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Interaction of a graphene sheet with a ferromagnetic metal plate
Anh D. Phan, N. A. Viet, Nikolai A. Poklonski, Lilia M. Woods, and Chi H. Le
Department of Physics, University of South Florida, Tampa, Florida 33620, USA
Institute of Physics, 10 Dao dan, Ba dinh, Hanoi, Vietnam
Physics Department, Belarusian State University, Minsk 220030, Belarus
School of Engineering, University of Greenwich, Medway, United Kingdom
(Received 24 July 2012; published 12 October 2012)
Dispersion forces, such as Casimir and van der Waals forces, can have a significant influence on the fabrication, handling, and assembly processes as well as the performance of micro- and nanodevices. In this paper, we investigate the Casimir force between a graphene sheet and a ferromagnetic metallic substrate in vacuum. The reflection coefficients, entering the expression for the force, are dependent on the graphene conductivity, which is described by the Kubo formalism. It is found that the magnetic response of the ferromagnet plays a significant role at low temperatures or high value of the graphene chemical potential. The numerical results also demonstrate that the thickness of the metallic plate has a minor influence on the Casimir force. This study may be useful for the design and operation of micro- and nanodevices.
DOI: 10.1103/PhysRevB.86.155419 PACS number(s): 78.20.Ls, 31.30.jh, 78.67.Wj, 12.20.Fv
I. INTRODUCTION
Micro- and nanotechnologies are considered as enabling technologies with exceptional economic capabilities. There are increasingly more products in today’s market in which the integrated micro- and nanoelectromechanical systems (MEMS/NEMS) are useful, because they allow for improved functionality, lower costs, and higher quality. With the decrease in the size of MEMS and NEMS, additional nanoscale surface forces, such as the Casimir and van der Waals forces, should be considered, especially in the areas of micro and nano machining, fabrication, manipulation, assembly, and metrology. Therefore, a fundamental understanding of the Casimir force has recently been under intense discussion.
The Casimir force can cause small elements in a device to stick together. Also, such nanoscale surface forces may overcome elastic restoring actions in the device and lead to stiction effects during the fabrication process. It has been recently shown, that Casimir forces may hamper the functioning of MEMS and NEMS devices by providing a pull-in instability. The Casimir force between two objects can induce further adhesion and stiction, leading to failures in devices. Particularly, when the size of a material is under the threshold length, the influence of the loading interaction on the design and manufacture of micro- and nanodevices becomes much more prominent.
The Casimir interaction originates from the quantum electromagnetic fluctuations between two objects. It provides a fundamental understanding about nanoscience and can play a significant role in the performance of devices. For over six decades, the Lifshitz theory has been employed to investigate this force in metal-metal, semiconductor-semiconductor, metal-superconductor, metamaterials, and graphene-graphene systems. The results of some configurations have been experimentally examined and have good agreement with theoretical calculations. The interaction between a nonmagnetic metal with a magnetodielectric material has also recently been discussed. These studies illustrate that the magnetic properties can significantly influence the Casimir pressure. Theoretical and experimental studies also show that it is possible to obtain a repulsive Casimir force in such systems, and the results could provide possible solutions to handle the stiction and adhesion problems found in MEMS/NEMS devices. In terms of theory, the calculations depend substantially on the model that describes the dielectric function of metals.
Graphene, an atomically thin layered material with novel properties, has gained a great deal of attention since its discovery. Researchers from a wide range of scientific fields have spent considerable effort in exploring its nature and its potential for practical applications. Recently obtained results demonstrate that graphene can be a promising candidate for the next-generation electronic devices.
In this paper, we calculate the Casimir force between a graphene layer and a ferromagnetic (FM) substrate, as shown in Fig. 1. The FM material is taken to be Fe described via dielectric and magnetic response properties. We utilize the Lifshitz theory to examine the role of the separation, temperature, and thickness of the substrate. We also investigate the influence of the magnetic response of the FM and show that in most cases its contribution is relatively small compared to the one from the dielectric response.
This paper is organized as follows: Sec. II presents detailed calculations of the thermal Casimir interactions. The results and discussion are given in Sec. III. Finally, Sec. IV presents the conclusions.
II. CASIMIR INTERACTION BETWEEN GRAPHENE AND A METAL SUBSTRATE
Here we calculate the Casimir force between a graphene sheet and a FM substrate in vacuum at a separation \( a \). The force per unit area at temperature \( T \) is given as
\[
F(a, T) = -\frac{k_B T}{\pi} \sum_{l=0}^{\infty} \left( 1 - \frac{1}{2} \delta_{l0} \right) \int_0^{\infty} q k_{1d} dq \left| r^{(1)}_{TE} \right|^2 + \left| r^{(1)}_{TM} \right|^2 \frac{\left( \left| r^{(2)}_{TE} \right|^2 \right)}{e^{2qa} - \left| r^{(2)}_{TE} \right|^2} \frac{\left( \left| r^{(2)}_{TM} \right|^2 \right)}{e^{2qa} - \left| r^{(2)}_{TM} \right|^2},
\]
where
\[
\left| r^{(1)}_{TE} \right| = \frac{\frac{1}{2} \left[ \sqrt{\frac{\epsilon_2^2 + 1}{\epsilon_2^2 + 3}} \frac{1}{\sqrt{3}} - 1 \right]}{\frac{1}{2} \left[ \sqrt{\frac{\epsilon_1^2 + 1}{\epsilon_1^2 + 3}} \frac{1}{\sqrt{3}} - 1 \right]},
\]
\[
\left| r^{(1)}_{TM} \right| = \frac{\frac{1}{2} \left[ \sqrt{\frac{\epsilon_2^2 + 1}{\epsilon_2^2 + 3}} \frac{1}{\sqrt{3}} + 1 \right]}{\frac{1}{2} \left[ \sqrt{\frac{\epsilon_1^2 + 1}{\epsilon_1^2 + 3}} \frac{1}{\sqrt{3}} + 1 \right]},
\]
\[
\left| r^{(2)}_{TE} \right| = \frac{\frac{1}{2} \left[ \sqrt{\frac{\epsilon_2^2 + 1}{\epsilon_2^2 + 3}} \frac{1}{\sqrt{3}} + 1 \right]}{\frac{1}{2} \left[ \sqrt{\frac{\epsilon_1^2 + 1}{\epsilon_1^2 + 3}} \frac{1}{\sqrt{3}} + 1 \right]} - 1,
\]
\[
\left| r^{(2)}_{TM} \right| = \frac{\frac{1}{2} \left[ \sqrt{\frac{\epsilon_2^2 + 1}{\epsilon_2^2 + 3}} \frac{1}{\sqrt{3}} - 1 \right]}{\frac{1}{2} \left[ \sqrt{\frac{\epsilon_1^2 + 1}{\epsilon_1^2 + 3}} \frac{1}{\sqrt{3}} - 1 \right]} - 1.
\]
where \( k_B \) is the Boltzmann constant, and \( r_{TM}^{(1,2)} \) and \( r_{TE}^{(1,2)} \) are the reflection coefficients corresponding, respectively, to the transverse magnetic (TM) and transverse electric (TE) field modes.
The reflection coefficients for the substrate are given as\(^{2,19,20}\)
\[
\begin{align*}
r_{TE}^{(1)} &= r_{TE}^{(1)}(i\xi_l, k_\perp) = \frac{\mu_1(i\xi_l)q_l - k_1}{\mu_1(i\xi_l)q_l + k_1}, \\
r_{TM}^{(1)} &= r_{TM}^{(1)}(i\xi_l, k_\perp) = \frac{\varepsilon_1(i\xi_l)q_l - k_1}{\varepsilon_1(i\xi_l)q_l + k_1},
\end{align*}
\]
where
\[
\begin{align*}
q_l &= q_l(i\xi_l, k_\perp) = \sqrt{k_1^2 + \mu_1(i\xi_l)\varepsilon_1(i\xi_l)}, \\
k_1 &= k_1(i\xi_l, k_\perp) = \frac{k_1^2 + \mu_1(i\xi_l)\varepsilon_1(i\xi_l)}{c^2}.
\end{align*}
\]
Note that \( k_\perp \) is the wave vector component perpendicular to the plane, \( c \) is the speed of light, and \( \xi_l = 2\pi k_B Tl/h \) are the Matsubara frequencies. The response properties of the FM metal are characterized by the dielectric function \( \varepsilon_1(i\xi_l) \) and the permeability function \( \mu_1(i\xi_l) \), which are frequency dependent along the imaginary axis \( (\omega_l = i\xi_l) \). We use the Drude model \( \varepsilon_{ID} \) and the plasma model \( \varepsilon_{1P} \) to describe the dielectric function,\(^{5,19,21}\)
\[
\begin{align*}
\varepsilon_{ID}(i\xi_l) &= 1 + \frac{\omega_p^2}{\xi_l + \gamma_p}, \\
\varepsilon_{1P}(i\xi_l) &= 1 + \frac{\omega_p^2}{\xi_l},
\end{align*}
\]
where \( \omega_p \) is the plasma frequency and the damping parameter is \( \gamma_p \). At room temperature, the \( l = 0 \) term of the Casimir-Lifshitz force in the metallic system is dominant.\(^{2,23}\) This allows us to consider the contribution of the static magnetic permeability \( \mu(0) \gg 1 \). For higher orders of \( l \), one should use \( \mu(i\xi_l) = 1 \).\(^{21}\) Both models lead to \( r_{TM}^{(1)}(0) = 1 \). However, we can obtain two different expressions for \( r_{TE}^{(1)}(0) \) when applying these two models,\(^{21}\)
\[
\begin{align*}
r_{TE,D}^{(1)}(0, k_\perp) &= \frac{\mu(0) - 1}{\mu(0) + 1}, \\
r_{TE,P}^{(1)}(0, k_\perp) &= \frac{\mu(0)k_\perp - c^2 k_\perp^2 + \mu(0)\omega_p^2}{\mu(0)k_\perp + c^2 k_\perp^2 + \mu(0)\omega_p^2}.
\end{align*}
\]
Here, \( r_{TE,D}^{(1)}(0, k_\perp) \) and \( r_{TE,P}^{(1)}(0, k_\perp) \) are the TE reflection coefficients corresponding to the Drude and plasma models, respectively.
For graphene, the reflection coefficients are found to be\(^{16,22}\)
\[
\begin{align*}
r_{TE}^{(2)} &= r_{TE}^{(2)}(i\xi_l, k_\perp) = -\frac{2\pi\sigma q_l/\xi_l}{1 + 2\pi\sigma q_l/\xi_l^2} , \\
r_{TM}^{(2)} &= r_{TM}^{(2)}(i\xi_l, k_\perp) = \frac{2\pi\sigma q_l/\xi_l}{1 + 2\pi\sigma q_l/\xi_l},
\end{align*}
\]
where \( \sigma \equiv \sigma(i\xi_l) \) is the two-dimensional (2D) conductivity described via the the Kubo formalism.\(^{16}\)
\[
\sigma(i\xi_l) = \frac{2e^2k_BT\ln(2)}{\pi \hbar^2 \xi_l} + \frac{e^2 \xi_l}{8\pi k_BT} \int_0^\infty \frac{\tanh(x) dx}{x^2} \left( \frac{\hbar^2}{4\pi k_B T} \right)^2.
\]
(7)
The first term in Eq. (7) corresponds to the intraband transitions, while the second term corresponds to the interband transitions. At low temperatures, the graphene conductivity \( \sigma(i\xi_l) \) approaches the universal value \( \sigma_0 = e^2/4\hbar \).
Using Eqs. (6) and (7), the TM reflection coefficient of graphene is given by
\[
r_{TM}^{(2)}(0, k_\perp) = 1 - \frac{2e^2k_BT\ln(2)}{\pi \hbar^2 \xi_l} + \frac{e^2 \xi_l}{8\pi k_BT} \int_0^\infty \frac{\tanh(x) dx}{x^2} \left( \frac{\hbar^2}{4\pi k_B T} \right)^2 .
\]
(8)
Equation (8) suggests \( r_{TM}^{(2)}(0, k_\perp) \) is approximately \( 0.162 \), and \( 0.325 \) eV, corresponding to the temperature \( 50\), \( 162 \), and \( 325 \) K, respectively.
The first Matsubara frequencies \( \xi_l \) are approximately \( 0.027, 0.162, \) and \( 0.325 \) eV, corresponding to the temperature \( 50, 300, \) and \( 600 \) K, respectively. As seen in Fig. 2, for \( l \geq 2 \), it is possible to substitute \( \sigma_0 \) for \( \sigma(i\xi_l) \) in Eq. (6) to calculate the reflection coefficients and the higher-order terms in the Casimir-Lifshitz force formula.
**FIG. 1.** (Color online) Schematics of a two-dimensional layer (graphene) and a substrate (FM metal) with thickness \( D \).
III. RESULTS AND DISCUSSION
In this section, we consider the Casimir interactions between graphene and a Fe metal plate. The parameters of Fe are $\omega_p = 4.09$ eV, $\gamma_p = 0.018$ eV, and $\mu(0) = 10^4$. As discussed above for $r_{TM}(0,k_{\perp}l)$ and $r_{TE}(0,k_{\perp}l)$, the TM contribution to the $l = 0$ term of the Casimir force is given by
$$F_{TM}^{(0)}(0,a,T) = -\frac{k_BT}{\pi} \int_0^\infty \frac{k_{\perp}^2 dk_{\perp}}{\omega_{p}^2 - \omega_{TM}(0,k_{\perp})^2} - \frac{k_BT\zeta(3)}{8\pi a^3}.$$ \hspace{1cm} (10)
This expression is identical to the term with $l = 0$ in the Casimir force between two metals. The sum of the $l \geq 1$ is much smaller than that of the metallic system due to the presence of the low graphene conductivity. As a result, the $l = 0$ term is the dominating term. Now, to calculate the contribution of the TE mode $F_{TE}^{(0)}(0,a,T)$ with $l = 0$, it is necessary to choose a good model for Fe. Both the plasma and Drude models, however, have been widely used to compute the Casimir interaction and fit with experimental data. The determination of the accuracy of the two models as compared to experimental data has been a controversial issue. In the following work, we utilize the plasma model to calculate the interactions. Thus $F_{TE}^{(0)}(0,a,T)$ is expressed by
$$F_{TE}^{(0)}(0,a,T) = \frac{k_BT}{2\pi} \int_0^\infty \frac{k_{\perp}^2 dk_{\perp}}{\omega_{p}^2 - \omega_{TE}(0,k_{\perp})^2} - 1.$$ \hspace{1cm} (11)
Note that $F_{TE}^{(0)}(0,a,T)$ is a unique term affected by the magnetic property of the ferromagnetic substrate. In Fig. 3, the ratio $F_{TM}^{(0)}/F_{TM}^{(0)}$ is less than 0.75% for distances $a$ in the $\mu m$ range at given temperatures. This indicates that the effect of $\mu(0)$ on the Casimir force is small. For this reason, Fe can be treated as a regular nonmagnetic metal $\mu(i\xi) = 1$.
For a finite-thickness iron slab $D$, the reflection coefficients of the metal material are modified as follows.\(^{20,32}\)
$$R_{TE,TM}(i\xi_{l},k_{\perp}) = R_{TE,TM}^{(1)} \frac{1 - e^{-2k_{\parallel}D}}{1 - (F_{TE,TM}^{(1)})^2 e^{-2k_{\parallel}D}}.$$ \hspace{1cm} (12)
To study the influence of thickness on the Casimir force, we rewrite Eq. (1) in the following way:
$$F(a,T) = F_{TM}^{(0)}(0,a,T) + F_{TE}^{(0)}(0,a,T) + F^{(1)}(a,T).$$ \hspace{1cm} (13)
Here, $F^{(1)}(a,T)$ is the sum of all $l \geq 1$ terms and is thickness dependent. Because $r_{TM}(0,k_{\perp}l) = 1$, therefore $F_{TM}^{(0)}(0,k_{\perp}l) = 1$. $F_{TM}^{(0)}(0,a,T)$ is given in Eq. (10) and it is independent of $D$. The insert in Fig. 3 shows that $F_{TM}^{(0)}(0,a,T)$ is much weaker than that for the thick plate and one can consider $F_{TM}^{(0)}(0,a,T) = 0$. Therefore, only $F^{(1)}(a,T)$ depends on the substrate thickness.
Figure 3 also shows that even $F^{(1)}(a,T)$ is weakly dependent on $D$ for practically all ranges since reduction of the thickness gives rise to a small decrease of the Casimir force. Because the thermal wavelength of graphene is $\lambda_T/200 \approx 38$ nm at room temperature, at distances beyond the thermal wavelength of a system, the contribution of the sum of $l \geq 1$ terms can be ignored. Thus the influence of $F^{(1)}(a,T)$ is not significant. This suggests that the graphene significantly interacts only with the nearest surface layers of the bottom substrate. We find that the universal graphene conductivity is the main reason for less than 2% difference as one compares the dispersion force between two graphene sheets with $F_{0}(a)$.\(^{16}\) This demonstrates that the approximate formula for the Casimir interaction equivalent to the $l = 0$ term of the Casimir-Lifshitz expression in this regime is $F_{app}(a,T) = -k_BT\zeta(3)/8\pi a^3$. In Fig. 4, we plot the normalized Casimir force with the full expression [see Eq. (1)] and the approximate expression. The $l = 0$ term is dominant and can replace the full expression of the Casimir interaction when $a \approx 0.8 \mu m$ for 300 K.
The critical $T_c$ of Fe is 1043 K. At $T > T_c$, the magnetic properties of the ferromagnetic material nearly vanish. Spins in the Fe slab are rearranged so that $\mu(i\xi) = 1$ at all frequencies. Nevertheless, the dielectric function is not affected by the directions of spins. Therefore, the plasma frequency and damping parameter are unchanged by temperature increases at $T \geq T_c$. If we consider the Casimir interaction between Fe and another metal, the phase transition leads to a significant change.
in the mutual interaction\textsuperscript{19,21} Due to the fact that graphene is quite transparent with the presence of the magnetic properties, the dispersion force is not affected significantly.
One notes that Eq. (7) is applicable, for undoped graphene with chemical potential $\mu_C = 0$. If $\mu_C \neq 0$, then the graphene conductivity becomes\textsuperscript{33}
\[ \sigma(\mu_C, i\xi) = \frac{e^2 k_B T \ln(2)}{\pi h^2 \xi} + \frac{e^2 k_B T \ln[1 + \cosh(\mu_C/k_B T)]}{\pi h^2 \xi} + \frac{e^2 \xi}{\pi} \int_0^\infty \frac{\sinh(E/k_B T)}{\cosh(E/k_B T) + \cosh(\mu_C/k_B T)} dE \times \frac{dE}{(h\xi)^2 + 4E^2}. \] (14)
The first two terms correspond to the intraband transitions; the last term is the interband component. Equation (14) shows that the intraband contribution to $\sigma(\mu_C, i\xi)$ still induces a nonzero value of $F_{TE}^{(2)}(0,k_{\perp})$. One way to control the graphene chemical potential is by an applied electric field $E_d$.\textsuperscript{34,35}
\[ \frac{\pi e^2 h^2 \nu_F^2}{e} E_d = \int_0^\infty E[f(E) - f(E + 2\mu_C)]dE, \] (15)
where $f(E)$ is the Fermi distribution function and $v_F = c/300$ is the graphene Fermi velocity. The chemical potential can also be influenced by doping.
In the limit of small chemical potential, $r_{TE}^{(2)}(0,k_{\perp})$ is represented as Eq. (9). For $\mu_C \gg k_B T$, the expression of the TE reflection coefficient with $l = 0$ is written as
\[ r_{TE}^{(2)}(0,k_{\perp}) \approx -\frac{4\sigma_0 \mu_C/(\pi \hbar c)}{k_{\perp} + 4\sigma_0 \mu_C/(\pi \hbar c)}. \] (16)
In Fig. 5, the Casimir interaction is calculated at low temperatures ($\leq 50$ K) and $\mu_C = 1$ eV, with and without the magnetic properties. Unlike the case of a pristine graphene sheet ($\mu_C = 0$ eV), the influence of permeability of Fe on the dispersion force is more pronounced at 10 K. The magnetic properties, however, have much smaller effect on the Casimir force at temperatures greater than 50 K. $F(a,T)$ is mainly determined by the interband conductivity of graphene. At 10 K, the contribution of the intraband on the Casimir force can be considerable compared to that of the interband conductivity. However, as the temperature increases, the interband contribution increases substantially, and causes a decrease in the contribution from intraband. For this reason, the magnetic properties nearly disappear at $T \geq 50$ K.
To further investigate the Casimir force dependence on chemical potential, we consider the fluctuation interactions at $a = 100$ nm and various temperatures versus $\mu_C$, as shown in Fig. 6. $F(a,T)/F_0$ changes from 0.018 to 0.034 at $T = 10$ K, and from 0.045 to 0.064 at $T = 300$ K, when $\mu_C$ varies in the regime below 1.2 eV. In addition, at higher temperatures, the curves of $F(a,T)/F_0$ are of the linear form.
IV. CONCLUSIONS
When designing and manufacturing micro- and nanodevices and components, it is important to understand the loading and the effects of related forces on the systems and their components, especially due surface forces such as the Casimir and van der Waals. In this study, a comprehensive investigation and discussion of the Casimir interaction between graphene and FM materials is presented. We discuss the Casimir force, which is a function of the graphene conductivity and the permeability constant of Fe. It is shown that the conductivity of graphene heavily depends on the chemical potential, which causes a difference between nonmagnetic and magnetic calculations at the low temperatures. For higher temperatures, the influence of the magnetic properties is small. One can apply a bias electric field to a graphene sheet to tailor the chemical potential of graphene in order to control the magnitude of the Casimir force. The numerical calculations demonstrate that the thickness of a metal slab had a minor influence on the Casimir force. The results from this study maybe useful for the design and operation of micro- and nanodevices utilizing magnetic materials at various temperature regimes.
ACKNOWLEDGMENTS
We give thanks to D. Drosdoff for discussions. This research was supported by the Nafosted Grant No. 103.06-2011.51.
L.M.W. acknowledges the US Department of Energy under Contract No. DE-FG02-06ER46297. N.A.P. acknowledges the financial support from the Belarusian Republican Foundation for Fundamental Research Grant No. F11V-001.
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| 2025-03-05T00:00:00 |
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Management of Upper Airway Leech Infestations
Kucuk Harun, MD
Abstract
Purpose: Upper airway foreign body is one of the most encountered clinical situations in otolaryngology practice. In rare conditions, a living organism may be a foreign body in the upper airway. In this study, we demonstrate 19 patients with leech infestations in nose, nasopharynx, and larynx. Methods: This study was enrolled with 19 patients between 2012 and 2016 in a regional state hospital. All of the patients were admitted to clinic with these complaints: epistaxis, hemoptysis, coughing, foreign body sensation, and bloody stool. Results: There were 12 male and 7 female patients. The leech was in the nose in 12 patients, in nasopharynx in 6 patients, and in the larynx in only 1 patient. All leeches are removed under local anesthesia (except laryngeal presentation). No bleeding and complication were seen after extraction of leech. Conclusion: Leech can be easily diagnosed and managed in the upper aero-digestive tract without any complication and leech-associated disease.
Keywords
leech, foreign body, epistaxis, upper airway
Introduction
A foreign body in the upper airway is a common clinical presentation in otolaryngology practice, with the recognition and removal of a foreign body an important part of daily practice for ear, nose, and throat (ENT) residents and otolaryngologists. The most commonly encountered inanimate foreign bodies include beads, pieces of paper, rubbers, legumes, and small parts of toys. In the pediatric population, an upper airway foreign body may be life threatening if it moves to the trachea or bronchi or obstructs the rima glottis. An unusual foreign body, a living organism like a leech, may sometimes be difficult to diagnose in otolaryngology practice.
Among animate foreign bodies, leeches, which are commonly encountered in rural areas, may be found in the upper aero-digestive tract. Leeches are water-living, blood-sucking parasites of various colors and lengths. They may enter the body via oral or nasal routes. Thereafter, they adhere to mucosa and suck blood from their host. The host does not recognize the leech as a foreign body, as the saliva of the host contains anesthetic and anticoagulant agents. As the organism grows in size, it may cause various symptoms, depending on its anatomic location. These symptoms include nosebleeds, hemoptysis, a foreign body sensation, and coughing. Herein, we describe 19 patients with leech infestations in the nose, nasopharynx, and larynx.
Patients and Methods
This was a retrospective study of 19 patients who were admitted to a regional state hospital between 2012 and 2016. The ethics committee of Samsun Medicana International Hospital approved this study. All patients’ data were obtained from the hospital’s database.
In terms of clinical features, all the patients had complaints of epistaxis, hemoptysis, a foreign body sensation, and bloody stools. All the patients were from rural areas and had a history of contact with polluted water.
All the patients underwent an ENT examination, including anterior rhinoscopy, which revealed the presence of a leech in all cases. Thus, there was no need for a radiological evaluation. Figures 1 to 4 show the worm-like mobile animate organism in the nose, nasopharynx, and larynx.
Results
There were 12 male and 7 female patients, with ages ranging from 5 to 60 years. The mean age was 15.7 years. The mean symptom onset time (ie, time of first bleeding) to diagnosis was 3.9 days. In terms of location, the leeches were in the nasal area ($n = 12$), nasopharynx ($n = 6$), and larynx ($n = 1$; Table 1). The laryngeal leech was removed under general anesthesia. In all
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1 Department of Otolaryngology, Samsun Medicana International Hospital, Samsun, Turkey
Received: May 07, 2019; accepted: June 07, 2019
Corresponding Author:
Kucuk Harun, MD, Medicana International Samsun Hospital, Sehit Mesut Birinci Caddesi No: 85 Canik, Samsun 55210, Turkey.
Email: [email protected]
the other cases, the leeches were removed using a forceps or clamp under local anesthesia with 4% lidocaine spray. None of the patients experienced bleeding after extraction of the leeches, and all patient-related complaints improved in a few days. Only 1 patient required an iron supplement due to anemia associated with leech-related bleeding. During the 1-year follow-up period of each case, there were no complications or leech-associated infectious diseases.
**Discussion**
Among patients who present to otolaryngology clinics and emergency departments with epistaxis or hemoptysis, the cause may be a foreign body in the nose or upper airway. Such foreign bodies are generally seen in the pediatric population but seldom in adults. A living organism is a rare type of
**Figure 1.** Endoscopic view of a leech in the nasopharynx of a 7-year-old girl. Black arrow: attachment points to the nasopharynx wall. Star: nasopharynx posterior wall. Square: posterior portion of the nasal septum.
**Figure 2.** An image showing a leech extending from the nasal entrance to the oropharynx.
**Figure 3.** A leech attached to (what exactly) in the interarytenoid region lying toward the tip of the epiglottis.
**Figure 4.** Appearance of one of the leeches after removal.
**Table 1.** Age, Sex, Symptoms, Localization, and Duration of the Complaints.
| Age | Sex | Symptoms | History | Location |
|-----|-----|---------------------------|---------|---------------|
| 7 | F | Epistaxis | 2 days | Nose |
| 14 | M | Epistaxis | 5 days | Nose |
| 40 | M | Hemoptysis | 14 days | Nasopharynx |
| 22 | M | Epistaxis | 5 days | Nasopharynx |
| 38 | M | Hemoptysis | 3 days | Nasopharynx |
| 5 | F | Epistaxis | 2 days | Nose |
| 7 | M | Epistaxis | 5 days | Nose |
| 6 | F | Epistaxis | 2 days | Nose |
| 10 | F | Foreign body sensation | 3 days | Nasopharynx |
| 60 | M | Epistaxis | 4 days | Nose |
| 12 | M | Hemoptysis | 1 day | Nasopharynx |
| 10 | M | Coughing, foreign body sensation | 2 days | Larynx |
| 6 | F | Epistaxis | 3 days | Nose |
| 17 | M | Blood in stool | 10 days | Nasopharynx |
| 14 | M | Epistaxis | 2 days | Nose |
| 5 | F | Epistaxis | 3 days | Nose |
| 8 | F | Foreign body sensation | 6 days | Nose |
| 8 | M | Direct visualization into the nose | 1 day | Nose |
| 11 | M | Epistaxis | 2 days | Nose |
Abbreviations: F, female; M, male.
foreign body. We described 19 cases of leech infestation and the clinical features.
Leeches that can cause parasitic infestations in humans can be divided into land-based and aquatic-based classes. Land-based leeches have strong jaws and can easily adhere to human skin. In contrast, aquatic-living leeches have weak jaws and require soft tissue to facilitate adherence. After a leech enters the human body, it starts to ingest blood. According to previous research, leeches can ingest blood meals averaging 890% of their weight and ingest about 9 mL of blood within 70.5 minutes. Leeches found in the upper aero-digestive tract are aquatic organisms and may cause severe anemia as a result of mucous membrane bleeding. Such leeches possess anticoagulant, hirudin, and histamine-like vasodilators, which support bleeding and result in epistaxis and haemoptysis. Aquatic-living leeches have previously been found in conjunctiva as well as in the vulva, vagina, urethra, esophagus, and trachea. When located in the nasopharynx, a leech may resemble a neoplasm.
Leech infestations can cause severe anemia, which may require a transfusion. None of the patients in the present study required a transfusion. Cundall et al described 3 cases of severe anemia due to leech infestation, with death due to blood loss in 1 case. Public awareness of leech infestation in endemic areas means that people present to the hospital shortly after symptoms occur. Early presentation can prevent fatal conditions. Recurrent epistaxis, living in an endemic area, or visiting endemic areas and contact with polluted water can provide clues for the clinician that a foreign body may be a leech.
There are some case reports and case series in the literature of upper aero-digestive tract infestations, in which various methods were used for leech removal. Chen et al used a forceps to extract a leech in a number of cases and electric shock in 1 case. Other researchers reported the use of hypertonic saline irrigation for leech extraction.
According to local knowledge in southeast part of Turkey, when a leech is squeezed for approximately 5 to 20 seconds at the midpoint of its body, it will spontaneously release its mouthparts from the mucosa to which it is attached. In the present cases, H. K. removed the leeches using this method. In the cases where the leech was in the nasal passage, a nasal polyp forceps was inserted into the nasal passage, and the leech was grasped at the midpoint of its body. As soon as it detached itself from the mucosa to which it was adhered, it was removed through the nasal passage. In the nasopharyngeal infestations, the lower part of the organism’s body extended into the oropharynx. Thus, in an oral cavity examination, it was easily visualized behind the soft palate and lateral to the tonsils. In these clinical presentations, the tongue was depressed using a tongue depressor. The organism was then held using a straight hemostatic clamp and removed via the oral route. This method is simple and easily applicable in the office setting, although the otolaryngologist must take extreme care not to drop the organism in the larynx. No complications were encountered in the present cases.
In conclusion, the present article describes our clinical experience of foreign body leech infestations and provides information on leech removal methods that may be of use to otolaryngologists, emergency department specialist, and ENT residents. Experienced otolaryngologists can easily diagnose a leech infestation in endemic areas and remove the leech from the upper aero-digestive tract. Living in rural areas where leeches are endemic and swimming in or drinking polluted water may provide clues for clinicians. Pressing the organism at the midpoint of its body for 5 to 20 seconds using a forceps will cause the organism to detach from the mucosa and aid extraction.
Author’s Note
This study was presented as oral presentation at International Hippocrates Congress on Medical And Health Sciences on March 1, 2019 to March 3, 2019, Ankara/Turkey.
Declaration of Conflicting Interests
The author(s) declared no potential conflicts of interest with respect to the research, authorship, and/or publication of this article.
Funding
The author(s) received no financial support for the research, authorship, and/or publication of this article.
References
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3. Bilgen C, Karci B, Uluoz U. A nasopharyngeal mass: leech in the nasopharynx. Int J Pediatr Otorhinolaryngol. 2002;64(1):73-76.
4. Cagli A, Celik H. An uncommon cause of epistaxis: nasopharyngeal hirudiniasis. Turkiye Parazitol Derg. 2015;39(2):171-173.
5. Chen WC, Chien CY, Yang CH, Li JH, Hwang CF. Nasal leech infestation: report of seven leeches and literature review. Eur Arch Otorhinolaryngol. 2010;267(8):1225-1229.
6. Demiroren K, Caliskan U. Unexpected result in the etiological approaching to an anemic case: a leech infestation. Pediatr Hema tol Oncol. 2003;20(7):547-550.
7. Cundall DB, Whitehead SM, Hechtel FO. Severe anaemia and death due to the pharyngeal leech Myxobdella Africana. Trans R Soc Trop Med Hyg. 1986;80(6):940-944.
8. Mansoor SN, Anwar Z, Sheen SN. Reach the leech: an unusual cause of hematuria. J Coll Physicians Surg Pak. 2016;26(2):156-157.
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Content-Based Features to Rank Influential Hidden Services of the Tor Darknet
Mhd Wesam Al-Nabki, Eduardo Fidalgo, Enrique Alegre, and Deisy Chaves
Abstract—The unevenness importance of criminal activities in the onion domains of the Tor Darknet and the different levels of their appeal to the end-user make them tangled to measure their influence. To this end, this paper presents a novel content-based ranking framework to detect the most influential onion domains. Our approach comprises a modeling unit that represents an onion domain using forty features extracted from five different resources: user-visible text, HTML markup, Named Entities, network topology, and visual content. And also, a ranking unit that, using the Learning-to-Rank (LtR) approach, automatically learns a ranking function by integrating the previously obtained features. Using a case-study based on drugs-related onion domains, we obtained the following results. (1) Among the explored LtR schemes, the listwise approach outperforms the benchmarked methods with an NDCG of 0.95 for the top-10 ranked domains. (2) We proved quantitatively that our framework surpasses the link-based ranking techniques. Also, (3) with the selected feature, we observed that the textual content, composed by text, NER, and HTML features, is the most balanced approach, in terms of efficiency and score obtained. The proposed framework might support Law Enforcement Agencies in detecting the most influential domains related to possible suspicious activities.
Index Terms—Tor, Darknet, Influence detection, Learning-to-Rank, Feature Extraction, Hidden Services.
1 INTRODUCTION
The Onion Router (Tor) network, which is known to be one of the most famous Darknet networks, gives the end-users a high level of privacy and anonymity. The Tor project was proposed in the mid-1990s by the US military researchers to secure intelligence communications. However, a few years later, and as part of their strategy for secrecy, they made the Tor project available for the public [1].
The onion domains proliferated rapidly and the latest statistics stated by the onion metrics website [1] has reported that the number of currently existing onion domains has increased from 30K to almost 90K between April 2015 and October 2019.
The community of the Tor network refers to an onion domain hosted in the Tor darknet by a Hidden Service (HS). Those services can be accessed via a particular web browser called Tor Browser or a proxy such as Tor2Web.
There are many legal uses for the Tor network, such as personal blogs, news domains, and discussion forums [2], [3]. However, due to its level of anonymity, Tor Darknet is being exploited by services traders allowing them to promote their products freely, including, but not limited to Child Sexual Abuse (CSA) [4], [5], drugs trading [5], [6], [7], [8], and counterfeit personal identifications [2], [10], [11].
The high level of privacy and anonymity provided by the Tor network obstructed the authorities monitoring tools from controlling the content or even identifying the IP address of the hosts who are behind any suspicious service.
We collaborate with the Spanish National Cybersecurity Institute (INCIBE), to develop tools that could ease the task of monitoring the Tor Darknet and detecting existing or new suspicious contents. These tools are designed to support the Spanish Law Enforcement Agencies (LEAs) in their surveillance of the Tor hidden services. An overview of two of our current contributions to the Tor monitoring tool is summarized in Figure [1].
The first contribution to the monitoring system presented in Figure [1] was a classification module, which detects and isolates the categories of suspicious onion domains that Spanish LEAs are interested in monitoring. For this task, we used our supervised text classifier presented in [11], which categorizes HSs into eight classes: Pornography, Cryptocurrency, Counterfeit Credit Cards, Drugs, Violence, Hacking, and
1. https://metrics.torproject.org/hidserv-dir-onions-seen.html
2. https://www.torproject.org/projects/torbrowser.html.en
3. https://tor2web.org/
4. In Spanish, it stands for the Instituto Nacional de Ciberseguridad de España
Counterfeit Money, and Counterfeit Personal Identification including Driving-License, Identification, and Passport.
The second module, which is also the focus of this work, addresses the problem of ranking the hidden services that were classified as suspicious. Once they are ranked, a police officer can prioritize her/his work by focusing on the most influential HSs, i.e., those which are in the first positions of the rank. In our previous work [2], we presented a ranking algorithm, called ToRank, to sort the onion domains by analyzing the connectivity of their hyperlinks, what was a linked-based approach. In this case, sharing the same objective, we propose a more rich solution for ranking them by analyzing as well the content of the domains.
One of the difficulties we faced was how to define the influence of a given onion domain based on its ability to attract the public. In this work, we assess the attractiveness of an onion domain, and we assign accordingly to it a score that reflects its influence among the other domains with similar content. Hence, the more attractive is a domain, the higher the score it receives. Using our text classifier, the ranking module we are proposing works at category-level and detects the influential HS in each category. Therefore, this paper aims to answer the following question: What are the most attractive onion domains in a determined area of activities?
The answer to this question could improve the capability of LEAs in keeping a close eye on the suspicious Hidden Services more influential by concentrating their efforts in monitoring them rather than the less influential ones. Moreover, in the case a Law Enforcement Agency takes a suspicious HS down, the proposed ranking module would recognize the same domain again if it still holds the same content, even if it were hosted under a different or new address. Similarly, when a new domain is introduced to the network for the first time, and it hosts suspicious content similar to an HS that was previously nominated as influential, the ranking module could capture it before becoming popular among Tor users. Therefore, LEAs will have the needed information to strike the suspicious domains preemptively earlier.
A straightforward strategy to detect the influential onion domains is to sort them by the number of clients’ requests that they receive, i.e., analyzing the traffic of the network. However, the design of the Tor network is oriented to preventing this behavior [12]. Chaabane et al. [13] conducted a deep analysis for the Tor network traffic through establishing six exit nodes distributed over the world with the default exit policy. However, this approach can not assess the traffic of onion domains that are not reachable through these exit nodes. Furthermore, it could be risky because the Tor network users could reach any onion domain, regardless of its legality, through the IP addresses of the machines dedicated to that purpose. Biryukov et al. [14] tried to exploit the concept of entry guard nodes [15] to de-anonymize clients of a Tor hidden service. However, this proposal will not be feasible as soon as the vulnerability is fixed.
Another strategy is to employ a link-based ranking algorithm such as ToRank [2], PageRank [16], Hyperlink-Induced Topic Search (HITS) [17], or Katz [18]. We explored it in our previous work [2], and we concluded that the main drawback of this approach lies in its dependency on hyperlinks connectivity between the onion domains [19]. Hence, if an influential but isolated domain exists in the network, this technique can not recognize it as an essential item.
In this paper, we present an alternative approach that incorporates several features that are extracted from the HSs into a Learning to Rank (LtR) schema [20]. Given a list of hidden services, our model ranks onion domains based on two key steps: content feature extraction and onion domain ranking. First, we represent each onion domain by a forty elements feature vector extracted from five different resources that are: 1) the textual content of the domain, 2) the textual Named Entities (NE) in the user-visible text like products names and organizations names, 3) the HTML markup code by taking advantage of specific HTML tags, 4) the visual content like the images exposed in the domain, and finally 5) the position of the targeted onion domain with respect to the Tor network topology. Second, the extracted features are cleaned and normalized to train a ranking function using the LtR approach to rank the domains and to propose top-k HSs as the most influential.
The ranking problem addressed in this paper is close to the field of Information Retrieval (IR) but with a significant difference. Both issues will retrieve a ranked list of elements similarly to how search engines work. For example, the Google search engine considers more than 200 factors to generate a ranked list of websites concerning a query [21]. However, in the context of our problem, we do not have a search term to order the results accordingly. Instead, our objective is to rank the domains based on a virtual query: What are the most attractive onion domains in a determined area of activities? Hence, this model adopts IR to solve the problem of ranking and detecting the most influential onion domain in the Tor network, but without having available a search term.
Nevertheless, the proposed framework is not only restricted to ranking the onion domains of the Tor network. It could be generalized and be adapted to different areas with slight modifications in the feature vector, as for example, document ranking, web pages of the Surface Web, or users in a social network, among others. Our focus on this field, based on the special sensitivity of the HS contents, motivates our application in the Tor network, and, additionally, we wanted to test the use of IR techniques for single query ranking problems.
The main contributions of this paper can be summarized in the following way.
- We propose a novel framework to rank the HSs and to detect the most influential ones. Our strategy exploits five groups of features extracted from Tor HSs via a Hidden Service Modeling Unit (HSMU). The extracted features are used to train the Supervised Learning-to-Rank Unit (SLRU). Our approach outperforms the link-based ranking technique, such as ToRank, PageRank, HITS, and Katz, when tested on samples of onion domains related to the marketing of drugs (Fig. 2).
- We evaluated 40 features extracted from five resources: 1) user-visible textual, 2) textual named entities, 3) the HTML markup code, 4) the visual content, and 5) features drawn from the topology.
of the Tor network. In particular, we address the effects of representing an onion domain by several variations of features on the ranking framework. We identify the most efficient combination of features compared to their cost of extraction in terms of the prediction time and the resources needed to build the features extraction model.
- To select the best LtR schema, we explore and compare three popular architectures: pointwise, pairwise, and listwise.
- Finally, we create a manually ranked dataset, that plays the role of ground truth for testing the models.
The rest of the paper is organized as follows. In Section 2 we summarize the related work. After that, Section 3 introduces the proposed ranking framework, including its main components. Section 4 presents the experimental settings along with the configuration of the framework units. Next, Section 5 addresses a case study to test the effectiveness of the proposed framework in a real case scenario. Finally, Section 6 presents the main conclusions of this work and introduces other approaches that we are planning to explore in the future.
## 2 Related Work
There are plenty of works tackling the study of the suspicious activities that take place in the Darknet of the Tor network, as are the illicit drugs markets, terrorist activities, arms smuggling, and violence, or cybercrime.
However, only a few of them have addressed the problem of analyzing the Darknet networks to detect the most influential domains. Some of them used approaches that depend on Social Networks Analysis (SNA) techniques to mine networks. Chen et al. conducted a comprehensive exploration of terrorist organizations to examine the robustness of their networks against attacks. In particular, these attacks were simulated by the removal of the items featured by either their high in-degree or betweenness scores.
Moreover, Al Nabki et al. proposed an algorithm, called ToRank, to rank and detect the most influential domains in the Tor network. ToRank represents the Tor network by a directed graph of nodes and edges, and the most influential nodes are the ones which removal would reduce the connectivity among the nodes. However, the link-based approaches would fail in evaluating the isolated nodes which do not have connections to the rest of the community. Therefore, as we show in the experiments section, this approach can not surpass any of the benchmarked LtR techniques.
Another different strategy was followed by Anwar et al., who presented a hybrid algorithm to detect the influential leaders of radical groups in the Darknet forums. Their proposal is based on mining the content of the user’s profiles and their historical posts to extract textual features representing their radicalness. Then, they incorporate the obtained features in a customized link-based ranking algorithm, based on PageRank, to build a ranked list of radically influential users.
A different perspective was followed by the study carried out by Birjukov et al., who exploits the entry guard nodes concept to de-anonymize clients of an onion domain in the Tor network. The popularity of onion domains in the Tor network is estimated by measuring its incoming traffic; however, this approach will not be feasible when the vulnerability is fixed.
The approach proposed in this work is entirely different and, to the best of our knowledge, is not present in the literature. We adopt a supervised framework that automatically learns how to order items following predefined ranking criteria. Concretely, we employ an LtR model to capture characteristics of a given ranked list and maps the learned rank into a new unsorted list of items.
LtR framework has been used widely in the field of IR and 2). Li et al. proposed an algorithm to help software developers in dealing with unfamiliar Application Programming Interface (API) by offering software documentation recommendations and by training an LtR model with 22 features extracted from four resources. Other examples are Agichtein et al. employed the RankNet algorithm to leverage search engine results by incorporating user behavior, or Wang et al. who presented an LtR-based framework to rank input parameters values of online forms. They used 6 categories of features extracted from user contexts and patterns of user inputs. Moreover, LtR has been employed for mining social networks or to detect and rank critical events in Twitter social network, but none of those aforementioned works addressed the study of Tor network from a content-analysis perspective.
## 3 Proposed Ranking Framework
In this paper, we present a supervised framework to rank Tor Hidden Services with the purpose of measuring the influence of each domain (Fig. 2). Our approach has two components: 1) Hidden Service Modeling Unit (HSMU), which analyzes and extracts features from a given onion domain, and 2) the Supervised Learning-to-Rank Unit (SLRU) that learns a function to order a collection of domains according to the pattern captured from previously sorted samples, a training set.
### 3.1 Hidden Service Modeling Unit
Given an onion domain \( d_i \in D \), where \( D \) is a set of onion domains, the HSMU analyzes \( d_i \) to extract features belonging to five different categories: text, named entity, HTML, visual content, and network topology. Then, the HSMU encodes those features into numerical values that represent the HSs analyzed.
#### 3.1.1 Text Features
The set of text features involves four types of descriptors constructed from the text in \( d_i \) that is visible to the user.
**Date and Time:** A binary feature to indicate whether \( d_i \) has been updated recently or not. A domain might be updated by its owner or after receiving reviews from customers concerning the offered service. We parsed the date and time patterns, and we compared them with a configurable threshold, computing this binary feature. This threshold is a particular date-time point, whereas the actions beyond it are considered obsolete.
Moreover, by counting these updates, we measured the number of recent changes that $d_i$ has received in the past. We refer to these two features by recently updated and updates_counts, respectively.
**HS Name**: The address of a hidden service consists of 16 characters, randomly generated. The prefix of an HS can be customized with tools like Shallot\(^5\), allowing that the onion domain address includes words attractive to the customers. For example, a drug marketplace could add the words Cocaine or LSD to its HS’s URL. Nevertheless, the customization process is extensively time-consuming; for example, customizing the first seven characters requires one day of machine-time while customizing 10 characters takes 40 years of processing.
To explore this characteristic, we split the concatenated words using a probabilistic approach based on English Wikipedia unigram frequencies thanks to Wordninja tool\(^6\). We obtained two features: (i) the number of human-readable words and (ii) the number of their letters. We named them as address_words_count and address_letters_count, respectively.
**Clones Rate**: the number of onion domains that host the same content under different addresses. After reviewing Darknet Usage Addresses Text (DUTA-10K) dataset\(^7\) we realized that some onion domains have almost the same textual content but hosted under different addresses. This feature, i.e., HS duplication, might reflect concerns of the domains’ owners about their services of being taken down by authorities. The clones_rate feature of $d_i$ reflects the frequency of the MD5 hash code of its text.
**Term Frequency-Inverse Document Frequency (TF-IDF) Vectorizer**: we used this text vectorization technique to extract and to weight domain-dependent keywords\(^41\). It allowed us to draw the following four features: 1) keyword_num: the number of words that are in common between the TF-IDF feature vector and the domain’s words - we consider these words as the keywords of the domain, 2) keyword_TF-IDF_Acc: the accumulated TF-IDF weights of the keywords, 3) keyword_avg_weight: the average weight of the keywords, and 4) keyword_to_total: the number of the domain’s words dived by the number of its keywords.
### 3.1.2 Named Entities Features
A textual Named Entity (NE) refers to a real proper name of an object, including, but not limited to, persons, organizations, or locations. To extract those named entities, our previous work\(^42\) adopted a Named Entity Recognition (NER)
model proposed by Aguilar et al. [43] to the Tor Darknet to recognize six categories of entities: persons (PER), locations (LOC), organizations (ORG), products (PRD), creative-work (CRTV), corporation (COR), and groups (GRP). We map the extracted NEs into the following five features:
**NE Number**: it counts the total number of entities in $d_i$ regardless of the category; we refer to this feature by $NE\_counter$.
**NE Popularity**: an entity is popular if its appearance frequency value is above or equal to a specific threshold that we set to five, as is explained in Section 4.2.2. For every category identified by the NER model, we use a binary representation to capture the existence of popular entities in the domain (1) or (0) otherwise. We refer to this feature as $popular\_NE_X$, where $X$ is the corresponding NER category.
**TF-IDF**: accumulates the TF-IDF weight of all the detected NE in $d_i$. This feature is denoted by $NE\_TF\_IDF$.
**TF-IDF Popular NE**: accumulated TF-IDF weight of the popular NE, and it is named $popular\_NE\_TF\_IDF$.
**Emerging NE**: the frequency of the emerging product entities in $d_i$. We used our previous work [6] based on K-Shell algorithm [44] and graph theory to detect these entities in the Tor Darknet. We denote this feature by $emerging\_NE$.
### 3.1.3 HTML Markup Features
Using regular expressions, we parse the HTML markup code of $d_i$ to build the following eight features:
**Internal Hyperlinks**: number of unique hyperlinks that share the same domain name as $d_i$. We denote it by $internal\_links$.
**External Hyperlinks**: refers to the number of pages referenced by $d_i$ on Tor network or in the Surface Web. We refer to this feature by $external\_links$.
**Image Tag Count**: denotes the number of images referenced in $d_i$. It is calculated by counting the <img> HTML tag in the HTML code of $d_i$. We denote it by $img\_count$.
**Login and Password**: a binary feature to indicate whether the domain needs login and password credentials or not. We use a regular expression pattern to parse such inputs. This feature is called $needs\_credential$.
**Domain Title**: a binary feature that checks whether the <title> HTML tag has a textual value or not. We call it $has\_title$.
**Domain Header**: a binary feature that analyzes if the <H1> HTML tag has a header or not. We named it $has\_H1$.
**Title and Header TF-IDF**: an accumulation of the TF-IDF weight for the $d_i$ title and header text. It is denoted by $TF\_IDF\_title\_H1$.
**TF-IDF Image Alternatives**: TF-IDF weight accumulation of the alternative text. Some websites use an optional property called <alt> inside the image tag <img> to hold a textual description for the image. This text becomes visible to the end-user to substitute the image in case it is not loaded properly. It is denoted as $TF\_IDF\_alt$.
### 3.1.4 Visual Content Features
The visual content could be an attractive factor for drawing the attention of end-users rather than the text, especially in the Tor HSs when the customer seeks to have a real image of the product before buying it. A suspicious services trader might incorporate real images of products to create an impression of credibility to a potential customer. However, the visual contents that are interesting for LEAs could be mixed up with other noisy contents, such as banners and images of logos. To isolate the interesting ones, we built a supervised image classifier that categorizes the visual content into nine categories, where eight of them are suspicious, and one is not. The definition of these categories is based on our previous works [2], [11], where we created DUTA dataset and its extended version DUTA-10K. The image classification model was built using Transfer Learning (TL) technique [45] on the top of a pre-trained Inception-ResNet V2 model [46]. The visual content feature vector has six dimensions distributed in the following manner:
**Image Count**: represents the total number of images in $d_i$, both suspicious and non-suspicious images regardless of their category. Suspicious stands for images that could contain illicit content. We denote these features by $total\_count$, $suspicious\_count$ and $noise\_count$, respectively.
**Average Classification Confidence**: represents the averaged confidence score of multiple images per category. These features are named $avg\_suspicious\_conf$ and $avg\_normal\_conf$, respectively.
**Majority Class**: a binary flag to indicate whether the majority of the images published in $d_i$ are suspicious or not. This flag is denoted by $suspicious\_majority$.
### 3.1.5 Network Structure Features
Additionally, we modeled the Tor network by a directed graph of nodes and edges. The nodes refer to onion domains and the hyperlinks between domains are captured by the edges. This representation allowed us to build the following seven features:
**In-degree**: refers to the number of onion domains pointing to the domain $d_i$. It is called $in\_degree$.
**Out-degree**: indicates the number of hidden services referenced by $d_i$, and it is named $out\_degree$.
**Centrality Measures**: for each domain $d_i$ in the Tor network graph, we evaluated three node’s centrality measures: $closeness$, $betweenness$, and $eigenvector$ [47]. In particular, the closeness measures how short the shortest paths are from $d_i$ to all domains in the network, and it is named $cls$. The betweenness measures the extent to which $d_i$ lies on paths between other domains, and it is named $btwn$. Finally, the eigenvector reflects the importance of $d_i$ for the connectivity of the graph and it is denoted $eigvec$.
**ToRRank Value**: ToRRank is a link-based ranking algorithm to order the items of a given network following their centrality [2]. We applied ToRRank to the Tor network to rank the onion domains, and we used the assigned rank as a feature of the node. Moreover, we used a binary flag to indicate whether
Our LtR schema aims to learn a function $f$ that projects a feature vector into a rank value $(d_{i,1}, d_{i,2}, ..., d_{i,n}) \xrightarrow{f} r_i$. Therefore, the goal of an LtR scheme is to obtain the optimal ranking function $f$ that ranks $D$ in a way similar to $R$. The learning loss function depends on the used LtR architecture, as explained in the following three subsections.
### 3.2.1 Pointwise
The loss function of the Pointwise approach considers only a single instance of onion domains at a time [49]. It is a supervised classifier/regressor that predicts a relevance score for each query domain independently. The ranking is achieved by sorting the onion domains according to yield scores. For this LtR schema, we explore the Multi-layer Perceptron (MLP) regressor [50].
### 3.2.2 Pairwise
It transforms the ranking task into a pairwise classification task. In particular, the loss function takes a pair of items at a time and tries to optimize their relative positions by minimizing the number of inversions comparing to the ground truth [51]. In this work, we use the RankNet algorithm [51], which is one of the most popular pairwise LtR schemes.
### 3.2.3 Listwise
This approach extends the pairwise schema by looking at the entire list of samples at once [52]. One of the most well-known listwise schemes is ListNet algorithms [53]. Given two ranked lists, the human-labeled scores and the predicted ones, the loss function minimizes the cross-entropy error between their permutation probability distributions.
## 4 Experimental Settings
To test our proposal, we designed an experiment to answer three research questions:
- What is the most suitable LtR schema for the task of ranking the onion domains in the Tor network and for detecting the influential ones?
- Which are the advantages of two different ranking approaches, the content-based and the link-based?
- And what is the best combination of features for the LtR model performance?
In this section, we discuss the motivation behind these questions, describing in detail the analytical approach that we conducted, and finally, we present our findings.
### 4.1 Evaluation Measure
The two most popular metrics for ranking Information Retrieval systems are Mean Average Precision (MAP) and Normalized Discounted Cumulative Gain (NDCG) [54], [55]. The main difference between the two is that the MAP assumes a binary relevance of an item according to a given query, while NDCG allows relevance scores in the form of real numbers. Two characteristics suggest the use of NDCG to evaluate the problem addressed in this paper. Thanks to the first component of the Tor network monitoring pipeline - the classification components-, all the addressed onion domains are already relevant to the query, and second, the
ground truth and the predicted rank produced by any of the previously commented LtR schemes are real numbers, not binary ones. To obtain the \( \text{NDCG} @ K \) of a given query, we calculate the \( \text{DCG} @ K \) flowing the next formula (Eq. 1):
\[
\text{DCG} @ K = G_1 + \sum_{i=2}^{K} \frac{G_i}{\log_2(i)}
\]
Where \( G_1 \) is the gain score at the first position in the obtained ranked list, \( G_i \) is the gain score of the item \( i \) in that list, and \( K \) refers to the first \( K \) items to calculate the \( \text{DCG} \). To obtain a normalized version of \( \text{DCG} @ K \) is necessary to divide it by \( \text{IDCG} @ K \), which is the ideal \( \text{DCG} @ K \) sorted by the gain scores in descending order (Eq. 2).
\[
\text{NDCG} @ K = \frac{\text{DCG} @ K}{\text{IDCG} @ K}
\]
### 4.2 Modules Configurations
#### 4.2.1 Hardware Configurations
Our experiments were conducted on a 2.8 GHz CPU (Intel i7) PC running Windows 10 OS with 16G of RAM. We implemented the ranking models using Python3.
#### 4.2.2 HSMU Configurations
In the TF-IDF text vectorizer, we set the feature vector length to 10,000 with a minimum frequency of 3, following our previous work [11]. We used a NER model trained on WNUT-2017 dataset [8]. To set the popularity threshold of the \( \text{popular NE}_i \) feature, we examined four values \((3, 5, 10, 15)\), and we assigned it to 5, experimentally. Additionally, we set the threshold of the \( \text{recently updated} \) feature to three months earlier to the dataset scraping date. To extract features from the HTML code, we used BeautifulSoup library [9]. To construct the Tor network graph, we used NetworkX library [10].
In the image classifier, we used the Transfer Learning (TL) technique with the pre-trained Inception-ResNet V2 model released by Google [11]. The model was trained and tested with a dataset of 9,000 and 2,700 samples, respectively, equally distributed over nine categories. The motivation behind selecting these categories is to have the same classes as in our text classifier [11]. The dataset was collected from Google Images using a chrome plugin called Bulk Image Downloader. Table 2 shows the image classifier performance per category.
#### 4.2.3 SLRU Configurations
We used the dataset described in Section 5.1 to train and test the three LtR models introduced in Section 3.2. Due to the small number of samples in the drug domain, 290, we conducted 5-fold cross-validation following recommendations from previous works [53]. On each iteration, three folds are used for training the ranking model, one fold for validation, and one fold for testing. For the three LtR models, the number of iterations is controlled by an early stopping framework, which is triggered when there is no remarkable change in the validation set at \( \text{NDCG} @ 10 @ 9 \).
The three LtR schemes commented in Section 3.2 share the same network structure but with different loss functions. The neural network has two layers, with 128 and 32 neurons, respectively. For non-linearity, a Rectifier Linear Unit (ReLU) activation function is used [57]. To avoid overfitting, the ReLU layer is followed by a dropout layer with a value of 0.5 [58].
### 5 Results and Discussion: Drugs Case Study
#### 5.1 Dataset Construction
Darknet Usage Text Addresses 10K (DUTA-10K) is a publicly available dataset proposed by Al-Nabki et al. [2] that holds more than 10K onion domains downloaded from the Tor network and distributed in 28 categories. In this case study, we address the ranking of the onion domains that were classified as Drugs in DUTA-10K. This category contains drugs-topics activities, including manufacture, cultivation, and marketing of drugs, in addition to drug forums and discussion groups. Out of 465 drug domains in DUTA-10K, we selected only English language domains what makes a total of 290 domains. This ranking approach could be adapted to any category of DUTA-10K, but we selected the drugs-related domains due to its popularity in the Tor network. We also want to stress that our approach is not only limited to web domains, and it could be extended to further fields such document ranking or influencers detection in social networks when a previously ranked list for training is available.
To create the content-based dataset, thirteen people, including the authors, ranked manually the 290 drugs-related domains, to build a dataset that served as ground truth. For keeping the consistency in the ranking criteria among the annotators, we created a unified questionnaire of 23 subjective binary questions (Table 3) that were answered by the annotators for each domain. The ground truth is built in a pointwise manner assigning an annotator a value to each domain, coming from answering to every question with a 1 or 0, that corresponds to Yes or No, respectively.
This process is repeated three times, assigning to each annotator a new batch of approximately 23 domains every time, different in each iteration. Thus, each onion domain is judged three times by three different annotators, and
| Category Name | F1 Score (%) |
|-----------------------------------|-------------|
| Counterfeit Credit Cards | 92.45 |
| Counterfeit Money | 96.78 |
| Counterfeit Personal Identification| 95.16 |
| Cryptocurrency | 94.60 |
| Drugs | 91.60 |
| Pornography | 98.53 |
| Violence | 93.80 |
| Hacking | 97.63 |
| Others | 86.78 |
8. https://noisy-text.github.io/2017/emerging-rare-entities.html
9. https://pypv.org/project/beautifulsoup4/
10. https://networks.github.io/
11. http://download.tensorflow.org/models/inception_resnet_v2_2016_08_30.tar.gz
as a result, each domain is represented by three binary
vectors of answers. Following the majority voting approach, we
unified these answers’ vectors of every hidden service
into a single vector of 23 dimensions, that correspond with
the number of questions. Finally, for a given domain, the
vector of answers is aggregated into a single real number,
a gain value, by adding up its elements, corresponding the
obtained sum with the ground truth rank of that domain.
The higher the gain value, the higher the rank an onion
domain obtains.
| Table 3 |
| --- |
| The binary questionnaire used to build a ground truth rank for the drugs onion domains. |
| Questions | Answers |
| --- | --- |
| Has a satisfactory FAQ? | Has a communication channel? |
| Has a professional design? | Has real images for the products? |
| Has a subjective title? | Sells between 2 to 10 products? |
| Provides safe shipping? | Domain name has a meaning? |
| Offers reward or discount? | Products majority are illegal? |
| Sell more than 10 products? | Still accessible in TOR network? |
| Shipping worldwide service? | Sells at least one popular product? |
| Reputation content? | Requires login/registration? |
| Accepts only Cryptocurrency? | Recently updated? |
| Can customers add a review/feedback? | Do you feel that this domain is trustable? |
| Need text spotting for the products’ images | Are you satisfied with the content of the domain? |
| Has more than 10 sub-pages? | Products majority are illegal? |
5.2 Learning to Ranking Schema Selection
In Section 3.2, we evaluated three well-known LtR schemes,
namely, pointwise, pairwise, and listwise, and for each one, we explored a supervised ranking algorithm: MLP, RankNet, and ListNet, respectively. We wanted to know what is the most suitable LtR schema for the task of ranking the onion domains in the Tor network and detecting the influential ones. Fig. 3 compares the three LtR algorithms in the onion domains in the Tor network and detecting the influential ones. Fig. 3 shows the superiority of the Listwise approach when each domain is represented by a vector of 40 features extracted from five different kinds of resources (Section 3.1). The same figure shows that the NDCG@1 of the ListNet is equal to one, which means that during the five folds of cross-validation, the algorithm ranked correctly the first domains tested, exactly as the ground truth. At NDCG@4, the curve starts dropping; however, the lowest NDCG value was 0.88 for K equals to 25. As also can be seen in Fig. 3, the pointwise approach, which is the MLP in our case, obtained the worst performance, which agrees with the conclusion of other researchers.
In addition to comparing the performance in terms of the NDCG@K, we registered the duration of the time required to train and to test each LtR model, i.e., starting from the moment the model receives a list of domains encoded by HSMU (Section 3.1) until it produces their rank. On average, for the five-folds, the ListNet model took 8.30 seconds for training and 0.88 seconds for testing. The RankNet took 7.35 seconds for training and 0.007 seconds for testing. Finally, the fastest one was the MLP model, which took 3.34 seconds for training and 0.0009 seconds for testing. This comparison shows that the ListNet model is the slowest one due to the complexity of its loss function comparing to the ones of the RankNet and the MLP algorithms.
5.3 Link-based versus Content-based Ranking
Having two distinct ranking strategies raises a question: which is the most suitable ranking approach? Content-based or link-based? To answer it, we explore four link-based algorithms, namely, ToRank, PageRank, Hyperlink-Induced Topic Search (HITS), and Katz. In particular, we compare the best LtR model of our approach, i.e., ListNet, which is considered as a supervised ranking algorithm, with the four link-based algorithms that are unsupervised. We represent the Tor network by a directed graph that consists of nodes and directed edges, where nodes represent the onion domains, and the hyperlinks between them are captured using the directed edges.
Comparison configuration. Unlike our approach, the link-based algorithms do not require training data. To obtain a fair comparison, we carried out 5-folds cross-validation with the same random seed for both ranking approaches. Then, we constructed a directed graph out of the testing nodes and applied the link-based algorithms; finally, both approaches were evaluated using the same test set. For the link-based algorithms, we evaluated several configuration parameters and selected the ones that obtained the highest NDCG (Table 4).
Fig. 4 shows that ListNet highly surpasses all the link-based ranking algorithms. We observe that the weakest LtR approach, i.e., MLP, which obtained a NDCG@10 of 0.71, outperforms the best link-based ranking algorithm, ToRank, which scored NDCG@10 of 0.69. This result emphasizes the importance of considering the content of domains rather than their hyperlinks connectivity only.
5.4 Feature Selection
In the previous sections, we concluded that ListNet outperforms the RankList and MLP content-based and the four
TABLE 4
The examined parameters for the link-based ranking algorithms. Bold numbers correspond to the selected configuration that achieved the highest \( NDCG \) value.
| Algorithm Name | Parameter | Evaluated values |
|----------------|-----------|------------------|
| PageRank | alpha | 0.5, 0.70, 0.75, 0.80, 0.85, 0.90 |
| | max_iter | 10, 100, 1000, 10000 |
| ToRank | alpha | 0.50, 0.70, 0.80, 0.90 |
| | beta | 0.1, 0.2, 0.3, 0.4, 0.5, 0.6 |
| HITS | max_iter | 10, 100, 1000, 10000 |
| Katz | alpha | 0.01, 0.1, 0.2, 0.3, 0.4, 0.6, 0.9 |
| | beta | 0.1, 0.3, 0.5, 0.7, 0.9, 1.0 |
| | max_iter | 10, 100, 1000, 10000 |
Fig. 4. A comparison between the content-based versus link-based ranking algorithms with respect to multiple values of \( K \). The horizontal axis refers to \( K \) value and the vertical one indicates the \( NDCG \) scores the algorithms obtained at each value of \( K \).
link-based algorithms when the proposed forty features represent an onion domain. However, the cost of these features varies. Some of them, such as the visual content, requires building a dedicated image classification model, while other features could be extracted merely using a regular expression. The cost is reflected in the time necessary to obtain the features and to build the ranking model, in addition to the inference time. On average, per domain, the prediction of the image classification model was the most expensive and took 109 seconds, followed by the NER model with 22 seconds, and then it was the text features that required 12 seconds. Finally, the HTML and the graph features were the fastest ones to be extracted, spending 3 and 2 seconds, respectively.
In the following, we want to answer the question: what is the feature or combination of features that produce the best performance of the LtR model? To answer this question, we conducted feature analysis for the best LtR model, the ListNet one, using features and combining them from the five different resources. To discover the best combination of features for the ranking system performance, we trained and tested five ListNet models for each source of features and compared their performance.
When we analyze only features coming from a single source, without combining them, it can be seen in Fig. 4 that the features that are extracted only from text, denoted by text and in clear green in this figure, achieves the highest \( NDCG@5 \) of 0.90. Very close to them is the model trained using only recognized named entities (NER) features, which obtains a \( NDCG@5 \) of 0.85. After that, using only features extracted from HTML, the ListNet model obtains a \( NDCG@5 \) of 0.81. In contrast, the graph features obtain the lowest \( NDCG@5 \) of 0.65, which indicates their weakness for ranking the onion domains, unlike the features that are extracted from the text, which have shown a significant and positive impact on the \( NDCG \) metric. Hence, we conclude that the features extracted from the user-visible text are more representative comparing to the ones coming from the visual characteristics of the domain or the graph ones.
After the previous analysis, we decided to investigate the effect of combining features from different sources, to measure the impact of those combinations on the model performance. In Figure 5, it can be seen that the performance increases when the top-3 individual features, i.e. text, NER, and HTML are fused. Also, those three features combined could obtain a \( NDCG \) close to the one yield by combining all the features (All). Consequently, we could remove the graph and the visual features and keep the ranking performance relatively high and very close to the case when all the features are used.
6 Conclusions and Future Work
The Tor network is overfull with suspicious activities that LEAs are interested in monitoring. By ranking the onion domains according to their influence inside the Tor network, LEAs can prioritize the domains to leverage the monitoring process.
In this paper, we created several ranking frameworks using Learning-to-Rank (LtR) to detect the most influential onion domains in the Tor darknet using different sources of features. Our purpose was to determine which is the best approach that allows the best performance with the lower complexity in the model creation. The proposed framework consists of two components. 1) Hidden Service Modeling Unit (HSMU), that represents an onion domain by 40 features that are extracted from five different resources: the domain user-visible text, the HTML markup of the web page, the named entities in the domain text, the visual content, and the Tor network structure; and 2) Supervised Learning-to-Rank Unit (SLRU), that learns how to rank the domains using LtR approach. To train the LtR model, we built a manually sorted dataset of 290 drugs-related onion domains.
We tested the effectiveness of our framework on a manually ranked dataset of onion domains related to drug trading. We explored and evaluated three common LtR algorithms: MLP, RankNet, and ListNet, considering that the method which obtained the highest \( NDCG \) is the best one. We found that the ListNet algorithm outperforms the rest of the ranking algorithms with a \( NDCG@10 \) of 0.95. Moreover, we contrasted our framework with four link-based ranking algorithms, and we observed that the MLP with a \( NDCG@10 \) of 0.71, which is the worst LtR algorithm, is better than the best link-based one, ToRank, which obtained a \( NDCG@10 \) of 0.69.
Given the superiority of the ListNet algorithm, we analyzed how the different kinds of features impact the ranking performance. We found that using only the features extracted from the user-visible textual content, including the text, the named entities, and HTML markup code, the model achieves a \( NDCG@4 \) of 0.97, exactly the same as the
model that uses all the features. However, at $NDCG@10$, the performance drops slightly to 0.88 comparing to 0.91 using the five different sources of features. Considering both the cost to obtain the features and to create the models and its score, we recommend the text-NER-HTML model because its cost is low, and its score is almost the same as the more complex approach that uses all the features.
In the future we plan to explore additional LtR methods from the listwise approach such as RankBoost [60] and LambdaMart [61]. Moreover, we will explore the StarSpace algorithm [62] that attempts to learn objects representations into a common embedding space that could be used to entities ranking and recommendation systems. Finally, in order to ease the process of building the training dataset, both in terms of time and the number of the labeled samples, we plan to explore the Active Learning technique [63], which selects the most distinct samples to be sorted by an expert.
**ACKNOWLEDGMENTS**
This work was supported by the framework agreement between the University of León and INCIBE (Spanish National Cybersecurity Institute) under Addendum 01 and 22.
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Warping Effects in Strongly Perturbed Metrics
Marco Frasca†‡, Riccardo Maria Liberati† and Massimiliano Rossi*†‡
MBDA Italia S.p.A., Via Monte Flavio, 45, 00131 Rome, Italy; [email protected] (M.F.); [email protected] (R.M.L.)
* Correspondence: [email protected]
† These authors contributed equally to this work.
Received: 15 October 2020; Accepted: 1 December 2020; Published: 7 December 2020
Abstract: A technique devised some years ago permits us to develop a theory regarding a regime of strong perturbations. This translates into a gradient expansion that, at the leading order, can recover the Belinsky-Kalathnikov-Lifshitz solution for general relativity. We solve exactly the leading order Einstein equations in a spherical symmetric case, assuming a Schwarzschild metric under the effect of a time-dependent perturbation, and we show that the 4-velocity in such a case is multiplied by an exponential warp factor when the perturbation is properly applied. This factor is always greater than one. We will give a closed form solution of this factor for a simple case. Some numerical examples are also given.
Keywords: general relativity; Schwarzschild solution; warp factor
1. Introduction
The study of Einstein equations in certain regimes is often restricted to solving them numerically [1]. The reason is that they form a set of nonlinear partial differential equations that are generally difficult to handle with analytical tools for most interesting situations. Often, the reason relies in the fact that no small parameter can be found to apply to standard perturbation techniques, while analytical solutions are very rare and difficult to find. Some years ago, a member of our group (Marco Frasca) proposed an approach based on earlier works on strongly perturbed systems [2]. It was shown that, under a strong perturbation in the formal limit running to infinity, the leading order perturbation series was firstly proposed by Belinsky, Kalathnikov, and Lifshitz for their famous BKL conjecture [3–5], as is known today.
Some decades ago, Alcubierre proposed a solution for the Einstein equations [6] that describes an observer moving with an unbounded velocity, provided that the condition of positivity of the energy is violated. A recent paper [7] (see also references therein) presents a short account of the Alcubierre metric and its interaction with dust. Indeed, many kinds of pathologies have emerged about it and the difficulties arise from the fact that this is an engineered metric that is imposed on the Einstein equations. It would be desirable to have a metric like this one emerging as a solution for the Einstein equations and conserving the positivity of the energy. A recent proposal works in such a direction [8]. This is possible by introducing a hyperbolic shift vector potential and the author shows how this can emerge from a plasma.
In this paper, we will show how a warp factor for the velocity can emerge when a strong perturbation is applied to a spherical symmetric metric. Thus, any Eulerian observer will have its velocity expanded when such perturbation acts. This extends and completes our preceding work [2]. We will obtain the exact solution for the leading perturbation equations and we will show how an exponential factor can emerge that is systematically greater than one. We emphasize that we are...
applying perturbation theory in a limit where the a perturbation applied to a given gravitational field is taken to be much greater than the unperturbed situation. This is the opposite limit to standard small perturbation theory and is based on the technique devised in [2].
The paper is so structured. In Section 2, we will introduce a technique to treat strongly perturbed systems. In Section 3, we apply this to the Einstein equations for a spherical symmetry metric with a time-dependent perturbation. In Section 4, we solve the leading order perturbation equations. In Section 5, we present the geodesic equations. In Section 6, we show how the expansion factor enters into the velocity, providing some examples and an analytic solution. In Section 7, conclusions are presented.
2. Strong Perturbations and Gradient Expansion
For our computations in general relativity, we need to study the case of a strong perturbation on a given metric: we select the Schwarzschild metric. In order to prove that a gradient expansion indeed represents a strong perturbation theory, we will study the following non-linear equation as a toy model for the Einstein equations that can represent Einstein equations in 1 + 1 dimensions [9–11]:
$$-\Box \phi + \lambda V'(\phi) = 0,$$
where the prime means derivative with respect to \( \phi \), \( \Box = \nabla^2 - \partial_t^2 \) with \( \partial_t \) being the time derivative, \( \partial_t \) is the wave operator, \( \phi \) is a scalar field and \( V(\phi) \) is its self-interaction with a coupling \( \lambda \). Here and in what follows, the speed of light is set \( c = 1 \). For 2-dimensional Einstein equations, this would be a Liouville equation [9–11]. We would like to apply perturbation theory in the formal limit of \( \lambda \to \infty \). This results in a non-trivial series in \( 1/\lambda \). We can accomplish our aim by rescaling the time variable [12]. We take \( t \to \sqrt{\lambda} t \) and the equation above becomes
$$-\nabla^2 \phi + \lambda \partial_t^2 \phi + \lambda V'(\phi) = 0. \quad (2)$$
Then, we take
$$\phi = \phi_0 + \frac{1}{\lambda} \phi_1 + \frac{1}{\lambda^2} \phi_2 + \ldots \quad (3)$$
and substitute this into Equation (2). This gives the following set of perturbative equations:
\[
\begin{align*}
\partial_t^2 \phi_0 &= -V'(\phi_0), \\
\partial_t^2 \phi_1 &= -V''(\phi_0)\phi_1 + \nabla^2 \phi_0, \\
\partial_t^2 \phi_2 &= -V''(\phi_0)\phi_2 - \frac{1}{2} V'''(\phi_0)\phi_1^2 + \nabla^2 \phi_1,
\end{align*}
\]
etc. \( (4) \)
We see that we have obtained a set of non-trivial equations that define the perturbation series in the formal limit \( \lambda \to \infty \). This approach can be applied, exactly in this way, to the Einstein equations. This also shows how consistent was the original BKL approach in [3–5]. Indeed, we have obtained a gradient expansion.
In order to see how this technique applies to Einstein equations, we express them in the Arnowitt–Deser–Misner (ADM) formalism as [1] (here and in the following Latin indexes \( i, j, \ldots \) run from 1 to 3, Greek indexes run from 0 to 3)
\[
\begin{align*}
\partial_t \gamma_{ij} - \beta^l \partial_l \gamma_{ij} &= \gamma_{ij} \partial_t \beta^l + \gamma_{ij} \partial_l \beta^l - 2\alpha K_{ij}, \\
\partial_i K_{ij} - \beta^l \partial_l K_{ij} &= K_{ij} \partial_t \beta^l + K_{ij} \partial_l \beta^l - 2\alpha K_{ij} K^l_j + \alpha KK_{ij} \\
&- \frac{1}{2} \alpha \gamma_{lm} \{ \partial_l \partial_m \gamma_{ij} + \partial_i \partial_j \gamma_{lm} - \partial_j \partial_i \gamma_{mj} - \partial_i \partial_j \gamma_{mi} \\
&+ \gamma^m_p ( \partial_i \gamma_{jm} + \partial_j \gamma_{im} - \partial_m \gamma_{ij} ) \partial_l \gamma_{mp} \}
\end{align*}
\]
\( (5) \)
\[ + \partial_t \gamma_{in} \partial_p \gamma_{jm} - \partial_i \gamma_{in} \partial_m \gamma_{jp} \]
\[ - \frac{1}{2} \gamma^{np} \left[ (\partial_t \gamma_{jm} + \partial_j \gamma_{im} - \partial_n \gamma_{ij}) \partial_p \gamma_{lm} + \partial_i \gamma_{in} \partial_p \gamma_{jm} \right] \]
\[ - \partial \Gamma_{\alpha} + \frac{1}{2} \gamma^{lm} (\partial_t \gamma_{jm} + \partial_j \gamma_{im} - \partial_m \gamma_{ij}) \partial_i \alpha \]
\[ + \alpha \left[ - 8 \pi G T_{ij} + 4 \pi G \gamma_{ij} (T - \rho) \right] , \tag{6} \]
where \( \partial_i = \partial / \partial x^i \), \( G \) is the Newton constant and the energy–matter tensor \( T_{ij} \) is given with the density \( \rho \), for a metric
\[ ds^2 = (-\alpha^2 + \gamma_{ij} \beta^i \beta^j) dt^2 + 2 \beta^i dx^i dt + \gamma_{ij} dx^i dx^j \tag{7} \]
with \( \alpha \) being the lapse function, \( \beta^i \) the shift vector, \( \gamma_{ij} \) the spatial part of the metric and \( K_{ij} \) the extrinsic curvature. For our purposes, we are not interested in constraint equations that are essential only for numerical computations. This set is amenable to the same treatment we applied to the preceding example. The procedure is identical: we introduce an ordering parameter \( \lambda \) that we will set to 1 to the end of computation. Then, we consider the perturbation series defined by
\[ \tau = \sqrt{\lambda} t , \tag{8} \]
\[ K_{ij} = \lambda \left( K_{ij}^{(0)} + \frac{1}{\lambda} K_{ij}^{(1)} + \frac{1}{\lambda^2} K_{ij}^{(2)} + \ldots \right) , \]
\[ \gamma_{ij} = \gamma_{ij}^{(0)} + \frac{1}{\lambda} \gamma_{ij}^{(1)} + \frac{1}{\lambda^2} \gamma_{ij}^{(2)} + \ldots , \]
\[ \alpha = \alpha_0 + \frac{1}{\lambda} \alpha_1 + \frac{1}{\lambda^2} \alpha_2 + \ldots . \]
Our gauge choice is to set the shift vector \( \beta_i = 0 \). This approach mirrors completely the standard computation for weak gravitational fields but implies that the perturbation is taken formally to reach infinity. This represents a situation where the perturbation overcomes the intensity of the gravitational field where it is applied. Typical situations where this technique could apply include black hole collisions, where, currently, only numerical computations or analytical techniques, working given certain approximations, are available [13]. Therefore, we obtain the following non-trivial set of equations (we have set \( \lambda = 1 \)):
\[ \partial_t \gamma_{ij}^{(0)} = -2 \alpha_0 K_{ij}^{(0)} , \tag{9} \]
\[ \partial_t \gamma_{ij}^{(1)} = -2 \alpha_1 K_{ij}^{(0)} - 2 \alpha_0 K_{ij}^{(1)} , \]
\[ \vdots \]
\[ \partial_t K_{ij}^{(0)} = -2 \alpha_0 K_{il}^{(0)} K_{j}^{(0)} + \alpha_0 K_{ij}^{(0)} K_{ij}^{(0)} , \]
\[ \partial_t K_{ij}^{(1)} = -2 \alpha_1 K_{il}^{(0)} K_{j}^{(0)} + 2 \alpha_0 K_{il}^{(1)} K_{j}^{(0)} - 2 \alpha_0 K_{ij}^{(1)} K_{ij}^{(1)} + \alpha_1 K_{ij}^{(0)} K_{ij}^{(0)} + \alpha_0 K_{ij}^{(0)} K_{ij}^{(1)} \]
\[ - \frac{1}{2} \alpha_0 \gamma_{jm}^{(0)} \left\{ \partial_t \partial_{m} \gamma_{ij}^{(0)} + \partial_j \partial_{m} \gamma_{im}^{(0)} - \partial_i \partial_{m} \gamma_{jm}^{(0)} - \partial_j \partial_{m} \gamma_{im}^{(0)} \right\} \]
\[ + \gamma_{ij}^{mp} \left\{ (\partial_t \gamma_{jm}^{(0)} + \partial_j \gamma_{im}^{(0)} - \partial_m \gamma_{ij}^{(0)}) \partial_p \gamma_{lm}^{(0)} \right\} \]
\[ + \partial \gamma_{jm}^{(0)} \partial_p \gamma_{mn}^{(0)} \left[ - \partial_t \partial_{m} \gamma_{ij}^{(0)} - \partial_p \gamma_{mn}^{(0)} \partial_t \gamma_{ij}^{(0)} - \partial_p \gamma_{mn}^{(0)} \partial_t \gamma_{ij}^{(0)} \right] \]
\[ - \frac{1}{2} \gamma_{ij}^{mp} \left\{ (\partial_t \gamma_{jm}^{(0)} + \partial_j \gamma_{im}^{(0)} - \partial_m \gamma_{ij}^{(0)}) \partial_p \gamma_{lm}^{(0)} + \partial \gamma_{jm}^{(0)} \partial_p \gamma_{mn}^{(0)} \right\} \]
\[ - \partial \gamma_{ij}^{(0)} \partial_0 + \frac{1}{2} \gamma_{ij}^{(0)} \left[ \partial_t \gamma_{jm}^{(0)} + \partial_j \gamma_{im}^{(0)} - \partial_m \gamma_{ij}^{(0)} \right] \partial \gamma_{ij}^{(0)} \]
\[ + \alpha^{(0)} \left[ - 8 \pi G T_{ij} + 4 \pi G \gamma_{ij}^{(0)} (T - \rho) \right] , \]
where one sees that the energy–matter tensor contributes to the next-to-leading order. We realize from these equations that the gradient terms—that is, components of the metric that vary spatially—are moved to the next-to-leading order. We will apply them in the following in the spherical symmetric case, assuming the Schwarzschild metric as the unperturbed solution. Here, and in the following, we avoid showing explicitly the energy–matter tensor as our perturbation series moves its contribution to the next-to-leading order. This implies that, at the leading order, an approximation for the energy–matter configuration can be taken to be that in absence of the gravitational field. This is consistent with our approach for strongly perturbed metrics.
Nevertheless, in order to gain insight into the main concept underlying this approximation scheme, let us consider the Reissner–Nördstrom metric of a charged black hole. This will be given by
$$ds^2 = - \left(1 - \frac{r_s}{r} + \frac{r_Q^2}{r^2}\right) dt^2 + \left(1 - \frac{r_s}{r} + \frac{r_Q^2}{r^2}\right)^{-1} dr^2 + r^2 d\theta^2 + r^2 \sin^2 \theta d\phi^2,$$
with $r_s = 2GM$ being the Schwarzschild radius for a mass $M$ and $r_Q^2 = GQ^2 / 4\pi\epsilon_0$ the scale introduced by the black hole charge $Q$ with $1/4\pi\epsilon_0$ the Coulomb constant. This is an exact solution for the Einstein–Maxwell equations. In our case, we assume that the electric field overcomes largely the gravitational contribution—that is, $r_Q \gg r_s$. This appears formally as a large perturbation on a Schwarzschild black hole and the approximate metric will be
$$ds^2 = - \left(1 + \frac{r_Q^2}{r^2}\right) dt^2 + \left(1 + \frac{r_Q^2}{r^2}\right)^{-1} dr^2 + r^2 d\theta^2 + r^2 \sin^2 \theta d\phi^2 + O(r_s/r).$$
This should be compared with the opposite dual limit $r_Q / r_s \ll 1$, which yields
$$ds^2 = - \left(1 - \frac{r_s}{r}\right) dt^2 + \left(1 - \frac{r_s}{r}\right)^{-1} dr^2 + r^2 d\theta^2 + r^2 \sin^2 \theta d\phi^2 + O(r_Q^2/r^2).$$
3. Strongly Perturbed Spherical Symmetry Metric
We assume a spherical symmetry metric in ADM formalism given by
$$ds^2 = -\alpha^2 dt^2 + \gamma_{rr} dr^2 + \gamma_{\theta\theta} d\theta^2 + \gamma_{\phi\phi} d\phi^2.$$
This implies a specific choice of the gauge where all the components of the shift vector, normally named $\beta_i$, are taken to be zero. Then, the perturbation $\alpha_1$ is applied to the lapse function as follows [1]:
$$\alpha^2 = \alpha_0^2 + \alpha_1.$$
Then, we specialize the set of Equation (9) to this case. Assuming the Schwarzschild solution as the unperturbed solution, the exterior solution is given by (again, $r_s = 2GM$ is the Schwarzschild radius)
$$\alpha_0^2 = \left(1 - \frac{r_s}{r}\right),$$
$$\gamma_{11}^{(0)} = \frac{1}{1 - \frac{r_s}{r}},$$
$$\gamma_{22}^{(0)} = r^2, \quad \gamma_{33}^{(0)} = r^2 \sin^2 \theta.$$
and the interior solution is
\[ a_0^2 = \frac{1}{4} \left( \frac{3}{r_s} - 1 \right)^2, \]
(17)
\[ \gamma_{11}^{(0)} = - \left( \frac{r^2}{r_s^2} \right)^{-1}, \]
\[ \gamma_{22}^{(0)} = r^2, \]
\[ \gamma_{33}^{(0)} = r^2 \sin^2 \theta, \]
where \( r_s \) is the value of the \( r \)-coordinate at the body’s surface. It is easy to see that both metrics are the same at the sphere surface for \( r = r_s \), granting continuity. We also have, with our gauge’s choice \( \beta_i = 0 \), the general formula
\[ K_{ij} = -\frac{1}{2\kappa} \partial_t \gamma_{ij}. \]
(18)
In our case, this is
\[ a^2 = a_0^2 + a_1 = a_0^2 + A f(r, t), \]
(19)
where \( A \) is the amplitude of the perturbation. We emphasize that the perturbations which we will consider are time-dependent. This yields
\[ \partial_t \gamma_{ij}^{(1)} = a_1 \frac{1}{\alpha_0} \partial_t \gamma_{ij}^{(0)} - 2\alpha_0 K_{ij}^{(1)}, \]
(20)
which reduces to
\[ \partial_t \gamma_{ij}^{(1)} = -2\alpha_0 K_{ij}^{(1)}, \]
(21)
as \( \gamma_{ij}^{(0)} \) does not depend on the time variable. Now, one has
\[ \partial_t K_{ij}^{(1)} = -2\alpha_1 K_{ij}^{(0)} K_{kl}^{(1)} K_{j}^{(0)} - 2\alpha_0 K_{ij}^{(1)} K_{j}^{(0)} - 2\alpha_0 K_{ij}^{(0)} K_{j}^{(1)} \]
\[ + \alpha_1 K_{ij}^{(0)} K_{kl}^{(1)} K_{j}^{(0)} + \alpha_0 K_{ij}^{(1)} K_{j}^{(0)} + \alpha_0 K_{ij}^{(0)} K_{j}^{(1)} \]
\[ + \alpha_1 K_{ij}^{(0)} K_{kl}^{(1)} K_{j}^{(0)} + \alpha_0 K_{ij}^{(1)} K_{j}^{(0)} + \alpha_0 K_{ij}^{(0)} K_{j}^{(1)} \]
\[ - \frac{1}{2} a_0 \gamma^{lm} \left\{ \partial_t \partial_m \gamma_{ij}^{(0)} + \partial_t \partial_l \gamma_{jm}^{(0)} - \partial_t \partial_l \gamma_{mj}^{(0)} - \partial_t \partial_l \gamma_{mj}^{(0)} \right\} \]
\[ + \gamma^{np} \left\{ (\partial_t \gamma_{jn}^{(0)} + \partial_t \gamma_{jn}^{(0)} - \partial_t \gamma_{jn}^{(0)}) \partial_t \gamma_{lm}^{(0)} \right\} \]
\[ + \partial_t \gamma_{jn}^{(0)} \partial_t \gamma_{jm}^{(0)} + \partial_t \gamma_{jn}^{(0)} \partial_t \gamma_{jm}^{(0)} \]
\[ + \partial_t \gamma_{jn}^{(0)} \partial_t \gamma_{jm}^{(0)} + \partial_t \gamma_{jn}^{(0)} \partial_t \gamma_{jm}^{(0)} \]
\[ - \partial_t \partial_t a_0 + \frac{1}{2} \gamma^{lm} \left\{ (\partial_t \gamma_{jn}^{(0)} + \partial_t \gamma_{jn}^{(0)} - \partial_t \gamma_{jn}^{(0)}) \partial_t \gamma_{lm}^{(0)} + \partial_t \gamma_{jn}^{(0)} \partial_t \gamma_{lm}^{(0)} \right\} \]
etc.
This set of equations, written in this way, is too difficult to manage. As we will see below, we can restate them to find an exact leading order solution.
It is correct to ask why the Birkhoff theorem does not apply in our case. The reason is that the problems we are treating are similar to that of the ringdown of a Schwarzschild black hole, where a strong perturbation, due to the collision between two black holes, modifies the metric, making it vary in time, after coalescence, until the oscillations are damped out and the spherical symmetry is recovered [14], in agreement with the Birkhoff theorem. It should be noted that such problems are better managed in the Kerr metric but we do not consider rotations to avoid too many computations cluttering the formulas.
4. Solving Perturbation Equations
In order to obtain more manageable equations, let us start from the following rewriting of the ADM equations of motion in exact form. We will obtain (as already stated, our gauge is $\beta_i = 0$)
$$\partial_t \gamma_{ij} = -2\alpha K_{ij},$$
$$\partial_t K_{ij} = \alpha \left[ R_{ij} - 2K_{il}K^l_j + KK_{ij} \right] - \partial_i \partial_j \alpha. \quad (23)$$
The Ricci tensor $R_{ij}$ refers to the $\gamma_{ij}$. We can exploit these equations for the diagonal elements to obtain
$$\partial_t \gamma_{11} = -2\alpha K_{11},$$
$$\partial_t \gamma_{22} = -2\alpha K_{22},$$
$$\partial_t \gamma_{33} = -2\alpha K_{33},$$
$$\partial_t K_{11} = \alpha \left[ R_{11} - 2K_{1l}K^l_1 + KK_{11} \right] - \partial_1^2 \alpha,$$
$$\partial_t K_{22} = \alpha \left[ R_{22} - 2K_{2l}K^l_2 + KK_{22} \right] - \partial_2^2 \alpha,$$
$$\partial_t K_{33} = \alpha \left[ R_{33} - 2K_{3l}K^l_3 + KK_{33} \right] - \partial_3^2 \alpha. \quad (24)$$
We notice that $K_j^l = \gamma^{jl}K_{ik}$ and $K = \gamma^{kl}K_{kl}$.
We expect that off-diagonal terms should be perturbatively negligible and so we neglect them here in view of a gradient expansion. Indeed, for $i \neq j$, we will have
$$K_{ij} = -\frac{\partial_t \gamma_{ij}}{2\alpha},$$
$$\partial_t K_{ij} = \alpha \left[ R_{ij} - 2K_{il}\gamma^l_j + \gamma^{kl}K_{ik}K_{lj} \right] - \partial_i \partial_j \alpha. \quad (25)$$
This will give
$$-\partial_t \left( \frac{\partial_t \gamma_{ij}}{2\alpha} \right) = \alpha \left[ R_{ij} + \frac{1}{2\alpha^2} \partial_t \gamma_{ii} \gamma^j_k \partial_t \gamma \gamma_{jk} + \frac{1}{4\alpha^2} \gamma^{kl} \partial_t \gamma_{ik} \partial_t \gamma_{lj} \right] - \partial_i \partial_j \alpha. \quad (26)$$
In a gradient expansion, where we neglect both $R_{ij}$ and $\partial_i \partial_j \alpha$ as we will show below, at the leading order, the off-diagonal terms will remain zero if they were zero initially because this is a solution for Equation (26) for $i \neq j$. Therefore,
$$\partial_t \gamma_{11} = -2\alpha K_{11},$$
$$\partial_t \gamma_{22} = -2\alpha K_{22},$$
$$\partial_t \gamma_{33} = -2\alpha K_{33},$$
$$\partial_t K_{11} = \alpha \left[ R_{11} - \gamma^{11}K_{11}^2 + \left( \gamma^{22}K_{22}^2 + \gamma^{33}K_{33}^2 \right)K_{11} \right] - \partial_1^2 \alpha,$$
$$\partial_t K_{22} = \alpha \left[ R_{22} - \gamma^{22}K_{22}^2 + \left( \gamma^{11}K_{11}^2 + \gamma^{33}K_{33}^2 \right)K_{22} \right] - \partial_2^2 \alpha,$$
$$\partial_t K_{33} = \alpha \left[ R_{33} - \gamma^{33}K_{33}^2 + \left( \gamma^{11}K_{11}^2 + \gamma^{22}K_{22}^2 \right)K_{33} \right] - \partial_3^2 \alpha. \quad (27)$$
These equations can be expressed in a single set of equations for the $\gamma$s as (the dot implies the derivation with respect to $\tau$)
$$\dot{\gamma}_{11}^2 = -2\alpha K_{11} - 2\alpha \dot{K}_{11} = \frac{\dot{\alpha}}{\alpha} \dot{\gamma}_{11} - 2\alpha^2 \left[ R_{11} - \gamma^{11} \frac{1}{4\alpha^2} \left( \dot{\gamma}_{11} \right)^2 + \frac{1}{4\alpha^2} \gamma^{22} \dot{\gamma}_{22} \dot{\gamma}_{11} + \frac{1}{4\alpha^2} \gamma^{33} \dot{\gamma}_{33} \dot{\gamma}_{11} \right] + 2\alpha \dot{\alpha}^2 \gamma_{11}^2,$$
\[ \frac{\partial^2 \gamma_{22}}{\partial t^2} = -2\alpha K_{22} - 2\alpha K_{22} = \frac{\alpha}{\dot{a}} \gamma_{22} - 2\alpha^2 \left[ R_{22} - \gamma_{22}^2 \frac{1}{4\alpha^2} \dot{\gamma}_{22}^2 + \frac{1}{4\alpha^2} \gamma_{11}^2 \gamma_{22} + \frac{1}{4\alpha^2} \gamma_{33}^2 \gamma_{22} \right] + 2 \alpha \dot{a}^2 \alpha, \]
\[ \frac{\partial^2 \gamma_{33}}{\partial t^2} = -2\alpha K_{33} - 2\alpha K_{33} = \frac{\alpha}{\dot{a}} \gamma_{33} - 2\alpha^2 \left[ R_{33} - \gamma_{33}^2 \frac{1}{4\alpha^2} \dot{\gamma}_{33}^2 + \frac{1}{4\alpha^2} \gamma_{11}^2 \gamma_{33} + \frac{1}{4\alpha^2} \gamma_{22}^2 \dot{\gamma}_{33} \right] + 2 \alpha \dot{a}^2 \alpha. \] (28)
and so on for the other components. As stated in Section 3, this set of equations can be solved perturbatively by the change in variable \( \tau = \sqrt{\lambda} t \) being \( \lambda \) just an ordering parameter that we will set to 1 until the end of the computations. This means that we can neglect spatial gradients at the leading order, yielding
\[ \frac{\partial^2 \gamma_{11}}{\partial t^2} = \frac{\dot{\gamma}_{11}}{\dot{a}} \frac{d}{d\tau} \left[ \ln a + \frac{1}{2} \ln \left( \frac{\gamma_{11}}{\gamma_{22} \gamma_{33}} \right) \right]. \] (30)
Then,
\[ \dot{\tau} \ln \gamma_{11} = \frac{d}{d\tau} \left[ \ln a + \frac{1}{2} \ln \left( \frac{\gamma_{11}}{\gamma_{22} \gamma_{33}} \right) \right], \] (31)
and finally
\[ \ln \gamma_{11} = \left[ \ln \left( \frac{\tau_k a}{\lambda_0} \right) + \frac{1}{2} \ln \left( \frac{\gamma_{11}}{\gamma_{22} \gamma_{33}} \right) \right], \] (32)
where we have properly fixed the integration constant in such a way that, in the absence of perturbation, the contribution from \( \alpha \) disappears, while dimensions are kept with the constant \( r_k = r_k \) for the exterior solution and \( r_k = r_k \) for the interior solution. This gives the following set of differential equations:
\[ \dot{\gamma}_{11} = \frac{\tau_k a}{\lambda_0} \sqrt{\frac{\gamma_{11}}{\gamma_{22} \gamma_{33}}} = \frac{\tau_k a}{\lambda_0} \gamma_{11}^{-\frac{1}{2}}, \]
\[ \dot{\gamma}_{22} = \frac{\tau_k a}{\lambda_0} \sqrt{\frac{\gamma_{22}}{\gamma_{11} \gamma_{33}}} = \frac{\tau_k a}{\lambda_0} \gamma_{22}^{-\frac{1}{2}}, \]
\[ \dot{\gamma}_{33} = \frac{\tau_k a}{\lambda_0} \sqrt{\frac{\gamma_{33}}{\gamma_{11} \gamma_{22}}} = \frac{\tau_k a}{\lambda_0} \gamma_{33}^{-\frac{1}{2}}. \] (33)
This set can be solved exactly by multiplying in the following way:
\[ \dot{\gamma}_{11} \gamma_{22} \gamma_{33} = \frac{\tau_k a}{\lambda_0} \gamma_{11}^{\frac{1}{2}}, \]
\[ \dot{\gamma}_{22} \gamma_{11} \gamma_{33} = \frac{\tau_k a}{\lambda_0} \gamma_{11}^{\frac{1}{2}}, \]
\[ \dot{\gamma}_{33} \gamma_{11} \gamma_{22} = \frac{\tau_k a}{\lambda_0} \gamma_{11}^{\frac{1}{2}}, \] (34)
and summing up the three equations obtained in this way, giving
\[ \dot{\gamma} = 3 \frac{\tau_k a}{\lambda_0} \gamma_{11}^{\frac{1}{2}}, \] (35)
which has as a solution
\[ \gamma(t) = \left[ \frac{3}{2} r_k a_0^{-1} \int_0^t a(t') dt' + \sqrt{\gamma(0)} \right]^2, \] (36)
and, e.g., one has
\[ \gamma(0) = |\gamma_{11}^{(0)} \gamma_{22}^{(0)} \gamma_{33}^{(0)}| = r^4 \sin^2 \theta \frac{1}{1 - \frac{r}{\tilde{r}}}. \] (37)
for the exterior solution. This yields the following set of equations:
\[ \begin{align*}
\dot{\gamma}_{11} &= \frac{r_k a_0^{-1} a}{2 r_k a_0^{-1} \int_0^t a(t') dt' + \sqrt{\gamma(0)}} \gamma_{11}, \\
\dot{\gamma}_{22} &= \frac{r_k a_0^{-1} a}{2 r_k a_0^{-1} \int_0^t a(t') dt' + \sqrt{\gamma(0)}} \gamma_{22}, \\
\dot{\gamma}_{33} &= \frac{r_k a_0^{-1} a}{2 r_k a_0^{-1} \int_0^t a(t') dt' + \sqrt{\gamma(0)}} \gamma_{33}.
\end{align*} \] (38)
These can be solved exactly by
\[ \begin{align*}
\gamma_{11}(t) &= \exp \left[ r_k a_0^{-1} \int_0^t dt'' \frac{a(t'')}{\sqrt{\gamma(0)}} \right] \gamma_{11}^{(0)}, \\
\gamma_{22}(t) &= \exp \left[ r_k a_0^{-1} \int_0^t dt'' \frac{a(t'')}{\sqrt{\gamma(0)}} \right] \gamma_{22}^{(0)}, \\
\gamma_{33}(t) &= \exp \left[ r_k a_0^{-1} \int_0^t dt'' \frac{a(t'')}{\sqrt{\gamma(0)}} \right] \gamma_{33}^{(0)}.
\end{align*} \] (39)
We can derive the volume expansion from Equation [6]
\[ \Theta = -\alpha \text{Tr} K = -\alpha \gamma^{ij} K_{ij} = \frac{1}{2} \gamma^{ij} \gamma_{ij}, \] (40)
and \( K_{ij} \) are given by Equation (18). Then,
\[ \Theta = \frac{3}{2} \frac{r_k a_0^{-1} a}{2 r_k a_0^{-1} \int_0^t a(t') dt' + \sqrt{\gamma(0)}} \exp \left[ r_k a_0^{-1} \int_0^t dt'' \frac{a(t'')}{\sqrt{\gamma(0)}} \right]. \] (41)
Here, we can see the first appearance of the expansion (warp) factor given by
\[ U(r, \theta, t) = \exp \left[ r_k a_0^{-1} \int_0^t dt'' \frac{a(t'')}{\sqrt{\gamma(0)}} \right]. \] (42)
As we will see, this is always greater than one.
5. Geodesic Equations
For the sake of completeness, we give below the geodesic equations in such a perturbed metric. For this aim, we need to consider
\[ ds^2 = -a^2(r, t) dt^2 + \gamma_{11}(r, \theta, t) d\theta^2 + \gamma_{22}(r, \theta, t) d\phi^2 + \gamma_{33}(r, \theta, t) d\phi^2. \] (43)
From this, it is easy to derive the Lagrangian,
\[ L = - \left( -a^2(r,t)^2 + \gamma_{11}(r,\theta,t)\dot{t}^2 + \gamma_{22}(r,\theta,t)\dot{\theta}^2 + \gamma_{33}(r,\theta,t)\dot{\phi}^2 \right)^{\frac{1}{2}}, \]
where the dot means derivative with respect to the proper time \( s \). Then, using the Euler–Lagrange equations, one has
\[
\frac{d}{ds} \left( a^2 \right) - \frac{1}{2} \frac{\partial a^2}{\partial t} \dot{t}^2 + \frac{1}{2} \frac{\partial \gamma_{11}(r,\theta,t)}{\partial t} \dot{t}^2 + \frac{1}{2} \frac{\partial \gamma_{22}(r,\theta,t)}{\partial \theta} \dot{\theta}^2 + \frac{1}{2} \frac{\partial \gamma_{33}(r,\theta,t)}{\partial \phi} \dot{\phi}^2 = 0,
\]
\[
\frac{d}{ds} (\gamma_{11}\dot{t}) + \frac{\partial \gamma_{11}(r,\theta,t)}{\partial r} \dot{r}^2 - \frac{\partial \gamma_{11}(r,\theta,t)}{\partial \theta} \dot{\theta}^2 - \frac{\partial \gamma_{33}(r,\theta,t)}{\partial \phi} \dot{\phi}^2 = 0,
\]
\[
\frac{d}{ds} (\gamma_{22}\dot{\theta}) - \frac{\partial \gamma_{22}(r,\theta,t)}{\partial \theta} \dot{\theta}^2 - \frac{\partial \gamma_{33}(r,\theta,t)}{\partial \phi} \dot{\phi}^2 = 0,
\]
\[
\frac{d}{ds} (\gamma_{33}\dot{\phi}) = 0.
\]
Then, finally
\[
\frac{d}{ds} \left[ a^2(r,t)\dot{t} \right] - \frac{1}{2} \frac{\partial a^2}{\partial t} \dot{t}^2 + \frac{1}{2} \frac{\partial \gamma_{11}(r,\theta,t)}{\partial t} \dot{t}^2 + \frac{1}{2} \frac{\partial \gamma_{22}(r,\theta,t)}{\partial \theta} \dot{\theta}^2 + \frac{1}{2} \frac{\partial \gamma_{33}(r,\theta,t)}{\partial \phi} \dot{\phi}^2 = 0,
\]
\[
\frac{d}{ds} \left[ \gamma_{11}(r,\theta,t)\dot{r} \right] + \frac{1}{2} \frac{\partial \gamma_{11}(r,\theta,t)}{\partial r} \dot{r}^2 - \frac{1}{2} \frac{\partial \gamma_{11}(r,\theta,t)}{\partial \theta} \dot{\theta}^2 - \frac{1}{2} \frac{\partial \gamma_{33}(r,\theta,t)}{\partial \phi} \dot{\phi}^2 = 0,
\]
\[
\frac{d}{ds} \left[ \gamma_{22}(r,\theta,t)\dot{\theta} \right] - \frac{1}{2} \frac{\partial \gamma_{22}(r,\theta,t)}{\partial \theta} \dot{\theta}^2 - \frac{1}{2} \frac{\partial \gamma_{33}(r,\theta,t)}{\partial \phi} \dot{\phi}^2 = 0,
\]
\[
\frac{d}{ds} \left[ \gamma_{33}(r,\theta,t)\dot{\phi} \right] = 0.
\]
For a full radial motion, we can set \( \theta = \pi/2 \), yielding
\[
\frac{d}{ds} \left[ a^2(r,t)\dot{t} \right] - \frac{1}{2} \frac{\partial a^2}{\partial t} \dot{t}^2 + \frac{1}{2} \frac{\partial \gamma_{11}(r,t)}{\partial t} \dot{t}^2 + \frac{1}{2} \frac{\partial \gamma_{33}(r,t)}{\partial \phi} \dot{\phi}^2 = 0,
\]
\[
\frac{d}{ds} \left[ \gamma_{11}(r,t)\dot{r} \right] + \frac{1}{2} \frac{\partial \gamma_{11}(r,t)}{\partial r} \dot{r}^2 - \frac{1}{2} \frac{\partial \gamma_{33}(r,t)}{\partial \phi} \dot{\phi}^2 = 0,
\]
\[
\frac{d}{ds} \left[ \gamma_{33}(r,t)\dot{\phi} \right] = 0.
\]
The last equation of the set can be integrated out to give
\[
\dot{\phi} = \frac{A}{\gamma_{33}(r,t)},
\]
where \( A \) is an integration constant. This can be substituted into the other two to give
\[
\frac{d}{ds} \left[ a^2(r,t)\dot{t} \right] - \frac{1}{2} \frac{\partial a^2}{\partial t} \dot{t}^2 + \frac{1}{2} \frac{\partial \gamma_{11}(r,t)}{\partial t} \dot{t}^2 + \frac{1}{2} \frac{\partial \gamma_{33}(r,t)}{\partial \phi} \dot{\phi}^2 = 0,
\]
\[
\frac{d}{ds} \left[ \gamma_{11}(r,t)\dot{r} \right] + \frac{1}{2} \frac{\partial \gamma_{11}(r,t)}{\partial r} \dot{r}^2 - \frac{1}{2} \frac{\partial \gamma_{33}(r,t)}{\partial \phi} \dot{\phi}^2 = 0.
\]
Now, we know from Equation (39) that
\[
\gamma_{11}(r,t) = U(r,t)\gamma_{11}^{(0)},
\]
\[
\gamma_{33}(r,t) = U(r,t)\gamma_{33}^{(0)},
\]
(50)
and then
\[
\frac{d}{ds} \left[ \gamma_{11}(r,t) \right] = -\frac{1}{2} \frac{\partial}{\partial r} \left[ \frac{A^2}{U^2(r,t) \gamma_{33}^{(0)}} \right] \frac{\partial}{\partial t} \dot{t}^2 + \frac{1}{2} \frac{\partial}{\partial r} \left[ \frac{A^2}{U^2(r,t) \gamma_{33}^{(0)}} \right] \frac{\partial}{\partial t} \dot{r}^2 = 0. \tag{51}
\]
This set can be solved only numerically. Therefore, this approach does not lend itself to a straightforward computation of the radial velocity.
6. Radial Velocity
We consider a particle of mass \( m \) moving in our metric. The definition of momenta is given by
\[
p_\alpha = g_{\alpha \beta} p_\beta. \tag{52}
\]
This yields the following dispersion relation:
\[
p_\alpha p_\alpha = -m^2. \tag{53}
\]
Similarly, we can derive the 4-velocity from this and it is given by
\[
u_\alpha = (\gamma_{11} \dot{r}, \gamma_{22} \dot{\theta}, \gamma_{33} \dot{\phi}). \tag{54}
\]
Then, the radial motion will be characterized by
\[
v_r = \frac{\gamma_{11} dr}{\gamma^{(0)}_{11} \dot{r}} = \frac{U(r, \theta, t)}{\alpha(r, \theta, t) \gamma_{11}^{(0)}} \frac{dr}{dt}. \tag{55}
\]
One obtains a warp factor, arising from the applied perturbation,
\[
U(r, t) = \exp \left[ r_k a_{(t')} \int_0^t dt'' \frac{a(t'')}{2 r_k a_{(0)} \int_0^t a(t') dt' + \sqrt{\gamma(0)}} \right], \tag{56}
\]
and we realize that, with this geometry, we can achieve exponential growth of the radial velocity depending on the applied perturbation.
We can provide a closed form solution for a very simple case, a toy model. We take for a perturbation
\[
a_1(t) = \frac{t}{\eta}, \tag{57}
\]
with \( \eta \) being a constant. This is a linear time increasing term. Then,
\[
a^2(r, t) = a_0^2(r) + \frac{t}{\eta}. \tag{58}
\]
Then,
\[
U(r, t) = \exp \left[ r_k a_{(0)}^{-1} \int_0^t dt'' \frac{\sqrt{a_0^2(r)} + \frac{t}{\eta}}{2 r_k a_{(0)}^{-1} \int_0^t \sqrt{a_0^2(r)} + \frac{t}{\eta} dt' + \sqrt{\gamma(0)}} \right]. \tag{59}
\]
This yields
\[
U(r, t) = \exp \left[ r_k a_0^{-1}(r) \int_0^t \exp \left( r_k a_0^{-1}(r) \eta \left[ \frac{3}{2} \left( a_0^2 + \frac{\nu}{\eta} \right)^{1/2} - \frac{2}{3} a_0 \right] + \sqrt{\gamma(0)} \right) \right]. \tag{60}
\]
and
\[
U(r, t) = \exp \left[ r_k a_0^{-1}(r) \frac{3}{2} \eta \int \frac{\chi(a_0^2 + t)}{a_0^2} \, dx \right] \tag{61}
\]
The final result is
\[
U(r, t) = a \left( a_0^2 + \frac{t}{\eta} \right)^{3/2} - b, \tag{62}
\]
with
\[a = r_k \eta a_0^{-1}(r)\]
and
\[b = r_k \eta - \sqrt{\gamma(0)}\]. We can see that this factor is always greater than one (this value is taken for \(t = 0\)) and increases as time increases.
From the formula for radial velocity, we can derive the force. This will be obtained by the first derivative of Equation (55). This yields
\[
\frac{dv_r}{d\tau} = \frac{d}{d\tau} \left[ \gamma_{11} \frac{dr}{d\tau} \right]. \tag{63}
\]
This gives, for a mass \(M\),
\[
F = M \frac{dv_r}{d\tau} = M \frac{dt}{d\tau} \frac{d\gamma_{11}}{d\tau} \frac{dr}{d\tau} + \gamma_{11} \frac{d^2r}{d\tau^2}. \tag{64}
\]
This gives,
\[
F = M \frac{dv_r}{d\tau} = M \frac{1}{a} \frac{d\gamma_{11}}{d\tau} \frac{dr}{d\tau} + \gamma_{11} \frac{d^2r}{d\tau^2}. \tag{65}
\]
In our toy model, we consider \(a_0 \approx 1\) and \(\gamma_{11}^{(1)} \approx 1\), so that
\[
\frac{d\gamma_{11}}{dt} = \frac{a}{\eta} \left( 1 + \frac{t}{\eta} \right)^{3/2} - \frac{db}{a} \frac{d\gamma_{11}}{dt} + \frac{a}{(a-b)^2} \frac{d^2r}{dt^2}. \tag{66}
\]
This yields,
\[
\frac{d\gamma_{11}}{dt} \approx \frac{r_k \left( 1 + \frac{t}{\eta} \right)^{3/2} + 2r \frac{dt}{dt}}{r^2} + \frac{r_k \eta \left( 1 + \frac{t}{\eta} \right)^{3/2} - r_k \eta + 2r^2 \frac{dr}{dt}}{r^4} \tag{67}
\]
Then, we obtain
\[
F \approx M \left( 1 + \frac{t}{\eta} \right)^{-1/2} \left[ \frac{r_k}{r^2} \left( 1 + \frac{t}{\eta} \right)^{3/2} + 2 \frac{dr}{r \, dt} + \frac{2r_k \eta \left( 1 + \frac{t}{\eta} \right)^{3/2} - 2r_k \eta + 2r^2 \frac{dr}{dt}}{r^4} \right] \frac{dr}{dt} + M \frac{r_k \eta \left( 1 + \frac{t}{\eta} \right)^{3/2} - r_k \eta + r^2 \frac{d^2r}{d\tau^2}}{r^2}. \tag{68}
\]
with the simple kinematic law of motion \( r(t) = r_0 + v_0 t \), it is easy to obtain
\[
F \approx M v_0 \frac{r_k}{r^2(t)} + 2M \left( 1 + \frac{t}{\eta} \right) - \frac{1}{2} \frac{v_0^2}{r(t)} + M \left( 1 + \frac{t}{\eta} \right)^{-\frac{1}{2}} \frac{2 r_k \eta \left( 1 + \frac{t}{\eta} \right)^{\frac{3}{2}} - 2 r_k \eta + 2 r^2(t)}{r^3(t)} v_0^2.
\]
(69)
Force is non-null and dependent on the initial velocity and the sphere radius. It is interesting to note that the force tends towards zero as time increases but this corresponds to the unphysical case of a perturbation which is never turned off. This equation simplifies significantly if we can neglect the terms dependent on \( r_k \). One has
\[
F \approx 3 M \left( 1 + \frac{t}{\eta} \right)^{-\frac{1}{2}} \frac{v_0^2}{r(t)}.
\]
(70)
This result is independent of the sphere geometry or the Schwarzschild radius. Such a perturbation is not completely physical. Thus, we considered some others with the characteristic of being practically realizable. Considering the interior solution, for a perturbation like \( a_1 = \Lambda t^2 \), we obtain Figure 1 and for a sinusoidal perturbation we get Figure 2.
Figure 1. Warp factor for a \( t^2 \) perturbation with an equation of motion \( r(t) = h_0 + v_0 t \).
Figure 2. Warp factor for a sin(\(\omega t\)) perturbation with frequency 1 MHz and equation of motion
\[ r(t) = h_0 + v_0 t + kt^2. \]
As expected from the toy model, the warp factor is always greater than one and can reach significantly large values depending on the applied perturbation.
7. Conclusions
We have solved the Einstein equations for a strong perturbation in the case of a spherical symmetry solution. In this case, the perturbation series reduces to the case of a gradient expansion and the equations are amenable to an exact analytical treatment. We were able to show that, when a perturbation is properly applied, there appears a multiplicative warp factor on the radial velocity that can, in this way, increase exponentially in time. This warp effect does not require significant energy and everything is completely in the realm of positive energy solutions of the Einstein equations, even if as a perturbation series.
We hope these results will find some application in the near future.
Author Contributions: All the authors contributed equally to the development of the computations, both analytical and numerical, at the core of the paper. All authors have read and agreed to the published version of the manuscript.
Funding: This research received no external funding.
Conflicts of Interest: The authors declare no conflict of interest.
References
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5. Belinsky, V.A.; Kalathnikov, I.M.; Lifshitz, E.M. A General Solution of the Einstein Equations with a Time Singularity. *Adv. Phys.* 1982, 31, 639–667. [CrossRef]
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7. Santos-Pereira, O.L.; Abreu, E.M.C.; Ribeiro, M.B. Dust content solutions for the Alcubierre warp drive spacetime. *Eur. Phys. J. C* 2020, 80, 786. [CrossRef]
8. Lentz, E.W. Breaking the Warp Barrier: Hyper-Fast Solitons in Einstein-Maxwell-Plasma Theory. *arXiv* 2020, arXiv:2006.07125.
9. Teitelboim, C. The Hamiltonian structure of two-dimensional space-time and its relation with the conformal anomaly. In *Quantum Theory of Gravity*; Christensen, S., Ed.; Adam Hilger: Bristol, UK, 1984; pp. 327–344.
10. Jackiw, R. Liouville field theory: A two-dimensional model for gravity? In *Quantum Theory of Gravity*; Christensen, S., Ed.; Adam Hilger: Bristol, UK, 1984; pp. 403–420.
11. D’Hoker, E.; Jackiw, R. Liouville Field Theory. *Phys. Rev. D* 1982, 26, 3517–3542. [CrossRef]
12. Frasca, M. Duality in perturbation theory. *Phys. Rev. A* 1998, 58, 3439–3442. [CrossRef]
13. Soffel, M.H.; Han, W.B. *Applied General Relativity*; Springer: Berlin/Heidelberg, Germany, 2019.
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© 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/).
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Onychomadesis in a 9-month-old boy with hand-foot-mouth disease
Ibrahim Mortada *, Rola Mortada and Mohamad Al Bazzal
Abstract
Background: Nail abnormalities in childhood are generally uncommon. Recently, onychomadesis is described as a rare, late complication of hand-foot-mouth disease, which is a viral illness commonly seen in the pediatric age group. It is therefore important to elucidate the presentation of this entity, especially in the context of the hand-foot-mouth disease.
Case presentation: We report a case of onychomadesis in a 9-month old Lebanese boy who presented to the emergency department with rapidly progressing nail changes involving all four extremities. These changes appeared few days after the healing of cutaneous lesions of hand-foot-mouth disease.
Conclusions: This case highlights the importance of recognizing the association between onychomadesis and hand-foot-mouth disease in order to avoid unnecessary treatment and to reassure the patient’s parents.
Keywords: HFMD, Onychomadesis, Nail shedding, Infectious diseases, Dermatology
Background
Onychomadesis, characterized by shedding of nails from the proximal nail beds, is often idiopathic, but can also be linked to certain medications, systemic illnesses, and viral infections including hand-foot-mouth disease (HFMD). HFMD is a common contagious disease, affecting mainly children under the age of 10, but also reported in adults [1]. This disease is characterized by vesicular rashes on hands, feet, and buttocks and ulcers in the oral mucosa, accompanied by occasional fever [2]. Enterovirus 71 and coxsackievirus A16 are the most common causative agents associated with the condition [3]. Onychomadesis, a rare complication occurring 4 to 6 weeks after the onset of the disease, is usually self-limited and does not require treatment [4]. Common nail abnormalities include leukonychia and Beau lines as well as partial or complete nail shedding [5]. The mechanism of onychomadesis remains to be elucidated, although onychomadesis usually implies that nail matrix proliferation was temporarily inhibited. Bettoli et al. suggest that periungual inflammation secondary to viral infection may be induced directly by viruses or indirectly by immunocomplexes and consequent distal embolism [6], while Cabrerizo et al. consider that the nail matrix is directly damaged by viral replication, based on the presence of Coxsackie virus 6 in shed nails [7].
In this paper, we describe the presentation of onychomadesis in a boy previously diagnosed with HFMD.
Case presentation
A 9-month-old boy presented to the emergency department at a tertiary health care center in Beirut in September with a two-day history of nail shedding involving all four extremities. The patient began to have changes in the nails 6 days following the resolution of painful vesicles on the hands, feet, and mouth accompanied by mild fever (temperature 38.3 °C), diagnosed as HFMD. The oral blisters had been interfering with feeding; however, the patient did not receive any treatment besides supportive care, leading to the spontaneous resolution of the vesicles. Nail changes began as a greenish-yellowish patch appearing at the...
beginning of the nails and spreading towards the free edge. The nails then started to shed from the lunula towards the free edge concomitantly with the appearance of slowly growing new, pink nails (Fig. 1). Beau lines, horizontal grooves running across the nail plates, were noted (Fig. 2).
Conclusions
To our knowledge, this is the first case of onychomadesis to be reported from the Middle East. We ought to highlight the importance of recognizing the association between HFMD and onychomadesis in order to avoid unnecessary treatment and to reassure the patient’s parents. Nevertheless, it is important to note that this is a rare presentation, and a thorough history and physical exam are necessary to identify the correct etiology and rule out other serious pathologies.
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soft tissue has not yet adhered to the peripheral structures and ocular movement is less likely to be restricted after surgery. However, in the late stage of trauma, fibrosis, scarring, and atrophy of soft tissues may cause diplopia, although tissue adhesion is mechanically separated during surgery.
The study was designed as a prospective study, which assured totality and accuracy in the data collection. Besides, measurement of orbital volume quantitatively confirmed the precision and effectiveness of the surgery. The weaknesses of this study included the small sample, which was limited by the strict inclusion criteria, and the follow-up period, which was not long enough to identify all possible complications.
In conclusion, the composite material of HDPP and titanium mesh combined their advantages to facilitate safe and effective repair of orbital blowout fractures. Studies of larger sample and longer follow-up period should be conducted in the future.
REFERENCES
1. de Silva DJ, Rose GE. Orbital blowout fractures and race. Ophthalmology 2011;118:1677–1680
2. Burnstine MA. Clinical recommendations for repair of orbital facial fractures. Curr Opin Ophthalmol 2003;14:236–240
3. Bilkey U, Alper M, Celik N, et al. Comparing the osteogenic capacities of bone substitutes: hydroxyapatite, high-density porous polyethylene, and bone collagen—a biochemical and histological analysis. J Craniofac Surg 2004;15:585–593
4. Jordan DR, Brownstein S, Dorey M, et al. Fibrovascularization of porous polyethylene (Medpor) orbital implant in a rabbit model. Ophthal Plast Reconstr Surg 2004;20:136–143
5. Liu XJ, Chen L, Song W, et al. Computed tomography imaging of Medpor: graph-cut algorithm and its accuracy. J Craniofac Surg 2012;23:758–761
6. Ellis E 3rd, Tan YH. Assessment of internal orbital reconstructions for blowout fractures: cranial bone grafts versus titanium mesh. J Oral Maxillofac Surg 2003;61:442–453
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8. Avashia VJ, Sastry A, Fan KL, et al. Materials used for reconstruction after orbital floor fracture. J Craniofac Surg 2012;23:1991–1997
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13. Vendenia N, Chao J, Ivanidze J, et al. A method for visualizing high-density porous polyethylene (Medpor, Porex) with computed tomographic scanning. J Craniofac Surg 2011;22:73–76
14. Scolozzi P, Momjian A, Heuberger J. Computer-aided volumetric comparison of reconstructed orbits for blow-out fractures with nonpreformed versus 3-dimensionally preformed titanium mesh plates: a preliminary study. J Comput Assist Tomogr 2010;34:98–104
15. Garibaldi DC, Lifft NT, Grant MP, et al. Use of porous polyethylene with embedded titanium in orbital reconstruction: a review of 106 patients. Ophthal Plast Reconstr Surg 2007;23:439–444
16. Kim CY, Jeong BJ, Lee SY, et al. Comparison of surgical outcomes of large orbital fractures reconstructed with porous polyethylene channel and porous polyethylene Titan Barrier implants. Ophthal Plast Reconstr Surg 2012;28:176–180
17. Mihora LD, Holck DE. Hematocyst in a barrier-covered porous polyethylene/titanium mesh orbital floor implant. Ophthal Plast Reconstr Surg 2011;27:117–118
18. Seiff SR, Good WV. Hypertropia and the posterior blowout fracture: mechanism and management. Ophthalmology 1996;103:152–156
Key Words: Modified free latissimus dorsi musculocutaneous flap, head and neck defects, reconstruction, oncologic surgery
Surgical defects on the head and neck region after tumor resection result in functional impairment such as swallowing and speech deficits.1,2 The reconstruction for postoperative defects on the head and neck region needs timely and adequate wound healing to optimize cosmetic appearance and function, to facilitate postoperative radiation, and to restore sensation if possible.2 Skin grafts, regional pedicled flaps, and distant free vascularized free flaps are the most frequently used methods in the reconstruction of postoperative defects of the head and neck.
The application of vascularized skin flaps on the head and neck reconstruction was first described in 1959.3 However, despite encouraging reports, it did not achieve popularity until the 1970s.4 Nowadays, microvascular surgery is a highly successful and relatively safe method for the reconstruction of head and neck defects and has largely become globally accepted means of repairing complex head and neck defects with an overall success rate of 94% to 96%.5,8
The free latissimus dorsi musculocutaneous flap (FLDMF) is one of the most commonly used flaps for the repair of complex head and neck defects.9–12 It contains the necessary muscular, cutaneous, and osseous elements that provide adequate tissue volume to fill the defects on a single common pedicle. Therefore, the FLDMF was used in the patients of our series with vast postoncologic surgical defects in the head and neck region.
In this article, we present a series of patients who had postoncologic surgical defects in the head and neck region and underwent reconstruction using the FLDMF. The objective of this study was to review these reconstructive cases regarding the oncological outcomes, complications, as well as the functional and aesthetic status of these patients.
MATERIALS AND METHODS
Patients
After the institutional review board approval by Sichuan Cancer Hospital, records of patients who underwent FLDMF procedures of reconstruction of defects in the head and neck region were reviewed retrospectively. In this study, the patients who presented to the department of head and neck surgery between 2004 and 2012 for free FLDMF reconstruction were included. The characteristics of the patients are summarized in Table 1. The medical records as well as the details of age, sex, follow-up, histology, primary or secondary nature of the tumor, tumor site, flap type, tumor stage, neoadjuvant and adjuvant radiation therapy, locoregional disease control, cosmetic outcome, and complications were analyzed. Surgical procedures were performed by the same surgeon team. Microvascular complications were attributed to either venous congestion (evident through pinprick examination, changes in flap color/consistency, and decreased venous Doppler signal) or arterial insufficiency (decreased arterial Doppler signal). Partial failure, acute total failure, and late total failure are considered as free flap complications.
Statistical Analysis
Descriptive variables were summarized as means for continuous variables and number (percentage) for categorical variables. Disease-free interval and disease-specific survival curves were illustrated using the Kaplan-Meier method. The Student’s t-test was applied to compare means between the groups. The κ statistic was carried out to analyze the intrarater reliability. The Pearson Chi-squared test was used to analyze the correlation between radiotherapy and postoperative complications. P < 0.05 was considered statistically significant. Statistical analysis was performed using SPSS 13.0 for Windows (SPSS Inc, Chicago, IL).
RESULTS
Patient Characteristics
The characteristics of the patients are summarized in Table 1. The median age of the patients was 58 years (range, 42–80 y), with 16 women and 20 men. The most common site of tumor was the parotid gland (n = 6), followed by adenoid cystic carcinoma of the acoustic duct (n = 4), eyeball involvement of maxillary sinus carcinoma (n = 4, Fig. 1), neck recurrence of nasopharyngeal carcinoma after radiation therapy (n = 4), recurrence of buccal squamous cell carcinoma (n = 4, Fig. 2), as well as recurrence and mandible involvement of squamous cell carcinoma in the tongue (n = 4). The majority of the patients (n = 24, 66.7%) had recurrent tumors, whereas the rest of the patients (33.3%) had primary tumors with stage IV. Fourteen patients (38.9%) had a history of prior
| Variables | No. Patients |
|-----------|--------------|
| Age (range), y | 58 (42–80) |
| Sex | |
| Male | 20 |
| Female | 16 |
| Tumor site | |
| Recurrence of parotid gland malignancies | 6 |
| Adenoid cystic carcinoma of acoustic duct | 4 |
| Eyeball involvement of maxillary sinus carcinoma | 4 |
| Neck recurrence and skin involvement of nasopharyngeal carcinoma after radiotherapy | 4 |
| Recurrence of buccal squamous cell carcinoma | 4 |
| Recurrence and mandible involvement of squamous cell carcinoma in the tongue | 4 |
| Eyeball involvement of basal cell carcinoma around angularis oculi medialis | 2 |
| Malignancy in neurofibromatosis type 1 on the nape | 2 |
| Recurrence of adenocarcinoma of lacrimal gland | 2 |
| Recurrence of basal cell carcinoma on the face after radiotherapy | 2 |
| Recurrence and skin involvement of thyroid cancer | 2 |
| T stage | |
| T1 | 0 |
| T2 | 0 |
| T3 | 0 |
| T4 | 4 |
| T stage | 32 |
| N stage | |
| N0 | 6 |
| N1 | 6 |
| N2 | 20 |
| N3 | 4 |
| Tumor | |
| Primary tumor | 12 |
| Recurrent tumor | 24 |
| Radiotherapy | |
| Prior radiotherapy | 14 |
| Postoperative radiotherapy | 10 |
radiation therapy, whereas 10 patients (27.8%) had postoperative radiation therapy.
Defects and Reconstruction
The areas of the defects vary from 52 cm² to 180 cm² (mean, 86.4 cm²). Thirty-seven FLDMFs were applied for 36 patients because 1 patient had another FLDMF transfer because of the necrosis of flap. The types of flap transferred included skin paddle overlying latissimus dorsi muscle (n = 28), 2 segmental latissimus dorsi flaps (n = 8), and latissimus dorsi perforator-based flap (n = 4). Of the 8 patients who underwent 2 segmental latissimus dorsi flaps transfer, 4 patients had through-and-through cheek defect because of buccal squamous cell carcinoma and the remaining 4 had large orbital-maxillary defects.
Complications
Sixteen of the 37 patients had complications at the recipient site (Table 2). The most common complication at the recipient site was hematoma (n = 6), followed by venous insufficiency (n = 4), infection (n = 3), partial flap necrosis (n = 2), and total flap necrosis (n = 1). One patient had total flap necrosis that happened 10 hours after the operation. The reoperation was carried out to replace the necrotic one with the heterolateral FLDMF. The rest of the 15 patients with complications at the recipient site healed finally. There were 8 patients who had complications at the donor site, in which 3 had delayed wound healing and 2 had necrosis of skin graft and had another skin grafting. There were 2 patients who had limited shoulder function after 7 months of follow-up. The limitations on the shoulder function moderately affected the daily activities. Systemic medical complications developed in 3 patients. Two patients had postoperative pneumonia, and the other one had both pneumonia and supraventricular tachyarrhythmia. The patients who had systemic complications are older than 80 years and had a history of hypertension.
Radiotherapy
There were 14 patients who received radiotherapy before the reconstructive surgery (55–73 Gy; median, 65 Gy). The patients who received radiotherapy before the surgery tend to have a higher risk for postoperative complications. There was a significant correlation between radiotherapy and postoperative radiotherapy analyzed by the Pearson Chi-squared test (P = 0.006, Table 3). Moreover, the only 1 flap failure happened in the patient who received curative intent radiotherapy (73 Gy). Ten patients received postoperative radiotherapy with median intent of 55 Gy.
| Type of Complication | No. Patients |
|------------------------------|--------------|
| Recipient Site | 16 |
| Hematoma | 6 |
| Venous insufficiency | 4 |
| Infection | 3 |
| Partial flap necrosis | 2 |
| Total flap necrosis | 1 |
| Donor site | 8 |
| Delayed healing | 3 |
| Necrosis of skin graft | 3 |
| Limited shoulder function | 2 |
| General medical complication | 3 |
| Pneumonia | 2 |
| Supraventricular tachyarrhythmia | 1 |
No flap failure was observed in the patients who received postoperative radiotherapy.
Disease Control and Survival
The median follow-up period was 32 months (range, 10–60 mo). Eighteen patients died during the follow-up period. The 5-year overall survival rate was 39.1%, and the median overall survival time was 53 months (Fig. 3A). Twenty patients developed a recurrence during the follow-up period. The 5-year disease-free survival rate was 22.1%. The median disease-free survival time was 37 months (Fig. 3B).
Aesthetic Outcome
Skin color, texture matches, and appearance of a surgical scar were evaluated by all patients and the operating surgeons. Aesthetic outcome was graded on the following 4-point scale: 1, poor; 2, moderate; 3, good; and 4, excellent. The self-assessed aesthetic results were excellent for 4 patients, good for 16 patients, moderate for 12 patients, and poor for 4 patients. However, the aesthetic outcomes evaluated by the surgeons were excellent for 6 patients, good for 18 patients, moderate for 8 patients, and poor for 4 patients. We considered good and excellent as satisfied; poor and moderate, as unsatisfied. Thus, 20 patients were satisfied with the aesthetic outcome, whereas the surgeons were satisfied with the aesthetic outcome of 24 patients. The K statistic was carried out to analyze the interrater reliability. The value of K was 0.538 (P = 0.001), suggesting that the ratings between the patients and the surgeons are largely similar.
Economic Results
The mean operative time was 8.2 hours, ranging from 6.5 to 9.5 hours. Postoperative intensive care recovery was used in 10 patients. The mean duration of hospitalization for the patients who had postoperative complications (23.5 d) was significantly longer than that for those who had no complication (15.5 d) (P = 0.014). The mean cost per patient was 62550 RMB (range, 51200–78430 RMB). Expenses for the patients who had postoperative complications were significantly higher than that for those who had no complication (P = 0.007).
DISCUSSION
Head and neck surgical defects after oncological resection of advanced carcinoma often involve different structures, with different functions and characteristics. The use of free flaps for the reconstruction of large defects in head and neck surgery is considered the first choice in the repair of defects after resection of head and neck cancer. Free flap transfer is a highly successful and reliable strategy for the repair of large defects in the head and neck region, associated with a low incidence of flap failure, promoting primary wound healing, preserving residual function, and ensuring effective deglutition and intelligible speech.
In recent years, fasciocutaneous (eg, anterolateral thigh and radial forearm flaps) and myocutaneous free flaps (eg, latissimus dorsi and rectus abdominis) have represented popular options for head and neck reconstruction. The FLDMF was used for the patients in this cohort because the defects were large (>7 cm in width), preventing the use of radial forearm flap. The anterolateral thigh flap was not used because no obvious perforator was detected using computed tomographic angiography.
The reported failure rate of FLDMF reconstruction in the head and neck region ranged from 0% to 8.4%.6,10,12 In our patients, the flap failed in 2.78% (1/36) of the cases. The total flap necrosis happened in the patient who had a history of radical radiation therapy (73 Gy). However, the flap failure happened in 10 hours after the surgery because of venous thrombosis. We therefore consider that the flap failure may not be attributed to the radiation therapy but to the surgical operation or improper postoperative anticoagulant therapy. This specific patient was 80 years old with hyperlipemia (4.35 mmol/L), which may be another candidate reason for the flap loss. However, there was no epidemiological or experimental evidence to suggest the correlation between hyperlipemia and flap failure. We will analyze this correlation in a larger sample in our further study.
Sixteen of the 37 patients (44.4%) had complications at the recipient site. The most common complication at the recipient site was hematoma (n = 6, 16.7%), followed by venous insufficiency (n = 4, 11.1%), infection (n = 3, 8.3), partial flap necrosis (n = 2, 5.5%), and total flap necrosis (n = 1, 2.8%). Pohlenz et al11 analyzed the surgical outcome and complications of 1000 microvascular free flaps performed at the authors’ institution. They reported that the hematoma and partial flap failure happened in 5.7% and 6.8% of patients, respectively, which is lower than our results. However, the total flap loss of latissimus in our study (2.8%) was lower than that in their report (8.4%). Considering the high rate of hematoma and partial flap failure rate in the early period of practice, we changed our operative procedure with ultrasonic scalpel energy and modified the method of drainage. Most of the patients in our cohort had recurrent disease or radiation therapy, which may be the potential reason why our patients had a higher rate of hematoma and partial flap loss. It has been reported that an increased risk for free flap failure in patients with previous surgery exist because of scarring and fibrosis secondary to previous surgery.13
Whether previous radiation therapy would increase the complication rate of free tissue transfer in the head and neck region remains controversial. Tabah et al14 suggested that previously irradiated patients had more incidence of local complication. On the contrary, no correlation between complication and preoperative radiation therapy was also reported.15–17 In our study, however, the previous radiation therapy (including radical and preoperative radiation therapy) was significantly correlated with an increased risk for recipient complications. However, owing to the limited number of samples, this correlation might be a false positive. Therefore, a larger sample size is needed to further analyze this question.
The donor-site complications include delayed healing, necrosis of skin graft, and limited shoulder function. There are 2 patients who complained of limited shoulder function after 7 months of
**TABLE 3.** Correlation Between Radiotherapy and Postoperative Complications
| Complication | With | Without |
|--------------------|------|---------|
| Radiotherapy | 10 | 6 |
| Without | 4 | 16 |
Pearson Chi-squared P = 0.009 (2-sided).
**FIGURE 3.** The survival curves of the patients: overall survival (A) and disease-free survival (B).
follow-up in our study. The limitations on the shoulder function mildly affected the daily activities. Giordano et al\textsuperscript{11} studied the long-term shoulder function of a patient who underwent FLDMF harvesting using objective measurements. They found a significant reduction in the range of motion in intrarotation and forward elevation in the long term after FLDMF procedure. However, insignificant loss of shoulder functionality has been reported by several studies\textsuperscript{18,19}. The contraries between the studies may be attributed to the small sample sizes, uneven follow-up time, and different methods in evaluating the function. Therefore, a larger sample size, a longer follow-up period, and objective measurements are needed to further clarify long-term shoulder dysfunction after FLDMF harvesting.
The 5-year overall survival and disease-free survival rates in our patients were 39.1% and 22.1%, respectively. All patients in this study had local advanced or recurrent diseases, which contributed to the low survival rate for our patients. Moreover, these patients had different types of cancer, including squamous cell carcinoma, adenocarcinoma, and basal cell carcinoma. These malignancies happened in almost all the anatomic region of the head and neck. Therefore, the survival data in our cohort do not reflect the general survival rate for patients with head and neck malignancies.
In general, the FLDMF is a useful strategy for the reconstruction of vast defects where voluminous tissue is needed to be transferred. However, a larger sample size and a longer follow-up time are needed to further analyze the risk factor for flap failure and long-term complication.
REFERENCES
1. Andry G, Hamoir M, Leemans CR. The evolving role of surgery in the management of head and neck tumors. Curr Opin Otolaryngol 2005;17:241–248.
2. de Bree R, Rinaldo A, Genden EM, et al. Modern reconstruction techniques for oral and pharyngeal defects after tumor resection. Eur Arch Otorhinolaryngol 2008;265:1–9.
3. Seidenberg B, Rosenak SS, Hurwitt ES, et al. Immediate reconstruction of the cervical esophagus by a revascularized isolated jejunal segment. Ann Surg 1959;149:162–171.
4. Rinaldo A, Shahe AR, Wei WI, et al. Microvascular free flaps: a major advance in head and neck reconstruction. Acta Otolaryngol 2002;122:779–784.
5. Nakatsuka T, Harri K, Asato H, et al. Analytic review of 2372 free flap transfers for head and neck reconstruction following cancer resection. J Reconstr Microsurg 2003;19:363–368.
6. Pohlenz P, Klett J, Schon G, et al. Microvascular free flaps in head and neck surgery: complications and outcome of 1000 flaps. Int J Oral Maxillofac Surg 2012;41:739–743.
7. Kademenis D, Mardini S, Moran SL. Reconstruction of head and neck defects: a systematic approach to treatment. Semin Plast Surg 2008;22:141–155.
8. Kim EK, Evangelista M, Evans GR. Use of free tissue transfers in head and neck reconstruction. J Craniofac Surg 2008;19:1577–1582.
9. Hiemer R, van Loon J, Goffin J, et al. Free latissimus dorsi flap transfer for subtotal scalp and cranium defect reconstruction: report of 7 cases. Microsurgery 2007;27:425–428.
10. Li BH, Jung HJ, Choi SW, et al. Latissimus dorsi (LD) free flap and reconstruction plate used for extensive maxillo-mandibular reconstruction after tumour ablation. J Craniofacial Surg 2012;40:e293–e300.
11. Giordano S, Kaaraiven K, Alavaikko J, et al. Latissimus dorsi free flap harvesting may affect the shoulder joint in long run. Scand J Surg 2011;106:202–207.
12. Girod A, Boissonnet H, Jouffray T, et al. Latissimus dorsi free flap reconstruction of anterior skull base defects. J Craniofacial Surg 2012;40:177–179.
13. Pohlenz P, Blessmann M, Heiland M, et al. Postoperative complications in 202 cases of microvascular head and neck reconstruction. J Craniofac Surg 2007;18:511–515.
14. Tabab RJ, Flynn MB, Acland RD, et al. Microvascular free tissue transfer in head and neck and esophageal surgery. Am J Surg 1984;148:498–504.
15. Bengtson BP, Schusterman MA, Baldwin BJ, et al. Influence of prior radiotherapy on the development of postoperative complications and success of free tissue transfers in head and neck cancer reconstruction. Am J Surg 1993;166:326–330.
16. Kiener JL, Hoffman WY, Mathes SJ. Influence of radiotherapy on microvascular reconstruction in the head and neck region. Am J Surg 1991;162:404–407.
17. Smolka W, Izukza T. Surgical reconstruction of maxilla and midface: clinical outcome and factors relating to postoperative complications. J Craniofac Surg 2005;13:1–7.
18. Glassy N, Perks GB, Mc Culley SJ. A prospective assessment of shoulder morbidity and recovery time scales following latissimus dorsi breast reconstruction. Plast Reconstr Surg 2009;122:1334–1340.
19. Button J, Scott J, Taghizadeh R, et al. Shoulder function following autologous latissimus dorsi breast reconstruction. A prospective three year observational study comparing quitting and non-quitting donor site techniques. J Plast Reconstr Aesthet Surg 2010;63:1505–1512.
Reconstruction of Full-Thickness Lower Eyelid Defect Using Superficial Temporal Artery Island Flap Combined With Auricular Cartilage Graft
Mei Yang, MD* Yanyong Zhao, MD†
Abstract: Full-thickness lower eyelid defect is one of common surgical diseases, which may lead to exposure keratopathy, corneal ulceration, and blindness. The aim of this study was to investigate the effect of superficial temporal artery island flap combined with auricular cartilage graft on the repair of full-thickness lower eyelid defect.
In this study, the reconstructions in 6 patients who had unilateral full-thickness lower eyelid defects due to ocular traumas or surgical resections of malignant tumors were carried out. The island flap of the frontal branch of superficial temporal artery reconstructed the outer layer and the total lower lid was supported with the plane of an auricular cartilage strip, offering a proper contour and physical strength to maintain a normal eyelid height. The follow-up time...
| 2025-03-06T00:00:00 |
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Use of endemic plants in dairy cattle breeding in the Middle Amur region
N F Klyuchnikova, M T Klyuchnikov, E M Klyuchnikova and L I Naumova
Far Eastern Scientific Research Institute of Agriculture, KHFITS FEB RAS 13, st. Klubnaya, Vostochnoe village, Khabarovsk Territory, Khabarovsk district, 680521, Russia
E-mail: [email protected]
Abstract. Preservation and maintenance of high productivity, reproductive capacity, productive longevity, and vitality is an urgent task of dairy farming. Modern dairy farming is characterized by a high level of mechanization of all production processes, a large concentration of animals in a confined space, constant exposure to various stressors against the background of increasing environmental pollution. This implies an increase in the adaptive abilities of the animal organism. The situation is aggravated by the transfer of animals to low-component rations and year-round stall keeping without active movement. The main role at the present stage of dairy farming development belongs to the strengthening of the fodder base and the organization of rational feeding of cattle. Only complete feeding ensures the practical realization of the genetically determined level of animal productivity, thereby contributing to the further increase in the efficiency of animal husbandry. Considering the problems of increasing the production of animal products in the conditions of the Khabarovsk Territory, the most important of them should be noted: increasing the biological value of the diet of animals by enriching the missing components. Due to the fact that the compound feed imported from other regions of Russia to the Far East does not always correspond to the required quality, chemical composition and nutritional value, therefore, in the Far East region, to increase the biological value of the animal diet, it is possible to use additives from local plant resources containing in its composition is a whole complex of biologically active substances, macro- and microelements. Domestic and world practice has convincingly proved that the use of biologically active substances in the feeding of animals and poultry makes it possible to obtain more products from them while reducing feed costs. Taking this factor into account, we have carried out studies on the use of flour from the roots and stems of the high teapot as a source of biologically active substances in the feeding of farm animals, as well as an alcoholic extract of the roots of the fox. Positive changes were noted in the experimental groups. During the reference period, the preparations of the high lure helped to stimulate the reproductive function of cows after calving, led to an earlier fertilization of cows and an increase in milk productivity during the milking period.
1. Introduction
An imbalance in diets for vital elements, a low level of feeding, a reduced quality of basic feed, a mismatch of the conditions of keeping animals with the physiological needs of the body against the background of an increase in the productive potential lead to metabolic disorders, to the emergence and development of pathological processes in the reproductive sphere, impaired reproductive function and early culling, and the greatest loss of offspring is associated with the death of embryos [1-2].
Most metabolic disorders occur in highly productive dairy and beef cattle. Signs of manifestation of these violations are an increase in barrenness, the birth of a weak offspring, a decrease in resistance to infectious diseases, live weight, productivity, deterioration in the quality of the products obtained. All of this ultimately leads to the premature culling of animals. As a result, the productive life of cows in highly productive herds has been reduced to critical values - 1.5-1.7 calving. Animals drop out of the herd in the most productive period, when they should receive the greatest amount of milk, or even before its onset [3-4]. According to L. Peshchuk, the duration of the use of animals less than 2.5 lactations leads to the fact that cows-mothers will begin to leave the herd before giving birth to their daughter. In this situation, the herd ceases to exist as an integral biological system. Mother cows leave the herd before they give birth to their daughter. This leads to the self-liquidation of the herd as a single biological system [5]. Dairy farming in the Far East region has low indicators of economically useful traits, including high barrenness and a short period of economic use of cows - on average, less than three lactations [6].
For the first time, veterinary medicine faced a massive manifestation of the borderline state of animal health, when the body, according to Avicenna, is "not healthy and not sick." Under existing conditions, it is advisable to revise the traditional views on the organization of veterinary care and animal feeding. For this, you can use the available means of natural origin. Among them are biologically active substances contained in plant extracts [7-9]. Natural fodder from wild plant resources can be used as an alternative to traditional synthetic antibiotics, which is quite relevant lately, because, along with solving the problems of realizing the genetic potential of productivity of farm animals and poultry, laid down in breeding work, agricultural producers face an important task of creating conditions for the production of environmentally friendly products with improved consumer properties. Since almost all farm animals and poultry can transfer nutrients from compound feeds necessary for human nutrition into products, its quality and consumer properties can vary depending on the composition of the feed rations. In this regard, interest has increased in the study of the use of natural plant (phytogenic or botanical) supplements in diets containing a complex of biologically active substances, allowing to obtain environmentally friendly products and not provoking the development of a large number of "medicinal diseases" that arise after treatment, including those transmitted through egg, milk and meat [10].
In the last decade, domestic and world practice has arguably proved that the use of biologically active substances in the diets of farm animals makes it possible to get more products from them while reducing feed costs. One of the solutions to this problem is the use of local natural fodder resources in the diets of farm animals, which make it possible to optimize the animals need for scarce nutrients and reduce the cost of fodder per unit of production and raising young animals [11]. The experience of using plant extracts in livestock practice shows that their full and rational use allows you to preserve and increase the livestock population, reduce the consumption of expensive chemotherapeutic agents, antibiotics and vitamins, and, therefore, reduce the cost and improve livestock products. They show themselves well in order to prevent, treat and improve the productive and reproductive performance of animals. This makes it possible for farms to reduce the cost of purchasing products from the chemical, microbiological, hydrolysis and other types of industry [12-13].
In this aspect, of undoubted interest in the conditions of the Middle Amur region are endemic medicinal plants, numbering more than 1000 species, including the famous Araliaceal family: real ginseng (Panax ginseng CA Mey), Eleutherococcus senticosus Maxim, Aralia manch Aralia mandshurica Rupr. Et Maxim), high bait (Echinopanax elatum Nakai), sessile acanthopanax (Acanthopanax sessiflorum Seem), seven-lobed calopanax (Kalopanax septemlobus).
In connection with the above, we carried out experiments on the correction of reproductive function and increasing the milk productivity of cows after calving with preparations of high enticement. Below is the characteristic of the high lure (Echinopanax elatum Nakai).
Zamaniha high - a shrub 0.5-3.0 m high, with lodging, rooting stems, with ascending aerial shoots, up to 2 cm in diameter, slightly branched, with numerous brittle thorns. Leaves are alternate, 5-7-lobed, large, rounded, up to 30 cm in diameter on long, hollow petioles. The leaf blade is bright green,
wrinkled, there are sparse thorns on top, on the bottom - with thorns along the veins and along the edges of the leaf and with spiny hairs. Blooms in June-July. The flowers are small, bisexual, yellowish-green, collected in simple umbrellas, which form a brush-like apical drooping inflorescence up to 20 centimeters long, densely covered with rusty-brown bristly hairs. Fruits ripen in August-September, spherical fleshy drupes 7-12 mm in diameter, leathery, with two bones. The color of the fruit is bright or yellow-red.
The main value of the zamaniha lies in long cylindrical roots with few thin roots. They contain alkaloids and triterpene glycosides, essential oil (2.7%), coumarins (up to 0.2%), flavanoids (up to 0.9%), resinous substances (up to 11.5%), and mineral salts. The complex of biologically active substances makes up 6.9% of the mass of air-dry roots, represented by the sum of saponin-echinokosides. The roots contain macronutrients (mg / g: K –12.30; Ca –34.60; Mg –2.70; Fe –0.46, as well as trace elements: manganese, copper, zinc, cobalt, strontium aluminum, barium, vanadium, selenium, nickel, lead, iodine. The plant concentrates selenium, barium, strontium.
In terms of the amount of biologically active substances, the first place is occupied by stems (9.5%), then roots - 8% and leaves - 7%. This makes it possible to rationally use a limited supply of natural raw materials. According to L. Vostrikov et al., The annual root collection limit is no more than 10 tons. Sukhomirov G.I. [14].
2. Materials and methods
The work was carried out in different years at dairy farms in the Khabarovsk Territory. The experiments were carried out by the group method, taking into account the age at calving, the level of previous productivity, and live weight. The animals were kept in the same conditions of feeding and housing, adopted in each farm. The first experiment was carried out in the autumn-winter period 2015-2016 in JSC "Danilovka". For this, 20 new-calving black-and-white cows were selected. Three groups of 10 heads were formed as the calving progressed during the months of January-February, taking into account the age at calving, the level of previous productivity. In the first experiment, the difference consisted in the fact that the cows of the first experimental group, starting from the second day after calving and for 30 days, were given an infusion of flour from the stalks of bait, collected after the autumn collection of roots, with feed. The dose of flour is 50 gram per head. The required amount of flour for each day was poured with boiling water in a ratio of 1:10 and left in a sealed container for about two hours. Then they were mixed with compound feed and fed to the cows before milking.
The animals of the second group were similarly given 100 gram of flour from the stalks of bait.
The third group served as a control; cows additionally received a similar amount of compound feed to the general economic ration.
In the second experiment, carried out in the winter stall period of 2016-2017, at JSC "Zarya", the animals during the first 10 days after calving were drunk with water an alcoholic extract of the roots of zamaniha at a dose of 0.1 ml per kg of live weight. Animals of the control group (22 heads) the same amount of 70% alcohol, diluted in 1000 ml of water.
In the winter stall period 2017-2018 at the dairy farm LLC "Sergeevo" conducted a comparative assessment of flour from the roots and stalks of bait according to a similar scheme of the first experiment. The cows of the first group were fed 100 gram of flour from the stalks, and the second group was fed 50 gram of high flour from the roots of zamaniha. The third group of animals served as control.
The reproductive ability of cows was assessed by the method of I.I. Homeland [15]. Throughout the entire accounting period (100 days), according to the results of control milking, which were carried out monthly, the milk productivity was taken into account individually from each animal. The mass fraction of fat was determined in the average milk sample.
Laboratory studies were carried out in the laboratory of the Dal Research Institute of Agriculture. All the material obtained was processed by the biometric method according to N.A. Plokhinsky [16] (table 1 and 2).
Table 1. Milk productivity indicators, 2015-2016 (M ± m).
| Group | Index | Experienced I | Experienced II | Control |
|----------------------|------------------------------------|---------------------|----------------------|-------------------|
| | Gross milk yield of natural fat content, kg | 1399.0±46.67 | 1423.5±42.08 | 1277.7±37.81 |
| | Average daily milk yield of natural fat content, kg | 13.99±0.25 | 14.23±0.29 | 12.77±0.51 |
| | Gross milk yield of 4% fat, kg | 1373.82±37.8 | 1393.6±40.2 | 1275.8±52.0 |
| | Average daily milk yield of 4% fat | 13.74±0.81 | 13.94±0.67 | 12.76±0.8 |
Table 2. Milk productivity of cows, 2016-2017 (M ± m).
| Group | Index | Control | Experienced |
|----------------------|------------------------------------|---------------|-------------|
| | Gross milk yield of natural fat content, kg | 1542.3±54.67 | 1785.8±46.65|
| | Average daily milk yield of natural fat content, kg | 15.42±0.90 | 17.86±0.80 |
| | Gross milk yield of 4% fat, kg | 1468.27±55.17 | 1702.76±37.8|
| | Average daily milk yield of 4% fat | 14.68±0.85 | 17.02±0.79 |
3. Results and Discussion
The data of the first experiment showed that the drug zamanhi contributed to the improvement of the reproductive function of cows. The period from calving to the first hunt was 53.2 ± 6.0 and 46.1 ± 7.0 days, respectively, in individuals of the 1st and 2nd groups and 59.4 ± 4.1 in the control group, and the service period was 79.5 ± 7.3 and 67.8 ± 6.3 days. The inclusion of flour from the stalks of zamanhi into the diet of cows during the first month after calving led to earlier fertilization of cows (on average by 10.4 and 22.1 days) compared to the control.
The data of the registration of the milk productivity of cows carried out monthly during the entire accounting period (100 days) after calving with the determination of the fat content in the average milk sample are given in table 1, which indicate an increase in the milk productivity of cows in the experimental groups during the milking period by 121.3-145.8 kg of natural fat milk and 98.2-117.8 kg of four percent fat, respectively, in relation to the animals of the control group.
In the winter stall period of 2016-2017, at the state farm of JSC Zarya, Khabarovsk region, 20 Holstein cows during the first 10 days after calving were drunk with water an alcoholic extract of the roots of bait at a dose of 0.1 ml per kg of live weight. Control animals (20 animals) have the same amount of 70% alcohol diluted in 1000 ml of water.
The results of the experiment testify to the positive effect of the alcoholic extract of the roots of the high tempest on the body of fresh cows. The period of isolation of lochia was on average 19.5 ± 5.1 days in the experimental group, in the control group - 22.3 ± 4.6 days. The first hunt began, respectively, 58.2 ± 6.1 and 68.6 ± 7.7 days after calving. The duration of the service period decreased by 46.1 days (from 192.8 ± 14 to 146.8 ± 13). The difference is significant at P <0.05; td = 2.43. Thus, the alcoholic extract of the roots of zamanikha high significantly improved the studied indicators of the reproductive function of cows and made it possible to inseminate animals 46.0 days earlier. The milk productivity of cows in the first 100 days of lactation increased on average in the group by 243.5 kg from 1542.3 kg in the control to 1785.8 kg in the experiment, the increase is significant at P <0.01 (table 2).
10 days after the end of the drug administration, blood was taken from 4 cows from each group for analysis. Analysis data indicate positive changes in the morphological composition of the blood of the experimental animals: hemoglobin 112.7 ± 0.5 g / l; erythrocytes 6.95 ± 0.1 10^{12} / l; leukocytes 8.67 ± 0.2 10^{9} / l. In the control, respectively - 103.8 ± 1.4; 6.1 ± 0.1; 8.15 ± 0.1 (P<0.1).
An increase in the content of erythrocytes and hemoglobin in the blood of animals of the experimental group indicates a more intensive metabolism in their bodies, a better ability to absorb oxygen during respiration, supplying organs to them, which is especially important during the period of intense lactation activity. An increase in the content of leukocytes indicates the activation of the body's defenses and is consistent with the literature data. The ratio of calcium and phosphorus in the...
blood was 2.39: 0.99. All the studied indicators characterizing the physiological state of animals indicate positive changes in the body of cows in the experimental group under the influence of an alcoholic extract of the roots of high teat.
In the winter stall period of 2017-1018, a comparative assessment of flour from the roots and stalks of high lure was carried out at the dairy farm of LLC Sergeevskoye in the Khabarovsk region according to the same scheme of the first experiment. The cows of the first group were fed 100 g of flour from the stalks, and the second group - 50 g of flour from the roots. The third group of animals served as control. Cows of all groups were kept in the same conditions of keeping and feeding. The number of cows in each group was 10 heads, selected on the basis of analogues. Due to the refusal of some of the animals to eat the steamed flour of the roots of zamanihi, they began to mix it with grinding oats or barley in dry form.
According to the data of primary zootechnical registration, the first insemination of cows on average in groups was carried out after 58.3 ± 3.4; 55.1 ± 2.7 and 64.5 ± 4.0 days after calving. The duration of the service period was respectively 76.3 ± 4.1; 68.8 ± 3.2 and 93.2 ± 5.3 days in the groups receiving flour from the stems, roots and the control group.
Studies have confirmed the positive effect of high lure on the reproductive capacity of cows and have shown the advantage of roots despite the dose reduced by half. Three cows from each group were tested twice a month later. By the amount of hemoglobin in the blood, animals of the experimental groups at the end of the first month after calving exceeded their peers who did not receive herbal stimulants by 7.5 and 9.3%, by the number of erythrocytes by 7.8 and 11.9%, which indicates an improvement in metabolism substances. This is also indicated by the increased content of total protein in blood serum by 0.39%, 0.59%, respectively.
4. Conclusion
The data of experiments on the study of the effect of high sediment preparations on the productive and reproductive indicators of cows after calving, carried out in different years and different farms on black-and-white and Holstein cows, allow us to recommend high sediment preparations to stimulate the reproductive function of cows after calving and increase milk productivity in milking period. Studies have confirmed the previously established fact in other members of the Araliev family - eleutherococcus prickly, acanthopanax sessile-flowered - the dependence of biological activity on the dosage form and plant parts.
References
[1] Dobson H, Smith R F, Royal M D, Knignt C H and Shltdon I M 2007 The high producing dairy cow and its reproductive performance. Reprod. Domest. Anim 42(2) 17-23
[2] Inskeep E K and Dailey R A 2005 Embryonic death in cattle. Vet. Clin. Food Anim 21 437-61
[3] Shtyreva I V and Rudishina N M 2015 Duration of economic use and milk productivity of black-and-white cows with different reasons for retirement (Bulletin of Altai State University) 6 89-92
[4] Molchanova N V and Filipchenko A A 2016 Reasons for retirement and the period of economic use of cows in a highly productive herd of black-and-white cattle (Bulletin of the Ryazan State Agrotechnological University named after PA Kostychev) 4 33-6
[5] Peshchuk L P 2002 Optimal terms of use of dairy cows and the reason for their culling. Dairy and beef cattle breeding 1 22-3
[6] Klyuchnikova N F and Klyuchnikov M T 2015 Lifetime productivity of Holstein cows depending on the season of first calving in the conditions of the Middle Amur region (Bulletin of Russian Agricultural Science) 2 15-8
[7] Podolnikov V E and Osipova A G 2018 Improving feed additive (OEC) "GUMEL LUX" as part of cow rations. Animal science 10 4-7
[8] Yarmots L P and Yarmots G A 2017 Use of biologically active substances in the diets of lactating cows. Feeding farm animals and forage production 11 39-45
[9] Kolyada A S and Frolov V D 1992 *Medicinal plants of Primorye: properties and applications* (Vladivostok) 66
[10] Cobic T and Milosevic M 1991 Efeti primenestimulatora rosta u foovnin junadi. *Nauka u praksi* 21(1) 65-86
[11] Tuayeva E V 2018 *Federal Scientific Center for Livestock - VIZH named after academician L.K. Ernst* (Dubrovitsy: Moscow region) 43
[12] Mezes M and Fuleky G 2003 Proc. Int. Symp. Food Quality Management for East European Countries. *Cluj-Napoca* 49-52
[13] Volgin V I, Komissarov I M and Protasov B I 2015 On some sources of feed premixes. *Animal science* 5 5-7
[14] Sukhomirov G I 2007 *Taiga nature management in the Russian Far East (World Wildlife Fund (WWF) Russia, Amur branch)* (Khabarovsk: RIOTIP) 384
[15] Rodin I I, Tarasov V R and Yakimchuk I V 1979 *Workshop on obstetrics, gynecology and artificial insemination of farm animals* (Moscow: Kolos) 280
[16] Plokhinsky N A 1969 *Guide to biometrics for livestock specialists* (Moscow: Kolos) 257
| 2025-03-04T00:00:00 |
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Review
Arguments for Using Direct Oral Anticoagulants in Cancer-Related Venous Thromboembolism
Roxana Mihaela Chiorescu 1,2, Mihaela Mocan 1,2,*, Mirela Anca Stoia 1,3, Anamaria Barta 1,4, Cerasela Mihaela Goidescu 1,5, Stefan Chiorescu 6 and Anca Daniela Farcaș 1,3
1 Internal Medicine Department, Iuliu Hatieganu University of Medicine and Pharmacy, 400012 Cluj-Napoca, Romania; [email protected] (R.M.C.); [email protected] (M.A.S.); [email protected] (A.B.); [email protected] (C.M.G.); [email protected] (A.D.F.)
2 Department of Internal Medicine, Emergency Clinical County Hospital, 400006 Cluj-Napoca, Romania
3 Department of Cardiology, Emergency Clinical County Hospital, 400006 Cluj-Napoca, Romania
4 Department of Cardiology, “Nicolae Stanciu” Heart Institute, 400001 Cluj-Napoca, Romania
5 Department of Cardiology, Military Emergency Hospital “C. Papilian”, 400132 Cluj-Napoca, Romania
6 Surgery Department, Iuliu Hatieganu University of Medicine and Pharmacy, 400012 Cluj-Napoca, Romania; [email protected]
*
Correspondence: [email protected]; Tel.: +40-765-258-870
Abstract: (1) Background: Patients with cancer with a hypercoagulable state present an increased incidence of venous thromboembolism (VTE). Neoplastic patients with concurrent VTE undergoing anticoagulant treatment face a series of issues. (2) The aim of the present paper is to systematically summarize current VTE management in patients with neoplasia and to review the current clinical evidence from meta-analyses of randomized controlled trials and guidelines regarding the administration of direct oral anticoagulants (DOACs) for cancer-associated VTE. (3) Search Strategy: We performed a review on meta-analyses of randomized controlled trials and guidelines in favor of the administration of DOACs in patients with cancer-associated VTE published in the last 6 years in the Medline (PubMed) and Embase databases. (4) Results: 21 meta-analyses, 14 randomized controlled studies comparing DOACs to VKAs and LMWH, and 7 national and international guidelines were identified. We identified five studies that show the antineoplastic effect of DOAC on experimental models. (5) Conclusions: DOACs can be seen as the first choice for VTE treatment in neoplastic patients who have a low risk of bleeding, who do not have severe renal impairment, and who are not undergoing treatments that could interact with DOAC’s mechanism of action.
Keywords: direct oral anticoagulants; cancer-associated venous thromboembolism
1. Introduction
Venous thromboembolism (VTE) is the second most frequent cause of death in patients with neoplasia undergoing chemotherapy, while the main cause of death in these patients is the progression of the neoplasm [1].
The association of cancer with VTE determines a 30 times higher risk of death as compared to the general population. The association of cancer with VTE increases the rate of mortality exponentially, which is 10 times higher than in the case of VTE patients without neoplasia and four times higher than in neoplastic patients without VTE [2].
The hypercoagulable state in neoplasia can be explained by the multiple physio-pathological mechanisms present in oncogenesis: (1) the production of procoagulant and angiogenic substances induced by tumor hypoxemia; (2) the changes in the thrombocyte–endothelium interaction and in the cascade of coagulation and fibrinolysis, i.e., there is an increase in the concentration of thrombocyte-activating factors (P-selectin, soluble CD40 ligand, and platelet factor); (3) changes in the concentration of the tissue factor responsible for the initiation of coagulation; (4) the synthesis of a protease capable of directly activating factor Xa [3].
Anticoagulant treatment in patients with cancer-associated VTE faces a number of problems such as increased risk of bleeding, high risk of VTE recurrence, interactions with the specific treatment of neoplasia, and the need for a long-term administration of the treatment. Recently, the standard of care of cancer-associated VTE consisted of subcutaneous low-molecular-weight heparin (LMWH) for an initial duration of 6 months, which was extended with either LMWH or vitamin K antagonists (VKA) for an indefinite duration, i.e., until the cancer was considered to be in remission [4]. The administration of LMWHs faces a series of drawbacks connected especially with the manner of administration, which leads to a decrease in treatment compliance and an increase in the risk of VTE recurrence [5].
The aim of the present paper was to systematically summarize current VTE management in patients with neoplasia and to review the current clinical evidence from meta-analyses of randomized controlled trials and guidelines in favor of the administration of DOACs in this category of patients.
2. Materials and Methods
2.1. Search Strategy
The search strategy was performed according to a predefined protocol and complied with the PRISMA guidelines [6], as shown in Figure 1.
**Figure 1.** The algorithm showing the identification of articles included in the review. * Other sources: references from meta-analyses and guidelines.
2.2. Information Sources
Two authors systematically searched the PubMed and Embase databases using the following combination of keywords: “cancer related thromboembolism DOAC”, “cancer thromboembolism DOAC”, “cancer thromboembolism dabigatran”, “cancer thromboembolism direct thrombin inhibitor”, “cancer thromboembolism rivaroxaban”, “cancer thromboembolism apixaban”, “cancer thromboembolism.
edoxaban”, “cancer thromboembolism factor Xa inhibitor”. Apart from these keywords, “the antineoplastic effect of DOAC on experimental models” was searched on Pub Med.
2.3. Eligibility Criteria
We included meta-analyses of large studies and of randomized controlled trials and practice guidelines of national and international societies, referring to DOAC prescription in patients with VTE associated with neoplasia. Two authors independently evaluated the studies for possible inclusion. Non-relevant studies were excluded based on their titles and abstracts. For potentially relevant studies, a full text was obtained. The research was restricted to meta-analyses of large studies and of randomized controlled trials and practice guidelines published in the past 6 years (January 2015–December 2020).
3. Results
The flow diagram of the evaluation process is shown in Figure 1. The literature search yielded a total of 393 related articles. After duplicates were removed, 42 articles remained.
3.1. Meta-Analyses
The 21 meta-analyses published in the past 6 years are shown in Table 1. Several meta-analyses focusing on the efficacy and safety of DOACs in cancer-associated VTE were identified. Efficiency was assessed according to the recurrence rate and safety as related to major bleeding and clinically relevant nonmajor bleeding (CRNMB). Comparisons between DOACs, LMWH, and VKAs were analyzed. The most important conclusion drawn from these extensive analyses was that DOACs demonstrate a similar efficiency and safety as compared to LMWH and VKAs in cancer-associated VTE [7,8].
| Meta-Analysis | Publication Year | Results |
|---------------|------------------|---------|
| 1. Sardar, P. [7] | 2015; 19,832 pts and 1197 pts. | DOACs administered in patients with cancer were found to be as safe and efficient as is the case in patients without cancer. Rivaroxaban might be effective and safe in patients with cancer, as compared to VKA [6]. |
| 2. Posch, F. [8] | 2015; 3242 pts | DOACs have similar efficacy and safety to LMWH in patients with cancer [7]. |
| 3. Mantha, S. [9] | 2015 | Apixaban appears to be safer than other oral anticoagulants, with a lower risk of bleeding in patients with cancer [8]. |
| 4. Boonyawat, K. [10] | 2017; 98,244 pts | When the influence of body weight on DOAC efficiency was assessed, the results showed that it is not recommended to adjust the doses of DOACs outside the already known limits [9]. |
| 5. Kahale, LA. [11] | 2017; 1486 pts | DOACs do not decrease mortality in cancer patients but may be responsible for more bleeding events [10]. |
| 6. Kahale, LA. [12] | 2018; 5167 | For long-term therapy for cancer-associated thrombotic events, DOACs, as compared to LMWH, may have an efficient antithrombotic effect, but safety issues arise because of an increased risk of major bleeding [11]. |
| 7. Vedovati, MC. [13] | 2018; 1430 pts | In patients with cancer and VTE, DOACs were showed to be safe and efficient as compared to LMWHs [12]. |
| 8. Xing, J. [14] | 2018; 667 pts | Rivaroxaban proved to be efficient and safe as compared to LWMH (enoxaparin for the prevention of recurrent thrombotic events in neoplastic patients). Thus, rivaroxaban was recommended as a therapeutic option for cancer-associated VTE [13]. |
| 9. Martinez, BK. [15] | 2018; 949 pts | Rivaroxaban demonstrated similar levels of safety (rate of major bleeding) and efficiency (recurrent VTE) to the other anticoagulants for patients with cancer-associated VTE. The mortality was lower than reported in many anticoagulation CAT trials [14]. |
Table 1. Cont.
| Meta-Analysis | Publication Year | Results |
|---------------|------------------|---------|
| 10. Park, H. [16] | 2018 | For the treatment of cancer-associated VTE, DOACs proved to be safer and more efficient as compared to VKA. DOACs could be one of the standard therapeutic options in neoplastic patients. Among DOACs, apixaban exhibited a better outcome [15]. |
| 11. Hong, Y. [17] | 2018 | Rivaroxaban was associated with a lower hospital admission rate as compared to LWMH [16]. |
| 12. Gómez-Outes, A. [18] | 2018; 29,844 pts | The type of anticoagulation made no difference in the overall survival or causes of death, while the presence of active cancer was associated with a poor outcome and a higher mortality rate [17]. |
| 13. Li, A. [19] | 2019 | DOACs proved to be more effective than LMWHs in secondary prevention of VTE. Unfortunately, DOACs had a low safety profile as a result of increasing the risk of major bleeding and CRNMB, even though the absolute risk differences were small (2–3%). Better compliance with DOACs than LMWHs was hypothesized to explain the differences in bleeding events [18]. |
| 14. Rossel, A. [20] | 2019; 4667 pts | DOACs proved efficient in secondary prevention of VTE in neoplastic patients but showed a low safety profile with an increased risk of bleeding as compared to LMWH [19]. |
| 15. Kirkilesis, Gl. [21] | 2019; 6980 pts | DOACs were more effective than LMWHs in preventing VTE recurrence but may carry a higher risk of major bleeding [20]. |
| 16. Massimiliano, Camilli [22] | 2020, 2894 pts | As compared to LMWH, DOACs were associated with a significantly lower risk of VTE recurrence and were not associated with an increased risk of major bleeding; however, they were associated with an increased risk of nonmajor bleeding and gastrointestinal bleeding [21]. |
| 17. Desai, R. [23] | 2020, 18,945 pts | DOACs proved to be more effective in secondary prevention of VTE and were associated with a small risk of CRNMB. DOACs were considered to only be safe in the appropriately selected neoplastic patients [22]. |
| 19. Sabatino, I. [24] | 2020; 2907 pts | DOACs demonstrated similar efficiency and safety to dalteparin in preventing CAT VTE recurrence. However, DOACs were associated with higher rates of nonmajor bleeding as compared with dalteparin, primarily in patients with gastrointestinal malignancies [23]. |
| 20. Desai, A. [25] | 2020; 4341 pts | DOACs were efficient in terms of lowering the risk of VTE or recurrent VTE in patients with cancer but demonstrated safety issues regarding the increased risk in major and nonmajor bleeding events without influencing the survival rate [24]. |
| 21. Molik, F. [26] | 2020; 2894 pts | DOACs for VTE treatment and secondary prophylaxis in neoplastic patients proved to be more effective than LMWH but with safety issues related to major and nonmajor bleeding events, especially in those with digestive cancers [25]. |
CAT—cancer-associated thrombosis; CRNMB—clinically relevant nonmajor bleeding; DOAC—direct oral anticoagulant; PE—pulmonary embolism; VKA—vitamin K antagonist; LMWH—low-molecular-weight heparin; VTE—venous thromboembolism.
3.2. Randomized Controlled Studies
Randomized controlled studies comparing DOACs to VKAs and LMWH respectively offer encouraging arguments with regard to the administration of DOACs in paraneoplastic VTE patients (Table 2). Multiple clinical trials compared the efficacy and safety of DOAC vs. LMWH administration in neoplastic patients with VTE. The VTE-recurrence risk was assessed, as was the risk of fatal and nonfatal hemorrhage recurrence under the two types of anticoagulants.
### Table 2. Randomized controlled studies comparing DOACs to VKAs and LMWH, respectively.
| Name of Study | DOAC | Active Cancer Randomization (n) | Efficacy End Point (Recurrent VTE) Rate HR (95% CI) | Safety End Point (Major Bleeding) Rate HR (95% CI) |
|-------------------|-----------------------|-------------------------------|---------------------------------------------------|-----------------------------------------------|
| **DOAC vs. VKA** | | | | |
| 1. RE-COVER I/II | Dabigatran | 114 vs. 107 | 3.5% vs. 4.7% 0.74 (0.20–2.7) | 13% vs. 9% 1.48 (0.64–3.4) |
| 2. EINSTEIN-DVT/PE| Rivaroxaban | 258 vs. 204 | 2% vs. 4% 0.62 (0.21–1.79) | 12% vs. 13% 0.82 (0.48–1.38) |
| 3. AMPLIFY | Apixaban | 88 vs. 81 | 3.7% vs. 6.4% 0.56 (0.13–2.37) | 2.3% vs. 5% 0.45 (0.08–2.46) |
| 4. HOKUSAI-VTE | Edoxaban | 85 vs. 77 | 2% vs. 9% 0.30 (0.06–1.51) | 19% vs. 26% 0.66 (0.34–1.27) |
| **DOAC vs. LMWH** | | | | |
| 5. SELECT-D | Rivaroxaban | 203 vs. 203 | 4% vs. 11% 0.43 (0.19–0.99) | 6% vs. 4% 1.83 (0.68–4.96) |
| 6. XALIA | Rivaroxaban | 146 vs. 223 | 3.4% vs. 4.5% 1.4% | 1.4% vs. 3.6% |
| 7. MSK | Rivaroxaban | 200 | 4.4% | 2.2% |
| 8. ADAM-VTE | Apixaban | 145 vs. 142 | 3.4% vs. 14.1% 0.26 (0.09–0.80) | 0% vs. 2.1% 0.9956 |
| 9. HOKUSAI-VTE CANCER | Edoxaban | 522 vs. 524 | 7.9% vs. 11.3% 0.09 | 6.9% vs. 4% 0.04 |
| 10. CARAVAGGIO | Apixaban | 576 vs. 579 | 5.6% vs. 7.9% 0.63 (0.37–1.07) | 3.8% vs. 4.0% 0.82 (0.40–1.69) |
| 11. CANVAS | Rivaroxaban, Apixaban, Edoxaban, Dabigatran | 811 | ongoing study | ongoing study |
| 12. CONKO-011 | Rivaroxaban | 450 | ongoing study | ongoing study |
| 13. CASTA-DIVA | Rivaroxaban | 159 | ongoing study | ongoing study |
| 14. COSIMO | Rivaroxabin | 528 | ongoing study | ongoing study |
CI—confidence interval; DOAC—direct oral anticoagulant; HR—hazard ratio; PE—pulmonary embolism; VKA—vitamin K antagonist; LMWH—low-molecular-weight heparin; VTE—venous thromboembolism.
3.3. **Guidelines Published in the Past 6 Years**
Guidelines published in the past 6 years that recommend the use of DOACs in neoplastic patients with VTE are summarized in Table 3. Practice guidelines play a crucial role in modern medicine. The information found in the guidelines was extracted from RCT and meta-analyses for the clinicians to apply in real-life patients.
| Society | Recommendations |
|---------|----------------|
| 1. Treatment algorithm in cancer-associated thrombosis: Canadian expert consensus (2018) [40] | 1. Does not mention anticoagulation counterindications.
2. DOACs are preferred to LMWH if the hemorrhagic risk is low, in the absence of gastrointestinal tumors, genitourinary tumors, and if there are no drug interactions.
3. The treatment is recommended for 3 months with re-evaluation at the end of the treatment for cancer evolution and type (active/inactive). |
| 2. ISTH (2018) [41] | 1. We suggest the use of specific DOACs (edoxaban or rivaroxaban) for acute VTE in patients with cancer who present a low risk of bleeding and no drug–drug interactions with current systemic therapy. LMWHs are considered an acceptable alternative.
2. Currently, edoxaban and rivaroxaban are the only DOACs with RCT evidence when compared to LMWH in cancer populations.
3. We suggest the use of LMWHs in cancer patients with an acute diagnosis of VTE and high risk of bleeding (luminal gastrointestinal cancer, genitourinary tract cancer, bladder or nephrostomy tubes, or in patients with active gastrointestinal mucosal abnormalities, such as duodenal ulcers, gastritis, esophagitis, or colitis).
4. We recommended individualized treatment by including patients' preferences and values. |
| 3. ESC (2019) [42] | 1. Weight-adjusted subcutaneous LMWH should be considered for the first 6 months over VKAs (IIa A).
2. Edoxaban should be considered as an alternative to LMWH in patients without gastrointestinal cancer (IIa B).
3. Rivaroxaban should be considered as an alternative to LMWH in patients without gastrointestinal cancer (IIa C).
4. Extended anticoagulation (> 6 months) should be considered for an indefinite period or until cancer is cured (IIa B).
5. Incidental PE should be managed as symptomatic PE if it involves segmental or more proximal branches, multiple subsegmental vessels, or a subsegmental vessel in association with confirmed DVT. |
| 4. ACCP (2019) [43] | 1. We suggest the use of specific DOACs for cancer patients with an acute diagnosis of VTE, low risk of bleeding, and no drug–drug interactions with current systemic therapy. LMWHs are an acceptable alternative.
2. Currently, edoxaban and rivaroxaban are the only DOACs with RCT evidence when compared to LMWH in cancer populations.
3. We suggest the use of LMWHs for cancer patients with an acute diagnosis of VTE and a high risk of bleeding (luminal gastrointestinal cancer and genitourinary tract cancer). |
| 5. ASCO (2019) [44] | 1. Initial anticoagulation may involve LMWH, UFH, fondaparinux, or rivaroxaban. LMWH is preferred over UFH for the initial 5–10 days of anticoagulation (evidence quality: high; strength of recommendation: strong) in patients initiating treatment with parenteral anticoagulation.
2. For long-term anticoagulation treatment, LMWH, edoxaban, or rivaroxaban are preferred for at least 6 months because of improved efficacy over VKAs (evidence quality: high; strength of recommendation: strong).
3. Anticoagulation with LMWH, DOACs, or VKAs beyond the initial 6 months should be offered to patients with active cancer, such as those with metastatic disease or those receiving chemotherapy.
4. The insertion of a vena cava filter may be offered as an adjunct to anticoagulation in patients with progression of thrombosis despite optimal anticoagulant therapy.
5. Incidental PE and deep vein thrombosis should be treated in the same manner as symptomatic VTE, given their similar clinical outcomes when compared to cancer patients with symptomatic events.
6. Anticoagulant use is not recommended in order to improve survival in patients with cancer without VTE. |
Table 3. Cont.
| Society | Recommendations |
|-----------------------------------------------------------------------|-----------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------|
| 6. Thrombosis and Hemostasis Society of Australia and New Zealand (2019) [45] | 1. For DVT or PE that is provoked by active cancer, treatment with therapeutic LMWH for at least 6 months should be administered (evidence: high; strength of recommendation: strong).
2. Patients with incidental PE should be treated in a similar way to patients with symptomatic cancer-associated thrombosis.
3. Edoxaban and rivaroxaban have been shown to be as efficacious as dalteparin in cancer-related thrombosis, but they are associated with an increased risk of major bleeding or CRNMB and, therefore, can be considered when appropriate. |
| 7. NCCN Guidelines Insights Cancer-Associated Venous Thromboembolic Disease (2019) [46] | 1. For noncatheter-associated DVT or PE, indefinite anticoagulation should be recommended while cancer is active, under treatment, or if risk factors for recurrence persist.
2. Apixaban is an option for anticoagulation in patients with cancer and should be limited to patients who refuse or have compelling reasons to avoid LMWH.
3. LMWH/UFH plus dabigatran is a potential treatment option for cancer-associated VTE and should be limited to those patients who refuse or have compelling reasons to avoid long-term LMWH.
4. LMWH followed by edoxaban is the first option for anticoagulation in cancer-associated VTE.
5. Rivaroxaban is an option for anticoagulation treatment of VTE in patients with cancer. Unlike single-agent apixaban, it is not limited to patients with compelling reasons to avoid LMWH.
6. For catheter-associated thrombosis, anticoagulant therapy should be administered if a catheter is in place. The recommended total duration of the therapy is at least 3 months. |
ISTH—International Society of Thrombosis and Hemostasis; ESC—European Society of Cardiology; ACCP—American College of Clinical Pharmacy; ASCO—American Society of Clinical Oncology; NCCN—National Comprehensive Cancer Network; DOAC—direct oral anticoagulant; VTE—venous thrombo-embolism; LMWH—low-molecular-weight heparins; UFH—unfractionated heparin; CNRMB—clinically relevant nonmajor bleeding; PE—pulmonary embolism; VKAs—vitamin K antagonists; RCT—randomized controlled trials.
3.4. DOACs beyond Anticoagulation: A Potential Antineoplastic Effect
The studies that assessed the antineoplastic effect in experimental models are presented in Table 4.
Table 4. The studies that showed a favorable antineoplastic effect of DOACs in experimental model.
| Authors | Cancer Model/No. of Animals (Mice) Per Experimental Group | Treatment (Dose, Mode, Duration, and Timing) | Results |
|--------------------------|------------------------------------------------------------|-------------------------------------------------------------------------------------------------------------|------------------------------------------------------------------------|
| DeFeo et al. (2010) [47] | syngeneic; orthotopic breast cancer model/4–10 | Dabigatran [45 mg/kg body weight twice a day (Mon–Fri) or 60 mg/kg once a day (Sat, Sun) by oral gavage for 4 weeks, beginning 1 day before tumor cell injection] | Reduced liver micrometastases (no significant effect on lung micrometastases) |
| | syngeneic; s.c. fibrosarcoma model/9 | Rivaroxaban [0.4 mg/g chow diet for 8 days, started 14 days after cancer cell inoculation] | ±50% reduction in tumor weight ±70% reduction in no. of macroscopic lung metastases |
| Graf et al. (2019) [47] | syngeneic; s.c. colorectal cancer model/9–11 | Rivaroxaban [0.4 mg/g chow diet for 9 days, started 12 days after cancer cell inoculation] | ±40% reduction in tumor volume |
| | spontaneous; breast cancer model/28 | Rivaroxaban [0.4 mg/g chow diet for 7 weeks, started from week 13 after birth] | reduction in no. of lung metastases |
| Sophie Featherby (2019) [48] | syngeneic the chorioallantoic membrane (CAM) model/3 | Apixaban (1 µg/mL) | Apixaban (1 µg/mL) partially reduced the growth of the implanted tumors |
4. Discussion
4.1. Meta-Analysis
Some of the most recently published meta-analyses comprising thousands of patients diagnosed with cancer-associated VTE showed that those treated with DOAC had a higher risk of bleeding [21,23,25]. Most of these bleedings were minor and were found especially in patients with gastrointestinal tumors. Desai R. et al. showed that DOACs are superior to VKA or LMWH for secondary prevention of VTE in patients with cancer, although they have an increased risk for nonmajor bleeding as compared to LMWH [23].
The interpretation of bleeding risks associated with DOACs is complex. Bleeding events associated with DOACs seem to be mostly related to mucosal bleeding. Upper digestive cancer and the use of edoxaban and rivaroxaban were frequently associated with more bleeding events [24,26].
Moreover, bleeding with DOACs may be related to their physiological and pharmacological mechanism of action. Thus, dabigatran, rivaroxaban, and edoxaban may have a topical anticoagulant effect that favors mucosal bleeding, tartaric acid found in dabigatran has a direct caustic effect, while rivaroxaban and edoxaban have pharmacodynamic differences leading to higher peak concentration [49]. To date, DOACs have not been evaluated for the bleeding risk of each representant. However, in one previous meta-analysis (published in 2013) of 43 trials utilizing DOACs for any indication including VTE (but excluding cancer), dabigatran and rivaroxaban were found to be associated with more digestive bleeding and nonmajor bleeding as compared to apixaban [50].
In this respect, Angelini et al. showed that, in presence of neoplasia, patients treated with anticoagulation experienced more bleeding events regardless of the type of DOAC used. Other factors influencing the risk of bleeding in cancer patients were as follows: renal impairment, obesity with a BMI ≥ 40 kg/m², the presence of metastatic disease, a moderate to severe thrombocytopenia, and tumor type. In this respect, the authors found
that regardless of the type of anticoagulant, patients with primary digestive neoplasia had more bleeding events than those with nondigestive cancers [51].
The arguments regarding the safety of different anticoagulants in cancer patients should be established by performing a subgroup meta-analysis of bleeding risk, stratified by cancer type and DOAC type.
4.2. Randomized Controlled Trials
The efficacy and safety of LMWHs as compared to VKAs was shown in the following studies: Meyer, Clot, Hull, Deitcher, and Cacht [52]. In these studies, the patients treated with LMWHs presented a lower VTE recurrence rate, without an increased risk of major bleeding, as compared to those treated with VKAs [53]. However, LMWH therapy is a burden both financially and socially, requiring daily subcutaneous injections that affect the quality of life. VKAs are sometimes used in cancer patients with increased bleeding risk or VTE recurrence because of the narrow therapeutic range and possible drug interactions found in cancer patients [54].
A number of recent studies show that DOACs have the same efficacy as VKAs and exhibit a better safety profile; thus, they are a potential therapeutic option in patients with paraneoplastic VTE [29,33,55–57]. The most important clinical trials that compared DOACs to VKAs in patients with neoplasia are as follows: RE-COVER I and II (dabigatran with VKA), EINSTEIN PE and DVT (rivaroxaban with VKA), AMPLIFY (apixaban with VKA), and Hokusai-VTE (edoxaban with VKA). The results of these clinical trials offer encouraging arguments with regard to the administration of DOACs in paraneoplastic VTE patients (Table 2).
The SELECT-D study included 406 patients with neoplasia and VTE. The subjects were randomly divided into two groups: the first group received rivaroxaban treatment (15 mg twice daily for 3 weeks and subsequently 20 mg once daily for 6 months); the second group received dalteparin treatment (200 IU/kg for 1 month and subsequently 150 IU/kg for 2–6 months). VTE recurrence 6 months into the treatment was 11% in the group undergoing dalteparin treatment and 4% in the group treated with rivaroxaban. The cumulative risk of major hemorrhages 6 months into the treatment was 4% with dalteparin treatment as compared to 6% with rivaroxaban treatment [31].
The ADAM-VTE study included 300 patients who were randomly divided into two groups: the first group was treated with apixaban (10 mg twice daily for 7 days and subsequently 5 mg twice daily for 6 months); the second group was treated with dalteparin (200 IU/kg for 1 month and subsequently 150 IU/kg for 6 months). The results of this study showed a lower hemorrhage and VTE-recurrence risk in the group treated with apixaban (recurrent VTE was 3.4% in the group treated with apixaban as compared to 14.1% in the group treated with dalteparin, major hemorrhages were 0% in the group treated with apixaban as compared to 2.1% in the group treated with dalteparin, and the incidence rate of major and nonmajor hemorrhages was the same in both groups, i.e., 9%) [34].
The CARAVAGGIO study is characterized as a multinational, randomized, investigator-initiated, open-label, non-inferiority trial with blinded central outcome adjudication. In this study, consecutive patients with cancer diagnosed with symptomatic or incidental acute proximal VTE/PE received either oral apixaban (a dose of 10 mg twice daily for the first week, followed by 5 mg twice daily for 6 months) or subcutaneous dalteparin (a dose of 200 IU per kilogram of body weight once daily for the first month, followed by 150 IU per kilogram once daily for 6 months). The primary outcome was recurrent VTE, which was objectively confirmed. Recurrent VTE frequency was higher in the dalteparin group (7.9%) as compared to the apixaban group (5.6%). On the other hand, no statistically significant differences regarding major bleeding were identified between the two groups (3.8% in the apixaban group and 4% in the dalteparin group). Thus, apixaban proved to be both effective and safe for the treatment of CAT VTE [35].
The Hokusai-VTE Cancer study included 1046 patients who were randomly divided into two groups: the first group was treated with LMWHs for 5 days and subsequently
with edoxaban (60 mg daily); the second group was treated with dalteparin (200 IU/kg during the first month, followed by 150 IU/kg). The edoxaban doses were adjusted to renal function and body weight (30 mg in the case of patients with an eGFR of 30–50 mL/min, weight < 60 kg, or in the case of an association with antiplatelet aggregation therapy). The risk of recurrent VTE was higher in the group treated with dalteparin, and the risk of major hemorrhages was greater in the group treated with edoxaban. The risk of recurrent VTE was 7.9% in the group treated with edoxaban as compared to 11.3% in the group under dalteparin treatment, and the risk of major hemorrhages was 6.9% in the group treated with edoxaban as compared to 4% in the group treated with dalteparin. The majority of hemorrhages in the group treated with edoxaban were gastrointestinal hemorrhages due to the gastrointestinal mucous membrane being affected by the toxic effects of the chemotherapeutic agents [30].
There are additional ongoing clinical studies that compare the efficacy and safety of DOAC vs. LMWH administration in neoplastic patients with VTE, e.g., CANVAS: dabigatran, rivaroxaban, apixaban, edoxaban vs. LMWH [36]; CONKO-011: rivaroxaban vs. LMWH [37]; CASTA-DIVA: rivaroxaban vs. LMWH [39]; COSIMO: rivaroxaban vs. LMWH [39].
There are several ongoing studies (one of them being the AVERT study) investigating the risk/benefit ratio in VTE prophylaxis in neoplastic patients with an intermediate and high risk of thrombosis.
4.3. Guidelines
In our review, we identified seven national and international guidelines that mention the baseline anticoagulant therapy in cancer patients suffering from VTE.
Until recently, higher adherence to the treatment has been considered one of the advantages of DOACs as compared to LWMH. Patients following an anticoagulant treatment with LMWH, which are administered by subcutaneous injection twice a day, were supposed to give up their treatment more frequently in favor of VTE recurrence [46,58,59]. Early this year, Schaefer et al. showed a similarly high rate (95%) of LMWH and DOAC adherence for patients with CAT. Thus, the authors recommend that anticoagulant therapy should not be guided by the probability of treatment compliance [5].
Edoxaban, rivaroxaban, and apixaban are the only DOACs that have been compared to LMWHs in clinical studies and are accepted for cancer-associated VTE. The use of rivaroxaban in the treatment of these patients is supported by an abundance of clinical evidence. DOACs are associated with a statistically significant lower risk of VTE recurrence in neoplastic patients but with a higher bleeding risk [20,60,61].
Some of the guidelines still recommend LMWH as the first-line therapy of cancer-associated VTE, while others recommend DOACs but in appropriate situations, i.e., no drug interactions with current cancer medication, a low risk of bleeding, and normal renal function. Thus, ESC [42] and ASCO [44] suggest the use of LMWH in patients with acute VTE diagnosis (during the first 7–10 days to 6 months) but prefer rivaroxaban to LMWH in patients without gastrointestinal cancer. On the other hand, ISTH [41] and ACCP [43] suggest DOACs in selected categories of patients with acute VTE, a low bleeding risk, and no drug interaction, and suggest LMWH in patients with a high bleeding risk (digestive cancer, genitourinary cancer, and digestive mucosal abnormalities, such as esophagitis, gastritis, colitis, etc.).
4.4. DOACs beyond Anticoagulation: A Potential Antineoplastic Effect?
To enhance the indication of DOACs in patients with VTE and cancer, several experimental studies were conducted with the aim of elucidating the possible antineoplastic effect of these drugs.
The antiangiogenetic effect was the first to be targeted in experimental studies. Angiogenesis is a consequence of inflammation and hemostatic disturbances and plays an essential role in tumor progression. Inflammation has a prothrombotic effect as it decreases
natural anticoagulants, activates platelets, or increases tissue factor (TF) expression. Moreover, both factor Xa (which represents the target of DOACs) and thrombin initiate and maintain angiogenesis and tissue fibrosis, thus promoting tumoral growth [36]. A schematic presentation of tumor angiogenesis is present in Figure 2. Therefore, experimental studies aimed at demonstrating the antitumoral growth effect of DOACs.
Figure 2. Schematic presentation of tumor angiogenesis (modified from others [36]). TF—tissue factor; PARs—protease-activated receptors.
The results of these studies on reducing the progression of tumors and metastases after DOACs were different and depended on the timing of DOACs and the type of cancer model used. Most of these experimental studies were performed with anticoagulant drugs that are only used in vitro [47]. We selected studies using DOACs approved for use in clinical practice.
The experimental in vitro and in vivo studies were extensively reviewed by Grandoni et al. [36]. Later, Najidh et al. identified nine publications that included a total of 19 in vivo experiments focusing on the effect of DOACs on tumor growth and metastasis [47]. These were animal models of fibrosarcoma, colorectal cancer, pancreatic cancer, melanoma, and breast cancer. Currently, dabigatran, rivaroxaban, and apixaban are the DOACs that have shown an angiogenetic effect.
Dabigatran acts by inhibiting thrombin, and studies on animals have demonstrated a decrease in tumor progression in breast cancer models when treatment is given immediately after the grafting of the neoplastic cells [47].
It has been proved that the timing of administering the treatment is an extremely important fact. However, two other experimental studies in breast cancer in animals showed that if dabigatran was administered when tumors were already established, it had no effect on the development of the primary tumor or on metastases. In a study of pancreatic cancer in mice, it was observed that if dabigatran was administered 1 week after inoculation of the cancer cells, it caused tumor growth, which is explained by the increase in intratumoral bleeding [47].
Rivaroxaban is included in the guidelines for the management of patients with cancer-associated VTE; however, studies showed different results depending on the cancer type. Graf et al. observed that rivaroxaban (0.4 mg/g chow diet) reduced fibrosarcoma weight by 50% and lung metastasis by 70% at 8 days after administration [62]. On the other hand, Maqsood et al. showed that rivaroxaban (0.5 mg/g chow diet) had no effect on tumor size
or tumoral cell proliferation (quantified by Ki-67-positive tumoral cells) when injected in a xenograft model of pancreatic cancer cells [63].
Another study compared the effect of LMWH (dalteparin and tinzaparín) with DOACs (apixaban and rivaroxaban) on cell proliferation and tumor growth in vitro and in vivo in melanoma and pancreatic cancer models. Dalteparin and tinzaparin reduced tumor growth and tumor invasion in vitro. Apixaban and rivaroxaban treatment did not influence tumor development. A study using the chorioallantoic membrane assay model in vivo demonstrated that in vivo LMWH had a beneficial effect in terms of reducing tumor vascularity and apixaban reduced the rate of tumor proliferation and tumor growth. The results of these studies were explained by the fact that LMWH acts on tumor development and tumor vascularization by inhibiting factor Xa, inhibiting NFκB cell activity, and decreasing tumor and endothelial cell adhesion through selectins and ICAM receptors [48].
Additional studies are required to determine the potential benefit of DOACs for primary tumor or distant metastasis reduction in laboratory settings before performing clinical studies.
4.5. Some Practical Considerations on the Use of DOACs in Cancer Patients
4.5.1. The Length of the Treatment
According to the current guidelines, the length of the anticoagulant treatment is 3–6 months. The treatment should be continued indefinitely in patients with active cancer, under chemotherapy, and multiple VTE risk factors [41,42,46]. The decision whether to extend the treatment should be reached following the periodic assessment of the hemorrhagic risk against the benefit of the treatment [45,46].
In cases where the VTE-recurrence risk is high, the anticoagulant treatment is administered over an extended period of time (over 3–6 months) [43,46,64]. Various risk scores may be used to stratify the patients’ recurrence risk vs. bleeding risk. The Ottawa score, for example, evaluates the 6-month VTE-recurrence risk considering the following variable: sex, cancer type, and previous history of VTE. In the modified score, female sex, lung cancer, and previous history of VTE is each given 1 point, breast cancer and cancer stage I and II receive −1 point [65].
The treatment for these patients needs to be structured according to the location of the neoplasm, major organ functions, patient compliance, concurrent medications, and the existence of other specific factors. For catheter-associated thrombosis, anticoagulant therapy should be administered if a catheter is in place. The recommended total duration of the therapy is at least 3 months [46]. For patients with VTE and cancer, extended anticoagulation (beyond the first 6 months) should be considered for an indefinite period or until the cancer is cured, and the therapeutic dose should be maintained [42,62].
4.5.2. High Risk of Major Bleeding
The hemorrhagic risk factors that must be taken into consideration are an age 65>, prolonged periods of immobilization, the presence of metastases, renal impairment (creatinine clearance below 30 mL/min), and history of digestive hemorrhages, hemorrhagic diathesis, and thrombocytopenia [3]. Currently, no bleeding scores are implemented; however, the IMPROVE score is an example of a bleeding score that is useful in clinical [41] practice. It comprises the following: history of gastroduodenal ulcer, bleeding in the 3 months prior, admission platelets <50,000/mm³, liver failure, ICU/CCU stay, CV catheter, active cancer, or rheumatic disease [66].
Thrombocytopenia is frequent in neoplastic patients. Its presence increases the risk of bleeding but does not decrease the risk of developing thrombosis. The current guidelines recommend that the anticoagulant treatment be continued, without dose reduction, in cases in which the platelet count exceeds 50,000/mm³. DOACs can be administered at a platelet count >50,000/mm³, and when the platelet level drops under 50,000/mm³, LMWH should be introduced instead. Each decision should be individualized [67]. In accordance with the ISTH and NCCN guidelines, anticoagulation should be stopped when the platelet
count is lower than 25,000/mm$^3$, while the ASCO guidelines recommend the withdrawal of the anticoagulants at a threshold of 20,000/mm$^3$ [41,44,46].
According to the current guidelines, DOACs are to be avoided in patients with a high risk of bleeding (luminal gastrointestinal, genitourinary, hematological neoplasms, with nephrostomy, or with an active gastroduodenal ulcer), and LMWHs should be administered instead [41,42].
4.5.3. Renal Impairment
The administration of DOACs is not generally recommended in the presence of renal impairment with a $<15$ mL/min/m$^2$ creatinine clearance. Under careful monitoring, in patients with a creatinine clearance of 15–50 mL/min/m$^2$, the following may be used: apixaban $2 \times 2.5$ mg/day, edoxaban (30 mg/day), and rivaroxaban (15 mg/day).
Although there are attempts to use DOACs in dialysis patients (apixaban $2 \times 2.5$ mg), the use of DOACs in the case of a creatinine clearance below 15 mL/min/m$^2$ and dialysis is contraindicated [45,59]. For apixaban, a dose reduction is recommended when two of the following three criteria are met: age $\geq 80$ years, weight $\leq 60$ kg, and serum creatinine $\geq 1.5$ mg/dL [41].
There are certain issues regarding DOACS dosing in RCT for VTE. Patients with CrCl $< 25$ mL/min were excluded from the trials testing apixaban, whereas patients with CrCl $< 30$ mL/min were excluded from those investigating rivaroxaban, edoxaban, and dabigatran. The dosages of dabigatran, rivaroxaban, and apixaban were not reduced in patients with mild–moderate renal dysfunction (CrCl between 30–60 mL/min), whereas edoxaban was given at a 30 mg dose in these patients [42]. During the first 3 weeks of treatment, it is not recommended to adjust the dose of Rivaroxaban, it should be maintained at 2 $\times\ 15$ mg/day, or it should be replaced by LWMH in cases with severe renal impairment.
Grandone et al. have recently published a statement paper regarding the use of DOACs in patients with renal impairment. The paper elegantly summarized the recommendation of three different international societies (2018–2019) regarding the dosing of DOACs adjusted to creatinine clearance and reviewed the real-life clinical trials focusing on DOACs in patients with renal impairment. The authors concluded that DOACs are recommended in patients with CKD, but close monitoring is necessary in order to avoid CRNMB [68].
4.5.4. Liver and Gastrointestinal Diseases
The oral intake of DOACs is an important drawback, as the absorption might be impaired by nausea and vomiting, symptoms which are relatively frequent in neoplastic patients undergoing chemotherapy.
DOACs absorption is influenced by the anatomic changes in the digestive tube. Rivaroxaban, dabigatran, and edoxaban must be avoided in patients with gastrectomies because they are absorbed in the distal part of the stomach and the proximal part of the small intestine, and they are dependent on gastric acidity for absorption. In such instances, apixaban should be administered because it is absorbed in the distal small bowel and in the ascending colon and is not pH-dependent for absorption [61].
Apixaban should be avoided in patients with intestinal resections and colectomies. Rivaroxaban, dabigatran, or edoxaban should be administered instead. Dabigatran is administered as capsules and should be avoided in the case of tube-fed patients [61].
Apixaban is not to be administered in cases in which transaminase levels are elevated to more than twice the upper limit, while rivaroxaban and edoxaban are not recommended when transaminase levels are three times the upper limit [61].
4.5.5. Interaction with Other Drugs
DOACs have fewer interactions than antivitamin K medication.
Drugs that induce CYP3A4, a cytochrome P450 component present in hepatic cells (rifampicin, carbamazepine, phenobarbital, valproic acid, doxorubicin, vinblastine, suni-
tinib, vandetanib, and dexamethasone) decrease the anticoagulant effect of apixaban and rivaroxaban. The drugs that inhibit CYP3A4 (dronedarone, diltiazem, clarithromycin, erythromycin, crizotinib, cyclosporine, and tacrolimus) increase the anticoagulant effect of rivaroxaban and apixaban [46].
The P glycoprotein (P-gp) transporter influences and modifies the absorption of dabigatran in the intestines. The P-gp inductors decrease the absorption and the anticoagulant action of dabigatran (rifampicin, dexamethasone, carbamazepine, phenobarbital, phenytoin, levetiracetam, valproic acid, doxorubicin, vinblastine, sunitinib, and vandetanib). The P-gp inhibitors (dronedarone, verapamil, amiodarone, quinidine, clarithromycin, erythromycin, ticagrelor, tacrolimus, cyclosporine, imatinib, and crizotinib) increase dabigatran absorption and its anticoagulant action. The edoxaban dose should be lowered to 30 mg/day when the P-gp inhibitors are concomitantly administered [69]. The interaction of DOACs with antineoplastic therapy is not fully understood and has not yet been investigated in large clinical trials. Bellesoeur et al. analyzed this interaction using the scarce evidence generated by real-life trials. They concluded that “the risk of pharmacokinetic drug–drug interaction with DOAC should be estimated taking account for clinical and biological parameters such as age, sarcopenia, inflammation, renal and hepatic impairment” [70].
4.5.6. Extreme Weight
In special cases such as extreme weight, which is frequent in the presence of neoplasia, pharmacological interferences, or suspected noncompliance, monitoring of the DOAC activity may be required. The recommended test for monitoring xabans is the chromogenic antifactory Xa assay. The ranges are 12–137 ng/mL for rivaroxaban and 34–230 ng/mL for apixaban. The recommended tests for monitoring dabigatran are the dilute thrombin time (DTT) test and the ecarin clotting time (ECT) test [46]. For patients weighing less than 60 kg, a lower dose of edoxaban (30 mg/dl) should be administered [42].
5. Conclusions
The anticoagulant treatment of cancer-associated VTE is difficult to administer because patients have a high risk of recurrence and bleeding.
DOACs exhibit a similar efficiency as VKAs for the treatment of cancer-associated VTE and a lower risk of bleeding. DOACs are more efficient and easier to administer as compared to LMWHs in the prevention of VTE recurrence, but they can be associated with a higher risk of bleeding.
Thus, we support the administration of DOACs as the first-choice treatment in cancer-associated VTE in patients who have a low risk of bleeding under anticoagulant treatment, who do not have severe renal impairment, and who are not undergoing treatments that could interact with the DOAC mechanism of action.
DOACs may also have an antineoplastic effect which depends on the type of cancer and on the early start of the treatment, but more studies are required to support this hypothesis.
Author Contributions: Conceptualization: R.M.C. and M.M.; software S.C. and C.M.G.; validation M.M. and A.D.F.; resources R.M.C.; data curation, A.B.; writing—original draft preparation, R.M.C. and A.B.; writing—review and editing, R.M.C. and M.M.; visualization, S.C. and M.A.S.; supervision, A.D.F. 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: Not applicable.
Acknowledgments: The authors want to thank Seulean Tudor for his great support in editing the manuscript.
Healthcare 2021, 9, 1287
Conflicts of Interest: The authors declare no conflict of interest.
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The biogeophysical climatic impacts of anthropogenic land use change during the Holocene
Article
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Smith, M. C., Singarayer, J. S., Valdes, P. J., Kaplan, J. O. and Branch, N. P. (2016) The biogeophysical climatic impacts of anthropogenic land use change during the Holocene. Climate of the Past, 12 (4). pp. 923-941. ISSN 1814-9332 doi: https://doi.org/10.5194/cp-12-923-2016 Available at https://centaur.reading.ac.uk/63319/
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The biogeophysical climatic impacts of anthropogenic land use change during the Holocene
M. Clare Smith¹, Joy S. Singarayer¹, Paul J. Valdes², Jed O. Kaplan³, and Nicholas P. Branch⁴
¹Centre for Past Climate Change and Department of Meteorology, University of Reading, Reading, UK
²School of Geographical Sciences, University of Bristol, Bristol, UK
³Institute of Earth Surface Dynamics, University of Lausanne, Lausanne, Switzerland
⁴School of Archaeology, Geography and Environmental Science, University of Reading, Reading, UK
Correspondence to: M. Clare Smith ([email protected])
Received: 29 August 2015 – Published in Clim. Past Discuss.: 1 October 2015
Revised: 11 March 2016 – Accepted: 15 March 2016 – Published: 15 April 2016
Abstract. The first agricultural societies were established around 10 ka BP and had spread across much of Europe and southern Asia by 5.5 ka BP with resultant anthropogenic deforestation for crop and pasture land. Various studies (e.g. Joos et al., 2004; Kaplan et al., 2011; Mitchell et al., 2013) have attempted to assess the biogeochemical implications for Holocene climate in terms of increased carbon dioxide and methane emissions. However, less work has been done to examine the biogeophysical impacts of this early land use change. In this study, global climate model simulations with Hadley Centre Coupled Model version 3 (HadCM3) were used to examine the biogeophysical effects of Holocene land cover change on climate, both globally and regionally, from the early Holocene (8 ka BP) to the early industrial era (1850 CE).
Two experiments were performed with alternative descriptions of past vegetation: (i) one in which potential natural vegetation was simulated by Top-down Representation of Interactive Foliage and Flora Including Dynamics (TRIFFID) but without land use changes and (ii) one where the anthropogenic land use model Kaplan and Krumhardt 2010 (KK10; Kaplan et al., 2009, 2011) was used to set the HadCM3 crop regions. Snapshot simulations were run at 1000-year intervals to examine when the first signature of anthropogenic climate change can be detected both regionally, in the areas of land use change, and globally. Results from our model simulations indicate that in regions of early land disturbance such as Europe and south-east Asia detectable temperature changes, outside the normal range of variability, are encountered in the model as early as 7 ka BP in the June–July–August (JJA) season and throughout the entire annual cycle by 2–3 ka BP. Areas outside the regions of land disturbance are also affected, with virtually the whole globe experiencing significant temperature changes (predominantly cooling) by the early industrial period. The global annual mean temperature anomalies found in our single model simulations were −0.22 at 1850 CE, −0.11 at 2 ka BP, and −0.03 °C at 7 ka BP. Regionally, the largest temperature changes were in Europe with anomalies of −0.83 at 1850 CE, −0.58 at 2 ka BP, and −0.24 °C at 7 ka BP. Large-scale precipitation features such as the Indian monsoon, the Intertropical Convergence Zone (ITCZ), and the North Atlantic storm track are also impacted by local land use and remote teleconnections. We investigated how advection by surface winds, mean sea level pressure (MSLP) anomalies, and tropospheric stationary wave train disturbances in the mid- to high latitudes led to remote teleconnections.
1 Introduction
The first agricultural societies were established in the Near East around 10 ka BP and had spread across most of Europe by 5.7 ka BP (Zohary et al., 2012) and to India by 9 ka BP (Tauger, 2013). In China domestication of millet and rice began about 8.5 ka BP, initially spreading more slowly than in Europe but reaching SE Asia by 5.5 ka BP (Roberts, 2013; Tauger, 2013). Agriculture was also independently developed in Mesoamerica, with maize possibly being cultivated as far back as 9 ka BP (Piperno et al., 2009), but, as in China, it spread slowly to other areas.
The most important anthropogenic alteration of the natural environment was the clearing of forests to establish cropland and pasture and the exploitation of forests for fuel and construction materials (Darby, 1956). This long history of anthropogenic land cover change (ALCC) has implications for regional hydrology and climate and possibly for global climate. Deforestation results in both biogeochemical and biogeophysical changes. The biogeochemical changes tend to increase temperature by the emission of greenhouse gases such as CO₂ and CH₄ (CH₄ emissions are influenced not just directly by deforestation but by irrigation in rice agriculture and by emissions from livestock and humans). The impacts of biogeophysical changes are many and varied, being dependent on the local climate, soil, and the natural vegetation that is being replaced, e.g. if natural savannah or grassland is replaced by crops the impact will not be as great as if woodland is replaced.
There are several mechanisms by which biogeophysical changes due to deforestation can affect regional climate. A combination of a reduction in aerodynamic roughness, in the root extraction of moisture, and in the capture of precipitation on the canopy leads to reduced evaporation and thus decreases the fluxes of moisture and latent heat from the surface to the atmosphere. These changes work to increase the local surface temperature (Lean and Rowntree, 1993). Conversely, the increase in surface albedo due to deforestation acts to decrease surface temperature by increasing the reflection of shortwave radiation. This is particularly true at high latitudes where snow on the ground is a factor for some of the year, and the snow-covered ground is no longer masked by the canopy of the forest. Generally, in mid- to high latitudes the albedo increase is considered to be the dominant effect, leading to a net cooling of the regional surface temperature, whereas in the moist tropics, the evaporation is more important and, therefore, a localised overall warming may result (Betts et al., 2007).
During the Holocene the climate has been influenced by natural forcings. Orbital variations have caused a decline in summer solar insolation in the Northern Hemisphere over the last 6000 years. During the same period concentrations of greenhouse gases such as CO₂ and CH₄ have been increasing. On decadal to centennial timescales, fluctuations in solar and volcanic activity have also had a climatic impact (Wanner et al., 2008; Schmidt et al., 2004). The impact of ALCC is superimposed on these natural forcings. The extent and timing of these early anthropogenic land surface changes is the subject of much debate, as is their role in changing Holocene climate. Ruddiman (2003) proposed the idea that anthropogenic impacts on greenhouse gases, and consequently climate change, began thousands of years ago as a consequence of early agriculture and have been increasing in amplitude ever since, which he termed “the early anthropogenic hypothesis”. The idea has been hotly debated in the literature (see, e.g., Broecker and Stocker, 2006; Joos et al., 2004; Singarayer et al., 2011; Mitchell et al., 2013; Kaplan et al., 2011). Whilst the early anthropogenic hypothesis may likely not account entirely for the pre-industrial rises in CO₂ and CH₄, there is no doubt that land use changes do have a climatic impact on both regional and global scales. The real debate is the scale of these effects of early agriculture.
Whilst paleoclimatic and archaeological evidence of anthropogenic land use changes exists, there are not enough sites to comprehensively determine continental-scale impacts of deforestation (Kaplan et al., 2009). Therefore, in order to better estimate impacts of anthropogenic land use, several databases of land use change have been developed. Examples of these include the HYDE 3.1 (History Database of the Global Environment; Goldewijk et al., 2011), Kaplan and Krumhardt 2010 (KK10; Kaplan et al., 2009, 2011), and Pongratz et al. (2008) models. Although the methodologies differ in the details, the basic premise of these models is that from an estimated database of historical population trends, anthropogenic deforestation is calculated based on population density and the suitability of land for crops or pasture.
To quantify the impact of ALCC on climate, data sets of past ALCC can be used in conjunction with climate models. Several studies have estimated the influence of pre-industrial ALCC on a global climate (He et al., 2014; Kutzbach et al., 2011; Pongratz et al., 2010). Globally, the biogeophysical effects of anthropogenic land use change have been estimated to cause a slight cooling that is offset by the biogeochemical warming, giving a net global warming (He et al., 2014; Pongratz et al., 2010). On the local to regional scale, in the most intensively altered landscapes of Europe, Asia, and North America, the biogeophysical effects can be comparable with the biogeochemical (He et al., 2014; Pongratz et al., 2010). In addition, Strandberg et al. (2014) used a regional climate model to evaluate the climatic effect of anthropogenic deforestation in Europe at 6 and 0.2 ka BP with both the HYDE 3.1 and KK10 ALCC scenarios. For the KK10 scenario at 6 ka BP, small but significant temperature differences were found in summer and, at 0.2 ka BP, changes up to ±1 °C were found over widespread areas in both summer and winter. Other authors (e.g. Oglesby et al., 2010; Cook et al., 2012) have modelled a decrease in precipitation in response to deforestation in Mesoamerica.
These existing studies are, however, limited in either temporal or spatial extent and do not address the question of when anthropogenically induced climate change first occurs. In this study global climate model simulations are used to provide a comprehensive evaluation of the influence that the biogeophysical effects of regional human-induced land cover change have had on the climate both globally and regionally throughout much of the Holocene. As described in detail in Sect. 2, the period under consideration is from 8 ka BP to the pre-industrial period (1850), and snapshot simulations with Hadley Centre Coupled Model version 3 (HadCM3) were run at 1000-year intervals. The results are highlighted in Sect. 3. For evaluation purposes palaeoclimate reconstructions from
Bartlein et al. (2011) and Marcott et al. (2013) have been compared with the results from the model runs (Sect. 4). The implications are discussed in Sect. 5.
2 Methodology
2.1 Model description
The climate simulations in this study were performed with the UK Hadley Centre coupled global climate model, HadCM3 (Gordon et al., 2000; Pope et al., 2000) with the Met Office Surface Exchange Scheme (MOSES2.1; Essery et al., 2003) and TRIFFID (Top-down Representation of Interactive Foliage and Flora Including Dynamics; Cox, 2001) dynamic vegetation. The experimental set-up is summarised in Table 1.
HadCM3, is a coupled atmospheric, ocean, and sea ice model. The atmospheric component has a horizontal resolution of 2.5° latitude and 3.75° longitude with 19 unequally spaced levels in the vertical and a 30 min time step. It has an Eulerian advection scheme and includes effects of CO₂, N₂O, CH₄, CFC11, and CFC12. The spatial resolution over the ocean is 1.25° by 1.25° with 20 unequally spaced layers extending to a depth of 5200 m. It also includes a 1.25° by 1.25° resolution model for the formation of sea ice with simple dynamics whereby the sea ice drifts on the ocean currents (Cattle and Crossley, 1995).
TRIFFID is coupled to the GCM (general circulation model) via MOSES every 10 days of the model run. Within TRIFFID, nine surface types are specified: five plant functional types (PFTs) and four non-vegetation types.
HadCM3 was widely used in both the third and fourth assessment reports of the Intergovernmental Panel on Climate Change (IPCC, 2001, 2007) and still performs well in a number of tests relative to other global GCMs (Covey et al., 2003; IPCC, 2007). For the fifth IPCC assessment, it has been superseded by Hadley Centre Global Environment Model version 2 (HadGEM2; Collins et al., 2011), but being relatively computationally efficient, HadCM3 can be the better choice for some palaeoclimate modelling applications as it allows more and/or longer runs to be conducted than would be possible with a higher-resolution model.
2.2 Project-specific model configuration
The version of HadCM3 used does not include interactive ice, carbon cycle, or methane and thus must be forced with prescribed changes in orbit, greenhouse gases, and ice-sheet evolution. Orbital parameters are taken from Berger and Loutre (1991), atmospheric concentrations of gases are determined from ice cores (CO₂ from Vostok (Petit et al., 1999; Loulergue et al., 2008) and CH₄, and N₂O from EPICA; Spahni et al., 2005), and the ice-sheet evolution is estimated using the ICE5G model of Peltier (2004). For further details of these natural forcings of the climate model, readers are referred to Singarayer et al. (2011).
To prescribe Holocene ALCC the KK10 data set of Kaplan et al. (2009, 2011) was used. The original data set has a 5’ spatial resolution and has modelled crop and pasture land use for every year from 8 ka BP to present. For this study the data at 1000-year intervals were taken (8, 7 ka BP, etc.) for both crop and pasture combined and upscaled to the spatial resolution of HadCM3 to formulate a time series of cropland masks (Fig. 1). Within TRIFFID the global crop area is designated by a cropland mask, which can only be occupied by agricultural-type vegetation (i.e. C₃ and C₄ grasses) or bare soil (Betts et al., 2007). Hence, the actual cropland is equivalent to the mask area, less inland water, urban, and ice tiles and less the area covered by non-grassland vegetation or bare soil. The crop mask area is not dynamically updated by climate data. The cropland area incorporates the natural C₃ and C₄ grass fractional areas before converting tree fractions.
For each simulation, the boundary condition forcings (orbit, greenhouse gases, and ice sheets) were specified, and in all simulations the initial conditions were the same, based on a spun-up early industrial simulation. Simulations were run for 1000 years. By the final 500 years of the simulation, the climate system had adjusted to a new surface equilibrium, and thus these final 500 years were averaged to result in the mean altered climatic conditions. The relatively long averaging period increases the signal-to-noise ratio between the modified and control climates and thus distinguishes between differences that are statistically significant but which can be hidden by decadal or multidecadal variability in shorter averaging periods. This is especially important for assessing the impact of agriculture in the earlier time slices of the Holocene when the land use change is small and localised.
3 Results
3.1 Surface air temperature
3.1.1 Local impacts of land use
In the regions where ALCC was significant, surface air temperature changes can be seen in all the time slice simulations (Figs. 2, 3, and 4), and for all time slices except 8 ka BP (not shown) the temperature anomalies in most regions are outside the normal range of variability, which is considered to be within 2 standard deviations of the mean. The anomalies are more pronounced in the JJA season (Fig. 2) than in DJF (Fig. 3). This is due to a combination of the land imbalance between the Northern and Southern Hemisphere, the lack of land surface changes in the extratropical Southern Hemisphere, and the enhanced effect of land surface changes during the season of greatest solar insolation and plant growth (which is JJA in the Northern Hemisphere).
The direct temperature response to ALCC varies with the degree of latitude but the relationship is not straightforward.
as it depends on local climate, soil, and the natural vegetation. In the extratropics, where the albedo effect is generally dominant, there is a trend towards increasing (negative) anomalies, with an increase in disturbance fraction (Fig. 5a for PI). At 7 ka BP the range of extratropical temperature anomalies within the areas of land disturbance is +0.1 to −1.2 °C (JJA) and +0.6 to −0.5 °C (DJF), by 4 ka BP it has increased to +0.4 to −2 °C (JJA) and +0.9 to −1 °C (DJF), and by the pre-industrial period (PI; 1850) it had reached +0.7 to −4 °C (JJA) and +0.3 to −2 °C (DJF). Although there are some positive temperature anomalies, the vast majority of grid points shows a negative temperature trend. Regions with the highest ALCC intensity show the largest negative temperature anomalies, in particular Europe and E Asia and China, where agricultural land use occurs earliest and has the highest concentration of land conversion (Figs. 2, 3, 4, and 5a).
The tropical response shows less of a trend because the impact of reduced evaporation is more significant, and thus there are conflicting signals between the cooling effect of increased albedo and the warming effect of reduced evaporation. In some tropical areas ALCC leads to net cooling, while in other areas net warming is simulated (Figs. 2, 3, 4, and 5a), partly dependent on the availability of moisture at the surface and partly on cloud cover changes (not shown). The main areas that show a warm anomaly response are southern Africa and India in JJA from 5 ka BP and the area bordering the Bay of Bengal in DJF where E India is warmer from 6 ka BP with warming extending to the east coast of the Bay of Bengal by 2 ka BP. The Indian JJA warming is enhanced by cloud feedbacks; a decrease in monsoon circulation leads to decreased cloudiness, thus increasing the shortwave radiation reaching the surface and warming the lower atmosphere. In contrast, tropical South America generally shows a net cooling in response to ALCC. Around the mid- to late Holocene the tropical temperature anomaly range within the areas of land disturbance is ±0.5 °C, and by the early industrial era (1850 CE) it has reached ±1 °C (Fig. 5a).
Analysis of the standard deviation of both the KK10 and control simulations indicated no significant changes in the amplitude of interannual variability of surface temperature or precipitation (using the f test statistic).
### 3.1.2 Remote impacts of land use
In addition to the local temperature changes described above, cooling can also be observed in regions remote from the areas of major ALCC, particularly in the Northern Hemisphere. The most intense cooling is always in the regions of ALCC but even as early as 7 ka BP in the JJA season our model simulations show a band of cooling that stretches across much of the extratropical Northern Hemisphere and the North Atlantic (Fig. 2). This cooling starts influencing the northern Pacific regions by 5 ka BP, and by the early industrial era the surface air temperature over most of the world’s land masses and much of the ocean is cooler due to the effects of ALCC in remote areas.
In the DJF season in the Northern Hemisphere, ALCC leads to cooling both locally and regionally starting at...
Figure 1. Fraction of anthropogenically disturbed land at 1000-year intervals from the late pre-industrial (1850 CE) period to 7 ka BP. The land disturbance data are based on the anthropogenic land use scenario KK10 (Kaplan et al., 2009, 2011).
7 ka BP (Fig. 3). The model simulations also show cooling in the Arctic and warming in Siberia. Cooling remote from the areas of major ALCC becomes more extensive by 3 ka BP, and most landmasses of the Northern Hemisphere are cooler than the control simulation by 2 ka BP. The Siberian warm anomaly has ceased by 3 ka BP, but it remains less affected by the cooling than other regions. In the Southern Hemisphere, cooling remains more localised until 2 ka BP, by which time the majority of the land surface is cooler than the control.
There is an increased temperature anomaly response for the same level of disturbance fraction in the later time slices (Fig. 5b), implying that the responses to the land use changes are not just due to the local effects. Some possible mechanisms for these remote impacts are large-scale circulation changes (such as stationary waves in the upper troposphere at mid- to high latitudes and monsoonal circulation changes), near-surface advection, and the amplifying factors of snow cover. These mechanisms will be discussed in more detail in Sect. 3.2 for atmospheric dynamics and Sect. 3.3.2 for snow cover changes. Changes to the natural vegetation cover (outside the regions of land use) due to the climatic impacts of land use were also investigated as a potential mechanism of further feedbacks but were not found to be significant.
3.2 Atmospheric dynamics
3.2.1 Upper tropospheric dynamics
There are several factors that can impact the dynamics of the upper troposphere in response to ALCC. Cooler surface air temperature means that the density of the air is greater and, therefore, the geopotential height in cooler regions will be lower (See Fig. 7c and d). The changes to mean sea level pressure (MSLP) described in Sect. 3.2.2 can change the areas of convergence and divergence leading to changes in regions of vertical motions. The unequal latitudinal distribution of the temperature anomalies, with the regions of greatest cooling in the midlatitudes of the Northern Hemisphere, affects the meridional temperature gradient leading to a change in baroclinicity, which has been shown to impact storm tracks (Yin, 2005).
In the JJA season from 7 ka BP there is a reduction in the 500 hPa geopotential height over the extratropical Northern Hemisphere in a pattern similar to the temperature pattern but more extensive, completely encircling the globe. From 3 ka BP onwards the height reduction expands southwards, so the geopotential height is lowered almost everywhere by pre-industrial times. The most intense reduction is always in a zonal belt across Europe and E Asia. The Southern Hemi-
sphere response from 5 ka BP appears to show a standing wave pattern affecting the subtropical highs.
In the DJF season a stationary wave in the anomaly field in both the Northern and Southern Hemisphere is apparent in all time slices but most pronounced at 4 ka BP (Fig. 7d). This is a recognised response to surface temperature anomalies as described in Hoskins and Karoly (1981) although, in this case, there are multiple thermal anomalies caused by ALCC. By 2 ka BP there is a reduction in 500 hPa geopotential height over most of the globe. Note that there are several areas that are not statistically significant in Fig. 7c and d, implying a large amount of variability. These geopotential height changes contribute to the simulated remote temperature changes by altering the regions of vorticity, which in turn influence the regions of ascent and descent and thus the MSLP, and surface climatic conditions. The geopotential height anomalies can also alter the pattern of the upper level winds, thus influencing surface storm tracks.
In particular, the positioning of the geopotential height anomalies in the earlier time slices (up to 4 ka BP, Fig. 7d) indicates an increased tendency towards a positive tropical–Northern Hemisphere (TNH) pattern (Barnston et al., 1991) with above average heights over the Bering Strait and Gulf of Alaska and northeastward of the Gulf of Mexico and be-
low average heights over eastern Canada. This would be expected to cause cooler temperatures over the continental United States by increasing the transport of cold polar air into the United States. In several time slices it can be seen that DJF temperature anomalies over the Bering Strait and Alaska (e.g. Fig. 3) show a warming pattern where there are positive geopotential height anomalies in Fig. 7c and d. The DJF temperature anomalies (warming) over Siberia up to 4 ka BP (Fig. 3) also relate to the stationary wave pattern. The decreased heights over the polar regions in most of the time slices are indicative of a positive Arctic oscillation (AO; Fig. 7b) which has been shown to be correlated with milder winters in Siberia (Tubi and Dayan, 2012).
3.2.2 Mean sea level pressure
Changes to MSLP can also have an effect on the climate system. The colder surface air temperature in the region of disturbance means reduced ascent in those regions and thus higher MSLP, and as discussed in Sect. 3.2.2 the changes in the upper troposphere can influence the surface conditions. The MSLP changes can be seen quite clearly in China from 6 ka BP and in Europe by 4 ka BP (Fig. 6 for PI JJA), although the DJF situation in Europe is less coherent, prob-
Figure 5. Relationship between the fraction of anthropogenically disturbed land (from KK10) and the resultant JJA temperature anomaly (°C): (a) for the late pre-industrial (1850 CE) period for extratropical and tropical grid cells; (b) for 7, 4, and 2 ka BP and late pre-industrial (1850 CE) time slices.
ably due to more remote influences such as the North Atlantic storm track. These MSLP changes could play a part in steering weather systems and thus influencing the climate in remote regions. For example, the JJA MSLP anomaly pattern (Fig. 7a and b) over the North and central Atlantic is indicative of a negative phase of the North Atlantic Oscillation (NAO), with above-normal pressure over the North Atlantic and below-normal pressure over the central Atlantic. This pattern is apparent from 5 ka BP. The NAO alters the intensity and location of the North Atlantic jet stream and storm track and thus the patterns of heat and moisture transport (Hurrell, 1995). A negative NAO would contribute to a tendency to wetter summers in all but the southernmost regions of Europe (Folland et al., 2009), and this was seen in the results described in Sect. 3.3.1. The DJF NAO shows a trend towards a positive NAO which could result in drier winters over the Mediterranean region (Hurrell et al., 2003), although it is difficult to ascertain whether this is the case as the pattern is not as consistent as in JJA.
3.2.3 Surface advection
Some of the cooling in regions adjacent to the areas of land disturbance is due to advection by low-level winds. In regions with a prevailing wind direction an advection pattern can be clearly seen. Figure 6 shows advection of cold air from the areas of land use change in east Asia to the east across the west Pacific and from the region of land disturbance in Mexico to the west across the east Pacific; this also affects the sea surface temperatures (SSTs) in these regions of the Pacific (not shown). In other areas where the surface wind direction is more variable the effect is more difficult to detect but probably does contribute to the spread of the cold anomaly outward from the region of land disturbance.
3.3 Hydroclimate
Our model simulations show precipitation changes in response to ALCC, but it should be noted that there are larger uncertainties in climate-model-simulated precipitation and other variables related to model dynamics than in temperature, which is primarily controlled by thermodynamics (Shepherd, 2014). Different climate models show a wide range of responses in their dynamics to palaeo- and future climate change scenarios, and we acknowledge that aspects of the precipitation anomaly patterns in this study may be less robust than those of other climate variables.
The precipitation responses to ALCC (Fig. 8 for JJA and Fig. 9 for DJF) tend to be caused by a response to large-scale circulation changes rather than being directly attributable to local land use. The European precipitation response in the DJF season is not entirely consistent throughout the time slices, but the general response is a slight decrease in precipitation around the western and Mediterranean coasts, with this dryness extending further into the continent by 1 ka BP. The simulations show that, in the JJA season, Europe has an increase in precipitation from 7 ka BP onwards compared to the control; the anomaly gradually grows in magnitude and extent, possibly influenced by the increased tendency to a negative North Atlantic Oscillation (NAO). Positive anomalies begin in the warm pool of the Gulf of Mexico and extend across the North Atlantic, following the track of positive anomalies to the 850hPa wind field (Fig. 10). In addition, as the cooler temperature anomalies extend quite high in the troposphere over Europe, this increases relative humidity throughout the low to mid-troposphere (not shown) and thus the likelihood of large-scale precipitation.
In India there is a decrease in monsoon precipitation from 5 ka BP, which then gradually increases in intensity. This is partly driven by the slightly cooler Indian subcontinent temperatures (Fig. 11) in the critical months for monsoon development and also by cooler temperatures in Europe and east Asia and increased snow cover on the Tibetan plateau. This leads to decreased monsoonal circulation and decreased cloudiness. There are also changes to the east Asian monsoon, with wetter conditions to the north and south of the region and drier conditions in the centre. This pattern is seen reasonably consistently from 4 ka BP onwards.
3.3.1 Intertropical Convergence Zone (ITCZ)
Analysis of the precipitation fields (Figs. 9 and 10) shows an overall southward migration of the ITCZ. These changes are most obvious in the Atlantic and Pacific oceans and over the continent of Africa. In the DJF season there are changes to the ITCZ in the western Pacific, but a consistent pattern is not seen until 3 ka BP when there is southward shift in
Figure 6. DJF surface temperature anomalies for KK10−control and KK10 surface winds for the late pre-industrial (1850 CE) and 2 ka BP.
Figure 7. Modifiers of climate in regions outside the areas of anthropogenic land use change. All anomalies are for KK10−control: (a) JJA MSLP changes at 1850 CE, with the stippling indicating grid boxes where the anomalies are significant at the 95 % level using Wilcoxon rank sum statistical analysis; (b) as (a) but for 4 ka BP; (c) DJF 500Pa geopotential height anomalies at 1850 CE demonstrating stationary wave pattern, with the stippling indicating grid boxes where the anomalies are significant at the 95 % level using Wilcoxon rank sum statistical analysis; (d) as (c) but for 4 ka BP.
the ITCZ over the Atlantic and coastal regions bordering the Atlantic leading by 2 ka BP to a decrease in precipitation in the interior of southern Africa and wetter conditions on the coasts. There is generally increased precipitation over the Indian Ocean and the Amazonian region of South America and a reduction over the Bay of Bengal, but this pattern is not entirely consistent throughout the time slices. Similarly, in the JJA season there are changes to the ITCZ throughout all the time slices, but these do not all show a consistent pattern. The most persistent changes are increased precipitation over the Pacific from 5 ka BP and over Central America from 7 ka BP and a southward shift from 2 ka BP. This southward shift in the ITCZ in the JJA season impacts the west African monsoon with lower precipitation in a belt across the monsoon region by 2 ka BP, although the west coast of North Africa is wetter.
The generally cooler temperatures in the Northern Hemisphere may influence the latitudinal position of the Hadley cell and thus the location of the ITCZ via the influence on the interhemispheric temperature gradient resulting in the
strengthening of the northward cross-equatorial energy transport (e.g. Kang et al., 2008). This shift south of the ITCZ to transport heat to the cooler Northern Hemisphere is seen in both the DJF and JJA seasons.
3.3.2 Snow cover
Lower surface air temperatures in the ALCC scenario relative to the control lead to an increase in winter snow accumulation (Fig. 12). This increase is seen by 5 ka BP, mostly in northern and mountainous regions. The areas affected gradually increase so that by 3 ka BP more temperate and lower-lying areas see increases in snow depth. The effects are most pronounced in North America and Europe. In regions outside the areas of permanent snow cover, increases in snow depth will delay the melting of the snow pack and thus result in a longer period of snow cover. The increased snow cover due to the cold temperature anomalies will cause additional cooling due to the increased albedo. This will be greatest in regions of deforestation where the snow-covered ground is no longer masked by the canopy of the forest. This increased snow cover would also lead to decreases in precipitation due to lower rates of moisture recycling over land. It should be noted that the modelling of snowfall is subject to the same uncertainties as described in Sect. 3.3.
Figure 8. JJA precipitation anomalies (mm day$^{-1}$) for KK10 minus control at time slices from the late pre-industrial period (1850 CE) to 7 ka BP. The stippling indicates grid boxes where the anomalies are significant at the 95 % level using Wilcoxon rank sum statistical analysis.
4 Temporal evolution of Holocene climate
In the control experiment the changes in orbital configuration, greenhouse gases (GHG), and ice sheets and sea level lead to monotonically increasing global temperatures through the Holocene (Fig. 13a). Analysis of previous experiments to assess the sensitivity to different natural forcings (data from Singarayer and Valdes, 2010; Singarayer et al., 2011) suggests that while the changes to orbital configuration effect a cooling in global temperature over the Holocene, this is outweighed by increases in greenhouse gases (~17 ppm CO₂ from 8 ka BP to late pre-industrial time), which result in overall warming. Cooling through the Holocene occurs in Northern Hemisphere summer, when forced with orbit and GHG variations, but is not as pronounced as when only forced by orbital variations. In winter, when HadCM3 is forced with orbit-only variation, there is little change in temperature, but when GHG increases are included, this becomes a warming over the Holocene, which then outweighs the reduced summer cooling. Whilst this contrasts with recent data compilations that suggest a general decline in global temperatures since the mid-Holocene (Marcott et al., 2013), it is within the range of other climate model responses when compared with the Paleoclimate Model Intercomparison Project 3 (PMIP3) mid-Holocene (MH) minus late pre-industrial (PI) temperature anomalies. Although palaeodata syntheses
**Figure 9.** DJF precipitation anomalies (mm day⁻¹) for KK10 minus control at time slices from the late pre-industrial period (1850 CE) to 7 ka BP. The stippling indicates grid boxes where the anomalies are significant at the 95 % level using Wilcoxon rank sum statistical analysis.
may suggest a cooling of Northern Hemisphere temperatures, there are regional and seasonal variations in the data such as that from the Bartlein et al. (2011; Fig. 14c) and Mauri et al. (2015) data compilations. In both these compilations and the combined proxy reconstructions of Wanner et al. (2008), the cooling is most evident over the higher-latitude Northern Hemisphere.
For our specific configuration of HadCM3 the inclusion of land use changes through the Holocene has a significant impact on the progression of modelled global average temperatures, such as to alter the direction of the multi-millennial trend described above, thus reducing the mismatch between the model simulations and the proxy reconstructions which show an extratropical cooling trend throughout the Holocene. The increasing magnitude and spread of ALCC through the Holocene reconstructed in KK10 counteracts the influence of increasing greenhouse gases, so that temperatures are effectively steady from 3 ka BP in HadCM3 (Fig. 14a). These global trends are composed of considerable heterogeneity on the regional scale. When the trends are broken down into zonal regions, it can be clearly seen that the difference in trends with/without land use is greatest in the northern extratropics (Fig. 13b), where the Holocene trend is modified from increasing temperatures to decreasing temperatures in the late Holocene by the addition of ALCC. There are impacts on mean temperatures in the tropics (Fig. 13c) and southern extratropics (Fig. 13d) but not sufficient to influence the direction of the Holocene trend.
MH minus PI anomalies of annual mean surface air temperature (Fig. 14a) show a near-global distribution of cooling, except over high-latitude sea ice regions, which are particularly influenced by changes in obliquity (higher in the MH than in the PI). The PMIP3 suite of models shows a similar pattern of surface air temperature anomalies. The cooling is most dramatic over the tropics and monsoonial regions, where changes in the seasonality of insolation (due to orbital precession variation) intensify monsoon circulation in the early and mid-Holocene and the resulting additional cloud cover reduces incoming shortwave radiation as well as increased surface water, altering the balance of sensible to latent heat fluxes. The inclusion of land use change in the KK10 experiment reduces the magnitude of MH cooling, especially in the midlatitudes. Over Europe and eastern North America the anomaly is reversed to a warming (i.e. over these regions the cooling from deforestation shown in Fig. 2 increases and outstrips the warming from greenhouse gases). These are also regions where there is the highest concentration of pollen reconstructions (Fig. 14c; Bartlein et al., 2011; Mauri et al., 2015). The influence of land use change improves the data–model comparison with the reconstruction by Bartlein et al. (2011) over these key areas (Fig. 14a–c). Likewise, when simulated top-level ocean temperatures are compared with SST data used within the Marcott et al. (2013) compilation, the inclusion of land use improves the data–model comparison (Fig. 14d and e). However, the largest MH warming in the model is in the summer months, whereas recent seasonal temperature reconstructions (also using pollen; Mauri et al., 2015) suggest that the largest and most widespread MH warming may have occurred in winter.
In contrast, using the KK10 ALCC scenario as a boundary condition to the climate model does not improve the agreement in annual mean MH−PI precipitation anomalies when compared to the palaeoclimate reconstruction of Bartlein et
temperature changes found in this study were greater, e.g., anomalies with those found by He et al. (2014) for 1850 CE are many similarities in the distribution of the temperature wave pattern. This may be particularly significant in producing the stationary global model simulations. The positioning of the major temperature anomalies has the advantages of higher spatial resolution and more detailed orography, but they may not include these potential impacts from the same land cover forcing in regional and remote atmospheric changes, possibly resulting in different detailed orography, but they may not include these potential uncertainties involved. The variability in the results from different models can be greater than the variability of the property that is being assessed (Pitman et al., 2009; de Noblet-Ducoudre et al., 2012; Brovkin et al., 2013). These inconsistencies have been attributed to disagreements in how land use change is implemented, the parameterisation of albedo, the representation of crop phenology and evapotranspiration, and the partitioning of available energy between latent and sensible heat fluxes (Pitman et al., 2009; de Noblet-Ducoudre et al., 2012; Boisier et al., 2012). The albedo and turbulent heat fluxes from our model simulations for the North America–Eurasia region (Fig. 16) are within the range of other climate model responses when compared with those from the Land-Use and Climate, IDentification of robust impacts (LUCID) set of experiments (Boisier et al., 2012). The negative turbulent and latent heat fluxes would offset some of the cooling due to the increased albedo. Although the largest albedo changes are in the DJF season the impact of this will be lessened due to the lower levels of incoming solar radiation in this season. Results could be further improved by the running of transient simulations that could capture events such as the Maunder minimum. A transient simulation response could result in different biogeophysical impacts to the ones achieved when using a long equilibrium simulation where the ocean–land–atmosphere system can reach more of a steady state and the climate sensitivity is different.
5 Discussion
Anthropogenic land cover change leads to climate change well beyond the core regions of land use early in the Holocene. These results suggest that regional ALCC has an effect on the atmospheric circulation, e.g. the ITCZ shift is a remote response on global scale. The implications of this finding are that regional models or atmospheric-only models would not simulate these atmospheric circulation changes as well as a global coupled model. In this study we observed multiple thermal anomalies (from intense regions of cooling directly over anthropogenic land use change), but the standing wave response of the geopotential height field would likely also be seen even for a single thermal source from just one region (Hoskins and Karoly, 1981). Regional models have the advantages of higher spatial resolution and more detailed orography, but they may not include these potential remote atmospheric changes, possibly resulting in different impacts from the same land cover forcing in regional and global model simulations. The positioning of the major temperature anomalies in the midlatitudes and at similar latitudes may be particularly significant in producing the stationary wave pattern.
Whilst these are the results from only one model, there are many similarities in the distribution of the temperature anomalies with those found by He et al. (2014) for 1850 CE and Pongratz et al. (2010) for the 20th century although the temperature changes found in this study were greater, e.g., a pre-industrial global annual mean temperature anomaly of $-0.23 \, ^{\circ} C$ as opposed to the $-0.17 \, ^{\circ} C$ estimated by He et al. (2014). Running similar simulations with a greater number of models would improve the robustness of the results particularly with respect to hydroclimate due to the high uncertainties involved. The variability in the results from different models can be greater than the variability of the property that is being assessed (Pitman et al., 2009; de Noblet-Ducoudre et al., 2012; Brovkin et al., 2013). These inconsistencies have been attributed to disagreements in how land use change is implemented, the parameterisation of albedo, the representation of crop phenology and evapotranspiration, and the partitioning of available energy between latent and sensible heat fluxes (Pitman et al., 2009; de Noblet-Ducoudre et al., 2012; Boisier et al., 2012). The albedo and turbulent heat fluxes from our model simulations for the North America–Eurasia region (Fig. 16) are within the range of other climate model responses when compared with those from the Land-Use and Climate, IDentification of robust impacts (LUCID) set of experiments (Boisier et al., 2012). The negative turbulent and latent heat fluxes would offset some of the cooling due to the increased albedo. Although the largest albedo changes are in the DJF season the impact of this will be lessened due to the lower levels of incoming solar radiation in this season. Results could be further improved by the running of transient simulations that could capture events such as the Maunder minimum. A transient simulation response could result in different biogeophysical impacts to the ones achieved when using a long equilibrium simulation where the ocean–land–atmosphere system can reach more of a steady state and the climate sensitivity is different.
**Figure 12.** DJF snow depth anomalies (cm) for KK10 minus control for the late pre-industrial period (1850 CE). The stippling indicates grid boxes where the anomalies are significant at the 95 % level using Wilcoxon rank sum statistical analysis.
**Figure 13.** Time series plots for the Holocene simulations from HadCM3. Panel (a): annual mean global surface air temperature (SAT) for the control simulation in grey, and KK10 simulation in black; panel (b): anomaly in northern extratropical (30–90° N) annual mean temperature from the equivalent simulation at 8 ka BP; panel (c): same as (b) but for the tropics (30° N–30° S); panel (d): same as (b) but for the southern extratropics (30–90° S).
From late preindustrial era simulations, one using observed atmospheric greenhouse gas concentrations and the other using greenhouse gas concentrations in a world with no anthropogenic emissions (based on linear projection from earlier Holocene trends from Kutzbach et al., 2011), He et al. (2014) estimated a net global warming of 0.9 °C due to the biogeochemical effects of ALCC, with between 0.5 and 1.5 °C warming in the areas of most intense land use changes. If we incorporate this degree of warming into our early industrial era (1850 CE) simulations, there would still be a net cooling in Europe, E Asia, and NE America with, e.g., a net cooling of up to 2 °C in parts of Europe. To put this in perspective, the IPCC (IPCC, 2014a) consider a temperature rise of more than 2 °C to be undesirable and that changes of 1 °C could have an impact on vulnerable ecosystems. However, the temperature changes in this study took place over a much longer period than the time frame considered in the IPCC and ecosystems and human societies would have had more time to adapt. The consequences of these changes for agricultural societies would vary depending on the pre-existing conditions. For example, in drier regions, where crops are more likely to be water limited, cooler, wetter summer conditions
may have been beneficial to the agricultural output although the risk of erosion would have been increased. The generally lower temperatures might also make societies more vulnerable to further transient cooling effects such as volcanic activity.
There are discrepancies between simulations of the mid-Holocene climate and the independent data-based reconstructions. Both the simulations from this study and virtually all the PMIP3 (Palaeoclimate Model Intercomparison 3; https://pmip3.lsce.ipsl.fr) models show a temperature increase from the mid-Holocene to the PI, whereas the Marcott et al. (2013) and Mann et al. (2008) (on a shorter timescale); reconstructions show a decrease. It is interesting to note that ALCC reduces this mismatch for HadCM3, especially in key areas such as Europe. Other factors that could lead to this discrepancy are uncertainties in the proxy reconstructions and deficiencies in climate models (e.g. Lohmann et al., 2013). These climate model deficiencies include low resolution and sensitivity and, importantly, their dependence on soil moisture, whereby energy is utilised for evaporation rather than for temperature increase.
This study shows a significant increase in precipitation over Europe with increasing land use, which means that the PI becomes wetter than the mid-Holocene, which leads to increases in soil moisture and changes in the sensible to latent heat flux balance, and, in combination with increased albedo caused by deforestation, this results in cooler temperatures for PI than MH. If the land–atmosphere coupling strength was different and soil moisture was strongly reduced with deforestation, it is likely that the cooling effect would be smaller (cf. Strandberg, 2014).
Further uncertainties arise from the robustness of the land use reconstructions, which is difficult to evaluate due to the lack of global-scale evidence for human impact on the Earth’s land surface. Much of the uncertainty comes from the lack of knowledge about the magnitude and distribution of the global human population and the rate of technological evolution and intensification through time. As part of our initial investigations simulations were also run using an alternative land use scenario (the HYDE 3.1 data set; Goldewijk et al., 2011). The HYDE 3.1 reconstruction has substantially lower levels of land use early in the Holocene (as compared with KK10), which resulted in a later development of consistent temperature anomalies at 4 ka BP (not shown) in comparison with the KK10 land use scenario. The decision was taken to proceed with the KK10 data due to its assumptions of a larger per capita land use earlier in the Holocene when agricultural methods were less efficient. Several ongoing international initiatives that aim to synthesise palaeoecological and archaeological data promise to lead to more robust reconstructions of Holocene ALCC in the future (e.g. the Past Global Changes (PAGES) LandCover6k project; http://www.pages-igbp.org/workinggroups/landcover6k/intro).
By the early industrial period, simulated biogeophysical temperature changes in the regions of land disturbance are of the same order of magnitude (e.g. 0.83 °C annual anomaly in the main agricultural areas of Europe) as the changes seen due to CO₂ increases during the industrial period (0.85 °C; IPCC, 2014b). Part of Ruddiman’s original hypothesis (Ruddiman, 2003) is that pre-industrial global warming caused by anthropogenic CO₂ or CH₄ emissions should have been ~2 °C at higher latitudes, but there was no evidence for this warming. Ruddiman (2003) attributed this to a natural cooling trend caused by decreasing summer insolation. This study suggests that biogeophysical effects of the land use changes may also have played a part in counteracting the warming due to anthropogenic greenhouse gas emissions, as acknowledged in Ruddiman (2013). The precipitation changes might also have an impact on the availability of water for rice irrigation and on natural wetlands, thus affecting the production of methane.
6 Conclusions
In our global model simulations that use a Holocene ALCC scenario as a boundary condition, a surface temperature response to the biogeophysical effects of ALCC is seen in regions of early land use such as Europe and SE Asia as early as 7 ka BP in the JJA season and throughout the entire annual cycle by 2–3 ka BP. Areas outside the major regions of ALCC are also affected, with virtually the whole globe experiencing significant temperature changes with a net global cooling of 0.22 °C by the pre-industrial period. Although the temperature changes are predominantly cooling, some regions such as India, southern Africa, and Siberia show warming as a response to ALCC. The greatest changes are generally seen in the JJA season, with a mean regional cooling of 1.4 °C experienced in Europe and 1 °C in E Asia in the early industrial period (1850 CE). Much of the precipitation response to the land use tends to be due to large-scale circulation changes such as a decrease in the intensity of the Indian monsoon, the southward movement of the ITCZ, and changes to the North
Figure 16. JJA and DJF albedo, latent heat flux (QLE), and turbulent heat flux (QT) anomalies for KK10 minus control for the late pre-industrial period (1850 CE) for the North America–Eurasia land surface.
Atlantic storm track. In Europe there is a slight decrease in precipitation in the DJF season and a more substantial increase in the JJA season. Some causal factors for the teleconnections are advection by surface winds, MSLP anomalies, and tropospheric stationary wave train disturbances in the mid- to high latitudes.
The potential for an early global impact of ALCC on climate strongly implied by this study suggests that due consideration of this should be taken in simulations covering the Holocene. The inclusion of ALCC in the model improves the model comparison for surface air temperature with the data-driven palaeoclimate reconstructions, especially in key areas such as Europe. The remote teleconnections seen in this study have implications for the regional modelling of land use change due to circulation changes that occur outside the domain of the regional model.
Overall, our model simulations indicate an increase in global surface air temperatures through the Holocene. Globally, the inclusion of ALCC data reduces the magnitude of this warming especially in the late Holocene when the temperatures remain relatively constant. Regionally, in the northern extratropics, this warming is reversed in the late Holocene. It should be noted that in this study it is not possible to distinguish the anthropogenic component of the biogeochemical changes as the same atmospheric CO$_2$ and CH$_4$ concentrations (from ice core measurements) are prescribed for both the KK10 and control simulations. However, the level of early industrial warming due to the biogeochemical impacts of ALCC predicted by He et al. (2014) would negate the early industrial biogeoophysical cooling seen in this study in all regions except for the most intensively altered landscapes of Europe, E Asia, and NE America.
Other caveats are the large uncertainties in the land use data and, therefore, in our understanding of the Holocene evolution of land surface–climate interactions as well as our ability to evaluate climate models. To reduce these uncertainties there is an urgent need to extend land cover reconstructions and the prehistory of land use globally (cf. PAGES LandCover6k initiative). It must also be stressed that these are the results from only one model and the use of equilibrium simulations may produce different results from a transient simulation. However, these uncertainties are more likely to impact the timing, intensity, and regional details of the changes rather than the overall trends and patterns.
Data availability
Data are available from the Bristol Research Initiative (BRIDGE, 2016) for the Dynamic Global Environment website: http://www.bridge.bris.ac.uk/resources/simulations. The relevant experimental runs are tdna (control) and tdpo (KK10).
Acknowledgements. M. Clare Smith is supported by a University of Reading doctoral scholarship. M. Clare Smith and Joy S. Singarayer would like to thank Sandy Harrison and Beni Stokker for useful discussions on land cover reconstructions. Jed O. Kaplan was supported by the European Research Council (313797 COEVLIVE).
Edited by: H. Goosse
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The Long Noncoding RNA MEG3 and its Target miR-147 Regulate JAK/STAT Pathway in Advanced Chronic Myeloid Leukemia
Zi-ye Li, Lin Yang, Xiao-jun Liu, Xing-zhe Wang, Yu-xia Pan, Jian-min Luo *
Department of Hematology, The Second Hospital of Hebei Medical University, Shijiazhuang, Hebei 050000, China
Abstract
Background: Long non-coding (Inc) RNAs plays an important role in chronic myeloid leukemia (CML). In this study, we aimed to uncover the mechanism of the IncRNA maternally expressed 3 (MEG3) and its target microRNA-147 (miR-147) in CML.
Methods: Sixty CML patients and 10 healthy donors were included in the study. The methylation of MEG3 and miR-147 promoter was determined by methylation-specific PCR. The relationship of MEG3 and miR-147 was explored by luciferase assay. The interactions of proteins were studied by RNA pull-down assay, RNA immunoprecipitation and co-immunoprecipitation.
Findings: Patients in accelerated phase CML (CML-AP) and blast phase CML (CML-BP) showed lower expressions of MEG3 and miR-147 and higher expressions of DNMT1, DNMT3B, MBD2, MECP2 and HDAC1 compared to the controls. These patients also showed a higher degree of methylation of MEG3 and miR-147 while there was a reduction after chidamide treatment. Furthermore, the overexpression of MEG3 and miR-147 inhibited cell proliferation both in vivo and in vitro, promoted apoptosis and decreased the expressions of DNMT1, DNMT3A, DNMT3B, MBD2, HDAC1 and MECP2. We also found MEG3 interacted with DNMT1, JAK2, STAT3, HDAC1, and TYK2, and JAK2 was bound to STAT3, STAT5 and MYC. More interestingly, JAK2 was bound to TYK2 by the bridge of MEG3.
Interpretation: LncRNA MEG3 and its target miR-147 may serve as a novel therapeutic target for CML blast crisis, and chidamide might have a potential clinical application in treating CML blast crisis.
© 2018 The Author(s). Published by Elsevier B.V. This is an open access article under the CC BY-NC-ND license (http://creativecommons.org/licenses/by-nc-nd/4.0/).
Keywords: IncRNA MEG3
Chronic myeloid leukemia blast crisis
Chidamide
miR147 and epigenetic
MEG3 may be an important molecule in the progression of CML. In the study, we explored the regulation mechanism of MEG3 on CML progression. Chidamide is a novel histone deacetylase inhibitor to treat cutaneous T-cell lymphoma. In this study, we detected the epigenetic regulation of MEG3 and regulation mechanism to further uncover the pathology of CML blast crisis, and the potential treatment effect of chidamide on CML blast crisis. Implications of all the Available Evidence
We found in our study that IncRNA MEG3 and its target miR-147 may serve as a novel therapeutic target for CML blast crisis, and chidamide might also have a potential clinical application in treating CML blast crisis.
1. Introduction
Chronic myeloid leukemia (CML) is a bone marrow clone malignancy characterized by the formation of the breakpoint cluster region (BCR) and Abelson murine leukemia (ABL) fusion gene that encodes BCR-ABL.p210 [1, 2]. The pathology of CML comprises three phases, namely chronic phase (CML-CP), accelerated phase (CML-AP), and blast phase (CML-BP). The CML-AP and CML-BP are the hallmarks of advanced CML. [3]. In clinic, tyrosine kinase inhibitors (TKIs) were primarily chosen for CML treatment, while some patients showed resistance to or cannot tolerate TKI administration. Therefore, it is urgent to explore novel therapeutic targets or potential medication. Development of CML is a complex process, many molecules play important roles, including long non-coding RNA (IncRNA) and microRNA (miRNA). It has been shown that IncRNA maternally expressed 3 (MEG3) can inhibit cancer cell proliferation and is associated with poor prognosis of cancer patients. MEG3 can inhibit cell proliferation in CML. MEG3 may be an important molecule in the progression of diseases including CML, while the regulation mechanism was not clear. Mir147, which is downregulated in colon cancer, suggesting that miR147 can act as tumor suppressor. The role of miR-147 in CML was unknown. In the study, we aimed to explore the role and regulation mechanism of MEG3 and miR147 in CML development to explore the novel therapeutic targets. Added Value of this Study
Besides IncRNAs, microRNAs (miRNAs) can also regulate the progression of diseases [11–14].
In addition to molecules, many genetic and molecular biological events were involved in the development of diseases including epigenetic regulation [15]. Epigenetics are the study of heritable changes in gene expression, without any alteration of the DNA sequence [16]. The abnormal methylation of promoter regions plays an important role in tumorogenesis, including human choriocarcinoma and squamous cell lung cancer [17, 18]. Furthermore, the study of IncRNA-associated methylation has gained increased attention [19, 20].
In the cells where methylation regulation occurs, the expressions of methylation related genes were significantly changed, such as DNMT1, DNMT3A, DNMT3B, MBD2, HDAC1, and MECP2. Histone deacetylases (HDACs) also involved epigenetic regulation. HDAC expression was increased in the majority of tumor cells and induces tumorogenesis. HDAC inhibitors (HDACis) are a novel family of drugs that achieved positive results in the treatment of hematological malignancies [21–23] and certain solid tumors [24]. HDACis interfere with the function of HDACs and reverse the effect of their overexpression [25, 26]. Chidamide is a novel HDACi that is approved to treat cutaneous T-cell lymphoma [26]. However, whether chidamide influences the epigenetic regulation of MEG3 and miR-147 in KCL22 and K562 cells remains largely unknown.
Therefore, we aimed to detect the epigenetic regulation of MEG3 and regulation mechanism to further uncover the pathology of CML blast crisis, and the potential treatment effect of chidamide on CML blast crisis in the study.
2. Materials and Methods
2.1. Collection of Bone Marrow Samples
The bone marrow samples of 60 CML patients and 10 healthy donors were collected at Department of Hematology of the Second Hospital of Hebei Medical University between May 2016 and June 2017 (Table 1). The bone marrow samples from 10 healthy donors were used as controls. In addition, we collected 3 CML-AP patients and 3 CML-BP patients to study the role of chidamide for treatment of CML. Peripheral blood mononuclear cells were isolated by lymphocyte separation. The inclusion criteria of patients were as follows: (i) diagnosis of CML via bone marrow morphology, immunology, molecular biology, and cytogenetic analyses; (ii) clear pathological staging; and (iii) availability of intact clinical data. The exclusion criteria were as follows: (i) significant organ dysfunction; (ii) pregnancy; and (iii) failure to provide informed consent. No chemotherapy was administered before the collection of the specimens. The study was approved by the Ethics Committee of the Department of Hematology of the Second Hospital of Hebei Medical University, and each patient signed an informed consent.
| Item | CML-CP (n = 30) | CML-AP (n = 15) | CML-BP (n = 15) |
|---------------------------|----------------|----------------|----------------|
| Age (years), median | 41.4 (9–65) | 49.1 (13–69) | 51.9 (20–69) |
| (range) | | | |
| Male/female, (n/n) | 20/10 | 9/6 | 10/5 |
| WBCs × 10⁹/(median | 221.4 (30.2–517) | 263.5 (47.4–396) | 69.5 (27.4–224) |
| (range) | | | |
| Hemoglobin level (g/l) | 94 (76–120) | 75 (61–105) | 62.4 (52–79) |
| Platelet count, 10⁹/median (range) | 518 (99–809) | 305 (32–725) | 35.5 (19–71) |
AP, accelerated phase; BP, blast phase; CML, chronic myeloid leukemia; CP, chronic phase; WBC, white blood cells.
transfection reagent (Life Invitrogen, Carlsbad, CA, USA) according with the LNA-ASO at a concentration of 80 nM, using the Oligofectamine control LNA-ASO were designed and synthesized by Saibaisheng Bioen (Carlsbad, CA). Purinamycin was used to screen the positive cells. MEG3 targeting controls or miR-147 mimics using lipo3000 (Life Invitrogen, Carlsbad, CA) and were transfected with LV-MEG3 or LV-control or miR-147 overexpression vector (Life Invitrogen, Carlsbad, CA). MiR-147 Invitrogen. The cDNA was cloned into the pLVX-hMEG3-Puro lentiviral mouth Junction, NJ, USA). The KCL22 and K562 cells or the patient-tomycin. Chidamide was purchased from MedChemExpress (Monmouth Junction, NJ, USA). The KCL22 and K562 cells were cultured in Iscove's modified Dulbecco's medium (Gibco, Beijing, China) containing 10% fetal bovine serum (FBS, KCL22 cells were maintained in our laboratory. The KCL22 and K562 cells were seeded into 6-well plates (5 × 10⁵/well) and were both either transfected with LV-MEG3 or LV-control, or transfected with the miR-147 mimics or miR-147 controls. Apoptosis was determined using an AnnexinV-FITC and PI kit (BD Biosciences, Franklin Lakes, NJ, USA) and was analyzed using a BD FACSCan II system (BD Biosciences). The patient-derived cells were also assayed using the apoptosis kit after treatment with chidamide, as described above.
2.7. Real-Time Polymerase Chain Reaction (RT-PCR)
The total RNA was isolated using the RNeasy Mini Kit (Qiagen, Valencia, CA, USA) and was reverse-transcribed to cDNA using RevertAid First Strand cDNA Synthesis Kit according to the manufacturer’s instructions (Thermo Fisher, USA). The reverse transcription reactions were conducted under the following conditions: 42 °C for 60 min; 25 °C for 5 min; and 70 °C for 5 min. The qPCR mixtures had a final volume of 20 μl and contained 1 μl of template cDNA, 0.5 μl of each sense and anti-sense primer, 10 μl of SYBR Green Mix (Invitrogen), and 8 μl of diethyl pyrocarbonate (DEPC)-treated water. The concentrations of primers for DNMT1, DNMT3A, DNMT3B, MBD2, MeCP2, and HDAC1 were as follows: 2 × All-in-OneTM qPCR Mix 10 μl; MiR-147 0.25 μM. The RT-qPCR conditions were as follows: denaturation at 95 °C for 5 min followed by 45 cycles of 95 °C for 15 s; 60 °C for 35 s; and 72 °C for 20 s in an ABI 7500 Real-Time Rotary Analyzer (Applied Biosystems, Thermo Fisher Scientific, Shanghai, China). The 2^−ΔΔCT method was used to calculate the relative gene expression. Each reaction was repeated for at least three times, independently. The primers were synthesized by Invitrogen and are shown in Table 3.
2.8. Detection of miR-147 Levels
The RNA in bone marrow mononuclear cells (BMMCs), KCL22 and K562 cell lines was extracted with Trizol (Invitrogen; Thermo Fisher Scientific, Inc., USA) and afterwards purified with the RNeasy Maxi kit (Qiagen, Germany) according to the provided instructions. Reverse transcription reactions and RT-qPCR were performed using miScript Reverse Transcription kit (Qiagen, Germany) and miScript SYBR® Green PCR kit (Qiagen, Germany). The mixtures for PCR to detect the level of miR-147 were as follows: 2 × All-in-OneTM qPCR Mix 10 μl, MiR-147 Primer 2 μl, Universal Adaptor PCR Primer 2 μl, cDNA 2 μl, and DEPC-treated water 4 μl. The concentration of primer was 0.2 μM. The programs for PCR were as follows: 95 °C for 1 min, and then 40 cycles of 95 °C for 10 s, 55 °C for 30 s and 70 °C for 30 s. After normalization to U6, the relative expression level of mature miR-147 was calculated with 2^−ΔΔCT method.
### Table 2
| Primer sequences of MEG3 ASO and NC ASO. | |
|----------------|----------------|
| MEG3 NC ASO | GACCTAGCTAGGTC GCTCTCAATGTC TCCAA |
| MEG3 ASO | |
ASO, acid-antisense oligonucleotide; NC, negative control; MEG3, maternally expressed 3.
### Table 3
| Primer sequences for RT-PCR. | |
|----------------|----------------|
| Gene | Primer | Product |
|----------------|----------------|
| MEG3 | Forward: 5′-CTCCCCCTTACGCTACCCAG-3′ Reverse: 5′-CTAGCCCGCTGCTACTACGGGT-3′ | 154 bp |
| DNMT1 | Forward: 5′-AGACACTGGTCAGCCCTTGG-3′ Reverse: 5′-CAATTGCTGCTGGGATTCATC-3′ | 116 bp |
| DNMT3A | Forward: 5′-CTGCTTTATTTCTCTTCTGCA-3′ | 141 bp |
| HDAC1 | Forward: 5′-CTCCCGGAGAAGCTCAGTGG-3′ Reverse: 5′-CTGCTTTGTATTCCCTTTTGCA-3′ | 181 bp |
| DNMT3B | Forward: 5′-ACACAGCTTCTCAACTGCTG-3′ Reverse: 5′-CTGCTTTGTATTCCCTTTTGCA-3′ | 124 bp |
| MEC2 | Forward: 5′-AATCAACACTCTCCTCAGAAA-3′ Reverse: 5′-CTGCTTTGTATTCCCTTTTGCA-3′ | 109 bp |
| MBD2 | Forward: 5′-CTCCGGCAAGGCGCATGTT-3′ Reverse: 5′-CTGCTTTGTATTCCCTTTTGCA-3′ | 175 bp |
| JAK2 | Forward: 5′-CCACCCCTCTGCCTCTCTCTG-3′ Reverse: 5′-CTGCTTTGTATTCCCTTTTGCA-3′ | 100 bp |
| STAT3 | Forward: 5′-TCTGCCACCAAGGAGTAACCA-3′ Reverse: 5′-CTGCTTTGTATTCCCTTTTGCA-3′ | 131 bp |
| STAT5 | Forward: 5′-TCTGCCACCAAGGAGTAACCA-3′ Reverse: 5′-CTGCTTTGTATTCCCTTTTGCA-3′ | 121 bp |
| miR-147 | Forward: 5′-GCCAGGGCGCATCTAATCTCTCTCTG-3′ | 82 bp |
| U6 | 5′-GCCAGGGCGCATCTAATCTCTCTCTG-3′ | 74 bp |
2.9. Methylation-Specific PCR
Genomic DNA was extracted, and the specific steps were performed according to the manufacturer’s instructions. Shanghai Generay Biotech Co. Ltd., Shanghai, China). The DNA concentration was detected, and the sulfito conversion of DNA was performed according to the instructions of the EZ DNA Methylation-Gold kit (Zymo USA Inc., Flemond Island, FL, USA). For all the reactions, the reaction mix contained bisulfite-modified DNA (2 μl), Zymo Taq PerMix (12.5 μl), water (8.5 μl), up-stream primer (1 μl), and downstream primer (1 μl). The PCR conditions were as follows: 95 °C for 10 min followed by 35 cycles of 30 s at 95 °C, 45 s at 54 °C for annealing; 45 s at 72 °C; and a final extension step of 7 min at 72 °C. The PCR products separated by 2% agarose gel (GoldView; Saibaisheng Bioengineering Co., Ltd., Beijing, China) electrophoresis as follows: MEG3 and miR-147 methylated (M) and MEG3 and miR-147 unmethylated (U) positive and negative methylation; MEG3 and miR-147 M and MEG3 and miR-147 U partial methylation; and MEG3 and miR-147, M-MSP Forward: 5′-GGGAATGTGATGCTTGGGCTTATG-3′ (174 bp), Reverse: 5′-GCGAATTATTATTTATATAGCCTTC-3′; MEG3 and miR-147 U-MSP Forward: 5′-TGGAGGTGTTATTACCGTATAGTTTGG-3′ (174 bp), Reverse: 5′-ATTGCGGCTTACTGAGGCTA-3′.
M, methylated; MSP, methylation-specific polymerase chain reaction; U, unmethylated.
2.11. Luciferase Assay
To assay the interaction between MEG3 and miR-147, wide type 3′-UTR region of MEG3 and the mutant 3′-UTR of MEG3 were cloned into the firefly luciferase gene reporter vector pmirGLO (Promega, Madison, WI, USA). The plasmid was synthesized by Invitrogen. The pmirGLO-MEG3 or pmirGLO-MEG3-MUT was co-transfected with miR-147 mimics or miRNA control (RiboBio, Guangzhou, China) into the 293 cells. The luciferase assays were performed using the dual-luciferase reporter assay system kit (Promega) according to the manufacturer’s instructions. The luciferase expression was analyzed by Modulus single-tube multimode reader (Promega). The relative luciferase expression equaled the expression of the Renilla luciferase divided by the expression of the firefly luciferase. All the assays were repeated for at least 3 times.
2.12. RNA Pull-Down Assay
The MEG3 binding proteins were determined using a Pierce Magnetic RNA-Protein Pull-Down Kit (Thermo Fisher Scientific Waltham, MA, USA) according to the manufacturer’s protocol. The MEG3 sense and MEG3 antisense IncRNAs were generated and incubated with the proteins from the KCL22 cells, and 100 ml of a silver staining solution were added to the MEG3 sense and MEG3 antisense IncRNA and protein mixture. The proteins were then collected for the mass spectrometry analysis.
2.13. RNA Immunoprecipitation
RNA immunoprecipitation was performed using the Magna RIP kit (EMD Millipore Co., Billerica, MA, USA). The complete KCL22 cell lysates were prepared in accordance with the manufacturer’s instructions and contained phosphatase and proteinase inhibitors. Next, we evaluated the connection and configuration of the antibody beads. The antibody beads were suspended and mixed with the sample after thawing and were then incubated at 4 °C overnight. The immunoprecipitation was completed after the suspension was placed on the magnetic frame and was washed with buffer for at least 6 times. Finally, the immuno co-purification products were collected, and the RNA was extracted and purified to determine the abundance of the target RNA.
2.14. Co-Immunoprecipitation
The protein was obtained from the cells using RIPA cell lysis buffer (Invitrogen) followed by quantification, using the bicinchoninic acid assay. The interacting proteins were precipitated using a JAK2 antibody (Abcam, USA), and SDS-PAGE was performed. The target protein was pulled down according to the electrophoresis bands. The protein in the gel had a reductive alkylating reaction, and the protein was digested in the gel. The samples were analyzed by Liquid Chromatography Coupled with Tandem Mass Spectrometry (LC MS/MS).
2.15. Mass Spectrometry
The gel was cut into small pieces of 1 mm × 1 mm square. The small gels were digested using in-gel trypsin in EP tubes for 15 h at 37 °C after the gels were washed and bleached. After the digestion reaction, 400 μl of peptide extract (50% ACN, 0.1% TFA) was added to the EP tubes immediately for 30 min at 37 °C. Then the protein was transferred to a new EP tube and performed peptide extraction. After the reaction, the samples were lyophilized in a freeze-dryer. The freeze-dried sample was immediately for 30 min at 37 °C. Then the MS analysis was performed on a Q Exactive (Thermo Fisher Scientific, San Jose, CA, USA). The liquid phase was UPLC water, with a C18 column that was 3 μm and 250
mm × 75 μm (Eksigent). The settings were as follows: 1.0 h chromatographic gradient; 3.0 μl/min chromatographic flow rate; and 10 strongest ions in the MS Spectrum for MS/MS Analysis. The protein database was Uniprot human, with a total of 20,214 protein sequences, and it was searched to identify the protein identities from the immunoprecipitation.
2.16. Xenograft Animal Experiments
Athymic male mice were purchased from the Animal Center of the Chinese Academy of Science (Shanghai, China) and were maintained in laminar flow cabinets under specific pathogen-free conditions. This study was approved by the Ethics Committee of the Department of Hematology of the Second Hospital of Hebei Medical University. The KCL22 cells were stably transfected with LV-MEG3 or empty vectors and were harvested from the cell culture plates. These cells were xenografted into BALB/c male nude mice. The tumor volumes and weights were measured every 5 days in the mice. The tumor volumes were measured as length × width × 0.5. At 35 days after the injection, the mice were sacrificed, and the tumor weights were measured and used for further analysis.
2.17. Statistical Analysis
The data are expressed as mean ± standard deviation (SD) and were analyzed using the SPSS 19.0 software (IBM Corp, Armonk, NY, USA). Significant differences between the groups were analyzed using a Student’s t-test or a one-way ANOVA for more than two subgroups. A chi-squared test was applied to compare the rates, and P < 0.05 was considered a statistically significant difference.
3. Results
3.1. MEG3 Expression and Promoter Methylation in Patients with Different Phases of CML
The expression levels of MEG3 were lower in the patients of different phases of CML than that in the healthy donors (P < 0.05, one-way ANOVA) (Fig. 1A). The expression levels of MEG3 in CML-AP patients and CML-BP patients were similar (P = 0.05, one-way ANOVA), but were lower than that in the CML-CP patients and healthy donors. The MEG3 promoter was not methylated in the healthy donors, but showed methylation in 6 CML-CP patients (20%) (N = 30). On the other hand, all CML-AP samples showed methylation of MEG3 promoter, and methylation can be detected in 100% of the CML-BP samples (Fig. 1B).
3.2. MEG3 Promoter Methylation after Chidamide Treatment in KCL22 and K562 Cells
Next, we assessed the MEG3 promoter methylation in KCL22 (a) and K562 (b) cells before and after chidamide treatment. The MEG3 promoter was methylated in the non-treated group, but was not in the treated group (Fig. 1C).
3.3. The Methyltransferase and HDAC1 mRNA and Protein Expression in Patients with Different Phases of CML
Then, we examined the mRNA expression of the DNA methyltransferases and HDAC1 in the CML samples by RT-qPCR. The mRNA expressions of DNA (cytosine-5)-methyltransferase (DNMT) 1, DNMT3B, MB2D, MECP2 (two methyl-CpG-binding proteins), and HDAC1 were higher in the CML-BP patients than in the healthy donors (P < 0.05, one-way ANOVA). The mRNA expression of DNMT3A, among any of the CML phases and healthy samples, was not statistically different (P > 0.05, one-way ANOVA). The mRNA expressions of DNMT1, DNMT3A, MB2D, MECP2, and HDAC1 were the highest in the CML-BP samples (Fig. 1D).
The protein expressions of DNMT1, DNMT3A, MB2D, MECP2, and HDAC1 were semi-quantitatively determined in the bone marrow samples of CML-CP, CML-AP, and healthy donors. Consistent with the RT-PCR results, the protein levels of DNMT1, DNMT3A, MB2D, MECP2, and HDAC1 were higher in the CML-AP and CML-BP patients than that in the CML-CP patients and healthy donors (P < 0.05, one-way ANOVA). The DNMT3A (b) level was not significantly different in the samples from the CML patients or the healthy donors (P > 0.05, one-way ANOVA), and the highest expression of DNMT1 (a), DNMT3B (c), MB2D (d), MECP2 (e), and HDAC1 (f) was found in the CML-BP patients (Fig. 1E and F).
3.4. Changes in mRNA and Protein Levels in CML Blast Cells after Chidamide Treatment
To determine the effect of HDACi on epigenetic regulation, the KCL22 and K562 cells were treated with three different concentrations of chidamide (10, 15, and 20 μmol/l). The mRNA expressions of DNMT1, DNMT3A, DNMT3B, MB2D, MECP2, and HDAC1 were decreased with the increase of concentration. The mRNA expression of MEG3 was significantly higher in the treatment of 20 μmol/l chidamide than that in the treatment of 10 μmol/l and 15 μmol/l chidamide in KCL22 cells (P < 0.05, one-way ANOVA), and was significantly higher in the treatment of 20 μmol/l chidamide and 15 μmol/l chidamide than that in the treatment of 10 μmol/l chidamide in K562 cells (P < 0.05, one-way ANOVA) (Fig. 2A and B).
Next, we treated the cells with the highest concentration of chidamide (20 μmol/l) and found that, by a semi-quantitative analysis, the protein expressions of DNMT1, DNMT3A, DNMT3B, MB2D, MECP2, and HDAC1 were lower in the treated group than that in the non-treated group in both KCL22 and K562 cells (P < 0.05, Student’s t-test) (Fig. 2C–F).
To assess the effect of chidamide on CML treatment, we treated the CD34+ cells which were isolated from the peripheral blood mononuclear cells of 3 CML-AP patients and 3 CML-BP patients. The expressions of DNMT1, DNMT3A, DNMT3B, MB2D, MECP2, and HDAC1 were lower in the treated group than that in the non-treated group, while the expression levels of MEG3 and miR-147, as well as cell viability and cell apoptosis were determined. We further confirmed that this effect was only seen in the three concentrations) decreased the mRNA and protein levels of DNMT1, DNMT3A, DNMT3B, MB2D, MECP2, and HDAC1 in CML-AP and CML-BP patients, while the expression levels of MEG3 and miR-147 were increased (Supplementary Fig. 1A–D). The treatment of chidamide also decreased cell viability in 3 CML-AP and 3 CML-BP patients (Supplementary Fig. 1E, F) and accelerated cell apoptosis (Supplementary Fig. 1G and H). These results...
indicated that chidamide might be potentially used for treating CML blast crisis.
3.5. Effect of MEG3 Overexpression on CML Blast Cells In Vivo and In Vitro
To determine the role of MEG3 in CML blast crisis, we first determined the mRNA levels of MEG3 in the BMMCs of healthy donors and in the K562 and KCL22 cells, and the results indicated that the mRNA level of MEG3 was lower in the KCL22 and K562 cells than in the BMMCs (a) \( P < 0.05 \) (one-way ANOVA) (Supplementary Fig. 2A). An overexpression vector for MEG3 was synthesized and was then transfected into the KCL22 (b) and K562 (c) cells, and MEG3 expression in the overexpression group was 7.3-fold and 6.4-fold higher than that in the empty vector group (\( P < 0.05 \), Student’s t-test) (Supplementary Fig. 2).
Fig. 2. Changes in mRNA and protein levels in CML blast cells after chidamide treatment. A & B. The mRNA levels of DNMT1, DNMT3A, DNMT3B, MBD2, MEC2, and HDAC1 after the KCL22 and K562 cells were treated by 10, 15, and 20 \( \mu \)mol/l chidamide were detected by RT-PCR. C. Chidamide treatment decreased the protein levels of DNMT1, DNMT3A, DNMT3B, MBD2, MEC2, and HDAC1 in KCL22 cells. D. Western blot was used to detect the protein levels of DNMT1, DNMT3A, DNMT3B, MBD2, MEC2, and HDAC1 in KCL22 cells. E. Chidamide treatment decreased the protein levels of these six proteins in K562 cells. F. Western blot was used to detect the protein levels of these six proteins in K562 cells. For Western blot, ACTB was used as a control. For Fig. 2A and B, the one-way ANOVA was used for data analysis. *: \( P < 0.05 \) compared to 10 \( \mu \)mol/l group. **: \( P < 0.01 \) compared to 10 \( \mu \)mol/l group. #: \( P < 0.05 \) compared to 15 \( \mu \)mol/l group. For Fig. 2C and E, the Student's t-test was used for data analysis. ***: \( P < 0.01 \) compared to control group.
Fig. 3. Effect of MEG3 overexpression on CML blast cells in vivo and in vitro. A. Overexpression of MEG3 inhibited KCL22 proliferation (a) and accelerated cell apoptosis (b and c). B. Overexpression of MEG3 inhibited K562 proliferation (a) and accelerated cell apoptosis (b and c). C. In the KCL22 cells, the mRNA (a) and protein (b and c) levels of the DNMT1, DNMT3A, DNMT3B, MBD2, MECP2, and HDAC1 were decreased in the MEG3 overexpression group. D. In the K562 cells, the mRNA (a) and protein (b) levels of DNMT1, DNMT3A, DNMT3B, MBD2, MECP2, and HDAC1 decreased in the MEG3 overexpression group. E, F and G. Overexpression of MEG3 inhibited tumor growth. Student’s t-test was used for data analysis. The comparison of cell apoptosis rate between LV-control group and LV-MEG3 group were analyzed using chi-squared test. *: P < 0.05 compared to LV-control group. **: P < 0.01 compared to LV-control group.
Fig. 2A. Cell proliferation (a) and apoptosis (b and c) assay results indicated that the overexpression of MEG3 inhibited proliferation \((P < 0.05, \text{Student's t-test})\) and induced apoptosis \((P < 0.05, \text{chi-squared test})\) in the KCL22 and K562 cells (Fig. 3A and B). To further detect whether MEG3 affected the proliferation of the KCL22 cells in vivo, the KCL22 cells were stably transfected with LV-MEG3 or a control vector and
Fig. 4. The relative luciferase activity was detected by a dual luciferase assay. A. The RNAup algorithm predicted the potential binding of miR-147 to MEG3, with a considerable sequence complementary in the indicated regions. B. The relative luciferase activity was not different between the miR-147 mimics group and the miR-147 control group. C. The relative luciferase activity was lower in the miR-147 mimic group compared to the miR-147 control group. D. In the KCL22 cells, MEG3 overexpression decreased the expression level of miR-147; E. In the K562 cells, MEG3 overexpression decreased the expression level of miR-147. F. The mRNA level of miR-147 was lower in CML-AP and CML-BP patients than that in the CML-CP patients and the healthy donors. G. The methylation of the miR-147 DNA promoter was not detected in the normal controls, and methylation can be detected in 37.5% of the CML-CP samples. All CML-AP samples showed methylation of the miR-147 promoter, and methylation can be detected in 100% of the CML-BP patients. H. After treatment with chidamide, the miR-147 was unmethylated in both the K562 (a) and KCL22 (b) cells. For 4B, C, D and E, Student’s t-test was used for data analysis. *: \(P < 0.05\) compared to NC group. **: \(P < 0.01\) compared to NC group. For 4F, the one-way ANOVA was used for data analysis. *: \(P < 0.05\) compared to NC group. **: \(P < 0.01\) compared to NC group. #: \(P < 0.05\) compared to CML-CP group. M, methylated; U, unmethylated.
Fig. 5. MiR-147 overexpression inhibited proliferation, promoted apoptosis, and affected the gene expression. A. The KCL22 cells were transfected with miR-147 control and miR-147 mimics. Compared with the control group, transfection with miR-147 mimics inhibited proliferation (a). The apoptosis rate of the miR-147 mimics group (Q2 + Q4 = 59.19%) was higher than that of the control group (Q2 + Q4 = 11.94%) (b and c). B. The K562 cells were transfected with miR-147-control and miR-147 mimics. Compared with the control group, transfection with the miR-147 mimics inhibited proliferation (a). The apoptosis rate of the miR-147 mimics group (Q2 + Q4 = 51.98%) was higher than that of the control group (Q2 + Q4 = 10.02%) (b and c). C. In the KCL22 cells, the mRNA levels of DNMT1, DNMT3A, DNMT3B, MBD2, MECP2, and HDAC1 decreased in the miR-147 mimics group (a); and the DNMT1, DNMT3A, DNMT3B, MBD2, MECP2, and HDAC1 protein levels decreased in the miR-147 mimics group (b and c). D. In the K562 cells, the mRNA levels of DNMT1, DNMT3A, DNMT3B, MBD2, MECP2, and HDAC1 decreased in the miR-147 mimics group (a); and the DNMT1, DNMT3A, DNMT3B, MBD2, MECP2, and HDAC1 protein levels decreased in the miR-147 mimics group (b and c). Student's t-test was used for data analysis. The comparison of cell apoptosis rate between miR-147 control group and miR-147 mimic group was analyzed using chi-squared test. *: P < 0.05 compared to miR-147 control group. **: P < 0.01 compared to miR-147 control group.
were inoculated into nude mice. Thirty-five days after the injection, the tumors that formed in the control group were substantially larger than those in the LV-MEG3 group (P < 0.05, Student's t-test) (Fig. 3E, F). Moreover, the tumor weight, at the end of the experiment, was markedly lower in the control vector group compared with the LV-MEG3 group (P < 0.05, Student's t-test) (Fig. 3G). Next, we determined the effect of MEG3 overexpression on the expression of DNA-modifying genes, and found that the mRNA (a) and proteins (b and c) expressions of DNMTI, DNMT3A, DNMT3B, MB2, MECP2, and HDAC1 were significantly decreased (P < 0.05, Student's t-test) (Fig. 3C and D).
3.6. Interaction of MEG3 with mir-147
LncRNAs and miRNAs usually act as a competing endogenous RNA (ceRNA). We searched the starBase2.0 database to identify the miRNAs that interact with MEG3. Results showed that mir-147 was the potential miRNA. A dual luciferase reporter assay was performed to verify the interaction between mir-147 and MEG3, and for this purpose, we generated luciferase reporter plasmids with wild-type or mutant MEG3 (Fig. 4A). The transfection of 293 cells with mir-147 mimics had no effect on the luciferase reporter activity of the wild MEG3 (P > 0.05, Student's t-test) (Fig. 4B), but significantly decreased the luciferase reporter activity of mutant-type MEG3 (P < 0.05, Student's t-test) (Fig. 4C). Furthermore, MEG3 overexpression decreased the expression of mir-147 (P < 0.05, Student's t-test) (Fig. 4D, E). In addition, we also detected the expression and methylation of MEG3 in healthy donors, CML-CP, CML-AP, and CML-BP patients. The results showed that the level of mir-147 was significantly lower in the samples of the different phases of CML than that in healthy donors (P < 0.05, one-way ANOVA) (Fig. 4F). MIR-147 was not methylated in the healthy donors and showed methylation in 8 (37.5%) of CML-CP patients (N = 30) (Fig. 4G). Next, we assessed mir-147 promoter methylation in K562 (a) cells KCL22 (b) before and after chidamide treatment. The promoter was methylated in the non-treated group, but was not in the treated group (Fig. 4H).
3.7. Mir-147 Overexpression Inhibited Proliferation, Promoted Apoptosis, and Affected the Expression of Epigenetically-Associated Genes
To determine the biological role of mir-147 in CML blast crisis, we first assessed the mir-147 mRNA levels in the BMMCs from healthy donors as well as in K562 and KCL22 cells, and the results indicated that the mir-147 level was lower in KCL22 and K562 cells than that in the BMMCs (a) (P < 0.05, one-way ANOVA) (Supplementary Fig. 2B). The mir-147 mimic and the mir-147 control were transfected into KCL22 and K562 cells. Mir-147 overexpression efficiently (16.3-fold in K562 and 2865 proteins in the sense group and 1852 proteins in the antisense group. Of the 586 proteins that were only found in the sense group, Janus kinase 2 (JAK2), signal transducer and activator of transcription 3 (STAT3), DNMT1, and tyrosine kinase 2 (TYK2) were associated with CML occurrence and development and were confirmed to interact with MEG3 by RNA immunoprecipitation (P < 0.05, Student's t-test) (Fig. 6A and B).
3.9. Co-Immunoprecipitation MS and Co-Immunoprecipitation WB
Of the 543 proteins identified in the experimental group and the 306 proteins identified in the control group, 216 proteins were only found in the experimental group and interacted with JAK2. Of these proteins, STAT3, STAT5, and MYC are known to be associated with the proliferation and apoptosis of cancer cells, and the Co-IP WB results showed that JAK2 interacted with TYK2 through MEG3 (Fig. 6C and D).
3.10. MEG3 Overexpression Substantially Reduced the Phosphorylation of JAK2 and STATs
To determine the effect of MEG3 on JAK2/STAT3 signaling, we overexpressed MEG3 and then performed qPCR and WB. In the KCL22 and K562 cells, the expression of MEG3 was both lowered in the MEG3-ASO group (P < 0.01, Student's t-test) (Fig. 6E and F). However, the overexpression of MEG3 decreased the mRNA expression (a) and proteins (b and c) phosphorylation of JAK2, STAT2, and STAT5 (P < 0.05, Student's t-test) (Fig. 6G and H).
3.11. STAT3 Regulated the Expression of MEG3
To explore the relationship between STAT3 and MEG3, we first treated K562 and KCL22 cells with cryptotanshione and niclosamide and found a decreased expression of pSTAT3 (Fig. 7A and C). Then, we detected the expression of MEG3 and found that treatment with cryptotanshione and niclosamide significantly increased MEG3 mRNA expression in both cell types (Fig. 7B and D). In addition, we used a siRNA targeting STAT3 and confirmed that STAT3 protein levels were reduced in both K562 and KCL22 cells (Fig. 7E and G). Furthermore, the knockdown of STAT3 increased the mRNA expression of MEG3 in both cell lines (Fig. 7F and H). These data revealed an inverse relationship between STAT3 and MEG3.
4. Discussion
CML is a hematopoietic stem cell clonal disorder characterized by a Philadelphia chromosome translocation, resulting in the generation of the Bcr-Abl oncogene encoding a constitutive kinase activity, which induces malignancy in white blood cells [3]. It accounts for approximately 15–20% of newly diagnosed leukemia in adults. Although TKIs, such as imatinib, have made a remarkable success in controlling CML, a significant proportion of CML patients still developed drug resistance to TKIs [4]. Therefore, it is crucial to comprehensively understand the underlying molecular mechanisms about the initiation and progression of CML and find novel therapeutic targets for the treatment of this disease. In this study, we investigated the important roles of a long noncoding RNA MEG3 and its target mir-147 in the regulation of the proliferation and apoptosis of cancer cells as well as the DNA methylation and the expression of histone deacetylation-related genes during the development of CML.
Accumulating evidence has suggested that LncRNAs play diverse roles in human tumorigenesis. Depending on the expression of these LncRNAs in specific tumors, they can function as suppressors or promoters. MEG3 is one of the most important LncRNAs, which has been demonstrated to be involved in multiple biological processes of normal human cells, such as gonadotrophs [27]. Recently, its low expression has been observed in many human cancers, such as bladder, bone marrow, breast, and liver cancers [28]. Consistent with these findings, we also...
RIP-PCR was performed to test if DNMT1, JAK2, TYK2, STAT3 and HDAC1 were bound to MEG3. A. In the K562 cells, the fold enrichment of lncRNA MEG3 was higher in the DNMT1, JAK2, TYK2, STAT3, and HDAC1 groups than that in the IgG group (**: $P < 0.01$ compared to the IgG group). Student’s $t$-test was used for data analysis. B. In the KCL22 cells, the fold enrichment of lncRNA MEG3 was higher in the DNMT1, JAK2, TYK2, STAT3, and HDAC1 groups than that in the IgG group (**: $P < 0.01$ compared to the IgG group). Student’s $t$-test was used for data analysis. C and D. The pull-down assays showed that MEG3 retrieved JAK2 and TYK2 in the KCL22 cells. The retrieved proteins were detected by immunoblotting. In the KCL22 cells, JAK2 interacted with TYK2. The knockdown of MEG3, but not si-NC, abrogated this interaction. E. In the KCL22 cells, the expression of MEG3 was lower in the ASO-MEG3 group (**: $P < 0.01$ compared to the ASO-NC group). Student’s $t$-test was used for data analysis. F. In the K562 cells, the expression of MEG3 was lower in the ASO-MEG3 group (**: $P < 0.01$ compared to the ASO-NC group). Student’s $t$-test was used for data analysis. G. In the KCL22 cells, the overexpression of MEG3 inhibited the mRNA (a) and phosphorylated protein (b and c) levels of JAK2, STAT3, and STAT5 (**: $P < 0.01$ compared to LV-control group). Student’s $t$-test was used for data analysis. H. In the K562 cells, the overexpression MEG3 decreased mRNA (a) and phosphorylated protein (b and c) levels of JAK2, STAT3, and STAT5 (**: $P < 0.01$ compared to LV-control group). Student’s $t$-test was used for data analysis.
found that the expression level of MEG3 was significantly lower in the different phases of CML patients than that of healthy donors. Notably, our results showed that the MEG3 promoter was methylated in CML-BP patients, while that was not found in healthy donors. Consistently, the methylated MEG3 promoter was also not found in KCL22 and K562 cells after the treatment of chidamide. Thus, these results
Fig. 7. STAT3 regulated MEG3. A. The KCL22 cells were treated with cryptotanshione and niclosamide (8 μmol/l and 1.5 μmol/l, respectively, for 48 h). A western blot was performed to assess pSTAT3 with ACTB as the loading control. B. MEG3 mRNA levels were assessed by real-time PCR after cryptotanshione and niclosamide treatment and were compared to the control group. C. The K562 cells were treated with cryptotanshione and niclosamide (6 μmol/l and 2 μmol/l, respectively, for 48 h). A western blot was performed to assess pSTAT3 with ACTB as the loading control. D. MEG3 RNA levels were assessed by real-time PCR after cryptotanshione and niclosamide treatment and were compared to the control group. E. STAT3 was knocked down in the KCL22 cells using siRNA and the level of STAT3 was assessed by a western blot with ACTB as the loading control. F. MEG3 expression was assessed by real-time PCR after STAT3 knockdown. For 7B and C, the one-way ANOVA was used for data analysis. For 7F and G, Student’s t-test was used for data analysis. **: P < 0.01 compared to the control group.
indicated that there might be a close relationship between the methylation status of MEG3 promoter and its expression level in the regulation of leukemia development, which needs to be investigated in future studies.
MicroRNAs (miRNAs) are a conserved family of small noncoding RNA molecules that post-transcriptionally regulate gene expression. MiR-147 is a recently identified cancer-related miRNA. However, studies have showed that miR-147 could be either oncogene or tumor suppressive gene in different types of human cancers. For example, MiR-147 was found to be up-regulated in human gastric and liver cancers, while was found to be down-regulated in human breast cancer [29]. Our findings showed that the expression level of miR-147 was significantly lower in the different phases of CML patients than that of healthy donors. Consistent with the result of MEG3, chidamide treatment also reversed the methylation status of MiR-147 promoter in KCL22 and K562 cells. Interestingly, the results of dual luciferase reporter assay showed that lncRNA MEG3 and miR-147 could regulate each other in a negative manner. One possible explanation of this is that there might be an unknown gene that is targeted by miR-147, and the effect of MEG3 and miR-147 on cell apoptosis might be mediated by this gene [30]. For example, Han et al., found that MEG3 aggravated hypoxia injury in PC12 cells by down-regulating miR-147, and miR-147 further negatively regulated Sox2 expression [31]. It should be noted that our co-immunoprecipitation results showed that JAK2 could interact with TYK2 through MEG3, suggesting that JAK2 might be the gene contributing to the negative interaction between MEG3 and miR147.
DNA methylation and histone deacetylation are two key mechanisms that affect gene expression and gene promoters [16]. The DNMT family of proteins, which includes DNMT1, DNMT3A, and DNMT3B, are mainly involved in the mediation of CpG island methylation [32], whereas the HDAC family regulates histone deacetylation [33]. Consequently, a complex which includes MB2D, MECP1, and HDACs was formed via the DNA methylation, histone deacetylation and the methylation-dependent binding of MECPP [34, 35]. Given that the methylation status of MEG3 and MiR-147 could be significantly regulated by HDAC inhibitor chidamide, we next detected the expression levels of the methylation-related genes including DNNT1, DNNT3A, DNNT3B, MB2D, HDAC1 and MECPP. The expressions of these proteins were higher in the CML-AP and CML-BP patients than that in the CML-CP patients and healthy individuals. Thus, we speculated that the lower expression levels of MEG3 and miR-147 in the patients with CML were possibly mediated by histone deacetylation and DNA methylation.
We next treated two CML blast phase cell lines KCL22 and K562 with different concentrations of chidamide and found that chidamide treatment led to increased MEG3 and miR-147 levels, which were negatively correlated with the mRNA levels of DNNT1, DNNT3A, DNNT3B, MB2D, MECPP and HDAC1. The effect of chidamide was also confirmed in CD34+ cells isolated from the peripheral blood mononuclear cells of CML patients. Furthermore, MEG3 and miR-147 overexpression inhibited proliferation and promoted apoptosis in these cells. Thus, we speculated that the activity of chidamide on the proliferation and apoptosis of cancer cells might be strongly associated with its inhibitory effects on HDAC1 expression, MB2D/MECP2 complex formation and MEG3 demethylation.
The JAK/STAT signaling pathway plays an important role in regulating cellular processes, such as apoptosis, differentiation, proliferation and migration [36]. The abnormal activation of JAK/STAT led to the occurrence and development of various types of cancers, including hematological malignancies and solid tumors [37–39]. To further study the regulatory role of MEG3 on cell proliferation and apoptosis during the development of CML blast crisis, RNA pulldown and immunoprecipitation assay followed by the mass spectroscopy analysis were performed. Our results showed that DNNT1, JAK2, STAT3, and TYK2 could bind with MEG3. Moreover, TYK2 and STAT3 interacted with JAK2, while knockdown of MEG3 abolished this interaction. Thus, we concluded that MEG3 might function as a bridge between JAK2 and TYK2. Indeed, in vitro cell assay showed that the overexpression of MEG3 decreased the protein levels of phosphorylated JAK2, STAT3, and STAT5. Therefore, we believed that MEG3 can regulate STAT3, at least partly, by inhibiting the phosphorylation of JAK/STAT. Another interesting finding of this study was that when we treated the K562 and KCL22 cells with cryptotanshione, niclosamide and siRNA to decrease the level of STAT3, the expression of MEG3 was significantly increased. These results indicate that there might be a negative feedback loop between MEG3 and STAT3, which needs to be confirmed in animal studies.
In conclusion, our results revealed that MEG3 might bind with miR-147 and regulate the progression of leukemia. We also provided a mechanism by which MEG3 and miR-147-mediated DNA methylation, histone deacetylation and JAK/STAT pathways might contribute to the antitumor effects of chidamide on the development of CML. Therefore, targeting the MEG3-miR-147 axis might represent a novel therapeutic application in leukemia.
Supplementary data to this article can be found online at https://doi.org/10.1016/j.ebiom.2018.07.013.
**Abbreviations**
| Term | Description |
|-----------------------|-----------------------------------------------------------------------------|
| MEG3 | maternally expressed 3 |
| CML | chronic myeloid leukemia |
| CP | chronic phase |
| AP | accelerated phase |
| BP | blast phase |
| LV | lentiviral vector |
| RIP | RNA immunoprecipitation |
| CoIP | co-immunoprecipitation |
| RT-qPCR | real time polymerase chain reaction |
| MACE | methylation-specific PCR |
| BCR | breakpoint cluster region |
| ABL | Abelson murine leukemia |
| TKIs | tyrosine kinase inhibitors |
| Esrp2 | epithelial splicing regulatory protein 2 |
| HDACs | histone deacetylases |
| HDACi | HDAC inhibitors |
| IMDM | Iscove’s modified Dulbecco’s medium |
| FBS | fetal bovine serum |
| LNA-ASO | locked nucleic acid-antisense oligonucleotide |
| MTT | 3’-4,5-dimethylthiazole-2-yl-2,5-diphenyltetrazolium bromide |
| DEPC | diethyl pyrocarbonate |
| RIPA | radio immune precipitation assay |
| SDS-PAGE | sulfate polyacrylamide gel electrophoresis |
| PVDF | polyvinylidene fluoride |
| SD | standard deviation |
| DNMT | DNA (cytosine-5)-methyltransferase |
| bcl-2 | B-cell lymphoma 2 |
| STAT5 | signal transducer and activator of transcription 5 |
| STAT3 | signal transducer and activator of transcription 3 |
| JAK2 | Janus kinase 2 |
**Funding**
None.
**Acknowledgements**
None.
**Conflicts of Interest**
The authors declare no conflicts of interest.
Author Contributions
ZL, LY, XL and JL made substantial contributions to design this study. LY contributed to patient collection. XW and YP contributed to solve the experimental technical problems. ZL did all the experiments and wrote the manuscript. LY, XL and JL analyzed the data.
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FINNIC ADJECTIVES FOR ‘TALL’
Vilja Oja
Institute of the Estonian Language
Abstract. In Finnic languages, the height of a tall person is described by the adjectives pitkä, korkea, suuri, iso and tobie, or their dialectal variants. The first three occur throughout the whole language group, carrying several meanings and serving to characterize many different objects, but in a general case their meanings do not coincide. The Finnic iso and the Karelian tobie are synonyms of the adjective suuri.
An analysis of their semantic relations and areal distribution has revealed that their areas in the sense of ‘tall’ (of a person) differ considerably from their general areas. The use of the adjectives korkea and suuri seems to be influenced by Indo-European contacts. The word tobie may be a Russian loanword in which a semantic change has taken place. As all of the words mentioned are multifunctional, the simple adjectives are often specified by being used in a compound construction where the final component has the stem kasyu- ‘stature’. This is especially appropriate in the case of the words meaning ‘big’ and referring to either height or adulthood. Such phrases or compounds are more frequent in the eastern part of the Finnic area, but they also occur in Estonian dialects. An analogous form of expression is used in Russian.
Keywords: concept ‘tall’, pitkä, suuri, korkea, etymology, onomasiological map, Finnic dialects
1. Introduction
It is common knowledge that the use of adjectives often depends on the object referred to, e.g. a tall tree is kõrge puu in Standard Estonian, but a tall man is pikk mees. The present study focuses on the words used to refer to a relatively tall height in persons, analysing their semantic relations and use in the dialects of closely related (Finnic) languages. As with most assessments, ‘tall’ is a relative notion referring not to a measurement, but to a height exceeding the average or expected height of the
object in question. As a result, an object (person included) may, depending on what it is being compared to, be classified as ‘tall’ in one case and as ‘short’ in another.
The adjectives used to describe human height in Finnic languages derive from five prototypes. Pitkä, suuri and korkea are used in multiple functions in all Finnic languages (see Sections 2–4), whereas iso and tobie occur in narrower areas (see Sections 5–6). The original source material was collected in the late 1970s by Finnic specialists using the questionnaire for the Atlas Linguarum Europae (ALE), with the following eliciting question for ‘tall’ in French: “Que dites-vous de quelqu’un qui est grand de taille? Il est ...” (ALE 1976: 42–43). Finnic dialects are represented in 263 of the 2631 ALE mapping points, i.e. 10% coverage of the atlas net (see ALE 2007: XXXIV–LXVII). Although ALE has no map for ‘tall’, the map added to the present article mainly follows the same grid. Additional material and examples of dialect usage have been drawn from dictionaries and collections of Estonian and Votic dialect vocabulary (EMSUKA). For easier reading, the orthography of the dialect examples has been simplified and unified.
2. *pitkä*
Nouns with the stem *pitk-* originate from the Uralic derivative *pið-kä* (< the Proto-Uralic stem *piðe-*), which is an ancestor of several Ugric and Samoyed words for ‘high’, ‘tall’ etc. (SKES 580–581, SSA 2: 377, Rédei 1988: 377–378). The most frequent phonetic variants occurring in Finnic dialects are as follows: the Finnish and Ingrian *pitkä*, Karelian *pitkä*, *pitk(ä)*, Vepsian *pitk*, Votic *pittšä, pittša, pittše*, pitš, Estonian *pikk, piikk*, *pitk* and Livonian *pitka*. In Finnish dialects, the word is one of the 100 most frequent, while in Estonian and Votic dialects its rank of frequency is 166 and 137, respectively (CED, Jussila et al. 1992). Adjectives with a *pitk*-stem denote a relatively great distance or duration. In the case of length in space, the words apply to very different objects, including various linear objects
(e.g. roads, pegs, ropes and ladders), rows of similar objects (e.g. trains, lines (of people) and fences), clothes and details of such (e.g. coats, skirts, sleeves and trouser legs), living beings and body parts (e.g. snakes, tails, necks, ears, limbs, hair, beards and nails) etc. (EKSS 4: 253–254, KKS 4: 318–319, NS 4: 356, PS 2: 485, VKS 4: 260–261).
The tall height of a person is referred to by *pitk*-adjectives in Finnish, Karelian, Vepsian, Estonian and Livonian. This is the common form of expression, dominant in North Estonian, Livonian, Vepsian and most of the Finnish dialects (see Map 1). As for southern Estonia, *pikk* is, in this context, characteristic of the Tartu dialect area only. Although the ALE collection contains no word of the *pitk*-stem representing Karelian or Votic dialects, a few examples can be found in dictionaries. An example from Olonets Karelian is *pitkü mužikku* ‘tall man’ (KKS 4: 318, Makarov 1990: 269). Also, Karelian has a compound with the final component -kazvoine (< kazvu ‘stature’ + adjective suffix), e.g. the Olonets *pitkükazvoine briha* ‘tall young man’, and the Border-Karelian dialect *heän oli vielä poika näi vallan … a hüvim pitkäkašvu näi* ‘he was still a boy, but of very tall stature’ (KKS 4: 320). Such compounds or phrases can be found in other languages as well, e.g. the Finnish *pitkäkasvuinen*, Estonian *pikakasvuine ~ pikka kasvu* and Livonian *pitkā ka’zzōks* (EMSUKA, NS 4: 357).
The Estonian word *pikk* is often used to refer to a tall and lean person, e.g. *pikäd mehed on peeniksed ja lõnkjad* ‘tall men are lean and loose-limbed’. *Pikk ja peenike* ‘tall and lean’ are often used as a pair. The same association is expressed in such similes as *pikk nagu kõrend (~ osi, ~ piitsavars, ~ piibuork)* ‘tall like a pole (~ horsetail, ~ whip handle, ~ pipe cleaner)’. Analogous examples are found in cognate languages: the Finnish *pitkä ja laiha* ‘tall and lean’ (NS 4: 356), and the Karelian [this person] *om pitkä kui sablas* ‘is tall like a pole’, and *oliham pitkä akka ..., hoikkañi še akka šemmoñii* ‘she was a tall woman …, such a slim woman’ (KKS 4: 318). People’s statures are compared by using the normal comparative and superlative forms, e.g. *Kuka on pisin?* ‘Who’s the tallest?’, *Näytät pitemmältä kuin*
Map 1. ‘tall’ (of a person) in Finnic dialects.
hän ‘You look taller than him’ (PS 2: 485), the North-Estonian peimes oli pitkem kut ruut ‘the groom was taller than the bride’, and isä ölli üks pikemist meestest ‘Father was one of the tallest men’ (EMSUKA).
3. korkea
Such Finnic words as the Finnish korkea and its variants¹, the Ingrian korkia, Karelian korke, korkei, korged, Vepsian korged, Votic kõrgkõa, Estonian kõrge and Livonian kuordo, are believed to be of genuine Finnic origin, while their Sami counterparts are regarded as Finnish loanwords (SKES 219, SSA 1: 403). In Estonian and Finnish dialects, the frequency is lower (the frequency rank is 635 in Estonian dialects, 738 in the Votic language, and 545 in Finnic dialects) than that of pitk-words (CED, Jussila et al. 1992). In all those languages, these adjectives generally mean 'high', with the following major sub-meanings: 1) extending above a horizontal level (of buildings, plants, surface forms etc.), 2) important (person, official, meeting etc.), 3) high-level (e.g. culture, education and research), 4) valuable, 5) of high degree (e.g. fever, blood pressure and old age), and 6) high (of voice or sound). Of these six meanings, the first, referring to great vertical extent, is the basic one, while the rest have traditionally been regarded as secondary or figurative senses (EKSS 2: 648–649, EMS 4 (17): 282–284, KKS 2: 327-8, NS 2: 490–491, PS 3: 180, SMS 8: 137–139, VKS 2: 356). In this sense, these adjectives apply to very many objects, whether natural or artificial, animate or inanimate, e.g. hills, trees, nettles, waves, houses, chimneys, fences, shelves, tubs, heels, foreheads and horses.
In some Finnish, Karelian, Vepsian, Ingrian and Votic dialects, an adjective with the stem kork- is used to refer to tall
¹ The areal distribution of the phonetic variants of the word korkea in Finnish dialects has been mapped for the Finnish dialect atlas (see Kettunen 1981, map 191).
stature. For example: the Finnish se oli vankka ukko, ei se oekein korkea ollu ‘this was a strong man, not too tall’, and min oon nin korkea jotta min yltyn kattoo ‘I am so tall that I can reach the ceiling’ (SMS 8: 137), the Olonec Karelian oliš ku kazvole korgiembaine ‘if only [he] was a little taller’ (Makarov 1990: 153), the West Votic tōin poika on kōrkōa ‘the other son is tall’, and the East Votic kōrkōa starikka ‘tall old man’ (VKS 2: 356). The Votic noun kōrkōuz, kōrkuuz ‘height’ derives from the same stem: sill on minu kōrkuuz ‘he is of my stature (= he is as tall as me)’. One example has survived from Livonian usage, päā jo kuordō ku sinaa ‘a head taller than you’, and one example from the Estonian North-Eastern Coastal dialect: ‘kōrge mies ‘tall man’ (EMSUKA). In parallel, the phrase kōrkōata kasvoa, meaning ‘of a tall stature’, is used, e.g. the Votic kōrkōa pojo, kōrkōata kasvoa ‘tall young man, of tall stature’ (EMSUKA). In Karelian dialects, there is a compound word with the final component -kašvuńi: korkiekašvuńi, korgiekazvońi ‘of a tall stature’ (KKS 2: 327), cf. Fin. korkeakasvuinen id. (NS 2: 491).
According to the collectors of Finnic material for ALE, the use of variants of the adjective korkea in the sense ‘of a tall stature’ is secondary in most dialects, preference being given to other words. However, this seems to be the main form of expression in Votic, and it is used in the Kukkuzi dialect, as well as in the Eastern and Western dialects (VKS 2: 356). In the eastern Finnic area, the use of korkea in this sense may have been influenced by Russian, where the adjective wysokij means both ‘high’ and ‘tall’, while the latter has the synonymous phrase wysokogo rosta ‘of tall stature’. In the Finnish dialects spoken in the Norwegian and Swedish territories, korkea has probably received semantic influences from Scandinavian languages, cf. the Norwegian høy ‘high’, en høy mann ‘a tall man’, and the Swedish hög ‘high’, hög(växt) ‘tall, of tall stature’.
4. **suuri**
An adjective with the stem *suur-* also occurs in all Finnic languages: the Finnish and Ingrian *suuri*, Karelian *suurī*, *suurī*, *šuuri* or *šurīi*, Vepsian *su(u)rī*, Votic *suur(ī)*, Estonian *suur* or *suurī* and Livonian *suurī*. Their origin probably lies in an Old Germanic loanword deriving from the Proto-Germanic *stiūra-* (EEW SKES 1136–1137, SSA 3: 225). According to the Corpus of Estonian Dialects, *suur* is one of the 50 most frequent words in most dialect areas (the average rank is 49), while in Votic it ranks 43rd, and in the frequency dictionary of Finnish dialects *suuri* is 89th (Jussila et al. 1992). The main senses of this adjective are: 1) big (of great bulk), large, capacious, 2) big, numerous, 3) strong, intensive, 4) very important, essential, and 5) long (of interval). Dictionaries usually start explaining the word with the semantic group 'big, large, capacious', where the adjective may describe practically any big object: buildings, vehicles, machines, various objects and details, mountains, roads, forests, bodies of water, cities, countries, celestial bodies, plants, animals, human beings, body parts of living beings etc. (EKSS 5: 407–409, Kettunen 1986: 125, KKS 5: 581–583, NS 5: 379–381, PS 3: 180, VKS 5: 308–310).
The height of objects, humans included, belongs to the same semantic group. Although in general the adjectives *suuri*, *korkea* and *pikā* are not synonymous, their semantic fields may partly coincide. For example, the Estonian phrases *suur tamm*, *pikk tamm* and *kõrge tamm* mean more or less the same thing: ‘a big and tall oak’. In the phrases *suur ruum* ‘large room’, *pikk ruum* ‘long room’ and *kõrge ruum* ‘high room’, the adjectives emphasize quite different characteristics of the room. The same applies to the word pairs *pikad püksid* ‘long-legged trousers’ and *suured püksid* ‘oversized trousers’. If a person is described as *suur*, the reference is often made to more than just height, i.e. the person is tall and of great bulk, e.g. the Karelian *akka suuri kui merenemā* ‘big woman
---
2 A map of the areal distribution of the phonetic variants of the word *suuri* in Karelian dialects can be found in the atlas of Karelian dialects (see Bubrih et al., Map 111).
like a “sea-mother” (of a very sizeable object’). Often tall stature and great physical strength are mentioned together, e.g. the Finnish *suuri ja vahva mies* ‘big and strong man’ (PS 3: 180), and the Estonian *suured tugevad mehed* ‘big strong men’ (EKSS 5: 407). Similar semantic relations hold for other Finnic languages.
All Finnic languages offer examples of the use of an adjective with the stem *suur-* as a reference to tall stature: the Karelian *oli tšoarilla poika, šuuri ja kaunis* ‘the Czar had a son, tall and handsome’, and *tämä mužik on šuuri* ‘this man is tall’ (KKS 5: 581–582), and the Estonian *suur kui kõrend* ‘tall like a pole’ (EMSUKA). In parallel with the simple adjective, compound words and phrases are used, the final component of which derives from the noun *kasv(u)*, e.g. the Estonian *suure kasvuga, suurt kasvu* (EMSUKA), Vepsian *suurt kazvu* (Zajceva and Mullonen 1972: 527), Finnish *suurikasvuinen* (NS 5: 381), and Karelian *oli yksi šuurikašvoi mieš* ‘[he] was a tall man’, and *hejjän lapset ollah kai suurikazvozet* ‘their children are said to be tall too’ (KKS 5: 583). The compound helps specify the meaning of the polysemantic adjective.
In the geographical area where Finnic languages are spoken, *suuri* is less widespread than *pitkä* in the above meaning in general, but several dialects prefer words with the stem *suur-*. This use seems to be most characteristic in the Ingrian and Livonian languages, in most of the South Estonian and Karelian dialects and in some East-Finnish ones. The use of a word meaning ‘big’ to describe a tall person may reflect semantic influences of Indo-European language contacts, cf. the Russian *bolšoj čelovek* (Dal: http://vidahl.agava.ru) and German *ein großer Mensch* (Agricola et al. 1972: 283).
5. *iso*
The adjective *iso* denotes the concept ‘big’ in Finnish (more often in Western dialects) and the Finnish-like Votic dialect of Kukkuzi. This is a derivative of the noun *isä* (< *isoī*) ‘father’, which has counterparts with the same stem in most of
the Uralic languages (SKES 109–110, SSA 1: 228–229, Rédei 1988: 78). Both synonyms iso and suuri are old words in literary Finnish, occurring in Mikael Agrikola’s prayer book Rucouskirja of 1544 (Jussila 1998: 69 and 254). In the frequency dictionary of Finnish dialects, iso ranks 79th, which is slightly higher than suuri, but the difference is not significant (Jussila et al. 1992).
Semantically, iso does not differ much from suuri. In its primary sense of ‘big, of great bulk’, iso is used to describe very many different objects: mountains, houses, rooms, windows, gardens, trees, stones, balls, cars, lakes, oversized articles of clothing, animals, human beings (also ‘adults’) etc. (PS 1: 297, SMS 4: 864 ff.). There is no difference between iso and suuri as references to the tall stature of a person, e.g.: sehä’ ol’ pitäjä’ isomija miehijä ja vankempija ‘this was one of the biggest and strongest men of the parish’, and meilä on kaikista [lapsista] issoin tuo Marjetta ‘Marjetta is the biggest of all our children’ (SMS 4: 865). In parallel with the simple adjective, such compound words as iso(n)kasvuinen, isonkasvaininen and iso(n) kokoinen are used (SMS 4: 871 and 874). In general, iso occurs more frequently in western Finnish dialects (Jussila et al. 1992: 5 and 185, SSA 1: 228). However, a tall person is mainly described as iso in the eastern dialect area, most frequently in Savo dialects (see Map), whereas in the western dialects, according to ALE materials, this sense of the word has been recorded from only two mapping points representing the Finnish dialect of Tornio spoken in northern Sweden.
6. tobie
The adjective tobie and its variants are used in the Eastern Finnic languages: the Karelian topie, tobju, tobj, tobđ, tobđe, and diminutive tobjahko, and the Central Vepsian tobj, tobg, tobň (KKS 6: 146, Zajceva and Mullonen 1972: 571). In Karelian and Vepsian, those adjectives mean ‘big’. The general meaning is divided into semantic subgroups analogously with words having the stem suur-, and the primary position is similarly occupied
by ‘of great bulk’ (KKS 6: 146). Thus the word may describe a big fish, room, forest, horse, potato, stone, tree etc. In the Lude dialect, the middle finger is called tobđ (or tohj) sořm (Kujola 1944: 434). In the Central Vepsian dialect, the word is also used to refer to higher age or adulthood, e.g. siña řeg itoi jo tobń ‘you have come of age now’, and ükš lapš om peń, a toĩñe tobģem ‘one child is little, the other is older’. The Vepsian dictionary has several entry words with that stem, e.g. the Central Vepsian tob-mad ‘great part (of something)’, and tobńeta, tobjeta ‘make bigger, enlarge’ and ‘grow’, and the South Vepsian tobmin ‘elder, governor over somebody’, tobmoota ‘to act as an elder, to order the others about’, and tobmuz ‘elder power’ (Zajceva and Mullanen 1972: 571).
The shape and areal distribution of the word suggests a combination of a stem borrowed from Russian and a genuine adjectival suffix. The Russian noun doba refers to concepts having to do with time, such as ‘time, moment and period’. In Russian dialects, the stem has also been used to express age, e.g. v moju dobu ‘in my age’, and On budet v tvoju dobu ‘he will be your age’ (Dal: http://vidahl.agava.ru, SRNG 8: 73). The Russian adjectives sdobnyj, udobnyj, nadobnyj, podobnyj, dobryj etc. derive from the same stem (Vasmer 1, 519–520). As revealed by the above analysis, the Finnic form of expression uses similar words for spatial and temporal length. Similar expressions also apply to the concepts ‘(child) of sufficient age or adult’ and ‘of tall stature’. Hence, it is quite likely that a loanword characterizing a time interval and age has, analogously with other adjectives of similar use, begun to be used in reference to spatial measures as well.
Examples of the stem being used in describing the tall stature of a person can mainly be found in South Karelian dialects, e.g. the Proper Karelian tobie rištikansa ‘a person of a tall stature’, and akk on pikkarane, ukko tobie ‘the woman is small, the man is tall’ (KKS 6: 146). In the Olonets Karelian, the noun tobjevus, of the same stem, has been used in the sense of ‘stature’ (e.g. tütär juo on muaman tobjevus ‘the daughter is already as tall as her mother’), while the verb form means ‘grow (up) tall’ (e.g. aigu tulow dai tobjevuw ‘the time will come and [he] will grow
up tall’) (Makarov 1990: 382). There is a compound word in the Lude dialect, tob’d’kazvoîne ‘of big stature’ (Kujola 1944: 434). In the ALE collection, tobie represents only the main dialects of the Lude Karelian dialect area: Halijärvi, Koikari and Pyhäjärvi, while in Halijärvi this is the primary word for ‘tall’, but secondary to the parallel variant suuri in the neighbouring dialects. For the present Map, the words collected for ALE have been supplemented with examples picked from the above-mentioned dictionaries.
7. Conclusion
In all Finnic languages, the adjectives pitkä, suuri and korkea, or their variants with the same stem, refer to a relatively large spatial or temporal measure, but in most cases their uses differ. The description of a tall person by using some variant of the adjective pitkä is the most widespread practice. Relevant examples can be drawn from all Finnic languages, but in the Finnish, Vepsian, North Estonian and Livonian dialects this is the primary way to express stature. Variants of suuri also occur in the same sense across the whole Finnic area, although the occurrence is rare in the Western Estonian and Finnish dialects. The use of adjectives with the stem kork- seems surprising at first sight. The word has been used to refer to tall stature in Votic, the Finnish enclaves in northern Norway and Sweden, in a couple of south-eastern Finnish dialects, the Hevaha dialect of Ingrian and in the Estonian Coastal dialect. The use of the adjectives korkea and suuri seems to have been influenced by Indo-European contacts (cf. the Russian vysokij ‘high, tall’, Norwegian en höy mann ‘tall man’, Swedish hög ‘high’, hög(växt) ‘tall, of tall stature’, German groß, and Russian bol’soj). Sometimes several adjectives are used in the same sentence, e.g. the Estonian (Otepää) sie on siis kõrge mies kui on õige pitk ja suur ‘a man is called kõrge if he is tall and big’ (EMS 4 (17): 283), and the South Estonian olli ka suur põik miiss ‘a truly big tall man he was’ (EMSKUUKA).
Variants of the Finnish iso and the Karelian-Vepsian tobie denote the concept ‘big’. The adjective iso is used for a tall
person in the Tornio dialect of Finnish and in the area running diagonally through Finland from Lake Oulujärvi to the Karelian Isthmus, most frequently in Savo dialects. Such a distribution, covering mainly the eastern dialects, differs considerably from the generally western distribution of the word. Possibly the eastern dialects sometimes use *iso* in place of the more usual *suuri* in order to emphasize certain semantic differences. Variants of *töbie* are only used in this sense in South Karelian dialects. It may be a Russian loanword (cf. Rus. *doba*) whose function of describing time and age has extended to cover spatial measures as well.
The polysemy of the adjectives discussed may cause misinterpretation, especially in the case of *suur(i)* and *iso*. It is not always clear without additional information whether an adjective refers to a person’s tall stature, sturdy build or adulthood. The quality ‘tall’ is specified with compound constructions, whose first component is an adjective of height and the final one derives from the noun *kasv(u)*. Although all of the adjectives discussed here participate in such compound words or phrases, most of the available examples involve the word *suur(i)*. This form of expression is the most productive in Karelian and South Estonian dialects.
**Acknowledgments**
For financing the study, I would like to express my gratitude to the Estonian Ministry of Education and Research project no. SF0050037s10 and the Estonian Science Foundation grant no. ETF9367.
**Address:**
Vilja Oja
Institute of the Estonian Language
Roosikrantsi 6
10119 Tallinn, Estonia
E-mail: [email protected]
References
Agricola, Erhard, Herbert Görner, and Ruth Küfner (1972) *Wörter und Wörterbuch zum deutschen Sprachgebrauch*. Leipzig: VEB bibliographisches Institut.
ALE 1976 = *Atlas Linguarum Europae: premier questionnaire, onomasiologie*. Antonius Angelus Weijnen, et al., eds. Vocabulaire fondamental préparé par Joep Kruijssen. Assen: Van Gorcum, 1976.
ALE 2007 = *Atlas Linguarum Europae (ALE)*. Vol. I, 7, *Commentaires*. Roma: Istituto Poligrafico e Zecca dello Stato, 2007.
Bubrih, Dmitri, A. A. Beljakov, and Aleksandra Punžina (1997) *Dialektologičeskij atlas karelskogo jazyka*. Karjalan kielen murrekartasto. Leena Sarvas, ed. Helsinki: Suomalais-Ugrilainen Seura.
Buck, Carl Darling (1949) *A dictionary of selected synonyms in the principal Indo-European languages: a contribution to the history of ideas*. Chicago and London: The University of Chicago Press.
CED = *Corpus of Estonian Dialects*. Available online at <http://www.murre.ut.ee>. Accessed on 10.02.2012.
Daľ, Vladimir (1880–1882) *Tolkovyj slovar’ živogo velikorusskogo jazyka*. On-line republicacija vypolnena na osnove II izdaniya. (Sovremennoe napisanie slov.) Available online at <http://vidahl.agava.ru>. Accessed on 27.02.2012.
EKSS = *Eesti keele seletav sõnaraamat*. Eesti kirjasuomen ensiesiintymiä. (Suomalaisen Kirjallisuuden Seuran Toimituksia, 696. Kotimaisten kielten tutkimuskeskuksen julkaisuja, 101.) Helsinki: Suomalainen Kirjallisuuden Seura.
EMS = *Eesti murrete sõnaraamat I–V*. Tallinn, 1994–.
EMSUKA = Archive of Estonian dialects and Finno-Ugric languages, Institute of the Estonian Language, Tallinn.
Jussila, Raimo (1998) *Vanhat sanat. Vanhan kirjasuomen ensiesiintymiä*. (Suomalaisen Kirjallisuuden Seuran Toimituksia, 696. Kotimaisten kielten tutkimuskeskuksen julkaisuja, 101.) Helsinki: Suomalainen Kirjallisuuden Seura.
Jussila, Raimo, Erja Nikunen, and Sirkka Rautoja (1992) *Suomen murteiden taa-juussanasto*. A frequency dictionary of Finnish dialects. (Kotimaisten kielten tutkimuskeskuksen julkaisuja, 66.) Helsinki: VAPK-kustannus.
Kettunen, Lauri (1938) *Livisches Wörterbuch mit grammatischer Einleitung*. (Lexica Societatis Fenno-Ugricae, 5) Helsinki: Suomalais-Ugrilainen Seura.
Kettunen, Lauri (1981) *Suomen murteet. Murrekartasto*. 4th ed. (Suomalaisen Kirjallisuuden Seuran toimituksia, 188.) Helsinki: Suomalaisen Kirjallisuuden Seura.
Kettunen, Lauri (1986) *Vatjan kielen Mahun murteen sanasto*. Jarmo Elomaa, Eino Koponen, and Leena Silfverberg, eds. (Castrenianummin toimitteita, 27.) Helsinki: Suomalais-Ugrilainen Seura.
KKS = *Karjalan kielen sanakirja* 1–6. Pertti Virtaranta and Raija Koponen, eds. (Lexica Societatis Fenno-Ugricae, 16. Kotimaisten kielten tutkimuskeskuksen julkaisuja, 25.) Helsinki: Suomalais-Ugrilainen Seura, 1968–2005.
Makarov, G.N. (1990) *Slovar' karel'skogo jazyka. Livvivskij dialekt.* Petrozavodsk: Kareljia.
Nirvi, R. E. (1971) *Inkeroismurteiden sanakirja.* (Lexica Societatis Fenno-Ugricae, 18.) Helsinki: Suomalais-Ugrilainen Seura.
NS = *Nykysuomen sanakirja.* Porvoo and Helsinki: Werner Söderström osakeyhtiö, 1951–1961.
PS = *Suomen kielen perussanakirja.* 4th ed. (Kotimaisten kielten tutkimuskeskuksen julkaisuja, 55.) Helsinki: Edita, Kotimaisten kielten tutkimuskeskus, 1996.
Rédei, Károly (1988) *Uralisches etymologisches Wörterbuch.* Unter Mitarbeit von Marianne Bakró-Nagy, Sándor Csúcs, István Erdélyi, László Honti, Éva Korenchy, Éva K. Sal und Edit Vértes. Wiesbaden: Otto Harrassowitz.
SKES = Erkki Itkonen, Yrjö H. Toivonen and Aulis J. Joki (1955–1981) *Suomen kielen etymologinen sanakirja.* (Lexica Societatis Fenno-Ugricae, 12.) Helsinki: Suomalais-Ugrilainen Seura.
SMS = *Suomen murteiden sanakirja* 4, 8. (Kotimaisten kielten tutkimuskeskuksen julkaisuja, 36.) Helsinki: Kotimaisten kielten tutkimuskeskus, Paimatuskeskus, 1994/Suomalaisen Kirjallisuuden Seura, 2008.
SRNG = *Slovar' russkih narodnyh govorov* 8. Leningrad: Nauka, 1972.
SSA = *Suomen sanojen alkuperä. Etymologinen sanakirja.* (Suomalaisen Kirjallisuuden Seuran toimituksia, 556. Kotimaisten kielten tutkimuskeskuksen julkaisuja, 62.) Helsinki: Suomalaisen Kirjallisuuden Seura, 1992–2000.
Zajceva, Marija and Marija Mullonen (1972) *Slovar’ vepsskogo jazyka.* Leningrad: Nauka, 1972.
VKS = *Vägja keele sõnaraamat.* Tallinn, 1990–2011.
Kokkuvõte. Vilja Oja: Mõistet ‘pikk’ väljendavad adjektiivid lääneresoome keeltes. Lääneresoome keeltes kirjeldatakse inimese pikka kasvu adjektiividega *pikkä, korkea, suuri, iso või tobie* ja nende murdevariantidega. Esimesed kolm on levinud kogu keelerühma ula-
tuses mitmes tähenduses ja sobivad väga paljude erinevate objektide iseloomustamiseks, kuid üldiselt nende tähendused ei kattu. Soome *iso* ja karjala *tobie* on adjektiivi *suuri* sünnonüümid. Murdesõnade semantilisi suhteid ja levikut analüüsisides selgus, et nende levik tähenduses ‘pikk’ (inimesest) erineb suuresti üldlevilast. Adjektiivide *korkea* ja *suuri* kasutus näib olevat mõjustatud kontaktidest indoeuroopa keeltega. Sõna *tobie* võib olla vene laen, kus võrreldes originaaliga on toimunud semantiline muutus. Et kõik kõnealused sõnad on multifunktionaalsed, on mõiste konkretiseerimiseks lihtadjektiivide baasil moodustatud kusv-tüvelise järelkomponendiga liitkonstruktsioone. Eriti vajavad täpsustust üldmõistet ‘suur’ väljendavad sõnad, millega kirjeldatakse nii inimese kasvu kui täisealisust. Selliseid ühendeid või liitsõnu kohtab sedamini läänemeresoomes, ent ka eesti murretes. Analoogilist väljendusviisi kasutatakse vene keeles.
**Märksõnad:** mõiste ‘pikk’, *suuri, korkea, tobie* etümooloogia, onomasioloogiline kaart, läänemeresoomes moodustatud kasutusid ja sõna *tobie* võib olla vene laen.
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CASE REPORT
Novel frame-shift mutation in PKP2 associated with arrhythmogenic right ventricular cardiomyopathy: a case report
Teresa Trenkwalder1,2, Isabel Deisenhofer1,2, Martin Hadamitzky3, Heribert Schunkert1,2 and Wibke Reinhard1,2*
Abstract
Background: Arrhythmogenic Right Ventricular Cardiomyopathy (ARVC) is an inherited disease mainly found in young people causing malignant arrhythmias which can result in sudden cardiac death. Due to unspecific symptoms the diagnosis of ARVC is still challenging and requires clinical testing and expert knowledge. Genetic testing of index patients is helpful in the primary diagnosis and further testing of family members may allow for prevention of sudden cardiac death.
Case presentation: We report a case of newly diagnosed ARVC where genetic testing identified a novel familial frame-shift mutation in the PKP2 gene. Screening of the family members identified both children and the father as mutation carriers following an autosomal-dominant inheritance pattern.
Conclusion: Our findings emphasize the importance of genetic family screening after the identification of a causative mutation in an index case.
Keywords: Arrhythmogenic right ventricular cardiomyopathy, PKP2, genetic testing
Background
Arrhythmogenic Right Ventricular Cardiomyopathy (ARVC) is a hereditary cardiac disease that predominantly affects the right and possibly the left ventricle and is pathologically characterized by progressive fibrofatty replacement of myocardium [1]. Clinically cardiac rhythm, i.e., palpitations, syncope and sudden cardiac death (SCD), or cardiac function, i.e., right- or bi-ventricular heart failure resembling dilated cardiomyopathy, may be affected. The diagnosis is based on the 2010 Task Force criteria including characteristic electrocardiographic, arrhythmic, structural and/or histological abnormalities [2]. The prevalence is estimated to be 1:1000 to 1:5000 with a mean age at diagnosis of 31 years (±13; range 4–64 years) [3]. ARVC is acknowledged to be a leading cause of ventricular arrhythmias and SCD in young, often athletic subjects below the age of 35 years [1, 2]. As much as 30 – 50 % of ARVC patients have a positive family history and ARVC most commonly follows an autosomal-dominant inheritance. However, incomplete penetrance and highly variable and age-dependent disease expression are observed [1].
Case presentation
A 43-year-old female presented with shortness of breath, chest discomfort and light-headedness while cross-country skiing. She was able to call the rescue service herself and upon arrival they detected a wide QRS complex tachycardia with left bundle branch block morphology and inferior axis at 190 bpm that was terminated by administration of 50 mg Ajmalin i.v. (Fig. 1a). In stable condition the patient was transferred to our emergency room for further evaluation. Medical history included repeated episodes of similar symptoms upon physical exertion, yet no syncope. The family history was remarkable of a survived sudden cardiac arrest of the patient’s father at the age of 86 years and recurrent syncopes during exercise of the patient's daughter.
The resting 12-lead ECG displayed T-wave inversion in leads V1-4 in the absence of bundle branch block configuration (Fig. 1b). Laboratory analysis showed mildly elevated troponin T. Echocardiography showed normal size and function of the left ventricle. However, the right ventricle (RV) was significantly enlarged with reduced function (Fig. 2a). Cardiac MRI displayed a reduced RV ejection fraction of 27 % with moderate RV enlargement and increased RV end-diastolic volume (128 ml) (Fig. 2b, c), as well as akinesia of the apical RV posterior wall with late enhancement in this area (Fig. 2d). The coronary angiogram was normal. 12 lead-Holter monitoring revealed numerous premature ectopic ventricular beats (>7000) and three episodes of sustained ventricular tachycardia around 200 bpm the longest lasting over 20 min with left bundle branch block configuration originating from the RV outflow tract (RVOT). In the electrophysiological study, 3D electroanatomic voltage mapping showed low voltage areas in the apical and basal inferior RV as well as the lateral and medial RV outflow tract. Isoproterenol infusion as well as programmed ventricular stimulation induced the clinically documented ventricular tachycardia (VT) as well as 3 other forms of RV-VT. Radiofrequency energy ablation guided by voltage and activation mapping successfully eliminated all induced VTs and reached non-inducibility of ventricular arrhythmias. Taken together the definite clinical diagnosis of late-onset arrhythmogenic right ventricular cardiomyopathy (ARVC) was made according to the modified Task Force criteria by Marcus et al. [2]. The patient fulfilled two major criteria of ARVC (MRI pathology, repolarization abnormalities) and one minor criterion (arrhythmia).
During the following days ventricular tachycardia could neither be recorded in repeated Holter monitoring nor induced by controlled exercise stress testing. Nevertheless, we recommended the implantation of an automated implantable cardiac defibrillator (ICD) for secondary prophylaxis of sudden cardiac death, which was initially refused by the patient. The patient agreed, however, to conduct genetic testing of common ARVC genes for eventual substantiation of the diagnosis. While DNA exon sequencing of the ARVC genes desmoglein 2 (DSG2), desmoplakin (DSP), ryanodine receptor 2 (RYR2), transmembrane protein 43 (TMEM43), desmocollin 2 (DSC2), junction plakoglobin (JUP) and transforming growth factor beta 3 (TGFβ3) showed no pathological findings, sequencing of the plakophilin-2 (PKP2) gene identified a new variant in exon 7 (performed at the Synlab, Mannheim, Germany). This heterozygous c1664delT deletion mutation has not yet been described in the literature (HGMD Professional 2014.1). However, a pathogenic effect of this mutation is very likely, since the frame-shift p.F555Sfs*8 prematurely terminates translation which probably leads to degradation of RNA or composition of an altered protein (Fig. 3a, b). Both mechanisms would result in loss of function of the mutated allele. Confronted with this result, the patient agreed to the ICD implantation.
**Fig. 1** a) 12-Lead ECG of the index patient (paper speed 25 mm/s) showing ventricular tachycardia with left bundle branch block morphology and inferior axis. b) Resting 12-Lead ECG upon admission to our hospital showing sinus rhythm (paper speed 50 mm/s). T-wave inversion is present in V1-V4.
implantation and a single-chamber ICD was successfully implanted. In the 6-months follow-up no sustained or non-sustained ventricular tachycardia was recorded in the ICD memory.
Predictive genetic testing of first-degree family members of the index patient for the new PKP2 mutation disclosed the familial heterozygous mutation in both children (ages 13 and 16) and the father of the patient. Neither her mother, nor her sister and her aunt were carriers of the mutation (Fig. 3c, Table 1). All carriers of the mutation underwent a comprehensive cardiological work-up including 12-lead ECG, exercise stress test, Holter monitoring, echocardiography and MRI of the heart (performed at Deutsches Herzzentrum München, Universitätsklinikum München-Großhadern, Germany).
The daughter showed an orthostatic reaction after stress testing resulting in dizziness and pre-syncopy but no arrhythmias were detected during this episode. At present, the remaining cardiological examinations were normal. The son presented with an epsilon potential in lead V1 in the resting ECG. The results of all other tests showed currently no abnormal findings. Nevertheless, with two major criteria being present, ARVC was diagnosed in the son. Both children were recommended to refrain from excessive physical exercise and to perform semi-annual cardiological check-ups. The 91-year old father of the index patient, currently still in good health, had a long-standing medical history of cardiac diseases, including sick sinus syndrome, implantation of a biologic aortic valve at the age of 81 and one episode of ventricular tachycardia that
![Echocardiography of index patient shows dilatation of the right ventricle. RVD1 (basal right ventricle): 42.5 mm (Mean value (95 % CI) 33 (31–35 mm)). RVD2 (mid right ventricle) 32.7 mm (Mean value (95 % CI) 28 (23–33 mm)). RVD3 (base to apex length) 58.6 mm (Mean value (95 % CI) 71 (67–75 mm)). Mean values (95 % CI) according to Rudski et al. [9]. b Cardiac MRI of the index patient reveals moderate enlargement of the right ventricle with an enddiastolic volume of 186 ml (standard value female 140 ± 37 ml) and (c) end systolic volume of 135 ml (standard value female 52 ± 22 ml) resulting in a highly reduced ejection fraction of 27 % (standard value female 64 ± 7 %). Furthermore, the apical posterior wall of the right ventricle showed akinesia and (d) late gadolinium enhancement identified apical fibrosis (yellow arrows) in the 4-chamber view. Standard values according to Hudsmith et al. [10].]
was successfully terminated with i.v. amiodarone at the age of 86, when he declined the implantation of an ICD. Echocardiography showed significant dilatation of the right ventricle with severely reduced function (TAPSE = 7 mm). Upon MRI the right ventricular ejection fraction was severely reduced (20 %) with akinesia and fibrosis of the lateral wall. Therefore, the diagnosis of ARVC was made.
Discussion
We report a case of a 43-year old female with newly diagnosed ARVC in whom genetic testing identified a novel frame-shift mutation in the PKP2 gene. Although the clinical diagnosis was established according to the 2010 Task Force criteria, the patient was reluctant to undergo ICD implantation, since she had not suffered from severe symptoms and felt that the intervention posed a substantial change to her daily life. In our case genetic testing was able to substantiate the diagnosis by the finding of a new frame-shift mutation in the PKP2 gene and to convince the patient of the need for the ICD implantation. Moreover, a comprehensive family screening detected the mutation in both of her children and her father following an autosomal-dominant inheritance. The disease
was also present in an advanced state in the father, and diagnosed in an early asymptomatic stage in the son, whereas the daughter had currently normal test results. While no sensible medical recommendations arose for the nonagenarian father, the teenage children of the patient are now confronted with the fact that they are asymptomatic disease and mutation carriers respectively. As a result, lifestyle modifications such as restraint from exhausting physical activity and cardiologic check-ups on a regular basis are warranted.
**Genetic testing in ARVC**
According to the Heart Rhythm Society/European Heart Rhythm Association’s Expert Consensus Statement genetic testing in ARVC can be useful for patients satisfying the 2010 Task Force diagnostic criteria and may be considered for patients with possible ARVC (1 major or 2 minor criteria), while it is not recommended for patients with only a single minor criterion. Mutation-specific genetic testing is recommended for family members after the identification of a causative mutation in an index case [4]. To date, mutations in eight genes are known to cause the disease (PKP2, DSG2, DSP, DSC2, RYR2, TGFBR3, JUP, TMEM43), with six of them encoding for proteins with importance for desmosomal structure or function (PKP2, DSG2, DSP, DSC2, JUP, TMEM43) [5]. Mutations in PKP2 are most common ranging from 10 – 78 % in ARVC patients [6, 7]. The overall yield of a current generation genetic test for a patient with the clinical diagnosis of ARVC approximates 50 % [7]. However, the frequency of rare variants in ARVC susceptibility genes in healthy volunteers, the so-called background rate of genetic variability, is estimated with 16 %, meaning that 1 in 6 healthy individuals would meet current criteria for a positive ARVC genetic test result [7]. Understanding the genetic variability including the importance of the genetic background mutation rate is important for the interpretation of a genetic test result. For comparison, in long-QT syndrome the rate of “mutations” without clinical phenotype in the three most frequently involved genes KCNQ1, KCNH2, and SCN5A is only 5 % [8]. Ideally, patients should be referred to specialized centers to perform the genetic test and test results have to be interpreted.
| Pedigree | Genetic testing | Clinical Data (Criteria for ARVC) |
|----------|----------------|----------------------------------|
| I.1 Aunt IP | wildtype sequence (no pathological finding) | Major (1)
• ARVC confirmed in first-degree relative |
| I.2 Father IP | c.1664delT | Major (2)
• Family history of a first-degree relative
• MRI: RV enlargement with akinesia and reduced RV function (20%)
• Identification of pathogenic mutation
Minor (1)
• Sustained VT of unknown axis |
| I.3 Mother IP | wildtype sequence (no pathological finding) | Major (1)
• ARVC confirmed in first-degree relative |
| II.2 Index patient (IP) | c.1664delT | Major (3)
• T-wave inversion (V1-4)
• MRI: RV enlargement with akinesia and reduced RV function (27%)
• Identification of pathogenic mutation
Minor (1)
• Sustained VT with left bundle branch block inferior axis |
| II.3 Sister IP | wildtype sequence (no pathological finding) | Major (1)
• ARVC confirmed in first-degree relative |
| III.1 Daughter IP | c.1664delT | Major (1)
• Identification of pathogenic mutation |
| III.2 Son IP | c.1664delT | Major (2)
• Epsilon wave in V1 (ECG)
• Identification of pathogenic mutation |
in light of clinical test results. Moreover, mutation characteristics seem to play a role in determining the probability of pathogenicity. Kapplinger et al. [7] found that radical mutations in ARVC susceptibility genes, such as in-frame and frame-shift insertions and deletions, splice junction, and nonsense mutations, are strongly associated with the disease (42.9 % in ARVC cases vs. 0.47 % in healthy controls, \( p < 9.8 \times 10^{-44} \)), whereas rare missense mutations are less likely to be related to ARVC and should be interpreted in the context of race and ethnicity, mutation location, and sequence conservation [7]. Radical mutations, as the frame-shift mutation in our patient, are found in approximately \( \frac{3}{4} \) of mutation-positive ARVC cases [7]. Despite the deleterious nature of this novel frame-shift mutation on the gene product the age of diagnosis in our patient and that of her father in particular is high. One can speculate whether this specific mutation goes along with a late-onset of symptoms and is comparatively “benign”, or whether other factors, such as genetic background and external influences (e.g., physical activity) affect the course of the disease. However, it is known that the presentation of ARVC can be highly variable even within families, which is of particular importance for the patient’s clinically asymptomatic children with positive genetic testing in whom preventive measures should be taken. In general our case suggests that genetic evaluation in ARVC can be helpful to establish the definite diagnosis and to influence clinical decision making, but should be viewed as one component of comprehensive clinical assessment and never replace clinical judgment.
**Conclusions**
We report a case of newly diagnosed ARVC where genetic testing identified a novel familial frame-shift mutation in the *PKP2* gene. Although not meant to override clinical judgment, the case shows that in index cases genetic testing can be helpful to establish the definite diagnosis and to guide treatment considerations. Among family members mutation-specific genetic cascade screening has diagnostic, prognostic and therapeutic implications. Interpretation of test results for ARVC is challenging and referring patients to specialty centers is strongly encouraged.
**Ethics statement and consent**
Written informed consent was obtained from the patient and all family members for publication of this case report and any accompanying images. A copy of the written consent is available for review by the Editor of this journal.
**Abbreviations**
ARVC: Arrhythmogenic Right Ventricular Cardiomyopathy (ARVC); DSC2: desmocollin 2; DSG2: desmoglein 2; DSP: desmoplakin; JUP: junction plakoglobin; PKP-2: plakophilin-2; RYR2: ryanodine receptor 2; TAPSE: tricuspid annular plane systolic excursion; TGF-B3: transforming growth factor beta 3; TMEM43: transmembrane protein 43.
**Competing interests**
None of the authors have any competing interests to declare.
**Authors’ contributions**
WR and HS provided clinical consultation. TT and WR analyzed the data and drafted the manuscript. MH and HS contributed clinical data. ID and HS helped to draft and revised the manuscript. All authors read and approved the final manuscript.
**Acknowledgments**
We thank the patient and the patient’s family to allow us to publish their clinical case. We would also like to thank Frau Dr. Britt-Maria Beckmann from the Universitätsklinikum München-Grosshadern, who provided us clinical information of the two children of the index patient.
**Author details**
1. Klinik für Herz- und Kreislaufkrankungen, Deutsches Herzcentrum München, Technische Universität München, Lazarettstr. 36, 80636 Munich, Germany. 2. Deutsches Zentrum für Herz- und Kreislaufforschung (DZHK) e.V., Partner Site Munich Heart Alliance, Munich, Germany. 3. Klinik für Radiologie und Nuklearmedizin, Deutsches Herzcentrum München, Technische Universität München, Munich, Germany.
Received: 17 June 2015 Accepted: 12 December 2015
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9. Rudski LG, Lai WW, Afilalo J, Hua L, Handschumacher MD, Chandrasekaran K, et al. Guidelines for the echocardiographic assessment of the right heart in adults: a report from the American Society of Echocardiography endorsed by the European Association of Echocardiography, a registered branch of the European Society of Cardiology, and the Canadian Society of Echocardiography. J Am Soc Echocardiogr. 2010;23(7):685–713. doi:10.1016/j.echo.2010.05.010. quiz 86–8.
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Lattice-aligned gallium oxynitride nanolayer for GaN surface enhancement and function extension
Junting Chen,1,2 Junlei Zhao,1 Sirui Feng,2 Li Zhang,2 Yan Cheng,2 Hang Liao,2 Zheyang Zheng,2 Xiaolong Chen,2 Zhen Gao,1 Kevin J. Chen,2 and Mengyuan Hua1
1 Department of Electrical and Electronic Engineering, Southern University of Science and Technology, Shenzhen 518055, China
2 Department of Electronic and Computer Engineering, The Hong Kong University of Science and Technology, Clear Water Bay, Kowloon, Hong Kong
Gallium nitride (GaN), as a promising alternative semiconductor to silicon, is of well-established use in photoelectronic and electronic technology. However, the vulnerable GaN surface has been a critical restriction that hinders the development of GaN-based devices, especially regarding device stability and reliability. Here, we overcome this challenge by converting the GaN surface into a gallium oxynitride (GaON) epitaxial nanolayer through an in-situ two-step “oxidation-reconfiguration” process. The oxygen plasma treatment overcomes the chemical inertness of the GaN surface, and the sequential thermal annealing manipulates the kinetic-thermodynamic reaction pathways to create a metastable GaON nanolayer with wurtzite lattice. This GaN-derived GaON nanolayer is a tailored structure for surface reinforcement and possesses several advantages, including wide bandgap, high thermodynamic stability, and large valence band offset with GaN substrate. These enhanced physical properties can be further leveraged to enable GaN-based applications in new scenarios, such as complementary logic integrated circuits, photoelectrochemical water splitting, and ultraviolet photoelectric conversion, making GaON a versatile functionality extender.
I. INTRODUCTION
In parallel with conventional silicon-based devices, tremendous efforts have been directed towards exploring stable compound semiconductor materials and their applications over the past decades, including silicon carbide [1], III-V compounds [2,3], and various oxides [4,5]. Amongst a large multitude of candidates, GaN-based devices have gained wide acceptance as one of the successfully commercialized compound semiconductor systems, not only in well-established photoelectronic devices, power electronics, radiofrequency power amplifiers [6,7], but also in emerging fields such as digital and quantum computing [8,9].
Nevertheless, at its cutting edge, the advance of the GaN-based device encounters bottleneck restrictions due to the vulnerable GaN surface, especially for electronic devices. The charging state of the GaN surface is easily changed by electric field through carrier trapping or detrapping, resulting in unstable electrical performance under switching operation, e.g., current collapse, threshold voltage shift, and worse block capability in GaN-based transistors [10]. Furthermore, electric field tends to crowd near the surface in many electronic device structures, making it a weak point suffering hot electron bombardment and piezoelectric stress [11]. Moreover, the exposed GaN surface is sensitive to the fabrication processes, exacerbating electric field non-uniformity and surface reliability issues. With GaN devices being scaled down toward emerging low-voltage applications, the surface effects are expected to be much more critical in the nano-scale devices featuring a large surface-to-volume ratio.
A common remedy for these aforementioned issues is to exquisitely passivate the GaN surface utilizing deliberate chemical reactions. Although different passivation methods are still developing at a fast pace [12,13], the conventional approaches rely on depositing dielectric layers on pristine GaN surface. However, compared to external deposition, to achieve an uncontaminated passivation/GaN interface and insensitivity to the initial conditions of pre-passivated surface, an internal passivation layer derived intrinsically from GaN is more favorable.
Oxides that can be formed by thermal oxidation (e.g., SiO₂ on Si [14]) are relatively stable under air exposure and in aqueous environments by chemical nature, and their wide bandgaps in general are well suited for dielectric layer. However, one essential difficulty of passivating GaN surface by oxidation is the chemically inert features of GaN surface. Conventional thermal treatment below the decomposition temperature of GaN (∼800 °C) is highly inefficient to form Ga₂O₃ intact nanolayers [2,15,16]. Only mono- or bi-layer oxides can be formed with limited thicknesses of sub-1 nm [17]. Instead of direct thermal oxidation, plasma-assisted process is a natural alternative approach to overcome the surface inertness of GaN with a higher reaction rate. Besides, another difficulty is that the fully oxidized Ga₂O₃ often adapts to the stable monoclinic β-phase with large lattice mismatch and different symmetry against hexagonal GaN (0001) substrate, resulting in high interface state density. Therefore, gallium oxynitride (GaON) nanolayer formed by partial oxidation of GaN is an alternative material of passivation, because of its better compatibility with GaN substrate.
Despite the promising features of plasma-assisted par-
tial oxidation as a surface passivation of GaN, investigation on achieving a metastable GaON epitaxial nanolayer on GaN is still at an immature stage, and the underlying formation mechanisms need a in-depth understanding. In this work, we will show a simple and robust oxidation-reconfiguration approach to achieve well-controlled near-surface (<5 nm) partial oxidation of GaN to enhance the surface and, moreover, lead to a versatile epitaxial nanolayer (GaON) on GaN surface. The GaON nanolayer is formed by a two-step oxidation process, using controllable remote oxygen plasma and sequential thermal annealing. Leveraging well-established experimental and computational methods, the formation mechanism and detailed structural and electrical characteristics of the GaON nanolayers are investigated. Control of the thickness, composition, and phase separation is readily accomplished by tuning the kinetic pathways of the intentional GaN-surface oxidation reaction. Finally, based on these findings of the nanosized GaON-on-GaN lamellar system, we demonstrate and discuss the potential applications in GaN-based power devices [18], GaN p-channel field effect transistors (p-FETs) [8], photoelectron-chemical (PEC) water splitting [19][20], and ultraviolet photodiodes [21][22]. This contribution can open up new prospects for future study on the GaON nanolayer as a versatile platform retaining intrinsic compatibility with a variety of GaN-based cutting-edge applications.
II. RESULTS AND DISCUSSION
A. Two-Step formation of GaON nanolayer
The two-step "oxidation-reconfiguration" process of the GaON nanolayer involves oxygen plasma treatment (OPT) followed by sequential high-temperature annealing in an N₂ atmosphere, as schematically illustrated in Figure 1. More detailed conditions of fabrication can be found in the Experimental Section. Compared with direct thermal oxidation, OPT can assist oxygen atoms in penetrating into GaN for several nanometers and overcome the chemical inertness of GaN in the ambient atmosphere. However, this far-from-equilibrium process can cause energetically unfavorable defect species, such as Frenkel pairs and extra O interstitials, to appear in the GaN lattice transiently. Therefore, high-temperature annealing is conducted subsequently to promote the defect healing process, where the O atoms will substitute the N atoms to form stable Oₕ sites [23], and release the additional N atoms to the gas phase. Moreover, rather unexpectedly, a segregation of the O composition is observed during the annealing, resulting in two distinct high- and low-oxygen-concentration layers, as illustrated in Figure 1b (after annealing). This aspect will be elucidated by more experimental characterizations later in this section.
One major advantage owing to oxygen incorporation is the enhanced thermal stability of the GaN surface. The bond formed between Ga and O is more energetically favorable and thermodynamically stable than that between Ga and N, since O has a lower electron affinity than N. Thus, better thermal stability of the GaON nanophas is expected, which is verified by the surface morphology after thermal annealing (Figure 1). After OPT, four groups of samples were annealed at 800/900/1000/1100 °C separately, and one group remained without annealing for reference. Another set of pristine GaN samples was only annealed but without OPT to verify the enhanced thermal stability of the GaON nanolayer. The initial surface of the GaN sample (before treatment) is of high quality with a small surface roughness (Rₛ) of 0.588 nm. Its comparison with the OPT-processed sample (w/o. OPT, w/o. annealing) confirms that OPT alone has no significant effect on the surface morphology, as clear atomic steps can be found in both samples. However, the further comparison between the annealed samples shows clearly different trends: for the samples without OPT, the samples start to decompose when the annealing temperatures reach 900 °C (w/o. OPT, 900 °C annealing) due to the facet-selected thermal decomposition of the GaN surface [24][25]. The "blanket spikes" appearing on the surface are the remaining Ga (oxidized in ambient conditions later) after the decomposition of GaN. As a comparison, the samples with OPT resist decomposition up to 1000 °C (w/. OPT, 1000 °C annealing). At 1100 °C, both samples with and without OPT have uniformly spaced hexagonal "etching pits" (small caves appearing at the surface), which indicate the bulk decomposition starting from the threading dislocation region [26]. The overall AFM images of all the samples can be found in Supplementary Information Figure S1.
A representative transmission electron microscopy (TEM) image of the GaON/GaN stack is shown in Figure 1b, which is obtained on the sample with OPT and 900 °C annealing. According to the line profile (right panel in Figure 1b), the average distance between two Ga planes (where the peak intensity appears) in the bulk GaN region (∼0.52 nm) is in good agreement with the lattice constant c (∼0.518 nm) of wurtzite GaN. However, noticeable lattice distortion can be seen near the surface, where the average distance between two Ga planes shrinks to 0.29 nm, and the total thickness of the distorted layer is 2.62 nm. A sharp boundary can be found between the distorted layer and the undistorted GaN lattice underneath.
Moreover, time-of-flight secondary-ion mass spectroscopy (ToF-SIMS) is adopted to probe the local composition of the near-surface region, as shown in Figure 1a. The thickness of the GaON nanolayer is determined by the full width at half maximum (FWHM) of the normalized intensity of the secondary O⁺ ion profiles. The ToF-SIMS measurements reveal that the OPT alone leads to an oxidized layer with a thickness of 2.94 nm, and the thickness extends to 3.36/3.99/4.91 nm after annealing at 800/900/1000 °C, respectively. Therefore, the thick-
FIG. 1. (a) The schematics of the two-step formation of GaON nanolayer on the GaN(0001) surface. (b) TEM image of the sample after OPT and 900 °C annealing, and the line profile of the pixel intensity along x direction indicating the two distinct layers with the different Ga-plane distances. (c) AFM-measured surface profiles of the samples after different treatments. The blanket spikes and etching pits are seen in the surface/bulk-decomposed samples. The scanning area of AFM is 5 × 5 µm². (d) Secondary O²⁻ ion intensity (used to indicate O concentration in the GaON nanolayers) from ToF-SIMS to analyze the samples after different treatments. More AFM images and full profiles of ToF-SIMS are shown in the Supplementary Information Figure S1-S2.
thicknesses of oxidized nanolayers are well controlled in the nm range and monotonically increase with the annealing temperatures. We note that the thickness measured from ToF-SIMS profiles is unambiguously larger than the one of the distorted layers seen in the TEM image (3.99 nm versus 2.62 nm). This result indicates that a part of the
oxide layer under the distorted layer can maintain the original wurtzite lattice, and hence not be identified in the TEM image, which will be further supported by the DFT calculation in the Section 2.2. The full profiles of ToF-SIMS are shown in the Supplementary Information Figure S2.
The degree of oxidation is further analyzed by X-ray photoelectron spectroscopy (XPS). To understand the bonding conditions of the GaON nanolayers, XPS measurements are conducted on different samples with varying durations of in-situ Ar⁺ sputtering and the take-off angles (ToA), as illustrated in Figure 2a. The spectra of the Ga-3d core level are used to analyze the local chemical bonding environments. The area ratios of the Ga-N, Ga-O, and Ga-Ga subpeaks to the corresponding total Ga-3d peaks (these ratios are referred to as the normalized intensity, \(I_x\)) are used to determine the composition of the nanolayer.
The sample with OPT and 900 °C annealing was first measured after every 10-second stepwise in-situ Ar⁺ surface sputtering, as shown in Figure 2a. Initially, the non-sputtered (at 0 s) nanolayer has a very high concentration of oxygen. After the first 10-s sputtering, the fraction of Ga-O bonds decreases drastically, whereas the fraction of Ga-N bonds increases rapidly, revealing a clear shift of the surface chemical bonding environment. From 10 to 30 s, the fraction of Ga-O bonds evolves slowly towards zero. This change in the slope of the Ga-O curve, together with the TEM image and the SIMS data, strongly evince the existence of a near-surface high-oxygen-concentration (HOC) nanolayer and an underneath low-oxygen-concentration (LOC) nanolayer. After 40 s, the fraction of Ga-O bonds keeps around a negligible value, suggesting that the GaON nanolayer has been completely sputtered. The rise of the Ga-Ga bond intensity is because of the preferential sputtering of the light atoms (O and N), leaving a thin layer of metallic Ga on the surface [27, 28].
The Ga-O/Ga-N bond ratio of the HOC-GaON layer can be directly obtained from the surface XPS profiles without sputtering, which is 9.68/7.77/9.44 after 800/900/1000 °C annealing, respectively (Figure 2). To obtain the XPS profiles of the underneath LOC-GaON nanolayers, the oxygen-rich layer needs to be removed by Ar⁺ sputtering for 20 s in-situ before the XPS measurements. Both the O/N atomic ratio \((x/y)\) and the thickness of the remaining LOC-GaON layer can be obtained from the angle-resolved XPS (ARXPS) data [29]. The Ga-O/Ga-N intensity ratios \(I_{Ga-O}/I_{Ga-N}\) in the Ga-3d core level are plotted against the take-off angle (ToA), as shown in Figure 2a. The \(I_{Ga-O}\) is contributed by the LOC-GaON nanolayer, while the \(I_{Ga-N}\) is from both the GaON nanolayer and the GaN substrate beneath. The \(x/y\) can be quantitatively extracted from \(I_{Ga-O}/I_{Ga-N}\) with the formula:
\[
\frac{I_{Ga-O}}{I_{Ga-N}} = \frac{1 - \exp \left[-d/\lambda \cos (\theta)\right]}{y/x + \exp \left[-d/\lambda \cos (\theta)\right]},
\]
where \(\lambda\) is the electron inelastic mean free path of 2.5 nm in GaN [30], \(d\) is the thickness of the remaining LOC-GaON nanolayer after sputtering, and \(\theta\) is the ToA. For the 800 °C-annealed sample, the extracted \(d\) is 0.97±0.08 nm, and \(x/y\) is 1.15/1; and for the 900 °C-annealed sample, the extracted \(d\) is 1.47±0.14 nm, and \(x/y\) is 0.54/1. The thickness of GaON nanolayer in the 900 °C-annealed sample is 0.50±0.22 nm thicker than that of the 800 °C-annealed sample, which is well consistent with the difference in the corresponding SIMS data (0.63 nm in Figure 2c). The more details of the XPS spectra are shown in Supplementary Information Figure S3, S4 and S5.
It is worth mentioning that this oxidation process is highly repetitive and tunable. The GaON nanolayer with various surface oxygen concentrations and thickness can be obtained as summarized in Table I, demonstrating its flexibility and wide application potential on the GaN-based device platform. The control of surface composition can be achieved by the total oxygen flux (controlled with time duration in Step I) [31], and the thickness of the GaON nanolayer can be tuned with annealing temperature in Step II.
B. Formation mechanism and band structure of GaON nanolayer
So far, we have systematically investigated the structural and compositional properties of the GaON nanolayer using different experimental methods and analyses. However, the exact driving force behind the formations of the initial plasma-oxidized nanolayer (Step I) and later the segregated HOC- and LOC-GaON nanolayers (Step II) remain unclear. We will elucidate the formation of the HOC- and LOC-GaON nanolayers with computational methods, but before that, how the oxygen plasma can overcome the chemical inertness of the GaN (0001) surface is discussed.
In principle, the initial plasma-assisted penetration depth of oxygen involves the codependency between the plasma and the substrate. The estimated average kinetic energy of oxygen ion in inductively coupled plasma (ICP) chamber is about ~10 eV which is about two orders of magnitude larger than that of a thermally heated oxygen gas (e.g. 0.165 eV/atom at 1000 °C). Therefore, the bond breaking caused by oxygen plasma is not only electron charge transfer through surface adsorption, which can be solely understood by chemical reaction theory, but rather a localized thermal spike and lattice distortion caused by inelastic ion collision within the threshold energy of surface sputtering. As a result, in our experiments Step I, the oxygen plasma create a highly active condition with negligible reaction energy barriers for oxidation, so the O atom will penetrate into GaN surface a few nanometers and stay in non-equilibrium transient configurations.
Thermodynamically, it is clear that the formation of the local substitutional \(O_N\) site is energetically favorable [23]. However, the overall supercell mapping
FIG. 2. (a) Illustration of XPS measurement setup applied in this work. The sample that being used (with OPT and different annealing time), the duration of in-situ Ar$^+$ sputtering, and the take-off angle (ToA) are the x-axis parameters in the following plots (b-d). (b) The XPS peak intensities of Ga-N, Ga-O, Ga-Ga bonds at different in-situ Ar$^+$ sputtering time. The measured sample is with OPT and 900 °C annealing. The curves are normalized to the total intensity of the corresponding Ga-3d core-level peaks. (c) The intensity ratios between Ga-O and Ga-N bond at the surface of the different samples (with OPT) are not significantly affected by the annealing temperatures. (d) The intensity ratio between Ga-O and Ga-N bond at different ToA of samples after OPT, 800/900 °C annealing, and 20 second of in-situ Ar$^+$ sputtering. The inset figures illustrate the fitted parameters from Equation [1]. More detailed analyses of the XPS data are shown in Supplementary Information Figure S3, S4 and S5.
TABLE I. (Al)GaON nanolayer originated from different fabrication parameters. The coil power and platen power are used to generate and control the oxygen plasma in the ICP chamber.
| Material | Step I: OPT | Step II: Annealing | Result |
|----------|-------------|---------------------|--------|
| | Power (W) | Duration (min) | Ambience | Surface Ga-O/Ga-N | Oxide Depth (nm) | [Ref.] |
| p-GaN | 50 | 20 | 5 | 800 °C N$_2$ | 9.68 | 3.36 | This work |
| p-GaN | 50 | 20 | 5 | 900 °C N$_2$ | 7.77 | 3.99 | This work |
| p-GaN | 50 | 20 | 5 | 1000 °C N$_2$ | 9.44 | 4.91 | This work |
| p-GaN | 50 | 30 | 4 | 800 °C N$_2$ | 5.40 | 4.30 | [31] |
| GaN | 10 | 10 | 10 | 780 °C NH$_3$ | 0.95 | unknown | [32] |
| AlGaN | 35 | 15 | 6 | 780 °C NH$_3$ | 0.30 | unknown | [11] |
through a wide range of oxygen composition is needed to understand the formation of the HOC- and LOC-GaON nanolayers, especially in the epitaxial nanolayer where the atomic strain induced by the GaN substrate can have
FIG. 3. (a) Chemical reaction equations with conditions: (i) stable reactants and (ii) in our experiments. (b) Enthalpy, $H$, of the different GaON states. The colored lines are the linear combinations of the reactants, i.e., GaN combined with three different GaO (and Ga+Ga$_2$O$_3$) states. The black curves are calculated using DFT. (c) Enthalpy of formation (heat of mixing), $\Delta H$, against the reference line of the reactants “GaN + GaO (relaxed)” as the orange line shown in (b). (d) A schematic illustration of the fast local oxygen substitution and the following segregation of the HOC and LOC nanolayers. The exemplary GaO$_{0.33}$N$_{0.67}$ configurations calculated by DFT are shown in Supplementary Information Figure S6.
On the one hand, considering the solid-state chemical reaction equation with the stable reactants as shown in Figure 3a (i), where the reactants on the left-hand side are GaN in the wurtzite phase, Ga$_2$O$_3$ in $\beta$-phase and Ga in the orthorhombic phase, and the product on the right-hand side is a neutrally charged GaO$_x$N$_{(1-x)}$ supercell with the $x$ fraction of the N sites randomly substituted by O atoms at different strain states (these states will be explained later). The solid-state reaction in our experiments (OPT and annealing) retains mainly the wurtzite GaN lattice, and the reaction proceeds with the one-to-one substitution of the N atoms by O atoms to form stable O$_N$ sites without universal phase transition to $\beta$-Ga$_2$O$_3$ structures [33, 34], therefore, the atomic ratio of Ga/(N+O) is set to be 1 in the calculations.
On the other hand, in our experiments, the non-thermal oxidation caused by OPT is a far-from-equilibrium process, so the referenced reaction is not initiated from the stable chemically segregated reactants Ga+Ga$_2$O$_3$, but can be the chemically mixed states such as unrelaxed wurtzite GaO, strain-relaxed wurtzite GaO, and lattice distorted GaO. The exemplary supercells of GaO in these strain states can be found in Supplementary Information Figure S6. Moreover, it can be clearly seen from the TEM image (Figure 1b) that, although the lattice constant of the top GaON layer is different from that of the wurtzite GaN, the GaON layer still maintains a certain crystallinity. As a result, the reactant that is most relevant to our experiments, as shown in Figure 3a (ii), should be “GaO (relaxed)”, where the lattice strain...
is released, and the hexagonal wurtzite lattice is not heavily distorted.
As shown in Figure 3, the enthalpy, $H$, in eV per chemical formula unit (eV/f.u.) is plotted against the fraction of oxygen, $x$, in the formula unit set as GaO$_2$N$_{(1-x)}$. The colored lines label the combination of reactants (GaO at different strain states combined with GaN) without chemical reaction, while the black data points are the calculated enthalpy of the “reacted” GaO$_2$N$_{(1-x)}$ supercells (product) at different strain states. Each black data point is averaged over five independent supercells with the corresponding $x$. Three strain states of the “reacted” GaO$_2$N$_{(1-x)}$ supercells (product) are considered: (a) static wurtzite lattice adopted to the lattice constants of perfect GaN with fixed-position O$_N$ sites (unrelaxed); (b) static lattice with internally relaxed O$_N$ sites (constraint); and (c) relaxed lattice in $z$-axis with fully relaxed O$_N$ sites ($z$-axis relaxed). In this way, the energy differences attributed to the internal O$_N$ relaxation and the external strain release can be clearly revealed. It is shown that the internal relaxation of the O$_N$ sites results in a main reduction in enthalpy, while the external strain release becomes significant only at the HOC region ($x > 0.5$). More essentially, the comparison of the $H$ between the products and the reference reactants gives the enthalpy of formation (heat of mixing) $\Delta H$ of this condition as shown in Figure 3.
As the orange line is the most relevant condition in our experiments, we further plot the enthalpy of formation (heat of mixing), $\Delta H$, of this condition as shown in Figure 3. The positive and negative $\Delta H$ values indicate endothermic and exothermic reactions, respectively. Intriguingly, a balanced point around $x = 0.33$ is seen in Figure 3. During the annealing process, both the internal local site and external strain are gradually relaxed to more stable states, and the migration of the O atoms should follow the same trend. Therefore, in a solid-state reaction with no external flux of the O atoms (as the annealing was conducted in N$_2$), the uniform system with a preset fraction of oxygen will tend to segregate into two HOC and LOC systems if the overall change in the $\Delta H$ is negative. Indeed, with reference to “(1-x)GaN + (x)GaO (relaxed)”, the energy landscape shows that the system (e.g., at $x = 0.5$) is energetically favorable to finally segregate into pure GaN and GaO$_{0.9}$N$_{0.1}$ systems, so the HOC and LOC nanolayers seen in the experiments can be explained as an intermediate metastable state before the full segregation.
The DFT calculated structures of the LOC-GaON are consistent with the TEM image (Figure 1j). As mentioned in Figure 2i, the $x/y$ in LOC-GaON of the 900 °C-annealed sample is 0.54 (±0.05)/1. Based on this ratio, the possible crystal structures are calculated ($x/y$ of 0.5/1 is used in the DFT calculation for simplicity), as shown the Supplementary Information Figure S6, in which the LOC-GaON exhibits the original wurtzite structure. As a result, only the HOC-GaON with the heavily distorted lattice can be identified in the TEM image, while the LOC-GaON layer is not distinguishable. Therefore, as shown in Figure 3i, we present a schematic illustration of the oxygen migration in GaN involving fast local substitution in $\mu$s time scale (based on the Arrhenius equation) and the slow overall segregation happening in minute time scale. The initial and final thickness of the GaON nanolayer is the same as the data in Figure 1.
In practical applications, the energy band diagram is essential for understanding and predicting the performance of the devices. Thus, understanding the band alignment of the GaON nanolayer to the GaN substrate is critical to pave the way for its device-level applications. The in-situ Ar$^+$ sputtering is used to remove all the GaON on the surface, so the GaN underneath is exposed for XPS characterization. By comparing the XPS spectra of the valence band (VB) levels, the offset of the VB maxima (VBM) between GaON and GaN can be determined. As shown in Figure 4a and b, using the N-1s core level as a reference, the VBM offset is 0.82 eV, and the VBM of the GaON nanolayer is lower than that of the GaN substrate. It is noticed that the Ga LMM Auger peaks (purple region in Figure 4a) and the additional bumped upper tail of GaN VB are originated from a thin layer of metallic Ga on the GaN surface introduced by in-situ Ar$^+$ sputtering (Ga-Ga curve in Figure 2i).
As for the conduction band (CB) offset, because the CB minimum (CBM) is mainly contributed by the Ga-$4s$ orbital, it is expected that the CBM offset should be rather minimal. Indeed, as shown in Figure 4, the density of states (DOS) from the DFT calculation indicates that the CBM offset is $\sim$0.1 eV. Here, the comparison is made between the pure GaN and pure Ga$_2$O$_3$ systems, where the VBMs are contributed by occupied N-2p for GaN and O-2p for Ga$_2$O$_3$, respectively. Therefore, a larger VBM offset ($\sim$1.37 eV) is seen. In contrast, the marginal CBM offset can be understood with respect to other similar common-cation compound semiconductors in terms of simple chemical trends of the band edge positions and the hydrostatic volume deformation potential of the Γ state [36, 37]. Specifically, in Ga-cation systems, the energies of the CBMs at Γ-point with insignificant shift indicate a small atomic volume deformation of Ga atom in different systems.
C. Device-level demonstration: Diodes and $p$-FETs
Based on the experimental and computational results, the GaON nanolayer is highly compatible with GaN-based platform by nature and can be readily integrated into electronic-device applications. Therefore, we further demonstrate its utility with Schottky junction diodes and GaN $p$-channel field effect transistors ($p$-FETs).
Figure 5a shows the schematic structure of the fabricated Schottky diode with the GaON nanolayer (GaON diodes), of which the fabrication process is described in
FIG. 4. (a) The XPS spectra of the sample after OPT and 900 °C annealing, before (upper panel) and after (lower panel) Ar⁺ sputtering. The peak of the N-1s core level and the VB are used to determine the valence band offset between GaN and GaON in (b). The difference of the Ga LMM Auger intensities is owing to the formation of the surface metallic Ga after Ar⁺ sputtering [35]. (b) Illustration of VB offset between GaN and GaON. (c) The DOS of pure wurtzite GaN and Ga₂O₃ calculated using DFT.
the Supplementary Information. The conventional diode without the GaON nanolayer (p-GaN diode) has also been fabricated on the same epi-structure for comparison. Owing to the large metal/GaON barrier as shown in the inset figure of Figure 5b, the GaON diodes exhibit an enhanced hole blocking capability with average two-order-of-magnitude smaller reverse-bias leakage current density compared with the conventional p-GaN diodes, and thus an enhanced current-regulating performance (Figure 5). Although the forward turn-on voltage ($V_{ON}$) of the diodes is increased (by ~0.47 V from linear extrapolation) with the GaON being introduced, the differential on-resistance ($R_{ON}$) of the diodes at the ON-state is seldomly affected (< 0.7%) by the GaON nanolayer. The additional $V_{ON}$ assists holes to overcome the additional barrier induced by the GaON when the GaON diode is fully turned on, after which the GaON would not further limit the transportation of holes, so the differential $R_{ON}$ is not affected. The increase on $V_{ON}$ is smaller than the VBM difference between GaON and GaN (0.47 eV versus 0.82 eV), probably due to the tunneling process, as the GaON nanolayer is only 3.99 nm in thickness. The uniformity of the GaON nanolayer on a large scale is revealed by analyzing 60 independent GaON diodes fabricated on two 2 × 2 cm² samples (with OPT, and annealed at 800/900 °C, respectively). The statistical distribution of the reverse leakage current at $V_{K} = 5$ V is shown in Figure 5. A reasonable uniformity with a standard deviation within 4.9% has been found, verifying the potential of the proposed GaON nanolayer in large-scale fabrication.
Figure 5 presents the schematic structure of the GaN p-FETs with a novel GaON/SiNx gate dielectric stack. For comparison, the GaON/SiNx dielectric stack of the devices is replaced with conventional Al₂O₃ in controlled samples. The device performance is summarized in Figure 5e and f. The GaN p-FETs with GaON/SiNx dielectrics have larger peak transconductance ($g_m$) and increased maximum channel current ($I_D$). In conventional Al₂O₃-gate devices, the Al₂O₃ is used to blocking holes transporting from the channel to the gate, and hence reduces the gate leakage current. However, at the Al₂O₃/p-GaN interface, a large number of trap states would be charged by holes at high gate bias. The trapped holes would deplete part of the holes in the p-FET channel, resulting in the reduction of the channel current [38]. As a consequence, in the conventional Al₂O₃-gate device, the $g_m$ drops greatly with $V_{GS} < -5$ V. To eliminate the influence of trap states in the gate region, a dielectric that has type-II alignment with p-GaN, such as SiNx in this demonstration, can be chosen. Such a type-II alignment allows the quick discharging of trapped holes through the VB of the SiNx, as the trap states are within the VBM-offset energy range between the p-GaN and SiNx. However, directly adopting SiNx will cause large gate leakage current, because there is no hole barrier from the chan-
FIG. 5. (a) Structure of fabricated GaON/GaN Schottky junction diode. (b) Comparison of the current densities between diodes with and without GaON nanolayer. $V_K$ stands for the cathode voltage. Inset figure is the energy band diagram of GaON/GaN Schottky junction diode. (c) Statistic histogram of the cathode current at $V_K$ of 5 V for 60 independent devices made on two 2 $\times$ 2 cm$^2$ samples (annealed at 800 and 900 °C, individually). (d) Structure of fabricated GaN $p$-FETs. The gate dielectric in controlled group is Al$_2$O$_3$, while it is GaON/SiNx stack in experimental group. (e) Transfer curves in log (left) and linear (right) scales of the GaN $p$-FETs with Al$_2$O$_3$ and GaON/SiNx gate dielectrics. (f) Transconductance ($g_m$) of the GaN $p$-FETs with Al$_2$O$_3$ and GaON/SiNx gate dielectrics. The detailed fabrication process is included in Supplementary Information Figure S7 and S8.
nel to the gate. This problem can be well-solved by inserting a hole-blocking GaON nanolayer. The GaON nanolayer has less trap states at its interface with $p$-GaN, because of its small lattice mismatch and similar symmetry against the hexagonal GaN. Although trap states can appear at the GaON/SiNx interface, the trapped holes can be quickly discharged through the VB of SiNx [39]. As a result, the $g_m$ in the GaON/SiNx-gate device maintains at reasonable values with $V_{GS} < -5$ V, benefiting to a higher maximum $I_D$.
In our previous works [8, 38–40], we have discussed other advantages of this unique GaON nanolayer in boosting the performance of GaN $p$-FETs. For example, the threshold voltage instability caused by interface trap states in conventional Al$_2$O$_3$-gate devices can also be greatly suppressed by this novel GaON/SiNx gate stack [38, 39]. Meanwhile, in GaN $p$-FETs, as junctionless devices, gate-recess is an intuitive way to realize normally-OFF operation [41], while the etching-induced damages would decrease the hole mobility in the channel of $p$-FETs, as the channel is very close to the etched interface. An oxidized layer would help to deplete the holes under the gate region, realizing buried-channel normally-OFF $p$-FETs without aggressive gate-recess [8, 40].
D. Discussion and outlook: GaON nanolayer with multifunction
So far, we have shown several superior structural and electronic properties of GaON nanolayer, such as enhanced thermal stability, large VB offset against GaN, and the two-step ”oxidation-reconfiguration” process with highly tunable and compatible plasma techniques. Moreover, we have demonstrated that the GaON nanolayer can be readily integrated into GaN-based electronic devices to enhance the device performance. In this section, we will further discuss potential applications of the GaON nanolayer as a multifunctional structure on a GaN-based platform according to its attractive characteristics.
The large VB offset against GaN makes GaON a naturally suitable dielectric for hole blocking. Compared with the conventional dielectric formed by deposition, GaON is in-situ converted from GaN, featuring an uncontaminated high-quality interface. Moreover, its high thermal stability allows a large thermal budget process, such as low-pressure chemical vapor deposition (LPCVD) [32], and metallization annealing.
A straightforward application of GaON is as gate dielectrics in the GaN-based transistors. Not only is it
FIG. 6. Schematic illustrations of the applicable scenarios of the GaON nanolayer: (a) GaN-based HEMT for power electronics and p-FET for CMOS technology; (b) passivation layer of photocathode in PEC water splitting; (c) dark-current-blocking layer in GaN-based UV photodetector.
beneficial for the p-FETs (“GaON (i)” in Figure 6a) as discussed in the previous section, the GaON nanolayer is also profitable in the n-channel GaN-based metal-insulator-semiconductor (MIS) HEMTs. As shown in Figure 6a, in a MIS-HEMT, the holes are mainly generated in the gate-to-drain access region from impact ionization, and these energetic holes will induce degradation of the dielectric by accelerated defects generation. This hole-induced degradation can result in a highly concerned reliability issue that deducts the high-temperature reverse-bias (HTRB) operating lifetime of the MIS-HEMT [42]. However, the degradation can be suppressed by a hole-blocking GaON layer (“GaON (ii)” in Figure 6a) at the interface between channel and dielectrics [32].
Another interesting feature of the GaON/GaN band alignment is the nearly flat CBM alignment despite a large VBM offset, remaining attractive in applications where require strong electron injection. As shown in Figure 6b, an instance is as a protection layer in photovoltaic-electrochemical (PEC) water-splitting application, which can potentially overcome the stability-efficiency trade-off of Si photocathode [43]. However, the CBM alignment between GaN and GaON is nearly flat as well, so the potential efficiency loss during the electron transportation across the interface is rather eliminated. More intriguingly, GaON nanolayer on non-polar GaN facet has been found to be more active than GaN in terms of hydrogen evolution reaction (HER), because of the much lower free energy of hydrogen adsorption on the Ga site compared to that of pure GaN non-polar facet [48]. Therefore, we note that it is highly promising that a large-scale GaON-nanolayer-decorated GaN layer (Figure 6b) can be used to protect Si photocathode with enhanced performance of PEC water-splitting devices.
One more application example is a GaN-based ultraviolet (UV) photodetector as shown in Figure 6c. The proposed GaON nanolayer can improve the device performance by suppressing the dark background current...
and thus enhancing the responsivity (sensitivity). Although GaN-based UV photodetector stimulates a lot of interest owing to its suitable detection range in UV, versatility and ability to serve in an extreme environment, a common challenge remains as the small photo-to-dark current ratio of less than $10^3$ [49, 50]. Therefore, an oxide layer, such as ZnO and ZrO$_2$, is usually used to suppress the dark current that is mainly carried by holes in VB $\beta$ [51, 52]. However, similar to the protection layer on Si photocathode, these oxides may undesirably reduce the photocurrent carried by photoelectrons if the interfacial CBM offset becomes large. Compared to other oxide materials, GaON nanolayer will not block the photon-generated electrons from the nearly-flat CBM alignment. Therefore, it can be used to improve the photo-dark current ratio by suppressing the dark current.
Apart from the desired band alignment with GaN, the large bandgap of GaON also brings potential benefits, such as stronger electric-field strength and hot-carrier immunity. Therefore, the responsivity of GaN photodetectors can be greatly improved through a field-enhanced exciton ionization process triggered by a high electrical field [53, 54]. By applying the GaON nanolayer, the device breakdown voltage can be boosted to a higher value [51], allowing enough operating room for a high electrical field that enables the field-enhanced exciton ionization process. With such strong hot-carrier immunity, the GaON nanolayer is also suitable as a reinforcement layer to enhance the reliability of p-GaN gate HEMTs, as shown in Figure 6a. For instance, the interface at AlGaN/passivation in the gate-to-drain access region (“(Al)GaON (iii)” in Figure 6a) would undergo hot-electron bombardment during high-power switching operations. The bombardment would generate new surface states that capture electrons, resulting in a degradation of dynamic on-resistance ($R_{ON}$) and a degradation of reverse blocking capability. The AlGaN/passivation interface can be reinforced by an (Al)GaON nanolayer, and therefore, can withstand more hot-carrier bombardment [11].
Similarly, at the Schottky-type p-GaN gate region (“GaON (iv)” in Figure 6a), the gate metal/p-GaN Schottky junction is also bombarded by hot electrons when a high gate voltage is applied, which will eventually lead to gate breakdown [55]. A GaON nanolayer between the gate metal and p-GaN can significantly enhance the gate reliability and breakdown voltage, originated from the high immunity of the hot-carrier bombardment of GaON [31].
As a final remark, we note that the potential applications of the GaON nanolayer are not limited to the discussed examples. Other recent studies on the GaON system, such as a smooth phase transition from GaN to $\beta$-Ga$_2$O$_3$ [56] and deep oxygen incorporation in bulk GaN [57], can extend the multifunctional utility of GaON in an unexpected way. For example, a possible GaN/Ga$_2$O$_3$ heterojunction with an intentionally embedded GaON nanolayer at the interface can make a high-quality transition layer in future GaN/Ga$_2$O$_3$-based devices.
### III. CONCLUSION
In this contribution, we proposed a well-controlled, large-scale, and yet few-step oxidation-reconfiguration approach to achieve metastable GaON epitaxial nanolayer on commercialized GaN platform. The construction as well as the formation mechanisms of the GaON nanolayer were clearly explained through well-established experimental and computational methods. The band alignment of the GaON nanolayer to the GaN substrate has been verified through experimental characterization and theoretical computation. The GaON nanolayer has been experimentally demonstrated to promote the performance of GaN-based Schottky diodes and p-FETs. Meanwhile, we discussed the employment of the GaON nanolayer as a multifunctional component in various kinds of applications, including GaN-based HEMTs for power electronics, p-FETs for CMOS technology, PEC water splitting, and photodetectors. This work can pave the way for future research on the GaON nanolayer as a multipurpose platform with inherent compatibility with a wide range of GaN-based cutting-edge applications.
### IV. EXPERIMENTAL AND CALCULATION SECTION
#### A. Fabrication and characterization
The GaN wafers (from Enkris Semiconductor Inc.) were firstly cleaned with acetone and buffered-oxide-etchant to remove the organic contaminates and native oxide respectively. In Step I, the samples were oxidized in an ICP chamber (Multiplex ICP from STS Inc.) with an O$_2$ flow of 30 sccm and platen/coil power of 20/50 W for 5 minutes. In Step II, the samples were annealed in N$_2$ at 800, 900, 1000 and 1100 °C, respectively for 55 minutes inside diffusion furnace (LB45 from ASM Inc.). All samples were stored in acetone and were isolated from the ambient atmosphere. The bright-field TEM image was taken with JOEL (JEM-ARM200F) microscopy. The further fabrication of GaON/p-GaN diodes is illustrated in Supplementary Information Figure S8. The details of AFM, SIMS and XPS characterizations are given in Supplementary Information as well.
#### B. Calculation details
DFT calculations were conducted using the Vienna Ab-initio Simulation Package (VASP) [57], employing the projected augmented-wave method [58]. The electronic states were expended in plane-wave basis sets with an energy cutoff of 700 eV. The Brillouin zone was sampled...
with a Γ-centered k-mesh grid with spacing 0.15 Å⁻¹ which was equivalent to a dense 9×9×6 grid for a hexagonal wurtzite GaN unit cell. Gaussian smearing with a width of 0.03 eV was used to describe the partial occupancies of the electronic states. We chose $10^{-7}$ eV and $5 \times 10^{-3}$ eV/Å as the energy and force convergence criteria for the optimization of the electronic and ionic structures, respectively. The Perdew-Burke-Ernzerhof (PBE) version of the generalized gradient approximation [59] was used for the initial configuration optimization and self-consistent energy calculations. The electronic densities of states were calculated using HSE06 hybrid functional with 32% of the exact Hartree-Fock exchange [60] to obtain correct bandgaps. More details is included in Supplementary Information.
**Supplementary Information**
Supplementary Figs. S1–S8, Tables S1, Experimental Details and Discussions.
**Acknowledgements**
This work was supported by the High-Level University Fund (G02236002 and G02236005) at the Southern University of Science and Technology (SUSTech). The computational resource was supported by the Center for Computational Science and Engineering at the Southern University of Science and Technology (SUSTech). The authors acknowledge the Nanosystem Fabrication Facility (NFF) (CWB) of the Hong Kong University of Science and Technology (HKUST) for the device fabrication. The TEM, SIMS and part of the XPS characterization of this research work was carried out in the Materials Characterization and Preparation Facility (MCPF) of the HKUST.
**Contributions**
M.H. and K.J.C. conceived the idea and supervised the project. J.C., S.F. and L.Z. fabricated the samples. J.Z. performed the DFT calculation. J.C., Y.C. and S.F. performed the TEM measurements and analysis. J.C. and J.Z. performed the SIMS measurements and analysis. J.C., J.Z., L.Z. and H.L. performed the XPS measurements and analysis. J.C. performed the AFM measurements and analysis. J.C. and J.Z. created the first draft of manuscript. J.C., Z.Z., X.C., Z.G., M.H. and K.J.C reviewed and edited the manuscript.
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The Herglotz variational principle for dissipative field theories
Jordi Gaset*, Manuel Lainz†, Arnau Mas‡, Xavier Rivas§.
December 1, 2022
Abstract
In the recent years, with the incorporation of contact geometry, there has been a renewed interest in the study of dissipative or non-conservative systems in physics and other areas of applied mathematics. The equations arising when studying contact Hamiltonian systems can also be obtained via the Herglotz variational principle. The contact Lagrangian and Hamiltonian formalisms for mechanical systems has also been generalized to field theories. The main goal of this paper is to develop a generalization of the Herglotz variational principle for first-order and higher-order field theories. In order to illustrate this, we study three examples: the damped vibrating string, the Korteweg–De Vries equation, and an academic example showing that the non-holonomic and the vakonomic variational principles are not fully equivalent.
Keywords: Herglotz variational principle, higher-order field theories, contact field theory, Korteweg–De Vries equation
MSC 2020 codes: 37K58, 37L05, 53D10, 35Q53
Contents
1 Introduction 2
2 The Herglotz principle in mechanics 3
2.1 Herglotz principle: implicit version 4
2.2 Herglotz principle: vakonomic version 5
2.3 Herglotz principle: nonholonomic version 7
3 The Herglotz principle for fields 8
3.1 Geometric structures 8
3.2 Herglotz principle for fields: non-holonomic version 10
3.3 Herglotz principle for fields: vakonomic version 11
3.4 Relations between both approaches 13
4 Higher-order Lagrangian densities 14
5 Examples 16
5.1 Vibrating string with damping 16
5.2 The non-holonomic and the vakonomic principles are not equivalent 17
5.3 The Korteweg–De Vries Lagrangian 17
6 Conclusions and outlook 18
References 23
*e-mail: [email protected] (ORCID: 0000-0001-8796-3149).
†e-mail: [email protected]. (ORCID: 0000-0002-2368-5853).
‡e-mail: [email protected] (ORCID: 0000-0003-0532-0938).
§e-mail: [email protected]. (ORCID: 0000-0002-4175-5157).
1 Introduction
It is well known that symplectic geometry is the natural geometric framework to study Hamiltonian mechanical systems [1, 2, 36, 45]. When dealing with time-dependent mechanical systems, cosymplectic geometry is the appropriate framework to work with [10, 12, 29]. These two geometric structures have been generalized to the so-called $k$-symplectic and $k$-cosymplectic structures in order to deal with autonomous and non-autonomous field theories [3, 25, 26, 27, 46, 50, 54, 55].
In recent years, the interest in dissipative systems has grown significantly. In part, this is due to the incorporation of contact geometry [4, 34, 42] to the study of non-conservative Lagrangian and Hamiltonian mechanical systems [6, 8, 20, 22, 31]. This approach has proved to be very useful in many different problems in areas such as thermodynamics, quantum mechanics, general relativity, control theory among others [7, 13, 18, 28, 33, 37, 42, 47, 49, 57, 58]. Recently, the notion of cocontact manifold has been developed in order to introduce explicit dependence on time [14, 53].
This growing interest has driven researchers to look for a generalization of $k$-symplectic and contact geometry in order to work with non-conservative field theories. This new geometric framework is called $k$-contact geometry, and has already been applied to the study of both Hamiltonian and Lagrangian field theories in the autonomous [30, 32, 51] and non-autonomous [52] cases. The contact formulation of mechanics has also been generalized to describe higher-order mechanical systems in [17]. The Skinner–Rusk formalism has also been studied in detail for both contact [15] and $k$-contact systems [39]. Recently, the notion of multicontact structure has been introduced [16], generalizing the multisymplectic framework to deal with non-conservative field theories. The Herglotz principle [23, 40, 41, 56] provides a variational formulation for contact Hamiltonian systems. There have been several attempts [35, 44] to generalize this theory to field theories.
In this paper we will derive this principle in a more general geometric language and compare it to the existing approaches. In order to do that, we will review three different formulations of the Herglotz principle in mechanics, the implicit version, the vakonomic version, and the non-holonomic version. In order to find a Herglotz principle for higher dimensions, we will generalize the vakonomic and the non-holonomic versions of the Herglotz principle for mechanical systems. We will see that the non-holonomic approach yields the same field equations as in the $k$-contact [32, 52] and multicontact [16] formalisms. On the other hand, in contrast to what happens in mechanics, using the vakonomic approach we obtain an additional condition that must be fulfilled. This new equation implies that the $k$-contact and multicontact Lagrangian formalisms are not fully equivalent to the vakonomic variational principle introduced in the present paper. One of the examples of the last section will illustrate this fact.
The vakonomic Herglotz variational principle for first-order field theories is then extended to a suitable Herglotz principle for higher-order non-conservative field theories. As an example, the Korteweg–De Vries equation [43] is discussed. This equation arises from a second-order Lagrangian and is used to model waves in shallow waters. In order to have a dissipative behaviour, we add a standard damping term to the Korteweg–De Vries Lagrangian and use the variational principle to derive a non-conservative version of the Korteweg–De Vries equation.
The organization of the paper is as follows. In first place, Section 2 offers a review of the Herglotz principle in mechanics. In particular, we see three different approaches: the implicit version, the vakonomic version and the non-holonomic version. Section 3 is devoted to extend the Herglotz variational principle from mechanics to field theory using the vakonomic and the non-holonomic approaches. In Section 4 we generalize the results given in Section 3 to the case of higher-order Lagrangian densities using the vakonomic variational principle.
Finally, Section 5 is devoted to study some examples of the theoretical framework developed
above. The first example deals with a first-order system consisting of a damped vibrating string with friction linear to the velocity. The second example shows that, as said before, the vakonomic variational principle for field theories and the $k$-contact formulations are not equivalent. We present an academic example consisting in taking the Lagrangian of the previous example and slightly modifying the damping term. In this case, we find a solution to the $k$-contact Euler–Lagrange equations that does not satisfy the additional condition arising from the vakonomic principle. The last example deals with the Korteweg–De Vries equation, which arises from a second-order Lagrangian.
Throughout this paper, all the manifolds are assumed to be real, connected and second countable. Manifolds and mappings are assumed to be smooth. The sum over crossed repeated indices is understood.
2 The Herglotz principle in mechanics
The Herglotz principle, in simple terms, might be explained as follows. Given a configuration manifold $Q$, consider a Lagrangian function $L : TQ \times \mathbb{R} \rightarrow \mathbb{R}$ depending on the positions $q^i$, the velocities $\dot{q}^i$ and an extra variable $z$ that we can think of as the action, but we will soon discuss its meaning in more detail. The Herglotz variational principle states that the trajectory of the system $c(t)$ is a critical point of the action $\zeta(1)$, satisfying $c(0) = q_0$, $c(1) = q_1$, $\zeta(0) = z_0$ and
$$\frac{dc}{dt} = L(c, \dot{c}, \zeta),$$
$$\zeta(0) = z_0.$$
We note that the action is given by
$$\zeta(1) = \int_0^1 \frac{dc}{dt} dt + \zeta(0) = \int_0^1 L(c(t), \dot{c}(t), \zeta(t)) dt + z_0,$$
which, if the Lagrangian does not depend on $z$, coincides with the usual Hamilton’s action up to a constant.
A slight modification of this principle, that is the one we will prefer in this paper, is to consider the action as the increment of $z$, that is,
$$\zeta(1) - \zeta(0) = \int_0^1 \frac{dc}{dt} dt = \int_0^1 L(c(t), \dot{c}(t), \zeta(t)) dt,$$
which coincides exactly with Hamilton’s action if the Lagrangian $L$ does not depend on $z$. Since both definitions of the action differ only by a constant $z_0$, their critical curves are the same. Indeed, they are the curves $c$ such that $(c, \dot{c}, \zeta)$ satisfy Herglotz’s equations:
$$\frac{\partial L}{\partial q^i} - \frac{d}{dt} \frac{\partial L}{\partial \dot{q}^i} = \frac{\partial L}{\partial q^i} \frac{\partial L}{\partial \zeta}.$$
To be more precise, we distinguish two possible equivalent interpretations of this principle. We can either understand it as an implicit action principle for curves $c$ on $Q$, or as a constrained but explicit action principle for curves $(c, \zeta)$ on $Q \times \mathbb{R}$. The three different ways to formalize the Herglotz principle that we will see in this section are based on [23]. Another version can be found in [19].
2.1 Herglotz principle: implicit version
For the first interpretation, we consider the (infinite dimensional) manifold $\Omega(q_0, q_1)$ of curves $c : [0, 1] \to Q$ with endpoints $q_0, q_1 \in Q$. The tangent space of $T_c\Omega(q_0, q_1)$, is the space of vector fields along $c$ vanishing at the endpoints. That is,
$$T_c\Omega(q_0, q_1) = \{\delta c \mid \delta c(t) \in T_{c(t)}Q, \delta c(0) = 0, \delta c(1) = 0\}.$$
Let $z_0 \in \mathbb{R}$ and consider the operator
$$Z_{z_0} : c \in \Omega(q_0, q_1) \mapsto Z_{z_0}(c) \in \mathcal{C}^\infty([0, 1] \to \mathbb{R}),$$
where $Z_{z_0}(c)$ is the only solution to the Cauchy problem
$$\begin{cases} \frac{dZ_{z_0}(c)}{dt} = L(c, \dot{c}, Z_{z_0}(c)), \\ Z_{z_0}(c)(0) = z_0, \end{cases}$$
that is, it assigns to each curve on the base space its action as a function of time. This map is well-defined because the Cauchy problem (5) always has a unique solution.
Now, the contact action functional maps each curve $c \in \Omega(q_0, q_1)$ to the increment of the solution of the Cauchy problem (5):
$$A_{z_0} : \Omega(q_0, q_1) \to \mathbb{R}$$
$$c \mapsto Z_{z_0}(c)(1) - Z_{z_0}(c)(0).$$
Note that, by the fundamental theorem of calculus,
$$A_{z_0}(c) = \int_0^1 L(c(t), \dot{c}(t), Z_{z_0}(c(t)))dt.$$
The following theorem states that the critical points of this action functional are precisely the solutions to Herglotz equation [21].
**Theorem 2.1** (Herglotz variational principle, implicit version). Let $L : TQ \times \mathbb{R} \to \mathbb{R}$ be a Lagrangian function and consider $c \in \Omega(q_0, q_1)$ and $z_0 \in \mathbb{R}$. Then, $(c, \dot{c}, Z_{z_0}(c))$ satisfies the Herglotz equations
$$\frac{d}{dt} \frac{\partial L}{\partial \dot{q}^i} - \frac{\partial L}{\partial q^i} = \frac{\partial L}{\partial \dot{q}^i} \frac{\partial}{\partial z},$$
if and only if $c$ is a critical point of the contact action functional $A_{z_0}$.
**Proof.** In order to simplify the notation, let $\psi = T_cZ(\delta v)$. Consider a curve $c_\lambda \in \Omega(q_0, q_1)$, namely a family of curves in $Q$ with fixed endpoints $q_0, q_1$ smoothly parametrized by $\lambda \in \mathbb{R}$, such that
$$\delta c = \frac{dc_\lambda}{d\lambda} \bigg|_{\lambda=0}.$$
Since $Z(c_\lambda)(0) = z_0$ for all $\lambda$, then $\psi(0) = 0$.
We compute the derivative of $\psi$ by interchanging the order of the derivatives using the differential equation defining $Z$:
$$\frac{d}{dt} \bigg|_{t=0} \frac{d}{d\lambda} Z(c_\lambda(t)) = \frac{d}{d\lambda} \bigg|_{t=0} L(c_\lambda(t), \dot{c}_\lambda(t), Z(c_\lambda)(t))$$
$$= \frac{\partial L}{\partial \dot{q}^i}(\chi(t))\delta c^i(t) + \frac{\partial L}{\partial q^i}(\chi(t))\delta \dot{c}^i(t) + \frac{\partial L}{\partial z}(\chi(t))\psi(t).$$
Hence, the function $\psi$ is the solution to the ODE above. Since $\psi(0) = 0$, necessarily,
$$
\psi(t) = \frac{1}{\sigma(t)} \int_0^t \sigma(\tau) \left( \frac{\partial L}{\partial q^i}(\chi(\tau)) \delta c^i(\tau) + \frac{\partial L}{\partial \dot{q}^i}(\chi(\tau)) \delta \dot{c}^i(\tau) \right) d\tau,
$$
where
$$
\sigma(t) = \exp \left( - \int_0^t \frac{\partial L}{\partial z}(\chi(\tau)) d\tau \right) > 0.
$$
Integrating by parts and using and that the variation vanishes at the endpoints, we get the following expression:
$$
T_cA(\delta c) = T_cZ(\delta c)(1) = \psi(1) = \frac{1}{\sigma(1)} \int_0^1 \delta c^i(t) \left( \sigma(t) \frac{\partial L}{\partial q^i}(\chi(t)) - \frac{d}{dt} \left( \sigma(t) \frac{\partial L}{\partial \dot{q}^i}(\chi(t)) \right) \right) dt,
$$
where we have used that
$$
\frac{d\sigma}{dt}(t) = - \frac{\partial L}{\partial z}(\chi(t)) \sigma(t).
$$
Since this must hold for every possible variation, we have
$$
\sigma(t) \left( \frac{\partial L}{\partial q^i}(\chi(t)) + \frac{d}{dt} \frac{\partial L}{\partial q^i}(\chi(t)) - \frac{\partial L}{\partial \dot{q}^i}(\chi(t)) \frac{\partial L}{\partial z}(\chi(t)) \right) = 0,
$$
thus obtaining the Herglotz equation.
\[\square\]
### 2.2 Herglotz principle: vakonomic version
Another way to understand this principle is to think of it as a constrained variational principle for curves on $Q \times \mathbb{R}$. This time, we will work on the manifold $\tilde{\Omega}(q_0, q_1, z_0)$ of curves $\tilde{c} = (c, \zeta) : [0, 1] \to Q \times \mathbb{R}$ such that $c(0) = q_0, c(1) = q_1, \zeta(0) = z_0$. Note that we do not constraint $\zeta(1)$. The tangent space at the curve $\tilde{c} \in \tilde{\Omega}(q_0, q_1, z_0)$ is given by
$$
T_{\tilde{c}}\tilde{\Omega}(q_0, q_1, z_0) = \{ \delta \tilde{c}(t) = (\delta c(t), \delta \zeta(t)) \in T_{\tilde{c}(t)}(Q \times \mathbb{R}) \mid \delta c(0) = 0, \delta c(1) = 0, \delta \zeta(0) = 0 \}.
$$
In this space, the action functional $\tilde{A}$ can be defined as an integral
$$
\tilde{A} : \tilde{\Omega}(q_0, q_1, z_0) \to \mathbb{R}
$$
$$
\tilde{c} \mapsto \zeta(1) - \zeta(0) = \int_0^1 \dot{\zeta}(t) dt.
$$
We will restrict this action to the set of paths that satisfy the constraint $\dot{c} = L$. For this, we consider the paths at the zero set of the constraint function $\phi_L$:
$$
\phi_L(q, \dot{q}, z) = z - L(q, \dot{q}, z).
$$
That is, we consider
$$
\tilde{\Omega}_L(q_0, q_1, z_0) = \{ \tilde{c} = (c, \zeta) \in \tilde{\Omega}(q_0, q_1, z_0) \mid \phi_L \circ \tilde{c} = \dot{c} - L(c, \dot{c}, \zeta) = 0 \}.
$$
Note that, since the Cauchy problem (5) has a unique solution, the elements $(c, \zeta) \in \tilde{\Omega}_L(q_0, q_1, z_0)$ are precisely $(c, \mathbb{Z}_{z_0}(c))$, where $c \in \Omega(q_0, q_1)$. That is, the map $\text{Id} \times \mathbb{Z}_{z_0} : \Omega(q_0, q_1) \to \tilde{\Omega}_L(q_0, q_1, z_0)$
given by \((\text{Id} \times \mathcal{Z}_{q_0}) (c) = (c, \mathcal{Z}_{q_0}(c))\) is a bijection, with inverse \((\text{pr}_Q)_* (c, \zeta) = c\). Moreover, the following diagram commutes
\[
\begin{array}{ccc}
A & \xrightarrow{\tilde{A}} & \mathbb{R} \\
\Omega(q_0, q_1) & \xrightarrow{\text{Id} \times \mathcal{Z}_{q_0}} & \tilde{\Omega}(q_0, q_1, z_0)
\end{array}
\]
(14)
Hence \((c, \zeta) \in \tilde{\Omega}(q_0, q_1, z_0)\) is a critical point of the functional \(\tilde{A}\) if and only if \(c\) is a critical point of \(A\). So the critical points of \(A\) restricted to \(\tilde{\Omega}(q_0, q_1, z_0)\) are precisely the curves that satisfy the Herglotz equations.
**Theorem 2.2** (Herglotz variational principle, vakonomic version). Let \(L : TQ \times \mathbb{R} \rightarrow \mathbb{R}\) be a Lagrangian function and let \((c, \zeta) \in \tilde{\Omega}(q_0, q_1, z_0)\). Then, \((c, \dot{c}, \zeta)\) satisfies the Herglotz equations:
\[
\frac{d}{dt} \frac{\partial L}{\partial \dot{q}} - \frac{\partial L}{\partial q} = \frac{\partial L}{\partial \dot{q}} \frac{\partial \dot{L}}{\partial \dot{z}},
\]
if and only if \((c, \zeta)\) is a critical point of \(\tilde{A}|_{\tilde{\Omega}(q_0, q_1, z_0)}\).
We will provide an alternative proof by directly finding the critical points of the functional \(\tilde{A}\) restricted to \(\tilde{\Omega}(q_0, q_1, z_0) \subseteq \tilde{\Omega}(q_0, q_1, z_0)\) using the following infinite-dimensional version of the Lagrange multiplier theorem (see [2] for more details).
**Theorem 2.3** (Lagrange multiplier Theorem). Let \(M\) be a smooth manifold and let \(E\) be a Banach space. Consider a smooth submersion \(g : M \rightarrow E\) such that \(A = g^{-1}(\{0\})\) is a smooth submanifold, and a smooth function \(f : M \rightarrow \mathbb{R}\). Then \(p \in A\) is a critical point of \(f|_A\) if and only if there exists \(\tilde{\lambda} \in E^*\) such that \(p\) is a critical point of \(f + \tilde{\lambda} \circ g\).
**Proof of Herglotz variational principle, vakonomic version.** We will apply this result to our situation. In the notation of the theorem, \(M = \tilde{\Omega}(q_0, q_1, z_0)\) is the smooth manifold. We pick the Banach space \(E = L^2([0, 1] \rightarrow \mathbb{R})\) of square integrable functions. This space is, indeed, a Hilbert space with inner product
\[
(\alpha, \beta) = \int_0^1 \alpha(t) \beta(t) dt.
\]
Recall that, by the Riesz representation theorem, there exists a bijection between \(L^2([0, 1] \rightarrow \mathbb{R})\) and its dual such that for every \(\hat{\alpha} \in L^2([0, 1] \rightarrow \mathbb{R})^*\) there exists \(\alpha \in L^2([0, 1] \rightarrow \mathbb{R})\) such that \(\hat{\alpha}(\beta) = \langle \alpha, \beta \rangle\) for all \(\beta \in L^2([0, 1] \rightarrow \mathbb{R})\).
Our constraint function is
\[
g : \tilde{\Omega}(q_0, q_1, z_0) \rightarrow L^2([0, 1] \rightarrow \mathbb{R})
\]
\[
\tilde{c} \mapsto (\phi_L) \circ (\tilde{c}, \dot{\tilde{c}}),
\]
where \(\phi_L\) is a constraint function locally defining \(A = g^{-1}(0) = \tilde{\Omega}(q_0, q_1, z_0)\).
By Theorem 2.3, \(c\) is a critical point of \(f = \tilde{A}\) restricted to \(\tilde{\Omega}(q_0, q_1, z_0)\) if and only if there exists \(\lambda \in L^2([0, 1] \rightarrow \mathbb{R})^*\) (which is represented by \(\lambda \in L^2([0, 1] \rightarrow \mathbb{R})\) such that \(c\) is a critical point of \(\tilde{A}_\lambda = \tilde{A} + \lambda \circ g\).
Indeed,
\[
\tilde{A}_\lambda = \int_0^1 L_\lambda(c(t), \dot{c}(t)) dt,
\]
where
\[
L_\lambda(q, z, \dot{q}, \dot{z}) = \dot{z} - \lambda \phi_L(q, z, \dot{q}, \dot{z}).
\]
Since the endpoint of $\zeta$ is not fixed, the critical points of this functional $\tilde{A}_\lambda$ are the solutions of the Euler–Lagrange equations for $L_\lambda$ that satisfy the natural boundary condition
$$\frac{\partial L_\lambda}{\partial \dot{z}}(c(1),\dot{c}(1)) = 1 - \lambda(1)\frac{\partial \phi_L}{\partial \dot{z}}(c(1),\dot{c}(1)) = 0.$$
Since $\phi_L = \dot{z} - L$, this condition reduces to $\lambda(1) = 1$.
The Euler–Lagrange equations of $L$ are given by
$$\frac{d}{dt} \left( \lambda(t) \frac{\partial \phi_L(c(t),\dot{c}(t))}{\partial \dot{q}^i} \right) - \lambda(t) \frac{\partial \phi_L(c(t),\dot{c}(t))}{\partial q^i} = 0,$$
(16a)
$$\frac{d}{dt} \left( \lambda(t) \frac{\partial \phi_L(c(t),\dot{c}(t))}{\partial z} \right) - \lambda(t) \frac{\partial \phi_L(c(t),\dot{c}(t))}{\partial \dot{z}} = 0,$$
(16b)
Since $\phi_L = \dot{z} - L$, the equation (16b) for $z$ is just
$$\frac{d\lambda(t)}{dt} = -\lambda(t) \frac{\partial L}{\partial z}.$$
Substituting on (16a) and dividing by $\lambda$, we obtain the Herglotz equations (15).
### 2.3 Herglotz principle: nonholonomic version
Another way to obtain the Herglotz equation of motion is through a non-linear non-holonomic principle, the so-called Chetaev principle [38]. Instead of restricting the space of admissible curves $\tilde{\Omega}_L(q_0, q_1, z_0) \subseteq \Omega(q_0, q_1, z_0)$ and find the critical points on this submanifold, we directly restrict the space of admissible variations, so that the differential of the action has to vanish only in a selection of variations. Hence, the solutions of this principle are not necessarily critical points of the action functional restricted to any space.
**Definition 2.4.** A section $\tilde{c} = (c, c_z) \in \tilde{\Omega}_L(q_0, q_1, z_0)$ satisfies the non-holonomic Herglotz variational principle if, and only if, $(c, \dot{c}, c_z)$ satisfies Herglotz’s equations:
$$\frac{d}{dt} \left( \frac{\partial L}{\partial \dot{q}^i} \right) - \frac{\partial L}{\partial q^i} = \frac{\partial L}{\partial \dot{q}^i} \frac{\partial L}{\partial z},$$
(17)
Then, the nonholonomic dynamics are given by [11, 38].
**Theorem 2.5** (Herglotz’s variational principle, nonholonomic version). Let $L : TQ \times \mathbb{R} \to \mathbb{R}$ be a Lagrangian function and let $\tilde{c} = (c, c_z) \in \tilde{\Omega}_L(q_0, q_1, z_0)$. Then $\tilde{c}$ satisfy the non-holonomic Herglotz variational principle if, and only if, $(c, \dot{c}, c_z)$ satisfies Herglotz’s equations:
3 The Herglotz principle for fields
In the literature, there exists a non-covariant formulation of the Herglotz principle for fields theories [35]. A more general approach is given in [44], although only a class of Lagrangian functions is considered, which we call Lagrangians with closed action dependence (see Definition 3.6).
The method presented in [44] uses an implicit argument, similar to the method presented in Section 2.1 for mechanical systems. We propose two alternative methods: the non-holonomic principle, which is compatible with the \( k \)-contact [30, 32], \( k \)-cocontact [52] and multicontact [16] formulations; and the vakonomic principle, which can be extended to higher-order Lagrangians.
Consider a Lagrangian function \( L(x^\mu, u^a, u^a_\mu, z^\mu) \) depending on the coordinates \((x^\mu)\) of an \( m \)-dimensional spacetime \( M \), the values of fields \( u^a \), their derivatives \( u^a_\mu \) at the point \( x \) and the variables \( z^\mu \) that, in this context do not represent the action, but the action density. In order to compute the action of a local field \( \sigma \) defined on \( D \subseteq M \), we find a vector field \( \zeta^\mu \) such that
\[
D_\mu \zeta^\mu = L.
\]
Then, the action is
\[
\int L d^n x = \int D_\mu \zeta^\mu d^n x = \int_{\partial D} \zeta^\mu \eta_\mu d\sigma,
\]
where \( \eta_\mu \) is the normal unit vector to the surface and \( d\sigma \) is the surface differential. The last equality follows from Stokes’ Theorem. Note that if \( M \) is one-dimensional, the action is just \( \zeta(1) - \zeta(0) \), and thus we recover the Herglotz action for mechanical systems.
The critical points of this action along the local fields \( \sigma \) with the same values on the boundary would be the solutions to the Herglotz field equations
\[
D_\mu \left( \frac{\partial L}{\partial u^a_\mu} \right) - \frac{\partial L}{\partial u^a} = \frac{\partial L}{\partial z^\mu}.
\]
These equations are obtained in [44] through an implicit argument, in a similar spirit to the proof of Theorem 2.1. Note that the Lagrangian theory of \( k \)-contact fields [32] provides the same equations.
However, we find two issues on this derivation of the variational principle. First of all, the definition of \( z^\mu \) in equation (18) depends on a metric on \( M \) in order to compute its divergence. This can be easily fixed by taking \( z^\mu \) to be components of a \((k-1)\)-differential form instead of a vector field.
The second issue is more subtle. The solution of (18) is not unique, and hence the action is not well-defined. This is not a problem if the Lagrangian does not depend on \( \zeta^\mu \), because in this case all the solutions to (18) differ only by an exact term, whose integral is zero, and does not contribute to the action, but this is not true in general. Indeed, \( \zeta \) may appear in equation (19). In [44] the authors assume some conditions on the Lagrangian in order to find a unique solution. Moreover, (18) might have no solutions and hence we will need to add more constraints in order to ensure the existence of solutions.
One way to fix this problem is to prescribe boundary conditions on (18) that make the solution unique. However, we will avoid this problem choosing a “constrained formulation” of this problem, in the same spirit of Theorems 2.2 and 2.5, instead of the “implicit” approach used in [44].
3.1 Geometric structures
Let \( M \) be an \( m \)-dimensional orientable manifold representing the spacetime and consider a fiber bundle \( E \to M \). Let \((x^\mu, u^a)\) be adapted coordinates on \( E \) and let \( d^n x = dx^1 \wedge \cdots \wedge dx^m \) be a
volume form on $M$. Then, we will denote $d^{m-1}x_{\mu} = i_{\nu}^{\mu} dx^{\nu} \in \Omega^{m-1}(M)$. The configuration space is the bundle $\pi : E \times M \Lambda^{m-1}m \rightarrow M$, because the action densities are $(m - 1)$-forms on $M$. The adapted coordinates of the first jet bundle $J^1(E \times M \Lambda^{m-1}M)$ are $(x^\mu, u_\mu^a, z^\nu, z'^\nu)$, where $z^\nu$ are the coordinates of $\Lambda^{m-1}(M)$ induced by the local basis $\{d^{m-1}x_\nu\}_{\nu=1,\ldots,m}$. We consider the first jet of the action densities because it is necessary to intrinsically define the constraint (18).
Given a coordinate system, the total derivative $D_\mu : \mathcal{C}^\infty(J^1(E \times M \Lambda^{m-1}M)) \rightarrow \mathcal{C}^\infty(J^2(E \times M \Lambda^{m-1}M))$, for $\mu = 1, \ldots, m$, is a derivation given by
$$D_\mu f = \frac{\partial f}{\partial x^\mu} + u_\mu^a \frac{\partial f}{\partial u^a} + z^{\nu} \frac{\partial f}{\partial z^\nu} + u_\mu^a \frac{\partial f}{\partial u_a^\nu} + z'^\nu \frac{\partial f}{\partial z'^\nu},$$
where $f \in \mathcal{C}^\infty(J^1(E \times M \Lambda^{m-1}M))$.
For any section $\rho : M \rightarrow E \times M \Lambda^{m-1}M$, the total derivative satisfies the property
$$(j^1 \rho)^*(D_\mu f) = \frac{\partial(j^1 \rho)^*f}{\partial x^\mu}.$$
Given a vector field $\xi \in \mathcal{X}(E \times M \Lambda^{m-1}M)$ with local flow $\gamma_\tau : E \times M \Lambda^{m-1}M \rightarrow E \times M \Lambda^{m-1}M$, its complete lift to $J^1(E \times M \Lambda^{m-1}M)$ is the vector field $\xi^1 \in \mathcal{X}(J^1(E \times M \Lambda^{m-1}M))$ whose local flow is $j^1 \gamma_\tau$. If $\xi \in \mathcal{X}(E \times M \Lambda^{m-1}M)$ is a vertical vector field with respect to the projection $\pi$
$$\xi = \xi^a \frac{\partial}{\partial u^a} + \xi^\nu \frac{\partial}{\partial z^\nu},$$
its complete lift is
$$\xi^1 = \xi^a \frac{\partial}{\partial u^a} + \left( \frac{\partial \xi^a}{\partial x^\mu} + u_\mu^b \frac{\partial \xi^a}{\partial u^b} + z^{\tau} \frac{\partial \xi^a}{\partial z^\tau} \right) \frac{\partial}{\partial u^a} + \xi^\nu \frac{\partial}{\partial z^\nu} + \left( \frac{\partial \xi^\nu}{\partial x^\mu} + u_\mu^b \frac{\partial \xi^\nu}{\partial u^b} + z'^\tau \frac{\partial \xi^\nu}{\partial z'^\tau}\right) \frac{\partial}{\partial z'^\nu}.$$
The Lagrangian density $\mathcal{L} : J^1(E \times M \Lambda^{m-1}M) \rightarrow \Lambda^m M$ is a fiber bundle morphism over $M$. In local coordinates, $\mathcal{L}(x^\mu, u_\mu^a, z^\mu) = L(x^\mu, u_\mu^a, z^\mu) d^m x$. In order to define intrinsically the constraint (18), we define the canonical differential action form as
$$\mathcal{D}S : J^1 \Lambda^{m-1}M \rightarrow \Lambda^m (M)$$
$$j^1 \alpha \longmapsto d\alpha.$$
The name is inspired by the canonical action form introduced in [16]. In local coordinates, it reads
$$\mathcal{D}S(z^\nu, z'^\nu) = z'^\nu d^m x.$$
Then, the constraint (18) can be written as
$$\Phi = \pi^* \mathcal{D}S - \mathcal{L} = 0,$$
where $\tau : J^1(E \times M \Lambda^{m-1}M) \rightarrow J^1 \Lambda^{m-1}M$ is the natural projection. In local coordinates, $\Phi = \phi d^m x$, with $\phi = z'^\nu$. The situation is described by the following commutative diagram [diagram not shown].
Given a submanifold $D \subseteq M$, the set of sections that satisfy the constraint $\Phi$ is denoted by
$$\Omega = \{ \rho \in \Gamma_D(E \times_M \Lambda^{m-1}M) \text{ such that } (j^1 \rho)^* \Phi = 0 \}.$$
Then, the action associated to $\mathcal{L}$ is:
$$\mathcal{A} : \Omega \rightarrow \mathbb{R}$$
$$\rho \mapsto \int_D (j^1 \rho)^* \mathcal{L}.$$
In general, the variations of this action are the elements tangent to $\rho$ which vanish at $\partial D$, which can be seen as the $\pi$-vertical vector fields along $\rho$. Thus, we define:
$$T_\rho \Gamma_D = \{ \xi : D \rightarrow T(E \times_M \Lambda^{m-1}M) \mid \xi(x) \in T_{\rho(x)}(E \times_M \Lambda^{m-1}M), \pi_\rho(x) = 0, \xi|_{\partial D} = 0 \}.$$
We want to find the sections which are “critical” for the action $\mathcal{A}$ under the constraint $\Phi$. As we have commented before, this problem is not well formulated. The constraint $\Phi$ involves velocities, and there are several non-equivalent ways to select which variations have to be taken [38]. Inspired by the case of contact mechanics [24], we will describe two different non-equivalent approaches: the non-holonomic and the vakonomic variational principles.
3.2 Herglotz principle for fields: non-holonomic version
The approach presented in this section is inspired on [5, 59, 38]. Let $D \subseteq M$ be an oriented manifold with compact closure and boundary $\partial D$. The vertical lift [48] is a morphism of vector bundles $S : T^*M \otimes J^1(E \times_M \Lambda^{m-1}M) \rightarrow V(\pi)$ over the identity of $J^1(E \times_M \Lambda^{m-1}M)$ such that, for any $j^1_x \phi \in J^1(E \times_M \Lambda^{m-1}M)$, $\beta \in T^*M \otimes J^1(E \times_M \Lambda^{m-1}M) V(\pi)$ and $f \in C^\infty(J^1_{\phi(x)}(E \times_M \Lambda^{m-1}M))$, we have:
$$S_{j^1_x \phi}(\beta)(f) = \frac{d}{dt} \bigg|_{t=0} f(j^1_x \phi + t\beta).$$
We have that $T^*M \otimes J^1(E \times_M \Lambda^{m-1}M) V(\pi)$ is the vector bundle associated to the affine bundle $\pi^1 : J^1(E \times_M \Lambda^{m-1}M) \rightarrow E \times_M \Lambda^{m-1}M$ and, hence, using the same coordinates $(x^\mu, u^a, z^\nu, u^\nu, z^\mu)$, the local expression of the vertical lift is
$$S = du^a \otimes \frac{\partial}{\partial x^\mu} \otimes \frac{\partial}{\partial u^a} + dz^\nu \otimes \frac{\partial}{\partial x^\mu} \otimes \frac{\partial}{\partial z^\nu}.$$
The dependence on the velocities of the constraint is implemented in the non-holonomic version as a force. This can be formalized in different ways. For instance, in [5] the authors use the vertical endomorphism. In our problem the constraint is given by the $m$-form $\Phi$ instead of a function, and we find that the vertical lift gives a more direct derivation of the equations. The vertical lift is a $(2,1)$-tensor, and we are interested in the contraction of both contravariant entrances with the form $d\Phi$:
$$\varphi = i_S d\Phi = \left( \frac{\partial \phi}{\partial u^a} du^a + \frac{\partial \phi}{\partial z^\nu} dz^\nu \right) \otimes \Lambda^m \cdot x_\mu.$$
**Definition 3.1.** A section $\rho \in \Omega$ satisfies the non-holonomic Herglotz variational principle if
$$T_\rho \mathcal{A}(\xi) = \int_D (j^1 \rho)^* (L_{\xi^1} \mathcal{L}) = 0.$$
for all vector fields $\xi \in T_\rho \Gamma_D$ such that
$$\varphi(\xi^1) = 0.$$
(23)
where $\mathcal{L}$ denotes the Lie derivative and $\varphi(\xi^1)$ is the contraction of $\xi^1$ with the first entrance of $\varphi$. In local coordinates, it reads
$$
\varphi(\xi^1) = \left(\frac{\partial \phi}{\partial u^a} \xi^a + \frac{\partial \phi}{\partial z^\mu} \xi^\mu\right) \otimes d^{m-1}x^\mu.
$$
**Theorem 3.2.** Let $\mathcal{L} : J^1(E \times_M \Lambda^{m-1}M) \rightarrow \Lambda^m M$ be a Lagrangian density and let $\rho \in \Omega$. Then, $j^1 \rho$ satisfies the Herglotz field equations
$$
D_\mu \left( \frac{\partial L}{\partial u^a_\mu} \right) - \frac{\partial L}{\partial u^a} = \frac{\partial L}{\partial u^a_\mu} \frac{\partial L}{\partial z^\mu}
$$
(24)
if, and only if, $\rho$ satisfies the non-holonomic Herglotz variational principle (Definition 3.1).
**Proof.**
$$
\int_D (j^1 \rho)^* (\mathcal{L}, \mathcal{L}) = \int_D (j^1 \rho)^* \left[ \xi^a \frac{\partial L}{\partial u^a} + \left( \frac{\partial \xi^a}{\partial x^\mu} + u^b_\mu \frac{\partial \xi^a}{\partial u^b} + z^\tau_\mu \frac{\partial \xi^a}{\partial z^\tau} \right) \frac{\partial L}{\partial u^a_\mu} \right]
$$
$$
+ \xi^a \frac{\partial L}{\partial z^\mu} + \left( \frac{\partial \xi^a}{\partial x^\mu} + u^b_\mu \frac{\partial \xi^a}{\partial u^b} + z^\tau_\mu \frac{\partial \xi^a}{\partial z^\tau} \right) \frac{\partial L}{\partial z^\mu} \right] \, d^m x
$$
$$
= \int_D (j^1 \rho)^* \left[ \xi^a \left( \frac{\partial L}{\partial u^a} - D_\mu \frac{\partial L}{\partial u^a_\mu} \right) \right] \, d^m x + \int_{\partial D} (j^1 \rho)^* \left[ \xi^a \frac{\partial L}{\partial u^a_\mu} \right] \, d^{m-1}x^\mu.
$$
If it vanishes for all $\xi$ satisfying equation (23), there exist functions $\lambda_\alpha \in \mathcal{E}^\infty(J^1(E \times_M \Lambda^{m-1}M))$ such that
$$
\frac{\partial L}{\partial u^a} - D_\mu \left( \frac{\partial L}{\partial u^a_\mu} \right) = \lambda_\alpha \frac{\partial \phi}{\partial u^a},
$$
$$
\frac{\partial L}{\partial z^\mu} = \lambda_\alpha \frac{\partial \phi}{\partial z^\mu}.
$$
Combining both equations and using the expression $\phi = z^\mu_\mu - L$, we see that $\lambda_\mu = \frac{\partial L}{\partial z^\mu}$ and
$$
D_\mu \left( \frac{\partial L}{\partial u^a_\mu} \right) - \frac{\partial L}{\partial u^a} = \frac{\partial L}{\partial u^a_\mu} \frac{\partial L}{\partial z^\mu}.
$$
(25)
The Herglotz field equations (24) are also called $k$-contact Euler–Lagrange equations [32].
### 3.3 Herglotz principle for fields: vakonomic version
The approach presented in this section is inspired by the vakonomic version of Herglotz principle [24], presented in Section 2.2.
In the vakonomic approach we only consider variations that transform sections that satisfy the constraints into sections that also satisfy the constraints. In other words, the lift of the variations to the first jet must be tangent to the submanifold defined by the constraints. Thus, we have the following variational principle. Let $D \subseteq M$ be an oriented manifold homeomorphic to a ball and with boundary $\partial D$.
11
Definition 3.3. A section $\rho \in \Omega$ satisfies the vakonomic Herglotz variational principle if
$$T_\rho A(\xi) = \int_D (j^1\rho)^*(L_{\xi_1}L) = 0$$
for every vector field $\xi \in T_\rho\Gamma_D$ such that $L_{\xi_1}\Phi = 0$.
This kind of constrained field theories has been studied, for instance, in [9]. By Theorem 2.3, we can rewrite this as a problem without constraints using Lagrange multipliers. We need to consider the Lagrangian
$$L_\Lambda = L + \lambda \Phi = (L + \lambda(z_\mu - L))\,d^m x = L_\lambda d^m x,$$
where $\lambda \in C^\infty(M)$ is a function to be determined called the Lagrange multiplier. Then, the action associated to $L_\lambda$ is
$$A_\lambda : \Omega \rightarrow \mathbb{R}$$
$$\rho \mapsto \int_D (j^1\rho)^*L_\lambda.$$
Corollary 3.4. A section $\rho \in \Omega$ satisfies the vakonomic Herglotz variational principle if, and only if,
$$T_\rho A_\lambda(\xi) = \int_D (j^1\rho)^*(L_{\xi_1}L_\lambda) = 0$$
for every vector field $\xi \in T_\rho\Gamma_D$.
The corresponding equations are given by the following theorem.
Theorem 3.5. Let $L : J^1(E \times_M \Lambda^{m-1}M) \rightarrow \Lambda^m M$ be a Lagrangian density and let $\rho \in \Omega$. Then, $j^1\rho$ satisfies the Herglotz field equations:
$$D_\mu \frac{\partial L}{\partial u^a} - \frac{\partial L}{\partial u^a} = \frac{\partial L}{\partial v^a_\mu} \frac{\partial L}{\partial z^\mu}$$
and the condition
$$D_\nu \frac{\partial L}{\partial z^\mu} = D_\mu \frac{\partial L}{\partial z^\nu},$$
if, and only if, $\rho$ satisfies the vakonomic Herglotz variational principle.
Proof. The problem is the usual non-constrained Hamilton variational problem for the Lagrangian $L_\lambda$. Considering variations with respect to $\delta u^a$ and $\delta z^\nu$ we obtain the set of equations
$$\frac{\partial L_\lambda}{\partial u^a} - D_\mu \left( \frac{\partial L_\lambda}{\partial u^a_\mu} \right) = 0,$$
$$\frac{\partial L_\lambda}{\partial z^\nu} - D_\mu \left( \frac{\partial L_\lambda}{\partial z^\nu_\mu} \right) = 0.$$
These equations are just the Euler–Lagrange equations when considering $u^a$ and $z^\nu$ as dynamical variables. Expanding equation (31), we have
$$(1 - \lambda) \frac{\partial L}{\partial z^\nu} - \frac{\partial L}{\partial x^\mu} = 0,$$
and combining it with equation (30), we find that
\[ 0 = (1 - \lambda) \frac{\partial L}{\partial u^a_\mu} - D_\mu \left( (1 - \lambda) \frac{\partial L}{\partial u^a_\mu} \right) = (1 - \lambda) \frac{\partial L}{\partial u^a_\mu} - (1 - \lambda) D_\mu \left( \frac{\partial L}{\partial u^a_\mu} \right) + (1 - \lambda) \frac{\partial L}{\partial z^\nu} \frac{\partial L}{\partial u^a_\mu}. \]
If \( \lambda \neq 1 \), we can divide by \( 1 - \lambda \) and obtain equation (28). However, in this case there are hidden conditions in equation (31). Taking \( g = \log(|1 - \lambda|) \), equation (31) implies
\[ dg = \pm \frac{\partial L}{\partial z^\nu} dx^\nu. \]
This has solution if and only if the right hand side is closed, namely if
\[ D_\nu \frac{\partial L}{\partial z^\mu} = D_\mu \frac{\partial L}{\partial z^\nu}. \tag{32} \]
If this condition is fulfilled, since \( D \) is homeomorphic to a ball,
\[ \frac{\partial L}{\partial z^\nu} dx^\nu = dh, \tag{33} \]
and so we pick \( g = h \).
### 3.4 Relations between both approaches
The main difference between the non-holonomic and the vakonomic approaches is the unexpected condition (29). It motivates the following definition.
**Definition 3.6.** A Lagrangian has *closed action dependence* if
\[ D_\mu \frac{\partial L}{\partial z^\mu} = D_\nu \frac{\partial L}{\partial z^\nu}. \tag{34} \]
for any pair \( 1 \leq \mu, \nu \leq m \).
This condition has two interesting interpretations: a variational one and a geometric one. The Lagrangian has closed action dependence if, and only if, the action of \( \rho = (\sigma, \zeta) \in \Omega \) only depends on \( \sigma \). Equation (32) is obtained by taking variations of the constrained action in the \( \zeta \) direction. Indeed, a Lagrangian has closed action dependence if, and only if, for any section \( \sigma : M \to E \), does not exist a family of sections \( \zeta_s : M \to \Lambda^{m-1}(M), s \in \mathbb{R} \), such that
\[ \left. \frac{d\zeta_s}{ds} \right|_{\partial D} = 0 \]
and satisfying the conditions
\[ d\zeta_s = \mathcal{L}(J^1 \sigma, \zeta_s) \quad \text{and} \quad \left. \frac{\partial A(\sigma, \zeta)}{\partial s} \right|_{s=0} \neq 0. \]
The reason is because, if \( \frac{\partial L}{\partial z^\mu} \) induces a closed form, by Stokes’ theorem the action only depends on the border, where the variation vanishes. This can be seen explicitly in the example presented in Section 5.2.
The geometric interpretation can be obtained as follows. Let \( L : J^1(E \times_M \Lambda^{m-1}M) \to \mathbb{R} \) be a Lagrangian function. Define the \( M \)-semibasic one-form \( \theta_L \in \Omega^1(J^1(E \times_M \Lambda^{m-1}M)) \) as
\[ \theta_L = \frac{\partial L}{\partial z^\mu} dx^\mu, \tag{35} \]
which is independent on the coordinates used to define it. The closed action dependence condition is equivalent to
\[ d\theta_L = 0. \] (36)
The form \( \theta_L \) is (minus) the dissipation form introduced in [16].
For Lagrangians with closed action dependence, both versions of the variational principle given in Definitions 3.1 and 3.3 are equivalent. Moreover, they coincide with the version proposed in [44] and the equations are the same as the ones derived from the \( k \)-contact [32] and multicontact [16] formalisms.
When the Lagrangian has not closed action dependence, both principles may be different. In Section 5.2, we provide an example where there are sections which are solutions of one variational principle but not the other. In this case, only the non-holonomic approach provides, in general, the same equations as the \( k \)-contact and multicontact formalisms.
4 Higher-order Lagrangian densities
Most of the relevant field theories are modelled by first-order Lagrangians with one notable exception, General Relativity, which is usually described with a second-order Lagrangian. Contact gravity is specially interesting as an example of modified gravity which may explain certain observations about the expansion of the universe [47]. The Herglotz field equations for the Hilbert Einstein Lagrangian with a linear term in the action have been derived in [47] and [33] with slightly different variational methods. The method used in [33] is, essentially, the vakonomic method presented in Section 3.3, showing how it can be expanded to higher-order Lagrangians. Hence, in this section we apply the vakonomic principle to higher-order Lagrangian densities.
Consider the \( r \)-th jet bundle \( J^r(E \times_M \Lambda^m M) \) of a fiber bundle \( E \rightarrow M \). Local coordinates of \( J^r(E \times_M \Lambda^m M) \) will be denoted as \((x^\mu, u^I)\), where \( I = (I_1, \ldots, I_m) \) is a multi-index such that \( 0 \leq |I| = I_1 + \ldots + I_n \leq r \). Given a local section \( \sigma : M \rightarrow E \), we denote by \( j^r \sigma : M \rightarrow J^rE \) its \( r \)-th prolongation.
Given a coordinate system, the total derivative \( D_\mu : \mathcal{C}^\infty(J^k(E \times_M \Lambda^m M)) \rightarrow \mathcal{C}^\infty(J^{k+1}(E \times_M \Lambda^m M)) \), for \( \mu = 1, \ldots, m \), is a derivation given by
\[
D_\mu f = \frac{\partial f}{\partial x^\mu} + \sum_{|J|=0}^k \left( u^a_{j+1} \frac{\partial f}{\partial u^a_{j+1}} + z^{r}_{j+1} \frac{\partial f}{\partial z^{r}_{j+1}} \right),
\]
where \( f \in \mathcal{C}^\infty(J^k(E \times_M \Lambda^m M)) \).
The Lagrangian density \( \mathcal{L} : J^r(E \times_M \Lambda^m M) \rightarrow \Lambda^m M \) is a fiber bundle morphism over \( M \). Locally, \( \mathcal{L} = Ld^m x \). The Herglotz operator [17] can be extended to fields.
**Definition 4.1.** Given a Lagrangian \( \mathcal{L} \) and an index \( 1 \leq \mu \leq m \), the Herglotz operator for fields is the linear operator
\[
D_\mu^\mathcal{L} : \mathcal{C}^\infty(J^r(E \otimes_M \Lambda^m M)) \rightarrow \mathcal{C}^\infty(J^{r+1}(E \otimes_M \Lambda^m M))
\]
\[
F \mapsto D_\mu^\mathcal{L}(F) = D_\mu F - F \frac{\partial \mathcal{L}}{\partial z^\mu}.
\]
In general, these operators are not derivations and, since
\[
\left( D^\mathcal{L}_\mu D^\mathcal{L}_\nu - D^\mathcal{L}_\nu D^\mathcal{L}_\mu \right) F = \left( D_\nu \frac{\partial \mathcal{L}}{\partial z^\mu} - D_\mu \frac{\partial \mathcal{L}}{\partial z^\nu} \right) F,
\]
they do not commute.
Lemma 4.2. The Herglotz operators commute if, and only if, the Lagrangian has closed action dependence.
For Lagrangians with closed action dependence, we can denote the successive applications of the Herglotz operator with multi-index notation as
\[ D_L^I = \prod_{\mu=1}^m (D_L^\mu)^{I_\mu}. \]
The constraint is implemented as in the first-order case, that is
\[ \Phi = (j^r \rho)^* \mathcal{D} - \mathcal{L} = 0, \quad (37) \]
where \( (\tau^r_1) : J^r(E \times M \Lambda^{m-1}M) \rightarrow J^1 \Lambda^{m-1}M \) is the projection. In local coordinates, \( \Phi = \phi d^m x \), with \( \phi = z^\mu_\mu - L \). Let \( D \subseteq M \) be an oriented manifold homeomorphic to a ball and with boundary \( \partial D \). The set of sections on \( D \) which satisfy the constraint is denoted by
\[ \Omega = \{ \rho \in \Gamma_D(E \otimes_M \Lambda^{m-1}M) \text{ such that } (j^r \rho)^* \Phi = 0 \}. \]
In the following definition we introduce the higher-order version of the vakonomic variational principle presented in Definition 3.3.
Definition 4.3. A section \( \rho \in \Omega \) satisfies the higher-order vakonomic Herglotz variational principle if
\[ T_{\rho} A(\xi) = \int_D (j^r \rho)^* (\mathcal{L}_\xi, \mathcal{L}) = 0, \quad (38) \]
for every vector field \( \xi \in T_{\rho} \Gamma_D \) such that \( \mathcal{L}_\xi \Phi = 0 \).
As before, we have an equivalent version of this variational principle based on Lagrange multipliers [9]. Consider the modified Lagrangian
\[ \mathcal{L}_\lambda = \mathcal{L} + \lambda \Phi = (L + \lambda(z^\mu_\mu - L)) d^m x = L_\lambda d^m x. \]
Then, the action associated to \( \mathcal{L}_\lambda \) is
\[ A_\lambda : \Omega \rightarrow \mathbb{R} \]
\[ \rho \mapsto \int_D (j^r \rho)^* \mathcal{L}_\lambda. \]
Corollary 4.4. A section \( \rho \in \Omega \) satisfies the higher-order vakonomic Herglotz variational principle if, and only if,
\[ \int_D (j^r \rho)^* (\mathcal{L}_\xi, \mathcal{L}_\lambda) = 0, \quad (39) \]
for every vector field \( \xi \in T_{\rho} \Gamma_D \).
Theorem 4.5. Let \( \mathcal{L} : J^r(E \otimes_M \Lambda^{m-1}M) \rightarrow \Lambda^m M \) be a Lagrangian density and let \( \rho \in \Omega \). Then, \( j^r \rho \) satisfies the higher-order Herglotz field equations
\[ \sum_I (-1)^{|I|} D_I^{\xi} \left( \frac{\partial L}{\partial u^a_I} \right) = 0 \]
and the condition
\[ D_\nu \frac{\partial L}{\partial z^\mu} = D_\mu \frac{\partial L}{\partial z^\nu}, \]
if, and only if \( \rho \) satisfies the higher-order vakonomic Herglotz variational principle.
Proof. We proceed in a similar way to the first-order case. The Euler–Lagrange equations of $L_\lambda$ are given by
$$\sum_I (-1)^{|I|} D_I \left( \lambda \frac{\partial L_\lambda}{\partial u_I^t} \right) = 0,$$
(40)
$$\lambda \frac{\partial L_\lambda}{\partial z^\nu} - D_\mu \left( \lambda \frac{\partial L_\lambda}{\partial z_{\mu}^\nu} \right) = 0.$$
(41)
Since $L_\lambda$ does only depend of $\zeta$ and its first derivatives, higher-order terms in equation (41) vanish. Taking into account the definition of $L_\lambda$, we have
$$\lambda \frac{\partial L_\lambda}{\partial x^\mu} \partial L_\lambda = 0.$$
(42)
Repeating the argument used in the first-order case, this has solution $\lambda(x^\mu)$ if and only if
$$D_\mu \left( \lambda \frac{\partial L_\lambda}{\partial x^\mu} \right) = 0.$$
That is, there only exist solutions where $L$ has closed action dependence. Hence, by equation (42), we see that, for any function $F$,
$$D_\mu ((1 - \lambda)F) = -D_\mu (\lambda F) = -\lambda D_\mu ^2 F.$$
Substituting the above expression in (40), we obtain the higher-order Herglotz field equations.
These equations are compatible with the ones derived in [33] for the Hilbert–Einstein Lagrangian.
5 Examples
5.1 Vibrating string with damping
In this example we are going to study how we can derive the equation of a vibrating string with damping from a Herglotz principle. It is well known that a vibrating string can be described using the Lagrangian formalism. Consider the coordinates $(t, x)$ for the time and the space. Denote by $u$ the separation of a point in the string from its equilibrium point, and hence $u_t$ and $u_x$ will denote the derivative of $u$ with respect to the two independent variables. The Lagrangian function for this system is
$$L_0(u, u_t, u_x) = \frac{1}{2} \rho u_t^2 - \frac{1}{2} \tau u_x^2,$$
(43)
where $\rho$ is the linear mass density of the string and $\tau$ is the tension of the string. We will assume that these quantities are constant. The Euler–Lagrange equation for this Lagrangian function is
$$u_{tt} = c^2 u_{xx},$$
where $c^2 = \frac{\tau}{\rho}$.
In order to model a vibrating string with linear damping, we can modify the Lagrangian function (43) so that it becomes a $k$-contact Lagrangian [32].
The new Lagrangian function $L$ is defined in the phase bundle $\oplus^2 TQ \times \mathbb{R}^2$, equipped with adapted coordinates $(u; u_t, u_x; z^t, z^x)$, and is given by
$$L(u, u_t, u_x, z^t, z^x) = L_0 - \gamma z^t = \frac{1}{2} \rho u_t^2 - \frac{1}{2} \tau u_x^2 - \gamma z^t,$$
where $\gamma \in \mathbb{R}$ is a constant accounting for the damping.
The Herglotz equation (20) for this Lagrangian $L$ reads
$$u_{tt} = c^2 u_{xx} - \gamma u_t,$$
which is the equation of a vibrating string with damping. The additional equation (29),
$$D_{\nu} \frac{\partial L}{\partial z} \equiv \left\{ -\partial_t \gamma = 0, \right.\left. -\partial_x \gamma = 0 \right\},$$
is trivially satisfied since $\gamma$ is constant, and hence the equations obtained are exactly the same as in the $k$-contact Lagrangian formalism introduced in [32]. The next example presents a case in which both approaches are not fully equivalent.
5.2 The non-holonomic and the vakonomic principles are not equivalent
Consider the Lagrangian
$$L(t, x, u, u_t, u_x, z^t, z^x) = \frac{1}{2} (u_t^2 + u_x^2) - u\gamma x z^x,$$
where $\gamma_x \neq 0$ is a constant. The Lagrangian function $L$ is regular in the sense of [16, 32]. This Lagrangian has not closed dependence action. The corresponding Herglotz field equations are
$$\gamma_x z^x + u_{xx} + u_{tt} + u t u_x = 0,$$
$$z^t + z^x = L.$$
A solution of these equations is the section $u(t, x) = t$, $z^x(t, x) = 0$ and $z^t(t, x) = \frac{t}{2}$. Nevertheless, for this section, we have
$$D_t \frac{\partial L}{\partial z^x} = D_x \frac{\partial L}{\partial z^t} \Rightarrow \gamma_x u_t = 0 \Rightarrow \gamma_x = 0,$$
which is not satisfied as long as $\gamma_x \neq 0$. Therefore, this section is a solution of the non-holonomic variational principle, but it is not a solution of the vakonomic variational principle. Therefore, both principles are not equivalent.
5.3 The Korteweg–De Vries Lagrangian
The Korteweg—De Vries (KdV) equation is used to model waves on shallow water [43]. This equation can be derived as the Euler-Lagrange equation of a second order Lagrangian. We will use the higher-order vakonomic Herglotz variational principle introduced in Definition 4.3 to derive the equations of motion of a contact analogue of the KdV Lagrangian.
KdV equation involves a scalar field over time and one dimension of space. Therefore, we consider a 2-dimensional base manifold $M$, with coordinates $(t, x)$. Then, in the second order jet $J^2(\mathbb{R} \otimes \Lambda^2 M)$ we consider the coordinates
$$(t, x, u, u_t, u_x, u_{xx}, u_{yy}, z^t, z^x, z^t_t, z^t_x, z^x_t, z^x_x, z^t_{tt}, z^t_{tx}, z^x_{tt}, z^x_{tx}, z^x_{xx}).$$
The standard KdV Lagrangian is
$$L_0 = \frac{1}{2} u_x u_t + u_x^3 - \frac{1}{2} u_{xx}^2.$$
(44)
The Euler–Lagrange equation one obtains from this Lagrangian is
\[ \partial_t \partial_x u + 6 \partial_x u \partial_x^2 u + \partial_x^4 u = 0. \] (45)
Let us now consider the KdV Lagrangian with a linear action coupling
\[ L = L_0 - \gamma \mu \zeta^\mu = \frac{1}{2} u_x u_t + u_x^3 - \frac{1}{2} u_x^2 - \gamma \mu \zeta^\mu. \] (46)
which has closed action dependence provided that \( \gamma \mu \) are the components of a closed form. This is a second order Lagrangian, so we need to use the Herglotz field equations derived in Theorem 4.5. The Herglotz field equation reads
\[ \partial_t \partial_x u + \frac{1}{2} (\gamma_x \partial_t u + \gamma_t \partial_x u) + 6 \partial_x u \partial_x^2 u + 3 \gamma_x (\partial_x u)^2 + \partial_x^4 u + (2 \gamma_x + \partial_x \gamma_x) \partial_x^3 u + \gamma_x^2 \partial_x^2 u = 0, \] (47)
along with the constraint
\[ z_t + z_x = L. \]
One sees that there are additional terms which are linear in the \( \gamma \mu \), which also appear in the first-order theory, as well as quadratic terms in \( \gamma \mu \) and involving their derivatives, which are characteristic of a second-order theory.
6 Conclusions and outlook
In this paper we have developed a generalization of the Herglotz variational principle [23, 41] for first-order and higher-order field theories. In order to do this, we have developed two non-equivalent approaches: the non-holonomic and the vakonomic versions. We have seen that the non-holonomic approach is equivalent to the \( k \)-contact [32, 52] and multicontact [16] geometric formulations of dissipative field theories. On the other hand, using the vakonomic principle, some new conditions arise. This fact motivates the introduction of the so-called Lagrangians with closed action dependence, for which both approaches are equivalent.
The differences between the non-holonomic and the vakonomic principles have been exemplified with an academic example which has a solution to its \( k \)-contact Euler–Lagrange equations that is not a solution to the Herglotz field equations arising from the vakonomic variational principle. This is because the Lagrangian considered has not closed action dependence.
We have also studied a first-order field theory, the damped vibrating string, for which the \( k \)-contact formalism and the Herglotz variational principle are fully equivalent. The last example consisted in modifying the Korteweg–De Vries Lagrangian by adding a standard dissipative term.
In [44], a variational principle for Lagrangians with closed action dependence is derived using an implicit argument. The extension of this approach to the general case will require a deeper analysis of equation (18). This might be clarifying to understand the condition of closed action dependence (34).
There are still many open problems in the geometrization of action-dependent field theories. In first place, it would be interesting to establish the relations among the different geometric frameworks (\( k \)-contact, \( k \)-cocontact and multicontact) and the variational principles presented in this work and previous one. Another relevant problem is the case of field theories described by singular Lagrangians.
There are some singular Lagrangians which are not compatible with the current geometric structures, not even a weakened version of them [14]. Nevertheless, we can derive their corresponding field equations via variational principles. We expect this work will help in the understanding of the underlying geometric structures of these singular Lagrangians.
Acknowledgments
The authors acknowledge fruitful discussions and comments from our colleague Miguel-C. Muñoz-Lecanda.
J. Gaset and X. Rivas acknowledge partial financial support from the Ministerio de Ciencia, Innovación y Universidades (Spain), projects PGC2018-098265-B-C33 and D2021-125515NB-21.
M. Lainz acknowledges partial financial support of the Spanish Ministry of Science and Innovation (MCIN/AEI/10.13039/501100011033), under grants PID2019-106715GB-C2 and “Severo Ochoa Programme for Centres of Excellence in R&D” (CEX2019-000904-S).
X. Rivas acknowledges partial financial support from Novee Idee 2B-POB II project PSP: 501-D111-20-2004310 funded by the “Inicjatywa Doskonałości - Uczelnia Badawcza” (IDUB) program.
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Spin-Voltaic Effect and its Implications
Igor Žutić
Condensed Matter Theory Center, Department of Physics, University of Maryland, College Park, Maryland 20742
Jaroslav Fabian
Institute for Theoretical Physics, Karl-Franzens University, Universitätsplatz 5, 8010 Graz, Austria
In an inhomogeneously doped magnetic semiconductor, an interplay between an equilibrium magnetization and injected nonequilibrium spin leads to the spin-voltaic effect—a spin analogue of the photo-voltaic effect. By reversing either the sign of the equilibrium magnetization or the direction of injected spin polarization it is possible to switch the direction of charge current in a closed circuit or, alternatively, to switch the sign of the induced open-circuit voltage. Properties of the spin-voltaic effect can be used to perform all-electrical measurements of spin relaxation time and injected spin polarization, as well as to design devices with large magnetoresistance and spin-controlled amplification.
Most of the existing applications using spin degrees of freedom in electronic systems exploit the magnetoresistive effects in magnetic nanostructures involving metals (paramagnetic and ferromagnetic) and insulators [1,2]. Considering semiconductors, on the other hand, offers flexibility in the doping and fabrication of a wide range of hetero- and nanostructures while the nonlinear current-voltage \((I-V)\) characteristics are suitable for amplification and implementing logic. Even though many materials, in their ferromagnetic state, can have a substantial degree of equilibrium carrier spin polarization, this alone is usually not sufficient for spintronic applications [3], which typically require current flow and/or manipulation of the nonequilibrium spin (polarization). Since the early work on shining circularly polarized light [4,5] and driving electrical current [6] to generate nonequilibrium spin polarization in semiconductors, the challenge has remained to understand what the implications are of such nonequilibrium spin [7].
We illustrate here the influence of nonequilibrium spin on \(I-V\) characteristics in magnetic \(p-n\) junctions [8,9], magnetic analogues of ordinary \(p-n\) junctions [11], and focus on the implications of the spin-voltaic effect [8–10]. Related phenomena of the spin-charge coupling [12,13] were introduced in metallic heterostructures by Silsbee and Johnson, following the theoretical proposals for electrical spin injection of Aronov and Pikus [14,15] (a recent account of electrical spin injection and a detailed list of references is given in [16,17]). In the context of semiconductors there is a long tradition of optically generating (for example, by shining circularly polarized light) spin-polarized carriers and spin-dependent electromotive force (spin emf) [18], reviewed in [19,20]. Both incoherent [21,22] and coherent [23,24] optical generation of spin currents have been demonstrated. In an applied magnetic field and using quantum point contacts, electrical spin injection and detection in semiconductor quantum dots [25] have been shown to have properties similar to spin-charge coupling [12,13].
Magnetic \(p-n\) junctions, which could demonstrate the spin-voltaic effect, have spatially dependent spin splitting of carrier bands—a consequence of doping with magnetic impurities and/or an applied magnetic field \(B\). Such a spin splitting can be realized using ferromagnetic semiconductors [26] or paramagnetic semiconductors in finite \(B\) where either the magnitude of \(B\) or the \(g\)-factor is spatially inhomogeneous. For simplicity, we address here the second realization, depicted in Fig. 1.
In the low injection regime it is possible to obtain the results for spin-polarized transport analytically and to decouple the contribution of electrons and holes [9]. In the \(p\) (\(n\)) region there is a uniform doping with \(N_a\) acceptors (\(N_d\) donors). Within the depletion region \((-x_L < x < x_R)\), we assume that there is a spatially dependent spin splitting of the carrier bands. Zeeman
splitting of the conduction band can be expressed as
\[ 2q\zeta = \mu_B g B, \]
where \( g \) is the \( g \)-factor for electrons, \( \mu_B \) is the Bohr magneton, \( q \) is the proton charge, and \( \zeta \) is the electron magnetic potential [8]. In contrast to metals, the magnitude of the \( g \)-factor can be significantly different from the free electron value, exceeding 500 in Cd_{0.95}Mn_{0.05}Se at low temperature [27] and attaining \( \approx 50 \) in InSb at room temperature. We further assume that the carriers obey the nondegenerate Boltzmann statistics and consider only the effect of spin-polarized electrons (the net spin polarization of holes can also be simply included [9]). The product of electron \((n)\) and hole \((p)\) densities in equilibrium (denoted with subscript “0”) is modified from the nonmagnetic \( p-n \) junction as [8]
\[ n_0p_0 = n_0^2 \cosh(\zeta/V_T) \]
(1)
where \( n_i \) is the intrinsic (nonmagnetic) carrier density and \( V_T = k_BT/q \), with \( k_B \) the Boltzmann constant and \( T \) temperature. In a nonmagnetic \( p-n \) junction, the carrier density \( J \) can be decomposed into electron and hole contributions \( J = J_n + J_p \), which in turn are proportional to the density of the nonequilibrium minority carriers, \( J_n \propto \delta n_L = n - n_0 = n_0[\exp(V/V_T) - 1]|_{x=x_L}, \)
\[ J_p \propto \delta p_R = p - p_0 = p_0[\exp(V/V_T) - 1]|_{x=x_R}, \]
evaluated at the two edges of a depletion region [11], and \( V \) is the applied bias. For a magnetic \( p-n \) junction, Eq. 1 implies that in the regime \( \zeta > V_T \), the density of minority electrons changes exponentially with \( B = (\zeta) \) and can give rise to exponentially large magnetoresistance [8,9]. Furthermore in the \( n-p-n \) magnetic bipolar transistor [28], from applying Eq. 1 to the base \( p \)-region, it follows that the current amplification also varies exponentially with \( B \).
Before discussing the implications of the injected nonequilibrium spin in a magnetic \( p-n \) junction (depicted in Fig. 1), it is helpful to recall two simpler situations. Consider first the usual photo-voltaic effect in a nonmagnetic \( p-n \) junction \((\zeta \equiv 0)\) illuminated entirely by unpolarized light. Photo-generated electron and holes will be swept away in opposite directions by the built-in electric field in the depletion region. This departure from equilibrium carrier densities (prior to the illumination) shifts the balance of the electron and hole currents which no longer add up to zero. If the leads are connected to the two ends of a \( p-n \) junction, a reverse charge current will flow. Conversely for an open circuit configuration, photo-generated carriers suppress the built-in field and create a net (open circuit) voltage measured at the two terminals. An analogous illumination by circularly polarized light can serve as a source of spin-polarized current–a spin-polarized solar cell [29]. However, while changing the degree of circularly polarized light (say, by reversing the helicity of an incident light) changes the degree of current spin polarization [29], there are no changes in \( I - V \) characteristics—the nonequilibrium spin does not affect the charge properties.
In a magnetic \( p-n \) junction carrier spin polarization \( P = s/n \), the ratio of the spin \( s = n_\uparrow - n_\downarrow \) and electron density \((n = n_\uparrow + n_\downarrow)\), can be changed from the equilibrium value \( P_0 = \tanh(\zeta/V_T) \) by shining circularly polarized light or by direct electrical spin injection as depicted in Fig. 1 (a) and (b), respectively. With the spatially dependent spin splitting, charge current will acquire an additional component—the spin-voltaic current \( J_{sv} \) caused by the nonequilibrium spin [8]. In the spin-voltaic effect the nonequilibrium spin, by diffusion (and drift) from the point where it is generated to the edge of depletion region \( \delta P_R \neq 0 \), see Fig. 1(a), disturbs the balance between the generation and recombination currents (Fig. 1) [8,9]. If \( \zeta > 0 \), and more spin up electrons are present at \( x_R \) \((\delta P_R > 0)\), the barrier for them to cross the region is smaller than the barrier for the spin down electrons, so more electrons flow from \( n \) to \( p \) than from \( p \) to \( n \), and positive charge current results. If there are more spin down electrons at \( x_R \) \((\delta P_R < 0)\), the current is reversed. In an open circuit geometry with a reversal of injected spin polarization \( \delta P_R \to -\delta P_R \) [30] the sign of the induced voltage will be switched [9], characteristic also for spin-charge coupling [12,13] and the electrical detection of injected spin in quantum dots [25]. An equivalent change of the sign for \( J_{sv} \) and the open circuit voltage can be realized by reversing the equilibrium magnetization i.e. \( \zeta \to -\zeta \) and, correspondingly, \( P_0 \to -P_0 \). Such a reversal can be achieved by changing \( B \to -B \) in the paramagnetic case, or by temporarily applying a finite \( B \) to flip the magnetization of a ferromagnetic region (in metallic multilayers this is feasible even at small fields \(< 10 \, G \) [1]). The total charge current can be expressed as spin equilibrium parts \( J_n \) and \( J_p \) and the spin-voltaic current \( J_{sv} \) generated by the nonequilibrium spin [10]
\[ J_{sv} \propto n_{0R}P_{0L}\delta P_R e^{V/V_T}, \]
(2)
which, unlike \( J_{n,p} \), can remain finite even as \( V \to 0 \), when \( J \to J_{sv} \) [8]. The product of the equilibrium magnetization and the nonequilibrium injected spin or, equivalently, \( P_{0L}\delta P_R \) also enters directly the current amplification in a magnetic bipolar transistor [28], which can be tuned by the controlling the spin-voltaic effect. Furthermore, Eq. 2 shows the sensitivity of \( J_{sv} \) to spin relaxation since \( \delta P_R \) depends on the effective distance \( d \) between the point of spin injection and the depletion region edge \( x_R \) [10]. The decay of the corresponding nonequilibrium spin can be characterized by the spin relaxation time \( T_1 \) and the corresponding length scale, the spin diffusion length \( L_{sn} = \sqrt{D_n T_1} \), where \( D_n \) is the electron diffusivity [29]. Figure 2 illustrates how the sensitivity of \( J_{sv} \) to spin relaxation could be used to perform all-electrical measurements of \( T_1 \) [10]. Consider an idealized situation where the injected spin is completely polarized. A long \( T_1 \) implies that the injected spin polarization will not be reduced at the depletion region edge, as shown in Fig. 2(a). The spin up electrons will then be easily
can be solved numerically by self-consistently combining
showed that a variation of an unknown
ing this procedure to the parameters of GaAs it was
background has then been effectively removed. By adapt-
ought by replacing $P_{\text{ad}} \rightarrow (P_{\text{ad}} - P_{\text{BR}})/(1 - P_{\text{ad}}^2)$. At higher applied bias, the corresponding problem can be solved numerically by self-consistently combining
Poisson’s and the appropriate continuity equations for spin and charge densities [8].
A materials realization of the spin-voltaic effect, similar to the usual photo-voltaic effect, is not limited to $p$-$n$ junction, and can also include heterojunctions and structures with Schottky barriers. Even though most of the currently studied ferromagnetic semiconductors [26], such as (Ga,Mn)As and (In,Mn)As, are $p$-doped with spin-polarized electrons rather then holes, they still have a spin splitting in the conduction band as depicted in Fig. 1(a), and could be suitable for the implementation of the spin-voltaic effect.
We thank S. Das Sarma and H. Munekata for useful discussions. This paper is based on the presentation at the International Workshop on Nanostructured Metallic Materials sponsored by Nanotechnology Research Network Center of Japan and Tohoku University Materials Research Center. This work was supported by DARPA, NSF-ECS, and the US ONR.
---
FIG. 2. Schematic representation of a conduction band in a magnetic $p$-$n$ junction. Spin relaxation of the injected spin is depicted in the limits of (a) long and (b) short spin relaxation time $T_1$. Applied bias $V$ changes the width of the depletion region and therefore changes the effective length between the injected spin and the depletion region edge.
transferred across the lower barrier in the depletion region, leading to large $J_{sv}$. In contrast, for a short $T_1$ sketched in Fig. 2(b), some of the injected spin up electrons will have their spin flipped. Those spin down electrons would go across the higher barrier (suppressed by $\propto \exp(\zeta / V_T)$ within the Boltzmann statistics as compared to the transfer of spin up electrons) and $J_{sv}$ is reduced. While these two limiting cases indicate that is possible to extract an unknown $T_1$ from $J_{sv}(T_1)$ at finite bias the total charge current $J$ could be dominated by $J_n$ and $J_p$ a large $T_1$-independent background ($J_{n,p}$ do not contain the nonequilibrium spin). It is therefore useful to use the symmetry properties of the individual contributions to the charge current with respect to the applied magnetic field [10]
$$J_{n,p}(-B) = J_{n,p}(B), \quad J_{sv}(-B) = -J_{sv}(B),$$
recalling that $\zeta \propto B$. Consequently, $I - V$ characteristics can be used to extract the $T_1$ and the degree of the injected spin polarization by measuring $J(V,B) - J(V,-B) = 2J_{sv}$ [10], where the large $T_1$-independent background has then been effectively removed. By adapting this procedure to the parameters of GaAs it was shown that a variation of an unknown $T_1$ by an order of magnitude would give a chance of approximately two orders of magnitude in $J_{sv}$ [10] and the spin relaxation time could be extracted from measured I-V curves.
To simplify the presentation, we have focused on a particular implementation of the spin-voltaic effect. Analytical results for a low injection regime, where $V < V_{\text{th}}(N_n N_d/n_i^2)$—the built-in potential [11], are also available in other cases [9]. For example, when both $p$ and $n$ regions are magnetic, the spin-voltaic current in Eq. 2 should be modified by replacing $P_{\text{ad}} \rightarrow (P_{\text{ad}} - P_{\text{BR}})/(1 - P_{\text{ad}}^2)$. At higher applied bias, the corresponding problem can be solved numerically by self-consistently combining
---
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Influence of organisational culture on the implementation of health sector reforms in low- and middle-income countries: a qualitative interpretive review
Rahab Mbau & Lucy Gilson
To cite this article: Rahab Mbau & Lucy Gilson (2018) Influence of organisational culture on the implementation of health sector reforms in low- and middle-income countries: a qualitative interpretive review, Global Health Action, 11:1, 1462579, DOI: 10.1080/16549716.2018.1462579
To link to this article: https://doi.org/10.1080/16549716.2018.1462579
© 2018 The Author(s). Published by Informa UK Limited, trading as Taylor & Francis Group.
Published online: 11 May 2018.
Article views: 14
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Influence of organisational culture on the implementation of health sector reforms in low- and middle-income countries: a qualitative interpretive review
Rahab Mbau and Lucy Gilson
School of Public Health and Family Medicine, University of Cape Town, Cape Town, South Africa; Health Policy and Systems Division, School of Public Health and Family Medicine, University of Cape Town, Cape Town, South Africa; Department of Global Health and Development, Faculty of Public Health and Policy, London School of Hygiene and Tropical Medicine, London, UK
ABSTRACT
Background: Health systems, particularly in low- and middle-income countries, are commonly plagued by poor access, poor performance, inefficient use and inequitable distribution of resources. To improve health system efficiency, equity and effectiveness, the World Development Report of 1993 proposed a first wave of health sector reforms, which has been followed by further waves. Various authors, however, suggest that the early reforms did not lead to the anticipated improvements. They offer, as one plausible explanation for this gap, the limited consideration given to the influence over implementation of the soft-ware aspects of the health system, such as organisational culture – which has not previously been fully investigated.
Objective: To identify, interpret and synthesise existing literature for evidence on organisational culture and how it influences implementation of health sector reforms in low- and middle-income countries.
Methods: We conducted a systematic search of eight databases: PubMed; Africa-Wide Information, Cumulative Index of Nursing and Allied Health Literature (CINAHL), Econlit, PsycINFO, SociINDEX with full text, Emerald and Scopus. Eight papers were identified. We analysed and synthesised these papers using thematic synthesis.
Results: This review indicates the potential influence of dimensions of organisational culture such as power distance, uncertainty avoidance, and in-group and institutional collectivism over the implementation of health sector reforms. This influence is mediated through organisational practices such as communication and feedback, management styles, commitment and participation in decision-making.
Conclusion: This interpretive review highlights the dearth of empirical literature around organisational culture and therefore its findings can only be tentative. There is a need for health policymakers and health system researchers to conduct further analysis of organisational culture and change within the health system.
Background
Health systems, particularly in low- and middle-income countries (LMICs), are commonly plagued by problems such as poor access and performance, as well as inefficient use, and inequitable distribution, of resources [1–3]. Recognising that such problems reflect system-wide deficiencies rather than weaknesses in particular health programmes or areas of service delivery, the World Bank proposed a first wave of ‘health sector reforms’, with the goals of improving health system efficiency, equity and effectiveness, in the World Development Report of 1993 [4]. The reforms emphasised at this time were decentralisation, user fees and social health insurance, pay for performance, public–private partnerships, contracting out of health services, and comprehensive primary health care [1,4–6]. Subsequent waves of similar reforms have been called for under the banner ‘health system strengthening’ [7] and, most recently, Universal Health Coverage [8]. For the most part, the reforms of focus largely address the hardware elements of the health system [9] – that is, the tangible and functional aspects of the system [10] that make up its basic building blocks: service delivery, health care financing, health workforce, leadership and governance, information, and medical products, vaccines and technology [11].
The changes resulting from the mid-1990s reforms were, however, varied [3], with authors such as Blaauw et al. [9] suggesting that the gains achieved were limited. Some authors specifically suggested that challenges resulted from the influence of health system software on reform implementation [9,12,13]. The software
elements of the health system refer to the intangible aspects that govern functions and relationships within the health system such as ideas, values, interests, power and norms [10] as well as organisational culture [9].
Indeed, since the early 2000s, organisational culture has been a key theme of debate in relation to the structural, or hardware, reforms in the health sector within high-income countries such as the USA and the UK. Policymakers and managers in these countries realised that structural reforms on their own cannot lead to the desired changes within the health systems [12–16]. Organisational culture is specifically noted as having the potential to shape the way that such reforms are put into action [12]. Whilst there are numerous definitions of organisational culture, all are based on a view of organisations as social systems characterised by social processes, behaviours and structures [17,18] and all understand culture to be shared social constructs such as beliefs, meanings, values, behaviour and norms [15,19,20]. Within a single organisation there may be several cultures linked to particular subgroups or units, and organisational culture is itself influenced by broader societal factors, including history and political culture [21].
In view of the potential importance of organisational culture as an influence on the implementation of health sector reforms at local level in LMICs, this qualitative synthesis was undertaken to take stock of the current knowledge base, to draw on relevant research, and, if possible, policy implications. In this aim it was in line with other, recent qualitative synthesis work (special issue of Health Policy and Planning 29[3], December 2014). It reviews existing empirical literature from LMICs to identify, interpret and synthesise evidence on organisational culture and its influence on the implementation of such reforms. The core review question is ‘How does organisational culture influence the implementation of health sector reforms in LMICs?’ In this synthesis, organisational culture is conceptualised as a system of values and practices that are socially constructed and shared by actors and influence their relationships, attitudes and behaviour towards changes, and can be manipulated or influenced, at least in part, through managerial strategies to enable achievement of the desired organisational goals. Practices refer to how things are done while values refer to judgements of how things should be done [22]. An organisation refers to a structured and formalised entity made up of a group of people who have come together for a common purpose [23].
**Methods**
This review employed an interpretive qualitative synthesis approach to interpret and synthesise findings from all forms of empirical studies whether qualitative, quantitative or mixed methods. Although founded on the principles of systematic review [24,25], such an approach goes beyond a review of literature to generate new concepts and meanings from synthesis of the collated work [25,26]. These new ideas are, in essence, analytic generalisations of potential relevance in settings beyond those specifically considered in the papers reviewed [27].
**Literature search**
We conducted a systematic electronic database search using key search terms (Figure 1) derived from the
**Organisational Culture OR institutional culture**
AND
health sector reform* OR Health Care Reform* OR Health Polic* OR “health system strengthening interventions” OR universal health coverage OR “user fee removal” OR “user fees” OR “pay for performance” OR “performance based financing” OR health sector strateg* OR “health system reform” OR “health reform” OR decentralization OR decentralisation OR politics OR contracting out OR outsourc* OR public private partnerships
OR comprehensive primary health care
AND
Implement*
AND
Developing Countr* OR Africa OR Asia OR Latin America OR Caribbean OR Pacific OR Middle East OR East Europe [30] OR transitional countr* OR low income countr* OR middle income countr* OR LMIC OR LMICs
**Figure 1.** Key search terms.
main concepts in the review question and strengthened by broader literature as well as consultations and inputs from LG (co-author), an experienced health policy and health systems researcher. The development of the search string and the subsequent literature search involved an iterative process that was done under the skilful assistance of a health science librarian from the University of Cape Town. We used eight databases that we considered relevant to the review due to their focus and accessibility to the primary reviewer. These databases included: PubMed, Africa-Wide Information, Cumulative Index of Nursing and Allied Health Literature (CINAHL), Econlit, PsycINFO, SocINDEX with full text, Emerald and Scopus. Multiple databases were included to minimise selection bias [28]. The initial search was conducted in PubMed and then translated to the other databases according to their appropriate controlled vocabulary and standardised terms of indexing [28]. To be as comprehensive as possible, the initial search in PubMed was carried out using country-specific names according to the 2012 LMICs filters developed by the Norwegian satellite of the Cochrane Effective Practice and Organisation of Care Group [29]. A comprehensive account of the literature search strategy used for each database and the dates of the last search are provided in the text in Supplementary material 1.
**Inclusion criteria**
We identified potentially relevant articles by first removing the articles that were not related to the health sector and those that had a high-income country focus. We downloaded the remaining papers into a data reference manager, RefWorks, for easier data management and removal of duplicates [28]. We then removed the duplicates and reviewed the titles and abstracts of the remaining articles against the inclusion criteria. We only included articles that were published in English, articles with full access, articles with a focus on LMICs, articles whose titles and abstracts contained the keywords and were relevant to the review question, articles published between 1 January 2000 and 31 December 2015, and articles with an empirical focus including qualitative, quantitative and mixed methods. The year 2000 was chosen as the start date for the search because it was the time when organisational culture came to be acknowledged as a potential influence over health sector reform implementation [12].
**Quality appraisal**
We included all the articles that met the inclusion criteria in this review irrespective of their quality. This approach recognised the limited number of articles retrieved and that, following the Cochrane Qualitative Research Methods Group [31], the value of each study may only become apparent in the synthesis rather than at the point of appraisal.
**Extraction and synthesis of data**
We extracted data from all the sections of the articles given that different reporting styles across academic disciplines means that relevant data may be presented in sections other than the findings section alone [32]. We used the thematic synthesis approach to analyse and synthesise the data [33]. RM initially read each of the articles line by line and identified and coded the texts, quotes and authorial judgments. Following Gilson et al. [34], authorial judgements were included as data because they offered more insight into the data presented in the studies. In an inductive process, we merged similar codes into descriptive themes related to values and practices and, where differences were found, these were resolved by consensus. These themes are presented in the Findings section. We then used the House et al. [22] dimensions of organisational culture (Table 1) to deductively interpret and synthesise the findings of the review. We selected this conceptual framework over others, such as Schein’s model [19], the culture web framework [35], Hofstede’s dimensions of organisational culture [36] and the competing values framework [21], for two reasons: (1) it had been piloted and tested across different sectors (telecommunication, finance and food processing sectors) in both higher- and lower-income countries, suggesting it was suitable for cross-cultural analysis [22]; (2) it both builds on the dimensions of organisational culture described by others scholars and reflects broader societal influences over its dimensions [22].
**Table 1. House et al. dimensions of organisational culture.**
| Dimension | Definition |
|--------------------|-----------------------------------------------------------------------------|
| Power distance | Extent of distribution and concentration of power across the organisation or society |
| Institutional collectivism | Extent to which the organisation or society encourages and rewards communal action and sharing of resources |
| In-group collectivism | Level of pride, satisfaction and loyalty shown by members towards their organisation or society |
| Uncertainty avoidance | Degree to which the members of an organisation or society avoid unknown circumstances or uncertainty by depending on accepted practices, rules or procedures |
| Gender egalitarianism | Extent to which the organisation or society minimises differences in roles and opportunities based on gender. |
| Aggressiveness | Extent to which members of an organisation or society are competitive and confrontational with each other |
| Humane orientation | Extent to which an organisation or society encourages and rewards altruistic behaviour |
| Future orientation | Extent to which organisations or societies develop plans and strategies for future |
| Performance orientation | Extent to which the organisation or society encourages excellence and awards improvement |
Results
The initial literature search generated 7650 articles. The majority of the articles were excluded because they were unrelated to the health sector and they had a focus in high-income countries (HICs). One hundred and seventeen articles were thought to be potentially relevant. Following the removal of duplicates, 102 articles remained and their titles and abstracts were screened against the inclusion criteria. Only seven articles were retrieved for full text reading with one additional article retrieved from searching the reference lists of these articles, generating a total of eight articles. This process is outlined in Figure 2 with reasons for article exclusion indicated at each stage.
Characteristics of the literature
The characteristics of the articles included in the review vary in terms of type of health sector reform considered, country and organisations of focus and methodology used, as outlined in Table 2. The organisations of focus in most of the papers were public health sector organisations (n = 7) involving either the public district health system or the national ministry of health.
Description of findings
The following section reports on the practices and values that were inductively identified from the retrieved articles as influencing the implementation of health sector reforms primarily within public health sector settings. These practices and values were identified from the interview reports, survey responses and observations (e.g. of district meetings) reported in the papers, as well as authorial judgements. These practices
Three of the six articles on decentralisation have the same first author and were carried out in Ghana but in different districts [37–39]. All articles offer insights into the influence of organisational culture over the implementation of the health sector reforms, with the articles on decentralisation offering more insight not only because they constituted the majority of the articles (n = 6), but also because they used case studies and qualitative methods to provide a rich description of the implementation experience and context. However, only one of the eight articles included in the review explicitly set out to study organisational culture and this study used a quantitative survey to assess organisational culture across a range of hospitals [40]. A full list and brief overview of these articles is provided in a table in Supplementary material 2.
Figure 2. Search flow diagram.
include communication, management styles, participation in decision-making and commitment. They do not, however, occur in isolation and interactions, and overlaps can be seen across them. Management styles and participation in decision-making showed marked overlap and are therefore presented under one finding. This section concludes with an interpretive synthesis and summary of the findings.
**Communication practices**
The majority of papers demonstrated weaknesses in communication practices as an influence over health reform implementation mostly, but not exclusively, in public health sector organisations [37–41]. These weaknesses convey implicit and explicit values judgements of how communication should be carried out as reported by participants or as interpreted and judged by the authors.
**Awareness, clarity and adequacy of information**
In Ghana, some public health workers and external stakeholders in the district health system were not aware of the decentralisation policy and its aims which undermined the support needed to implement the reform:
‘I am not aware of the decentralisation programme … I don’t also know the aims for decentralisation’ [38].
Public health workers and other stakeholders also reported receiving little or no information on major reforms from public district health system managers. This further undermined health workers’ knowledge of the reform and its objectives and slowed the implementation of the reform [37]. Interestingly, senior health managers held the opinion that members of the staff should only receive information that was relevant to them:
‘Staff are not supposed to be given all the information, only information that concerns them or what they need to know is made available to them’ [37].
The lack of awareness and inadequate information resulted in dysfunctional interactions between the district health team, public health workers and external stakeholders [37–39]. It also led to an attachment to the old values and systems of doing things which limited the implementation of the decentralisation policy in Ghana:
[W]eak communication and information sharing contributed to the limited understanding of reform. This constrained reform implementation because, instead of opening up to the challenges and opportunities brought about by the reform, health workforces continued to hold onto the old value system and its style of service management in an era of change [37].
In Nigeria, public health workers and those from one mission hospital reported that information was not openly shared in their hospitals. This was perceived as an area of weakness that required strengthening in order to support the implementation of the comprehensive health sector reform [40].
**Timeliness of information and feedback**
Public health workers and district stakeholders across Ghana’s district health system reported that district health managers did not provide information in time:
The only problem was that mostly the district assembly received the information late [37].
We only hear of the programmes either on radio or when the programme is finished [37].
Public health workers also complained about non-response and delays in receiving feedback from their managers. In contrast, information sharing and provision of feedback among senior public health managers was perceived to occur frequently:
‘District health directors and managers communicate and share relevant information with senior managers, and they do so frequently; and, they do regular follow-up for feedback, either by telephone or written note’ [37].
According to Sakyi [37], delays and lack of feedback arose from heavy dependence on the top-down style of communication which led to centralisation of information among the public health managers. This prevented public health workers and external stakeholders from learning about the reform process which subsequently constrained the implementation of the decentralisation policy.
| Table 2. Characteristics of the literature. |
|---------------------------------------------|
| Type of health sector reform | Country and organisations of focus | Methodology |
| Decentralisation (n = 6) | Brazil (n = 2); Public sector district health system | Ethnographic studies (n = 2) |
| Comprehensive health sector reform to strengthen primary health care (n = 1) | Uganda (n = 1); National Ministry of Health | Case study (n = 1) |
| Public-private partnerships between the State and Civil Society Organisations (n = 1) | Nigeria: 4 hospitals; Three public sector hospitals and one not-for-profit mission hospital | Quantitative study |
| | India, Partnership between two civil society organisations and the public state | Multi-site ethnographic studies |
**Effectiveness of forms of communication**
In Ghana, reports by public health workers and district stakeholders indicate that the usual forms of government communication, such as circulars, letters, memos and reports, were not being used effectively to share information on management decisions which limited their knowledge of the decentralisation policies [37,38]:
‘Although we know that there is a decentralised policy in the system, we have not officially been informed and had not got any written document about it so we are not very clear about its content’ [38].
In Uganda, the use of circulars and written communication, as opposed to face-to-face communication, were seen as the cause of poor communication between the Ministry of Health and the district health system. This resulted in poor support for the restructuring process required for the decentralisation policies at the district level.
‘It seems obvious that in Uganda, circulars and written communication in general may not suffice as carrying contexts. Important processes such as the critical face-to-face relationship, the “co-presence” in space and time, need to be directly and clearly established’ [41].
In India, the government and one Civil Society Organisation (CSO) used posters to convey messages of equal participation in decision-making as part of decentralising health care planning to the local level. However, the effectiveness of this communication was undermined by the broader social and gender hierarchies that limited participation in these councils [42].
**Management styles**
Three kinds of management styles were described in the reviewed articles: authoritarian, participative and consultative [37–39,41–44]. These management styles had different influences on the implementation of health sector reforms, as seen below.
**Authoritarian management**
Authoritarian management was often characterised by hierarchy and centralisation of power and communication. In Ghana, public sector hierarchical structures were seen as barriers to the decentralisation policy because they negatively affected the attitude, behaviour and interactions of different actors in the district health system:
‘The way the structures are put up here does not help; the policy is not well practised here because it is a one person’s administration’ [38].
Atkinson et al. [44] examined public health system decentralisation in three districts (one rural, one urban and one metropolitan) in Brazil. They observed that decision-making power in the rural district was centralised to the district prefect – a political figure – who never consulted health staff or members of the health council. As a result, the health secretariat and staff lacked autonomy and voice in decision-making, which led to the poor implementation of the reform policy [44].
In India, members of the Civil Society Organisations (CSOs) who had partnered with the State of India to promote rural health reported that the State dominated the partnership. This dominance highlighted the bureaucratic and hierarchical nature of the government, which led to asymmetry in the State–CSOs partnership with varying forms of conflict that challenged and threatened the sustainability of the State–CSOs partnerships. The dominance also stifled the autonomy of the CSOs and limited the effectiveness of the CSO–government partnership [42]:
‘When we work with you we have lost the liberty. Because we think according to you, we plan according to you, we get our salary according to you. So that is the reason why we are not doing well’ [42].
Perceptions of loss of power by some of the actors at the regional and central public administration in Ghana were judged as barriers to the implementation of the decentralisation policy [38]. In Uganda, the paternalistic attitude of Ministry of Health staff towards the district health system and the attachment to the traditional way of managing programmes within the Ministry of Health – in the face of the restructuring process and decentralisation – were seen as ‘bureaucratic resistance to decentralisation’ [41]. This resulted in poor ownership of the restructuring and decentralisation policies by public officials at the district level.
Authoritarian management was also inferred from reports of hierarchical reporting lines among actors in the health system. For example, managers in Ghana’s Sekyere district health system were required to seek approval from the regional administration prior to making any decisions:
In the event of any needed change, health directors had to seek prior permission and must wait until approval is granted from regional or headquarters before any action could be taken [39].
‘The top would have to come in before we are able to take decisions’ [38].
Reporting lines between Ghana’s district health system and the regional departments formed barriers to decision-making and implementation of the decentralisation policy. In addition, conflict over reporting lines between the district assembly officials and district health officials in Ghana’s Sekyere district
undermined cooperation and collaboration, which further weakened implementation of the decentralisation policy in this district [39].
**Participative management**
In participative management, public health managers encouraged the participation of their own health workers and external stakeholders in the reform process. In Brazil’s metropolitan district, the district health secretary’s style of management was participative because the secretary encouraged the participation of health workers in decision-making. However, the secretary did not engage the district health council because of the assumption that the district health council (made up of both health workers and lay members of the community) was a bureaucratic intervention. As a result, the council no longer convened, which slowed the implementation of the decentralisation policy [44]. In Nigeria, hospital managers encouraged team work and participation of the staff in planning for the health sector reforms. This style of management was seen as a supportive element of culture for the reform process [40]. On the other hand, public health managers in Ghana did not encourage external stakeholder (district assemblies, non-governmental organisations [NGOs] and private providers) participation in planning and decision-making. This undermined the stakeholders’ knowledge of the ongoing decentralisation reforms and weakened the implementation of the policy [37,39]. Public health workers and external stakeholders in Ghana’s district health system considered participation in decision-making essential for the successful implementation of the decentralisation policy [37–39].
**Consultative management**
Interview reports from external stakeholders in Ghana indicate that it was an uncommon practice for the district health managers to consult health workers and external stakeholders on management issues including major reforms:
‘The district management does not give information, or consult us about any health management issues or major health decision’ [37].
The poor consultation and involvement of stakeholders resulted in their exclusion from the decentralisation reform process, which weakened the support needed for the implementation of the decentralisation reform [37]:
‘Professional associations were not informed or effectively absorbed into the health reform programme’ [37].
In Brazil’s urban district health system, the district health secretary employed a consultative style of management. As a result, the decentralisation policy was judged as better implemented in the urban district than in the rural and metropolitan districts [44].
**Commitment**
Commitment of district health managers to the districts and to the reforms was judged as an important aspect of the social organisation that influenced the implementation of the decentralisation policy in Brazil [43,44]. For instance, health managers in Brazil’s urban district health system were observed to be the most committed to the reform objectives in terms of the language used and adherence to the procedures outlined in the reforms when compared to the managers and health workers in the rural and metropolitan districts. Consequently, decentralisation policy was better implemented in the urban district than in the metropolitan and rural districts [43,44]. In Ghana’s Nkwanta district, health managers reported poor commitment to and lack of ownership of the decentralisation policy because they felt that the headquarters largely imposed the reforms on them. Poor commitment and lack of ownership created barriers to the decentralisation policy [39].
In Nigeria, inferences on commitment were made at both the hospital level and the managers’ level. At hospital level, commitment was inferred from the health workers’ report that both public and mission hospital activities and images were consistent with the objectives of the reforms. These hospitals were also seen to have the capacity to innovate towards the reforms. At managerial level, health managers from both public and mission hospitals were committed to representing the interests of the hospitals to external stakeholders and to steering the organisation towards achieving the objectives of the health sector reforms. These aspects of organisational culture were strong enough to support the implementation of the health sector reforms [40].
**Influence of the wider social and political context**
The influence of political culture on the implementation of the decentralisation policy was judged as particularly marked in Brazil’s rural district compared to Brazil’s urban and metropolitan districts [44] such that the decentralisation reform had little impact on increasing local voice and autonomy [43,44]. Authorial observations of Brazil’s rural district showed that the district prefect – a political figure – retained all the decision-making power, thereby disempowering the district health secretary and limiting the participation of the health workers in decision-making. In addition, authorial judgments indicate that the disposition and behaviour of the district health secretary towards the health sector
reforms in Brazil’s district health systems mirrored what was valued by the political leaders including the district prefect. In this regard, the prevailing political culture in Brazil’s rural district hindered the implementation of the decentralisation [43,44]. According to Atkinson et al. [44], political culture and social organisation had the potential to negatively influence the implementation of the decentralisation policy across Brazil:
‘The extent to which aspects of social organisation and political culture enable or hinder implementation indicates a mixed influence but one which is sufficiently negative.’
In Ghana’s Nkwanta district, political interference by those in authority formed a barrier to the implementation of the decentralisation policy [38], while in India efforts by the Indian government and the CSOs to increase local participation in decision-making in the village health councils as part of the decentralisation of health planning were limited by the wider social and gender hierarchies [42].
**Synthesis of the findings**
The study of culture within organisations is largely interpretive and founded on the notion that the behaviour and actions of the members are influenced by rules, orders, incentives and ‘common frames of reference’ [45]. In the previous section, we presented the range of practices and values inductively identified from the papers that point to the influence of public sector organisational culture over reform implementation. In this section we seek to deepen understanding of these influences through synthesis and further interpretation, drawing on four of the organisational cultural dimensions proposed by House et al. [22]: power distance, in-group collectivism, uncertainty avoidance and institutional collectivism. These four dimensions are those most clearly visible in the identified organisational practices. As summarised in Figure 3, moreover, the organisational practices identified inductively seem to mediate the influence of these particular and interacting dimensions of organisational culture over the implementation of health system reforms, and all are themselves influenced by the broader sociopolitical context.
*Power distance* is characterised by varying concentrations and distributions of power across the health systems, with varying impacts on organisational practices and implementation of reforms. For instance, the presence of a large power distance in the district health system – characterised by centralisation of power to the district managers – not only disempowered the junior managers, but also limited the autonomy, local voice and participation in decision-making by health workers and external stakeholders as seen across Brazil’s and Ghana’s case studies. This weakened the implementation of the decentralisation policy in both countries [37–39,43,44]. This large power distance also negatively affected the commitment of managers and health workers in Brazil’s rural district [43,44] and in Ghana’s Sekyere district [39], which further weakened the implementation of the decentralisation policy. In Ghana, the presence of a large power distance led to the concentration of communication among the senior public health managers and to the dependence on top-down style of
**Figure 3.** Framework of the relationship between dimensions of organisational culture, organisational practices and implementation of health sector reforms. Adapted from Jaakko et al. [46]. The boundary of the organisation is represented by a dotted line to show the influence of the wider political and social context.
communication. This resulted in poor communication and feedback practices between the managers and health workers, which led to poor implementation of the decentralisation reform at the district level [37–39]. In India, the large power distance between the government and the CSOs limited the autonomy of the CSOs and threatened the sustainability of the partnership [42]. On the other hand, the presence of a small power distance was associated with participative and consultative styles of management as well as increased participation of health workers and stakeholders in decision-making, as seen in Brazil’s urban district, leading to better implementation of the reform compared to the rural and metropolitan districts [44]. The above case studies therefore suggest that the extent of power distance within the health system can shape the implementation of the reforms through its influence on management styles, participation in decision-making, communication and commitment.
High institutional collectivism can be inferred from local health systems that valued team work and collective action from both the members of the organisation and the external stakeholders. For instance, Brazil’s urban health system valued collective consultation and participation of health workers and stakeholders in decision-making. The district health secretary consulted and engaged the stakeholders in regular health council meetings. This created an enabling environment for the implementation of the decentralisation policy, which proceeded with fewer challenges compared to the metropolitan and rural districts [43,44]. However, local health systems with low institutional collectivism did not encourage collective action in decision-making for the reform process from either their members or external stakeholders, as seen in Brazil’s rural district [44], in Ghana’s district health system [37–39] and in Uganda [41]. Low collectivism, therefore, undermined both intra-organisational and inter-organisational support for the reforms, which resulted in the poor implementation of the health sector reforms in these studies. It can therefore be inferred and interpreted from these studies that the extent to which the organisation values institutional collectivism will influence the management style as well as level of health worker or stakeholder participation in decision-making.
High in-group collectivism was expressed by managers in Brazil’s urban district who showed more commitment to the district and to the decentralisation reform than the managers in the rural and metropolitan district. This commitment was judged to lead to better implementation of the reform in the urban district [43,44]. High in-group collectivism can also be inferred in the Nigerian study, where health workers expressed confidence in the capacity of their managers to steer the organisation towards achieving the reform objectives by aligning organisational activities to the reform objectives, which supported the reform process [40].
Uncertainty avoidance was inferred from Ghana’s district health system where, despite health workers’ perception of needed change, no decisions could be made without the approval of senior managers. The heavy dependence on rules and approval to guide decision-making despite needed change is suggestive of high uncertainty avoidance. Unfortunately, this slowed decision-making for the implementation of the reforms [38]. In Uganda, the attachment to the traditional practice of managing vertical programmes by Ministry of Health officials in the face of decentralisation and restructuring underscores organisational rigidity to change and hence high uncertainty avoidance, which also limited the implementation of these policies [41]. On the other hand, an organisation’s capacity to innovate, as reported by the health workers in Nigeria, is suggestive of low uncertainty avoidance, which was seen to support implementation of the reforms [40].
Beyond these dimensions of organisational culture, the reviewed literature also provided evidence of the influence of the wider social and political culture on organisational practices and subsequently on the implementation of the health sector reforms. This influence was particularly felt in Brazil’s rural district health system where the prevailing political culture and attitudes of political leaders influenced the management styles and extent of participation of health managers and health workers in decision-making [43,44]. Political culture in Brazil and political interference in Ghana’s Nkwanta district [38] limited the implementation of the decentralisation policy. In India, social and gender hierarchies limited participation in decision-making, which undermined the efforts to decentralise health planning under the State–CSOs partnership [42].
Discussion
There has been growing interest in the notion of organisational culture and its potential influence in the health sector in HICs. However, organisational culture has been little examined in health system studies in LMICs. This paper, therefore, presents a review of empirical literature with two aims: (a) to identify and synthesise findings about organisational culture and its influence on the implementation of health sector reforms in LMICs, and (b) to provide analytic generalisations that can inform health policy and systems research. The retrieval of only a few papers can be seen as a limit of this synthesis; however, analytic generalisation is possible and it provides the following insights.
Using thematic analysis, this review identified four organisational practices that influenced the implementation of health sector reforms in public health sector organisations across different country settings: communication, management styles, participation in decision-making, and commitment. To deepen understanding of these organisational practices as dimensions of organisational culture, they were further synthesised and interpreted using the dimensions of power distance, in-group collectivism, institutional collectivism and uncertainty avoidance [22].
Articulating the nature of the influence of organisational culture on the implementation of health sector reforms was largely based on judgements and new insights beyond those of the primary studies, in keeping with the aim of an interpretive synthesis [25]. The interpretations arrived at in this review suggest that: (a) power distance impacts on communication, management styles, commitment and participation in decision-making; (b) institutional collectivism impacts on management practices and participation in decision-making; (c) uncertainty avoidance impacts on decision-making and commitment; and (d) in-group collectivism impacts on commitment, as summarised in Figure 3 above.
The multiple linkages between these cultural dimensions and organisational practices highlight the complexity of the notion of culture within organisations. Nevertheless, the interpretations arrived at in this synthesis can be supported by wider literature. Power distance is expected in any society or organisation, with some showing more inequality than others [47]. As seen in this review, power distance varied across the district health systems in different countries, as seen across the three district health systems in Brazil. The influence of power distance on the style of management and participation in decision-making is not peculiar to the health sector. A large multi-country study on the influence of culture on managers’ behaviour across different continents, including Africa, showed that in a hierarchical culture managers tended to rely on rules, procedures and their superiors during decision-making and less on their subordinates [48]. Similarly, the influence of power distance and collectivism on organisational practices appeared to overlap, leading to different forms of management styles (authoritarian, consultative or participatory) and participation in decision-making. Interestingly, both power distance and collectivism have also been shown to correlate in various country settings, leading to various forms of participatory decision-making depending on the extent to which both cultural dimensions are valued and practised within the organisation [49].
The effect of the broader social and political culture on organisational culture and implementation of health sector reforms is supported by Gilson and Erasmus [50], who recognised that organisations are embedded within the wider society and can therefore be influenced by societal values.
This review has the following implications for health policy and systems research. First, given the dearth of literature, it underscores the need for more empirical studies on organisational culture and its influence on reform implementation in the health sector. It is possible that these studies may generate new insights on how different dimensions of organisational culture, values and practices influence changes in the health sector which may be useful for health system development. As highlighted in Figure 3, such understanding must also consider the influence of the broader sociopolitical context. Second, the framework presented in Figure 3 provides a useful starting point for future researchers to test and build the knowledge base on organisational culture and reforms in the health sector. This framework may also support further cross-paper or cross-context analysis in interpretive synthesis work and qualitative empirical research. Third, future researchers can also build on this interpretive synthesis – for example, by considering unpublished literature and literature from HICs, as well as by expanding and translating the literature search strategy to other data bases accessible to them. This would address a limitation of this review which excluded articles published in languages other than English and unpublished literature. Lastly, the broad and inclusive scope of organisational culture makes its interpretation difficult. We therefore recommend that future researchers work in teams when studying and analysing organisational culture, in order to generate a richer analysis drawing on the different perspectives and experiences of the research team.
With regard to the implications for health managers and policymakers, the findings of this review suggest the value of identifying dimensions of organisational culture which can influence the implementation of health sector reforms indirectly by influencing organisational practices. Due to the limited number of articles reviewed, no conclusions can be made on which dimensions of organisational culture provide the most influence on the implementation of health sector reforms – although it can be inferred that power distance was an important influence on organisational practices. Understanding culture can, then, facilitate the development and negotiation of ‘mutually agreeable approaches to conflict resolution, problem solving, decision making, and management practices’ [22], all of which characterised the implementation of the reforms across the different settings in the reviewed literature. It is important that improvement strategies are adapted to the local context [47] as what works in one context may not necessarily work in another. The importance of organisational culture in the health sector cannot be overemphasised.
Conclusion
This interpretive synthesis suggests the potential influence of dimensions of organisational culture such as power distance, in-group collectivism, institutional collectivism and uncertainty avoidance on the implementation of health sector reforms. Their influence appears to be mediated through organisational practices such as management styles, participation in decision-making, communication and commitment. However, the analytic generalisations drawn from this synthesis are limited by the few papers retrieved. More empirical research on organisational culture in LMIC health systems is needed in order to deepen understanding of its influence on health reform implementation and health system development.
Acknowledgments
The authors express their sincere appreciation to Tamzyn Suliaman of the Health Science Library at the University of Cape Town who helped with the development of the literature search string and navigation of the data bases used in this review.
Author contributions
LG conceptualised the study. RM conducted the literature search and performed the initial analysis. Both authors contributed to further analysis. RM wrote the first draft of the manuscript. LG provided review comments. Both authors contributed to subsequent drafts. Both authors approved the final draft of the journal manuscript.
Disclosure statement
No potential conflict of interest was reported by the authors.
Ethics and consent
Ethical approval for this review was not required because the authors used publicly available literature.
Funding information
None.
Paper context
The World Development Report of 1993 led to the introduction of health sector reforms with the aim of improving efficiency, effectiveness and responsiveness of health systems globally. The implementation of these reforms has, however, resulted in limited improvement. One plausible explanation for this is the inattention to organisational culture, which is thought to be more likely to impede change. This review uses existing empirical literature to explore evidence on organisational culture and its influence on the implementation of health sector reforms in low- and middle-income countries.
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Clinical Characteristics and Prognostic Analysis of Pregnancy-Related Acute Kidney Injury
Minjie Hu
XinHua Hospital Affiliated to Shanghai Jiaotong University School of Medicine
Haidong Huang
XinHua Hospital Affiliated to Shanghai Jiaotong University School of Medicine
Xuantong Dai
XinHua Hospital Affiliated to Shanghai Jiaotong University School of Medicine
Fujun Lin
XinHua Hospital Affiliated to Shanghai Jiaotong University School of Medicine
Junfeng Shi
XinHua Hospital Affiliated to Shanghai Jiaotong University School of Medicine
Wei Lu (✉ [email protected])
XinHua Hospital Affiliated to Shanghai Jiaotong University School of Medicine
Research Article
Keywords: pregnancy-related acute kidney injury, continuous renal replacement therapy, maternal and infant outcomes
Posted Date: November 30th, 2021
DOI: https://doi.org/10.21203/rs.3.rs-1074697/v1
License: This work is licensed under a Creative Commons Attribution 4.0 International License. Read Full License
Abstract
Objective: To investigate the clinical characteristics and prognosis of pregnancy-related acute kidney injury (PR-AKI) and provide a basis for improving maternal and infant outcomes.
Methods: Seventy pregnant women admitted to the surgical intensive care unit of Xinhua Hospital affiliated to Shanghai Jiaotong University School of Medicine from January 2010 to December 2020 were included; 31 were screened out according to KDIGO-AKI criteria. We retrospectively analyzed their clinical characteristics and prognosis and analyzed risk factors for different pregnancy outcomes with logistic regression analysis.
Results: A total of 31 PR-AKI patients were enrolled. The mean age of onset was 30.08±0.63 years, and the mean gestational age was 33.02±7.64 weeks. Six cases (19.45%) were in stage 1, six cases (19.35%) were in stage 2, and 19 cases (61.29%) were in stage 3. The continuous renal replacement therapy (CRRT) group comprised 13 cases (41.94%): one (7.69%) in stage 1, one (7.69%) in stage 2, and 11 (84.62%) in stage 3. The non-CRRT group comprised 18 cases (58.06%): five (27.78%) in stage 1, five (27.78%) in stage 2, and eight (44.44%) in stage 3. The mean time of commencing renal replacement therapy was 2.08±1.26 days after admission, and the serum creatinine (SCr) level at the beginning of treatment was 352.68±196.58 μmol/L. Renal function recovered completely in 18 cases (58.06%), comprising four (22.22%) in the CRRT group and 14 (77.78%) in the non-CRRT group, and three cases of partial renal function recovery occurred in the CRRT group. Eventually, seven patients (22.58%) died, of whom four (57.14%) were in the non-CRRT group, and all were in stage 3. The causes of death were postpartum hemorrhage, septic shock, and acute fatty liver during pregnancy. Three patients (42.86%) died in the non-CRRT group: two in stage 3 and one case in stage 1. The causes of death were severe preeclampsia and acute fatty liver during pregnancy. Multi-factor logistic regression analysis showed that gestational weeks (OR=0.456, P=0.023), platelet count (OR=0.989, P=0.02), hemoglobin (OR=1.017, P=0.022), and uric acid (OR=1.017, P=0.022) were associated risk factors for maternal adverse pregnancy outcomes of PR-AKI (P<0.05).
Conclusions: The incidence of PR-AKI is high, the outcomes of maternal renal function are better, and the proportion of adverse fetal outcomes is higher. CRRT can effectively improve the prognosis of patients with PR-AKI, stabilize the internal environment, and affect hemodynamics slightly. It is currently one of the main ways to treat severe PR-AKI. Maternal and infant outcomes are related to the severity of PR-AKI.
Introduction
Acute kidney injury (AKI) is a critical pregnancy complication needing particular attention. It seriously affects the life and health of the pregnant woman and the fetus. In recent years, due to increased access to maternal and infant healthcare, the incidence of pregnancy-related AKI (PR-AKI) has decreased significantly. Research has reported that the incidence of PR-AKI among pregnant women is around 0.005% in developed countries [1] and 0.81%–11.5% in developing countries [2–6]. However, little
epidemiological data exists on PR-AKI in China. A multi-center study retrospectively analyzed all pregnant women with PR-AKI in 25 hospitals in China from 2013 to 2015. It found that the incidence of PR-AKI was 7.3% [7], indicating that AKI is a common and serious pregnancy complication in China. It not only increases the mortality of pregnant women but also increases the mortality of perinatal infants by 3.4 times [8]. Therefore, early and reasonable diagnosis and treatment of PR-AKI are related to the safety of women and fetuses. Continuous renal replacement therapy (CRRT) has played an essential role in treating AKI, including stabilizing hemodynamics and the internal environment [9], and is the primary treatment for critically ill pregnant women with PR-AKI. According to the KDIGO-AKI criteria, 31 patients with PR-AKI were admitted to the surgical intensive care unit (SICU) of our hospital from January 2010 to December 2020. The etiology of PR-AKI, maternal and infant prognosis, CRRT efficacy, and analysis of risk factors for adverse pregnancy outcomes were retrospectively analyzed to improve awareness of PR-AKI, highlight early diagnosis and treatment, reduce mortality, and improve maternal and infant outcomes.
Materials And Methods
Subjects
Clinical data were collected and analyzed of 31 pregnant women admitted to Xinhua Hospital affiliated with the School of Medicine of Shanghai Jiaotong University from January 2010 to December 2020. The average age was 30.08±0.63 years. Six patients were in the second trimester, with an average gestational age of 23.67±5.00 weeks; 17 patients were in the third trimester, with an average gestational age of 34.38±3.00 weeks; patients cases were in the puerperium, with an average gestational age of 36.72±4.46 weeks. The etiology of PR-AKI was acute fatty liver of pregnancy (AFLP) in eight cases (25.8%); preeclampsia or eclampsia (PE/E) in seven cases (22.6%); infectious or hemorrhagic shock in five cases (16.1%); chronic kidney disease (CKD) in three cases (9.7%); postpartum hemorrhage (PPH), pregnancy with chronic high blood pressure, and other unknown reasons in two cases each (6.4%); and pregnancy complicated with severe infections and ANCA-associated vasculitis in one case each (3.23%). The patients were divided into 13 who received CRRT and 18 who did not. The KDIGO staging criteria released in March 2012 were used to stage PR-AKI [10]. According to the onset time of AKI, the patients were divided into three groups: AKI in the second trimester, AKI in the third trimester, and AKI in the puerperium. The characteristics of the three groups of patients are shown in Table 1.
Related definitions
The definition of AKI followed KDIGO guidelines [10]. Severe AKI was defined as patients receiving renal replacement therapy [2]. PR-AKI was defined as a rapid decline in renal function and accumulation of metabolic waste during pregnancy [11]. CKD was defined following K/DOQI guidelines [12]. Acute exacerbation of CKD (AKI on CKD or A/C) was defined as a reduction in the patient’s renal function by 50% from the original level in the short term due to various causes [13]. The KDIGO-AKI staging criteria [10] were used to stage the patients.
Prognostic evaluation
**CRRT curative effect:** (1) Effective: recovery of renal function, delivery of live baby, improvement and discharge.
(2) Ineffective: Renal replacement therapy still needed after discharge; death or treatment abandonment.
**Recovery of renal function:** (1) Complete recovery: serum creatinine (SCr) and urine output return to normal range.
(2) Partial recovery: SCr or urine output not fully recovered to normal levels, but renal replacement therapy not required after assessment.
(3) No recovery: SCr not returned to normal or continuing to rise, urine output not returned to normal range, and renal replacement therapy needing to be continued.
**Pregnancy outcomes:** (1) Good: smooth vaginal delivery or cesarean section, good fetal development, full-term delivery, birth weight $\geq 2500 \text{ g}$, Apgar score 1 minute $\geq 8$ points.
(2) Poor: mainly including stillbirth, neonatal death, miscarriage, premature delivery, neonatal asphyxia, neonatal growth restriction, neonatal deformity, precious baby, fetal distress, placental abruption, premature rupture of membranes, birth weight $<2500 \text{ g}$, Apgar score 1 minute $<8$ points.
**Treatments**
**Conservative treatment:** The patient’s condition was evaluated, and the causal treatment was given according to KDIGO-AKI criteria, supplemented by symptomatic support treatment.
**CRRT treatment:** According to the disease severity, 13 patients were transferred to the ICU for CRRT treatment, using CVVH and CVVHDF modes. We adjusted time and dosage according to the condition. The type and dosage of anticoagulants were determined according to the state of the patients.
**Observation indicators:** SCr measured before admission was taken as the baseline value for AKI staging. (1) Basic information: age, gestational age, pregnancy number, delivery number, prenatal examination, hospitalization days. (2) Laboratory examination: white blood cell count (WBC), neutrophil %, neutrophil/lymphocyte % (NLR), platelet count (PLT), hemoglobin (HB), SCr, blood urea nitrogen (BUN), alanine aminotransferase (ALT), aspartate transaminase (AST), uric acid, albumin (ALB), Na$^+$, K$^+$, HCO$_3^-$, lactic acid, vital signs (blood pressure, heart rate, respiration, blood oxygen saturation) were measured every 1 hour during CRRT treatment. (3) Maternal and infant outcomes.
**Data analysis**
SPSS 23.0 software was used for statistical analysis. Normally distributed measurement data is represented by the mean ± standard deviation, and comparison between groups used the t-test. Non-
normal distribution measurement data is represented by the median and interquartile range, and comparison between groups used the Wilcoxon rank-sum test. Count data used the $\chi^2$ test. Single-factor logistic regression analysis was used for risk factor analysis to screen related factors. The variables with significant differences in single-factor analysis were analyzed by stepwise multivariate logistic regression analysis. P<0.05 was considered statistically significant, and P<0.01 was considered statistically very significant.
Table 1 Basic information of 31 patients with PR-AKI
# Results
## Maternal outcomes
| | All patients n=31 | Second trimester n=6 | Third trimester n=17 | Puerperium n=8 |
|-----------------------|-------------------|----------------------|----------------------|---------------|
| **Age (years)** | 29.16±4.97 | 31.33±7.94 | 27.41±3.78 | 31.25±3.45 |
| **Gestational age (weeks)** | 32.91±5.98 | 23.67±5.00 | 34.38±3.00 | 36.72±4.46 |
| **Cesarean section (%)** | 26 (83.87) | 6 (23.08) | 16 (73.08) | 5 (19.23) |
| **Primipara (%)** | 18 (58.06) | 4 (22.22) | 10 (55.56) | 4 (22.22) |
| **Twin pregnancy (%)** | 5 (16.13) | 0 | 4 (80.00) | 1 (20.00) |
| **Number of pregnancies** | 1.94±1.24 | 2.50±1.87 | 1.76±1.03 | 1.88±1.13 |
| **Number of deliveries** | 1.23±0.56 | 1.33±0.52 | 1.24±0.66 | 1.13±0.35 |
| **Termination weeks** | | | | |
| ≥37 weeks (%) | 11 (35.48) | 0 | 5 (45.45) | 6 (54.55) |
| 28 to <37 weeks (%) | 14 (45.16) | 1 (7.14) | 11 (78.57) | 2 (14.29) |
| 12 to <28 weeks (%) | 5 (16.13) | 5 | 0 | 0 |
| Unterminated (%) | 1 (3.23) | 0 | 1 | 0 |
| **In-hospital days** | 24.61±17.55 | 27.00±25.61 | 27.35±17.09 | 17.00±9.71 |
| **In-ICU days** | 12.03±10.13 | 7.00±5.69 | 14.00±11.33 | 11.63±9.59 |
| **APACHE II scores** | 12.77±7.30 | 10.50±6.66 | 10.88±5.73 | 18.50±8.44 |
| **AKI stage** | | | | |
| AKI stage 1 (%) | 6 (19.40) | 2 (33.33) | 3 (50.00) | 1 (16.67) |
| AKI stage 2 (%) | 6 (19.40) | 2 (33.33) | 3 (50.00) | 1 (16.67) |
| AKI stage 3 (%) | 19 (61.29) | 2 (10.53) | 11 (84.62) | 6 (31.58) |
| **Obstetric complications** | | | | |
| PE/E (%) | 8 (25.81) | 2 (33.33) | 4 (23.53) | 2 (25.00) |
| PPH (%) | 2 (6.45) | 0 | 1 (5.88) | 1 (12.50) |
| Shock (%) | 5 (16.13) | 1 (16.67) | 1 (5.88) | 3 (37.50) |
| AFLP (%) | 7 (22.58) | 0 | 5 (29.41) | 2 (25.00) |
| CKD (%) | 3 (9.68) | 2 (33.33) | 1 (5.88) | 0 |
Of the 31 patients with PR-AKI, 13 were in the CRRT group, including five cases of AFLP (38%) and three cases of septic or hemorrhagic shock (23%). The remaining 18 patients received non-replacement therapy (39%), including seven cases of PE/E (39%), three cases of AFLP (16%), and three cases of septic shock (16%), as shown in Figure 1. In the CRRT group, four patients (31%) had complete recovery of renal function, three (23%) had partial recovery of renal function but ended substitution therapy, and four (31%) died. In the group with complete recovery of renal function, the average CRRT included six treatment times, and the average cumulative treatment duration was 61.54 hours. In the group with partial recovery of renal function, the average CRRT included five treatment times, and the average cumulative treatment duration was 51.5 hours. Compared with the partially recovered renal function group, the complete recovery group had more CRRT treatment times, longer cumulative treatment durations, and better maternal and infant outcomes.
Among the 18 cases in the non-CRRT group, 13 had complete renal function recovery, one received renal replacement therapy, one did not recover renal function and delivered a stillbirth, and three died. In the CRRT group, WBC, neutrophil %, NLR, AST, AST, serum uric acid, and SCr were significantly lower than before CRRT treatments (P<0.05). Lactic acid, BUN, albumin, Na⁺, and K⁺ were lower than before CRRT treatments, but with no statistical difference, as shown in Table 2.
Table 2 Comparison of laboratory examinations before and after CRRT treatment
| | Before treatment | After treatment | T/Z value | P-value |
|----------------------|------------------|----------------|-----------|---------|
| WBC (×10⁹/L) | 22.10±6.27 | 9.70±7.04 | 4.009 | 0.002 |
| N % | 91.17±4.64 | 61.98±20.31 | 4.987 | 0.000 |
| NLR | 3.92 (4.50) | 4.80 (7.93) | -3.667 | 0.000 |
| BUN (mmol/L) | 16.41±11.45 | 11.65±9.38 | 1.233 | 0.241 |
| SCr (μmol/L) | 363.25±202.99 | 177.85±149.85 | 4.061 | 0.002 |
| Uric acid (mmol/L) | 522.21±133.05 | 247.05±136.85 | 4.940 | 0.000 |
| ALT (U/L) | 70.00 (89.00) | 29.00 (31.00) | -2.515 | 0.012 |
| AST (U/L) | 96.00 (79.50) | 32.00 (67.00) | -2.130 | 0.033 |
| ALB (g/L) | 29.93±11.87 | 31.11±8.01 | -1.725 | 0.110 |
| Na⁺ (mmol/L) | 133.38±7.41 | 139.29±5.86 | -2.284 | 0.041 |
| K⁺ (mmol/L) | 4.52±0.90 | 4.01±0.54 | 2.115 | 0.056 |
| Lactic acid (mmol/L) | 4.80 (7.93) | 1.85 (5.68) | -1.421 | 0.155 |
| PLT (×10⁹/L) | 85.54±52.06 | 206.08±111.09 | -3.154 | 0.008 |
**Fetal outcomes**
Fetal outcomes are summarized in Table 3. The 31 patients with PR-AKI delivered 35 newborns, including 25 parturients (83.33%) with a single pregnancy, 5 parturients (16.67%) with a twin pregnancy, and 26 cesarean sections (83.9%). Among the newborns, eight (22.86%) were full-term, 17 (48.57%) were premature, and one (2.86%) was post-term. Five died, with a mortality rate of 14.26%, and 22 were transferred to NICU (62.86%). Seven newborns had a birth weight ≥2500 g (20.00%), 10 had a birth weight ≥1500g but <2500 g (28.57%), and eight had a birth weight <1500 g (22.86%). Among the three groups, the best pregnancy outcomes were in the puerperium group, and the worst were in the second trimester group (P<0.05). These results are consistent with those reported in the literature [2].
Table 3 Fetal outcomes
| Outcomes | Number | Second trimester | Third trimester | Puerperium |
|--------------------------------|--------|------------------|-----------------|------------|
| Infants (%) | 35 | 6 (17.14) | 20 (57.14) | 9 (25.71) |
| Term infants (%) | 8 | 0 | 4 (50.00) | 4 (50.00) |
| Pre-term infants (%) | 17 | 3 (17.65) | 10 (58.82) | 4 (23.53) |
| Post-term infants (%) | 1 | 0 | 0 | 1 (100.00) |
| Stillbirths (%) | 5 | 3 (60.00) | 2 (40.00) | 0 |
| Severe asphyxia (%) | 5 | 1 (20.00) | 1 (20.00) | 3 (60.00) |
| Birth weight, g | | | | |
| ≥2500 (%) | 7 | 0 | 4 (57.14) | 3 (42.86) |
| ≥1500 but <2500 (%) | 10 | 0 | 9 (90.00) | 1 (10.00) |
| <1500 (%) | 8 | 3 (37.50) | 5 (62.50) | 0 |
| Apgar scores | | | | |
| 1 minute | 6.48±3.24 | 5.53±1.16 | 7.00±3.31 | 5.50±3.73 |
| 5 minutes | 7.85±2.63 | 6.67±1.53 | 8.06±2.90 | 7.83±2.32 |
| 10 minutes | 9.00±2.08 | 6.67±1.53 | 9.19±2.58 | 9.67±0.82 |
| Transfer to NICU (%) | 22 (62.86) | 3 (13.64) | 15 (68.18) | 4 (18.19) |
| Loss to follow-up (%) | 3 (8.57) | 0 | 0 | 3 (100.00) |
**Characteristics of the CRRT group**
A total of 13 patients with PR-AKI received CRRT treatment. The mean timing of the CRRT intervention was 1.92±1.12 days after admission, the mean number of treatments was 7.09±7.39, and the mean cumulative treatment time was 63.31±45.43 hours. The main causes were AFLP in five cases (38.46%), infectious or hemorrhagic shock in three cases (23.08%), severe preeclampsia in one case (7.69%), and postpartum hemorrhage in one case (7.69%); two cases were A/C. Among the 13 patients was one with AKI stage 1, where the primary disease was chronic glomerulonephritis, who received CRRT treatments 29 times and long-term renal replacement therapy after delivery. The infant had a poor prognosis due to low birth weight with severe asphyxia. In the one case of AKI stage 2, with a main cause of Alphard with twin pregnancy, CRRT treatments were more frequent, and the commencement time of CRRT was earlier. As expected, the prognosis was good, and the newborns survived. In the 11 cases of AKI stage 3, three partially recovered renal function, two progressed to end-stage renal disease, and four died; three newborns did not survive.
**Analysis of adverse pregnancy outcomes and risk factors in PR-AKI patients**
Among the 31 patients with PR-AKI, 25 (80.6%) had poor fetal outcomes, including five stillbirths, five cases of neonatal asphyxia, 18 premature births, 10 low birth weight infants, and eight deficient birth weight infants. Six patients had good fetal outcomes. The gestational age, platelet count, and hemoglobin of patients with good fetal outcomes were significantly higher than those with poor fetal outcomes (all $P<0.05$). BUN and uric acid were significantly lower than those with poor fetal outcomes (all $P<0.05$). No significant difference existed between the age, the number of pregnancies and deliveries, NLR, ALT, AST, albumin, SCr, and the composition ratio of CKD patients (all $P>0.05$), as shown in Table 4.
Table 4 Comparison of PR-AKI patients with different fetal outcomes
| | Good outcomes (n=6) | Poor outcomes (n=25) |
|-------------------------|---------------------|---------------------|
| Age ($x^2±s$, years) | 28.17±2.64 | 29.4±5.40 |
| Gestational weeks ($x^2±s$, weeks) | 39.26±1.53$^{\dagger}$ | 31.62±5.50 |
| Number of pregnancies ($x^2±s$, times) | 2.00±1.26 | 1.88±1.27 |
| Number of deliveries ($x^2±s$, times) | 1.33±0.52 | 1.20±0.58 |
| NLR ($x^2±s$) | 12.15±4.19 | 27.07±20.70 |
| Platelet count ($x^2±s$, $\times 10^9$/L) | 217.13±122.87$^{\dagger}$ | 90.24±84.88 |
| Hemoglobin ($x^2±s$, g/L) | 94.19±13.21$^{\dagger}$ | 74.48±20.78 |
| ALT ($x^2±s$, U/L) | 34.22 (153.10) | 68.00 (116.00) |
| AST ($x^2±s$, U/L) | 44.00 (313.26) | 102.10 (165.50) |
| Albumin ($x^2±s$, g/L) | 33.75±1.47 | 27.99±12.66 |
| BUN ($x^2±s$, mmol/L) | 11.87±4.28$^{\dagger}$ | 19.47±10.98 |
| SCr ($x^2±s$, $\mu$mol/L) | 178.94±137.46 | 294.02±211.54 |
| Uric acid ($x^2±s$, $\mu$mol/L) | 262.41±167.00$^{\dagger}$ | 586.87±144.52 |
| CKD (n, %) | 2 (33.33%) | 1 (4.00%) |
| AKI Stage (n, %) | | |
| Stage 1 | 1 (16.67%) | 11 (44.00%) |
| Stage 2 | 1 (16.67%) | 3 (12.00%) |
| Stage 3 | 4 (66.67%) | 11 (44.00%) |
Compared with poor pregnancy outcomes: P<0.01.
Logistic regression analysis was performed on these factors. Gestational age (OR=0.456, P=0.023), platelet count (OR=0.989, P=0.02), hemoglobin (OR=1.017, P=0.022), and uric acid (OR=1.017, P=0.022) were risk factors for poor fetal outcomes in PR-AKI patients (Table 5). Age, number of pregnancies, parity, NLR, ALT, AST, plasma, albumin, SCr, and CKD did not affect pregnancy outcomes (P>0.05).
Table 5 Logistic regression analysis of risk factors for adverse fetal outcomes
| Variables | Regression coefficients | Standard error | Wald | P-value | OR |
|---------------|-------------------------|----------------|-------|---------|-----|
| Gestational weeks | -0.786 | 0.345 | 5.204 | 0.023 | 0.456 |
| PLT | -0.011 | 0.005 | 5.421 | 0.020 | 0.989 |
| HB | -0.050 | 0.027 | 3.573 | 0.059 | 0.951 |
| Uric acid | 0.017 | 0.007 | 5.241 | 0.022 | 1.017 |
Discussion
Significant changes occur in renal hemodynamics, renal tubules, and endocrine function during pregnancy. The mechanism of PR-AKI is multifaceted. During pregnancy, due to the significant increase in cardiac output, renal blood flow in the second trimester can increase by around 85%, and glomerular filtration rate (GFR) can increase by 50%, leading to significantly high filtration in the second trimester. Late GFR decreased by about 20% and returned to average around 3 months after delivery. The excretion of metabolites such as BUN and SCr increased, and the concentration of SCr decreased to 44 µmol/L. Feng et al. [14] reported that SCr over 70 µmol/L was considered abnormal. In our study, the diagnosis of PR-AKI was mainly based on KDIGO-AKI criteria, all of which are in line with SCr ≥ 70 µmol/L. Due to the increase in coagulation factors and fibrinogen during pregnancy, the blood is in a hypercoagulable state, prone to microvascular thrombosis and disseminated intravascular coagulation (DIC), which is an essential pathophysiological basis for acute renal injury [15]. Among the pregnant women with PR-AKI in our study, the CRRT group included five cases of secondary DIC, which promoted the occurrence or aggravated the severity of AKI. Three patients in the non-CRRT treatment group, combined with DIC, had a prolonged course of treatment, and their pregnancy outcomes were also affected to varying degrees. During pregnancy, due to the influence of estrogen and progesterone, prostaglandin E2 has effects such as inhibiting ureteral peristalsis and dextrorotation of the uterus on the right ureter. The right side of the ureter is severely hydronephrotic [14]. This physiological change increases the probability of urinary tract infections and promotes the progression of PR-AKI.
In developing countries, the leading causes of PR-AKI include infectious abortion, postpartum sepsis, PE, and PPH [16–18]. In developed countries, they are PE/E, hemolysis–liver elevated enzymes–low platelet (HELLP) syndrome, thrombotic microangiopathy (TMA), placental abruption, and AFLP [19]. AFLP is a critical and severe obstetric complication. According to the literature, the incidence of PR-AKI caused by
AFLP is 2–4.3% [20]. In our study, AFLP accounted for 25.8% of cases, and PE/E accounted for 22.6%, significantly lower than in foreign research [21]. A possible reason is that more pregnant women with severe AKI were included. As the leading cause of PR-AKI, PE is worthy of attention. In recent years, its risk factors have been more common, such as increased maternal age, diabetes, multiple births, and heart failure [22]. Duley [23] reported that PE seriously affects pregnant women; 8% of pregnancies develop PE, which carries threats in terms of maternal mortality and neonate survival. Shock is another crucial cause of PR-AKI. In our study, PR-AKI caused by shock accounted for 16.1% of cases, similar to rates reported before [24]. Prakash et al. [3] conducted a study of 85 patients with AKI in the third trimester and puerperium and found that PE, HELLP syndrome, AFLP, prenatal and postpartum hemorrhage, and puerperal infection were the leading causes. However, notably, the etiology of PR-AKI is complex, and multiple factors often act synergistically [25].
Comprehensive treatment of PR-AKI is crucial, including three aspects: active treatment of the primary disease, symptomatic and supportive treatment, and renal replacement therapy. Dialysis treatment is essential in the clinic. Dialysis indications mainly include hyperkalemia, volume overload, uremic encephalopathy, and acidosis. Compared with IHD, CRRT has the advantages of high solute clearance, less impact on patient hemodynamics, and being conducive to managing water and electrolytes. It is currently the main way to treat AKI with severe comorbidities and is widely used in critically ill patients [26–27]. In our study, 13 (41.9%) pregnant women underwent CRRT treatment; nine (69.2%) had improved renal function. Eighteen (58.1%) were treated conservatively; 15 (83.3%) had improved renal function, and three (16.7%) died. Foreign studies have reported that the rate of renal replacement therapy in patients with PR-AKI reached 70–100% [28–29]. The main reason for the low rate of replacement therapy in our study was that the proportion of pregnant women with AKI stage 1–2 was relatively large.
As long as patients with PR-AKI are given timely, effective, and correct treatment, most can recover their renal function [30], and the return of renal function is reasonable. In this study, renal function improved in 20 cases, and the effective rate of treatment on PR-AKI was 64.5%. Seventeen patients recovered completely, with a PR-AKI cure rate of 54.8%, similar to that reported in a previous study [31]. Seven patients died, giving a mortality rate of 22.6%, higher than reported in the research (11.4–16.2%) [32–34]. The reason is that the pregnant women included in our study were all critically ill patients in the SICU with a severe underlying condition. The rates of renal function recovery in AKI stages 1, 2, and 3 were 83.3%, 66.7%, and 63.2%, respectively, indicating that the maternal prognosis of PR-AKI is related to the stage. The 31 PR-AKI patients gave birth to 35 newborns; the neonatal survival rate was 74.3%, and the proportion of adverse outcomes was relatively high. Among the infants were 17 premature babies (48.6%), 10 low birth weight infants (28.6%), eight deficient birth weight infants (22.9%), and five stillbirths (14.3%, lower than the 29.8% reported in domestic studies) [8]. The reason may be the gradual improvement of obstetric care and maternal and infant healthcare technology.
The pregnancy outcomes of PR-AKI are related to multiple factors. Logistic regression analysis showed that gestational age, platelet count, hemoglobin, and uric acid were risk factors for poor pregnancy
outcomes in patients with PR-AKI, indicating that the second trimester of pregnancy, low platelet counts, anemia, and high uric acid increased the occurrence of adverse pregnancy outcomes.
**Conclusion**
In summary, PR-AKI is a severe complication of pregnancy, with a high incidence and a high proportion of adverse maternal and infant outcomes. Timely and effective renal replacement therapy can improve the prognosis of pregnant women, and its timing needs to be further studied. Renal function and maternal and infant outcomes are related to the severity of PR-AKI. Therefore, pregnancy monitoring and early intervention must be strengthened to improve maternal and infant outcomes.
**Abbreviations**
KDIGO Kidney Disease: Improving Global Outcomes
K/DOQI Kidney Disease Outcomes Quality Initiative
NICU Neonatal intensive care center
CVVH Continuous veno - venous hemofiltration
CVVHDF Continuous veno - venous hemodiafiltration
**Declarations**
**Acknowledgements**
We would like to acknowledge the whole team members involved in the management.
**Funding**
This study has been conducted with the support of The Western Medicine Guidance Project of Shanghai Science and Technology Commission, grant no. 19411968000.
**Availability of data and materials**
The datasets used and analysed during the current study available from the corresponding author on reasonable request.
**Authors’ contributions**
HMJ and LW carried out the retrospective review of the data, participated in the design, writing and organization of the manuscript. LW, HHD and SJF conceived of the study and designed of it. HMJ, LFJ and DXT participated in the collect and analysis data of the case.
All authors read and approved the final manuscript.
**Ethics approval and consent to participate**
This research study was conducted retrospectively from data obtained for clinical purposes. We consulted with the Bioethics Committee of Xinhua Hospital affiliated to Shanghai Jiaotong University School of Medicine who determined that our study did not need ethical approval. A Bioethics Committee's official statement of ethical approval was granted from the Xinhua Hospital affiliated to Shanghai Jiaotong University School of Medicine. The study was conducted according to the principles of the Declaration of Helsinki and its amendments. Informed consent was obtained from all subjects.
**Consent for publication**
Not applicable.
**Competing interests**
None of the authors have any competing interest to declare.
**Footnotes**
**Publisher’s Note**
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**Contributor Information**
Minjie Hu, Email: [email protected].
We Lu, Email: [email protected].
Junfeng Shi, Email: [email protected].
Haidong Huang, Email: [email protected].
Xuantong Dai, Email: [email protected].
Fujun Lin, Email: [email protected].
**References**
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6. Patel ML, Sachan R, Radheshyam, Sachan P. Acute renal failure in pregnancy: Tertiary centre experience from north Indian population. Niger Med J. 2013 May;54(3):191-5. doi: 10.4103/0300-1652.114586. PMID: 23900700; PMCID: PMC3719246.
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8. Liu Y, Ma X, Zheng J, Liu X, Yan T. Pregnancy outcomes in patients with acute kidney injury during pregnancy: a systematic review and meta-analysis. BMC Pregnancy Childbirth. 2017 Jul 18;17(1):235. doi: 10.1186/s12884-017-1402-9. PMID: 28720086; PMCID: PMC5516395.
9. Stucker F, Ponte B, Tataw J, Martin PY, Wozniak H, Pugin J, Saudan P. Efficacy and safety of citrate-based anticoagulation compared to heparin in patients with acute kidney injury requiring continuous renal replacement therapy: a randomized controlled trial. Crit Care. 2015 Mar 18;19(1):91. doi: 10.1186/s13054-015-0822-z. PMID: 25881975; PMCID: PMC4364313.
10. Khwaja A. KDIGO clinical practice guidelines for acute kidney injury. Nephron Clin Pract. 2012;120(4):c179-84. doi: 10.1159/000339789. Epub 2012 Aug 7. PMID: 22890468.
11. Liu YM, Bao HD, Jiang ZZ, Huang YJ, Wang NS. Pregnancy-related Acute Kidney Injury and a Review of the Literature in China. Intern Med. 2015;54(14):1695-703. doi: 10.2169/internalmedicine.54.3870. Epub 2015 Jul 15. PMID: 26179522.
12. National Kidney Foundation. K/DOQI clinical practice guidelines for chronic kidney disease: evaluation, classification, and stratification. Am J Kidney Dis. 2002 Feb;39(2 Suppl 1):S1-266. PMID: 11904577.
13. Wu VC, Huang TM, Lai CF, Shiao CC, Lin YF, Chu TS, Wu PC, Chao CT, Wang JY, Kao TW, Young GH, Tsai PR, Tsai HB, Wang CL, Wu MS, Chiang WC, Tsai IJ, Hu FC, Lin SL, Chen YM, Tsai TJ, Ko WJ, Wu KD. Acute-on-chronic kidney injury at hospital discharge is associated with long-term dialysis and mortality. Kidney Int. 2011 Dec;80(11):1222-30. doi: 10.1038/ki.2011.259. Epub 2011 Aug 10. Erratum in: Kidney Int. 2012 Apr;81(7):708. PMID: 21832983.
14. Krane NK, Hamrahian M. Pregnancy: kidney diseases and hypertension. Am J Kidney Dis. 2007 Feb;49(2):336-45. doi: 10.1053/j.ajkd.2006.10.029. PMID: 17261438.
15. Taber-Hight E, Shah S. Acute Kidney Injury in Pregnancy. Adv Chronic Kidney Dis. 2020 Nov;27(6):455-460. doi: 10.1053/j.ackd.2020.06.002. PMID: 33328061; PMCID: PMC7751749.
16. Jayakumar M, Prabahar MR, Fernando EM, Manorajan R, Venkatraman R, Balaraman V. Epidemiologic trend changes in acute renal failure--a tertiary center experience from South India. Ren Fail. 2006;28(5):405-10. doi: 10.1080/0886022060689034. PMID: 16825090.
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18. Prakash J, Vohra R, Wani IA, Murthy AS, Srivastava PK, Tripathi K, Pandey LK, Usha, Raja R. Decreasing incidence of renal cortical necrosis in patients with acute renal failure in developing countries: a single-centre experience of 22 years from Eastern India. Nephrol Dial Transplant. 2007 Apr;22(4):1213-7. doi: 10.1093/ndt/gfl761. Epub 2007 Jan 31. PMID: 17267539.
19. Vijayan M, Avendano M, Chinchilla KA, Jim B. Acute kidney injury in pregnancy. Curr Opin Crit Care. 2019 Dec;25(6):580-590. doi: 10.1097/MCC.0000000000000656. PMID: 31524717.
20. Drakeley AJ, Le Roux PA, Anthony J, Penny J. Acute renal failure complicating severe preeclampsia requiring admission to an obstetric intensive care unit. Am J Obstet Gynecol. 2002 Feb;186(2):253-6. doi: 10.1067/mob.2002.120279. PMID: 11854645.
21. Bouaziz M, Chaari A, Turki O, Dammak H, Chelly H, Ammar R, Nasri A, Ben Algia N, Bahloul M, Ben Hamida C. Acute renal failure and pregnancy: a seventeen-year experience of a Tunisian intensive care unit. Ren Fail. 2013 Oct;35(9):1210-5. doi: 10.3109/0886022X.2013.819767. Epub 2013 Jul 26. PMID: 24021030.
22. Lunn MR, Obedin-Maliver J, Hsu CY. Increasing incidence of acute kidney injury: also a problem in pregnancy? Am J Kidney Dis. 2015 May;65(5):650-4. doi: 10.1053/j.ajkd.2014.11.007. Epub 2015 Jan 7. PMID: 25577135.
23. Duley L. The global impact of pre-eclampsia and eclampsia. Semin Perinatol. 2009 Jun;33(3):130-7. doi: 10.1053/j.semperi.2009.02.010. PMID: 19464502.
24. Sivakumar V, Sivaramakrishna G, Sainaresh VV, Sriramnaveen P, Kishore CK, Rani ChS, Jagadeesh K. Pregnancy-related acute renal failure: a ten-year experience. Saudi J Kidney Dis Transpl. 2011 Mar;22(2):352-3. PMID: 21422644.
25. Prakash J, Ganiger VC, Prakash S, Iqbal M, Kar DP, Singh U, Verma A. Acute kidney injury in pregnancy with special reference to pregnancy-specific disorders: a hospital based study (2014-2016). J Nephrol. 2018 Feb;31(1):79-85. doi: 10.1007/s40620-017-0466-y. Epub 2018 Jan 4. PMID: 29302904.
26. Fülöp T, Zsom L, Tapolyai MB, Molnar MZ, Rosivall L. Volume-related weight gain as an independent indication for renal replacement therapy in the intensive care units. J Renal Inj Prev. 2016 Nov 6;6(1):35-42. doi: 10.15171/jrip.2017.07. PMID: 28487870; PMCID: PMC5414517.
27. Connor MJ Jr, Karakala N. Continuous Renal Replacement Therapy: Reviewing Current Best Practice to Provide High-Quality Extracorporeal Therapy to Critically Ill Patients. Adv Chronic Kidney Dis. 2017 Jul;24(4):213-218. doi: 10.1053/j.ackd.2017.05.003. PMID: 28778360.
28. Silva GB Jr, Monteiro FA, Mota RM, Paiva JG, Correia JW, Bezerra Filho JG, Macedo RN, Lima RS, Daher EF. Acute kidney injury requiring dialysis in obstetric patients: a series of 55 cases in Brazil. Arch Gynecol Obstet. 2009 Feb;279(2):131-7. doi: 10.1007/s00404-008-0682-8. Epub 2008 May 28. PMID: 18506463.
29. Arora N, Mahajan K, Jana N, Taraphder A. Pregnancy-related acute renal failure in eastern India. Int J Gynaecol Obstet. 2010 Dec;111(3):213-6. doi: 10.1016/j.ijgo.2010.06.026. Epub 2010 Sep 25. PMID: 20870228.
30. Miguil M, Salmi S, Moussaid I, Benyounes R. Insuffisance rénale aiguë hémodialysée en obstétrique [Acute renal failure requiring haemodialysis in obstetrics]. Nephrol Ther. 2011 Jun;7(3):178-81. French. doi: 10.1016/j.nephro.2010.12.003. Epub 2011 Jan 11. PMID: 21227762.
31. Aggarwal RS, Mishra VV, Jasani AF, Gumber M. Acute renal failure in pregnancy: our experience. Saudi J Kidney Dis Transpl. 2014 Mar;25(2):450-5. doi: 10.4103/1319-2442.128621. PMID: 24626025.
32. Kabbali N, Tachfouti N, Arrayhani M, Harandou M, Tagnaouti M, Bentata Y, Laouad I, Ramdani B, Bayahia R, Ouailim Z, Houssaini TS. Outcome assessment of pregnancy-related acute kidney injury in Morocco: A national prospective study. Saudi J Kidney Dis Transpl. 2015 May-Jun;26(3):619-24. doi: 10.4103/1319-2442.157426. PMID: 26022044.
33. Hassan I, Junejo AM, Dawani ML. Etiology and outcome of acute renal failure in pregnancy. J Coll Physicians Surg Pak. 2009 Nov;19(11):714-7. PMID: 19889269.
34. Godara SM, Kute VB, Trivedi HL, Vanikar AV, Shah PR, Gumber MR, Patel HV, Gumber VM. Clinical profile and outcome of acute kidney injury related to pregnancy in developing countries: a single-center study from India. Saudi J Kidney Dis Transpl. 2014 Jul;25(4):906-11. doi: 10.4103/1319-2442.135215. PMID: 24969215.
Figures
Figure 1
Comparison of etiology between CRRT and non-CRRT groups
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Improving Word Translation Disambiguation by Capturing Multiword Expressions with Dictionaries
Lars Bungum, Björn Gambäck, André Lynum, Erwin Marsi
Norwegian University of Science and Technology
Sem Sælands vei 7–9; NO—7491 Trondheim, Norway
{bungum,gamback,andrely,emarsi}@idi.ntnu.no
Abstract
The paper describes a method for identifying and translating multiword expressions using a bi-directional dictionary. While a dictionary-based approach suffers from limited recall, precision is high; hence it is best employed alongside an approach with complementing properties, such as an n-gram language model.
We evaluate the method on data from the English-German translation part of the cross-lingual word sense disambiguation task in the 2010 semantic evaluation exercise (SemEval). The output of a baseline disambiguation system based on n-grams was substantially improved by matching the target words and their immediate contexts against compound and collocational words in a dictionary.
1 Introduction
Multiword expressions (MWEs) cause particular lexical choice problems in machine translation (MT), but can also be seen as an opportunity to both generalize outside the bilingual corpora often used as training data in statistical machine translation approaches and as a method to adapt to specific domains. The identification of MWEs is in general important for many language processing tasks (Sag et al., 2002), but can be crucial in MT: since the semantics of many MWEs are non-compositional, a suitable translation cannot be constructed by translating the words in isolation. Identifying MWEs can help to identify idiomatic or otherwise fixed language usage, leading to more fluent translations, and potentially reduce the amount of lexical choice an MT system faces during target language generation.
In any translation effort, automatic or otherwise, the selection of target language lexical items to include in the translation is a crucial part of the final translation quality. In rule-based systems lexical choice is derived from the semantics of the source words, a process which often involves complex semantic composition. Data-driven systems on the other hand commonly base their translations nearly exclusively on cooccurrences of bare words or phrases in bilingual corpora, leaving the responsibility of selecting lexical items in the translation entirely to the local context found in phrase translation tables and language models with no explicit notion of the source or target language semantics. Still, systems of this type have been shown to produce reasonable translation quality without explicitly considering word translation disambiguation.
Bilingual corpora are scarce, however, and unavailable for most language pairs and target domains. An alternative approach is to build systems based on large monolingual knowledge sources and bilingual lexica, as in the hybrid MT system PRESEMT (Sofianopoulos et al., 2012). Since such a system explicitly uses a translation dictionary, it must at some point in the translation process decide which lexical entries to use; thus a separate word translation disambiguation module needs to be incorporated. To research available methods in such a module we have identified a task where we can use public datasets for measuring how well a method is able to select the optimal of many translation choices from a source language sentence.
In phrase-based statistical MT systems, the translation of multiword expressions can be a notable source of errors, despite the fact that those systems explicitly recognize and use alignments of sequential chunks of words. Several researchers have approached this problem by adding MWE translation tables to the systems, either through expanding the phrase tables (Ren et al., 2009) or by injecting the MWE translations into the decoder (Bai et al., 2009). Furthermore, there has been some interest in automatic mining of MWE pairs from bilingual corpora as a task in itself: Caseli et al. (2010) used a dictionary for evaluation of an automatic MWE extraction procedure using bilingual corpora. They also argued for the filtering of stopwords, similarly to the procedure described in the present paper. Sharoff et al. (2006) showed how MWE pairs can be extracted from comparable monolingual corpora instead of from a parallel bilingual corpus.
The methodology introduced in this paper employs bilingual dictionaries as a source of multiword expressions. Relationships are induced between the source sentence and candidate translation lexical items based on their correspondence in the dictionary. Specifically, we use a deterministic multiword expression disambiguation procedure based on translation dictionaries in both directions (from source to target language and vice versa), and a baseline system that ranks target lexical items based on their immediate context and an n-gram language model. The n-gram model represents a high-coverage, low-precision companion to the dictionary approach (i.e., it has complementary properties). Results show that the MWE dictionary information substantially improves the baseline system.
The 2010 Semantic Evaluation exercise (SemEval’10) featured a shared task on Cross-Lingual Word Sense Disambiguation (CL-WSD), where the focus was on disambiguating the translation of a single noun in a sentence. The participating systems were given an English word in its context and asked to produce appropriate substitutes in another language (Lefever and Hoste, 2010b). The CL-WSD data covers Dutch, French, Spanish, Italian and German; however, since the purpose of the experiments in this paper just was to assess our method’s ability to choose the right translation of a word given its context, we used the English-to-German part only.
The next section details the employed disambiguation methodology and describes the data sets used in the experiments. Section 3 then reports on the results of experiments applying the methodology to the SemEval datasets, particularly addressing the impact of the dictionary MWE correspondences. Finally, Section 4 sums up the discussion and points to issues that can be investigated further.
2 Methodology
The core of the disambiguation model introduced in this paper is dictionary-based multiword extraction. Multiword extraction is done in both a direct and indirect manner: Direct extraction uses adjacent words in the source language in combination with the word to be translated, if the combination has an entry in the source-to-target language (SL–TL) dictionary. Indirect extraction works in the reverse direction, by searching the target-to-source (TL–SL) dictionary and looking up translation candidates for the combined words. Using a dictionary to identify multiword expressions after translation has a low recall of target language MWEs, since often there either are no multiword expressions to be discovered, or the dictionary method is unable to find a translation for an MWE. Nevertheless, when an MWE really is identified by means of the dictionary-based method, the precision is high.
Due to the low recall, relying on multiword expressions from dictionaries would, however, not be sufficient. Hence this method is combined with an n-gram language model (LM) based on a large target language corpus. The LM is used to rank translation candidates according to the probability of the n-gram best matching the context around the translation candidate. This is a more robust but less precise approach, which servers as the foundation for the high-precision but low-recall dictionary approach.
In the actual implementation, the n-gram method thus first provides a list of its best suggestions (currently top-5), and the dictionary method then prepends its candidates to the top of this list. Consequently, n-gram matching is described before dictionary-based multiword extraction in the following section. First, however, we introduce the data sets used in the experiments.
(a) AGREEMENT in the form of an exchange of letters between
the European Economic Community and the Bank for Interna-
tional Settlements concerning the mobilization of claims held by
the Member States under the medium-term financial assistance
arrangements
{bank 4; bankengesellschaft 1; kreditinstitut 1; zentralbank 1; fi-
nanzinstitut 1}
(b) The Office shall maintain an electronic data bank with the par-
ticulars of applications for registration of trade marks and entries
in the Register. The Office may also make available the contents
of this data bank on CD-ROM or in any other machine-readable
form.
{datenbank 4; bank 3; datenbanksystem 1; daten 1}
(c) established as a band of 1 km in width from the banks of a
river or the shores of a lake or coast for a length of at least 3 km.
{ufer 4; flussufer 3}
Table 1: Examples of contexts for the English word bank
with possible German translations
| Context | German Translation |
|---------|--------------------|
| Trial and test instances were extracted from two other corpora, JRC-Acquis (Steinberger et al., 2006) and BNC (Burnard, 2007). The trial data for each language consists of five nouns (with 20 sentence contexts per noun), and the test data of twenty nouns (50 contexts each, so 1000 in total per language, with the CL-WSD data covering Dutch, French, Spanish, Italian and German). Table 1 provides examples from the trial data of contexts for the English word bank and its possible translations in German. Gold standard translations were created by having four human translators picking the contextually appropriate sense for each source word, choosing 0–3 preferred target language translations for it. The translations are thus restricted to those appearing in Europarl, probably introducing a slight domain bias. Each translation has an associated count indicating how many annotators considered it to be among their top-3 preferred translations in the given context. |
| In this way, for the English lemma bank, for example, the CL-WSD trial gold standard for German contains the word Bank itself, together with 40 other translation candidates, as shown in Table 2. Eight of those are related to river banks (Ufer, but also, e.g., Westbank and Westjordanland), three concern databases (Datenbank), and one is for blood banks. The rest are connected to different types of financial institutions (such as Handelsbank and Finanzinstitut, but also by association Konto, Weltausfuhr, Banknote, Geldschein, Kredit, etc.). |
2.2 N-Gram Context Matching
N-gram matching is used to produce a ranked list of translation candidates and their contexts, both in order to provide robustness and to give a baseline performance. The n-gram models were built using the IRSTLM toolkit (Federico et al., 2008; Bungum and Gambar), 2012) on the DeWaC corpus (Baroni and Kilgarriff, 2006), using the stopword list from NLTK (Loper and Bird, 2002). The n-gram matching procedure consists of two steps:
1. An n\textsuperscript{th} order source context is extracted and the translations for each SL word in this context are retrieved from the dictionary. This includes stopword filtering of the context.
2. All relevant n-grams are inspected in order from left to right and from more specific (5-grams) to least specific (single words).
For each part of the context with matching n-grams in the target language model, the appropriate target translation candidates are extracted and ranked according to their language model probability. This results in an n-best list of translation candidates.
Since dictionary entries are lemma-based, lemmatization was necessary to use this approach in combination with the dictionary enhancements. The source context is formed by the lemmata in the sentence surrounding the focus word (the word to be disambiguated) by a window of up to four words in each direction, limited by a 5-gram maximum length. In order to extract the semantically most relevant content, stopwords are removed before constructing this source word window. For each of the 1–5 lemmata in the window, the relevant translation candidates are retrieved from the bilingual dictionary. The candidates form the ordered translation context for the source word window.
The following example illustrates how the translation context is created for the focus word ‘bank’.
First the relevant part of the source language sentence with the focus word in bold face:
1. The BIS could conclude stand-by credit agreements with the creditor countries’ central [bank] if they should so request.
For example, using a context of two words in front and two words after the focus word, the following source language context is obtained after a preprocessing involving lemmatization, stopword removal, and insertion of sentence start (\texttt{<s>}) and end markers (\texttt{</s>}):
2. country central [bank] request [\texttt{</s>}]
From this the possible n-grams in the target side context are generated by assembling all ordered combinations of the translations of the source language words for each context length: the widest contexts (5-grams) are looked up first before moving on to narrower contexts, and ending up with looking up only the translation candidate in isolation.
Each of the n-grams is looked up in the language model and for each context part the n-grams are ordered according to their language model probability. Table 3 shows a few examples of such generated n-grams with their corresponding scores from the n-gram language model. The target candidates (italics) are then extracted from the ordered list of target language n-grams. This gives an n-best list of translation candidates from which the top-1 or top-5 can be taken. Since multiple senses in the dictionary can render the same literal output, duplicate translation candidates are filtered out from the n-best list.
### 2.3 Dictionary-Based Context Matching
After creating the n-gram based list of translation candidates, additional candidates are produced by looking at multiword entries in a bilingual dictionary. The existence of multiword entries in the dictionary corresponding to adjacent lemmata in the source context or translation candidates in the target context is taken as a clear indicator for the suitability of a particular translation candidate. Such entries are added to the top of the n-best list, which represents a strong preference in the disambiguation system.
Dictionaries are used in all experiments to look up translation candidates and target language translations of the words in the context, but this approach is mining the dictionaries by using lookups of greater length. Thus is, for example, the dictionary entry Community Bank translated to the translation candidate Commerzbank; this translation candidate would be put on top of the list of prioritized answers.
Two separate procedures are used to find such indicators, a direct procedure based on the source context and an indirect procedure based on the weaker target language context. These are detailed in pseudocode in Algorithms 1 and 2, and work as follows:
#### Source Language (SL) Method (Algorithm 1)
If there is a dictionary entry for the source word and one of its adjacent words, search the set of translations for any of the translation candidates for the word alone. Specifically, transla-
| n | n-gram | LM score |
|---|--------|----------|
| 5 | land mittig bank nachsuchen [\texttt{</s>}] | Not found |
| 4 | mittig bank nachsuchen [\texttt{</s>}] | Not found |
| 3 | mittig bank nachsuchen | Not found |
| 3 | kredit anfragen [\texttt{</s>}] | -0.266291 |
| 2 | mittig bank | -3.382560 |
| 2 | zentral blutbank | -5.144870 |
| 1 | bank | -3.673000 |
Table 3: Target language n-gram examples from lookups of stopword-filtered lemmata country central bank request reported in log scores. The first 3 n-grams were not found in the language model.
Algorithm 1
SL algorithm to rank translation candidates (tcands) for SL lemma b given list of tcands
1: procedure FINDCAND(list rlist, SL-lemma b, const tcands) ▶ rlist is original ranking
2: &comblemmas ← list(previouslemma(b) + b + nextlemma(b)) ▶ Find adjacent lemmata
3: for lem ∈ comblemmas do
4: c ← sl-dictionary-lookup(lem) ▶ Look up lemma in SL→TL dict.
5: if c ∈ tcands then rlist ← list(c + rlist) ▶ Push lookup result c onto rlist if in tcands
6: end if
7: end for
8: return rlist ▶ Return new list with lemmata whose translations were in tcands on top
9: end procedure
Algorithm 2
TL algorithm to rank translation candidates (tcands) for SL lemma b given list of tcands
[The ready-made TL tcands from the dataset are looked up in TL-SL direction. It is necessary to keep a list of the reverse-translation of the individual tcand as well as the original tcand itself, in order to monitor which tcand it was. If the SL context is found in either of these reverse lookups the matching tcand is ranked high.]
1: procedure FINDCAND(list rlist,SL-lemma b, const tcands) ▶ rlist is original ranking
2: for cand ∈ tcands do ▶ Assemble list of TL translations
3: translist ← list(cand, tl-dictionary-lookup(cand)) + translist ▶ Append TL→SL lookup results of tcands with cand as id
4: end for
5: for cand, trans ∈ translist do ▶ If trans contains either SL lemma
6: if previouslemma(b) || nextlemma(b) ∈ trans then ▶ append this cand onto rlist
7: rlist ← list(cand) + rlist
8: end if
9: end for
10: return rlist ▶ Return tcands list; top-ranking tcands whose SL-neighbours were found in TL→SL lookup
11: end procedure
tions of the combination of the source word and an adjacent word in the context are matched against translation candidates for the word.
Target Language (TL) Method (Algorithm 2)
If a translation candidate looked up in the reverse direction matches the source word along with one or more adjacent words, it is a good translation candidate. TL candidates are looked up in a TL→SL dictionary and multiword results are matched against SL combinations of disambiguation words and their immediate contexts.
For both methods the dictionary entry for the target word or translation candidate is matched against the immediate context. Thus both methods result in two different lookups for each focus word, combining it with the previous and next terms, respectively. This is done exhaustively for all combinations of translations of the words in the context window. Only one adjacent word was used, since very few of the candidates were able to match the context even with one word. Hence, virtually none would be found with more context, making it very unlikely that larger contexts would contribute to the disambiguation procedure, as wider matches would also match the one-word contexts.
Also for both methods, translation candidates are only added once, in case the same translation candidate generates hits with either (or both) of the methods. Looking at the running example, stopword filtered and with lemmatized context:
(3) country central bank request
This example generates two source language multiword expressions, central bank and bank request. In the source language method, these word combina-
tions are looked up in the dictionary where the zentralbank entry is found for central bank, which is also found as a translation candidate for bank.
The target language method works in the reverse order, looking up the translation candidates in the TL–SL direction and checking if the combined lemmata are among the candidates’ translations into the source language. In the example, the entry zentralbank:central bank is found in the dictionary, matching the source language context, so zentralbank is assumed to be a correct translation.
2.4 Dictionaries
Two English-German dictionaries were used in the experiments, both with close to 1 million entries (translations). One is a free on-line resource, while the other was obtained by reversing an existing proprietary German-English dictionary made available to the authors by its owners:
- The GFAI dictionary (called ‘D1’ in Section 3 below) is a proprietary and substantially extended version of the Chemnitz dictionary, with 549k EN entries including 433k MWEs, and 552k DE entries (79k MWEs). The Chemnitz electronic German-English dictionary2 itself contains over 470,000 word translations and is available under a GPL license.
- The freely available CC dictionary3 (‘D2’ below) is an internet-based German-English and English-German dictionary built through user generated word definitions. It has 565k/440k (total/MWE) EN and 548k/210k DE entries.
Note that the actual dictionaries are irrelevant to the discussion at hand, and that we do not aim to point out strengths or weaknesses of either dictionary, nor to indicate a bias towards a specific resource.
3 Results
Experiments were carried out both on the trial and test data described in Section 2.1 (5 trial and 20 test words; with 20 resp. 50 instances for each word; in total 1100 instances in need of disambiguation). The results show that the dictionaries yield answers with high precision, although they are robust enough to solve the SemEval WSD challenge on their own.
For measuring the success rate of the developed models, we adopt the ‘Out-Of-Five’ (OOF) score (Lefever and Hoste, 2010b) from the SemEval’10 Cross-Lingual Word Sense Disambiguation task. The Out-Of-Five criterion measures how well the top five candidates from the system match the top five translations in the gold standard:
$$OOF(i) = \frac{\sum_{a \in A_i} freq_1(a)}{|H_i|}$$
where $H_i$ denotes the multiset of translations proposed by humans for the focus word in each source sentence $s_i$ (1 ≤ i ≤ N, N being the number of test items). $A_i$ is the set of translations produced by the system for source term $i$. Since each translation has an associated count of how many annotators chose it, there is for each $s_i$ a function $freq_i$ returning this count for each term in $H_i$ (0 for all other terms), and $maxfreq_i$ gives the maximal count for any term in $H_i$. For the first example in Table 1:
$$H_1 = \{\text{bank, bank, bank, bank, zentralbank, bankengesellschaft, kreditinstitut, finanzinstitut}\}$$
$$freq_1(\text{bank}) = 4$$
$$freq_1(\text{finanzinstitut}) = 1$$
$$maxfreq_1 = 4$$
and the cardinality of the multiset is: $|H_1| = 8$. This equates to the sum of all top-3 preferences given to the translation candidates by all annotators.
For the Out-Of-Five evaluation, the CL-WSD systems were allowed to submit up to five candidates of equal rank. OOF is a recall-oriented measure with no additional penalty for precision errors, so there is no benefit in outputting less than five candidates. With respect to the previous example from Table 1, the maximum score is obtained by system output $A_1 = \{\text{bank, bankengesellschaft, kreditinstitut, zentralbank, finanzinstitut}\}$, which gives $OOF(1) = (4 + 1 + 1 + 1 + 1)/8 = 1$, whereas $A_2 = \{\text{bank, bankengesellschaft, nationalbank, notenbank, sparkasse}\}$ would give $OOF(1) = (4 + 1)/8 = 0.625$.
---
2http://dict.tu-chemnitz.de/
3http://www.dict.cc/
### Table 4: F$_1$-score results for individual dictionaries
| Dictionary | Source language | Target language | All language |
|------------|----------------|----------------|-------------|
| | D1 | D2 | comb | D1 | D2 | comb | comb |
| Top | 8.89| 6.99| 8.89 | 22.71| 24.43| 25.34| 24.67 |
| Low | 0.00| 0.00| 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
| Mean | 2.71| 0.99| 3.04 | 8.35 | 7.10 | 9.24 | 10.13 |
### Table 5: Precision scores for all terms filtering out those instances for which no candidates were suggested
| Dictionary | Source language | Target language | All language |
|------------|----------------|----------------|-------------|
| | D1 | D2 | comb | D1 | D2 | comb | comb |
| coach | 1.00| 0.00| 1.00 | 0.21 | 0.00 | 0.21 | 0.21 |
| education | 0.83| 0.67| 0.83 | 0.47 | 0.62 | 0.54 | 0.53 |
| execution | 0.00| 0.00| 0.00 | 0.17 | 0.22 | 0.17 | 0.17 |
| figure | 1.00| 0.00| 1.00 | 0.51 | 0.57 | 0.55 | 0.55 |
| job | 0.88| 0.20| 0.94 | 0.45 | 0.78 | 0.46 | 0.44 |
| letter | 1.00| 0.00| 1.00 | 0.66 | 0.75 | 0.62 | 0.66 |
| match | 1.00| 1.00| 1.00 | 0.80 | 0.50 | 0.80 | 0.80 |
| mission | 0.71| 0.33| 0.71 | 0.46 | 0.37 | 0.36 | 0.36 |
| mood | 0.00| 0.00| 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
| paper | 0.68| 0.17| 0.68 | 0.53 | 0.35 | 0.55 | 0.55 |
| post | 1.00| 1.00| 1.00 | 0.39 | 0.48 | 0.45 | 0.48 |
| pot | 0.00| 0.00| 0.00 | 1.00 | 1.00 | 1.00 | 1.00 |
| range | 1.00| 1.00| 1.00 | 0.28 | 0.37 | 0.30 | 0.30 |
| rest | 1.00| 0.67| 1.00 | 0.60 | 0.56 | 0.56 | 0.58 |
| ring | 0.09| 0.00| 0.09 | 0.37 | 0.93 | 0.38 | 0.38 |
| scene | 1.00| 0.00| 1.00 | 0.50 | 0.42 | 0.44 | 0.50 |
| side | 1.00| 0.00| 1.00 | 0.21 | 0.16 | 0.23 | 0.27 |
| soil | 1.00| 1.00| 1.00 | 0.72 | 0.58 | 0.66 | 0.69 |
| strain | 0.00| 0.00| 0.00 | 0.51 | 0.88 | 0.55 | 0.55 |
| test | 1.00| 1.00| 1.00 | 0.62 | 0.52 | 0.57 | 0.61 |
| Mean | 0.84| 0.74| 0.84 | 0.50 | 0.56 | 0.49 | 0.51 |
### Table 6: Number of instances with a translation candidate (‘Mean’) and the total number of suggested candidates
| Most Freq | Most Freq Aligned | 5-gram + Dict | All Dict Comb | VSM Model |
|-----------|-------------------|---------------|--------------|-----------|
| Top | 51.77 | 68.71 | 52.02 | 52.74 | 24.67 | 55.92 |
| Low | 1.76 | 9.93 | 14.09 | 15.40 | 0.00 | 10.73 |
| Mean | 21.18 | 34.61 | 30.36 | 36.38 | 10.13 | 30.30 |
### Table 7: Overview of results (F$_1$-scores) on SemEval data
For assessing overall system performance in the experiments, we take the best (‘Top’), worst (‘Low’), and average (‘Mean’) of the OOF scores for all the SL focus words, with F$_1$-score reported as the harmonic mean of the precision and recall of the OOF scores. Table 4 shows results for each dictionary approach on the test set, with ‘D1’ being the GFAI dictionary, ‘D2’ the CC dictionary, and ‘comb’ the combination of both. Target language look-up contributes more to providing good translation candidates than the source language methodology, and also outperforms a strategy combining all dictionaries in both directions (‘All comb’).
Filtering out the instances for which no candidate translation was produced, and taking the average precision scores only over these, gives the results shown in Table 5. Markedly different precision scores can be noticed, but the source language method again has higher precision on the suggestions it makes than the target language counterpart.
As shown in Table 6, this higher precision is offset by lower coverage, with far fewer instances actually producing a translation candidate with the dictionary lookup methods. There is a notable difference in the precision of the SL and TL approaches, coinciding with more candidates produced by the latter. Several words in Table 5 give 100% precision scores for at least one dictionary, while a few give 0% precision for some dictionaries. The word ‘mood’ even has 0% precision for both dictionaries in both directions.
Table 7 gives an overview of different approaches to word translation disambiguation on the dataset. For each method, the three lines again give both the best and worst scoring terms, and the mean value for all test words. The maximum attainable score for each of those would be 99.28, 90.48 and 95.47, respectively, but those are perfect scores not reachable for all items, as described above (OOF-scoring). Instead the columns Most Freq and Most Freq aligned give the baseline scores for the SemEval dataset: the translation most frequently seen in the corpus and the translation most frequently aligned in a word-aligned parallel corpus (Europarl), respectively. Then follows the results when using only a stopword-filtered 5-gram model built with the IRSTLM language modeling kit (Federico and Cettolo, 2007), and when combining the 5-gram model with the dictionary approach (5-gram + Dict).
The next column (All Dict Comb) shows how the dictionary methods fared on their own.
bined dictionary approach has low recall (see Table 6) and does not alone provide a good solution to the overall problem. Due to high precision, however, the approach is able to enhance the n-gram method that already produces acceptable results. Finally, the column VSM Model as comparison gives the results obtained when using a Vector Space Model for word translation disambiguation (Marsi et al., 2011).
Comparing the dictionary approach to state-of-the-art monolingual solutions to the WTD problem on this dataset shows that the approach performs better for the Lowest and Mean scores of the terms, but not for the Top scores (Lynum et al., 2012). As can be seen in Table 7, the vector space model produced the overall best score for a single term. However, the method combining a 5-gram language model with the dictionary approach was best both at avoiding really low scores for any single term and when comparing the mean scores for all the terms.
4 Discussion and Conclusion
The paper has presented a method for using dictionary lookups based on the adjacent words in both the source language text and target language candidate translation texts to disambiguate word translation candidates. By composing lookup words by using both neighbouring words, improved disambiguation performance was obtained on the data from the SemEval’10 English-German Cross-Lingual Word Sense Disambiguation task. The extended use of dictionaries proves a valuable source of information for disambiguation, and can introduce low-cost phrase-level translation to quantitative Word Sense Disambiguation approaches such as N-gram or Vector Space Model methods, often lacking the phrases-based dimension.
The results show clear differences between the source and target language methods of using dictionary lookups, where the former has very high precision (0.84) but low coverage, while the TL method compensates lower precision (0.51) with markedly better coverage. The SL dictionary method provided answers to only between 1.5 and 3.25 of 50 instances per word on average, depending on the dictionary. This owes largely to the differences in algorithms, where the TL method matches any adjacent lemma to the focus word with the translation of the pre-defined translation candidates, whereas the SL method matches dictionaries of the combined lemmata of the focus word and its adjacent words to the same list of translation candidates. False positives are expected with lower constraints such as these. On the SemEval data, the contribution of the dictionary methods to the n-grams is mostly in improving the average score.
The idea of acquiring lexical information from corpora is of course not new in itself. So did, e.g., Rapp (1999) use vector-space models for the purpose of extracting ranked lists of translation candidates for extending a dictionary for word translation disambiguation. Chiao and Zweigenbaum (2002) tried to identify translational equivalences by investigating the relations between target and source language word distributions in a restricted domain, and also applied reverse-translation filtering for improved performance, while Sadat et al. (2003) utilised non-aligned, comparable corpora to induce a bilingual lexicon, using a bidirectional method (SL→TL, TL→SL, and a combination of both).
Extending the method to use an arbitrary size window around all words in the context of each focus word (not just the word itself) could identify more multiword expressions and generate a more accurate bag-of-words for a data-driven approach. Differences between dictionaries could also be explored, giving more weight to translations found in two or more dictionaries. Furthermore, the differences between the SL and TL methods could be explored further, investigating in detail the consequences of using a symmetrical dictionary, in order to study the effect that increased coverage has on results. Testing the idea on more languages will help verify the validity of these findings.
Acknowledgements
This research has received funding from NTNU and from the European Community’s 7th Framework Programme under contract nr 248307 (PRESEMT). Thanks to the other project participants and the anonymous reviewers for several very useful comments.
References
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Elementary Integral Series for Heun Functions
With an Application to Black-Hole Perturbation Theory
Pierre-Louis Giscard · Aditya Tamar
Received: date / Accepted: date
Abstract Heun differential equations are the most general second order Fuchsian equations with four regular singularities. An explicit integral series representation of Heun functions involving only elementary integrands has hitherto been unknown and noted as an important open problem in a recent review. We provide explicit integral representations of the solutions of all equations of the Heun class: general, confluent, bi-confluent, doubly-confluent and triconfluent, with integrals involving only rational functions and exponential integrands. All the series are illustrated with concrete examples of use. These results stem from the technique of path-sums, which we use to evaluate the path-ordered exponential of a variable matrix chosen specifically to yield Heun functions. We demonstrate the utility of the integral series by providing the first representation of the solution to the Teukolsky radial equation governing the metric perturbations of rotating black holes that is convergent everywhere from the black hole horizon up to spatial infinity.
Keywords Heun Equations · Integral Representation · Path Sums · Volterra equation · Neumann Series · Teukolsky Equation
PACS 02.30.Hq · 02.30.Rz · 04.70.Bw · 04.70.-s
1 Introduction
The study of Heun equations has generated significant interest in both mathematics and physics lately. From a mathematical standpoint, recent results
Pierre-Louis Giscard
Univ. Littoral Côte d’Opale, UR 2597, LMPA, Laboratoire de Mathématiques Pures et Appliquées Joseph Liouville, F-62100 Calais, France.
E-mail: [email protected]
Aditya Tamar
Independent Researcher, Delhi, India.
E-mail: [email protected]
have uncovered a relation between Heun equations and other equations of paramount importance for physics. For example, it was found by means of antiquantisation procedures [68] and monodromy preserving transformations [72] that the Heun equations share a bijective relationship with Painlevé equations [68,71,69]. This permitted in-depth studies on the integral symmetry properties of equations of the Heun class [11] and to determine generating polynomial solutions of the Heun equation by formulating a Riemann-Hilbert problem for the Heun function [18]. The reduction of certain Heun equations under non-trivial substitutions to hypergeometric equations has also been possible by means of pull-back transformations based on Belyi coverings [79] and polynomial transformations [48,50].
In contrast, in spite of the increasing use of Heun functions in physics (in quantum optics [82,57], condensed matter physics [15,17], quantum computing [27], two-state problems [66,39] and more [35]), few studies [35,36] have specifically focused on determining their properties most relevant to physical applications. For example, the lack of integral expansions of these functions involving only elementary integrands has been clearly identified as a major obstacle when extracting physical meaning from the mathematical treatment of black holes quasinormal modes [35,36], yet remains unaddressed in the mathematical literature. The present work tackles this issue by determining a novel integral representation of the Heun equations involving elementary functions that is tailored to physical applications. In particular, we demonstrate the applicability of the novel integral representation to the Teukolsky equation [77] that governs the metric perturbations of rotating black holes and further explore which physical observables pertinent to black hole perturbation theory can be obtained from the integral form. The present progress in integral representation is enabled by the method of path-sum [29], which generates the linear Volterra integral equation of the second kind satisfied by any function involved a system of coupled linear differential equations with variable coefficients.
This paper is organised as follows. In Section 2 we give the minimal necessary background on Heun equations. This section concludes in §2.4 with a review of existing integral representations of Heun functions and their major drawback as noted in the recent mathematical-physics literature. Section 3 is a self-contained presentation of the novel, elementary integral representations of all functions of Heun class, illustrated with concrete examples. This section contains none of the proofs, all of which are deferred to Appendix A. Then, in Section 4 we give the elementary integral series representation of the solution to the Teukolsky radial equation. This representation is the first one to be convergent from the black hole horizon up to spatial infinity. This stands in contrast to the state-of-the-art MST formalism [51], that uses two hypergeometric series (one convergent at the horizon and the other at infinity) that must then be matched after an analytic continuation procedure. This last step requires the introduction of an auxiliary parameter lacking physical correspondence, at the very least obscuring the physical picture. The convergence of the integral series over the entire domain from the black hole horizon up to spa-
tial infinity therefore alleviates the need for such parameters lacking physical correspondence when calculating solutions of the Teukolsky radial equation. These solutions are of primary importance for computing quantities of physical interest such as gravitational wave fluxes [26] and quasinormal modes [84]. We conclude in §5 with a brief discussion of the novel integral series and future prospects of the method of path-sum from which they stem for solving the coupled system of Teukolsky angular and radial equations.
2 Heun Differential Equations
2.1 Mathematical Context
The most general linear, homogenous, second order differential equation with polynomial coefficients is given by the Fuchsian equation [70] which has the following form
\[ P(z) \frac{d^2 y(z)}{dz^2} + Q(z) \frac{dy(z)}{dz} + R(z)y(z) = 0, \quad z \in \mathbb{CP}^1, \]
where \( \mathbb{CP}^1 \) is the Riemann sphere. In the above equation, if the function \( K_{QP} = Q(z)/P(z) \) has a pole of at most first order and \( K_{RP} = R(z)/P(z) \) has a pole of at most second order at some singularity \( z = z_0 \), then \( z_0 \) is called a Fuchsian singularity, otherwise it is an irregular singularity. The above equation is a Fuchsian equation if all its singularities are Fuchsian singularities. Now, any Fuchsian equation with exactly four singular points can be mapped onto a Heun equation [32] by transformation in dependent or independent variables. These transformations are called s-homotopic and Möbius transformations respectively. The Heun equation is a straightforward generalisation of the hypergeometric equation, a Fuchsian equation with exactly three singular points [70].
2.2 General Heun Equation
As mentioned in the Introduction, the Heun differential equation is the most general Fuchsian equation with four regular singularities. The canonical form of the equation, also known as the General Heun Equation (GHE) is given by the following equation and conditions:
\[ \frac{d^2 y(z)}{dz^2} + \left[ \frac{\gamma}{z} + \frac{\delta}{z-1} + \frac{\epsilon}{z-t} \right] \frac{dy(z)}{dz} + \frac{\alpha \beta z - q}{z(z-1)(z-t)} y(z) = 0, \quad (1) \]
where \( q \in \mathbb{C} \) is called the accessory parameter. The corresponding Riemann-P symbol is as follows:
\[
\begin{pmatrix}
0 & 1 & a & \infty \\
0 & 0 & 0 & \alpha \\
1 - \gamma & 1 - \delta & 1 - \epsilon & \beta
\end{pmatrix}
\]
where the parameters satisfy the Fuch’s condition:
\[ 1 + \alpha + \beta = \gamma + \delta + \epsilon \]
The GHE has four singular points at \( z = 0, 1, t, \infty \). Concerning its solutions, Maier, completing a task initiated by Heun himself has shown that solutions of the GHE have Coxeter group \( D_4 \) as their automorphism group [49]. This means that 192 solutions can be generated using the symmetries of \( D_4 \), much more than the 24 solutions of the Gauss Hypergeometric equation determined by Kummer [81]. We refer the reader to [49] for the complete list of solutions and their relations as well as to [70] for a further discussion of their properties.
For specific parameter values the Heun equation reduces to other well-known equations of importance: e.g. setting \( \epsilon = 0, \gamma = \delta = 1/2 \) yields the Mathieu equation, which has found widespread applicability in the theoretical and experimental study of vibration phenomenon [16,54], electromagnetic scattering from elliptic waveguides [34,93], ion traps in mass spectrometry [61], stability of floating ships [63]. Furthermore, the confluent form of the Heun equation has found wide ranging applications in quantum particle confinement and interaction potentials [44,53] and in the Stark effect [67,70].
2.3 Confluent Heun Equations
The GHE contains 4 regular singularities. If we apply a confluence procedure to two of its singularities such that we get an irregular singularity, we call the resultant equation a confluent Heun equation (CHE). The CHE contains at least one irregular singular point besides the regular singular points. We can construct local solutions in the vicinity of this irregular singular point by the means of (generally divergent) Thomé series [70]. The number of parameters in the CHE are reduced by one. Thus by applying the confluence procedure laid out in [70] to the singularities at \( z = t \) and \( z = \infty \) in equation 2, we get the CHE:
\[
\frac{d^2 y(z)}{dz^2} + \left[ \gamma + \frac{\delta}{z} + \frac{1}{z-1} + \epsilon \right] \frac{dy(z)}{dz} + \alpha z - q \frac{y(z)}{z(z-1)} = 0. \tag{2}
\]
By continuing application of the confluence procedure, we obtain the bi-confluent Heun equation
\[
\frac{d^2 y(z)}{dz^2} + \left[ \gamma + \delta + \epsilon z \right] \frac{dy(z)}{dz} + \alpha z - q \frac{y(z)}{z} = 0, \tag{3}
\]
and related doubly-confluent Heun equation
\[
\frac{d^2 y(z)}{dz^2} + \left[ \frac{\delta}{z^2} + \gamma + \frac{1}{z} \right] \frac{dy(z)}{dz} + \alpha z - q \frac{y(z)}{z^2} = 0, \tag{4}
\]
as well as the triconfluent Heun equation
\[ \frac{d^2 y(z)}{dz^2} + \left[ \gamma + \delta z + \epsilon z^2 \right] \frac{dy(z)}{dz} + (\alpha z - q)y(z) = 0. \]
(5)
We refer the reader to [70] for further general informations on these functions.
2.4 Integral representations of Heun functions
Erdélyi was the first to give an integral equation relating the values taken at two points by a general Heun function [21]. His equation, a Fredholm integral equation, involves an hypergeometric kernel and can be used to obtain a series representation of Heun functions as sums of hypergeometric functions with coefficients determined via recurrence relations. Applications of this result in the special cases of Mathieu and Lamé equations were discussed by Sleeman [72]. Naturally, since Erdélyi’s breakthrough many mathematical works on Heun equations were concerned with integral transformations involving Heun functions. In particular, based on the work of Carlitz [11], Valent found an integral transform for the Heun equation in terms of Jacobi polynomials [78]; Ishkhanyan gave expansions of the confluent Heun functions involving incomplete beta functions [38]; El Jaick and coworkers [20] provided novel transformations and classified expansions for Heun functions involving hypergeometric kernels; and Takemura found an elliptic transformation relating Heun’s functions for different parameters based on the Weierstrass sigma function [76]. This brief list of contributions is far from exhaustive, we refer to the recent review [35] for more details.
The common feature of all of these integral transforms is that they contain higher transcendental functions which makes them physically opaque and of limited use for practical calculations. In addition, the resulting series representations for the Heun functions have insufficient radiuses of convergence [??] causing difficulties for black hole perturbation theory (see Section ??). These issues were noted in the recent review [35] on Heun’s functions, the current state of research on this being described as follows:
“No example has been given of a solution of Heun’s equation expressed in the form of a definite integral or contour integral involving only functions which are, in some sense, simpler... This statement does not exclude the possibility of having an infinite series of integrals with ‘simpler’ integrands”.
In this work, we constructively prove the existence of such a representation for all types of Heun’s functions and for all parameters, in the form of infinite series of integrals whose integrands involve only rational functions and exponentials of polynomials. Furthermore, we show that the series converges everywhere except at the singular points of the Heun function. We show that any Heun function, general or (bi-, doubly-, tri-)confluent, is a sum of exactly two functions each of which satisfy a linear Volterra equation of the second kind with explicitly identified elementary kernels. In particular, any Heun function $H(z)$ itself satisfies a linear integral Volterra equation of the second
kind with such an elementary kernel if either there is at least one non-singular point \( z_0 \in \mathbb{R} \) where \( H(z_0) = H'(z_0) \) or there is a point where \( H(z_0) = 0 \).
3 Elementary integral series for all types of Heun functions
Owing to the emphasis of the present work on concrete results and a physical application, all the technical mathematical proofs are deferred to Appendix A.
3.1 Notation
The * notation is useful to denote iterated integrals. Let \( K(z, z_0) \) be a function of two variables that is continuous over \([z_0, z]\). We denote \( K(z, z_0) = K^n(z, z_0) \) and, for any integer \( n > 1 \),
\[
K^{*n}(z, z_0) = \int_{z_0}^{z} K^{*(n-1)}(z, \zeta_1) K(\zeta_1, z_0) d\zeta.
\]
In other terms \( K^{*n} \) is the Volterra composition \([80]\) of \( K \) with itself \( n \)-times. The only type of integral series that is required to present all results of this section is the following
\[
G(z, z_0) := \sum_{n=1}^{\infty} K^{*n}(z, z_0),
\]
\[
= K(z, z_0) + \int_{z_0}^{z} K(z, \zeta) K(\zeta_1, z_0) d\zeta_1 + \int_{z_0}^{z} \int_{\zeta_1}^{z} K(z, \zeta_2) K(\zeta_2, \zeta_1) K(\zeta_1, z_0) d\zeta_2 d\zeta_1 + \cdots,
\]
see also Eq. (29). In the appendix, we show that once \( z_0 \) is fixed, the above series converges over any subinterval of \( \mathbb{R} \) which does not contain a singularity of \( K(z, z_0) \). A bound on the convergence speed of the series is also provided.
The function \( G(z, z_0) \) defined above, is solution to the linear Volterra integral equation of the second kind
\[
G(z, z_0) = K(z, z_0) + \int_{z_0}^{z} K(z, \zeta) G(\zeta, z_0) d\zeta,
\]
or, in * notation, \( G = K + K \ast G \). Thus, the function \( G \) can either be evaluated from the integral series or by solving the above Volterra equation.
3.2 Results
We emphasize that all results stated remain valid for complex parameter values. This is crucial notably when forming solutions of the Teukolsky equation in the study of quasinormal modes, for which the frequency parameter takes complex values (see Eq. [21]).
**Corollary 1 (General Heun Equation)** Let $H_G(z)$ be solution of the General Heun Equation,
$$
\frac{d^2 H_G(z)}{dz^2} + \left[ \frac{\gamma + \delta}{z} + \frac{\epsilon}{z-1} + \frac{\alpha \beta z - q}{z(z-1)(z-t)} \right] \frac{dH_G(z)}{dz} + \frac{\alpha \beta z - q}{z(z-1)(z-t)} H_G(z) = 0,
$$
with initial conditions $H_G(z_0) = H_0$ and $\dot{H}_G(z_0) = H_0'$, assuming that $z_0 \in \mathbb{R}$ is not a singular point of $H_G$. Denote $I$ the largest real interval that contains $z_0$ and does not contain any singular point of $H_G$. Then, for any $z \in I$,
$$
H_G(z) = H_0 + \int_{z_0}^{z} G_1(\zeta, z_0) d\zeta + (H_0' - H_0) \left( e^{z-z_0} - 1 + \int_{z_0}^{z} (e^{z-\zeta} - 1) G_2(\zeta, z_0) d\zeta \right),
$$
where $G_i$ = $\sum_{n=1}^{\infty} K_i^{*n}$ and
$$
K_1(z, z_0) = 1 + e^{-z} \int_{z_0}^{z} \left\{ \zeta^\gamma \left( \frac{\zeta-1}{\zeta} \right)^\delta \left( t - \zeta \right)^\epsilon \left( \frac{q - \alpha \beta z}{(z-1)(z-t)} \right) \right\} d\zeta,
$$
$$
K_2(z, z_0) = \left( \frac{q - \alpha \beta z}{(z-1)(z-t)} \right) \left( \frac{\zeta^\gamma \left( \frac{\zeta-1}{\zeta} \right)^\delta \left( t - \zeta \right)^\epsilon}{\zeta - z \delta} \right) - \frac{\epsilon}{z-1} - \frac{\gamma}{z-1} - 1 - \frac{\delta}{z-1} - 1.
$$
**Example 1 (Elementary integral series converging to a general Heun function)**
In order to illustrate concretely the above corollary, consider the following General Heun equation (here with arbitrary parameters),
$$
\frac{d^2 H_G(z)}{dz^2} + \left[ \frac{2}{z} + \frac{7}{z-1} + \frac{-1}{z-4} \right] \frac{dH_G(z)}{dz} + \frac{(3/2)z - 1}{z(z-1)(z-4)} H_G(z) = 0, \quad (7)
$$
with initial conditions $H_G(6) = H_0(6) = 1$. Here, the largest real interval containing 6 and none of the singular points 0, 1, and $t = 4$ is $I = [4, +\infty[$. Thus Corollary [1] indicates that for any $z \in [4, +\infty[$,
$$
H_G(z) = 1 + \int_{z_0}^{z} G_1(\zeta, z_0) d\zeta,
$$
$$
= 1 + \sum_{n=1}^{\infty} \int_{6}^{z} K_1^{*n}(\zeta, 6) d\zeta,
$$
$$
= 1 + \int_{6}^{z} K_1(\zeta, 6) d\zeta + \int_{6}^{z} \int_{6}^{\zeta} K_1(\zeta, \xi) K_1(\xi, 6) d\xi d\zeta + \cdots.
$$
with the kernel $K_1$ given by
$$K_1(z, z_0) = 1 - e^{-z} \frac{(z - 4)}{z^2(z - 1)^2} \int_{z_0}^{z} e^{\zeta_1} \frac{(\zeta_1 - 1)}{(\zeta_1 - 4)^2} \left(2\zeta_1^3 + 10\zeta_1^2 - 67\zeta_1 + 14\right) d\zeta_1.$$
In Fig. (4), we show a purely numerical evaluation of $H_G(z)$ together with analytical estimates based on the first few orders of the above series, i.e. we give $H_G^{(m)}(z) := 1 + \sum_{n=1}^{m} \int_{6}^{z} K_1^*(\zeta, 6) d\zeta$, with $m = 1, 2, 3$ and $m = 6$. This exhibits the convergence of the Neumann series representation of the path-sum formulation of a general Heun function, as predicted by the theory.
**Fig. 1** **Convergence to a general Heun function with elementary integrals.** Numerical evaluation of the general Heun function solution of Eq. (7) (solid black line), together with the first integral approximands of it: $H_G^{(1)}(z)$ (dotted magenta line), $H_G^{(2)}(z)$ (dashed blue line) and $H_G^{(6)}(z)$ (solid blue line, very close to the numerical solution). For orders $m \geq 9$, we reach the numerical solution to within machine precision. Note that the integral series given here is convergent on $z \in [4, +\infty]$ but we show only the interval $z \in [6, 26]$ for illustration purposes.
The results above continue to hold should e.g. $z_0 = 3$, in which case $I = [1, 4]$; $z_0 = 1/2$ implying $I = [0, 1]$; or $z_0 = -20$ giving $I = [-\infty, 0]$. In other terms, the integral representation given for the General Heun function is valid everywhere on $z \in \mathbb{R}\{0, 1, t = 4\}$ but can only be used in an interval $I$ where initial conditions for $H_G$ are available.
Corollary 2 (Confluent Heun Equation) Let \( H_C(z) \) be solution of the Confluent Heun Equation,
\[
\frac{d^2 H_C(z)}{dz^2} + \left( \frac{\gamma}{z} + \frac{\delta}{z-1} + \epsilon \right) \frac{d H_C(z)}{dz} + \frac{\alpha z - q}{z(z-1)} H_C(z) = 0,
\]
with initial conditions \( H_C(z_0) = H_0 \) and \( \dot{H}_C(z_0) = H'_0 \), assuming that \( z_0 \neq 0 \) and \( z_0 \neq 1 \). If \( z_0 < 0 \), let \( I = ]-\infty,0[ \), if \( 0 < z_0 < 1 \) let \( I = ]0,1[ \), and else for \( z_0 > 1 \) let \( I = ]1, +\infty[ \). Then, for any \( z \in I \),
\[
H_C(z) = H_0 + H_0 \int_{z_0}^{z} G_1(\zeta, z_0) d\zeta + (H'_0 - H_0) \left( e^{z-z_0} - 1 + \int_{z_0}^{z} (e^{z-\zeta} - 1) G_2(\zeta, z_0) d\zeta \right),
\]
where \( G_i = \sum_{n=1}^{\infty} K_i^n \), \( i = 1, 2 \), and
\[
\begin{align*}
K_1(z, z_0) &= 1 + e^{-z} \int_{z_0}^{z} \left\{ e^{\zeta} \gamma(\zeta-1) \delta e^{\zeta} \right\} d\zeta, \\
K_2(z, z_0) &= \left( \frac{q - \alpha z}{(z-1)z} - \frac{\gamma}{z} - \frac{\delta}{z-1} - \epsilon - 1 \right) e^{z-z_0} - \frac{q - \alpha z}{(z-1)z}.
\end{align*}
\]
Example 2 (Convergence to a Confluent Heun function) Let us now consider the following Confluent Heun function \( H_C(z) \) satisfying
\[
\frac{d^2 H_C(z)}{dz^2} + \left( \frac{3}{z} + \frac{2(2/3)}{z-1} + \frac{4}{z} \right) \frac{d H_C(z)}{dz} + \frac{5z - 1}{z(z-1)} H_C(z) = 0 \tag{8}
\]
with initial conditions \( H_C(-5) = 0 \) and \( H'_C(-5) = 1 \). Suppose that we wish to evaluate \( H_C \) on the interval \( z \in ]-\infty,0[ \), i.e. on both sides \( z < z_0 \) and \( z > z_0 \) of the conditions at \( z_0 = -5 \). Then Corollary 2 indicates that, for any \( z \in ]-\infty,0[ \), we have
\[
H_C(z) = e^{z+5} - 1 + \int_{-5}^{z} (e^{z-\zeta} - 1) G_2(\zeta, -5) d\zeta,
\]
with \( G_2 = \sum_{n=1}^{\infty} K_2^n \) and
\[
K_2(z, z_0) = \frac{3(5z - 1) - e^{z-z_0}(3z+4)(5z-3)}{3(z-1)z}.
\]
We emphasize that these results hold for all \( z \in ]-\infty,0[ \) since this interval is divergence free, more precisely \( K_2 \) is bounded continuous on any compact subinterval of \( ]-\infty,0[ \) and the integral series for \( G_2 \) is thus guaranteed to converge on this entire domain (this is shown in the appendix). Note that when considering \( z < z_0 \), all integrals remain the same as for \( z > z_0 \).
In Fig. (2) below, we show a purely numerical evaluation of $H_C(z)$ together with the truncated integral series approximations
$$H_C^{(m)}(z) := \int_{-5}^{z} (e^{z-\zeta} - 1) \left( 1 + \sum_{n=1}^{m} K_2^n(\zeta,-5) d\zeta \right),$$
$$= \int_{-5}^{z} (e^{z-\zeta} - 1) \left( 1 + K_2(\zeta,-5) + \int_{z}^{\zeta} K_2(\zeta,\zeta_1)K_2(\zeta_1,-5) d\zeta_1 + \cdots \right).$$
Since kernel $K_2$ is singular at $z = 0$ just as $H_C$ is, we expect the convergence speed of the integral series to slow down when approaching the singular point, as predicted by the bound of Eq. (30) presented in the appendix. This does not preclude analytically obtaining the correct asymptotic behavior for $H_C(z)$ as $z \to 0^-$. Indeed this follows from the behavior of $K_2$ under the same limit. We demonstrate such a procedure in \S 4.4.
Fig. 2 Convergence to a Confluent Heun function with elementary integrals over the interval $]-\infty,0]$. Numerical solution of the Eq. (8) (solid black line) with conditions $H_C(-5) = 0$, $H_C'(-5) = 1$, together with its integral approximands as per Eq. (9), $H_C^{(2)}(z)$ (dotted magenta line), $H_C^{(20)}(z)$ (dot-dashed red line) and $H_C^{(40)}(z)$ (dashed blue line, very close to the numerical solution). Convergence near $z = 0$ is slowed down due to $K_2$ being singular at $z = 0$ just as $H_C$ is. Still, the integral series is convergent over the entire domain $z \in ]-\infty,0]$, a crucial property for perturbative black hole theory that is unique to the present approach. Here as in subsequent examples we plot the various functions over smaller intervals for $z$, for illustration purposes.
Corollary 3 (Biconfluent Heun Equation) Let $H_B(z)$ be solution of the Biconfluent Heun Equation,
\[
\frac{d^2 H_B(z)}{dz^2} + \left[ \frac{\gamma}{z} + \delta + \epsilon z \right] \frac{dH_B(z)}{dz} + \frac{\alpha z - q}{z} H_B(z) = 0,
\]
with initial conditions $H_B(z_0) = H_0$ and $H_B'(z_0) = H_0'$, assuming that $z_0 \neq 0$.
If $z_0 > 0$, denote $I = [0, +\infty[$ otherwise let $I = ]-\infty, 0]$. Then, for any $z \in I$,
\[
H_B(z) = H_0 + H_0 \int_{z_0}^{z} G_1(\zeta, z_0)d\zeta + (H_0' - H_0) \left( e^{z-z_0} - 1 + \int_{z_0}^{2}(e^{z-\zeta} - 1)G_2(\zeta, z_0) d\zeta \right),
\]
where $G_i = \sum_{n=1}^{\infty} K_i^{*n}$, $i = 1, 2$, and
\[
K_1(z, z_0) = 1 + e^{-z} \sum_{n=0}^{\infty} \left\{ \frac{\zeta_1^n}{z} e^{\zeta_1 - \frac{1}{2}(z-\zeta_1)(2\delta + \epsilon(z+1))} \left( \frac{q - \alpha\zeta_1}{\zeta_1} - \frac{\gamma}{\zeta_1} - \delta - \zeta_1\epsilon - 1 \right) \right\} d\zeta_1,
\]
\[
K_2(z, z_0) = \left( \frac{q - \alpha z}{z} - \frac{\gamma}{z} - \delta - z\epsilon - 1 \right) e^{z-z_0} - \frac{q - \alpha z}{z}.
\]
Example 3 (Evaluating a Biconfluent Heun function via Volterra equations) Let us now consider the following Biconfluent Heun function $H_B(z)$ satisfying
\[
\frac{d^2 H_B(z)}{dz^2} + \left[ \frac{(1/10)}{z} + 1 + 6z \right] \frac{dH_B(z)}{dz} + \frac{(-1)z - 2}{z} H_B(z) = 0,
\]
with initial conditions $H_B(2/3) = 0$ and $H_B'(2/3) = -4$. Then Corollary 3 indicates that for $z > 0$,
\[
H_B(z) = 2 + 2 \int_{2/3}^{2} G_1(\zeta, 2/3)d\zeta - 6 \left( e^{z-2/3} - 1 + \int_{2/3}^{2}(e^{z-\zeta} - 1)G_2(\zeta, 2/3) d\zeta \right),
\]
with $G_i = \sum_{n=1}^{\infty} K_i^{*n}$ for $i = 1, 2$, and
\[
K_1(z, z_0) = 1 + \int_{z_0}^{2} \frac{(19 - 10\zeta(6\zeta + 1))e^{-(z-\zeta)(3\zeta + 3z^2 + 2)}}{10\zeta_0^{10}z_0^{10}} d\zeta,
\]
\[
K_2(z, z_0) = \frac{(19 - 10z(6z + 1))e^{z-z_0} - 10(z + 2)}{10z}.
\]
Instead of evaluating functions $G_1$ and $G_2$ as the integral series, we may directly solve the linear integral Volterra equations that they satisfy, see Eq. (11). Such equations are very well behaved and numerically easy to solve, so that we can evaluate $H_B$ thanks to Eq. (11) with high numerical accuracy. In Fig. 3, we show the numerical evaluation of $H_B(z)$ obtained using a standard differential equations numerical solver versus the procedure described above.
Corollary 4 (Doubly-confluent Heun Equation) Let $H_D(z)$ be solution of the Doubly-confluent Heun Equation,
$$\frac{d^2 H_D(z)}{dz^2} + \left[ \frac{\delta}{z^2} + \frac{\gamma}{z} + 1 \right] \frac{dH_D(z)}{dz} + \frac{\alpha z - q}{z^2} H_D(z) = 0$$
with initial conditions $H_D(z_0) = H_0$ and $H_D'(z_0) = H_0'$, assuming that $z_0 \neq 0$. If $z_0 > 0$, denote $I = [0, +\infty[$; otherwise let $I = ]-\infty, 0[$. Then, for any $z \in I$,
$$H_D(z) = H_0 + H_0 \int_{z_0}^{z} G_1(\zeta, z_0) d\zeta + (H_0' - H_0) \left( e^{z-z_0} - 1 + \int_{z_0}^{z} (e^{z-\zeta} - 1) G_2(\zeta, z_0) d\zeta \right),$$
where $G_i = \sum_{n=1}^{\infty} K_i^n$, $i = 1, 2$, and
$$K_1(z, z_0) = 1 + e^{-z} \int_{z_0}^{z} \left( \frac{\zeta}{z} \right)^{\gamma} e^{-\frac{\delta}{z} + \frac{\gamma}{z} + \frac{1}{z}} \left( q - \frac{\alpha}{\zeta} \right) \zeta 1 - \frac{\delta}{\zeta} - \frac{\gamma}{\zeta} - 2 \right) d\zeta,$$
$$K_2(z, z_0) = \frac{q - \alpha z}{z^2} - \frac{\delta}{z^2} - \frac{\gamma}{z} - 2 \right) e^{z-z_0} - q - \frac{\alpha z}{z^2}.$$
Example 4 (Convergence to a Doubly-Confluent Heun function) Let us now consider the following Doubly-Confluent Heun equation, once again with arbitrarily chosen parameters for the example,
$$\frac{d^2 H_D(z)}{dz^2} + \left[ \frac{(-2)}{z^2} + \frac{1}{z} + 1 \right] \frac{dH_D(z)}{dz} + \frac{10z - (-1)}{z^2} H_D(z) = 0$$
(12)
with initial conditions \( H_D(1) = H'_D(1) = 1/2 \). Then Corollary 4 indicates that for \( z \in [0, +\infty[ \),
\[
H_D(z) = \frac{1}{2} + \frac{1}{2} \sum_{n=1}^{\infty} \int_1^z K_1^n(\zeta, 1) d\zeta,
\]
with
\[
K_1(z, z_0) = 1 + e^{-z-z_0} \int_{z_0}^z e^{2z_1+\zeta} \frac{1}{\zeta} (1 - 2\zeta^2 + 11\zeta) d\zeta.
\]
In Fig. 4 below, we show a purely numerical evaluation of \( H_D(z) \) together with analytical approximations based on the first few orders of the above series, i.e. we give \( H^{(m)}_D(z) := 1 + \sum_{n=1}^{m} \int_1^z K_1^n(\zeta, 1) d\zeta \), with \( m = 3, 5, 8 \). This demonstrates again the convergence of the Neumann series representation of a general Heun function, as predicted by the theory. Here the exact \( H_D(z) \) and \( H^{(m)}_D(z) \) become indistinguishable for \( m \geq 9 \).
Corollary 5 (Triconfluent Heun Equation) Let \( H_T(z) \) be solution of the Triconfluent Heun Equation,
\[
\frac{d^2 H_T(z)}{dz^2} + \left[ \gamma + \delta z + \epsilon z^2 \right] \frac{dH_T(z)}{dz} + (\alpha z - q)H_T(z) = 0,
\]
with initial conditions \( H_T(z_0) = H_0 \) and \( \dot{H}_T(z_0) = H'_0 \). Then, for any \( z \in \mathbb{R} \),
\[
y(z) = H_0 + H_0 \int_{z_0}^{z} G_1(\zeta, z_0) d\zeta + (H'_0 - H_0) \left( e^{z-z_0} - 1 + \int_{z_0}^{z} (e^{z-\zeta} - 1) G_2(\zeta, z_0) d\zeta \right),
\]
where \( G_i = \sum_{n=1}^{\infty} K^*_i n \), \( i = 1, 2 \) and
\[
K_1(z, z_0) = 1 - e^{-\frac{1}{6}\pi i(\gamma + 2z^2 + 3z + 6)} \int_{z_0}^{z} e^{\frac{1}{6}\pi i(\gamma + 3\zeta^2 + 2z^2 + 6)} (\zeta(\alpha + \delta + \epsilon) + \gamma - q + 1) d\zeta,
\]
\[
K_2(z, z_0) = -(\epsilon z^2 + (\alpha + \delta) z - q + \gamma + 1) e^{z-z_0} - (q - z\alpha).
\]
Example 5 (Convergence to a complex-valued Triconfluent Heun function) Consider the Triconfluent Heun function defined as the solution to
\[
\frac{d^2 H_T(z)}{dz^2} + \left[ 2 - z + 7z^2 \right] \frac{dH_T(z)}{dz} + (z - (2 + i))H_T(z) = 0, \tag{13}
\]
where \( i^2 = -1 \), and with initial conditions \( H_T(-5) = H'_T(-5) = 2 \). Corollary 5 indicates that for \( z \in \mathbb{R} \),
\[
H_D(z) = 2 + 2 \int_{z_0}^{z} G_1(\zeta, -10) d\zeta,
\]
with \( G_1 = \sum_{n=1}^{\infty} K^*_1 n \) and
\[
K_1(z, z_0) = 1 - e^{-\frac{1}{6}\pi i(3-14z)^2 + 3z^2} \int_{z_0}^{z} e^{-\frac{1}{6}\pi i(3-14\zeta^2 + 3\zeta^2 + 1 - i)} d\zeta.
\]
We show in Fig. [5] convergence to the complex-valued triconfluent Heun function by the integral series
\[
H_T^{(n)}(z) := 2 + 2 \int_{z_0}^{z} \sum_{n=1}^{\infty} K^*_1 n(\zeta, -10) d\zeta,
\]
\[
= 2 + 2 \int_{z_0}^{z} K_1(\zeta, -10) d\zeta + \int_{z_0}^{z} \int_{z_0}^{z} K_1(z, \zeta_1) K_1(\zeta_1, -10) d\zeta_1 d\zeta + \cdots
\]
With this example, we emphasize that all the integrals representations obtained here remain valid for complex-valued Heun functions.
Having focused on concrete evaluations of various Heun functions in the illustrative examples, we now turn to using the elementary integral series in the field of black hole physics.
Fig. 5 Convergence to a complex-valued Triconfluent Heun function with elementary integrals. Numerical solution of the Eq. (13) (solid black line), together with its integral approximands $H^{(1)}_T(z)$ (dotted magenta line), $H^{(3)}_T(z)$ (dot-dashed red line) and $H^{(6)}_T(z)$ (dashed blue line). Top figure: real parts of these quantities. Bottom figure: imaginary parts of these quantities. Note that the integral series provided is convergent over the entire real line, we here show only the interval $z \in [-5, 7]$ for illustration purposes.
4 Application to Black-Hole Perturbation Theory
4.1 Motivations
The theory of metric perturbations of Kerr black holes is governed by the Teukolsky equation [77]. This equation provides the basic mathematical framework to study the stability of Schwarzschild [25] and Kerr black holes [11] and yields physical insights in the broader field of gravitational wave astrophysics [65]. With the advent of event detections by LIGO [1,2], obtaining a better analytical grasp over the solutions of the Teukolsky equation is paramount in modeling the ringdown stage [47] of a binary black hole merger using accurate waveform templates [55].
In the frequency domain, the Teukolsky equation can be decoupled into radial and angular components [77]. Determining the analytical solutions of the radial equation has been an active area of research since the first formulation of the equations [52,65]. To this end, state-of-the-art approaches all rely on the same strategy: i) obtain two series expansions of the solution, one convergent near the black hole horizon the other at spatial infinity; and ii) match both expansions at some intermediate radial point. The standard implementation of this strategy, due to Mano, Suzuki and Takasugi (MST) [52,51], relies on a series of hypergeometric functions at the black hole horizon and of Coulomb wave functions at spatial infinity. Matching both expansions requires the introduction of an auxiliary parameter $\nu$. We stress that this parameter is not part of the original parameters of the Teukolsky equation. Rather $\nu$ is a mathematical checkpost introduced to establish the convergence and matching of the hypergeometric and Coulomb series [26]. The MST strategy successfully yields accurate numerical data for studying gravitational wave radiation from Kerr black holes [65,28]. It is “the only existing method that can be used to calculate the gravitational waves emitted to infinity to an arbitrarily high post-Newtonian order in principle.” [65]. At the same time, it has been explicitly recognised that the mathematical complexity of the formalism obscures physical insights into the problem [65]. In particular, the auxiliary parameter $\nu$, which has been called “renormalised angular momentum” to make it more palatable, has limited correspondence to physical phenomenon, if any.
More recently, explicit, analytic solutions to the Teukolsky equation have been established in terms of Heun functions [8]. Yet, Cook and Zalutskiy [13] note that in order to extract physical quantities of interest out of this approach, one is forced to revert to Leaver’s formalism [45] because “the series solution around $z = 1$ has a radius of convergence no larger than 1, far short of infinity”. Thus, just as for the MST formalism the problem is, in essence, that we are lacking a single representation of the solution to the Teukolsky radial equation that is convergent from the black hole horizon up to spatial infinity. The integral series provided in this work addresses this issue completely since it converges on this entire domain, thereby retaining the crucial features of the MST formalism that lead to its widespread applicability, while also not
requiring any auxiliary, unphysical parameter. In a similar vein, we can assert that our formalism is suited for practical numerical and even analytical calculations since the integral series are rapidly convergent, and their asymptotic behavior is analytically available. We may therefore also hope that the integral series representation will help solve the well-recognised computational difficulties that emerge from the MST formalism when applied to gravitational wave physics, in particular for the two body problem [7], and in the gravitational self force program [33,40].
For completeness, we begin with a brief discussion of the theory of the Teukolsky equation and its reduction to Heun form. We then give the series representation of its solution. Finally, we establish its asymptotics at both the black hole horizon \((z \to 1^+)\) and spatial infinity \((z \to +\infty)\).
4.2 The Teukolsky Equation : background
The Teukolsky Equation [77] is a gauge invariant equation [24] that governs the curvature perturbations of the Kerr black hole [56]. By making use of the Newman-Penrose formalism [59], the single master equation for the spin \((s)\) weighted scalar wave function \(s\psi\) in Boyer-Lindquist co-ordinates \([t,r,\theta,\phi]\) and the Kinnersley tetrad [42] is written as:
\[
\left(\frac{r^2 + a^2}{\Delta} - a^2 \sin^2 \theta\right) \frac{\partial^2 s\psi}{\partial t^2} + \left(\frac{4Ma r}{\Delta}\right) \frac{\partial^2 s\psi}{\partial t \partial \phi} + \left[\frac{a^2}{\Delta} - \frac{1}{\sin^2 \theta}\right] \frac{\partial^2 s\psi}{\partial \phi^2} - \frac{4s}{\Delta} \left[Mr - r \cos \theta \right] \frac{\partial s\psi}{\partial \phi} + 4s \left[\frac{M(r^2 - a^2)}{\Delta} - \frac{r - ia \cos \theta}{\Delta} + (s^2 \cot^2 \theta - s) s\psi = 4\pi \Sigma T\right]
\]
where the auxiliary variables are given by:
\[
\Sigma \equiv r^2 + a^2 \cos^2 \theta, \Delta \equiv r^2 - 2Mr + a^2
\]
Here, \(M\) is the mass of the black hole, \(a\) is its angular momentum (per unit mass), \(T\) is the source term built from the energy-momentum tensor [77] and the spin parameter \(s = 0, \pm 1/2, \pm 1, \pm 2 \pm 3/2\) for scalar, neutrino, electromagnetic, gravitational and Rarita-Schwinger [12] fields respectively. It reduces to the Bardeen-Press equation [5] in the non-rotating \((a = 0)\) case.
The equation (14) can be separated in time [33] and frequency domain [77]. The latter can be performed for the vacuum case \((T = 0)\) by the following separation ansatz:
\[
s\psi(t,r,\theta,\phi) = e^{-i\omega t} e^{im\phi} S(\theta) R(r).
\]
For the radial function \(R(r)\) we obtain the Teukolsky Radial Equation (TRE):
\[
\Delta^{-s} \frac{d}{dr} \left[\Delta^{s+1} \frac{dR(r)}{dr}\right] + \left[\frac{K^2 - 2is(r-M)K}{\Delta} + 4is\omega r - \lambda\right] R(r) = 0,
\]
where
where,
\[ K \equiv (r^2 + a^2)\omega - am, \quad \lambda \equiv sA_{lm}(a\omega) + a^2\omega^2 - 2am\omega. \]
For the angular equation, we make \( x \equiv \cos \theta \). Now the function \( S(\theta) = sS_{lm}(x; a\omega) \) is the spin weighted spheroidal function [10] which gives the solution for the Teukolsky Angular Equation (TAE):
\[
\partial_x \left[ (1 - x^2)\partial_x sS_{lm}(x; c) \right] + \left[ (cx)^2 - 2csx + s \right]
+ sA_{lm}(c) - \frac{(m + sc)^2}{1 - x^2} sS_{lm}(x; c) = 0,
\]
where \( c = a\omega \) is the oblateness parameter, \( m \) is the azimuthal separation constant and \( sA_{lm}(c) \) is the angular separation constant. The equations 17 and 19 are coupled equations which require simultaneous evaluation of the parameters \( \omega \) and \( sA_{lm}(c) \). Given a value for \( sA_{lm}(c) \), we can solve 17 for the complex frequency \( \omega \) and given the latter, we can solve 19 as an eigenvalue problem for \( sA_{lm}(c) \).
4.3 Teukolsky Radial Equation in Heun Form
We now reduce the Teukolsky Radial Equation to the non-symmetrical Heun form, which allows us to represent its solution with the results of Section. 3. There is one small consideration to be noted: depending on the sign of the spin \( s \) we wish to operate in, certain parameters of the CHE form of the TAE and TRE flip their signs as given in [8]. However this is not of relevance for our purposes since our main aim is to work with the CHE form of the equations that obviously remains irrespective of the sign of the spin parameter.
The radial function \( R(r) \) solution to Eq. 17 has three singularities: an irregular singular point at \( r = \infty \) and two regular singular points corresponding to the roots of \( \Delta = 0 \), which are
\[ r_{\pm} = M \pm \sqrt{M^2 - a^2} \]
The values \( r_{\pm} \) correspond to the event and Cauchy horizon respectively (for an in-depth introduction to the notation and terminology on back-hole mathematics, we refer the reader to [56]). Having identified these, we may now map the Teukolsky Radial Equation into an Heun equation. We close following the standard treatment [13]. We begin by letting the radial function \( R \) be of the form
\[ R(r) = (r - r_+)^\zeta(r - r_-)^\eta e^{\xi r} H(r), \]
where the parameters \( \zeta, \xi, \eta \) are given by
\[
\zeta = \pm i\omega \equiv \zeta_\pm, \quad \xi = -\frac{2 \pm (s + 2i\sigma_+)}{2} \equiv \xi_\pm, \\
\eta = -s \pm \frac{(s - 2i\sigma_-)}{2} \equiv \eta_\pm, \quad \sigma_\pm = 2Mr_{\pm} - ma \]
\[ r_+ - r_- \right]. \]
With the dimensionless variables
\[ \bar{r} \equiv \frac{r}{M}, \quad \bar{a} \equiv \frac{a}{M}, \quad \bar{\omega} \equiv M\omega, \quad \bar{\zeta} \equiv M\zeta, \]
we transform the radial coordinate \( r \) into the dimensionless variable \( z \) defined by
\[ z = \frac{r - r_-}{r_+ - r_-} = \frac{\bar{r} - \bar{r}_-}{\bar{r}_+ - \bar{r}_-}. \]
Now, any of the eight possible combinations of the parameters \( \{\zeta, \xi, \eta\} \) given in Eqs. \( \text{(21)} \) will reduce the Teukolsky Radial Equation \( \text{(17)} \) into the following equation for the auxiliary function \( H \),
\[ \frac{d^2 H(z)}{dz^2} + \left( \frac{\gamma}{z} + \frac{\delta - 1 + 4p}{z - 1} \right) \frac{dH(z)}{dz} + \frac{4\alpha p z - \sigma}{z(z - 1)} H(z) = 0 \tag{22} \]
which is a Confluent Heun equation. Here, the following variables have been introduced to clarify the equation,
\[ p = (\bar{r}_+ - \bar{r}_-)^2 \bar{\zeta}, \quad \alpha = 1 + s + \xi + \eta - 2\bar{\zeta} + \bar{\omega} \bar{\zeta}, \]
\[ \gamma = 1 + s + 2\eta, \quad \delta = 1 + s + 2\xi, \]
\[ \sigma = sA_{lm}(\bar{a}\bar{\omega}) + \bar{a}^2\bar{\omega}^2 - 8\omega^2 + p(2\alpha + \gamma - \delta) + \left( 1 + s - \frac{\gamma + \delta}{2} \right) \left( s + \frac{\gamma + \delta}{2} \right). \tag{23} \]
Furthermore, the local solutions at the singularities have the exact same form for all eight combinations of the parameters \( \{\zeta, \xi, \eta\} \) given in Eqs. \( \text{(21)} \). More precisely, we get
\[ \lim_{z \to 0} R(z) \sim z^{-s+i\sigma_0} \quad \text{or} \quad z^{-i\sigma_0}, \tag{24a} \]
\[ \lim_{z \to 1} R(z) \sim (z - 1)^{-s+i\sigma_0} \quad \text{or} \quad (z - 1)^{i\sigma_0}, \tag{24b} \]
\[ \lim_{z \to \infty} R(z) \sim z^{-1-2s+2i\omega} e^{i(r_+ - r_-)\omega z} \quad \text{or} \quad z^{-1-2i\omega} e^{-i(r_+ - r_-)\omega z}. \tag{24c} \]
Now, the above forms correspond to behaviour of the perturbations at the boundary conditions of the event and Cauchy horizon and spatial infinity. By suitable choice of the signs in \( \text{24a}, \text{24b}, \text{and} \text{24c} \) we can obtain expressions for quantities of physical interest such as Quasinormal Modes and Totally Transmitting Modes \[13\]. Also, see \[60,74,73,83\] for applications of the Heun form of the Teukolsky equations. The equation can be solved by various methods such as Frobenius series about the singular points \[8\] and continued fractions \[45\].
4.4 Representation of the Teukolsky radial function convergent on $[1, +\infty[$
4.4.1 Elementary integral series
The solution of the Confluent Heun equation \cite{22} satisfied by the auxiliary function $H(z)$ is described by Corollary (2). Since the singular points are located at $z = 0, 1, +\infty$, given any initial conditions for $H(z_0)$ and $\dot{H}(z_0)$ at $z_0 \in [1, +\infty]$, the integral series representation of $H(z)$ is guaranteed to converge on the entire domain $[1, +\infty[$. This crucial property stands in stark contrast with the hypergeometric and Coulomb series, which converge close to 1 and to $+\infty$, respectively. Because of this, we do not need to introduce the unphysical parameter $\nu$.
Recall that the Teukolsky radial function $R$ and auxiliary function $H$ are related by Eq. (20). The auxiliary function is a confluent Heun function given by the following integral series representation, convergent for any $z \in [1, +\infty[$,
$$H(z) = H_0 + H_0 \int_{z_0}^{z} G_1(\zeta, z_0) d\zeta + (H_0' - H_0) \left(e^{z-z_0} - 1 + \int_{z_0}^{z} (e^{z-z} - 1) G_2(\zeta, z_0) d\zeta \right),$$
where $G_i = \sum_{n=1}^{\infty} K_i^n$, $i = 1, 2$, and
$$K_1(z, z_0) = 1 + e^{-(1+4p)z} z^{-\gamma}(z-1)^{-\delta} \times \int_{z_0}^{z} \left\{ e^{(1+4p)\zeta} \zeta^{-\gamma} (\zeta-1)^{\delta} \left( \frac{\sigma - 4\alpha p \zeta}{(\zeta-1)\zeta} - \frac{\delta}{\zeta-1} - 4p - 1 \right) \right\} d\zeta,$$
$$K_2(z, z_0) = (\frac{\sigma - 4\alpha p z}{(z-1)z} - \frac{\gamma}{z-1} - 4p - 1) e^{z-z_0} - (\frac{\sigma - 4\alpha p z}{(z-1)z}).$$
Here we assumed $z_0 \in [1, +\infty[$ then $H_0 := H(z_0)$, $H_0' := \dot{H}(z_0)$ and all parameters are given by Eq. (23).
Witnessing to the fact that the above representation is convergent for all $z \in [1, +\infty[$, we here recover the asymptotic behavior of $H(z)$ in both limits $z \to 1^+$ and $z \to +\infty$. We emphasize that this is not possible with any single series representation of $H(z)$, which converges either in the vicinity of $1^+$ or of $+\infty$.
4.4.2 Asymptotic behavior for $z \to +\infty$
From now on, we write $F(z) \sim_{a.e.}$ to present the leading term of the asymptotic expansion of the function $F(z)$, disregarding constant factors. For example, we would write $1 + 2/z \sim_{a.e.} z^{-1}$ as $z \to 0$.
We begin by determining the asymptotic behavior of $K_1(z, z_0)$ for $z \gg 1$. This depends on two cases: $p = 0$ and $p \neq 0$. We suppose first that $p = 0$ and assume that $\delta + \gamma > 0$. In this situation, the confluent Heun function becomes a well understood hypergeometric function \cite{22,55} for which we will nonetheless
show that we recover the correct asymptotic behavior. Setting \( p = 0 \) we get, as \( z \to +\infty \),
\[
K_1(z, z_0) \sim_{a.e.} 1 + e^{-(1+4p)z}z^{-\gamma}(z-1)^{-\delta}\left(-e^{z\gamma+\delta} + e^{z_0^-\gamma+\delta}\right),
\]
\[
\sim_{a.e.} e^{-z^{-\gamma}e^{z_0^-\gamma+\delta}}.
\]
Then \( K_1(z, z_0) \) is asymptotically the product of a function depending only
on \( z \) and of a function depending only on \( z_0 \). This property is sufficient to
determine the asymptotic behavior of \( G_1 \) in closed-form\(^1\)
\[
G_1(z, z_0) \sim_{a.e.} e^{-z^{-\gamma}e^{z_0^-\gamma+\delta}} e^{\int_{z_0}^z e^{-\zeta^{-\gamma}e^{\zeta+\delta} d\zeta}} = (z_0/z)^{\delta+\gamma}
\]
implies that \( \int_{z_0}^z G_1(\zeta, z_0) d\zeta \sim_{a.e.} z^{1-\delta-\gamma} \) for \( z \to +\infty \). Analyzing \( K_2 \) and \( G_2 \) yields the same results. Indeed, with \( p = 0 \), we have
\[
K_2(z, z_0) \sim_{a.e.} \left(-\frac{1}{z}(\gamma+\delta) - 1\right) e^{z^{-z_0}},
\]
which is the product of a function of \( z \) and a function \( z_0 \) so we determine
\[
G_2(z, z_0) \sim_{a.e.} \left(-\frac{1}{z}(\gamma+\delta) - 1\right) e^{z^{-z_0}e^{-(z-z_0)(z_0/z)^{\gamma+\delta}}},
\]
that is \( G_2 \sim_{a.e.} z^{-\gamma-\delta} \). From there \( e^{z^{-z_0} - 1 + \int_{z_0}^z e^{z^{-z_0}} - 1)G_2(\zeta, z_0) d\zeta \sim_{a.e.} z^{1-\gamma-\delta} \). Thus for \( p = 0 \) and \( \delta + \gamma > 0 \), we get \( H(z) \sim_{a.e.} z^{1-\gamma-\delta} \) regardless of the conditions at \( z_0 \) and provided \( \delta + \gamma > 0 \), as expected\(^2\). Further cases arise for \( \delta + \gamma \leq 0 \) but we do not discuss these here as they correspond to well
known hypergeometric results.
Let us now suppose that \( p \neq 0 \). Then, since
\[
e^{4pz\zeta}(\zeta-1)^{\delta}f(\zeta) = -e^{4p\zeta}\zeta^{\gamma+\delta}\left(\frac{4\alpha p + \gamma + \delta}{\zeta} + 4p + O(1/\zeta^2)\right),
\]
we have, asymptotically for \( z \to +\infty \),
\[
K_1(z, z_0) \sim_{a.e.} 1 - e^{-4pz}z^{-\gamma}z^{-\delta} \times z^{\gamma+\delta}\left(e^{4pz} - 4pE_{-\gamma-\delta+1}(-4pz)\right).
\]
where \( E_n(z) \) is the exponential integral function, with asymptotic expansion
\( E_n(x) \sim_{a.e.} e^{-x}/x \) as \( x \to +\infty \). This result greatly simplifies \( K_1 \), reducing it to
\[
K_1(z, z_0) \sim_{a.e.} -\frac{\alpha}{z} \text{ as } z \to +\infty.
\]
This allows us to determine the asymptotic behavior of \( G_1 \) straightforwardly as
\[
G_1(z, z_0) \sim_{a.e.} -\frac{\alpha}{z} e^{\int_{z_0}^z -\alpha/\zeta d\zeta} = -\alpha z^{-1-\alpha},
\]
\(^1\) This is because the solution of a linear Volterra integral equation of the second kind
with kernel \( K_1(z, z_0) = k(z)l(z_0) \) is known exactly\(^2\).
and therefore \( \int_{z_0}^{z} G_1(\zeta, z_0) d\zeta \sim_{a.e.} z^{-\alpha} \) for \( z \to +\infty \).
We proceed similarly for \( K_2 \) and \( G_2 \). We have \( K_2(z, z_0) = f(z)e^{z-z_0} + O(1/z) \), so that asymptotically \( K_2(z, z_0) \sim_{a.e.} f(z)e^{z-z_0} \) for \( z \to +\infty \). Then \( K_2(z, z_0) \) is asymptotically the product of a function depending only on \( z_0 \) and of a function depending only on \( z \). We therefore obtain
\[
G_2(z, z_0) \sim_{a.e.} e^{z-z_0} f(z)e^{\int_{z_0}^{z} f(\zeta) d\zeta}, \text{ as } z \to +\infty.
\]
The right-hand side is
\[
e^{z-z_0} f(z)e^{\int_{z_0}^{z} f(\zeta) d\zeta} = e^{-4p(z-z_0)} \left( \frac{z_0 - 1}{z - 1} \right)^\delta \left( \frac{z_0}{z} \right)^{\gamma + \sigma} \left( \frac{1 - z_0}{1 - z} \right)^{4\alpha p - \sigma} \times \frac{1}{z(z - 1)}(1 - z(\gamma + \delta + 4p(\alpha + z - 1) + z - 1) + \sigma)
\]
which yields the asymptotic result,
\[
G_2(z, z_0) \sim_{a.e.} e^{-4pz - 4\alpha p - \delta - \gamma}, \text{ as } z \to +\infty.
\]
This implies that
\[
\left( e^{z-z_0} - 1 + \int_{z_0}^{z} (e^{z-\zeta} - 1)G_2(\zeta, z_0) d\zeta \right) \sim_{a.e.} e^{-4pz - 4\alpha p - \delta - \gamma}.
\]
Gathering our results, we conclude that when \( p \neq 0 \),
\[
H(z) \sim_{a.e.} z^{-\alpha} \quad \text{or} \quad H(z) \sim_{a.e.} e^{-4pz - 4\alpha p - \delta - \gamma}, \text{ as } z \to +\infty,
\]
which gives the same asymptotic behavior as obtained from series designed to converge when \( z \to +\infty \). The result for \( p = 0 \) yields the correct asymptotics of the hypergeometric function obtained in this case.
4.4.3 Asymptotic behavior for \( z \to 1^+ \)
In this situation, we begin with
\[
K_1(z, z_0) \sim_{a.e.} 1 + e^{-(1+4p)(z-1)^{-\delta}} \int_{z_0}^{z} \left( e^{(1+4p)\zeta} (\zeta - 1)^{\delta-1} (e + c'(\zeta - 1)) \right) d\zeta,
\]
where \( e = \sigma - 4\alpha p - \delta \) and \( c' = \gamma + 4p + 1 \). In order to progress without presenting cumbersome equations, denote \( F(\zeta) \) the following indefinite integral
\[
F_3(\zeta) := \int e^{(1+4p)\zeta} (\zeta - 1)^{\delta} d\zeta,
\]
\[
\quad = -e^{4p+1}(\zeta - 1)^{\delta+1}E_{-\delta}(-(1+4p)(\zeta - 1)),
\]
where \( E_{-\delta} \) is the generalized Laguerre function.
where $E_n(x)$ is the exponential integral function. In particular $E_n(x) \sim_{a.e.} x^{n-1}c_1 + c_2$ as $x \to 0^+$ and where $c_1$ and $c_2$ are non-zero real constants that are irrelevant here. This implies $F_\delta(\zeta) \sim_{a.e.} (\zeta - 1)^{1+\delta}$. Now given that
$$K_1(z, z_0) = 1 + e^{-(1+4\rho)z}(z-1)^{-\delta}(cF_{\delta-1}(z) - c'F_{\delta-1}(z_0) + cF_{\delta}(z) - c'F_{\delta}(z_0)).$$
then
$$K_1(z, z_0) \sim_{a.e.} 1, \text{ as } z \to 1^+.\] This implies that $G_1(z, z_0) \sim_{a.e.} e^{z-z_0}$ and therefore $\int_{z_0}^{z} G_1(\zeta, z_0) d\zeta \sim_{a.e.} 1$ as $z \to 1^+$.
For $K_2$ and $G_2$ we begin by noting that for $z$ close to $1$,
$$K_2(z, z_0) \sim_{a.e.} \frac{4\alpha p}{z-1}(1 - e^{z-z_0}) - \frac{\delta}{z-1}, \text{ as } z \to 1^+.\]$$
from which it follows that $G_2(z, z_0) \sim_{a.e.} (z-1)^{-\delta}$ for $z \to 1^+$, and therefore
$$\left(e^{z-z_0} - \int_{z_0}^{z} (e^{z'-\zeta} - 1)G_2(\zeta, z_0) d\zeta\right) \sim_{a.e.} (z-1)^{1-\delta}, \text{ as } z \to 1^+.\]$$
Note that this assumes that $\delta > 0$. If this is not the case, then the asymptotics is $O(1)$.
Gathering our results, we get that
$$H(z) \sim_{a.e.} 1 \text{ or } (z-1)^{1-\delta}, \text{ as } z \to 1^+.\]$$
which gives the same asymptotic behavior as obtained from series representations of $H(z)$ for $z$ close to $1$ \cite{58,13,62}.
4.5 Remarks on the Teukolsky Angular Equation
The Teukolsky angular equation \cite{19} has two regular singular points at $x = \pm 1$ and an irregular singular point at infinity. Just like the radial equation, we can transform it to either the Bocher symmetrical form \cite{13} or the non-symmetric canonical form of the confluent Heun equation \cite{8}. It follows that any solution to the angular equation has an integral series representation as described in this work.
The radial and angular Teukolsky equations are coupled equations, as shown e.g. by the presence of the frequency parameter $\omega$ and of the angular eigenvalue $A_{lm}$ in both the angular and radial equations. Therefore, when it comes to determining physical quantities of interest, such as quasinormal modes, the two equations must be solved simultaneously (we refer the reader to \cite{68,45,23,37} for methods to that end). While using integral series to solve both the radial and angular equations separately and then match the solutions is feasible, a truly ambitious alternative approach would be solve the coupled system directly with the path-sum formalism. Indeed, natively this formalism was designed to solve systems of coupled (differential) equations with variable
coefficients. So much so that in order to solve the Heun equations and get an integral series representation from path-sum, the first step (see Appendix A) is to map any Heun equation back onto a system of coupled differential equations. We believe such an approach to be feasible not only for the system comprising the angular and radial Teukolsky equations, but also for the underlying pair of coupled equations in the Penrose-Newmann formalism from which Teukolsky obtained his equation [77]. This is beyond the scope of this work.
5 Conclusion
In this work, we present novel integral series representations for all functions of Heun class. The major advantage of these representations is that 1) they involve only elementary integrands (rational and exponential functions); 2) they are unconditionally convergent everywhere except at the singular points of the Heun function being studied; and 3) they demonstrate that all functions of Heun class can be obtained from one or at most two Volterra equations of the second kind. Points 1) and 2) above are crucial in order to obtain physically well-behaved solutions of the homogenous Teukolsky radial equation by means of Heun functions, as this necessitates a series representation that is convergent from the black hole horizon up to spatial infinity. This is not feasible with state-of-the-art techniques involving hypergeometric and Coulomb series representations of confluent Heun function. The former is convergent only near the horizon while the later is convergent only at spatial infinity. In order to match both representations of the solutions, a book-keeping unphysical parameter has to be introduced which, at the very least, obscures the physical picture. Unlike the above MST strategy, the integral series proposed here converge over the entire spatial domain from the horizon up to infinity, thus bypassing the need for parameters that are not already present in the Teukolsky equation.
While this work is devoted to establishing the well-posedness of the integral series formalism, the next obvious step is to use it to actually compute quantities of physical interest for the rapidly growing field of gravitational wave astrophysics. These include gravitational wave fluxes [26], quasinormal modes [47,13] and totally transmitting modes [13], all of which should now be accessible without Leaver’s method (which suffers from numerical stability issues) nor the MST strategy. We hope that the formalism can also help resolve mathematical difficulties that arise in implementing the MST formalism in the various aspects of the two body problem in general relativity [7,40].
Finally, we stress that our novel mathematical results were obtained by applying the method of path-sum to Heun’s equation. This method, relying on the algebraic combinatorics of walks on graphs, was originally designed to solve systems of coupled differential equations and compute matrix functions. While it already proved successful in the fields of quantum dynamics, matrix theory and combinatorics, we think that this work opens new venues for its use
in ordinary differential equations and general relativity. In particular, path-
sum is natively adapted to solve directly the system of coupled equations
which, in the Penrose-Newman formalism, underlies the Teukolsky equation.
Acknowledgements P.-L. G. is supported by the Agence Nationale de la Recherche young
researcher grant No. ANR-19-CE40-0006.
A Appendix: Proof of the results
The method of proof is as follows: we map the Heun equation onto a system of two coupled linear first order differential equations with variable coefficients. The solution of such systems is given by a formal object called a path-ordered exponential, which we present below. Then we use the path-sum method to evaluate this path-ordered exponential. Finally we extract the desired Heun function from the path-sum solution.
A.1 Path-ordered exponentials
All the results are corollaries of the general purpose method of path-sum, which permits the exact calculation of path-ordered exponentials of finite variable matrices. The path-ordered exponential $U(z)$ of a variable matrix $M(z)$ is the unique matrix solution to the system of coupled first order ordinary linear differential equations with variable coefficients encoded by $M(z)$, i.e.
$$\frac{d}{dz}U(z,z_0) = M(z).U(z,z_0), \quad (25)$$
and such that for all $z_0$, $U(z_0,z_0) = \text{I}d$ is the identity matrix of relevant dimension. The solution of Eq. (25) is the path-ordered exponential $U(z,z_0)$ of $M$, denoted
$$U(z,z_0) = \mathcal{P}\int_{z_0}^{z} M(\zeta)d\zeta,$$
where $\mathcal{P}$ the path-ordering operator,
$$\mathcal{P}\{M(\zeta_2)M(\zeta_1)\} = \begin{cases} M(\zeta_2)M(\zeta_1), & \text{if } \zeta_2 \geq \zeta_1 \\ M(\zeta_1)M(\zeta_2), & \text{otherwise}. \end{cases}$$
We refer the reader to [19] for the origins of this notation.
Although used primarily to gain analytical understanding into the dynamics of quantum systems driven by time-dependent forces, path-sum relies solely on the algebraic combinatorics of walks on graphs that is valid irrespectively of the nature or size of the matrix $M$. It is also only distantly related to the famous Feynman’s path-integrals. The interest here is that when calculating path-ordered exponentials, the method natively generates integral representations of the solutions. The strategy thus consists in calculating the ordered exponential of a matrix $M(z)$ designed so that the solution of Eq. (25) should involve the desired Heun’s function.
In order to recover an integral representation for all of Heun’s functions, remark that Eqs. (1)–5) all take the form
$$y''(z) - B_1(z)y'(z) - B_2(z)y(z) = 0, \quad (26)$$
We thus focus on obtaining the integral representation of the solution of Eq. (26) in terms of integrals involving $B_1$ and $B_2$, irrespectively of what these functions are. To this end, we begin by exhibiting a matrix $M(z)$ whose path-ordered exponential involves a function solution to Eq. (26).
**Proposition 1.** Let $y(z)$ be a solution of Eq. (26) with initial conditions $y(z_0) = y_0$ and $y'(z_0) = y'_0$. Let
$$M(z) = \begin{pmatrix} 1 & 1 \\ B_1(z) + B_2(z) - 1 & B_1(z) - 1 \end{pmatrix},$$
and let $U(z, z_0) := \mathcal{P} e^{\int_{z_0}^z M(\zeta) d\zeta}$ be the path-ordered exponential of $M$. Then
$$y(z) = y_0 U_{11}(z, z_0) + (y'_0 - y_0) U_{12}(z, z_0).$$
**Proof.** By direct differentiation. Let $\psi(z) = (\psi_1(z), \psi_2(z))^T$ such that $\dot{\psi}(z) = M(z).\psi(z)$. This implies
$$\dot{\psi}_1 = \psi_1 + \psi_2, \quad \dot{\psi}_2 = (B_1 + B_2 - 1)\psi_1 + (B_1 - 1)\psi_2,$$
where we omitted the $(z)$ arguments to alleviate the notation. Then
$$\ddot{\psi}_1 = \psi_1 + (B_1 + B_2 - 1)\dot{\psi}_1 + (B_1 - 1)(\ddot{\psi}_1 - \dot{\psi}_1),$$
which is
$$\ddot{\psi}_1 - (B_1 - 1 + 1)\dot{\psi}_1 - (B_1 + B_2 - 1 - B_1 + 1)\psi_1 = 0,$$
i.e. $\ddot{\psi}_1 - B_1 \dot{\psi}_1 - B_2 \psi_1 = 0$. This is precisely Eq. (26). Now, since $\psi_1(z_0) = y_0$ is the desired initial condition, and since $\dot{\psi}(z_0) = M(z_0).\psi(z_0)$, then to get $\psi_1(z_0) = y'_0$ we must have $\psi_2(z_0) = y'_0 - y_0$. From there and given that $\psi(z) = U(z, z_0).\psi(z_0)$, we obtain
$$\psi_1(z) = y_0 U_{11}(z, z_0) + (y'_0 - y_0) U_{12}(z, z_0),$$
which completes the proof.
A.2 Path-sum formulation
We may now use the method of path-sum to calculate the path-ordered exponential of $M$ to recover the desired integral representations. We first state and prove the general result concerning Eq. (26) before giving its corollaries in the specific cases of the general Heun, confluent, biconfluent, doubly-confluent and triconfluent Heun functions.
**Theorem 1** Let $M(z)$ be given as in Eq. (27), let $U(z, z_0)$ be its path-ordered exponential. Then
$$U_{11}(z, z_0) = 1 + \int_{z_0}^{z} G_1(\zeta, z_0) d\zeta,$$
where $G_1(z, z_0)$ satisfies the linear integral Volterra equation of the second kind
$$G_1(z, z_0) = K_1(z, z_0) + \int_{z_0}^{z} K_1(z, \zeta) G_1(\zeta, z_0) d\zeta,$$
with kernel
$$K_1(z, z_0) = 1 + e^{-z} \int_{z_0}^{z} \left( e^{\zeta} e^{\zeta} B_1(\zeta') d\zeta' (B_1(\zeta) + B_2(\zeta) - 1) \right) d\zeta.$$
Furthermore,
$$U_{12}(z, z_0) = \int_{z_0}^{z} (e^{z-\zeta} - 1) (1 + G_2(\zeta, z_0)) d\zeta,$$
where $G_2(z, z_0)$ satisfies the linear integral Volterra equation of the second kind
$$G_2(z, z_0) = K_2(z, z_0) + \int_{z_0}^{z} K_2(z, \zeta) G_2(\zeta, z_0) d\zeta,$$
with kernel
$$K_2(z, z_0) = (B_1(z) + B_2(z) - 1) e^{z-z_0} - B_2(z).$$
Given that a linear Volterra integral equations of the second kind always has an explicit solution in the form of a Neumann series of the kernel obtained from Picard iteration, we present below the ensuing elementary integral series representations for the solution $y_0 U_{11}(z, z_0) + (y_0' - y_0) U_{12}(z, z_0)$ of Eq. (26).
This will be greatly facilitated by Volterra compositions, presented in the proof of the Theorem.
**Remark 1** If the initial conditions are such that $y_0 = y_0'$, then by Proposition 1, the solution $y(z)$ is directly proportional to $U_{11}$. By Theorem 1 this implies that the derivative $\dot{y}(z)$ of the solution of Eq. (26) satisfies a linear Volterra integral equation of the second kind with kernel $K_1$ given above. In other terms, any solution of any Heun equation which has at least one point $z_0$ for which $y(z_0) = y'(z_0)$ satisfies such a Volterra integral equation with kernel $K_1$. This is the first known integral equation satisfied by Heun functions in terms of elementary functions. Similarly if $y(z_0) = 0$, then the solution $y(z)$ is proportional to $U_{12}$, itself an integral of $G_2$ which satisfies a linear Volterra integral equation of the second kind.
Proof. The central mathematical concept enabling the path-sum formulation of path-ordered exponentials is the ∗-product. This product is defined on a large class of distributions [30], however for the present work only its definition on smooth functions of two variables is required. For such functions the ∗-product reduces to the Volterra composition, a product between functions first expounded by Volterra and Péres in the 1920s [80] and which had largely fallen out of use by the early 1950s for a reason that appears, retrospectively, to be the lack of a mathematical theory of distributions. The Volterra composition of two smooth functions of two variables \( f(z, z_0) \) and \( g(z, z_0) \) is
\[
(f \ast g)(z, z_0) = \int_{z_0}^{z} f(z, \zeta) g(\zeta, z_0) d\zeta \Theta(z - z_0),
\]
with \( \Theta(\cdot) \) the Heaviside theta function under the convention that \( \Theta(0) = 1 \).
This extends to functions of less than two variables, for example if \( h(z) \) is a smooth function of one variable, then
\[
(h \ast g)(z, z_0) = h(t') \int_{z_0}^{z} g(\zeta, z_0) d\zeta \Theta(z - z_0),
\]
\[
(g \ast h)(z, z_0) = \int_{z_0}^{z} g(z, \zeta) h(\zeta) d\zeta \Theta(z - z_0).
\]
That is, the variable of \( h(z) \) is always treated as the left variable of a function of two variables.
The identity element for the ∗-product is the Dirac distribution, denoted \( 1_* \equiv \delta(z - z_0) \), an observation which we here accept without proof as it would require presenting the full theory of the ∗-product [30]. Similarly we accept without proof that for any bounded function \( f(z, z_0) \) of two variables, \( f^{*0} = 1_* \), while \( f^{*1} = f \) and \( f^{*n+1} = f \ast f^{*n} = f^{*n} \ast f \) [80]. Furthermore, if \( f \) is bounded the Neumann series \( \sum_{n=0}^{\infty} (f^{*n})(z, z_0) \) converges superexponentially and thus unconditionally [46] to an object, called the ∗-resolvent \( R_f \) of \( f \), given by
\[
R_f(z, z_0) = \sum_{n=0}^{\infty} (f^{*n})(z, z_0),
\]
\[
= \delta(z - z_0) + f(z, z_0)\Theta(z - z_0) + \int_{z_0}^{z} f(z, \zeta_1) f(\zeta_1, z_0) d\zeta_1 \Theta(z - z_0) + \int_{z_0}^{z} \int_{\zeta_1}^{z} f(z, \zeta_2) f(\zeta_2, \zeta_1) f(\zeta_1, z_0) d\zeta_2 d\zeta_1 \Theta(z - z_0) + \cdots.
\]
Seeing this as stemming from a Picard iteration entails an additional property of ∗-resolvents, namely that they solve the Volterra equation of the second kind with kernel \( f \),
\[
R_f = 1_* + f \ast R_f, \tag{28}
\]
or, in explicit integral notation, and showing all distributions
\[
R_f(z, z_0) = \delta(z - z_0) + \int_{z_0}^{z} f(z, \zeta) R_f(\zeta, z_0) d\zeta \Theta(z - z_0).
\]
Thus we have $R_f \ast (1_\ast - f) = 1_\ast$ and are therefore justified in writing $R_f = (1_\ast - f)^{*-1}$. In order to avoid distributions altogether, it is more convenient to define $G_f := R_f - 1_\ast$ and rewrite Eq. (28) as
$$G_f = f + f \ast G_f,$$
which is an ordinary linear integral Volterra equation of the second kind. The Neumann integral series obtained from Picard iterations for $G_f$ as above is now
$$G_f(z, z_0) = \sum_{n=1}^\infty f^{*n}(z, z_0),$$
and it is a well-established result [46] that the convergence of this series is guaranteed provided $f$ is continuous and bounded. In this case, truncating the series at order $m$, yields a relative error of at most
$$\left| G_f(z, z_0) - \sum_{n=1}^m f^{*n}(z, z_0) \right| \leq \frac{\kappa_f^m}{m!}$$
with $\kappa_f := \sup_{\zeta, \zeta' \in [z_0, z]} |f(\zeta, \zeta')|$. Path-sum expresses the path-ordered exponential of any finite variable matrix in terms of a finite number of Volterra compositions and $*$-resolvents. The path-sum formulation of the path-ordered exponential of the $2 \times 2$ matrix $M(z)$ is
$$U_{11}(z) = 1 \ast R_1,$$
$$R_1 = (1_\ast - M_{11} - M_{12} \ast (1_\ast - M_{22})^{*-1} \ast M_{21})^{*-1},$$
where the $*$-multiplication by 1 on the left is a short-hand notation for an integral with respect to the left variable, since for any $f$ smooth, $(1_\ast f)(z, z_0) = \int_{z_0}^z f(\zeta, z_0) d\zeta \Theta(z - z_0)$. Furthermore, since $M_{22}$ depends on a single variable, its $*$-resolvent can be shown to be
$$(1_\ast - M_{22})^{*-1} = 1_\ast + M_{22} e^{1_\ast M_{22}},$$
or equivalently
$$(1_\ast - M_{22})^{*-1}(z, z_0) = \delta(z - z_0) + M_{22}(z) e^{\int_{z_0}^z M_{22}(\zeta) d\zeta} \Theta(z - z_0).$$
Now the form of $U_{11}$ as claimed in the theorem follows upon writing the $*$-products as explicit integrals with $M$ given by Proposition. [1]. For $U_{12}$, the path-sum formulation reads
$$U_{12} = 1 \ast (1_\ast - M_{11})^{*-1} \ast M_{12} \ast R_2,$$
where
$$R_2 = (1_\ast - M_{22} - M_{21} \ast (1_\ast - M_{11})^{*-1} \ast M_{12})^{*-1},$$
and the theorem result for $U_{12}$ follows upon writing the $*$-products as explicit integrals with $M$ given by Proposition. [1]
Since $R_1$ and $R_2$ are *-resolvents, we may express them as the unconditionally Neumann series involving the corresponding kernels $K_1$ and $K_2$, i.e. $R_i = 1 + \sum_{n=1}^{\infty} K_i^{*n}$ or equivalently $G_i = \sum_{n=1}^{\infty} K_i^{*n}$, $i = 1, 2$. This yields an explicit representation for the solution of Eq. (26) as series of elementary integrals:
**Theorem 2** Let $y(z)$ be the unique solution of
$$y''(z) - B_1(z)y'(z) - B_2(z)y(z) = 0,$$
such that $y(z_0) = y_0$ and $y'(z_0) = y'_0$. Then
$$y(z) = y_0 + \int_{z_0}^{z} G_1(\zeta, z_0)d\zeta + (y'_0 - y_0) \int_{z_0}^{z} (e^{z-\zeta} - 1)(1 + G_2(\zeta, z_0))d\zeta,$$
where $G_1$ and $G_2$ satisfy linear Volterra integral equations of the second kind with kernels respectively given by
$$K_1(z, z_0) = 1 + e^{-z} \int_{z_0}^{z} \left\{ e^{\zeta} B_1(\zeta) d\zeta \right\} d\zeta,$$
$$K_2(z, z_0) = (B_1(z) + B_2(z) - 1)e^{z-z_0} - B_2(z).$$
In consequence, $G_1$ and $G_2$ have the following representation as integral series involving elementary integrands,
$$G_i(z, z_0) = \sum_{n=1}^{\infty} K_i^{*n}(z, z_0),$$
(29)
$$= K_i(z, z_0) + \int_{z_0}^{z} K_i(z, \zeta_1)K_i(\zeta_1, z_0)d\zeta_1 + \int_{z_0}^{z} \int_{\zeta_1}^{\zeta_2} K_i(z, \zeta_2)K_i(\zeta_2, \zeta_1)K_i(\zeta_1, z_0)d\zeta_2d\zeta_1 + \sum_{n=2}^{\infty} \int_{z_0}^{z} \int_{\zeta_1}^{\zeta_2} \cdots \int_{\zeta_{n-1}}^{\zeta_n} K_i(z, \zeta_n)K_i(\zeta_n, \zeta_{n-1})K_i(\zeta_{n-1}, \zeta_{n-2})K_i(\zeta_{n-2}, \zeta_1)K_i(\zeta_1, z_0)d\zeta_{n}d\zeta_{n-1}d\zeta_{n-2}d\zeta_1 + \cdots,$$
for $i = 1, 2$. The series representation is guaranteed to converge to $G_i$ everywhere except at the singular points of $K_i$. More precisely, let $]z_0, z_1[$ be an open interval over which $K_i$ is divergent free and let $\kappa_i := \sup_{\zeta, \zeta' \in ]z_0, z_1[; \zeta \geq \zeta'} |K_i(\zeta, \zeta')|$. Then
$$\left| G_i(z, z_0) - \sum_{n=1}^{m} K_i^{*n}(z, z_0) \right| \leq \frac{\kappa_i^m}{m!}.$$
(30)
This immediately provides the Corollaries of the main text for the general Heun, confluent, biconfluent, doubly-confluent and triconfluent Heun’s functions upon replacing $B_1$ and $B_2$ appearing in Eq. (26) and Theorem 2 with their values as dictated by Eqs. (14).
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LTL to Büchi Automata Translation:
Fast and More Deterministic*
Tomáš Babiak, Mojmír Křetínský, Vojtěch Řehák, and Jan Strejček
Faculty of Informatics, Masaryk University
Botanická 68a, 60200 Brno, Czech Republic
{xbabiak, kretinsky, rehak, strejcek}@fi.muni.cz
Abstract. We introduce improvements in the algorithm by Gastin and Oddoux translating LTL formulae into Büchi automata via very weak alternating co-Büchi automata and generalized Büchi automata. Several improvements are based on specific properties of any formula where each branch of its syntax tree contains at least one eventually operator and at least one always operator. These changes usually result in faster translations and smaller automata. Other improvements reduce non-determinism in the produced automata. In fact, we modified all the steps of the original algorithm and its implementation known as LTL2BA. Experimental results show that our modifications are real improvements. Their implementations within an LTL2BA translation made LTL2BA very competitive with the current version of SPOT, sometimes outperforming it substantially.
This is a full version of [1] published at TACAS 2012.
1 Introduction
A translation of LTL formulae into equivalent Büchi automata plays an important role in many algorithms for LTL model checking, LTL satisfiability checking etc. For a long time, researchers aimed to find fast translations producing Büchi automata with a small number of states. This goal has led to the developments of several translation algorithms and many heuristics and optimizations including input formula reductions and optimizations of produced Büchi automata, see e.g. [3,9,11,12,10,7].
As the time goes, the translation objectives and their importance are changing. In particular, [17] demonstrates that for higher performance of the subsequent steps of the model checking process, it is more important to minimize the number of states with nondeterministic choice than the number of all states in resulting automata. Note that there are LTL formulae, e.g. $FGa$, for which no equivalent deterministic Büchi automaton exists. Further, model checking practice shows that one LTL formula is usually used in many different model checking
* The authors are supported by The Czech Science Foundation, grants 102/09/H042 (Babiak), 201/09/1389 (Křetínský), P202/10/1469 (Řehák, Strejček), P202/12/G061 (Křetínský, Řehák, Strejček), and P202/12/P612 (Řehák).
tasks. Hence, it pays to invest enough computation time to get high quality (more deterministic and/or minimal) automata as it may reduce computation time of many model checking tasks.
The new objectives lead to the developments of algorithms focusing on quality of produced automata. For example, [5] presents an effective algorithm translating LTL formulae of the fragment called obligation (see [14]) into weak deterministic Büchi automata (WDBA). Moreover, WDBA can be minimized by the algorithm of [13]. There is also a SAT-based algorithm searching for minimal (nondeterministic) Büchi automata [8]. The main disadvantage of all the mentioned determinization and minimization algorithms is their long running time which limits their use.
Our research returns to the roots: we focus on a fast translation producing a relatively good output. This approach is justified by the following facts:
- The mentioned algorithms producing high quality automata often need, for a given LTL formula, some equivalent automaton as an input.
- The mentioned algorithms are usually feasible for short formulae only or for formulae with a simple structure.
- Given a fresh LTL formula, it can be useful to run vacuity checks, namely satisfiability of the formula and its negation, to detect bugs in the formula. In these checks, time of the LTL to automata translation can be more significant than time needed for subsequent computations (see [16]). Hence, we need a fast translator to support an early detection of bugs in formulae.
Considering the speed of an LTL to Büchi automata translation, LTL2BA [11] and SPOT [7] are two leading tools. Based on extensive experiments on LTL satisfiability checking, [16] even states:
*The difference in performance between SPOT and LTL2BA, on one hand, and the rest of explicit tools is quite dramatic.*
Each of the two tools is based on different algorithms.
In LTL2BA, the translation proceeds in three basic steps:
1. A given LTL formula is translated into a very weak alternating automaton (VWAA) with a co-Büchi accepting condition.
2. The alternating automaton is then translated into a transition-based generalized Büchi automaton (TGBA), i.e. a generalized Büchi automaton with sets of accepting transitions instead of accepting states.
3. The generalized automaton is transformed (degeneralized) into a Büchi automaton (BA).
Each of the three automata is simplified during the translation.
SPOT translates a given LTL formula to a TGBA using a tableau method presented in [3]. The TGBA is then translated to a BA. Note that the model checking algorithm natively implemented in SPOT works directly with TGBAs. Prior to a translation, both LTL2BA and SPOT try to decrease the number of temporal operators in a given input formula by applications of reduction rules.
While the LTL to automata translation in SPOT is under the gradual development following the current trends (see [6] for improvements made in the last four years), LTL2BA underwent only one minor update in 2007 since its creation in 2001. In particular, SPOT reflects the changes in objectives. Therefore, SPOT usually produces more deterministic and smaller automata than LTL2BA, while LTL2BA is often a bit faster.
**Our contribution.** We introduce several modifications of LTL2BA on both algorithmic and implementation levels. We suggest changes in all the steps of the translation algorithm. Our experimental results indicate that each modified step has a mostly positive effect on the translation. The new translator, called LTL3BA, is usually faster than the original LTL2BA and it produces smaller and more deterministic automata. Moreover, comparison of LTL3BA and the current version of SPOT (run without WDBA minimization that is very slow) shows that the produced automata are of similar quality and LTL3BA is usually faster.
Some modifications employ an observation that each LTL formula containing at least one *always* operator and at least one *eventually* operator on each branch of its syntax tree (with possible exceptions of branches going to the left subformula of any *until* or *release* operator) is prefix invariant. We call them *alternating* formulae. Indeed, validity of each alternating formula on a given word $u$ depends purely on a suffix of $u$. In other words, it is not affected by any finite prefix of $u$. We apply this observation to construct new rules for formula reductions. Further, the observation justifies some changes in constructions of VWAA and TGBA. Intuitively, a state of a VWAA corresponds to a subformula that has to be satisfied by the rest of an accepted word. If the corresponding subformula is an alternating formula, then the state can be temporarily suspended for finitely many steps of the automaton.
Other changes in a VWAA construction are designed to lower nondeterminism. This is also a motivation for new simplification rules applied on intermediate automata. These rules remove some transitions of the automaton and hence reduce the number of nondeterministic choices in produced automata. The original simplification rules can be seen as special cases of the new rules. An effective implementation of this simplification required to change representation of transitions. Further, we add one ad-hoc modification speeding up the translation of selected (sub)formulae. Finally, we modify a simplification rule merging some states of resulting BA.
The rest of the paper is organized as follows. The next section recalls the definitions of LTL, VWAA, and TGBA. Section 3 focuses on alternating formulae and its properties. Sections 4, 5, and 6 present new rules for formula reductions, modified translation of LTL to VWAA (including generalized simplification of VWAA), modified translation of VWAA to TGBA, and modified rule for simplification of BA, respectively. Finally, Section 8 is devoted to experimental results. The last section summarizes the achieved improvements.
2 Preliminaries
In this section, we recall the definition of LTL and definitions of VWAA and TGBA as presented in [11].
Linear Temporal Logic (LTL) The syntax of LTL [15] is defined as follows
\[ \varphi ::= tt \mid a \mid \neg \varphi \mid \varphi \lor \varphi \mid \varphi \land \varphi \mid X \varphi \mid \varphi U \varphi, \]
where \( tt \) stands for true, \( a \) ranges over a countable set \( AP \) of atomic propositions, \( X \) and \( U \) are temporal operators called next and until, respectively. The logic is interpreted over infinite words over the alphabet \( \Sigma = 2^{AP'} \), where \( AP' \subseteq AP \) is a finite subset. Given a word \( u = u(0)u(1)u(2)\ldots \in \Sigma^\omega \), by \( u_i \) we denote the \( i^{th} \) suffix of \( u \), i.e. \( u_i = u(i)u(i+1)\ldots \).
The semantics of LTL formulae is defined inductively as follows:
\[
\begin{align*}
& u \models tt \quad \text{iff} \quad a \in u(0) \\
& u \models \neg \varphi \quad \text{iff} \quad u \not\models \varphi \\
& u \models \varphi_1 \lor \varphi_2 \quad \text{iff} \quad u \models \varphi_1 \text{ or } u \models \varphi_2 \\
& u \models \varphi_1 \land \varphi_2 \quad \text{iff} \quad u \models \varphi_1 \text{ and } u \models \varphi_2 \\
& u \models X \varphi \quad \text{iff} \quad u_{i+1} \models \varphi \\
& u \models \varphi_1 U \varphi_2 \quad \text{iff} \quad \exists i \geq 0 . \ ( u_i \models \varphi_2 \text{ and } \forall 0 \leq j < i . \ u_j \models \varphi_1 )
\end{align*}
\]
We say that a word \( u \) satisfies \( \varphi \) whenever \( u \models \varphi \). Two formulae \( \varphi, \psi \) are equivalent, written \( \varphi \equiv \psi \), if for each alphabet \( \Sigma \) and each \( u \in \Sigma^\omega \) it holds \( u \models \varphi \iff u \models \psi \). Given an alphabet \( \Sigma \), a formula \( \varphi \) defines the language \( L^\Sigma(\varphi) = \{ u \in \Sigma^\omega \mid u \models \varphi \} \). We often write \( L(\varphi) \) instead of \( L^{2^{AP'}}(\varphi) \), where \( AP \) denotes the set of atomic propositions occurring in the formula \( \varphi \).
We extend the LTL with derived temporal operators:
- \( F \varphi \) called eventually and equivalent to \( tt U \varphi \),
- \( G \varphi \) called always and equivalent to \( \neg F \neg \varphi \), and
- \( \varphi R \psi \) called release and equivalent to \( \neg (\neg \varphi U \neg \psi) \).
In the following, temporal formula is a formula where the topmost operator is neither conjunction, nor disjunction. A formula without any temporal operator is called state formula. Note that \( a \) and \( tt \) are both temporal and state formulae. An LTL formula is in positive normal form if no operator occurs in the scope of any negation. Each LTL formula can be easily transformed to positive normal form using De Morgan’s laws for operators \( \lor \) and \( \land \), equivalences for derived operators, and the following equivalences:
\[
\begin{align*}
& \neg(\varphi_1 U \varphi_2) \equiv \neg \varphi_1 R \neg \varphi_2 \\
& \neg(\varphi_1 R \varphi_2) \equiv \neg \varphi_1 U \neg \varphi_2 \\
& X \varphi \equiv X \neg \varphi
\end{align*}
\]
**Büchi Automata (BA)** A BA is a tuple $B = (Q, \Sigma, \delta, I, F)$, where
- $Q$ is a finite set of states,
- $\Sigma$ is a finite alphabet,
- $\delta : Q \to 2^{\Sigma \times Q}$ is a total transition function,
- $I \subseteq Q$ is a set of initial states, and
- $F \subseteq Q$ is a set of accepting states.
Automaton $B$ is deterministic if and only if $|I| = 1$ and $|\delta(q, a)| \leq 1$ for all $q \in Q$ and $a \in \Sigma$.
A run $\rho$ of $B$ over an infinite word $w = w(0)w(1)w(2)\ldots \in \Sigma^\omega$ is a sequence $\rho = q_0q_1q_2\ldots$, where $q_0 \in I$ is an initial state and $q_{i+1} \in \delta(q_i, w(i))$ for all $i \geq 0$. The run $\rho$ is accepting if some accepting state occurs infinitely often in the sequence $q_0q_1q_2\ldots$. An infinite word $w$ is accepted by an automaton $B$ if some run of $B$ over $w$ is accepting.
We denote by $L(B)$ the language accepted by $B$, i.e. the set of all words over $\Sigma$ accepted by an automaton $B$.
**Very Weak Alternating co-Büchi Automata (VWAA)** A VWAA is a tuple $A = (Q, \Sigma, \delta, I, F)$, where
- $Q$ is a finite set of states, and we let $Q' = 2^Q$,
- $\Sigma$ is a finite alphabet, and we let $\Sigma' = 2^\Sigma$,
- $\delta : Q \to 2^{\Sigma' \times Q'}$ is a transition function,
- $I \subseteq Q'$ is a set of initial states,
- $F \subseteq Q$ is a set of accepting states, and
- there exists a partial order on $Q$ such that, for each state $q \in Q$, all the states occurring in $\delta(q)$ are lower or equal to $q$.
Note that the transition function $\delta$ uses $\Sigma'$ instead of $\Sigma$. This enables to merge transitions that differ only by action labels. We sometimes use a propositional formula $\alpha$ over $AP$ to describe the element $\{a \in \Sigma \mid a \text{satisfies } \alpha\}$ of $\Sigma'$.
A run $\sigma$ of VWAA $A$ over a word $w = w(0)w(1)w(2)\ldots \in \Sigma^\omega$ is a labelled directed acyclic graph $(V, E, \lambda)$ such that:
- $V$ is partitioned into $\bigcup_{i=0}^{\infty} V_i$ with $E \subseteq \bigcup_{i=0}^{\infty} V_i \times V_{i+1}$,
- $\lambda : V \to Q$ is a labelling function,
- $\{\lambda(x) \mid x \in V_0\} \subseteq I$, and
- for each $x \in V_i$, there exist $\alpha \in \Sigma'$, $q \in Q$ and $O \in Q'$ such that $w(i) \in \alpha$, $q = \lambda(x)$, $O = \{\lambda(y) \mid (x, y) \in E\}$, and $(\alpha, O) \in \delta(q)$.
A run $\sigma$ is accepting if each branch in $\sigma$ contains only finitely many nodes labelled by accepting states (co-Büchi acceptance condition). A word $w$ is accepted if there is an accepting run over $w$.
We denote by $L(A)$ the language accepted by $A$, i.e. the set of all words over $\Sigma$ accepted by an automaton $A$.
Transition Based Generalized Büchi Automata (TGBA) A TGBA is a tuple \( G = (Q, \Sigma, \delta, I, F) \), where
- \( Q \) is a finite set of states,
- \( \Sigma \) is a finite alphabet, and we let \( \Sigma' = 2^\Sigma \)
- \( \delta : Q \rightarrow 2^{\Sigma' \times Q} \) is a total transition function,
- \( I \subseteq Q \) is a set of initial states, and
- \( T = \{ T_1, T_2, \ldots, T_m \} \) where \( T_j \subseteq Q \times \Sigma' \times Q \) are sets of accepting transitions.
A run \( \rho \) of TGBA \( G \) over a word \( w = w(0)w(1)w(2)\ldots \in \Sigma^\omega \) is a sequence of states \( \rho = q_0q_1q_2\ldots \) where \( q_0 \in I \) is an initial state and, for each \( i \geq 0 \), there exists \( \alpha \in \Sigma' \) such that \( w(i) \in \alpha \) and \( (\alpha, q_{i+1}) \in \delta(q_i) \). A run \( \rho \) is accepting if for each \( 1 \leq j \leq m \) it uses infinitely many transitions from \( T_j \). A word \( w \) is accepted if there is an accepting run over \( w \).
We denote by \( L(G) \) the language accepted by \( G \), i.e. the set of all words over \( \Sigma \) accepted by an automaton \( G \).
3 Alternating Formulae
We define the class of alternating formulae together with the classes of pure eventuality and pure universality formulae introduced in [9]. Let \( \varphi \) ranges over general LTL formulae. The following abstract syntax equations define the classes pure eventuality formulae \( \mu \), pure universality formulae \( \nu \), and alternating formulae \( \xi \):
\[
\begin{align*}
\mu ::= & \mathsf{F} \varphi \mid \mu \lor \mu \mid \mu \land \mu \mid X \mu \mid \varphi \mathsf{U} \mu \mid \mu \mathsf{R} \mu \mid G \mu \\
\nu ::= & G \varphi \mid \nu \lor \nu \mid \nu \land \nu \mid X \nu \mid \nu \mathsf{U} \nu \mid \varphi \mathsf{R} \nu \mid F \nu \\
\xi ::= & G \mu \mid F \nu \mid \xi \lor \xi \mid \xi \land \xi \mid X \xi \mid \varphi \mathsf{U} \xi \mid \varphi \mathsf{R} \xi \mid F \xi \mid G \xi
\end{align*}
\]
Note that there are alternating formulae, e.g. \((a \mathsf{U} (G b)) \land (c \mathsf{R} (G f))\), that are neither pure eventuality formulae, nor pure universality formulae. Properties of the respective classes of formulae are summarized in the following lemmata.
Lemma 1. \[9\] Every pure eventuality formula \( \mu \) satisfies the following:
\[ \forall w \in \Sigma^\omega, u \in \Sigma^* : w \models \mu \rightarrow uw \models \mu \]
Further, every pure universality formula \( \nu \) satisfies the following:
\[ \forall w \in \Sigma^\omega, u \in \Sigma^* : uw \models \nu \rightarrow w \models \nu \]
In other words, pure eventuality formulae define left-append closed languages while pure universality formulae define suffix closed languages.
Lemma 2. Every alternating formula \( \xi \) satisfies the following:
\[ \forall w \in \Sigma^\omega, u \in \Sigma^* : uw \models \xi \iff w \models \xi \]
In other words, each alternating formula defines a \textit{prefix-invariant} language.
\textbf{Proof.} The proof proceeds by induction on the structure of \( \xi \). We assume that \( w \in \Sigma^\omega \) is an arbitrary infinite word and \( u \in \Sigma^* \) is an arbitrary finite word.
\( \xi = G\mu \) – The semantics of \( G \) operator directly provides one implication, namely \( uw \models G\mu \iff w \models G\mu \). As \( \mu \) is a pure eventuality formula, Lemma \[\text{I}\] gives us \( \forall u' \in \Sigma^* : w \models \mu \implies u'w \models \mu \). This implies \( w \models G\mu \implies uw \models G\mu \). In total, we get \( w \models G\mu \iff uw \models G\mu \).
\( \xi = F\nu \) – The semantics of \( F \) operator directly provides one implication, namely \( w \models F\nu \iff uw \models F\nu \). As \( \nu \) is a pure universality formula, Lemma \[\text{I}\] gives us \( \forall u' \in \Sigma^* : u'w \models \nu \implies w \models \nu \). This implies \( uw \models F\nu \implies w \models F\nu \). In total, we get \( w \models F\nu \iff uw \models F\nu \).
\( \xi = \varphi U \xi_1 \) – From the induction hypothesis, it follows that \( F\xi_1 \implies \xi_1 \). Hence, \( \varphi U \xi_1 \equiv \xi_1 \) holds. Thus, the statement coincides with the induction hypothesis.
\( \xi = \varphi R \xi_1 \) – From the induction hypothesis, it follows that \( \xi_1 \implies G\xi_1 \) and thus also \( \xi_1 \implies \varphi R \xi_1 \). As \( \varphi R \xi_1 \implies \xi_1 \), we get \( \varphi R \xi_1 \equiv \xi_1 \). Hence, the statement coincides with the induction hypothesis.
\( \xi = \xi_1 \lor \xi_2 \) or \( \xi = \xi_1 \land \xi_2 \) or \( \xi = X\xi_1 \) or \( \xi = F\xi_1 \) or \( \xi = G\xi_1 \) – In all these cases, the statement easily follows from the induction hypothesis. \( \Box \)
\textbf{Corollary 1.} Every alternating formula \( \xi \) satisfies \( \xi \equiv X\xi \).
Hence, in order to check whether \( w \) satisfies \( \xi \) it is possible to skip an arbitrary long finite prefix of the word \( w \).
We use this property in new rule for formula reduction. Further, it has brought us to the notion of alternating formulae \textit{suspension} during the translation of LTL to Büchi automata. We employ suspension on two different levels of the translation: the construction of a VWAA from an input LTL formula and the transformation of a VWAA into a TGBA.
\section{Improvements in Reduction of LTL Formulae}
Many rules reducing the number of temporal operators in an LTL formula have been presented in [\text{IL}] and [\text{9}]. In this section we present some new reduction rules. For the rest of this section, \( \varphi, \psi \) range over LTL formulae and \( \gamma \) ranges over alternating ones.
\[
\begin{align*}
X\varphi \land X\psi &\equiv X(\varphi \land \psi) & \varphi U \gamma &\equiv \gamma & F\gamma &\equiv \gamma & X\gamma &\equiv \gamma \\
X\varphi \lor X\psi &\equiv X(\varphi \lor \psi) & \varphi R \gamma &\equiv \gamma & G\gamma &\equiv \gamma
\end{align*}
\]
The following equivalences are valid only on assumption that \( \varphi \) implies \( \psi \).
\[
\begin{align*}
\psi U (\varphi U \gamma) &\equiv \psi U \gamma & \varphi \land (\psi \land \gamma) &\equiv (\varphi \land \gamma) \\
(\psi R \gamma) R \varphi &\equiv \gamma R \varphi & \psi \lor (\varphi \lor \gamma) &\equiv (\psi \lor \gamma) \\
\varphi U (\gamma R (\psi U \rho)) &\equiv \gamma R (\psi U \rho)
\end{align*}
\]
Further, we have extended the set of rules deriving implications of the form \( \varphi \Rightarrow \psi \). The upper formula is a precondition, the lower one is a conclusion.
\[
\begin{align*}
G\varphi & \Rightarrow \psi \\
G\varphi & \Rightarrow X\psi \\
\varphi & \Rightarrow F\psi \\
X\varphi & \Rightarrow F\psi \\
\varphi & \Rightarrow X\psi
\end{align*}
\]
5 Improvements in LTL to VWAA Translation
First, we recall the original translation of LTL to VWAA according to \cite{11}. The translation utilizes two auxiliary operators:
- Let \( \Sigma' = 2^\Sigma \), and let \( Q' = 2^Q \). Given \( J_1, J_2 \in 2^{\Sigma' \times Q'} \), we define \( J_1 \otimes J_2 = \{(\alpha_1 \cap \alpha_2, O_1 \cup O_2) \mid (\alpha_1, O_1) \in J_1 \text{ and } (\alpha_2, O_2) \in J_2\} \).
- Let \( \psi \) be an LTL formula in positive normal form. We define \( \overline{\psi} \) by:
\begin{itemize}
\item \( \overline{\psi} = \{\psi\} \) if \( \psi \) is a temporal formula,
\item \( \overline{\psi_1 \land \psi_2} = \{O_1 \cup O_2 \mid O_1 \in \overline{\psi_1} \text{ and } O_2 \in \overline{\psi_2}\} \),
\item \( \overline{\psi_1 \lor \psi_2} = \overline{\psi_1} \cup \overline{\psi_2} \).
\end{itemize}
Let \( \varphi \) be an LTL formula in positive normal form. An equivalent VWAA with a co-Büchi acceptance condition is constructed as \( \mathcal{A}_\varphi = (Q, \Sigma, \delta, I, F) \), where \( Q \) is the set of temporal subformulae of \( \varphi \), \( \Sigma = 2^{AP(\varphi)} \), \( I = \overline{\varphi} \), \( F \) is the set of all \( U \)-subformulae of \( \varphi \), i.e. formulae of the type \( \psi_1 U \psi_2 \), and \( \delta \) is defined as follows:
\[
\begin{align*}
\delta(tt) &= \{(\Sigma, \emptyset)\} \\
\delta(p) &= \{(\Sigma_p, \emptyset)\} \text{ where } \Sigma_p = \{a \in \Sigma \mid p \in a\} \\
\delta(\neg p) &= \{(\Sigma_{\neg p}, \emptyset)\} \text{ where } \Sigma_{\neg p} = \Sigma \setminus \Sigma_p \\
\delta(X\psi) &= \{(\Sigma, O) \mid O \in \overline{\psi}\} \\
\delta(\psi_1 U \psi_2) &= \Delta(\overline{\psi_2}) \cup \{(\Sigma, \underbrace{\{(\psi_1 U \psi_2)\}}_{\Delta(\psi_1) \otimes \{(\Sigma, \{\psi_1 U \psi_2\})\}})\} \\
\delta(\psi_1 R \psi_2) &= \Delta(\overline{\psi_2}) \otimes \{(\Sigma, \underbrace{\{(\psi_1 R \psi_2)\}}_{\Delta(\psi_1) \cup \{(\psi_1 R \psi_2)\}})\}
\end{align*}
\]
\[
\Delta(\psi) = \delta(\psi) \text{ if } \psi \text{ is a temporal formula}
\]
\[
\begin{align*}
\Delta(\psi_1 \lor \psi_2) &= \Delta(\psi_1) \cup \Delta(\psi_2) \\
\Delta(\psi_1 \land \psi_2) &= \Delta(\psi_1) \otimes \Delta(\psi_2)
\end{align*}
\]
Using the partial order “is a subformula of” on states of \( \mathcal{A}_\varphi \), one can easily prove that \( \mathcal{A}_\varphi \) is very weak.
Improved Translation In order to implement the suspension of alternating formulae, we modify the way the transition function \( \delta \) handles the binary operators \( U, R, \lor, \land \). The original transition function \( \delta \) reflects the following identities:
\[
\begin{align*}
\varphi_1 U \varphi_2 & \equiv \varphi_2 \lor (\varphi_1 \land X(\varphi_1 U \varphi_2)) \\
\varphi_1 R \varphi_2 & \equiv \varphi_2 \land (\varphi_1 \lor X(\varphi_1 R \varphi_2))
\end{align*}
\]
However, if $\varphi_1$ is an alternating formula we apply the relation $\varphi_1 \equiv X \varphi_1$ to obtain the following identities:
$$\varphi_1 \lor \varphi_2 \equiv \varphi_2 \lor (X \varphi_1 \land X(\varphi_1 \lor \varphi_2))$$
$$\varphi_1 \land \varphi_2 \equiv \varphi_2 \land (X \varphi_1 \lor X(\varphi_1 \land \varphi_2))$$
Using these identities, the formula $\varphi_1$ is effectively suspended and checked one step later. Similarly, in the case of disjunction or conjunction, each disjunct or conjunct corresponding to an alternating formula is suspended for one step as well. Correctness of these changes clearly follows from properties of alternating formulae. Note that $\delta$ is defined over formulae in positive normal form only. The translation treats each formula $F \varphi$ as $tt U \varphi$ and each formula $G \varphi$ as $\neg(tt R \varphi)$.
We introduce further changes to the transition function $\delta$ in order to generate automata which exhibits more determinism. In particular, we build a VWAA with only one initial state. Similarly, each state corresponding to a formula of $X$ generates only one successor corresponding to $\varphi$. These changes can add an extra initial state and an extra state for each $X$-subformula comparing to the original construction. However, this drawback is often suppressed due to the consecutive optimizations during the construction of a TGBA.
Now we present a modified construction of VWAA. Given an input LTL formula $\varphi$ in positive normal form, an equivalent VWAA with a co-B"uchi acceptance condition is constructed as $A' = (Q, \Sigma, \delta, I, F)$, where $Q$ is the set of all subformulae of $\varphi$, $\Sigma$ and $F$ are defined as in the original construction, $I = \{\varphi\}$, and $\delta$ is defined as follows:
$$\delta(tt) = \{(\Sigma, \emptyset)\}$$
$$\delta(p) = \{(\Sigma_p, \emptyset)\} \text{ where } \Sigma_p = \{a \in \Sigma \mid p \in a\}$$
$$\delta(\neg p) = \{(\Sigma_{\neg p}, \emptyset)\} \text{ where } \Sigma_{\neg p} = \Sigma \setminus \Sigma_p$$
$$\delta(X \varphi) = \{(\Sigma, \{\psi\})\}$$
$$\delta(\varphi_1 \lor \varphi_2) = \Delta(\varphi_1) \cup \Delta(\varphi_2)$$
$$\delta(\varphi_1 \land \varphi_2) = \Delta(\varphi_1) \otimes \Delta(\varphi_2)$$
$$\delta(\varphi_1 \lor \varphi_2) = \begin{cases}
\Delta(\varphi_1) \cup \Delta(\varphi_2) & \text{if } \varphi_1 \text{ is alternating}, \\
\Delta(\varphi_1) \otimes \Delta(\varphi_2) & \text{otherwise}.
\end{cases}$$
$$\delta(\varphi_1 \land \varphi_2) = \begin{cases}
\Delta(\varphi_1) \cup \Delta(\varphi_2) & \text{if } \varphi_1 \text{ is alternating}, \\
\Delta(\varphi_1) \otimes \Delta(\varphi_2) & \text{otherwise}.
\end{cases}$$
$$\Delta(\psi) = \begin{cases}
\{(\Sigma, \{\psi\})\} & \text{if } \psi \text{ is a temporal alternating formula}, \\
\delta(\psi) & \text{if } \psi \text{ is a temporal formula that is not alternating}.
\end{cases}$$
Motivation for our changes in the translation can be found in Figures 1 and 2. Each figure contains (a) the VWAA constructed by the original translation and (b) the VWAA constructed by our translation with suspension. Figure 1 shows the effect of suspension of alternating subformula $G \varphi a$ in computation of transitions leading from the initial state. It can be easily proved that whenever
one start with a formula reduced according to Section 4, then each suspension of an alternating temporal subformula leads just to reduction of transitions in the resulting VWAA, i.e., no state is added. On the other hand, if an alternating non-temporal subformula $\psi$ is suspended or the new definition of $\delta(X\psi)$ is used, then the resulting VWAA can contain one more reachable state corresponding to the formula $\psi$. However, other states may become unreachable and, in particular, the automaton can also have more deterministic states as illustrated by Figure 2.
**Optimization of VWAA** In the original algorithm, the VWAA is optimized before it is translated to a TGBA. In particular, if there are two transitions $t_1 = (q, \alpha_1, O_1)$ and $t_2 = (q, \alpha_2, O_2)$ satisfying $\alpha_2 \subseteq \alpha_1$ and $O_1 \subseteq O_2$, then $t_2$ is removed as it is implied by $t_1$.
We suggest a generalization of this principle: if $O_1 \subseteq O_2$ then replace the label $\alpha_2$ in $t_2$ by $\alpha_2 \land \neg \alpha_1$. If $O_1 = O_2$, replace both transitions by the transition $(q, \alpha_1 \lor \alpha_2, O_1)$. Note that if $\alpha_2 \Rightarrow \alpha_1$, i.e. $\alpha_2 \subseteq \alpha_1$, then $\alpha_2 \land \neg \alpha_1 \equiv \neg tt$
and transition $t_2$ can be removed as before. Our generalized optimization rule increase determinism of the produced VWAA as illustrated by automata (c) of Figures 1 and 2.
6 Improvements in VWAA to TGBA Translation
First, we recall the translation of VWAA to TGBA introduced in [11]. Let $A_\varphi = (Q, \Sigma, \delta, I, F)$ be a VWAA with a co-Büchi acceptance condition. We define $G_A = (Q', \Sigma, \delta', I, T)$ to be a TGBA where:
- $Q' = 2^Q$, i.e. a state is a set of states of $A_\varphi$ and represents their conjunction,
- $\delta''(\{q_1, q_2, \ldots, q_n\}) = \bigotimes_{i=1}^{n} \delta(q_i)$ is the non-optimized transition function,
- $\delta'$ is the optimized transition function defined as the set of ≼-minimal transitions of $\delta''$ where the relation ≼ is defined by $t_1 ≼ t_2$ iff $t_1 = (O, \alpha_1, O_1)$, $t_2 = (O, \alpha_2, O_2)$, $\alpha_2 \subseteq \alpha_1$, $O_1 \subseteq O$, and $\forall T_f \in T$, $t_2 \in T_f \Rightarrow t_1 \in T_f$, and
- $T = \{T_f \mid f \notin O' \} \cup \{((\beta, O'') \in \delta(f), \alpha \subseteq \beta \text{ and } f \notin O'' \subseteq O'\}$.
Improved Translation Our algorithm for a VWAA to TGBA translation differs from the original one only in definition of $\delta$, where we also integrate the idea of suspension of alternating formulae. Recall that each state $q_i$ of a VWAA is a subformula of an input LTL formula and each state of a TGBA is identified with a conjunction of states of a VWAA. Let $O = \{q_1, \ldots, q_n\}$ be a state of a TGBA. Then transitions leading from $O$ in a TGBA correspond to combinations of transitions leading from $q_1, \ldots, q_n$ in a VWAA. If $q_i$ is an alternating formula and thus it satisfies $q_i \equiv Xq_i$, we can effectively decrease the number of transition combinations that need to be considered during computation of $\delta'(O)$ provided we suspend a full processing of $q_i$ to the succeeding states of the TGBA. More precisely, for the purpose of computation of $\delta'(O)$, we set $\delta(q_i) = \{(\Sigma, \{q_i\})\}$. To construct a TGBA equivalent to the VWAA, we have to ensure that $q_i$ will not be suspended forever during any accepting run of the TGBA. Hence, we enable suspension only in the states that are not on any accepting cycle in a TGBA.
Let $M$ be the minimal set containing all VWAA states of the form $\psi R \rho$ and all subformulae of their right operands $\rho$. One can observe each TGBA state lying on some accepting cycle is a subset of $M$. The VWAA states outside $M$, called progress formulae, push TGBA computations towards accepting cycles. Suspension is enabled in a TGBA state only if it contains a progress formula. However, if all progress formulae in a TGBA state are alternating, their suspension is not allowed (as suspended progress formulae would not enforce any progress).
Formally, for each TGBA state $O = \{q_1, q_2, \ldots, q_n\}$ we define $\delta''(O)$ as follows:
$$\delta''(O) = \bigotimes_{i=1}^{n} \delta_O(q_i),$$
where
Fig. 3. A VWAA $\mathcal{A}_\psi$ corresponding to $GF_a \land Fb$.
Fig. 4. A TGBA $G_\psi$ corresponding to the VWAA of Figure 3.
$\delta_\phi(q_i) = \begin{cases} \{(\Sigma, \{q_i\})\} & \text{if } O \text{ contains a progress non-alternating formula} \\
\delta(q_i) & \text{and } q_i \text{ is an alternating formula,} \\
\delta(q_i) & \text{or } O \text{ contains a progress formula} \\
\delta(q_i) & \text{and } q_i \text{ is an alternating non-progress formula,} \\
\end{cases}$
We have obtained better results when we restrict the definition of progress formulae to temporal progress formulae.
Note that the original translation of VWAA to TGBA uses a correct but non-intuitive definition of accepting sets $T_f$. In fact, our modification is correct only if we change the definition of these sets to intuitive one: for each accepting state $f$ of the VWAA with a co-Büchi acceptance, we compute a set $T_f$ to contain all TGBA transitions that do not contain any VWAA transition looping in $f$. Formally, $T = \{ T_f \mid f \in F \}$ where
$T_f = \{ (O, \alpha, O') \mid f \notin O' \text{ or } (\exists (\beta, O'') \in \delta(f), \exists (\gamma, O''') \in \bigotimes_{f' \in O \setminus \{f\}} \delta(f') \text{ such that } f \notin O'', \alpha = \beta \land \gamma, \text{ and } O' = O'' \cup O''' \}$.
Incorrectness of the improved VWAA to TGBA translation in connection with the original definition of accepting sets is illustrated by the TGBA $G_\phi$ of Figure 5 constructed from the VWAA $\mathcal{A}_\phi$ of Figure 6. Thanks to the accepting cycle between states $\{1, 2, 4\}$ and $\{1, 2, 5\}$, automaton $G_\phi$ accepts the infinite word $w = ((p_1, p_2)\{p_3\})^\omega$. Note that $w \not\models GFq$ and hence also $w \not\models \psi \land GFq$. Thus, $w$ is not accepted by VWAA $\mathcal{A}_\phi$ as $\mathcal{A}_\phi$ corresponds to the formula $\varphi = \psi \land GFq$. Figure 7 depicts the TGBA $G'_\varphi$ automaton produced by the improved translation with the new definition of accepting sets. One can easily see that $G'_\varphi$ does not accept $w$.
To demonstrate the effect of suspension during the construction of a TGBA, consider the VWAA $\mathcal{A}_\psi$ for the formula $\psi = GFa \land Fb$ depicted in Figure 3. The construction of an equivalent TGBA $G_\psi$ starts in the initial state $\{1, 2\}$ that corresponds to a conjunction of states 1 and 2 of $\mathcal{A}_\psi$. Figure 8 depicts the transitions of $G_\psi$ leading from the initial state when constructed by (a) the
Fig. 5. A VWAA $A_\psi$ corresponding to formula $\varphi = \psi \land GFq$, where $\psi = (X(p_1 R p_2) \lor (\neg p_1 \cup p_3)) \cup p_1$.
Fig. 6. A TGBA $G_\varphi$ corresponding to the VWAA of Figure 5 constructed using original definition of accepting sets.
Fig. 7. A correct TGBA $G'_\varphi$ corresponding to the VWAA of Figure 5 constructed using modified definition of accepting sets.
original translation of [11] and by (b) our translation with suspension. Note that the state 1 corresponding to the alternating formula $\text{GF}a$ is suspended in the TGBA state $\{1,2\}$ as the state 2 corresponds to a non-alternating progress formula $\text{F}b$. In both cases, the TGBA has two sets of accepting transitions, $T_2$ and $T_3$. Each transition in the TGBA is labelled by a propositional formula over $AP$ and by a subset of $\{2,3\}$ indicating to which sets of $T_2,T_3$ the transition belongs.
Comparing to the original VWAA to TGBA translation without any optimizations, the application of suspension leads to automata with fewer states. However, if we enable the optimizations suggested in [11], the original translation often constructs automata with the same number of states as our translation with suspension. For example, in the TGBA constructed from the VWAA of Figure 3, the optimizations merge states $\{1,2,3\}$ and $\{1,3\}$ with $\{1\}$, respectively. In this particular case, both approaches lead to the same automaton $G_\psi$ as shown in Figure 4. However, this is not the case in general. Using suspension, automata with either more or less states can be constructed. However, the translation with suspension is usually slightly faster.
In addition, we detect that both the original and the improved algorithms spend a lot of time when computing transitions of TGBA states equivalent to a formula of the form $\rho = \text{G}\alpha_0 \land \bigwedge_{1 \leq i \leq n} \text{GF}\alpha_i$ where $n \geq 0$ and $\alpha_0, \alpha_1, \ldots, \alpha_n$ are formulae without any temporal operator. As such TGBA states are very frequent in practice, we use an optimization that detects these TGBA states and directly constructs the optimal transitions.
7 Optimization of BA
We slightly modify one optimization rule suggested in [11]. It is applied on a resulting BA. The rule says that states $q_1$ and $q_2$ of a BA can be merged if $\delta(q_1) = \delta(q_2)$ and $q_1 \in F \iff q_2 \in F$. This rule typically fails to merge the states with a self loop. We suggest to add a new rule where the condition $\delta(q_1) = \delta(q_2)$ is replaced by $\delta(q_1)[q_1/r] = \delta(q_2)[q_2/r]$, where $r$ is a fresh artificial state and $\delta(q)[q/r]$ is a $\delta(q)$ with all occurrences of $q$ as a target node replaced by $r$.
![Fig. 8. Transitions leading from state $\{1,2\}$ in the TGBA constructed from the VWAA of Figure 3 by (a) the translation of [11] and by (b) our translation with suspension.](image-url)
| Translator | Benchmark1 | Benchmark2 |
|--------------------|------------|------------|
| | States | Trans. | Time | det. BA | States | Trans. | Time | det. BA |
| SPOT | 1561 | 5729 | 7.47 | 55 | 14697 | 95645 | 68.46 | 221 |
| SPOT+WDBA | 1587 | 5880 | 10.81| 88 | 13097 | 77346 | 5916.45 | 373 |
| LTL2BA | 2118 | 9000 | 0.81 | 25 | 24648 | 232400 | 18.57 | 84 |
| LTL3BA(1) | 1621 | 5865 | 1.26 | 27 | 17107 | 129774 | 22.25 | 92 |
| LTL3BA(1,2) | 1631 | 6094 | 1.41 | 54 | 15936 | 115624 | 9.04 | 237 |
| LTL3BA(1,2,3) | 1565 | 5615 | 1.41 | 54 | 14113 | 91159 | 8.53 | 240 |
| LTL3BA(1,2,3,4) | 1507 | 5348 | 1.38 | 54 | 13244 | 85511 | 8.30 | 240 |
Table 1. Comparison of translators on two sets of random formulae. Time is in seconds, 'det. BA' is the number of deterministic automata produced by the translator. Note that, using WDBA minimization, SPOT failed to translate 6 formulae of Benchmark2 within the one hour limit. In order to see the effect of WDBA minimization to other formulae, we state in braces the original results increased by the values obtained when these 6 formulae were translated without WDBA minimization.
8 Implementation and Experimental Result
We have implemented all the modifications suggested in the previous sections (and formula reduction rules suggested in [9]) in order to evaluate their effect. The implementation is based on LTL2BA and therefore called LTL3BA. Besides the changed algorithms, we also made some other, implementation related changes. In particular, we represent transition labels by BDDs and transitions are represented by C++ STL containers.
In this section, we compare LTL3BA with LTL2BA\(^1\) (v1.1) and SPOT\(^2\) (v0.7.1\(^3\)) For the comparison of results, we use \texttt{lbbt} testbench tool \cite{lbtt} to measure, for each translator, the number of states and transitions of resulting automata, and the time of the computation. Further, we extend \texttt{lbbt} to count the number of produced deterministic automata. To be able to compare the results, we set SPOT (option \texttt{-N}) to output automata in the form of never claim for SPIN as that is the output of LTL2BA as well. All experiments were done on a server with 8 processors Intel\(^®\) Xeon\(^®\) X7560, 448 GiB RAM and a 64-bit version of GNU/Linux. However, all three translators are single threaded, therefore, they can utilize only one CPU core.
\(^1\) Available online at \url{http://www.lsv.ens-cachan.fr/~gastin/ltl2ba/index.php}
\(^2\) Available online at \url{http://spot.lip6.fr/wiki/}
\(^3\) In version version 0.7.1, SPOT contains a small bug in TGBA degeneralization. We reported this problem to authors and they provided a corresponding fix which we have applied. Therefore, the version of SPOT we have actually used differs a bit from the current version 0.7.1 that is publicly available.
To solve the problem with different representation of transitions in automata produced by different tools, we count all transitions leading from a state \(q\) to a state \(r\) as one.
First we compare the translators on two sets, Benchmark1 and Benchmark2, of random formulae generated by lbtt. Benchmark1 contains 100 formulae of the length 15–20 and their negations. Benchmark2 contains 500 formulae of the length 15–30 and their negations. The exact lbtt parameters used to generate the formulae are in Appendix A. Table 1 presents the cumulative results of translations of all formulae in the two sets. The table also illustrates the gradual effect of modifications of each step of the translation (1,2,3,4 refers to modifications introduced in Sections 4, 5, 6, and 7 in the respective order; e.g. LTL3BA(1) uses the original algorithm with our formula reduction while LTL3BA(1,2,3,4) refers to the translation with all the suggested modifications). Finally, the table contains the results for SPOT with WDBA minimization, which has the longest running time but provides the best results. The automata produced by LTL3BA are in sum slightly better than the automata produced by SPOT. Further, LTL3BA seems to be much faster.
Further, we compare the execution time of translators running on parametric formulae from [11] and [16]. We use SPOT with the recommended option -r4, i.e. with the input formula reduction as the only optimization. To get a comparable settings of LTL3BA, we switched off the generalized optimization of VWAA. We gradually increase the parameter of the formulae until a translator fails to finish the translation in one hour limit. The results are depicted in Figure 9, Figure 10 and Figure 11.
It is worth mentioning that each automaton produced by LTL3BA for $\theta_n$ has around half the number of states and half the number of transitions than
Fig. 10. Running times of LTL to BA translators on parametric formulae of [16] (the vertical axes are logarithmic and represent time in seconds, while the horizontal axes are linear or logarithmic and represent the parameter $n$).
The graphs show that, in general, LTL3BA is slightly slower than LTL2BA and faster than SPOT on small formulae. With increasing parameter, LTL3BA outperforms LTL2BA (with exception of $S(n)$ where LTL2BA fails before its running time reaches the limit), while SPOT sometimes remains slower, but sometimes eventually outperform LTL3BA.
Finally, we compared SPOT and LTL3BA on parametric formulae from [2]:
$$
\alpha_n = F(p_1 \land F(p_2 \land \ldots \land Fp_n) \ldots) \land F(q_1 \land F(q_2 \land \ldots \land Fq_n) \ldots)
$$
$$
\beta_n = F(p \land X(p \land \ldots \land Xp) \ldots) \land F(q \land X(q \land \ldots \land Xq) \ldots)
$$
$$
\beta'_n = F(p \land X^2p \land \ldots \land X^{n-1}p) \land F(q \land Xq \land X^2q \land \ldots \land X^{n-1}q)
$$
$$
\psi_n = GFp_1 \land GFp_2 \land \ldots \land GFp_n
$$
$$
\xi_n = F[pq \lor Fp_2 \lor \ldots \lor Fp_n]
$$
In 2009, Cichoń et al. [2] introduced the four parametric formulae and shown that their BA representations obtained by both LTL2BA and SPOT are far away from their minimal representations (or uncomputable even for the parameter \( n \leq 20 \)). Two years later in [6], the authors of SPOT announced that they are able to compute all the mentioned formulae in minimal form. We have recomputed the results for all \( n \leq 20 \) by SPOT and LTL3BA and realized that LTL3BA returns also the minimal automata but 8 times faster. More precisely, the overall computation of SPOT took more than 13 minutes (802 seconds), while the computation of LTL3BA took less than 2 minutes (95 seconds).
### 9 Conclusion
We have focused on LTL to BA translations with the stress on their speed-up while maintaining outputs of a good quality. We have introduced several modifications of LTL2BA on both algorithmic and implementation levels. Among others, we have identified an LTL subclass of “alternating” formulae, validity of which does not depends on any finite prefix of the word.
Our experimental results indicate that our modifications have a mostly positive effect on each step of the translation. The new translator called LTL3BA is usually faster than the original LTL2BA and it produces smaller and more deterministic automata. Moreover, comparison of LTL3BA and the current version of SPOT (run without WDBA minimization that is very slow) shows that the produced automata are of similar quality and LTL3BA is usually faster.
LTL3BA has served as an experimental tool to demonstrate that our modifications are improvements and their applicability to other LTL to BA translations is a subject of further research.
LTL3BA is publicly available under GPL at:
http://sourceforge.net/projects/ltl3ba/
Acknowledgments. The authors would like to thank three anonymous referees and Alexandre Duret-Lutz for valuable comments.
References
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2. J. Cichoń, A. Czubak, and A. Jasiński. Minimal Büchi automata for certain classes of LTL formulas. In DEPCOS-RELCOMEX’09, pages 17–24. IEEE, 2009.
3. J.-M. Couvreur. On-the-fly verification of temporal logic. In FM’99, volume 1708 of LNCS, pages 253–271. Springer, 1998.
4. M. Daniele, F. Giunchiglia, and M. Y. Vardi. Improved automata generation for linear temporal logic. In CAV’99, volume 1633 of LNCS, pages 249–260. Springer, 1998.
5. C. Dax, J. Esinger, and F. Klaedtke. Mechanizing the powerset construction for restricted classes of ω-automata. In ATVA’07, volume 4762 of LNCS, pages 223–236. Springer, 2007.
6. A. Duret-Lutz. LTL translation improvements in Spot. In VECoS’11, eWiC. British Computer Society, 2011.
7. A. Duret-Lutz and D. Poitrenaud. SPOT: An extensible model checking library using transition-based generalized Büchi automata. In MASCOTS 2004, pages 76–83. IEEE, 2004.
8. R. Ehlers and B. Finkbeiner. On the virtue of patience: Minimizing Büchi automata. In SPIN 2010, volume 6349 of LNCS, pages 129–145. Springer, 2010.
9. K. Etessami and G. J. Holzmann. Optimizing Büchi Automata. In CONCUR’00, volume 1877 of LNCS, pages 153–167. Springer, 2000.
10. C. Fritz. Constructing Büchi automata from linear temporal logic using simulation relations for alternating Büchi automata. In CIAA ’03, volume 2759 of LNCS, pages 35–48. Springer, 2003.
11. P. Gastin and D. Oddoux. Fast LTL to Büchi Automata Translation. In CAV’01, volume 2102 of LNCS, pages 53–65. Springer, 2001.
12. D. Giannakopoulou and F. Lerda. From States to Transitions: Improving Translation of LTL Formulae to Büchi Automata. In FORTE’02, volume 2529 of LNCS, pages 308–326. Springer, 2002.
13. C. Löding. Efficient minimization of deterministic weak omega-automata. *Information Processing Letters*, 79(3):105–109, 2001.
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17. R. Sebastiani and S. Tonetta. “More Deterministic” vs. “Smaller” Büchi Automata for Efficient LTL Model Checking. In *CHARME 2003*, volume 2860 of *LNCS*, pages 126–140. Springer, 2003.
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A lbt parameters used for formulae generation
Here are the precise parameters for lbt to produce the sets Benchmark1 and Benchmark2 of random formulae. Note that we also added negations of these formulae to the sets.
Benchmark1 (100 formulae + their negations):
Size = 15...20
Propositions = 8
AbbreviatedOperators = Yes
GenerateMode = Normal
OutputMode = NNF
PropositionPriority = 50
TruePriority = 1
FalsePriority = 1
AndPriority = 10
OrPriority = 10
XorPriority = 0
EquivalencePriority = 0
BeforePriority = 0
StrongReleasePriority = 0
WeakUntilPriority = 0
UntilPriority = 30
DefaultOperatorPriority = 15
The parameters for Benchmark2 (500 formulae + their negations) are the same except the first one, where set:
Size = 15...30
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Fluctuations in the average daily personality of the United States capture both meaningful affective responses to world events (e.g., changes in anxiety or well-being) and broader psychological responses. We estimate the change in national personality in the months following the onset of the COVID-19 pandemic and investigate fluctuations in personality states during the year 2020 using data from an ongoing personality assessment project. We find significant and meaningful change in personality traits since the beginning of the pandemic, as well as evidence of instability in personality states. When evaluating changes from the first few months of 2020 to the period of social distancing related to COVID-19 restrictions, the social traits reflected an unexpected "deprivation" effect such that mean self-ratings increased in the wake of restricted opportunities for social interaction. Changes in mean levels of the affective traits were not significant over the same months, but they did differ significantly from the average levels of prior years when looking at shorter time intervals (rolling 7-day averages) around prominent national events. This instability may reflect meaningful fluctuations in national personality, as we find that daily personality states are associated with other indices of national health, including daily COVID-19 cases and the S&P index. Overall, the use of personality measures to capture responses to global events offers a more holistic picture of the U.S. psyche and of personality change at the national level.
Substantial prior work has documented that personality traits differ across geographic regions (Allik & McCrae, 2004; McCrae & Terracciano, 2005; Schmitt et al., 2007; Wei et al., 2017) and that such differences are associated with important psychological (Steel & Ones, 2002), economic (de Vries et al., 2011; Kirkcaldy et al., 1998), political (Barceló, 2017; Connelly & Ones, 2008; Rentfrow et al., 2009), and health outcomes (McCann, 2010; Rentfrow et al., 2015). National traits, for example, are associated with GDP and subjective well-being (Kirkcaldy et al., 1998), while state-level traits predict income inequality (de Vries et al., 2011) and voting patterns (Rentfrow et al., 2009). The relationships between personality and outcomes at the state- and country-level are often stronger than similar relationships at the person-level (Steel & Ones, 2002), suggesting that regional and national personality contains important information for policy-makers.
To date, the study of national personality has occurred in the context of cross-cultural research, in which trait levels and outcomes are compared between-countries. However, just as personality is known to change and fluctuate within a single person (Caspi et al., 2005; Fleeson & Jayawickreme, 2015), we might also expect changes and fluctuations in personality within countries over time. The potential for change in personality at the level of nations poses serious consequences for the long-term outcomes of countries. However, personality change at the nation-level has remained largely unstudied because such change either happens slowly over time (requiring continuous assessment across decades) or in the face of a strong and sudden situation that greatly affects a large proportion of the population.
But the COVID-19 pandemic created a quasi-experimental condition, during which we have reason to suspect the personality of the United States has changed. Moreover, the year 2020 included multiple major news events and situations which may have also contributed to noticeable changes in national personality. Importantly, even if national personality is stable in the long-term, short-term fluctuations in some traits could prove to have measurable impact on the psychological and physical health of the nation.
To illustrate the notions of personality change and fluctuation in the context of the pandemic, we describe the example of trait Sociability. If a person, Peter, wanted to change his level of Sociability, he would be advised that trait change is possible, if difficult, through changes in daily-life processes (Quintus et al., 2020; Wrzus & Roberts, 2017) and that he should target behaviors related to Sociability (Stieger et al., 2020). For example, Peter might start work-
ing in cafes instead of solo-occupant offices, or plan more frequent social outings with groups. If Peter were able to change his daily habits for long enough, he may begin to experience more durable and less intentional increases in his trait Sociability. Scaling this process up to change the personality of a nation would require consistent change in daily processes for many citizens of a country. Millions of Americans would need to engage in new daily behaviors in more or less the same direction, simultaneously. Under normal circumstances, it would be unlikely for the personalities of countries, or other large groups, to change substantially in a short period of time (Elleman et al., 2018; Rentfrow et al., 2008, 2013).
Even so, short-term changes or fluctuations in the personality states of nations may have import. In March and April of 2020, public health officials called for American citizens to “flatten the curve,” or slow the rate of spread of the coronavirus, through the use of social distancing (Matrajt & Leung, 2020; Thunström et al., 2020). In essence, the call was for Americans to engage in active, if short-term, personality change: reduce Sociability for a period of 2-3 weeks in an effort to measurably reduce viral spread and maintain public health. Again, we note here the distinction between lasting long-term change in personality and fluctuations in personality states. We do not claim that engagement in social distancing is a form of long-term personality change, nor is there currently evidence that the personalities of individuals changed in consistent ways during the first weeks of the pandemic (Sutin et al., 2020).
Yet personality states reflect both affective fluctuations and situation-specific behaviors (Wilson et al., 2017) and provide meaningful insight into the psychological experience of individuals. Fluctuations in personality at the national level likely hold information relevant to more transitory concerns of a country, especially with regard to less stable outcomes, such as some economic indicators or, during a pandemic, public health and well-being. Early work points to increases in loneliness and decreases in well-being during the first months of the pandemic (Gubler et al., 2020; Zacher & Rudolph, 2020); based on these findings, changes to other personality states also seemed likely.
We note that change in nation-level personality may result from multiple situations. As described above, an unusual situation affecting most or all persons in a country would be one example. Another example would be a situation that has a large effect on a subset of the population. With that in mind, consider the potential for personality change following the killing of George Floyd, the Black Lives Matter protests, the lead-up to the national election, and the sitting president’s refusal to concede the election. Regardless of political orientation, one would concede that such events were highly emotional and potentially disruptive for at least a subset of the US population, and thus may precipitate short-term fluctuations in national personality.
Fluctuations in personality traits may be assessed through the application of indices originally developed for research on affective dynamics (Marwaha et al., 2014; Ong & Ram, 2016). These indices – marking the variability, instability, and inertia of psychological states – have been applied at the person-level to understand manifestations of personality disorders (Wright & Simms, 2016) and other pathologies. Recent focus on intraindividual personality suggests that the assessments of state dynamics can better characterize persons than trait levels (Danvers et al., 2020; Sosnowska et al., 2019).
The current study assesses (1) the degree of personality change in the United States after the pandemic began, (2) the fluctuations in personality states during 2020, and (3) the extent to which fluctuations in states are meaningful, as defined by their associations with other indices of national health, both physical (COVID-19 cases) and financial (S&P closing prices). To answer these questions, we use data (N = 40,887) collected through the SAPA-Project (Condron et al., 2017; Condon & Revelle, 2015), an ongoing personality assessment platform that collects data on thousands of personality items continuously. Such ongoing data collection allows for assessment of change without reliance on retrospective reports. Though the data collected through the SAPA-Project are cross-sectional, there is considerable precedent in psychological research for using large-scale cross-sectional data sets to estimate normative longitudinal trends in personality change (Roberts & Mroczek, 2008; Soto et al., 2011).
Methods
Data collection and participants
Personality data was collected as part of the Synthetic Aperture Personality Assessment (SAPA) project, an international online personality assessment tool (Condon & Revelle, 2015). Participants were motivated to complete the survey in exchange for customized feedback about their personality. Participants could answer as many questions as they chose, from 25 to 250 personality questions; more feedback was given to participants who answered more questions. Responding was also optional for all demographic prompts except age, gender, and a question asking whether participants had previously completed the survey. This data collection protocol was approved by the University of Oregon Institutional Review board to have Exempt Status, including informed consent. All methods were carried out in accordance with guidelines and regulations. Participant data for this sample were collected between the dates of January 1 and December 31, 2020 (inclusive). Participants were included in these analyses if they reported residing in the United States (N = 40,887).
Participants (67% female) ranged from 15- to 90-years-old (M = 25.29, SD = 11.34). Participants are generally healthy, with 61% (N = 25,981) of those responding to a single item rating of self-reported health as very good or excellent. Of those who reported employment status (84%), the majority were either currently employed (45%; N = 15,391) or a student (39%; N = 13,375).
Measures
Personality was assessed using the hierarchical SAPA Personality Inventory (SPI-135) (Condon, 2017), which allowed us to calculate scores on both the Big Five traits as well as 27 narrow, unidimensional traits. The Big Five are widely used for the assessment of personality though often criticized for being overly-broad (Condon et al., 2021; Mõttus.
et al., 2020), whereas the assessment of more narrow traits, including Sociability, can paint a more nuanced picture of the ways in which personality is (or is not) changing and fluctuating in the United States during the COVID-19 pandemic. While this measure can be scored to generate estimates for each of the broad Big Five traits and 27 narrow traits, we pre-registered our analyses for this study to focus on the Big Five trait of Neuroticism and the five narrow traits most highly correlated with Neuroticism: Adaptability, Anxiety, Emotional Stability, Irritability, and Well Being. As with other hierarchical frameworks for measuring personality, the scores within each level of the hierarchy are independent and the scores across levels of the hierarchy are somewhat dependent. In other words, some of the questions used to derive Neuroticism estimates (at the level of the broad Big Five dimensions) are also used for one (but not more than one) of the narrow 27 traits lower down in the hierarchy.
Each person’s Big Five trait scores were calculated by taking the average response to the 14 items in each trait scale ($\alpha_N = 0.90; \alpha_E = 0.88; \alpha_A = 0.85; \alpha_C = 0.86; \alpha_O = 0.80$). Because the narrow traits are unidimensional, we used IRT-scoring to estimate person scores on those traits, providing more precise estimates than a traditional sum score approach. Reliability for IRT-scored scales is best conveyed through test information curves as shown in Figures S1-5 (see osf.io/6anw7). Cronbach’s alphas are not typically appropriate in this case, but we note that they ranged from a low of .66 (Easy-Goingness) to a high of .90 (Well Being). All trait measures were T-scored (scaled to a mean of 50 and a standard deviation of 10) for ease of interpretation.
We estimate national personality at the daily level by aggregating responses from all participants who provided data on a given day ($N_{\text{per day}}$ ranged from 18 to 282, with an average of 111.14). In addition, we weighted responses by participant characteristics – age, gender, race, and education – using raked weights (Lu & Gelman, 2003) derived using U.S. Census data, in an effort to maximize sample similarity across days and also better represent the population of the nation. In order to reduce systematic variance due to biased participation by time (e.g., perhaps introverts are more likely to participate on weekends), we calculated a seven-day smoothed average, thereby eliminating day-of-week effects.
We also included daily indices of the country’s physical and financial health. Here, we report analyses using the S&P 500 closing price and daily COVID-19 cases, as reported by The New York Times. We also examined the correlations of personality states with daily deaths from COVID-19, 10-year treasury bond rates, and stock market volatility (VIX); these results were similar to what is presented here, and corresponding figures can be found in the Supplemental Materials (Figures S6-8).
These analyses were pre-registered (osf.io/vpbfm) and hypotheses were specified for affective traits (i.e., Neuroticism and related narrow traits). We note here that the pre-registration was for data collected through June 1. Given the time required to complete the analyses, we chose to extend correlation analyses through December, so as to estimate more generalizable and timely effect sizes. In a prior iteration of these analyses, trait Sociability was also strongly associated with both indices discussed herein, while Conscientiousness was unrelated.
Results
Changes in personality traits
To assess the degree to which national personality has changed during the COVID-19 pandemic, we compared personality in the months following the declaration of the national emergency (March 13–June 1, 2020) to personality in the months preceding the declaration (January 1–March 12, 2020). Change in personality traits from before to after the national emergency declaration are shown in Figure 1. After March 13, we see increases in Extraversion and related narrow traits, including Humor, Sociability, Sensation Seeking, and Attention Seeking. Such change is surprising, as this suggests that scores for social traits increased, on average, in the sample under social distancing and lockdown orders. Though the underlying mechanism is unclear given the cross-sectional nature of these data, it is unlikely that changes in these traits reflect changes in daily behaviors; as the opportunities for socializing and pursuing sensation- and attention-seeking behaviors were more limited than usual. Alternative explanations follow directly from the deprivation of these opportunities. Perhaps the lockdown prompted higher rates of participation from more extraverted individuals, or the deprivation of lockdown changed respondents’ self-appraisals, on average, with respect to the restricted behaviors. Notable increases in Compassion and Art Appreciation support the latter interpretation more than the former, as these were also affected by lockdown restrictions (e.g., going to museums, believing in the importance of art) and fear of contagion (e.g., concern about others, sympathy for those who are worse off). In other words, we may not think of ourselves as extraverts and art aficionados until we are prohibited from social gatherings and cultural events. We also note observed decreases in Emotional Stability (e.g., feeling overwhelmed by emotions, strong changes in mood) and Authoritarianism (e.g., respecting authority, following rules).
To account for the possibility that these changes may be subject to seasonal fluctuation independent of the national emergency, we computed the amount of change across the same period in 2019 (i.e., change in average daily personality from January 1, 2019 through March 12, 2019 and March 13, 2019 to June 1, 2019) and 2018 (change from January 1–March 12 to March 13–June 1), as well as the difference in change. These results are depicted in Supplementary Material Figures S12-15. We found little evidence of national personality trait change in the equivalent time period in 2019; after adjusting for multiple comparisons, only two of 32 traits (Introspection and Attention Seeking) were significantly different in the spring 2019 compared to winter 2019. However, six trait change estimates were significant in 2018. (Eight were significant in 2020.) We note that traits which changed in 2018 were largely different from those that changed in 2020 (Agreeableness, Orderliness, Intellect, and Trust decreased, while Impulsivity increased). Common to both years, Emotional Stability decreased from Winter to Spring. Moreover, comparisons of trait change using standardized effect sizes suggest that change during 2020 for
traits Extraversion \(d = 0.93\), Humor \(d = 1.22\), and Sociability \(d = 0.83\) – as well as Art Appreciation \(d = 1.07\) – were quite large by comparison to 2018. Overall, these analyses suggest that daily national personality levels did change after the declaration of the national emergency, and that these changes were not merely expected seasonal changes.
Change analyses yielded two surprising results: (1) increases in social traits, discussed above, and (2) a lack of change in trait Neuroticism and related narrow traits, including Anxiety and Well-Being (the exception being decreases in Emotional Stability). Given the focus on mental health during social distancing, the lack of change in these traits was unexpected and suggested that the use of two time-points for change analyses poorly represents the real-world processes of change. Perhaps levels of Anxiety and Neuroticism increase just before and/or after the start of the national emergency, but as American citizens become accustomed to their new daily lives, these traits return to baseline. Or perhaps various large-scale events push and pull these traits in different directions. Rising case counts, for example, may lead to increases in anxiety, while federal stimulus bills lead to decreases. In other words, while there may not be significant overall differences between winter and spring, we may see significant fluctuations in traits in the year 2020. Expanding beyond spring, there were a number of large-scale events which had the potential to impact at least subsets of the population.
To explore this possibility further, we created several exploratory figures, representing the 7-day rolling average of trait levels across the year. These figures also include the dates of key events during 2020, such as the killing of George Floyd, the start of the school year, and the presidential election. Figure 2 shows the national trends for Anxiety, and figures for the other traits are included in the supplementary material (Figures S14-S20). In Figure 2, we see some evidence that large events impacted national personality. For example, the presidential election coincided with the highest levels of Anxiety, while in prior years, Anxiety was below average levels during this time of year. In addition, Anxiety tended to be high throughout the Fall of 2020, perhaps due to both the political election and instability in school openings. However, we do not see similar trends in Anxiety coinciding with the killing of George Floyd or the summer of protests. Overall, these figures present mixed evidence for the impact of national events on national personality.
Fluctuations in personality traits
We examine the daily fluctuations of personality states using a dynamics approach (Ong & Ram, 2016). Through this approach, we assess three indices of fluctuation: variability, instability, and inertia. For all analyses, we use the weighted daily averages (not smoothed), in order to avoid artifactual results; we use all days from January 1 through December 31. We caution against comparing broad traits to narrow ones in the analyses of variability and instability, given that broad traits were assessed with a greater number of items that are less highly correlated. These differences in psychometric properties may contribute systematically to differences in amounts of variance. Inertia results, on the other hands, are in a standardized format.
As can be seen in Figure 3A, national traits had similar levels of variability across days, suggesting that traits deviated from the country’s average level to the same extent. Traits were scored at the person-level such that all traits had a mean of 50 and standard deviation of 10. When aggregated to the day level, we see an expected reduction in variability, although not equally across traits. Conscientiousness and Openness were the most variable of the Big Five, although not statistically significantly so. We interpret these results to suggest that personality traits, broad and narrow, were relatively similar in terms of their variability across days. That is, no one trait was unchanging. Yet while traits were similar in their levels of variability, there were notable differences in instability, or the amplitude and tendency with which national personality was likely to change from one day to the next (see Figure 3B). Instability was measured using the mean square successive difference (Ong & Ram, 2016). Large values of instability suggest that, from one day to the next, national personality levels are likely to change and the magnitude of this change is large. Take
for example, Attention Seeking; this was the least stable of the narrow traits. If Attention Seeking is high on a Tuesday, we would not be surprised to see it drop precipitously on Wednesday or bounce back again on Thursday. Compare this to Sociability. If Sociability is high on Thursday, we would expect it to be high on Friday. A note of caution that these effect sizes are unstandardized, so cutoffs for “high” and “low” instability are difficult to estimate. Rather, we suggest the relative comparison of traits is more informative. The pattern of instability suggests that interpersonal traits are the most variable. Consider that Attention Seeking showed great instability, followed by Adaptability and Humor. On the other hand, Honesty, Intellect, Emotional Stability, and Introspection were more stable. This pattern suggests important day-to-day changes in interpersonal traits, perhaps reflecting changing attitudes about socializing, or perhaps even changing attitudes about communality with fellow Americans, as social and political events became increasingly divisive during 2020.
Finally, we examine the inertia of personality states (Figure 3C), as measured by the autocorrelation (Ong & Ram, 2016), or the correlation of trait levels one day with the next. Inertia is similar to instability (in the opposite direction), in that it indexes the likelihood of change from one day to the next. However, unlike instability, it does not account for the amplitude of change. None of the inertia estimates were significantly different from zero, in part driven by the lower power of this study to detect effects smaller than $r = .10$; in other words, there was no evidence that the nation persisted in specific personality states across multiple days. In combination with the instability analyses, the inertia findings suggest that personality traits are likely to fluctuate from day to day. However, this may also be driven by the use of a cross-sectional study, in which sampling error may, even after weighting, obscure some group-level trends.
### Trait fluctuations associated with national health
Our results suggest that some national personality traits changed since the national emergency was declared, and that even for traits which did not change, there were fluctuations in national personality states during 2020. It remains to be seen whether these fluctuations are meaningful or reflected in other aspects of national activity. To evaluate this, we examine the associations between personality states and other indices of national economic and public health. More specifically, we examined the correlations between daily personality states and daily new cases of COVID-19 and the closing prices of the S&P 500.
The 7-day moving averages for all affective traits were associated with one or more of the physical health and financial indicators (see Figure 4 for correlations with COVID-19 cases and Figure 5 for correlations with financial markets). Trait Neuroticism was strongly associated with both outcomes—increases in both daily COVID-19 cases and, perhaps surprisingly, S&P500 closing prices. Correspondingly, there are large positive correlations between these outcomes and Anxiety and Irritability, and negative associations with Well-Being and Adaptability. Counter-intuitively, Easy-goingness was also positively associated with COVID-19 cases and the S&P closing prices, although we note that this trait is somewhat more reflective of low industriousness than emotion generally.
Figure 3. Personality state dynamics
Bars represent bias corrected and accelerated 95% confidence intervals estimated using bootstrapping.
**a. Variability in personality states.** Bars represent the standard deviation of the national daily states; the standard deviation value is also printed next to the bar. Longer bars (higher values) indicate greater levels of variability.
**b. Instability in national states,** as measured using the mean square of successive difference (MSSD) from one day to the next. Bars present the value of the MSSD. Longer bars indicate greater instability, which captures both the tendency to change and change amplitude.
**c. Inertia in national states,** as measured using the autocorrelation. Positive values indicate that on any day, the nation is more likely than not to be in a similar state as the day before, while negative values indicate that the nation is more likely to have changed.
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Personality States of the Union
Collabra: Psychology
Conscientiousness was negatively associated with both outcomes, which may correspond to the generally positive relationship of this trait with health outcomes (Bogg & Roberts, 2004; Weston et al., 2015) and also its association with risk avoidance (Ehsani et al., 2015; Hampson et al., 2000). Extraversion and associated lower traits (including Sociability, Humor, Charisma) were negatively associated with new COVID-19 cases and S&P prices, suggesting an overall decrease in Extraversion during the year.
**Discussion**
In summary, the present research found evidence for change in national personality traits after the onset of the COVID-19 pandemic, specifically increases in trait Extraversion and associated narrow traits (e.g., Sociability, Humor, and Sensation Seeking). Fluctuations in social traits were also associated with increased numbers of new daily COVID-19 cases and drops in the S&P500, suggesting that these changes and fluctuations in national personality are connected with larger psychological processes that impact both daily lives and long-term outcomes for the country. There was no supporting evidence that these changes were driven by annual or seasonal changes. While it remains a possibility that some or all of this change was driven by a shift in sampling characteristics (i.e., lockdowns increased the likelihood that more extraverted individuals participated in the survey because they could no longer socialize), other changes during the lockdown period suggest that more substantive factors were involved. These changes include increases in Art Appreciation, Compassion, and Emotional Expressiveness, and decreases in Emotional Stability and Authoritarianism. Changes in these traits are less readily explained by shifts in participant sampling than the circumstantial factors of pandemic-induced restrictions and suffering.
Mean-level increases in affective traits (e.g., Neuroticism) were not found, but analysis of personality state dynamics revealed substantial instability in daily national state Neuroticism and related traits, such as Well-Being, Anxiety, and Irritability. These fluctuations are meaningful (i.e., not simple sampling error), as evidenced by their substantial correlations with other national indices, though challenging to interpret with respect to personality theory. One explanation is methodological. Consistent with recognition that affective traits are more labile than other personality traits (Gross et al., 1998), the appropriate time frame for assessing change in these traits is likely distinct from the months-long window used to compare trends before and after the lockdown.
These findings shed light on another methodological issue as well. Unlike short-term fluctuations in the affective traits, mean-level changes in social traits during the lockdown run counter to expectations based on the behavioral or "act frequency" conception of traits (Buss & Craik, 1983). Mean self-ratings increased due to the deprivation of opportunities to engage in social behaviors, whether due to a change in the make-up of respondents and/or increased self-appraisals of social tendencies. This highlights the merits of informant-reports with respect to convergent validity. The use of national indices of personality traits for tracking changes over time (Baugh et al., 2021) would be substantially improved by the inclusion of informant-reports as a means of distinguishing these deprivation effects from changes in behavioral frequency. The collection of informant-reports should be prioritized in subsequent research on changes in personality at the national level.
This study adds to the growing literature on regional personality (Rentfrow et al., 2008), especially national person-
ality, by being among the first to consider how national personality changes over short intervals and in response to a significant global crisis. Our work points to the utility of measures of narrow traits in this field, as the narrow and unidimensional state fluctuations were those most highly correlated with daily national outcomes. Future research should examine the associations of daily fluctuations in national personality with other metrics of import to economists, public health advisors, and others who work in policy, to understand the psychological underpinnings of these outcomes. Moreover, additional work should seek to model the underlying causal processes; it remains unknown whether fluctuations in traits cause these outcomes or are reflections of other processes.
Changes and fluctuations in Humor speak to the possibility of the bidirectional processes. We propose that changes in traits provide insight into how a nation chooses to react to emergencies. Humor is used to facilitate interpersonal relationships (Ziv, 2010); compare the relatively higher levels of humor during the spring of 2020 to the low levels in the fall and winter. Humor rose when the nation faced an emergency that was perceived to affect all its citizens. It can be argued that no person’s life was untouched by the pandemic, at least in terms of day-to-day routines. However, as the summer approached, it became apparent that all citizens were not affected equally. By the time of the presidential election, American citizens were no longer fighting a pandemic together, but fighting each other for control of the federal government. Correspondingly, Humor— and attempts to build community— plummeted.
The current study only examines change through December 31, so a remaining question is the extent to which the observed changes in national personality are lasting. However, regardless of the long-term impact on personality, even short-term changes in these traits may have substantial impact on national outcomes, given the associations between daily fluctuations and other indices. Especially if there is evidence that some personality states cause outcomes (rather than the other way around), even changes lasting a week or only a few days could have repercussions lasting months or years. For example, it was notable to see no change in affective traits (Neuroticism, Anxiety, etcetera) over longer intervals, but to see substantial short-term instability in these traits and strong associations with national indices of health.
Statistical power in this study was limited by the length of data collection ($N_{days} = 366$ days in 2020), despite the large number of participants who provided data. While greater statistical power could be achieved by widening the time frame, we believe that days outside this time period constitute a different population from the days of interest to this study, at least with regard to historical years. The year 2020 was a unique time in the nation’s history, with major news related to (1) the COVID-19 pandemic, the national emergency, and state-ordered lockdowns, (2) social unrest and injustice, and (3) a major political election in which a sitting president refused to support a peaceful transfer of power. While the United States has been troubled by public health, political, and civil emergencies in the past, we cannot think of a time when we have grappled with all three simultaneously. Moreover, the Internet and social media have connected the average citizen to these issues with more regularity and intimacy than ever before. With that in mind, we do not view the current study as an attempt to find the definitive and context-independent associations between personality fluctuations and outcomes, but rather a demonstration that change and fluctuations in nation-level personality are meaningful, informative, and worthy of consideration by researchers and policymakers alike.
Importantly, the cross-sectional design of the current work is a significant limitation. Given this design, we cannot make strong claims about personality change within individuals, nor can we say definitively that the findings herein are not driven by a shift in sampling characteristics during this period. To do so would require either large-scale longitudinal data collection with high frequency assessments or, in cross-sectional data, carefully randomized sampling of participants to reduce the potential of bias due to “opt-in” participation.
While much attention has been paid to the well-being of the nation during the COVID-19 pandemic, the present research points to the importance and utility of national personality as a focus of study. Our findings suggest that national personality is impermanent, and that fluctuations in personality states are meaningfully linked to important outcomes. Future research may be able to harness this information for better understanding of national health and psychology-informed policy intervention.
**Author Contributions**
Contributed to conception and design: DMC, SJW
Contributed to acquisition of data: DMC, SJW
Contributed to analysis and interpretation of data: SJW, DMC
Drafted and/or revised the article: SJW, DMC
Approved the submitted version for publication: DMC, SJW
**Competing Interests**
Authors have no known conflicts of interest to disclose.
**Data Accessibility Statement**
Pre-registration of this work can be accessed through the Open Science Framework (OSF) at [https://osf.io/ypbfn](https://osf.io/ypbfn).
Submitted: October 19, 2021 PST, Accepted: November 22, 2021 PST
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Antioxidant modulation of nevirapine induced hepatotoxicity in rats
Olufunsho AWODELE 1, Temidayo POPOOLA 1, Kunle ROTIMI 1, Victor IKUMAWOYI 1, Wahab OKUNOWO 2
1 Department of Pharmacology, Therapeutics and Toxicology, College of Medicine, University of Lagos, PMB 12003, Lagos-Nigeria
2 Department of Biochemistry, College of Medicine University of Lagos, PMB 12003, Lagos-Nigeria
ABSTRACT
HIV/AIDS related mortality has been dramatically reduced by the advent of antiretroviral therapy (ART). However, ART presents with associated adverse effects. One of such adverse effects is hepatotoxicity observed with nevirapine (NVP) containing ART. Since previous studies showed that NVP hepatotoxicity may be due to oxidative stress via generation of oxidative radicals, this study sought to evaluate the protective effects of antioxidants in alleviating NVP induced hepatotoxicity. Rats were divided into 6 groups with 8 animals per group and received doses of the antioxidants jobelyn (10.7 mg/kg/day), vitamin C (8 mg/kg/day), vitamin E (5 mg/kg/day) and/or NVP (6 mg/kg/day) for 60 days. The animals were sacrificed on day 61 by cervical dislocation, blood samples were collected for biochemical and hematological examination. The liver of the sacrificed animals was weighed and subjected to histopathological examination. There was a statistically significant (p<0.05) elevation in MDA level observed in the NVP group as compared with control. The results further showed non-significant decreases in the levels of MDA in the NVP plus antioxidant groups, except vitamin C, when compared with the NVP alone group. Vitamin E and Vitamin E plus C treated groups showed significantly (p<0.05) higher levels of SOD, CAT and GSH. The results also showed statistically significantly (p<0.05) lower levels of ALT and AST in the antioxidant treated groups. Histopathological assessment of the liver extracted from the rats showed no visible pathology across the groups. Observations from this study suggest a potentially positive modulatory effect of antioxidants and may be indicative for the inclusion of antioxidants in nevirapine containing ART.
KEY WORDS: ART; nevirapine; jobelyn; vitamin C; vitamin E
Introduction
The human immunodeficiency virus (HIV) is a retrovirus known to be the cause of acquired immune deficiency syndrome (AIDS). About 39 million people globally are living with HIV with high morbidity/mortality data in sub-Saharan Africa including Nigeria (WHO 2006). HIV/AIDS related mortality has however been dramatically reduced by the advent of antiretroviral therapy (ART) (Emejulu et al., 2010). Current ART guidelines involve the combination of antiretroviral drugs – referred to as highly active antiretroviral therapy (HAART) – which hamper the growth of the HIV virus, eventually leading to decreased viral load, thereby prolonging the life span and improving the quality of life of the patient (Hughes et al., 2011).
A drawback to the use of ART includes adverse effects associated with these antiretroviral drugs (Elias et al., 2012). One of such adverse effects is hepatotoxicity, frequently reported in patients taking nevirapine (NVP) containing ART (WHO, 2006). Case reports, clinical trials and other studies have linked NVP with hepatotoxicity in HIV patients taking NVP containing ART (Elias et al., 2013). NVP has been reported to be associated with early hypersensitivity reactions and late onset hepatotoxicity leading to elevation of liver enzymes (Soriano et al., 2008; Elias & Brambaiba, 2013; Elias et al., 2013).
The WHO therefore recommends the use of NVP with caution and regular monitoring in patients who have baseline elevations of liver enzymes and in co-infections with hepatitis B or C viruses (WHO, 2006). In January and March 2005, the US Food and Drug Administration (USFDA, 2005) and the European Medicines Agency (EMEA, 2005), respectively, issued warnings in NVP package inserts against the initiation of NVP in adult women with CD4 count above 250 cells/ml or in men with...
a count of above 400 cells/ml, because of a higher risk of hepatotoxicity.
Oxidative stress (defined as an imbalance between the antioxidant and pro-oxidant systems, with the shift towards the pro-oxidant system) is a common feature in liver hepatotoxicity (Elias et al., 2013). The term is usually used to describe the damage caused by reactive oxygen species (ROS) to tissues or organs. Collectively, ROS can lead to oxidation of proteins, DNA, peroxidation of lipids and ultimately cell death. Evidence shows oxidative stress as a factor in the progression of drug induced hepatotoxicity (Yamamoto et al., 2005; Kashou and Agarwal, 2011).
Recent studies have also shown that antiretroviral drugs (including NVP) induce oxidative stress via generation of oxidative radicals, which may be associated with their toxicological effects (Valle et al., 2013). Given that the antioxidant system prevents tissue damage (and consequent loss of function) caused by oxidative radicals during a period of persistent oxidative stress, and that the provision of simple, inexpensive micronutrient supplements as an adjunct to HAART may have several cellular and clinical benefits, such as reduction in mitochondrial toxicity and oxidative stress (Drain et al., 2007), it may be important to evaluate the role of this system (including exogenous antioxidants) in ameliorating drug (NVP) induced hepatotoxicity.
This study seeks to evaluate the protective anti-oxidative effects of different exogenous antioxidants (jobelyn, vitamin C and vitamin E) in alleviating NVP induced hepatotoxicity. The investigation into possible tissue protective roles of these antioxidants was done by measurement of oxidative stress parameters, serum levels of liver function enzymes and by evaluating the histopathological features of the liver in the experimental animals used for the study.
The findings from this study are expected to provide a scientific basis for further investigations into the inclusion of exogenous antioxidants in NVP containing regimens currently used in antiretroviral therapy.
**Methodology**
**Drugs**
Nevirapine was obtained from the HIV/AIDS Clinic of the University of Lagos Teaching Hospital, while vitamin E, vitamin C and jobelyn (*Sorghum bicolor* leaf extract) were obtained from Health – Plus Pharmacy, Domino, Yaba.
**Animals**
The animals used in this study were 4–6 week-old male albino rats with average weight of 140g. They were obtained from the Laboratory Animal Centre of the College of Medicine, University of Lagos, Idr-Araba. They were housed and kept in standard environmental conditions with access to standard rodent feed and clean water (pH 7.0) ad libitum and acclimatized for a period of two weeks before experimental procedures. The investigation conforms to The Guide for the Care and Use of Laboratory Animals published by the U. S. National Institutes of Health (NIH Publication No. 85-23, revised 1996) for studies involving experimental animals.
**Treatment groups**
The animals were divided into six groups, each containing eight rats. The antioxidant groups were pretreated with jobelyn (10.7 mg/kg), vitamin C (8 mg/kg) or vitamin E (5 mg/kg) for two weeks before the administration of nevirapine (6 mg/kg). All treatments were administered orally.
- **Group 1** (control): normal saline (10 ml/kg/day) throughout the treatment period
- **Group 2**: nevirapine (6 mg/kg/day) for a period of 60 days
- **Group 3**: jobelyn (10.7 mg/kg/day) for two weeks then a combination of nevirapine (6 mg/kg /day) and jobelyn (10.7 mg/ kg/day) for 60 days
- **Group 4**: vitamin C (8 mg/kg/day) for two weeks then a combination of nevirapine (6 mg/kg/day) and vitamin C (8 mg/kg/day) for 60 days
- **Group 5**: vitamin E (5 mg/kg/day) for two weeks then a combination of nevirapine (6 mg/kg/day) and vitamin E (5 mg/kg/day) for 60 days
- **Group 6**: vitamin C (8 mg/kg/day) and vitamin E (5 mg/kg/day) for two weeks followed by a combination of nevirapine (6 mg/kg/day), vitamin C (8 mg/kg/day) and vitamin E (5 mg/kg/day) for 60 days
**Biochemical and hematological examination**
On the 61st day after termination of administration of the drugs, the rats were anesthetized and sacrificed by cervical dislocation. Blood samples were collected through the retro-orbital plexus vein of the eye for biochemical and hematological determination.
The fully automated clinical chemistry analyzer (Hitachi 912, Boehringer Mannheim, Germany) was used to determine the levels of aspartate aminotransferase (AST), alanine aminotransferase (ALT), alkaline phosphatase (ALP), urea, creatinine, albumin, total protein, bilirubin, cholesterol, triglyceride, serum catalase (CAT), superoxide dismutase (SOD), reduced glutathione (GSH), malondialdehyde (MDA) and the fully automated clinical hematological analyzer (Pentra-XL 80, Horiba ABX, USA) was used to determine the levels of white blood cells, red blood cells, hemoglobin, hematocrit (packed cell volume), platelet, mean cell hemoglobin concentration (MCHC) and mean cell hemoglobin (MCH).
**Histopathological examination**
Qualitative data on liver weight of the albino rats were assessed by carefully dissecting the liver from the sacrificed animal into normal saline contained in a sample bottle. Isolated livers were dried and weighed using Mettler sensitive weighing balance. The weight of each liver was standardized to 100g body weight of each animal. After weighing, each liver was fixed in 10% formalin in labeled bottles. Tissues were processed routinely and embedded in paraffin wax. Sections of 5μ thickness were...
cut, stained with hematoxylin and eosin and examined under the light microscope by a pathologist.
**Statistical analysis**
Results were expressed as mean ± SEM. The data were subjected to one way analysis of variance (ANOVA) test and differences between samples were determined by Dennett’s Multiple Comparison Test, using the Graph Pad Prism (statistical) soft ware. Results were considered to be significant at p<0.05.
**RESULTS**
Table 1 presents the mean weight (g) ± SEM of the liver extracted from male rats following administration of the drugs. The results show no statistically significant (p<0.05) variation in liver weight among the treatment groups.
Table 2 shows the effects of drug treatments on liver antioxidant enzymes and MDA. There was a statistically significantly (p<0.05) higher level of MDA in the NVP group as compared with the control group. The combination of NVP and antioxidant groups showed non-significant decreases in MDA levels as compared with NVP alone, except the vitamin C combination group. The vitamin E treated group showed a statistically significantly (p<0.05) higher level of SOD, CAT and GSH when compared with other groups, with the exception of the vitamin C plus vitamin E treated group for SOD. The vitamin E treated group showed a statistically significantly higher level of white blood cells when compared with other groups, with the exception of the vitamin C plus vitamin E treated group compared with the control group. There was also a significantly (p<0.05) higher level of AST in the jobelyn group when compared with the vitamin C and vitamin E groups. A significantly (p<0.05) higher level of TP and urea was recorded in the antioxidant treated rats and control group compared with the NVP group.
Table 3 shows the effects of drug treatment on serum biochemical parameters. There were statistically significantly (p<0.05) lower levels of ALT, AST in the antioxidant treated groups and the control group compared with the nevirapine group, with an exception observed in the jobelyn group where there was no significantly lower level of AST and ALT when compared with the NVP group; however all the antioxidant groups show statistically significantly (p<0.05) higher levels of AST and ALT compared with the control group. There was also a significantly (p<0.05) higher level of AST in the jobelyn group when compared with the vitamin C and vitamin E groups. A significantly (p<0.05) higher level of TP and urea was recorded in the antioxidant treated rats and control group compared with the NVP group.
Table 4 shows the in vivo effects of drug treatments on hematological parameters. There was a statistically significantly (p<0.05) lower level of white blood cells in the NVP and antioxidant groups compared with the control group. A significantly higher level of white blood cells was found in the antioxidant groups compared with the NVP group. Other hematological parameters show no statistically significant (p<0.05) variations among the groups.
Histopathological assessment of the liver extracted from the rats after drug exposure showed no visible pathology across the groups (Table 5).
### Table 1. Effect of nevirapine and exogenous antioxidants on liver weight.
| Treatment | Weight (g)/100 g BW |
|----------------------|---------------------|
| Control | 7.21±1.148 |
| NVP | 6.61±0.822 |
| Jobelyn + NVP | 6.23±1.007 |
| Vitamin C + NVP | 5.91±1.616 |
| Vitamin E + NVP | 7.33±1.337 |
| Vitamin C + Vitamin E + NVP | 7.29±1.748 |
Data are expressed as mean ± SEM (n=8)
*represents results where p<0.05 as compared with control,
*represents results where p<0.05 as compared with NVP
*represents results where p<0.05 as compared with jobelyn + NVP
*represents results where p<0.05 as compared with vitamin C + NVP
*represents results where p<0.05 as compared with vitamin E + NVP
*represents results where p<0.05 as compared with vitamin C + vitamin E + NVP
NVP is nevirapine; CAT is serum catalase; SOD is superoxide dismutase; GSH is reduced glutathione; MDA is malondialdehyde
SEM is standard error of mean
### Table 3a. Effect of exogenous antioxidant on serum biochemical parameters of treated rats.
| Treatment | ALT (μ/l) | AST (μ/l) | ALP (μmol/l) | BIL (μmol/l) | CHOL (mmol/l) | TG (mmol/l) |
|--------------------|----------------|----------------|--------------|--------------|---------------|-------------|
| Control | 26.76±6.41 | 112.16±15.74 | 153.20±33.21 | 18.44±0.26 | 2.49±0.15 | 1.22±0.048 |
| NVP | 56.10±1.66 | 213.82±4.16 | 188.12±15.23 | 20.28±1.19 | 2.28±0.16 | 2.16±0.76 |
| Jobelyn + NVP | 39.62±0.79 | 190.66±2.63 | 218.96±13.41 | 20.28±1.19 | 2.28±0.16 | 2.16±0.76 |
| Vitamin C + NVP | 37.10±3.71 | 139.54±2.31 | 203.24±12.90 | 17.66±5.42 | 2.25±0.14 | 2.13±0.27 |
| Vitamin E + NVP | 40.50±3.15 | 274.24±13.28 | 274.24±12.90 | 16.64±5.42 | 2.20±0.14 | 2.08±0.77 |
| Vitamin E + Vitamin C + NVP | 39.70±3.04 | 168.73±2.96 | 176.67±3.30 | 17.30±1.20 | 1.90±0.24 | 1.24±0.39 |
Data are expressed as mean ± SEM (n=8)
* represents results where p<0.05 as compared with control,
# represents results where p<0.05 as compared with NVP,
$ represents results where p<0.05 compared with jobelyn + NVP,
% represents results where p<0.05 as compared with Vitamin C + NVP,
& represents results where p<0.05 as compared with Vitamin E + NVP,
### Table 3b: Effect of exogenous antioxidant on serum biochemical parameters of treated rats.
| Treatment | ALB (g/l) | TP (g/l) | UREA (mmol/l) | CREA (μmol/l) | GLU (mmol/l) |
|--------------------|----------------|---------------|---------------|---------------|--------------|
| Control | 41.88±3.15 | 67.06±2.29 | 4.26±0.80 | 43.67±3.83 | 1.48±0.65 |
| NVP | 38.60±4.18 | 54.54±2.34 | 2.82±0.19 | 26.57±8.50 | 2.20±1.15 |
| Jobelyn + NVP | 42.20±0.42 | 66.72±1.00 | 5.08±0.71 | 35.07±5.09 | 2.26±0.47 |
| Vitamin C + NVP | 40.66±2.58 | 68.08±1.66 | 4.64±1.17 | 40.07±4.84 | 1.82±0.36 |
| Vitamin E + NVP | 35.96±4.89 | 65.22±2.63 | 4.18±0.25 | 42.88±4.34 | 1.94±0.77 |
| Vitamin E + Vitamin C + NVP | 41.33±2.71 | 56.0±2.13 | 4.50±0.95 | 35.13±3.47 | 1.93±0.30 |
Data are expressed as mean ± SEM (n=8)
* represents results where p<0.05 as compared with control,
# represents results where p<0.05 as compared with NVP,
$ represents results where p<0.05 compared with jobelyn + NVP,
% represents results where p<0.05 as compared with Vitamin C + NVP,
& represents results where p<0.05 as compared with Vitamin E + NVP,
### Table 4. Effect of exogenous antioxidants on hematological parameters of treated rats.
| Treatment | RBC (10^9/l) | WBC (10^9/l) | PCV (%) | PLAT (10^9/l) | HB (g/dl) | MCH (pg) | MCHC (g/dl) |
|--------------------|--------------|--------------|---------|---------------|-----------|----------|-------------|
| Control | 7.42±0.52 | 11.2±0.52 | 49.32±3.70 | 638.40±48.96 | 13.00±1.06 | 17.42±0.71 | 26.14±0.847 |
| NVP | 6.41±0.59 | 5.82±0.27 | 42.56±8.39 | 672.0±121.05 | 11.80±1.41 | 18.28±0.74 | 26.48±0.76 |
| Jobelyn + NVP | 6.65±0.60 | 8.76±1.11 | 50.0±2.95 | 685.0±40.50 | 13.22±0.54 | 18.02±0.85 | 26.10±0.718 |
| Vitamin C + NVP | 7.41±0.76 | 9.06±0.99 | 45.70±6.13 | 738.20±115.82 | 12.28±1.50 | 17.04±0.47 | 26.12±0.492 |
| Vitamin E + NVP | 6.91±0.29 | 9.18±0.33 | 47.81±1.10 | 712.40±107.90 | 12.66±0.65 | 17.72±1.08 | 25.50±2.001 |
| Vitamin E + Vitamin C + NVP | 7.53±0.95 | 8.36±0.97 | 49.77±1.05 | 670.33±68.14 | 13.03±0.58 | 18.13±0.20 | 25.90±1.179 |
Data are expressed as mean ± SEM (n=8)
* represents results where p<0.05 as compared with control,
# represents results where p<0.05 as compared with NVP,
$ represents results where p<0.05 compared with jobelyn + NVP,
% represents results where p<0.05 as compared with Vitamin C + NVP,
& represents results where p<0.05 as compared with Vitamin E + NVP,
NVP is nevirapine; RBC is red blood cells; WBC is white blood cells; HB is hemoglobin; PCV is packed cell volume; PLAT is platelets; MCH is mean corpuscular hemoglobin; MCHC is mean corpuscular hemoglobin concentration; SEM is standard error of mean.
Discussion
Nevirapine is an important component of HAART and has been clinically proven to be hepatotoxic in HIV patients taking NVP containing ART (Elias et al., 2013). Our previous study (Awodele et al., 2011) showed that the hepatotoxic effect of zidovudine plus combined anti-TB drugs, possibly due to free radical generation, was modulated by NEUTROSEC® (a combination of vitamins and amino acids) in animal models. Due to the relevance and interesting results obtained from the above-mentioned study, a clinical trial model of this research was proposed with the goal to improve pharmacotherapy and limit adverse effects (hepatic toxicity) of patients on these medications. The present study was designed to evaluate the possible modulation of jobelyn and other nutritional antioxidants in nevirapine (NVP) induced hepatotoxicity.
The results showed statistically significant \( p < 0.05 \) increase in MDA concentration in the NVP treated group compared with the control group. As the quantitation of MDA is widely used as an indicator of lipid peroxidation (Simsek et al., 2006), this finding indicates an NVP induced increase in lipid peroxidation and agrees with the suggestion of Zalen et al., 2010. Lipid peroxidation radicals have been shown to increase cell membrane permeability, decrease cell membrane fluidity, inactivate membrane proteins and cause a loss of polarity across mitochondrial membranes, ultimately leading to mitochondrial toxicity, a mechanism attributable to NVP induced hepatotoxicity (Wei et al., 1998; Elias et al., 2013). There were however no statistically significant differences only slight reductions in MDA levels between the NVP group and the NVP plus antioxidant treated groups, suggesting that an increase in the concentrations of antioxidants may be needed to induce significant reductions.
GSH, a major endogenous antioxidant participates directly in neutralizing free radicals and ROS as well as maintaining antioxidants such as vitamin C and E in their reduced active form (Scholz et al., 1964). Since vitamin E inhibits glutathione S-transferase (GST) in humans (Haaf ten et al. 2001), the high level of GSH in the vitamin E plus NVP group may be secondary to GST inhibition, thereby preventing the conjugation of GSH catalyzed by GST (Douglas, 1987; Costagliola & Menzione, 1990) leading to accumulation of GSH.
The high level of GSH will definitely contribute to the antioxidant system (Onyema et al., 2006). When vitamin E is depleted due to its oxidation, glutathione reduces tocopheroxyl radicals to tocopherol and is itself oxidized, however in the presence of exogenous supply of vitamin E, glutathione is maintained in its reduced state (Hess, 1993). This may also account for the significantly higher level of GSH in the vitamin E treated group compared with the NVP treated group, as obtained in the study.
The statistically significantly higher levels of the other enzymes, SOD and CAT, observed in the vitamin E plus NVP treated group when compared with the control indicate that vitamin E stimulates the antioxidant systems in the rat liver (Onyema et al., 2006; Zelen et al., 2010). Since higher levels of MDA in NVP exposed rats suggest that NVP stimulated lipid peroxidation, which will result in the formation of aldehydic and reactive by-products, and which, in turn, decrease the GSH content (Gurer et al., 2001), it seems plausible that vitamin E can improve the antioxidant defense system via inhibiting the lipid peroxidation process, thereby mitigating the consumption of GSH. The same mechanism, rather than a direct effect on the enzymes, could also explain the beneficial effects of vitamin E on CAT and SOD (Gurer et al., 2001).
Vitamin C supplementation has been reported to increase the level of GSH (Carol et al., 1993), however in our study the NVP plus vitamin C group showed a statistically nonsignificantly \( p < 0.05 \) higher level of GSH compared with the other groups. The vitamin C/vitamin E/NVP combination also showed no significant effects on CAT compared with other groups; there were however, statistically significantly higher levels of GSH and SOD compared with the control. Overall, these results suggest that a combination of vitamin C/vitamin E offers no advantage over vitamin E or even vitamin C alone in modulating oxidative stress associated NVP induced hepatotoxicity. Jobelyn showed no significant increase in the antioxidant systems when compared with the other exogenous antioxidants; this suggests that jobelyn has lower antioxidant effects in NVP induced hepatotoxicity when compared with vitamins E and C.
In an evaluation of the effect of micronutrient supplementation in HIV-positive persons receiving HAART, a non-randomized intervention study assessed the effects of either a low-dose or high-dose antioxidant regimen (mainly vitamins A, C, and E and selenium) for 12 weeks on antioxidant defenses, oxidative stress, and plasma viral load (Batterham et al., 2001). The results showed that antioxidant supplements significantly increased antioxidant defenses but had no significant effect on oxidative stress or plasma viral load. No significant differences were observed between rats supplemented with low-dose and those supplemented with high-dose antioxidants. A summary of the review work by Drain et al. (2007) suggests that intervention studies with antioxidants found increased oxidative defenses, but only one of these studies found decreased oxidative stress.
However, Drain et al. (2007) pointed out that micronutrients may play a role in reducing mitochondrial dysfunction and metabolic complications, which are
### Table 5. Summary of histopathological assessment of rat liver exposed to drug treatment.
| Treatment | OBSERVATION |
|----------------------------|-------------|
| Control | Normal |
| NVP | Normal |
| Jobelyn + NVP | Normal |
| Vitamin C + NVP | Normal |
| Vitamin E + NVP | Normal |
| Vitamin E + Vitamin C + NVP| Normal |
commonly experienced by HIV-positive persons receiving HAART. This conclusion was based on reports which state that selenium supplements were shown to stimulate glutathione peroxidase activity (a measure of antioxidant defenses) and reduce NF-kB activation in HIV-1 infected cells (Sappey et al., 1994; Taylor et al., 1997; Zhao et al., 2000), along with a study of 120 HIV-positive adults receiving HAART that found that a greater total intake of vitamin E was associated with fewer outcomes of HAART associated metabolic complications (including body fat redistribution, dyslipidemia, and insulin resistance) due to changes in the ratio of plasma reduced to oxidized glutathione and oxygen free radicals (Gavrila et al., 2003).
Serum markers of hepatocellular injury ALT, AST and ALP in the NVP group were significantly ($p<0.05$) higher when compared with the control group and the antioxidant groups. The high levels of these markers observed in the NVP group might be a result of hepatic injury caused by NVP induced oxidative stress (Elias et al., 2013). The lower level of AST in the Vitamin C and Vitamin E treated groups was statistically significant when compared with control, NVP and jobelyn groups. These findings further suggest that jobelyn offers no advantage in modulating NVP induced hepatotoxicity compared with vitamin C and vitamin E. The Vitamin C/vitamin E combination as antioxidant shows no advantage over vitamin C and vitamin E used individually in preventing nevirapine induced elevation of AST.
It should however be noted that ALT, AST and ALP levels are usually elevated also in cases of injury to other organs, like kidney, brain, and heart (Bain, 2003). The value of total proteins is helpful in differentiating between hepatic injury and injury to other organs as the majority of plasma proteins are produced in the liver (Thapa & Walia, 2007). There was a significantly ($p<0.05$) lower level of total protein in the NVP group when compared with the vitamin C plus NVP and the jobelyn plus NVP groups, indicative of hepatocellular injury due to NVP, since the total protein level is often reduced during hepatocellular injury (Singh et al., 2011).
There was also a significantly ($p<0.05$) lower level of urea in the NVP group compared with the antioxidant group, suggesting that the exogenous antioxidants (vitamin E, vitamin C and jobelyn) protected against NVP induced decreased urea production. In hepatotoxicity there is generally a lower level of urea (Singh et al., 2011). Hematological analysis showed slight variations among the groups which were not statistically significant, with the exception of the white blood cell count which showed a statistically significant ($p<0.05$) lower count for the NVP group compared to other groups, suggesting that NVP induces a low white blood cell count. This is at variance with the work of Umar et al. (2007) where nevirapine was found to have no effect on the white blood cell count.
Histological examination revealed no visible pathology in any of the groups studied. This may be due to a homeostatic mechanism through which restoration takes place after tissue injury (Clancy et al., 2002) or the tissue suffered only minor injury due to short exposure to NVP. Biochemical alterations and anomalies have been repeatedly reported to precede marked organ damage after long-term continuous exposure.
**Conclusion**
Nevirapine remains an essential component in antiretroviral therapy despite evidence that it carries a risk of hepatotoxicity associated with oxidative stress. Observations from the presented study suggest potential positive modulatory effects of antioxidants and may be indicative for the inclusion of antioxidants, particularly vitamin E, in nevirapine containing ART. However, further studies are needed to ascertain these findings.
**Conflicts of interest**
All authors declare no conflicts of interest.
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Absconding During Inpatient Care from a Tertiary Psychiatric Hospital: A Comparative Study
Dileep Kumar Verma1, Sourav Khanra1, Nishant Goyal1, Basudeb Das1, Christoday Raja Jayant Khess1, Sanjay Kumar Munda1, Daya Ram1
ABSTRACT
Background: Absconding from psychiatric hospitals is of great concern for patients and caregivers. Absconding affects not only the treatment and safety of these patients but also patient’s caregivers and the community. Further investigation is needed to examine the pattern of this event and the characteristics of patients who abscond. Hence, our study was aimed to examine the sociodemographic and clinical profiles of inpatients who absconded from a psychiatric hospital in five years and to compare them with matched controls.
Methods: A retrospective chart review of inpatients who absconded and matched control inpatients during the specified period of five years from January 2014 to December 2018 was done at a psychiatric hospital. Each control was matched with a corresponding absconding case on the following order: (a) admission ward, (b) admission period, (c) diagnosis, and (d) age. Results: Among 20,052 adult admissions during the specified period, 38 patients absconded, with a rate of 1.8 per 1,000 admissions. Most of them were male, from a younger age group, diagnosed with schizophrenia or mood disorder, and having comorbid substance use disorder, irritable affect, impaired judgment, and absent insight. Most of the events occurred within the first two weeks of admission. About 11% of them had a history of prior absconding from the hospital.
Conclusion: Knowledge about the associated sociodemographic and clinical profile would help clinicians and mental health care professionals to prevent absconding. Further risk assessment using a patient’s profile would help to reduce absconding events from psychiatric hospitals in the future.
Key Messages: Most of the inpatients who absconded were male, from a younger age group, diagnosed with schizophrenia or mood disorder, with comorbid substance use disorder and had irritable affect, impaired judgment, and absent insight. Most incidents of absconding occurred during the first two weeks following admission.
leave after his authorized period of leave had expired.45 Broadly, absconding has been defined by researchers as leaving hospital without permission.45,62,63 Often, studies have found that those who abscond are young, male, diagnosed with schizophrenia, and have a short duration of stay and a previous history of absconding. Some studies have found significantly lower rates of absconding in general hospitals than psychiatric hospitals or psychiatric wards.64–69 This might be due to differences in inpatients’ clinical profiles and hospital environment.69 A recent review revealed that patients abscond to find relief, and to regain power and control over their lives. Absconding has been viewed as a means of seeking freedom.69 A few studies from India also have investigated this.68–71 A literature review by Stewart and Bowers69 has shown that a few studies had included control groups but very few among them had used matched controls to examine absconding events. Also, India has witnessed a significant shift in mental health care services over the last three decades. Earlier, only a few psychiatric hospitals provided mental health care services. With the establishment of general hospital psychiatry units at medical colleges, mental health care services have become more accessible than before. Mental health care services took a more deinstitutionalized approach, and all restrictive approaches were abolished from psychiatric care settings. Among a few studies from India, only one by Gowda et al.74 recently examined the characteristics of the patient who abscond during inpatient care at a psychiatric hospital. Hence, the study was aimed to examine the sociodemographic and clinical profiles of adult inpatients who absconded in a specified period and to compare them with matched controls.
Methods
The study was conducted at a psychiatric hospital in India. Under adult psychiatry, the institute has three units for male patients, three units for female patients, and a dedicated unit for addiction psychiatry. Patients aged more than 18 years are admitted in these units. There is an open ward system, where the patients are admitted and managed with no/least restrictive measures. The institute has a boundary wall surrounding the campus and a main gate for entry and exit. The wards are adequately staffed with nurses and attendants across three fixed shifts of duty spanning over 24 hours. The staffing pattern is fixed for a type of shift (morning, evening, and night) across wards, based on the number of beds available for that ward. Each morning shift has 3–5 nursing personnel and 2–3 ward attendants, apart from the housekeeping staff, which is largely outsourced.
Approval was obtained from the Institutional Ethics Committee before collecting data. A separate register is maintained in the institute to record the absconding events. After an inpatient is reported missing in count from any ward during the mandatory headcount at the beginning and/or end of each shift, the information is passed to the treating team and hospital administration. A thorough search is conducted in the hospital premises. The local police station is also informed simultaneously. If the patient cannot be traced inside the hospital area and he/she fails to return to the hospital before midnight of the same day, either by himself/herself or by assistance, he/she is considered as absconding. Such events are recorded in the absconding register.
A list of case record file (CRF) numbers of patients who absconded between January 1, 2014 and December 31, 2018 was made from the register. Corresponding admission register of each case was accessed and searched for the admission period of that case. Parallely, from other admitted inpatients of that admission period, a control was selected, matched with the diagnosis and age of the corresponding absconding case. Thus, each control was matched with the corresponding absconding case in the following order: (a) admission ward (admitted and residing in the same unit and ward as in each case of absconding) (b) admission period (the time period of admission during which the absconding case was admitted), (c) diagnosis, and (d) age. The method of chart review was followed for data collection. Sociodemographic information was recorded. Details for the event of absconding were collected. For clinical profiles, mental status examinations (MSE) done both during the admission and before the event of absconding were reviewed. As a part of the protocol of the institute, all the patients were examined regularly twice a day, in the morning and evening, and the clinical notes were recorded in CRFs. The MSE is structured and comprehensive in the case records. For cases, the most recent MSE before absconding was reviewed. For controls, the MSE most proximal to the date and time of absconding of the corresponding case was recorded. This was done to match immediate external factors around the event of absconding.
Statistical Analysis
Statistical analysis was performed, using the level of statistical significance of \( P < 0.05 \), in the Statistical Package for the Social Sciences (SPSS) version 22.0 for Windows. Sociodemographic characteristics and clinical profile of the sample were analyzed by descriptive statistics. Those records where either history was not available or MSE could not be elicited or did not specify psychopathology were excluded from the analysis. Chi-square test was used to assess discrete variables. Fisher’s exact test and Yates’ continuity correction was applied wherever applicable. After checking skewness, Student’s t or Mann–Whitney U test was applied for continuous variables.
Results
There was a total of 20,052 admissions in adult psychiatry in the specified period. During this period, 38 patients had absconded. Thus, the rate of absconding was 1.8/1000 admissions (0.18%).
Sociodemographic and Clinical Characteristics
Table 1 shows the sociodemographic characteristics of absconding cases and matched controls. The mean(±SD) age was 27.95 ± 6.96 years in the absconding cases. Most of the absconding cases were male (44.7%, n = 34). There was no difference in sex between the groups as the controls were selected from the same admission ward of the corresponding absconding cases. Other
### Table 1: Comparison of Sociodemographic Variables between Groups (N = 76)
| Characteristics | Absconding cases | Control | χ²/f/t/U | P |
|----------------------------------------|-------------------|---------|---------|-------|
| **Type of admission** | | | | |
| Voluntary | 36(47.4) | 38(50) | 0.51 | 0.47 |
| Under special circumstances | 2(2.6) | 0(0.0) | | |
| **Age (in years)** | | | | |
| Means ± SD | 27.94 ± 6.96 | 28.02 ± 6.74 | -0.05 | 0.96 |
| **Age group (in years)** | | | | |
| 18–30 | 25(32.9) | 26(34.2) | | 0.21 | 1.00 |
| 31–40 | 11(14.5) | 10(13.2) | | | |
| ≥41 | 2(2.6) | 2(2.6) | | | |
| **Sex** | | | | |
| Male | 34(44.7) | 34(44.7) | 0.00 | 1.00 |
| Female | 4(5.3) | 4(5.3) | | | |
| **Marital status** | | | | |
| Unmarried | 17(22.4) | 18(23.7) | | 1.08 | 0.81 |
| Married | 21(27.6) | 19(25) | | | |
| Others | 0(0.0) | 1(1.3) | | | |
| **Religion** | | | | |
| Hindu | 22(28.9) | 29(38.2) | | 4.22 | 0.13 |
| Muslim | 15(19.7) | 7(9.2) | | | |
| Others | 1(1.3) | 2(2.6) | | | |
| **Education** | | | | |
| Illiterate | 8(10.5) | 2(2.6) | | 5.03 | 0.09 |
| Below graduation | 24(31.6) | 32(42.1) | | | |
| Graduation and above | 6(7.9) | 4(5.3) | | | |
| **Occupation** | | | | |
| Unemployed | 13(17.1) | 17(22.4) | | 1.19 | 0.93 |
| Employed | 2(2.6) | 2(2.6) | | | |
| Labourer | 9(11.8) | 7(9.2) | | | |
| Students | 4(5.3) | 3(3.9) | | | |
| Others | 10(13.2) | 9(11.8) | | | |
| **Address** | | | | |
| Rural | 23(30.3) | 26(34.2) | 4.99 | 0.07 |
| Semi urban | 10(13.2) | 3(3.9) | | | |
| Urban | 5(6.6) | 9(11.8) | | | |
| **Distance of address from hospital** | | | | |
| <200 km | 10(13.2) | 9(11.8) | | 1.52 | 0.48 |
| 201–400 km | 12(15.8) | 8(10.5) | | 0.23 | 0.80 |
| >400 km | 16(21.1) | 21(27.6) | | | |
| **State where the patient belongs to** | | | | |
| Jharkhand | 14(18.4) | 12(15.8) | | 0.23 | 0.80 |
| Others | 24(31.6) | 26(34.2) | | | |
| **Family type** | | | | |
| Nuclear | 12(15.8) | 9(11.8) | | 0.59 | 0.60 |
| Extended/joint | 26(34.2) | 29(38.2) | | | |
| **Socioeconomic status** | | | | |
| Below poverty line | 9(11.8) | 5(6.6) | | 1.84 | 0.42 |
| Above poverty line | 27(35.5) | 29(38.2) | | | |
| **Family income (₹/month)** | | | | |
| <10,000 | 26(34.2) | 26(34.2) | | 2.32 | 0.58 |
| 10,000–50,000 | 8(10.5) | 8(10.5) | | | |
| >50,000 | 2(2.6) | 0(0.0) | | | |
| Not known | 2(2.6) | 4(5.3) | | | |
| **Informants** | | | | |
| Parents | 21(27.6) | 20(26.3) | | 3.88 | 0.29 |
| Siblings | 7(9.2) | 13(17.1) | | | |
| Spouse | 4(5.3) | 3(3.9) | | | |
| Relatives and others | 6(7.9) | 2(2.6) | | | |
| **Social support** | | | | |
| Good/satisfactory | 25(32.9) | 26(34.2) | | 0.06 | 1.00 |
| Poor | 13(17.1) | 12(15.8) | | | |
| **Primary caregivers** | | | | |
| Family | 34(44.7) | 37(48.7) | | 0.85 | 0.35 |
| Relative and others | 4(5.3) | 1(1.3) | | | |
| **Family attitude** | | | | |
| Concerned | 23(30.3) | 24(31.6) | | 0.05 | 1.00 |
| Ignorant | 15(19.7) | 14(18.4) | | | |
| **Relationship with family members** | | | | |
| Cordial | 13(17.1) | 16(21.1) | | 0.50 | 0.63 |
| Strained | 25(32.9) | 22(28.9) | | | |
χ²: Chi-Square test, f: Fisher's exact test, level of significance accepted at P < 0.05, y: Yate's continuity correction, t: Student's t test.
sociodemographic characteristics were comparable between the groups, except for a trend toward a more well-adjusted premorbid personality observed among controls (P = 0.05). Though patients with absconding had a higher proportion of substance use disorder as a co-morbid diagnosis, no significant difference between the groups was observed (P = 0.49). Most cases in both groups had no physical comorbidity, and no significant difference was found between the groups (P = 1.00). The mean duration of stay in the hospital was 14.76 ± 12.31 and 41.68 ± 25.05 days in the absconding group till the event of absconding and the control group, respectively, with a significant difference between the groups (P = 0.005). More absconding cases (22.4%, n = 17) than controls (9.2%, n = 7) had irritable affect. More patients in the control group (n = 13) than in the absconding group (n = 5) had perceptual abnormalities (P = 0.04). Most of the cases in both the groups had impaired judgment and poor insight about illnesses at the time of admission. Table 3A shows the comparison of MSE findings between the groups at admission.
### Mental Status Examination at the Time of Admission
More cases of absconding had loud and overproductive speech (32.9%, n = 25) than controls (25%, n = 19). There was a significant difference in affect between the groups at the time of admission (P = 0.001). Table 2 shows a comparison of the clinical profiles of the groups.
| Table 2. Comparisons of Clinical Profiles between Groups (N = 76) |
|---------------------------------------------------------------|
| Characteristics | Absconding cases (n = 38(%)) | Control cases (n = 38(%) | χ²/ft/U | P |
| Age of onset (years) Means ± SD | 20.02 ± 7.78 | 21.50 ± 6.53 | -0.35 | 0.72 |
| Age of onset group | Before 18 years | 15(19.7) | 16(21.1) | 0.05 | 1.00 |
| | After 18 years | 23(30.3) | 22(28.9) | 0.32 | 0.44 |
| Duration of Illness | <6 months | 9(11.8) | 4(5.3) | 2.37 | 0.37 |
| | 6 months to 2 years | 4(5.3) | 4(5.3) | 0.00 | 1.00 |
| | >2 years | 25(32.9) | 26(33.3) | 0.76 | 0.51 |
| Treatment history | No | 12(15.8) | 9(11.8) | 1.02 | 0.44 |
| | Yes | 25(32.9) | 29(38.2) | 0.76 | 0.51 |
| Past psychiatric illness | Absent | 30(39.5) | 27(35.5) | 0.63 | 0.59 |
| | Present | 8(10.5) | 11(14.5) | 0.39 | 0.75 |
| Past medical illness | Absent | 33(43.4) | 31(40.8) | 0.39 | 0.75 |
| | Present | 5(6.6) | 7(9.2) | 0.32 | 0.57 |
| Family history of psychiatric illness | Absent | 19(25.0) | 18(23.7) | 0.00 | 1.00 |
| | Present | 19(25.0) | 20(26.3) | 0.76 | 0.38 |
| Forensic history | Absent | 33(43.4) | 33(43.4) | 0.00 | 1.00 |
| | Present | 5(6.6) | 5(6.6) | 0.00 | 1.00 |
| Premorbid personalitya | Well adjusted | 24(31.6) | 31(40.8) | 3.70 | 0.05 |
| | Not well adjusted | 12(15.8) | 4(5.3) | 0.12 | 0.90 |
| Number of hospitalizations | Single | 25(32.9) | 24(31.6) | 0.05 | 0.81 |
| | Multiple | 13(17.1) | 14(18.4) | 0.21 | 0.64 |
| Diagnosis | Affective disorders | 14(18.4) | 16(21.1) | 1.81 | 0.74 |
| | Schizophrenia and related disorders | 15(19.7) | 15(19.7) | 0.00 | 1.00 |
| | Substance use disorders | 7(9.2) | 7(9.2) | 0.00 | 1.00 |
| | Others | 2(2.6) | 0(0.0) | 0.00 | 1.00 |
| Comorbid diagnosis | Affective disorders | 4(5.3) | 2(2.6) | 3.44 | 0.49 |
| | Schizophrenia and related disorders | 0(0.0) | 1(1.3) | 0.00 | 1.00 |
| | Substance use disorders | 15(19.7) | 10(13.2) | 0.00 | 1.00 |
| | Others | 4(5.3) | 5(6.6) | 0.76 | 0.38 |
| | None | 15(19.7) | 20(26.3) | 0.76 | 0.38 |
| Comorbid physical illness | Present | 9(11.8) | 9(11.8) | 0.00 | 1.00 |
| | Absent | 29(38.2) | 29(38.2) | 0.00 | 1.00 |
| Treatment | Antidepressant/mood stabilizers only | 0(0.0) | 1(1.3) | 0.00 | 1.00 |
| | Antipsychotics only | 9(11.8) | 10(13.2) | 0.00 | 1.00 |
| | ECT only | 3(3.9) | 3(3.9) | 0.00 | 1.00 |
| | Any combinations of above | 26(34.2) | 24(31.6) | 0.00 | 1.00 |
| Duration of stay in the hospital (days) | Means ± SD | 14.76 ± 12.31 | 41.68 ± 25.05 | 198.5*** | <0.001*** |
| | Median | 9.50 | 37.50 | 0.00 | 1.00 |
| | Interquartile range | 14.25 | 22.00 | 0.00 | 1.00 |
χ²: Chi-Square test, f: Fisher’s exact test, U: Mann–Whitney U, t: Student’s t test, y: Yate’s continuity correction. Level of significance accepted at P < 0.05. ***P < 0.001. *Five patients were excluded from the analysis.
There was a significant difference in affect between the groups (P = 0.001). Affect was found irritable among more cases of the absconding group (32.9%, n = 25) than the controls (11.8%, n = 9). Most of the patients in the absconding group had no insight (47.4%, n = 36). Table 3B shows the comparison of MSE findings between the groups before the time of absconding.
**Factors Related to Events of Absconding**
Table 4 shows various factors related to the absconding behavior. The mean duration of stay till the date of absconding was 14.76 ± 12.31 days. The most common timing was 8 AM to 2 PM (28.95%, n = 11). The most common mean chosen was scaling the boundary wall (34.21%, n = 13), followed by escaping through the main gate (21.05%, n = 8). For 28.94% (n = 11) of the absconding cases, the means chosen for absconding could not be recorded as the patients, when traced later, did not share the details of the same.
**Discussion**
Our study examined all the absconding events from the inpatient care of a psychiatric hospital over a period of five years. The strengths of our study were not missing any cases of absconding and close matching between the cases and controls. Admission period and admission ward were matched, as these might influence immediate environmental factors such as, level of supervision, security level, and clinical management protocols. As psychiatric diagnoses are often heterogeneous in nature and dependent upon a constellation of psychopathologies, matching diagnosis helped us examine several clinical factors, including psychopathologies not attributable to the difference in the diagnosis between the groups. A similar matching protocol had been adopted by research that investigated absconding from an inpatient setting and other uncommon hospital events like inpatient suicide. As the controls were matched for the admission ward and admitted under the same unit of the corresponding absconding case, both the groups became matched for sex too. Another strength was that we reviewed the MSE at two time points.
The rate of absconding in our study was 1.8 incidents per 1,000 admissions. This rate is low compared to previous studies, where the rate ranged from 1.8% to 17.2%. A systematic review found the rates to be substantially lower for locked wards (1.34/100 admissions) compared to open wards (7.96/100 admissions). Despite being an open ward system, comprehensive management, including continuous risk assessment, monitoring, and supervision by treating teams consisting of a psychiatrist, clinical psychologist, psychiatric social worker, psychiatric nurse, and ward attendants
might have reduced absconding, accounting for the lower rate in our study. Different rates across the world might be due to a difference in the type of security measures, type of hospital care, the presence of forensic patients, legal measures, and multiple other factors.1
Most of the total sample in our study was admitted as voluntary admission under Mental Health Act 1987 and subsequently as independent admission under Mental Healthcare Act 2017 in both the cases and the control group. In contrast to this, most studies have demonstrated an increased prevalence of involuntary admission among inpatients who abscond.6,9,13,33 A recent study by Gowda et al.,24 at a psychiatric hospital, also showed that most patients who absconded had involuntary admission. However, a case-control study by Bowers et al.1 did not demonstrate the above finding and instead suggested that the escaping incidents might be more officially reported among involuntary patients than the voluntary ones. In our study, the mean hospital stay for the absconding group was 14.8 days. Though a recent study found that a longer duration of stay is predictive of absconding,16 other studies found that most absconding occurred during the first two weeks following admission. This may be because, during the initial two weeks of inpatient care, adjusting to the hospital environment happens and the illness is often most acute.16,33
We did not find any significant difference regarding marital status between the groups. A recent case-control study by Khirmarnia et al.15 showed no significant difference between those who absconded and those who did not, in terms of age and marital status. A few studies have found a higher rate of absconding among unmarried inpatients.4,33 Our study did not find any difference in religion between the groups, which is consistent with the findings from other studies.4,33 However, some studies have a different finding.1,5,34–36 Like other studies, most of the absconding cases in our study were male and from a younger age group.16,22,24,30,33 Similarly, John et al.30 also found a smaller proportion of females than males and speculated that the low rate among the women might be due to the culturally inculcated restrictions on women. On the contrary, Khirmarnia et al.15 and Dickens and Campbell4 did not find any significant difference between absconding cases in men and women. Cultural shift over time or difference in the setting might have caused this finding.19
While Gowda et al.24 found that most patients who absconded belonged to lower socioeconomic status, our study did not find any such difference between the groups. In our study, most of the patients in the absconding group belonged to joint or extended family. In contrast, Gowda et al.24 had found that most of them belonged to a nuclear family.
The absconding patients and the controls did not differ in the age of onset, duration of illness, history of past treatment, history of psychiatric or medical illness, history of family illnesses, or the presence of forensic history. The most common diagnosis in the absconding group was schizophrenia and related disorders, followed by affective disorders and substance use disorders.
| TABLE 3b. Comparison of the Latest Mental Status Examination Before Leave (N = 76) |
|---------------------------------------------------------------|
| Characteristics | Absconding cases n = 38 (%) | Control n = 38 (%) | χ²/df | P |
|---------------------------------------------------------------|
| Motor behaviour |
| Increased | 10 (13.2) | 12 (15.8) | 0.38² | 0.93 |
| Decreased | 3 (3.9) | 3 (3.9) |
| Normal | 25 (32.8) | 23 (30.3) |
| Speech |
| Loud and over productive | 12 (15.8) | 14 (18.4) | 2.14⁴ | 0.58 |
| Mute/decreased productivity | 4 (5.3) | 7 (9.2) |
| Normal | 22 (28.9) | 17 (22.4) |
| Affect |
| Euphoric/related | 12 (15.8) | 10 (13.2) | 18.83⁴ | 0.001** |
| Irritable | 15 (19.7) | 3 (3.9) | 18.83⁴ | 0.001** |
| Depressed | 1 (1.3) | 3 (3.9) |
| Dysphoric | 7 (9.2) | 6 (7.9) |
| Constricted | 3 (3.9) | 11 (14.5) |
| Euthymic | 0 (0.0) | 5 (6.6) |
| Thought (stream, form and possession) |
| Poverty of thought/FTD | 3 (3.9) | 2 (2.6) | 0.91² | 1.00 |
| Thought alienation | 1 (1.3) | 2 (2.6) |
| Obsessive and compulsive | 1 (1.3) | 1 (1.3) |
| No abnormality detected | 33 (43.4) | 33 (43.4) |
| Thought (content) |
| No abnormality detected | 7 (9.2) | 12 (15.8) | 2.23³ | 0.11 |
| Delusions | 25 (32.9) | 19 (25.0) |
| Depressive cognitions | 4 (5.3) | 3 (3.9) |
| Perceptual abnormality |
| Present | 5 (6.6) | 11 (14.5) | 3.16 | 0.09 |
| Absent | 30 (39.5) | 23 (30.3) |
| Judgment |
| Impaired test, social, and personal | 25 (32.9) | 9 (11.8) | 17.47³ | <0.001*** |
| Impaired social and personal | 11 (14.5) | 15 (19.7) |
| Impaired personal | 2 (2.6) | 13 (17.1) |
| Intact | 0 (0.0) | 1 (1.3) |
| Insight |
| Grade-I | 36 (47.4) | 18 (23.7) | 21.64³ | <0.001*** |
| Grade-II | 1 (1.3) | 14 (18.4) |
| Grade-III | 1 (1.3) | 5 (6.6) |
| Grade-IV and above | 0 (0.0) | 1 (1.3) |
χ²: chi-square test, f: Fisher’s exact test, level of significance accepted at P < 0.05, FTD: formal thought disorder. *P < 0.05, **P < 0.01, ***P < 0.001. aSix patients were excluded from analysis. bSeven patients were excluded from the analysis.
This finding is also supported by previous descriptive and case-control studies, which found psychotic illness to be a common factor predicting absconding events.\textsuperscript{5,12,22,40,47,19} A few studies have also found increased rates of affective illness, substance use, and personality disorders.\textsuperscript{10,38,39}
A significantly higher proportion of patients who absconded had irritable affect both at the time of admission and around the time of absconding. Also, those who absconded had less perceptual abnormalities than controls at admission, which could explain the absence of perceptual abnormality among the absconding cases at the time of absconding too. This is consistent with Khisty et al.\textsuperscript{19} who speculated that being more guarded than controls might be the reason why they were less likely to report hallucinations.
There was a significant difference in judgment and insight around the event of absconding between the groups. Patients of the absconding group had grade II or better insight (P < 0.001). A recent study from a psychiatric hospital in India also found a higher prevalence of absconding among patients who had an absent insight.\textsuperscript{24}
About 10% of cases had a history of prior absconding from the hospital in the previous admissions. This proportion is less than what was found by Meehan et al.,\textsuperscript{40} who found that one-third of those who absconded had a similar history in their previous hospitalizations. The reason behind this discrepancy might be the improvement in the psychiatric management of inpatients, including the physical structure and environment of the psychiatric care facility.
Most of the events occurred during the daytime and early morning or evening hours, as compared to early morning clustering observed in another study.\textsuperscript{40} Khisty et al.\textsuperscript{19} found that most incidents occurred during the daytime (09:00 hr to 18:00 hr). Several factors might contribute to this. Leaving the hospital ward may be easier during the daytime because at that time, almost in any hospital, much more people move around or visit, thereby making it less difficult to make way for the exit. Dickens and Campbell\textsuperscript{1} reasoned that often, at nighttime, even open wards are locked by night staff, which seems to be relevant in our study too. A literature review\textsuperscript{1} did not find any common patterns, which might be due to the variations in the hospitals, organization of shifts among hospitals, settings, hospital protocols, and countries.
The most common mean chosen for absconding was scaling through the boundary wall, followed by escaping through the main gate, manipulating other patients or their guardians, during a referral to other medical centers for physical illness, and by manipulating the workers. A study by Yasini et al.\textsuperscript{41} found that high numbers of absconding take place from the main door of the hospital, followed by other sites (walls, windows, etc.). Agreeing with previous researchers, we speculate that increased staffing would help by improving the monitoring and observation of inpatients and the understanding of their psychological and nursing care needs.\textsuperscript{5,40,41}
Our study suffered from a few limitations. For about one-third of the absconding cases, the means chosen to abscond were not shared by the patients and hence could not be recorded. Reasons for absconding have not been examined as well in our study. Qualitative information could not be examined. We included a modest period of observation of five years only. Limitations of a retrospective design based on CRF review need a mention.
**Conclusion**
Most of the inpatients who absconded were male, from a younger age group, from joint or extended family, diagnosed with schizophrenia or mood disorder, and having comorbid substance use disorder, irritable affect, impaired judgment, and absent insight. Most incidents of absconding happened during the first two weeks following admission. About one-tenth of those who absconded had a similar history. Most of the events occurred during daytime and early morning or evening hours, and the most common means chosen were scaling the boundary wall and passing through the main gate. Our study adds to the existing sparse literature on the nature and pattern of absconding and the profile of those inpatients who abscond from a psychiatric hospital. Further research should focus on this event with a longer period of observation and should include
---
**TABLE 4. Factors Related to Absconding (N = 38)**
| Characteristics | Number (%) |
|------------------------------------------|------------|
| Time of missing | |
| 3 am—8 am | 10(26.32) |
| 8 am—2 pm | 11(28.95) |
| 2 pm—8 pm | 9(23.68) |
| 8 pm—3 am | 8(21.05) |
| Mean chosen to abscond | |
| Through the main gate | 8(21.05) |
| Scaling the boundary wall | 13(34.21) |
| By manipulating workers | 1(2.63) |
| During referral to a medical centre for management of a physical illness | 2(5.26) |
| By manipulating other patients/their guardians | 3(7.89) |
| Details unspecified | 11(28.94) |
| Past history of absconding | |
| No | 3(10.53) |
| Yes | 34(89.47) |
| Duration of stay before absconding (days)| |
| Means ± SD | 14.76 ± 12.31|
| Median | 9.50 |
| Interquartile range | 14.25 |
References
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10. Hunt IM, Windfuhr K, Swinson N, et al. Suicide amongst psychiatric in-patients who abscond from the ward: a national clinical survey. BMC Psychiatr 2010; 10: 14.
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16. Dolan M and Snowden P. Leaves from a medium secure unit. J Forensic Psychiatry 1994; 5: 275–286.
17. Raynes AE and Patch WD. Distinguishing features of patients who discharge themselves from psychiatric ward. Compr Psychiatry 1971; 12: 473–479.
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20. Clark N, Kyiimba E, Bowers L, et al. Absconding: nurses views and reactions. J Psychiatr Ment Health Nurs 1999; 6: 219–224.
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Linking decision and utility theories to financial information usefulness and company performance: A study applied to Portuguese's certified accountants
Albertina Paula Monteiroa, Catarina Cepêdaa and Amélia Silvaa*
*Porto Accounting and Business School, Polytechnic of Porto, CEOS PP, Portugal
ABSTRACT
The role accounting plays in decision-making in business is a broad topic that has driven academics. This paper is grounded on decision and utility theories. It investigates the Certified Accountants' perception of financial information (FI) usefulness and the company's performance. Based on data collected through a survey applied to certified accountants, this study develops and evaluates an original theoretical model using the Structural Equations Model (SEM). The results reveal that manager's gender and academic qualifications influence the perception of FI usefulness. Non-owner managers and older companies also attach more significance to FI in decision making. The managers who attribute the most usefulness to FI in decision-making are those of companies with higher performance. Additionally, the results show that the FI usefulness is a mediator variable in the relationship between the characteristics above and company performance. This research helps all stakeholders improve decision-making, studying past events with FI to predict future results and consequently increase the company's success.
© 2021 by the authors; licensee Growing Science, Canada
Keywords: Certified Accountants
Financial Information usefulness
Company Performance
Decision Making
Utility Theory
Decision Theory
1. Introduction
Human decision-making is a complex process. It comprises risks and cost-benefits appraisals; it occurs within specific contexts and affects persons with idiosyncratic mindsets. Traditional economic models rely on the basic assumption that human beings are rational. In the business world, very often, this rationality is associated with the use of financial information. The behavioral schools of finance and accounting launched new research streams to explain neuronal aspects of human decision-making and behaviors (Artienwicz, 2016). Previous research identified biological, emotional, and neurologic factors that affect rationality, namely impulsivity, limbic system, intuition, experience, age, morality, etc. The concept of neurocognition aims to capture all that complexity of the decision process (Cesar, Jerônimo & Carneiro, 2012). Nevertheless, as pointed out by Botchway and Rashedi (2020:1) “accounting information plays a decision-facilitating role since it possesses value relevance capabilities to enhance decision making”. Indeed, in a highly intertwined and connected business environment, financial information gained a prominent role. It became the language of the globalized economy. Classic literature explains this phenomenon with two interrelated theories. According to Fishburn (1970, p. 1), “decision making serves as the foundation on which utility theory rests”. Utility theory is related to people's preferences and the assumption that this preference will numerically bring usefulness to the person (Fishburn, 1968). On the other hand, the barriers that hinder success in decision-making are the focus of decision theory. Research within this theory has shown that managers face difficult decisions (Maguire and Albright, 2005), which can be mitigated if they have access to accurate and reliable FI. The Lack of FI is a barrier to the foundations of this theory.
Decision-making is a term related to how people make choices between desirable alternatives (Edwards, 1954). Bachrach and Baratz (1962) create the term “non-decisions” that are hidden questions on which one simply decides not to decide (Bachrach and Baratz, 1962), maybe because the decision would not be useful or benefit the person or group of people. Miller and Wilson (2006, p. 294) refer that in literature “is clearly a contrast between seeing decision-making as a functional prerequisite of effective organization and seeing it as a maelstrom of political activity and sectional conflict, where power games are played out in an arena which is only partially open to view, and this accounts in part for the differences in approaches to research and discussion”.
According to neoclassical economic assumptions, individuals usually act as maximizing entrepreneurs, who make decisions in a sequential and linear process (Mintzberg, Raisinghani, & Theoret, 1976). Decision-making is necessary because according to structural functionalism, more complex companies have a greater need to make rational decisions and, in this sense, key decisions are necessary for the functioning of companies. (Miller & Wilson, 2006). Management is involved with several types of activities and decisions which entail quality and reliable accounting information (Soudani, 2012). Decision-making involves the use of various types of information, highlighting FI, information generated from an accounting information system.
For Salehi, Rostami and Mogadam (2010, p. 188), FI “plays an important role in the process of managing an enterprise's activity”. According to Soudani (2012, p. 50), “accounting information systems are considered as important organizational mechanisms that are critical for effectiveness of decision management and control in organizations”. Successful management of organizations implies the use of FI, because successful decision-making refers to the ability of firms' decision makers to manage problems successfully (Powell, 1987; White, Pothos & Busemeyer, 2015). According to Haleem and Teng (2018) the accounting system provides useful information to stakeholders for decision making, which can determine the organization's success.
The same is to say that the use of FI is a semiquinone condition for the success of companies. In fact, Hope and Vyas (2011) and Cepêda and Monteiro (2020) conclude that FI usefulness of financial information and business performance are statistically correlated. Business performance is a consequence of the usefulness of FI; however, the literature suggests the existence of antecedent variables, such as individual characteristics of managers and the company characteristics where manager performs functions (Amoako, 2013; Florin, 2014; Tang & Liu, 2016; Santos, Dorow & Beuren, 2016). In Portugal, 99.9% of the business fabric are Micro, Small and Medium Enterprises (SMEs) (Pordata, 2019), so most managers fall into family businesses. The death rate of companies is around 12%, which is largely influenced by SMEs.
However, Bertolami, Artes, Gonçalves, Hashimoto, and Lazzarini (2018) refer that many SMEs do not survive their first years of life due to lack of market knowledge, business management experience, and financial problems, given their maturity. Besides that, companies with some maturity also face insolvency processes. Thus, a better understanding of the factors that influence the performance of companies is necessary, as it can contribute to the survival and growth of companies and, consequently, enhance the economic country development. Failure of relevant and true information may have compromised good decision-making (Maguire & Albright, 2005), resulting in a disastrous outcome. This situation requires a better understanding of the manager characteristics (individuals and context) that influence his behavior in decision-making and with consequent impact on the company's performance. Managers and accountants are responsible for the timely and accurate disclosure of FI. It is crucial to understand how accountants perceive managers' attitudes regarding FI they co-produce through annual reports. In this context, this study, based on usefulness and decision and utility theories, aims to analyze the relationship between FI usefulness in decision-making and business performance, taking into account the decision behavioral and utility theories. Specifically, the objective is to analyze whether the individual manager characteristics (gender and academic qualifications) and the company (size, manager non-owner, and seniority) influence the FI usefulness and, consequently, its performance. This research is relevant for the literature development, as it evaluates an original model for managers, in the sense that it identifies the factors that contribute to the success of Portuguese companies using the two theories as a theoretical basis. On the other hand, most of the literature focuses only on the study of decision-making based on the manager's beliefs in allocating financial resources, and the study at hand will also consider the formation of probability beliefs about potential returns on various assets (Latane and Tuttle, 1965).
The structure of this paper is as follows: the next section introduces the main topics related to the empirical research and presents the investigation hypotheses. The following sections develop the procedures and samples used to test the research hypotheses. In the penultimate and last section, empirical findings are discussed, and the research conclusions and implications are presented.
2. Literature reviews and hypotheses development
2.1 Decision-making and decision theory
Lindblom (1959) refers that incrementalism dispelled the myth that decision-making was a linear process. This author refers that each actor involved will have their problem perception and its solution. For White et al. (2015), successful decision-making refers to the ability of corporate decision-makers to find a better solution or the most lucrative solution among several alternatives. The “way a decision-maker should assess evidence depends on how the task is framed” (Mock et al., 2008). However, there are three types of decision making: sporadic (subject to major disruption, and with great opportunity for negotiation); fluid (faster, flows into formal meetings with fewer impediments and delays); and restricted (flows less than the...
Decision makers need FI to support their choices, that is, information of both qualitative and quantitative nature (Smith, 2020). This author mentions that as much data, in real-time, can help the decision-makers to make the best choices. In addition, the usefulness of accounting information, which integrates the entire system of internal control, is a valuable decision mediator (Huian, 2020). Hence, the usefulness of accounting information is considered as a key outcome of maintaining the quality of internal control (Phornlaphatrachakorn, 2019). Following the International Accounting Standards Board (IASB), the main purpose of FI general purpose is to provide useful information about the reporting entity to stakeholders so that they can make appropriate economic decisions (Huian, 2020). The quality of internal control plays a key role in determining and driving the competitive advantage, performance, success, and survival of companies in rigorous markets and competitive environments (Phornlaphatrachakorn, 2019). Decision theory is a fundamental pillar for understanding decision making, in turn decision success can increase if the manager assigns usefulness to the FI produced by accountants (Sajady et al., 2012). Thus, the utility theory should be considered in the decision-making process (Fishburn, 1968).
2.2 The usefulness of Financial Information and utility theory
According to Fishburn (1968), utility theory is related to people's preference and the assumption that this preference will numerically bring usefulness to the person (Fishburn, 1968). The key result of the theory, for Wang, Lee, Augenbroe and Paredis (2017, p.79) “is the expected utility theorem, which states that a decision-maker should select the alternative with the greatest expected utility”. This theory is based on the assumptions of accounting, which aim to produce useful information for all FI stakeholders. FI usefulness refers to information capable of making a difference in the decision-making of users of financial statements because it has confirmatory value, predictive value or both (Frendy & Semba, 2017). FI lets stakeholders use available FI “FI are prepared so that information can be used by stakeholders to better understand and manage the firm” (Carragher and Auken, 2013). SMEs owners generally lack management knowledge and have difficulty interpreting financial statements, this difficulty prevents owners from extracting the usefulness of FI (Auken, 2005). However, the difficulty in analyzing and interpreting the FI can jeopardize business survival (Çaliyurt, 2011). FI provides useful information to a wide range of users, its internal and external users (Ibicioglu et al., 2010). All FI produced must be reliable, relevant and accurate to be analyzed and processed by users in order to be a fundamental pillar in decision-making (Popescu, 2009). The great usefulness of accounting information can help provide and improve better decision-making and improve and increase the competitive advantage, performance, and success of companies (Phornlaphatrachakorn, 2019). Financial Statements are one of the main sources of information for financial analysis (Monea, 2013). The profit and loss account reports company financial performance over a given period, this financial statement summarizes all income and expenses and reports the results (Monea, 2013, p. 143). The cash flow statements information, in conjunction with profit and loss statement and the balance sheet, have decision-making relevance to external and internal user groups (Sharma & Jones, 1998). Financial statements are designed to provide useful information regarding the financial position, performance, and changes in the financial position of companies for a particular time. Being that one of the great purposes in its use is to predict future gains and dividends (Ibicioglu, Kocabiyik, & Dalgar, 2010). The financial statements, from the point of view of an investor, are essential for forecasting the future, from the point of view of a manager, they are useful to help anticipate future conditions and for planning actions that will affect the company's
future statements (İbicioglu et al., 2010). The notice 8254/2015 of July 29 of the Portuguese official gazette states that the qualitative characteristics that make FI useful in decision-making are:
- Understandability - The FI must be readily understandable by users and cannot “be excluded merely on the grounds that it may be too difficult for certain users to understand”.
- Materiality - The FI is material when “its omission or inaccuracy influences the economic decisions of users taken on the basis of the financial statements”.
- Relevance – Information has the quality of relevance when it influences how economic decisions users make when evaluating past, present, or future events or confirming, or correcting, or correcting, such as their past evaluations.
- Comparability – users must be able to compare an entity's financial statements over time in order to identify trends in its financial position and performance.
- Credibility – Information is credible unless it contains significant errors, is not biased, and users can be confident that it accurately represents objectives and what is reasonably expected to present. To have credibility, any information in the financial statement must be completed. Any omission can make the information false, misleading and lacks credibility or become irrelevant.
In fact, the financial statements are the result of all the information processed over time and, at the same time, they become an essential FI tool and of the decision-making process. (Monea, 2013). This is true when the accountant, in preparing financial statements, has taken into consideration the qualitative characteristics that make information useful in the decision-making of the various stakeholders. However, individual investors rarely use FI prepared by accounting, this behavior increases the risk of loss of investments (Ezamaa et al., 2018). In his opinion, in addition to education, and the interpretation of legislation, national and international institutions should facilitate the interpretation of FI, which is one of the most important sources of information in the decision-making process. Managers, when analyzing the FI, must understand and interpret the financial data in order to attribute the due usefulness to the FI, facilitating the decision-making process. (Çaliyurt, 2011). Managers not only want to analyze the organization's performance, but they also want to know how the organization has achieved those goals (Smith, 2020). Financial performance focuses on companies' income and distribution of expenditures (Edwards and Pinkerton, 2020) and is one of the indicators that shows an organization's operation and efficiency in achieving its financial goals (Omondi-Ochieng, 2019; Karamoy & Tulung 2020). Thus, in addition to financial performance, companies are increasingly concerned with information transparency (Bennett, James and Klinkers, 2017). Such transparency is only possible with an effective accounting system that respects all the qualitative characteristics of FI (İbicioglu et al., 2010). Thus, this system is one of the most effective tools in the management decision-making process, as it allows the collection and organization of FI on various business, banking and other transactions, making it a critical aid for management in business operation (Amoako, 2013). According to Çaliyurt (2011), all companies and their FI have their own characteristics, so decisions are influenced by the company characteristics and individual characteristics of decision-makers according to utility theory with the assumption on decision theory. Ma, Bartnik, Haney and Kang (2017, p. 2), show that manager characteristics influence decision making, for example, “ethical leadership is not only associated with a leader trait (e.g., honesty, integrity and trustworthiness) and ethical behaviours (e.g., openness, concern, fairness and ethical decision making) but also linked to value-based management”.
According to Çaliyurt (2011), most studies state that female managers tend to make decisions on financial issues based on the opinion of their husbands, families, and friends, instead of being taken according to the science of financial management. The research results affirm that in businesswomen are not good at decision-making because they do not have business skills and do not have sufficient education in financial management (Çaliyurt, 2011). In the study by Zeng and Wang (2015), it is possible to conclude that female managers do not focus on the opportunity cost of money and moderate the problem of excess investment in free cash flow, being possible to verify that at this level, they are more conservative than male managers. Okafor and Amalu (2010) state that female entrepreneurship, when the business is constituted, focuses a lot on the survival and growth of the business, neglecting other factors that lead to failures in business implementation. In this context, we formulate the first hypothesis:
H1: Managers’ Gender influences the usefulness they attach to FI in decision making.
Academic qualifications attainment influences the understanding of FI importance. In addition, if a business owner is educated at a higher level, he will have greater success and ease in building, analyzing and implementing the management control systems needed in the business (Amoako, 2013). Ezamaa et al. (2018) report that managers often have difficulty interfering with FI factor that diminishes its usefulness. According to Amoako (2013), only with a level of higher education is it possible to succeed in understanding challenges posed by business management. In this context, we formulate the second hypothesis:
H2: Managers with academic qualifications at the level of higher education attribute more usefulness to FI in decision making.
The importance of examining contextual factors of companies as an example of company size has been particularly addressed in the literature (Sharma & Jones, 1998; Cepèda & Monteiro, 2020; Fujianti, 2018; Alonso-Almeida, 2015; Liargovas & Skandalis, 2010; Wood, 1991). Companies and their financial statements have different characteristics, so decisions are influenced by company characteristics (Çaliyurt, 2011). Decision-making in small businesses involves several factors that make
the process complex. One of these factors may be the company characteristics (for example, the level of revenue can serve as a proxy for the company size); the company level can affect many small business decisions. (Carraher & Auken, 2013). In this context, we formulate the third hypothesis:
**H3:** Managers of larger companies attach greater usefulness to FI in decision making.
In the study by Amoako (2013), results indicate that the majority of owners, because they do not have sufficient management knowledge, do not feel comfortable using FI to make their decisions. According to Amoako (2013), owners do not appreciate the need to keep accounting records, lack necessary accounting knowledge, and blame costs of hiring accounting professionals. In this context, we formulate the fourth hypothesis:
**H4:** Managers who are not company owners attribute more usefulness to FI in decision making.
İbicıoglu et al. (2010) report that, compared with large firms, small firms have less liquidity, have more volatile cash flows, rely on short-term financing, and are more likely to experience financial difficulties and constraints. These authors further state that failure rates in small businesses are unacceptably high. The cause of this situation, according to Amoako (2013), may be related to the fact that micro-company managers assign less importance to FI in decision making. In this context, the following hypothesis of this investigation is defined:
**H5:** Managers of older companies attribute more usefulness to FI in decision making.
According to contingency theory, contingent factors affect, as technologies and business environment, affect the design and functioning of organizations, as well as its performance “Given its importance in everyday life and professional settings, there is a growing body of research that seeks to examine if decision-makers are proficient in hypothesis evaluation and whether performance can be enhanced” (Mock et al., 2008, p. 124). Company performance “is one type of effectiveness indicator” (Richard, Devinney, Yip and Johnson, 2009, p. 722) and it has always motivated and guided company actions (Folan and Browne, 2005). Literature suggests that there is “a multidimensional conceptualization of organizational performance related predominately to stakeholders, heterogeneous product, market circumstances and time” (Richard et al., 2009, p. 718). According to these authors (p. 719), measuring business performance is essential for managers to assess where firms stand in relation to their rivals and how companies evolve and perform over time. Ruf, Muralidhar, Brown, Janney and Paul (2001) use measures of financial performance as return on equity, return on sales, and sales growth. Several authors measure company performance through profitability, growth, and market share (Dhanaraj and Beamish, 2003; Richard et al. 2009). Other authors adopt a dynamic guideline to measure performance by asking the respondent evolution of results in the last 3 years (Sousa, Martínez-López, and Coelho (2008). Previous empirical studies have analyzed the relationship between company performance and FI usefulness (Hope & Vyas, 2011; Soudani, 2012; Cepêda & Monteiro, 2020). These authors provide statistical support for this relationship. In this context, we formulate the following hypothesis:
**H6:** FI usefulness significantly influences the company performance.
Literature suggests that the people are different from each other. Understanding the individual traits of people is important when these characteristics can influence their professional behavior (Trikı, Cook and Bay, 2015). Personality traits, as a way of being, thinking, acting, among others, influence the choices and perceptions of professionals in a particular area of work. Montenegro and Rodrigues (2020) study, applied in Portugal, show that the gender, age, academic education, accounting ethics education and experience influence accountants' judgments. Cepêda and Monteiro (2020) verify that as managers’ individual characteristics (e.g., academic qualifications and management skills) have impact on perception about the FI usefulness and that the variables FI usefulness and business performance are statistically correlated. Furthermore, Kallerberg and Leight (1991) indicate that manager's gender relevance to small companies’ performance is a critical issue in survival and organizational success. In this context, we expected that managers’ individual characteristics have an impact directly on the FI usefulness and indirect on firm performance, Therefore, in this study we formulate the following research hypothesis.
**H7:** FI usefulness in decision-making has a mediating effect on the relationship between individual manager characteristics and company performance.
This hypothesis gives rise to two sub-hypotheses:
**H7.1:** FI usefulness in decision-making has a mediating effect on the relationship between manager gender and company performance.
**H7.2:** FI usefulness in decision-making has a mediating effect on the relationship between managers Academic qualifications and company performance.
Previous research also shows that the characteristics of the companies where managers work (e.g., size, age and accounting standards) have an impact on the importance they attach to IF (Cepêda & Monteiro, 2020). On the other hand, there is empirical
evidence that firms' performance is influenced by the distinctive characteristics of firms (Fama & French, 1992). Despite the scarcity of studies in this area, there are no studies that analyze the FI usefulness mediating effect on the relationship between individual characteristics company and companies’ performance, although there are fundamentals in this regard (Mukhametzyanov & Nugaev, 2016). Thus, in this study we intend to test the last investigations hypotheses:
H8: FI usefulness in decision-making has a mediating effect on the relationship between company characteristics and company performance.
This hypothesis gives rise to three sub-hypotheses:
H8.1: FI usefulness in decision-making has a mediating effect on the relationship between size and company performance.
H8.2: FI usefulness in decision-making has a mediating effect on the relationship between non-owner managers and company performance.
H8.3: FI usefulness in decision-making has a mediating effect on the relationship between age (seniority) company performance.
The hypotheses defined above are evident in the operational model that we propose for this research.
2.3 Conceptual model and methodology of the study
Operational model
This research aims to analyze the FI usefulness determinants related to manager's individual characteristics (gender and academic qualifications) and context factors (size, manager-owner and age) and analyses its impact in the company's performance. The operational model is present in Fig. 1.
2.4 Measuring instruments development
To achieve the proposed objective, this study is based on a quantitative approach, which involves applying an online survey to certified accountants (available on the Certified Accountants website1). This survey is directed to certified accountants because they are the ones who prepare and produce companies FI and can evaluate FI usefulness, depending on the type of information that is usually produced and what is actually requested by the manager.
---
1 CAA website: https://www.occ.pt/
In this study, the survey application to accountants was in collaboration with the Certified Accountants Association (CAA), which agreed to publish the survey on its institutional website. In this way, it was possible to collect responses quickly, at no cost and in large quantities, and to guarantee data confidentiality (Gillham, 2000). Given the large number of Certified Accountants (about 72,000), this study opts for a non-probabilistic statistic. A survey-based study was carried out to test the proposed model. The questionnaire was pre-tested with higher education teachers on the accounting area and accounting professionals to detect problems related to instruction/questions wording and clarity. The questionnaire's final version included questions about the firm (size, owner and age) and managers (gender and academic qualifications), FI usefulness in decision-making and company performance. To measure company and manager variables, several questions were asked in the questionnaire: Regarding company age, respondents were motivated to enter a number that corresponded to company age; regarding whether the manager is the company owner or not, respondents were asked to answer either (1) no or (2) yes; as for companies size, accountants answered this question taking different options into account, namely: (1) micro entity, (2) small entity, (3) medium entity or (4) large entity; to know managers gender was asked if this was (1) female or (2) male. Finally, to measure academic qualifications, we asked whether company managers had higher education, (1) no or (2) yes. To measure FI usefulness, we used the items shown in Table 1. We measured company performance using Murphy, Trailer and Hill's (1996) measurement scale (6 items) Table 2. The items of each dimension were evaluated on a Likert scale of 5 points.
### Table 1
**FI Usefulness**
| FI usefulness | Author(s) |
|-------------------------------------------------------------------------------|----------------------------------------|
| 1. Company managers give due importance to financial indicators in the decision-making process. | Jaffar, Selamat, Ismail and Hamzah (2012) |
| 2. Company managers beyond FS requests another type of FI. | Amoako (2013). |
| 3. Company managers attach great value to FI. | Bondt and Thaler (1995) |
### Table 2
**Company's Performance**
| Company Performance | Author(s) |
|-----------------------------------------------------------------------------------|----------------------------------------|
| 1. Turnover has increased over the last 3 years. | Murphy, Trailer and Hill (1996) |
| 2. The business has been very lucrative. | |
| 3. The company has expanded its activity in the last 3 years. | |
| 4. The company has increased its market share in the last 3 years. | |
| 5. The company size has increased in the last 3 years. | |
| 6. The number of employees has increased in the last 3 years. | |
2.5 Survey administration and sample
The survey was carried out with Portuguese's certified accountants enrolled in the CAA in May 2017 to August 2018. We emphasize that professionals, in order to perform the function of certified accountant must be compulsorily enrolled in CAA. The link to access the online survey was made available on CAA website. During data collection, a total of 285 questionnaires were received, 250 of which were usable because 35 respondents do not currently practice. In data analysis, we used SPSS statistical software (version 19) and LISREL (version 8.8).
3. Results
3.1 Sample Characteristics
Findings show that the sample is mostly composed of men (56.8%), by individuals over 50 years old (65.6%), higher education (80.8%), experience for more than 10 years (81.6%) and that currently assume accounting in more than one company (65.6%). Accountants', in their replies, took into consideration company and managers that, by the nature and wealth of information allowed them, with more knowledge, to respond to this inquiry. Regarding managers under analysis, 80% are male, 57.6% have higher education, 56% work in micro-entities, 27.2% in small entities, 14.4% in medium-sized companies and 2.4% in large companies, and 88.8% managers are business enterprise owners. Most companies belong to the services sector (57.6%), with 25.6% of the commercial sector and 16.8% of industry. About three-quarters of companies have started business more than 10 (years) ago and more than half of the companies have been in the market for more than 20 years.
3.2 Structural equation model
In this study, to prepare the data and assess whether it meets the requirements to be subjected to an SEM analysis, we proceeded to a preliminary data analysis. Then we proceeded to an SEM evaluation. Analysis using the structural equation model involves two steps, the measurement model, and the structural model assessment.
The maximum likelihood estimation method was used to evaluate the measurement model (Hair, Anderson, Tatham and Black, 1998). This method, when using covariance matrices, calculates more reliable estimates (Diamantopoulos & Siguaw, 2000). In the analysis, we find moderate violations of normality main assumptions. However, this method is considered robust against normality assumption violations (Diamantopoulos & Siguaw, 2000). The measurement model, the unidimensionality of the constructs, as well as reliability and validity (convergent and discriminant) were analyzed. Table 3 provides measurement model evaluation results. Confirmatory factor analysis rejected 1 item in the company performance dimension (business has been very profitable). In first-order models, all items correspond statistically with their factor, demonstrating the unidimensionality of the factor. All loads of observed variables have values, proving the existence of convergent validity of the constructs (≥ 0.70) (Garver & Mentzer, 1999). All latent variables have values greater than 0.60, which proves the reliability of the scales (Bagozzi & Yi, 1988). Finally, the value of the extracted average variance (> 0.50) shows discriminant validity of the constructs (Fornell & Larcker, 1981).
| Table 3 | Measurement model results |
|--------------------------------------------------|-----------------------------|
| **Construct and items** | **Standardized loading** |
| **Usefulness of FI (CR= 0.879, AVE= 0.79)** | |
| Company managers give due importance to financial indicators in decision-making process | 0.95 |
| Company managers beyond the FS requests another type of FI. | 0.95 |
| Company managers beyond the FS requests another type of FI. | 0.76 |
| **Company Performance (FC= 0.94, MVE= 0.71)** | |
| Turnover has increased over the last 3 years. | 0.84 |
| The company has expanded its activity in the last 3 years. | 0.92 |
| The company has increased its market share in the last 3 years. | 0.97 |
| The company size has increased in the last 3 years. | 0.92 |
| The number of employees has increased in the last 3 years. | 0.70 |
Notes: CR = composite reliability; AVE = average variance extracted. All loadings are statistically significant at p<0.001.
The structural model was estimated in order to test the hypotheses proposed. In this study, the parameters of the analysis do not confirm models fit ($\chi^2$ (51) = 184.90; p < 0.05, CFI = 0.94, GFI = 0.90, NNFI = 0.91, RMSEA = 0.10). We present in Table 3 testing results hypothesis.
| Table 4 | Testing results hypotheses |
|--------------------------------------------------|-----------------------------|
| **Parameters** | **Standardized coefficients** | **t-value** | **R^2** | **Hypotheses** | **Results** |
| Gender – FI usefulness | -0.11 | -3.18(*) | | H1 | Supported |
| Academic qualifications – FI usefulness | 0.11 | 2.53(*) | 0.30 | H2 | Supported |
| Company non-owner - FI usefulness | -0.06 | -2.50(*) | | H3 | Supported |
| Age (seniority) - FI usefulness | 0.45 | 2.56(*) | | H4 | Supported |
| Size - FI usefulness | -0.02 | -0.22 | | H5 | Not supported |
| FI usefulness - company performance | 0.27 | 4.30(*) | 0.17 | H6 | Supported |
Note: (*) Sig. value p<0.01.
As we can see in Table 4, of the 6 direct hypotheses, only 1 was rejected (H5). The revised structural model was estimated after eliminating the relationship between company size and FI usefulness since in the initial evaluation, it is not statically significant. Parameters of the analysis confirm the models fit ($\chi^2$ (44) = 19.20; p < 0.05, CFI = 0.95, GFI = 0.90, NNFI = 0.93, RMSEA = 0.08). We present in Table 4 the testing result hypothesis for the revised model.
| Table 5 | Testing result hypothesis (revised model) |
|--------------------------------------------------|-----------------------------|
| **Parameters** | **Standardized coefficients** | **t-value** | **R^2** | **Hypotheses** | **Results** |
| Gender – FI usefulness | -0.11 | -3.46* | | H1 | Supported |
| Academic qualifications - FI usefulness | 0.11 | 2.93* | 0.29 | H2 | Supported |
| Company’s non-owner - FI usefulness | -0.06 | -2.67* | | H3 | Supported |
| Age (seniority) - FI usefulness | 0.42 | 3.69* | | H4 | Supported |
| FI usefulness - company performance | 0.26 | 4.34* | 0.12 | H6 | Supported |
Note: (*) Sig. value p<0.01.
The results show that based on decision theory and utility theory and the Portuguese economic context: (1) managers gender has an impact on FI usefulness. However, it is not male managers who attribute greater usefulness to FI, but female; (2) the managers with higher education attach greater usefulness to FI; (3) older companies' managers and non-owners attribute greater usefulness to FI in decision-making and; (4) managers who attribute most usefulness to FI are managers of better-performing companies. Results allow direct hypothesis support of H1, H2, H3, H4 and H6. In this study, we also analyzed indirect relationships, that is, the mediating effect of individual characteristics of manager and company features on company performance through FI usefulness. We tested mediating effect significance by using the Aroian test (Baron & Kenny, 1986). The results found show that managers gender and academic qualifications directly impact FI usefulness and have an indirect effect in company’s performance of - 0.03 (-0.11 × 0.26; p<0.01; Z= -3.20) and 0.03 (0.11×0.26; p<0.01; Z= -2.66), respectively. Indirect effects of company age and non-owner managers on company performance is 0.12 (0.42x26; p<0.01; Z= -2.80) and -0.02 (-0.06x0.26; p<0.01; Z= -2.60), respectively. Results allow support to hypothesis H7.1, H7.2, H8.2, and H8.3.
4. Discussion and Conclusion
For good management, it is necessary to use and analyze FI, both for analyzing past mistakes and predicting future decisions. This study aims to explore consequent antecedents of FI usefulness with utility theory and decision theory assumption. As antecedents, we consider managers' and companies' characteristics and resulting company performance. In this study, we developed and evaluated a theoretical model using SEM. Based on 250 certified accountants' opinions, results show that managers' individual characteristics, such as gender and academic qualifications, have an influence on the usefulness that managers attribute to FI in decision making. This way made it possible to verify that, it is in fact women and managers who have higher qualifications that attribute greater usefulness to FI. These results are consistent with Okafor, Amalu (2010), and Amoako (2013) studies. Regarding contextual characteristics, results indicate that non-proprietary managers of older companies attach greater importance that is produced by accounting in decision-making that goes against the fundamentals of Carraher and Auken (2013) and Amoako (2013). In terms of direct relationships, we just did not find a significant relationship between company size and usefulness of financial information, not meeting the results of Carraher and Auken (2013). It was also possible to conclude that FI usefulness significantly influences company performance against the foundations of Hope and Vyas (2011), Soudani (2012) and Cepeda and Monteiro (2020).
This paper contributes to the literature, as we present evidence, with the assumptions on utility and decision theory, on the relationship between managers individual characteristics and company, the usefulness of FI, and business performance, by using Structured Equations Model (SEM) and Certified Accountants. Given the high rate of bankruptcies in the Portuguese business fabric, this research becomes very relevant for accounting and management professionals. It provides a better understanding of Portuguese managers and companies' characteristics that influence the usefulness of FI in the decision-making process. Models are only approximations of reality and are based on theoretical assumptions. Thus, this study has some limitations, namely in terms of survey sample size, since we use a convenience sample that limits results generalization. Another survey limitation is that investigation it's not applied directly to managers, as this investigation is time-limited, we chose to apply the survey to certified accountants as the answer is easier to obtain on the one hand. On the other hand, they are aware of the usefulness that managers attribute to FI as a function of FI requested by the manager.
In future research, we suggest analyzing other variables associated with managers' individual characteristics (e.g., management skills, experience, and age) and the company (e.g., degree of internationalization). The frequency with which FI is requested may determine its usefulness; therefore, we suggest future investigation to include this variable in the FI usefulness dimension and check whether Non-Financial Information determines the usefulness of FI in decision-making. We recommend applying this study directly to managers to compare the results obtained and apply it in different countries where large companies' samples are more significant.
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© 2021 by the authors; licensee Growing Science, Canada. This 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/).
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A New Zn(II)-containing Coordination Polymer for Photocatalytic Degradation of Organic Dyes and Treatment Activity on Atherosclerosis via Reducing the Vcam-1 Expression
Yan Hao, Hou-Zhi Yu, and Hai-Tao Yuan
Department of Cardiology, Shandong Provincial Hospital Affiliated to Shandong University, Jinan, Shandong, CHINA
Abstract: By employment of a rigid tripodal nitrogen-containing heterotopic ligand tris(1-imidazolyl) benzene (Htib), a new fluorescent Zn(II)-containing coordination polymer \([\{Zn(tib)\}_3(NO_3)_2(H_2O)_3\}_n\) (1) with a rare two-fold interpenetrating (3,6)-connected pyr network topology has been successfully prepared under the solvothermal reaction conditions. Under the condition of visible light irradiation, rhodamine B (RhB) and methylene blue (MB) could be degraded with good performance. In the biological function study, the cytotoxicity of the synthetic was evaluated with CCK-8 detection kit on human umbilical vein endothelial cells (HUVEC). The inhibitory effect of compound on vcam-1 expression in the vascular endothelial cells was evaluated by RT-PCR. The effect of the complex on the inflammatory response in the vascular endothelial cells was determined via ELISA test of IL-1β and TNF-α. The results of pose scoring software as well as molecular docking was conducted to explore the interaction between compounds and VCAM, which might provide latent regulatory mechanisms along with binding sites for compounds.
Key words: coordination polymer, photocatalytic degradation, vascular endothelial, molecular docking
1 Introduction
Coordination polymers (CPs) formed by organic bridging ligands as well as transition metal ions generate more and more interest in recent years, not only their broad applications prospects in material science field, but also their excellent performance and latent applications in electrochemistry, magnetism, catalysis, photochemistry along with biochemistry, and their attractive topologies as well as structures. Organic dyes are one of the major pollutants in wastewater, the treatment of wastewater is a significant problem. Since the photocatalytic degradation of phenol with MOF-5 was first reported, photocatalytic degradation of phenol via organic dyes based on CPs under visible light or ultraviolet has been rapidly developed because of its low cost as well as high efficiencies. However, the number of CPs-based photocatalysts used for visible light irradiation is relatively small, because many CPs usually have low stability under the condition of visible light irradiation, rhodamine B (RhB) and benzimidazole are attached to rigid benzene ring, forming a number of rigid nitrogen-containing tripodal ligands. Recent literatures have revealed that the imidazole-based ligands are good candidates for building coordination polymers with excellent water stabilities, and some of them have already used in the photocatalytic degradation or adsorption of organic dyes. For instance, Zhang’s group has reported that Co-based CPs assembled using 1,3,5-tris-(1-imidazolyl) benzene ligands show good dyes degradation capacity. In this study, by employment of a rigid tripodal nitrogen-containing heterotopic ligand tris(1-imidazolyl) benzene (Htib), a new fluorescent Zn(II)-containing coordination polymer \([\{Zn(tib)\}_3(NO_3)_2(H_2O)_3\}_n\) (1) with a rare two-folded interpenetrating (3,6)-connected pyr network topology has been successfully prepared under the solvothermal reaction conditions. The prepared complex 1 was completely measured by single crystal X-ray diffraction as well as elemental analysis. Under the condition of visible light irradiation, rhodamine B (RhB) and...
methylene blue (MB) have fine photocatalytic degradation performance. We proposed the photocatalytic mechanism, and then confirmed it. In biological research, the protective effect of compound on atherosclerosis was evaluated. Firstly, the CCK-8 results indicated the compound has no cytotoxicity on HUVEC, and the RT-PCR detection of vcam-1 in vascular endothelial cells indicated that this important adhesion molecule in progression of AS could be significantly reduced by compound treatment. Then, the ELISA detection of TNF-α and IL-1β revealed that the inflammatory level in the vascular endothelial cells was also been inhibited via compound. By calculating pose and docking scores, the latent binding patterns between target proteins and synthetic compounds were discussed.
2 Experimental
2.1 Chemicals and measurements
All the reagents as well as solvents are analytical grade and can be applied without deep purification. Using the Perkin-Elmer 240C elemental analyzer to obtain elemental results of C, N and H element content. With Avatar 360 (Nicolet) infrared spectrometer we collected FT-IR spectra (KBr pellets) in the region of 4000-400 cm⁻¹. Utilizing Shimadzu UV-3101PC instrument we carried out ultraviolet—visible spectra. Applying the Edinburgh Instrument FL/FS-920 fluorescent spectrometer we recorded fluorescent spectra under room temperature.
2.2 Preparation and characterization for [Zn(tib)₃(NO₃)_2]·6H₂O
We added Zn(NO₃)₂·6H₂O which is 0.3 mmol and 0.0409 g and tib of 0.3 mmol and 0.0828 g, mixed them to form a mixture, sealed it into a Teflon-lined stainless steel Parr bomb of 25 mL which has 10 mL deionized H₂O, heated it for 3 days at 140°C, and then cooled it to room temperature. We acquired a small white crystals of 1 with block-like (the yield is 72% on the basis of Zn(NO₃)₂·6H₂O), and then washed by using deionized ethanol and water. Anal. Calc. for Anal. Calcd for C₉₅H₇₃N₁₁₂Zn: C, 46.31; H, 3.63; N, 25.20%; found: C, 46.69; H, 3.43; N, 25.55%. IR (KBr, cm⁻¹): 3385 (m), 2360 (w), 1944 (w), 1829 (w), 1610 (m), 1583 (m), 1446 (m), 1398 (w), 1315 (w), 1186 (w), 1142 (w), 1109 (w), 1051 (w), 1014 (w), 922 (w), 905 (w), 862 (w), 810 (w), 779 (m), 746 (w), 709 (w), 670 (w), 635 (w), 592 (w), 526 (w), 477 (w), 426 (w).
By using Oxford Xcalibur E diffractometer we acquired X-ray data of compound 1. Utilizing CrysAlisPro software for the sake of analyzing intensity data and convert them into HKL files. The original structural models of complexes 1 was constructed through SHELXS program according to the direct method and corrected by utilizing SHELXL-2014 program based on the least-squares method. Mixing all the non-H atoms of complex 1 which have anisotropic parameters, and the whole H atoms were fixed to their connected C atoms geometrically through applying AFIX commands. Table 1 describes the numerical information as well as crystallographic parameters reorganized for compound 1.
2.3 Cell Counting kit-8 detection
The cytotoxicity of the compound was evaluated on HUVEC with CCK-8 detection kit under the guidance of the instructions with some modification. In brief, the HUVEC cells in the logarithmic growth phase were collected and seeded into 6-well plates at the concentration of 5 × 10⁵ cells/well, and the cells were cultured in an incubator at the condition of 37°C, 5% CO₂ humidified atmosphere. When the cells research confluence of 70-80%, serious dilutions of the compound (1, 2, 4, 8, 10, 20, 40, 80, 100 μM) were added into wells for 24 h incubation. After that, the cells were harvested and centrifuged at 800 rpm for 5 min. The culture medium was discarded, and the 10% CCK-8 (Dojindo Laboratories, Kumamoto, Japan) in 100 μL medium without FBS was added into wells for 2 h incubation at 37°C in the dark. Subsequently, the absorbance of each well was measured with Thermo Scientific Microplate Reader at 450 nm. The Cell viability curves were calculated
and plotted according to the absorbance values. Three replicate wells were used to determine each point.
2.4 RT-PCR detection of vcam-1
15 New Zealand rabbits were used in this experiment, the rabbits were randomly divided into three different groups \( (n=5) \). The control group (received sham-operation), model group (received endothelium injury without treatment) and the treatment group (received endothelium injury with compound treatment). After the construction of endothelium injury model, the compound was given daily for 14 days treatment. At the end of this treatment, the carotid artery segments were harvested for the detection of relative expression of vcam-1 with RT-PCR preformation. This experiment was performed according to the protocols precious introduced with some modification. The primer used in this experiment were \( vcam-1: \) GGACCA-CATCTAGCTGACA and TTTGACTGTGATCGGCTTCCC, \( \text{gapdh: AATGGGCAGCCGGTTAGGAAA and GC-}
2.5 ELISA detection of IL-1β and TNF-α
After the endothelium injury model construction and compound treatment, the level of inflammatory response in the animals as evaluated by the ELISA measurement of TNF-α and IL-1β in the endothelium tissues. In brief, at the end of this treatment, the carotid artery segments were harvested, grinded and suspended in PBS, the content of TNF-α and IL-1β was measured via ELISA detection kit following the instructions. This experiment was repeated at least three time. The results were presented as mean ± SD.
2.6 Molecular Docking
Discovery Studio 3.0 serves is a commercial software that can predict latent binding pattern between protein and small molecule, thus, it was selected a platform for carrying out molecular docking simulation. Its advantage is that it has been customized at the aim of better developing high-precision scoring function. We derived ligand structure from the crystal structure measured via X-ray, and from protein data bank (PDB) we downloaded it. The VCAM protein crystal structure (PDB ID: 1VSC) was utilized to predict the docking, and the coordination posture was scored for the high resolution. The gesture scoring module as well as Libdock tool were utilized for preparing the structures of receptor and ligand for molecular docking simulation. The grid frame length is set at 40, which is enough large to cover the whole docking bag, including double helix chains along with protein parts.
3 Results and Discussion
3.1 Molecular structures
The hydrothermal reaction is a fine choice for preparing coordination polymers which have excellent water stability. Such a reaction condition usually involves reaction of the starting materials in a highly sealed reaction container using the pure water as the solvents. High temperature and high pressures accompanies with the reaction process. Complex 1 chemical formula was established by elemental analysis as well as single crystal X-ray diffraction, the formula was \( \left[ \text{Zn} \left( \text{tib} \right) \right] \left( \text{NO}_3 \right) \left( \text{H}_2\text{O} \right) \). Complex 1 could not be dissolved in the common solvents such as water, DMF, EtOH and so on. The refinement results as well as structural solution based on crystal data collected at room temperature reflect that cubic space group Ia-3, and represents a three-dimensional porous framework. According to Fig. 1a, 1’s asymmetric unit contains one sixth of a crystallographically independent \( \text{Zn(II)} \) ion, one third of \( \text{NO}_3 \) ion, as well as one third of \( \text{O}_2 \) ion. Every \( \text{Zn(II)} \) is surrounded via six nitrogen atoms, formed by two six imidazolyl nitrogen atoms in six different tib ligands. We can described the coordination geometry which around the center of \( \text{Zn(II)} \) as a warped octahedron. The \( \text{Zn-N} \) bond distance is 2.182 (6) Å, which belongs to the normal range values reported in other \( \text{Zn(II)} \)-based coordination polymers based on the N-donor ligands. The tib ligand has \( \text{C}_6 \) axis through the center of benzene ring, this means that three imidazolyl groups cannot be distinguished during assembly (Fig. 1a). The tib ligand, as an isoligand, binds to three randomly oriented \( \text{Zn(II)} \) ions. Each \( \text{Zn(II)} \) ion links six tib ligands, and each tib ligand links three \( \text{Zn(II)} \) ions, so combining \( \text{Zn(II)} \) ions as well as tib ligands cause a complex three-dimensional framework (Fig. 1c). At the aim of better understanding the relationship between tib ligands as well as \( \text{Zn(II)} \) ions, three-dimensional framework topological structure is analyzed. Simply put, the tib ligand is connected with three \( \text{Zn(II)} \) ions, which can be regarded as three connecting nodes, while \( \text{Zn(II)} \) ion is connected with six tib ligands, which can be regarded as six connecting nodes. Then, the obtained network is a pyr network connected by two peaks (3,6). Its Schläfli symbol is \( \left[ 6^3 \right] \left[ 12 \right] \left[ 8^3 \right] \) \( \left[ 6^3 \right] \), as shown in TOPOS analysis. Such a single network includes large gaps, so the two single networks penetrate into each other, forming a pyr framework of double mutual penetration (Fig. 1d).
To check the phase purity of the products, powder X-ray diffraction (PXRD) experiments have been carried out for complex 1. The peak positions of the experimental and simulated PXRD patterns are in good agreement with each other, indicating that the crystal structures are truly representative of the bulk crystal products (Fig. 2a). The differences in intensity may be owing to the preferred orientation of the crystal samples. The thermal stability of complex 1 was determined in the temperature range of J. Oleo Sci. 69, (1) 55-63 (2020)
The thermal stability of 1 was investigated from the ambient temperature to 800°C under the N₂ atmosphere. The thermal decomposition of 1 occurs in three main stages with the structure remaining approximately unchanged up to ca. 400°C. Given that the first two losses overlap, they have been considered together as a unique loss in the range ca. 21–390°C. Overall, 1 loses in this range approximately 6.5% of the total weight, which agrees well with the release of three water molecules per formula unit (calculated value of 6.8%).
### 3.2 Photocatalytic degradation of organic dyes.
Free tib and 1’s solid-state luminescence were measured at room temperature. When title compound is excited at 328 nm, there is a strong emission peak at 394 nm (Fig. 2a). For comparison, when excited at 312 nanometers, free tib ligands reveals emission at 412 nanometers. 1’s strong emission is due to charge transfer in ligands. We determined crystal 1’s optical diffuse reflectance spectra under room temperature. Via extrapolating the linear part of absorption edge, 1’s energy band gap (Eg) was 2.30 eV, indicating its latent semiconductor properties (Fig. 3b).
The photocatalytic properties of photocatalysts were investigated using organic dyes Rhodamine B (rhB) along with methylene blue (MB) as dye models. The photocatalytic properties of 1 for MB degradation under the irradiation of visible light were studied. After 15, 30, 45 and 60 minutes of the irradiation of visible light, MB degradation efficiency under catalyst 1 was 33.2%, 56.3%, 73.6% and 86.2%, respectively (Fig. 3c). After 75 minutes, MB degradation
efficiency can up to 92.8%. Compared with above experiment, in the blank experiment which only H\textsubscript{2}O\textsubscript{2} MB degradation ratestructure were 16.4, 34.2 and 58.7 \textdegree\textsubscript{C}, respectively, for commercial inorganic oxide semiconductor titanium dioxide (\textlessthan20 nm) as well as titanium dioxide (\textgreateq60 nm) after the irradiation of visible-light for 75 minutes. 1 for MB degradation photocatalytic efficiencies were more than that of TiO\textsubscript{2} (\textgreateq60 nm). TiO\textsubscript{2} (\textlessthan20 nm) for MB degradation photocatalytic efficiencies were higher than that of TiO\textsubscript{2}. After 15, 30, 45, 60, 75, 90 and 105 minutes irradiation of visible light, RhB under catalyst 1 degradation efficiencies are 18.8, 36.5, 52.7, 64.9, 73.1, 80.2 and 85.2 \textdegree\textsubscript{C}, respectively (Fig. 3d). After 2 hours, RhB degradation efficiency can up to 90.6 \textdegree\textsubscript{C}. Compared with above experiment, in the blank experiment which only H\textsubscript{2}O\textsubscript{2}, MB degradation efficiencies were 2.8, 16.3 as well as 41.5 \textdegree\textsubscript{C}, respectively, for commercial inorganic oxide semiconductor titanium dioxide (\textlessthan20 nm) as well as titanium dioxide (\textgreateq60 nm) after the irradiation of visible light for 2 hours. 1 for RhB degradation photocatalytic efficiencies were more than that of TiO\textsubscript{2} (\textgreateq60 nm). TiO\textsubscript{2} (\textlessthan20 nm) for RhB degradation photocatalytic efficiencies were higher than that of TiO\textsubscript{2}. Thus, 1 is a fine photocatalyst for degrading RhB as well as MB. At the aim of understanding RHB and MB photocatalytic degradation mechanism under the action of catalyst (1), photocatalytic experiments were carried out under ammonium oxalate (AO, h\textsuperscript{+} scavenger), mannitol (OH scavenger), and benzoquinone (BQ, O\textsuperscript{2-} scavenger) as well as other various scavengers. Under AO, mannitol and BQ, MB degradation efficiency reduced from 92.8 \textdegree\textsubscript{C} for 1 to 80.7, 54.3 and 23.2 \textdegree\textsubscript{C}, respectively. Experimental results reveal that h\textsuperscript{+} was the major active substance, \textsuperscript{\textregistered}OH radical and O\textsuperscript{2-} promoted the degradation of MB to some extent. Under AO, mannitol and BQ, MB degradation efficiencies reduced from 90.4 \textdegree\textsubscript{C} for 1 to 58.7, 11.4 and 3.2 \textdegree\textsubscript{C}, respectively. Experiment results reveal that h\textsuperscript{+} and the \textsuperscript{\textregistered}OH radical were major active substance, and O\textsuperscript{2-} promoted the degradation of RhB to some extent.
The reaction kinetics model has an important role in the development of a photocatalytic degradation process for industrial application, because it can explain the effects of the necessary parameters on the photodegradation reaction rate, independently of the shape and configuration of the reactor. The Langmuir–Hinshelwood (L–H) kinetic model has been used for the photodegradation of many organic compounds such as dyes. This model is widely accepted to explain the kinetics of photodegradation processes. ln(C\textsubscript{0}/C\textsubscript{t}) versus time was plotted for photodegradation of RhB using 1 (Fig. 4). The experimental data fit well, with R\textsuperscript{2}>0.99, which indicates that the experimental data can be described by the pseudo-first order kinetics model. The slope of this linear plot indicates the first order rate constant of 1 is 0.12 min\textsuperscript{-1}, which is larger than that of some CP-based materials under the similar conditions\textsuperscript{21–23}.
Fig. 3 (a) Free tib and 1 solid-state luminescence under room temperature; (b) 1’s Solid-state optical diffuse-reflectance spectra; MB photocatalytic degradation efficiencies (c) and RhB (d) solutions utilizing photocatalyst 1, under scavenger AO, mannitol and BQ, or commercial (60 nm, 20 nm) TiO\textsubscript{2} and blank.
3.3 Cytotoxicity of the compound on HUVEC
CCK-8 detection kit was performed to detect the cytotoxicity of the synthetic compound on HUVEC. The HUVEC were treated with serially diluted compound for 24 h, with Oxaliplatin was used as the positive control drug. The absorbance values at 570 nm was measured, which reflect the cancer cells viability after compound treatment. As the CCK-8 results shown in Fig. 5, the compound did not show any inhibitory effect on the viability of the HUVEC cells, while the positive drug could reduce the viability of the cells to about 18% after 24 h treatment. This result indicated that the compound has no cytotoxicity on HUVEC, which was recommended for the following experiment.
3.4 Compound reduced the relative expression level of vcam-1
VCAM-1 has a significant function in AS course, which involved in the adhesion of cells, cells and extracellular matrix components. Recent reports revealed that the content of VCAM-1 in the vascular cell determines the consequence of the AS development. Thus, in this experiment, we firstly constructed the animal model and then evaluated the effect of compound on vcam-1 relative expression in the intravascular cells. As the results showed in the Fig. 6, at the 7th and 14th day after compound treatment, the expression of vcam-1 in the model group was significant increased compared with the control group, however, this up-regulated expression could be obviously reduced by the compound treatment to about the normal level.
3.5 Compound reduced the content of IL-1β and TNF-α
The various factors leading AS will ultimately cause the pathological processes of chronic inflammation, reflected as increased level of inflammatory cytokines TNF-α and IL-1β. So, in this study, the inhibitory effect of compound in reducing the level of inflammatory response in intravas-
Coordination Polymer, Photocatalytic Degradation
3.6 Molecular Docking
These results indicated that VCAM proteins have latent binding affinity with synthesized compounds, but their latent interaction modes are still missing. To further understanding possible binding patterns between VCAM protein and synthesized compound, pose scoring as well as molecular docking was carried out. Figure 8A exhibits the whole view of the possible binding pattern, where we can observe that the yellow rod of the compound indicates that it has been processed in the docking bag. From the surface view, the multiple functional groups of the compound showed potentials of interaction with VCAM. The surface binding view shown in Fig. 8B clearly reveals the binding interaction between receptors and ligands. It can be observed that the functional groups of this compound showed latent binding ability on the binding surface between predicted binding site and helix chain, which may affect the efficacy of VCAM. The compound interacts with mono receptor of VCAM protein, forming polar contacts with Glu96, His98 and Ser100. Other than other residues, hydrophobic interactions are reinforced by Leu124, Ile126, Gly131 and Leu134. The compound obtains a docking score as 78.5364, which reveals a moderate binding ability.
4 Conclusion
In conclusion, we have made a luminescent Zn(II)-based coordination polymer by using a rigid tripodal nitrogen-containing heterotopic ligand tris(1-imidazolyl)benzene (Htib). The prepared complex 1 was completely measured
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Fig. 6 Reduced relative expression level of vcam-1 in intravascular cells after compound treatment. After the model construction and compound treatment, the carotid artery segments were harvested for the detection of relative expression of vcam-1 with RT-PCR.
Fig. 7 Reduced TNF-α and IL-1β level in intravascular cells after compound treatment. After the model construction and compound treatment, the carotid artery segments were harvested, and the TNF-α and IL-1β level was detected via ELISA test.
by single crystal X-ray diffraction as well as elemental analysis. Under the condition of the irradiation of visible light, rhodamine B (Rhb) and methylene blue (MB) could be degraded with a good performance. In biological study, we aimed to explore new candidates for the treatment of atherosclerosis. The CCK-8 results indicated the compound has no cytotoxicity on HUVEC. Next, the protective effect of compound was evaluated in the constructed animal model. The RT-PCR determination of \( vcam-1 \) in vascular endothelial cells indicated that the compound could significantly inhibit the expression of \( vcam-1 \). Besides, the ELISA detection of TNF-\( \alpha \) and IL-1\( \beta \) revealed that the inflammatory level in the vascular endothelial cells was also been inhibited by compound. The results from molecular docking provided latent binding patterns between targeted protein (VCAM) and synthesized compound, indicating the possible binding mode and regulation mechanism for the compound.
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Association Between Baseline Diastolic Blood Pressure and the Efficacy of Intensive vs Standard Blood Pressure-Lowering Therapy
Andrew J. Foy, MD; Edward J. Filippone, MD; Eric Schaefer, PhD; Matt Nudy, MD; Mohammed Ruzieh, MD; Anne-Marie Dyer, MS; Vernon M. Chinchilli, PhD; Gerald V. Naccarelli, MD
Abstract
IMPORTANCE Low diastolic blood pressure (DBP) has been found to be associated with increased adverse cardiovascular events; however, it is unknown whether intensifying blood pressure therapy in patients with an already low DBP to achieve a lower systolic blood pressure (SBP) target is safe or effective.
OBJECTIVE To evaluate whether there is an association of baseline DBP and intensification of blood pressure–lowering therapy with the outcomes of all-cause death and cardiovascular events.
DESIGN, SETTING, AND PARTICIPANTS This cohort study analyzed patients who were randomized to intensive or standard BP control in the Action to Control Cardiovascular Risk in Diabetes–Blood Pressure (ACCORD-BP) trial and Systolic Blood Pressure Intervention Trial (SPRINT). Data were collected from September 1999 to June 2009 (ACCORD-BP) and from October 2010 to August 2015 (SPRINT). Data were analyzed from December 2020 to June 2021.
EXPOSURES Baseline DBP as a continuous variable.
MAIN OUTCOMES AND MEASURES All-cause death and a composite cardiovascular end point (CVE) that included cardiovascular death, nonfatal myocardial infarction, and nonfatal stroke.
RESULTS A total of 14,094 patients (mean [SD] age, 66.2 [8.9] years; 8504 [60.4%] men) were included in this analysis. There were significant nonlinear associations between baseline DBP and all-cause death (eg, baseline DBP 50 vs 80 mm Hg: hazard ratio [HR], 1.48; 95% CI, 1.06-2.08; \( P = .02 \)) and the composite CVE (eg, baseline DBP 50 vs 80 mm Hg: HR, 1.45; 95% CI, 1.27-3.04; \( P = .003 \)) observed among all participants. Findings for the interaction between baseline DBP and treatment group assignment for all cause death did not reach statistical significance. For intensive vs standard therapy, the HR of death for a baseline DBP of 50 mm Hg was 1.80 (95% CI, 0.95-3.39; \( P = .07 \)) and that for a baseline DBP of 80 mm Hg was 0.77 (95% CI, 0.59-1.01; \( P = .05 \)). Overall, there was no interaction found between baseline DBP and treatment group assignment for the composite CVE. Over the range of baseline DBP values, significant reductions in the composite CVE for patients assigned to intensive vs standard therapy were found for baseline DBP values of 80 mm Hg (HR, 0.78; 95% CI, 0.62-0.98; \( P = .03 \)) and 90 mm Hg (HR, 0.74; 95% CI, 0.55-0.98; \( P = .04 \)).
CONCLUSIONS AND RELEVANCE This pooled cohort study found no evidence of a significant interaction between baseline DBP and treatment intensity for all-cause death or for a composite CVE. These results are hypothesis generating and merit further study.
JAMA Network Open. 2021;4(10):e2128980. doi:10.1001/jamanetworkopen.2021.28980
Open Access. This is an open access article distributed under the terms of the CC-BY License.
Introduction
Since the publication of the landmark Systolic Blood Pressure Intervention Trial (SPRINT), the focus in treating hypertension has been on systolic blood pressure (SBP). However, this ignores observational data showing a J-shaped curve for diastolic blood pressure (DBP), where adverse cardiovascular events and mortality increase as DBP decreases below critical levels (<60 mm Hg). It has been postulated that pharmacological treatment to achieve a lower SBP target in persons whose DBP is already low may worsen patient outcomes. To test this hypothesis, we performed a pooled cohort analysis combining participants from SPRINT with those of the similarly designed Action to Control Cardiovascular Risk in Diabetes–Blood Pressure (ACCORD-BP) trial to assess whether there is an association between baseline DBP and treatment intensity on patient outcomes.
Methods
This cohort study was reported in adherence with the Strengthening the Reporting of Observational Studies in Epidemiology (STROBE) reporting guideline. The study met all criteria for exemption by the institutional review board at Penn State College of Medicine. Informed consent was waived because data were deidentified.
The designs and outcomes of ACCORD-BP and SPRINT have been reported previously, and patient-level data from each trial were obtained from the Biologic Specimen and Data Repository Information Coordinating Center of the National Institutes of Health. In brief, ACCORD-BP was a randomized trial of 4733 patients with diabetes with elevated cardiovascular risk assigned to either intensive (ie, SBP <120 mm Hg) or standard (ie, SBP <140 mm Hg) BP control and followed for a median of 4.7 years. SPRINT randomized 9361 patients without diabetes with elevated cardiovascular risk to either intensive or standard BP control, using the same targets as ACCORD-BP, and followed them for a median of 3.3 years.
Statistical Analysis
We used a Cox proportional hazards model to test the association between baseline DBP as a continuous variable and the outcomes of interest. These outcomes were all-cause mortality and a composite cardiovascular end point (CVE) that included cardiovascular death, nonfatal myocardial infarction (MI), or nonfatal stroke. This composite CVE was chosen because it was the primary composite end point of the ACCORD-BP trial and because each of these individual end points was included in the composite primary end point of the SPRINT trial. The completed analysis included the following variables measured at baseline: DBP, age, sex, history of MI, history of congestive heart failure, history of peripheral vascular disease, history of stroke, estimated glomerular filtration rate at baseline, treatment group (intensive vs nonintensive), stratification factor for study (SPRINT vs ACCORD-BP), and stratification factor for site. To allow for nonlinear associations with outcomes, we used a restricted cubic spline with 4 df. The level of significance was set to a 2-sided P < .05, and the hazard ratios (HRs) and corresponding 95% CIs were reported from these models. We also showed the association in graphical form using the log hazard scale.
A separate Cox proportional hazards regression model was used to test for an interaction between baseline DBP as a continuous variable and treatment group assignment. The outcomes were all-cause mortality and the aforementioned composite CVE. The completed analysis included all variables used in the model described already but included the additional variable of interaction between treatment group and DBP. To allow for nonlinear associations with outcomes, we used a restricted cubic spline with 4 df. The level of significance was set to P < .05, and the HRs and corresponding 95% CIs were reported from these models. We also showed the associations in graphical form using the log hazard scale.
For representative purposes, baseline characteristics are presented for all patients stratified by baseline DBP less than 60 mm Hg and greater than or equal to 60 mm Hg. The change in SBP and
DBP values from baseline to 12 months is also presented for these DBP subgroups based on treatment group assignment (intensive vs nonintensive).
Analyses were generated using SAS STAT software version 9.4 for Windows (SAS Institute). Data were analyzed from December 2020 to June 2021.
Results
The data included 14,094 participants (mean [SD] age, 66.2 [8.92] years; 8,504 men [60.3%]), with 4,733 (33.6%) coming from ACCORD and 9,361 (66.4%) coming from SPRINT. The overall number of patients who died was 672 (4.8%), and the number experiencing the combined CVE was 893 (6.3%). More patients died from noncardiovascular causes (392 patients) than cardiovascular causes (280 patients) (Table 1). The median (IQR) baseline DBP was 77 (70-85) mm Hg (Table 1). A distribution plot of baseline DBP values for all participants is provided in Figure 1. In total, 97 patients (0.7%) had at least 1 missing baseline value involving comorbid conditions and were excluded when fitting the models. There were significant associations between baseline DBP (modeled nonlinearly) and all-cause death (eg, baseline DBP 50 vs 80 mm Hg: HR, 1.48; 95% CI, 1.06-2.08; P = .02; baseline DBP 110 vs 80 mm Hg: HR, 2.15; 95% CI, 1.30-3.56; P = .003) and the composite CVE (eg, baseline DBP 50 vs 80 mm Hg: HR, 1.45; 95% CI, 1.27-3.04; P = .003; baseline DBP 110 vs 80 mm Hg: HR, 1.96; 95% CI, 1.27-3.04; P = .003). The resulting estimated associations were U-shaped (Figure 2).
When analyzed as a continuous variable, findings for the association between baseline DBP and treatment group assignment for the outcome of all-cause death did not reach statistical significance (Figure 2). No interaction was seen between baseline DBP and treatment group for the composite CVE (Figure 2). HRs and corresponding P values from the Cox model are provided in Table 2 for intensive vs standard groups.
For intensive vs standard therapy, for a baseline DBP of 50 mm Hg, the HR of death was 1.80 (95% CI, 0.95-3.39; P = .07); for 60 mm Hg, the HR was 1.12 (95% CI, 0.84-1.50; P = .43); for 70 mm Hg, the HR was 0.82 (95% CI, 0.65-1.02; P = .08); for 80 mm Hg, the HR was 0.77 (95% CI, 0.59-1.01; P = .05); for 90 mm Hg, the HR was 0.85 (95% CI, 0.59-1.20; P = .35), for 100 mg Hg, the HR was...
0.79 (95% CI, 0.48-1.28; \(P = .34\)); for 110 mm Hg, the HR was 0.64 (95% CI, 0.25-1.64; \(P = .35\)) (Table 2). For intensive vs standard therapy, significant reductions in the composite CVE were found for DBP values of 80 mm Hg (HR, 0.78; 95% CI, 0.62-0.98; \(P = .03\)) and 90 mm Hg (HR, 0.74; 95% CI, 0.55-0.98; \(P = .04\)) (Table 2).
Figure 1. Histogram of Baseline Diastolic Blood Pressure Values Among Participants of the Action to Control Cardiovascular Risk in Diabetes–Blood Pressure and Systolic Blood Pressure Intervention Trial Trials
Figure 2. Log Hazard Plots of Baseline Diastolic Blood Pressure and All-Cause Death and the Composite Cardiovascular End Point
Log hazard plots of the baseline DBP and all-cause mortality and baseline DBP and the composite cardiovascular end point are shown overall (A and B) and according to treatment group assignment (C and D). Shaded areas in A and B denote 95% CIs.
There were 800 participants with baseline DBP less than 60 mm Hg and 13,277 with baseline DBP greater than or equal to 60 mm Hg. Individuals with baseline DBP less than 60 mm Hg were older (mean [SD] age, 73.6 [8.7] vs 65.7 [8.7] years) and had 3-fold higher risk of dying (74 patients [9.3%] vs 598 patients [4.5%]) than those with baseline DBP greater than or equal to 60 mm Hg (Table 3). Baseline SBP and DBP values were similar for those assigned to intensive vs standard control at baseline in both subgroups; however, by 12 months there were significant differences in achieved levels (Table 3). For individuals with baseline DBP less than 60 mm Hg, the mean (SD) SBP and DBP values at 12 months for the intensive and standard therapy groups were 122.4 (14.9) and 56.3 (9.0) mm Hg and 134.2 (14.9) and 62.4 (9.6) mm Hg, respectively. For those with baseline DBP greater than or equal to 60 mm Hg, the mean (SD) SBP and DBP values at 12 months for the intensive and standard therapy groups were 121.0 (13.8) and 68.8 (9.6) mm Hg and 135.6 (13.7) and 76.0 (10.4) mm Hg, respectively.
Discussion
In this pooled cohort analysis of patients from the ACCORD-BP and SPRINT trials, we tested the association between baseline DBP and patient outcomes. We also tested for an association between baseline DBP and treatment group assignment with respect to patient outcomes. Our results confirm prior observations of a nonlinear association between DBP and patient outcomes that appears U-shaped. No statistically significant interactions were observed, however, with respect to DBP and treatment group assignment for all-cause mortality or the composite CVE. This undermines the traditional J-curve hypothesis relating low DBP with reduced coronary perfusion and events.
Although we acknowledge our findings do not establish the existence of an interaction between baseline DBP and treatment group assignment for the outcome of all-cause death, we think it would be imprudent to dismiss possible associations altogether. Treatment effect heterogeneity emerges from a few essential risk dimensions, including (1) the risk of the primary study outcome, (2) competing risk, (3) the risk of treatment-related harm, and (4) direct treatment-effect modification. In individuals with lower baseline DBP values, factors unrelated to blood pressure may be associated with death more so than for individuals with higher DBP. Patients whose baseline DBP was less than 60 mm Hg compared with those with higher values were at 3-fold higher risk of dying (9% vs 3%), were significantly older (73.6 vs 65.7 years), and had higher rates of all comorbid conditions (Table 3). It is also not implausible to speculate that such individuals would be at increased risk of treatment-related harm, both measured and unmeasured and that they would not recover the same from adverse events as healthier subjects (adverse events were significantly increased in ACCORD-BP and SPRINT in the intensive therapy groups), and finally, that lowering blood pressure would not yield the same benefits as in those generally healthier subjects. A limitation of this analysis is that it did not look at serious adverse events in relation to baseline DBP, but this was intentional.
| DBP by treatment interaction, intensive vs nonintensive, mm Hg | All-cause mortality | Composite cardiovascular end point |
|---------------------------------------------------------------|---------------------|-----------------------------------|
| | HR (95% CI) | P value | HR (95% CI) | P value |
| Overall | Not applicable | .13 | Not applicable | .88 |
| 50 | 1.80 (0.95-3.39) | .07 | 0.77 (0.44-1.33) | .35 |
| 60 | 1.12 (0.84-1.50) | .43 | 0.85 (0.66-1.10) | .22 |
| 70 | 0.82 (0.65-1.02) | .08 | 0.85 (0.69-1.03) | .10 |
| 80 | 0.77 (0.59-1.01) | .05 | 0.78 (0.62-0.98) | .03 |
| 90 | 0.85 (0.59-1.20) | .35 | 0.74 (0.55-0.98) | .04 |
| 100 | 0.79 (0.48-1.28) | .34 | 0.67 (0.45-1.01) | .05 |
| 110 | 0.64 (0.25-1.64) | .35 | 0.60 (0.26-1.37) | .22 |
Abbreviations: DBP, diastolic blood pressure; HR, hazard ratio.
owing to the different definitions and adjudication procedures used for defining these events within the trials.
The notion of treatment effect heterogeneity for common interventions in high-risk patients is not unprecedented in cardiovascular medicine. An example of this within an individual trial can be found in the Sudden Cardiac Death in Heart Failure Trial,9 where there was a significant association of heart failure class and implantable cardioverter-defibrillator therapy with mortality. Patients with New York Heart Association class III heart failure derived no benefit from implantable cardioverter-defibrillator therapy but those with New York Heart Association class II heart failure benefited greatly. The 5-year mortality rates in the New York Heart Association classes III and II placebo groups were 46% and 32%, respectively.9 This same dynamic can be seen across trials as well. In the Study to Evaluate the Use of Rosuvastatin in Subjects on Regular Hemodialysis trial,10 a high-risk population of dialysis patients derived no benefit from statin therapy. The rates of death and nonfatal MI in the control group of this population were 14 per 100 person-years and 2.5 per 100 person-years, respectively.10 Contrary to this, in the Justification for the Use of Statins in Prevention: An International Trial Evaluating Rosuvastatin trial,11 a much lower risk population of patients who were
### Table 3. Baseline Characteristics of Individuals With Baseline DBP Less Than and Greater Than or Equal to 60 mm Hg Along With Blood Pressure Control at Baseline and 12 Months
| Variable | Participants, No. (%) |
|-----------------------------------------------|-----------------------------------------------|
| | DBP < 60 mm Hg (n = 800) | DBP ≥ 60 mm Hg (n = 13,277) |
| **Age, y** | | |
| Mean (SD) | 73.6 (8.7) | 65.7 (8.7) |
| <50 | 0 | 111 (0.8) |
| 50-59 | 68 (8.5) | 3629 (27.3) |
| 60-69 | 183 (22.9) | 5379 (40.5) |
| 70-79 | 343 (42.9) | 3210 (24.2) |
| ≥80 | 206 (25.8) | 948 (7.1) |
| **Sex** | | |
| Male | 472 (59.0) | 8026 (60.5) |
| Female | 328 (41.0) | 5251 (39.5) |
| **Myocardial infarction** | | |
| | 115 (14.4) | 1295 (9.8) |
| **Congestive heart failure** | | |
| | 46 (5.8) | 483 (3.6) |
| **Peripheral vascular disease** | | |
| | 88 (11.0) | 575 (4.3) |
| **Stroke** | | |
| | 29 (3.6) | 326 (2.5) |
| **Estimated glomerular filtration rate, mean (SD), mL/min/1.73 m²** | 68.4 (23.7) | 79.0 (25.4) |
| **Diabetes** | | |
| Uncomplicated | 94 (11.8) | 2118 (16.0) |
| End-organ damage | 167 (20.9) | 2352 (17.7) |
| **BP control, mean (SD), mm Hg** | | |
| **Baseline** | | |
| **SBP** | | |
| Intensive therapy | 127.0 (15.4) | 140.2 (15.6) |
| Standard therapy | 128.1 (15.7) | 140.3 (15.1) |
| **DBP** | | |
| Intensive therapy | 54.9 (3.8) | 78.8 (10.4) |
| Standard therapy | 55.2 (3.7) | 78.7 (10.3) |
| **12 mo** | | |
| **SBP** | | |
| Intensive therapy | 122.4 (14.9) | 121.0 (13.8) |
| Standard therapy | 134.2 (14.9) | 135.6 (13.7) |
| **DBP** | | |
| Intensive therapy | 56.3 (9.0) | 68.9 (9.6) |
| Standard therapy | 62.4 (9.6) | 76.0 (10.4) |
Abbreviations: BP, blood pressure; DBP, diastolic blood pressure; SBP, systolic blood pressure.
in generally good health derived a significant benefit from statin therapy. The same rates of death and
nonfatal MI in the control group of this population were 1.25 per 100 person-years and 0.33 per 100
person-years, respectively.11
In the recently published International Study of Comparative Health Effectiveness with Medical
and Invasive Approaches-Chronic Kidney Disease trial,12,13 patients with advanced chronic kidney
disease derived no benefit from an invasive compared with conservative strategy and were more
likely to experience a stroke or a composite of death from any cause or initiation of dialysis. The
3-year rates of death and nonfatal MI in the control group of this population were 27.8% and 15.9%,
respectively.12,13 In the main trial,14,15 which excluded CKD patients with chronic kidney disease, fewer
events were experienced in the invasive group, and there was a significant reduction in angina and
no evidence of harm. The 3-year rates of death and nonfatal MI in the control group of this population
were 4.3% and 8.5%, respectively.14,15
Our study is not the first to look for an interaction between intensive therapy and baseline DBP
in an intention-to-treat fashion. In a reanalysis of SPRINT-only patients, Beddhu et al16 did not find
an interaction between baseline DBP and all-cause death, the composite CVE, or chronic kidney
disease events when DBP subgroups were analyzed on the basis of quintiles, or when the lowest
quintile was compared with the remaining cohort. There are several notable differences between this
study16 and ours. First, the use of SPRINT-only patients would reduce power to detect any subgroup
interactions, if present. Second, their method only considered baseline DBP as a dichotomous
variable (based on quintiles) and in doing so, they included many patients with DBPs much greater
than 60 mm Hg in their lowest quintile (the mean [SD] DBP of this group was 61 [5] mm Hg).16 Our
analysis of DBP as a continuous variable suggests the interaction occurs very near the 60 mm Hg
mark. Finally, in their analysis they do report a P value for the interaction between baseline DBP and
treatment intensity on all-cause death of .29.16 Although this is far from the traditional bounds of
what is considered statistically significant, it may not be trivial. P values for testing interactions may
be considered hypothesis-generating at lower thresholds than the 95% mark used for hypothesis
testing and confirmation.
Li and colleagues17 studied the association between DBP and outcomes for patients in the
ACCORD-BP and SPRINT trials among patients who achieved a SBP less than 130 mm Hg. Among
such patients, those with treated DBP lower than 60 mm Hg had higher rates of events. Their
findings are consistent with our study and many others in the past that have looked at baseline and
achieved DBP levels and found associations between lower values and outcomes. We did this by
looking at baseline DBP as a continuous variable and found significant nonlinear associations with
all-cause death and a composite CVE among patients in the ACCORD-BP and SPRINT trials (Figure 2).
However, these observations in themselves do not directly address the question of whether starting
or intensifying therapy in patients with DBP values less than a certain number to achieve a lower SBP
target is effective or not. To the best of our knowledge, only this study and the one by Beddhu et al16
address this question directly.
It should not be construed from our data or the other studies mentioned here that patients with
low DBP should have deintensification of therapy with the aim of increasing DBP. The question
addressed by our study is whether therapy can be safely intensified to lower SBP in such patients.
Strengths and Limitations
Our study has both strengths and limitations. The main strength is the use of individual patient data
from 2 large, randomized clinical trials conducted in the same manner, including both patients with
and without diabetes. Limitations include the lack of a significant number of patients with stroke at
baseline and the low number of patients whose baseline DBP was less than 60 mm Hg.
Conclusions
In conclusion, this pooled cohort analysis of patients enrolled in the ACCORD-BP and SPRINT trials supports the existence of a nonlinear association between baseline DBP and patient outcomes as previously reported. More importantly, it suggests that among patients whose baseline DBP was greater than 60 mm Hg, intensifying therapy to achieve an SBP target of 120 mm Hg could reduce death and cardiovascular events. It does not allow us to conclude the same for patients whose baseline DBP is 60 mm Hg or below since intensifying therapy may not reduce the risk of dying and could possibly increase it. This topic merits further investigation.
4. Bhatt DL. Troponin and the J-curve of diastolic blood pressure: when lower is not better. J Am Coll Cardiol. 2016;68(16):1723-1726. doi:10.1016/j.jacc.2016.08.007
5. Cushman WC, Evans GW, Byington RP, et al; ACCORD Study Group. Effects of intensive blood-pressure control in type 2 diabetes mellitus. N Engl J Med. 2010;362(17):1575-1585. doi:10.1056/NEJMoa1001286
6. Dahabreh IJ, Hayward R, Kent DM. Using group data to treat individuals: understanding heterogeneous treatment effects in the age of precision medicine and patient-centred evidence. Int J Epidemiol. 2016;45(6):2184-2193. doi:10.1093/ije/dyw125
7. Kent DM, van Klaveren D, Paulus JK, et al. The predictive approaches to treatment effect heterogeneity (PATH) statement: explanation and elaboration. Ann Intern Med. 2020;172(1):W1-W25. doi:10.7326/M18-3668
8. Burke JF, Hayward RA, Nelson JP, Kent DM. Using internally developed risk models to assess heterogeneity in treatment effects in clinical trials. Circ Cardiovasc Qual Outcomes. 2014;7(1):163-169. doi:10.1161/CIRCOUTCOMES.113.000497
9. Bardy GH, Lee KL, Mark DB, et al; Sudden Cardiac Death in Heart Failure Trial (SCD-HeFT) Investigators. Amiodarone or an implantable cardioverter-defibrillator for congestive heart failure. N Engl J Med. 2005;352(3):225-237. doi:10.1056/NEJMoa043399
10. Fellström BC, Jardine AG, Schmieder RE, et al; AURORA Study Group. Rosuvastatin and cardiovascular events in patients undergoing hemodialysis. N Engl J Med. 2009;360(14):1395-1407. doi:10.1056/NEJMoa0810177
11. Ridker PM, Danielson E, Fonseca FA, et al; JUPITER Study Group. Rosuvastatin to prevent vascular events in men and women with elevated C-reactive protein. N Engl J Med. 2008;359(21):2195-2207. doi:10.1056/NEJMoa0807646
12. Bangalore S, Maron DJ, O’Brien SM, et al; ISCHEMIA-CKD Research Group. Management of coronary disease in patients with advanced kidney disease. N Engl J Med. 2020;382(17):1608-1618. doi:10.1056/NEJMoa1915925
13. Spertus JA, Jones PG, Maron DJ, et al; ISCHEMIA-CKD Research Group. Health-status after invasive or conservative care in coronary and advanced kidney disease. N Engl J Med. 2020;382(17):1619-1628. doi:10.1056/NEJMoa1916374
14. Maron DJ, Hochman JS, Reynolds HR, et al; ISCHEMIA Research Group. Initial invasive or conservative strategy for stable coronary disease. N Engl J Med. 2020;382(15):1395-1407. doi:10.1056/NEJMoa1915922
15. Spertus JA, Jones PG, Maron DJ, et al; ISCHEMIA Research Group. Health-status outcomes with invasive or conservative care in coronary disease. N Engl J Med. 2020;382(15):1408-1419. doi:10.1056/NEJMoa1916370
16. Beddu S, Chertow GM, Cheung AK, et al; SPRINT Research Group. Influence of baseline diastolic blood pressure on effects of intensive compared with standard blood pressure control. Circulation. 2018;137(2):134-143. doi:10.1161/CIRCULATIONAHA.117.030848
17. Li J, Somers VK, Gao X, et al. Evaluation of optimal diastolic blood pressure range among adults with treated systolic blood pressure less than 130 mm Hg. JAMA Netw Open. 2021;4(2):e2037554. doi:10.1001/jamanetworkopen.2020.37554
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PROTOGENE: turning amino acid alignments into bona fide CDS nucleotide alignments
Sébastien Moretti, Frédéric Reinier, Olivier Poirot, Fabrice Armougom, Stéphane Audic, Vladimir Keduas and Cédric Notredame*
Information Génomique et Structurale, CNRS UPR2589, Institute for Structural Biology and Microbiology (IBSM), Parc Scientifique de Luminy, 163 Avenue de Luminy, FR 13288, Marseille cedex 09, France
Received February 14, 2006; Revised and Accepted March 20, 2006
ABSTRACT
We describe Protogene, a server that can turn a protein multiple sequence alignment into the equivalent alignment of the original gene coding DNA. Protogene relies on a pipeline where every initial protein sequence is BLASTed against RefSeq or NR. The annotation associated with potential matches is used to identify the gene sequence. This gene sequence is then aligned with the query protein using Exonerate in order to extract a coding nucleotide sequence matching the original protein. Protogene can handle protein fragments and will return every CDS coding for a given protein, even if they occur in different genomes. Protogene is available from http://www.tcoffee.org/.
INTRODUCTION
Although they constitute the material with which primary biological databases are made of, nucleotide sequences are rarely used when it comes to analyzing proteins. The reason is that evolutionary models designed for comparing nucleic acids are often too simplistic and almost never take into account the constraints associated with the coding nature of gene sequences. In practice, biologists dealing with proteins are often encouraged to use protein databases and associated tools to build their models. However, the transposition of these results onto the bona fide nucleotide sequences is time-consuming. This limitation can be an issue, especially when reconstructing phylogenetic trees of closely related species or when looking for conserved nucleotide patterns within multiple coding sequences.
In theory, the task of turning a protein multiple sequence alignment (MSA) into the associated CDS (CoDing Sequence) MSA is trivial. Yet in practice things can prove more complicated for a variety of simple reasons: unknown gene names, MSAs of domain or partial protein sequence, incomplete database annotation, and the ever faster evolution of genomic resources. Of course, each of these problems can usually be solved manually, on a case by case basis, but altogether they tend to hamper the establishment of automatic procedures for seamlessly connecting the protein and the nucleotide worlds.
When comparing protein and nucleotide sequences, efficient methods exist to either align CDSs using their coding potential (1–3) or thread CDSs onto a pre-established protein sequences (protal2dna: http://bioweb.pasteur.fr/seqanal/interfaces/protal2dna.html and pal2nal (http://www.bork.embl-heidelberg.de/pal2nal/) but all these tools require the user to preprocess the data, gather the appropriate CDSs and make sure these are compatible with any subdomain extracted from the original protein sequence. To the best of our knowledge, no tool is available online to automatically identify the nucleotide sequence (genomic or transcript) associated with a protein partial sequence (domain or fragment) and process it to replace that protein with its bona fide CDS while retaining the original alignment.
We developed a fully automated program named Protogene (PROtein TO GENE) that when given a protein sequence alignment (pairwise or multiple) returns the corresponding CDS alignment. Protogene searches RefSeq (4) and NR with BLAST (5) in order to identify the transcript or genomic sequence(s) most likely to be associated with the original protein sequences. The sequences thus identified are processed by Exonerate (6) in order to extract a portion of CDS matching perfectly the original protein sequence. This CDS is re-introduced within the MSA to replace the original protein. Although every attempt is made to identify the genuine protein CDS, a conservative post-filtering step is still needed to eliminate any sequence that may not have been correctly processed. Protogene is not a gene finding tool and depends entirely on the pre-established proteomes found in RefSeq and NR. We have put the emphasis on robustness and reliability rather than...
exhaustiveness. In our hands, Protogene returns a bona fide
CDS for 95% of the sequences and fails on ~5%. Whenever
the missed sequences matter, it is up to the user to explore the
labyrinth of nucleotide databases and discover the glitch that
breaks the information chain between the protein and its CDS.
Protogene is available on http://www.tcoffee.org/.
METHODS
Server pipeline
Figure 1 shows Protogene’s flow chart. Each sequence within
the provided MSA is treated individually. The first step is a
BLASTp (5) against the RefSeq (4) protein database. Matches
against RefSeq are only accepted when associated with an
alignment that displays 100% identity and 100% coverage
with the query sequence (i.e. 100% of the query sequence
residues aligned with identical residues). Multiple hits with
the same score are all kept. If no suitable hit is found in
RefSeq, the query sequence is BLASTed against the NR non-
redundant protein sequence database, with a lowered accep-
tance threshold (95% identity, 95% coverage). NCBI EFetch
and EUtils utilities (http://eutils.ncbi.nlm.nih.gov/entrez/
query/static/eutils_help.html) are then used to fetch the nucle-
otide sequences associated with the query sequence. Exonerate
is finally used to extract a CDS matching perfectly the original
protein sequence (be it a full-length protein or just a fragment).
Exonerate is able to splice introns and can handle genomic and
transcript sequences alike. Mismatches between the query and
the CDS are indicated with NNN codons. It is up to the user to
decide whether these are sequences errors, polymorphisms or
identification errors. The user may also request automatic back-
translations using the IUC ambiguity code for unmatched amino
acids. CDSs are returned along with some basic annotation
including the nucleotide sequence accession number, the source
organism and the RefSeq/NR accession number. CDSs where
>5% of the nucleotides have had to be replaced with Ns are
considered unreliable and discarded with an explicit mention in
the output.
It is important to point out that when several proteins from
different organisms have a perfect identity with the original
query, each corresponding nucleotide sequence is integrated
within the final alignment, leaving it to the user to remove the
nucleotide sequences he is not interested in (see the Histone
example in the next section). To ease this selection, the final
alignment is reported in FASTA format. Nucleotide sequences
gathered from the NCBI are kept in cache for 2 weeks, thus
insuring faster second runs when reanalyzing a dataset with
minor modifications.
Distribution
The Protogene server is available from http://www.tcoffee.
org/. It relies on a collection of Perl scripts and two external
programs: BLAST and Exonerate. BLAST searches against
NR and RefSeq are made using the gigablaster service (http://
www.igs.cnrs-mrs.fr/).
USING PROTOGENE
We provide three simple examples of how Protogene can be
used to rapidly and efficiently ask simple questions regarding
protein sequence conservation at the nucleotide level. The first
one is an analysis of the CLP Serine protease family. Serine is
the only amino acid coded by two sets of codons (UCN and
AGY) that cannot be interconverted by a single point muta-
tion. Class switches, appear however to be very frequent and
the question whether they arise from double mutations has
been the subject of intense scrutiny and debate (7). Given a
collection of protein sequences, Protogene makes it straight-
forward to analyze the codon conservation of the serine.
Figure 2 shows the output obtained after cutting and pasting
the Pfam (8) seed MSA of the CLP Serine Protease family
(PF00574). This alignment is not made of complete proteins
but restricted to the serine protease domain. For each domain,
Protogene managed to identify at least one corresponding gene
and also reported identical protein sequences coming from
closely related genomes. Figure 2 represents the portion of
this alignment containing the conserved Serine that is part of
the catalytic triad. In a second test, we evaluated Protogene’s
Figure 1. Protogene flow chart sequences are first BLASTed against RefSeq. If
no match is found, they are then BLASTed against NR. Nucleotide sequences
are fetched from NCBI and processed with Exonerate to yield CDSs that
perfectly match the original protein.
Figure 2. Protagene output on the CLP Serine Protease family. The Seed MSA of the PFAM profile entry (PFAM PF00574) was processed by Protagene. The portion of the alignment containing the Serine active site classes are indicated in yellow (UCN) and green (AGY).
ability to process a complete eukaryotic domain sequence dataset. For that purpose we selected the 209 human trypsin like serine proteases listed in the SMART database (9) (SM00020). These are protein domains processed using a SMART Hidden Markov Model. Protogene returned the CDSs associated with 253 protein sequences found in RefSeq and NR (157 in RefSeq and 96 in NR). Out of the 209 original human sequences, 4 matched equally well a chimpanzee protein (thus prompting the return of the associated Chimpanzee CDSs) and 66 matched two distinct human entries (thus prompting the return of 66 extra Human CDSs). Of the original sequences 26 could not be associated with an acceptable CDS: 20 did not pass the BLAST step (i.e. no suitable match was found in RefSeq or NR) and the 6 remaining could not be properly processed by exonerate against the nucleotide sequences indicated by the database annotation.
Our third example (Figure 3) addresses the question of nucleotide sequence conservation in the Histone H2A family. Histones are notoriously conserved proteins and in the present case, launching a Protogene analysis on the Human H2A sequence (SwissProt P28001) returned 5 perfect matches in RefSeq, resulting in 5 CDSs being reported: Human, Cow, Rat, Mouse and Dog. The alignment is shown of Figure 3. Such a nucleotide alignment of perfectly conserved protein sequences is ideal for phylogenetic studies or motif discoveries. It is worth pointing out that although it is identical, the Chimpanzee Histone was not reported by Protogene because it is not included in RefSeq. This finding reveals the heavy bias of Protogen toward model systems included in RefSeq. The systematic use of NR rather than RefSeq could help solve this problem, but this would come at the cost of a more complex output.
CONCLUSION
In this paper we describe Protogene, a web server that makes it possible to turn a protein MSA into the corresponding CDS MSA, using bona fide genomic or transcriptome data. Protogene is meant to be a simple yet powerful data exploration tool. Its purpose is to rapidly ask simple questions, with an emphasis on accuracy and robustness rather than sensitivity.
ACKNOWLEDGEMENTS
We thank Guy Slater for his advice on the use of Exonerate, NCBI team for their help with EFetch and EUtis tools. We thank Prof. Jean-Michel Claverie (head of IGS) for stimulating discussions and support. The development was supported by CNRS (Centre National de la Recherche Scientifique), Sanofi-Aventis Pharma SA., Marseille-Nice Génopole and the French National Genomic Network (RNG). Funding to pay the Open Access publication charges for this article was provided by CNRS.
Conflict of interest statement. None declared.
REFERENCES
1. Bininda-Emonds,O.R. (2005) transAlign: using amino acids to facilitate the multiple alignment of protein-coding DNA sequences. BMC Bioinformatics, 6, 156.
2. Stocsits,R.R., Hofacker,I.L., Fried,C. and Stadler,P.F. (2005) Multiple sequence alignments of partially coding nucleic acid sequences. BMC Bioinformatics, 6, 160.
3. Wernersson,R. and Pedersen,A.G. (2003) RevTrans: multiple alignment of coding DNA from aligned amino acid sequences. Nucleic Acids Res., 31, 3537–3539.
4. Wheeler,D.L., Barrett,T., Benson,D.A., Bryant,S.H., Canese,K., Chetvernin,V., Church,D.M., DiCuccio,M., Edgar,R., Federhen,S. et al. (2006) Database resources of the National Center for Biotechnology Information. Nucleic Acids Res., 34, D173–D180.
5. Altschul,S.F., Gish,W., Miller,W., Myers,E.W. and Lipman,D.J. (1990) Basic local alignment search tool. J. Mol. Biol., 215, 403–410.
6. Slater,G.S. and Birney,E. (2005) Automated generation of heuristics for biological sequence comparison. BMC Bioinformatics, 6, 31.
7. Averof,M., Rokas,A., Wolfe,K.H. and Sharp,P.M. (2000) Evidence for a high frequency of simultaneous double-nucleotide substitutions. Science, 287, 1283–1286.
8. Finn,R.D., Mistry,J., Schuster-Bockler,B., Griffiths-Jones,S., Hollich,V., Lassmann,T., Moxon,S., Marshall,M., Khanna,A., Durbin,R. et al. (2006) Pfam: clans, web tools and services. Nucleic Acids Res., 34, D247–D251.
9. Letunic,I., Copley,R.R., Pils,B., Pinkert,S., Schultz,J. and Bork,P. (2006) SMART 5: domains in the context of genomes and networks. Nucleic Acids Res., 34, D257–D260.
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Research Article
FE Modeling for Bolted Wood Connection Using a Porous Constitutive Model
Huazhang Zhou¹,² and Xiaoqiang Zhou²
¹Key Lab of Structures Dynamic Behaviour and Control (Harbin Institute of Technology), Ministry of Education, Harbin 150090, China
²School of Civil Engineering, Harbin Institute of Technology, Harbin 150090, China
Correspondence should be addressed to Huazhang Zhou; [email protected]
Received 4 October 2020; Revised 18 November 2020; Accepted 12 December 2020; Published 28 December 2020
Copyright © 2020 Huazhang Zhou and Xiaoqiang Zhou. 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.
According to the facts of localized crushing failure of bolt groove in wood connection with enough end distance and the three-phase composites of wood with solid (wood substance), water, and gas, a confined compression test for the wood cylinder was conducted for achieving constitutive relation under the complex stress state in wood groove. A porous constitutive model was developed according to the confined compression experiments. Then, the constitutive model was implemented in a finite element modeling of mental dowel-type fasteners in wood-to-wood connections to analyse the load-carrying capacity parallel to the grain. Through changing the thicknesses of centre members and side members of wood connections made of a similar wood species, Pinus Sylvestris var. Mongolica, the effects of thickness combinations of centre members and side members on the failure modes and load-carrying capacity of bolted wood connection including numerical simulations and experiments were compared. The failure modes, including the yielding of centre member, the yielding of side member, and the yielding of the bolt, as well as the rigid rotation of the bolt, all reappeared by the finite element modeling with the porous constitutive model. The predicted deformation shapes and load-displacement relations of bolted wood connections were compared with experimental ones, and good correlations were observed. This paper presents a new approach to simulate the local embedment crushing of bolt groove in wood connections.
1. Introduction
Finite element (FE) numerical simulation of the localized problem in wood structure is always a difficult issue due to the inevitable differences between FE results and experiment results. The reasons causing the differences involve the high variable mechanical properties of wood, differences between clear wood and structural wood, size effect, defects of wood, effect of moisture content, duration of load, and even the test method for material parameters for the localized compression wood. Hence, to reduce the differences between FE simulation and experiment, some hypotheses were adopted in FE modeling to calibrate the mechanical parameters. For example, Moses reduced the initial modulus to cover the work-hardening behaviour of wood, and a multiplier 0.01 was used in the modeling [1]. Guan adopted a modification factor of the empirical modulus to simulate the stiffness of the flat nail embedment test, where a multiplier 0.25 was used [2]. Barrett developed a FE modeling using a foundation material model and limit foundation zone around bolt hole of 4.5 times of diameter of the bolt to simulate the localized problem of nailed connections in wood [3]. Sandhaas developed a continuum damage mechanics model including eight types of failure modes to simulate the performance of timber joints with the slotted-in steel plate, where the size effect for fracture energy was taken into consideration by means of the characteristic element length [4]. By utilizing the modification factors, the simulation results were consistent with those of corresponding experiments. However, the modification factors are always...
empirical coefficients which are dependent on the experiences of sophisticated engineers.
Difference induced by the test method for mechanical parameter is also one source for the differences between simulation results and experiment results. The mechanical parameters for the constitutive model in FE modeling were usually determined through uniaxial compression or tension tests. However, in bolted wood connection, the stress state in wood groove is not uniaxial one. Localized wood groove is restrained by lateral wood, which usually deforms along the direction parallel to the grain including shear deformation and crushing deformation components. However, a stress-strain relation from the uniaxial test cannot describe accurately the stress state in wood groove. On the other hand, the dowel-bearing strength test specified in ASTM D5764-97a only specifies the average embedment strength of groove [5]. The embedment strength is also different with the strength from the uniaxial test due to different stress states. Hence, a confined compression test of the wood cylinder was conducted to obtain the real deformation-compression relation in wood groove. A new approach to simulate the localized issue of wood groove in bolted connection by applying the porous constitutive model for wood groove was established to mitigate the dependency on the experiences.
A three-dimensional (3D) FE modeling developed in this paper is based on the phenomena of failure process and failure model of wood groove in bolted connection. During the contacting between bolt and wood groove, localized wood groove is compressed and wood void becomes less and less. If without enough end distance (7d) for the connection, wood groove will crack along the direction of load and shear failure will happen. However, for the connection with enough end distance, only localized wood will be crushed and then plastic hinge may appear in the bolt. In the process of groove crushing, the embedment stiffness of connection changes with the changing of the contact state. At the beginning of contact, embedment stiffness is small. Then, it becomes bigger and nearly keeps a constant. When groove crush is happening, embedment stiffness increases steeply which means that groove becomes compact and the wood void becomes small. In the numerical modeling, the effect of embedment stiffness and strength will be reflected in the porous constitutive by the corresponding relationship between void ratio of wood and pressure on the porous medium.
2. Porous Constitutive Model for Wood
Wood can be seemed as a three-phase medium which is composed of wood solid, liquid, and gas. The wood substance components of wood are the product of wood parenchyma. The liquid component is usually water, and the gas component is usually air. The gaps between the wood substance are called voids. The voids may contain air, water, or both. The void ratio \( e \) is the proportion of the volume of voids with respect to the volume of wood substance [6]. Volume of wood changes due to the water expelled from the voids. Mechanical behaviour of wood is also largely dependent on the proportion of wood solids versus voids.
When wood is localized compressed, crushing failure is one of typical failure modes and its void ratio becomes less and less. In the elastic stage, the relationship between void ratio and compression stress can be described by a differential equation, the change of the void ratio and the change of logarithm of the equivalent pressure stress [7], shown in the following equation:
\[
de = -k \, d \left[ \ln \left( p + p^3 \right) \right],
\]
\[
p = \frac{1}{3} \left( \sigma_R + \sigma_T + \sigma_L \right),
\]
where \( e \) is the void ratio of wood; \( p \) is the equivalent pressure stress; \( \sigma_R \), \( \sigma_T \), and \( \sigma_L \) are stress components in the directions of radius, tangent, and longitude, respectively; \( k \) is the value of the logarithmic bulk modulus, a dimensionless material parameter, which is the slope of the curve between void ratio and the logarithm of the equivalent pressure stress when wood is confined compressed, and it describes the detailed shape of void ratio vs. stress; and \( p^3 \) is the tensile strength of wood.
After using the equivalent pressure stress, the total stress and deviator stress have the following relationships [7]:
\[
\sigma = S - \rho I,
\]
\[
S = 2Ge,
\]
where \( \sigma \) is the total stress; \( S \) is the deviator stress; \( I \) is a unit matrix; \( G \) is the shear modulus; and \( e \) is the deviator strain [7], which can be expressed as
\[
e = \varepsilon - \frac{1}{3} \varepsilon_{vol} I,
\]
where \( \varepsilon \) is the total strain and \( \varepsilon_{vol} \) is the logarithmic volumetric strain; and \( \varepsilon_{vol} = \ln \left( \frac{dV}{dV_0} \right) \), where \( V \) is the volume of wood and \( V_0 \) is the initial volume of wood. Then, the stress and strain can be solved by the above equations.
3. Confined Compression Test of Wood
A setup for the confined compression test was devised to conduct the experiments for obtaining the relationship between void ratio of wood and equivalent pressure in the direction of parallel to grain, shown as in Figure 1(a). A wood cylinder made of the species of Pinus Sylvestris var. mongolica was inserted into the steel block through a round hole bored in the block. Then, the wood cylinder was compressed by a steel cylinder which was fit to the hole. The diameters of the wood cylinder and the hole are both 20 mm. After sanded by the sand paper, the wood cylinder was inserted in the hole. During the test, the compression velocity of the cylinder was controlled at a rate of 0.5 mm/min [5, 8] and the compression load and displacement were recorded. The information for wood cylinders is shown in Table 1.
Seven wood cylinders with different initial density and different initial void ratio were compressed parallel to grain. Figure 1(b) shows the typical crushing failure mode of the cylinder. The wood cylinders were shortened, and diagonal
cracks appeared. Figure 2 shows the curves of stress versus elongation parallel to grain from the confined compression testsof wood cylinders.
Based on the relationship among three components including wood substance, water, and void [9], the initial void ratio of wood can be expressed by
\[ e_0 = \frac{(1 + w)\rho_{wp}}{\rho_0} - 1 = \frac{(1 + w)\rho_{wp}S}{m_0} - 1, \]
where \( e_0 \), \( w \), and \( \rho_0 \) are initial void ratio, moisture content, and density of wood, respectively; \( \rho_{wp} \) is the density of the wood solids, for different wood species, \( \rho_{wp} = 1.50 - 1.56 \text{ g/cm}^3 \), and here an average value [6] was applied; and \( S, l_0 \), and \( m_0 \) are the cross-section area, initial length, and mass of wood cylinder specimens, respectively. The initial void for wood cylinder specimens is shown in Table 1.
For the confined compression test, the longitudinal strain is not zero, while the tangent strain and radial strain are both zero, which can be derived by the following equation:
\[
\begin{bmatrix}
\frac{1}{E_L} & \frac{v_{SL}}{E_L} & \frac{v_{TL}}{E_T} \\
\frac{v_{LR}}{E_L} & \frac{1}{E_R} & -\frac{v_{TR}}{E_T} \\
\frac{v_{LT}}{E_L} & \frac{v_{RT}}{E_R} & \frac{1}{E_T}
\end{bmatrix}
\begin{bmatrix}
\sigma_L \\
\sigma_R \\
\sigma_T
\end{bmatrix}
= \begin{bmatrix}
\varepsilon_L \\
0 \\
0
\end{bmatrix}.
\]
Then, the radial stress and tangent stress can be expressed by the longitudinal stress, shown in the following equations:
\[ \sigma_R = \frac{v_{LR} + v_{LT}v_{TR}}{1 - v_{RT}v_{TR}} \frac{E_R}{E_L} \sigma_L, \]
(7)
\[ \sigma_T = \frac{v_{LT} + v_{LR}v_{RT}}{1 - v_{RT}v_{TR}} \frac{E_T}{E_L} \sigma_L, \]
(8)
For the tested wood species, the elastic ratio and Poisson’s ratio [10] are shown in Table 2. After applying the elastic ratio and Poisson’s ratio, the equivalent stress of the confined compression wood cylinder can be solved, \( \sigma_R = 0.041\sigma_L, \) \( \sigma_T = 0.031\sigma_L, \) and \( p = -0.357\sigma_L, \) respectively.
4. FE Modeling and Validation of Embedment Crushing of Wood Groove
4.1. 3D FE Modeling for Bolted Wood Connection. A 3D FE modeling for bolted connection in wood was created using C3D8 solid elements in ABAQUS [7]. Surface contact between wood groove and steel bolt was taken into consideration with the coefficient of friction of 0.15 [11]. The material property of perfect porous elasto-plasticity was assigned to the wood groove zone around the three times of bolt diameter according to crushing deformation in experiment results and FE calculation. A Drucker–Prager plasticity was assigned to wood in the groove zone. The material angle of friction of wood was set as 11°, and dilation angle was zero [4]. An orthotropic elasticity property was assigned to other zones of wood. A perfect elasto-plasticity property was assigned to the steel bolt. The requisite material properties used in FE modeling are listed in Table 3. Here, the properties of clear wood were assigned to the pin groove due to the fact that the wood without defects was usually chosen to make joints and only localized crushing occurred at the joint zone with enough end distance (7d). The dependent relationship of the logarithmic bulk modulus on change of void ratio was implemented in a user defined subroutine UFIELD in which a user defined field variable was defined as the void ratio of each integrate point in the FE software ABAQUS [7].
4.2. Test of Single Bolted Wood Connection. To validate the FE modeling with the perfect elasto-plastic porous constitutive model, 12 lateral resistance tests of single bolt connection of wood made of the species of Pinus sylvestris var. mongolica were conducted in the direction of parallel to grain according to ASTM D5652 [8]. The dimensions of centre member and side member of connections are all 150 mm in the direction of parallel to grain and 80 mm in the direction of perpendicular to grain, shown as in Figure 4. The diameters of the bolt and groove are 10.5 mm and 13 mm, respectively. The side distance is 40 mm and end distance is 100 mm for every connections. Four groups of thickness combinations for connection specimens, three samples per
\[
\Delta e = e_0 - e = \frac{\Delta h}{h_0} (1 + e_0),
\]
where \( \Delta e \) is the change of void ratio of wood, \( h_0 \) is the initial length of the wood cylinder, and \( \Delta h \) is the compressive deformation of the wood cylinder. After calculating the equivalent stress \( \rho \) and \( \Delta e \), curves of the equivalent stress versus the change of void ratio can be obtained, shown as in Figure 3.
Comparing the curves from the experiments of seven wood cylinders in Figure 3(a), the curves of different cylinders with different initial void ratios are close to each other except the specimen S5. However, an average curve of equivalent stress versus change of void ratio can reflect the compression behaviour of wood with the boundary condition of confined restrain. Based on equation (1), the logarithmic bulk modulus of wood was calculated by the average curve. From the average curve shown in Figure 3(b), it can be found that the logarithmic bulk modulus \( k \) is not a constant, which reflects three stages of the contact between wood groove and bolt. At the beginning of compression, the logarithmic bulk modulus decreases rapidly until bolt and wood groove contact closely. Then, it nearly keeps a constant. Finally, it climbs rapidly at the same time plasticity is yielded in wood groove. Here, a regressed relationship between the logarithmic bulk modulus \( k \) and the change of void ratio \( \Delta e \) was expressed by equation (10) using a polynomial based on the average curve:
\[
k = 17.910 - 1.279 \times 10^3 \Delta e + 4.116 \times 10^4 \Delta e^2 - 6.850 \times 10^5 \Delta e^3 + 6.343 \times 10^6 \Delta e^4 - 3.298 \times 10^7 \Delta e^5 + 9.000 \times 10^8 \Delta e^6 - 9.980 \times 10^9 \Delta e^7.
\]
Table 3: The material properties for FE modeling.
| Requisite constants | Value |
|----------------------------------------------------------|-------------|
| Elastic modulus of wood parallel to grain | 9000 N/mm² |
| Yield stress of wood crushing parallel to grain of wood | 40.0 N/mm² |
| Tension strength parallel to grain of clear wood | 112.9 N/mm² |
| Average initial void ratio of wood cylinders | 2.944 |
| Elastic modulus of steel bolt | 2.06 × 10⁵ N/mm² |
| Poisson’s ratio of steel bolt | 0.3 |
| Yield stress of steel bolt | 235 N/mm² |
*The data are from experiments.
Figure 3: Compression curves of confined compressed wood cylinders parallel to the grain: (a) equivalent stress versus change of void ratio; (b) the logarithmic bulk modulus versus change of void ratio.
Table 4: Thickness combinations for bolted wood connections.
| | Combination 1 | Combination 2 | Combination 3 | Combination 4 |
|------------------------|---------------|---------------|---------------|---------------|
| Thickness of centre member, $t_{cm}$ (mm) | 40 | 40 | 60 | 60 |
| Thickness of side member, $t_{sm}$ (mm) | 30 | 10 | 30 | 60 |
Figure 5: Typical failure models of bolt connection with different thickness combinations both in tests and FE simulations: (a) combination 1: $t_{cm} = 40$ mm and $t_{sm} = 30$ mm; (b) combination 2: $t_{cm} = 40$ mm and $t_{sm} = 10$ mm; (c) combination 3: $t_{cm} = 60$ mm and $t_{sm} = 30$ mm; (d) combination 4: $t_{cm} = 60$ mm and $t_{sm} = 60$ mm.
Figure 6: Stress contours for wood grooves in (a) centre member and (b) side member (combination 1).
combination, were prepared, whose detail thicknesses are shown in Table 4.
4.3. Validation of FE Modeling. The deformations of all tested connections from different thickness combinations are shown in Figure 5. For each combination, one typical deformed connection and all three deformed bolts are exhibited in the same figure, including these from the tested connection and numerical modeling. The deformation of FE modeling shows good agreement with the experiment observation. Localized crushing failure of pin groove and plastic hinges in the steel bolts appears in different connections. It is obvious that crushing failure did appear at the compressive pin groove, and stress contours for combination 1 are shown in Figure 6. The stress concentration phenomenon and local crushing deformation occur under the contact surface between bolt and groove. The number of plastic hinges in bolts depends on the thickness ratio between the centre member and side member. For the combination 2, the thickness of side member is the thinnest among the four combinations, crushing failure appeared in side member, and the rigid body deformation happened in the bolt. Hence, there was no plastic hinge in the bolt in combination 2. Meanwhile, in combination 4, there were three plastic hinges in the bolt and two hinges in each shear plane. The FE modeling with perfect elasto-plastic porous constitutive exhibits the practicability to simulate the deformation of wood connection including localized deformation of groove and bolt’s deformation.
The load-displacement curves for all tested connections and FE simulations are shown in Figure 7. All curves showed the changes of stiffness of bolted connection. The stiffness becomes less and less with the increase in deformation when the localized wood and steel bolt come into plasticity. The
ultimate load from FE results was very close to the maximum loads among three experiment results. While the diameter of the bolt is large and wood members are thin, the yield of groove also can be simulated. The six yield modes for single shear and four yield modes for double shear can all be modeled by the FE modeling. Comparing the deformations of experiments and FE simulations, although the initial stiffness by FE modeling is a little bigger than those of experiments, the overall simulated curves are general accordant with those of experiment curves. The possible reason is that the contact gap between bolt and wood groove brings additional deformation. Hence, the initial stiffness in simulation is more than that of experiment.
5. Conclusions
A method to simulate the localized crushing failure of wood groove in bolted wood connection applying a perfect elastoplasticity porous constitutive model was developed. According to the three-phase composites of wood with solid, water, and gas, wood void ratio expression was derived. A confined compression of the wood cylinder was conducted for void ratio versus stress relationship. The tests can simulate the real stress state in wood groove and provide the FE parameter of wood species for numerical simulation. A relationship between wood void ratio and compression stress was established. The empirical constitutive model for localized crushing wood was validated by the good agreement between experiments and numerical simulations for bolted wood connection with enough end distance (7d). The FE modeling also can predict the load bearing capacity of the all yield modes for single shear and double shear. Its application may be expanded to simulate complex bolted connection in wood structures, such as multiple fastener connections.
Data Availability
The 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.
Acknowledgments
The authors thank the financial support of National Key Research and Development Program of China (no. 2019YFD1101001).
References
[1] D. M. Moses, Constitutive and analytical models for structural composite lumber with applications to bolted connections, Ph.D. Dissertation, University of British Columbia, Vancouver, Canada, 2000.
[2] T. Zhou and Z. W. Guan, “A new approach to obtain flat nail embedding strength of double-sided nail plate joints,” Construction and Building Materials, vol. 25, no. 2, pp. 598–607, 2011.
[3] H. Jung-Pyo and D. Barrett, “Three-dimensional finite-element modelling of nailed connections in wood,” Journal of Structural Engineering, vol. 136, no. 6, pp. 715–722, 2010.
[4] S. Carmen, Mechanical behaviour of timber joints with slotted-in steel plates, Ph.D. Dissertation, Technology University Delft, Delfts, Netherlands, 2012.
[5] ASTM D 5764-97a, Standard Test Method for Evaluating Dowel-Bearing Strength of Wood and Wood-Based Products, American Society for Testing and Materials, West Conshohocken, PA, USA, 2002.
[6] F. F. P. Kollmann, A. Wilfred, and J. R. Cote, Principles of Wood Science and Technology. 1 Solid Wood, Springer-Verlag New Yourk Inc, New York, NY, USA, 1968.
[7] D. S. Simulia, ABAQUS 6.14. ABAQUS Theory Guide, Dassault Systèmes Simulia Corp., Johnston, RI, USA, 2014.
[8] ASTM D 5652-95, Standard Test Methods for Bolted Connections in Wood and Wood-Based Products, American Society for Testing and Materials, West Conshohocken, PA, USA, 2002.
[9] M. D. Wood, Soil Behaviour and Critical State Soil Mechanics, Cambridge University Press, Cambridge, UK, 1990.
[10] D. W. Green, E. Winandy Jerrold, and E. Kretschmann David, Mechanical Properties of Wood, Wood as an Engineering Material, Forest Products Laboratory, Madison, WI, USA, 1999.
[11] W. Simpson and T. W. Anton, Physical Properties and Moisture Relations of Wood: Wood Handbook, Wood as an Engineering Material, Forest Products Laboratory, Madison, WI, USA, 1999.
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Introduction
Astaxanthin (Figure 1) is the main carotenoid pigment found in microorganisms (the yeast Phaffia rhodozyma and the algae Haematococcus pluvialis), aquatic animals and many of the seafood including salmon, trout, red sea bream, shrimp, lobster and fish eggs. It is also present in birds such as flamingoes and quails. Availability of astaxanthin has also been reported in mangrove flora, under different tidal conditions.
Figure 1 Structure of Astaxanthin.
The mangroves of Indian Sundarbans, being a reservoir of several bioactive substances may serve as future source of astaxanthin, although very few works have been carried out on this particular subject. Astaxanthin has several essential biological functions in animals and is known as a free radical quencher and powerful antioxidant reagent. Industrially, astaxanthin has been commercially exploited as a pigmentation source and feed supplement for marine fish aquaculture and poultry. It is evident, therefore, that astaxanthin is a molecule with potential to the pharmaceutical, food, cosmetic and medical fields.
The industrial production of astaxanthin has been successful in many parts of the world through series of chemical reactions, but the synthetic type is not similar to that found in nature as its stability and activity is lower than that of natural product. Therefore attention has been diverted for searching the natural source of astaxanthin. The deltaic complex of Indian Sundarbans at the apex of the Bay of Bengal (21°13′ to 22°40′ N latitude and 88°03′ to 89°07′ E longitude) sustains 34 species of true mangroves, which are specialized floral community found at the land-sea interface in the estuarine and coastal ecosystems (Figure 2).
These plants are characterized with the presence of pneumatophores, prop roots, still roots and viviparous germination and are exposed to tidal inundations twice in every 24 hours in this part of the Indian subcontinent. The important ecological requisites for the growth of these plants are water salinity (ranging from 2% to 30%), pH (around 8.00), tidal inundation and clayey-silty soil substratum typical for deltaic complex. Considering the immense ecological and economic benefits of these plants, the Govt. of India (Ministry of Environment and Forests) has taken up several programmes of afforestation and nursery development in and around Indian Sundarbans and hence proper back-up of raw materials exists in this region that can serve as natural source of astaxanthin.
Materials and methods
Sagar Island is the largest island of Indian Sundarbans (located between 21°31′ N to 21°53′ N latitude and 88°02′ E to 88°15′ E meridians) with an approximate area of 145sq.km. The entire network of the present programme consists of the sampling of five dominant mangrove species from the northern and southern tips of Sagar Island during April, 2016. These two sampling stations are drastically
Abstract
The astaxanthin level in the leaves of five dominant mangrove species, sampled from two different stations of Sager Island in western Indian Sundarbans region was studied during April, 2016. The two sampling stations selected at the northern and southern tips of the island exhibited drastic variation with respect to aquatic salinity, although other parameters like surface water temperature, pH, D.O. and nutrients were more or less uniform. Relatively higher astaxanthin level was observed in the high saline zone (southern tip) of the island, which indicates the regulation of astaxanthin level in the mangrove plants by ambient aquatic salinity. The inundated leaves of the selected mangrove plants showed more astaxanthin level in comparison to the exposed ones. The astaxanthin content of the mangrove leaves was in the order Heritiera fomes > Avicennia alba > Avicennia marina > Avicennia officinalis > Sonneratia apetala in both the sampling stations which points towards the species specificity of the carotenoid pigment.
Keywords: mangroves, astaxanthin, Indian sundarbans, tidal influx, salinity gradient
Volume 1 Issue 2 - 2017
Kakoli Banerjee,1 Goutam Roy Chowdhury,2 Abhijit Mitra1
1School of Biodiversity & Conservation of Natural Resources, Central University of Orissa, India
2Chancellor, Techno India University, India
Correspondence: Abhijit Mitra, Department of Marine Science, University of Calcutta, 35 B. C. Road, Kolkata 700 019, India, Tel: 9831269550, Email [email protected]
Received: April 25, 2016 | Published: May 03, 2017
MOJ Bioorganic & Organic Chemistry
Submit Manuscript | http://medcraveonline.com
Astaxanthin level of dominant mangrove floral species in Indian sundarbans
Astaxanthin level of dominant mangrove floral species in Indian Sundarbans
different from each other with respect to salinity as the northern tip of the island lies within the Hugli estuarine stretch, whereas the southern tip is located at the confluence of the river Hugli and the Bay of Bengal. Leaves of the selected species were collected during the low tide period from two different portions (submerged lower zone and exposed upper zone) of the same plant. The lower region of the tree is inundated during the high tide condition and the upper region of the same plant remains unexposed to tidal water. The collected leaves were thoroughly washed with ambient water followed by deionized water and oven dried at 110°C overnight. The estimation of carotenoid were separately carried out for each species through spectrophotometric method after extraction with DMSO and acetone and finally the carotenoid value was converted to astaxanthin percent as per the expression: Percent astaxanthin=Carotenoids (mg) extracted/ sample weight (mg)×80.
Water samples of both the stations were also collected simultaneously for analyzing the physico-chemical variables (surface water temperature, salinity, pH, DO, nitrate, phosphate and silicate) as per the standard methods.12
Results and discussion
The astaxanthin level in the selected mangrove species exhibits significant spatial variation (Table 1).
| Station | Mangrove species | Astaxanthin content (mg/kg) | Submerged | Exposed |
|---------------|------------------------|-----------------------------|-----------|---------|
| Kachuberia | Avicennia alba | 485.08 | 313.02 | |
| (salinity range: 1‰ to 9‰) | Avicennia marina | 409.66 | 298.73 | |
| | Avicennia officinalis | 388.02 | 267.44 | |
| | Sonneratia apetala | 156.14 | 94.32 | |
| | Heritiera fomes | 619.20 | 386.25 | |
| | Avicennia alba | 513.95 | 353.20 | |
| Sagar south | Avicennia marina | 449.36 | 340.13 | |
| (salinity range: 12‰ to 28‰) | Avicennia officinalis | 420.10 | 310.41 | |
| | Sonneratia apetala | 225.21 | 130.42 | |
| | Heritiera fomes | 680.22 | 391.02 | |
Table 1: Astaxanthin content in five mangrove species collected from two different stations of Sagar Island, Sundarbans during April 2016
The two sampling stations in the present programme are drastically different with respect to surface water salinity although other parameters are more or less uniform (Table 2).
Table 2: Physico-chemical variables of water samples collected from two different stations of Sagar Island, Sundarbans during April, 2016
| Parameters | Northern tip | Southern tip |
|---------------------------------|--------------|--------------|
| Surface water temp (°C) | 33.0±0.02 | 32.2±0.01 |
| pH | 8.0±0.01 | 8.2±0.01 |
| Salinity (psu) | 8.5±0.31 | 27.23±0.44 |
| DO (mg/l) | 5.82±0.23 | 6.01±0.19 |
| NO₃ (µgat/l) | 15.32±0.31 | 16.2±0.39 |
| PO₄ (µgat/l) | 1.72±0.05 | 1.45±0.04 |
| SiO₄ (µgat/l) | 85.90±1.07 | 91.24±0.98 |
The proximity of the southern tip of Sagar Island to Bay of Bengal may be attributed to high aquatic salinity in this zone. The relatively higher astaxanthin level in the plant parts collected from the southern tip of Sagar Island may be related to stress posed by high aquatic salinity. Similar variations of the pigment level with geographic location have been pointed out by several workers.13 In both the sampling stations, a uniformity was observed with respect to astaxanthin level of the mangrove leaves and it is in the order Heritiera fomes > Avicennia alba > Avicennia marina > Avicennia officinalis > Sonneratia apetala (Table 1). Astaxanthin occurs in several different forms and can be classified into stereoisomer’s, geometric isomers and free or esterified forms. All these forms are found in various natural sources e.g., the predominant stereoisomers of astaxanthin found in the Antarctic krill Euphausia superba is 3R,3R and the majority of this is esterified.14-16 The relative distribution of esters and optical isomers in some organisms is shown in Table 3. The level of astaxanthin detected in the mangrove floral species of Indian Sundarbans is less than the existing natural mega-reservoir of astaxanthin like Phaffia rhodozyma,17 Whyte18 and Haematococcus pluvialis.21 However considering the huge biomass of mangrove leaves in and around the area of Sundarban Biosphere Reserve (SBR), the standing stock of the carotenoid pigment has high probability to reach the point of compensation (requirement), provided few back-up nurseries in the region for extraction of bioactive substances are maintained.
The relatively higher astaxanthin content in the submerged leaves of mangrove plants confirms the synthesis of the pigment under stress condition. However, more studies are needed to establish the role of tidal influx and subsequent salinity fluctuation of the ambient aquatic phase on astaxanthin level in the mangrove floral parts. The present data may serve as baseline information on the regulatory role of tidal submergence on astaxanthin level in the estuarine and coastal vegetation. The enhancement of astaxanthin production under stressed condition of organisms is a matter of interest and several researches are still being undertaken to pinpoint the reaction pathway of astaxanthin production by inducing stress of varied nature. Many yeasts have been described with an increase ability to produce carotenoids when they grow under unfavorable environment.22 The enhancement of the accumulation of astaxanthin in cysts of Haematococcus pluvialis
Citation: Banerjee K, Chowdhury GY, Mitra A. Astaxanthin level of dominant mangrove floral species in Indian Sundarbans. MOJ Biorg Org Chem. 2017;1(2):25–28. DOI: 10.15406/mojboc.2017.01.00008
under salt stress conditions has been reported both in the dark and
light by several workers.\textsuperscript{23-31} The present study has pointed higher
astaxanthin level in those leaves of the mangroves that are inundated
for 10 to 12 hours by tidal waters (ambient water salinity during the
period of investigation was 8.50\% in the northern tip of Sagar Island
and 27.23\% in the southern tip of Sagar island) thus exposed to stress
caused by aquatic salinity. The steep enhancement of astaxanthin
level in the inundated Sundari leaves \textit{(Heritiera fomes)} irrespective
of the sampling stations (space) clearly reflects the highest degree of
stress posed by water salinity on this species. \textit{Heritiera fomes}, being
fresh water loving mangrove species cannot tolerate high salinity\textsuperscript{22}
and hence acceleration of astaxanthin production may probably be
a part of its adaptation to cope with the stenohaline condition of
coastal and estuarine environment that becomes acute during high
tide. The astaxanthin level of mangrove flora is thus a function of its
physiological system, which is extremely species specific.
| Astaxanthin | Free | Diester | Monoester | Ratio optical isomers |
|---------------------------------|------|---------|-----------|-----------------------|
| *Euphausia superba* (Antarctic krill) | 5 | 64 | 31 | 9:21:70 |
| *Thysanoessa inermis* (Antarctic krill) | 4 | 61 | 35 | 55:07:38 |
| *Calanus finmarchicus* (Marine copepod) | 11 | 46 | 43 | 83:03:14 |
| *Acanthephyra purpurea* (Deep sea shrimp) | 20 | 43 | 37 | 20:44:15 |
| *Cancer pagurus shell* (Edible crab shell) | 58 | 22 | 13 | 20:24:56 |
| *Phaffia rhodozyma* (Red yeast) | 100 | | | 98:+:+ |
| *Haematococcus pluvialis* (Alga) | 5 | 59 | 22 | 4:8:88 |
*The free and esterified astaxanthin and ratio of optical isomers is based on refs 15-18.
In both plant and animal kingdoms, the protective role of
astaxanthin to tide over unfavorable environmental conditions is very
prominent. This carotenoid pigment plays many important functions
in fishes, crustaceans and several aquatic animals like improved
protection against oxidation and photo-oxidation, reproduction
and development, immune response, resistance to diseases and
communication system. Recent research shows that astaxanthin acts
like a vitamin for salmon. Now-a-day astaxanthin is used as a source
of pigmentation for fish in aquaculture and for eggs in the poultry
industry.\textsuperscript{35} It also recognized as having a higher antioxidant activity
than other carotenoids,\textsuperscript{34,35} Kobayashi\textsuperscript{36} and hence has a great role to
play in the sector of aqua cultural feed and poultry feed production.
The present research has immense relevance in the framework of
Indian Sundarbans as several small scale mangrove based astaxanthin
industries like cattle feed, fish feed, poultry feed units can be set up
involving the local people.
This will not only improve the quality of products, but can bind
substantial number of island dwellers in the matrix of alternative
livelihood schemes, who otherwise are engaged in illegal intrusion
in the mangrove forest for exploitation of natural resources, poaching
of wild animals, honey collection, prawn seed collection and several
anti-conservation related activities.
**Acknowledgements**
This research is a part of GRC Vision 2025 programme, which is
the brain child of Chancellor, TIU to eradicate poverty, over population
and pollution initially at local scale and then at regional and global
scales. The road map for this programme includes the promotion of
Green technology, Agri-Biotechnology, Hydroponics, Zero Emission
transportation and low cost fly ash based structures and propagating
the same through special Franchise Model developed by Prof. Sujoy
Biswas, CEO of TIU, and West Bengal.
**Conflict of interest**
The author declares no conflict of interest.
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Factors Influencing Electric Vehicle Penetration in the EU by 2030: A Model-Based Policy Assessment
Stergios Statharas *, Yannis Moysoglou, Pelopidas Siskos, Georgios Zazias and Pantelis Capros
E3MLab, Department of Electrical and Computer Engineering, National Technical University of Athens, 9 Iroon Politechniou Street, Zografou Campus, 15773 Athens, Greece
* Correspondence: [email protected]
Received: 21 June 2019; Accepted: 11 July 2019; Published: 17 July 2019
Abstract: The European Commission (EC) has set ambitious CO₂ emission reduction objectives for the transport sector by 2050. In this context, most decarbonisation scenarios for transport foresee large market penetration of electric vehicles in 2030 and 2050. The emergence of electrified car mobility is, however, uncertain due to various barriers such as battery costs, range anxiety and dependence on battery recharging networks. Those barriers need to be addressed in the 2020–2030 decade, as this is key to achieving electrification at a large scale in the longer term. The paper explores the uncertainties prevailing in the first decade and the mix of policies to overcome the barriers by quantifying a series of sensitivity analysis scenarios of the evolution of the car markets in the EU Member States and the impacts of each barrier individually. The model used is PRIMES-TREMOVE, which has been developed by E3MLab and constitutes a detailed energy-economic model for the transport sector. Based on model results, the paper assesses the market, energy, emission and cost impacts of various CO₂ car standards, infrastructure development plans with different geographic coverage and a range of battery cost reductions driven by learning and mass industrial production. The assessment draws on the comparison of 29 sensitivity scenarios for the EU, which show that removing the barriers in the decade 2020–2030 is important for electrification emergence. The results show that difficult policy dilemmas exist between adopting stringent standards and infrastructure of wide coverage to push technology and market development and adverse effects on costs, in case the high cost of batteries persists. However, if the pace of battery cost reductions is fast, a weak policy for standards and infrastructure is not cost-effective and sub-optimal. These policies are shown to have impacts on the competition between pure electric and plug-in hybrid vehicles. Drivers that facilitate electrification also favour the uptake of the former technology, the latter being a reasonable choice only in case the barriers persist and obstruct electrification.
Keywords: transport sector decarbonisation; electric vehicles; energy-economy model; transport modelling; recharging infrastructure; battery costs; CO₂ standards
1. Introduction
In its Clean Planet for all [1] and European Strategy for low-emission mobility [2] initiatives, the European Commission (EC) confirmed the adoption of ambitious CO₂ emission reduction objectives for the transport sector to 2050. The EC strategy aims at reaching at least a 60% reduction in greenhouse gas (GHG) emissions in transport by 2050 relative to 1990. This target was originally set in the White Paper [3]. Electrification of mobility is a valid option for supporting decarbonisation in the transport sector if electricity generation is also low in carbon emissions. Both options are part of the European strategy for energy and climate policies.
Electric vehicles, including battery electric vehicles (BEVs), plug-in hybrids (PHEVs) and range extenders (REEVs), started to slowly emerge in the markets during the last decade. The sales recorded
an increase from 436.9 thousand units in 2017 to 636.5 thousand units in 2018, according to the European Alternative Fuels Observatory [4]. The increase in sales is noticeable, but there is room for improvement. Car manufacturers need to invest further to be able to deliver affordable alternatives to the EU car market, within a transition aiming at achieving CO\(_2\) emission reduction targets by 2030. The current planning foresees a reduction of average CO\(_2\) emissions of new car registrations in 2030 by 37.5\% relative to 2021.
Several long-term scenarios foresee electrification of car mobility at least in the period after 2030 as a cost-effective option for decarbonisation in the EU and other countries. The usual scenarios combine electrification with a drop of battery costs driven by massive production and development of a large network for battery recharging [5–10].
Although the long-term picture seems clear enough according to studies found in the literature, the developments anticipated to take place in the early stages still remain uncertain. The decade 2020-2030 is crucial in preparing the grounds for the massive transition towards electrification. Investments in recharging infrastructure have to start as soon as possible, as its existence is important for the adoption of electric cars by consumers and range anxiety is considered a major obstacle. The battery industry needs to undergo technological restructuring, at least in the EU, and also invest in the learning potential. Decreasing battery costs is also decisive for consumers, as at present, electric cars are expensive compared to conventional technologies. Policy interventions intended to trigger the technology adoption process are also uncertain and seem costly in case it is decided to rely on car subsidisation.
The present paper explores the decade 2020–2030 while focusing on factors that may lead to successes or failures for the launching of the electric car market. Overcoming barriers deserves to become a policy priority, as it is of high importance, especially in the early stages of the electrification. A vast literature identified and analysed such barriers, including cost barriers [11,12], technical features of cars implying range anxiety [13–16] and dependence on availability and coverage of battery recharging networks [17,18]. The analysis presented in [19] confirmed that the barriers negatively impact on consumers’ perception of electric cars, causing uncertainty and reluctance to invest. Fiscal measures (i.e., subsidies) to incentivise the adoption of electric vehicles are proposed in the literature [20,21] together with innovative business models [22] for car marketing and the development of the recharging infrastructure [23–25].
Research and development policies and public-private partnerships are also important for tapping into the learning potential of batteries [26]. CO\(_2\) car standards, if anticipated to decrease over time, is an appropriate policy measure for building confidence about the development of a large market for batteries and electric cars in the future. Long-term visibility is the major precondition for the industry to embark in massive investment in new technologies and transform the car manufacturing sector on a large scale [27]. The development of battery recharging networks is at the discretion of public policy, either directly, in case investment is made by bodies subject to public regulation (e.g., distribution system operators and other licensed bodies), or indirectly, in case the state adopts the relevant legislative framework, also allowing private bodies to invest. All the factors mentioned in this paragraph require successful coordination and appropriate timeliness of decisions and construction works, in an aim to avoid market coordination failures, which are usual in such large endeavours.
This paper aims to provide a quantitative analysis of the factors influencing electric vehicle penetration in the EU in 2030. Model-based analyses of this type often assess the impacts of individual barriers or policy instruments [28–31]. However, there is a lack of comparative impact assessments of all the barriers/factors that influence the market uptake of electro-mobility technology.
The quantitative assessment uses a large set of scenarios-sensitivities (projection for the EU until 2030) performed using the PRIMES-TREMOVE energy economic model, developed by E3MLab. The model allows for an evaluation of the impacts of each barrier type on the market, and of the cost-benefit of policies that could remove those barriers. The analysis covers all 28 EU member states (MS), but the results presented in this paper are for the EU28, as a whole.
The barriers under consideration are split into: (1) Techno-economic uncertainty factors such as battery costs and vehicle range autonomy; (2) recharging infrastructure regarding coverage and timeliness of development. The model runs for a sensitivity analysis assuming different learning rates for the reduction of capital costs of batteries, which rely on data drawn from the literature.
The analysis considers three alternative trajectories for the development of the recharging infrastructure until 2030. The minimum case assumes development only in urban areas and almost no coverage outside of highly populated areas. The maximum case assumes a timely development of recharging infrastructure also outside the urban zones, mainly using fast recharging stations.
Regarding policy options, the paper uses the model to evaluate the impacts of various levels of CO₂ standards on cars until 2030. The comparative assessment of model results (in total 29 cases) focuses on costs from the perspective of consumers and emission reductions on the horizon of 2030.
The paper is structured as follows: Section 2 presents the methodology; Section 3 presents a business-as-usual scenario; Section 4 presents the design of the sensitivity analysis scenarios and the corresponding model results; finally, Section 5 provides a short discussion and concludes the paper.
2. Methodology: Brief Presentation of the PRIMES-TREMOVE Transport Model
PRIMES-TREMOVE [32] is a large-scale economic-engineering model of passenger and freight transport and is part of the PRIMES modelling suite, a family of linked models covering all aspects of the energy system and the demand and supply sectors (see [33]). Recent applications of the PRIMES-TREMOVE model are found in [34,35]. PRIMES-TREMOVE projects are in future transport activity, the allocation of mobility to various transport modes (both road and non-road), the choice of technology for the dynamic renewal of the transport fleet, the use of the fleet in various trip types, the consumption of energy, emissions and costs. The dynamic projections cover the period until 2050 and 2070 by 5-year steps and for each European MS. The base year of the model is 2015. Figure 1 shows a schematic flowchart illustrating the interactions of the actors related to passenger transportation of households, as modelled in PRIMES-TREMOVE.
PRIMES-TREMOVE solves an equilibrium problem with equilibrium constraints and involves individual models for the demand of mobility and the supply by transport services and self-supply using private cars. The model solves a structural microeconomic optimisation problem for each decision-maker, with embedded technical constraints referring to transport engineering and behavioural parameters reflecting preferences, as well as to policy-related parameters that influence decisions. The decision-making problem runs dynamically in a sequential manner keeping track of all vintages of transport technologies.
Based on evolving technical and economic features of technologies and under the influence of policies, decision makers may purchase new transport means by making choices over a variety of candidate technologies and fuels, and may also consider a scrappage of old vintages. The demanders of mobility follow nested choices to allocate mobility and trip types to the transport modes, determine their rate of use and select technologies for investment. The choice controlling functions follow the discrete choice theory to adequately depict the heterogeneity of behaviours and decision circumstances and thus overcome the limitations of the representative agent hypothesis. The choice functions use utility and cost functions as arguments, which embed several parameters used to reflect behavioural factors (uncertainty, perceived costs, risk perception), as well as penalty factors to reflect technical, infrastructural and resource limitations, and policy-reflecting parameters.
The model simulates the balancing of demand and supply of transport services and self-mobility, through the concept of the generalised cost of transport which includes congestion (time of use), externalities and other factors along with costs. The model solves a mixed complementarity equilibrium problem, using the generalised cost of transport as a dual variable associated with the demand-supply balance. In a way, the model varies the generalised cost, which in turn influences the demand and supply behavioural modelling until reaching a balance. The cost of transport also includes transport fares that the model calculates endogenously on a cost-plus basis, eventually including subsidies for
certain public transport means. The mixed complementarity equilibrium also includes overall policy constraints, reflecting policy targets, and uses the associated dual variables to influence demand and supply. The targets may concern emissions, efficiency and renewable energy targets.
![Diagram of the structure of modelling passenger transportation]
**Figure 1.** Schematic representation of the structure of modelling passenger transportation.
Households are modelled to choose new vehicle equipment from a set of fleet and fuel choices provided by car manufacturers. Vehicle purchasing prices, as set by the manufacturing industry, change dynamically following cost-efficiency improvement curves that draw from engineering studies. Car manufacturers price their portfolio of electric vehicles (EVs) depending on the evolution of battery costs. Households compare costs, convenience and congestion to make a decision which also depends on penalty factors in case the density and coverage of refuelling/recharging infrastructure are not adequate. The model also includes subjective factors as additional costs. In this manner, the model captures travelling inconvenience (range anxiety), technical risk perceptions (regarding maintenance and performance), imperfect information and the opportunity cost of funding capital costs to reflect
the consumer conservatism towards choosing a new technology like an EV. The various cost elements constitute component of the generalised unit cost of transport services.
The model represents public policy based on fiscal instruments (e.g., subsidies, tax exemptions, etc.), tolling and congestion pricing, CO₂ or efficiency standards applying on vehicle manufacturing, overall policy targets and the extent and timeliness of infrastructure development. The model applies a penalty mechanism specifically by vehicle technology type, to discourage the production of vehicle varieties that do not comply with the standard, CO₂ or efficiency or both. The model captures the effects of the refuelling and recharging infrastructure by splitting the trip types into stylised geographic areas (i.e., metropolitan, other urban, highways, and other roads). In addition, the model includes public policy, e.g., campaigns aiming to increase the awareness of the new technology and reduce the subjective surcharges and thus enable the emergence of the new technology in the markets.
3. Business-As-Usual Scenario
3.1. BAU Scenario Background
The business-as-usual scenario (BAU) projects the development of the EU passenger transport system following trends which assume the implementation of currently adopted national and EU policies and measures, but no new measures in the future. The set of policies and measures included in the BAU scenario is in line with the Reference Scenario 2016 of the European Commission [36]. In particular, the BAU scenario does not include the most recent policies targeting car manufacturers (i.e., the post-2020 targets on car manufacturers). The projections of the business-as-usual scenario also consider member state-specific policies, such as mandatory blending obligations of biofuels, as well as incentives for the promotion of vehicles with advanced powertrains, such as subsidies, lower taxation and premiums and plans to support the electrification in private road transport. The BAU scenario follows the technology cost assumptions of the Reference Scenario 2016 and assumes a relatively pessimistic trajectory by 2030 (i.e., they are assumed to reach approx. 300 $/kWh by 2030). These assumptions are generally in line with the least optimistic developments from the analysis in [26].
3.2. BAU Scenario Results
Table 1 shows the main results of the business-as-usual (BAU) scenario related to passenger activity, energy consumption and CO₂ emissions from passenger cars. The activity of passenger cars increases by 0.8% p.a., driven by income growth and increased motorisation rates in the low-income EU Member States. The projection assumes that car manufacturers comply with the CO₂ emission standards, by marketing vehicles based on advanced internal combustion engines (ICE) and some of them equipped with a hybrid system on their powertrain. The share of vehicles with conventional ICE powertrains reduces in the BAU, mainly because of the penetration of full hybrids and to a less extent, plug-in hybrids. Despite a relative decline in their use, conventional ICE powertrains remain dominant in the market until 2030, as the scenario assumes no additional policies.
The policies promoting electrification are weak in the BAU scenario, and remain at the discretion of national governments. Thus, they are not sufficient to drive the penetration of electric cars in the BAU scenario, and in 2030, electrification remains a niche market with a maximum penetration of 7% for passenger mobility in the EU. The stock of EV vehicles represents only 5% of the entire fleet of passenger cars in 2030.
Table 1 shows the main results of the business-as-usual (BAU) scenario related to passenger activity, energy consumption and CO₂ emissions from passenger cars. The activity of passenger cars increases by 0.8% p.a., driven by income growth and increased motorisation rates in the low-income EU Member States. The projection assumes that car manufacturers comply with the CO₂ emission standards, by marketing vehicles based on advanced internal combustion engines (ICE) and some of them equipped with a hybrid system on their powertrain. The share of vehicles with conventional ICE powertrains reduces in the BAU, mainly because of the penetration of full hybrids and to a less extent, plug-in hybrids. Despite a relative decline in their use, conventional ICE powertrains remain dominant in the market until 2030, as the scenario assumes no additional policies.
The policies promoting electrification are weak in the BAU scenario, and remain at the discretion of national governments. Thus, they are not sufficient to drive the penetration of electric cars in the BAU scenario, and in 2030, electrification remains a niche market with a maximum penetration of 7% for passenger mobility in the EU. The stock of EV vehicles represents only 5% of the entire fleet of passenger cars in 2030.
The demand for oil products for cars decreases by 1.5% p.a. in the period from 2010 to 2030, mainly due to currently applied car standards. The share of biofuels in the energy mix is mainly driven by the legally binding target of 10% renewable energy in the transport sector (RES-T target) and by the reduction target mandated by the Fuel Quality Directive, and its amendment as in the ILUC Directive (EU 2015/1513). The legislation drives an increase in biofuels, which succeed to cover only 7% of the energy consumption of private cars by 2020. Beyond 2020, the amounts of biofuels remain relatively stable, assuming no further tightening of the RES-T targets in the BAU scenario. CO₂ emissions from
passenger cars decrease over time (1.3% p.a.), driven by the efficiency gains driven by the current car standards. The reductions seem to slow down after 2020, as the scenario assumes no new policies.
Table 1. Key results of the business-as-usual scenario related to passenger cars.
| Transport Activity (Billion p-km) | 2010 | 2020 | 2025 | 2030 |
|----------------------------------|-------|-------|-------|-------|
| Conventional diesel ICE | 2199 | 2380 | 2286 | 2216 |
| Full hybrid diesel | 2 | 168 | 367 | 488 |
| Plug-in diesel | 0 | 36 | 62 | 112 |
| Conventional gasoline ICE | 1979 | 1595 | 1378 | 1212 |
| Full hybrid gasoline | 4 | 174 | 345 | 460 |
| Plug-in gasoline | 0 | 43 | 74 | 121 |
| LPG/CNG/Flexi fuelled vehicles | 149 | 268 | 298 | 314 |
| Battery electric | 0 | 25 | 56 | 129 |
| Fuel cell | 0 | 0 | 2 | 9 |
| **Total** | 4333 | 4690 | 4867 | 5060 |
| **Share of conventional ICE** | 96% | 85% | 75% | 68% |
| **Share of full hybrids** | 0% | 7% | 15% | 19% |
| **Share of LEV ( )* ** | 0% | 2% | 4% | 7% |
| Energy consumption (Mtoe) | 2010 | 2020 | 2025 | 2030 |
|----------------------------------|-------|-------|-------|-------|
| Gasoline | 86.0 | 61.5 | 54.9 | 50.5 |
| Diesel | 83.8 | 79.7 | 76.2 | 74.3 |
| LPG/CNG | 6.4 | 10.0 | 10.6 | 10.8 |
| Biofuels | 7.5 | 11.1 | 10.6 | 10.4 |
| Electricity | 0.0 | 0.6 | 1.1 | 2.1 |
| Hydrogen | 0.0 | 0.0 | 0.0 | 0.2 |
| **Total** | 183.6 | 162.9 | 153.3 | 148.3 |
| **Share of diesel** | 46% | 49% | 50% | 50% |
| **Share of gasoline** | 47% | 38% | 36% | 34% |
| **Share of biofuels** | 4% | 7% | 7% | 7% |
| **CO₂ emissions (million tons)** | 2010 | 2020 | 2025 | 2030 |
| | 525 | 451 | 422 | 404 |
(* ) Low Emission Vehicles (LEV) include Plug-in hybrids (PHEV), Battery Electric Vehicles (BEV) and hydrogen fuel-cell powered vehicles (FCEV).
4. Sensitivity Analysis Runs: Design and Results
4.1. Design of the Scenarios
The model runs for sensitivity analysis which are variants of the main transport decarbonisation scenarios. The general policy context of a decarbonisation scenario assumes that all decision-makers in all sectors, including the transport sector, are aware of ambitious emission reduction targets for 2050 and anticipate structural changes in technology choices and energy markets. This awareness may induce a removal of non-market barriers, at least partially, and the easiness of market uptake of clean and advanced technologies in all sectors. It also induces good visibility of enlarged future markets for new technologies, which enables tapping into the potential of learning by manufacturers and technology developers. In this context, battery manufacturing also benefits and expects a high potential of cost reduction in the future, accompanied by an improvement of performance. At the same time, positive anticipation of electrification incites private investors and public policy-makers to develop a recharging and refuelling infrastructure for clean alternative fuels with adequate timeliness and sufficient coverage of urban and non-urban areas. Hence, current barriers impeding market uptake of EVs are alleviated.
Although the long-term prospects seem robust, the transition during the early stages of the process appear to be uncertain from various points of view. To explore these uncertainties, the paper
quantifies several sensitivity analysis scenarios which evaluate the impacts of market barriers related to infrastructure availability and battery costs, as well as several policy options for CO₂ standards. In particular, the paper discusses the impacts of different battery cost trajectories and varying degrees of coverage, and electricity recharging network availability in the presence of different CO₂ standards for car manufacturers. The sensitivities consider three different time series of CO₂ standards for the period until 2030, all foreseeing a decrease in the standard over time. The three standard cases are different from those presented in the announcements of the European Commission for the CO₂ standard for cars until 2030.
The assumptions on the evolution of the market barriers in the respective scenarios-sensitivities are discussed in more detail below.
4.1.1. Assumptions on the Development of Battery Costs
The evolution of battery costs is a key factor for market acceptance of electric vehicles by the consumers since batteries can considerably increase the purchasing price of the vehicle. The literature suggests that there is high uncertainty with regards to the cost reduction possibilities of the battery unit cost (usually expressed in terms of €/kWh). However, recent publications suggest that the learning potential may be higher than the estimated levels, as a considerable reduction of battery costs has taken place over the last 2–3 years, at a much faster pace than anticipated a few years ago.
This study considered three alternative trajectories regarding the development of battery costs until 2030, assuming optimistic, pessimistic and expected battery costs. The data draw on [26]. Battery costs decrease from 2020 onwards and influence market sales in the EU car fleet mainly between 2025 and 2030. In the pessimistic scenario (low learning case), battery costs reduce down to approximately 300 $/kWh in 2030 (same as in the BAU scenario). In the most optimistic scenario (high learning case), the cost is assumed to approach 120 $/kWh. The medium trajectory (medium learning case) assumes that costs decrease to 200 $/kWh in 2030. The battery costs appear in the model in the form of additional costs for the BEVs and PHEVs.
4.1.2. Assumptions on the Development of Recharging Infrastructure
The market uptake of electric vehicles strongly depends on future availability of recharging infrastructure and the degree of its coverage. A well-developed network of recharging points is likely to increase consumer acceptance of electric vehicles by reducing uncertainty regarding range anxiety. The model distinguishes the following cases regarding the development of the recharging infrastructure:
- **Level I**: Slow home charging points (3 kW AC), providing a full charge usually within 8 h. They are designed to equip the homes of EV users and can provide a full charge of the vehicle overnight.
- **Level II**: Semi-fast (22 kW AC) public charging points, located at parking lots and supermarkets and providing a full charge with 2-4 h, and
- **Level III**: Fast (50 kW DC) charging points, providing a full charge within approx. 15–20 min. Fast charging points aim to provide vehicle users with additional battery autonomy for longer trips and with charging times as close as possible to the duration of a typical refuelling at a conventional petrol station. These points are more likely to be located on central nodes outside metropolitan areas.
The scenario design considers three alternative options for the coverage of the recharging infrastructure until 2030.
(i) In the worst case scenario, users of electric vehicles can charge their vehicles mainly at their residences (i.e., Level-I charging points), as there is only minimum coverage of other places in urban areas, and almost no coverage outside highly populated areas.
(ii) The medium case assumes that the coverage of the recharging infrastructure develops in clusters within urban areas (mostly Level-II charging stations). The users driving within urban areas do not face recharging limitations, however, the coverage outside urban zones is minimum.
(iii) In the best case scenario, there is also a timely development of recharging infrastructure, but coverage is much broader also outside the urban zones, mainly based on fast recharging stations (Level-III stations).
The model uses data ratios of the number of electric cars being served by type of recharging point, drawn from the literature [37,38]. The size of the recharging infrastructure is endogenous in the model depending on the assumptions about the pace of investment and the geographic priorities of development, in conjunction with the size of the EV car market and its distribution by geographic area. For this calculation, the model makes the following typical assumptions:
- Level-I private home chargers, mainly deploying in urban areas, can serve 4 EVs per 3 chargers on average, as in highly populated regions space limitations apply.
- Level-II charging stations can serve 20 EVs per station in the early stages of infrastructure development and can serve 17 EVs per station when the infrastructure is large.
- The Level-III charging stations can serve approx. 100 EVs per station.
- The assumed ratios consider the possibility that the EVs owners may not fully recharge their car at home but only partially. They may also use Level-II charging stations to serve commuting and leisure mobility travelling. A broad development of the infrastructure can facilitate fast recharging and thus it can include the development of Level-III charging stations. Fast DC charging points mainly facilitate inter-urban mobility for EV cars.
The model includes the electricity recharging infrastructure costs as part of the total transport system costs and the total investment expenditures. The recovery of infrastructure costs is endogenously modelled. An additional fee is added to the prices of electricity for consumers charging the batteries. The authors assume a business model for the infrastructure that applies tariffs based on the calculation of the present value of a regulated asset basis divided by the present value of expected demand for electricity for battery recharging over a long period. In this way, a levelized unit cost of the infrastructure that is fully recouped by the fee applying on electricity prices can be calculated. The same approach is applied for the recovery of incremental investment expenditures needed to reinforce the electricity distribution system to accommodate the additional demand due to the recharging of batteries. An additional fee for the grid reinforcements applies on electricity prices for electric car users, defined so as to recoup the corresponding investment expenditures.
4.1.3. Sensitivity Analysis on the Policy Intervention
The European Commission has clearly announced the evolution of CO\textsubscript{2} emission standards that apply, on average, to the sales of car manufacturers in the EU. The policy foresees a reduction in the value of the standard (i.e., 37% reduction in 2030 relative to 2021). The application of the standard refers to a recently revised test cycle of emission measurements (WLTP, Worldwide Harmonised Light Vehicle Test Procedure, which replaced the NEDC, New European Driving Cycle).
For analytical purposes, the modelling considers different reduction paces of CO\textsubscript{2} car standards, to assess the relationship between the standards and the barriers, which concern battery costs, range anxiety and infrastructure availability.
Table 2 summarises the assumptions about the standards in the various cases modelled. The targets assumed by the model are based on the NEDC test cycle and not on the WLTP test cycle. The most optimistic scenario assumes a standard of 70 gCO\textsubscript{2}/km in 2030, while the least optimistic a standard of 80 gCO\textsubscript{2}/km. As already stated, the scenario that represents a business-as-usual case assumes the same target throughout the projection period.
Table 2. Stringency of CO\textsubscript{2} car standards.
| Policy Intensity for CO\textsubscript{2} Car Standards (gCO\textsubscript{2}/km) | 2021 | 2025 | 2030 |
|-----------------------------------------------|-------|-------|-------|
| High Stringency (70) | 95 | 80 | 70 |
| Medium Stringency (75) | 95 | 85 | 75 |
| Low Stringency (80) | 95 | 90 | 80 |
| BAU | 95 | 95 | 95 |
Table 3 defines sensitivity scenarios as combinations of policy intensity for infrastructure, battery cost reduction and CO\textsubscript{2} car standards. The table also shows the scenario acronyms.
Table 3. Overview of scenario configuration.
| Scenario Names | Infrastructure Coverage | Battery Costs and Performance | CO\textsubscript{2} Car Standard in 2030 (gCO\textsubscript{2}/km) |
|----------------|-------------------------|------------------------------|----------------------------------------------------------------|
| MI_MT_80 | MI—Medium level | MT—medium learning | 80 |
| MI_MT_75 | MI—Medium level | MT—medium learning | 75 |
| MI_MT_70 | MI—Medium level | MT—medium learning | 70 |
| MI_LT_80 | MI—Medium level | LT—low learning | 80 |
| MI_LT_75 | MI—Medium level | LT—low learning | 75 |
| MI_LT_70 | MI—Medium level | LT—low learning | 70 |
| MI_HT_80 | MI—Medium level | HT—high learning | 80 |
| MI_HT_75 | MI—Medium level | HT—high learning | 75 |
| MI_HT_70 | MI—Medium level | HT—high learning | 70 |
| LI_MT_80 | LI—Low level | MT—medium learning | 80 |
| LI_MT_75 | LI—Low level | MT—medium learning | 75 |
| LI_MT_70 | LI—Low level | MT—medium learning | 70 |
| LI_LT_80 | LI—Low level | LT—low learning | 80 |
| LI_LT_75 | LI—Low level | LT—low learning | 75 |
| LI_LT_70 | LI—Low level | LT—low learning | 70 |
| LI_HT_80 | LI—Low level | HT—high learning | 80 |
| LI_HT_75 | LI—Low level | HT—high learning | 75 |
| LI_HT_70 | LI—Low level | HT—high learning | 70 |
| HI_MT_80 | HI—Low level | MT—medium learning | 80 |
| HI_MT_75 | HI—Low level | MT—medium learning | 75 |
| HI_MT_70 | HI—Low level | MT—medium learning | 70 |
| HI_LT_80 | HI—High level | LT—low learning | 80 |
| HI_LT_75 | HI—High level | LT—low learning | 75 |
| HI_LT_70 | HI—High level | LT—low learning | 70 |
| HI_HT_80 | HI—High level | HT—high learning | 80 |
| HI_HT_75 | HI—High level | HT—high learning | 75 |
| HI_HT_70 | HI—High level | HT—high learning | 70 |
| LI_LT_65 | LI—Low level | LT—low learning | 65 |
4.2. Model Results
4.2.1. Impacts on Market Shares of EVs
The model projects the EV market shares until 2030 by scenario depending on the assumptions of each scenario, as shown in Table 3.
Figure 2, based on the model results, illustrates how several combinations of CO\textsubscript{2} car standards, infrastructure coverage and cost reduction of batteries drive the market share of EV cars in the EU in 2030. The variation range of the share is large. The minimum is 7% and the maximum is 18%. The drivers do matter for the share of EVs and the model projections go further until 2050. Due to lack of space, this paper does not show the projections after 2030. Nevertheless, it becomes clear that the share achieved in 2030 also matters for the share in the period after 2030, and at least until 2040.
Therefore, it is proposed that the policy choices behind the three drivers are of strategic importance for car mobility electrification.
High infrastructure coverage and high reduction of battery costs can lead to the highest EV market share in 2030 when combined with the most stringent CO₂ standard. Conversely, the lowest EV market
share in 2030 occurs when the pessimistic assumptions prevail for both the infrastructure and the battery costs, while the less stringent CO$_2$ standard also applies.
Based on the model’s results, it is inferred that the tightening of the CO$_2$ regulation on car manufacturers is a strong driver of EV market penetration in all cases assumed in the scenarios, irrespective of the particular assumptions made for costs and infrastructure. More specifically, the EVs reach 18% of the total car fleet in 2030 under the assumptions of the best-case scenario, assuming the tightest regulation (70 gCO$_2$/km). The model’s results show that the stock of BEVs and PHEVs increases by 2.6 percentage points and 2.0 percentage points respectively in 2030, when tightening the standard to 65 gCO$_2$/km compared to a scenario with a 70 gCO$_2$/km standard.
The model’s results show that the combination of stringent CO$_2$ car standards and high battery cost reduction can lead to similar levels of penetration of electric vehicles under high battery cost reduction and high infrastructure coverage, but only when combined with low policy intervention (i.e., 80 gCO$_2$/km). However, the adoption of strict standards (i.e., 70 gCO$_2$/km) is the main driver of market penetration of EVs and is effective even when the coverage of infrastructure is low (only in urban zones). In this case, EV cars conquer the urban mobility markets.
In case of a low reduction of battery costs, adopting more stringent CO$_2$ standards, i.e., from 80 to 70 gCO$_2$/km, can add six percentage points to the share of EVs in 2030, irrespective of the infrastructure coverage. Low coverage of the infrastructure leads to a drop of EV shares of 2–3 percentage points, on average across the scenarios. When the standard is set at 80 gCO$_2$/km, the other two factors imply that the EV shares have a maximum variation of 8 percentage points. However, when the standard is at 70gCO$_2$/km, the variation in terms of EV share is 3 percentage points.
All three factors appear to have significant impacts on the market uptake of electric cars by 2030 in the EU. The authors consider the model’s results for 2030 as a sample of meta-data that are used for statistical analysis.
Based on the meta-data, the CO$_2$ standard seems to have the largest impact, as the range of the median values of EV shares reach 6 pp. in 2030. The same range reaches 3 pp. for the infrastructure and battery costs. Figure 3 illustrates the effect of the three factors on the share of EVs in 2030, by plotting each factor alone. The dots represent EV market shares in 2030 for the various model runs.
To get a better insight into the simultaneous effects of the three factors on EV shares in 2030, a multiple regression estimation is performed which attempts to explain the EV market share through the logarithms of the values of the three factors. For the regression, the authors use the number of recharging points for the infrastructure, the unit cost of batteries and the value of the CO$_2$ car standard in 2030. As shown in Table 4, all three factors are highly significant statistically, as also is the multiple regression. The elasticity values (ratio of percentage changes) derived from a log-linear model are 0.23 for the infrastructure, −0.26 for the cost of batteries and −3.01 for the value of the CO$_2$ car standard.
Table 4. The results of multiple regression for the EV market shares in 2030.
| | Coefficient | Standard Error | t-Statistic | Lower t0.025(23) | Upper t0.975(23) | p-Value |
|---------------------|-------------|----------------|-------------|------------------|------------------|----------|
| Constant term | 1.766293 | 0.0828365 | 21.32655 | 1.594933 | 1.937654 | 0 |
| Infrastructure | 0.0282036 | 0.0022486 | 12.542546 | 0.0235519 | 0.0328552 | 9.10 × 10⁻¹² |
| Battery costs | −0.03139 | 0.0027207 | −11.537332 | −0.037018 | −0.025762 | 4.82 × 10⁻¹¹ |
| CO₂ car standard | −0.374582 | 0.0187071 | −20.023536 | −0.413281 | −0.335884 | 4.44 × 10⁻¹⁶ |
Adjusted R-squared = 0.964, F = 230.455825, p-value = 0.00000
CO₂ standards are highly important as stringent standards may eliminate EV competitors. Improved ICE engines and mainly the use of (non-plugin) hybrids can compete with EVs only up to a certain extent and can lose shares in the market if the CO₂ standard is below a certain threshold. At the same time, other alternatives to EVs such as fuel cell cars or ICE cars, using entirely carbon-neutral fuels (e.g., e-fuels, or fully fungible advanced biofuels), are not expected to be mature or available in the market until 2030. According to the results shown above, a policy ambitiously combining the three factors can induce 2–3 times the higher market share of the EVs in 2030, compared to a weak policy for all the three factors. A policy implication is that the decade 2020–2030 is important for successfully launching the EV car market regarding infrastructure development and the achievement of cost reduction in the battery industry, while stringent CO₂ car standards need to accompany structural policies during the same decade.
4.2.2. Impacts on the Relative Sales of Battery Electric Vehicles and Plug-in Hybrids
The choice of the type of electric vehicles, i.e., the uptake of BEVs versus PHEVs, also depends on the three factors that vary among the scenarios. The model’s results seem to indicate that the most important factor influencing the choice of the type of electric vehicle is the cost of batteries, as they evolve in the future. In scenarios including high battery cost reduction, the share of BEVs in the total fleet of electric vehicles is high, to the detriment of PHEVs. Inverse shares occur in scenarios that include low battery cost reductions. Figure 4 presents the relative shares of BEVs and PHEVs across all scenarios for 2025 and 2030.
BEVs are likely to get the lowest shares in the BAU scenario (27% and 33% for 2025 and 2030, respectively) in comparison to PHEVs, which get two-thirds of the market for electric cars. The BAU conditions, i.e., lowest end for all three factors, are detrimental to the market uptake of BEVs. Their shares in the BAU are the lowest among all scenarios.
The maximum share of BEVs in the total stock of EVs in 2030 occurs when the cost of batteries achieves the lowest values, and when infrastructure develops at the highest possible coverage. The reason is that BEVs can achieve significant savings in fuel expenditures compared to any other technology (including PHEVs), and this advantage pays off when capital costs are the lowest possible due to the decrease in battery costs. Range anxiety is also the lowest possible, due to the maximum possible development of the infrastructure. In the most optimistic battery cost reduction scenarios, the relative share of BEVs compared to PHEVs is likely to range from 56% to 67% in 2030.
Contrastingly, when capital costs are less competitive for the BEVs due to the high battery costs and range anxiety is significant due to the low density of the infrastructure, the shares of the BEVs in the total fleet of EVs is low. They could reach a share of 50% in the case of medium developments for battery costs and infrastructure, and even less than 40% in the most pessimistic developments scenario for battery costs and infrastructure. The contrast between shares in 2030 is much lower in 2025, as the electric vehicles market is still small.
Figure 4. Market shares of BEVs and PHEVs in the total fleet of electric cars.
As expected, the stringency of CO$_2$ standards is more beneficial for the BEVs as they are purely electric and emit no carbon dioxide compared to the PHEVs. However, as the CO$_2$ standards in 2030 are not yet below the threshold that can eliminate PHEVs, the impact on the choice of electric car types is limited compared to the effects of the other two factors.
The plots in Figure 5 show that the shares of BEVs in the total fleet of electric cars in 2030 are strongly and negatively correlated with battery costs, albeit weakly correlated with the development of infrastructure and the stringency of CO$_2$ standards. The authors further perform a multiple regression of the share of BEVs in the fleet of electric cars in 2030 explained by the three factors. Table 5 shows the statistical results. The regression is highly significant in statistical terms, but the battery costs are the only variable for which there is full statistical confidence. Statistically, the other two factors are of small significance. Therefore, the statistical analysis confirms that for 2030, the cost of batteries is the decisive factor for the market success of pure electric cars to the detriment of plug-in electric hybrid cars. The value of elasticity of the share of pure electric cars within the fleet of electric cars in 2030, depending on battery costs, is roughly $-0.40$. The stringency of CO$_2$ standards has a positive influence for the promotion of the BEVs to the detriment of the plug-in technology, as found in the statistical analysis, but the statistical significance of the coefficient is doubtful. This is related, however, to the range of CO$_2$ standards assumed in the scenarios, as it does not include highly stringent standards because they are not relevant for the horizon until 2030.
process and cannot happen in a short interval (e.g., ten years), as building the infrastructure and policies of biofuels, as, by assumption, biofuels develop as liquid fuels blended with mineral oil fuels by 2030. It seems difficult to develop fungible advanced biofuels, at least on a significant scale, on the 2030 horizon, as the production technologies have not yet reached the necessary technology readiness level. Electricity, therefore, seems to displace biofuels, albeit modestly, in the sensitivity scenarios, which is...
**Figure 5.** The distribution of the shares of BEVs in the total fleet of EVs in the EU in 2030.
**Table 5.** The results of multiple regression for the shares of BEVs in total EVs in the EU in 2030.
| | Coefficient | Standard Error | t-Statistic | Lower t0.025(23) | Upper t0.975(23) | p-Value |
|-------------------------|-------------|----------------|-------------|------------------|-----------------|-----------|
| Constant term | 0.779071 | 0.28181 | 2.764532 | 0.196104 | 1.362039 | 0.0110316 |
| Infrastructure | 0.0265788 | 0.0076499 | 3.474418 | 0.0107539 | 0.0424037 | 0.002052 |
| Battery costs | −0.203444 | 0.0092559 | −21.980087 | −0.222592 | −0.184297 | 0 |
| CO₂ car standard | 0.149722 | 0.0636415 | 2.352852 | 0.0180694 | 0.281375 | 0.0275711 |
Adjusted R-squared = 0.950, F = 166.910151, p-value = 8.88 × 10⁻¹⁶
4.2.3. Impacts on Final Energy Demand
As expected, in the BAU scenario, the petroleum products dominate fuel consumption by cars in the EU by 2030, maintaining a share close to 90% of the total, as restructuring policies are by this assumption weak in this scenario. Electrification is promoted in all alternative scenarios, albeit with policies of different intensity. Achieving maturity in the market for battery-based vehicles is a tedious process and cannot happen in a short interval (e.g., ten years), as building the infrastructure and achieving battery cost reductions need significant development time.
Consequently, the share of electricity in total energy consumption of cars remains relatively modest in the alternative scenarios for 2030 and range between 2–6%, depending on the intensity of the supporting policies. However, the consumption of electricity increases between 60% and 260% in the scenarios compared to the levels of BAU in 2030, as shown in Table 6. The range of the increase appears to be small at a first glance, but getting close to the high end of this range is important in cases where this is seen as the basis for launching the full transition to the electrification of cars in the period after 2030. Also, electric cars are roughly three times more efficient than ICE cars, and thus the relatively modest amounts of electricity consumption are not indicative of the share of EVs in the total stock of cars in 2030 in the alternative scenarios.
As shown in Table 6, the reduction in the consumption of petroleum products ranges between 6% and 16% in 2030 compared to the BAU, and of course, the largest decrease corresponds to the maximum intensity of the policies, which at the same time induce the highest demand for electricity among the sensitivity scenarios.
The decrease in consumption of petroleum products also implies a reduction in the consumption of biofuels, as, by assumption, biofuels develop as liquid fuels blended with mineral oil fuels by 2030. It seems difficult to develop fungible advanced biofuels, at least on a significant scale, on the 2030 horizon, as the production technologies have not yet reached the necessary technology readiness level. Electricity, therefore, seems to displace biofuels, albeit modestly, in the sensitivity scenarios, which is...
paradoxical from a climate policy perspective, but at the same time also explicable, due to the lack of advanced biofuel technologies. The stringency of the CO$_2$ car standards also drives an increase in the consumption of gaseous fuels in 2030, as the emission factor is slightly lower than petroleum products (at least for natural gas).
Table 6. Energy consumption of private cars in 2030 in the EU (difference and % change from BAU).
| | Electricity | Biofuels | Petroleum Products | Gaseous Fuels | Total Fuels |
|----------------|-------------|----------|--------------------|---------------|-------------|
| | Mtoe | % Change from BAU | Mtoe | % Change from BAU | Mtoe | % Change from BAU | Mtoe | % Change from BAU | Mtoe | % Change from BAU |
| BAU | 2.14 | 10.39 | 131.86 | 3.93 | 148.32 |
| LI_LT_80 | 2.90 | 36% | 10.65 | 2% | 123.46 | −6% | 4.49 | 14% | 141.51 | −5% |
| MI_LT_80 | 3.40 | 59% | 10.42 | 0% | 123.07 | −7% | 4.37 | 11% | 141.25 | −5% |
| LI_MT_80 | 3.49 | 63% | 10.45 | 1% | 123.66 | −6% | 4.34 | 10% | 141.94 | −4% |
| HI_LT_80 | 3.86 | 80% | 10.27 | −1% | 122.09 | −7% | 4.31 | 10% | 140.53 | −5% |
| LI_HT_80 | 4.11 | 92% | 10.30 | −1% | 123.23 | −7% | 4.23 | 8% | 141.86 | −4% |
| LI_LT_75 | 4.25 | 98% | 10.60 | 2% | 115.87 | −12% | 4.77 | 21% | 135.48 | −9% |
| MI_MT_80 | 4.34 | 103% | 10.17 | −2% | 121.85 | −8% | 4.24 | 8% | 140.61 | −5% |
| MI_LT_75 | 4.74 | 121% | 10.30 | −1% | 115.68 | −12% | 4.56 | 16% | 135.32 | −9% |
| LI_LT_75 | 4.88 | 128% | 10.34 | 0% | 116.50 | −12% | 4.56 | 16% | 136.27 | −8% |
| MI_LT_75 | 5.01 | 134% | 10.01 | −4% | 120.13 | −9% | 4.20 | 7% | 139.34 | −6% |
| HI_LT_75 | 5.10 | 138% | 10.12 | −3% | 115.46 | −12% | 4.45 | 13% | 135.14 | −9% |
| LI_LT_77 | 5.29 | 147% | 10.58 | 2% | 110.76 | −16% | 4.71 | 20% | 131.34 | −11% |
| HI_LT_77 | 5.39 | 152% | 10.16 | −2% | 117.09 | −11% | 4.39 | 12% | 137.03 | −8% |
| MI_MT_75 | 5.40 | 152% | 9.96 | −4% | 119.79 | −9% | 4.15 | 6% | 139.30 | −6% |
| LI_MT_75 | 5.42 | 153% | 10.03 | −3% | 116.34 | −12% | 4.34 | 11% | 136.14 | −8% |
| MI_LT_75 | 5.78 | 170% | 10.25 | −1% | 110.62 | −16% | 4.50 | 15% | 131.16 | −12% |
| HI_MT_75 | 5.94 | 178% | 9.85 | −5% | 115.78 | −12% | 4.24 | 8% | 135.81 | −8% |
| LI_MT_70 | 6.00 | 180% | 10.28 | −1% | 111.48 | −15% | 4.51 | 15% | 132.27 | −11% |
| MI_MT_70 | 6.12 | 186% | 9.84 | −5% | 116.47 | −12% | 4.19 | 7% | 136.62 | −8% |
| HI_MT_70 | 6.22 | 190% | 10.05 | −3% | 110.38 | −16% | 4.37 | 11% | 131.03 | −12% |
| HI_LT_70 | 6.51 | 204% | 9.71 | −6% | 116.92 | −11% | 4.10 | 4% | 137.24 | −7% |
| HI_MT_70 | 6.53 | 205% | 9.93 | −4% | 111.37 | −16% | 4.30 | 9% | 132.14 | −11% |
| LI_LT_70 | 6.57 | 207% | 10.06 | −3% | 112.15 | −15% | 4.37 | 11% | 133.15 | −10% |
| HI_LT_70 | 6.92 | 223% | 9.63 | −7% | 115.07 | −13% | 4.08 | 4% | 135.70 | −9% |
| HI_MT_70 | 7.01 | 227% | 9.74 | −6% | 111.15 | −16% | 4.18 | 6% | 132.08 | −11% |
| MI_MT_70 | 7.14 | 233% | 9.72 | −6% | 112.09 | −15% | 4.16 | 6% | 133.10 | −10% |
| HI_LT_70 | 7.78 | 263% | 9.52 | −8% | 111.45 | −15% | 4.04 | 3% | 132.79 | −10% |
The meta-data generated by the model for the sensitivity analysis scenarios allowed a statistical analysis of the dependence of electricity consumption on the three factors analysed in this paper, namely infrastructure, battery costs and CO$_2$ car standards.
As shown in Figure 6, all three factors appear to exert a significant influence on electricity consumption in 2030. The increase in the coverage of the recharging infrastructure influences electricity consumption positively. The infrastructure alone can induce 1.3 Mtoe in 2030 of additional electricity demand compared to the BAU. The reduction in battery costs is also an important driver pushing consumption of electricity upwards. Battery cost reductions can drive 1.8 Mtoe of additional electricity demand. The largest positive effect on electricity consumption derives from the CO$_2$ standards, which alone can increase demand for electricity by 2.0 Mtoe on average.
The statistical analysis for the market shares of battery-based cars, as presented above in Table 4, has led to similar conclusions, showing, in fact, there is a strong positive correlation (value of elasticity 1.05) between the consumption of electricity and the market share of electric cars in 2030. However, a similar analysis, presented in Table 5, concerning the market share or the BEVs has found a weak correlation of the shares with demand for electricity, probably because the BEV technology is very efficient in the consumption of electricity.
The multiple regression of electricity consumption, as seen in Table 7, using the three factors as independent variables, confirms that the CO₂ car standard exerts the highest inducement of electricity demand reduction among the three factors. The statistical significance of the regression is robust and the statistical confidence is very high for all the estimated coefficients. The values of the coefficients coincide with elasticity values, the most important of which is the elasticity for CO₂ car standards.
Table 7. The results of multiple regression for electricity consumption by cars in the EU in 2030.
| | Coefficient | Standard Error | t-Statistic | Lower t0.025(23) | Upper t0.975(23) | p-Value |
|----------------------|-------------|----------------|-------------|------------------|------------------|--------------|
| Constant term | 15.968025 | 1.045763 | 15.269256 | 13.804699 | 18.131351 | 1.57 × 10⁻¹³ |
| Infrastructure | 0.222129 | 0.0283877 | 7.824837 | 0.163405 | 0.280854 | 6.26 × 10⁻⁸ |
| Battery costs | -0.335291 | 0.0343474 | -9.761768 | -0.406345 | -0.264238 | 1.20 × 10⁻⁹ |
| CO₂ car standard | -3.173947 | 0.236167 | -13.439442 | -3.662494 | -2.685399 | 2.23 × 10⁻¹² |
Adjusted R-squared = 0.928, F(1,23) = 112.379595, p-value = 6.98 × 10⁻¹⁴
It is worth examining statistically the correlation of the three policy factors with total energy consumption by cars in 2030, with the aim of evaluating the implications for energy efficiency, which is among the main objectives of the EU policy during the period until 2030.
As depicted in Figure 7, the distributions seen separately for each of the factors clearly indicate that only the stringency of the CO₂ car standards has a robust causality with total final energy consumption of cars in 2030, towards improving the energy efficiency of car transport as a whole. The various car standards considered in the analysis imply a range of impacts on energy consumption that varies by 10 Mtoe in 2030 in the EU. The other two factors seem to be poorly correlated with total energy consumption of cars in 2030. The multiple regression, presented in Table 8, confirms the same statistical inference. Both the infrastructure and the battery costs are not statistically significant regarding the effects on total final energy consumption by cars in 2030, whereas there is strong statistical confidence regarding CO₂ car standards. According to this estimation, the value of elasticity of total final energy consumption with respect to the stringency of the CO₂ car standards is 0.45, which is noticeable despite the relatively small penetration of electric cars in the total car fleet by 2030. Thus, CO₂ standards are also beneficial for the energy efficiency policy target.
The changes in fleet composition and fuel consumption imply corresponding changes in the CO₂ emissions calculated as tank-to-wheel (TTW) emissions. The reduction in CO₂ emissions is a common feature of all sensitivity scenarios, in comparison to the BAU scenario, which by assumption includes a non-stringent CO₂ car standard set at 95 gCO₂/km for the entire period until 2030. Figure 8 shows the decline of CO₂ emissions in 2030 in the sensitivity analysis scenarios.
The main driver of emissions reduction is the stringency of the CO₂ car emissions since, as already explained, the level of the standard is a major driver for the increase in electricity demand and at the same time, reduction in total energy consumption. The standards enable energy efficiency improvement both via electrification and the uptake of highly efficient conventional cars. As electricity has zero direct emissions in final demand uses, a reduction in carbon emissions follows the increase in the demand for electricity. The set of scenarios assuming low stringency (80 gCO₂/km) involve a range of reductions in CO₂ emissions, namely 8% in the car segment, compared to BAU, whereas the highest stringency (70 gCO₂/km) approximately doubles emission reductions in 2030, i.e., 15% less than in the BAU, in 2030.
### Table 8. The results of multiple regression for total final energy consumption by cars in the EU in 2030.
| Coefficient | Standard Error | t-Statistic | Lower t0.025(23) | Upper t0.975(23) | p-Value |
|----------------------|----------------|-------------|------------------|------------------|-----------|
| Constant term | 3.012871 | 0.107147 | 28.118948 | 3.234522 | 0 |
| Infrastructure | −0.0079325 | 0.00290856 | −2.727291 | −0.0139493 | 0.0120103 |
| Battery costs | −0.00373267 | 0.00351919 | −1.060662 | −0.0110127 | 0.299855 |
| CO₂ car standard | 0.454467 | 0.0241973 | 18.781744 | 0.504523 | 1.89×10⁻¹⁵|
Adjusted R-squared = 0.932, F(1,24) = 179.162842, p-value = 3.77×10⁻¹⁵
Table 8. The results of multiple regression for total final energy consumption by cars in the EU in 2030.
| Coefficient | Standard Error | t-Statistic | Lower t0.025(23) | Upper t0.975(23) | p-Value |
|-------------------|----------------|-------------|-------------------|-------------------|----------|
| Constant term | 3.012871 | 0.107147 | 28.118948 | 2.79122 | 3.234522 |
| Infrastructure | -0.0079325 | 0.00290856 | -2.727291 | -0.0139493 | 0.0120103|
| Battery costs | -0.00373267 | 0.00351919 | -1.060662 | -0.0110127 | 0.00354732|
| CO2 car standard | 0.454467 | 0.0241973 | 18.781744 | 0.404411 | 0.504523 |
Adjusted R-squared = 0.932, F(1,24) = 179.162842, p-value = 3.77×10^-15
4.2.4. Impacts on CO2 Emissions
The changes in fleet composition and fuel consumption imply corresponding changes in the CO2 emissions calculated as tank-to-wheel (TTW) emissions. The reduction in CO2 emissions is a common feature of all sensitivity scenarios, in comparison to the BAU scenario, which by assumption includes a non-stringent CO2 car standard set at 95 gCO2/km for the entire period until 2030. Figure 8 shows the decline of CO2 emissions in 2030 in the sensitivity analysis scenarios.
The main driver of emissions reduction is the stringency of the CO2 car emissions since, as already explained, the level of the standard is a major driver for the increase in electricity demand and at the same time, reduction in total energy consumption. The standards enable energy efficiency improvement both via electrification and the uptake of highly efficient conventional cars. As electricity has zero direct emissions in final demand uses, a reduction in carbon emissions follows the increase in the demand for electricity. The set of scenarios assuming low stringency (80 gCO2/km) involve a range of reductions in CO2 emissions, namely 8% in the car segment, compared to BAU, whereas the highest stringency (70 gCO2/km) approximately doubles emission reductions in 2030, i.e., 15% less than in the BAU, in 2030.
4.2.5. Impacts on Car Mobility
The increasing stringency of CO2 car standards drives the uptake of electric and more efficient cars, which are more expensive than conventional technologies, at least during the period until 2030. If at the same time the technology progress of batteries is not sufficiently strong, battery costs are expected to be high, and thus the high purchasing costs of electric cars increase the cost of mobility by cars as borne by consumers. According to the model’s logic, an increase in the cost of transport by car implies a reduction of car transport activity, as consumers shift towards public transport and possibly also to less mobility if the cost impact is significant.
Conversely, if the adequate reduction in battery costs accompanies the stringency of the CO2 car standards, then the impact on transport costs by car is alleviated, and the reaction of consumers away from cars is mitigated.
Consequently, successfully tapping into the learning potential of batteries during the period until 2030 is an important condition for the acceptance of public policy targeting stringent CO2 standards in the same period. A mismatch between battery costs and CO2 standards can increase car transport costs for consumers. The ensuing social and economic adverse effects may challenge the policy-setting of standards.
The model results show, as depicted in Figure 9, that in the scenarios involving the highest reduction in battery costs, activity of car transportation reduces by only 0.4% to 0.5% down from activity levels in the BAU, irrespective of the intensity of the rest of the driving policies. In contrast, the lowest reduction in battery costs could imply a reduction in car transport activity above 1% in 2030, compared to the BAU, if at the same time policy-making adopts the most stringent CO2 car standards. However, if the policy adopts less stringent CO2 car standards (80 gCO2/km), the reduction in car transport activity is expected to be limited to 0.4% in 2030, compared to the BAU.
Thus, the sensitivity scenario results suggest that it is important to coordinate the expected pace of battery cost reduction and the rhythm of the decrease in the CO$_2$ car standard. This is difficult to achieve in practice, as high uncertainty surrounds technological progress. From a different angle, it is important for investors in technology and industry development of batteries and electric cars to have a clear long-term visibility of the rhythm of a decrease in CO$_2$ car standards, in order to make long-term investment commitments which are necessary to enable a fast pace technology cost reduction. Therefore, policy-makers have a challenging dilemma regarding standards, as they commit ambitiously, decreasing standards and risk facing adverse social effects, or moderate the stringency and the time length of commitments addressing concerns about economic and social impacts, and risk not being sufficient in order to enable technology progress and industrial development at full potential.
4.3. Comparison of Policy-Options Regarding Cost-Effectiveness
Each sensitivity scenario includes a different combination of policies regarding the three factors examined in this paper. Using the model’s results per scenario, it is worth evaluating the cost-effectiveness of the various combinations of the policy options. As far as costs are concerned, total transport costs are studied, and as far as effectiveness is concerned, CO$_2$ emissions are considered. The comparisons are meant as relative changes of costs and emissions compared to the BAU. The total transport cost calculation includes annuity payments for capital (for the purchasing of vehicles) and operating costs comprising fuel purchasing costs, as well as variable non-fuel and fixed operation and maintenance costs.
Theoretically, cost and effectiveness are inversely related to each other, as higher emission abatement usually implies higher costs. The results of the sensitivity scenarios plotted in Figure 10 confirm that the correlation between costs and effectiveness is negative. The figure shows cumulative cost differences from the BAU and cumulative emission abatement, compared to the BAU, during the period 2015–2040.
**Figure 9.** Change of passenger car transport activity, relative to the BAU, in the EU in 2030.
The CO2 standard becoming more stringent implies higher emission abatement, as the line moves to the right in the figure. At the same time, the lines shift upwards, which means that the costs increase when the cost reduction is higher. Further, their slope decreases when cost reduction is higher, which implies that the cost increase per unit of emission abatement (i.e., the marginal cost of abatement) is lower when battery cost reduction is high, compared to the cases where battery cost reduction is low.
An obvious statement, illustrated in Figure 10, is that the higher the cost reduction in battery costs, the higher the cost-effectiveness of emissions abatement. The graph shows three district lines grouping the different cases regarding cost reduction in battery costs. The lines move downwards when the cost reduction is higher. Further, their slope decreases when cost reduction is higher, which implies that the cost increase per unit of emission abatement (i.e., the marginal cost of abatement) is lower when battery cost reduction is high, compared to the cases where battery cost reduction is low.
The same graph shows three lines which group the cases regarding the level of the standard. The CO2 standard becoming more stringent implies higher emission abatement, as the line moves to the right in the figure. At the same time, the lines shift upwards, which means that the costs increase per unit of emissions abated when the standard becomes more stringent.
If scenario A (i.e., a policy combination) leads to higher emissions and higher costs than scenario B, it is inferred that the former is inferior to the latter from a cost-effectiveness perspective and should therefore not be taken into consideration.
For example, the high development of infrastructure and high reduction in battery costs is a more cost-effective combination than a medium or low development of infrastructure and a medium reduction of battery costs. However, as the policy instruments cannot guarantee certainty about the reduction pace of battery costs, the cost-effectiveness comparisons conditionally on the battery cost improvement need to be performed. There is no clear winner among the scenarios assuming a low reduction of battery costs, as increasing the development of infrastructure implies higher costs but also lower emissions.
A similar trade-off holds for the group of scenarios applying a medium development of infrastructure and for those applying a high development of infrastructure. The comparison of cost-effectiveness across the three groups with different paces of cost reduction of batteries indicates that successful technology progress can be very beneficial for both costs and emissions. The benefits
in both dimensions are much larger than the range of trade-offs that concern the development of infrastructure. In other words, the most important factor enabling high cost-effectiveness is the pace of the reduction of battery costs.
The right-hand side graph in Figure 10 confirms that battery costs are of crucial importance for costs needed to reduce emissions of CO$_2$ in car transportation. A low pace of cost reductions for batteries imply a two times higher average cost of CO$_2$ emission abatement compared to the pace of cost reduction when it is high. The differences in average abatement costs due to the extent of infrastructure development are much smaller than cost differences due to battery costs. Only the battery cost factor can sort the average abatement costs in monotone order. The value of the standard cannot drive alone a monotone order of average abatement costs, which implies that the optimum choice of the standard is conditional on the reduction achievement for battery costs.
5. Conclusions
This paper quantitatively assessed the impacts of three key factors that drive market penetration of electric cars, in the medium term, until 2030. These factors are battery costs, the coverage of the recharging infrastructure network and the CO$_2$ car standards. All three factors depend on policy choices, both directly and indirectly. The future cost of batteries depends on the volume of investment in technology improvement and massive industrial production, while the volume of investment crucially depends on the long-term visibility of the market size, which in turn also depends on the policy. The development of infrastructure depends on policy directly, when developed by regulated bodies, and indirectly, as conditions influenced by policy may or may not attract private investment in infrastructure. Finally, the CO$_2$ car standards, directly set by policy, are of high importance when it is anticipated that they will further reduce with regulatory certainty in the future.
To analyse the impact of these factors on EV market shares, the PRIMES-TREMOVE energy economic model was used for the transport sector, and a large number of projections were quantified which assumed different combinations for the three driving factors. Moreover, the model’s results were used as meta-data to perform comparisons and statistical inferences regarding causalities.
The authors conclude that all three factors have a non-negligible influence on the market shares of electric cars in the EU for the year 2030. Statistical analysis of the meta-data derived from the sensitivity scenarios shows that all three factors have a statistically significant impact on the market share of electric vehicles. The impacted range of EVs shares, as driven by the three factors, is large, namely between 7% and 18% in 2030.
The factor with the comparatively larger influence is the reduction of battery costs. High reduction implies a high share of EVs, irrespective of the intensity of the two other factors. A low reduction implies that even if the two other factors are at their maximum intensity (among the options examined in this analysis), the market share of EVs remains lower than in the case of a high reduction of costs. However, high intensity of policies implies 3 to 5 percentage points higher shares of EVs, compared to a policy of low intensity. Therefore, given the uncertainty surrounding future battery costs, it is worth increasing the intensity of policies for infrastructure and standards as a hedging instrument in case the policy targets electrification of car mobility. However, if cost reduction in battery costs proves to be low and at the same time the policy on standards is stringent, there may be non-negligible cost increases for consumers of car transportation. However, if policymakers refrain from adopting stringent standards to avoid the risk of affordability, the signal to technology and infrastructure developers is expected to be weak, and therefore the risk of low progress in both developments is likely to be high. Policy-making needs to balance the risks of cost increases and non-enabling technology progress. However, if the pace of battery cost reductions was known to be fast, a weak policy for standards and infrastructure is not cost-effective and sub-optimal with respect to the potential benefits from electrification. To investigate further the influence of possible reduction of battery costs, this study quantified an additional sensitivity scenario assuming high development of the recharging infrastructure, 70 gCO$_2$/km for the standards and battery costs reaching as low as 73 $/kWh in 2030 [39].
The results show that total EV share reaches 21% in 2030 i.e., 3 pp. higher compared to the HI_HT_70 scenario. BEVs increase their share by 1.7%, while PHEVs by 1.3%. Therefore, faster progress of the battery technology, compared to the assumptions used in the model-based analysis, can be a decisive factor for the market share of electric cars in 2030. A policy combining the three factors ambitiously can induce 2–3 times a higher market share of EVs in 2030, compared to a weak policy for all the three factors. A policy implication is that the decade 2020–2030 is important for successfully launching the EV car market regarding the infrastructure development and the achievement of cost reduction in the battery industry, while stringent CO₂ car standards need to accompany structural policies during the same decade.
Regarding the competition between BEVs and PHEVs, under specific conditions, the two electric vehicle types can represent two respective vehicle options that target different market segments.
- Due to their currently low range autonomy and limited coverage of recharging infrastructure, BEVs fit better urban transport commuting trips. PHEVs, on the contrary, inherit the benefits of the ICE conventional cars and can provide long-range trips running on the ICE when electricity depletes. Unconstrained mobility constitutes an advantage of PHEVs over BEVs, as the latter increasingly depend on the existence of a network of charging points.
- PHEVs are also cheaper, as they have a lower battery capacity compared to BEVs. The model’s findings show that once BEVs overcome their competitive disadvantage over PHEVs (low range, much higher purchasing price), they may become the dominant technology type (between the two). The dominance of BEVs over PHEVs, however, require a transition period before the former reaches adequate maturity. The transition period may vary from 5 to 10 or even more years, depending on the level of technical progress of the battery technology.
The low coverage of recharging infrastructure (i.e., mostly home charging points) acts as a stronger market barrier to BEVs, which are fully dependent on the existence of a well-developed network of charging points. PHEVs are also influenced but to a lower extent. The authors, therefore, conclude that the policies addressing the three barriers have impacts on the competition between pure electric and plug-in hybrid vehicles. Drivers that facilitate electrification also favour the uptake of the former technology, the latter being a reasonable choice only in case the barriers persist and obstruct electrification.
Furthermore, it has been shown that electrification is beneficial for energy efficiency. The analysis found that CO₂ car standards are an effective instrument for inducing the reduction of energy consumption in car transportation. The scenarios showed that standards were also an effective instrument for reduction of CO₂ emissions, as expected. Stringent standards can achieve above 15% of CO₂ emission reductions in the EU by 2030, compared to the BAU scenario.
Recent model-based studies for the car market in the EU find similar results. An application of the TIMES model in [40] has shown that the CO₂ car standards played an important role in emission reduction and promoted electrification, while in particular a stringent standard at 70 gCO₂/km may effectively reduce emissions significantly, already in 2030. Other model-based studies [7,29,31,40,41] differ in their results regarding which type of electric vehicle, i.e., BEV or PHEV, is likely to be the dominant choice in the future. However, they all share the view, which is also similar to our results, that factors such as battery cost reduction, removal of range anxiety and efficiency promotion greatly favour the choice of BEV.
The successful market uptake of EVs needs to also overcome barriers, other than economic and technological, which are related to the reluctance and conservatism of consumers. While the functional forms and the structure of the model allow the simulation of such factors, the authors acknowledge that further research needs to be carried out to quantify these factors and estimate which policy measures would effectively overcome consumer conservatism and reluctance in the uptake of EVs.
Finally, it should be stated that the authors acknowledge certain limitations in their analysis. An important limitation is the relatively low spatial resolution of the model (currently four region types),
since the model employed is not a transport network model. Moreover, range anxiety mostly applies to inter-urban trips of higher distance (in km), and therefore, a higher resolution would represent dependence on range anxiety in a more accurate manner.
**Author Contributions:** Conceptualization, P.C. and P.S.; Methodology, P.C., P.S. and S.S.; Software, S.S. and Y.M.; Validation, G.Z., P.C. and P.S.; Formal Analysis, S.S. and Y.M.; Investigation, S.S.; Data Curation, P.S. and S.S.; Writing-Original Draft Preparation, P.C., P.S. and S.S.; Writing-Review & Editing, P.C.; Visualization, G.Z. and S.S.; Supervision, P.S. and P.C.
**Funding:** This research received no external funding.
**Acknowledgments:** This research did not receive any specific grant from funding agencies in the public, commercial, or not-for-profit sectors.
**Conflicts of Interest:** The authors declare no conflict of interest.
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Extracting Exact Answers to Questions Based on Structural Links
Wei Li, Rohini K. Srihari, Xiaoge Li, M. Srikanth, Xiuhong Zhang, Cheng Niu
Cymfony Inc.
600 Essjay Road, Williamsville, NY 14221. USA.
{wei, rohini, xli, srikanth, xzhang, cniu}@cymfony.com
Keywords: Question Answering, Information Extraction, Semantic Parsing, Dependency Link
Abstract
This paper presents a novel approach to extracting phrase-level answers in a question answering system. This approach uses structural support provided by an integrated Natural Language Processing (NLP) and Information Extraction (IE) system. Both questions and the sentence-level candidate answer strings are parsed by this NLP/IE system into binary dependency structures. Phrase-level answer extraction is modelled by comparing the structural similarity involving the question-phrase and the candidate answer-phrase.
There are two types of structural support. The first type involves predefined, specific entity associations such as Affiliation, Position, Age for a person entity. If a question asks about one of these associations, the answer-phrase can be determined as long as the system decodes such pre-defined dependency links correctly, despite the syntactic difference used in expressions between the question and the candidate answer string. The second type involves generic grammatical relationships such as V-S (verb-subject), V-O (verb-object).
Preliminary experimental results show an improvement in both precision and recall in extracting phrase-level answers, compared with a baseline system which only uses Named Entity constraints. The proposed methods are particularly effective in cases where the question-phrase does not correspond to a known named entity type and in cases where there are multiple candidate answer-phrases satisfying the named entity constraints.
Introduction
Natural language Question Answering (QA) is recognized as a capability with great potential. The NIST-sponsored Text Retrieval Conference (TREC) has been the driving force for developing this technology through its QA track since TREC-8 (Voorhees 1999). There has been significant progress and interest in QA research in recent years (Voorhees 2000, Pasca and Harabagiu 2001).
QA is different than search engines in two aspects: (i) instead of a string of keyword search terms, the query is a natural language question, necessitating question parsing, (ii) instead of a list of documents or URLs, a list of candidate answers at phrase level or sentence level are expected to be returned in response to a query, hence the need for text processing beyond keyword indexing, typically supported by Natural Language Processing (NLP) and Information Extraction (IE) (Chinchor and Marsh 1998, Hovy, Hermjakob and Lin 2001, Li and Srihari 2000). Examples of the use of NLP and IE in Question Answering include shallow parsing (Kupiec, 1993), semantic parsing (Litkowski...
Identifying exact or phrase-level answers is a much more challenging task than sentence-level answers. Good performance on the latter can be achieved by using sophisticated passage retrieval techniques and/or shallow level NLP/IE processing (Kwok et al. 2001, Clarke et al. 2001). The phrase-level answer identification involves sophisticated NLP/IE and it is difficult to apply only IR techniques for this task (Prager et al. 1999). These two tasks are closely related. Many systems (e.g. Prager et al 1999; Clark et al 2001) take a two-stage approach. The first stage involves retrieving sentences or paragraphs in documents as candidate answer strings. Stage Two focuses on extracting phrase-level exact answers from the candidate answer strings.
This paper focuses on methods involving Stage Two. The input is a sentence pair consisting of a question and a sentence-level candidate answer string. The output is defined to be a phrase, called answer-point, extracted from the candidate answer string. In order to identify the answer-point, the pair of strings are parsed by the same system to generate binary dependency structures for both specific entity associations and generic grammatical relationships. An integrated Natural Language Processing (NLP) and Information Extraction (IE) engine is used to extract named entities (NE) and their associations and to decode grammatical relationships. The system searches for an answer-point by comparing the structural similarity involving the question-phrase and a candidate answer-phrase. Generic grammatical relationships are used as a back-off for specific entity associations when the question goes beyond the scope of the specific associations or when the system fails to identify the answer-point which meets the specific entity association constraints. The proposed methods are particularly helpful in cases where the question-phrase does not correspond to a known named entity type and in cases where there are multiple candidate answer-points to select from.
The rest of the paper is structured as follows: section 1 presents the NLP/IE engine used, sections 2 discusses how to identify and formally represent what is being asked, section 3 presents the algorithm on identifying exact answers leveraging structural support, section 4 presents case studies and benchmarks, and section 5 is the conclusion.
1 NLP/IE Engine Description
The NLP/IE engine used in the QA system described here is named InfoXtract™. It consists of an NLP component and IE component, each consisting of a set of pipeline modules (Figure 1). The NLP component serves as underlying support for IE. A brief description of these modules is given below.
- **Part-of-Speech Tagging**: tagging syntactic categories such as noun, verb, adjective, etc.
- **Shallow Parsing**: grouping basic linguistic units as building blocks for structural links, such as Basic Noun Phrase, Verb Group, etc.
- **Asking-point Identification**: analysis of question sentences to determine what is being asked
• **Semantic Parsing**: decoding grammatical dependency relationships at the logical level between linguistic units, such as Verb-Subject (V-S), Verb-Object (V-O), Head-Modifier (H-M) relationships; both active patterns and passive patterns will be parsed into the same underlying logical S-V-O relationships.
• **Named Entity Tagger**: classifying proper names and other phrases to different categories such as Person, Organization, Location, Money, etc.
• **Entity Association Extractor**: relating named entities with predefined associations such as Affiliation, Position, Age, Spouse, Address, etc.
The NE tagger in our system is benchmarked to achieve close to human performance, around or above 90% precision and recall for most categories of NE. This performance provides fundamental support to QA. Many questions require a named entity or information associated with a named entity as answers. A subset of the NE hierarchy used in our system is illustrated below:
**Person**: woman, man
**Organization**: company, government, association, school, army, mass-media
**Location**: city, province, country, continent, ocean, lake, etc.
**Time Expressions**: hour, part-of-day, day-of-week, date, month, season, year, decade, century, duration
**Numerical Expressions**: percentage, money, number, weight, length, area, etc.
**Contact expressions**: email, address, telephone, etc.
The Entity Association module correlates named entities and extracts their associations with other entities or phrases. These are specific, predefined relationships for entities of person and organization. Currently, our system can extract the following entity associations with high precision (over 90%) and modest recall ranging from 50% to 80% depending on the size of grammars written for each specific association.
**Person**: affiliation, position, age, spouse, birth-place, birth-time, etc.
**Organization**: location, staff, head, products, found-time, founder, etc.
Entity associations are semantic structures very useful in supporting QA. For example, from the sentence *Grover Cleveland, who in June 1886 married 21-year-old Frances Folsom,...* the IE engine can identify the following associations:
- Spouse: Grover Cleveland ← Frances Folsom
- Spouse: Frances ← Grover Cleveland
- Age: Frances Folsom ← 21-year-old
A question asking about such an association, say, Q11: *Who was President Cleveland’s wife*, will be parsed into the following association link between a question-phrase ‘Who’ and the entity ‘Cleveland’ (see Section 2): *Spouse: Cleveland → Who*. The semantic similarity between this structure and the structure *Spouse: Grover Cleveland → Frances Folsom* can determine the answer point to be ‘Frances Folsom’.
The Semantic Parsing module decodes the grammatical dependency relationships: V-S, V-O, V-C (Verb-Complement), H-M of time, location, reason, manner, purpose, result, etc. This module extends the shallow parsing module through the use of a cascade of handcrafted pattern matching rules. Manual benchmarking shows results with the following performance:
- H-M: Precision 77.5%
- V-O: Precision 82.5%
- V-S: Precision 74%
- V-C: Precision 81.4%
In our semantic parsing, not only passive patterns will be decoded into the same underlying structures as active patterns, but structures for verbs such as *acquire* and for de-verbal nouns such as *acquisition* lead to the same dependency links, as shown below.
*AOL acquired Netscape in 1998*.
- V-S: acquired ← AOL
- V-O: acquired ← Netscape
- H-M: acquired ← in 1998 (time-modifier)
*Netscape was acquired by AOL in 1998*.
- V-S: was acquired ← by AOL
V-O: was acquired ← Netscape
H-M: was acquired ← in 1998 (time-modifier)
the acquisition of Netscape by AOL in 1998... →
V-S: acquisition ← by AOL
V-O: acquisition ← of Netscape
H-M: acquired ← in 1998 (time-modifier)
These links can be used as structural support to answer questions like Who acquired Netscape or which company was acquired by AOL.
Obviously, our semantic parser goes one step further than parsers which only decode syntactic relationships. It consumes some surface structure variations to provide the power of comparing the structural similarity at logical level. However, compared with the entity association structures which sits at deep semantic level, the logical SVO (Subject-Verb-Object) structures still cannot capture semantic relations which are expressed using different head verbs with different structures. An example is the pair: *X borrows Y from Z* versus *Z lends Y to X*.
2 Asking Point Link Identification
Asking point link identification is a crucial step in a QA system. It provides the necessary information decoded from question processing for a system to locate the corresponding answer-points from candidate answer strings.
The Asking-point (Link) Identification Module is charged with the task of parsing *wh*-phrases in their context into three categories: NE Asking-point, Asking-point Association Link and Asking-point Grammar Link. Asking Point refers to the question phrases with its constraints that a corresponding answer-point should satisfy in matching. Asking-point Link is the decoded binary relationship from the asking point to another unit in the question.
The identification of the NE asking point is essentially mapping the *wh*-phrase to the NE types or subtypes. For example, *which year* is mapped to [which year]/NeYear, *how old* mapped to [how old]/NeAge, and *how long* mapped to [how long]/NeLength or [how long]/NeDuration, etc.
The identification of the Asking-point Association Link is to decide whether the incoming question asks about a predefined association relationship. For Asking-point Association Link, the module needs to identify the involved entity and the asked association. For example, the Asking-point Association Link for *How old is John Smith* is the AGE relationship of the NePerson John Smith, represented as *AGE: John Smith ← [how old]/NeAge*.
The *wh*-phrases which may or may not be mapped to NE asking points and whose dependency links are beyond predefined associations lead to Asking-point Grammar Links, e.g. *How did Julian Hill discover nylon?*. This asking-point link is represented as *H-M: discover ← [How]/manner-modifier*. As seen, an asking-point grammar link only involves generic grammatical constraints: in this case, the constraints for a candidate answer-point to satisfy during matching are H-M link with ‘discover’ as head and a phrase which must be a modifier of manner.
These three types of asking points and their possible links form a natural hierarchy that can be used to facilitate the backoff strategy for the answer-point extraction module (see Section 3): Asking-point Association Link → Asking-point Grammar Link → NE Asking Point. This hierarchy defines the sequence of matching steps which should be followed during the answer-point extraction.
The backoff from Asking-point Association Link to Asking-point Grammar Link is necessary as the latter represents more generic structural constraints than the former. For example, in the sentence *where is IBM located*, the Asking-point Association Link is *LOCATION: IBM ← [where]/NeLocation* while the default Grammar Link is *H-M: located ← [where]/location-modifier*. When the specific association constraints cannot be satisfied, the system should attempt to locate an answer-point by searching for a location-modifier of the key verb ‘located’.
The NE asking point constraints are also marked for asking-point association links and those asking-point grammar links whose *wh*-phrases can be
mapped to NE asking points. Backing off to the NE asking point is required in cases where the asking-point association constraints and grammatical structural constraints cannot be satisfied. For *How old is John Smith*, the asking-point grammar link is represented as $H-M: \text{John Smith} \leftrightarrow [\text{how old}] / \text{NeAge}$. If the system cannot find a corresponding AGE association or a modifier of NeAge for the entity *John Smith* to satisfy the structural constraints, it will at least attempt to locate a candidate answer-point by enforcing the NE asking point constraints NeAge. When there is only one NeAge in the answer string, the system can extract it as the only possible answer-point even if the structural constraints are not honored.
3 Answer Point Identification
The answer-point identification is accomplished through matching the asking-point to candidate answer-points using the following back-off algorithm based on the processing results of the question and the sentence-level candidate answer string.
1. If there is Asking-point Association Link, call $\text{Match}(\text{asking-point association link, candidate answer-point association link})$ to search for the corresponding association to locate answer-point
2. If step (1) fails and there is an asking-point grammar link, call $\text{Match}(\text{asking-point grammar link, candidate answer-point grammar link})$ to search for the corresponding grammar link to locate the answer-point
3. If step (2) fails and there is an NE asking point, search for the corresponding NEs: if there is only one corresponding NE, then extract this as the answer-point else mark all corresponding NEs as candidate answer-points
The function $\text{Match}(\text{asking-point link, candidate answer-point link})$ is defined as (i) exact match or synonym match of the related units (synonym match currently confined to verb vs. de-verbal noun); (ii) match the relation type directly (e.g. $V-S$ matches $V-S$, AGE matches AGE, etc.); (iii) match the type of asking point and answer point (e.g. NePerson asking point matches NePerson and its sub-types NeMan and NeWoman; ‘how’ matches manner-modifier; etc.): either through direct link or indirect link based on conjunctive link (ConjLink) or equivalence link (S-P, subject-predicative or appositive relations between two NPs).
Step (1) and Step (2) attempt to leverage the structural support from parsing and high-level information extraction beyond NE. It is worth noticing that in our experiment, the structural support used for answer-point identification only checks the binary links involving the asking point and the candidate answer points, instead of full template matching as proposed in (Srihari and Li, 2000).
Full template matching is best exemplified by the following example. If the incoming question is *Who won the Nobel Prize in 1991*, and the candidate answer string is *John Smith won the Nobel Prize in 1991*, the question template and answer template are shown below:
$$
\begin{align*}
\text{win} & \quad \text{NePerson [Who]} \\
V-S: & \quad \text{NP [the Nobel Prize]} \\
V-O: & \quad \text{NeYear [1991]} \\
H-M: & \quad \text{NeYear [1991]}
\end{align*}
$$
The template matching will match the asking point *Who* with the answer point *John Smith* because for all the dependency links in the trees, the information is all compatible (in this case, exact match). This is the ideal case of full template matching and guarantees the high precision of the extracted answer point.
However, in practice, full template matching is neither realistic for most of cases nor necessary for achieving the objective of extracting answer points in a two-stage approach. It is not realistic because natural language semantic parsing is such a challenging problem that a perfect dependency tree (or full template) which pieces together every linguistic unit is not always easy to decode. For
InfoXtract, in most cases, the majority, but not all, of the decoded binary dependency links are accurate, as shown in the benchmarks above. In such situations, insisting on checking every dependency link of a template tree is too strong a condition to meet. On the other hand, it is actually not necessary to check all the links in the dependency trees for full template matching. With the modular design and work division between sentence level candidate answer string generation module (Stage One) and answer-point extraction from the candidate answer strings (Stage Two), all the candidate answer strings are already determined by previous modules as highly relevant. In this situation, a simplified partial template matching, namely, ‘asking/answer point binary relation matching’, will be sufficient to select the answer-point, if present, from the candidate answer string. In other words, the system only needs to check this one dependency link in extracting the answer-point. For the previous example, only the asking/answer point binary dependency links need to be matched as illustrated below:
V-S win←[Who]/NePerson
V-S win←[John Smith]/NeMan
Some sample results are given in section 4 to illustrate how answer-points are identified based on matching binary relations involving asking/answer points.
4 Experiments and Results
In order to conduct the feasibility study on the proposed method, we selected the first 100 questions from the TREC-8 QA track pool and the corresponding first candidate answer sentences for this preliminary experiment. The Stage One processing for generating candidate answer sentences was conducted by the existing ranking module of our QA system. The Stage Two processing for answer-point identification was accomplished by using the algorithm described in Section 3.
As shown in Table 1, out of the 100 question-answer pairs we selected, 9 have detected association links involving asking/answer points, 44 are found to have grammar links involving asking/answer points.
| | detected | correct | fail | precision | recall |
|-------------------------|----------|---------|------|-----------|--------|
| Association Links | 9 | 8 | 1 | 89% | 8% |
| Grammar Links | 44 | 39 | 6 | 89% | 39% |
| NE Points (Baseline) | 76 | 41 | 35 | 54% | 41% |
| Overall performance | 86 | 71 | 14 | 83% | 71% |
As for NE asking points, 76 questions were identified to require some type of NE as answers. Assume that a baseline answer-point identification system only uses NE asking points as constraints, out of the 76 questions requiring NEs as answers, 41 answer-points were identified successfully because there was only one NE in the answer string which matches the required NE type. The failed cases in matching NE asking point constraints include two situations: (i) no NE exists in the answer string; (ii) multiple NEs satisfy the type constraints of NE asking points (i.e. more than one candidate answer-points found from the answer string) or there is type conflict during the matching of NE asking/answer points. Therefore, the baseline system would achieve 54% precision and 41% recall based on the standard precision and recall formulas:
\[
\text{Precision} = \frac{\text{Correct}}{\text{Detected}}
\]
\[
\text{Recall} = \frac{\text{Correct}}{\text{Relevant}}.
\]
In comparison, in our answer-point identification system which leverages structural support from both the entity association links and grammar links as well as the NE asking points, both the precision and recall are raised: from the baseline 54% to 83% for precision and from 41% to 71% for recall. The significant improvement in precision and recall is attributed to the performance of structural matching in identifying exact answers. This demonstrates the benefits of making use of sophisticated NLP/IE technology, beyond NE and shallow parsing.
Using grammar links alone, exact answers were identified for 39 out of the 44 candidate answer-points satisfying the types of grammar links in 100 cases. During matching, 6 cases failed either due to the parsing error or due to the type conflict.
between the asking/answer points (e.g. violating the type constraints such as manner-modifier on the answer-point for ‘how’ question). The high precision and modest recall in using the grammar constraints is understandable as the grammar links impose very strong constraints on both the nodes and the structural type. The high precision performance indicates that grammar links not only have the distinguishing power to identify exact answers in the presence of multiple NE options but also recognize answers in the absence of asking point types.
Even stronger structural support comes from the semantic relations decoded by the entity association extraction module. In this case, the performance is naturally high-precision (89%) low-recall (8%) as predefined association links are by nature more sparse than generic grammatical relations.
In the following, we illustrate with some examples with questions from the TREC-8 QA task on how the match function identified in Section 3 applies to different question types.
Q4: How much did Mercury spend on advertising in 1993? → asking-point grammar link: V-O spend ← [How much]/NeMoney
A: Last year the company spent Pounds 12m on advertising. → candidate answer-point grammar link: V-O spent ← [Pounds 12m]/NeMoney
Answer-point Output: Pounds 12m
This case requires (i) exact match in its original verb form between spend and spent; (ii) V-O type match; and (iii) asking/answer point type NeMoney match through direct link.
Q63: What nuclear-powered Russian submarine sank in the Norwegian Sea on April 7, 1989? → asking-point grammar link: H-M submarine ← [What]
A: NEZAVISIMAYA GAZETA on the Komsomolets nuclear-powered submarine which sank in the Norwegian Sea five years ago: → candidate answer-point grammar link: H-M submarine ← Komsomolets
Answer-point Output: Komsomolets
This case requires (i) exact match of submarine; (ii) H-M type match; and (iii) asking/answer point match through direct link: there are no asking point type constraints because the asking point goes beyond existing NE. This case highlights the power of semantic parsing in answer-point extraction. Since there are no type constraints on answer point,1 candidate answer points cannot be extracted without bringing in structural context by checking the NE type. Most of what-related asking points such as those in the patterns ‘what/which…N’, ‘what type/kind of …N’ go beyond NE and require this type of structural relation checking to locate the exact answer. The case below is another example.
Q69: What did Shostakovich write for Rostropovich? → asking-point grammar link: V-O write ← [What]
A: The Polonaise from Tchaikovsky’s opera Eugene was a brief but cracking opener and its brilliant bluster was no sooner in our ears than forcibly contradicted by the bleak depression of Shostakovich’s second cello concerto, Op. 126, a late work written for Rostropovich in 1966 between the thirteenth and fourteenth symphonies. → candidate answer-point grammar link:
V-O written ← [a late work]/NP
S-P [Op. 126]/NP ← [a late work]/NP
Answer-point Output: Op. 126
This case requires (i) exact match in its original verb form between written and write; (ii) V-O type match; and (iii) asking/answer point match through indirect link based on equivalence link S-P. When there are no NE constraints on the answer point, a proper name or an initial-capitalized NP is preferred over an ordinary, lower-case NP as an answer point. This heuristic is built-in so that ‘Op. 126’ is output as the answer-point in this case instead of ‘a late work’.
Q79: What did Shostakovich write for Rostropovich?
A: The Polonaise from Tchaikovsky’s opera Eugene was a brief but cracking opener and its brilliant bluster was no sooner in our ears than forcibly contradicted by the bleak depression of Shostakovich’s second cello concerto, Op. 126, a late work written for Rostropovich in 1966 between the thirteenth and fourteenth symphonies.
1 Strictly speaking, there are some type constraints on the answer point. The type constraints are something to the effect of ‘a name for a kind of ship’ which goes beyond the existing NE types defined.
Conclusion
This paper presented an approach to exact answer identification to questions using only binary structural links involving the question-phrases. Based on the experiments conducted, some preliminary conclusions can be arrived at.
- The Entity Association extraction helps in pinpointing exact answers precisely
- Grammar dependency links enable the system to not only identify exact answers but answer questions not covered by the predefined set of available NEs/Associations
- Binary dependency links instead of full structural templates provide sufficient and effective structural leverage for extracting exact answers
Some cases remain difficult however, beyond the current level of NLP/IE. For example,
Q92: Who released the Internet worm in the late 1980s? → asking point link:
V-S (released, NePerson[Who])
A: Morris, suspended from graduate studies at Cornell University at Syracuse, N.Y., is accused of designing and disseminating in November, 1988, a rogue program or “worm” that immobilized some 6,000 computers linked to a research network, including some used by NASA and the Air Force. → answer point link:
V-S (disseminating, NePerson[Morris])
In order for this case to be handled, the following steps are required: (i) the semantic parser should be able to ignore the past participle postmodifier phrase headed by ‘suspended’; (ii) the V-O dependency should be decoded between ‘is accused’ and ‘Morris’; (iii) the V-S dependency should be decoded between ‘designing and disseminating’ and ‘Morris’ based on the pattern rule ‘accuse NP of Ving’ → V-S(Ving, NP); (iv) the conjunctive structure should map the V-S (‘designing and disseminating’, ‘Morris’) into two V-S links; (v) ‘disseminate’ and ‘release’ should be linked somehow for synonym expansion. It may be unreasonable to expect an NLP/IE system to accomplish all of these, but each of the above challenges indicates some directions for further research in this topic.
We would like to extend the experiments on a larger set of questions to further investigate the effectiveness of structural support in extracting exact answers. The TREC-9 and TREC 2001 QA pool and the candidate answer sentences generated by both NLP-based or IR-based QA systems would be ideal for further testing this method.
5 Acknowledgement
The authors wish to thank Walter Gadz and Carrie Pine of AFRL for supporting this work. Thanks also go to anonymous reviewers for their valuable comments.
References
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**Abstract:** Aptamers are short fragments of nucleic acids, DNA or RNA that have the ability to bind selected proteins with high specificity and affinity. These properties allow them to be used as an element of biosensors for the detection of specific proteins, including viral ones, which makes it possible to design valuable diagnostic tools. The influenza virus causes a huge number of human and animal deaths worldwide every year, and contributes to remarkable economic losses. In addition, in 2020, a new threat appeared—the SARS-Cov-2 pandemic. Both disease entities, especially in the initial stage of infection, are almost identical in terms of signs and symptoms. Therefore, a diagnostic solution is needed that will allow distinguishing between both pathogens, with high sensitivity and specificity; it should be cheap, quick and possible to use in the field, for example, in a doctor’s office. All the mentioned properties are met by aptasensors in which the detection elements are specific aptamers. We present here the latest developments in the construction of various types of aptasensors for the detection of influenza virus. Aptasensor operation is based on the measurement of changes in electric impedance, fluorescence or electric signal (impedimetric, fluorescence and electrochemical aptasensors, respectively); it allows both qualitative and quantitative determinations. The particularly high advancement for detecting of influenza virus concerns impedimetric aptasensors.
**Keywords:** aptasensors; aptamers; influenza; flu; virus
1. Introduction
There are many viruses in the environment that infect humans, other animals or both, around it. Some of them contribute to the development of diseases. The most pathogenic viral strains can cause diseases leading to permanent damage to health and even death. However, they always contribute to economic losses [1,2]. In order to avoid the undesirable consequences of either viral, health and economic infections, not only effective therapeutic solutions are necessary, but most of all, reliable, effective and quick diagnostic methods with high sensitivity and specificity, which, as a result of the diagnosis, will allow for either appropriate treatment, quarantine or both [3–5].
There are many viruses that are extremely dangerous to humans. Among them, one of the most important is the influenza virus, which not only easily mutates, causing further epidemics in humans and animals, but some of its strains also cause infections with low survival rates. A particularly important strain in this context is the H5N1 avian influenza virus, which causes severe economic losses and causes death in farmed poultry. Moreover, under favorable circumstances it also infects people, causing an infection characterized by high, as much as 60% mortality [6–8]. A classic example of the
lethal human influenza virus potential was the Spanish flu, which decimated the world’s population between 1918 and 1920, causing over 50 million deaths worldwide [9]. There are also many other dangerous viruses, such as HBV or HCV. They constitute a serious health problem contributing to liver dysfunction and even the development of hepatocellular carcinoma in humans [10,11]. There are also deadly viruses such as Ebola for which there is still no effective treatment. At the turn of 2013/2014, the virus spread widely through African countries. There are serious and well-founded concerns about its expansion to other geographic regions [12]. Apart from those mentioned, there are many other viruses, such as HIV, Zika, et cetera, which also constitute a serious diagnostic and therapeutic problem [13,14]. The year 2020 also brought a whole new challenge in the form of the SARS-CoV-2 virus that causes COVID-19. This is an extremely unfortunate event because the death rate caused by the virus is relatively high and the virus itself is highly contagious. An extremely unfavorable coincidence is the fact that initial symptoms of SARS-CoV-2 infection are deceptively similar to infection with the group virus.
It seems that the key to efficiently dealing with the expansion of viruses dangerous for humans is a quick and correct diagnosis, often also involving the differentiation of infections with a similar course as in the case of the influenza virus and SARS-CoV-2. Among the standard diagnostic methods used in the detection of viral infections, enzyme-linked immunosorbent assay (ELISA) and molecular methods based on the polymerization chain reaction dominate [15–17]. The first have a major disadvantage—they allow detection of infection at the time of developing immunity, in other words, antibody production. This process usually takes place a few days or weeks after infection, which makes it impossible to make a quick and reliable diagnosis right after infection, and additionally prevents the application of immediate pharmacological prevention. The second group of diagnostic methods, based on the polymerization chain reaction, for the detection of viral nucleic acid is very sensitive and allows the detection of infection in a period incomparably shorter than that of immunoenzymatic methods. However, their use is extremely costly and therefore not routinely used. Moreover, in the case of both types of methods, their use is time-consuming [15–19]. Aptamers seem to be an alternative to the above-mentioned problems of virological diagnostics, the use of which guarantees high sensitivity and specificity of detection, and is also relatively cheap. The use of aptamers as components of virological sensors is a promising panacea for the problems of currently used diagnostic solutions [15,20,21].
Aptamers are short (usually no longer than 90 nucleotides) fragments of nucleic acids, DNA or RNA that bind selected proteins (as well as other chemical molecules) in a specific manner and with high affinity. They show a number of advantages over monoclonal antibodies: they are stable at room temperature, homogeneous, easy to modify and, above all, simple and cheap to obtain [8,22]. Aptamer molecules are obtained by the SELEX method (systematic evolution of ligands by exponential enrichment) developed and used for the first time by the Tuerk and Gold teams [23] and Elington and Szostak in 1990 [24]. Briefly, this technique relies on repeated cycles of selection and replication of a combinatorial library of DNA or RNA molecules of a specified length in vitro under selected conditions by the recipient. Since the first application of this method, many variations of this technique have been developed that either accelerate the aptamer production, enhance or both; either the specificity, affinity or both; of these molecules for target molecules. The process of obtaining aptamers, as well as their more in-depth characteristics, is not the subject of this study, therefore, in order to find out more about these issues, we encourage you to read our other article, where these issues are presented in detail [8]. Binding of target proteins with high specificity and affinity by aptamers often results in their function being blocked. Such action can be of great importance in the treatment of various diseases, including viral ones. Much research has already been carried out in this area. However, the high specificity and affinity of the binding of target molecules by aptamers have made them attractive not only for therapeutic but also diagnostic applications, where quick and reliable diagnosis in the case of viral diseases is often crucial and may favor either the prompt treatment of the patient (if therapy exists), its isolation or both, which in turn prevents further spread of the disease [3–5,25].
The use of aptamers in the diagnosis and therapy of diseases brings great benefits and is the subject of many research projects. The authors of extensive review papers compare their properties in comparison with monoclonal antibodies, probably due to the fact that they are a direct competition for this diagnostic tool. However, this technique is not without disadvantages, although they remain in significant disproportion compared to the advantages. The most important of them are listed in Table 1.
| Advantages | Disadvantages |
|------------|---------------|
| - short duration of chemical synthesis (a few days) | - aptamer sequence determination using the SELEX technique is long-lasting (several months) |
| - relatively low cost of production | - SELEX carries extremely high costs |
| - high stability of the obtained particles—no variability between batches | - small size contributes to a high rate of excretion from the body |
| - low immunogenicity | - unmodified aptamers are susceptible to degradation by serum nucleases |
| - affinity and specificity similar to monoclonal antibodies | |
| - the possibility of increasing the affinity to the analyte by increasing the rounds of SELEX (systematic evolution of ligands by exponential enrichment) | |
| - high selectivity | |
| - the ability to selectively adjust to selected extracellular and intracellular targets (proteins, nucleotides, amino acids, small molecules, ions, viruses, living cells) | |
| - the possibility of their immobilization on many surfaces and coupling with nanoparticles and drugs | |
| - small particle size compared to monoclonal antibodies ensures higher sensitivity and lowers the limits of detection of analytes | |
| - ability to regenerate and re-use (renaturation after denaturation allows rebinding of the analyte) | |
| - possibility of chemical modification without loss of binding capacity or performance | |
| - possibility of adaptation to operation in non-standard temperatures, solvents, buffers | |
In our previous article, “Aptamers in diagnostics and treatment of viral infection” published in 2015 in the journal “Viruses”, we presented in detail the current research and clinical achievements regarding the diagnosis and therapy of viral diseases with the use of aptamers. Since then, there have been many new and noteworthy reports on virological diagnostics. When creating this study, we decided to review these solutions with particular attention to the influenza virus, as in our opinion, research into the diagnosis of this virus seems to be the most advanced. In addition, due to the current epidemiological threat caused by the SARS-CoV-2 virus, the infection of which resembles the course of an influenza virus infection, the solutions for the detection of the influenza virus developed so far may be of great importance in the differentiation of both infections. This is even more significant in that research into the use of aptamers in the detection of the SARS-CoV virus-2 requires time is just starting. The current work is a kind of update of the content of the article mentioned above—it focuses on the current reports on the use of aptamers in the diagnosis of the influenza virus.
2. Flu Virus Diagnosis
The influenza virus, along with SARS-CoV-2 infection, represents one of the most challenging challenges in virology today. It is an enveloped virus [31]. Its molecules contain seven (influenza type C and D) or eight (influenza type A and B) single-stranded negative-sense RNA segments that make up its genome. The genome encodes, among others, matrix protein M1 and viral nucleoproteins, which are used to distinguish its three main types—there are three types: A, B and C [31]. In turn, on the surface of the influenza particles there are two types of glycoproteins that have been encoded in the genome—hemagglutinin and neuraminidase. The differences in their structure have become the basis for distinguishing subtypes of influenza viruses [31,32]. Type A and B viruses can infect humans [31]. Type A viruses seem to pose the greatest threat to humans, mainly due to the phenomena of drift and genetic shift, which are easily affected [33,34]. This phenomenon most often concerns the viral hemagglutinin of the virus—a protein involved in the process of infection of host cells (attaching to their surface and penetrating into them). Neuraminidase is involved in the transmission of the virus. In nature, there are 15 types of hemagglutinin and 9 types of neuraminidase, which are the basis for the differentiation of influenza A virus type [32]. The variability resulting from the phenomena of drift and genetic shift is the main cause of difficulties in the development of vaccines and drugs against this type of virus. These phenomena also affect the design of diagnostic solutions, which they do not facilitate either [33,34].
A particularly important case, which receives a lot of attention and research, is the avian influenza virus—H5N1 [35,36], that belongs to the group of influenza type A viruses. Until 2012, according to FAO findings, it caused epidemics that resulted in nearly 400 million deaths among farmed poultry, which contributed to significant economic losses (over USD 20 trillion) for farmers around the world [37]. The first cases were found in 1990 in Southeast Asia and later also in the Middle East and Europe [35]. However, what is extremely worrying, cases were also reported in sixteen countries around the world, among people [38]. Their occurrence is favored, in the case of the avian influenza virus, by the high frequency of mutations and the ease of reassortment of this strain with other strains of the influenza virus [35]. Infection with influenza type A virus causes infections of the upper respiratory system, which are manifested by fever, nasal congestion and headache [39,40]. Between years 2003 and 2016, 844 cases of infection with this strain in humans were detected, according to a report by the World Health Organization. They were characterized by a very high, as much as 53% mortality (449 deaths) [38]. In 2013, the first case of human infection with the H7N9 strain of avian influenza was also confirmed, which, like the H5N1 strain, is characterized by high mortality in humans, reaching over 36% [41,42]. The strains of influenza type A virus—H1N1 and H3N2—are also the most infectious strains of this virus for humans and can cause large and rapidly spreading epidemics [43,44].
B influenza type viruses only infect humans and seals. The ailments they cause are usually much less severe than those caused by infection with the group of type A viruses [45]. The severity of symptoms caused by infection with C influenza type is even less.
The threat and economic losses associated with the outbreak of a potential epidemic prompted us to undertake further research aimed at developing not only therapeutic measures, but most of all, diagnostic solutions that will ensure the possibility of immediate, on the spot, detection of the virus and taking immediate preventive actions. A significant drawback of the currently used solutions is the long waiting time for the result, the release of which is preceded by a relatively long time necessary to perform analysis in laboratory conditions [34,35,46], while it has been proven that the initiation of antiviral treatment within 24 h (e.g., Tamiflu preparation) from the onset of symptoms significantly reduces the duration of the infection and its severity. This fact significantly influences the activities of scientists whose aim is to accelerate the diagnostic process, and thus reduce the negative effects of infection with influenza viruses [40,47]. The most frequently used analyses are three groups of methods: viral cultures for the multiplication of the virus and its subsequent identification, genetic methods consisting of the detection of the viral genome and immunological methods consisting of the detection of antiviral antibodies or virus antigens. The first group of methods includes RT-PCR
and real-time polymerase chain reaction (PCR), and the second group of ELISA tests or rapid influenza diagnostic test (RITD). The use of the former is very time-consuming and expensive—analysis cannot be performed on site; the test material must be collected from the patient and sent to the laboratory, which extends the identification time and postpones the initiation of treatment (e.g., the anti-influenza preparation Tamiflu should be administered within 24–48 h from the onset of symptoms, which in the case of using this type of diagnostic methods becomes impossible) [48]. The second group of methods, in turn, is often characterized by insufficient sensitivity and specificity (cross-reactions against other viruses and pathogens were observed during detection due to the production of insufficiently specific antibodies) [49] compared to molecular methods. For example, RITD tests have extremely low diagnostic sensitivity (10–70%), resulting in a high number of false negative results. In the case of classic ELISA tests, they more often rely on the detection of antibodies than the virus itself [33,35,46,50–54]. Methods based on the culture of cells, most often PMK (primary rhesus monkey cell line) and MDCK (Madin–Darby canine kidney cell line) infected with the virus isolated from patients, favor its multiplication and effective and easier identification on the basis of viral antigens present in numerous cultures. However, this method is extremely time-consuming and labor-intensive. It takes 3–14 d to determine the type of virus [55].
Biosensors are an interesting alternative to the diagnostic methods currently used to detect viruses. These are devices that use a biological element capable of specifically capturing a viral particle, for example, it may be an aptamer. Most often, it is combined with a processing unit which, due to the binding of the target molecule by a specific aptamer, emits a signal depending on the type of biosensor, which is synonymous with the detection of a specific pathogen [35]. In our previous work [8], we reported that at least several research teams had developed aptasensors to detect influenza viruses, including avian influenza. They used, inter alia, the surface plasmon resonance method [56–60], quartz crystal microbalance [61–64], the phenomenon of fluorescence [65,66] as well as electrochemical processes [67–71]. At that time, the proposed solutions were characterized by higher sensitivity and specificity than the constructed immunosensors [36], but they did not meet the requirements for solutions that could be used “in the field”. First of all, the use of aptasensors was relatively time-consuming and cost-intensive, and was characterized by a rather complicated methodology. For example, using a sensor based on the SPR technique required about 90 min to obtain results, while a waiting time of no more than 30 min is expected for fast detection methods. It seems that a lot has changed in this regard over the last five years, so we again took information on the latest advances in virological diagnostics using aptasensors, which are presented later in this paper.
One of the molecules most frequently targeted for aptamer detection in influenza virus is hemagglutinin. It is a protein that plays a key role in the process of infection of host cells, as well as in the formation of immunity. It is known that the production of antiviral antibodies mainly involves the production of molecules directed against this particular viral protein. It occurs on the surface of the virus as a trimeric spike [64].
3. Impedimetric Aptasensors
One of the most frequently used and developed biosensors in the diagnosis of influenza virus, including the avian subtype H5N1 (but not only), are impedimetric detectors. This is due to the possibility of their miniaturization and low production costs, which is always an important factor determining the development of a given technology. Their operation is based on electrochemical changes occurring in the tested material, the occurrence and subsequent detection of which allows confirming or excluding the presence of the molecules sought. First of all, impedimetric techniques measure the actual changes of impedance or resistance that occur when a target molecule binds to a biosensor. The methods of detecting these changes depend on marking elements (direct or indirect labeling) or can be label-free. In addition, it has been proven that the use of selected materials such as, for example, gold nanoparticles, carbon nanotubes and others, in the construction of impedimetric aptasensors or their elements (most often microelectrodes included in biosensor) multiplies detected
signal changes, which increase the sensitivity of the test. Moreover, additional advantages resulting from the combination of an impedimetric biosensors with different types of microelectrodes are: the fast kinetics of the reaction, shorter detection time resulting from the fast sensor response and what was mentioned earlier—the amplification of the emitted signal in relation to the background signal, which allows for minimizing the volume of the tested sample [35,72,73]. In addition, the use of a connection often minimizes the amount of preparatory steps needed to be performed with the test material. This improves the psychological comfort of a diagnosticians work and reduces the risk of infection resulting from more frequent contact with the tested material [73]. Aptamers have proven to be effective detectors of viral particles that could be used in virological biosensors. Their use is associated with a very low background signal, high repeatability of results and high sensitivity of the device [33,35]. For most solutions, three times the maximum standard deviation of the measurement made for the control sample, which is the so-called background signal, was adopted as the standard for the lower detection limit [36,74].
Lum et al. developed an impedance biosensor containing a DNA aptamer capable of detecting H5N1 avian influenza virus particles. The described sensor uses a gold electrode placed in a microflow chamber, which is coated with streptavidin in such a way that it can interact and bind the detection element on its surface—a biotinylated aptamer specific for the H5N1 virus. The presence of the virus in the tested material was confirmed by the increase in the impedance magnitude, which was directly proportional to the virus concentration in the tested material and resulted from the blockage of the ion flow caused by the binding of the virus by a specific aptamer coated on the microelectrode. The biosensor allowed for selective detection of H5N1 avian influenza virus. The presence of other types of influenza virus in tested material, such as H1N1, H2N2 and H7N2 did not interfere with the detection process. It was a direct evidence for high specificity of the constructed biosensor. The high specificity of the sensor resulted not only from the presence of the aptamer, but also from the lack of the need to perform the blocking procedure. As a consequence, when aptamers are used, the background noise is significantly reduced, which increases the specificity of biosensors. Moreover, the biosensor constructed by Lum et al. was also characterized by high sensitivity. The attainable detection limit was not lower than in previous solutions constructed by the same [75] and other research teams [64]—the sensor allowed detection of the virus in the amount of 0.0128 hemagglutinin units (HAU). Hemagglutination (HA) stands for agglutination of red blood cells induced by the presence of virus. One HA unit (HAU) is the amount of virus needed to agglutinate an equal volume of a standardized RBC suspension, or one HAU in a virus suspension is measured by the amount of virus dilutions made equal to the amount of HA titers [35]. Use of described biosensor for virus detection was fast (only 30 min). This was due to elimination of the need to mark the tested material and also elimination of the necessity of its condensation. Moreover, for the first time, the time, sensitivity and, above all, the form of the biosensor achieved, enabled its possible use in the field. Previously, the proposed solutions [64] with similar time parameters and detection sensitivity were not adapted to use outside the laboratory [76]. The aptasensor designed by Lum et al. was miniature, had low energy requirements and was easy to use [35].
An aptasensor constructed in an analogous way (biotinylated DNA aptamer [64], streptavidin-coated gold microelectrode, impedance measurement) also using a similar method of operation as that designed by Lum et al. [35], was edited by Karash et al. [36]. It was used to detect the same virus strain—H5N1—whose particles were inactivated. The aptamer used was characterized by high virus binding affinity; the dissociation constant was 4.65 nM. One of the basic differences in the approach was the use of the microelectrode blocking step during the analysis, which was performed with the use of polyethylene glycol, and the use of a signal amplifier—thiocyanuric acid, which created a kind of cross-linking binding gold nanoparticle covalently linked with aptamers, which increased the generated impedance signal at least 48 times [36]. Although the solution proposed by Karash et al. was slightly less sensitive and longer in execution than that proposed by Lum et al., the limit and time of detection were satisfactory [35,36]. The detection limit for the discussed aptasensor was
0.25 HAU for the purified virus and 1 HAU for the virus introduced into swabs collected from the trachea of breeding poultry. The first of the mentioned detection thresholds is lower than in the case of the conventional RT-PCR test (0.5 HAU) and higher than the detection threshold of the real-time PCR method (possible detection of 0.125 HAU of the virus). On the other hand, the performance of the real-time PCR test is significantly more expensive, longer and, above all, must be performed in a laboratory. In the case of the described aptasensor, the detection can take place on site, in the field. On the other hand, the specificity of the aptasensor was confirmed in the presence of influenza virus strains other than H5N1, which generated only a minimal impedance signal. Even 90% similarity of the hemagglutinin sequence of the H5N2 avian influenza virus strain did not cause it to bind to the aptamer, which proved its high specificity for the H5N1 strain. The detection time was 45 min when using the variant without signal booster. A sample with a volume of only 30 microliters was enough to carry out the reaction, which is an unquestionable advantage in the case of having very small samples. Moreover, Karash et al. made a concise economic analysis for the proposed solution, stating that the total cost of making a single sensor, excluding the cost of the personnel performing the test, is only $13, of which the main cost is the microelectrode constituting the core of the aptasensor. The authors of the study speculate that mass production would reduce the total cost of one test to as low as $3 [36]. Moreover, the construction of aptasensors based on the solution proposed by the authors of the publication was cheaper than in the cases postulated by other authors. For example, the generation of an aptasensor proposed by Wang et al. using quartz crystal electrode generated a cost of nearly $20/test [64], and the production of microfluidic chips proposed by Lum et al. [35] cost as much as $100/chip. The cost-quality ratio of the compared tests (their sensitivity, specificity and execution time) seems to be in favor of the solution proposed by Karash et al. [35,36,64].
A solution based on the detection of the avian influenza virus using an electrochemical impedance spectroscopy using an aptasensor was also proposed by Kirkegaard et al. Their main goal was to reduce the detection time and sensor production costs. For this purpose, instead of conventional metallic electrodes, they used an electrode made of PEDOT:PSS (poly (3,4-ethylenedioxythiophene) polystyrene sulfonate) [39]. Such electrodes are much easier to manufacture than conventional metal electrodes. Moreover, the cost of materials necessary for their production is significantly lower, and their stability and conductivity are sometimes higher than in the case of traditional electrodes [77]. The primary biological component responsible for the capture of H1N1, H3N2 and H2N2 avian influenza particles was the hemagglutinin-specific single-stranded A22 DNA aptamer of the virus, which had already been selected by the team of Jeon et al. [78], and finally it was modified by introducing TC-tag into its structure, which made it possible to immobilize it on the surface of the created electrode. According to the authors of the study, the developed aptasensor enabled detection in no more than 30 min [39]. The goals set by the team were achieved, although there is no information in the publication about the sensitivity of the developed solution.
Bai et al. developed sensors to detect a different strain of influenza A, H1N1. For its construction, a DNA aptamer was used, which was selected against inactivated whole particles of this virus. Typically, this approach produces aptamers that are specific for conserved regions of viral antigens. The authors developed two diagnostic tests. The first—the ELONA test—was the equivalent of the ELISA test, in which monoclonal antibodies were replaced with molecules of a selected aptamer. This allowed obtaining the H1N1 detection limit (LOD) defined as the signal-to-noise ratio value, S/N = 3 at the level of 0.3 ng/µL. The second diagnostic device constructed with the use of the selected aptamer was the electrochemical impedance aptasensor, the use of which allowed achieving a sensitivity of 0.9 pg/µL—nearly 300 times lower than in the case of the designed ELONA test. The thiolated aptamer was immobilized on the surface of the gold microelectrode. The constructed aptasensor allowed for one-step detection without prior lysis of viral particles or extraction of their proteins. In addition, it showed significant specificity—it detected the H1N1 and H3N2 influenza virus strains. Interestingly, the research team observed that lower aptamer density on the electrode surface favored an increase in specificity, while its increase favored an increase in sensitivity at the expense of sensor specificity.
The latter observation, in particular, may be important when analyzing samples with a very low content of viral particles—as in the case of, for example, throat swabs [33].
4. Fluorescent Apatasensors
An important type of aptasensor is also those based on the measurement of fluorescence. Many other diagnostic methods are based on the detection of this phenomenon. These methods are used routinely nowadays mainly due to the high sensitivity and ease of performing the procedure [34].
In recent years, Pang et al. have developed a solution that enables the detection of H5N1 avian influenza virus hemagglutinin in human plasma. For this purpose, they used Ag-SiO$_2$ nanoparticles coated with an aptamer rich in guanine residues. Interestingly, this aptamer underwent conformational changes depending on whether there were molecules of the detected protein in its vicinity or not [34]. It has been proven many times that nucleic acids showing the II-order structure, including aptamers obtaining the G-quadruplex structure, are able to bind various dyes and induce their fluorescence [79].
The team of Pang et al. used an aptamer with just such properties. It was able to obtain G-quadruplex structures in the presence of viral hemagglutinin and consequently to bind Thiazole Orange—a dye that only emits fluorescence upon binding to a conformationally altered aptamer [80]. Importantly, any fluorescence-based diagnostic method must be strong enough. In the case of the solution proposed by Pang et al., the fluorescence signal was repeatedly amplified as a result of the use of Ag-SiO$_2$ nanoparticles [34,66]. In the proposed solution, the background signal emitted by the free Thiazole Orange present in the reaction mixture was remarkably low. The viral protein was detected in human plasma in a one-step process, as early as 30 min and at a concentration of only 3.5 ng/mL (the detection limit for the aqueous protein solution was even lower, only 2 ng/mL). It was a solution that, due to the extremely short detection time, according to the authors, could be used to detect the virus directly at the site of sample collection. It was faster, more sensitive and more specific than enzyme immunoassays used for the same purpose [34].
In turn, Tseng et al. proposed a detection method specific for the influenza virus of the H1N1 type. In order to detect it, they used a microfluidic system with a sandwich-based system and fluorescence emission. The virus capture was possible, as in the previous cases, thanks to the incorporation of an aptamer into the system, characterized by very high specificity and binding affinity for virus particles. Two identical aptamers were used in the designed test—one detected the virus, the other increased the specificity of the reaction and was responsible for the emission of fluorescence since it was conjugated to the fluorescent marker. As in the solution proposed by Pang et al., this time the detection time was also very short and did not exceed 30 min, and the entire process was automated. The detection limit of the designed solution was only 0.032 HAU, which, according to the authors of the study, made the designed test comparable in terms of sensitivity with tests involving the use of monoclonal antibodies or PCR techniques [54] and approximately 30 times more sensitive than conventionally used serological solutions of the RIDT type [81]. What is more, the authors of the study pointed out that the use of aptamers brings many benefits, since it is known that they are more stable (in various temperature and humidity ranges), easier to store and cheaper to obtain (chemical synthesis) than monoclonal antibodies in standard enzyme immunoassays applications today [26,54].
Among the achievements in the field of fluorescent sensors is the aptasensor developed by Wang et al. The solution proposed by the authors made it possible to detect three different types of influenza virus, including two type A—H1N1, H3N2—and influenza B virus type.
As in the previously mentioned cases, the detection element was a fluorescently labeled DNA aptamer. It was integrated with a relatively small microfluidic system. This aptamer predictably changed its conformation depending on the type and concentration of ions present in the environment. These changes enabled the simultaneous detection of various types of influenza virus in no more than 20 min and with a detection limit of 3.2 HAU, which makes the described microfluidic system a potential tool for on-site diagnostics in the office of, for example, a doctor [40].
5. Electrochemical Aptasensors
The diagnosis of influenza virus is quite often based on the use of electrochemical immunosensors. The principle operation of this type of technique is based on a chemical reaction between the sensor and a chemical substance, during which an electric signal is generated with intensity proportional to the content of the tested factor. The speed of electrochemical analyses, as well as their high sensitivity, selectivity and simplicity in performing determinations, make them suitable for real-time virus detection [82]. Currently, there is a lot of research in this field, and below are selected projects that undoubtedly deserve attention.
The clinical need for rapid differentiation of influenza virus subtypes is directly related to their differential susceptibility/susceptibility to treatment. This mainly concerns the H1N1 and H3N2 subtypes that are widespread in humans. Accordingly, the team of Bhardwaj et al. in 2019 [83] presented the characteristics of two candidates for ssDNA aptamers for the selective detection of influenza AH1N1 virus (V46 and V57—dissociation constants were 19.2 nm and 29.6 nm, respectively), the action of which is based on targeting the recombinant mini-hemagglutinin protein (mini-HA—the stable stem region of HA) and whole H1N1 viruses. In the course of the conducted analysis, the authors observed that the V46 aptamer exhibits greater affinity for mini-HA and the H1N1 virus subtypes. For this reason, in a further stage of the research, it was incorporated into an indium tin oxide-based electrochemical sensor. The results of the analysis turned out to be very promising as the detection limit for the H1N1 virus was 3.7 plaque forming units per milliliter (PFU/mL), and its selectivity was confirmed by distinguishing six H1N1 virus strains from four different influenza A virus subtypes. Therefore, the authors’ suggestion is understandable that the use of the V46 aptamer in combination with an electrochemical sensor may find application in the rapid differentiation of the H1N1 subtype of the influenza virus, and possibly also may be useful in its neutralization, which will certainly find therapeutic application. Moreover, the detection of H1N1 virus using this aptasensor is faster than standard ELISA assays and nucleic acid based techniques.
Furthermore, Bhardwai’s team and colleagues constructed a vertical flow-based paper immunosensor for the rapid electrochemical and colorimetric detection of the H1N1 influenza virus with high sensitivity [84]. For this purpose, a sample pad with two pore sizes/DP was used—double pore size, a conjugate cartridge and a nitrocellulose membrane strip. The DP sample pad constructed in this way had the desired filtration properties, which was confirmed by using fluorescent beads, showing that only small-sized bio-particles such as viruses can pass through it. The measurements were performed using the electrochemical impedance spectroscopy (EIS) technique, where working, opposing and reference electrodes were used, which were, respectively, a gold paper electrode, carbon paste electrode and Ag/AgCl electrode. The thus constructed measuring set made it possible to detect the H1N1 virus at the concentration of 3.3 PFU/mL (PBS) and 4.7 PFU/mL (saliva). At the same time, the color signal emitted by the free HRP-Ab was assessed by means of a colorimetric scanner. Its use made it possible to detect the virus in the titers of 1.34 PFU/mL (PBS) and 2.27 PFU/mL (saliva). According to the authors, the simultaneous use of these two methods will help to reduce the number of false results, and the device for simultaneous qualitative and quantitative analysis will simplify and speed up the diagnosis of the influenza virus.
The H1N1 influenza virus, due to its dangerous impact on human health, especially in children and the elderly, has become the subject of research by Kushawa et al. [85]. The authors, looking for quick diagnostic methods, were the first to apply the procedure of acquiring aptamers with the use of multiple targets SELCOS (systemic enrichment of ligands by competitive selection), also known as competitive non-SELEX, in which, unlike the techniques used so far, the polymerase chain reaction (PCR) is not used. The aptamers obtained in this way show the ability to detect targets with a very similar structure, which proves their extremely high selectivity. The aptamer obtained in this way was used as an element of the electrochemical diagnostics system (Apta-DEPSOR) allowing the selection of aptamer pools with high affinity (for H1N1 KD (dissociation constant) = 82 pM, for H3N2 KD = 88 pM) and low cross activity. This study used a single-use, three-electrode screen-printed (DEP) chip. This three-electrode
electrochemical analysis system uses a carbon working electrode, a counter electrode and an Ag/AgCl reference electrode. The electrochemical detection was based on the Au NPs electro-oxidation reaction. An increase in DPV (differentiation pulse voltammetry) signal was observed with an increase in Au NPs captured by the H1N1 protein on the surface of the working electrode. A reduction in the DPV signal was in turn observed when most of the H1N1 protein was captured by the aptamer strands in the solution. This aptasensor detected H1N1 in the dynamic range of 0.4–100 µg/mL, and the LOD was 0.51 µg/mL. This research represents a huge step towards the real transfer of the rapid and reliable diagnosis of the H1N1 virus to the field.
6. Conclusions
The diagnosis of viral diseases requires not only the use of sensitive and specific methods, but they must also be fast, cheap and widely available. An ideal diagnostic test should be possible in the doctor’s office and the result should be available in a short time. This is crucial in preventing the spread of epidemics of viral diseases such as the flu and COVID-19.
Aptamers are a specific, clean, cheap and quick solution with enormous potential in the diagnosis of viral diseases. Numerous studies summarized in this paper have demonstrated their effectiveness in detecting pathogenic strains causing influenza in humans and other animals. First of all, the progress of biological and technical sciences allowed for the miniaturization of the applied solutions, significantly simplified them and lowered the cost of their production and implementation. Even before 2015, the results of research work and the use of aptasensors in the diagnosis of diseases caused by viruses did not allow their use in the field, outside the laboratory. Currently, the solutions developed have mostly solved old problems. Among the aptasensors dedicated to the detection of the influenza virus, various solutions are used, including impedimetric, fluorescent and electrochemical. In particular, research and impedimetric aptasensors show, in our opinion, very advanced and the best relative results. Before their use, however, final studies confirming the effectiveness of their use are necessary. These studies should be performed as quickly as possible, since the potential of aptasensors in the diagnosis of viral diseases, including influenza, seems to be enormous, and the widespread COVID-19 epidemic, due to the similarity of symptoms of the influenza infection will require reliable diagnostic tools differentiating infections by influenza viruses and SARS-CoV-2, especially in the approaching period of increased flu cases in the northern hemisphere.
Author Contributions: E.W., T.W. and E.P. conceived the review topic and wrote the manuscript; E.W. compiled the table and wrote the manuscript; P.K. corrected and edited the manuscript. All authors have read and agreed to the published version of the manuscript.
Funding: This research received no external funding
Conflicts of Interest: The authors declare no conflict of interest.
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Linkage disequilibrium across two different single-nucleotide polymorphism genome scans
Juan Manuel Peralta*1,2, Thomas D Dyer2, Diane M Warren2, John Blangero2 and Laura Almasy2
Address: 1Centro de Investigación en Biología Celular y Molecular, Ciudad de la Investigación, Universidad de Costa Rica, San José, Costa Rica and 2Genomics Computing Center, Department of Genetics, Southwest Foundation for Biomedical Research, San Antonio, TX 78227-5301, USA
Email: Juan Manuel Peralta* - [email protected]; Thomas D Dyer - [email protected]; Diane M Warren - [email protected]; John Blangero - [email protected]; Laura Almasy - [email protected]
* Corresponding author
Abstract
Linkage disequilibrium (LD) content was calculated for the Genetic Analysis Workshop 14 Affymetrix and Illumina single-nucleotide polymorphism (SNP) genome scans of the Collaborative Study on the Genetics of Alcoholism samples. Pair-wise LD was measured as both D' and r^2 on 505 pedigree founder individuals. The r^2 estimates were then used to correct the multipoint identity by descent matrix (MIBD) calculation to account for LD and LOD scores on chromosomes 3 and 18 were calculated for COGA’s tttd3 electrophysiological trait using those MIBDs. Extensive LD was observed throughout both marker sets, and it was higher in Affymetrix’s more dense SNP map. However, SNP density did not solely account for Affymetrix’s higher LD. MIBD estimation procedures assume linkage equilibrium to construct genotypes of non-genotyped pedigree founder individuals, and dense SNP genotyping maps are likely to contain moderate to high LD between markers. LOD score plots calculated after correction for LD followed the same general pattern as uncorrected ones. Since in our study almost half of the pedigree founders were genotyped, it is possible that LD had a minor impact on the LOD scores. Caution should probably be taken when using high density SNP maps when many non-genotyped founders are present in the study pedigrees.
Background
Single nucleotide polymorphisms (SNPs) are ubiquitous throughout the human genome. SNPs are more closely spaced than microsatellites and they permit the construction of very high-density genome screening maps. Methods that rely on SNPs are very easy to automate (no electrophoresis, easy allele calling), and will probably be more cost effective than microsatellites for performance high-throughput genotyping.
Yet, several properties of SNP maps remain unclear. Kruglyak [1] evaluated the usefulness of diallelic markers for linkage analysis by evaluating how many of them would be needed to extract the same amount of genetic information as microsatellites. With the help of simulation, he concludes that a 1–2 cM diallelic map will be equivalent or even superior to the conventional 5–10 cM microsatellite map, even in cases in which allele frequencies of the diallelic markers are far from the ideal 50/50 ratio. More recently, Goddard and Wijsman [2] pointed out the relevance of marker information, map accuracy, and flexibility of analysis as important factors to consider for diallelic maps. They argue in favor of clustered SNP maps, with 2–3 SNPs per cluster.
The impact of linkage disequilibrium (LD) on linkage studies has also been the subject of some discussion [3] and analysis [4], and this issue still raises several questions. For instance, the estimation of multipoint identity-by-descent (MIBD) matrices generally assumes that haplotypes for non-genotyped founders can be imputed using the product of the marker allele frequencies involved, effectively implying that the haplotype markers are in linkage equilibrium (LE). Because SNPs are much more closely spaced than traditional microsatellites, the assumption that the markers are in LE can be easily violated. The effect that such departures from LE will have on the LOD score statistic is yet unclear.
Polymorphism information content (PIC) [7-9] was also calculated for each SNP marker and each two-SNP marker haplotype (treated as a single 4-allele marker). All LD and PIC measures were assigned to the average genetic distance between the markers forming each pair.
The effect that such departures from LE will have on the LOD score statistic is yet unclear.
Methods
SNP genotypes from the clean GAW14 COGA datasets were selected from Affymetrix's GeneChip Mapping 10 K Array (AMA) and Illumina's Linkage Panel III (ILP). A total of 11,120 Affymetrix and 4,720 Illumina SNP markers (SNPs) were present in the final clean datasets, but only 10,084 and 4,599 of those SNPs, respectively, were used for this analysis. One thousand and thirty-six Affymetrix and 121 Illumina markers were not included in the first dataset that was distributed for GAW 14. Those markers became available after a substantial part of the work presented here was done and therefore were not included in the analysis. COGA pedigree founders (n = 505; 240 genotyped, 265 not genotyped) were chosen as a representative sample of unrelated individuals, and only their genotypes were included in the LD analysis.
LD was measured pairwise as $D'$ and $r^2$ [5]. Pairs were composed of SNP markers from the same chromosome and dataset, and all consecutive adjacent marker pairs were constructed for the 22 autosomes. Pairs constructed for AMA and ILP SNPs will be referred as AMASnP and ILPSnP, respectively. The expectation-maximization (EM) method implemented in GENECOUNTING [6] was used to obtain maximum-likelihood frequency estimates of the required two-marker haplotypes. As pointed out by Schaid et al. [3], the EM algorithm does not assume LE between markers. Sex chromosomes were not included in the analysis. To assess the degree of spurious LD present in the sample, unlinked markers from chromosomes 1 and 2 were combined systematically in pairs, starting at 0 cM and moving towards the opposite telomere. LD between them was measured as described above.
Affymetrix and Illumina SNP genotyping of samples from the Collaborative Study on the Genetics of Alcoholism (COGA) for the Genetic Analysis Workshop 14 (GAW14) provide an excellent opportunity to investigate certain properties of SNP genome screening maps. It also leads to the comparison of several aspects of both company products, one of the most obvious being the performance of the highly dense Affymetrix in comparison with the more sparse Illumina array.
Here, our main objective is to explore empirically the extent of LD that is present in the two complete SNP genome scans of real DNA samples and its effect on the LOD score.
Results
Overall, pair-wise haplotype frequencies were estimated for a median of 488 Illumina (range = 486–520) and 490 Affymetrix (range = 276–520) SNP haplotypes per chromosome. Nineteen AMA SNPs had to be discarded from the analysis because they were not polymorphic in the sample. Except for chromosomes 19 and 22 AMA had a more dense marker coverage of each chromosome.
Random LD between unlinked markers was found to be low, for both $r^2$ and $D'$, in ILP (mean $r^2 = 4.35 \pm 0.34 \times 10^{-3}$, mean $D' = -2.45 \pm 5.22 \times 10^{-3}$) as well as in AMA (mean $r^2 = 5.51 \pm 0.29 \times 10^{-3}$, mean $D' = -7.44 \pm 10.09 \times 10^{-3}$). But variance was greater in AMA's $r^2$ and $D'$ ($F_{749,380} = 1.43, p < 0.0001$ and $F_{749,380} = 7.35, p < 0.0001$, respectively). Only 0.26% ($N = 380$) ILPSnP showed $|D'| \geq 0.5$, while 6.85% ($n = 759$) AMASnP did. All ILPSnP and AMASnP $r^2$ values for unlinked markers were below 0.06.
We analyzed 10,065 AMA and 4,598 ILP linked SNP pairs. Of all AMASnP, 8,096 (80.44%) were pairs in which the
distance between the SNPs was \( \leq 1 \) cM, while only 1,242 (27.01\%) ILPSnP were formed by markers at that spacing. The mean distance between the two SNPs in a pair was significantly different \((T_{10064,4597} = 24.56, p < 0.0001)\) between AMA (3.08 ± 0.07 × 10\(^{-1}\) cM), and ILP (7.48 ± 0.16 × 10\(^{-1}\) cM) pairs. Variance in distance between AMASnP SNPs was significantly lower \((F_{10064,4597} = 0.44, p < 0.0001)\) than between ILPSnP SNPs.
Figure 1 shows AMASnP and ILPSnP \( r^2 \) and D' LD frequency plots for all 22 chromosomes. The extent of LD, measured either as \( r^2 \) or D', is much more conspicuous between AMASnP. Most of the observed \( r^2 \) values are \( \leq 0.2 \) for both SNP sets, but |D'| values show maximum frequencies at values \( \leq 0.2 \) and >0.8 only for Affymetrix SNPs. At a SNP spacing within a pair \( \leq 1 \) cM, 3,241 (40.03\%) of all AMASnP had measures of |D'| \( \geq 0.5 \), while only 37 (2.98\%) of all ILPSnP did. At the same \( \leq 1 \) cM spacing, 960 (11.87\%) AMASnP and 8 (0.64\%) ILPSnP pairs had an \( r^2 \geq 0.5 \) measure.
Mean PIC values were found to be significantly lower \((T_{10064,4597} = 90.18, p << 0.0001)\) for AMA (0.2853 ± 0.0006) than for ILP (0.3536 ± 0.0003) SNPs. PIC was also significantly lower \((T_{10064,4597} = 85.56, p < 0.0001)\) for AMA (4.92 ± 0.01 × 10\(^{-1}\)) than for ILP (6.41 ± 0.01 × 10\(^{-1}\)) haplotypes. Total PIC variance was significantly higher in AMA than in ILP for both SNPs \((F_{10064,4597} = 8.28, p << 0.0001)\) and haplotypes \((F_{10064,4597} = 3.21, p << 0.0001)\).
Using AMA uncorrected MIBDs, the ttd3 trait phenotype maximum LOD peaks were 2.94 at 58 cM from 18p-ter and 3.34 at 211 cM from 3p-ter, while ILP's uncorrected MIBDs gave LOD peaks of 2.73 at 58 cM from 18p-ter and 3.63 at 213 cM from 3p-ter. Figure 2 shows a plot of the region with the highest LOD scores obtained for the AMA and ILP SNP sets at the different arbitrary \( r^2 \) thresholds used. LOD score curves tended to follow the same general pattern of LODs calculated using the uncorrected MIBDs, with three exceptions that are worth mentioning: a shift from 58 cM to 61 cM (chromosome 18) in the location of the maximum LOD when AMA's 0.2 MIBD was used; and both, a 8-cM shift from 58 cM to 66 cM (chromosome 18) and a shift from 213 cM to 215 cM (chromosome 3) when ILP's 0.2, 0.4, and 0.6 MIBDs were used.
Discussion
As both the AMA and ILP genome scans show, extensive LD is present throughout the genome. Yet it is more extensive within AMA haplotypes, something which per se is not surprising, given that AMA's higher marker density causes SNPs to be more closely spaced. What's striking is that for markers under the same < 1-cM marker spacing, AMA shows a much higher proportion of LD than ILP (~40\% vs ~3\% respectively, see Results). This suggests that...
there might be reasons, other than marker spacing, that affect LD content. For instance, Affymetrix and Illumina certainly have different protocols to select the SNPs that are in their AMA and ILP products. Differences in the SNP selection procedure might explain why we observed significantly more LD in the Affymetrix product.
The AMA and ILP genome scans also differ in the quantity of SNP and haplotype information. PIC was much more variable in the AMA dataset, and it was consistently lower for both SNPs and haplotypes. One possible explanation for this is that closely spaced markers became redundant because of the high LD present between them.
What seems to be clear is that LD is a common feature of the genome. Tsunoda et al. [13] focused on 77,176 SNPs, located in 14,271 genes, genotyped for 1,128 chromosomes also found regions of the genome showing extensive LD.
John et al. [4] also recently published an empirical comparison between SNP and microsatellite whole-genome scans. They used Affymetrix GeneChip Mapping 10 K Arrays and found areas of LD. They reported that across a 40-cM region of chromosome 6, 45% of the SNP pairs had an \( r^2 \geq 0.4 \). John et al. [4] tried to correct the IBD calculations for high LD, using only SNPs that were in LE, and found "modest" changes in linkage results [4]. But because removing SNPs that show LD results decreases the information content present for the linkage, they tried unsuccessfully to compensate for it by replacing them with haplotypes generated by the EM algorithm.
Here, we explored the effect of LD on the LOD score by accounting for the amount of it in the founder individuals, at different stringencies (\( r^2 \) thresholds), when creating the MIBD matrices. We found "modest" LOD score changes in magnitude, as John et al. did. But those modest changes in magnitudes were able to shift the location of the maximum LOD score even by a great genetic distance (10 cM, see Figure 2). Because we do not know the true location of the quantitative trait locus (QTL) affecting COGA's ttdt3 is (or if such a QTL exists), it is impossible for us to determine the relevance that this finding might have for QTL/gene mapping.
In spite of this, the main features of the LOD score curves remain the same, suggesting that the MIBD estimation algorithm used might be robust enough to tolerate the violation of its implicit assumption of LE. Another possible, and maybe more likely, explanation could be that the COGA families analyzed here do not provide a good framework to test for the effect of LD on LODs through MIBD estimation. Because we had genotypes for about half the founders, few founder haplotypes had to be estimated during MIBD construction by means of marker allele frequencies. In effect, that could diminish the impact of LD on the LOD scores by means of fewer violations of the LE assumption. If this is indeed the case, then LD could potentially be a serious problem for studies that have many non-genotyped founder individuals in their pedigrees.
Finally, one more practical issue deserves consideration. These technologies generate vast amounts of information that will be statistically analyzed. Those statistical analyses have a non-trivial computational cost associated with them. Users of these technologies have to evaluate the wet-laboratory savings they bring in light of the not-so-evident computational and statistical costs that will be needed after data collection. Affymetrix's approach is more costly in this sense, not because it produces a higher volume of information to be analyzed, but because part of it is redundant and time and/or resources need to be allocated for its analysis.
Conclusion
SNP genotyping technologies are becoming more widespread and allow for very high density (less than a centi-morgan) whole-genome scans. But as marker map density increases, so does LD content. We showed that considerable LD exists between markers in both the Affymetrix and Illumina SNP genotyping sets, and it is more pronounced in Affymetrix's denser map. Since all methods used to calculate MIBDs assume LE when estimating haplotypes of non-typed founder individuals, the effect of violating this assumption using highly dense SNP maps in which LD is more the rule than the exception needs to be considered. We observed modest changes in LOD score magnitude and shifts in the position of the maximum LOD after correcting for LD in the MIBDs. But the effect of LD on LOD scores might not always be this subtle and it may be adverse in studies where a large number of founder individuals are not genotyped.
Abbreviations
AMA: Affymetrix GeneChip Mapping 10 K Array
COGA: Collaborative Study of the Genetics of Alcoholism
EM: Expectation maximization
GAW14: Genetic Analysis Workshop 14
ILP: Illumina Linkage Panel III
LD: Linkage disequilibrium
LE: Linkage equilibrium
MIBD: Multipoint identity by descent
QTL: Quantitative trait locus
PIC: Polymorphism information content
SNP: Single-nucleotide polymorphism
Authors' contributions
JMP performed the statistical analysis and drafted the manuscript. TD did the data cleanup and helped with the preparation of the MIBD matrices. LA designed the study, participated in its coordination, and helped to draft the manuscript. DMW selected the chromosomes, the trait, and the model for the linkage analysis. JB participated in the design of the study.
Acknowledgements
This work was supported in part by NIH grants MH59490, MH61622 and HL70751.
References
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Multifactor dimensionality reduction analysis for detecting SNP-SNP, SNP-environment interactions associated with polycystic ovarian syndrome among South Indian women
Abstract
Background: Polycystic Ovarian Syndrome (PCOS) is the most common cause of female anovulatory infertility, with a prevalence of 8-10% among women of reproductive age, characterized by clinical or biochemical androgen excess, ovulatory dysfunction and polycystic ovaries. It is a multifactorial disorder which is determined by the interaction of multiple genetic and environmental factors. Many candidate genes have been proposed as important contributors to PCOS. One of the greatest challenges facing human geneticists is the identification and characterization of susceptibility genes for common complex multifactorial human diseases. This challenge is partly due to the limitations of parametric-statistical methods for detection of gene effects that are dependent completely or partially on interactions with other genes with environmental factors. Multifactor-dimensionality reduction (MDR) has power to identify interactions among two or more loci in relatively small samples, and reduces dimensionality of multilocus information and improves identification of polymorphism combinations associated with disease risk.
Aim: Our aim is to identify the effect of gene – gene, and gene- environmental interactions associated with PCOS disease risk using MDR.
Materials and methods: Prospective genetic case-control study, involving 204 women with PCOS and 204 healthy, sex and age matched controls. Anthropometric and biochemical profile were taken in a well-designed proforma. Isolation of DNA by salting out method and genotype analysis was done for all the study population using PCR-RFLP. MDR analysis of SNPs and SNP–environmental interactions were done.
Results: MDR statistical version (MDR_3.0.2) showed the strong interaction between Calpain-10-FSHR, and TNF-α-IGF2. Moderate interaction is noticed between LHCGR, TNF-α/IGF2, and weak interaction between LHCGR and FSHR/CAPN-10. Correlation is seen between TNF-α and IGF2, synergistic interaction seen between FSHR and Calpain-10, whereas LHCGR is independently interacting with the disease. SNP-environmental interactions also revealed impact of individual factor and their combination with SNP has shown significant effect in disease risk.
Conclusion: SNP-SNP, SNP-Environmental factors interaction analysis using MDR software revealed the role of various genes and environmental factors in combination are increasing the disease risk effectively, and helps in better understanding of the reproductive and metabolic abnormalities and management of the PCOS.
Keywords: polycystic ovary syndrome, multifactor dimensionality reduction, SNP
Introduction
Polycystic ovarian syndrome (PCOS) is the leading cause of menstrual irregularities and anovulatory infertility which is now essentially known as androgen excess disorder with varying degrees of reproductive and metabolic abnormalities determined by the interaction of multiple genetic and environmental factors. We focused on the candidate gene analysis of PCOS in the South Indian women by analyzing a panel of five candidate genes (Tumor necrosis factor alpha A, Insulin growth factor 2, Calpain 10, Follicular stimulating hormone receptor and Leutinising hormone G protein coupled receptor) involved in insulin action and secretion, gonadotropin action and regulation and hyperandrogenism. The genetic association of the above candidate genes with PCOS susceptibility were studied. However in the case of complex genetic disorders, it is usually observed that inspite of a small effect of an individual SNP, the genetic effects of combinations of functionally relevant SNPs may synergistically contribute to increased disease risk. One of the biggest challenges in human genetics is identifying polymorphisms, or mutations, that increases the disease risk. This challenge is partly due to the limitations of parametric statistical methods (i.e., those in which a hypothesis about the value of a statistical parameter is made) for detection of gene effects that are dependent completely or partially on interactions with other genes and with environmental exposures. Multifactor dimensionality reduction (MDR) was developed for detecting gene–gene and gene-environment interactions in case-control studies with relatively small sample size.
Materials and methods
Ethics Statement
This study was approved by the institutional ethical committee (Vasavi hospital and research centre) and informed written consent was obtained from all subjects. In this prospective case-control study, we included 204 PCOS patients from Anu’s fertility center, Somajiguda, Hyderabad, India from July 2011 to January 2013.
Inclusion criteria
Subjects were ranged in age from 17 to 35 years and were diagnosed using the 2006-Androgen Excess Society (AES) Criteria. Hyperandrogenism, clinical or biochemical and either oligo-ovulation or Polycystic ovarian morphology.
Exclusion criteria
Women excluded from the study were those with inherited disorders like congenital adrenal hyperplasia, androgen secreting neoplasms, androgenic/anabolic drug use or abuse, Cushing syndrome, syndromes of severe insulin resistance, thyroid dysfunction and hyperprolactinemia. We have recruited 204 controls from a tertiary care hospital, Kamineni academy of medical sciences and research center, LB Nagar, Hyderabad. Controls ranged from 17-35 years and did not show hirsutism, acne or male-type alopecia and had regular menstrual cycles and none of them satisfied any of the AES-2006 criteria. All the control subjects also underwent an ultrasonographic examination, and women who had any pathologic findings like polycystic ovaries were excluded from the study.
Collection of blood samples, DNA isolation, and SNP Analysis by using PCR-RFLP
Two milliliters of peripheral blood was collected in EDTA for DNA isolation according to the method routinely used in our laboratory, and 5 ml of blood in plain vial for serum preparation from all the patients and controls along with clinical data, personal history and family history. We carried out PCR - RFLP to screen the polymorphisms of TNFα, IGF2, CAPN-10, FSHR, LHCGR genes.
Table 1 Comparison of anthropometric parameters between PCOS and controls using mean and standard deviation
| Parameter | Patients(n=204) | Controls(n=204) | P value |
|-------------------------|-----------------|-----------------|---------|
| Age(years) | 28±3.6 | 28±5.1 | 1 |
| Body mass index (kg/m²) | 27.1±4.93 | 23.4±3.2 | <0.0001 |
| Waist circumference (inches) | 37±4.3 | 30.36±3.3 | <0.0001 |
| Hip circumference(inches) | 39.4±4.1 | 38.1±3.7 | 0.0008 |
| Waist to Hip ratio | 0.93±0.04 | 0.79±0.05 | <0.0001 |
Table 2 Comparison of biochemical parameters between PCOS and controls using mean and standard deviation
| Parameter | Patients (n=204) | Controls (n=204) | P value |
|--------------------------|------------------|------------------|---------|
| Fasting glucose (gm/dl) | 88±8.6 | 86.85±7.1 | 0.0678 |
| Fasting insulin (Uu/ML) | 16.9±7.26 | 6.66±3.19 | <0.0001 |
| Homa Score | 3.73±3.8 | 1.44±0.75 | <0.0001 |
| Lh (IU/L) | 11.97±6.08 | 5.5±3.8 | <0.0001 |
| Fsh (IU/L) | 5.48±1.98 | 7.9±5.4 | 0.0002 |
| LH/FSH | 2.62±1.2 | 1.5±1.2 | <0.0001 |
We framed our analysis of genetic polymorphisms in four steps: 1. SNP-SNP interaction analysis using different combinations among the candidate gene panel. 2. SNP-Environment interaction analysis. 2.a. SNP-Clinical interaction analysis between each genetic polymorphic locus and clinical factors considered as categorical variables. 2.b. SNP-Biochemical interaction analysis between each genetic polymorphic locus and biochemical factors considered as categorical variables. 2.c. SNP-Hormonal interaction analysis between each genetic polymorphic locus and hormonal factors considered as categorical variables. TNFα, IGF2, CAPN-10, FSHR, LHCGR genes were involved in SNP-SNP, SNP-Environment (SNP-Clinical, SNP-Biochemical & SNP-Hormonal) interaction analysis.
For SNP-SNP interaction analysis, we considered five genes (TNFα, IGF2, CAPN-10, FSHR and LHCGR), for gene-clinical: six factors (acne, hirsutism, central obesity, fertility, menarche age, menstrual period), for SNP-Biochemical: nine factors (fasting glucose, fasting Insulin, HOMA score, LH, FSH, LH/FSH, HDL, Triglycerides, TNF serum levels), for SNP-Hormonal: four factors (free testosterone, total testosterone, androstenedione, DHEA) were considered.
Statistical analysis
A p-value of <0.05 was considered statistically significant. Multifactor dimensionality reduction (MDR) software was used for carrying out SNP-SNP and SNP-Environment interaction analysis.
Results
Anthropometric, biochemical and hormonal findings showed significant differences between PCOS and Controls (Table 1–4). Increased BMI and HOMA is associated with IGF2, FSHR and LHCGR gene polymorphism. Increased LH, LH/FSH and DHEA is associated with FSHR and LHCGR gene polymorphism. Increased FTS is associated with IGF2 and FSHR gene polymorphism. The variants of TNFα C850T, Apa1 IGF2 A820G, FSHR Ser680Asn and LHCGR A312G showed 5.7, 7.6, 1.98, & 3.36 folds risk of developing PCOS in our population. CAPN-10 UCSNP-43 did not show any risk association with PCOS in our population.
Multifactor dimensionality reduction analysis for detecting SNP-SNP, SNP-environment interactions associated with polycystic ovarian syndrome among South Indian women
Table 3 Comparison of Hormonal parameters between PCOS and controls using mean and standard deviation
| Parameter | Patients (n=204) | Controls (n=204) | P value |
|----------------------------|-----------------|-----------------|---------|
| Cholesterol (mg/dl) | 161.57±30 | 162.7±33 | 0.8904 |
| Hdl (mg/dl) | 40.21±10.21 | 45±13.4 | <0.0001 |
| Triglycerides (mg/dl) | 126.14±5.2 | 97±49 | <0.0001 |
| Tnf-α (pg/ml) | 13.24±10.6 | 5.6±3.86 | <0.0001 |
Table 4 Summary table for significant observation in genotype/allele frequency analysis for individual genes
| Gene | rs ID | Location | Allele | PCOS (N=204) | Controls (N=204) | Odds ratio (95% C.I.) | P-value |
|---------------|--------|----------|--------|-------------|-----------------|-----------------------|-----------|
| TNF-α | rs1799724 | Exon | C | 382 | 302 | 5.1569 | P<0.0001 |
| C850T | | | T | 26 | 106 | (3.27-8.12) | |
| IGF2 Apal | rs 680 | 3’UTR | A | 244 | 375 | 7.639 | P<0.0001 |
| A820G | | G | G | 164 | 33 | (5.08-11.47) | |
| Calpain 10 | rs 3792267 | Intron 3 | G | 347 | 328 | 0.7207 | P=0.0793 |
| UCSNP-43 | | A | A | 61 | 80 | (0.5-1.039) | |
| FSHR | rs 6166 | Exon 10 | G | 161 | 230 | 1.98 | P<0.0001 |
| Ser680Asn | | A | A | 247 | 178 | (1.5-2.6) | |
| LHCGR | Rs 2293275 | Exon 10 | G | 242 | 199 | 1.5311 | P=0.0026 |
| S312N | | A | A | 166 | 209 | (1.16-2.01) | |
SNP-SNP, SNP-environmental, SNP-biochemical and SNP-hormonal interaction analysis
The multifactorial dimensionality reduction analysis revealed significant contribution of four allelic variants i.e. TNF-α, IGF2, FSHR, and LHCGR in modulating the PCOS risk (Figure 1). CAPN-10 was the only polymorphism evaluated which did not show any association. The shorter the line connecting to attributes the stronger the interaction. The color of the line indicates the type of interaction. Red suggests that there is synergistic relationship (epistasis), Yellow suggests independence, Green and blue suggests redundancy or correlation (Figure 2). When the interaction of five gene polymorphisms was evaluated using MDR statistical version (MDR_3.0.2) showed the strong interaction between Calpain-10-FSHR, and TNF-α-IGF2. Moderate interaction is noticed between LHCGR, TNF-α/IGF2, and weak interaction between FSHR and LHCGR/FSHR/CAPN-10. Correlation is seen between TNF-α and IGF2, synergistic interaction seen between FSHR and Calpain-10, whereas LHCGR is independently interacting with the disease. The interaction graph presents that A820 A/G IGF2 Apal SNP (24.28%), 850 C/T TNF-α (12.24%), 680 G/A FSHR (4.36%), 312 A/G LHCGR (4.10%), UCSNP-43 G/A CAPN-10 (0.71%) polymorphism have independent effects for developing PCOS (Figure 3) (Table 5). There were found independent effects with 0.40% between menarche age and 312A/G LHCGR polymorphism and also found that central obesity, hirsutism, menstrual period, acne, fertility, menarche age, have independent effects for PCOS developing 85.72% entropy for central obesity, followed by 78.81 %,73.67%, 72.87%, 63.93%, 4.68% of entropy. TNF-α, IGF2, CAPN-10 and FSHR showed correlation effects with negative entropy (Figure 4) (Table 6). The interaction graph showed combination of TNF-α-fasting glucose, IGF2-fasting glucose, IGF2-HDL, IGF2-FSH, CAPN10-fasting glucose, CAPN10-HDL, CAPN10-fasting insulin, CAPN10-LH/FSH, FSHR-LH, FSHR-HDL, FSHR-fasting insulin, LHCGR-HOMA, LHCGR-LH, LHCGR-TG, LHCGR-TNFα showed synergistic effect with 0.46% of entropy followed by 0.47%, 1.02%, 0.40%, 0.53%, 0.63%, 0.42%, 0.09%, 0.08%, 0.35%, 0.38%, 0.29%, 0.17%, 0.62%, 0.47%, 0.29% of entropy. It was also found that the combination of TNF-α, IGF2, CALP10-10, FSHR with serum TNF-α showed synergism with negative entropy (Table 7). The interaction graph presents that Androstenedione, FTS, DHEA, TTS have independent effects for PCOS developing with 27.50% of entropy for central obesity, followed by 26.99%, 16.23%, 7.93% of entropy. It was found that combination of FSHR-TTS, CALP10-AND, CAPN10-DHEA, CALP10-TTS, and CALP10-FTS are risk factors for PCOS, showed independence effects with 0.97%, followed by 1.09%, 0.41%, 0.34% and 0.03% of entropy (Figure 5) (Table 8).
Citation: Thathapudi S, Erukambattu JS, Putcha UK, et al. Multifactor dimensionality reduction analysis for detecting SNP-SNP, SNP-environment interactions associated with polycystic ovarian syndrome among South Indian women. Int J Mol Biol Open Access. 2019;4(2):59–65. DOI: 10.15406/ijmboa.2019.04.00098
Multifactor dimensionality reduction analysis for detecting SNP-SNP, SNP-environment interactions associated with polycystic ovarian syndrome among South Indian women
Figure 1 Circle graph representing gene-gene interaction of insulin resistance and hypothalamo-pituitary-gonadotropin axis pathway in PCOS.
Figure 2 Dendogram representing gene-gene interaction of insulin resistance and hypothalamo-pituitary-gonadotropin axis pathway.
Figure 3 Circle graph representing interaction between gene–clinical factors.
Citation: Thathapudi S, Erukambattu JS, Putcha UK, et al. Multifactor dimensionality reduction analysis for detecting SNP-SNP, SNP-environment interactions associated with polycystic ovarian syndrome among South Indian women. Int J Mol Biol Open Access. 2019;4(2):59–65. DOI: 10.15406/ijmboa.2019.04.00098
Multifactor dimensionality reduction analysis for detecting SNP-SNP, SNP-environment interactions associated with polycystic ovarian syndrome among South Indian women
Figure 4 Circle graph representing interactions between gene and biochemical factors.
Figure 5 Circle graph representing gene–androgen levels interaction of five gene polymorphisms in PCOS as compared to controls.
Table 5 SNP-SNP interactions in each loci combination category
| Loci combinations | SNP combinations | Balanced accuracy values | CV consistency | p-value |
|-------------------|------------------|--------------------------|----------------|---------|
| Two loci | TNF, IGF2 | 0.7868 | 10 | 0.0002 |
| | TNF, CAPN10 | 0.6667 | 10 | 0.0195 |
| | TNF, FSHR | 0.7108 | 10 | 0.0068 |
| | TNF, LHCGR | 0.6691 | 10 | 0.018 |
| | IGF2, CAPN10 | 0.7794 | 10 | 0.003 |
| | IGF2, FSHR | 0.7794 | 10 | 0.003 |
| | IGF2, LHCGR | 0.7598 | 6 | 0.0009 |
| | CAPN10, FSHR | 0.5711 | 8 | 0.3638 |
| | CAPN10, LHCGR | 0.5711 | 10 | 0.2862 |
| | FSHR, LHCGR | 0.5613 | 10 | 0.4335 |
| Three loci | TNF, IGF2, CAPN10| 0.7721 | 10 | 0.0004 |
| | TNF, IGF2, FSHR | 0.777 | 10 | 0.0003 |
| | TNF, IGF2, LHCGR | 0.8064 | 10 | 0.0002 |
| | IGF2, CAPN10, FSHR| 0.7696 | 10 | 0.0005 |
| | IGF2, CAPN10, LHCGR| 0.7574 | 10 | 0.001 |
| | CAPN10, FSHR, LHCGR| 0.576 | 10 | 0.3304 |
| | CAPN10, FSHR, TNF| 0.6618 | 10 | 0.0361 |
| | TNF, FSHR, LHCGR | 0.6936 | 10 | 0.0108 |
| | IGF2, FSHR, LHCGR| 0.7574 | 9 | 0.001 |
| Four loci | TNF, IGF, CAPN10, FSHR | 0.7353 | 10 | 0.0026 |
| | TNF, CAPN10, FSHR, LHCGR| 0.625 | 10 | 0.1056 |
| | LHCGR, CAPN10, FSHR, IGF2| 0.7206 | 10 | 0.0048 |
| | TNF, IGF2, FSHR, LHCGR| 0.7574 | 7 | 0.001 |
| | TNF, IGF2, CAPN10, LHCGR| 0.7868 | 10 | 0.0002 |
| Five loci | IGF2, TNF, CAPN10, FSHR, LHCGR| 0.7255 | 10 | 0.0039 |
Citation: Thathapudi S, Erukambattu JS, Putcha UK, et al. Multifactor dimensionality reduction analysis for detecting SNP-SNP, SNP-environment interactions associated with polycystic ovarian syndrome among South Indian women. Int J Mol Biol Open Access. 2019;4(2):59–65. DOI: 10.15406/ijmboa.2019.04.00098
Multifactor dimensionality reduction analysis for detecting SNP-SNP, SNP-environment interactions associated with polycystic ovarian syndrome among South Indian women
Table 6 Gene-Environment (clinical) interactions
| Loci combinations | SNP combinations | Balanced accuracy values | CV consistency | p-value |
|-------------------|-----------------------------|--------------------------|----------------|---------|
| 6 Loci | FSHR, LHCGR, CAPN10, TNF, IGF2, Acne | 0.9412 | 10 | <0.0001 |
| | FSHR, LHCGR, CAPN10, TNF, IGF2, Central obesity | 0.9755 | 10 | <0.0001 |
| | FSHR, LHCGR, CAPN10, TNF, IGF2, Hirsutism | 0.9583 | 10 | <0.0001 |
| | FSHR, LHCGR, CAPN10, TNF, IGF2, Fertility | 0.9289 | 10 | <0.0001 |
| | FSHR, LHCGR, CAPN10, TNF, IGF2, Menarche age | 0.7525 | 10 | 0.0012 |
| | FSHR, LHCGR, CAPN10, TNF, IGF2, Menstrual period | 0.9436 | 10 | <0.0001 |
Table 7 Gene-Environment (Biochemical) interactions
| Loci combinations | SNP combinations | Balanced accuracy values | CV consistency | p-value |
|-------------------|--------------------------------|--------------------------|----------------|---------|
| 6 Loci | FSHR, LHCGR, CAPN10, TNF, IGF2, Fasting Insulin | 0.799 | 10 | 0.0001 |
| | FSHR, LHCGR, CAPN10, TNF, IGF2, Homa Score | 0.7623 | 5 | 0.0008 |
| | FSHR, LHCGR, CAPN10, TNF, IGF2, LH | 0.799 | 10 | 0.0001 |
| | FSHR, LHCGR, CAPN10, TNF, IGF2, LH/FSH | 0.7181 | 10 | 0.0047 |
| | FSHR, LHCGR, CAPN10, TNF, IGF2, Triglycerides | 0.7181 | 10 | 0.005 |
| | FSHR, LHCGR, CAPN10, TNF, IGF2, HDL | 0.7377 | 10 | 0.0023 |
| | FSHR, LHCGR, CAPN10, TNF, IGF2, Serum TNF | 0.7328 | 10 | 0.0009 |
Table 8 Gene-Environment (Hormonal) interactions
| Loci combinations | SNP combinations | Balanced accuracy values | CV consistency | p-value |
|-------------------|-----------------------------------------|--------------------------|----------------|---------|
| 6 Loci | FSHR, LHCGR, CAPN10, TNF, IGF2, Total Testosterone | 0.6569 | 10 | 0.0335 |
| | FSHR, LHCGR, CAPN10, TNF, IGF2, Free Testosterone | 0.723 | 10 | 0.0006 |
| | FSHR, LHCGR, CAPN10, TNF, IGF2, DHEA | 0.6446 | 10 | 0.0086 |
| | FSHR, LHCGR, CAPN10, TNF, IGF2, Androstenedion | 0.7475 | 10 | 0.0003 |
Discussion
Complex multifactorial disorders are manifested as a result of interactions between multiple genetic and environmental factors because the effect of any single genetic variation will likely be dependent on other genetic variations (gene-gene interaction or epistasis) and environmental factors (gene-environment interaction). MDR addresses concerns about inaccurate parameter estimates and low power for identifying interactions in relatively small sample sizes. MDR is a nonparametric and genetic model-free approach. In MDR, genotypes are pooled into high risk and low risk groups, effectively reducing the dimensionality of the genotype predictors from N dimensions to one dimension. The new one-dimensional multi locus genotype variable is evaluated for its ability to classify and predict disease status using cross-validation and permutation testing. In the dendrogram, color of the line indicates the type of interaction. Red and Orange suggest there is a synergistic relationship (i.e. epistasis). Yellow suggests independence. Green and Blue suggest redundancy or correlation. The shorter the line connecting two attributes the stronger the interaction (Epistasis blog). Cordell reviewed, multifactor dimensionality reduction has emerged as one important new method for detecting statistical epistasis in genetic association studies. MDR was a nonparametric method and genetic model-free data mining and machine learning strategy for identifying combinations of discrete genetic and environmental factors. PCOS is a multifactorial disorder which is determined by the interaction of multiple genetic and environmental factors. Many candidate genes have been proposed as important contributors to PCOS. We focused on the candidate gene analysis of PCOS in the South Indian women by analyzing a panel of five candidate genes (Tumor necrosis factor alpha, Insulin growth factor 2, Calpain 10, Follicular stimulating hormone receptor and Leutinising hormone G protein coupled receptor) involved in insulin action and secretion, gonadotropin action and regulation and hyperandrogenism. The genetic association of the above candidate genes with PCOS susceptibility were studied. The variants of TNFα C850T, Apal IGF2 A820G, FSHR Ser680Asn and LHCGR A312G showed 5.7, 7.6, 1.98, & 3.36 folds risk of developing PCOS in our population. CAPN-10 UCSNP-43 did not show any risk association with PCOS in our population. Although the candidate genes and the underlying biological pathways analyzed in this study have been previously implicated in the etiology of PCOS, their SNP-SNP interactions, SNP-environment interactions have not been described before. Therefore to identify the complex biological relationships between the molecular pathological pathways leading to PCOS, we attempted to understand the epistasis phenomenon involved in PCOS etiology through SNP-SNP interaction, SNP-environment interaction analysis. In the individual gene analysis, four out of five genes indicated significant associative patterns with PCOS, and Calpain-10 did not show any contribution, but it showed a positive interaction with FSHR and TNF-α polymorphism. The first
Citation: Thathapudi S, Erukambattu JS, Putcha UK, et al. Multifactor dimensionality reduction analysis for detecting SNP-SNP, SNP-environment interactions associated with polycystic ovarian syndrome among South Indian women. Int J Mol Biol Open Access. 2019;4(2):59–65. DOI: 10.15406/ijmboa.2019.04.00098
Multifactor dimensionality reduction analysis for detecting SNP-SNP, SNP-environment interactions associated with polycystic ovarian syndrome among South Indian women
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Sujatha Thathapudi, Jayashankar Erukkambattu, Uma Addepally, et al. Association of follicle-stimulating hormone receptor gene Ser680Asn (rs6166) polymorphism with Polycystic Ovarian Syndrome. Int J Reprod Contracept Obstet. 2016;5(9):3126–3132.
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Pilot Sleep Behavior across Time during Ultra-Long-Range Flights
Jaime K. Devine 1,*, Jake Choynowski 1, Caio R. Garcia 2, Audrey S. Simoes 2, Marina R. Guelere 2, Bruno de Godoy 2, Diego S. Silva 2, Philipe Pacheco 2 and Steven R. Hursh 1,3
1 Institutes for Behavior Resources, Inc., Baltimore, MD 21218, USA; [email protected] (J.C.); [email protected] (S.R.H.)
2 Azul Linhas Aéreas Brasileiras, 06460-040 Sao Paulo, Brazil; [email protected] (C.R.G.);
[email protected] (A.S.S.); [email protected] (M.R.G.);
[email protected] (B.D.G.); [email protected] (D.S.S.);
[email protected] (P.P.)
3 Institutes for Behavior Resources, Johns Hopkins University School of Medicine, Baltimore, MD 21205, USA
* Correspondence: [email protected]; Tel.: +1-410-752-6080 (ext. 132)
Abstract: Fatigue risk to the pilot has been a deterrent for conducting direct flights longer than 12 h under normal conditions, but such flights were a necessity during the COVID-19 pandemic. Twenty (N = 20) pilots flying across five humanitarian missions between Brazil and China wore a sleep-tracking device (the Zulu watch), which has been validated for the estimation of sleep timing (sleep onset and offset), duration, efficiency, and sleep score (wake, interrupted, light, or deep Sleep) throughout the mission period. Pilots also reported sleep timing, duration, and subjective quality of their in-flight rest periods using a sleep diary. To our knowledge, this is the first report of commercial pilot sleep behavior during ultra-long-range operations under COVID-19 pandemic conditions. Moreover, these analyses provide an estimate of sleep score during in-flight sleep, which has not been reported previously in the literature.
Keywords: sleep score; sleep duration; sleep timing; time zones; COVID-19; aviation
1. Introduction
Pilots operating routes that are long-haul (LH), defined as flight duty periods (FDPs) longer than 6 h, or ultra-long-range (ULR), defined as FDPs longer than 12 h, routinely suffer from fatigue due to sleep disruption [1–3]. Schedule mitigation and in-flight napping are fatigue countermeasures used to reduce sleep pressure during LH/ULR flights and aviation is one of the most regulated industries with regards to fatigue [4–9]. Maintaining a home base time zone schedule during ULR rosters may help pilots avoid fatigue related to circadian misalignment or jet lag [2]. However, local environmental and social time cues strongly influence even pilots who have been instructed to retain a home base time schedule [2].
Several studies have also shown that pilot sleep quality is diminished during layovers and in-flight rest periods [3,5,10]. Diminished sleep quality not only reduces total sleep duration, but is less restorative than sleep of equal duration in a bedroom environment [3]. The restorative value of sleep, as estimated through subjective fatigue and objective performance, is related to sleep architecture—namely, slow wave sleep (SWS) and rapid eye movement (REM) sleep stages [11,12]. Polysomnography (PSG) is the gold standard to assess sleep stages, but is considered an impractical method for collecting sleep information in operational environments [13]. Consumer sleep trackers cannot measure sleep architecture, but many offer a non-equivalent sleep score under the assumption that sleep stages N1 and N2 are comparable to light sleep, SWS is comparable to deep sleep, and REM is its own category [14–17]. It should be noted that while sleep score
refers to sleep as being light or deep, CSTs do not measure the brain waves necessary to determine sleep depth [18,19]. Reliable estimation of sleep architecture during LH/ULR rosters, particularly during in-flight sleep, is important toward understanding the quality of sleep across aviation operations. Estimation of sleep scoring is a preliminary step toward that goal.
Pilot fatigue constitutes a well-anticipated threat to aviation safety, but the estimation of fatigue risk and sleep behavior for specific flight rosters has been informed by scientific examination of fatigue factors during actual or simulated aviation operations. Data cannot be collected during operations which never occur, but the COVID-19 pandemic resulted in unprecedented commercial aviation operations, including ULR direct round-trip flights between Brazil and China.
Operators adapted to the unique operating conditions imposed by global lockdowns as best as possible given the limited information and tools available to predict fatigue. Brazil-based Azul Airlines, for example, estimated pilot fatigue using a biomathematical model prior to conducting five separate humanitarian missions to China between May and July of 2020 [20]. During missions, pilots wore a validated wrist actigraph (the Zulu watch, Institutes for Behavior Resources Inc., Baltimore, MD, USA [21]) and reported the sleep duration and quality of their in-flight rest periods using a sleep diary. Each mission consisted of four flight legs between 11–15 h long each going from: (1) Brazil to a layover destination in Europe, (2) the layover destination to a destination in China to pick up COVID-19 relief supplies, (3) China to a return layover destination, and finally, (4) the return layover destination to the home airport in Brazil. Pilots were each provided a 9 h rest opportunity per FDP, and were instructed to remain on a home base schedule, i.e., west Brazilian local time (UTC-5).
The Zulu watch is a commercial sleep tracker designed for use in operational environments which has been validated against PSG and actigraphy for sleep-wake determination and against PSG for the estimation of sleep score [21]. Two-min epochs within sleep events which are recorded by the Zulu watch are categorized as either interrupted sleep, light sleep, or deep sleep. It should be noted that the Zulu watch estimates sleep score based on wrist movement using a tri-axial accelerometer and on-wrist detection using a galvanic sensor. Specific differences between NREM–REM sleep stages cannot be estimated by accelerometry alone, but wrist movement can identify bouts of immobility which are known to correspond to periods of restful sleep that could include NREM and REM [22,23]. Previous studies have compared sleep scoring in commercial wearables or mobile apps against PSG under the assumption that sleep stages N1 and N2 are comparable to light sleep, SWS is comparable to deep sleep, and REM is its own category [14–17]. The Zulu watch does not include a category for REM sleep.
The data analyzed in this manuscript was collected by Azul Airlines’ human factors team; secondary use of the data was granted to the science team at the Institutes forBehavior Resources (IBR). The goals of the current analyses are three-fold. The first goal is to describe observed sleep behavior during pandemic-specific ULR flight conditions and thus, establish an expectation of rest patterns in the hopefully unlikely event of future global public health emergencies. The second goal is to describe patterns of sleep behavior and sleep score across ULR in-flight and layover sleep events with respect to pilots’ flight schedules and local night as a precedence for future investigations. The third goal is to evaluate the accuracy of Zulu watch measures of sleep duration and sleep timing estimation in operations compared against sleep diary. The Zulu watch has been validated in the laboratory, but the true test of its utility is (a) the ability to accurately measure sleep timing and duration compared to self-report in real-world operations and (b) the ability of Zulu watch measurements to inform assumptions about sleep behavior in real-world situations such as ULR flight rosters. Agreement between Zulu watch measures of sleep timing (i.e., sleep onset time and offset time) and sleep duration, compared to sleep diary report of sleep timing and duration during FDP in-flight sleep, was examined using Pearson’s r correlation, paired samples t-tests, and Bland–Altman plots. Taking these three study goals
together, this paper constitutes the first report of sleep behavior and estimation of sleep score during in-flight sleep for commercial pilots flying ULR missions across multiple time zones under global pandemic conditions.
2. Results
2.1. Pilot Participation
In total, 40 pilots flew the Brazil-China routes between May and July 2020 for Azul’s humanitarian missions. Missions ranged from 96 h to 132 h in length. Missions 1, 2, and 5 departed in the afternoon (between 14:00 and 16:00 UTC-5) while Missions 3 and 4 departed in the early morning (between 01:30 and 03:00 UTC-5). Each mission consisted of 4 FDPs which ranged in length from 11 to 14 h each, 1 turnaround period in China, which lasted between 3 to 6 h without deplaning, and 2 layover periods in Europe which lasted between 20 to 41 h. Thirty-two (32) out of 40 (80%) pilots crewing a COVID-19 humanitarian mission completed the sleep diary and 22 out of 40 (55%) wore a Zulu watch continuously during the mission period. Twenty (20; 50%) pilots completed both the sleep diary and wore the Zulu watch. Only pilots who both completed the sleep diary and provided Zulu watch data (N = 20) have been included in these analyses. Fifteen (N = 15) participants provided Zulu and diary data for all 4 flight legs; N =3 participants provided Zulu and sleep diary data for 3 out of the 4 flight legs; N =1 participant provided Zulu watch data for all FDPs, but only completed the sleep diary for 3 out of 4 FDPs and N = 1 participant completed the sleep diary for all 4 FDPs, but only wore the Zulu watch for 3 out of the 4 flight legs.
2.2. Sleep Timing and Sleep Duration across Mission Hours
Pilots reported between 0 to 3 separate sleep events per FDP by diary. In comparison, Zulu watches recorded between 0 to 6 sleep events for the same FDP. FDPs include time allocated for commuting and preparation. Sleep duration was not reported during layover or turnaround. There was only one instance in which a pilot did not report any sleep and no sleep event was recorded by the Zulu watch during a flight leg. For FDPs during which sleep occurred, sleep duration ranged between 30–520 min as reported by diary and 20–518 min for Zulu watch. Sleep occurred across 24 h of the day. On average, pilots reported sleeping for 237 ± 43 min and sleeping once within a 24–h period. Average sleep duration per 24 h as measured by the Zulu watch was 368 ± 55 min; average TST per 24 h was 321 ± 56 min as measured by the Zulu watch, with pilots sleeping between 2 to 3 times within a 24-h period in contrast to sleep diary report of 1 sleep episode. Figure 1 depicts each pilot participants’ sleep behavior with respect to mission FDPs and local night across all hours of the missions. Time is reported in hours elapsed since mission start rather than in base, local, or GMT time to avoid confusion about sleep behavior as pilots circumnavigated the globe.
Pilot sleep opportunities during FDPs were determined in-flight by the crew. Sleep opportunities were decided ad libitum by pilots during layovers, and pilots were instructed not to sleep during the turnaround periods in China. Pilots were confined to the aircraft during turnaround in China, but their activities were not restricted during layover periods. The timing of pilot sleep with respect to the end of the previous FDP or the start of the subsequent FDP ranged from 0 min to 2527 min (approximately 42 h). In contrast, pilot sleep began, on average, 50 ± 70 min after the onset of local night. There were no differences between sleep onset with regard to local night depending on whether pilots were sleeping in-flight or during a layover period (t = 0.19, p = 0.85).
Figure 1. Pilot Participant Sleep During COVID-19 Humanitarian Missions. Sleep timing and sleep duration across COVID-19 humanitarian missions as measured by Zulu watch and sleep diary. (a) Pilots’ sleep episodes occurring across each mission hour as measured by Zulu watch compared to sleep diary reports of sleep during FDPs are depicted by color-matched thin (Zulu watch) and thick (diary) lines. FDPs are indicated by light blue boxes; local night is indicated by gray boxes. (b) Comparison of sleep duration as measured by Zulu watch and Zulu watch TST compared to diary sleep duration across all mission FDPs, layovers, and turnaround. * represents significance at $p \leq 0.05$.
2.3. Sleep Quality and Sleep Score across Missions
Distribution of sleep quality across categories (Excellent, Good, Fair, and Poor) is depicted in Figure 2a. Pilots reported “Good” sleep quality for the majority of in-flight sleep. There were 81 diary reports of sleep quality in total. Percentages of interrupted, light, deep sleep, and overall sleep efficiency (SE) as measured by Zulu watch are depicted in Figure 2b. Average SE during in-flight sleep was 85% ± 8%. Pilots’ sleep was classified as deep sleep for 70% ± 12%, light sleep for 15% ± 7%, and interrupted sleep for 15%±8% of TST. Differences in sleep quality ratings and Zulu watch sleep score percentages were statistically non-significant across all FDPs and missions (all \( p > 0.05 \)).
Figure 2. Subjective Sleep Quality, Sleep Efficiency, and Sleep Score Across Mission Flight Legs.
(a) Diary reports of sleep quality during in-flight sleep across all missions FDPs. Pilots only reported sleep quality during in-flight sleep. The graph depicts “Excellent” sleep in green, “Good” sleep in orange, “Fair” sleep in yellow, and “Poor” sleep in red. The breakdown of sleep quality ratings by percentage are reported for each flight leg.
(b) Sleep efficiency and sleep score categories as measured by Zulu watch.
2.4. Agreement between Zulu Watch and Diary Measurements of Sleep
Average sleep duration per sleep event was 281 ± 126 min by sleep diary compared to 204 ± 134 min for Zulu watches. Diary sleep duration was positively correlated with Zulu sleep duration ($r = 0.75, p \leq 0.001$) and TST ($r = 0.75, p \leq 0.001$), but paired samples t-tests showed that diary reports of sleep duration were significantly higher than Zulu watch sleep duration ($t = 5.24, p \leq 0.001$) or TST ($t = 6.49, p \leq 0.001$). Sleep onset times were positively correlated between Zulu watch and diary ($r = 0.74, p \leq 0.001$), as was time of final awakening ($r = 0.62, p \leq 0.001$). Between 40%–56% of the variance in Zulu sleep duration ($R^2 = 58\%$) or TST ($R^2 = 41\%$) could be explained by sleep diary measurements. Diary-reported sleep onset explained 55% of variance in Zulu watch sleep onset ($R^2 = 58\%$) and diary-reported final awakening explained 38% of Zulu watch final awakening ($R^2 = 45\%$). Sleep onset time and time of final awakening were not significantly different between Zulu watch and diary (all $p > 0.05$). Figure 3 summarizes the Bland–Altman plots of the mean difference, bias, and limits of agreement for Zulu watch and sleep diary measures of sleep duration, diary sleep duration compared to Zulu TST, time of sleep onset, and time of final awakening.
3. Discussion
It must first be mentioned that the circumstances of the 5 ULR flights profiled in this manuscript are exceptional. The purpose of Azul’s humanitarian missions was to bring respirators, COVID rapid tests, and medical supplies from mainland China back to Brazil. The humanitarian goal of these missions served as a uniquely motivating factor for each pilot who participated in the missions. Azul Airlines had not previously conducted flights to China, and the pilots were unfamiliar with the destination airports within China. While the missions were conducted by commercial airline pilots on a commercial aircraft, there were no passengers or cabin crew aboard. Pilots were permitted to sleep in either crew rest facilities or in the business class section, per their preference. Moreover, pilots were restricted from leaving the aircraft while in China, and while they were permitted to move freely during layovers in Europe, shutdowns related to COVID-19 most likely
limited the availability of social activities. Because these ULR flights were conducted under unprecedented global pandemic conditions, pilot behavior may not generalize to all ULR operations.
Pilots slept between 5 to 6 h per 24-h period despite being afforded 9 h of sleep opportunity per FDP and between 20 to 40 h of free time during layovers. Using sleep diary data, sleep duration was less than 4 h per 24-h period. It must be noted that sleep diary did not include reports of sleep during layover periods and should not be considered an accurate total of 24-h sleep. Estimations of daily sleep duration were further limited due to the fact that flights departed Brazil at variable hours of the day and crossed multiple time zones continuously throughout the mission. Parameters for “daily” estimations of sleep are normally defined with hourly cutoffs, such as noon to noon [24]. These cutoffs could have been retained using Brazil time (UTC-5) except that 3 of the 5 missions departed in the afternoon while 2 departed shortly after midnight. To avoid complications when comparing between all flights, “daily” estimates of sleep were defined as sleep intervals ending within a 24-h period starting with mission hour 0. Sleep duration per 24-h period were not significantly different depending on whether flights departed during the afternoon versus the early morning. While preliminary, these data suggest that pilots during ULR travel may experience shortened sleep (~5–6 h per day) even when provided sufficient opportunities for sleep and under conditions of limited social distractions. Insufficient pilot sleep during ULR flights could have implications for fatigue risk management or pilot well-being.
Despite being instructed to remain on home base time, the logistical necessity of coordinating in-flight sleep opportunities with co-pilots and severe limitations to social time cues, pilots tended to initiate sleep within an hour of the onset of local night. The clustering of pilot sleep around local night can most clearly be seen in Figure 1a. The timing of pilot sleep with respect to FDPs was vastly more variable, occurring anywhere from 0 to 42 h apart. These findings indicate that environmental light cues may influence sleep behavior over the course of ULR transmeridian travel over and above logistical considerations such as the timing of work or adherence to a home schedule.
Understanding the quality of pilot sleep during ULR operations is important for the mitigation of fatigue. There is a lack of previous data examining sleep quality in the context of aviation or in-flight sleep. In this study, neither subjective nor objective sleep quality changed significantly over the course of the mission. Sleep efficiency remained in a normal range (above 80%) throughout all FDPs and layovers, and pilots largely rated their sleep as “good” or “fair”. Estimation of sleep score remained consistent as well, with the majority of TST being spent in “deep sleep”. However, actigraphy devices have a problem with low specificity [25–27], meaning that they are not very good at picking up awakenings during sleep intervals. The specificity of the Zulu watch to identify awakenings during a sleep interval compared to PSG under laboratory conditions is 26% [21]. Moreover, while sleep score estimation by the Zulu watch has been tested against gold-standard PSG under laboratory conditions, no investigations of sleep score or sleep architecture have ever been conducted during in-flight sleep. While these data represent a step towards understanding the impact of ULR travel on sleep quality, the limitations of the technology must be acknowledged. Extensive future research and advancements in device specificity will be required in order to determine whether sleep quality is truly resilient to transmeridian travel or not.
Another aim of the current analyses was to evaluate agreement between sleep diary and Zulu watch measures of sleep timing and duration. Zulu watch measures of sleep were moderately, though not strongly, correlated with diary measures. Time of sleep onset and final awakening were similar between diary and Zulu watches. However, pilots consistently reported longer sleep duration than was recorded by the Zulu watch. This finding is consistent with previous findings that sleep duration measured by actigraphy is shorter than sleep diary report [28–30]. Pilots only reported in-flight sleep, so we could not test agreement between diary and the Zulu watch before or after the mission or during
layover periods. It is possible that turbulence or background movement of the airplane in flight could falsely register an awakening on the Zulu watch. However, considering the low specificity of the Zulu watch and actigraphy devices in general, this possibility is not highly likely.
In some ways, the testing of Zulu watch measures of sleep against a diary was akin to comparing apples and oranges. The Zulu watch considered periods of awakening as the termination of a sleep episode, while pilots may have reported the total amount of time during which they attempted sleep, regardless of whether any sleep occurred. For this reason, multiple Zulu watch sleep intervals occurred over the course of one diary entry. Despite our best efforts to objectively compare the two measures, researcher bias may have influenced the results. An additional limitation is that the data were collected for operational purposes rather than for scientific study. Since the available data was restricted to the mission period, this precluded the examination of the role of pilot demographics, sleep or medical history, or other potential intervening variables on rest patterns during the missions. The Human Factors team at Azul did an exceptional job of collecting quality data which could be evaluated for scientific purposes post hoc, but this was not a controlled experimental study.
Validation testing methodology has been established for a laboratory environment [31], but there is little guidance for what constitutes proper validation of sleep measurement in a real-world environment. Validity testing against sleep diary is one method that is feasible in an operational environment, but relies on the assumption that diaries are accurate measures of sleep. Diary report of sleep can differ from gold-standard PSG or actigraphy measurements [28,29,32,33]. This constitutes a limitation to sleep research in general, and closing the validation gap is a goal for future research [34]. Previous studies have compared self-report to actigraphy but these comparisons have been made either under controlled conditions or in specialty populations that are not directly comparable to airline pilots [24,28–30,32,35]. Explained variance between measures of sleep duration or timing have been reported in these previous studies. In this study, explained variance for comparisons of sleep timing and duration was below or slightly above 50%. It is difficult to interpret this finding without context from the literature, which constitutes a study limitation. Understanding sleep patterns during duty periods is an important step forward toward mitigating fatigue in operational environments, but the distraction caused by data collection during a mission is itself a safety risk. While it is impossible to say whether the subjective assessment of sleep or the objective measurement is more representative of actual sleep under the circumstances of testing in the field, it is worthwhile to note that pilots were able to passively provide data through the Zulu watch more consistently over the mission than they were able to provide sleep diary report.
4. Materials and Methods
4.1. Participants
Participants were recruited through Azul Airlines’ Human Factors Safety Department. Participants provided written informed consent for their participation. All missions were considered eligible for participation regardless of gender, ethnicity, age (over 18), sleep habits, or health status. Secondary use of de-identified data for research purposes was approved by Salus Institutional Review Board and these analyses were conducted in accordance with the Declaration of Helsinki.
4.2. Procedures
Mission flights were designed to be carried out with 2 relay crews consisting of 8 pilots. There were 4 flight legs to each mission: (1) Brazil to a European layover destination; (2) layover to China; (3) China to a return layover destination; and (4) layover to Brazil. Each flight leg was approximately 12 h and the planned available rest time for each crew member per stage was approximately 9 h. The crews were organized so that all pilots would be available to work during any flight leg and that no one pilot would need to fly
extra time. In-flight rest periods were freely chosen by the crew during the mission. Each flight leg was approximately 12 h and the available rest time for each crew member per stage was approximately 9 h. Aircrew were instructed to remain on home base Brazilian time throughout the mission.
Pilots were assigned the Zulu watch (Institutes for Behavior Resources, Inc., Baltimore, MD, USA [21]) in May 2020 prior to COVID-19 support missions and wore the watches continuously until the completion of their mission (between May and July, 2020). Crews returned the watch to airline researchers directly upon returning to Brazil from their mission. Data were downloaded by airline researchers using the Zulu Data Extraction application (Institutes for Behavior Resources, Inc., Baltimore, MD, USA, Version 2.0). Pilots completed a sleep diary during FDPs.
4.3. Sleep Measures
4.3.1. Zulu Watch
The Zulu watch hardware device collects activity data in 2-min epochs and automatically scores sleep duration and sleep efficiency on-wrist based on a proprietary algorithm for sleep–wake determination. Devices were programmed to detect multiple sleep intervals per day and can detect sleep intervals which are as short as 20 min in duration. Data were then exported as one summary file of all scored sleep interval information and as multiple 2-min epoch-by-epoch (EBE) data files for each day during the mission study period. Zulu watch scored sleep interval summary files included sleep onset time and sleep offset time reported as mm/dd/yyyy hh:mm, sleep duration in minutes, and SE as a percentage for any events determined to be a sleep interval by the Zulu watch.
Epoch data are scored as on-wrist “On” or off-wrist “Off”. Epochs are scored in a separate data column as 0 for periods of wake, 1 for restless or interrupted sleep, 2 for light sleep, and 3 for deep sleep. The Zulu watch uses a proprietary algorithm to estimate sleep score using only motion and on-wrist detection and cannot differentiate between sleep stages. Zulu watch sleep scoring should be considered an estimation of locomotor inactivity rather than an estimate of neurophysiological sleep architecture.
4.3.2. Sleep Diary
The pilots reported the start time and end time (as mm/dd/yyyy hh:mm), sleep duration in hours and minutes, and categorical subjective quality of any sleep intervals occurring during FDPs. Subjective sleep quality was rated on a 4-point scale as either Poor, Fair, Good, or Excellent by pilots. Pilots were not asked to complete the sleep diary during layovers or ground time in China. All times were reported in Brazilian time.
4.4. Reformatting Data for Consistency between Zulu Watch and Diary Measurements
The Zulu watch automatically determines sleep onset and sleep offset regardless of whether the wearer is still attempting sleep. For this reason, while the Zulu watch can provide a measure of sleep duration similar to total sleep time (TST), it does not provide an estimate of time in bed (TIB). Conversely, pilots reported the amount of time that they dedicated to sleep, which more closely resembles a measurement of TIB. However, the term “time in bed; TIB” cannot be considered an accurate description of sleep opportunities in the current analyses since none of the sleep events reported in this manuscript occurred in a bed or bedroom environment. Because of the constitutional difference in data reporting, multiple Zulu watch sleep events occurred over the course of a single diary-reported event. In order to most accurately compare Zulu watch measurements against diary, all minutes of sleep duration recorded by Zulu watch within proximity to 1 diary-reported sleep event were summed. Sleep onset time and sleep offset time were selected from the earliest occurring Zulu watch sleep interval and last occurring Zulu watch sleep interval data, respectively. An estimate of time dedicated to sleep as measured by the Zulu watch was computed as the minutes occurring between the earliest-occurring Zulu watch sleep onset time and the last-occurring sleep offset time for comparison against diary sleep duration.
For the purposes of these analyses, sleep duration will refer to time dedicated to sleep (a proxy for TIB), and TST will refer to the time recorded as sleep by the Zulu watch in minutes.
4.5. Data Analysis
All statistics were computed using Excel 2013, STATA version 15, and RStudio version 1.3.959. Sleep duration is defined as time (in minutes) dedicated to sleeping based on Zulu watch or diary. Total sleep duration per flight leg was computed by summing all minutes of sleep recorded or reported occurring during each flight leg. Total sleep duration across 24 h were computed by summing all minutes of sleep recorded or reported in which the wake-up time occurred within a 24-h period starting at mission hour 0. The number of daily sleep intervals (DSI) was determined by counting the number of sleep events recorded or reported for each 24-h period starting at mission hour 0. All date/time data were converted to west Brazilian home base time zone (UTC-5) for consistency. Sleep onset and offset times as reported by Zulu and sleep diary were converted from UTC-5 date time format to numeric values for statistical analysis. Distance between sleep onset and FDPs or local night were computed by subtracting the sleep start time from the end time of previous FDP or start time of subsequent FDPs or by subtracting sleep start time from the start time of local night. Local night start times were extracted from the Sleep, Activity, Fatigue, and Task Effectiveness Fatigue Avoidance Scheduling Tool (SAFTE-FAST) biomathematical modeling software. Differences between sleep distance from night by FDP versus layover were examined using Student’s t-test. Differences in sleep quality ratings and Zulu watch sleep score percentages across flight legs and between missions were compared using repeated measures mixed model analysis. Percent explained variance was evaluated using adjusted $R^2$ values. Paired samples t-tests were run to compare differences between Zulu watch and diary-reported measures of in-flight sleep. Mean difference scores were additionally computed between sleep onset time, sleep offset time and sleep duration. Bland–Altman plots examined the mean difference between measures of sleep and single sample t-tests were conducted to determine if a statistically significant difference existed between mean difference scores. Limits of agreement were computed (mean difference ± 1.96 SD) to indicate the range in which the differences between the two measures would occur with 95% probability [36]. The strength of the association between Zulu watch and diary report for measures of sleep onset, offset, and duration was calculated using Pearson correlation coefficients.
5. Conclusions
This is the first report of sleep behavior and sleep score estimation in pilots operating ULR flights during global pandemic conditions to our knowledge. Pilots tended to sleep during local night despite being instructed to adhere to home base time schedule and having to coordinate sleep opportunities with their co-pilots. Subjective sleep quality, SE, and percentage of interrupted, light, and deep sleep remained consistent across the missions, and were not indicative of diminished sleep quality. Zulu watch and diary measures of sleep were similar, but pilots reported longer sleep duration than was measured by the Zulu watch. These analyses can help inform the management of fatigue risk in the planning or future ULR flights or pandemic flight conditions.
Author Contributions: Conceptualization, J.K.D., C.R.G. and S.R.H., methodology, J.K.D., C.R.G., A.S.S., M.R.G., B.d.G., D.S.S. and P.P.; data collection, C.R.G., A.S.S., M.R.G., B.d.G., D.S.S. and P.P.; formal analysis, J.K.D., J.C., S.R.H.; data curation, J.C., C.R.G. and A.S.S.; writing—original draft preparation, J.K.D.; writing—review and editing, J.K.D. and J.C., S.R.H.; supervision, C.R.G. and S.R.H.; project administration, C.R.G., A.S.S., M.R.G., B.d.G., D.S.S. and P.P.; All authors have read and agreed to the published version of the manuscript.
Funding: This research received no external funding.
Institutional Review Board Statement: The study was conducted according to the guidelines of the Declaration of Helsinki, Secondary use of de-identified data for research purposes was approved by Salus Institutional Review Board for the Institutes for Behavior Resources, INC. (Protocol Number Azul2020; 3 August 2021).
Informed Consent Statement: Informed consent was obtained from all subjects involved in the study.
Data Availability Statement: Data for this study is owned by Azul Airlines and is not publicly available.
Acknowledgments: The authors would like to acknowledge and thank the pilots who flew the COVID-19 humanitarian flights.
Conflicts of Interest: The authors declare no direct conflicts of interest. The Institutes for Behavior Resources sells the Zulu watch as a research tool. Authors J.K.D., L.P.S., and S.R.H. are affiliated with the Institutes for Behavior Resources but do not benefit financially or non-financially from sale of the Zulu watch.
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31. Depner, C.M.; Cheng, P.C.; Devine, J.K.; Khosla, S.; de Zambotti, M.; Robillard, R.; Vakulin, A.; Drummond, S.P.A. Wearable technologies for developing sleep and circadian biomarkers: A summary of workshop discussions. Sleep 2020, 43. [CrossRef]
32. Aili, K.; Astrom-Paulsson, S.; Stoetzer, U.; Svartengren, M.; Hillert, L. Reliability of Actigraphy and Subjective Sleep Measurements in Adults: The Design of Sleep Assessments. J. Clin. Sleep Med. 2017, 13, 39–47. [CrossRef]
33. Matthews, K.A.; Patel, S.R.; Pantesco, E.J.; Buysse, D.J.; Kamarck, T.W.; Lee, L.; Hall, M.H. Similarities and differences in estimates of sleep duration by polysomnography, actigraphy, diary, and self-reported habitual sleep in a community sample. Sleep Health 2018, 4, 96–103. [CrossRef] [PubMed]
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variation further, we conducted (1) quantitative analyses of facility-level versus provid-
er-level variation, and (2) qualitative interviews with emergency department providers.
**Methods.** For each hospitalization, we predicted the probability of anti-MRSA and anti-PAE use by fitting machine learning models from 75 patient variables. We estimated the predicted risk of anti-MRSA/anti-PAE and facility features among patients hospitalized at upper versus lower 10% facilities after controlling for patient characteristics. We plotted density curves with the variance attributed to facility and provider alone and together. We then interviewed 16 emergency department (ED) prov-
iders at 8 VA facilities using a cognitive task analysis.
**Results.** Among 215,803 hospitalizations at 128 VA facilities 1/1/2006-
12/31/2016, 31% reported empiric anti-MRSA and 29% reported empiric anti-
PAE antibiotics. Hospitalizations at upper-decile facilities had a 50% and 45%
adjusted probability of receiving anti-MRSA and anti-PAE antibiotics, compared to
15% and 20% in the lower-decile facilities. Facility features most predictive of
anti-MRSA or anti-PAE use after adjusting for patient characteristics were com-
plexity level (33% and 30% in high versus 15% and 20% in low complexity facilities).
Variation in empiric anti-MRSA and anti-PAE use was almost completely at the facility level (Figure 1). Providers reported social influences from the opinions of other providers during decision-making and a high trust in guidelines and order
sets. Consideration of pathogens was not mentioned by any providers at high-pre-
scribing facilities.
**Conclusion.** Variation in empiric use of anti-MRSA and anti-PAE antibiotics in pneumonia clustered nearly completely at the facility level. ED providers report so-
cial influences during decision-making and a high trust in guidelines and order
sets. Guidelines, order sets, and facility-level clinical champions that promote consideration of pathogens could be important strategies for de-adoption.
**Disclosures.** All Authors: No reported disclosures.
### 1311. Population-based Mortality Rates of Clinical Syndromes Potentially Associated with Pneumococcal Disease in Argentina from 2008-2018
Noelia Giglio, MD1; Norberto Babic, MD2; Marina Gabriela Birck, n/a3; Cintia Parellada, MD, PhD2; Ricardo Gutierrez Children’s Hospital, Buenos Aires, Buenos Aires, Argentina; IQVIA, São Paulo, Sao Paulo, Brazil; IQVIA Brazil, São Paulo, Sao Paulo, Brazil; MSD Argentina, Buenos Aires, Argentina; MSD Brazil, Sao Paulo, Sao Paulo, Brazil
**Session:** P-73. Respiratory Infections - Bacterial
**Background.** In 2012, the 13-valent conjugate vaccine (PCV13) for children <
2 years was introduced in the Argentinean National Immunization Program (NIP) with
sustained coverage >80% since then. The 23-valent polysaccharide vaccine (PPSV23)
has been available for ≥65 years and at-risk populations in NIP since 2001 and
in 2017, it was replaced by the sequential regimen (PCV13/PPSV23). The 2013
National Survey of Risk Factors estimated a coverage of 23.1% for ≥65 years and
16.2% for at-risk populations. We evaluated mortality rates of clinical syndromes
potentially associated with pneumococcal disease (PPD) in a 10-year period by age
groups, before (2008-2011) and after childhood PCV introduction (2013-2018) in
the NIP in Argentina.
**Methods.** All age-deaths cases related to clinical syndromes PPD were obtained
from Dirección de Estadísticas e Información de la Salud between 2008-2018. ICD-
10 codes were used to define PPD: pneumonia (J13-J18) and invasive disease (sepsis
- A44.0; A41.2; A49.2; meningitis - G00.2; G03.9; and other - M00.1, J86.7, J90.39,J95.3).
The yearly mortality rate was calculated per 100,000 people, estimated by the
national census, and stratified by age groups. The percentage of change was the
difference between the average rate in the pre (2008-2011) and post-vaccination (2013-
2018) periods.
**Results.** In total, 65,947 deaths due to pneumonia (56.7%) and invasive disease
(43.3%) occurred from 2008 and 2018. In the younger age groups (< 1, 1-4, 5-17),
144% a reduction was seen in both invasive disease and pneumonia compared to
pre-childhood vaccination period, mainly in infants (from 2.2 to 10.2 per 100,000
people). In adult population, a less pronounced reduction was noted in mortality by
invasive disease, however an inverse trend occurred in pneumonia in the age groups
18-49 years, 50-59 years, and 60-69 years, from 1.9 to 2.1 (7%), 9.3 to 10.2 (10%) and
18.3 to 19.2 (5%) per 100,000 people, respectively (Fig 1).
**Mortality rate change (%) pre and post pneumococcal childhood introduction**
### 1312. Evaluation of a Multiplexed PCR Pneumonia Panel in a Tertiary Care Medical Center
Erin Su, BA in Molecular Biology1; Rosemary She, MD2; Keck School of Medicine, chino hills, California; University of Southern California, Los Angeles, CA
**Session:** P-73. Respiratory Infections - Bacterial
**Background.** Syndromic PCR testing for lower respiratory pathogens may give rapid, actionable results to aid in management decisions for suspected pneumonia cases. We sought to evaluate the performance of a multiplexed PCR pneumonia panel compared to routine microbiologic work-up in a tertiary care patient population.
**Methods.** Sputum and bronchoalveolar lavage (BAL) samples from Keck Medical Center (Los Angeles, CA) inpatients submitted for clinical microbiology work-up Dec
2019-Jun 2020 were tested by a multiplexed PCR panel (FilmArray Pneumonia Panel, BioFire Diagnostics). We compared panel results for typical bacterial pathogens to those of quantitative culture and susceptibility testing. We retrospectively determined the incidence of non-panel respiratory pathogens as detected by standard of care tests in this patient cohort.
**Results.** 68 of 180 samples yielded 80 positive bacterial PCR results: 34 were detected by both PCR panel and culture and 46 by PCR panel only, yielding a sensi-
tivity of 100% (34/34) for pathogens detected and specificity of 73.1% (114/156) among negative cultures (normal flora or no growth). Concordant results had PCR Bin values
2×10^5 copies/mL whereas all 18 targets detected at 10^4 copies/mL were culture-neg-
ative. Among resistance gene targets, the panel detected 12 MRSA specimens, of which
MRSA grew in 4 cultures; E. coli and CTX-M in 1 specimen from which grew normal flora; and multiple gram-negative organisms and KPC in 1 specimen from which
culture isolated carbapenem-resistant P. aeruginosa. Quantification from positive
BAL cultures (n=25) correlated weakly with PCR Bin values (R-squared=0.17). Non-
PCR panel pathogens were detected in 22 of 180 (12.2%) specimens through routine
methods (16 molds, 3 AFB, and 3 non-fermenter gram-negative bacteria).
**Conclusion.** The pneumonia panel had excellent sensitivity for its target bacterial pathogens, but results were often positive in negative cultures. This could be due to antecedent antibiotic therapy, differences in reporting threshold versus culture, or in-
ability of PCR to discern results from normal flora. Non-panel pathogens were detected in a significant proportion in our population. The pneumonia panel should be imple-
mented and interpreted carefully with consideration of antimicrobial stewardship.
**Disclosures.** All Authors: No reported disclosures.
### 1313. Disease Burden and Real-world Clinical Practice for the Treatment of Hospital-Acquired Bacterial Pneumonia Using a Japanese Large-scale Claims Database: A Retrospective Cohort Study
Masahiro Kimata, PhD1; Yousuke Aoki, MD, PhD2; Adachi Noriaki, n/a3; Takeshi Akiyama, MS3; Akiko Harada, n/a3; MSD K.K., Tokyo, Japan, Tokyo, Tokyo, Japan; Saga University, Saga, Japan; IQVIA Solutions Japan, Tokyo, Tokyo, Japan
**Session:** P-73. Respiratory Infections - Bacterial
**Background.** With an aging population and increasing healthcare utilization, the frequency of hospital-acquired pneumonia (HAP) is expected to increase. Since
### Figure 1. Mortality rate change (%) of clinical syndromes potentially associated with pneumococcal disease before (2008-2011) and after infant vaccination introduction (2013-2018) in Argentina.
**Conclusion.** Mortality rates declined mostly for infants, and despite the differ-
ences observed for the older population, it remains significant. Evaluation of mortality trends are key for decision-making process on current and future prevention strategies using pneumococcal vaccines.
**Disclosures.** Norberto Giglio, MD, Merck Sharp & Dohme Corp (Consultant); Pfizer (Other Financial or Material Support, Speaker); Sanofi (Other Financial or Material Support, Speaker) Marina Gabriela Birck, n/a; IQVIA (Independent Contractor) Guillerme Julian, BSc, MSc, IQVIA (Independent Contractor) Virginia Verdaguer Babic, MSc, MSD Argentina (Employee) Cintia Parellada, MD, PhD, MSD Brazil (Employee, Shareholder)
HAP is life threatening, appropriate diagnosis and treatment are required; however, large-scale Japanese data focusing on patient profiles and treatment patterns is lacking.
**Methods.** The demographics and treatment patterns of HAP were examined using a large-scale Japanese claims database from Jan. 2016 to Apr. 2018. The HAP population included patients who received injection antibiotics ≥3 consecutive days after admission, but not within 2 days after admission, and those whose reason for hospitalization was not pneumonia but had a diagnosis of pneumonia after hospitalization (based on ICD-10 codes).
**Results.** 2,968 HAP patients (mean age 77 years, 64.9% male) contributing 2,973 hospital episodes were included. The 12-month pre-index mean Charlson Comorbidity Index (CCI) score was 4.0±3.1 (mean±SD), CCI score ≥4 comprised 44.0%. Most HAP episodes (77.6%) occurred ≥25 days after hospitalization. During the 12-month pre-index period including outpatients, 64.9% of patients had some type of pneumonia record, 9.1% had VAP (ventilator associated pneumonia) records, and 7.4% had anti-MRSA prescription records. For post-index HAP treatment, ampicillin/sulbactam (36.4%, 8.2±5.3 days), and piperacillin/tazobactam (22.0%, 8.8±4.4 days) were frequently prescribed as the first antibiotic prescription. Ceftaxime (19.4%) and meropenem (9.8%) were also frequently prescribed. Examinations prescribed during HAP, 30.5% blood culture tests, 28.2% sputum examinations and 29.2% urine antigen tests. The overall mortality rate of HAP in the overall hospitalization post-index was 22.0%, in which 14.4% of deaths occurred within 30 days. The mean (±SD) length of overall hospital stay was 49.9 (±34.2) days (113 days for HAP period), with 12.4% ICU use and 17.6% ventilator use. The median total cost during hospitalization was ¥1,924,848.18 ($19,248).
**Conclusion.** The data revealed patient characteristics, treatment patterns, mortality rates and healthcare costs in Japanese HAP patients. This database approach should prove useful for discussing antibiotics usage trends in highly aging Japan.
**Disclosures.** Masahiro Kimata, PhD, MSDK K.K., Tokyo, Japan (Employee) Yosuke Aoki, MD, PhD, MSDK K.K., Tokyo, Japan (Other Financial or Material Support, Honorarium for Lecturing) Naohi Zilberberg, n/a; Andrew F. Shorr, MD, MPH, MBA; EviMed Research Group, LLC, Goshen, MD; Optistatin, LLC, Longmeadow, MA; Merck & Co., Inc., Kenilworth, New Jersey; EviMed Research Group, LLC & University of Massachusetts, Amherst, Amherst, Massachusetts; Medstar Washington Hospital Center, Washington, DC
**Session:** P-73. Respiratory Infections - Bacterial
**Background.** Nosocomial pneumonia (NP) remains associated with excess morbidity and mortality. The effect of NP on other measures of outcome and quality, such as re-admission at 30 days, remains unclear. Moreover, differing types of NP may have varying impacts on re-admissions.
**Methods.** We conducted a multicenter retrospective cohort study within the Premier Research database, a source containing administrative, pharmacy, and microbiology data. The rate of rehospitalization at 30 days following the index discharge varied among important outcomes and quality, such as re-admission at 30 days, remains unclear. Moreover, differing types of NP may have varying impacts on re-admissions.
**Results.** Among 17,819 patients with NP, 14,123 (79.3%) survived to discharge, of which 2,151 (15.2%) required an acute readmission within 30 days of discharge. Of these, 106 (4.9%) were RaP, and the remainder were RaO. At index hospitalization, RaP patients were older (mean age (SD) 67.4 [±13.9] vs. 63.0 [±15.2] years), more likely to have hypertension, diabetes, and chronic obstructive pulmonary disease (COPD), and more likely to require acute care during hospitalization (48.6% vs. 44.3%, p = 0.01). Of these 106, 93 (87.7%) were RaP and 13 (12.3%) were RaO. At 30 days follow-up, 76 (71.7%) of RaP patients were discharged alive, and 29 (26.9%) died. The rate of rehospitalization at 30 days following the index discharge was 22.0%, in which 14.4% of deaths occurred within 30 days. The mean (±SD) length of overall hospital stay was 49.9 (±34.2) days (113 days for HAP period), with 12.4% ICU use and 17.6% ventilator use. The median total cost during hospitalization was ¥1,924,842.18 ($19,248).
**Conclusion.** The data revealed patient characteristics, treatment patterns, mortality rates and healthcare costs in Japanese HAP patients. This database approach should prove useful for discussing antibiotics usage trends in highly aging Japan.
| 2025-03-04T00:00:00 |
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Astragaloside IV alleviates senescence of vascular smooth muscle cells through activating Parkin-mediated mitophagy
Huijun Li1 · Jialin Xu1 · Yanan Zhang2 · Lei Hong3 · Zhijian He1 · Zhiheng Zeng1 · Li Zhang1
Received: 12 April 2022 / Accepted: 18 July 2022 / Published online: 4 August 2022
© The Author(s) 2022
Abstract
Astragaloside IV (AS-IV), as one of the main active components of Astragalus membranaceus, has been reported to have cardiovascular protective effects. However, the role and molecular mechanism of AS-IV in vascular senescence have not been clearly stated. The in vitro aging model was constructed using bleomycin (BLM) in vascular smooth muscle cells (VSMCs). Cell senescence were assessed through Western blotting analysis of aging markers, flow cytometry, and the β-galactosidase (SA-β-Gal) kit. Mitophagy was determined through transmission electron microscopy, TMRM staining, and Western blotting analysis of p62. A model of aging blood vessels was induced by d-gal. The vascular wall thickness of mice was also evaluated by H&E staining. Our data proved that AS-IV plays an anti-senescent role in vitro and in vivo. Results showed that AS-IV effectively improved mitochondrial injury, raised MMP, and mediated mitophagy in BLM-induced senescent VSMCs and d-gal induced aging mice. Parkin expression strengthened AS-IV’s anti-senescent function. In conclusions, AS-IV attenuated BLM-induced VSMC senescence via Parkin to regulate mitophagy. Therefore, AS-IV-mediated Parkin might be a latent therapeutic agent and target for VSMC senescence.
Keywords Astragaloside IV · Senescence · Vascular smooth muscle cells · Parkin · Mitophagy
Introduction
Senescence is a prevalent phenomenon in nature and is a necessary procedure for organisms [1]. With the aging of the global population, the incidence of cerebrovascular and cardiovascular diseases (CVDs) such as atherosclerosis, myocardial infarction, hypertension, heart failure, and stroke, has dramatically increased [2, 3]. Based on 2015 data from the United States, the average incidence of first-episode cardiovascular events in people aged 80 years was 74 [4]. Study confirmed that vascular smooth muscle cell (VSMC) senescence is the main pathological mechanism of CVDs [5]. Senescent VSMCs are characterized by growth arrest, cytoskeleton stiffness, and increased secretion of inflammatory factors [6]. Study proved that senescent VSMCs can be detected in human atherosclerotic plaques, but they are almost undetectable in normal vascular tissues [7]. By secreting multiple cytokines and growth factors, senescent VSMCs can change the local microenvironment of tissues, induce inflammatory responses and vascular sclerosis, and aggravate the process of related diseases [8]. However, the occurrence and development mechanism of VSMC senescence still lacks in-depth study.
Autophagy is a key way for cells to clear senescent or damaged organelles or proteins, which is essential for maintaining homeostasis [9]. Mitophagy refers to the process by which cells selectively clear mitochondria through the mechanism of autophagy [10]. In the early stage of disease, mitophagy can maintain cell homeostasis in a compensatory way, but long-term mitophagy results in cell decompensation and apoptosis [11]. Abnormal mitophagy is closely associated with cellular senescence [12]. Under normal conditions,
mitophagy can clean up mitochondria that have lost their function, thereby preventing cells and protecting senescence [13]. In the aging state, the function of mitophagy declines, causing the gradual accumulation of damaged mitochondria, which further aggravates the senescence process [14]. Moderate autophagy is crucial to ameliorate mitochondrial dysfunction and delay the senescence of VSMCs [15]. Therefore, mitophagy may be a vital target for the therapy of VSMC senescence. Further exploration of therapeutic drugs that can affect mitophagy is crucial to VSMC senescence.
Astragalus membranaceus (AM), as a traditional Chinese medicine, has the functions of strengthening the exterior and reducing sweat, healing sores, reinforcing Qi and promoting diuresis [16]. AM also has multiple pharmacological activities such as antioxidation, immunomodulation, anti-inflammation and anti-ischemic brain injury [17, 18]. Astragaloside IV (AS-IV) is the main active saponin ingredient extracted from AM [19]. Pharmacological studies also verified that AS-IV has anti-inflammatory, anti-oxidation, anti-apoptosis, and other pharmacological effects [20]. Moreover, AS-IV has liver protection, anti-aging, anti-stress, anti-hypertension, and antibacterial properties [21, 22]. Study also found that AS-IV can increase the content of superoxide dismutase (SOD) in cardiomyocytes. However, it is still not completely clear whether AS-IV plays an anti-aging role by regulating mitophagy in VSMCs.
In the current study, we further uncovered the therapeutic effect of AS-IV on VSMC senescence, and preliminarily verified the influences of AS-IV on mitochondrial dysfunction and autophagy. Moreover, we also analyzed the possible regulatory mechanism of AS-IV in BLM-induced VSMCs. Thus, we confirmed the protective role and mechanism of AS-IV on VSMC senescence, suggesting that AS-IV might be a novel therapeutic drug for VSMC senescence.
Animal and model of aging
Male BABL/C mice of SPF grade (6 weeks, weight: 18 ± 20 g) were provided by the Experimental Animal Center of Guangdong Pharmaceutical University. All mice were kept in the SPF animal laboratory at a constant temperature of 18–20 °C, a humidity of 50%–80%, sterile water, and standard feed. The animal experiments formed the Guidelines of the International Committee on Laboratory Animals. The experimental animal study was approved by The First Affiliated Hospital of Guangdong Pharmaceutical University (approval NO. gyfgyzr030).
To construct an in vivo model of vascular aging, α-galactose was used in this experiment. Fifty mice were randomly divided into 5 groups: the control group, aging model group (α-gal), AS-IV low concentration group (α-gal + LD-AS-LV), AS-IV medium concentration group (α-gal + MD-AS-LV), and AS-IV high concentration (α-gal + HD-AS-LV) group. Except for the control group, the other four groups received D-galactose daily for 8 weeks at a dose of 150 mg/kg/day. While receiving the α-galactose injection, the animals were treated with astragaloside IV (Sigma) by gavage. Specifically, two weeks after receiving the first α-galactose injection, the animals received daily intragastric administration of astragaloside IV at doses of 20, 40, and 80 mg/Kg for 2 weeks. At the end of the experiment, the animals were anesthetized with pentobarbital and subjected to systemic vascular perfusion. Subsequently, the animals in each group were dissected and the blood vessels were collected for subsequent experiments.
Cell treatment
Parkin-overexpressed plasmids and Parkin shRNAs were purchased from HanBio Biotechnology (HanBio, Shanghai, China). In brief, BLM-induced VSMCs cells were transfected with these plasmids using Lipofectamine 3000 (Invitrogen) in accordance with the detailed specification. BLM-induced VSMCs were given different doses of AS-IV (10, 50, or 100 μM) and Mdivi-1 (1 μM). After 48 h of treatment with AS-IV, plasmids, or other drugs, the cells were collected for subsequent assays.
Mitochondria isolation
Mitochondria and cytosolic fractions were isolated from cells and tissues with a commercially available kit (89,874, Thermo Fisher Scientific, Waltham, MA, USA) according to the manufacturer’s instructions.
Materials and methods
Cell culture
Human vascular smooth muscle cells (hVSMCs) were purchased from BeNA Culture Collection (BNCC332960). hVSMCs were cultured in F-12 K (ATCC, Catalog No. 30-2004) complete growth medium. To make the complete growth medium, the following components were added to the F-12 K base medium: 0.05 mg/ml ascorbic acid, 0.01 mg/ml insulin, 0.01 mg/ml transferrin, 10 ng/ml sodium selenite, 0.03 mg/ml Endothelial Cell Growth Supplement (ECGS), fetal bovine serum (Unovl Biotechnology, 107-FBS-500) to a final concentration of 10%, HEPES to a final concentration of 10 mM, and TES to a final concentration of 10 mM. Cells were cultured at 37 °C and 5% CO₂.
Western blot
The treated VSMCs and the aorta of mice were collected from each group, and the total proteins were extracted through the use of RIPA lysis buffer (Beyotime, China). After quantification, the total protein (20 μg) in each group was subjected to electrophoresis and transferred onto the prepared PVDF membranes (Millipore). Then the membranes were exposed to 5% skim milk for 1.5 h, incubated with rabbit anti-primary antibodies overnight at 4 °C, and goat anti-secondary antibodies (Abcam, ab6721, 1:10,000) for 2 h. The protein blots were observed using the chemiluminescent reagent (Millipore, Burlington, MA, USA). The primary antibodies included p16 (Beyotime, AF1069, 1:1000), p21 (ProteinTech, 10,355–1-AP, 1:3000), Drp1 (Abcam, ab184247, 1:1000), and Parkin (Boster, PB9307, 1:1500). GAPDH expression was set as the internal reference.
Transmission electron microscopy (TEM)
The collected samples were fixed using 2.5% glutaraldehyde at 4 °C, dehydrated with acetone, and embedded. The embedded tissues were sliced into 80 nm slices and placed in a copper mesh. After staining with lead citrate and uranium acetate, the ultrastructure of the tissue samples was observed using a JEM-100CX microscope (JEOL, Japan).
TMRM staining and detection
The treated VSMCs were incubated at 37 °C for 45 min in a solution containing 2 mM CaCl₂, 1.25 mM KH₂PO₄, 2 mM MgSO₄, 3 mM KCl, 156 mM NaCl, and the TMRM probe (25 nM). The cells were subsequently observed using laser confocal microscopy. The positive cells were detected by flow cytometry (parameters: excitation wavelength 543 nm, generation wavelength 605 nm). The results were analyzed with FlowJo software (BD, USA).
Flow cytometer
Cells were fixed with paraformaldehyde, and then SPiDER-βGal working solution was added, and the samples were incubated at 37 °C for 30 min. The cells were then digested with trypsin and resuspended in MEM medium and detected by flow cytometry (parameters: excitation wavelength 488 nm, generation wavelength 530 nm). The results were confirmed with FlowJo software (BD, USA).
H&E staining
The aorta of mice was first subjected to a series of treatments, including fixation (4% paraformaldehyde), dehydration (gradient ethanol), and embedding in paraffin. Then the tissues were cut into continuous 4 μm slices. The slices were dewaxed with xylene I, xylene II, dehydrated with 95%, 90%, 80%, and 70% ethanol, and washed with distilled water. Then the slices were processed with Harris hematoxylin, 1% hydrochloric acid alcohol, 0.6% ammonia, and eosin. After dehydration (gradient ethanol) and transparency (xylene), the pathological structure was observed with a microscope.
Immunofluorescent (IF) assay
Briefly, immunofluorescent staining of the treated VSMCs and aorta of mice in fixed paraffin sections was used to analyze the distribution of p16, p21, and Parkin proteins. Microwave ovens were used for antigen retrieval in a citrate solution for 20 min. Endogenous peroxidase activity was blocked using 3% hydrogen peroxide for 15 min and rinsing in PBS. The glass slides that had crawled cells were sealed with sealing solution (5% donkey serum, Solarbio Science and Technology Co., Ltd., Beijing, China) was dripped at room temperature for 30 min. Each slide had a sufficient amount of diluted primary antibodies (p16: Beyotime, AF1069, 1:100); p21 (ProteinTech, 10,355–1-AP, 1:3000); Parkin (Boster, PB9307, 1:1500). GAPDH expression was set as the internal reference.
Enzyme-linked immunosorbent assay (ELISA)
Blood samples from mice were collected, and centrifuged to obtain serum. The concentration of β-galactosidase was tested with the β-Gal ELISA kit (Meimian Biotechnology, MM-1118M2) in line with the manufacturers’ instructions.
Statistical analysis
All data from three independent experiments were displayed as the mean ± SD. Data analysis was conducted using SPSS 20.0 software (SPSS, Inc.) with one-way ANOVA. P < 0.05 denoted that the statistical result was statistically significant.
Results
AS-IV ameliorated the senescence of BLM-induced VSMCs
To investigate the preventive effect of AS-IV on VSMC senescence, we first used BLM to induce the senescence of VSMCs, which were also given different doses of AS-IV. Western blotting data showed that expressions of p16, p21, and DcR2 were raised in the BLM group compared with the control group, while the upregulation of p16, p21, and DcR2 expressions was markedly weakened by the introduction of AS-IV in a concentration dependent manner (Fig. 1A). Flow Cytometer data showed that the percentage of β-galactosidase positive cells in VSMCs was elevated in the BLM-treated VSMCs, while treatment with AS-IV dramatically reduced the amount of β-galactosidase induced by BLM in a concentration dependent manner (Fig. 1B). Next, results of β-galactosidase staining showed that the senescence of VSMCs (cells in blue) was increased in the BLM group compared to the control group, while addition of AS-IV attenuated the increase of SA-β-galactosidase in BLM-induced VSMCs (Fig. 1C). In general, these results proved that BLM induced senescence-like VSMCs, and AS-IV has a prominent relieving role on VSMC senescence induced by BLM.
Fig. 1 AS-IV ameliorated the senescence of BLM-induced VSMCs. BLM-treated VSMCs were given different doses of AS-IV. A Western blot exhibited the expression changes of p16, p21, and DcR2, and the protein levels were quantified on the gray scale. B The population of β-galactosidase was tested using flow cytometer, and quantitative analysis was conducted. C After processing with AS-IV, the SA-β-galactosidase kit was used to evaluate the senescence of BLM-induced VSMCs. Magnification, 200×, scale bar=50 μm. L low dose, M medium dose, H high dose. *P < 0.05, ***P < 0.001
AS-IV protected VSMCs from senescence by mediating mitochondrial quality and mitophagy
Subsequently, we further verified the impacts of AS-IV on mitochondrial injury and autophagy of BLM-stimulated VSMCs. TMRM-staining data first indicated that MMP was lost in the BLM group, while AS-IV could markedly aggrandize the MMP of BLM-induced VSMCs (Fig. 2A). Then TEM results showed that AS-IV promoted mitophagy (yellow arrow) in BLM-induced senescent VSMCs. Specifically, there was swelling in mitochondrial compartment, dissolution, shedding, and decrease of mitochondrial
**Fig. 2** AS-IV improved mitophagy and attenuated mitochondrial membrane potential loss in BLM-induced VSMCs. A After administration of AS-IV, MMP was identified by TMRM staining in BLM-induced VSMCs. Magnification, 200×, scale bar = 50 μm. B TEM was used to observe the influence of AS-IV on the mitochondrial structure of BLM-induced VSMCs. C Flow Cytometer was used to assess the impact of AS-IV on the TMRM + fluorescent intensity in BLM-stimulated VSMCs. D P62 expression was examined by Western blot in BLM-induced VSMCs, which were given AS-IV, and the P62/TOMM20 value was determined. E Expression of Parkin was measured by Western blot in BLM-induced VSMCs. LD low dose, MD medium dose, HD high dose. *P < 0.05, **P < 0.05, ***P < 0.001
induced VSMCs. However, the results of TEM showed that the morphology of mitochondria in BLM-induced cells gradually recovered with the treatment of AS-IV (Fig. 2B, yellow arrow). In order to quantitatively analyze the mitochondrial membrane potential of the cells in each group, the cells were treated with the TMRM probe, and then the potential was detected by flow cytometry. As shown in Fig. 2C, the loss of membrane potential was significantly increased after BLM treatment. As the concentration of AS-IV increased, the loss of MMP was mitigated (Fig. 2D). To further confirm the level of mitophagy, Western blot was used to detect the expression level of P62, the substrate of mitophagy. As shown in Fig. 2D, the expression level of P62 was significantly upregulated in VSMCs treated with BLM, while AS-IV effectively reduced the P62 expression level. While, BLM suppressed expression of Parkin in VSMCs and AS-IV treatment recovered the expression of Parkin (Fig. 2E). To sum up, the data showed that AS-IV can notably increase MMP and mediate autophagy in BLM-induced VSMCs.
Mitophagy inhibitor, Mdivi-1, effectively affected the anti-senescent function of AS-IV.
Based on the roles of AS-IV in the maintenance of mitochondrial fusion and division balance, and the induction of autophagy in BLM-induced VSMC, we further investigated whether autophagy mediators exert a key effect on the senescence of VSMCs. Thus, after treatment with AS-IV, we used the mitophagy inhibitor (Mdivi-1) to treat BLM-treated VSMCs. As shown in Fig. 3A, Mdivi-1 up-regulated p16, p21, and DcR2 in BLM-induced VSMCs. (Fig. 3A). Flow cytometry showed that the loss of mitochondrial membrane potential of VSMCs induced by BLM was higher after Mdivi-1 treatment than in the AS-IV group (Fig. 3B). The results of β-galactosidase staining showed that the aging characteristics of VSMCs induced by BLM were alleviated after AS-IV treatment. However, AS-IV showed up-regulation of senescent characteristics after Mdivi-1 treatment (Fig. 3C). In short, the mitophagy mediator played a key regulatory role in BLM-induced senescent-like VSMCs.
Mitophagy inhibitor, Mdivi-1, affected the protective function of AS-IV on mitochondrial quality and mitophagy
Likewise, through rescue experiments, we further verified whether autophagy/mitophagy mediators can change the impacts of AS-IV on mitochondrial morphology, mitochondrial membrane potential, and autophagy in BLM-induced VSMCs. As shown in Fig. 4A, mitophagy was inhibited by Mdivi-1. The mitochondria were swollen and their cristae were destroyed (Fig. A). Flow cytometry results showed that Mdivi-1 treatment hindered the protective effect of AS-IV on mitochondrial membrane potential loss (Fig. 4B). The results of Western blot showed that expression of P62 induced by BLM was significantly up-regulated, and the expression level of P62 was significantly down-regulated after AS-IV treatment. (Fig. 4C). In summary, these findings revealed that the mitophagy mediator can regulate AS-IV’s role on mitochondrial quality in BLM-induced VSMCs.
Parkin-dependent mitophagy attenuated the cellular senescence induced by BLM
As concluded above, mitophagy acts as a mediator in cellular senescence induced by BLM. Therefore, we further explored whether overexpression or knockdown of Parkin could affect the effects of BLM-induced VSMC senescence. First, changing expression of Parkin in VSMCs was done. As shown in Fig. 5A, overexpression of Parkin or AS-IV delivery significantly downregulated p16, p21, and DcR2 in BLM-induced VSMCs, while, knockdown of Parkin reversed the suppression of p16, p21, and Drp2 by AS-IV (Fig. 5B). Flow cytometry data also disclosed that Parkin overexpression or AS-IV delivery dramatically rescued the mitochondrial membrane potential loss in BLM-induced VSMCs (Fig. 5B), while, knockdown of Parkin impaired the inhibitive role of AS-IV on P62 expression (Fig. 5C). As shown in Fig. 5D, Parkin overexpression reversed the suppression by BLM. Figure 5D also presented that the elevation of Parkin expression induced by AS-IV treatment in VSMCs was reversed by Parkin shRNA (Fig. 5D). As a whole, we showed that AS-IV repressed senescence and activated autophagy in BLM-induced VSMCs by upregulating Parkin.
AS-IV attenuated senescence and mitophagy in the aging mouse model
More importantly, we also investigated the influence of AS-IV on the senescence and mitophagy in the aging mouse model. H&E staining results showed that the vascular tissue of the model group (D-Gal) showed a large amount of inflammatory cell infiltration, nuclear staining deepened, and the nucleus showed signs of enlargement. This phenomenon gradually changed with the treatment of AS-IV (Fig. 6A). The results of immunofluorescence and Western blot showed that expressions of P21, p16, and DcR2 were up-regulated in the n-Gal group, while expressions of P21, p16, and DcR2 were inhibited by AS-IV treatment (Fig. 6B–E). Further kit test results showed that the level of β-galactosidase significantly decreased with the increase of the AS-IV dose (Fig. 6G). Western blot results showed that the expression level of Parkin was decreased in the n-Gal group, while AS-IV treatment led to the reverse of Parkin expression, while Drp1 showed the opposite trend (Fig. 6F). The results
suggest that there is a correlation between Parkin-mediated mitophagy and α-Gal-induced senescence.
**Discussion**
CVDs refers to ischemic or hemorrhagic diseases of the heart, brain and systemic tissues caused by hyperlipidemia, blood viscosity, atherosclerosis, and hypertension [23]. CVDs are characterized by high morbidity, high recurrence, high mortality, and high disability rate[24]. As a multi-factor disease, the pathogenesis of CVDs is increasingly complicated. Therefore, further research on the pathogenesis and effective drugs of CVDs is of great significance for its treatment.
Cellular senescence is the phenomenon in which cells stop dividing due to irreversible cell cycle arrest [1]. It has been reported that VSMC senescence is a key mechanism
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**Fig. 3** Mitophagy mediators regulated the functions of AS-IV on BLM-induced VSMC senescence. BLM-treated VSMCs were given AS-IV, and then exposed to the autophagy inducer (Torin 1) or mitophagy inhibitor (Mdivi-1). A Western blot was used to assess the protein levels of P62, p21, and DCR2, and quantitative analysis of the protein was also determined. B Flow Cytometer was used to analyze the population of β-galactosidase in each group. C Cellular senescence was evaluated using a SA-β-galactosidase kit in each group. Magnification, 200×, scale bar=50 μm. *P<0.05, **P<0.01, ***P<0.001
Astragaloside IV alleviates senescence of vascular smooth muscle cells through activating...
in the pathogenesis of CVDs [25]. VSMC is the main cell type in vascular walls, and the functional status and activity of VSMCs can directly affect the structure and function of the vascular wall. Phenotypic transformation and functional changes of VSMCs with aging can result in pathological changes of vascular senescence, such as thickening of the vascular wall, decreased elasticity, and enlargement of the lumen [8]. BLM is a chemotherapeutic agent that has been reported to induce cell senescence [26]. To investigate the changes in senescent-related characteristics of VSMCs and its possible regulatory factors, we used BLM to construct a senescent cell model. The main features of cell senescence include increased activity of SA-β-gal, formation of a senescent-associated heterochromatin focus (SAHF) in the nucleus, increased expression of DCR2, and activation of p16 and p21 pathways [27]. Our results revealed that the introduction of BLM can cause an increase of these senescent-related indicators in VSMCs, indicating that BLM can induce VSMC senescence. In our current research, we also used BLM to induce VSMC senescence.
Studies revealed that AM has a wide range of biological activities and curative effects, and has a broad prospect in the treatment of respiratory, digestive, cardiovascular, and immune system diseases [28]. The active substances of AM have been confirmed to play positive roles in the regulation of the oxidative/antioxidant balance and inflammatory response [19]. Among them, AS-IV, as the primary active ingredient of AM, has antiviral, metabolic regulation, antioxidant, tumor inhibition, and other biological functions [29, 30]. With the deepening of AS-IV researches, AS-IV has vital pharmacological effects in the remedy of CVDs, anti-hyperglycemia, anti-aging, and other aspects [31, 32]. Thus, AS-IV has a certain anti-aging role. In our study, the results showed that AS-IV treatment can downregulate p16, p21, and DcR2 and weaken SA-β-galactosidase and SAHF in BLM-induced VSMCs, suggesting that AS-IV can alleviate VSMC senescence. In vivo results also revealed that AS-IV can delay senescence and improve mitochondrial injury in the aging mouse model.
There are multiple causes of cell senescence, such as DNA damage, ROS production caused by oxidative stress, and activation of proto-oncogenes [33]. The study proved that AS-IV can effectively reduce endogenous ROS production [34]. The production of intracellular ROS mainly comes from the mitochondrial respiratory chain. It was reported that mitochondrial dysfunction is both a sign of aging and an initial cause of aging [35]. Mitochondria are found in most cell types and are the main productive structures. Mitochondrial fusion and division are the basis of mitochondrial function [36]. Under normal conditions, mitochondrial fusion and division maintain a dynamic balance to maintain the stable morphology, structure, and function of mitochondria in cells [37]. Currently, mitochondrial fusion proteins include Mfn1 and Mfn2, and mitochondrial
division proteins include DRP1 [38]. In our study, we discovered that AS-IV can downregulate Drp1 and upregulate Mfn2 in BLM-induced VSMCs, indicating that AS-IV can maintain the balance of mitochondrial fusion and division in the process of VSMC senescence. Moreover, our results verified that the mitochondrial division inhibitor (Mdivi-1) can reverse the inhibition of AS-IV on BLM-induced VSMC senescence, indicating the importance of mitochondrial fusion and division in the prevention of AS-IV-mediated BLM-induced VSMC senescence.
Autophagy is a self-protection mechanism by which eukaryotic cells can remove cellular cohesion and damaged organelles to maintain homeostasis [39]. With the deepening of autophagy-related studies, autophagy has become the key regulatory mechanism of cellular senescence [6]. In mammals, autophagic protein deficiency can cause the accumulation of misfolded proteins and aberrant mitochondria in cells, leading to premature senescence and organ dysfunction [40]. Autophagy and senescence are mediated by multiple signaling pathways. Among them, mTOR, a serine-threonine protein kinase, is the key to the regulation of cell senescence and autophagy [41]. As a crucial negative regulator of autophagy, mTOR can induce autophagy by regulating the production of Atg1/ULK [42]. Study revealed that mitophagy can participate in the pathophysiological processes of various CVDs [43]. In our study, we further proved that AS-IV can downregulate mitochondrial P62 and upregulate mitochondrial LC3 in BLM-induced VSMCs, suggesting that AS-IV can enhance autophagy in the process of VSMC senescence.
Furthermore, we also screened AS-IV-mediated mitophagy-related proteins in BLM-induced VSMCs and found that Parkin has the greatest regulating potential in AS-IV-mediated senescence VSMC delay. Parkin, as an E3 ubiquitin ligase, can degrade misfolded proteins by the ubiquitin proteasome pathway [44]. Also, Parkin, as
Astragaloside IV alleviates senescence of vascular smooth muscle cells through activating a potential anti-aging factor, can prevent inflammation and fibrosis and alleviate diabetes-associated myocardial and nerve injury [45, 46]. Research also uncovered that Parkin is related to VSMC senescence [47]. Our current study further disclosed that AS-IV can repress senescence and mitochondrial injury and active autophagy in BLM-induced VSMCs by upregulating Parkin.
**Conclusions**
Our current study demonstrated that AS-IV prevented cellular senescence through mediating mitophagy in VSMCs and vascular tissues via regulating Parkin expression (Fig. 7). This study suggested that AS-IV-mediated Parkin...
might be a latent therapeutic agent and target for VSMC senescence.
Supplementary Information The online version contains supplementary material available at https://doi.org/10.1007/s13577-022-00758-6.
Acknowledgements This work was supported by the National Natural Science Foundation of China (No. 81774241, 82174467). We also thanks to Dr. Edward C. Mignot, Shandong University, for linguistic advice.
Author contributions LZ and ZHZ contributed to the conception and design of the study. JLX and HJL performed the main experiments. YNZ, LH, and ZJH performed the additional experiments. LZ, ZHZ and HJL wrote the manuscript. All authors contributed to manuscript revision, read, and approved the submitted version.
Declarations
Conflict of interest None.
Human and animal rights The experimental animal study was approved by The First Affiliated Hospital of Guangdong Pharmaceutical University (approval NO. gyfygzr030).
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/.
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Star Formation in a Turbulent Framework: From Giant Molecular Clouds to Protostars
Dávid Guszejnov\textsuperscript{1}\textsuperscript{*} and Philip F. Hopkins\textsuperscript{1}
\textsuperscript{1}TAPIR, Mailcode 350-17, California Institute of Technology, Pasadena, CA 91125, USA
To be submitted to MNRAS, 7 March 2016
ABSTRACT
Turbulence is thought to be a primary driving force behind the early stages of star formation. In this framework large, self-gravitating, turbulent clouds fragment into smaller clouds which in turn fragment into even smaller ones. At the end of this cascade we find the clouds which collapse into protostars. Following this process is extremely challenging numerically due to the large dynamical range, so in this paper we propose a semi-analytic framework which is able to model star formation from the largest, giant molecular cloud (GMC) scale, to the final protostellar size scale. Due to the simplicity of the framework it is ideal for theoretical experimentation to explore the principal processes behind different aspects of star formation, at the cost of introducing strong assumptions about the collapse process. The basic version of the model discussed in this paper only contains turbulence, gravity and crude assumptions about feedback, nevertheless it can reproduce the observed core mass function (CMF) and provide the protostellar system mass function (PSMF), which shows a striking resemblance to the observed IMF, if a non-negligible fraction of gravitational energy goes into turbulence. Furthermore we find that to produce a universal IMF protostellar feedback must be taken into account otherwise the PSMF peak shows a strong dependence on the background temperature.
Key words: stars: formation – turbulence – galaxies: evolution – galaxies: star formation – cosmology: theory
1 INTRODUCTION
Finding a comprehensive description of star formation has been one of the principal challenges of astrophysics for decades. Such a model would prove invaluable to understanding the evolution of galactic structures, binary star systems and even the formation of planets.
It has been long established that stars form from collapsed dense molecular clouds (McKee & Ostriker 2007a). Currently the most promising candidate for a driving process is turbulence, as it can create subregions with sufficiently high density so that they become self-gravitating on their own, while also exhibiting close to scale-free behavior (in accordance with the observations of Larson 1981; Bolatto et al. 2008). These fragments are inherently denser than their parents so they collapse faster, quasi-independent from their surroundings. However, once they turn into stars they start heating up the surrounding gas (by radiation, solar winds or supernova explosions) preventing it from collapsing and forming stars (see Fig. 1). This process is inherently hierarchical so it should be possible to derive a model that follows it from the scale of the largest self-gravitating clouds, the GMCs ($\sim 100$ pc), to the scale of protostars ($\sim 10^{-5}$ pc). This is not possible in direct hydrodynamic simulations due to resolution limits, but can be treated approximately in analytic and semi-analytic models.
This paradigm has been explored by Padoan et al. (1997) and Padoan & Nordlund (2002), then made more rigorous by Hennebelle & Chabrier (2008) who attempted to create an analytic model analogous to Press & Schechter (1974), which approximates the background density field as a Gaussian random field. A similar model was developed by Zamora-Avilés et al. (2012), however that did not rely on turbulence. Later Hopkins (2012a) expanded on these works by adopting the excursion set formalism to find the distribution of the largest self-gravitating structures, which was found to be very similar to the observed distribution of GMCs. Similarly Hopkins (2012b) found that the distribution of the smallest self-gravitating structures fit well the observed CMF. Building on these results Hopkins (2013a) generalized the formalism to be applicable to systems with different equations of state and turbulent properties.
Observed cores are sub-sonic and show no clear signs of fragmentation and the CMF looks very similar to the IMF apart from a factor of $\sim 3$ shift in the mass scale (Offner et al. 2014). However, if no other physics is assumed other than isothermal turbulence and grav-
ity, during the collapse the cores develop strong turbulence and eventually sub-fragment into smaller objects (Goodwin et al. 2004; Walch et al. 2012a, for discussion see Krumholz 2014). This implies that some additional physics must play a role, but there is no clear consensus on what it could be: magnetic fields (Nakano & Nakamura 1978; McKee & Ostriker 2007b), radiation (Krumholz 2011), cooling physics (Jappsen et al. 2005) etc. Using a cooling physics motivated “stiff” EOS Guszejnov & Hopkins (2015) incorporated the time dependent collapse of the cores into the excursion set formalism and found that the distribution of protostars closely reproduced the observed IMF.
These excursion set models did successfully reproduce the CMF, IMF and the GMC mass function, however they had several shortcomings. First, they did not account for the differences in formation and collapse times of clouds of different sizes (e.g. small clouds form faster and collapse faster). Secondly, the excursion set formalism describes the density field around a random Lagrangian point. This means that the spatial structure of a cloud can not be modeled directly (e.g. there is no way to find if a cloud forms binary stars). Finally, there is no self consistent excursion set model that follows from the GMC to the protostar scale (i.e. Hopkins 2012b covered scales between the galactic disk and cores, Guszejnov & Hopkins 2015 between cores and protostars). We believe these shortcomings can be overcome by moving away from the analytic excursion set formalism and instead adopting a simple semi-analytical approach with the same random field assumption. This framework would allow us to follow the evolution self gravitating clouds while resolving both the GMC and protostellar scales and preserving spatial information. In this paper we will outline a possible candidate for such a model.
The paper is organized as follows. Sec. 2 provides a general overview of the model, including the primary assumptions and approximations and briefly outlines its numerical realization. Sec. 3 shows the simulated time evolution of the CMF and the protostellar system mass function (PSMF) which shows a striking similarity to the IMF. Sec. 3.2 also discusses the effects of having a temperature independent equation of state on the peak of the PSMF and the universality of the IMF. Finally, Sec. 4 discusses the results and further applicability of the model.
2 METHODOLOGY
In short, instead of doing a detailed hydrodynamical simulation involving gravity and radiation, our model assumes a simple stationary model for the density field, collapse of structures at constant virial parameter and an equation of state that depends on cloud properties. Starting from a GMC sized cloud it evolves the density field as the cloud collapses and pumps turbulence (this is not a bad approximation, see Robertson & Goldreich 2012; Murray & Chang 2015; Murray et al. 2015). Note that our assumptions do not necessarily mean that all clouds have supersonic turbulence. Paper II has shown that if a medium has a “stiff” equation of state ($\gamma > 4/3$), then turbulence is dampened during collapse. Since it is observed that dense, low mass cores are subsonic while high mass, low density clouds are supersonic some form of physics is needed to remove the turbulent energy. For that purpose we are using an equation of state that becomes stiff at high densities, which in combination with the constant virial parameter assumption makes dense clouds sub-sonic, arresting fragmentation.
In the model, at each time step we search for self gravitating structures which we treat as new fragments, for which the process is repeated in recursion until a substructure is found that collapses to protostellar scale without fragmenting. Our assumptions will be discussed in more detail in the following subsections while a step-by-step description of the algorithm is provided in Appendix A.
Our model is a modified version of the excursion set model used by Guszejnov & Hopkins (2015) (henceforth re-
ferred to as Paper I) using the theoretical foundation of Hopkins (2013a) (henceforth referred to as Paper II). Due to the significant overlap between models we show only the essential equations and emphasize the differences and their consequences. If the reader is familiar with Paper I we suggest skipping to Sec. 2.3.
2.1 The Density Field
It is known that the density field in the cases of both sub and supersonic, isothermal flows follows approximately lognormal statistics (for corrections see Hopkins (2013b)). This means that if we introduce the density contrast \( \delta(x) = \ln[\rho(x)/\rho_0] + S/2 \), with \( \rho(x) \) as the local density, \( \rho_0 \) as the mean density and \( S \) as the variance of \( \ln \rho \), it would follow a close to Gaussian distribution\(^1\), thus
\[
P(\delta|S) \approx \frac{1}{2\pi S} \exp \left( -\frac{\delta^2}{2S} \right).
\]
(1)
It is a property of normal and lognormal random variables that a linear function of these variables will also be normal/lognormal, thus the averaged density in a region has lognormal equilibrium statistics whose properties are prescribed by turbulence. Following Paper II this yields
\[
S(\lambda) = \int_0^\lambda \Delta S(\lambda) d\ln \lambda \approx \int_0^\lambda [1 + b^2M^2(\lambda)] d\ln \lambda,
\]
(2)
where \( \lambda \) is the averaging scale, \( M(\lambda) \) is the Mach number of the turbulent velocity dispersion on scale \( \lambda \) and \( b \) is the fraction of the turbulent kinetic energy in compressive motions, which we take to be about 1/2 (this is appropriate for an equilibrium mix of driving modes, see Federrath et al. 2008 for details. Paper I experimented with \( b \sim 1/4-1 \) and found no qualitative differences).
It is important to note that although \( \rho \) is lognormal which means \( \delta \) is Gaussian, there is significant spatial correlation (i.e. \( \rho \) can not change instantly over arbitrarily small spatial intervals) so it is not possible to model the density field as a spatially independent random field. To circumvent this issue we solve the problem in Fourier space since \( \delta(k) \) is also lognormal, while there is little correlation between modes so it is acceptable to assume them to be independent (note: having correlated modes in Fourier space introduces only mild effects on the final mass functions, see Appendix A of Paper II for details). Combined with the fact that the number of modes in the \([k, k + dk]\) range is \( dN(k) = 4\pi k^2 dk n_k \), where \( n_k \) is the mode density, we get the variance for an individual density contrast mode is
\[
S_{\text{mode}}(k) = \frac{\ln(1 + b^2M(k)^2)}{4\pi k^3 n_k}.
\]
(3)
Paper II showed that to realize a steady state density contrast field with such variance and zero mean, the Fourier component \( \delta(k, t) \) must evolve as
\[
\delta(k, t + \Delta t) = \delta(k, t) (1 - \Delta t/\tau_k) + \epsilon \sqrt{2S_{\text{mode}}(k)\Delta t/\tau_k},
\]
(4)
where \( \epsilon \) is a Gaussian random number with zero mean and unit variance while \( \tau_k \sim v_t(k)/\lambda \) is the turbulent crossing time on scale \( \lambda \sim 1/k \), and the turbulence dispersion obeys \( v_t^2(\lambda) \propto \lambda^{p-1} \) thus \( \tau_k \propto \lambda^{p-2} \) (in our simulations we use \( p = 2 \), appropriate for supersonic turbulence, see (Murray 1973; Schmidt et al. 2009; Federrath 2013)).
2.1.1 The Equation of State
It is easy to convince oneself that a purely isothermal or polytropic equation of state (EOS) would be a very poor description of the complex physical processes contributing to the cooling and heating of clouds, however, modeling these processes in detail would require full numerical simulations. Instead we try to find a simple, heuristic EOS that captures the behaviors critical to our calculation. One of the most important effect during collapse is the transitioning from the state where the cooling radiation efficiently escapes from the cloud to the state where the cloud becomes optically thick to it and heats up as it contracts. As the virial parameter is assumed to be constant, this leads to a decrease in turbulence, which effectively arrests fragmentation. This is essential to reproduce the IMF shape as pure isothermal collapse would
\[\text{Figure 2.}\] Time evolution of the distribution of density in a parent GMC of \(10^5 M_\odot\). This is a mass weighted average of the density distribution of all substructures in the parent cloud (which are all assumed to be lognormal with different parameters), thus the low mass end is set by the lowest density structure which is the parent cloud while the high mass end is a power law due to the power law like distribution of fragments (see Fig. 4). There is also a clear trend as the high mass end tail rises in time. This is caused by the formation of new self gravitating substructures (Federrath & Klessen 2013).
lead to an infinite fragmentation cascade. We adopt the same effective polytropic EOS model as Paper I where for small time steps (compared to the dynamical time):
\[ T(x, t + \Delta t) = T(x, t) \left( \frac{\rho(x, t + \Delta t)}{\rho(x, t)} \right)^{\gamma(t)-1}, \]
where \( \gamma(t) \) is the effective polytropic index of the cloud at time \( t \).
One of the main goals and advantages of our framework is that it allows the exploration of different physical EOS models simply and efficiently. For example, let us consider a toy model where the effective EOS is not volume-density \((n)\) dependent: \(E\) EOS model based on works like Masunaga & Inutsuka 2000; Glover & Mac Low 2007 that follows the form
\[ \gamma(n) = \begin{cases}
0.8 & n < 10^7 \text{cm}^{-3} \\
1.0 & 10^7 < \frac{n}{\text{cm}^{-3}} < 10^{10} \\
1.4 & n > 10^{10} \text{cm}^{-3}
\end{cases}. \]
Simulations have shown that this leads to a ‘turnover’ only at extremely low masses (\(\sim 0.001 \text{M}_\odot\), Fig. 9 later), making the IMF nearly a pure power-law at the observable masses. We will explore model and some of its physical consequences for observables in more detail in a future paper, but explicitly show below that our semi-analytic model also captures this behavior. This is a valuable vindication both of the accuracy of the semi-analytic model (compared to full numerical simulations), and of the need for additional physics to establish the turn-over of the IMF.
For purposes of this study, let us assume that we do not know the detailed origin of such physics (it may be due to magnetic fields, or radiative heating, for example, both of which we will explore in detail in follow up papers). The simplest approach, and one commonly adopted in numerical simulations, is to parametrize their effects via an ‘effective equation of state’. Motivated by the work on radiative feedback from [Bate 2009; Krumholz 2011], let us consider a toy model where the effective EOS is not volume-density but surface-density \((\Sigma)\) dependent:
\[ \gamma(\Sigma) = \begin{cases}
0.7 & \Sigma \leq 3 \text{M}_\odot/\text{pc}^2 \\
0.094 \ln \left( \frac{\Sigma}{3 \text{M}_\odot/\text{pc}^2} \right) + 0.7 & 3 \text{M}_\odot/\text{pc}^2 < \Sigma < 5000 \text{M}_\odot/\text{pc}^2 \\
1.4 & \Sigma \geq 5000 \text{M}_\odot/\text{pc}^2
\end{cases}. \]
This is the same EOS as we used in Paper I. Note that the “turnover” where this becomes “stiff” is at much lower surface densities than we would obtain if we modeled cooling physics alone (Glover & Mac Low 2007) which would essentially give the same answer as our \(\gamma(n)\) case above (for a comparison of the two types of EOS models, see Guszejnov et al. 2015). Instead, we are assuming some form of physics makes the EOS stiffen at much higher surface densities – we choose the particular value here \textit{empirically}, because it provides a reasonable fit to the observed IMF. We will then explore the consequences of such a parametrization, for the IMF and its time-evolution in different clouds.
### 2.2 Collapse: criterion and evolution
It has been shown in Paper I and Paper II that the critical density for a \((\text{compared to the galactic disk})\) small, homogeneous, spherical region of radius \(R\) to become self gravitating is
\[ \rho_{\text{crit}}(R) = \frac{1}{1 + \mathcal{M}_{\text{edge}}^{1/2} \left( \frac{R}{R_0} \right)^{-2}} \left( \frac{T(R)}{T_0} + \mathcal{M}_{\text{edge}}^{1/2} \left( \frac{R}{R_0} \right)^{p-1} \right), \]
where the two terms represent thermal and turbulent energy respectively, \(T(\lambda)\) is the temperature averaged over the scale \(\lambda\), while \(T_0\) is the mean temperature of the whole collapsing cloud and we used the following scaling of the turbulent velocity dispersion and Mach number \(\mathcal{M}\)
\[ \mathcal{M}^2(R) = \frac{\sigma_v^2(R)}{(\sigma_v^2(\rho_0))} = \mathcal{M}_{\text{edge}}^{1/2} \left( \frac{R}{R_0} \right)^{p-1}, \]
where \(R_0\) is the size of the self gravitating parent cloud and \(p\) is the turbulent spectra index, so the turbulent kinetic energy scales as \(E(R) \propto R^p\); generally \(p \in [5/3; 2]\), but in this paper, just like in Paper I we assume \(p = 2\) as is appropriate for supersonic turbulence.
It should be noted that the fragmentation process is complex even in the idealized case of homologous collapse (see Hanawa & Matsumoto 1999; Noormousi & Hennebelle 2015). This means that our method of finding self gravitating subregions using Eq. 8 is a strong approximation, however, a proper treatment would require drastically more computation power which would go against one of the primary goal of the framework: the rapid exploration of parameter space and testing of physical models.
Our goal is to create a model that resolves clouds from GMC to protostellar scales, so the initial structures of the model are the GMCs which themselves are self gravitating (first crossing scale in the excursion set formalism). This means they must satisfy Eq. 8, for which spherical clouds \((M(R) = (4\pi/3)R^3 \rho(R))\) in isothermal parents yields the mass-size relation:
\[ M = \frac{M_{\text{sonic}}}{2} \frac{R}{R_{\text{sonic}}} \left( 1 + \frac{R}{R_{\text{sonic}}} \right). \]
Note that for very high mass clouds a correction containing the angular frequency of the galactic disk would appear, however this term is small (see Paper II for details). Eq. 10 introduces \(R_{\text{sonic}}\) which is the sonic length, the scale on which the turbulent velocity dispersion is equal to the sound speed, so in an isothermal cloud using the scaling of Eq. 9, we expect
\[ R_{\text{sonic}} = R_0 \mathcal{M}_{\text{edge}}^{-2/(p-1)}. \]
Meanwhile \(M_{\text{sonic}}\) is defined as the minimum mass required for a sphere with \(R_{\text{sonic}}\) radius to start collapsing so
\[ M_{\text{sonic}} = \frac{2}{Q_{\text{coll}}} \frac{c_s^2 R_{\text{sonic}}}{G}, \]
where \(G\) is the gravitational constant and \(Q_{\text{coll}}\) is the virial parameter for a sphere of the critical mass for collapse (see Eq. 15 later). For reasonable galactic parameters and temperatures \(R_{\text{sonic}} \approx 0.1 \text{pc}\) and \(M_{\text{sonic}} \approx 6.5 \text{M}_\odot\) (assuming we use the value for \(Q_{\text{coll}}\) we specify in Sec. 2.2.1).
Since the GMC in question has just started collapsing, the turbulent velocity at its edge must (initially) obey the turbulent power spectrum. Thus \(v_s^2(R) \propto R\) for the supersonic and \(v_s^2(R) \propto R^{2/3}\) (the Kolmogorov scaling) for the subsonic case. Using the mass-size relation of Eq. 10 leads
to the following fitting function
\[
\frac{(1 + M_{\text{edge}}^2) M_{\text{edge}}}{1 + M_{\text{edge}}^{-1}} = \frac{M}{M_{\text{onic}}},
\]
which exhibits scalings of $M \propto M^4$ for the subsonic and $M \propto M^2$ for the supersonic case respectively, and (coupled to the size-mass relation above) very closely reproduces the observed linewidth-size relations (Larson 1981; Bolatto et al. 2008; Lada & Lada 2003). Note that dense regions will deviate from this scaling, as observed (see references above), because collapse “pumps” energy into turbulence (Robertson & Goldreich 2012; Murray & Chang 2015; Murray et al. 2015).
2.2.1 Evolution of Collapsing Clouds
One of the key assumptions of the previous models in Paper I and Paper II is that the kinetic energy of collapse pumps turbulence (Robertson & Goldreich 2012; Murray & Chang 2015; Murray et al. 2015) whose energy is dissipated on a crossing time. As turbulent motion provides support against collapse, the collapse can only continue after this extra energy has been dissipated by turbulence (see Sec. 9.2 in Paper II for details). This leads to the following equation for the contraction of the cloud:
\[
\frac{d\bar{r}}{dt} = -\bar{r}^{-1/2} \left(1 - \frac{1}{1 + M_{\text{edge}}^2(\bar{r})}\right)^{3/2},
\]
where $t(t) = \bar{R}(t)/R_0$ is the relative size of the cloud at time $t$ while $\bar{r} = t/t_0$ is time, normalized to the initial cloud dynamical time $t_0 \approx 2Q_{\text{coll}}^{-3/2} (GM_0/R_0^2)^{-1/2}$ (see Paper II for derivation). In this case the initial dynamical time ($t_0$) and the crossing time only differ by a freely-defined order unity constant, so in our simulations we consider them to be equal without loss of generality.
The other key assumption of the model is that collapse happens at constant virial parameter. We define $Q_{\text{coll}}$ as
\[
Q_{\text{coll}} \equiv \frac{GM}{k^2} = c_s^2 + v^2 = c_s^2 (1 + M_{\text{edge}}^2). \tag{15}
\]
Note that $Q_{\text{coll}}$ is not the Toomre $Q$ parameter, merely the ratio of kinetic energy to potential energy needed to destabilize the cloud, thus the higher $Q_{\text{coll}}$ the more unstable clouds are to fragmentation. One can find $Q_{\text{coll}}$ using the Jeans criterion:
\[
0 \geq \omega^2 = \left(c_s^2 + v^2\right) k^2 - 4\pi G \rho,
\]
which for the critical case ($\omega = 0$) leads to
\[
Q_{\text{coll}} = \frac{3}{k^2 R^2}. \tag{17}
\]
One would be tempted to substitute in $k = 2\pi/R$, but that would be incorrect, as we have a spherical overdensity with R radius to which the corresponding sinusoidal wavelength is not R. We therefore chose $k = \frac{2\pi}{R}$ which yields $Q_{\text{coll}} = 12/\pi^2 \approx 1.2$. Note that all formulas contain $c_s^2/Q_{\text{coll}} \propto T/Q_{\text{coll}}$ so an uncertainty in the virial parameter is degenerate with an uncertainty in the initial temperature.
Combined, the above equations completely describe the collapse of a spherical cloud, as the EOS (Eq. 5-7) sets the temperature and thus the sound speed. Using that, Eq. 15 provides the edge Mach number, which allows us using Eq. 14 to calculate the contraction speed.
2.3 Differences from previous models
So far we are following the same assumptions as Paper I and Paper II, however, instead of simulating a stochastic density field averaged on different scales around a random Lagrangian point (the basis of analytic excursion set models) we use a grid in space and time. This means that we directly evolve the $\delta(k)$ modes to simulate the density field. This allows us to preserve spatial information as we now have information about the relative positions and velocities of substructures.
Having a proper density field not only allows us to take basic geometrical effects into account (as substructures are still assumed to be spherical) but it also allows a proper application of the self gravitation condition of Eq. 8. The excursion set formalism finds the smallest self gravitating structure a point is embedded in. The problem is that this “last crossing” structure may have further self gravitating fragments which do not contain the aforementioned point. These substructures will form protostars of their own (see Fig. 1) leaving their parent cloud with less mass which in turn might not be self gravitating anymore. This is not addressed in excursion set models which instead simply assume 100% of the mass ending up in protostars of different sizes (which of course is not realistic), while the proposed grid model predicts only about 5% (see Sec.3.2), which in fact depends on the physical assumptions of the model (i.e. how to deal with unbound material).
It should be noted that like the model of Paper I, in this first study we include no explicit feedback mechanism. Instead the model utilizes a few crude approximations to account for the qualitative effects of feedback. First, it is assumed that the clouds that becomes unbound by fragmentation stop collapsing and “linger” for a few dynamical times (during which they may form new self gravitating fragments) before being heated up/blown up/disrupted by feedback from the newly created protostars in such a fashion that they can no longer participate in star formation². Note that this assumption is made for convenience, it is not inherent in the code as it is possible to implement direct feedback prescriptions. Similarly magnetic fields are neglected in this base model, but can be easily implemented into the framework. Like in Paper I we neglected the effects of accretion and protostellar fragmentation when comparing to the IMF as the protostellar system mass function (from now on PSMF) is already a good enough qualitative fit so their effects are assumed to be modest (except for the very high and low mass ends where fragmentation could provide a high mass cut off while accretion could affect the turnover point, see McKee & Offner 2010 for details on the protostellar mass function). We would also like to note that it is possible to apply a crude implementation of supernova feedback by simply stopping the evolution after a few Myrs (when enough supernovae have exploded to unbind the GMC). Since the simulation provides a time dependent output, it can be done during post-processing. Of course, the point of our frame-
² For example photoionization can destroy the molecular cloud (Dale et al. 2012; Walch et al. 2012b; Geen et al. 2015), while both supernovae (Iffrig & Hennebelle 2015) and outflows (Arce et al. 2007) can provide momentum for turbulence or ejection.
work is that one could easily add models for feedback, and/or accretion if desired. We would like to note that using hydrodynamical simulations would allow a much more realistic treatment of certain details of the problem, however the large dynamic range ($10^{-5} - 100$ pc) and the long range gravitational interactions make such attempts extremely computationally intensive, preventing one from getting substantial statistics. A further issue with direct hydrodynamical simulations is that they involve the full, detailed form of all physical interactions, making it harder to pinpoint the primary driving mechanisms behind certain phenomena.
In summary we propose a semi-analytical model which has negligible computational cost and still captures phenomena (e.g. spatial correlation, motion of objects, complicated time dependence) which are beyond the capabilities of the analytical excursion set formalism. Our intention in this paper is not to present a “complete” model of star formation, but rather to illustrate the power of this approach with a first study involving only turbulence and self-gravity.
3 EVOLUTION OF THE IMF AND CMF IN GMCS
In this section we present an application of the model for simulating the collapse of an ensemble of GMCs (distributed following the first crossing mass function obtained by Hopkins 2012b, see Fig. 3). This includes simulating a number of GMCs of different masses where the initial conditions are set by Eq. 9 and Eq. 10. The clouds are assumed to start with fully formed turbulence (as GMCs form out of an already turbulent medium) which means that before simulating the collapse the density field is initialized to have the appropriate lognormal distribution. The output of the code contains the formation time and properties (e.g. mass, position, velocity) of individual protostars along with snapshots of the hierarchical structure of bound objects at different times. In Sec. 3.1 we investigate the latter and compare the distribution of nonfragmented structures with the observed CMF. Later, in Sec. 3.2 we discuss the time evolution of PSMF and how it relates to the IMF and whether it can be universal without invoking feedback physics.
3.1 Fragmentation and self-gravitating substructures: the observed CMF
It is well known that during their collapse clouds fragment into smaller self-gravitating structures (see Fig. 1). It is instructive to see how much mass is bound in structures of different sizes. Fig. 4 shows the time evolution of the number of structures of different sizes counting all “clouds-in-clouds”, which follows a distribution similar to the observed IMF and CMF (for quick overview see Offner et al. 2014), however it has a significantly shallower slope\(^3\) of roughly $M^{-0.5}$. The distribution is established fairly quickly and is maintained until the collapse of the parent cloud ends. This mass function of bound structures is consistent with the cloud in cloud picture shown in Fig. 1 in that there is a vast hierarchy of bound structures embedded in each other.
Observationally finding the substructure of a GMC is very challenging (although see Rosolowsky et al. 2008), most observers instead concentrate on the so called cores which are collapsing clouds that have no self gravitating fragments. Figure 5 shows the total CMF (time and mass averaged
---
\(^3\) In this paper the approximate high mass end behavior is estimated by fitting a power law between $0.5 M_\odot$-$100 M_\odot$. The error presented in the figures only account for the uncertainty in the fitting.
over an ensemble of GMCs following the distribution shown in Fig. 3) for different initial parameters. The simulated CMF reproduces the shape of observed results, having both a turnover point and a slightly shallower high mass slope ($\sim M^{-1.15}$) than the canonical Salpeter result of $\sim M^{-1.35}$ for the IMF (see Offner et al. 2014).
Fig. 6 clearly shows that there is very small difference between the CMF turnover masses and high mass slopes between GMCs of different sizes after 1 Myr. This is because early collapse is roughly isothermal so these clouds all have the same characteristic fragment mass ($M_{\text{crit}}$, see Eq. 20 for details). Systems which are on the same linewidth-size relation (i.e. they form out of the same turbulent cascade) will always have the same $M_{\text{sonic}}, M_{\text{crit}}$ (see Hennebelle & Chabrier 2008; Hopkins 2012b). During later evolution the GMCs heat up at a different pace as the dynamical times are different. Meanwhile Fig. 7 shows that there is a clear trend of increasing turnover mass with time in each cloud. This phenomenon and its possible cause is further investigated in Sec. 3.2. This trend is not visible in case of the physical EOS of Eq. 6 as the peak is well below the stellar mass scales (see Fig. 9). Nevertheless, this scenario shows that in the absence of a dominant $M_{\text{crit}}$ the initial CMF turns over around the sonic mass scale (as shown by previous analytical works e.g. Hennebelle & Chabrier 2008; Hopkins 2012b), but this mass scale gets “forgotten” during the fragmentation cascade.
3.2 Evolution of the PSMF
We now examine the mass function of the final collapsed objects, the protostellar system mass function (PSMF).
In Fig. 8 we show that parent clouds of all masses produce similar to Salpeter scalings the high mass end with lower mass clouds producing slightly steeper slopes. Also, there is a clear trend of increasing turnover mass with increasing parent mass, unlike the case of the CMF (See Fig. 6). It is worth noting that the GMC mass function is top heavy, which means that the high mass clouds dominate the integrated mass function. If we accept this result then it suggests a possible observational bias of the IMF as most observations focus on smaller clouds in the Milky Way. Also, turbulent fragmentation does not produce a cloud mass dependent “maximum stellar mass”.
The increasing turnover mass for both PSMF and CMF is related to the equation of state. In a turbulent cloud, self gravitating fragments of different sizes form, which (according to the EOS of Eq. 7) have different effective polytropic indices. According to the EOS there exists a threshold in the surface density ($\Sigma_{\text{crit}}$) above which $\gamma > 4/3$, stabilizing the cloud against further fragmentation. Thus it is instructive to find the critical mass ($M_{\text{crit}}$) corresponding to $\Sigma_{\text{crit}}$. Using the collapse condition of Eq. 8 and expanding up to linear order in $\gamma$ around 1 (this is a good approximation during most of the cloud’s lifetime as the collapse starts at close to isothermal conditions) yields that $\Sigma > \Sigma_{\text{crit}}$ requires that
$$R < R_{\text{crit}} = R_0 \frac{\gamma (\Sigma_{\text{crit}} / \Sigma_0)}{\Sigma_0} \left(1 + M_{\text{edge}}^2\right)^{-1} - M_{\text{edge}}^2 + \gamma - 1,$$
where $R$ is the fragment radius and $R_0$, $\Sigma_0$, $\gamma = \gamma (\Sigma_0)$ are the radius, surface density and the effective polytropic index of the parent cloud. From Eq. 18 we can find the critical mass $M_{\text{crit}} = 4\pi R^2 \Sigma_{\text{crit}}$ below which fragments are unlikely to collapse (note: according to the EOS of Eq. 7 the critical surface density $\Sigma_{\text{crit}} \approx 2400 M_\odot / pc^2$). These formulas can
yields then:
\[
\text{a density dependent EOS where the}
\]
shows the time evolution of the time and ensemble
Chabrier
Time evolution of the CMF in a \(10^6 \, M_\odot\) parent GMC using the \(\gamma(\Sigma)\) EOS of Eq. 7. The plot is normalized so that integrated mass corresponds to the mass of gas bound in self gravitating clouds relative to the total mass of the parent GMC, which explains the downwards trend since less and less gas is bound in cores as more protostars are produced and the cloud gets heated by contraction. The high mass power law fitting is done according to Footnote 3. There is a clear trend in the turnover mass (the peaks are denoted with solid circles) which increases significantly while preserving the overall shape of the function (e.g. high mass slope). Right: Time evolution of the CMF in a \(10^6 \, M_\odot\) parent GMC using the physically motivated EOS of Eq. 6 (a density dependent EOS where the transition point to the \(\gamma > 1\) regime is calculated from cooling physics). As expected the CMF has a peak around the sonic mass at early times, however, that feature gets “washed out” by the fragmentation cascade which is not arrested by this EOS until very small scales.
Figure 7. Left: Time evolution of the CMF in a \(10^6 \, M_\odot\) parent GMC using the \(\gamma(\Sigma)\) EOS of Eq. 7. The plot is normalized so that integrated mass corresponds to the mass of gas bound in self gravitating clouds relative to the total mass of the parent GMC, which explains the downwards trend since less and less gas is bound in cores as more protostars are produced and the cloud gets heated by contraction. The high mass power law fitting is done according to Footnote 3. There is a clear trend in the turnover mass (the peaks are denoted with solid circles) which increases significantly while preserving the overall shape of the function (e.g. high mass slope). Right: Time evolution of the CMF in a \(10^6 \, M_\odot\) parent GMC using the physically motivated EOS of Eq. 6 (a density dependent EOS where the transition point to the \(\gamma > 1\) regime is calculated from cooling physics). As expected the CMF has a peak around the sonic mass at early times, however, that feature gets “washed out” by the fragmentation cascade which is not arrested by this EOS until very small scales.
be simplified by assuming isothermal collapse (\(\gamma \simeq 1\)) and that the parent GMC is highly supersonic (\(M_{\text{edge}} \gg 1\)), Eq. 11 yields then:
\[
R_{\text{crit}} \approx \frac{R_0 \Sigma_0}{M_{\text{edge}} \Sigma_{\text{crit}}} = \frac{R_{\text{sonic}} \Sigma_0}{\Sigma_{\text{crit}}}. \tag{19}
\]
Using the mass-size relation of Eq. 10 and that \(R_0 \gg R_{\text{sonic}}\) we obtain
\[
M_{\text{crit}} \approx \frac{4\pi R_{\text{sonic}}^2 \Sigma_{\text{crit}}}{16\pi R_{\text{sonic}}^2 \Sigma_{\text{crit}}} = \frac{M_{\text{sonic}}^2}{4\pi G^2 Q_{\text{coll}}^2 \Sigma_{\text{crit}}} \propto \frac{T^2}{\Sigma_{\text{crit}}}. \tag{20}
\]
The critical mass only depends on the cloud temperature and the equation of state. A similar sensitivity to the initial temperature has been found by \(\text{Bate} (2009)\) using a Jeans mass argument. Assuming that there exists a critical density \(\rho_{\text{crit}}\) where some physics terminates the fragmentation cascade the corresponding Jeans mass will simply be \(\propto T^{3/2}\). It is easy to see that this is the same result one would get when trying to find the critical mass using a \(\gamma(\eta)\) EOS.
Fig. 9 shows the time evolution of the time and ensemble averaged PSMF for different initial \(M_{\text{crit}}\) values (the different critical masses in these cases arise from having different \(\sigma/Q_{\text{coll}} \Sigma_{\text{crit}}\); where we fix \(Q_{\text{coll}}\) and \(\Sigma_{\text{crit}}\) and vary \(\Sigma_{\text{init}}\), for definition see Eq. 20) which all produce a shape similar to the IMF but with different peak masses. If we compare the results to the canonical IMF fitting functions of \(\text{Kroupa} (2002)\) and \(\text{Chabrier} (2005)\), then it is clear that the average PSMF always reproduces the Salpeter scalings however the turnover point is heavily influenced by \(T/Q_{\text{coll}} \Sigma_{\text{crit}}\). Since \(Q_{\text{coll}}\) is a constant this implies that the average temperature of the cloud could have a significant effect on the turnover point if \(\Sigma_{\text{crit}}\) is constant. Meanwhile, Fig. 9 also shows that the physical EOS of Eq. 6 has such a low characteristic mass that the resulting PSMF in the stellar mass range is just a power law. Nevertheless, the position of the peak is still sensitive to the initial conditions (\(\propto T^{3/2}\)), if one extends the plot to substellar mass scales.
Fig. 10 shows how this critical mass evolves in time for our default model assumptions (\(\Sigma_{\text{crit}} = \text{const.}\)). It is clear that \(M_{\text{crit}}\) correlates well with the peaks of the PSMF of the corresponding time interval.
This increase of the critical mass with time has an interesting consequence. Fig. 11 shows that the average time
of formation monotonically increases with the protostellar system mass.
So, if the equation of state does not depend on temperature (e.g. our $\gamma(\Sigma)$ is invariant) then the turnover mass shows a strong ($\propto T^2$) dependence on the initial conditions which would likely lead to a non-universal IMF ($\propto T^{3/2}$ in the $\gamma(n)$ case). A possible solution to this issue is if $\Sigma_{\text{crit}}$ from Eq. 20 has a temperature dependence. This perfectly plausible, just recall that the effective EOS is just a crude approximation of complex cooling physics. Bate (2009) argues that radiative feedback effectively weakens the dependence of the Jeans mass on density, making the turnover mass less sensitive to initial conditions. A similar example is provided by Krumholz (2011), where the initially formed protostar ‘seed’ heats up its environment, preventing it from collapsing. This dense cloud is heated up to $T_{\text{heating}} \propto M^{3/8} R^{7/8} \approx \Sigma^{3/8}$ by the accretion luminosity from the protostar\(^4\), which, using our EOS language, roughly translates to $\Sigma_{\text{crit}} \propto T^2$ which would produce a constant $M_{\text{crit}}$ and thus a universal IMF.
In a paper in preparation we will explore this feedback model in a fully spatially-dependent framework. For now, let us consider a simple experiment where $\Sigma_{\text{crit}} \propto T^2$.
Fig. 12 compares the results of two simulations, one with $\Sigma_{\text{crit}} = \text{const.}$ and one with $\Sigma_{\text{crit}} \propto T^2$. Although the latter still shows some time dependence, the shifting of the peak is greatly reduced, making it more consistent with observations, even though the only assumption about feedback was that it prevents collapsed cores from accreting from their
---
\(^4\) One can derive this temperature by assuming an optically thick cloud in equilibrium that is heated by accretion luminosity $L_{\text{acc}} \sim M \Psi \sim M/t_{\text{ff}} \Psi \propto M^{3/2} R^{-3/2}$ and cooled by thermal radiation $L_{\text{cool}} \sim 4\pi R^2 \sigma_{\text{SB}} T_{\text{heat}}^4$.
---
**Figure 9.** Evolution of the averaged PSMF (normalized to integrated mass) for different initial critical masses (set by having different $T/Q_{\text{cool}} \Sigma_{\text{crit}}$ values, for definition see Eq. 20) compared to results using the “traditional” EOS of Eq. 6 and the canonical IMF of Kroupa (2002) and Chabrier (2005). The PSMF is averaged both over time (assuming the age of GMCs is uniformly distributed in the [0,5] Myr range) and the GMC mass function (following Fig. 3). We included the standard $M_{\text{crit}} = 0.03 M_\odot$ (solid red), an $M_{\text{crit}} = 0.08 M_\odot$ (solid blue) and an $M_{\text{crit}} = 0.2 M_\odot$ (solid black) scenarios with the $\gamma(\Sigma)$ EOS along with a run which had the physically motivated $\gamma(n)$ EOS of Eq. 6. For realistic temperatures ($10-30$ K) the critical mass of the latter is well below the stellar mass range so the PSMF becomes a pure power law. Meanwhile, for the $\gamma(\Sigma)$ EOS case the PSMF shape is similar for different critical masses, and there is a clear shift of the peak to higher masses with increasing $M_{\text{crit}}$. In all cases the high mass end is close to the Salpeter result.
**Figure 10.** The peak masses of the PSMF of different time intervals (solid line with symbols) and the critical mass (dashed lines) for different parent GMC masses according to Eq. 18. The critical mass correctly predicts the qualitative evolution of the peak mass.
**Figure 11.** Average time of formation for protostars of different masses (the error bars represent the standard deviation) in a model with an invariant EOS. There is a clear trend of more massive protostars forming at later times (which is consistent with the shifting of the turnover mass in Fig. 10), however the scatter is comparable to this difference. Nevertheless it is clear that most massive stars only start forming after roughly a Myr after the cloud starts collapsing. Changing this requires additional physics beyond turbulence, gravity and cooling.
surroundings. Note that our aim with this experiment was only to demonstrate what would be required from a purely EOS based model to produce an invariant IMF, any other physics that sets the critical mass of the EOS constant would achieve similar results.
An important question of star formation is what fraction of the gas ends up in stars. The analytical excursion set models like in Paper I could not answer that question as they assume by default that 100% of the mass ends up in bound structures similar to the Press-Schecter model (Press & Schechter 1974) of dark matter halos which they are based on. However, our semi-analytic framework here allows us to explore different assumptions for the time-dependent behavior of both bound and unbound gas, and thus (in principle) to make predictions for this quantity.
In the “basic” models presented in this paper, we assume that whenever a core collapses and forms a star, any remaining mass in its parent cloud which is no longer self-gravitating (once the core is fully collapsed) is simply thrown out of the system. This is meant to represent a very crude toy model for the effects of feedback (from e.g. protostellar jets) on the parent sub-clumps from which the stars form. With this assumption, we find an integrated star-formation efficiency (after all mass either turns into stars or is unbound) of $\sim 5 – 10\%$ for GMCs of all sizes. Interestingly, this is almost completely independent of the EOS we assume (either constant $\Sigma_{\text{crit}}$ or $\Sigma_{\text{crit}} \propto T^2$), as long as it terminates the fragmentation cascade at roughly the same point. Of course, if we assume this gas remains bound to the total system, so it is simply recycled back to the “top level” of the original fragmentation hierarchy until it is consumed (which obviously corresponds to a no-feedback case), then we trivially predict that eventually all gas turns into stars. Of course, the effects of realistic feedback are much more complex than these simplistic assumptions, and we could adopt arbitrarily complex models (for example, evolving each protostar and tracking explicitly location-dependent photo-ionization feedback, which we then use to explicitly calculate whether gas is unbound from the system). We note this result simply to demonstrate the utility of these semi-analytic models for rapidly exploring different assumptions regarding the effects of feedback.
4 CONCLUSIONS
The aim of this paper is to provide a general framework for the modeling of star formation through turbulent fragmentation from the scale of GMCs to the scale of stars in order to quickly test the effects of different assumptions and new physics. Such a tool could allow theorists to explore different models and parameters before committing significant resources towards a detailed numerical simulation. We propose a semi analytical extension of the model of Guszejnov & Hopkins (2015) (Paper I) that we believe is detailed enough to capture the physics essential for modeling the formation of stars without being too demanding numerically. Just like the analytical excursion set models it does not simulate turbulence directly, instead it assumes that the density follows a locally random field distribution whose parameters evolve in time so that virial equilibrium is satisfied. This is an assumption about turbulent collapse that needs to be tested in future work. The density field is directly resolved on a grid which preserves spatial and time information allowing the implementation of more detailed physics (e.g. proper checking for self gravitation, time dependent cloud collapse) and the analysis of the spatial structure. This is not possible in the excursion set formalism which describes the density field around a random Lagrangian point. This also means that unlike the analytical models noted 100% of the mass ends up in protostars.
The presented form of the model contains only the minimally required physics (turbulence, self gravity, some equation of state). It is however possible to integrate more sophisticated models to provide a more accurate description of these processes. Also, since the output of our model contain the time dependent evolution of the CMF and the PSMF, one can easily apply corrections during post processing to account for effects like protostellar fragmentation or supernova feedback (stop the evolution when enough SNe exploded).
By applying this framework to modeling the collapse of giant molecular clouds, we found that even the basic model qualitatively reproduces the observed core mass function. The CMF evolution has little dependence on the mass of the parent GMC mass.
Another result of the simulation is the mass distribution of all bound structures in the cloud. This appears to have the same shape as the CMF with a shallower slope of roughly $M^{-0.3}$ at the massive end. These clearly show the hierarchy of bound structures.
One of the main results of our basic model is the protostellar system mass function (PSMF) which is obtained by following the collapse of an ensemble of GMCs following a GMC mass function determined by Hopkins (2012b). As in Paper I we found that the PSMF is qualitatively very similar to the observed IMF: it exhibits a close to Salpeter slope almost independent of the initial conditions, while the turnover mass is mainly set by the equation of state and the initial temperature.
Due to the minimalistic nature of the model we managed to pinpoint the physical quantities influencing the different features of the PSMF and thus the IMF. We found that the Salpeter slope at the high mass end is a clear consequence of turbulence (as shown before in Paper I) where the inclusion of extra physics only causes slight deviation from the pure power law behavior. Furthermore we found that in a medium with a stiff equation of state the actual turnover point in leading order is set by the local temperature ($M_{\text{crit}} \propto T^2 / \Sigma_{\text{crit}}$).
We found that if we assume a $\gamma(\Sigma)$ equation of state then the PSMF for protostars of the same age changes as the parent cloud collapses: the turnover mass increases with time. This can be explained by the increase of $M_{\text{crit}}$. This leads to a quadratic dependence of the turnover mass on the initial temperature which is inconsistent with the observed universality of the IMF. This means that it is not possible to derive a universal IMF with an equation of state that has no temperature dependence. One way to 'fix' the model is by implementing the feedback from protostars. Using the assumptions of Krumholz (2011) in leading order the heating from the protostars cancel the aforementioned quadratic scaling (due to $\Sigma_{\text{crit}} \propto T^2$), leading to a close to universal turnover mass.
Figure 12. PSMF for protostars in a parent GMC of $10^5 M_\odot$ for an EOS with $\Sigma_{\text{crit}} = \text{const}$ (left) and for an EOS with $\Sigma_{\text{crit}} \propto T^2$ (right). The solid circles show the peaks, which move considerably less for the $\Sigma_{\text{crit}} \propto T^2$ case. As implied by Eq. 20, if $\Sigma_{\text{crit}} \propto T^2$ then $M_{\text{crit}} = \text{const}$, and the IMF becomes invariant.
ACKNOWLEDGMENTS
We thank Ralf Klessen and Mark Krumholz for their insights and inspirational conversations throughout the development of this work. Support for PFH and DG was provided by an Alfred P. Sloan Research Fellowship, NASA ATP Grant NNX14AH35G, and NSF Collaborative Research Grant #1411920 and CAREER grant #1455342. Numerical calculations were run on the Caltech computer cluster “Zwicky” (NSF MRI award #PHY-0990291) and allocation TG-AST130039 granted by the Extreme Science and Engineering Discovery Environment (XSEDE) supported by the NSF.
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APPENDIX A: BASIC SIMULATION ALGORITHM
In this appendix we detail step-by-step how the basic version of the simulation works (see flowchart of Fig. A1), but note that it can be greatly expanded with new physics, as long as the fundamental assumption (locally random density modes) is kept.
(1) We begin with a GMC sized cloud whose initial parameters (mass, radius, temperature, density, edge Mach number, sound speed etc.) are derived from its mass \( M \), the sonic mass \( M_{\mathrm{sonic}} \) and length \( R_{\mathrm{sonic}} \), using the mass-size relation of Eq. 10 and linewidth-size relation of Eq. 9. These are all initialized on a 3D spatial grid, of resolution \( N \times N \times N \) chosen such that the final statistics converge (we found this happens at \( N \geq 16 \)). The density field is initialized assuming that it is lognormal (variance set according to Eq. 3) using the full density power spectrum model (transforming to Fourier space and back), while the temperature field follows the density according to the desired equation of state.
(2) We take timestep \( \Delta t \) (\( \Delta t \ll t_{\mathrm{dyn}} \) and \( \Delta t \ll t_{\mathrm{cross}}(d) \), where \( d = 2R/N \) is the spatial resolution of the grid). This means:
(a) Global contraction of the cloud (all scales shrink, density uniformly increases) according to Eq. 14.
(b) The density perturbation power spectrum \( \delta(k) \) is updated following Eq. 4, which assumes density mode statistics obey a local “random walk” in phase space. The actual density field is calculated by Fourier transforming to real space and normalizing the field with the cloud mass (this way mass is conserved).
(c) The temperature field is updated according to new densities and the chosen EOS (see Eq. 5).
(d) The cloud scale Mach number is updated according to our assumption that the virial parameter is constant during collapse.
(3) We now check whether any self-gravitating substructures have formed by using a Monte Carlo method that involves placing spheres of all possible sizes at random positions and testing them using the collapse criterion of Eq. 8.
(4) If such a region is found it is “removed” temporarily and expanded into its own grid. This new grid will have a higher spatial resolution than its parent, thus density modes on the newly available small scales need to be initialized (larger modes are inherited from previous grid). We then repeat steps (2)-(4) on this new grid. This means that during the evolution of its fragments the parent cloud is “frozen” in time. This is motivated by the fact that the dynamical time of fragments is smaller as \( t_{\mathrm{dyn}} \propto 1/\sqrt{\rho} \), so they evolve “fast” compared to their parents. Note that all clouds keep track of physical time, so it is possible to properly date the formation times of protostars and clouds.
(5) The time evolution of each cloud/grid continues until:
(a) The cloud reaches the protostellar size scale \( (R < R_{\mathrm{min}}) \), below which it is assumed to have formed a protostar.
(b) The cloud is still self-gravitating after a number of dynamical times \( (t > t_{\max})^5 \). After this limit is reached the cloud is assumed to have cooled and collapsed through other means. Essentially, this represents non-fragmenting cores.
(c) The cloud stops being self-gravitating. This can happen if a cloud loses enough of its mass that it becomes unbound. Since virial equilibrium is enforced this means no turbulence, which means no more fragmentation. In the model presented above these clouds are not forming stars or contributing to the mass of the protostars forming from their fragments, instead this material is “thrown away” (this represents “feedback” in some sense, see Sec. 2.3). Note that it is possible within the framework to return this unbound material to the parent GMC where it may form stars, but for simplicity in the presented model we chose not to do that.
(6) Clouds that formed protostars are removed the properties of the protostars are cataloged. We then return to the parent cloud and continue its evolution from Step (4).
(7) This continues until 100% of the original original mass of the cloud is either in protostars or unbound. The final output is the catalog of protostars. Note that it is also possible to get the CMF by exporting the properties of bound structures at a specified time. The whole process is repeated for large number of initial GMCs (with different random seeds) to gain adequate statistics.
\[ \text{MN} \]
Start cloud evolution with $\rho(x)$, $T(x)$, $R$ and $M_{\text{edge}}$ as input. Initialize turbulence. Prepare $\delta(k, 0)$ using FFT.
Evolve global parameters and $\delta(k, t)$ one time step. Calculate $\rho$ and $T$ fields at $t + dt$.
Is there a fragmenting subregion?
Is the cloud still self-gravitating?
Recursively follow the subregion using current state as initial conditions.
Continue evolving for one dynamical time. If no fragments have formed throw away the unbound material.
The cloud collapsed to a protostar. Write data, return to parent.
Figure A1. Basic algorithm of fragmentation code. The bold numbers in each box show which step from Appendix A they represent. See Appendix A for more detailed description.
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Toughness study of Borided, Borided and induction modified AISI 4340 steel
T Sivakumar1,*, M Prince2, P Gopalakrishnan3
1Department of Mechanical Engineering, Malla Reddy College of Engineering and Technology, Hyderabad.
2Department of Mechanical Engineering, Sri Krishna College of Technology, Kovaipudur, Coimbatore.
3Department of Metallurgical Engineering, PSG College of Technology, Coimbatore.
*Author for correspondence E-mail: [email protected]
Abstract. In this study, pack boriding is done on AISI 4340 steel in steel containers for 3 hours at 950°C. Boriding results in the formation of FeB or Fe2B columnar microstructure at the case. Such microstructure brings about a high brittleness of the boride layer. Induction surface modification is done on Borided samples to bring down the surface hardness. We put an effort to enhance the toughness of boride layer using 30 kW power high frequency induction heat source. The toughness of borided, borided and induction surface modified specimens are evaluated by shear punch test. Cylindrical punch of 4 mm diameter is used in this test. The toughness is calculated from the load-displacement curve. Induction modified specimens exhibit 38% improvement in toughness as compared with borided specimens. This improvement in toughness may be due to blunting of acicular boride structure in to a globular structure at the interface, smooth hardness gradient and formation of single phase Fe2B microstructure as a result of induction surface modification.
1. Introduction
The AISI 4340 is a low alloy steel, widely used as a material for manufacturing of different types of gears, shafts owing to the exceptional combinations of good mechanical and fatigue properties [1]. However, this steel has inadequate surface hardness when it is used in tribological applications [2]. Thus, its surface modification is necessary to improve the hardness. Boriding is one of the capable surface modification techniques to produce very hard surfaces on steels [3-4]. Boriding on steels can offer higher surface hardness (1400 – 2100 HV), as compared to carburizing (700 – 850 HV), nitriding (600 – 1100 HV) and carbo-nitriding (940 – 1000 HV) [5]. Borided steels offer wear resistance analogous to that of sintered carbides [6].
As Boriding on steels can be done through different methods like pack, molten salt and gas boriding [7-8]. This process is carried out in the temperature range of 700°C to 1000°C for 1-12 hours in the presence of suitable boriding mixture [9-10]. During this process distribution of boron into the surface of the steel takes place, two phase microstructure (Fe2B and FeB) and superficially, directional saw tooth microstructure is framed [11]. Eyre [12] reported that Fe2B and FeB phases formation based on the boron potential. If the boron potential is 8.83%, Fe2B phase only forms in the case; at 16.3% of boron, FeB phase also forms over and above Fe2B. The Fe2B phase forms nearby to the core and the FeB phase forms in close proximity to the surface. Two phase microstructure (FeB+Fe2B), pores in the case, anisotropic distribution of boron in the case, high process time, high process temperature result...
in poor toughness and ductility [13]. The effective use of borided components is restricted due to high brittleness.
For improving the toughness of the boride layer or/and borided steel, several kinds of surface engineering techniques have been tried by the researchers. The full disappearance of FeB layer is observed as a result of post diffusion annealing on borided steels, by heating the borided steels at 950°C for 6-8 hours [14-16]. Multicomponent boriding is suggested as one of the effective method to enhance the toughness of borided steels by carefully choosing the alloying elements such as copper, aluminium, chromium, silicon and nickel along with diffusion of boron [17-19]. Superplastic boronising is reported as an effective method to result in equiaxed boride grains with high toughness [20-24]. However, this is comparatively harder technique to be used for standard engineering components. Interrupted boriding is suggested as another alternative method to enhance the toughness and ductility of borided steels with fewer disturbances to the core [25]. Laser surface modification of as-borided steels results in significant improvement in the toughness due to the formation globular microstructure and better hardness gradient [26]. By doing laser treatment, surface hardness decreases and simultaneously toughness and ductility increases appreciably by reducing the degree of non-uniformity of the borided layer and generating residual compressive stresses [27].
In this investigation, an attempt is made to study the improvement in toughness of borided 4340 steel using induction surface modification.
2. Experimental details
2.1. Base Material
A medium carbon low alloy steel (0.39 C, 1.4 Ni, 0.8 Cr, 0.6 Mn, 0.3 Si, 0.4 Mo, balance Fe) is used as a base material (AISI 4340) for boriding. The steel specimens are normalized before boriding. The steel has a hardness of 449±5 HV (at 100 g load). Specimens of 12 mm diameter and 0.6 mm thickness are used for shear punch test.
2.2. Boriding and Induction surface modification
Boriding is done on AISI 4340 steel sheets of 18 mm diameter, 0.600 mm thickness using pack process (paste method) in a furnace at 950°C for 3 hours.
The borided surfaces are modified using 30 kW power high frequency induction heating machine. The gap between the coil and specimen is kept constant as 3.5mm. The input voltage is kept constant as 210V. The induction coil is fixed stationary. The specimens are moved at four different feed rates. A protective paste is applied on the exterior (surface) of the specimen to avoid oxidation.
After this treatment, the specimens are studied metallographically. The microstructures are observed using Zeiss axiovert optical microscope at suitable magnifications. The microhardness along the case was measured using Mitutoyo microhardness tester at a load of 100 g. The phase analyses are carried out using Shimadzu X-ray diffractometer, using Cu Kα radiation. The toughness of borided, borided and induction surface modified specimens are evaluated by shear punch test using small specimen of about 18 mm diameter and 0.6 mm thickness as per ASTM D732-10. The shear punch test is performed on a computerized materials testing system (FINE Testing Industries, Model TFNP 25KN) with a load cell of 25 kN capacity and an optical encoder with 1000 pulse per minute for uninterrupted monitoring of the applied load and a data acquisition system measuring punch head displacement. The shear punch experimental setup utilizes a flat cylindrical punch of about 4 mm in diameter. The load on the punch is calculated as a function of the punch journey and the graph of load vs. displacement is made. The material selected for both the die and punch is A2 air hardened tool steel (RC 58).
3. Results and discussions
The optical microstructure of borided specimen is shown in Figure 1. The microstructure shows typical two phase (Fe$_2$B – FeB) acicular boride needles for an average length of 100 µm.
The above figure 2 (a-d) give details an optical microstructures of borided and induction modified specimens treated at feed rates of 8.7, 9.7, 10.5, 11.5 mm/s. It is found that induction surface modification of borided specimens treated at a feed rates less than or equal to 9.7 mm/s results in the deterioration of the case microstructure. Figure 2 (c & d) show the improved modification of the case with increasing feed rates, with apparent sign of rounding of acicular boride needles at the interface.
resulting in possible improvement of toughness of boride layer. It is observed that by increasing the induction power, acicular nature of boride layer disappears significantly. The compactness of the boride layer increases with increase in induction power. Figure 2 (d) also demonstrate the development of spherical boride particles proximity to the surface. The average case depth of induction modified specimen treated at 11.5 mm/s was 72 µm. The case depth decreases may be due to dilution of boron from case to core. Further, it is apparent from the present investigation that a minimum feed rate of 11.5 mm/s is necessary to cause effective microstructural modification. Characteristic directional growth of the thermo-chemical diffusion based treatment vanished due to induction treatment as similar like laser treatment [27].
Figure 3. shows XRD pattern of borided specimen. XRD pattern illustrates the presence of Fe₃B and FeB phase in the borided case. This two phase boride microstructure exhibits inferior mechanical properties as reported by many researchers [3, 6, 11 and 13].
Figure 4 shows XRD pattern of induction modified specimen treated at a feed rate of 11.5 mm/s. The absence of hard brittle phase (FeB) has been observed from the XRD pattern. XRD pattern explains the presence of single phase Fe₃B in the induction modified surface. The single phase Fe₃B microstructure exhibits better ductile behavior as compared with dual phase microstructure as reported by many researchers [3, 6, 11 and 13].
Figure 5. Microhardness profiles of borided, induction modified at a feed rate of 11.5 mm/s.
The above figure 5, shows the microhardness profiles (ASTM E384) of the borided specimen and borided and induction modified specimen with feed rate of 11.5 mm/s. The average peak surface hardness measured from borided specimen is 1700 HV. This peak surface hardness is caused by the presence hard FeB phase present on the case. The microhardness is observed in the range between 800 HV – 1700 HV approximately. There is a great variation in the microhardness of the borided case indicates greater inhomogeneity of boron distribution in the case. The average peak surface hardness of induction modified specimen is 1100 HV. The micro hardness is found to vary between 1000 HV – 1100 HV approximately. Microstructural refinement due to induction modification results in better distribution of boron and other alloying elements in the case. The decrease in surface hardness and less scatter in hardness across the section are due to effective homogenization happened during induction modification.
Figure 6. A comparison of load vs punch displacement plot from a shear punch test of borided specimen and borided, induction modified specimen treated at 11.5 mm/s.
The mechanical properties such as ductility, strength and toughness of borided and borided and induction modified were estimated from the load-displacement curve shown in the figure 6. The shear
punch test is preferred method for the evaluation of mechanical properties of thin coatings. Shear punch test is based on blanking process, consisting of clamping a small thin sheet between the die and punch [26].
It is found that induction modification is the cost effective method to break down the acicular needle of conventionally borided steel as compared to laser modification. Borided and induction modified specimens exhibit lesser tensile strength as compared to the only borided specimens. The strength of the induction modified borided specimen is lowered be due to drop in the surface hardness. The notch angle between boride layer and iron substrate in the case of conventional boriding is around 90⁰C. It is observed from the optical microstructures that induction modification results in reducing the notch angle significantly. Because of reduction in notch angle, toughness is improved significantly. 38% improvement is estimated from the shear punch curve.
4. Conclusions
Acicular microstructure is replaced by globular microstructure in the induction surface modified borided AISI 4340 steels. Due to effective homogenization, lesser hardness scatter is observed. Such lesser hardness gradient leads to single phase of Fe-B microstructure on the surface. Thus, toughness in induction modified boride steel is enhanced by 38%.
Acknowledgments
The authors thankfully recognize All India Council for Technical Education (20/AICTE/RIFD/RPS (Policy II) 6/2012-13, dated 20.01.2013), New Delhi for providing the financial support for procuring shear punch test machine. The authors wish to show gratitude to Mr.Madhu, managing partner of M/s. Sri Vishnu Induction Hardening, Coimbatore for providing facilities to carry out induction modification trials. Also, the authors are grateful to the management of PSG college of Technology, Coimbatore for allowing us to carry out all the research facilities available in the Department of Metallurgical Engineering.
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A Surgical Reduction Technique for Posterior Cruciate Ligament Avulsion Fracture in Total Knee Arthroplasty: A Comparison Study
CURRENT STATUS: UNDER REVIEW
Journal of Orthopaedic Surgery and Research BMC
Wei Lin
Hebei Medical University Third Affiliated Hospital
Jinghui Niu
Hebei Medical University Third Affiliated Hospital
Yike Dai
Hebei Medical University Third Affiliated Hospital
Huaxing Zhang
Hebei General Hospital
Jing Zhu
Hebei General Hospital
Fei Wang
Hebei Medical University Third Affiliated Hospital
[email protected] Corresponding Author
DOI: 10.21203/rs.2.22829/v4
SUBJECT AREAS
Orthopedic Surgery
KEYWORDS
posterior cruciate ligament; avulsion fracture; cruciate retaining; total knee arthroplasty.
Abstract
**Background:** Posterior cruciate ligament (PCL) avulsion fracture of tibia is an uncommon but serious complication during primary cruciate retaining total knee arthroplasty (TKA). The first objective of this report was to conduct a retrospective cohort study to investigate the incidence and potential risk factors of PCL avulsion fracture in primary cruciate-retaining TKA. The second objective was to assess the functional outcomes of the knee after reduction of PCL avulsion fracture.
**Methods:** From January 2014 to January 2016, 56 patients who experienced PCL avulsion fracture of tibia in primary cruciate-retaining TKA were included in study group. Patients in this group underwent reduction of avulsion fracture. In this period, we selected 224 patients (control group) for comparison. Patients in this group also underwent the same TKA but no PCL avulsion fracture occurred. Range of motion of the knee and Knee Society Scores were assessed. The forgotten joint score was used to analyze the ability to forget the joint. Differences were considered statistically significant at $p < 0.05$.
**Results:** In our series, the incidence of PCL avulsion fracture was 4.6%. There was no significant differences ($p > 0.05$) with regard to preoperative or postoperative range of motion of the knee, final 4 year mean clinical score in study and control groups 92.4 ± 2.7 and 93.6 ± 1.9, respectively, and mean functional scores of 85.1 ± 1.8 and 87.1 ± 1.2, respectively.
**Conclusions:** The incidence of PCL avulsion fracture of tibia is relatively high. Older age and female gender were two risk factors of fracture in primary cruciate-retaining TKA. Reduction of PCL avulsion fracture with high-strength line can achieve good stability and function of the knee.
**Background**
Osteoarthritis is a chronic joint disease that affects more than 100 million people in the world [1]. The knee joint is the most frequently affected joint, and total knee arthroplasty (TKA) is an effective method for the treatment of end-stage knee osteoarthritis [2]. In a posterior cruciate ligament (PCL) retaining TKA, PCL avulsion fracture of tibia is an uncommon but serious complication. However, the outcomes of reinsertion and reduction of PCL are rarely reported.
Both PCL and anterior cruciate ligament contribute stability of the knee. Therefore, it is difficult to assess PCL function alone in TKA. The PCL drives more physiological knee and provides a part of...
proprioceptive feedback by decreasing paradoxical roll forward and allowing the femur to execute a controlled rollback during flexion [3-5]. A large number of different techniques have been used to protect the PCL from injury. Liabaud et al [6] reported the use of the bone island technique to protect the PCL and to preserve as much PCL as possible. That is the initial reason for using a cruciate-retaining knee prosthesis. In cruciate-retaining TKA, careful evaluation of the gap balance and tension of PCL are mandatory to prevent postoperative knee stiffness and instability. When performing a trial reduction, if the flexion gap is too tight, a PCL avulsion fracture may occur accidentally. Usually, this fracture is an incomplete fracture. It is not necessary to convert to a posterior-stabilized TKA, because the flexion gap will become too tight. In this setting, whether to reduce the PCL avulsion fracture or not becomes a controversial issue. Kim et al [7] reported the incidence of tibial-sided PCL avulsion fracture during the primary cruciate-retaining TKA, but they did not attempt to reduce the fracture. As the result, a non-healing fracture, instability of the knee, and a failed TKA are the major concerns. Currently, few surgeons reported the reduction of PCL avulsion fracture of tibia in primary cruciate-retaining TKA.
The first objective of this report was to conduct a retrospective cohort study to investigate the incidence and potential risk factors of PCL avulsion fracture in primary cruciate-retaining TKA. The second objective was to assess the functional outcomes of the knee after reduction of PCL avulsion fracture.
Materials And Methods
Institutional Review Board Approval was obtained before the study commenced. From January 2014 to January 2016, 56 patients who experienced PCL avulsion fracture of tibia in primary cruciate-retaining TKA were included in study group. Patients in this group underwent reduction of avulsion fracture. In this period, a total of 1216 primary cruciate-retaining TKAs were performed. Matching at a 1:4 ratio with regard to age, gender, body mass index (BMI) and follow up time, we selected 224 patients (control group) for comparison. Patients in this group also underwent the same TKA but no PCL avulsion fracture occurred. Our eligibility criteria were (1) unilateral knee osteoarthritis; (2) a primary cruciate-retaining TKA; (3) a knee with flexion-contracture deformity < 15°; and (4) a varus deformity.
< 20°. Patients who had knee instability, valgus knee, or stiff knee were excluded. All operations were performed in our center by senior orthopaedic surgeons (WF. et al) using the same surgical techniques.
**Surgical technique**
In both groups, as described by Kim et al [7], all primary cruciate-retaining TKAs were performed through the conventional midline skin incision. The distal femur cut was made with an intramedullary guide as the consultation to choose the right size of knee prosthesis. The anterior and posterior femoral condyles were resected with a battery-powered saw. For tibial resection, we made a bone island to protect the tibial attachment of PCL. Using an extramedullary cutting guide, a piece of 12 mm thick bone was resected. The retroversion angle was 5° to 10°. Soft tissue balance was measured using a tensor/balancer device as described by Sasanuma et al [8]. If the gap was too tight, an additional bony resection and soft tissue release were performed appropriately. During insertion and removal of trial components, if a PCL avulsion fracture of the tibia occurred accidentally (Fig. 1), reinsertion and reduction of PCL avulsion fracture were performed, this procedure was performed in study group. A high-strength suture with needle was passed through the tibia plateau (Fig. 2). The distal insertion of PCL was sutured with the high-strength suture, and a high-strength suture knot was secured on the anterior cortex of the tibia (Fig. 3). The fracture was reduced, and the prosthesis was implanted to restore the gap balance. With the knee flexed, the high-strength suture was tightened and tied at the front of the tibia tubercle before bone cement dried. Thus, the high-strength suture was fixed with dried bone cement. All patients used the same knee prosthesis (LINK, Germany, Gemini MK II). After the total knee prosthesis was implanted, the wound was closed in layers.
**Postoperative managements**
All patients received the same postoperative pain control and rehabilitation programs. Muscle exercises on the lower limbs and range of motion exercises ideally started one day after surgery [9]. All the patients were required to walk with crutches to support part of the weight. As soon as the patients regained adequate quadriceps control, crutches would be discontinued.
**Outcome evaluation**
Assessments were performed by a senior orthopaedic surgeon (DYK) who did not attend the treatments. Range of motion of the knee and Knee Society Scores (KSS; including clinical and functional scores of the knee) [10] were assessed. For comparing the postoperative status of the osteoarthritic patients after TKA, we used the forgotten joint score (FJS; a 12-item questionnaire with a maximum of 100) to analyze the ability to forget the joint [11]. Higher scores represented better results. Knee stability was assessed with drawer test by the senior orthopaedic surgeon (DYK). Fracture healing was defined as a callus bridging the fracture fragment on X-ray.
**Statistical analysis**
In order to determine whether age, gender, body mass index, preoperative range of motion, and component size were the potential risk factors of PCL avulsion fracture, we used logistic regression to analyze the correlation. Normality of continuous variables were checked with Shapiro-Wilks test. If the data were normally distributed, the two groups were compared using student t-test; on the contrary, a non-parametric test was selected. Categorical variables were checked with chi-square test or Fisher’s exact test. Logistic regression was used to identify the potential risk factors of PCL avulsion fracture. The data were analyzed with SPSS 19.0 (SPSS, Chicago, Illinois, USA). Differences were considered statistically significant at $p < 0.05$.
**Results**
In study group, complete reduction was achieved and maintained in all patients. Based on radiographic evaluation, fracture healing occurred in all patients within 3 months (Fig. 4). No patient experienced knee instability. No patient walked with an assistive device, and no patient underwent a revision surgery.
Patient demographics and outcomes of both groups were summarized in Tables 1 and 2. In our series, the incidence of PCL avulsion fracture was 4.6% (56: 1216) in primary cruciate-retaining TKA. We found no significant differences between study and control groups with regard to age, gender, body mass index, size of components, or follow-up period. We found no significant difference with regard to preoperative or postoperative range of motion of the knee. At the final follow-up, the mean clinical scores of study and control groups were 92.4±2.7 and 93.6±1.9, respectively ($p = 0.248$). The mean
functional scores were 85.1±1.8 and 87.1±1.2, respectively ($p = 0.066$). We found no significant statistical difference in regard to FJS ($p = 0.426$). The results of logistic regression analysis demonstrated that older age and female gender were two risk factors of PCL avulsion fracture (Table 3).
Discussion
Our study found that the incidence of avulsion fracture in primary cruciate-retaining TKA is relatively high, and older age and female gender are the two risk factors. Our reinsertion and reduction technique is a reliable treatment for PCL avulsion fracture. By using the technique, acceptable PCL function is maintained, which provides sufficient stability to the knee during movement.
There are few studies that investigate patient-reported outcomes of PCL reduction in primary cruciate-retaining TKA. Kim et al [7] showed that the incidence of tibial-sided PCL avulsion fractures was 1.7%, and female gender was the only risk factor. However, they did not reduce the PCL avulsion fracture and the function of PCL was assessed based on the comparison between the pre- and post-operative range of motion of the knee. In our comparison cohort study, we assessed the function of PCL based on both the objective scores (Knee Society Scores) and subjective scores (FJS). Those multiple assessments enable the creation of a more comprehensive understanding of PCL function, ultimately leading to more accurate and appropriate clinical conclusions.
In our experience, PCL avulsion fractures may occur when an en bloc tibial resection is performed. The fractures may be related to a high (12 mm thickness) tibial osteotomy as required by the instructions for fitting the prosthesis. Older age and female gender are two risk factors, because osteoporosis affects mostly older women. We believe that this technique is more applicable to incomplete PCL avulsion fracture, and as the repair has not been biomechanical tested, but yet is being used for a very important function to ensure PCL stability post-operatively. When the flexion gap is too tight or PCL reinsertion is difficult, soft tissue release is appropriate, and soft tissue balance was confirmed using a tensor/balancer device as described by Sasanuma et al [8]. In addition, we used posterior stabilized prosthesis that provided greater stability of the knee in flexion.
Both the anterior cruciate ligament and PCL play important roles in maintaining optimal knee stability.
In our study, resecting the anterior cruciate ligament may cause instability of the affected knee joint, but PCL has also been recognized as the limiting factor for the posterior translation of the tibia when the knee flexion is greater than 30° [6, 12]. Patients can tolerate the loss of PCL at rest, but this kinematic change often leads to severe knee dysfunction [13]. Some studies showed that preservation of PCL probably promoted patient proprioception, leading to an increased patient satisfaction and knee feeling more ‘normal’ after TKA [12, 14]. This finding corresponds to the FJS in our study. The FJS is a newly developed scoring system in recent years, which is often used to measure patients’ ability of forgetting joint replacement or joint awareness in daily life. In daily activities, people often don’t realize their healthy joints, so we take the lack of awareness of normal healthy joints (forgotten joints) as the standard to assess the outcomes after TKA [11]. The FJS is affected by many factors, but we found that reduction of PCL avulsion fracture in primary TKA achieved acceptable FJS after 4 years. Therefore, we believe that reinsertion of PCL allows the femur to carry out a controlled rollback when the knee is flexed, in line with normal knee kinematics. The PCL maintains the stability of the knee, contributes to good gap balance, and helps to maintain good proprioception [15].
The proper tension of PCL is an important success factor in cruciate-retaining TKA [9]. Excessive release of the ligaments may result in worse outcomes [16-19]. In many cases, the PCL insertion may be damaged during the tibial cut, which raises a question about how much the PCL is actually preserved [16, 20-24]. Some surgeons argued that a posterior-stabilized TKA with a spine-cam mechanism is an alternative when the PCL is sacrificed. Moreover, whether the PCL should be preserved has been discussed for nearly 30 years. Either a cruciate-retaining TKA or a posterior-stabilized TKA has its advantages and disadvantages of process, clinical outcomes, kinematics, and lifespan [9,24,25]. In a human cadaveric study, Kennedy et al [27] compared the kinematics of the knees after tibial resection with vs without preservation of the intact PCL, anterior lateral bundle, and posterior medial bundle. They found that the anterior lateral bundle and posterior medial bundle were the main stabilizers of the knee joint and serve primarily to resist the posterior translation of the tibia. Consequently, the surgeons should do their best to prevent PCL avulsion fractures in cruciate-
Our research has several limitations. The retrospective study has a potential bias and weaknesses. The small number of PCL avulsion fracture decreases the power of the research. Surgeon preference, experience, and ability may influence ascertaining the effects of TKA. The follow-up period of 4 years is insufficient to fully assess the outcomes of PCL reduction.
Conclusions
Our research showed that the incidence of PCL avulsion fracture of tibia is 4.6%. Older age and female gender were the two risk factors in primary cruciate-retaining TKA. Reduction of PCL avulsion fracture with high-strength suture can achieve good stability and function of the knee.
Abbreviations
PCL: posterior cruciate ligament; TKA: total knee arthroplasty; ROM: range of motion; KSS: knee society score; FJS: forgotten joint score; BMI: body mass index.
Declarations
Ethics approval
This study was approved by the Third Hospital of Hebei Medical University and followed the Declaration of Helsinki. Informed consent was received from all patients.
Consent for publication
Not applicable.
Availability of data and materials
The detailed data and materials of this study were available from the corresponding author through emails on reasonable request.
Competing interests
The authors declare that they have no competing interests.
Funding
Not applicable.
Authors' contributions
FW designed the study. WL, JHN, and YKD performed the experimental work. HXZ, JZ, WL evaluated the data. WL wrote the manuscript. All authors read and approved the final manuscript.
Acknowledgments
The authors would like to thank all the staff of the participating departments.
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23. Cinotti G, Sessa P, Amato M, Ripani FR, Giannicola G. Preserving the PCL during the tibial cut in total knee arthroplasty. *Knee Surg Sports Traumatol Arthrosc.* 2017;25(08):2594-2601.
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versus gap technique. *Int Orthop*. 2014;38:531-537.
27. Kennedy NI, Wijdicks CA, Goldsmith MT, LaPrade, RF. Kinematic analysis of the posterior cruciate ligament, part 1: the individual and collective function of the anterolateral and posteromedial bundles. *Am J Sports Med*. 2013;41:2828-2838.
**Tables**
Table 1 Patient demographics for study and control groups
| Demographics | Study group | Control group | p-Value |
|-------------------------|-------------|---------------|---------|
| Total patients | 56 | 221 | - |
| Age (years) | 70.6 ± 4.2 | 66.3 ± 6.8 | 0.041 |
| BMI (kg/m²) | 27.3 ± 4.2 | 28.5 ± 3.6 | 0.183 |
| Gender | | | 0.048 |
| Male | 12 (21.4 %) | 78 (35.3 %) | - |
| Female | 44 (78.6 %) | 143 (64.7 %) | - |
| Component sizes | | | |
| Femur | 3 (1–6) | 3 (1–6) | 0.251 |
| Tibia | 3 (1–7) | 4 (1–7) | 0.362 |
| Follow-up (years) | 4.1 ± 0.3 | 4.2 ± 0.4 | 0.661 |
BMI, body mass index; mean±standard deviation.
Table 2 Clinical and functional outcomes for study and control groups
| | Study group | Control group | p-Value |
|-----------------------|-------------|---------------|---------|
| **ROM** | | | |
| Preop | 96.2 ± 8.4 | 97.1 ± 8.7 | 0.651 |
| Last Follow-up | 115.6 ± 7.2 | 117.9 ± 6.8 | 0.495 |
| **KSS** | | | |
| Clinical score | | | |
| preop | 36.6 ± 4.2 | 37.1 ± 3.6 | 0.774 |
| Last Follow-up | 92.4 ± 2.7 | 93.6 ± 1.9 | 0.248 |
| **Functional score** | | | |
| preop | 38.1 ± 4.2 | 38.3 ± 3.1 | 0.819 |
| Last Follow-up | 85.1 ± 1.8 | 87.1 ± 1.2 | 0.066 |
| **FJS** | | | |
| Last Follow-up | 82.5 ± 3.4 | 83.1 ± 2.8 | 0.426 |
KSS, Knee Society Score; FJS, Forgotten Joint Score; Preop, Preoperation; mean±standard deviation.
Table 3 Logistic regression analysis of the risk factors
| | Odds ratio | 95% CI | p-Value |
|------------------|------------|-----------------|---------|
| age (years) | 1.875 | 1.617–5.292 | 0.032 |
| gender | 1.927 | 1.031–7.138 | 0.041 |
| BMI (kg/m²) | 0.724 | 0.732–1.031 | 0.731 |
| preoperative ROM | 0.816 | 0.831–1.021 | 0.417 |
| component sizes | 0.853 | 0.819–1.052 | 0.513 |
BMI, body mass index; ROM, range of motion; CI, confidence interval.
Figures
Figure 1
Intraoperative photo showing a PCL avulsion fracture (arrow).
Figure 2
The PCL is sutured with a high-strength line (arrow).
The PCL is sutured with a high-strength suture.
Figure 4
Lateral X-ray showing bone healing after 3 months.
| 2025-03-05T00:00:00 |
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Cosmological Quantum Metrology
Jieci Wang1,2, Zehua Tian2, Jiliang Jing2 and Heng Fan∗1
1Beijing National Laboratory for Condensed Matter Physics, Institute of Physics, Chinese Academy of Sciences, Beijing 100190, P. R. China,
2Department of Physics, and Key Laboratory of Low Dimensional Quantum Structures and Quantum Control of Ministry of Education, Hunan Normal University, Changsha, Hunan 410081, China.
We investigate the cosmological quantum metrology of Dirac fields in a two-dimensional asymptotically flat Robertson-Walker spacetime, which describes the universe well. We show that the expansion of the universe generates quantum Fisher information (QFI) between modes of the Dirac particles. Meanwhile, the QFI gives optimal bounds to the error of the quantum parameter estimations under the influence of universe expansion. We demonstrate the possibility for high precision estimation of parameters that appear in the expanding universe including the volume and expansion velocity. We find that the precision of the estimation can be improved by choosing special measurements that are marked by mass of the Dirac particles.
PACS numbers: 03.67.-a, 06.20.-f, 04.62.+v
Introduction.—Quantum metrology is mainly to study the ultimate limit of precision in estimating a physical quantity if quantum physics is considered [1]. Classically, for a given measurement scheme, the effect of statistical errors can be reduced by repeating the same measurement and averaging the outcomes. Explicitly, by repeating the measurements $N$ times separately, the uncertainty about the measured parameter $\Theta$ will be reduced to the standard quantum limit $\Delta \Theta \simeq 1/\sqrt{N}$. However, if the quantum properties are exploited such as the squeezed or entangled states are used as probe system which undergoes an evolution depending on the parameters to be estimated, the precision can be enhanced such that the uncertainty will approach the Heisenberg limit $\Delta \Theta \simeq 1/N$ which beats the standard quantum limit [2]. This has been realized in gravitational wave observation [3]. Recently, the study of quantum metrology has been applied to the area of relativistic quantum information [4–14]. It is shown that quantum metrology methods can be exploited to improve probing technologies of Unruh-Hawking effect [15, 16] and gravitation [17]. Most recently, it is found that quantum metrology can be employed to estimate the Unruh temperature of a moving cavity at experimental reachable acceleration [18, 19]. These preliminary results are of great importance for the observation of relativistic effects in a laboratory [20] and pace-based quantum information processing tasks [21, 22].
It is remarkable that the universe expands acceleratingly, which is discovered through the observations of Type Ia supernovae [24, 25]. The accurate measurement of the expansion velocity of the universe is significant not only for estimating the age of our universe but also for the study of dark energy. Currently, the expansion velocity is mainly measured through distance measurement [26, 27], which is hardly be performed and easily be interfered. In this work, we propose a quantum metrology technique to estimate the expansion velocity of the universe in Robertson-Walker (RW) metric [28–32], which describes an isotropic and homogeneous expanding universe. The RW universe is widely regarded as the Standard Model of the present-day cosmology [33]. We study a system of a vacuum state for Dirac fields in the asymptotically past but evolves to an entangled fermion and antifermion state as the expanding of the universe. By applying quantum metrology strategy on the final states, the precision of the estimated parameter can be related to the quantum Fisher information (QFI) [34]. We analytically calculate the QFI in terms of the mass $m$ of the Dirac particles and module $k$ of the wave vector. Such process corresponds to finding the set of measurements that allows us to estimate the expansion velocity [17] with the highest precision. Our proposal is independent of the measurement on the velocities and distances of the galaxies. We demonstrate that the dynamic spacetime background actually creates QFI. At the same time, information about the history of the expanding universe can be extracted from measurements on the states in the asymptotic future region, while the ultimate precision limit is related with QFI. We then find that the precision of the estimation can be improved by choosing the proper measurements that marked by the mass of the Dirac particles. As far as we know, this is the first time that the quantum metrology is studied in the cosmological background. Our work opens a new avenue for the development of quantum detection and estimation technologies for cosmological parameters in the expanding universe.
Quantum Metrology and Fisher information.—The aim of quantum metrology is to determine the value of a parameter with higher precision than classical approaches, by using entanglement and other quantum resources [1]. A key concept for the metrology is Fisher information [34], which relates with the result $\xi$ of a positive operator valued measurement
*Corresponding author, Email: [email protected]
(POVM) \{ \hat{E}(\xi) \} and takes the form
\begin{equation}
\mathcal{F}_\xi(\Theta) = \sum_\xi P(\xi|\Theta) \left( \frac{\partial \ln P(\xi|\Theta)}{\partial \Theta} \right)^2 ,
\end{equation}
where \( P(\xi|\Theta) \) is the probability with respect to a chosen POVM and the corresponding measurement result \( \xi \) and \( \Theta \) is the parameter to be estimated. According to the classical Cramér-Rao inequality [35], the mean square fluctuation of the unbiased error for \( \Theta \) is
\begin{equation}
\Delta \Theta \geq \frac{1}{\sqrt{\mathcal{F}_\xi(\Theta)}}.
\end{equation}
Furthermore, the Fisher information is \( n\mathcal{F}_\xi(\Theta) \) for \( n \) repeated trials of measurement, which leads to Cramér-Rao Bound (CRB) on the phase uncertainty, \( n(\Delta \Theta)^2 \geq \frac{1}{\mathcal{F}_\xi(\Theta)} \) which gives the maximum precision in \( \Theta \) for a particular measurement scheme. Optimizing over all the possible quantum measurements provides an lower bound [2], i.e.,
\begin{equation}
n(\Delta \Theta)^2 \geq \frac{1}{\mathcal{F}_\xi(\Theta)^2} \geq \frac{1}{\mathcal{F}_{Q}(\Theta)} ,
\end{equation}
where \( \mathcal{F}_Q(\Theta) \) is the quantum Fisher information (QFI). Usually, the QFI can be calculated from the density matrix of the state by the maximum \( \mathcal{F}_Q(\Theta) := \max_\xi \mathcal{F}_\xi(\Theta) \) which is saturated by a particular POVM and defined in terms of the symmetric logarithmic derivative (SLD) Hermitian operator \( \mathcal{L}_\Theta \)
\begin{equation}
\mathcal{F}_Q(\Theta) = \text{Tr} \left( \rho_\Theta \mathcal{L}_\Theta^2 \right) = \text{Tr} \left[ (\partial_\Theta \rho_\Theta) \mathcal{L}_\Theta \right] ,
\end{equation}
where
\begin{equation}
\partial_\Theta \rho_\Theta = \frac{1}{2} \{ \rho_\Theta , \mathcal{L}_\Theta \} ,
\end{equation}
where \( \partial_\Theta \equiv \frac{\partial}{\partial \Theta} \) and \( \{ , \} \) denotes the anticommutator.
Quantization of Dirac fields in the RW universe.— In quantum field theory, particles are excitations of quantum fields [31]. To study the quantum metrology for Dirac fields (or particles) in the RW spacetime [28–31], we introduce the local tetrad field
\begin{equation}
g^{\mu\nu} = e^\mu_a(x)e^\nu_b(x)\eta^{ab} ,
\end{equation}
where \( g^{\mu\nu} \) and \( \eta_{ab} \) are metrics of the RW spacetime and Minkowski spacetime, respectively. The covariant Dirac equation for field \( \Psi \) with mass \( m \) in a curved background reads [36]
\begin{equation}
i\gamma^\mu(x) \left( \frac{\partial}{\partial x^\mu} - \Gamma^\mu_\rho \right) \Psi = m \Psi .
\end{equation}
We solve the Dirac equation in a two-dimensional RW spacetime, which is proved to embody all the fundamental features of the higher dimensional counterparts [29]. The corresponding line element reads
\begin{equation}
ds^2 = [a(\eta)]^2(\ d\eta^2 - dx^2) ,
\end{equation}
where the dimensionless conformal time \( \eta \) is related to cosmological time \( \tau \) by \( a(\eta) = \int a^{-1}(\tau)\ d\tau \). We consider a special case, as presented in [29 31 32 37], the conformal factor \( a(\eta) \) can be written as
\begin{equation}
a(\eta) = 1 + \epsilon (1 + \tanh \rho \eta) ,
\end{equation}
where \( \epsilon \) and \( \eta \) are positive real parameters, corresponding to the total volume and the expansion velocity of the universe [29 31], respectively. Note that \( a(\eta) \) is constant in the far past \( \eta \to -\infty \) and far future \( \eta \to +\infty \), which means that the spacetime tends to a flat Minkowskian spacetime asymptotically. In the asymptotic past (in)- and future (out)-regions the vacuum states and one-particle states may be well defined. In this special spacetime background the spin connections read
\begin{equation}
\Gamma_\mu = \frac{1}{4} \frac{\partial a(\eta)}{a(\eta)} [\gamma_\mu , \gamma_0] ,
\end{equation}
where \( \partial a(\eta) = \frac{\partial a(\eta)}{a(\eta)} \). To solve the Dirac equation Eq. (7) in the metric Eq. (8), we re-scale the field as
\begin{equation}
\Psi = a^{-3/2} \gamma^\nu \partial_\nu - m a(\eta) )\psi ,
\end{equation}
and the dynamic equation evolves to
\begin{equation}
\eta^{\mu\nu} \partial_\mu \partial_\nu \psi - \frac{\partial}{\partial \eta} m a(\eta) \psi - [m a(\eta)]^2 \psi = 0 .
\end{equation}
Moreover, by introducing the flat spinors \( U_d \) and \( V_d \) that satisfy the relations \( \bar{\eta}^0 U_d = -iU_d \) and \( \bar{\eta}^0 V_d = iV_d \), we can represent the re-scaled solution \( \psi \) into a radial and temporal separable form, that is \( \psi := N^{(+)\psi} (\eta) U_d e^{i k^x x} \) (or \( \psi := N^{(+)\psi} (\eta) V_d e^{i k^x x} \)). Here the functions \( \psi^\pm_k \) obey the following coupled differential equation
\begin{equation}
\psi^+_k (\pm) + \left[ k^2 + m^2 a(\eta)^2 + im\tilde{a}(\eta) \right] \psi^\pm_k = 0 .
\end{equation}
Actually \( \psi^+_k (+) \) and \( \psi^+_k (-) \) are positive and negative frequency modes with respect to conformal time \( \eta \) near the asymptotic past and future, i.e. \( \psi^+_k (\pm) (\eta) \approx \mp \omega_{in/out} \psi^\pm_k (\eta) \) with \( \omega_{in/out} = \sqrt{|k|^2 + m^2 a^2 (\eta \to \mp\infty)} \) and \( |k|^2 = k^2 \). In the asymptotic past region, the positive and negative frequency solutions [29 32 38] of Eq. (13) are
\begin{equation}
\psi^\pm_{in} = \exp \left[-i \omega(\pm) \eta - \frac{i \omega(\mp)}{\rho} \ln(2 \cosh \rho \eta) \right] \times \sum_{n=0}^{\infty} \left[ \rho + i \zeta_{in}^\pm \right] \Lambda^\pm_n \frac{\Lambda^\pm_n}{2^n \eta} ,
\end{equation}
where \( [n] = n(n+1) \ldots (q+n-1) \), \( \Lambda^\pm_n = [1 + \tanh(\rho \eta)]_n \), \( \zeta_{in}^\pm = \omega_{in} (\pm) \pm m \epsilon \) and \( \omega_{in} = (\omega_{out} + \omega_{in})/2 \). Similarly,
one may obtain the modes of the Dirac fields that behaving as positive and negative frequency modes in the asymptotic future region
\[ \psi_{\text{out}}^{(\pm)} = \exp \left[ -i\omega_{(+)} \eta - \frac{i\omega_{(-)}}{\rho} \ln(2 \cosh \rho \eta) \right] \times \sum_{n=0}^{\infty} \frac{[\rho + i\omega_{(n)}]_{\eta}}{[\rho + i\omega_{(n)}]_{\eta}} \Lambda_{n}^{n} 2 \eta \rho^{n}, \] (15)
where \( \Lambda_{n}^{n} = [1 - \tanh(\rho \eta)]^{n} \). It is now possible to quantize the field and find the relation between the vacuum state in the asymptotic future region and that in asymptotic past. Such relation can be described by a certain set of Bogoliubov transformations \([3]\) between in and out modes
\[ \psi_{\text{in}}^{(\pm)}(k) = A_{k}^{\pm} \psi_{\text{out}}^{(\pm)}(k) + B_{k}^{\pm} \psi_{\text{out}}^{(\mp)}(k), \] (16)
where \( A_{k}^{\pm} \) and \( B_{k}^{\pm} \) are Bogoliubov coefficients that take the form,
\[ A_{k}^{\pm} = \sqrt{\frac{\omega_{\text{out}}}{\omega_{\text{in}}}} \frac{(1 - \frac{\omega_{\text{in}}}{\rho}) \Gamma(-i\omega_{(n)}/\rho)}{(1 - \frac{\omega_{\text{out}}}{\rho}) \Gamma(-i\omega_{(n)}/\rho)}, \]
\[ B_{k}^{\pm} = \sqrt{\frac{\omega_{\text{out}}}{\omega_{\text{in}}}} \frac{(1 + i\omega_{(n)}/\rho) \Gamma(i\omega_{(n)}/\rho)}{(1 + i\omega_{(n)}/\rho) \Gamma(i\omega_{(n)}/\rho)}. \] (17)
We can see that the Dirac field undergoes a \( \Theta_{i} \)-dependent Bogoliubov transformation, where \( \Theta_{i} = \epsilon, \rho \) are the parameters that we want to estimate.
To find the relation between the asymptotic past and future vacuum states, we use the relationship between the operators
\[ b_{\text{in}}(k) = \left[ A_{k}^{\ast} b_{\text{out}}(k) + B_{k}^{\ast} \chi(k) a_{\text{out}}^{\dagger}(-k) \right], \] (18)
where \( \chi(k) = \frac{\omega_{\text{out}}}{\omega_{\text{in}}} \frac{\omega_{\text{in}}}{\rho} - \frac{\omega_{\text{in}}}{\rho} \). Imposing \( b_{\text{in}}(k)|0\rangle_{\text{in}} = 0 \) and the vacuum normalization \( \langle 0 | 0 \rangle_{\text{in}} = 1 \), we obtain the asymptotically past vacuum state in terms of the asymptotic future Fock basis
\[ |0\rangle_{\text{in}} = \sqrt{1 + |\gamma_{k} F\rangle_{\text{out}}^{2}} |1\rangle_{\text{out}}^{\text{out}} - \frac{|\gamma_{k} F\rangle_{\text{out}}}{1 + |\gamma_{k} F\rangle_{\text{out}}^{2}} |1\rangle_{\text{out}}^{\text{out}} \] (19)
where
\[ |\gamma_{F}\rangle_{\text{out}}^{2} = \frac{\zeta_{(-)}^{+} \sinh \left( \frac{\pi \zeta_{(-)}^{+}}{\rho} \right)}{\zeta_{(-)}^{\mp} \sinh \left( \frac{\pi \zeta_{(-)}^{\mp}}{\rho} \right)} \frac{\sinh \left( \frac{\pi \zeta_{(+)}^{+}}{\rho} \right)}{\sinh \left( \frac{\pi \zeta_{(+)}^{\mp}}{\rho} \right)}. \] (20)
We can see that the system which was a natural vacuum state \( |0\rangle_{\text{in}} \) of Dirac field in the asymptotically past region evolves to an entangled particle and antiparticle state as the expansion of the universe. Particles and antiparticles were produced and entangled by gravity during the expanding and the information about the velocity of the expansion is codified in the final states.
**Quantum Metrology in the expanding universe.**—Our aim is to study how precisely one can in principle estimate the cosmological parameters that appear in the expansion of the universe. Specifically, we will estimate the volume \( \epsilon \) and the expansion velocity \( \rho \) of the universe based on the quantum Cramer–Rao inequality. Thus we should at first calculate the operational QFI in terms of the Bogoliubov coefficients which encode in the estimated parameters. The reduced density matrix corresponding to particle modes is found to be
\[ \phi_{k}^{\rho} = \frac{1}{(1 + |\gamma_{k} F\rangle_{\text{out}}^{2})} \langle 0 | 0 \rangle + |\gamma_{k} F\rangle_{\text{out}}^{2} |\gamma_{k} F\rangle_{\text{out}}^{2} \langle 1 | 1 \rangle, \] (21)
which is obtained after tracing out the antiparticle modes \( n_{-} \) and all other modes with different \( k \) since the modes of the out states are unique for all inertial particle (or antiparticle) detectors \([23]\). Assuming that now we live in the universe that corresponds to the asymptotic future of the spacetime, we can estimate the volume and the expansion velocity of the universe by taking measurements on the particle state. In this system, the states of the Dirac fields act as the probes, which is prior available. Now our main task is to find the optimal estimation strategy, i.e., finding an optimal measurement realizing the QFI that allows us to estimate the parameters with the highest precision. The symmetric logarithmic derivative operator \( L_{\Theta_{i}} \) is given by \( \mathcal{L}_{\Theta_{i}} = \frac{1}{2} (j \partial_{\Theta_{i}} (\rho_{k}^{F})) \| j \rangle \langle j \| \), where \( j(\neq l) = (0, 1) \) and the QFI is found to be
\[ \mathcal{F}_{Q}(\Theta_{i}) = \frac{1}{(1 + |\gamma_{k} F\rangle_{\text{out}}^{2})} \langle \partial_{\Theta_{i}} \rho_{k}^{F} (\rho_{k}^{F})^{\dagger} \rangle^{2} \]
\[ + \frac{1}{(1 + |\gamma_{k} F\rangle_{\text{out}}^{2})} \langle \partial_{\Theta_{i}} (\rho_{k}^{F})^{2} \rangle \] (22)
where the expanding parameters \( \rho \) and \( \epsilon \) are encoded.
**FIG. 1:** (Color online) The QFI of the Dirac fields vs the expansion velocity \( \rho \) for different \( \epsilon \). The values of \( \epsilon \) for each line with increasing gap length are 0.2, 0.4, 0.6, 0.8, and 1.0, corresponding to the color sequence red, orange, green, blue and purple, respectively. Both \( m \) and \( k \) are fixed with \( m = k = 1 \).
In Fig. 1 we plot the QFI of the Dirac fields in an expanding universe as a function of expansion velocity \( \rho \) for different...
It is shown that the expansion generates QFI between certain modes of the Dirac particles that are only influenced by the expansion of the universe. The QFI first increases and then decreases as the increase of both ρ and ε. We can see that the QFI of the final states depends sensitively on the cosmological parameters, which means that the expansion of the universe has a significant effect on the precision of quantum metrology. Conversely, information about the history of the expanding universe can be extracted from the measurements on the final states in the asymptotic future region, in which the QFI shows the limit on the precision of the measurements.
For a further study, we calculate the optimal bound for the error in the estimation process by using Eqs. (3) and (22). In Fig. 2 we plot the optimal bounds (Δρ)² and (Δε)² (dashed line) in the estimation of the volume ε and the expansion velocity ρ of the universe over the mass m of the Dirac particles. It is shown that the optimal bounds behave almost the same when we estimate ε or ρ. It is found that the bounds decrease rapidly as the increase of mass for the light Dirac particles (for example neutrinos). In the standard cosmology model, relic neutrinos act as witnesses and participants for landmark events in the history of the universe from the era of big-bang nucleosynthesis to the era of large scale structure formation [39, 40]. It is shown that the relic neutrinos are crucial for estimating the age of our universe and its fate. It is also shown that the bounds become very small (the order of magnitude 10⁻¹²) as the measurements repeated a number of times for the medium weight Dirac particles (for example the strange and charm quarks).
In Fig. 3 we plot the optimal bounds (Δθ)² in the estimation of the volume ε (dashed line) and the expansion velocity ρ of the universe over k. The parameters are fixed with ρ = ε = k = 1. The measurements repeated n = 10¹¹ times.
Discussion and summary.— We studied the cosmological quantum metrology by incorporating the effect of universe expansion in quantum parameter estimation. The expanding spacetime background has a significant effect on the value of QFI. The expansion velocity of the universe can be estimated from the measurements on the final states of the Dirac particles (for example the neutrinos) in the asymptotic future region. This cosmologic quantum metrology goes beyond the classical method though may not achieve the Heisenberg limit. As mentioned before, the expansion velocity is currently measured through the distance measurement. Such a method requires measuring both the velocities and distances of the supernovae [26, 27] and is hardly be performed and easily be interfered for the following three reasons. First, the supernovae explosions are very rare events, so the probability of seeing one nearby is very low. Second, the supernovae interact gravitationally with their neighbours and the velocities become perturbed, inducing “proper” motions that are superimposed onto the overall expansion. Third, performing an accurate extragalactic distance measurement is far more difficult because the distances depend on the expansion velocity itself [26, 27]. Our proposal is based on the local measurements on the final states of Dirac particles which are detectable in cosmic rays [41] or cosmic neutrino background [42]. According to the standard cosmology, the relic neutrinos are abundant particles ranking only second to the cosmic microwave background in the present-day universe [40, 43]. One of the most important task of the neutrino detectors, for example the IceCube in the Antarctica, the Super-Kamiokande and Sudbury Neutrino Observatory (SNO) located underground, are exploring the background of neutrinos produced in the Big Bang. Thus, the measurements can be performed once the relic neutrinos has been detected in the observatories.
sive understanding of quantum metrology in the background of cosmology will enable us to make the necessary estimation technologies that affected by the expansion the universe.
This work is supported by 973 program through 2010CB922904, the National Natural Science Foundation of China under Grant Nos. 11305058, 11175248 and CAS.
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Spatio-Temporal Clustering of Hand, Foot, and Mouth Disease at the County Level in Guangxi, China
Yi-hong Xie1,2,3, Virasakdi Chongsuvivatwong2*, Zhenzhu Tang1, Edward B. McNeil2, Yi Tan1
1 Guangxi Zhuang Autonomous Region Center for Disease Prevention and Control, Nanning, Guangxi, China, 2 Epidemiology Unit, Faculty of Medicine, Prince of Songkla University, HatYai, Songkla, Thailand, 3 International Field Epidemiology Training Program (IFETP), Bureau of Epidemiology, Ministry of Public Health, Bangkok, Thailand
Abstract
Background: Amid numerous outbreaks of hand, foot and mouth disease (HFMD) in Asia over the past decade, studies on spatio-temporal clustering are limited. Without this information the distribution of severe cases assumed to be sporadic. We analyzed surveillance data with onset dates between 1 May 2008 to 31 October 2013 with the aim to document the spatio-temporal clustering of HFMD cases and severe cases at the county level.
Methods: Purely temporal and purely spatial descriptive analyses were done. These were followed by a space-time scan statistic for the whole study period and by year to detect the high risk clusters based on a discrete Poisson model.
Results: The annual incidence rate of HFMD in Guangxi increased whereas the severe cases peaked in 2010 and 2012. EV71 and CoxA16 were alternating viruses. Both HFMD cases and severe cases had a seasonal peak in April to July. The spatio-temporal cluster of HFMD cases were mainly detected in the northeastern, central and southwestern regions, among which three clusters were observed in Nanning, Liuzhou, Guilin city and their neighbouring areas lasting from 1.2 to 2.5 years. The clusters of severe cases were less consistent in location and included around 40–70% of all severe cases in each year.
Conclusions: Both HFMD cases and severe cases occur in spatio-temporal clusters. The continuous epidemic in Nanning, Liuzhou, Guilin cities and their neighbouring areas and the clusters of severe cases indicate the need for further intensive surveillance.
Introduction
Hand, foot, and mouth disease (HFMD) is a common infectious disease mostly affecting children under 5 years of age. Over the past decade, many small and large outbreaks have been reported in Asia [1–8]. In China, HFMD has been a notifiable disease since May, 2008 after two consecutive years of large outbreaks affected more than 46,000 persons [9,10]. Over six million cases had been reported up to the end of 2012 in China. Guangxi is one of the serious HFMD epidemic provinces in China. A substantial increase in cases has been reported since 2008 with an incidence rate of 449.4 per 100,000 population reported in 2012. The number of severe cases (2,236) and fatalities (123) in that year was ranked first among 31 provinces in China.
Spatio-temporal clustering indicates the composite of place and time i.e. where and when the incidence is abnormally high. Identification of spatio-temporal clusters allows public health officials to understand the disease nature and launch timely surveillance and intervention programs at the correct site. However, most of the previous studies on spatial variation were separated from the temporal ones. Studies on smaller units (for example at the county level) and the spatio-temporal composite analyses are very limited [27,28], and no studies on severe cases have been reported.
Methods
Study area
Guangxi is located in southern China at latitude 20.54N to 26.24N and longitude 104.26E to 112.04E, which covers a total
area of 236,700 km² with a population of 46.5 million in 2012. There are 14 prefecture level divisions and 113 county level divisions in Guangxi. The population size at the county level ranges from 112,777 to 1,510,509 people. The distribution of main highways and railways in Guangxi are shown in Figure 1. There are four main cities (Baise, Nanning, Liuzhou and Guilin city), which are major transit centers linking the west to the northeast of the province.
Data sources
The daily data of HFMD cases and severe cases from 1 May 2008 and 31 October 2013 were obtained from the China Information System for Disease Control and Prevention, which is an online, real-time surveillance system. All HFMD cases need to be reported to this system within 24 hours after diagnosis since HFMD was classified as a class “C” notifiable disease on May 2008 [31]. In Guangxi, this system covered all the hospitals at or above the township level. The information entered into the system includes name, age, gender, address, occupation, date of onset, date of diagnosis, type of diagnosis (clinical or lab confirmed), status (severe or non-severe), and laboratory test results. The diagnostic criteria of HFMD cases, severe cases and the procedure of laboratory test follow the HFMD Clinical Diagnosis and Treatment Guideline [32–34]. A severe case is defined as having fever, rash with blisters on the palms, soles and/or buttocks, and with neurological, respiratory or circulatory complications such as myoclonia, acute flaccid paralysis, encephalitis, cardiopulmonary failure or pulmonary edema. Each severe case must be confirmed by at least two experts at or above county level.
Table 1. Incidence and pathogen of HFMD in Guangxi, 1 May 2008 to 31 October 2013.
| Year | Incidence | Severe cases | Deaths | Number of laboratory confirmed cases (%) |
|------|-----------|--------------|--------|------------------------------------------|
| | Number of cases | Rate (/10⁵) | Total | EV7 | Cox A16 | Other |
| 2008 | | | | 219 | (28/191) | 85 | (38.8) | 11 | (5.0) | 123 | (56.2) |
| 2009 | | | | 386 | (14/372) | 60 | (15.5) | 139 | (36.0) | 187 | (48.5) |
| 2010 | | | | 2403 | (1412/991) | 1713 | (71.3) | 128 | (5.3) | 562 | (23.4) |
| 2011 | | | | 3027 | (256/2771) | 727 | (24.0) | 1380 | (45.6) | 920 | (30.4) |
| 2012 | | | | 5421 | (1622/3799) | 3284 | (60.0) | 469 | (8.7) | 1668 | (30.8) |
| 2013 | | | | 2358 | (153/2205) | 223 | (9.5) | 686 | (29.1) | 1449 | (61.5) |
| Total | | | | 13814 | (3485/10329) | 6092 | (44.1) | 2813 | (20.4) | 4909 | (35.5) |
Notes:
1From 1 May, 2Until 31 October
2Numbers in brackets are the numbers of severe/non-severe cases among all the laboratory confirmed cases.
3Numbers in brackets are the percentage of positive cases among all the laboratory confirmed cases.
Figure 1. The distribution of main highways and railways in Guangxi and the location of four major transit centers.
Data sources
The daily data of HFMD cases and severe cases from 1 May 2008 and 31 October 2013 were obtained from the China Information System for Disease Control and Prevention, which is an online, real-time surveillance system. All HFMD cases need to be reported to this system within 24 hours after diagnosis since HFMD was classified as a class “C” notifiable disease on May 2008 [31]. In Guangxi, this system covered all the hospitals at or above the township level. The information entered into the system includes name, age, gender, address, occupation, date of onset, date of diagnosis, type of diagnosis (clinical or lab confirmed), status (severe or non-severe), and laboratory test results. The diagnostic criteria of HFMD cases, severe cases and the procedure of laboratory test follow the HFMD Clinical Diagnosis and Treatment Guideline [32–34]. A severe case is defined as having fever, rash with blisters on the palms, soles and/or buttocks, and with neurological, respiratory or circulatory complications such as myoclonia, acute flaccid paralysis, encephalitis, cardiopulmonary failure or pulmonary edema. Each severe case must be confirmed by at least two experts at or above county level.
Data analysis
Data management was done using R version 3.0.2. The incidence of all cases, severe cases and an analysis of pathogens over the 66 months were presented in graphs using R. The purely spatial distribution of HFMD cases and severe cases was shown in thematic maps using Quantum GIS.
A retrospective space-time scan statistic was applied to detect high risk clusters of HFMD cases and severe cases by using SaTScan™ software (version 9.1) with a discrete Poisson model. The space-time scan statistic is defined by a cylindrical window with a circular geographic base and with height corresponding to time [35]. The cylindrical window moves over space and time scanning for an elevated risk within the space-time window as compared to outside the window. The null hypothesis assumes that HFMD cases are randomly distributed. The alternative hypothesis for each scanning window is that there is an elevated risk inside the window as compared to outside [35]. The difference of the incidence inside and outside each window was calculated by the log likelihood ratio (LLR) [36]. Significant results (based on Monte Carlo simulation) from these were defined as a cluster. Among the statistically significant clusters, the cluster with the maximum LLR indicates one that is least likely to have occurred by chance which is thus the most likely cluster. Secondary clusters were those in rank order after the most likely cluster, based on their likelihood ratio test statistic. The relative risk of each cluster is the ratio of the estimated risk within the cluster to that outside the cluster [35].
In this study, we initially scanned the entire study period from 1 May 2008 to 31 October 2013. Further yearly scans were done to observe changes in clustering and to control the time trend in the whole study period [35]. As there is no consensus and optimal maximum-size of the spatial cluster size setting [37,38], we firstly used the recommended value of 50% of the population in the spatial window to avoid the pre-selection bias [35]. To explore small to middle-sized clusters, we conducted the scan again at every 10% interval down to 10%. The scan results of HFMD cases in the entire 66 month study period were demonstrated by the 50%, 20% and 10% values. The severe cases and yearly scan results were displayed using a value of 20% as it is believed to have more power to detect the true cluster [26,38].
For each run, we set the number of Monte Carlo replications to 999. The height of the cylindrical window which reflects time was set to be 50% of the scan timeframe and the clusters reported without geographical overlap. R software was used to illustrate the spatio-temporal cylinders of the 66 months data. Quantum GIS was used to visualize the yearly scan results.
Results
Demographic characteristics
From 1 May 2008 to 31 October 2013, there were 796,072 HFMD cases notified in Guangxi with an annual incidence rate of 298.3/100,000 population. Among these cases, there were 5,636 (0.71%) severe cases reported which included 350 fatalities. The incidence rate in males (323/100,000 population) was higher than in females (217/100,000 population, P value < 0.01). 68.4% of HFMD cases and 83.7% of fatalities were aged under 3 years. 19.8% of HFMD cases and 8.9% of fatalities were preschool attending children.
A total of 3,485 severe cases (314 fatalities) were confirmed by laboratory testing. Among the confirmed cases, EV71, CoxA16 and other enteroviruses accounted for 80.2%, 2.8% and 17.0% of severe cases and 93.0%, 1.6% and 5.4% of fatalities, respectively.
Table 1 summarizes the incidence and pathogens by year. The incidence rate of HFMD cases increased over time (P value for linear trend = 0.017) while severe cases peaked in 2010 and 2012. For pathogens, other enteroviruses appeared consistently in the background in all years. Among the distinct viruses, the predominant pathogen alternated between EV71 and CoxA16.
Temporal dimension
The monthly distribution of HFMD cases, severe cases and laboratory confirmed cases are illustrated in Figure 2. A general rising trend of HFMD cases was evident with clear seasonality and large and small alternating peaks. From 2008 to 2012, the first large peak occurred between April to July followed by smaller peaks in September to November. A different seasonal pattern was seen in 2013 when the epidemic started relatively late and lasted longer, with a higher peak occurring from August to October. The two distinct peaks of severe cases were seen from April to July. All
Table 2. Spatial-temporal clusters of HFMD in Guangxi, China, from 1 May 2008 to 31 October 2013 (setting 10% of the population as the maximum spatial cluster size).
| Cluster period | Cluster center/Radius | Number of counties in the cluster | Cases per 10^5 person years | RR* |
|-------------------------|-----------------------|-----------------------------------|-----------------------------|-----|
| 1 May 2010-30 Sep 2010 | (21.52 N, 109.46 E)/66 km | 3 | 885 | 2.95|
| 1 Mar 2011-30 Sep 2013* | (22.55 N, 107.81 E)/80 km | 10 | 862 | 3.10|
| 1 Apr 2011-30 Sep 2013 | (24.33 N, 109.32 E)/76 km | 11 | 695 | 2.45|
| 1 Apr 2012-31 Jul 2012 | (24.25 N, 105.33 E)/217 km | 16 | 1589 | 5.39|
| 1 Apr 2012-31 Jul 2013 | (25.60 N, 110.59 E)/56 km | 8 | 917 | 3.12|
| 1 Apr 2012-30 Jun 2012 | (22.54 N, 110.06 E)/41 km | 4 | 1292 | 4.33|
| 1 Apr 2012-30 Jul 2012 | (22.82 N, 109.21 E)/48 km | 3 | 1039 | 3.47|
| 1 Apr 2012-30 Nov 2012 | (24.49 N, 111.24 E)/111 km | 10 | 637 | 2.13|
| 1 May 2012-31 May 2012 | (23.45 N, 110.51 E)/0 km | 1 | 951 | 3.15|
*The most likely cluster.
*All P-values < 0.001. RR: relative risk.
doi:10.1371/journal.pone.0088065.t002
viruses also had a seasonal pattern but with inconsistent predominant type. The peak of severe cases was consistent with the peak of EV71 confirmed cases. CoxA16 predominated only in 2011 whereas other enteroviruses appeared to co-oscillate with EV71 and CoxA16 in the beginning of the surveillance period and became relatively persistent after 2011. It is however, not possible to tell from these graphs whether the outbreaks were confined to certain areas only.
Spatial dimension
The spatial distribution of HFMD cases by year is shown in Figure 3. Over the years, especially after the disease was well established in 2010, there were clear differences in the incidences among counties. Relatively high incidence rates appeared in the northeastern-southwestern belt whereas the northwestern and southeastern parts had relatively low incident rates. To check whether there was any temporal continuation of the increased incidence in certain areas, a spatio-temporal integration was done.
Spatio-temporal analysis
In the entire 66 month study period, one large cluster consisting of 56 counties centered in the west and lasting from April 2011 to September 2013 was detected when setting 50% of the population as the maximum spatial cluster size (Figure 4A). The cluster contained a considerable proportion of low risk areas when complemented by in Figure 3. When the maximum spatial cluster size was set to 20% of the population, four clusters were detected (Figure 4B), two of them lasting for approximately 2.5 years from April 2011 to September 2013 were located in the southwestern and central part of the province. Two shorter clusters were detected in the east and lasted 4 months from April to July 2012. When the maximum spatial cluster size was set to 10%, nine small clusters were detected (Figure 4C). Details of each of these clusters are shown in Table 2. The nine clusters varied in geographic and temporal sizes. The first cluster took place in the southern part of the province in the middle of 2010. Two long-lasting clusters located along the southwestern to northeastern belt, which included 10 counties around Nanning city and 11 counties around Liuzhou city started in 2011 and continued until 2013. Six clusters, five starting in April 2012 and one in May 2012, each lasted for a few months, except one which continued until the middle of 2013 (consisting of 8 counties around Guilin city). The most western occurring cluster consisted of 16 counties and had high intensity (RR = 5.39) but lasted only 3 months. In all of the 66 months, there were no clusters detected in 2008 and 2009 when the incidence was relatively low.
For the severe cases, we illustrated only the 20% scale (Figure 4D). The first cluster occurred in 2010 in the northeast and included 17 counties around Guilin city with very high intensity (RR = 39.7) in 2010. The other three clusters in 2012 were detected in the southern (14 counties around Nanning), northern and central (21 counties around Liuzhou) and eastern (9 counties around Wuzhou) part of the province. All clusters occurred between April and July.
As the incidence of HFMD cases increased over time and the number of severe cases fluctuated each year, an analysis using the whole study period can only detect clusters in high incidence periods. To observe the cluster change and control for the temporal trend in the whole study period, scans were conducted in each year setting 20% of the population as the maximum spatial cluster size. The results are shown in Figure 5. In each year, apart from the most likely cluster, several secondary clusters with relative risk ranging from 1.5 to 9.3 were also detected. Most of clusters were located in the northeastern, central and southwestern parts of the province and occurred from April to July. There were also 2–3 small secondary clusters observed in the southeast. The most likely cluster in 2013 and four small secondary clusters in 2009, 2011 and 2013 occurred in the second peak period from August to October.
The yearly spatial distribution (red dots) and spatio-temporal clusters of severe cases are illustrated in Figure 6. There were 18 clusters detected. The most likely and secondary clusters of severe cases covered more than half of the counties in 2010 and 2012 when thousands of severe cases occurred. The cluster sizes were relatively small and the locations were less consistent in the other years. The severe cases included in the clusters accounted for 52.0%, 68.0%, 63.6%, 40.5%, 54.3% and 40.0% of all cases in the 6 years from 2008 to 2013, respectively. Four cluster centers were repeated in two different years.
Discussion
Under the increasing trend of HFMD in Guangxi, we have demonstrated that both HFMD cases and severe cases had a spatio-temporal cluster pattern. For HFMD cases, in addition to seasonality (April to July), spatio-temporal analyse revealed that certain clusters lasted longer than one year. These clusters were located in Nanning, Liuzhou, Guilin city and their neighbouring areas along the southwestern-northeastern belt. In each year, around 40%–70% of the severe cases were aggregated within the clusters.
The incidence rate of HFMD in Guangxi increased by more than a factor of five from 2008 to 2013, which was higher than the average level in China [39] and neighboring provinces of Guangdong [27] and Guizhou [40]. A similar situation occurred in Singapore between 2001 and 2007 [7]. Similar to previous studies from USA and Singapore [7,41], the current study found that EV71 and CoxA16 had an alternating pattern. The predominant pathogen in 2010 and 2012 was EV71 while in
Figure 6. Spatial distribution (red dots) and spatio-temporal clusters of severe HFMD cases in Guangxi, China, from 1 May 2008 to 31 October 2013 (by year).
doi:10.1371/journal.pone.0088065.g006
strongly associated with severity and fatality [9,17,42].
In our study, a large cluster (50% scale) occupies half of the study area and contained a considerable proportion of low risk areas. In Hong Kong, two peaks per year were detected between 2001 to 2009 [6]. In mainland China, the seasonality depends on the region. Some provinces [28,44] have a single peak per year while others have two [27,44]. Our data fall into the latter group. Similar to our findings, the epidemic period in mainland China was reported from April to July with the highest peak occurring in April or May [26,44].
The spatio-temporal scan results are sensitive to the parameter choices related to cluster scaling. A maximum spatial cluster size that is too large would detect a cluster that contains some low risk areas and thus much larger than the true cluster, and significant clusters could be missed using a parameter that is too small [37]. In our study, a large cluster (50% scale) occupies half of the study area and contained a considerable proportion of low risk areas. More small clusters with higher elevation in risk were detected using the 10% and 20% scale setting. These small clusters may produce more usable and informative results to epidemiologist for disease prevention initiatives or etiologic investigations [39,40].
We found three clusters lasting from 1.2 to 2.5 years located in the capital city (Nanning), an industrial city (Liuzhou), a tourism city (Guilin) and their neighbouring areas along a southwestern-northeastern belt. These cities are located on the major transit centers of highways and railways in Guangxi. This finding is consistent with previous reports that clusters are more commonly observed in areas of high population density and mobility [6,45,46], which also indicates that the disease may be transmitted along highways and railways. The yearly scan results show that most of the clusters lasted for 2–3 months and occurred in the first of the two peaks during the year, which is consistent with a previous study at the provincial level [26] but the duration were shorter than a study from GuangDong [27]. Although the center of the most likely cluster varied every year, the locations of clusters were concentrated in the southwestern, central and northeastern parts of the province.
The number of severe cases in each year fluctuated based on the predominant pathogen. Varying sizes of clusters were also detected in each year. These findings are different from many previous descriptive studies which reported that severe cases were distributed sporadically [47]. Lack of proper spatio-temporal analysis makes it difficult to reveal clustering for relatively rare events.
The limitation of this study is in the nature of the circular spatial scan statistic, which does not allow for irregular geographic shapes. In addition, as HFMD was in increasing trend, the small clusters in the early years could not be detected when data from all 66 months were used. We remedied this limitation by scanning each year separately, which has the disadvantage of losing information of each year on the continuation of the clusters. The data set used in this study also has some limitations. The sensitivity and positive predictive value of the HFMD surveillance systems in Guangxi and the other provinces in China have not been assessed. The surveillance system in Guangxi and the whole of China has only been in operation since 2008. A longer period of time for trend analysis is probably needed.
In conclusion, both HFMD cases and severe cases have spatio-temporal clusters. The continuous epidemic in Nanning, Liuzhou, Guilin cities and their neighbouring counties as well as moving clusters of severe cases indicate the need to address prevention and control measures in these areas.
Acknowledgments
We would like to thank Dr. Vorasith Somsrirutchai, Dr. Alan Geater in the Epidemiology Unit, Prince of Songkla University and Mr. Tang Xianyan from Guangxi Medical University for their valuable suggestions.
Author Contributions
Conceived and designed the experiments: YX VC. Analyzed the data: YX VC EM. Contributed reagents/materials/analysis tools: ZT YT YX. Wrote the paper: YX. Interpreted the results: YX VC.
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Awareness of Cervical Cancer and Attitude Toward Human Papillomavirus and Its Vaccine Among Ghanaians
Emmanuel Kwateng Drokow 1, Liu Zi 2, Qian Han 1, Clement Yaw Effah 3, Clement Agboyibor 4, Evans Sasu 5, Gloria Selorm Akpabla 6, Francis Foli 7 and Kai Sun 8
1 Department of Radiation Oncology, Zhengzhou University People’s Hospital and Henan Provincial People’s Hospital Henan, Zhengzhou, China, 2 Department of Radiation Oncology, First Affiliated Hospital of Xi’an Jiaotong University, Xi’an, China, 3 College of Public Health, Zhengzhou University, Zhengzhou, China, 4 School of Pharmaceutical Sciences, Zhengzhou University, Zhengzhou, China, 5 Department of Radiotherapy, National Centre for Radiotherapy and Nuclear Medicine, Korle Bu Teaching Hospital, Accra, Ghana, 6 Department of Internal Medicine, Tianjin Medical University, Tianjin, China, 7 Department of Internal Medicine, Seventh-Day Adventist Hospital, Takoradi, Ghana, 8 Department of Haematology, Zhengzhou University People’s Hospital and Henan Provincial People’s Hospital Henan, Zhengzhou, China
Background: Cervical cancer (CC) is the fourth most commonly diagnosed cancer among women. Ghana is a low-middle-income country with annual diagnosed cases of 3,151 and 2,119 deaths. The high prevalence rate of cervical cancer in Ghana is mainly due to ineffective preventive measures and insufficient knowledge about the disease. Therefore, our objective was to evaluate the level of knowledge and awareness of cervical cancer and attitude toward human papillomavirus and its vaccine among Ghanaians.
Methods: This descriptive cross-sectional survey on the awareness of cervical cancer and attitude toward human papillomavirus and its vaccine was carried out from March 2019 to February 2020. SPSS v. 23.0 was used in the data analysis. The participants’ demographic characteristics, knowledge of cervical carcinoma, human papillomavirus vaccine and HPV, and the likelihood to be vaccinated were represented as percentages and frequencies. The difference between males and females was assessed using the chi-square test. The logistic regression analysis was used to evaluate the relationship of possible related indicators with the willingness to receive the HPV vaccine. A $p < 0.05$ was considered statistically significant.
Results: A total of 1,376 participants were involved in the final analysis. Among the 1,376 participants involved in this survey, 1,240 participants (90.1%) representing 456 males (33.1%) and 784 females (57.0%) were aware of the terminology “cervical cancer” with a significant $p = 0.001$. When stratified by gender, women had significantly greater knowledge, compared to men in terms of “cervical cancer being common in middle age (35–50) females” (75.5 vs. 67.5%, respectively, $p \leq 0.001$). When stratified by gender, women had significantly greater knowledge of human papillomavirus (54.5 vs. 43.6%, respectively, $p < 0.001$) and the human papillomavirus vaccine (39.3 vs. 33.1%, respectively, $p = 0.019$) compared to men.
INTRODUCTION
Carcinoma of the cervix (CC) is the fourth most commonly diagnosed cancer among women with an annual new registered case of 569,847 and 311,365 deaths worldwide (1, 2). Human papillomaviruses (HPV) have been shown to be one of the most common pathogens transmitted through sexual contact in the cervix, and chronic infections of the cervix with high-risk human papillomavirus is required before cervical cancer can develop or occur (3). The HPV-18 and HPV-16 genotypes cause about 70% of the worldwide cervical cancer cases (4). When measured/estimated by sites, the cervix accounts for about 90% of human papillomavirus attributable global cancers, with two-thirds of that occurring in low and middle-income nations (5). This is primarily attributed to a lack of health insurance coverage in screening programs and a well-established nationwide screening system. Nevertheless, the WHO guide on the control of cervical cancer stated that the success of cervical cancer prevention and control mainly depends on cervical carcinoma screening programs (CCSP) and human papillomavirus vaccinations (6). The highest morbidity rates of cervical cancer were recorded in South–Eastern and South Central Asia, South-America, and sub-Saharan Africa (7). The age-standardization rates (ASR) per 100,000 women annually in West-Africa vary from 53.6 in Guinea, 39.5 in Ghana, 33.0 in Nigeria, 30 in Togo, and 28.6 in Burkina Faso in comparison to the 15.2 globally (8). The level of awareness and knowledge of cervical cancer etiology and HPV vaccination in women, to a great extent, influences their participation in screening and vaccination programs. Ghana is a low-middle-income country with annual diagnosed cases of 3,151 and 2,119 deaths, according to the 2018 ICO/IARC summary reports (9). These statistics, however, are prone to underestimate the actual nation’s disease burden, as there exist imparity in the event of cervical cancer screening for females with different geographical and demographical indicators across the nation (10). In addition, most women in rural areas may not avail themselves during cervical cancer screening and HPV vaccination due to lack of knowledge, insufficient funding for health service, and high poverty rates (11). It has been generally acknowledged that health disparities are largely influenced by sociodemographic factors like welfare, unemployment, education, social and health care services, work environment, housing, and living (12). The high uptake and effective implementations of the HPV vaccines depend on the general public comprehension of HPV infections, and their ability to understand the efficacy of the HPV vaccines in preventing cervical cancer (13–16). Some studies have shown that encouragement from close relatives can influence the participation of women in cervical cancer screening and consenting to the children’s vaccination. Ndejjo et al. (17) reported that Ugandan women who knew someone who had previously participated in the screening program would avail themselves to be screened. Furthermore, Anyebe et al. (18) and Cunningham et al. found that the willingness of women participating in cervical cancer screening was influenced by their husbands’ or partners’ decision in helping or encouraging them (18, 19). White et al. (20) also reported that most women in Zambia discuss their screening decisions with their close relatives or people within their immediate social circle. These pieces of evidence indicate that women who receive encouragement from their family, friends, or partners are more likely to participate in the screening program. Studies by Chao et al. (21) and Spencer et al. (22) also demonstrated the effect of women’s attitudes in relation to human papillomavirus vaccination uptake in their children. They observed that daughters whose mothers undertook screening were more prone to get the vaccination than those whose mothers did not test or wanted to avoid screening personally. Hence, it was realistic to conclude that females who undergo screening are more willing to have their children vaccinated. Additionally, variables like cultural and religious values were reported to affect health practices. Modibbo et al. (23) noticed that those religious beliefs were a barrier to cervical screening. Consequently, a study by Masika et al. (24) discovered that certain religious beliefs were against vaccination. Past studies on HPV in Ghana focused on the prevalence rate and genotype. Domfeh et al. (25) reported a prevalence rate of 10.7% in 75 women seen in the outpatient department. Yar et al. (26) also reported a prevalence rate of 76.6% in 107 women who tested HIV negative and 42.0% in 100 women who tested HIV positive. Thus, no study has been conducted on the awareness of HPV and its vaccines. Furthermore, given that Cervarix vaccine has been introduced in Ghana, research on the perception of women in relation to human papillomavirus vaccinations are extremely important to assess the effects of past educational programs and further aid the decision-making process to promote these HPV vaccines. We, therefore, conducted this study to assess cervical cancer and HPV awareness, HPV vaccine, and the readiness of both men and women to receive these vaccinations since HPV can cause throat cancer, anal cancer, and genital warts in men. We hypothesized that females who are aware of cervical cancer are most likely to participate in vaccination and screening programs. We also hypothesized that religious beliefs have negative influence on the willingness to receive HPV vaccination.
**Conclusion:** Majority of the respondents had poor knowledge regarding cervical cancer risk factors, symptoms, HPV, and its vaccine. Hence, this indicates a wakeup call for government to increase the awareness and knowledge level via the media and health professionals.
**Keywords:** Ghana, cervical cancer, vaccines, human papillomavirus, awareness
MATERIALS AND METHODS
Study Population
This descriptive cross-sectional survey on the awareness of cervical cancer and attitude toward human papillomavirus and its vaccine was carried out from March 2019 to February 2020. The study population included (i) a Ghanaian resident, either male or female, (ii) must be 18 years and above, (iii) not deaf and dumb, and (iv) women with no history of HPV vaccination. The target population of men and women mostly resided in either Accra, Kumasi, or Takoradi. These three cities were chosen due to their population density and the availability of cervical cancer screening programs. The questionnaires were designed after a comprehensive review of literature from past studies and then approved by experts (27–29). The soundness and legitimacy of the questionnaire were further verified by a review panel of two experts each in oncology, gynecology and obstetrics, and research methodology prior to the pilot survey. Three questions associated with symptoms and signs were modified, and two questions not related to the topic were deleted according to the comments from the expert. Afterwards, a pilot study was conducted with 30 respondents on the pre-final template to determine the questionnaire’s clarity. Findings from the current and pilot study demonstrated that Cronbach’s alpha was >0.70. Cronbach’s alpha evaluates the internal reliability or consistency of a given dataset. The questionnaire-based survey was undertaken after all participants had given written consent, with their anonymity, and confidentiality maintained. The exclusion criteria included women diagnosed with cervical cancer, women with some gynecological condition, and participants who did not provide their consent. The sample size was determined using the minimum sample size formula; thus, “n = Z2 P(1 - P)/d2; where, n = sample size; Z = z statistic for a level of confidence. For the level of confidence of 95%, which is conventional, the Z-value is 1.96. P = expected prevalence or proportion (in proportion of one; if 46%, P = 0.46), and d = precision (in proportion of one, if 5%, d = 0.05)” (16). The calculated sample size was 382 using an expected proportion or prevalence (p) of 46%; P = 0.46 (13), considering a 95% confidence interval (CI) and a 5% marginal error. To cover for heterogeneity in the targeted population and further ensure that maximum responses were received, we increased the sampling size and targeted about 1,500 participants. Simple random sampling was used to attain the targeted sample size.
Data Collection
The selection of group and the designing of our questionnaire was based on (30) Theory of Triadic Influence (TTI) and McLeroy et al. (31) Social Ecological Model (SEM). The Theory of Triadic Influence considers a “3 × 3 frameworks with environmental streams of influence, interpersonal, and intrapersonal crossed by proximal, distal, and ultimate levels of influence.” The Social-Ecological Model (SEM) considers public policy, community, institutional, interpersonal, and intrapersonal as levels of influence for health-related attitudes. Many theoretical concepts are shared by these frameworks, even though these frameworks differ in variable and structure interaction thus, integrating them in this study. Each question in this survey was adapted and modified from previously published articles, and experts’ opinions and was written in English in clear and straightforward language.
To aid the respondents answer the questions easily and quickly, the questions covered in the questionnaires, was categorized into sociodemographic, knowledge on cervical cancer, knowledge of HPV vaccine and HPV, the willingness to receive the HPV vaccination themselves and also having their children vaccinated, the rationale for not being willing to be vaccinated and the acceptability to pay for the human papillomavirus vaccination by themselves and interview quality evaluation. The cervical cancer section was subcategorized into (a) knowledge about cervical cancer, (b) knowledge about cervical cancer symptoms, and (c) knowledge about risk factors of cervical cancer. Knowledge of cervical cancer was evaluated if a participant responded that they were aware of cervical carcinoma by stating that one has heard or knows about cervical cancer. The participant’s knowledge regarding the risk factors (“Can HPV infection cause cervical cancer?” “long term use of oral contraceptives pills,” “smoking,” “unprotected sexual practices,” “multiparity,” “Immunocompromised/HIV-AIDS,” “early age at marriage”) and symptoms (“lower abdominal pain,” “bleeding after sexual intercourse,” “bleeding in between periods,” “vaginal discharge with foul smell,” “weight loss,” “post-menopausal bleeding,” and “asymptomatic”) of cervical carcinoma was evaluated. A 30-point score was used to evaluate cervical cancer knowledge. Five points were allocated to every sub-section of knowledge; hence participants were required to range between 0 and 30 scores. One point was allocated to each true response, and zero points to the incorrect response. Participants who responded only “Yes” to the questionnaire’s first statement, “Do you know about cervical cancer?” were assigned a knowledge score. Participants’ level of knowledge while calculating the knowledge score was categorized using Bloom’s cut off point (32). Participants who had from 24 to 30 point were regarded as having excellent knowledge with right answers of 80–100%, participants who scored from 18 to 23 point were regarded as having moderate knowledge with right answers of 60–79%, and participants who scored <18 points were lastly regarded as having poor knowledge with right answers of less than 60%. Information on cervical carcinoma was given to all participants to bridge the knowledge disparity after the end of the cervical cancer sub-section.
HPV awareness was evaluated with the phrase, “Have you heard of HPV?” Participants who responded “yes” to this statement were regarded to have knowledge about HPV. The knowledge on HPV vaccine was evaluated in the same manner. Some previous studies have reported these questions (29). Other relevant questions such as, “Is HPV infection a sexually transmitted infection?,” “Is a persistent infection of high-risk HPV the leading cause of cervical cancer and other HPV cancer types?,” “Can the HPV vaccine prevent cervical cancer and other HPV cancer types?,” and “Must the HPV vaccination be received before the first sexual intercourse?” were preliminary used in evaluating participants’ knowledge concerning human papillomavirus and its vaccine. Similar questions used by past
studies (28) in evaluating the HPV vaccination acceptability by asking, “Are you willing to vaccinate your current or future children both male and female?” “Are you willing to vaccinate yourself?” and “Will you accept that you pay for the HPV vaccination by yourself?” were also used in this study. Specific questions contained three possible outcomes (don’t know, no, yes); however, the “don’t know” option was regarded as an incorrect response.
Data Analysis
SPSS v. 23.0 was used in the data analysis. The participants’ demographic characteristics, knowledge of cervical carcinoma, human papillomavirus vaccine and HPV, and likelihood to be vaccinated were represented by percentages and frequencies. The difference between males and females was assessed using the chi-square test. The logistic regression analysis was used to evaluate the relationship of possible related indicators with the willingness to receive the HPV vaccine. Indicators in the univariate model were integrated into a multivariate logistic regression, in which confidence intervals of 95% and the adjusted odds ratio were estimated. A stratified assessment was conducted to determine whether gender affected the factors correlated with the willingness to be vaccinated. A $p < 0.05$ was considered statistically significant.
RESULTS
Sociodemographic Characteristics
Of the total 1,500 survey respondents, 124 answered the questionnaires with inconsistent and incomplete responses. After eliminating the inconsistent and incomplete questionnaires, the remaining questionnaires were analyzed and the total response rate was 91.73%. A total of 1,376 participants were involved in the final analysis. Table 1 represents the sociodemographic characteristic of the participants. The participants mean age was 35.5 [Standard Deviation (SD) ±6.4] years. A total of 532 (38.7%) were males, and the remaining 844 (61.3%) were females. Among them, 1,316 (95.6%; males = 496, females = 820) were Christians. The proportions of ethnicity based on Akan, Ewe, Ga, and others were 71.8, 12.8, 7.3, and 8.1%, respectively. Five-point eight percent of the participants had been educated at the senior high school level and below. Sixteen-point, six percent of the respondents, were not on any insurance policy, and 46.8% had a monthly income of <2,000 Ghana cedis equivalent to $350. Fifty-one-point, 1% of the respondents, were working, and 39.5% were students. Majority of the respondents were single (86.9%) and 61.0% (males = 292, females = 548) had their first sexual intercourse at age 18 years old and above with 47.4% (males = 220, females = 432) having only “one sexual partner in the past 6 months.” Statistical significance was noticed in most of the sociodemographic variables except medical insurance, marital status, and age.
Knowledge About Cervical Cancer
Among the 1,376 participants involved in this survey, 1,240 participants (90.1%) representing 456 males (33.1%) and 784 females (57.0%) were aware of the terminology “cervical cancer.” When stratified by gender, women had significantly greater knowledge, compared to men in terms of “cervical cancer being common in middle age (35–50) females” (75.5
| Sociodemographic characteristics | Gender | Chi-square | p-value |
|----------------------------------|--------|------------|---------|
| **Age** | | | |
| <40 | 508 (95.5) | 804 (95.3) | 0.142a | 0.974a |
| 40–60 | 20 (3.8) | 32 (3.8) | | |
| Above 60 | 4 (0.8) | 8 (0.9) | | |
| **Tribe** | | | |
| Akan | 396 (74.4) | 592 (70.1) | | |
| Ewe | 64 (12.0) | 112 (13.3) | 11.127b | 0.011b |
| Ga | 24 (4.5) | 76 (9.0) | | |
| Others | 48 (3.5) | 64 (4.7) | | |
| **Religion** | | | |
| Christian | 496 (93.2) | 820 (97.2) | | |
| Muslim | 28 (5.3) | 20 (2.4) | 14.472a | 0.001a |
| Traditionalist | 4 (0.8) | 4 (0.5) | | |
| Others | 4 (0.8) | 0 (0) | | |
| **Education** | | | |
| Junior high school or below | 4 (0.8) | 4 (0.5) | | |
| Senior high school | 20 (3.8) | 48 (5.7) | 5.246a | 0.133a |
| College/graduate and above | 508 (95.5)| 788 (93.4) | | |
| Not applicable | 0 | 4 (0.5) | | |
| **Occupation** | | | |
| Student | 232 (43.6)| 312 (37.0) | | |
| Working | 252 (47.4)| 452 (53.6) | 11.215b | 0.011b |
| Retired | 12 (2.3) | 8 (0.9) | | |
| Unemployed | 36 (6.8) | 72 (8.5) | | |
| **Marital status** | | | |
| Single/divorced/widow | 468 (88.0)| 728 (86.3) | 0.843b | 0.359b |
| Married | 64 (12.0) | 116 (13.7) | | |
| **Medical Insurance** | | | |
| No insurance | 104 (19.5)| 124 (14.7) | | |
| NHIS | 264 (88.4)| 612 (72.5) | 5.716b | 0.126b |
| Commercial Insurance | 28 (5.3) | 44 (5.2) | | |
| Company Insurance | 36 (6.8) | 64 (7.6) | | |
| **Age at sex debut (year)** | | | |
| <18 | 76 (14.3)| 72 (8.5) | | |
| >18 | 292 (54.9)| 548 (64.9) | 27.567b | <0.001b|
| Don’t know | 48 (9.0) | 36 (4.3) | | |
| None | 116 (21.8)| 188 (22.3) | | |
| **Age at menarche (year)** | | | |
| <12 | 0 | 144 (17.1) | | |
| >12 | 0 | 660 (78.2) | 1.813.155a<0.001a|
| Unknown | 0 | 40 (4.7) | | |
| Not applicable for male | 532 | 0 | | |
aFisher’s exact analysis was performed for tables which had at least one expected value <5 in the cells. bPearson Chi-square test was performed for tables with 0 expectant cell count. The color values means Fisher’s exact analysis was used.
vs. 67.5%, respectively, \( p \leq 0.001 \). These participants were examined further to test their knowledge on some risk factors and symptoms of cervical cancer, as presented in Tables 2–4. Majority of the respondents were aware of “bleeding after sexual intercourse (correctly identified by 51.8% of men and 70.4% of women, \( p \leq 0.001 \)),” “lower abdominal pain (correctly identified by 59.6% of men and 71.9% of women, \( p \leq 0.001 \))” and “vaginal discharge with foul smell (correctly identified by 61.4% of men and 68.4% of women, \( p \leq 0.001 \))” as being the dominant cervical cancer symptoms. Likewise, a high proportion among the respondents regarding the risk factors “Human papillomavirus infection (correctly identified by 47.4% of men and 55.6% of women, \( p = 0.010 \))” and “unprotected sexual practices (correctly identified by 50.9% of men and 63.8% of women, \( p \leq 0.001 \))” was noticed. Our survey respondents were ranked in each sub-category according to their level of knowledge. Respondents were asked regarding sources of information on cervical carcinoma and the main sources were social media/radio/television (\( N = 851, 68.8 \)), nurses/doctor (\( N = 507, 40.9 \)), newspapers/magazines (\( N = 255, 20.7 \)), and relatives/family (\( N = 221, 17.8 \)).
### Knowledge About HPV and Its Vaccine
As presented in Table 5 of the participant who answered the questions, 50.3% (\( N = 692 \)) have “heard of HPV,” and only 36.9% have “heard of the HPV vaccine.” When stratified by gender, women had significantly greater knowledge of human papillomavirus (54.5 vs. 43.6%, respectively, \( p < 0.001 \)) and the human papillomavirus vaccine (39.3 vs. 33.1%, respectively, \( p = 0.019 \)) compared to men.
Among the respondents who have heard of HPV, 59.8% (\( N = 414 \)) of the respondents were aware that HPV infection is transmitted through sexual contact (correctly identified by 48.7% of men and 65.4% of women, \( p < 0.001 \)) and 75.1% of the respondents were aware that “the persistent infection of high-risk HPV is the leading cause of cervical cancer and other HPV cancer types” with a significant \( p < 0.001 \). Furthermore, among respondents with knowledge of the HPV vaccine, only 55.9% (\( N = 284, p < 0.001 \)) knew that cervical cancer could be prevented with the HPV vaccine. Additionally, only 21.7% (\( N = 110, p = 0.001 \)) knew that “HPV vaccination is needed before first sexual intercourse.”
### TABLE 3 | Knowledge on cervical cancer symptoms answered by only participants who have heard of cervical cancer.
| Symptoms | Gender | Chi-square | \( p \)-value |
|------------------------------|------------|------------|---------------|
| | Male (\( N = 456 \)) | Female (\( N = 784 \)) | |
| Asymptomatic (no symptoms) | Yes 96 (21.1) | 252 (32.1) | 18.75 <0.001 |
| | No 136 (29.8) | 220 (28.1) | |
| | Don’t know 224 (49.1) | 312 (39.8) | |
| Post-menopausal bleeding | Yes 200 (43.9) | 424 (54.1) | 15.315 <0.001 |
| | No 20 (4.4) | 44 (5.6) | |
| | Don’t know 236 (51.8) | 316 (40.3) | |
| Weight loss | Yes 180 (39.5) | 420 (53.8) | 23.226 <0.001 |
| | No 56 (12.3) | 80 (10.2) | |
| | Don’t know 220 (48.2) | 264 (36.2) | |
| Vaginal discharge with foul smell | Yes 280 (61.4) | 536 (68.4) | 6.739 <0.001 |
| | No 32 (7.0) | 52 (6.6) | |
| | Don’t know 144 (31.6) | 196 (25.5) | |
| Bleeding in between periods | Yes 212 (46.5%) | 484 (61.7) | 29.448 <0.001 |
| | No 20 (4.4) | 36 (4.6) | |
| | Don’t know 224 (49.1) | 264 (33.7) | |
| Bleeding after sexual intercourse | Yes 236 (51.8) | 552 (70.4) | 62.377 <0.001 |
| | No 20 (4.4) | 52 (6.6) | |
| | Don’t know 200 (43.9) | 180 (23.0) | |
| Lower abdominal pain | Yes 272 (59.6) | 564 (71.9) | 19.905 <0.001 |
| | No 32 (7.0) | 36 (4.6) | |
| | Don’t know 152 (33.3) | 184 (23.5) | |
Values are presented as number (%). The \( \chi^2 \)-square test was used and \( p < 0.001 \) was considered as statistically significant.
*Only participants who have heard of cervical cancer answered these questions.*
TABLE 4 | Knowledge on cervical cancer risk factors answered by only participants who have heard of cervical cancer.
| Risk factors | Gender | Chi-square | p-value |
|--------------------------------------------------|--------|------------|---------|
| | Male | Female | |
| (N = 456) | (N = 784) | | |
| Early age at marriage | | | |
| Yes | 88 (19.3) | 168 (21.4) | 3.544 | 0.170 |
| No | 204 (44.7) | 308 (39.3) | | |
| Don't know | 164 (36.0) | 308 (39.3) | | |
| Immunocompromised/Human immunodeficiency virus/AIDS | | | |
| Yes | 160 (35.1) | 276 (35.2) | 7.048 | 0.029 |
| No | 128 (28.1) | 172 (21.9) | | |
| Don't know | 168 (36.8) | 338 (42.9) | | |
| Multiparity (giving birth to more than 3 children) | | | |
| Yes | 48 (10.5) | 112 (14.3) | 8.511 | 0.015 |
| No | 220 (48.2) | 316 (40.3) | | |
| Don't know | 188 (41.2) | 356 (45.4) | | |
| Unprotected sexual practices | | | |
| Yes | 232 (50.9) | 500 (63.8) | 25.342 | <0.001 |
| No | 52 (11.4) | 92 (11.7) | | |
| Don't know | 172 (37.7) | 192 (24.5) | | |
| Smoking | | | |
| Yes | 192 (42.1) | 388 (49.5) | 14.575 | 0.001 |
| No | 40 (8.8) | 96 (12.2) | | |
| Don't know | 224 (49.1) | 300 (38.3) | | |
| Long term use of oral contraceptives pills | | | |
| Yes | 208 (45.6) | 396 (50.5) | 14.216 | 0.001 |
| No | 28 (6.1) | 84 (10.7) | | |
| Don't know | 220 (48.2) | 304 (38.8) | | |
| Human papillomavirus (HPV) infection | | | |
| Yes | 216 (47.4) | 436 (55.6) | 9.117 | 0.010 |
| No | 16 (3.5) | 32 (4.1) | | |
| Don't know | 224 (49.1) | 316 (40.3) | | |
In general, 80.5% (N = 1,108) respondents were willing to have the HPV vaccination. Likewise, women had significantly greater willingness, compared to men (89.6 vs. 66.2%, respectively, p < 0.001). A total of 83.9% of women were willing to vaccinate their current and future children. Furthermore, the major reasons for respondents refusing to undertake the HPV vaccinations were “worrying about the safety of vaccine (30.2%),” “the HPV vaccine has not been widely accepted (13.1%),” “worrying about the price (13.1%),” and “worry about the effectiveness (12.7%).” Participants who said no to the payment for the HPV vaccine suggested that, WHO (70.4%) and the government (60.5%) should ensure the free supply of the HPV vaccine.
**Willingness to Receive HPV Vaccine and Its Associated Factors**
The bivariate regression analysis demonstrated a significant relationship exists between the willingness to be vaccinated and age, religion, economic status, education, age at first sex, participants with knowledge of cervical, HPV and its vaccine. This finding showed age 18–35 years (OR = 1.475; 95%CI = 1.142–1.591), respondents who are Christians (OR = 1.275; 95%CI = 0.729–1.459), college/graduate students (OR = 1.218; 95%CI = 1.054–1.878), respondents who had their first sex at age above 18 years (OR = 1.670; 95%CI = 1.484–1.929), respondents with monthly income 2,000–3,999 Ghana cedis (OR = 1.686; 95%CI = 1.136–2.501), respondent with knowledge about CC (OR = 0.541; 95%CI = 0.364–0.803), respondent who have heard of HPV (OR = 0.760; 95%CI = 0.581–0.993) and heard of HPV vaccine (OR = 0.870; 95%CI = 0.657–1.150) were more willing to receive the HPV vaccinations. Hence, a strong association between these variables and a respondent willingness to be vaccinated. Table 6 shows the outcome of the univariate and multivariate logistics analysis.
**DISCUSSION**
Advancement in understanding cervical carcinoma has been effective in acknowledging its preventive nature (33). It is firmly known that effective screening and HPV vaccination, to a large extent, will significantly decrease the prevalence of the disease (33, 34). For effective prophylaxis and screening, it is of paramount significance to understand the beliefs, perceptions, and knowledge of the general public. The assertion was that females who were aware of cervical carcinoma are most likely to participate in vaccination and screening programs. Our findings confirmed the hypothesis when a participant responded that they know about cervical cancer, HPV, and its vaccine. This was evident in both women and men. Men who know of cervical carcinoma were most likely to offer encouragement to their partners to participate in vaccination and screening programs. The knowledge of respondents confirmed the effectiveness (12.7%). Participants who said no to the payment for the HPV vaccine suggested that, WHO (70.4%) and the government (60.5%) should ensure the free supply of the HPV vaccine.
Our study findings showed that majority (90.1%) of the participants were knowledgeable of the term cervical cancer which is higher when compared with other similar studies in developing countries such as Pakistan, Ethiopia, and Zambia and where the percentage of participants knowledgeable of the term cervical cancer were 51.3, 76.8, and 36.8%, respectively (29, 37, 38). The variation may be attributable to the dissemination of information through various mass media and the availability of screening programs in Ghana. The knowledge of respondents on cervical cancer showed that 63.8% of participants know of cervical cancer risk factors.
Among these risk factors, “human papillomavirus infection” and “unprotected sexual practices” were correctly and highly identified as cervical cancer risk factors. This finding is lower when compared to past studies conducted in South Africa, Bhutan, Malaysia, and Ukraine (39–42). This lack of awareness normally leads to the higher death rate related with CC because women who are not enlightened about these risk factors will not undertake the appropriate preventive actions.
Regarding awareness of cervical cancer symptoms, respondents were aware of symptoms such as “vaginal discharge with a foul smell,” “bleeding after sexual intercourse,” and “bleeding in-between period” (67.8, 63.5, and 56.1%, respectively).
respectively). Our results indicate that much effort is needed to educate the general public, especially women of cervical cancer symptoms, since failure to recognize these symptoms or late presentation can result in delaying medical care, resulting in poor prognosis and higher death rates.
There is no doubt that basic knowledge is essential in encouraging women to patronize preventive actions. This is in line with the intrapersonal level regression findings for SEM, where basic knowledge concerning cervical cancer was the key predictor of attitude (38). Communities based educational programs have been shown to be effective in increasing preventive practices, knowledge, and awareness (43). Social media /radio/television, nurses/doctors, and newspapers/magazines were found as reliable information sources and they could offer potential targets for performing interventional studies intended to improve awareness of cervical cancer in Ghana. It was presumed that females who receive backing from close relatives could influence the participation of women in cervical cancer screening. The findings back the assertion about women participating in screening. It was observed that women’s recognized that the acceptance of spouses, families, and friends affected their screening practices. This result is consistent with another study conducted in Zambia that assessed that relatives and peers often spurred women’s choice to screen (20). Ndejjo et al. (17) reported that Ugandan women who knew someone who had previously participated in the screening program would avail themselves to be screened. Furthermore, Anyebe et al. (18) and Cunningham et al. (19) found that the willingness of women participating in cervical cancer screening was influenced by their husbands’ or partners’ respectively). Our results indicate that much effort is needed to educate the general public, especially women of cervical cancer symptoms, since failure to recognize these symptoms or late presentation can result in delaying medical care, resulting in poor prognosis and higher death rates.
There is no doubt that basic knowledge is essential in encouraging women to patronize preventive actions. This is in line with the intrapersonal level regression findings for SEM, where basic knowledge concerning cervical cancer was the key predictor of attitude (38). Communities based educational programs have been shown to be effective in increasing preventive practices, knowledge, and awareness (43). Social media /radio/television, nurses/doctors, and newspapers/magazines were found as reliable information sources and they could offer potential targets for performing interventional studies intended to improve awareness of cervical cancer in Ghana. It was presumed that females who receive backing from close relatives could influence the participation of women in cervical cancer screening. The findings back the assertion about women participating in screening. It was observed that women’s recognized that the acceptance of spouses, families, and friends affected their screening practices. This result is consistent with another study conducted in Zambia that assessed that relatives and peers often spurred women’s choice to screen (20). Ndejjo et al. (17) reported that Ugandan women who knew someone who had previously participated in the screening program would avail themselves to be screened. Furthermore, Anyebe et al. (18) and Cunningham et al. (19) found that the willingness of women participating in cervical cancer screening was influenced by their husbands’ or partners’
| Items | Total (N = 1,376) | Male (N = 532) | Female (N = 844) | p-value |
|---------------------------------------------------------------------|------------------|---------------|-----------------|---------|
| Have you heard of HPV? | | | | |
| Yes | 692 (50.3) | 232 (43.6) | 460 (54.5) | <0.001 |
| No | 684 (49.7) | 300 (56.4) | 384 (45.4) | |
| Is HPV infection a sexually transmitted infection?a | | | | |
| Yes | 414 (59.8) | 113 (48.7) | 301 (65.4) | <0.001 |
| No | 278 (40.2) | 119 (51.3) | 159 (34.6) | |
| Is persistent infection of high-risk HPV the leading cause of cervical cancer and other HPV cancer types?a | | | | |
| Yes | 520 (75.1) | 155 (66.8) | 365 (79.3) | <0.001 |
| No | 172 (24.9) | 77 (33.2) | 95 (20.7) | |
| Have you heard of the HPV vaccine? | | | | |
| Yes | 508 (36.9) | 176 (33.1) | 332 (39.3) | <0.001 |
| No | 868 (63.1) | 356 (66.9) | 512 (60.7) | |
| Can the HPV vaccine prevent cervical cancer and other HPV cancer types?b | | | | |
| Yes | 284 (55.9) | 80 (45.5) | 204 (61.4) | <0.001 |
| No | 224 (44.1) | 96 (54.5) | 128 (38.6) | |
| Must the HPV vaccination be received before the first sexual intercourse?b | | | | |
| Yes | 110 (21.7) | 52 (29.5) | 58 (17.5) | 0.001 |
| No | 398 (78.3) | 124 (70.5) | 274 (82.5) | |
| Are you willing to vaccinate yourself? | | | | |
| Yes | 1,108 (80.5) | 352 (66.2) | 756 (89.6) | <0.001 |
| No | 268 (19.5) | 180 (33.8) | 88 (10.4) | |
| Are you willing to vaccinate your current or future children both male and female?c | | | | |
| Yes | 900 (81.2) | 266 (75.6) | 634 (83.9) | <0.001 |
| No | 208 (18.8) | 86 (24.4) | 122 (16.1) | |
| What are your reasons for unwillingness to take the HPV vaccine | | | | |
| Worry about the safety | 81 (30.2) | 38 (21.1) | 43 (48.9) | 0.001 |
| The HPV vaccine has not been widely accepted | 35 (13.1) | 23 (12.8) | 12 (13.6) | |
| Worry about the price | 35 (13.1) | 15 (8.3) | 20 (22.7) | |
| Worry about the effectiveness | 34 (12.7) | 28 (15.6) | 6 (6.8) | |
| Not considering themselves at risk of cervical cancer | 30 (11.2) | 27 (15.0) | 3 (3.4) | |
| The vaccine is not protective | 28 (10.4) | 26 (14.4) | 2 (2.3) | |
| Other reasons | 25 (8.6) | 23 (12.8) | 2 (2.3) | |
| Will you accept that you pay for the HPV vaccination by yourself?d | | | | |
| Yes | 331 (29.9) | 145 (41.2) | 186 (24.6) | <0.001 |
| No | 777 (70.1) | 207 (58.8) | 570 (75.4) | |
Values are presented as number (%). The chi-square test was used and p < 0.05 was considered as statistically significant. aParticipants who have heard of human papillomavirus (HPV) answered these questions, bParticipants who have heard of the HPV vaccine answered these questions, cParticipants who are not willing to take the HPV vaccine answered the question, dParticipants who are willing to take the HPV vaccine answered the question.
TABLE 6 | Variables associated with the willingness to receive HPV.
| Variables | Willingness to receive HPV vaccination | Willingness to receive HPV vaccination |
|--------------------|--------------------------------------|--------------------------------------|
| | Odd Ratio 95% CI | Adjusted odd ratio 95% CI |
Gender
- Male: 1
- Female: 0.228 (0.171–0.303)
Age
- 18–35: 1.475 (1.142–1.591)
- 36–60: 0.600 (0.154–2.344)
- Above 60: 1
Tribe
- Akan: 1.639 (0.729–3.085)
- Ewe: 0.769 (0.380–1.557)
- Ga: 1.500 (0.729–3.085)
- Others: 1
Religion
- Christian: 1.275 (0.729–1.591)
- Muslim: 1.151 (0.523–2.233)
- Traditionalist: 1
Education
- Junior high school or below: 1
- Senior high school: 0.700 (0.700–3.037)
- College/graduate and above: 1.218 (1.054–1.878)
Occupation
- Student: 1.254 (0.801–2.287)
- Working: 0.832 (0.492–1.408)
- Retired: 2.933 (2.933–8.117)
- Unemployed: 1
Marital status
- Single/divorced/widow: 1
- Married: 1.213 (0.830–1.774)
Medical Insurance
- No insurance: 1
- NHIS: 0.676 (0.480–0.952)
- Commercial Insurance: 1.536 (0.864–2.730)
- Company Insurance: 0.419 (0.213–0.822)
Monthly Income (GH Cedis)
- <2,000: 1
- 2,000–3,999: 1.686 (1.136–2.501)
- 4,000–5,999: 2.205 (1.062–4.577)
- 6,000–9,999: 1.102 (0.360–3.378)
- Above 10,000: 2.205 (0.649–7.485)
Age at first sex
- <18: 1
- >18: 1.670 (1.484–1.929)
Number of sexual partners in the past 6 months
- 1: 1
- >2: 2.369 (1.549–3.625)
Do you know about cervical cancer?
- Yes: 0.541 (0.364–0.803)
- No: 1
Have you heard of HPV?
- Yes: 0.760 (0.581–0.993)
- No: 1
Have you heard of HPV vaccine?
- Yes: 0.870 (0.657–1.150)
- No: 1
The bold values are reference values.
decisions in helping or encouraging them. In addition, with the exception of men, women would be more prone to have their daughter's vaccinated if they gain approval from their spouses. It can be proposed that there exists an association between women needing support and participating in taking preventive programs. This suggests that the Ghanaian community is a patriarchal community in which men have a significant influence on the households—indicating that men must be included as a target group for the effectiveness of cervical cancer preventive programs.
Religious beliefs were believed to hinder screening and vaccine uptake. The findings contradict this hypothesis in that there was no influence of religion on screening choices, but rather religion had a good impact on the acceptability of vaccination. This is contradictory to other nations where religion was observed to hinder uptake of vaccination (24, 44). About 95.6% of the respondents acknowledged being Christians, and this improved the likelihood of having themselves vaccinated. This indicates that Ghanaian churches can play a part in enhancing vaccinations program in Ghana. The potential reason is that it is known that certain Christian denominations consciously enlighten their members on medical problems such as cervical cancer. These explanations are insufficient since the participant's Christian denominations were not evaluated. Again, beliefs vary from one Church to another. Likewise, the truthfulness of the information given by the churches requires further investigation.
Previous studies on HPV awareness with a large sample size reported that the percentage of women knowledgeable of HPV ranged from 15.0 to 44.9% (45–48). We noticed a greater percentage of 54.5% in only women, while the total percentage among all the respondents was 50.3%. This finding is lower when compared with results from developed nations since the percentage of women knowledgeable of the human papillomavirus was 71.8, 61.6, and 87.7% in Australia, United Kingdom, and the United States, which indicates that women in developed countries might be more knowledgeable of HPV (49). Furthermore, 36.9% of women were aware of the HPV vaccine. This outcome is slightly higher than what
was reported in Chinese women by Lin et al. (28) (21.0%). Nevertheless, women’s knowledge of the human papillomavirus vaccine is still far from women in economically developed nations where governmentally funded HPV vaccination program has been implemented per WHO recommendation (49). The possible relationship between HPV awareness and its vaccine and socioeconomic characteristics requires further investigation because populations showed a variety of socioeconomic, ethnic, cultural, and other inequalities in published surveys.
Even though there was a higher willingness of participants to accept the vaccination, the primary complaints among participants not willing to accept the vaccination were how safe the vaccine is, in addition to the acceptability of it worldwide and the price of the vaccine. This finding is similar to a study by (50), where participants were willing to undertake the vaccination at a free cost or receives a subsidy from the government (51). Endarti et al. further showed that the knowledge of vaccine effectiveness increased the willingness of people to undertake vaccination (51). Hence, the government may use the media houses to educate people on the efficacy of the vaccine. In addition, the economic status may play an important part in the acceptance of the vaccine because our study showed that the likelihood of respondents paying for the vaccination was relatively low in the general population sample, which corresponds with the assumption that the majority of the respondents had lower-income rates. However, it was also striking that higher income earners and participant with company insurance were less willing to pay for vaccination and this can be attributable to the fact that majority of the higher income earners have company or private insurance hence their unwillingness to pay for the vaccination but instead, wants the insurance companies to cover the cost for the vaccination. Again, a greater comprehension of how insurance coverage and certain variables influence HPV vaccination uptake is required to allow potential interventions to be planned, therefore our next research will concentrate on this.
In our survey, most Ghanaians claim to be affiliate with the Christian religion. Hence improvement in the vaccine coverage can be increased with clergy’s the support since the majority of these churches are mostly arraigned of refusing western medication due to biblical and moral values. Again, regular visitation to Church must be taken to motivate church members to participate in vaccination programs and further ensure that accurate information on cervical cancer is disseminated during their health talk. There is a need for the general public to be educated to understand the significance of the vaccination in addition to risk factors, symptoms, and screening of cervical carcinoma due to low knowledge and awareness highlighted in our study. Furthermore, community-based programs and interventional strategies must be targeted at both women and men because men were an influential element in the acceptability of the HPV vaccination by women.
Some limitations need to be highlighted. First, study participation was voluntary. Hence, most of the participants may have been those who demonstrated greater interest in the subject. Secondly, the study was limited to three cities in Ghana; therefore, the entire population cannot be generalized to our findings. Thus, the participants in the study constitute a representative sample. Also, different results will be obtained from new studies targeting rural communities and different residential areas. Thirdly, our survey centered on acceptability instead of uptake of the HPV vaccine; thus, it is uncertain if the intentions of participants to be vaccinated would turn into actions. Lastly, due to different educational backgrounds, some participants may not have completely grasped the questions, contributing to possible bias.
Taking into account the findings of this survey, certain policies can be implemented. First of all, it is important to ensure that screening facilities for cervical carcinoma are accessible in all health centers. Because of low awareness, probably providing such services in all health centers will result in an effective outreach between women and healthcare providers who may visit the health center for certain health purposes. In regards to the HPV vaccines, the higher willingness among respondents to accept the vaccine was a good sign. Since reproductive age in Ghana starts very early, it is, however, essential to begin vaccinations early in adolescence. HPV vaccines can be added to the normal vaccination program as an effective-cost solution, or “community-based vaccine drives” can be launched via the Ministry of Health. In principle, advancement in acceptance of vaccines, along with changes in behavior, would have a huge influence on Cervical Cancer Prevention in Ghana.
DATA AVAILABILITY STATEMENT
The raw data supporting the conclusions of this article will be made available by the authors, without undue reservation.
ETHICS STATEMENT
The studies involving human participants were reviewed and approved by Zhengzhou University and Henan Provincial People’s Hospital. The patients/participants provided their written informed consent to participate in this study.
AUTHOR CONTRIBUTIONS
ED wrote and presented the original draft. LZ and QH were involved in data curation and visualization. CE, CA, GA, ES, and FF were involved in methodology, software, analysis, review and editing. KS was involved in supervision.
FUNDING
This study was partially supported by the National Natural Science Foundation of China (Nos. 81971508, 81471589, and 81273259), the Health Bureau of Henan Province, P.R. China (No. 201201005), and the foundation and frontier research grant of Henan provincial science and technology bureau, P.R. China (Nos.112300410027 and 132102310120).
ACKNOWLEDGMENTS
We thank all participants involved in this survey.
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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 © 2020 Drokow, Zi, Han, Efijah, Agboyibor, Sasu, Akpabla, Foli and Sun. 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.
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Effects of renal denervation on cardiac oxidative stress and local activity of the sympathetic nervous system and renin-angiotensin system in acute myocardial infarcted dogs
Qiaoli Feng†, Chengzhi Lu2†, Li Wang2, Lijun Song3, Chao Li2 and Ravi Chandra Uppada1
Abstract
Background: This study sought to evaluate the therapeutic effects of renal denervation (RDN) on acute myocardial infarction (MI) in canines and explore its possible mechanisms of action.
Methods: Eighteen healthy mongrel dogs were randomly assigned to either the control group, the MI group or the MI + RDN group. To assess cardiac function, left ventricular ejection fraction (LVEF), left ventricular end-diastolic dimension (LVEDD), left ventricular end-systolic dimension (LVESD) and fraction shortening (FS) were recorded. Additionally, haemodynamic parameters such as left ventricular systolic pressure (LVSP), left ventricular end-diastolic pressure (LVEDP) and heart rate (HR) were measured. Cardiac oxidative stress levels were evaluated based on the expression of p47phox mRNA, malondialdehyde (MDA), anti-superoxide anion free radical (ASAFR) and activity of superoxide dismutase (SOD). To measure the local activity of the sympathetic nervous system (SNS) and renin-angiotensin system (RAS), the levels of tyrosine hydroxylase (TH), angiotensin II (AngII), angiotensin-converting enzyme 2 (ACE2), angiotensin (1–7) [Ang(1–7)], and Mas receptor (MasR) in myocardial tissues were recorded. The expression of TH in renal tissue and serum creatinine were used to assess the effectiveness of the RDN procedure and renal function, respectively.
Results: We found that MI deteriorated heart function and activated cardiac oxidative stress and the local neurohumoral system, while RDN partially reversed these changes. Compared with the control group, parameters including LVEDD, LVESD, LVEDP and the levels of ASAFR, MDA, p47phox, ACE2, Ang(1–7), MasR, AngII and TH-positive nerves were increased (all $P < 0.05$) in myocardial infarcted dogs; meanwhile, LVEF, FS, LVSP and SOD expression were decreased (all $P < 0.05$). However, after RDN therapy, these changes were significantly improved ($P < 0.05$), except that there were no significant differences observed in FS or LVSP between the two groups ($P = 0.092$ and 0.931, respectively). Importantly, the expression of TH, AngII and Ang(1–7) was positively correlated with MDA and negatively correlated with SOD. Between-group comparisons demonstrated no differences in serum creatinine ($P = 0.706$).
(Continued on next page)
Conclusions: RDN attenuated cardiac remodelling and improved heart function by decreasing the level of cardiac oxidative stress and the local activity of the SNS and RAS in cardiac tissues. Additionally, the safety of the RDN procedure was established, as no significant decrease in LVSP or rise in serum creatinine was observed in our study.
Keywords: Renal denervation, Acute myocardial infarction, Oxidative stress, Sympathetic nervous system, Renin-angiotensin system
Background
The incidence of acute myocardial infarction (MI) has increased over time. Chronic heart failure (CHF) is a common complication of acute MI, which places substantial burden on the health care system. Complicated pathophysiologic mechanisms participate in the development of HF, among which the whole-body and local cardiac sympathetic nervous system (SNS) and renin-angiotensin system (RAS) contribute significantly to the pathogenesis of CHF. Recently, oxidative stress has been demonstrated to play a pivotal role in ventricular remodelling after MI. In the clinical setting, drugs targeting these two systems, such as angiotensin-converting enzyme inhibitors (ACEI), angiotensin receptor blockers (ARB), mineralocorticoid receptor antagonists, and beta-blockers, have been the mainstay of management for post-MI HF. Additionally, anti-oxidative therapy has attracted increasing attention in the cardiovascular field. However, despite intensive therapeutic treatment, a large number of patients continue to experience worsening of HF symptoms. Thus, it remains necessary to explore new therapeutic approaches for the treatment of MI and its complications.
Previously published studies have shown that renal denervation (RDN) provides significant benefits in delaying the progression of cardiac hypertrophy [1], attenuating left ventricular (LV) remodelling and improving cardiac function [2]. The activities of the systemic SNS and RAS [3, 4] were shown to be decreased by RDN through interruption of the renal sympathetic efferent and afferent nerves [5]. However, the effects of RDN on cardiac-specific SNS and RAS activity and oxidative stress have not been investigated. In the present study, we used an established canine MI model to explore the related mechanisms, and thus further validate that RDN could be used as a new treatment for post-MI remodelling and HF.
Methods
Animals
Eighteen healthy mongrel dogs (male:female, 8:10), weighing 15 ~ 18 kg, were used in this study (and were provided by the Experimental Animal Centre in Tianjin). The experiments were carried out in strict accordance with the guide for the care and use of laboratory animals. The animals were kept under a 12/12-h light/dark cycle and fed with regular chow and water ad libitum.
Experimental groups and conditions
All experimental mongrel canines were randomly divided into three groups. (1) The control group (n = 6) received only a coronary angiogram, followed by a renal arteriogram one week later. (2) The MI group (n = 6) underwent an established procedure inducing MI and, one week later, underwent a renal arteriogram. (3) The MI + RDN group (n = 6) underwent the MI-inducing procedure, followed by renal denervation one week later.
Myocardial infarction
All animals were anesthetized with 6% sodium pentobarbital (30 mg/kg, intravenous (IV)), with an additional 50 mg given as needed through IV injection every 30 to 60 min, according to the reaction of the animals. The dogs were placed on the operating table in a supine position. Using a Mac-Lab (GE, United States) hemodynamic detection system, electrocardiography (ECG) and vital signs were monitored. The right iliac region was shaved and disinfected, and then a venous pathway was established. The right femoral artery was punctured, and then a 6 F guiding wire was inserted through the sheath, followed by the injection of 1000 IU heparin. After verifying the coronary anatomy, a bolus of gelatine sponge (1 mm in diameter) was injected into the distal end of the fist diagonal branch of the left anterior descending artery, as described previously [6]. Coronary angiography was performed again 10 min later to confirm interruption of the blood flow in the distal vessels. The operation lasted 60–90 min.
Renal denervation
Under pentobarbital sodium (30 mg/kg, IV) anaesthesia, bilateral renal denervation was performed in the MI + RDN group; meanwhile, in the control and MI groups, the operation was the same except that the nerves were kept intact. The right femoral groins were shaved prior to connecting the radio frequency ablation apparatus (IBI-1500 T, IBI, United States). The temperature of the radiofrequency ablation instrument was set at 43 °C, at a power of 10 W, for a duration of 90 s. The right femoral artery was punctured, and a 6 F guiding wire was inserted through the guiding sheath. Renal angiography was performed to determine the location of the renal artery. The ablation electrode (6 F ablation catheter tip, electrode length of 4 mm) was then inserted, and radiofrequency ablation was performed with a high frequency in the renal artery (diode power of 10 W, for a duration of 90 s). After the procedure was completed, the electrode was pulled out.
frequency (RF) energy was applied to the endothelial lining. The catheter tip was placed in the proximal portion of the renal artery main trunk, and the ablation procedure was conducted by applying RF energy in the renal artery distally to proximally and circumferentially. Then, the catheter was withdrawn 1–2 cm to generate another ablation location. Renal angiography was performed again to validate that the catheter tip was well-attached to the vessel wall before ablating at the new target site. This procedure was repeated three to four times in the renal artery, and then the same RF energy was applied to the contralateral renal artery.
**Transthoracic echocardiography**
To evaluate LV function and cardiac chamber structure, echocardiography was performed at baseline and 4 weeks after MI (CX50, Philips, Netherlands). Parameters such as the left ventricular ejection fraction (LVEF), left ventricular end-diastolic dimension (LVEDD), left ventricular end-systolic dimension (LVESD) and fraction shortening (FS) were recorded. LVEF was measured using X-plane imaging and was calculated as follows: (L V V m a x - L V V m i n ) / L V V m a x . Three consecutive cardiac cycles were observed, and the average values were recorded as the final cardiac parameters.
**Detection of haemodynamics**
Haemodynamic parameters were detected at baseline and at 4 weeks post-MI. The right femoral artery was punctured, and a 6 F pigtail catheter was used to perform LV angiography. The heart rate (HR), left ventricular systolic pressure (LVSP), and left ventricular end-diastolic pressure (LVEDP) of each animal were measured using the Mac-Lab system.
**Enzyme-linked immunosorbent assay (ELISA)**
The myocardial expression of AngII and Ang(1–7) were detected using a commercial ELISA kit (Huamei Biological Co., Wuhan, China). The reaction system and standard curves were established according to the kit's instructions.
**Real-time reverse transcription polymerase chain reaction (RT-PCR)**
We used RT-PCR analysis to assay the mRNA expression of angiotensin-converting enzyme 2 (ACE2) and MasR in the LV. Total RNA extraction was performed according to the instructions provided with the Trizol reagent (CWbio. Co. Ltd, Cat# CW0581). Template cDNA was prepared from total RNA using the HiFi-MMLV cDNA reverse transcription kit (CWbio. Co. Ltd, Cat# CW0744). Quantitative PCR (Q-PCR), using an ABI7500 (Applied Biosystems, United States), was performed in triplicate for the amplification of target genes, while GAPDH was selected as an endogenous control.
Each sample was run in duplicate with the following thermocycler protocol: an initial step 95 °C for 10 min, followed by 45 cycles at 95 °C for 15 s and 60 °C for 30 s. The PCR mix contained 0.4 uL (10 μmol) of forward and reverse primers, 10 uL of 2× UltraSYBR Mixture (CWbio. Co. Ltd, Cat# CW 0956), 2 uL of template cDNA and RNase-free water to a final volume of 20 uL. Melting curve analysis was used to confirm the specificity and identify of the PCR products, and relative gene expression changes were measured using the delta-delta Ct method, where \( X = 2^{-\Delta \Delta Ct} \). The primer sequences used are listed below in Table 1.
---
**Immunohistochemistry analysis**
Cardiac expression of TH was detected by immunohistochemistry. Myocardial tissues were fixed with formalin, and after embedding and dehydrating, the LV tissue was sliced into 4-um sections. The sections were treated with 0.01 M citrate buffer (pH 6.0) for 10 min in a microwave oven, and the samples were then washed with PBS after cooling to room temperature. The sections were incubated overnight at 4 °C with primary antibody and again with biotinylated secondary antibody, followed by the addition of streptavidin-conjugated horseradish peroxidase. Immunohistochemistry staining for TH was performed using the DAB staining system according to the manufacturer's instructions. Then, the nuclei were counterstained with haematoxylin. Three sections from each group were chosen for TH detection, and the amount of TH was assessed in five randomly chosen high-power fields from each sample. The investigator was blinded to the specimen’s source. The raw data were converted to an immunohistochemical score (IHS) to show the immunoreactivity of TH-positive nerves using an image analysis-based system [7].
**Statistical analysis**
Experimental data were analysed using SPSS version 20.00 software. Quantitative data are presented as the mean ± standard deviation. Each experiment was performed in triplicate for each group. The significance of differences between the groups for haemodynamic parameters was determined using one-way analysis of variance (ANOVA) followed by Tukey’s multiple comparison test. The differences were considered significant when \( P < 0.05 \). "P" values of lower than 0.05 were considered significant. The rest of the differences were considered nonsignificant (NS).
---
**Table 1 Specific primers for Q-PCR**
| Gene names | Primers | Product size (bp) |
|------------|---------|------------------|
| ACE2 | Forward: 5'- TTCAGCACAGTGGATCATCA-3' | 95 |
| | Reverse: 5'- CAAGTATAAAGCCTCCTGA-3' | |
| MasR | Forward: 5'- TGAGCAACAAAGGTGAAGTC-3' | 124 |
| | Reverse: 5'- AGGCCATCCGGTACTACAA-3' | |
| P47phox | Forward: 5'- TGATGCTGTGACCTACGCAC-3' | 136 |
| | Reverse: 5'- AGGCTCCTCTGGTCCATCA-3' | |
| GAPDH | Forward: 5'- CCGGCCGCTTACACGCAC-3' | 138 |
| | Reverse: 5'- CGGCCAGCCAGTCCAGACG-3' | |
mean ± SD. Group comparisons were subjected to analysis of variance (ANOVA), followed by the Newman-Keuls multiple comparison test to identify significant differences between individual groups. *P < 0.05 was considered statistically significant.
**Results**
One dog died due to a malignant arrhythmia on the 1st day in the MI group, and one dog died on the 3rd day in the MI + RDN group. There were no deaths in the control group.
**Baseline parameters**
Dogs in each group were assessed for LVEDD, LVESD, FS, LVEF, LVEDP, LVSP and HR before MI (shown in Table 2) and there were no significant baseline differences between the three groups.
**Cardiac function and haemodynamic parameters at 4 weeks post-MI**
At 4 weeks post-MI, compared to the control group, dogs from the MI and MI + RDN groups showed increased LVEDD, LVESD and LVEDP, while the LVEF, FS and LVSP values were all reduced. Importantly, compared with the MI group, parameters such as LVEF, LVEDD, LVESD and LVEDP were significantly improved in the MI + RDN group, but no significant difference was observed in FS and LVSP (*P = 0.092 and *P = 0.931, respectively). Additionally, there were no significant differences in HR among the three groups (shown in Table 3).
**Cardiac oxidative stress levels**
As shown in Fig. 1, the cardiac infarct border zone was obtained to assess oxidative stress levels. At 4 weeks post-MI, the activities of MDA, p47phox, and ASAFR were all increased compared to the control group, while RDN treatment significantly reduced these changes (shown in Fig. 1a-c). SOD activity in the control, MI, and MI + RDN groups was 159.77 ± 11.90 U/mg prot, 105.14 ± 7.66 U/mg prot and 140.01 ± 14.10 U/mg prot, respectively (shown in Fig. 1d).
**Activity of the cardiac RAS**
Compared with the control group, the expression of AngII, ACE2, Ang(1–7) and MasR in myocardial tissue was significantly increased in the MI and MI + RDN groups. After intervention with RDN, the levels of AngII, ACE2, Ang(1–7) and MasR were significantly decreased in the RDN-treated group compared to the MI group (shown in Fig. 2a-d).
**Activity of the cardiac SNS**
Four weeks post-MI, the relative expression of TH-positive nerves in the myocardial tissue from the control, MI and MI + RDN groups was 66.82 ± 13.09, 134.16 ± 12.06, and 101.14 ± 3.91, respectively. Compared with the control group, the amount of TH-positive nerves was markedly elevated in the MI and MI + RDN groups. Importantly, a decrease in TH-positive nerves was seen in the MI + RDN group compared with the MI group (shown in Fig. 3a-b).
**Correlation analysis**
The expression of TH, AngII and Ang(1–7) was positively correlated with MDA (all *P < 0.05) and negatively correlated with SOD (all *P < 0.05). The correlation indexes are listed in Table 4.
**TH-positive nerves in renal tissue**
Four weeks after MI, the relative expression of TH-positive nerves in renal tissue in the control, MI and MI + RDN groups was 93.44 ± 10.86, 102.26 ± 18.98, 75.69 ± 14.67, respectively. A decrease in TH-positive nerves was seen in the MI + RDN group compared to the MI group, while no significant difference (*P = 0.071) was observed between the control and MI + RDN groups (shown in Fig. 4a-b).
Comparison of serum creatinine at 4 weeks post-MI in each group
The serum creatinine levels in the control, MI and MI + RDN groups were 56.00 ± 19.12 μmol/L, 62.20 ± 12.79 μmol/L and 64.80 ± 20.40 μmol/L, respectively. No difference in serum creatinine among the three groups was detected (P = 0.706, shown in Fig. 5).
Discussion
Mounting evidence suggests that RDN is beneficial at improving cardiac function in both experimental animals and clinical patients. Hu et al. found that RDN was superior to monotherapy with a beta blocker, ACEI or ARB in decreasing plasma norepinephrine (NE) levels and improving cardiac function in rats with MI [8]. A significant improvement in diastolic function and a
lowered LV mass index were also seen in RDN-treated refractory hypertension patients [9]. The present study showed that cardiac function was deteriorated after MI and that RDN inhibited the process of ventricular remodelling and improved cardiac function. Acute MI results in an increase in SNS and RAS activity in both the whole body and local myocardial tissues, which is proportional to the severity of post-MI HF [10, 11]. Additionally, reactive oxygen species (ROS), as the main effectors of oxidative stress, play an important role in the ventricular remodelling that occurs after MI [12]. Many studies have shown that RDN is effective at reducing the whole-body activity of the SNS and RAS. In our study, we explored the effect of RDN on cardiac oxidative stress and local activity of the SNS and RAS.
Previous studies have demonstrated that antioxidant therapy distinctly inhibits oxidative stress, delays ventricular remodelling and improves cardiac function after MI [13, 14]. Oxidative stress results from imbalance of the antioxidant and oxidant systems, which leads to excessive ROS production. The biological effects of nicotinamide adenine dinucleotide phosphate (NADPH) oxidase, one of the principle sources of ROS in the cardiovascular system [15], are regulated by antioxidant enzymes such as SOD and catalase. The NADPH p47phox subunit, composed of 390 amino acids, acts as a connector between the components of the membrane and cytoplasm and is essential for NADPH oxidase activation [16] and interstitial fibrosis [17]. MDA, the lipid peroxidate product, is used as a measure of the body’s oxidative levels. SOD is a vital antioxidant enzyme and effectively clears free oxygen radicals. In our study, we found that RDN reduced the high level of oxidative stress after MI. In addition, the activity of ASAFR in dogs from the MI + RDN group was lower than in those from the MI group. Regarding this phenomenon, we propose that RDN reduces the myocardial oxidative level mainly through decreasing the generation of superoxide rather than increasing the activity of ASAFR, which clears superoxide production.
It is well known that chronic sustained sympathetic over-activity results in the aggravation and deterioration of HF. Previously published studies have shown that RDN can reduce HR, NE overflow and muscle SNS activity [18–20]; meanwhile, RDN has also demonstrated beneficial effects in various conditions with high SNS activity, such as resistant hypertension, HF, malignant arrhythmia, impaired glucose tolerance and chronic renal dysfunction [1, 21–23]. Research has further demonstrated that TH-positive nerves can be used as an
**Fig. 3** a TH immunohistochemical staining at the infarct border zone of nerve fibres (×400). Compared with the control group, the TH nerve fibres in the MI and MI + RDN groups were increased. However, after treatment with RDN, the quantity of TH nerve fibres was significantly decreased, and an orderly appearance of fibres was observed. b Expression of TH-positive nerves in cardiac tissues. * P < 0.05 vs. control group # P < 0.05 vs. MI group.
### Table 4 Correlation analysis
| | TH (IHS) | AngII (pg/mL) | Ang(1–7) (pg/mL) |
|------------------|----------|---------------|------------------|
| MDA (nmol/mg prot) | 0.900 | 0.876 | 0.832 |
| SOD (nmol/mg prot) | −0.818 | −0.674 | −0.806 |
indirect indicator of sympathetic activity [24]. In our research, the effectiveness of removing sympathetic nerve activity by RDN was demonstrated by the decrease in TH-positive fibres in renal tissues. Moreover, the relative expression of TH nerve fibres, which reflects the local activity of the SNS, was also down-regulated in cardiac tissue, suggesting that RDN lowered the over-activation of the SNS in myocardial tissues.
The RAS is also a crucial mediator of myocardial fibrosis, pathological hypertrophy and HF [25, 26]. The adverse effects of the RAS on cardiovascular disease are mainly due to increased AngII, which exerts its effects through the classical ACE-AngII-AT1R axis. Importantly, the ACE2-Ang(1–7)-MasR axis, known as an endogenous counter-regulator of the RAS, has been confirmed to be protective in CHF [27]. The development of cardiovascular disease has been found to involve to both axes of the RAS [28]. ACE2’s major biological function is converting AngII into Ang(1–7), which is the physiological antagonist of AngII [29–31]. Ang(1–7) exerts vasodilatory, anti-proliferative, anti-inflammatory, and protective effects through activation of MasR. Previous studies have shown that ACE2 is increased in MI or HF [32–35]. As reported previously, the ACE2 gene was upregulated in HF patients and was associated with the degree of LVEDD and LVEF loss [36]. In agreement with previous investigations, our study showed that AngII and the compensatory ACE2-Ang(1–7)-MasR axis were increased in MI dogs, although these changes were reversed by ablation of renal sympathetic nerves. The exact mechanisms for the decreased expression of ACE2-Ang(1–7)-MasR after RDN are not fully understood; we speculate that RDN effectively inhibits LV dilatation and modifies cardiac function by reducing the activation of AngII to a significantly higher degree, which in turn leads to a relatively weakened compensatory mechanism. Importantly, a previous study reported that the enhanced ACE2 and Ang(1–7) levels were significantly increased in MI + RDN group compared with MI and control groups.
**Fig. 4 a** TH immunohistochemical staining of nerve fibres in renal tissue (×400). Compared with the MI group, the density of TH nerve fibres was decreased in the MI + RDN group; no difference was observed between the control and MI + RDN groups. **b** Expression of TH-positive nerves in renal tissues. # P < 0.05 vs. MI group.
**Fig. 5** Serum creatinine levels at 4 weeks post-MI in each group. No differences were observed in serum creatinine among the three groups.
Cardiac SNS, RAS and oxidative stress mutually influence each other. AngII-induced phosphorylation of p47phox [16] and myocardial hypertrophy induced by ROS mediate various signalling pathways [37]. Moreover, the AngII type 1 receptor (AT1R) blocker irbesartan and Ang(1–7) blocked NADPH oxidase activation and thus restored systolic function and cardiac flow in an animal study [38, 39]. Other studies have shown that ROS increase SNS activity both in the central and peripheral nervous systems [40]. In our study, we found that RDN lowered the expression of AngII, MDA and TH-positive nerve fibres in the heart, and the change in MDA was positively correlated with AngII and TH. Our preliminarily hypothesis is that RDN improves cardiac function by reducing the activity of the cardiac AngII-ROS-SNS axis, which needs to be confirmed in future research.
Safety issues related to the procedure for RDN have attracted great attention. The REACH Pilot study evaluated the safety of RDN for HF, and no significant reduction in blood pressure or other haemodynamic disturbances were observed [1]. Mahfoud et al. found that RDN reduced the renal resistance index without decreasing the glomerular filtration rate (GFR), and no renal artery stenosis or dissection was recorded [41]. Hering et al. demonstrated that RDN had no negative influence on patients with renal insufficiency [23]. In the present study, the LVSP and serum creatinine level showed no significant difference after RDN compared with the non-RDN treated group, thereby demonstrating the short-term safety of the RDN procedure.
Conclusion
RDN exerts a protective effect against acute MI, which may be attributed to antioxidant effects and a decrease in the local activity of the SNS and RAS. In conclusion, RDN may serve as a new therapeutic treatment for MI patients by blocking these adverse mechanisms.
Limitations
With regard to our study, some limitations should be considered. First, myocardial infarction was only validated by the pathological specimen and echocardiography, and we did not evaluate the infarct size, which reduces the persuasion to a certain extent. Second, the number of subjects was not large enough, which may have affected our statistical analysis. Third, due to lack of a control + RDN group, the effects of the intervention could not be excluded completely. Finally, the observation time was short. To confirm the validity of these results, studies both in humans and animals should be undertaken on a larger scale and with a longer observation time.
Abbreviations
ACE2: Angiotensin converting enzyme 2; ACEI: Angiotensin-converting enzyme inhibitors; AMI: Acute myocardial infarction; Ang(1–7): Angiotensin 1 through 7; AngII: AngiotensinII; ARB: Angiotensin receptor blockers; ASA: Anti-superoxide anion free radical; AT1R: AngII type 1 receptor; CHF: Chronic heart failure; ELISA: Enzyme-linked immunosorbent assay; FS: Fraction shortening; GFR: Glomerular filtration rate; HR: Heart rate; IHS: Immunohistochemical score; LVEDD: Left ventricular end-diastolic dimension; LVEDP: Left ventricular end-diastolic pressure; LVEF: Left ventricular ejection fraction; LVED: Left ventricular end-systolic dimension; LVSP: Left ventricular systolic pressure; MasR: Mas receptor; MDA: Malondialdehyde; NADPH: Adenine dinucleotide phosphate; NE: Noradrenaline; OPCR: Quantitative PCR; RAS: Renin-angiotensin system; RDN: Renal sympathetic denervation; RF: Radio frequency; RT-PCR: Real-time reverse transcription polymerase chain reaction; SNS: Sympathetic nervous system; SOD: Superoxide dismutase; TH: Tyrosine hydroxylase
Acknowledgements
We thank all the researchers who participated in this work.
Funding
This work was supported by the research plan of the Tianjin Application Foundation and Advanced Technology (NO.14JCYJQC26100) and the Science and Technology foundation of Tianjin Health and Family Planning Committee (NO.15KG131 and NO.2014KY11).
Availability of data and materials
Data sharing is not applicable to this article as no datasets were generated during the current study.
Authors’ contributions
Study design and model building: CL, LS and CL. Data collection: LS and LW. Data analysis: QF and RU. Manuscript writing: QF and CL. Final approval of the manuscript: CL. All authors read and approved the final manuscript.
Competing interests
The authors declare that they have no competing interests.
Consent for publication
Not applicable.
Ethics approval
All experimental protocols were approved by the local animal care and use committee (the Animal Experimental Ethics Association of Tianjin First Centre Hospital). The methods were carried out in accordance with the approved guidelines.
Author details
1First Center Clinic College of Tianjin Medical University, Tianjin First Central Hospital, Tianjin, China. 2Department of Cardiology, Tianjin First Central Hospital, 24 Fukang Road, Nankai District, Tianjin 300192, China. 3Department of Digestion, Tianjin First Central Hospital, Tianjin, China.
Received: 21 June 2016 Accepted: 9 February 2017
Published online: 17 February 2017
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Wake pattern and wave resistance for anisotropic moving objects
Michael Benzaquen¹, Alexandre Darmon² and Elie Raphaël¹†
¹PCT, UMR CNRS 7083 Gulliver, ESPCI ParisTech, 10 rue Vauquelin, 75005 Paris, France
²EC2M, UMR CNRS 7083 Gulliver, ESPCI ParisTech, 10 rue Vauquelin, 75005 Paris, France
(Received 8 April 2014)
We present a theoretical study of gravity waves generated by an anisotropic moving disturbance. We model the moving object by an elliptical pressure field of given aspect ratio $W$. We study the wake pattern as a function of $W$ and the longitudinal hull Froude number $Fr = V/\sqrt{gL}$, where $V$ is the velocity, $g$ the acceleration of gravity and $L$ the size of the disturbance in the direction of motion. For large hull Froude numbers, we analytically show that the rescaled surface profiles for which $\sqrt{W}/Fr$ is kept constant coincide. In particular, the angle outside which the surface is essentially flat remains constant and equal to the Kelvin angle, and the angle corresponding to the maximum amplitude of the waves scales as $\sqrt{W}/Fr$, thus showing that previous work on the wake’s angle for isotropic objects can be extended to anisotropic objects of given aspect ratio.
We then focus on the wave resistance and discuss its properties in the case of an elliptical Gaussian pressure field. We derive an analytical expression for the wave resistance in the limit of very elongated objects, and show that the position of the speed corresponding to the maximum wave resistance scales as $\sqrt{gL}/\sqrt{W}$.
1. Introduction
The influence of Lord Kelvin’s theory [Kelvin 1887] on the study of water waves and particularly on the wake pattern that falls behind an object moving at constant speed is no longer to be proved. His work revealed a certain universality of the wake pattern, that everyone can notice when looking at the waves produced by objects as different as swans or sailing boats. One of his most remarkable results concerns the well-known constant wake angle $\phi_K \simeq 19.47^\circ$, delimiting a region outside which the water remains essentially unperturbed. Since Lord Kelvin’s first results, a lot of efforts have been done to extend his work [Lighthill 1978, Barnell & Noblesse 1986, Lamb 1993, Johnson 1997], for instance to nonlinear waves [Dias & Kharif 1999], or waves in the presence of vorticity [Ellingsen & Brevik 2014, Ellingsen 2014]. Recently the constancy of the wake angle has been contested [Rabaud & Moisy 2013]. Indeed, in their analysis of airborne images, Rabaud and Moisy showed that, for large hull Froude numbers $Fr = V/\sqrt{gL}$, where $V$ is the object velocity, $g$ the acceleration of gravity and $L$ the typical size of the object in the direction of motion, the angle of the wake decreases and scales as $1/Fr$. In response to these intriguing observations, we recently [Darmon et al. 2014] presented an analytical study of the wake pattern as a function of the Froude number and showed that the delimiting angle of the wake actually remains constant for all $Fr$, therefore comforting Lord Kelvin’s theory. We also provided an explanation to the airborne observations of Rabaud and Moisy by analytically proving that, for an axisymmetric object of typical
† Email address for correspondence: [email protected]
size $L$, the angle corresponding to the maximum amplitude of the waves decreases as $Fr$ is increased, scaling as $1/Fr$ for large Froude numbers.
The main issue that arose from our previous study (Darmon et al. 2014) is that an axisymmetric object does not correctly reflect the real geometry of boats (Dias 2014). Indeed, boats have elongated shapes with aspect ratios typically ranging between 0.1 and 0.5, with the exception of overcrafts which actually display a cylindrical symmetry. For elongated objects, the emphasis has been placed on the planing regime in the limit of small aspect ratios (Casling 1978; Taravella & Vorus 2011). The important feature that needs to be considered when it comes to hull design, is the so-called wave resistance, or wave drag, a force resulting from the generation of surface waves. Indeed, a well profiled hull notably reduces the wave resistance thus improving the velocity performances of the ship. Along with wake patterns, wave resistance has been widely studied both at practical (Peri et al. 2001; Darrigol 2005) and theoretical levels (Havelock 1908; Wehausen 1973; Lighthill 1978).
We here present a theoretical study on anisotropic moving objects. In the first part, we focus on the wake pattern. After recalling the main ingredients of the physical model, we calculate the surface displacement induced by an elliptical moving pressure distribution and discuss its main features. In particular, we investigate the universality of the wake pattern as a function of the aspect ratio of the moving disturbance and the longitudinal hull Froude number. In the second part, we derive the expression of the wave resistance for an anisotropic moving disturbance and focus on the case of an elliptical Gaussian pressure field. In the limit of very elongated objects, we obtain interesting analytical results on the scaling of the velocity corresponding to the maximum of the wave resistance.
2. Wake pattern
For gravity waves, the surface displacement generated by a pressure field $p(x, y)$ moving in the $-x$ direction with constant speed $V$ can be written in the frame of reference of the moving perturbation as (Havelock 1908, 1919; Darmon et al. 2014):
$$\zeta(x, y) = -\lim_{\varepsilon \to 0} \int \int \frac{dk_x dk_y}{4\pi^2 \rho} \frac{\hat{p}(k_x, k_y) e^{-i(k_x x + k_y y)}}{\omega(k)^2 - V^2 k_x^2 + 2i\varepsilon K k_x^2},$$
where $k = (k_x^2 + k_y^2)^{1/2}$, $\hat{p}(k_x, k_y)$ is the Fourier Transform of $p(x, y)$, $\rho$ is the water density and $\omega(k) = (gk)^{1/2}$ is the dispersion relation for pure gravity waves. Let us nondimensionalise the problem through $x = LX; y = LY; k_x = K_X/L; k_y = K_Y/L; k = K/L; p = pgLP; \hat{p} = pgL^3\hat{P}; \varepsilon = (gL)^{1/2} \varepsilon$ where $L$ is the typical size of the pressure field $p(x, y)$ in the direction of motion. This yields $\zeta(x, y) = (L/4\pi^2) Z(X, Y)$ where:
$$Z(X, Y) = -\lim_{\varepsilon \to 0} \int \int dK_X dK_Y \frac{K_Y \hat{P}(K_X, K_Y) e^{-i(K_X X + K_Y Y)}}{K - Fr^2 K_X^2 + 2i\varepsilon Fr K_X^2},$$
and where $Fr = V/\sqrt{gL}$ is the longitudinal hull Froude number. In order to account for the anisotropic geometry of a real ship’s hull in a simple manner, we consider an elliptical pressure field of the form:
$$P(X, Y) = F \left( X^2 + \frac{Y^2}{W^2} \right)$$
(2.3)
where $W = l/L$ is the aspect ratio of the ellipse of major diameter $L$ and minor diameter $l$. Consistently with this choice, we let the elliptical change of variables:
$$X = \tilde{R} \cos \tilde{\varphi} \quad K_X = \tilde{K} \cos \tilde{\theta}$$
$$Y = W\tilde{R} \sin \tilde{\varphi} \quad K_Y = W^{-1}\tilde{K} \sin \tilde{\theta}.$$ \hspace{1cm} (2.4)
This leads to $Z(X,Y) = Z(\tilde{R},\tilde{\varphi})$ where:
$$Z(\tilde{R},\tilde{\varphi}) = -\lim_{\varepsilon \to 0} \int K dK d\tilde{\theta} \frac{\sqrt{W^2 \cos^2 \tilde{\theta} + \sin^2 \tilde{\theta}} \tilde{P}(\tilde{K}) e^{-i\tilde{K} \tilde{R} \cos(\tilde{\theta} - \tilde{\varphi})}}{\sqrt{W^2 \cos^2 \tilde{\theta} + \sin^2 \tilde{\theta}} - V \tilde{K} \cos^2 \tilde{\theta} + 2i V \sqrt{W} \cos \tilde{\theta}},$$ \hspace{1cm} (2.5)
and where $V = Fr\sqrt{W}$ and $\tilde{P}(\tilde{K}) = W^{-1}\tilde{P}(K_X,K_Y)$. The interest of the elliptical change of variables in Eq. (2.5) is that the Fourier transform of the pressure field is now a function of the single variable $\tilde{K}$. This, as we shall see later, implies that our previous derivation with an axisymmetric pressure field (Darmon et al. 2014) is applicable to the case of an elliptical pressure field. Using the Sokhotski-Plemelj formula (see e.g. [Appel 2007]) to perform the integral over $\tilde{K}$ yields $Z(\tilde{R},\tilde{\varphi}) = Z_0(\tilde{R},\tilde{\varphi}) + G(\tilde{R},\tilde{\varphi})$ where $G(\tilde{R},\tilde{\varphi})$ is a rapidly decreasing function with the distance to the perturbation and where:
$$Z_0(\tilde{R},\tilde{\varphi}) = i\pi \int_{-\pi/2}^{\pi/2} d\tilde{\theta} \frac{(W^2 \cos^2 \tilde{\theta} + \sin^2 \tilde{\theta}) \tilde{P}(\tilde{K}_0) e^{-i\tilde{K}_0 \tilde{R} \cos(\tilde{\theta} - \tilde{\varphi})}}{V^4 \cos^4 \tilde{\theta}},$$ \hspace{1cm} (2.6)
where $\tilde{K}_0 = \sqrt{W^2 \cos^2 \tilde{\theta} + \sin^2 \tilde{\theta}}/(\sqrt{V^2 \cos \tilde{\theta}})$. The integral in Eq. (2.6) is of the form $\int d\tilde{\theta}H(\tilde{\theta}) e^{i\phi(\tilde{\theta})}$ and may be approximated through the method of the steepest descent. For $\tilde{R}/V > 1$, the integrand oscillates rapidly and there are two stationary points $\tilde{\theta}_1$ and $\tilde{\theta}_2$ given by $\phi'(\tilde{\theta}) = 0$. One can then write $Z_0(\tilde{R},\tilde{\varphi}) \simeq i\pi(Z_{01}(\tilde{R},\tilde{\varphi}) + Z_{02}(\tilde{R},\tilde{\varphi}))$, where $Z_{01}$ corresponds to the transverse waves and $Z_{02}$ corresponds to the diverging waves. For large Froude numbers, the transverse waves vanish compared to the diverging waves (Darmon et al. 2014), so that within this limit we shall only consider the latter:
$$Z_{02}(\tilde{R},\tilde{\varphi}) = Q(\tilde{R},\tilde{\varphi}) e^{i(\phi(\tilde{R},\tilde{\theta}_2(\tilde{\varphi}))+\frac{i\pi}{2})},$$ \hspace{1cm} (2.7)
where $Q(\tilde{R},\tilde{\varphi})$ is the envelope of the wave signal:
$$Q(\tilde{R},\tilde{\varphi}) = \sqrt{\frac{2\pi}{|\partial^2\phi(\tilde{R},\tilde{\theta}_2(\tilde{\varphi})),\tilde{\varphi}|}} H(\tilde{\theta}_2).$$ \hspace{1cm} (2.8)
For small elliptical angles $\tilde{\varphi}$, the stationary point $\tilde{\theta}_2$ reads $\tilde{\theta}_2(\tilde{\varphi}) = \pi/2 + 2\tilde{\varphi}$, and the envelope $Q(\tilde{R},\tilde{\varphi})$ of the waves eventually becomes in the small $\tilde{\varphi}$ approximation:
$$Q(\tilde{R},\tilde{\varphi}) \simeq \frac{1}{4} \frac{\pi}{\tilde{R}} \frac{1}{V^3 \tilde{\varphi}^{5/2}} \tilde{P} \left( \frac{1}{4 V^2 \tilde{\varphi}^2} \right).$$ \hspace{1cm} (2.9)
It is worth mentioning here that we recover a very similar expression to that of the isotropic case (Darmon et al. 2014), where the hull Froude number $Fr$ has been replaced by $V$, and $\varphi$ by $\tilde{\varphi}$. Let us now change the variables back to real polar coordinates $(R,\varphi)$:
$$R = \tilde{R} \left( \cos^2 \tilde{\varphi} + W^2 \sin^2 \tilde{\varphi} \right)^{1/2}$$ \hspace{1cm} (2.10a)
$$\varphi = \arctan(W \tan \tilde{\varphi}).$$ \hspace{1cm} (2.10b)
For small angles, Eqs. (2.10) become:
$$R \simeq \tilde{R}$$ \hspace{1cm} (2.11a)
Combining Eq. (2.9) and Eq. (2.11) and defining the rescaled envelope in real polar coordinates \( Q(R, \varphi) = \sqrt{\mathcal{W}} \tilde{Q}(\tilde{R}, \tilde{\varphi}) \) one gets:
\[
Q(R, \varphi) \simeq \frac{1}{4} \sqrt{\frac{\pi}{R}} \frac{U^3}{\varphi^{5/2}} \tilde{P} \left( \frac{U^2}{4 \varphi^2} \right), \tag{2.12}
\]
where \( U = \mathcal{W} \mathcal{V}^{-1} = \sqrt{\mathcal{W}} Fr^{-1} \). This shows that the rescaled envelope \( Q(R, \varphi) \) depends on the aspect ratio \( \mathcal{W} \) and the rescaled Froude number \( \mathcal{V} \) only through the single variable \( \sqrt{\mathcal{W}} Fr^{-1} \). In other terms, for large Froude numbers and small angles, profiles resulting from moving disturbances with the same \( \sqrt{\mathcal{W}} Fr^{-1} \) coincide when multiplied by \( \sqrt{\mathcal{W}} \) (see Fig. 1). In particular the angle \( \varphi_{\text{max}} \) corresponding to the maximum amplitude of the waves reads:
\[
\varphi_{\text{max}} \sim \sqrt{\mathcal{W}} Fr. \tag{2.13}
\]
This explains why objects with very low aspect ratio, such as rowing boats, usually display a small maximum amplitude angle even though their longitudinal hull Froude number is not very high as they are propelled by man power.
To illustrate these analytical results, we then perform a numerical evaluation of the integral in Eq. (2.6) with an elliptical Gaussian pressure field whose dimensionless Fourier transform reads:
\[
\tilde{P}(K, \theta) = \frac{f_0}{\rho g L^3} \exp \left[ -\frac{K^2}{4\pi^2} \left( \cos^2 \theta + \mathcal{W}^2 \sin^2 \theta \right) \right], \tag{2.14}
\]
where \( f_0 \) is the total integrated pressure force. The resulting rescaled surface profiles are displayed in Fig. 1. Here, rescaled means multiplied by \( \sqrt{\mathcal{W}} \). Each relief plot corresponds to given values of \( Fr \) and \( \mathcal{W} \) and is plotted as a function of \( \tilde{X} = X/\Lambda \) and \( \tilde{Y} = Y/\Lambda \) where \( \Lambda = 2\pi Fr^{-2} \) is the dimensionless wavelength. The parameters \( Fr \) and \( \mathcal{W} \) are varied respectively along the horizontal axis and the vertical axis on a logarithmic scale. In all graphs the angle \( \varphi_{\text{max}} \) indicating the maximum amplitude of the waves is signified with a solid red line and the Kelvin angle \( \varphi_{\text{K}} \) with a black dashed line. On each diagonal, signified by a grey stripe, the value of the ratio \( U = \sqrt{\mathcal{W}} Fr^{-1} \) is kept constant. The first row (\( \mathcal{W} = 1 \)) corresponds to the isotropic case. Firstly, one can see that for any set of parameters \( (Fr, \mathcal{W}) \) the angle delimiting the region outside which the surface remains essentially flat is constant and equal to the Kelvin angle \( \varphi_{\text{K}} \). Secondly, on a given diagonal \( (\sqrt{\mathcal{W}} Fr^{-1} = cst) \), all the profiles seem identical to the naked eye, therefore comforting the analytical results found in the previous section. Finally, looking closely, one can note that the agreement between different profiles on the same diagonal becomes all the more true as we go towards higher values of \( Fr \), as predicted by the analytical study.
3. Wave Resistance
The waves generated by the moving disturbance continually remove energy to infinity. This translates into a drag force $R$ experienced by the disturbance, often referred to as the wave drag or the wave resistance. We here investigate the wave resistance experienced by the disturbance, using the method proposed by Havelock (Havelock [1908, 1919]), according to whom the wave resistance is the total resolved pressure in the direction of
motion:
$$R = - \int \int dx \, dy \, p(x, y) \, \partial_z \zeta(x, y) \, .$$ \hspace{1cm} (3.1)
Inserting Eq. (2.1) into Eq. (3.1) yields (Raphaël & de Gennes 1996):
$$R = \lim_{\varepsilon \to 0} \int \int \frac{dk_x \, dk_y}{4\pi^2 \rho} \, \frac{ik_x \, k \, |p(k_x, k_y)|^2}{\omega^2(k) - V^2 k_y^2 + 2i\varepsilon \, V \, k_x} \, .$$ \hspace{1cm} (3.2)
Changing to dimensionless variables consistently with the previous section, switching to polar coordinates, and inserting the dimensionless elliptical Gaussian pressure field defined in Eq. (2.14) into Eq. (3.2) leads to:
$$R = \lim_{\varepsilon \to 0} \left( \frac{f_0^2}{4\pi^2 \rho \, l^3} \int \int dk \, d\theta \, \frac{iK^2 \, \cos \theta \, \exp \left( - \frac{K^2}{2\pi^2} \left( \cos^2 \theta + \frac{W^2}{2} \sin^2 \theta \right) \right)}{1 - Fr^2 \, K \, \cos^2 \theta + 2i\varepsilon \, Fr \, \cos \theta} \right) \, .$$ \hspace{1cm} (3.3)
Performing the integral over $K$ in Eq. (3.3) yields:
$$R = \frac{f_0^2}{2\pi \rho \, l^3} \, f(V, W) \, ,$$ \hspace{1cm} (3.4)
where:
$$f(V, W) = \frac{W^3}{V^6} \, \int_0^{\pi/2} \frac{d\theta}{\cos^5 \theta} \, \exp \left( - \frac{W^2}{2\pi^2 V^4} \left( \frac{W^2}{\alpha^4} + \frac{1}{\alpha^2} \right) \right) \, .$$ \hspace{1cm} (3.5)
Equations (3.4) and (3.5) are central as they give the wave resistance of an elliptical Gaussian pressure field as a function of the dimensionless parameters $V$ and $W$. In order to seek for a limit form of the wave resistance at low aspect ratios, and guided by the fact that the integrand is dominant in the vicinity of $\pi/2$, this being all the more true for large values of $V$ and small values of $W$, we develop the integrand in the vicinity of $\pi/2$ at the lowest relevant order in $\theta$ and let the change of variables $\alpha = \pi/2 - \theta$. This yields:
$$f(V, W) \simeq \frac{W^3}{V^6} \, \int_0^{\pi/2} \frac{d\alpha}{\alpha^5} \, \exp \left( - \frac{W^2}{2\pi^2 V^4} \left( \frac{W^2}{\alpha^4} + \frac{1}{\alpha^2} \right) \right) \, .$$ \hspace{1cm} (3.6)
Furthermore, aiming for a Gaussian like analytical integral, we let the change of variables $m = 1/\alpha^2$. This leads to:
$$f(V, W) \simeq \frac{W^3}{2V^6} \, \int_{4/\pi^2}^\infty dm \, m \, \exp \left( - \frac{W^2}{2\pi^2 V^4} \left( W^2 m^2 + m \right) \right) \, .$$
$$\simeq e^{- \frac{2W^2 + \pi^2}{8V^2 W}} \, \left[ 4\pi^2 V^2 - \pi^3/2 \sqrt{2} \, e^{(\pi^2 + 8W^2)/2 \pi^2 V^4} \, \text{erfc} \left( \frac{\pi^2 + 8W^2}{2\pi \sqrt{2} V^2} \right) \right] \, ,$$ \hspace{1cm} (3.7)
where $\text{erfc} = 1 - \text{erf}$ is the complementary error function (Abramowitz & Stegun 2012).
In the limit of small aspect ratios $W$, $f(V, W)$ scales as $1/W$ and:
$$\lim_{W \to 0} W \, f(V, W) = \frac{\pi^2}{2V^2} \, \frac{\pi^3/2 \sqrt{2}}{8V^4} \, \exp \left( \frac{1}{8\pi^2 V^4} \right) \, \text{erfc} \left( \frac{1}{2\pi \sqrt{2} V^2} \right) \, .$$ \hspace{1cm} (3.8)
Equation (3.8) provides an analytical limit of the wave resistance at very low aspect ratios $W$. The fact that this limit is independent of $V$ shows that $V$ is the relevant variable to describe the problem of anisotropic moving objects. Figure 2 displays $W \, f(V, W)$ as
given by Eq. (3.7) as a function of \( \mathcal{V} \) for different values of the aspect ratio \( \mathcal{W} \). The red dashed curve corresponds to the limit regime \( \mathcal{W} \to 0 \) as given analytically by Eq. (3.8).
As one can see, the curves converge to the limit regime \( \mathcal{W} \to 0 \) as the aspect ratio is decreased, the convergence being faster at large \( \mathcal{V} \). In the limit of small aspect ratios, the position of the maximum of wave resistance \( \mathcal{V}_{\text{max}} \) is obtained numerically by solving \( \frac{d}{d\mathcal{V}} (\lim_{\mathcal{W} \to 0} \mathcal{W} f(\mathcal{V}, \mathcal{W})) = 0 \); one gets \( \mathcal{V}_{\text{max}} \simeq 0.3702 \). Recalling that \( \mathcal{V} = \mathcal{F}_r \sqrt{\mathcal{W}} \), one has the scaling of the position of the maximum of wave resistance in terms of Froude number:
\[
\mathcal{F}_r_{\text{max}} \sim \frac{1}{\sqrt{\mathcal{W}}} ,
\]
or identically in terms of real speed:
\[
\mathcal{V}_{\text{max}} \sim \sqrt{\frac{gL}{\mathcal{W}}} = \sqrt{gL} \sqrt{\frac{L}{l}} .
\]
It is known that for cylindrical objects of size \( L \), the position of the maximum of wave resistance scales as \( \sqrt{gL} \) (Stoker 1992). Equation (3.10) shows that in our case, the scaling is that of the cylindrical object multiplied by the square root of the inverse aspect ratio. Note that, in order to discuss the amplitude of wave resistance rather than the position of its maximum, one must prescribe how the total integrated force \( f_0 \) behaves with the dimensions of the distribution. For example, one could have \( f_0 \) proportional to the area \( Ll = L^2 \mathcal{W} \), and given that the wave resistance behaving as \( f_0^2 \), the relevant quantity to plot would be \( \mathcal{W}^2 f(\mathcal{V}, \mathcal{W}) \).
4. Conclusion
In this study, we performed a theoretical analysis of the wake pattern and the wave resistance of an anisotropic moving disturbance. In order to account for anisotropy in a simple manner, we modelled the disturbance by an elliptical pressure distribution. In section 2, we derived the expression of the surface displacement and analysed it as a function of two relevant dimensionless parameters. We showed that the angle delimiting the wake region remains constant and equal to the Kelvin angle $\varphi_K = 19.47^\circ$; and that, at large Froude numbers, the angle corresponding to the maximum amplitude of the waves scales as $\sqrt{W/\text{Fr}}$ where $W$ is the aspect ratio of the elliptical disturbance and $\text{Fr}$ is the longitudinal hull Froude number. This notably extends the results of our previous study [Darmon et al. 2014] that focused on isotropic moving objects. In section 3, we derived the expression of the wave resistance for an elliptical Gaussian pressure field and analysed it as a function of the same relevant dimensionless parameters. We obtained a limit analytical expression for the case of very small aspect ratios, and showed that the position of the maximum of wave resistance in terms of real speed scales as that of a cylindrical object multiplied by the square root of the inverse aspect ratio. We believe this study is of interest as it reveals the main physical features of waves created by anisotropic moving objects, closer to the real geometry of ships than axisymmetric objects.
5. Acknowledgements
We wish to thank A. C. Maggs for fruitful discussions.
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Effect of line defects on the electrical transport properties of monolayer MoS\textsubscript{2} sheet
Amretashis Sengupta\textsuperscript{1∗}, Dipankar Saha\textsuperscript{1}, Thomas A. Niehaus\textsuperscript{2}, Santanu Mahapatra\textsuperscript{1}
\textsuperscript{1}Nano Scale Device Research Laboratory, Department of Electronic Systems Engineering, Indian Institute of Science, Bangalore 560012, India
\textsuperscript{2}Institute I - Theoretical Physics, University of Regensburg, 93040 Regensburg, Germany
(Dated: January 21, 2014)
We present a computational study on the impact of line defects on the electronic properties of monolayer MoS\textsubscript{2}. Four different kinds of line defects with Mo and S as the bridging atoms, consistent with recent theoretical and experimental observations are considered herein. We employ the density functional tight-binding (DFTB) method with a Slater-Koster type DFTB-CP2K basis set for evaluating the material properties of perfect and the various defective MoS\textsubscript{2} sheets. The transmission spectra is computed with a DFTB-Non-Equilibrium Greens Function (NEGF) formalism. We also perform a detailed analysis of the carrier transmission pathways under a small bias and investigate the phase shifts in the transmission eigenstates of the defective MoS\textsubscript{2} sheets. Our simulations show a 2-4 folds decrease in carrier conductance of MoS\textsubscript{2} sheets in the presence of line defects as compared to that for the perfect sheet.
I. INTRODUCTION
Two dimensional (2-D) transition metal dichalcogenides, especially MoS\textsubscript{2} has shown great promise as an alternate channel material for next generation electron devices \cite{1,2} due to their intrinsic non-zero band gap, which gives them a distinct advantage over graphene for logic circuit applications. Apart from this, 2-D materials offer enhanced electrostatic integrity, optical transparency and mechanical flexibility. Thus a great activity, in both experimental and computational research, has started to understand the electrical properties of atomically thin, layered MoS\textsubscript{2} crystals \cite{1-8}.
Although a number of studies have been conducted on possible enhancement/ degradation of MoS\textsubscript{2} electrical properties, not much focus has been given to defects and deformations in MoS\textsubscript{2} sheets. Point defects, dislocations, grain boundary effects can significantly impact the carrier transport in 2-D MoS\textsubscript{2} channels. Intrinsic crystallographic faults like line defect in single layer MoS\textsubscript{2} can occur due to stoichiometry changes in the S shell during fabrication. Recently Enyashin et. al. \cite{6} have reported experimental results on the various type of line defects present in 2-D MoS\textsubscript{2}. However their report is more focussed on defect formation and dynamics, rather than examining how such defects could alter the electrical properties of MoS\textsubscript{2} sheets. This paper reports a computational study on the impact of such line defects on the electrical transport properties of monolayer MoS\textsubscript{2} sheets. We investigate four different types of line defects with the density functional tight-binding (DFTB) method in QuantumWise ATK. We compute the density of states (DOS), transmission spectra, transmission eigenstates and the pathways for electron and hole transport in such defective and perfect sheets.
II. METHODOLOGY
Fig. 1 shows the various line defects in sheets of 2-D MoS\textsubscript{2} considered for our studies. We consider a monolayer MoS\textsubscript{2} sheet having length of 5 nm and width of 2.5 nm. Such supercell dimensions are considered sufficient for accurately simulating the electronic properties of a periodic sheet of MoS\textsubscript{2} as reported by other groups \cite{9-12}. As shown in Fig. 1, the first type of defect henceforth referred to as defect-I has two zigzag edges joined in a bridging network of both S and Mo atoms. Defects-II and III have only Mo, as the bridging atom. Defect-III, differs from defect-II in the sense of the presence of an additional almost Stone-Wales type defect in the bridging Mo atoms alternating honeycombs. Defect IV consists of only S as the bridging atom and does not display any other variants as in defect-III. The defects are consistent with the results of Enyashin et. al. [6]
To calculate the electrical properties of our supercell we employ density functional tight binding (DFTB) theory in QuantumWise ATK 13.8.0 \cite{13}. We use a 9×1×9 Monkhorst-Pack k-grid \cite{14} and employ the Slater-Koster
The density matrix \[ \mathcal{R} \] used to solve the Poisson equation is given by
\[
[\mathcal{R}] = \int_{-\infty}^{\infty} \frac{dE}{2\pi} A(E,k,x) f_0(E_k,x - \eta)\]
where \( A(E_k,x) \) is the spectral density, \( E_k,x \) the energy of the conducting level, \( \eta \) being the chemical potential of the contacts, \( f_0(\cdot) \) is the Fermi function. For NEGF studies, a multi-grid poisson solver is employed using Dirichlet boundary conditions on the left and right faces (i.e. the electrodes) and periodic boundary conditions along the width of the supercell. The electrode temperatures are considered 300 K. The carrier density \( n_{tot} \) is evaluated from the NEGF formalism and put into the Poisson solver to self-consistently and iteratively evaluate the potential \( U_{SCF} \). The converged values of the carrier density and the self-consistent potential are used to calculate the transmission matrix \( \mathcal{I}(E,V) \)
\[
\mathcal{I}(E,V) = \text{trace}[A_L \varphi_R] = \text{trace}[A_R \varphi_L] \]
For the transmission spectra we use the Krylov self-energy calculator [13] with the average Fermi level being set as the energy zero parameter.
The transmission pathways are evaluated by splitting the transmission coefficient into local bond contributions \( \mathcal{I}_{i,j} \). The pathways are such that, if the system is divided into 2 parts \( a \) and \( b \) then the pathways across the boundary between \( a \) and \( b \) sum up to the total transmission coefficient as [13,17,18]
\[
\mathcal{I} = \sum_{i \in a, j \in b} \mathcal{I}_{i,j} \]
To find the transmission eigenstates of the sheet, the transmission matrix can be written as
\[
\mathcal{I}_{nm} = \sum_k t_{nk} t_{km}^\dagger \]
where \( t_{nk} \) is the transmission amplitude from Bloch state \( \psi_n \) in the left electrode to Bloch state \( \psi_k \) in the right electrode. The transmission coefficient is given by the trace of the transmission matrix \( \mathcal{I} = \sum_n \mathcal{I}_{nn} \). The transmission eigenstates are obtained by propagating the linear combination of the Bloch states
\[
\sum_n \ell_{\alpha,n} \psi_n \]
with transmission eigenvalue \( \lambda_{\alpha} \).
### III. RESULTS AND DISCUSSIONS
In Fig. 2 (a)-(b), we show the density of states (DOS) and the normalized transmission spectra of the perfect MoS\(_2\) sheet under consideration. From Fig. 2 (a) a forbidden gap of 1.84 eV is estimated between the valence band (VB) maxima and conduction band (CB) minima of the material. This is in accordance with reported band gap of 1.78 eV of perfect MoS\(_2\) sheets. [7]-[12] The most significant contributions to the DOS come from the p and d orbitals of Mo and S atoms. If we see the normalized transmission spectra for the perfect sheet as in Fig. 2 (b), we find two distinct peaks at 1.5 eV and -1.68 eV. Upon the application of a small bias of 0.2 V (on either the left or right electrode keeping the other terminal ground) we observe the edges of the transmission spectra drawing slightly closer to the Fermi level. This signifies availability of a greater number of conducting channels both in CB and VB.
In Fig 3, we have the DOS of the various defective sheets under consideration. Here we observe the states to be more evenly spread out, having much less sharper peaks in the DOS compared to perfect MoS\(_2\) sheet. The
defect states are seen to exist in considerable density even in the formerly forbidden gap of the perfect MoS$_2$. This indicates the possibility of a semiconductor to semi-metal transition (depending on the contribution of these defect states to the carrier transmittance) of the MoS$_2$ sheets in the presence of the line defects.
From the transmission spectra in Fig. 4 of the various sheets in the presence of the line defects, we observe that the staircase like behavior of the spectra (as seen for the perfect sheet) no longer persists and the defect states near the Fermi level (as seen in the DOS plots) do not contribute much to the number of transmission channels. To study the reason for this behavior we conduct studies on the transmission eigenstates and the carrier transmission pathways of the different sheets. It should be noted that the transmission spectra shown in Fig. 4, has been normalized in order to gain a better understanding of the relative contribution of various energy bands to the total transmission spectra of the MoS$_2$ sheets. We show mostly the region near the Fermi level of the spectra, since for small bias this is the most significant part of the transmission spectra that contributes to carrier transport. With a small applied bias on either left/ right terminal of the sheets, the contributions of the various available channels seem to undergo some minor redistribution. Under such bias, the transmission peaks, signifying most transparent channels for carrier conduction for defect-I are observed at 1.33 and -1.88 eV. For defect-II the peaks are at 1.56 eV and -1.92 eV, for defect III these are 1.54 eV, -1.72 eV and for defect IV the peaks are at 1.54 eV and -1.74 eV respectively.
In our studies we consider the elastic scattering in the channel for electron/ hole transport. Therefore it is of interest to look into the transmission eigenstates and the transmission pathways for the defective sheets. In order to visualize the transmission eigenstates and pathways we select the energy values corresponding to maximum transmission (as in Fig. 4) for each case. For the electron transmission eigenstates and the transmission pathways the energy state corresponding to the transmission peak on the VB are considered. For the hole transmission it is the energy state corresponding to the transmission peak on the CB that are considered.
From Fig. 5 (a)-(b), we see that there exists a certain periodic pattern in the phase of the transmission eigenstates for the perfect case. In the case of the line defects this periodic pattern is no longer preserved and a varying degree of randomness in phase sets in for both the electron and the hole transmission eigenstates. Among the defects in case of defect-II, there exists an interesting pattern of about $\frac{\pi}{2}$ phase shift of the peak transmission eigenstate across the line defect for electron transport. Also for the hole transmission eigenstate, there exist about $\frac{\pi}{2}$ phase difference across the line defect in defect II. It is defect-I that seems to have the most random variance of phase, followed by defect-IV and III. The high degree of randomization in the phase
of the transmission eigenstates due to the defects, can signify lesser transmission across the defective sheets, and suppress conductance of the defective sheets. Fig. 6 (a)-(b), shows the electron and hole transmission pathways for the various systems under consideration. The relative scale factor and the threshold values are as mentioned in the methodology section, and they are kept the same for all the pathway plots. From the plots we see that the pathways for electron and hole transmission at the respective CB and VB transmission peaks are identical in case of perfect sheet of MoS$_2$. This is in accordance with the closely matching values of electron and hole effective masses for perfect MoS$_2$ sheets as reported in our earlier work.[19] However for the line defects, the transmission pathways differ significantly for electrons and holes. In defect-I, the number of available transmission paths near the defect site seems more for electron transport compared to that for hole transport, also the magnitude of transmission through these pathways is higher compared to that for the holes. In defect-I the transmission path between the Mo atoms around the line defect has
FIG. 6. (a) Electron and (b) Hole transmission pathways plotted for an applied bias of 0.2 V, at the CB transmission peak for electrons and VB transmission peak for holes.
the highest magnitude of electron conductance as seen in Fig. 6(a). The same pathways do not seem equally conducive to hole transport, as evident from Fig. 6(b). However away from the defect site, there exist lesser number of paths for electrons than that for holes in defect-I.
For defect-II also, there exist a larger number of paths near the defect for electron transport than that for hole transport. Same is observed for defects-III and IV. Overall in all the defects we observe some highly electron conducting paths between the metallic atoms (Mo-Mo) around the defects. However for hole transport this route does not offer any enhanced carrier transport (Mo-Mo) around the defects. However for hole transport, the S-S pathway is weakly conducive in either electron or hole transport.
In Fig 7, we show the absolute value of transmission spectra of the perfect and the various defective sheets under a small applied bias of 0.2 V. It is worth mentioning here that the transmission spectra shown earlier in Fig. 2(b) and Fig. 4, are normalized to provide a better view of how the relative contribution of various energy bands to the total transmission of the channel (MoS$_2$ sheet) evolve under applied bias. In order to understand the carrier conductance through the channel, it is the absolute value of the transmission that is more significant than the normalized $\Sigma(E,V)$. As seen in the Fig 7 the magnitude of transmission through the perfect sheet is significantly larger than that for the defective ones. The defect states have a slight contribution to transmission near the energy levels of 1 eV and -1 eV, whereas the transmission for the perfect sheet in these regions is somewhat lesser. Also for the defective sheets the levels are less discrete and do not have the staircase behavior as in the perfect sheet. At the corresponding transmission peaks, the value of $\Sigma(E,V)$ for the perfect sheet is 2–4 times that of the various defective sheets.
This indicates a high degree of suppression of carrier transmission in presence of the line defects in MoS$_2$ sheet.
**IV. SUMMARY**
Here we report the impact of four different types of line defects on the electrical transport properties of mono-layer MoS$_2$ sheets. The defects with different configurations and Mo and S as the bridging atoms, based on recent experimental evidence, are studied with the DFTB-NEGF formalism for their transport behavior. Our studies show that although a moderate amount of defect states are induced near the Fermi level due to these line-defects, the carrier transport through these defect states is rather limited and the overall transmission is highly scattered in presence of these line defects. The suppressed carrier transmission is also reflected in the high degree of defect induced randomization in the phase of the transmission eigenstates. The lowering of transmission in the defective sheets and the elastic scattering at the defect centres were evident from the transmission pathways. Our studies show a sizeable decrease in carrier conductance in MoS$_2$ sheets due to the presence of line defects as compared to that for the perfect sheet. Such results are very significant considering the future application of MoS$_2$ monolayer sheets for MOSFET applications.
**ACKNOWLEDGMENTS**
Dr. A Sengupta thanks DST, Govt. of India, for the DST Post-doctoral Fellowship in Nano Science and Technology. This work was supported by the Department of Science and Technology, Government of India, under grant no: SR/S3/EECE/0151/2012.
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Chart-Text: A Fully Automated Chart Image Descriptor
Abhijit Balaji¹, Thuvaarakkesh Ramanathan, Venkateshwarlu Sonathi
SPI Technologies India Private Limited, Chennai, India
{B.Abhijit, R.Thuvaarakkesh, T.Venkateshwarlu}@spi-global.com
Abstract
Images greatly help in understanding, interpreting and visualizing data. Adding textual description to images is the first and foremost principle of web accessibility. Visually impaired users using screen readers will use these textual descriptions to get better understanding of images present in digital contents. In this paper, we propose Chart-Text a novel fully automated system that creates textual description of chart images. Given a PNG image of a chart, our Chart-Text system creates a complete textual description of it. First, the system classifies the type of chart and then it detects and classifies the labels and texts in the charts. Finally, it uses specific image processing algorithms to extract relevant information from the chart images. Our proposed system achieves an accuracy of 99.72% in classifying the charts and an accuracy of 78.9% in extracting the data and creating the corresponding textual description.
Keywords: Computer vision, Chart data extraction, Information retrieval, Object detection
1 Introduction
Images are an excellent medium for data representation and interpretation. For the images present in digital contents to be useful to people with visual challenges, it is mandatory for the content creators to provide a corresponding textual description. This process of providing textual description for an image is termed as Alternative Text (Alt-Text). These Alt-Texts are present as part of E-books and other similar digital contents that are read aloud to users with visual challenges using screen readers. This process of creating textual description for images is a highly time consuming manual process. Moreover, for the same image the textual description varies from person to person. Thus, standardizing these Alt-Texts poses a challenge. Hence, having a system that can create textual description of the images will boost the credibility and the productivity of the content creators. It also enhances the accessibility of the digital content to people with visual challenges.
To address this, we developed Chart-Text, a system that can create textual description given a chart image.
Our proposed Chart-Text system creates complete textual description of 5 different type of chart images namely: pie charts, horizontal bar charts, vertical bar charts, stacked horizontal bar charts and stacked vertical bar charts. Our system achieves an accuracy of 99.72% in classifying the charts and an accuracy of 78.9% in extracting the data and creating the corresponding Alt-Text.
The paper is organized as follows: First, we discuss a few related works in section 2. Then, we describe the dataset that we used to create the system in section 3. In section 4, we provide the proposed methodology for extracting information from chart images. Then, we provide the results along with sample input and outputs.
¹ - Corresponding Author
An interactive demo of the project is available at http://ml.spi-global.com:8000/
2 Related works
We built our system by leveraging past research works in areas such as image classification, object detection, localization and optical character recognition. A few different systems have been built using the above approaches. Most of these systems are semi-automated except for [1].
ReVision [2] is one of the initial systems developed for automatically redesigning charts to improve graphic depictions to help users in understanding the data better. It first classifies the type of chart and then uses traditional image processing algorithms to extract the marks and the data from the charts. Then, ReVision applies heuristics to map the marks and the related data extracted from the graphs. Finally, the system combines the existing information extracted from the charts and comes up with an easily decipherable visualization.
ChartSense [3] is a system similar to ReVision but has a better performance in classifying the chart type. This increase in performance is attributed to the deep learning based image classifier as compared to the traditional image processing based classifier in ReVision. ChartSense overall is a semi-automatic system that uses input from users to further improve detection accuracy. ChartSense applies an interactive data extraction algorithm most appropriate for the identified chart type. In addition, ChartSense provides a set of simple interactions to fine-tune the result, enabling more accurate data extraction.
Financial analysis includes many visualizations and scatter plots are widely used. To further facilitate data inspections, analysis and financial modeling, it is necessary to extract information from the scatter plots. Scatteract [1] is a fully automated solution developed to achieve the purpose of performing scatter plot data extraction. It combines deep learning and image-processing algorithms to identify the scatterplot components and OCR to extract the text information from the scatterplots.
3 Dataset
Chart-Text uses both image classification and object detection models, which require a large number of annotated images to train. To the best of our knowledge, there is no publicly available dataset that satisfies our needs. We chose to follow the method given in [1] and generated images using Matplotlib [4]. We generated 5000 training and 1000 testing images for each of pie charts, horizontal bar charts, vertical bar charts, stacked horizontal and stacked vertical bar charts. We used the same set of training images for the classifier and the object detector. Thus, we have five classes for classification: horizontal bar charts, vertical bar charts, stacked horizontal bar charts and stacked vertical bar charts and seven classes for object detection as given in Table 1. We randomized the plot aesthetics as given below. This is adopted from [1].
Plot aesthetics:
- Plot style (default styling values e.g. “classic”, “seaborn”, “ggplot”, etc.)
- Size and resolution of the plot
- Number of style variations on the points
- Point styles (markers, sizes, colors)
- Padding between axis and tick values, axis and axis-labels, and plot area and plot title
- Axis and tick’s locations
- Tick sizes if using non-default ticks
- Rotation angle of the tick values, if any
- Presence and style of minor ticks
- Presence and style of grid lines
- Font and size of the tick values
- Fonts, sizes and contents of the axis-labels and plot title
- Colors of the plot area and background area
Table 1. Labels present in the procedurally generated dataset for text position detection.
| Class | Presence in charts |
|-----------|----------------------------------------|
| Chart title | All charts |
| X value | Except pie charts |
| Y value | Except pie charts |
| X label | Except pie charts |
| Y label | Except pie charts |
| Label | Only pie charts |
| Legend | Randomly present in pie charts and definitely present in stacked horizontal and stacked vertical bar charts |
4 Chart-Text system:
Chart-Text system comprises a deep learning based classifier and a deep learning based object detector. The classifier identifies the type of the input chart and the object detector detects the various text regions in the charts. Optical character recognition is applied to extract the texts from the bounding boxes identified by the object detector. Further, the system extracts the relevant data from the charts using chart specific image processing algorithms. Finally, all extracted information is sent as input to predetermined text templates (one template per type of chart) to generate the final Alt-Text. We address each of the above steps in detail in the following sections.
4.1 Charts classification:
Recently, Deep Neural Networks (DNN), particularly Convolutional Neural Networks (CNNs) have excelled in recognizing objects in the images [5]. CNNs are a type of neural network architecture specially made to deal with image data. CNNs typically consist of Convolutional Layer, Max Pooling layer and Fully Connected layers. Convolution layer tangles nearby pixels to abstract their meaning. Pooling layer extracts representative specimens from the result of the convolution layer to reduce computational time. The fully connected layer does conventional neural network learning. Of different CNN architectures available publicly, we choose MobileNet [6] as our CNN architecture. They achieve a similar accuracy to VGG-16 [7] using far fewer parameters on ImageNet [8]. MobileNet achieves 70.6% accuracy using only 4.6 million parameters compared to VGG-16’s 71.5% using 138 million parameters.
4.1.1 Training the classifier:
We used Keras [9] with Tensorflow [10] backend to train the classification network on our data. We resized the images to a fixed size of $224 \times 224 \times 3$ and normalized them before feeding into the network. We used transfer learning [11] by initializing the network with ImageNet weights. We used SGD as our optimizer with Nesterov momentum and trained it for 50 epochs. The learning rate (LR) schedule we used is as follows: we start with a LR of 0.0001 and reduce it by a factor of 30% after every 20 epochs. We used a mini-batch size of 64 and the network was trained on Nvidia Tesla M60 (2 GPUs with 8GB memory each) for approximately 3.5 hours. The performance of the classifier is discussed in the results section.
4.2 Text position detection
Detecting objects in an image is a common problem in computer vision. The task involves putting bounding boxes around objects of interest in the image. In Chart-Text we use object detection to localize and classify chart title, x-label, y-label, x-values, y-values, labels and legends as described in the dataset section. There are various object detection systems but, all state of the art object detection systems uses deep
learning. We use Faster R-CNN [12] as our object detection model because, as [13] argues, this achieves the best accuracy for small object detection when compared to YOLO[14], SSD[15] and R-FCN[16] with the trade-off being the inference speed.
4.2.1 Training the object detector
We used Tensorflow’s Object detection API to train the Faster R-CNN object detection model. We used Inception-V2[17] as our fixed feature extractor. We resized all the incoming images while preserving their aspect ratio in such a way that their shorter side is at least 500 pixels. We trained the network for 50,000 iterations with a mini-batch size of 1. We used the following anchor box sizes: [0.25, 0.5, 0.75, 1.0, 1.5] (w.r.t to a base size of 256 pixels) and the following aspect ratios: [0.5, 1.0, 2.0]. The total training time was about 4 hours on an Nvidia Tesla M60. After training, given a chart image, the model outputs 300 bounding boxes with confidence scores and class names. We only keep the detections with a confidence score greater than or equal to 0.5. We chose this number based on validation experiments.
4.3 Extracting text from charts
To extract text information from the charts we apply Optical character recognition (OCR) to the bounding boxes output from our object detection model. We use Google’s open source Tesseract [18] as our OCR engine. Out of the box, it comes pre-trained to recognize several fonts and styles. It is possible to retrain it on custom fonts but we use it as it is. As pointed out in [1], the OCR accuracy is higher for horizontally aligned text. We use the following algorithm to align the text image horizontally:
1. We convert the image to grey scale and threshold it to obtain a binary image.
2. We fit a minimum bounding rectangle to the binary image and measure the angle made by the rectangle w.r.t. the horizontal.
3. We rotate the image using the calculated angle in the opposite direction to align the text image with the horizontal.
We also found that rescaling the aligned image so that its height is 130 pixels significantly improves OCR accuracy. The above procedure is very similar to the one given in [1].
Figure 1: example of horizontally aligning text images to facilitate OCR using Tesseract OCR engine.
4.4 Extracting data from charts
In this section, we present the chart specific image processing algorithms that we use to extract relevant data marks from the chart images. As the data extraction process is unique for every type of chart, we first provide the underlying assumptions and then describe the specific image processing algorithm.
4.4.1 Horizontal and vertical bar charts
We assumed that horizontal and vertical bar charts do not contain 3D effects. The algorithm
for horizontal and vertical bar extraction is as follows:
1. We convert the image to grayscale and then use a median filter with a kernel size of 7 to remove noises.
2. We threshold the image and perform area opening morphological operation to remove any remaining small objects.
3. We label the regions, perform connected components analysis and fit a minimum bounding rectangle to each of the labelled region to identify and extract different bars.
4. We use OpenCV [19] and DIPlib [20] to perform the above-mentioned operations.
Here, we do not consider the chart orientation (horizontal or vertical) as this is taken care of by the classifier, and this method works irrespective of the chart orientation.
4.4.2 Stacked horizontal and vertical bar charts
Similar to horizontal and vertical bar charts, we assume that the charts do not have 3D effects. Additionally, we also assume that there are no texts inside the stacked bars and each stack has a distinct color. We follow the same procedure as horizontal and vertical bar charts to extract different bars. In addition, after extracting the individual bars we use a local search algorithm to extract the stacks. We confine our search space to the bars extracted from the connected component analysis. The local search algorithm is as follows:
1. We find the midpoint of the two edges of the rectangle along its length. For horizontal bar charts lengthwise is the x-axis and for vertical bar charts lengthwise is the y-axis.
2. With these two points as start and end points, we move along the line made by them and detect sudden changes in pixel values between two adjacent pixel points. We take the center of those pixel points as the border or the edge point separating two adjacent stacks.
3. The process continues until we find all the stacks inside all the bars.
For all the 4 types of bar charts we calculate a ratio called as chart to pixel ratio. We calculate this ratio by extracting the numbers and position of y values (horizontal charts) or x values (vertical charts). We define the chart to pixel ratio as the ratio of two consecutive x or y values extracted using OCR and the corresponding distance between the centroids of their bounding boxes. We use this ratio to scale the bars to the chart coordinate system from the pixel coordinate system.
4.4.3 Pie chart
We assume pie charts do not have 3D effects, each wedge has a distinct colour, and the corresponding labels are present adjacent to the wedge. We adopted a similar approach to the one given in [3]. The approach is explained in detail below:
1. We use Canny edge detection to create an edged image of the pie chart.
2. We fit a robust circle to the pie using RANSAC. We use RANSAC because it is more efficient in ignoring outliers while fitting a circle.
3. We sample 1000 pixels uniformly along the fitted circle whose radius is 0.2*R. Where, R is the radius of the fitted circle.
4. We traverse the sampled points sequentially and detect sudden change in pixel intensity between two adjacent pixel points. We take the center of those two pixel points as the border point between wedges.
5. After detecting the border points, we measure the clockwise angle between them with respect to the center of the fitted circle to determine the angle of each wedge.
5 Results
5.1 Classifier and Detector results
Our Chart-Text system achieved a classification accuracy of 99.72% on the procedurally
generated test set. The normalized confusion matrix for classification is given in Table 2. It is evident from the confusion matrix that the classifier misclassified three stacked vertical bar chart images as vertical bar chart and four horizontal bar chart images as stacked horizontal bar charts and six stacked horizontal bar chart images as horizontal bar chart.
Understanding where the CNN is looking in the image to classify is very important to understand the generalizing capability of the network. Grad-Cam [21] visualizations give insights on which part of the image maximally activates the neurons to predict that particular class. We generated Grad-Cam images to verify whether the network attends to correct part of the image when it predicts a particular class. Figure 2 shows a few samples of Grad Cam results. These images show that the network attends to the correct part of the image while classifying.
Similarly, we evaluate the performance of the text position detection (object detection) model on the procedurally generated test set. Generally, the performance of an object detector is measured by the mean-average-precision (mAP) metric. The mAP for each class at an Intersection over Union (IOU) of 50% is given in Table 3.
### Table 2. Normalized Confusion Matrix
| True Label | Predicted Label | Horizontal bar chart | Pie chart | Stacked horizontal bar chart | Stacked vertical bar chart | Vertical bar chart |
|-----------------------------|----------------------------------|----------------------|-----------|-------------------------------|----------------------------|-------------------|
| Horizontal bar chart | 0.996 | 0.0 | 0.004 | 0.0 | 0.0 | 0.0 |
| Pie chart | 0.0 | 1.0 | 0.0 | 0.0 | 0.0 | 0.0 |
| Stacked horizontal bar chart| 0.006 | 0.0 | 0.994 | 0.0 | 0.0 | 0.0 |
| Stacked vertical bar chart | 0.001 | 0.0 | 0.0 | 0.996 | 0.003 | 1.0 |
| Vertical bar chart | 0.0 | 0.0 | 0.0 | 0.0 | 1.0 | 0.0 |
**Figure 2:** Grad-Cam images (clockwise) first image, depicts the pixel regions which maximally activate the class ‘horizontal bar chart’. Second image, depicts the pixel regions which maximally activate the class ‘pie chart’. Third image depicts the pixel regions which maximally activate the class ‘vertical bar chart’.
### Table 3: Mean Average Precision metric for the Object detection model
| Class | mAP at 0.5IOU |
|----------------|---------------|
| Chart title | 0.9796 |
| Pie Label | 0.9304 |
| Legend | 0.8857 |
| X label | 0.9486 |
| X value | 0.9365 |
| Y label | 0.9478 |
| Y value | 0.9313 |
### 5.2 Alt-Text accuracy
The performance of Alt-Text generation is dependent on accuracy of the extracted text from the charts and the precision of the calculated values from the chart. To evaluate the performance of the complete system in generating the Alt-Text on the procedurally generated plots we define two evaluation metrics.
**Text accuracy**: We define that the extracted text is true positive if the Levenshtein distance ratio between the extracted text and the ground truth text is greater than 80%. We use 80% instead of a 100% match because, the texts are randomly generated and in some cases have special characters in them. Mathematically:
\[
\frac{\text{Dist}(P,T)}{\text{Alignment distance}} \geq 0.8
\]
Where, Dist is Levenshtein distance, P is the predicted string and T is ground truth string.
**Value accuracy**: we define that the calculated value is true positive if and only if the difference between the calculated value and ground truth-value is within 2%. Mathematically:
\[
\left| \frac{\text{Calculated value} - \text{True value}}{\text{True value}} \right| \leq 0.2
\]
For each image belonging to a particular class, we calculate the mean text and value accuracies and average them across all the images of that particular class and report this average text and value accuracies for each of the five classes in Table 4.
### Table 4. Average text and value accuracies of all the 5 types of charts
| Class | Average text accuracy (%) | Average value accuracy (%) |
|------------------------|---------------------------|----------------------------|
| Pie chart | 85 | 80.7 |
| Horizontal bar chart | 82.3 | 76.4 |
| Vertical bar chart | 83.5 | 76.5 |
| Stacked horizontal bar chart | 80.47 | 71.64 |
| Stacked vertical bar chart | 81.2 | 70.12 |
### 6 Conclusion
In this paper, we introduced Chart-Text, a fully automated system that completely describes horizontal bar charts, vertical bar charts, stacked horizontal bar charts, stacked vertical bar charts and pie charts. We developed an original approach to extract data from stacked bar charts. One more important contribution in Chart-Text is our deep learning based object detection model that is used to detect and classify chart title, pie labels, x values, y values, x labels, and y labels. Our method is generic and can be extended it to other chart types such as line charts, scatter plots, area charts, histograms etc.
Even though our system performs considerably well on the procedurally generated dataset, the performance on data from web and other sources plummets. This is primarily because most charts from web and other sources are graphically enhanced and typesetted for better visual appearance. Further investigations on improving Chart-Text’s generalization capability is needed. The ultimate goal of Chart-Text is to act as an end-to-end fully automatic system that extracts information from charts to create complete textual description of it so that the chart images become more accessible to people with vision impairments.
7 Examples
Here, we provide a few Alt-Texts generated by our Chart-Text system. These example input images are generated using Matplotlib.
**Alt-Text:** The stacked vertical bar graph depicts 'Sales in the Dress Store'. The graph is plot between 'Units sold' y axis over 'Days of the week' x axis for '(Shirts, Skirts, Trousers, Accessories)'. The Units sold for the corresponding Days of the week are (Monday Accessories = 20, Shirts = 24, Skirts = 19, Trousers = 13), (Thursday Accessories = 31, Shirts = 35, Skirts = 19, Trousers = 15), (Saturday Accessories = 28, Shirts = 29, Skirts = 26, Trousers = 17), (Friday Accessories = 3, Shirts = 36, Skirts = 24, Trousers = 18), (Tuesday Accessories = 21, Shirts = 26, Skirts = 11, Trousers = 16), (Wednesday Accessories = 46, Shirts = 41, Skirts = 8, Trousers = 19), (Sunday Accessories = 25, Shirts = 25, Skirts = 7, Trousers = 11). (All Values estimated)
Alt-Text: The stacked horizontal bar graph depicts 'Sales in the Dress Store'. The graph is plot between 'Units sold' x axis over 'Days of the week' y axis for '(Shirts, Trousers, Skirts)'. The Units sold for the corresponding Days of the week are (Monday Trousers = 11, Skirts = 17, Shirts = 21), (Thursday Trousers = 12, Skirts = 17, Shirts = 31), (Saturday Trousers = 14, Skirts = 23, Shirts = 25), (Friday Trousers = 15, Skirts = 21, Shirts = 32), (Tuesday Trousers = 13, Skirts = 10, Shirts = 23), (Wednesday Trousers = 16, Skirts = 7, Shirts = 36), (Sunday Trousers = 9, Skirts = 6, Shirts = 22). (All Values estimated)
Alt-Text: The vertical bar graph depicts 'Dog name percentages in 1960'. The graph is plot between 'Percentages of dog names' y axis over 'Names of the dogs' x axis. The Percentages of dog names for the corresponding Names of the dogs are Others = 48, Elvis = 34, Rover = 26, Spot = 23, Fido = 18. (All Values estimated)
**Horizontal Bar Chart**
Alt-Text: The horizontal bar graph depicts 'Favorite Genre of Movie'. The graph is plotted between 'Number of people (X 100)' x-axis over 'Movie Genres' y-axis. The Number of people (X 100) for the corresponding Movie Genres are Action = 1896, Comedy = 3187, Crime = 2393, Romance = 1300, Scifi = 3187. (All Values estimated)
**Pie Chart**
Alt-Text: The pie chart depicts 'On Demand Services Market Share'. It has 5 parts (Dubai, New York, London, Mumbai, Singapore) to it and percentage for each are Dubai: 11%, New York: 18%, London: 27%, Mumbai: 13%, Singapore: 32%. (All Values estimated)
Alt-Text: The stacked vertical bar graph depicts 'Market Share of Nuts'. The graph is plotted between 'Market share (%)' y axis over 'Year' x axis for ['Cashewnut, Walnuts, Almonds']. The Market share (%) for the corresponding Year are (2015 Cashewnut = 22, Walnuts = 28, Almonds = 33), (2017 Cashewnut = 43, Walnuts = 41, Almonds = 41), (2016 Cashewnut = 65, Walnuts = 29). (All Values estimated)
8 Bibliography
[1] M. Cliche, D. Rosenberg, D. Madeka, and C. Yee, “Scatteract: Automated Extraction of Data from Scatter Plots,” in Lecture Notes in Computer Science, 2017, pp. 135–150.
[2] M. Savva, N. Kong, A. Chhajta, L. Fei-Fei, M. Agrawala, and J. Heer, “ReVision: Automated Classification, Analysis and Redesign of Chart Images.”
[3] D. Jung et al., “ChartSense: Interactive Data Extraction from Chart Images,” 2017.
[4] J. D. Hunter, “Matplotlib: A 2D Graphics Environment,” Comput. Sci. Eng., vol. 9, no. 3, pp. 90–95, 2007.
[5] A. Krizhevsky, I. Sutskever, and G. E. Hinton, “ImageNet Classification with Deep Convolutional Neural Networks,” Commun. ACM, vol. 60, no. 6, pp. 84–90, 2017.
[6] A. G. Howard et al., “MobileNets: Efficient Convolutional Neural Networks for Mobile Vision Applications,” Apr. 2017.
[7] K. Simonyan and A. Zisserman, “Very Deep Convolutional Networks for Large-Scale Image Recognition,” Sep. 2014.
[8] O. Russakovsky et al., “ImageNet Large Scale Visual Recognition Challenge,” Int. J. Comput. Vis., vol. 115, no. 3, pp. 211–252, 2015.
[9] F. Chollet, Keras. 2015.
[10] M. Abadi et al., TensorFlow: Large-Scale Machine Learning on Heterogeneous Systems. 2015.
[11] J. Yosinski, J. Clune, Y. Bengio, and H. Lipson, “How Transferable are Features in Deep Neural Networks?”
[12] S. Ren, K. He, R. Girshick, and J. Sun, “Faster R-CNN: Towards Real-Time Object Detection with Region Proposal Networks,”
IEEE Trans. Pattern Anal. Mach. Intell., vol. 39, no. 6, pp. 1137–1149, 2017.
[13] J. Huang et al., “Speed/Accuracy Trade-Offs for Modern Convolutional Object Detectors,” in 2017 IEEE Conference on Computer Vision and Pattern Recognition (CVPR), 2017.
[14] J. Redmon, S. Divvala, R. Girshick, and A. Farhadi, “You Only Look Once: Unified, Real-Time Object Detection,” in 2016 IEEE Conference on Computer Vision and Pattern Recognition (CVPR), 2016.
[15] W. Liu et al., “SSD: Single Shot MultiBox Detector,” in Lecture Notes in Computer Science, 2016, pp. 21–37.
[16] J. Dai, Y. Li, K. He, and J. Sun, “R-FCN: Object Detection via Region-based Fully Convolutional Networks,” Dec. 2015.
[17] C. Szegedy, V. Vanhoucke, S. Ioffe, J. Shlens, and Z. Wojna, “Rethinking the Inception Architecture for Computer Vision,” in 2016 IEEE Conference on Computer Vision and Pattern Recognition (CVPR), 2016.
[18] A. Kay, Tesseract: An Open-Source Optical Character Recognition Engine. 2007.
[19] G. Bradski, The OpenCV Library. 2008.
[20] L. Cris and S. Erik, DIPlib: Quantitative Image Analysis in C++, MATLAB and Python.
[21] R. R. Selvaraju, M. Cogswell, A. Das, R. Vedantam, D. Parikh, and D. Batra, “Grad-CAM: Visual Explanations from Deep Networks via Gradient-Based Localization,” in 2017 IEEE International Conference on Computer Vision (ICCV), 2017.
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RESEARCH
TGF-β2 enhances expression of equine bone marrow-derived mesenchymal stem cell paracrine factors with known associations to tendon healing
Drew W. Koch1,2, Lauren V. Schnabel1,2*, Ilene M. Ellis1, Rowan E. Bates1 and Alix K. Berglund1,2*
Abstract
Background: Mesenchymal stem cells (MSCs) secrete paracrine factors and extracellular matrix proteins that contribute to their ability to support tissue healing and regeneration. Both the transcriptome and the secretome of MSCs can be altered by treating the cells with cytokines, but neither have been thoroughly investigated following treatment with the specific cytokine transforming growth factor (TGF)-β2.
Methods: RNA-sequencing and western blotting were used to compare gene and protein expression between untreated and TGF-β2-treated equine bone marrow-derived MSCs (BM-MSCs). A co-culture system was utilized to compare equine tenocyte migration during co-culture with untreated and TGF-β2-treated BM-MSCs.
Results: TGF-β2 treatment significantly upregulated gene expression of collagens, extracellular matrix molecules, and growth factors. Protein expression of collagen type I and tenascin-C was also confirmed to be upregulated in TGF-β2-treated BM-MSCs compared to untreated BM-MSCs. Both untreated and TGF-β2-treated BM-MSCs increased tenocyte migration in vitro.
Conclusions: Treating equine BM-MSCs with TGF-β2 significantly increases production of paracrine factors and extracellular matrix molecules important for tendon healing and promotes the migration of tenocytes in vitro.
Keywords: Mesenchymal stem cell, Tenocyte, TGF-β, Equine, Tendon, RNA-sequencing, Paracrine factors, Extracellular matrix
Background
Mesenchymal stem cells (MSCs) are fibroblast-like cells that can be isolated from various tissues including bone marrow, adipose, peripheral blood, and cord blood. Although MSCs can be directed to differentiate into cartilage, fat, and bone in vitro, there is little evidence to support that MSCs engraft and differentiate into new tissue once injected in vivo [1]. Instead, MSCs secrete numerous paracrine factors that recruit and support the differentiation of endogenous progenitor cells, promote angiogenesis, inhibit apoptosis, and modulate local immune responses [2]. Extracellular matrix (ECM) proteins secreted by MSCs may also directly contribute to tissue healing or be used to generate acellular scaffolds for tissue engineering [3–5]. MSCs are therefore of interest as a regenerative therapy to enhance the endogenous healing of injured tissues.
Due to the lack of inherent healing capacity within the tendon, improved therapies for tendon regeneration are...
needed to promote return to functionality after injury. Bone marrow-derived MSCs are currently used to treat tendon injuries in horses and are actively being investigated in preclinical research and clinical trials for treating human tendon injuries as well. Horses with superficial digital flexor tendon (SDFT) injuries treated with autologous MSCs had reduced reinjury rates, improved fiber alignment, and less inflammatory cell infiltrate compared to horses that did not receive MSCs [6–8]. In a rat Achilles tendon repair model, tendons treated with BM-MSCs had higher maximum load to failure and stiffness compared to control tendons as well as increased expression of pro-tendon healing factors, scleraxis and tenomodulin [9]. However, results from human clinical trials using MSCs to treat musculoskeletal injuries have failed to meet the expectations set by preclinical animal models. A number of factors have likely contributed to this including immunocompatibility, cell quality and dose, and inconsistent culture protocols [10–12]. Current trends in MSC research are therefore focused on improving the consistency and quality of MSCs to increase their therapeutic efficacy.
There is considerable interest in in vitro priming or “licensing” of MSCs to enhance their secretome and increase the expression of paracrine factors specific for the type of injury or disease being treated. Previous research has focused primarily on priming MSCs with inflammatory cytokines like IFN-γ, TNF-α, or IL-1β to increase expression of growth factors and anti-inflammatory cytokines from MSCs [13]. We previously published that allogeneic equine BM-MSCs cultured with TGF-β2 have reduced MHC I surface expression and cell-mediated cytotoxicity in vitro while retaining their abilities to suppress T cell proliferation and secrete PGE2 and TGF-β1 [14]. However, TGF-β is known to affect the expression of other cytokines, growth factors, and extracellular matrix molecules that may affect the MSC functions and the efficacy of MSC therapy [15, 16].
The purpose of this study was to determine how TGF-β2 changes the transcriptome of MSCs with an emphasis on secreted factors relevant to tendon healing in equine BM-MSCs. Through use of RNA-sequencing, western blotting, and a tenocyte migration assay, we discovered that TGF-β2-treated BM-MSCs have enhanced expression of extracellular matrix molecules including collagen and tenascin-C and, similar to untreated MSCs, increase tenocyte migration, all of which may improve their therapeutic efficacy for in vivo tendon healing.
**Methods**
**Animal use and welfare**
A total of 13 systemically healthy horses were utilized in this study for sternal bone marrow harvest as approved under protocol #19–628 for sedated bone marrow collection or #20–454 for postmortem collection by the Institutional Animal Care and Use Committee of North Carolina State University. All horses were between the ages of 6–16 years of age, were Thoroughbred or Thoroughbred crosses, and an equal number of mares and geldings were used in each experiment. The SDFT obtained for tenocyte isolation was collected from a 16 year old Thoroughbred horse euthanized for reasons unrelated to this study as approved under protocol #20–454.
**MSC isolation and culture**
Bone marrow aspirates were collected aseptically from the sternum of horses using 11-gauge Jamshidi bone marrow aspirate biopsy needles under standing sedation with local lidocaine anesthesia or immediately post-euthanasia. Bone marrow aspirates were purified via Ficoll-Paque Plus (GE Healthcare) gradient centrifugation. Isolated cells were cultured in standard media containing 1 g/dl glucose DMEM (Corning), 10% fetal bovine serum (Atlanta Biologicals), 2 mM L-glutamine, 100 U/ml penicillin and streptomycin, and 1 ng/ml recombinant human basic fibroblast growth factor (bFGF)(Corning). When cultures reached 80% confluency, MSCs were passaged with Accutase cell-dissociation solution (Innovative Cell Technologies) and plated at a density of 6,250 cells per cm² on 100 mm tissue culture plates. BM-MSCs were passaged for 2 to 4 passages prior to use. Cell count and viability at each passage were determined using a Cellometer® Auto 2000 and ViaStain™ AOPI Staining Solution (Nexcellor Bioscience LLC). BM-MSCs were treated by adding 1 ng/ml recombinant human TGF-β2 (BioLegend) to the media as previously described for 3 passages prior to RNA-sequencing or for 72 h for all other analyses [17]. We have previously published that MSC isolated and cultured using this protocol are positive for CD29, CD44, and CD90 and negative for LFA-1 and CD45 [17].
**RNA-sequencing**
Total RNA was extracted from paired P3 or P4 untreated and TGF-β2-treated BM-MSCs from four horses using the RNeasy Mini kit (Qiagen). Libraries were generated and poly(A) enriched using 1 ug of RNA as input. Indexed samples were sequenced using a 150 base pair paired-end protocol on a HiSeq 2500 (Illumina) according to the manufacturer’s protocol. Sequence reads were trimmed to remove possible adaptor sequences and nucleotides with poor quality using Trimmomatic v.0.36. The trimmed reads were mapped to the EquCab 3.0 using the STAR aligner v.2.5.2b. Unique gene hit counts were calculated using featureCounts from the Subread package.
v.1.5.2. Using DESeq2, a comparison of gene expression between the untreated and TGF-β2-treated BM-MSCs was performed. The Wald test was used to generate p values and log2 fold changes. Genes with an adjusted p value of < 0.05 and log2 fold change > 1 were determined to be differentially expressed for each comparison. The quantification and poly(A) selection of mRNA, library preparation, sequencing, and bioinformatics were outsourced to GENEWIZ, Inc.
**Protein lysate collection and western blotting**
BM-MSCs from four additional horses not used for RNA-sequencing were cultured on 100 mm tissue culture plates in control media or media containing 1 ng/ml TGF-β2 for 72 h. The plates were washed with ice cold phosphate buffered saline (PBS) before adding 350 μl of cold RIPA Lysis and Extraction Buffer (Thermo Scientific) with 1X Halt Protease Inhibitor Cocktail (Thermo Scientific). Plates were scraped on ice and the contents transferred to a microcentrifuge tube and incubated on ice for 15 min. Microcentrifuge tubes were then centrifuged at 14,000 g for 10 min. The protein lysate supernatant was collected and frozen at – 80 °C until used. For western blotting, 20 μg of protein lysate was boiled at 100 °C for 5 min with 1X Laemmli buffer and 5% 2-mercaptoethanol and resolved using an Any kD Criterion TGX gel (Bio-Rad). Protein was transferred to a PVDF membrane using a Trans-Blot Turbo Blotting System (Bio-Rad). The membrane was blocked with 5% non-fat dry milk before blotting the membrane with rabbit anti-human type I collagen antibody (Novus Biologicals, NBP168942) or rabbit anti-human tenascin-C antibody (Millipore Sigma, AB19011) [18] both at 1:500 in tris-buffered saline with 0.1% Tween-20 detergent. A mouse anti-human beta-actin antibody was used as a loading control at 1:10,000 (Invitrogen, clone 15G5A11/E2). The membrane was probed overnight at 4 °C before adding mouse anti-rabbit IgG-HRP secondary antibody (Cell Signaling Technology) at 1:2000 or goat anti-mouse IgG-HRP secondary antibody (Invitrogen) at 1:2000 for 1 h at room temperature. The membrane was incubated with Clarity Western ECL Substrate (Bio-Rad) for 5 min before imaging. Images were captured by a luminescent image analyzer with a CCD camera (Bio-Rad). Quantification of expression levels was calculated using ImageJ software (NIH), and values were expressed in arbitrary units relative to beta-actin (ACTB).
**MSC and tenocyte co-culture**
To determine the effects of paracrine factors from TGF-β2-treated BM-MSCs on tendon, tenocytes were isolated from a forelimb equine SDFT similar to previously published methods [19]. The SDFT palmar to the third metacarpal bone was aseptically dissected and the tendon was transported in sterile PBS with 100 U/ml penicillin and streptomycin and transferred to a tissue culture hood. Under aseptic conditions, 5 mm × 5 mm × 5 mm tendon explants were created ensuring the center of the SDFT was isolated and para- tenon excluded. Explants were digested for 12–18 h in media containing 1 g/dl glucose DMEM (Corning) supplemented with 10% fetal bovine serum (Atlanta Biologicals), 100 U/ml penicillin and streptomycin, 2 mM L-glutamine, 20 μg/ml α-ketoglutaric acid, and 50 μg/ml ascorbic acid and 0.3% collagenase type I (Gibco). Following digestion, media was filtered through a 100 μm Nylon cell strainer before centrifuging the cell solution at 800 g. Viability and cell count were obtained, and cells were cultured on 100 mm tissue culture plates at 8800 cells per cm² in tenocyte media (as previously mentioned, without collagenase). Tenocytes were passaged with trypsin–EDTA (0.25%) when plates became confluent and subcultured to P2 prior to co-culture.
Untreated or TGF-β2-treated BM-MSCs from five additional horses and on horse also used for western blotting were seeded onto Transwell® polycarbonate membrane inserts (MilliporeSigma) in tenocyte media at a density of 20,000 cells per cm². Tenocytes were similarly plated in Transwell inserts at 20,000 cells per cm² as a control and to standardize nutrient deprivation between treatment groups. Cells were allowed 24 h to attach on inserts before adding to scratch wound wells for co-culture. Tenocytes were plated at a density of 6,250 cells per cm² in the wells of a 12-well tissue culture plate and allowed to grow to confluency. Twenty-four hours prior to tenocyte wounding, tenocytes were transitioned to serum-free tenocyte media. A single vertical scratch wound was created in each well using a 200 μl pipette tip. The media was then aspirated, wells were washed twice with PBS, and serum-free tenocyte media was replaced. Images were taken at baseline and then every 12 h for 48 h at three separate locations along each scratch wound using an IX83 inverted microscope and cellSens™ software (Olympus). All images were obtained with the Transwell inserts removed, and to ensure the same location was imaged at each time point, a plate map was created and saved within cellSens™ software. Using Adobe Photoshop, the pixel area of the scratch wound at each location for all treatment groups was measured at baseline (time 0) and then each subsequent time point. The percent closure was calculated by averaging the three locations for each treatment group at each time point using the equation: \( \frac{((\text{Average Area} \text{ Time } 0 - \text{ Average Area Time } x))/\text{Average Area Time } 0} \times 100 \) where “x” represents time.
Statistical analysis
The functional enrichment analysis of RNA-sequencing data was performed using g:Profiler (version e104_eg51_p15_3922dba) with g:SCS multiple testing correction method applying significance threshold of 0.05 [20]. Western blot data were normalized by log transformation and analyzed using paired one-tailed t tests with a null hypothesis of no difference using JMP Pro 15 (SAS Institute Inc.). The percent wound healing data for the tenocyte scratch assays were analyzed using a one-way repeated measures ANOVA followed by a Tukey’s test for multiple comparisons using Prism 9.0 (GraphPad).
Results
Differentially expressed genes in TGF-β2-treated BM-MSCs
To identify global changes in gene expression after TGF-β2 treatment, RNA-sequencing was performed on matched untreated and TGF-β2-treated BM-MSCs from four donor horses. We observed 2467 significant differentially expressed genes (DEGs) in total with 1148 genes upregulated and 1319 genes downregulated (Fig. 1a). The genes with the largest increase in expression were INHBE, a member of the TGF-β superfamily, IFGBP5, an insulin-like growth factor binding protein, and RELN, a glycoprotein involved in neuronal migration. The genes with the largest decrease in expression were SCARA5, a ferritin receptor, PDE1A, a phosphodiesterase involved in cAMP signaling, and C30H1orf115, an uncharacterized homolog of the human gene C1orf115. Gene ontology (GO) enrichment analysis was performed to identify the top overrepresented terms in the entire DEG set. The top ten molecular functions (MF), biological processes (BP), and cellular components (CC) for this data are listed in Fig. 1b. Among the overrepresented GO terms relevant to tendon healing were extracellular matrix, collagen-containing extracellular matrix, tissue development, cell adhesion molecule binding, and growth factor activity. For the top 200 upregulated genes, all significant GO terms for MF, BP, CC, Kyoto Encyclopedia of Genes and Genomes (KEGG) pathways, and human phenotype ontology (HP) are shown in Additional file 1: Fig. S1.
Collagen expression is upregulated in TGF-β2-treated BM-MSCs
Twenty-eight different types of collagens have been described, although types I, II, III, IV, V, VI, VII, XI, XII, XV, and XVIII are the most common [21, 22]. Normal, healthy tendon is composed primarily of type I collagen. Regenerative therapies for tendons aim to increase type I collagen and limit persistence of type III collagen that is secreted during the proliferative phase of tendon healing, but is structurally weaker. In BM-MSCs treated with TGF-β2, collagen types I, IV, V, VIII, XI, XII, XV, and XVIII were significantly upregulated compared to untreated BM-MSCs (Fig. 2a). COL1A1 and COL1A2 were by far the most abundant collagen transcripts detected in both untreated and TGF-β2-treated equine BM-MSCs followed by COL5A1, COL5A2, and COL12A1. COL11A1, which has been shown to regulate type I collagen fibril assembly [23, 24], had the greatest Log2 fold change in TGF-β2-treated BM-MSCs compared to untreated. Both subunits associated with type V collagen were upregulated, which may support collagen fibrillogenesis [25]. Gene transcripts of type II and type III collagens were not detected by RNA-sequencing. Protein expression of alpha-1 type I collagen from untreated and TGF-β2-treated BM-MSCs from 4 different donor horses was measured by western blot (Fig. 2b). Prominent bands could be detected around both 180 kDa and 35 kDa, which likely correspond to the procollagen alpha-1 chain and procollagen type I carboxy-terminal propeptide, respectively [26, 27]. All horses expressed significantly more total alpha-1 type I collagen from TGF-β2-treated BM-MSCs than untreated (p = 0.0001) (Fig. 2b). This significant increase in collagen production by TGF-β2-treated BM-MSCs may be beneficial in improving healing in tissues like tendons where collagen production is critical to the structure, integrity, and function of the tissue.
Extracellular matrix genes and enzymes are differentially expressed in TGF-β2-treated MSCs
Numerous other non-collagenous ECM genes linked to healthy tendon or tendon healing were upregulated in TGF-β2-treated BM-MSCs including tenascin-C, biglycan, elastin, and fibronectin (Fig. 3a). Tenascin-C is a known marker of tenogenic differentiation and tendon ECM; it plays an important role in cell migration during wound healing, collagen fibril organization, and creates a de-adhesive ECM environment during injury repair [28, 29]. Protein expression of tenascin-C was confirmed to be significantly upregulated in TGF-β2-treated BM-MSCs compared to untreated BM-MSCs (p = 0.0005) (Fig. 3b). Of the tendon relevant ECM genes, only tenascin-X (TNXB) was downregulated in TGF-β2-treated
Differentially expressed genes (2,467)
- Upregulated (1,148)
- Downregulated (1,319)
Fig. 1 (See legend on previous page.)
BM-MSCs. Along with increases in collagen expression, increases in ECM protein expression from TGF-β2-treated BM-MSCs may assist and enhance tendon repair and healing.
Also important to the ECM in tendon healing are the enzymes that assist with remodeling, collagen cross-linking, and regulation of growth factors. Matrix metalloproteinase-9 (MMP9) is suggested to play a role in early tendon remodeling [30] and was downregulated in TGF-β2-treated BM-MSCs (Fig. 3c). Tissue inhibitors of metalloproteinase, TIMP3 and TIMP4, were also downregulated in TGF-β2-treated BM-MSCs, although expression of TIMP1 and TIMP2 was unaffected by TGF-β2 treatment. LOX and LOXL2, which encode lysyl oxidase family members and are involved in cross-linking of collagen and elastin, had high levels of transcript detected in BM-MSCs and were significantly upregulated in TGF-β2-treated BM-MSCs. The timing of expression and coordination between secreted ECM subunits and enzymes that contribute to tendon ECM remodeling, maintenance, and healing are not well understood, so it is still unclear how significantly the changes in these secreted factors might affect the healing tendon.
Cytokines and growth factors are differentially expressed in TGF-β2-treated BM-MSCs
Cytokines and growth factors regulate tendon healing by stimulating angiogenesis, extracellular matrix production, tenocyte proliferation, and modulating immune responses. Gene expression of several important cytokines and growth factors relevant to tendon healing was upregulated in TGF-β2-treated BM-MSCs compared to untreated controls (Fig. 4). Cytokines with the greatest upregulation in TGF-β2-treated BM-MSCs included bone-derived neurotropic factor (BDNF), interleukin-11 (IL-11), insulin-like growth factor-1 (IGF-1), and acidic fibroblast growth factor (FGF1). We attempted to measure IGF-1 protein expression from BM-MSCs using a commercial anti-human IGF-1 ELISA kit and an anti-human IGF-1 antibody in a western blot, but no protein could be detected (data not shown). Human IGF-1 and equine IGF-1 have 98% homology, but high levels of transcripts of five IGF binding proteins, IGFBP2, IGFBP4, IGFBP5, IGFBP6, and IGFBP7, were also detected in untreated and TGF-β2-treated BM-MSCs. IGFBPs can block antibody binding to IGF-1, which may have affected our ability to measure protein expression in cell culture supernatant and cell lysate [31, 32]. ANGPT1 and ANGPTL4, which may promote angiogenesis and tenocyte migration and cell cycle progression in injured tendons [33, 34], were downregulated in TGF-β2-treated BM-MSCs, but VEGFA, VEGFB, and VEGFC isoforms were not differentially expressed. PGE2 and TGF-β1 have been identified in the horse as the primary cytokines responsible for immunomodulation [35], and these were not differentially expressed in TGF-β2-treated BM-MSCs. This is supported by our previous work that did not find any significant difference in the concentrations of PGE2 and TGF-β1 in modified one-way mixed leukocyte reactions with untreated and TGF-β2-treated BM-MSCs [14].
BM-MSCs increase tenocyte migration
Migration of tenocytes to the site of tendon damage following injury is an important initial step in the repair process [36]. To determine if the changes in the
secretome of TGF-β2-treated BM-MSCs affect tenocyte migration, untreated and TGF-β2-treated BM-MSCs were indirectly co-cultured with tenocytes in a standard scratch assay. Tenocyte scratch wound closure was significantly improved with untreated BM-MSCs at 24 and 48 h and with TGF-β2-treated BM-MSCs at 24, 36, and 48 h (Fig. 5a). A significant difference between untreated and TGF-β2-treated BM-MSC groups was measured only at 36 h (Fig. 5b). An effect on tenocyte migration was noted between BM-MSCs from different horses ($p < 0.0001$), which is consistent with the known variation in the quantity of paracrine factors secreted from outbred species like humans and horses [37, 38]. Based on these results, the secretome of TGF-β2-treated BM-MSCs does not appear to be detrimental to tendon migration following wounding in an in vitro scratch wound assay.
**Discussion**
Treatment of tendon injuries is a major challenge in human and veterinary orthopedic medicine, and the goals of regenerative therapies are to improve the tendon biochemical composition and biomechanical strength while reducing clinical reinjury rates. Advances in the understanding of MSC biology have led us to explore modulating cell function in an effort to improve MSC therapy for tendon injuries. In this study, we investigated changes in gene and protein expression of paracrine factors and ECM components related to tendon healing in equine...
BM-MSCs treated with TGF-β2. Using RNA-sequencing, we identified gene expression of numerous secreted factors important for tendon healing including COL1A1 and COL1A2, TNC, LOX, IGF-1, and FGF1 which were upregulated in TGF-β2-treated BM-MSCs compared to untreated MSCs. Further, when grown together in coculture, both untreated and TGF-β2-treated BM-MSCs enhanced migration of equine tenocytes.
The clinical outcome of MSC therapy is dependent on both the quality and viability of the cells [39–42]. As seen in both the RNA-seq results and western blots, there were significant differences in the production of paracrine factors and ECM components between individual horses. This is consistent with reports that the quality of autologous MSCs can be affected by individual genetic backgrounds, health status, and age [43–45]. As shown in this study, the quantity of paracrine factors important for tendon healing can be increased by treating BM-MSCs with TGF-β2. Additionally, BM-MSCs from older horses may grow more slowly, but treating BM-MSCs with TGF-β2, provided bFGF is also included in the culture media, increases the yield of cells even from older horses [17]. Treating BM-MSCs with TGF-β2 could therefore potentially improve the efficacy of autologous therapy from patients who might otherwise be less than ideal candidates for MSC therapy including older patients. TGF-β2 also reduces MHC class I expression on MSCs, which reduces the cell-mediated immunogenicity of allogeneic BM-MSCs [14, 17]. In this study, we used different horses across experiments and still saw similar increases in both gene and protein expression of type I collagen and tenascin-c in the TGF-β2-treated MSCs.
Even though BM-MSCs were treated with TGF-β2 for a much shorter period of time than the BM-MSCs used for RNA-seq, both type I collagen and tenascin-c protein expression was significantly upregulated. This is consistent with previously published in vitro and in vivo studies that have shown significant improvements in wound healing or clinical signs following treatment with MSCs licensed with cytokines for 24 or 48 h [40, 46–48]. Therefore, a short duration treatment of TGF-β2 is likely sufficient to significantly enhance the secretome of BM-MSCs and improve the efficacy of both autologous and allogeneic BM-MSC therapy, although more studies are needed to confirm this.
Type I collagen is the primary collagen of healthy tendon ECM. With aging and injury, the ECM contains higher levels of type III collagen along with more disorganized fibers [49]. Therefore, a strategy to improve tendon healing would include a shift to decrease deposition of type III collagen and concurrent remodeling into type I collagen. In western blots, TGF-β2-treated BM-MSCs had increased expression of the pro-alpha-1 chain and procollagen type I carboxy-terminal propeptide (PICP), which can only originate from synthesized type I collagen and is used as a marker of type I collagen production [50]. Increased PICP in the BM-MSC cultures may be due to both upregulation of type I procollagen and BMP1, which cleaves the carboxy terminus of type I procollagen [51]. BMP1 was upregulated in TGF-β2-treated BM-MSCs, although the log2 fold change was slightly less than 1. TGF-β2 treatment also enhanced BM-MSC gene expression of two of the three type V collagen alpha chains, which are incorporated into the type I collagen triple helix during collagen maturation in tendon tissue [22]. Tendon ECM development may be further supported through BM-MSC secretion of tenascin-C, which has been shown to enhance tendon stem cell migration and remodeling and accelerate restoration of tissue matrix after exogenous administration [52]. Therefore, TGF-β2-treated BM-MSCs may improve the composition of the tendon ECM during healing through direct secretion of both the collagenous and non-collagenous tendon ECM.
While many of the secreted factors upregulated following treatment could impart benefit to a healing tendon, others may be associated with fibrosis under certain conditions. IL-11 is a poorly understood pleiotropic cytokine belonging to the IL-6 family which plays a role in stromal cell proliferation, tissue healing and homeostasis, as well as fibrosis, but its role in tendon injury and repair is not well characterized [53–55]. Like TGF-β, BMP-2 drives extracellular matrix expression and can promote fibrosis in chronic tendon inflammation, although it also promotes tenocyte migration [56, 57]. HGF, an inhibitor of myofibroblast differentiation and TGF-β-induced fibrosis
[58], is downregulated in TGF-β2-treated BM-MSCs. Due to the inherent complexity of biologic systems, the timing and cell specificity of cytokine and cytokine receptors involved in fibrosis, and our minimal understanding of what is required for a tendon to remodel to its native composition and strength [59], there are still many unknowns about the full effects of TGF-β2-treated BM-MSCs on tendon healing. Further research into how TGF-β2-treated BM-MSCs affect tenocyte gene expression and function is necessary to better predict any potential adverse effects. Additionally, while we do not see any overt morphologic changes in the BM-MSCs after adding TGF-β2 [17], in vivo testing in preclinical animal models is needed to confirm that TGF-β2-treated BM-MSCs do not promote ectopic bone or cartilage formation as some of the upregulated secreted factors are also involved in osteo-chondrogenic development.
Co-culture assays with BM-MSCs and tenocytes demonstrated that BM-MSC paracrine factors enhanced tenocyte migration. Other studies have established the role of migration in improved tendon healing [36, 57] and that MSC paracrine factors enhance cellular migration
and proliferation of tenocytes as well as corneal epithelial cells and dermal fibroblasts [60–62]. Chen et al. determined that this tenocyte-specific response in improved cell migration was due to activation of the ERK1/2 pathway by MSC paracrine factors, although the exact factors responsible were not elucidated [60]. FGF1, TGF-β2, and IL-11, all which were upregulated in TGF-β2-treated BM-MSCs, can activate MAP kinase signaling as can angiotensin, prostaglandins, and platelet derived growth factors [63–66]. In this study, both untreated and TGF-β2-treated BM-MSCs significantly improved migration of tenocytes. While TGF-β2-treated BM-MSCs only showed an enhanced effect on migration over untreated BM-MSCs at a single time point, 36 h, it is not clear from this in vitro study if this difference would significantly enhance healing in vivo. However, migration is a single outcome measure and future studies investigating if TGF-β2-treated BM-MSCs improve tendon healing will focus more in depth on modulation of tenocyte function including ECM production and secretion of paracrine factors.
Genome-wide transcriptional analysis of equine BM-MSCs has not been extensively investigated despite the horse being an important large animal translational model for testing MSC regenerative therapies in musculoskeletal injuries [67, 68]. Harman et al. used single-cell RNA-seq to compare equine MSCs between tissue sources, but the focus of the reported data was on differences in phenotypic markers and expression of C-X-C motif chemokine ligand 6 (CXCL6) [69]. Although some cell functions can be inferred across species, differences in MSC phenotype and function have been previously identified in the horse including differences in important immunomodulatory factors [38, 70, 71]. Through RNA-sequencing, we revealed which secreted factor genes relevant to tendon healing are and are not expressed in equine BM-MSCs allowing for future comparisons between other species including humans and mice. We have also shown that TGF-β2 enhances gene expression of collagens, ECM matrix proteins, matrix remodeling enzymes, and growth factors in BM-MSCs. MSCs licensed with inflammatory cytokines typically have significant increases in immunomodulatory factors rather than collagen and other ECM-related proteins. As immunomodulatory factors play a critical role in tissue healing, treating BM-MSCs with both TGF-β2 and an inflammatory cytokine prior to treatment may enhance the paracrine function of MSCs in additional ways that are relevant to treatment of tendon injuries and should be further investigated. One limitation of this study is that it focuses primarily on the changes in gene expression in BM-MSCs following TGF-β2 treatment. However, the results from the RNA-seq do give us a better understanding of what proteins equine BM-MSCs potentially secrete, which allows us to better plan future experiments to characterize the entire secretome. Additional research into the changes in protein expression of BM-MSC secreted factors is also necessary to understand mechanisms of BM-MSC-mediated tissue repair and the differences in the BM-MSC secretome between the horse and the human for translational relevance.
Conclusion
In this study, we demonstrated that treating equine BM-MSCs with TGF-β2 significantly increased production of secreted factors associated with tendon healing and maintained the ability of BM-MSCs to promote tenocyte migration. Increasing the expression of growth factors, collagens, and other extracellular matrix molecules from BM-MSCs by treating the cells with TGF-β2 prior to in vivo use may improve the consistency of secreted factor production and cell quality. More in vitro research into which BM-MSC secreted factors are most important for improving tendon healing is still needed as are preclinical animal models to investigate if manipulation of the secretome of BM-MSCs using TGF-β2 results in enhanced therapeutic efficacy for tendon injury.
Supplementary Information
The online version contains supplementary material available at https://doi.org/10.1186/s13287-022-03172-9.
Additional file 1. Figure S1. GO terms, adjusted p value, and -log10 (adjusted p value) for the top 200 upregulated genes in TGF-β2-treated BM-MSCs.
Acknowledgements
The authors would like to thank the NCSU Laboratory Animal Resources staff for their help with animal care and handling and James Robertson for help with statistical analysis.
Author contributions
AB, LS, and DK contributed to study conception and design. AB and DK collected the data. DK, LS, IE, RB, and AB analyzed and interpreted the data. AB and DK performed statistical analysis and drafted the manuscript. All authors read and approved the final manuscript.
Funding
This work was supported by National Institutes of Health Grants K01OD027037 (AB), Morris Animal Foundation Grant D18EQ-055 (LS, AB), T32OD011130 (DK) and T35OD11070 (IE).
Availability of data and materials
The raw sequence data and normalized cells counts reported in this paper have been deposited in the Gene Expression Omnibus (GSE207394). All other data are available upon reasonable request.
Declarations
Ethics approval and consent to participate
The Institutional Animal Care and Use Committee of North Carolina State University approved the use of horses in these studies.
Consent for publication
Not applicable.
Competing interests
The authors declare that they have no competing interests.
Author details
1. Department of Clinical Sciences, College of Veterinary Medicine, North Carolina State University, Raleigh, NC, USA.
Received: 3 July 2022 Accepted: 7 September 2022
Published online: 16 September 2022
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RESEARCH ARTICLE
Diagnostic and prognostic impact of cytokeratin 18 expression in human tumors: a tissue microarray study on 11,952 tumors
Anne Menz1, Timo Weitbrecht1, Natalia Gorbokon1, Franziska Büscheck1, Andreas M. Luebke1, Martina Kluth1, Claudia Hube-Magg1, Andrea Hinsch1, Doris Höflmayer1, Sören Weidemann1, Christoph Fraune1, Katharina Möller1, Christian Bernreuther1, Patrick Lebok1, Till Clauditz1, Guido Sauter1, Ria Uhlig1, Waldemar Wilczak1, Stefan Steurer1, Sarah Minner1, Eike Burandt1, Rainer Krech2, David Dum1, Till Krech1,2, Andreas Marx1,3 and Ronald Simon1*
Abstract
Background: Cytokeratin 18 (CK18) is an intermediate filament protein of the cytokeratin acidic type I group and is primarily expressed in single-layered or "simple" epithelial tissues and carcinomas of different origin.
Methods: To systematically determine CK18 expression in normal and cancerous tissues, 11,952 tumor samples from 115 different tumor types and subtypes (including carcinomas, mesenchymal and biphasic tumors) as well as 608 samples of 76 different normal tissue types were analyzed by immunohistochemistry in a tissue microarray format.
Results: CK18 was expressed in normal epithelial cells of most organs but absent in normal squamous epithelium. At least an occasional weak CK18 positivity was seen in 90 of 115 (78.3%) tumor types. Wide-spread CK18 positivity was seen in 37 (31.9%) of tumor entities, including adenocarcinomas of the lung, prostate, colon and pancreas as well as ovarian cancer. Tumor categories with variable CK18 immunostaining included cancer types arising from CK18 positive precursor cells but show CK18 downregulation in a fraction of cases, tumor types arising from CK18 negative precursor cells occasionally exhibiting CK18 neo-expression, tumors derived from normal tissues with variable CK18 expression, and tumors with a mixed differentiation. CK18 downregulation was for example seen in renal cell cancers and breast cancers, whereas CK18 neo-expression was found in squamous cell carcinomas of various origins. Down-regulation of CK18 in invasive breast carcinomas of no special type and clear cell renal cell carcinomas (ccRCC) was related to adverse tumor features in both tumors (p ≤ 0.0001) and poor patient prognosis in ccRCC (p = 0.0088). Up-regulation of CK18 in squamous cell carcinomas was linked to high grade and lymph node metastasis (p < 0.05). In summary, CK18 is consistently expressed in various epithelial cancers, especially adenocarcinomas.
Conclusions: Down-regulation or loss of CK18 expression in cancers arising from CK18 positive tissues as well as CK18 neo-expression in cancers originating from CK18 negative tissues is linked to cancer progression and may reflect tumor dedifferentiation.
Keywords: Cytokeratin 18 (CK18), Tissue microarray, Immunohistochemistry
© The Author(s) 2021. 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/.
Introduction
Cytokeratin 18 (CK18) belongs to the cytokeratin acidic type 1 group (CK9-CK12) and is encoded by a gene located at chromosome 12q13 (Moll et al. 1982; Waseem...
et al. 1990). CK18 is an intermediate filament protein that forms heteropolymers with its co-expressed complementary type II keratin partner CK8, which assembles into keratin filaments—the major structural component in the cytoplasm of epithelial cells (Moll et al. 1982; Fuchs and Weber 1994). CK18 is primarily expressed in single-layered or “simple” epithelial tissues of, for example, the liver, kidney, breast, prostate, gastrointestinal tract as well as in cancers arising from CK18 positive epithelial cells (Oshima et al. 1996; Cajaiba et al. 2006; Skinnider et al. 2005; Faridi et al. 2018). Beside the important structural function, CK18 was also shown to play a role in apoptosis (Caulin et al. (2000); Gilbert et al. 2001), cell cycle progression (Galarneau et al. 2007), and cancer-related signaling pathways. For example, CK18 hypoglycosylation is linked to decreased Akt1 kinase activity and reduced cell survival (Rotty et al. 2010). CK18 upregulation was described to be associated with decreased cell motility and invasiveness via the Wnt-pathway (Yee et al. 2010), and CK18 may be involved in the control of the ERK1/2-MAPK pathway (Zhang et al. 2006; Gilbert et al. 2004).
In surgical pathology, CK18 is used as an epithelial marker to identify CK18 positive adenocarcinomas that arise from different CK18 positive normal epithelia (Oshima et al. 1996; Weng et al. 2012). CK18 expression was also suggested as a potential prognostic marker. For example, decreased CK18 expression was found to be related to tumor progression in breast and colorectal cancers (Woellle et al. 2004; Knosel et al. 2006). Elevated CK18 protein levels were found to be associated with unfavorable tumor features in oral and esophageal squamous cell carcinomas (Makino et al. 2009; Fillies et al. 2006) as well as in non-small cell lung cancers (Zhang et al. 2016). CK18 antibodies have been used as diagnostic cancer markers for more than thirty years (Oshima et al. 1996). However, the literature on the prevalence of CK18 expression is controversial for many cancers (Walker et al. 2007; Shao et al. 2012; Bartek et al. 1991; Malzahn et al. 1998; Young et al. 2002; Lyda and Weiss 2000; Broers et al. 1988; Hsu et al. 2010; Ueda et al. 1993; Lam et al. 2001; Moll et al. 1993; Levy et al. 1992; Notohara et al. 2000; Akiba et al. 2016; Shimonishi et al. 2000; Yoshikawa et al. 1998; Sinard 1999; Poniecka and Alexis 1999; Balm et al. 1996; Nanda et al. 2012; Agaimy et al. 2012; Miettinen and Fetsch 2000; Raju 1988; Chen et al. 2011; Ishida et al. 2017; Nhung et al. 1999; Safadi et al. 2019). For example, CK18 positivity has been described in 30% to 100% of oral squamous cell carcinomas (Nanda et al. 2012; Safadi et al. 2019), 0% to 100% of non-small cell lung cancers (Chen et al. 2011; Nhung et al. 1999), and 0% to 43% of esophageal squamous cell carcinomas (Makino et al. 2009; Ishida et al. 2017). These conflicting data are likely to be caused by the use of different antibodies, immunostaining protocols, and criteria to determine CK18 positivity in these studies.
To better understand the prevalence and significance of CK18 expression in cancer, a comprehensive study analyzing a large number of neoplastic and non-neoplastic tissues under highly standardized conditions is needed. Therefore, CK18 expression was analyzed in more than 14,000 tumor tissue samples from 115 different tumor types and subtypes as well as 76 non-neoplastic tissue categories by immunohistochemistry (IHC) in a tissue microarray (TMA) format in this study.
**Materials and methods**
**Tissue microarrays (TMAs)**
Our normal tissue TMA was composed of 8 samples from 8 different donors for each of 76 different normal tissue types (608 samples on one slide). The cancer TMAs contained a total of 14,579 primary tumors from 115 tumor types and subtypes. Detailed histopathological data on grade, pT and pN status were available from 4191 cancers (breast, kidney, bladder, various kinds of squamous cell carcinoma). Clinical follow up data were available from 1178 breast cancer and 847 kidney cancer patients with a median follow-up time of 49/39 months (range 1–88/1–250). The composition of both normal and cancer TMAs is described in detail in the results section. All samples were from the archives of the Institutes of Pathology, University Hospital of Hamburg, Germany, the Institute of Pathology, Clinical Center Osnabrueck, Germany, and Department of Pathology, Academic Hospital Fuert, Germany. Tissues were fixed in 4% buffered formalin and then embedded in paraffin. The TMA manufacturing process was described earlier in detail (Dancau et al. 2016; Kononen et al. 1998). In brief, one tissue spot (diameter: 0.6 mm) was transmitted from a cancer containing donor block (> 70% cancer cells) in an empty recipient paraffin block. The use of archived remnants of diagnostic tissues for manufacturing of TMAs and their analysis for research purposes as well as patient data analysis has been approved by local laws (HmbKHG, §12) and by the local ethics committee (Ethics commission Hamburg, WF-049/09). All work has been carried out in compliance with the Helsinki Declaration.
**Immunohistochemistry**
Freshly cut TMA sections were immunostained on one day and in one experiment. Slides were deparaffinized and exposed to heat-induced antigen retrieval for 5 min in an autoclave at 121 °C in pH 7.8 buffer. Primary antibody specific for CK18 (mouse monoclonal, MSVA-118, MS Validated Antibodies, GmbH, Hamburg, Germany) was applied at 37 °C for 60 min at a dilution of 1:300. Bound antibody was then visualized using the EnVision
Kit (Agilent, CA, USA) according to the manufacturer’s directions. For tumor tissues, the percentage of positive neoplastic cells was estimated, and the staining intensity was semiquantitatively recorded (0, 1+, 2+, 3+).
For statistical analyses, the staining results were categorized into four groups. Tumors without any staining were considered negative. Tumors with 1+ staining intensity in \( \leq 70\% \) of cells and 2+ intensity in \( \leq 30\% \) of cells were considered weakly positive. Tumors with 1+ staining intensity in \( > 70\% \) of cells, 2+ intensity in 31–70%, or 3+ intensity in \( \leq 30\% \) were considered moderately positive. Tumors with 2+ intensity in \( > 70\% \) or 3+ intensity in \( > 30\% \) were considered strongly positive.
Statistics
Statistical calculations were performed with JMP 14 software (SAS Institute Inc., NC, USA). Contingency tables and the chi\(^2\)-test were performed to search for associations between CK18 and tumor phenotype. Survival curves were calculated according to Kaplan–Meier. The Log-Rank test was applied to detect significant differences between groups.
Results
Technical issues
A total of 11,952 (82.0%) of 14,579 tumor samples were interpretable in our TMA analysis. The remaining 2627 (18.0%) samples were not analyzable due to the lack of unequivocal tumor cells or loss of the tissue spot during the technical procedures. On the normal tissue TMA, a sufficient number of samples was always interpretable per tissue to determine the CK18 expression.
CK18 in normal tissues
CK18 was highly expressed in epithelial cells of the stomach (except parietal cells), duodenum, ileum, appendix, colon, rectum (Fig. 1a), gall bladder, pancreas (weaker staining in Islet cells than in acinus cells; Fig. 1b), endometrium, endocervix, alveolar cells of the lung, cytотrophoblast and syncytiotrophoblast of the placenta,
 Cytokeratin 18 (CK18) expression in normal tissues. The images show strong CK18 staining in epithelial cells from rectum (a) and pancreas (b), a zonal staining variability in the liver (c), strongly positive umbrella cells and a gradually decreasing staining intensity from superficial to basal urothelial cells in the bladder (d), strong positivity in acinus cells but absent staining in basal cells of the breast epithelium (e) and a complete lack of staining in squamous epithelium of the oral mucosa (f).
and in all cells of the adenohypophysis (variable staining intensity). Liver tissue exhibited a zonal variability in hepatocyte staining ranging from negative to strongly positive (Fig. 1c). Bile ducts were always positive. Urothelium of the kidney and urinary bladder showed a strong staining in umbrella cells and a gradually decreasing staining intensity from superficial to basal urothelial cells (Fig. 1d). Salivary glands showed strong staining of serous and mucinous cells but somewhat weaker positivity in excretion ducts, especially in large ones. Some ducts only showed few positive cells or complete CK18 negativity. In the kidney, proximal and distal tubuli as well as collecting ducts were CK18 positive. In the ovary, follicular cells and follicular cysts stained positive as well as some cells of the corpus luteum. A strong positive staining of glandular cells with weaker and probably absent staining in basal cells was seen in prostate, respiratory mucosa of bronchus and paranasal sinuses, epididymis, seminal vesicle, and breast glands (Fig. 1e). In lymph nodes, tonsil, spleen, and thymus delicate fibrillar staining caused by CK18 positive fibroblastic reticulum occurred mainly in the interfollicular area. In the thymus, some cellular components of Hassal bodies were CK18 positive, and merkel cells in the skin and hair follicles were CK18 positive. CK18 was absent in all mesenchymal tissues, the stroma of the ovary, posterior lobe of the pituitary gland, brain, bone marrow, lymph nodes, spleen and lymphocytes in tonsil and thymus. Staining was also negative in all squamous epithelia from esophagus, skin, lip, oral cavity (Fig. 1f), tonsil, and anal canal, hair follicles, sebaceous glands, testis (except some weak staining in some Sertoli cells in 2 of 8 samples), adrenal gland (except some cells with weak staining in 1/8 samples), aorta, heart, striated muscle, skeletal muscle, myometrium, muscular wall of the gastrointestinal tract, kidney pelvis, and the urinary bladder, corpus spongiosus of the penis, bone marrow.
A detailed description of the immunostaining results is given in Table 1 and Fig. 3.
**CK18 expression, tumor phenotype, and prognosis**
The relationship between CK18 expression and clinicopathological data could be analyzed in two cancer types derived from CK18 positive precursor cells (breast and kidney cancer), one cancer type derived from epithelium with variable CK18 expression (urinary bladder) as well as in 230 squamous cell carcinomas of various organs of origin (n=8), but all derived from squamous epithelia that are normally CK18 negative (Table 2, Fig. 4). Reduced or absent CK18 immunostaining was associated with high UICC stage (p=0.001), high Thoenes grade (p=0.0086), advanced tumor stage (p<0.0001), and poor prognosis in clear cell renal cell cancers (p=0.0088) and with high grade and unfavorable molecular features such as ER/PR negativity (p<0.0001 each)—but not with patient outcome—in invasive breast carcinomas of no special type. In squamous cell carcinomas, CK18 up-regulation was preferentially seen in cancers with advanced stage (13.2%/136 pT1-2 vs 27.7%/94 pT3-4; p=0.0154), presence of lymph node metastasis (14.7%/95 pN0 vs 26.1%/92; p=0.0354) and high grade (14.9%/134 G1-2 vs 28.0%/75 G3; p=0.0767, data not shown). In bladder cancer, the CK18 expression pattern varied between subgroups. Within 1,353 patients that were treated by cystectomy, CK18 expression was unrelated to pathological parameters and patient outcome, however.
**Discussion**
The standardized analysis of 11,952 cancers by IHC gives a comprehensive overview on CK18 staining in malignant tumors. The most valuable result of our study is a ranking order of CK18 positivity across a broad range of tumor entities which enables an estimate of the relative biologic importance of CK18 for individual tumor types and—together with the absolute numbers obtained in our analysis—a better assessment of the diagnostic impact of CK18 immunostaining results in specific diagnostic situations. The S-shaped curve of the CK18 expression frequencies found across 115 different tumor types reflects that frequent and intense CK18 immunostaining is commonly seen in cancers derived from CK18 positive normal cell types while most other tumors are often CK18 negative. 37 of 115 analyzed tumor entities (32.2%) showed CK18 positivity in >97% of cases. Sporadic negative cases in the range of ≤3% in these cancer types may well be caused by technical issues. Some unexpected negative staining always occurs in TMAs because not all tissues are properly fixed in all areas (Tapia et al. 2004). Unequal immunostaining in tissues results in an
immunostaining gradient across a tissue block and can result in false negative immunostaining, if TMA cores are taken from areas with poor reactivity (Fraune et al. 2020).
The group of cancers with variable CK18 immunostaining results including significant fractions of patients with CK18 positive and CK18 negative cancers, is heterogeneous in nature. This category contains cancer types arising from CK18 positive precursor cells but showing CK18 downregulation in a fraction of cases, tumor types arising from CK18 negative precursor cells but undergoing CK18 upregulation in a fraction of cancers, neoplasia's derived from tissues with variable CK18 expression in benign precursors, and tumors with a mixed differentiation. The latter group contains tumors with a mixed glandular/squamous differentiation such as endometroid carcinomas of the uterus where adenomatous but not squamous epithelia stain positive as well as epithelial-mesenchymal tumors such as carcinosarcoma of the uterus and ovary, phyllodes tumor of the breast, teratoma of the testis or malignant mesothelioma. In these tumors, glandular epithelial but not mesenchymal tumor areas stain positive.
Cancers that markedly downregulate CK18 in a relevant fraction of cases include renal cell and breast cancers. True downregulation can easily be distinguished from artificial staining deficiency by presence of strongly staining normal cells in the same tissue spot. The analysis of larger cohorts of kidney and breast cancers for which clinical follow-up data were available identified significant associations of reduced CK18 immunostaining with unfavorable tumor phenotype and—in case of clear cell renal cell carcinoma—poor patient prognosis. These findings are consistent with earlier studies in breast cancer and may reflect a tendency towards a worse prognosis in cancer cells with an impaired cell differentiation (Woelfle et al. 2004; Willipinski-Stapelfeldt et al. 2005). That various cancer types that are by default poorly differentiated such as small cell carcinomas or anaplastic thyroid cancer showed lower CK18 positivity rates than their better differentiated counterparts is also consistent with the concept of a CK18 expression loss during tumor progression.
Fig. 2 Cytokeratin 18 (CK18) expression in tumors. The images show diffuse strong CK18 staining in a colorectal carcinoma (a), an invasive breast carcinoma of no special type (b), a clear cell carcinoma of the kidney (c), and a squamous cell carcinoma of the cervix uteri (d). CK18 immunostaining is focal in a squamous cell carcinoma of the larynx (e) and absent in another renal cell clear cell carcinoma (f).
| Entity | On TMA (n) | CK18 immunostaining |
|-------|-----------|---------------------|
| | Analyzable (n) | Negative (%) | Weak (%) | Moderate (%) | Strong (%) | Positive (%) |
| Tumors of the skin | | | | | | |
| Pilomatrixoma | 35 | 28 | 100.0 | 0.0 | 0.0 | 0.0 | 0.0 |
| Basal cell carcinoma | 48 | 42 | 100.0 | 0.0 | 0.0 | 0.0 | 0.0 |
| Benign nevus | 29 | 23 | 100.0 | 0.0 | 0.0 | 0.0 | 0.0 |
| Squamous cell carcinoma of the skin | 50 | 44 | 93.2 | 6.8 | 0.0 | 0.0 | 6.8 |
| Malignant melanoma | 48 | 43 | 100.0 | 0.0 | 0.0 | 0.0 | 0.0 |
| Merkel cell carcinoma | 46 | 43 | 32.6 | 16.3 | 23.3 | 27.9 | 67.4 |
| Tumors of the head and neck | | | | | | |
| Squamous cell carcinoma of the larynx | 50 | 43 | 72.1 | 25.6 | 0.0 | 2.3 | 27.9 |
| Oral squamous cell carcinoma (floor of the mouth) | 50 | 43 | 93.0 | 7.0 | 0.0 | 0.0 | 7.0 |
| Pleomorphic adenoma of the parotid gland | 50 | 42 | 23.8 | 50.0 | 19.0 | 7.1 | 76.2 |
| Warthin tumor of the parotid gland | 49 | 47 | 0.0 | 40.4 | 36.2 | 23.4 | 100.0 |
| Basal cell adenoma of the salivary gland | 15 | 15 | 6.7 | 50.0 | 6.7 | 26.7 | 93.3 |
| Tumors of the lung, pleura and thymus | | | | | | |
| Squamous cell carcinoma of the lung | 77 | 66 | 39.4 | 48.5 | 7.6 | 4.5 | 60.6 |
| Small cell carcinoma of the lung | 20 | 16 | 18.8 | 12.5 | 50.0 | 18.8 | 81.3 |
| Malignant mesothelioma | 48 | 40 | 12.5 | 12.5 | 15.0 | 60.0 | 87.5 |
| Mesothelioma, other types | 28 | 18 | 11.1 | 33.3 | 16.7 | 38.9 | 88.9 |
| Mesothelioma, epithelioid | 39 | 26 | 3.8 | 11.5 | 34.6 | 50.0 | 96.2 |
| Tumors of the female genital tract | | | | | | |
| Squamous cell carcinoma of the vagina | 48 | 20 | 90.0 | 5.0 | 0.0 | 5.0 | 10.0 |
| Squamous cell carcinoma of the vulva | 50 | 33 | 100.0 | 0.0 | 0.0 | 0.0 | 0.0 |
| Squamous cell carcinoma of the cervix | 50 | 35 | 88.6 | 2.9 | 0.0 | 8.6 | 11.4 |
| Adenocarcinoma of the cervix uteri | 50 | 38 | 0.0 | 13.2 | 23.7 | 63.2 | 100.0 |
| Endometrioid endometrial carcinoma | 236 | 212 | 0.5 | 14.2 | 22.2 | 63.2 | 99.5 |
| Endometrial serous carcinoma | 82 | 53 | 1.9 | 15.1 | 34.0 | 43.4 | 92.5 |
| Carcinosarcoma of the uterus | 48 | 38 | 21.1 | 26.3 | 34.2 | 18.4 | 78.9 |
| Endometrial clear cell carcinoma | 8 | 7 | 0.0 | 57.1 | 42.9 | 0.0 | 100.0 |
| Endometrial carcinoma, low differentiated G3 | 13 | 12 | 33.3 | 33.3 | 25.0 | 8.3 | 66.7 |
| Endometrial stromal sarcoma | 12 | 10 | 100.0 | 0.0 | 0.0 | 0.0 | 0.0 |
| Endometrioid carcinoma of the ovary | 115 | 86 | 1.2 | 4.7 | 26.7 | 67.4 | 98.8 |
| Entity | On TMA (n) | CK18 immunostaining |
|----------------------------------------|------------|---------------------|
| | Analyzable (n) | Negative (%) | Weak (%) | Moderate (%) | Strong (%) | Positive (%) |
| Serous carcinoma of the ovary | 567 | 495 | 0.8 | 13.7 | 31.9 | 53.5 | 99.2 |
| Mucinous carcinoma of the ovary | 97 | 75 | 0.0 | 17.3 | 18.7 | 64.0 | 100.0 |
| Clear cell carcinoma of the ovary | 54 | 47 | 8.5 | 34.0 | 31.9 | 25.5 | 91.5 |
| Carcinosarcoma of the ovary | 47 | 41 | 22.0 | 14.6 | 24.4 | 39.0 | 78.0 |
| Brenner tumor | 9 | 8 | 62.5 | 37.5 | 0.0 | 0.0 | 37.5 |
| Invasive breast carcinoma of no special type | 1391 | 1001 | 3.6 | 21.8 | 23.5 | 50.9 | 96.2 |
| Lobular carcinoma of the breast | 294 | 229 | 0.4 | 21.0 | 26.6 | 52.0 | 99.6 |
| Medullary carcinoma of the breast | 26 | 22 | 59.1 | 18.2 | 9.1 | 13.6 | 40.9 |
| Tubular carcinoma of the breast | 27 | 17 | 0.0 | 23.5 | 17.6 | 58.8 | 100.0 |
| Mucinous carcinoma of the breast | 58 | 35 | 0.0 | 11.4 | 37.1 | 51.4 | 100.0 |
| Phyllodes tumor of the breast | 50 | 32 | 0.0 | 37.5 | 21.9 | 40.6 | 100.0 |
| Adenomatous polyp, low-grade dysplasia | 50 | 41 | 0.0 | 0.0 | 0.0 | 100.0 | 100.0 |
| Adenomatous polyp, high-grade dysplasia| 50 | 44 | 0.0 | 0.0 | 2.3 | 97.7 | 100.0 |
| Adenocarcinoma of the colon | 1932 | 1750 | 2.6 | 2.3 | 9.9 | 85.3 | 97.4 |
| Adenocarcinoma of the small intestine | 10 | 5 | 0.0 | 0.0 | 0.0 | 100.0 | 100.0 |
| Gastric adenocarcinoma, diffuse type | 226 | 161 | 5.6 | 32.3 | 28.6 | 33.5 | 94.4 |
| Gastric adenocarcinoma, intestinal type| 224 | 156 | 7.1 | 23.7 | 19.2 | 50.0 | 92.9 |
| Gastric adenocarcinoma, mixed type | 62 | 59 | 5.1 | 25.4 | 22.0 | 47.5 | 94.9 |
| Adenocarcinoma of the esophagus | 133 | 70 | 1.4 | 12.9 | 7.1 | 78.6 | 98.6 |
| Squamous cell carcinoma of the esophagus| 124 | 63 | 68.3 | 22.2 | 0.0 | 9.5 | 31.7 |
| Squamous cell carcinoma of the anal canal | 50 | 33 | 75.8 | 15.2 | 9.1 | 0.0 | 24.2 |
| Cholangiocarcinoma | 130 | 112 | 1.8 | 17.0 | 29.5 | 51.8 | 98.2 |
| Hepatocellular carcinoma | 50 | 49 | 8.2 | 28.6 | 20.4 | 42.9 | 91.8 |
| Ductal adenocarcinoma of the pancreas | 612 | 523 | 1.0 | 16.8 | 25.6 | 56.6 | 99.0 |
| Pancreatic/Ampullary adenocarcinoma | 89 | 76 | 5.3 | 6.6 | 25.0 | 63.2 | 94.7 |
| Acinar cell carcinoma of the pancreas | 13 | 12 | 0.0 | 0.0 | 16.7 | 83.3 | 100.0 |
| Entity | On TMA (n) | CK18 immunostaining |
|--------|------------|---------------------|
| | Analyzable (n) | Negative (%) | Weak (%) | Moderate (%) | Strong (%) | Positive (%) |
| Tumors of the urinary system | | | | | | |
| Tumors of the male genital organs | | | | | | |
| Tumors of endocrine organs | | | | | | |
### Table 1 (continued)
| Entity | On TMA (n) | CK18 immunostaining |
|------------------------------------------------------------------------|------------|---------------------|
| | Analyzable (n) | Negative (%) | Weak (%) | Moderate (%) | Strong (%) | Positive (%) |
| Follicular thyroid carcinoma | 158 | 150 | 0.0 | 2.0 | 34.0 | 64.0 | 100.0 |
| Medullary thyroid carcinoma | 107 | 98 | 1.0 | 6.1 | 33.7 | 59.2 | 99.0 |
| Anaplastic thyroid carcinoma | 45 | 43 | 41.9 | 32.6 | 14.0 | 11.6 | 58.1 |
| Adrenal cortical adenoma | 50 | 36 | 91.7 | 5.6 | 0.0 | 2.8 | 8.3 |
| Adrenal cortical carcinoma | 26 | 20 | 70.0 | 10.0 | 0.0 | 20.0 | 30.0 |
| Phaeochromocytoma | 50 | 42 | 100.0 | 0.0 | 0.0 | 0.0 | 0.0 |
| Appendix; neuroendocrine tumor (NET) | 22 | 15 | 0.0 | 8.3 | 0.0 | 91.7 | 100.0 |
| Colorectal, neuroendocrine tumor (NET) | 10 | 10 | 0.0 | 0.0 | 10.0 | 90.0 | 100.0 |
| Ileum, neuroendocrine tumor (NET) | 49 | 45 | 0.0 | 2.2 | 2.2 | 95.6 | 100.0 |
| Lung, neuroendocrine tumor (NET) | 19 | 18 | 0.0 | 11.8 | 17.6 | 70.6 | 100.0 |
| Pancreas, neuroendocrine tumor (NET) | 102 | 79 | 1.3 | 5.1 | 31.6 | 62.0 | 98.7 |
| Colorectal, neuroendocrine carcinoma (NEC) | 11 | 9 | 33.3 | 22.2 | 22.2 | 22.2 | 66.7 |
| Gallbladder, neuroendocrine carcinoma (NEC) | 4 | 4 | 50.0 | 0.0 | 25.0 | 25.0 | 50.0 |
| Pancreas, neuroendocrine carcinoma (NEC) | 13 | 7 | 28.6 | 28.6 | 0.0 | 42.9 | 71.4 |
| Tumors of hematopoietic and lymphoid tissues | | | | | | | |
| Hodgkin Lymphoma | 45 | 39 | 100.0 | 0.0 | 0.0 | 0.0 | 0.0 |
| Non-Hodgkin Lymphoma | 48 | 41 | 100.0 | 0.0 | 0.0 | 0.0 | 0.0 |
| Tumors of soft tissue and bone | | | | | | | |
| Tenosynovial giant cell tumor | 45 | 43 | 100.0 | 0.0 | 0.0 | 0.0 | 0.0 |
| Granular cell tumor | 53 | 32 | 100.0 | 0.0 | 0.0 | 0.0 | 0.0 |
| Leiomyoma | 50 | 32 | 100.0 | 0.0 | 0.0 | 0.0 | 0.0 |
| Angiomyolipoma | 91 | 74 | 98.6 | 1.4 | 0.0 | 0.0 | 1.4 |
| Angiosarcoma | 73 | 55 | 87.3 | 7.3 | 3.6 | 1.8 | 12.7 |
| Dermatofibrosarcoma protuberans | 21 | 16 | 100.0 | 0.0 | 0.0 | 0.0 | 0.0 |
| Ganglioneuroma | 14 | 11 | 100.0 | 0.0 | 0.0 | 0.0 | 0.0 |
| Kaposi sarcoma | 8 | 5 | 100.0 | 0.0 | 0.0 | 0.0 | 0.0 |
| Leiomyosarcoma | 87 | 70 | 100.0 | 0.0 | 0.0 | 0.0 | 0.0 |
| Liposarcoma | 132 | 98 | 100.0 | 0.0 | 0.0 | 0.0 | 0.0 |
| Malignant peripheral nerve sheath tumor (MPNST) | 13 | 12 | 100.0 | 0.0 | 0.0 | 0.0 | 0.0 |
| Myofibrosarcoma | 26 | 24 | 100.0 | 0.0 | 0.0 | 0.0 | 0.0 |
| Neurofibroma | 117 | 103 | 100.0 | 0.0 | 0.0 | 0.0 | 0.0 |
Squamous cell carcinomas are the best examples of epithelial tumors that are typically CK18 negative but can upregulate CK18. Even though CK18 immunostaining was not at all observed in any normal squamous epithelium samples from the lung, tonsil, skin, anal canal, oral cavity, or lip, a positive CK18 immunostaining was observed in 8 of 9 analyzed squamous cell carcinoma subtypes. That CK18 immunostaining was sometimes seen at high levels in these squamous cell carcinomas further demonstrates that these findings reflect true overexpression and not just a faint non-specific antibody binding. Our notion, that CK18 upregulation reflects aberrant differentiation or dedifferentiation in these cancers is supported by significant associations of elevated CK18 protein levels with high pT stage and presence of nodal metastasis that could be
| Table 2 Cytokeratin 18 immunostaining and tumor phenotype | n | CK18 Immunostaining | p |
|---------------------------------------------------------|---|---------------------|---|
| Invasive breast carcinoma of no special type | | Negative (%) | Weak (%) | Moderate (%) | Strong (%) |
| All cancers | 935| 3.6 | 22.2 | 23.9 | 50.3 |
| pT1 | 497| 4.2 | 18.9 | 25.0 | 51.9 | 0.0611 |
| pT2 | 333| 2.4 | 26.1 | 23.7 | 47.8 |
| pT3-4 | 73 | 6.9 | 19.2 | 16.4 | 57.5 |
| Grade 1 | 147| 0.0 | 16.3 | 21.1 | 62.6 | <0.0001 |
| Grade 2 | 479| 2.1 | 19.0 | 26.7 | 52.2 |
| Grade 3 | 308| 7.8 | 30.2 | 20.5 | 41.6 |
| pN0 | 439| 3.2 | 20.1 | 23.9 | 52.9 | 0.6092 |
| pN+ | 299| 2.7 | 23.1 | 25.8 | 48.5 |
| HER2 negative | 697| 4.0 | 20.8 | 22.0 | 53.2 | 0.1689 |
| HER2 positive | 89 | 1.1 | 18.0 | 30.3 | 50.6 |
| ER negative | 160| 15.0| 33.8 | 23.1 | 28.1 | <0.0001 |
| ER positive | 589| 0.5 | 16.6 | 22.8 | 60.1 |
| PR negative | 308| 8.8 | 28.6 | 24.0 | 38.6 | <0.0001 |
| PR positive | 472| 0.4 | 15.7 | 22.7 | 61.2 |
| Non-triple negative | 619| 0.8 | 17.5 | 22.5 | 59.3 | <0.0001 |
| Triple negative | 107| 20.6| 37.4 | 21.5 | 20.6 |
| Clear cell renal cell carcinoma | | | | | |
| All cancers | 674| 48.7| 30.4 | 14.1 | 68 |
| ISUP 1 | 217| 42.9| 35.5 | 15.2 | 65 | 0.1312 |
| ISUP 2 | 218| 50.5| 28.4 | 13.8 | 7.3 |
| ISUP 3 | 189| 51.3| 30.2 | 13.2 | 5.3 |
| ISUP 4 | 40 | 67.5| 17.5 | 5.0 | 100 |
| Fuhrmann 1 | 32 | 37.5| 34.4 | 21.9 | 63 | 0.2311 |
| Fuhrmann 2 | 399| 46.4| 31.6 | 15.0 | 7.0 |
| Fuhrmann 3 | 194| 52.1| 30.9 | 11.3 | 5.7 |
| Fuhrmann 4 | 48 | 62.5| 16.7 | 10.4 | 10.4 |
| Thoenes 1 | 239| 41.0| 33.9 | 17.6 | 7.5 | 0.0086 |
| Thoenes 2 | 369| 51.8| 30.1 | 12.7 | 5.4 |
| Thoenes 3 | 65 | 60.0| 20.0 | 7.7 | 12.3 |
| UICC 1 | 294| 37.4| 36.1 | 19.0 | 7.5 | 0.0010 |
| UICC 2 | 34 | 50.0| 32.4 | 11.8 | 5.9 |
| UICC 3 | 87 | 58.6| 20.7 | 11.5 | 9.2 |
| UICC 4 | 70 | 57.1| 34.3 | 7.1 | 1.4 |
| pT1 | 391| 40.2| 35.8 | 16.1 | 7.9 | <0.0001 |
| pT2 | 72 | 59.7| 25.0 | 11.1 | 4.2 |
| pT3 | 266| 61.7| 21.4 | 11.2 | 5.8 |
| pN0 | 114| 55.3| 26.9 | 7.9 | 7.9 | 0.5327 |
| pN+ | 16 | 43.8| 25.0 | 18.8 | 12.5 |
| pM0 | 102| 39.2| 35.3 | 15.7 | 9.8 | <0.0001 |
| pM+ | 73 | 64.4| 31.5 | 4.1 | 0.0 |
| Urinary bladder cancer | | | | | |
| All cancers | 1353| 37.0 | 25.4 | 18.0 | 19.7 |
| pTa G2 low | 109 | 41.3 | 11.9 | 23.9 | 22.9 | <0.0001 |
| pTa G2 high | 100 | 36.0 | 20.0 | 24.0 | 20.0 |
| pTaG3 | 144| 18.8| 27.8 | 24.3 | 29.2 |
identified in a combined analysis of our 230 squamous cell carcinomas with available clinico-pathological data. These findings fit with data from several earlier studies suggesting a link between CK18 positivity and unfavorable clinico-pathological features and outcome in squamous cell carcinomas of the lung, esophagus, oral cavity, and pharynx (Makino et al. 2009; Broers et al. 1988; Nanda et al. 2012; Nhung et al. 1999; Safadi et al. 2019; Yang et al. 2018; Afrem et al. 2016).
The role of CK18 is less clear in tumor entities derived from tissues with variable CK18 expression such as in liver and urinary bladder cancer. In our analysis of 1353 urothelial carcinomas, 37% were completely negative and 20% of all cancers were considered strongly positive. That a marked difference in CK18 immunostaining was seen between pTa and pT2-4 urothelial carcinomas is consistent with the striking genomic differences between these tumor categories (summarized in (Knowles and Hurst 2015)). The absence of a statistically significant impact
### Table 2 (continued)
| n | CK18 Immunostaining | p |
|--------|---------------------|---------|
| | Negative (%) | Weak (%) | Moderate (%) | Strong (%) |
| pT ≥ 2 G3 | 921 | 39.9 | 28.0 | 14.8 | 17.4 |
| pT ≥ 2 G3 sarcomatoid | 18 | 33.3 | 33.3 | 11.1 | 22.2 |
| pT ≥ 2 G3 small cell cancer | 18 | 66.7 | 33.3 | 0.0 | 0.0 |
| pN0 | 293 | 36.5 | 26.6 | 16.7 | 20.1 | 0.2540 |
| pN+ | 170 | 27.7 | 29.4 | 18.2 | 24.7 |
**Fig. 4** Cytokeratin 18 (CK18) immunostaining and patient prognosis. All bladder cancer patients had at least pT2 cancers and were treated by cystectomy.
of CK18 expression on clinico-pathological features and outcome of pT2-4 carcinomas treated by cystectomy argues against a functional role of CK18 for cancer progression. CK18 plays a role in various cellular processes, such as securing the structure of the cytoplasm and mitochondria that are not directly related to cancer aggressiveness (Coulombe and Wong 2004). Considering the continuous increase of CK18 expression from basal and intermediate cells to the superficial and umbrella cells of the bladder epithelium, various levels of CK18 in cancer cells may also be related to the specific cell of origin.
Our data enable a comprehensive assessment of potential diagnostic applications of CK18 IHC. The close to 100% prevalence of CK18 expression in gastrointestinal cancers supports the concept of using CK18 measurement for metastasis detection (Oshima et al. 1996; Makino et al. 2009). The most useful diagnostic application of CK18 IHC may be the distinction of seminomas from other germ cell tumors of the testis. Only 12 of 204 analyzed seminomas (6%) but all of 88 embryonal carcinomas and yolk sack tumors of the testis showed CK18 expression. This finding is in line with data from an RNA and protein expression study identifying CK18 expression in seminomas.
as one of the strongest discriminators of seminomatous versus non-seminomatous testicular germ cell tumors (Biermann et al. 2007). Pan-cytokeratin antibodies are often being included in diagnostic IHC panels to be used for the distinction of testicular cancer subtypes. In this context, cytookeratin positivity argues against seminoma which ideally should show either none or only weak cytookeratin staining. Considering that pan-cytokeratin staining is found in >20% of seminomas and in >80% of non-seminomas (summarized in (Emerson and Ulbright (2005))), the use of cytokeratin 18 showing positivity in 2.5% of seminomas and 100% of embryonal carcinoma of the testis as well as 100% of yolk sack tumors in our study might be preferable for testicular cancer subtyping. It appears conceivable that an antibody targeting just CK18 offers better specificity than an antibody targeting multiple cytokeratins.
Importantly, all prevalence’s described in this study are specific to the reagents and the protocol used in our laboratory. It is almost certain, that the use of different antibodies, protocols and interpretation criteria have jointly caused highly diverse literature data on CK18 expression in cancer (summarized in Fig. 5). It is well known, that different antibodies designed for the same target protein can vary to a large extent in their binding properties and that protocol modifications greatly impact the rate of immunostained cases (Saper 2009). However, the abundant data generated in this study would potentially make it possible to adjust a protocol for CK18 immunostaining and interpretation in a way that resulted in comparable frequencies of CK18 positivity. For that purpose, it might be sufficient to use smaller collections of tumors with high positivity rate such as adenocarcinomas of the prostate or the colorectum and of tumors with low positivity rates such as squamous cell carcinomas of various types to develop a protocol that results in comparable data as provided in this study.
Conclusions
Our data show that CK18 is consistently expressed in various epithelial cancers, especially adenocarcinomas. Both loss of CK18 expression in cancers derived from CK18 positive precursor cells and neo-expression in malignancies derived from CK18 positive precursors tend to be linked to unfavorable tumor phenotype and disease outcome. Distinction of seminomas from other germ cell tumors of the testis appears to be the strongest diagnostic application of CK18 IHC.
Abbreviations
Akt1: Serine/threonine-protein kinase; CK18: Cytokeratin 18; ER: Estrogen receptor; ERK: Extracellular signal-regulated kinase; IHC: Immunohistochemistry; ISUP: International Society of Urological Pathology; MAPK: Mitogen-activated protein kinase; PR: Progesterone receptor; TMA: Tissue microarray; UICC: International Union Against Cancer.
Acknowledgements
We are grateful to Melanie Witt, Inge Brandt, Maren Eisenberg, Christina Möller-Koop, and Süße Seekamp for excellent technical assistance.
Authors’ contributions
AM, RS, MIK, DH, KM, SW, TC, CH-M, AH contributed to conception, design, data collection, data analysis and manuscript writing. AM, TW, NG, FB, AL, CF, CB: immunohistochemistry analysis. RK, TK, AM: conception and design, collection of samples. PL, DD, SS, RU, SM, EB: data collection and data analysis. AM, GS, WW, RS: study supervision. All authors read and approved the final manuscript.
Funding
Open Access funding enabled and organized by Projekt DEAL.
Availability of data and materials
All data generated or analyzed during this study are included in this published article.
Ethics approval and consent to participate
The usage of archived diagnostic left-over tissues for manufacturing of tissue microarrays, their analysis for research purposes and patient data analysis has been approved by local laws (HmbKHG, §12,1) and by the local ethics committee (Ethics commission Hamburg, WF-049/09). All work has been carried out in compliance with the Helsinki Declaration.
Consent for publication
Not applicable.
Competing interests
The Institute of Pathology of the UKE receives royalties on the sale of CK18 clone MSVA-118 from MS Validated Antibodies GmbH (owned by a family member of GS).
Author details
1 Institute of Pathology, University Medical Center Hamburg-Eppendorf, Martinistr. 52, 20246 Hamburg, Germany. 2 Institute of Pathology, Clinical Center Osnabruuck, Osnabrueck, Germany. 3 Department of Pathology, Academic Hospital Fuerth, Fuerth, Germany.
Received: 21 October 2020 Accepted: 18 January 2021
Published online: 15 February 2021
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Cell-penetrating peptide conjugates to enhance the antitumor effect of paclitaxel on drug-resistant lung cancer
Ziqing Duan1, Cuitian Chen1, Jing Qin1, Qi Liu1, Qi Wang2, Xinchun Xu3, and Jianxin Wang1
1Department of Pharmaceutics, School of Pharmacy, Fudan University & Key Laboratory of Smart Drug Delivery, Ministry of Education, Shanghai, PR China, 2Institute of Clinical Pharmacology, Guangzhou University of Traditional Chinese Medicine, Guangzhou, PR China, and 3Shanghai Xuhui Central Hospital, Shanghai, PR China
Abstract
To conquer the drug resistance of tumors and the poor solubility of paclitaxel (PTX), two PTX-cell-penetrating peptide conjugates (PTX-CPPs), PTX-TAT and PTX-LMWP, were synthesized and evaluated for the first time. Compared with free PTX, PTX-CPPs displayed significantly enhanced cellular uptake, elevated cell toxicity, increased cell apoptosis, and decreased mitochondrial membrane potential (ΔΨm) in both A549 and A549T cells. PTX-LMWP exhibited a stronger inhibitory effect than PTX-TAT in A549T cells. Analysis of cell-cycle distribution showed that PTX-LMWP influenced mitosis in drug-resistant A549T tumor cells via a different mechanism than PTX. PTX-CPPs were more efficient in inhibiting tumor growth in tumor-bearing mice than free PTX, which suggested their better in vivo antitumor efficacy. Hence, this study demonstrates that PTX-CPPs, particularly PTX-LMWP, have outstanding potential for inhibiting the growth of tumors and are a promising approach for treating lung cancer, especially drug-resistant lung cancer.
Keywords
Paclitaxel, low molecular weight protamine, TAT, conjugate, cell-penetrating peptide, drug-resistant lung cancer
Introduction
Lung cancer is a fatal disease with high incidence and mortality rates (Siegel et al., 2012). As a cytotoxic microtubule-stabilizing agent extracted from Taxus brevifolia (Pacific Yew) (de Hoon et al., 2012) and a commonly used drug to treat lung cancer in the clinic (Xu et al., 2016), paclitaxel (PTX) has made a significant contribution on improving the quality of life and prolonging the survival time of lung cancer patients. However, drug resistance has become a serious challenge in the application of PTX (Zuo et al., 2010; Rasco et al., 2010; Ferrara et al., 2016). The mechanisms of drug resistance can be divided into pump resistance and non-pump resistance (Minko et al., 2013). Pump resistance plays an important role and is primarily caused by membrane-bound active drug efflux pumps such as P-glycoprotein, multidrug resistance-associated proteins, and breast cancer resistance proteins (Patel et al., 2013). As a transmembrane adenosine triphosphate (ATP)-dependent efflux pump presenting in a great diversity of tumors (Yusuf et al., 2003), P-glycoprotein efflux pump is the most widely reported mechanism of PTX resistance (Yusuf et al., 2003; Luqmani, 2005). Overexpression of P-glycoprotein in cancer cells leads to decreased accumulation of PTX and reduced antitumor efficacy. Many studies (Zunino & Capranico, 1990; Nicholson, 2000; Galletti et al., 2007; Vasile et al., 2007; Vasilie et al., 2015) have also revealed that non-pump mechanisms, including but not limited to drug degradation, mutation of tubulin/microtubule system, antiapoptotic defense, and DNA repair, also participate in the development of PTX resistance.
To conquer this problem, many efforts have been made to diminish or circumvent the activity of efflux pumps. The discovery of efflux pump inhibitors has attracted much attention, and co-delivery of anticancer drugs with efflux transporter inhibitors has shown potential for reversing drug resistance in tumors (Patil et al., 2009; Song et al., 2009). However, applications of the inhibitors are hindered by their lack of specificity, poor bioavailability, adverse effects and limited clinical activities (van Zuylen et al., 2000; Pusztai et al., 2005; Kibria et al., 2014). With the development of nanomedicine, some researchers (Susa et al., 2009; Wang et al., 2011) have demonstrated that nanoparticles can help antitumor drugs bypass efflux pumps by preventing the
exposure of antitumor drugs and transporting them into cells through endocytic pathway. However, in order to overcome drug resistance using nanocarrier strategies, antitumor drugs should remain incorporated in nanoparticles until internalization (Wang et al., 2015b). Considering most nanoparticles are designed to disassemble at the tumor site and release their cargo, the clinical anti-drug-resistant effect of nanoparticles still needs to be assessed cautiously.
Modifying the structure of anti-cancer drugs is another effective strategy to circumvent drug resistance (Liang & Yang, 2005; Ferrara et al., 2016). According to a recent study (Minko et al., 2013), antitumor drugs excluded by efflux pumps need to conform to three essential properties: having a relatively low molecular weight, capable of mimicking the substrate of an efflux pump and being internalized into cells through passive diffusion. Therefore, modifying the molecular structure of a drug and/or changing the mechanism of drug internalization could, in theory, bypass efflux pumps (Minko et al., 2013; Vargas et al., 2014). Meanwhile, conjugating anti-cancer drugs with functional molecules, such as proteins, peptides, monoclonal antibodies, polymers, glycans, or other molecules, can deliver the drugs into cancer cells through active uptake rather than passive diffusion (Liang et al., 2012; Li et al., 2013; Murakami et al., 2013; Teow et al., 2013; Wang et al., 2015a). Many scientists have focused their attention on developing new antitumor drug conjugates to overcome efflux pumps and thus the drug resistance of tumors. For example, ANG1005, the conjugate of PTX and an anti-cancer drug conjugate, was designed to enhance the ability of PTX to cross the P-gp efflux pump and enhancing the ability of PTX to cross the blood–brain barrier (Regina et al., 2008). Han (Han et al., 2014) designed a triphenylphosphonium–doxorubicin conjugate and successfully applied it toward reversing the drug resistance of breast cancer cells. Luo (Luo et al., 2015) synthesized a novel xyloglucan–mitomycin C/doxorubicin conjugate and used it to achieve an extraordinary in vivo antitumor effect in multidrug-resistant HepG2 cells.
Cell-penetrating peptides (CPPs) have been used as efficient tools for delivering pharmaceuticals and nanosystems into cells (Xia et al., 2011; Chen et al., 2014; Zhong et al., 2015). Some antitumor drugs, such as doxorubicin (Soudy et al., 2013; Zhang et al., 2013) and methotrexate (Szabo et al., 2016), have been conjugated to CPPs and obtained the ability to overcome drug resistance. As a first-line antitumor drug, PTX has serious limits that need to be addressed. In addition to its limited antitumor effect on drug-resistant cancer cells, the hydrophobicity of PTX is also a problem that needs to be solved when developing PTX formulations. Because most CPPs are hydrophilic, conjugating PTX to CPPs can not only enhance the transport of PTX into tumor cells and then inhibiting drug resistance, but also make PTX-CPPs water-soluble, thus avoiding the use of inorganic solvents, such as Cremophor EL. Among the CPPs, TAT (GGGYGRKRRQRRR), derived from HIV (Dalian, China), N-(2-Aminoethyl) maleimide trifluoroacetate salt was purchased from Sigma-Aldrich Co., LLC (St. Louis, MO). Trifluoroacetic acid (TFA), 3-(4,5-dimethylthiazol-2-yl)-2,5-diphenyl tetrazolium bromide (MTT), N-hydroxysuccinimide (NHS), N-(3-dimethylaminopropyl)-N'ethylcarbo-diimide hydrochloride (EDC), and N,N-diisopropylcarbodiimide (DIEA) were purchased from aladdin-e.com (Shanghai, China). JC-1, propidium iodide (PI) and annexin V-FITC were purchased from Univ Biological Technology Co., Ltd. (Shanghai, China). Dichloromethane (DCM) and anhydrous dimethyl sulfoxide (DMSO) were purchased from Sinopharm Chemical Reagent Co., Ltd. (Shanghai, China).
Cell culture
Non-small cell lung cancer cell line A549 and the PTX-resistant version of the same cell line, A549T, were kindly provided by Professor Yongzhuo Huang (Shanghai Institute of Materia Medica, Chinese Academy of Sciences). Both cell lines were grown in RPMI-1640 medium containing 10% fetal bovine serum and 100 μg/mL antibiotics (streptomycin and penicillin) at 37 °C in a humidified incubator with 5% CO₂.
Synthesis of the PTX-LMWP conjugate
Synthesis of PTX-SA
Succinic acid (SA) has a bis-carboxylic acid moiety and can react with the hydroxyl group in PTX on an equimolar basis to form a PTX-SA conjugate, which can be further linked with the primary amino group of LMWP via its free carboxyl group. Briefly, PTX (100 mg, 0.117 mmol) and succinic acid (20 mg, 0.169 mmol) were dissolved in 20 mL of anhydrous DCM. DIPEA (100 μL) was then added to the mixture as a catalyst. The reaction was performed with continuous stirring for 12 h at room temperature. As examined by thin layer chromatography (10:90, methanol:chloroform, v/v), PTX completely disappeared from the reaction mixture, and a new compound, PTX-SA, was formed. The resulting solution was condensed with a rotary evaporator. The residue was purified using a silica gel column and eluted with a chloroform–methanol mixture (10:0.5, v/v) to afford pure PTX-SA, which was then dried.
using a rotary evaporator (Scheme 1). 1H NMR (CDCl₃, 400 MHz): δ ppm 1.15 (s, 3H), 1.24 (s, 3H), 1.26–1.30 (m, 2H), 1.69 (s, 3H), 1.81–1.91 (m, 1H), 1.93 (s, 3H), 2.13–2.14 (m, 1H), 2.23 (s, 3H), 2.33–2.43 (m, 2H), 2.45 (s, 3H), 2.51–2.63 (m, 2H), 2.63–2.80 (m, 3H), 3.82 (d, 1H, J = 7.2 Hz), 4.18–4.31 (AB, 2H, J = 42.8 Hz), 4.4–4.5 (m, 1H), 4.99 (d, 1H, J = 7.6 Hz), 5.55 (d, 1H, J = 7.2 Hz), 5.71 (d, 1H, J = 7.2 Hz), 5.97–6.04 (m, 1H), 6.25 (s, 1H), 7.1 (d, 1H, J = 9.2 Hz), 7.33–7.37 (m, 1H), 7.39–7.47 (m, 6H), 7.48–7.60 (m, 3H), 7.59–7.66 (m, 2H), 7.78 (d, 2H, J = 7.2 Hz), 8.16 (d, 2H, J = 6.8 Hz). [M + H]⁺ HRMS (MALDI-TOF) m/z: 954.3523 (Supplementary material, Figures S1 and S2).
Synthesis of PTX-LMWP
Conjugation of SA with PTX resulted in the formation of a monocarboxylic acid group, which was further connected to the primary amino group in LMWP. Briefly, PTX-SA (100 mg, 0.104 mmol), EDC (200 mg, 1.043 mmol) and NHS (24 mg, 0.208 mmol) were dissolved in 5 mL of anhydrous DMSO and stirred at room temperature for 2 h. Then, LMWP and DIPEA (50 µL) were added, and the reaction solution was maintained under stirring at room temperature. The molar ratio of LMWP to PTX-SA was maintained at 1:1. The reaction was supervised by ultra-performance liquid chromatography (UPLC, BEH C18 column, 1.7 µm, 2.1 × 50 mm). The flow rate was 0.3 mL/min, with the mobile phase starting at 90% solvent A (0.1% TFA in water) and 10% solvent B (0.1% TFA in acetonitrile) at 0 min and transitioning to 40% solvent A and 60% solvent B at 10 min. The retention time for PTX-LMWP was 6.6 min. After 24 h, 1 mL of phosphate-buffered saline (PBS, pH = 5.0) was added to stop the reaction, and the product was purified by semi-preparative high performance liquid chromatography (HPLC; Eclipse XDB-C18, 9.4 × 250 mm). The flow rate was 3 mL/min, with the mobile phase starting at 70% solvent A and 30% solvent B (0 min) and transitioning to 10% solvent A and 90% solvent B (30 min). Solvent A and solvent B were the same as for the analytical UPLC method. Finally, the solution collected from semi-preparative HPLC was lyophilized for 2 d (Scheme 1). 1H NMR (D₂O and DMSO-d₆, 600 MHz): δ ppm 0.75–0.86 (m, 6H), 0.93–1.01 (m, 5H), 1.39–1.58 (m, 30H), 1.61–1.78 (m, 16H), 1.86–1.97 (m, 1H), 2.08 (s, 3H), 2.13–2.22 (m, 5H), 2.26–2.47 (m, 6H), 2.53–2.63 (m, 4H), 3.13–3.37 (m, 4H), 3.51–3.67 (m, 5H), 3.71 (t, 3H, J = 16.8 Hz), 3.85–3.9 (m, 2H), 3.95–4.12 (m, 7H), 4.13–4.31 (m, 12H), 4.89 (d, 2H, J = 9.6 Hz), 5.27 (t, 2H, J = 9.6 Hz), 5.38 (d, 2H, J = 7.2 Hz), 5.43–5.48 (m, 7H), 5.75–5.83 (m, 2H), 7.16 (t, 1H, J = 7.2 Hz), 7.36–7.46 (m, 4H), 7.48 (t, 2H, J = 7.2 Hz), 7.53–7.56 (m, 1H), 7.62–7.68 (m, 2H), 7.73 (t, 1H, J = 7.2 Hz), 7.81 (d, 2H, J = 7.2 Hz), 7.96 (d, 2H, J = 7.2 Hz). [M + H]⁺ HRMS (MALDI-TOF) m/z: 2816.4023 (Supplementary material, Figures S3, S4 and S5).
Synthesis of the PTX-TAT conjugate
Synthesis of PTX-SA-MAL
There are three primary amino groups in TAT, including two lysine amino acid residues in its sequence. If TAT was conjugated with PTX through the reaction of a primary amino group and a carboxylic acid group in the same way as LMWP, a complicated mixture including at least three types of PTX-TAT conjugates would be generated because of the random reaction of PTX-SA with one or more of the three primary amino groups in TAT. In addition, because the lysine amino acid residues play a crucial role in the transduction function of TAT (Park et al., 2002), reacting the primary amino groups of the lysines would decrease the ability of TAT to translocate into cells. To avoid the occurrence of these issues, N-(2-aminoethyl) maleimide trifluoracetate salt, a heterobifunctional cross-linker, was first reacted with PTX-SA. Briefly, PTX-SA (100 mg, 0.104 mmol), EDC (200 mg, 1.043 mmol), and NHS linker, was first reacted with PTX-SA. Briefly, PTX-SA (100 mg, 0.104 mmol), dissolved in 10 mL of PBS, pH 7.0. The solution was then stirred at room temperature for 2 h. Then, N-(2-aminoethyl)maleimide trifluoracetate salt (30 mg, 0.118 mmol, dissolved in 10 mL of PBS, pH 7.0) was added. The resulting solution was stirred for 12 h. Then, acetonitrile was removed with a rotary evaporator, and DCM (10 mL) was added as an extractive solvent to remove excessive EDC and NHS. The water phase was abandoned, and the organic phase was concentrated with a rotary evaporator. The residue of the organic phase was purified with a silica gel column and eluted with a chloroform:ethyl acetate mixture (4:10, v/v) to obtain pure PTX-SA-MAL (Scheme 1).$^1$H NMR (DMSO-d6, 600 MHz): $\delta_{ppm}$ 0.968 (s, 3H), 0.998 (s, 3H), 1.212 (s, 1H), 1.416–1.449 (m, 1H), 1.470 (s, 3H), 1.534–1.667 (m, 1H), 1.739 (s, 3H), 1.758–1.816 (m, 1H), 2.080 (s, 3H), 2.209 (s, 3H), 2.230–2.340 (m, 3H), 2.512–2.624 (m, 2H), 3.055–3.158 (m, 2H), 3.390 (t, 2H, $J = 6$ Hz), 4.034–4.126 (m, 1H), 4.627 (s, 1H), 4.886 (d, 1H, $J = 10$ Hz), 4.926 (s, 1H), 5.308 (d, 1H, $J = 9.2$ Hz), 5.386 (d, 1H, $J = 7.2$ Hz), 5.495 (t, 1H, $J = 8.4$ Hz), 5.788 (t, 1H, $J = 8.8$ Hz), 6.264 (s, 1H), 6.977 (s, 2H), 7.132–7.188 (m, 1H), 7.389–7.446 (m, 4H), 7.446–7.511 (m, 2H), 7.517–7.574 (m, 1H), 7.620–7.684 (m, 2H), 7.692–7.753 (m, 1H), 7.833 (d, 2H, $J = 6.8$ Hz), 7.958 (d, 2H, $J = 7.2$ Hz), 8.000 (t, 1H, $J = 6$ Hz), 9.210 (d, 1H, $J = 8.4$ Hz). [M + H]$^+$ HRMS (MALDI-TOF) m/z: 2910.3787 (Supplementary material, Figures S8, S9 and S10).
Synthesis of PTX-TAT
Linking a heterobifunctional cross-linker to PTX-SA provided a maleimide group that could react with the thiol group of TAT. Briefly, PTX-SA-MAL (100 mg, 0.093 mmol) and TAT (200 mg, 0.109 mmol) were dissolved in a solution comprising 5 mL of acetonitrile and 10 mL of PBS (pH 7.0). The solution was then stirred at room temperature for 1 h. The reaction was monitored by UPLC using the same column and analytical method as that used for PTX-LMWP. The retention time for PTX-TAT was 6.2 min. The solution was purified by semi-preparative HPLC, also using the same method as that used for PTX-LMWP. The collected semi-preparative HPLC elution was lyophilized immediately (Scheme 1).$^1$H NMR (D$_2$O and DMSO-d6, 600 MHz): $\delta_{ppm}$ 0.946 (s, 3H), 0.959 (s, 3H), 1.206–1.375 (m, 7H), 1.445 (s, 3H), 1.471–1.614 (m, 18H), 1.625–1.830 (m, 14H), 1.837–1.928 (m, 2H), 2.064 (s, 3H), 2.159 (s, 6H), 2.252–2.362 (m, 4H), 2.546–2.636 (m, 3H), 2.682–2.746, 2.896–2.959 (brs, 4H), 2.773 (t, 4H, $J = 7.2$ Hz), 3.095–3.267 (m, 6H), 3.332–3.451 (m, 3H), 3.470–3.558 (m, 2H), 3.583–3.799 (m, 7H), 3.799–3.920 (AB, 3H), 3.941 (t, 1H, $J = 6.0$ Hz), 3.986 (s, 2H), 4.021–4.092 (m, 2H), 4.102–4.230 (m, 8H), 4.864–4.929, 5.327–5.385 (AB, brs, 4H), 5.231–5.287, 5.385–5.444 (AB, brs, 4H), 5.711–5.806 (m, 2H), 6.212 (s, 1H), 6.619–6.704, 6.974–7.067 (AA’BB’; 4H), 7.090–7.136 (m, 1H), 7.363–7.421 (m, 4H), 7.455 (t, 2H, $J = 7.8$ Hz), 7.536 (t, 1H, $J = 7.2$ Hz), 7.632 (t, 2H, $J = 7.8$ Hz), 7.719 (t, 1H, $J = 7.2$ Hz), 7.765 (d, 2H, $J = 7.2$ Hz), 7.923 (d, 2H, $J = 7.8$). [M + H]$^+$ HRMS (MALDI-TOF) m/z: 2910.3787 (Supplementary material, Figures S8, S9 and S10).
Cellular uptake assay
The cellular uptake experiment was implemented basing on the protocol designed by Meng with some modifications (Meng et al., 2011). Briefly, A549 and A549T cells were cultivated in chambered 24-well plates with 5% CO$_2$ at 37 °C for 48 h. Then, the adherent cells were washed twice with PBS. Each of the three drugs was diluted in cell medium at concentrations of 10 μM and 20 μM and added to the chambers. The cells were incubated for 2 h and washed four times with PBS after incubation. After that, the cells were scraped from the wells and quantitatively transferred to Eppendorf centrifuge tubes. The resulting cell/saline suspensions were sonicated for 20 cycles of 2 s each with 2 s of rest between each cycle using a probe sonicator. The lysed cell solution was centrifuged at 7000 g for 30 min at 4 °C. Then, 100 μL of the supernatant was withdrawn carefully and tested with UPLC (BEH C18, 1.7 μm, 2.1 × 50 mm). The flow rate was 0.3 mL/min, and the mobile phase consisted of 55% solvent A (PBS, pH = 5) and 45% solvent B (acetonitrile). To further test the change in cellular uptake against incubation time, the drugs (20 μM) were added to the cells, and the cells were then incubated for different times, ranging from 15 min to 4 h. The other steps of the experiment were performed as described above.
Cytotoxicity study
The inhibitory activities of the drug samples on cell growth were evaluated using a 3-(4,5-dimethylthiazol-2-yl)-2,5-diphenyltetrazolium bromide (MTT) colorimetric assay. A549 and A549T cells were harvested by trypsinization and resuspended at a concentration of 2 × 10^4 cells/mL in fresh culture medium. Then, the cells were seeded at a density of 5000 cells per well in 96-well plates. After 48 h of incubation at 37 °C with 5% CO$_2$, the culture medium was replaced with 200 mL of medium containing one of the three drug samples, PTX, PTX-LMWP, or PTX-TAT. The concentration of the drugs ranged from 0.1 μM to 100 μM. After 24 h of incubation, the drug-containing media were replaced with 200 mL of MTT (5 mg/mL) solution was added to each well. The plate was incubated for an
additional 4 h, and then, 200 mL of DMSO was added to each well to dissolve any formed purple formazan crystals. The plates were vigorously shaken before measuring the relative color intensity. The absorbance at 570 nm of each well was measured with a plate reader.
Cell apoptosis detection
Cell apoptosis was determined by an annexin V-FITC/PI assay. The externalization of phosphatidylserine, a result of early stage apoptosis, was detected by FITC-annexin V protein staining, and the membrane damage due to late-stage apoptosis was detected by the binding of PI to nuclear DNA. Briefly, $2 \times 10^5$ A549 and A549T cells were plated in 6-well plates and incubated for 24 h. After exposure to the different drugs at a concentration of $10 \mu M$ for 48 h, the cells were harvested by trypsinization, washed in PBS twice and incubated in the dark for 10 min at room temperature in 500 $\mu L$ of binding buffer containing annexin V-FITC ($1 \mu g/mL$) and PI ($1 \mu g/mL$). The cells were immediately analyzed by flow cytometry (Becton Dickinson, Franklin Lakes, NJ). The fluorescence intensity of annexin V-FITC was measured at an excitation/emission wavelength of 488/530 nm and that of PI was measured at an excitation/emission wavelength of 488/617 nm. Approximately 10 000 cells were analyzed in each of the samples. Each assay was repeated in triplicate.
Mitochondrial membrane potential ($\Delta \psi _m$) determination
Changes in the mitochondrial membrane potential ($\Delta \psi _m$) were detected using JC-1 and analyzed with flow cytometry. Briefly, A549 and A549T cells were seeded at a density of $1 \times 10^5$ cells/mL in 6-well plates and exposed to the drugs ($10 \mu M$) for 48 h. The control experiments were performed by adding only culture medium. Then, the cells were harvested by trypsinization, washed in PBS twice, incubated with JC-1 ($5 \mu g/mL$) at $37^\circ C$ for 10 min in the dark, and finally analyzed by flow cytometry (Becton Dickinson, Franklin Lakes, NJ). Each assay was repeated in triplicate. JC-1 accumulates in mitochondria that have a high membrane potential and then dimerizes due to the high local concentrations achieved. Dimerized JC-1 emits red fluorescence, while monomeric JC-1 emits green fluorescence. The results are expressed as a ratio of red to green fluorescence. High values indicate that the cells have an intact mitochondrial membrane potential, while low values suggest the cells are in the early stage of apoptosis.
Cell-cycle analysis
To analyze the effect of the PTX-CPP conjugates on the cell cycle distribution, A549 and A549T cells were seeded at a density of $1 \times 10^5$ cells/mL in 6-well plates and then exposed to $5 \mu M$ PTX, PTX-TAT, or PTX-LMWP solution for 48 h. After that, the cells were harvested by trypsinization, washed in PBS twice, and fixed in 70% cold ethanol for 24 h at 4°C. The fixed cells were washed in cold PBS and then resuspended in 0.5 mL of PBS containing 50 $\mu g/mL$ PI, 0.1% Triton-X-100, 0.1% sodium citrate, and 100 $\mu g/mL$ RNase. After incubation at 4°C for 30 min, the fluorescence-activated cells were sorted. The cellular DNA content was analyzed by flow cytometry (Becton Dickinson, Franklin Lakes, NJ). Each analysis contained at least 10 000 cells. The changes in cell distribution at each cell-cycle phase were observed, and the results are displayed in histograms. The percentages of cells in different cell cycles were then recorded. Each experiment was performed in triplicate, and the results were expressed as the mean ± SD.
Antitumor efficacy
The protocol to evaluate the in vivo antitumor efficacy of the PTX-CPP conjugates was approved by the ethics committee of Fudan University. Four-week-old female BALB/c nude mice were purchased and housed in the Animal Care Facilities in the School of Pharmacy, Fudan University. BALB/c mice bearing subcutaneous tumors were used as an animal model for the evaluation of the anticancer activities of PTX-LMWP and PTX-TAT. The subcutaneous tumor xenograft model was established by inoculating $2 \times 10^6$ A549 or A549T cells (in $100 \mu L$ of cell culture medium) into the subcutaneous tissue of the armpit of the right anterior limb (Gu et al., 2014). Tumor size was measured with Vernier calipers for the largest (length) and smallest (width) superficial visible diameters of the protruding tumor mass through the skin. Tumor volumes were calculated according to the following formula: volume $= 0.52 \times W^2 \times L$, where $W$ and $L$ represent the width and the length, respectively (Lee et al., 2011). The drugs were administered 2 weeks after tumor implantation, when the size of the tumors reached approximately 100–150 mm$^3$. Test compounds included (I) PBS solution (control), (II) PTX ($1000 \mu M$), (III) PTX-LMWP ($1000 \mu M$), and (IV) PTX-TAT ($1000 \mu M$). Each experimental group contained six mice. The mice were treated ($100 \mu L$ volume) three times over 8 d via peritumoral injection. Tumor volumes were measured at 2-d intervals. At the end of the experiment, the mice were sacrificed, and necropsies were performed. The tumors were removed, weighed and fixed with formalin.
Results
Cellular uptake assay
The cellular uptake of PTX was evaluated in A549 and A549T cells. As shown in Figure 1(A), the results indicated that both A549 and A549T cells treated with PTX-CPPs had higher cellular uptake of PTX than cells incubated with PTX ($p < 0.01$), regardless of the concentration was 10 $\mu M$ or 20 $\mu M$. As shown in Figure 1(B), the cellular uptake of PTX-CPPs increased with prolonged incubation time in both cell lines. The uptake of PTX-LMWP was stronger than that of PTX-TAT in A549 cells at all incubation times ($p < 0.05$), but this phenomenon was not observed in A549T cells.
Cytotoxicity study
The cytotoxic efficiency of PTX and PTX-CPPs toward tumor cells was measured in A549 and A549T cells. The concentration of PTX and PTX-CPPs ranged from 0.01 nM to 100 000 nM. LMWP and TAT peptides were also selected in
the same molar concentrations as PTX to test the toxicity of the CPPs. In MTT assay, all cells exposed to PTX/PTX-CPPs exhibited a typical dose-dependent curve. The viability of A549 cells was higher than 80% when the concentration of PTX was below 1 nM. When the concentrations of PTX and PTX-CPPs ranged from 100 nM to 100 000 nM, the cell viabilities decreased to 40%. As shown in Figure 2(A), from 1 nM to 100 nM, the survival curves of the cells treated with PTX-CPPs declined more sharply than that of the cells treated with PTX. In A549T cells, no effect on cell viability was observed in response to either PTX-CPPs or PTX when the concentrations were below 1000 nM because of the drug resistance of these tumor cells. Meanwhile, the cell viabilities of the PTX-CPP groups were notably decreased compared with those of the PTX groups when the concentration changed from 1000 nM to 100 000 nM. No harmful effect was observed in A549 or A549T cells treated with TAT or LMWP alone.
GraphPad Prism software (GraphPad Software, Inc., La Jolla, CA) was used to calculate the IC₅₀ of PTX and the PTX-CPPs. As shown in Figure 2(B), in both A549 cells and A549T cells, the IC₅₀ values of PTX-LMWP and PTX-TAT, which were 33.5% and 47.2% of PTX in A549 cells and 21.5% and 39.5% of PTX in A549T cells, respectively, were decreased significantly compared with that of PTX (p<0.01). The observed IC₅₀ value of PTX-LMWP was remarkably lower than that of PTX-TAT in A549T cells (p<0.01), while this phenomenon was not observed in A549 cells.
Cell apoptosis
As shown in Figure 3(A,B), the Q1, Q2, Q3, and Q4 regions represent necrotic cells (PI+/annexin V−), late apoptotic cells (PI+/annexin V+), early apoptotic cells (PI−/annexin V+) and viable cells (PI−/annexin V−), respectively. The apoptosis results revealed that PTX-CPPs induced early apoptosis and/or late apoptosis in more tumor cells than PTX. From Figure 3(C), it can be seen that PTX induced late apoptosis in only 13.03% of A549 cells. After the treatment with PTX-TAT or PTX-LMWP, the percentage of late apoptotic A549 cells sharply increased to 72.57% or 84.03%, respectively (p<0.01). PTX-LMWP had a better ability to induce late apoptosis in A549 cells than PTX-TAT (p<0.05). In A549T cells, PTX-TAT and PTX-LMWP induced late apoptosis in 54.20% and 55.75% of cells, respectively, while PTX only induced late apoptosis in 16.10% of cells (p<0.01). The percentages of early apoptotic A549T cells induced by PTX-TAT and PTX-LMWP were 23.15% and 38.10%, respectively, both of which were significantly higher than that of PTX (p<0.01). Obviously, the effect of PTX-LMWP on inducing early apoptosis in A549T cells was stronger than that of PTX-TAT (p<0.05).
Mitochondrial membrane potential (Δψ/m)
The effects of PTX and PTX-CPPs on the mitochondrial membrane potential (Δψ/m) in A549 cells and A549T cells are shown in Figure 4(A,B). The x-axis and the y-axis display the JC-1 monolayer signals and JC-1 aggregate
signals, respectively. Q1 + Q2 and Q3 + Q4 represent the aggregate form and monomeric form of JC-1, respectively. The results indicated that PTX and PTX-CPPs significantly reduced the Δψ/m in both A549 and A549T cells compared with the control cells (p < 0.01). PTX-CPPs induced more severe collapse of the Δψ/m than PTX in both cell lines (p < 0.01). In addition, in A549T cells, treatment with PTX-LMWP resulted in significant breakdown of the Δψ/m compared with the PTX-TAT treatment (p < 0.05). However, the same result was not observed in A549 cells.
Cell-cycle analysis
The effects of PTX and PTX-CPPs on the cell-cycle distribution of A549 and A549T cells were displayed in Figure 5. In A549 cells, exposure to PTX and PTX-CPPs substantially increased the percentages of cells in G2/M phase cell-cycle arrest compared with the control cells (p < 0.01), and significantly higher percentages of G2/M phase cells were observed in PTX-CPP-treated cells than the cells treated with PTX (p < 0.05). In A549T cells, the fitting result showed that a large number of A549T cells were induced into tetraploids with exposure to PTX and PTX-TAT, and PTX-TAT-treated A549T cells showed higher tetraploid-G2/M phase arrest than those incubated with PTX (p < 0.05). In contrast, A549T cells treated with PTX-LMWP demonstrated limited generation of tetraploids but a large number of cells in diploid-S phase cell-cycle arrest. Compared with the control cells, the percentages of diploid-G0/G1 phase A549T cells in the PTX and PTX-CPP groups were extremely reduced (p < 0.01), which was similar to the results in A549 cells.
Antitumor efficacy
A549 and A549T tumor cells xenografted into nude mice were used for the in vivo efficacy study. As shown in Figure 6, A549 tumor growth in mice treated with PTX-CPPs was significantly suppressed, and the size of tumors reduced continuously compared with the control (p < 0.05) from 20 to 30 d. PTX treatment also had a significant antitumor effect in A549 tumor-bearing mice after 26 d (p < 0.05). Furthermore, PTX-TAT and PTX-LMWP produced more convincing growth inhibition of A549 tumors than PTX in nude mice (p < 0.05). The volume of tumor was decreased approximately 1.51–1.77-fold and 1.45–1.80-fold, respectively, from 22 to 30 d. PTX did not show satisfactory antitumor efficacy in A549T-tumor bearing mice, and there was no significant difference in the tumor volumes between the control and PTX groups. PTX-TAT and PTX-LMWP still had a considerable antitumor effect compared with the control or PTX (p < 0.05) after 6 d and displayed 1.74–1.52-fold and 1.74–1.58-fold reductions, respectively, in tumor volume from 6 to 24 d compared with the PTX group. After 24 or 30 d, all tumor-bearing mice were sacrificed. The tumors were dissected and weighed. The tumor inhibition rates (%) in A549 tumor-bearing mice receiving PTX-LMWP and PTX-TAT were 62.92% and 63.32%, respectively. Both showed significant inhibition (p < 0.05) compared with the 31.06% inhibition rate of PTX. Meanwhile, the inhibition rates (%) in A549T tumor-bearing mice injected with PTX-TAT and PTX-LMWP were 42.47% and 43.13%, respectively. Compared with the inhibition rate in the group treated with PTX, which was only 11.0%, the inhibitory abilities of PTX-LMWP and PTX-TAT
were a significant improvement \((p<0.05)\). However, no significant difference was observed between the inhibitory effects of PTX-TAT and PTX-LMWP.
**Discussion**
Here, we have developed two novel conjugates, PTX-LMWP and PTX-TAT, to enhance the cellular uptake and antitumor efficacy of PTX, especially in drug-resistant tumor cells. To synthesize PTX-LMWP, a two-step procedure was used starting with 2′-hemisuccinylation of PTX through a previously reported reaction (Safavy et al., 2004; Khandare et al. 2006; Gao et al., 2009). Conjugation of PTX-SA to the LMWP peptide was performed using a previously described NHS/EDC method (Pan et al., 2016). However, direct reaction of PTX-SA with TAT would produce a complicated reaction mixture, including at least three forms of PTX-TAT conjugates, due to the random reaction of PTX-SA with the three primary amino groups of TAT. Therefore, many previous reports utilized a heterobifunctional cross-linker to synthesize TAT conjugates (Christie et al., 2004; Wei et al., 2009; van Bracht et al., 2014; Li et al., 2015). In this article, we chose a simple procedure of covalently bonding PTX-SA to N-(2-aminoethyl) maleimide using the NHS/EDC method to form PTX-SA-MAL, and then TAT was reacted with PTX-SA-MAL to form PTX-TAT conjugate.
The results of cellular uptake demonstrated that PTX-CPPs could enhance the accumulation of PTX in A549 and A549T cells compared with PTX, which confirm that CCPs can facilitate the uptake of cargo (Nakase et al., 2012). The uptake mechanism of CPPs has been deeply researched but still remained elusive (Guo et al., 2016). It is also unknown whether CPPs enter cells with or without the mediation of specific receptors (Farkhani et al., 2014).
Figure 3. Cell apoptosis after incubating with 10μM PTX or PTX-CPPs for 48 h. (A) Apoptosis of A549 cells. (B) Apoptosis of A549T cells. (C) Quantification of apoptosis data. *\(p<0.05\); **\(p<0.01\).
Nonetheless, it is a common consensus (Fonseca et al., 2009) that energy-dependent endocytosis and energy-independent direct translocation are two major cellular uptake mechanisms of CPPs. Small molecules linked with CPPs can enter cells quickly via direct translocation. In contrary, uptake of large cargos attached to CPPs may due to the energy-dependent endocytosis with slow rates. The direct translocation contains several different models (Guo et al., 2016) such as transient pore formation, carpet-like model, membrane-thinning model, and transitory membrane structure formation. The common features of these models are that CPPs bind to the plasma membrane via electrostatic interaction first, and then CPPs induce membrane destabilization or inverted micelle inside the lipid bilayer, leading to the uptake of CPPs. Previous research (Song et al., 2015) proved that TAT peptide could induce the formation of transient natural pore in membrane. Kawamoto (Kawamoto et al., 2011) illustrated that arginine-rich peptides permeated the plasma membrane via the formation of inverted micelle. LMWP peptide is an arginine-rich peptide. Based on the literatures and considering the small molecular weight of PTX, we can speculate that PTX-TAT and PTX-LMWP may enter the tumor cells via energy-independent direct translocation pathway. The uptake of PTX-TAT and PTX-LMWP increased without obviously saturate phenomenon when the incubation time was prolonged. The results suggest that the uptake of both conjugates may be mediated via energy-independent pathway. The uptake results of two conjugates are coincidence with our speculation. Efflux pump is a promiscuous transmembrane protein, thus PTX-CPPs can easily bypass the efflux pump via the transient pore or inverted micelle in membrane, which may be the reason that
Figure 4. JC-1 forms and Δψm values of A549 and A549T cells. All cells were exposed to drugs at 10 μM for 48 h. (A) The distribution of different JC-1 forms in A549 cells. (B) The distribution of different JC-1 forms in A549T cells. (C) Ratio of red to green fluorescence in A549 and A549T cells. *p < 0.05; **p < 0.01.
PTX-CPPs conjugates can overcome the drug resistance of A549T cells.
Apoptosis is a kind of programmed cell death. The decrease of mitochondrial membrane potential is often a symbol of early apoptosis (Jiang et al., 2015). As a cationic dye, JC-1 can bind with polarized mitochondria in healthy cells and emit red fluorescence. Whereas in apoptotic cells, it can disperse from depolarized mitochondria to cytosol and emit green fluorescence. Thus, the disruption of mitochondrial membrane potential ($\Delta\psi$/m) can be indicated by a switch from red to green fluorescence. According to previous researches (Pawar et al., 2014; Jelinek et al., 2015), PTX has been shown to activate the mitochondrial pathway of apoptosis. In this study, we observed significant reductions of the $\Delta\psi$/m in A549 and A549T cells after application of PTX and PTX-CPPs.
These data suggest that PTX-CPPs also induce cell apoptosis through mitochondrial pathway. PTX-CPPs displayed enhanced cell toxicity, greater apoptosis, and a greater reduction in the $\Delta\psi$/m in both sensitive and drug-resistant cells compared with PTX, and this result may be ascribed to the extremely elevated accumulation of PTX-CPPs in cells. It is interesting that in A549 cells, PTX-LMWP and PTX-TAT exhibited different degrees of cellular uptake but manifested similar cell toxicities and effects on the $\Delta\psi$/m, which indicates that the increased uptake of PTX-LMWP is not sufficient to exert a more considerable antitumor efficacy. In contrast, there was no significant difference between the cellular uptake of PTX-LMWP and PTX-TAT in A549T cells, while the cell toxicity, the effects on apoptosis and the $\Delta\psi$/m of the two conjugates were quite different, indicating that the diverse
Figure 5. Cell-cycle profiles of A549 and A549T cells treated with 5 µM PTX or PTX-CPPs. (A) Cell-cycle distribution of A549 cells. (B) Cell-cycle distribution of A549T cells. (C) Quantification of cell cycle data. *p < 0.05; **p < 0.01.
anti-drug resistance mechanisms of PTX-TAT and PTX-LMWP may influence their antitumor efficiency in A549T cells.
The cell-cycle assessment showed that PTX-CPPs could induce more G2/M phase arrest compared with PTX and the control. This phenomenon may be attributed to the increased accumulation of PTX in A549 cells caused by LMWP and TAT. After treatment with PTX and PTX-CPPs, a large number of tetraploids were found in A549T cells. As is known, PTX can stabilize microtubules (Tian et al., 2014), hinder normal kinetochore-microtubule attachment and activate spindle assembly checkpoint, and subsequently lead to mitotic arrest and cell death (Ganem et al., 2007). However, after going through a process known as mitotic slippage, some cells are induced into apoptosis, while others can slowly recover from the arrest of the spindle assembly checkpoint and re-enter the G1 phase as tetraploids, thus escape the apoptosis induced by PTX (Flores et al., 2011; Topham & Taylor, 2013; Chi et al., 2014). Many studies revealed that polyploid cancer cells, especially tetraploids, displayed clear correlation with drug resistance (Puig et al., 2008; Ogden et al., 2015; Zhou et al., 2015). It is reasonable that A549T cells, as a drug-resistant cancer cell line, experienced an apparent tetraploid mitotic process after treatment with PTX and PTX-CPPs. Interestingly, PTX- and PTX-TAT-treated A549T cells had obvious tetraploid-G2/M phase arrest, but PTX-LMWP mostly induced diploid-G0/G1 and diploid-S phase arrest. Although the reason is still unclear, the phenomenon illustrates that PTX-LMWP has a different mechanism of anti-drug resistance with PTX and PTX-TAT. Considering tetraploid morphology is strongly associated with drug resistance, the small percentage of cells exhibiting tetraploid mitotic phase arrest indicates that PTX-LMWP is powerful in overcoming the drug resistance of A549T cells.
The in vivo antitumor assay showed that PTX-CPPs had stronger inhibitory effects on tumor volume and tumor weight than the control and PTX in both cell lines, consistent with the cell toxicity, cell apoptosis, and ΔT/m results. The result confirms that PTX-CPPs are more effective in slowing the growth of solid tumors, particularly drug-resistant tumors. However, there was no difference between PTX-TAT and PTX-LMWP in the inhibition of A549T tumors, which does not agree with the results of in vitro studies. Considering that all in vitro experiments were tested in cells with a single
Figure 6. Anticancer efficacy of the drugs on tumor cell xenografts in female nude mice. (A) Tumor volume profiles. (B) Weights of tumors from mice after 24 or 30 d. (C) Photos of tumors separated from mice. *p < 0.05; **p < 0.01.
membrane, PTX-LMWP may have a higher capacity to penetrate single-cell membranes and induce apoptosis or death compared with PTX-TAT. However, the xenografted tumors in the nude mice recruited dense tumor tissues, which were likely much harder to be penetrated than a single cell in vitro (Lee et al., 2011). Thus, PTX-LMWP may not have sufficient ability to permeate solid A549T tumors more deeply than PTX-TAT. However, PTX-LMWP still showed a significant antitumor effect in both sensitive and drug-resistant tumors in vivo, and the effects of PTX-LMWP and PTX-TAT were both much stronger than that of PTX.
**Conclusion**
In summary, two new conjugates, PTX-TAT and PTX-LMWP, were synthesized successfully. Both conjugates were more efficient in permeating tumor cells and inducing cell toxicity and apoptosis in both sensitive and drug-resistant lung cancer cells than PTX. Cell-cycle analysis showed that PTX-CPPs induced more G2/M phase cell-cycle arrest in A549 cells. With the emergence of tetraploid A549T cells, the cell-cycle distribution of A549T cells was very different from that of A549 cells. This result suggests that PTX-LMWP has a different mechanism of influencing mitosis in drug-resistant lung tumor cells than PTX and PTX-TAT. The in vivo antitumor efficacy study confirms that PTX-CPPs could significantly inhibit the growth of both sensitive and drug-resistant tumors. Compared with PTX-TAT, PTX-LMWP exhibited much stronger effects on cell toxicity and apoptosis. The results of this study highlight the potential of PTX-CPPs, especially PTX-LMWP, which are promising for clinical application in the treatment of drug-resistant cancers.
**Declaration of interest**
The authors declare no competing financial interests. The authors thank the National Basic Research Program of China (No. 2013CB 932500), the National Natural Science Foundation of China (No. 81361140344), and the Development Project of Shanghai Peak Disciplines-Integrated Medicine (No. 20150407) for financial support.
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Supplementary material available online
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A SERM increasing the expression of the osteoblastogenesis and mineralization-related proteins and improving quality of bone tissue in an experimental model of osteoporosis
Abstract
Raloxifene is an antiresorptive drug, selective estrogen receptor modulator (SERM) used in the treatment of osteoporosis. Objective: To evaluate proteins related to bone repair at the peri-implant bone in a rat model of osteoporosis treated with raloxifene. Material and Methods: 72 rats were divided into three groups: SHAM (healthy animals), OVX (ovariectomized animals), and RLX (ovariectomized animals treated with raloxifene). Raloxifene was administered by gavage (1 mg/kg/day). Tibial implantation was performed 30 days after ovariectomy, and animals were euthanized at 14, 42, and 60 days postoperatively. Samples were collected and analyzed by immunohistochemical reactions, molecular analysis, and microtomographic parameters. Results: RLX showed intense staining of all investigated proteins at both time points except for RUNX2. These results were similar to SHAM and opposite to OVX, showing mild staining. The PCR gene expression of OC and ALP values for RLX (P<0.05) followed by SHAM and OVX groups. For BSP data, the highest expression was observed in the RLX groups and the lowest expression was observed in the OVX groups (P<0.05). For RUNX2 data, RLX and SHAM groups showed greater values compared to OVX (P<0.05). At 60 days postoperatively, microtomography parameters, related to closed porosity, showed higher values for (Po.N), (Po.V), and (Po) in RLX and SHAM groups, whereas OVX groups showed lower results (P<0.05); (BV) values (P=0.009); regarding total porosity (Po.tot), RLX group had statistically significant lower values than OVX and SHAM groups (P=0.009). Regarding the open porosity (Po.V and Po), the SHAM group presented the highest values, followed by OVX and RLX groups (P<0.05). The Structural Model Index (SMI), RLX group showed a value closer to zero than SHAM group (P<0.05). Conclusions: Raloxifene had a positive effect on the expression of osteoblastogenesis/mineralization-related proteins and on micro-CT parameters related to peri-implant bone healing.
Keywords: Raloxifene. Immunohistochemistry. Osteoporosis. Dental implants. WNT signaling.
Introduction
Post-menopausal osteoporosis is the main skeletal disorder with high incidence found in society, being characterized by reduced bone mass due to estrogen deficiency and decreased intestinal absorption of calcium, resulting in increased bone fragility and fracture susceptibility19. Studies evidenced that one of the signaling pathways of these proteins, as the canonical pathway, has very importance in the knowledge of osteoporosis and drug action used in their treatment2.
Many drug therapies were developed for osteoporosis treatment. Among them, we highlight raloxifene, a second generation Selective Estrogen Receptor Modulator (SERM) approved for use in the prevention and treatment of osteoporosis in postmenopausal women. Raloxifene acts by mimicking estrogen actions in the bone tissue and cholesterol metabolism (reducing total cholesterol and LDL levels), playing a role in the regulation of osteoblast lineage cells and bone remodeling5,15.
Bisphosphonates are the most commonly used drugs for osteoporosis treatment, mainly alendronate, and have shown great results by increasing bone mineral density and decreasing the risk of bone fracture in post-menopausal women29 However, the long-term use of these drugs is associated with the emergence of medication-related osteonecrosis of the jaw (MRONJ), increasingly common in patients who underwent oral surgeries, such as implants placement21.
The activity of non-collagenous bone matrix proteins synthesized by osteoblasts during the calcium deposition process, such as osteocalcin, osteopontin, and bone sialoprotein, is important in the process of bone matrix maturation and mineralization, and regulates the functional activity of bone cells10. Osteocalcin is an important marker of bone mineralization, representing the final stage of bone formation and demonstrating its importance for better understanding bone remodeling13.
Clinical studies have demonstrated the positive effect of raloxifene by preventing bone loss and decreasing the risk of bone fracture in post-menopausal women, besides having no relationship with breast cancer4,5. Furthermore, pre-clinical studies have shown the positive role of raloxifene in the alveolar bone14,15. However, few in vivo studies showed the effect of this drug on osteoblastogenesis proteins during peri-implant healing.
The reason for choosing raloxifene in peri-implant healing of osteoporosis conditions instead of other drugs, such as bisphosphonates, is because this drug is the only one to present a nearly physiologic effect, acting on estrogen receptors. Besides that, this drug can inhibit bone resorption and promote bone formation. On the other hand, bisphosphonates are described as anti-resorptive drugs which, in the long-term, can damage bone turnover, inhibit bone resorption, and do not promote bone formation, prevailing a poor quality and old bone, in addition to be related with medication-related osteonecrosis of the jaw (MRONJ).
Thus, this study aimed to evaluate new proteins belonging to the WNT/β-catenin pathway and other proteins related to bone repair and morphometric parameters at the bone-implant interface in induced-osteoporosis rat model treated with raloxifene.
Material and Methods
Animals
This study followed ethical principles and was approved by the Ethics Committee on Animal Use of FOA-UNESP under the protocol number 2012/01096. For this study, 72 4-month-old rats (Rattus norvegicus albinus, Wistar), weighing approximately 250 grams, were obtained from the central vivarium of FOA-UNESP. The animals were divided into three groups: SHAM – rats submitted to sham surgery and fed a balanced diet; OVX – rats submitted to bilateral ovariectomy and fed a low calcium diet (osteoporotic) without medical treatment; RLX – rats submitted to bilateral ovariectomy and fed a low calcium diet (osteoporotic) with raloxifene treatment.
The animals were kept in cages and fed a balanced diet (NUVILAB, Curitiba, PR, Brazil) containing 1.4% Ca++ and 0.8% P, and given water ad libitum. After completion of sham surgeries and ovariectomies, animals in the SHAM group continued to receive rations of the balanced diet, whereas animals in the other two groups were switched to a diet containing 0.1% Ca++ and 0.5% P (RHOSTER Ind. Com., Vargem Grande Paulista, SP, Brazil).
Estrous cycle classification
The rats were placed in individual cages for daily
observation of estrous cycle. The technique used was described by Long and Evans (1922) and consisted of introducing 1-2 drops of physiological serum into the vagina, which was then aspirated and placed on a histology slide for microscopic visualization. After observation of two or three regular cycles, animals were selected.
**Induction of osteoporosis**
Osteoporosis was induced in animals by using a combination of bilateral ovariectomy and 4-week treatment with a low calcium and phosphate diet, as previously described by Teófilo, et al. (2004) and Ramalho-Ferreira, et al. (2016). The development of osteoporosis was confirmed by obtaining cortical bone mineral density (BMD) values from SHAM and OVX rats using computerized micro-tomography (SkyScan 1176, Bruker MicroCT, Aartse-Laar, Belgium). We confirmed that BMD in animals not subjected to ovariectomy and who received a normal diet was 0.35255 g/cm³, as compared to 0.12525 g/cm³ in ovariectomized animals. This fact confirmed the presence of osteopenia in the latter group, which is characteristic of the osteoporotic rat model.
**Bilateral ovariectomy**
RLX and OVX rats were anesthetized, and incisions in both flanks were subsequently performed to expose the ovaries, which were then surgically removed. Rats from the SHAM group were subjected to the same procedure. However, the ovaries were exposed and not removed.
**Drug treatment**
Raloxifene treatment (1 mg/kg/day) began eight days after ovariectomy by oral gavage of aqueous solution containing the drug dissolved. The course of treatment lasted until the end of the experiment (euthanasia of animals), totaling 44, 72, and 90 days of oral administration in RLX and OVX groups, according to the periods of analysis.
**Tibia implantation surgery**
Thirty days after drug treatment, the animals were fasted for eight hours prior to the surgery, and were sedated using a combination of 50 mg/kg intramuscular ketamine (Vetaset, Fort Dodge Animal Health Ltd, Campinas, SP, Brazil) and 5 mg/kg xylazine hydrochloride (Dopaser, Laboratory Calier of Brazil Ltda., Osasco, SP, Brazil). Rats received mepivacaine hydrochloride (0.3 ml/kg) and scandicaine (2%) with epinephrine (1:100,000) (Septodont, France) for local anesthesia and the maintenance of operative field hemostasis.
After animals were sedated, a trichotomy was performed in the medial portion of the left and right tibias, and antisepsis of the incision region was performed using polyvinylpyrrolidone iodine disinfectant (10% povidone, Riodeine Degermante, Rioquimica, São José do Rio Preto, SP, Brazil). An incision was then made with a number 15 blade (Feather Industries Ltd., Tokyo, Japan) in the left and right tibial metaphysis regions, followed by divulsion of the soft tissue to expose the bone for implantation.
One hundred-eight commercially grade for titanium double acid-etched surface implants (cpTi, Implalife Biotechnology, Jales, SP, Brazil) were installed in the left and right tibias of the rats. The implants measured 2.0 mm in diameter and 4.0 mm of long square-edge module. A milling was performed with a 1.4 mm diameter spiral cutter mounted on an electric motor (BLM 600; Driller, São Paulo, SP, Brazil) at 1000 rpm, with 0.9% isotonic sodium chloride irrigation (Physiological; Biosintética Laboratories Inc., Ribeirão Preto, SP, Brazil). It was done a manually installation with a square digital key.
Immediately at the end of the surgical procedure, the tissues were relocated and sutured with a 4-0 vicryl thread (Ethicon, Johnson & Johnson, São José dos Campos, SP, Brazil) in a deep plane and with a monofilament thread (nylon 5-0; Ethicon, Johnson & Johnson) for the skin plane. All the animals received a Pentabiotic injection (0.1 ml/kg; Fort Dodge Saúde Animal Ltda, Campinas, SP, Brazil) during the immediate postoperative period.
**Decalcified tissues**
Euthanasia was performed at 14 (n=6) and 42 days (n=6), with the left and right tibiae removed and immediately fixed in 10% buffered formaldehyde solution (Reagents Analytical, Dental-Hospital Dynamics Ltd., Catanduva, SP, Brazil) for 48 hours, and then soaked in water for 24 hours. The tissue was then decalcified in 10% EDTA solution for 6 weeks and then dehydrated using a gradually increasing alcohol solution gradient. Diaphanization was performed with xylene, and then the samples were finally embedded in paraffin. The tissue block was cut at a thickness of 5 µm using a microtome, and sections were mounted on...
Calcified tissues
Euthanasia was performed at 60 days (n=6) with the left and right tibiae removed and immediately fixed in 10% buffered formaldehyde solution (Sigma-Aldrich, St. Louis, MO, USA) for 48 hours, then soaked in water for 24 hours and subsequently stored in 70% ethanol until scanning X-ray beam analysis using a digital computed micro-tomography system.
Immunohistochemical analysis
For immunohistochemistry analysis, polyclonal goat antibodies (Santa Cruz Biotechnology, Dallas, Texas, EUA) were used as primary antibodies against Runx-related transcription factor 2 (RUNX-2; SC-8566), osteopontin (OPN; SC-10591), and osteocalcin (OCN; SC-365797) to characterize the osteoblastic phenotype, as well as beta-catenin (β-catenin; SC-59737) and WNT-10a pathway (Santa Cruz Biotechnology - SC-6280, Dallas, Texas, EUA), proteins responsible for stem cell differentiation in bone tissue formed during osseointegration.
Immunostaining was visualized using the indirect immunoperoxidase detection method. Blocking of non-specific reactions was performed through the inactivation of endogenous peroxidase using a solution of 3% hydrogen peroxide (Merck, Kenilworth, NJ, USA), 1% bovine serum albumin (Sigma-Aldrich, St. Louis, MO, USA), and 20% of skim milk powder. Antigen retrieval was achieved using citrate phosphate buffer (pH 6.0) in the presence of moist heat.
The secondary antibody used was a biotinylated goat antibody produced in rabbit (Pierce Biotechnology, Rockford, IL, USA), which was treated with biotin and streptavidin (Dako, Glostrup, Denmark), Elite Kit, Avidin and Biotin (Vector Laboratories, Burlingame, Ca, EUA). Diaminobenzidine (Dako, Glostrup, Denmark) was used as the chromogen. Counterstaining was performed with Harris hematoxylin.
Staining was evaluated through a semi-quantitative analysis – the assignation of different “scores”\(^1\) to the presence of immunostained cells in the repaired region of the peri-implant bone. Analysis was performed using light microscopy (LeicaR DMLB, Heerbrugg, Switzerland), and assigned scores represented: no staining (0), mild staining (1), moderate staining (2), and intense staining (3). Higher scores reflected an increased area of diaminobenzidine-stained cells. The scores of the evaluator were subjected to Kappa test, in which the index was adjusted to >0.8, indicating that the observed values were consistent. Absence of immunostaining was observed when the primary antibody was substituted by the serum of the host species, acting as a negative control for the secondary antibody.
PCR analysis
Implants were removed through reverse torque and the peri-implant tissue was collected, washed in phosphate buffered saline, and stored in liquid nitrogen. Total RNA was extracted with Trizol reagent (Promega Corporation, Madison, WI, USA) and converted into cDNA (Life kit; Life Technologies, Invitrogen, Carslbad, CA, USA). Real time PCR was performed with the Step One Plus (Applied Biosystems, Waltham, MA USA) using SYBR Green (Applied Biosystems, Waltham, MA, USA). Beta-actin and beta-2 microglobulin (Life Biotechnologies, Invitrogen, Carslbad, CA, USA) were used for normalization of RUNX2, BSP, ALP, and OC expression by Delta CT method.
Micro CT – description of two-dimensional (2D) and three-dimensional (3D) morphometric calculations
The parameters used in this study were adopted in accordance with the guide for evaluation of bone microarchitecture in rodents using micro computed tomography.\(^1\) CTAnalyzer software (Skyscan, Leuven, Belgium) was used to perform 2D and 3D morphometry. Standardization of the region of interest (ROI) was performed by demarcating a rectangular area in the central slice of the implant that occupied a region corresponding to the valleys between the 3rd and 5th threads of the implant. The rectangular area was approximately 0.5 mm in length and 0.8 mm in width.
From that first demarcation, two new rectangular areas occupying the same regions of the implant were demarcated at 50 slices in the proximal and distal directions relative to the bone where the implant was installed, thus a total volume of 100 slices (874.3 μm) was examined.
After ROI standardization, the sequence of images was converted to grayscale by using a scale ranging from 0 to 255, with a minimum value of 70 and a maximum value of 100 in all groups. These amounts were determined based on the visualization of the cancellous bone structure, located in the region of interest.
Micro-tomography parameters analyzed were bone...
volume (BV), porosity parameters (Po.N; Po.V and Po) and Structural Model Index (SMI), which evaluates the trabecular geometry.
**Statistical analysis**
Regarding the micro-CT analysis, all data were initially subjected to homoscedasticity test (Shapiro–Wilk). BV and Po-tot parameters were subjected to Kruskal-Wallis non-parametric test. A P value <0.05 was interpreted as statistically significant. Structural Model Index (SMI) parameter showed non-parametric data under Kruskal-Wallis test. Thus, it was applied a Tukey post-test and all values in which P<0.05 were considered statistically significant.
**Results**
**Immunohistochemical analysis**
Representative slices and scores of immunohistochemistry may be visualized in Figures 1 to 5.
In general, the β-catenin, Wnt, and RUNX2 proteins that indicate the presence of osteogenic cell differentiation showed greater labeling for RLX groups when compared with OVX groups, regardless period of analysis (14 and 42 days postoperatively), but not for RUNX2 at 42 days, which showed mild labeling.
Concerning the mineralization proteins (osteopontin and osteocalcin) for both periods, RLX groups showed moderate labeling whereas OVX groups showed mild labeling.
**Molecular (PCR) analysis**
The gene expression of osteocalcin and ALP showed higher values for RLX group (P<0.05), followed by SHAM and OVX groups (P>0.05). In addition, there was no statistically significant difference between control groups (SHAM vs OVX), SHAM showed a tendency to greater values when compared to OVX (Figures 6A and B).
For BSP data, the highest expression was observed in RLX groups and the lowest expression, in OVX groups.
---
**Figure 1** - (A) Photomicrographs in a higher original objective (x40) of the different groups (SHAM, OVX, and RLX) and periods (14 and 42 days), in which is possible to observe an increased area of diaminobenzidine-stained cells (brown areas) around the peri-implant bone where the biomarker WNT were intense, represented by black arrows, denoting an improvement in the bone formation; (B) The chart shows the scores submitted to the Kappa test, in which the index was adjusted to >0.8, representing the expression of WNT among the groups and in both periods; (C and D) Photomicrographs in a higher original objective (x100) about the 14 and 42 days of peri-implant bone healing from RLX group showing an intense labeling of WNT pathway represented by red arrows.
For RUNX2 data, RLX and SHAM groups showed greater values compared to OVX group (P<0.05) (Figure 6D). The interaction between SHAM and RLX groups showed similar results.
3D radiographic evaluation (Micro-CT)
Regarding the bone volume, we observed that RLX group tended to have higher bone volume values, followed by OVX and SHAM groups, as noted by the mean shown in the chart. However, there was no statistically significant difference between the groups (P>0.05) (Figure 7).
As for the total bone porosity, RLX group had statistically significant lower total bone porosity than OVX and SHAM groups. (P<0.05) (Figure 8A). Total volume of pore space showed higher values for SHAM group compared to OVX and RLX groups, respectively, and between OVX and RLX (P<0.05) (Figure 8B).
The microtomography parameters related to closed porosity showed higher values for number of pores (Po.N), volume of pores (Po.V), and percentage of pores (Po) in RLX and SHAM groups, whereas OVX groups showed lower results (P<0.05) (Figures 8C-E). Values of closed pores surface were higher for SHAM group followed by OVX and RLX groups (P<0.05) (Figure 8F).
Regarding the porosity open (Po.V and Po), we observed higher values for SHAM group followed by OVX and RLX groups (P<0.05) (Figures 8G and H).
As for SMI data, RLX group showed values closer to zero, while SHAM group showed values closer to three, which means more parallel trabeculae and higher bone density (P<0.05) (Figure 9).
Discussion
We suggested that raloxifene can stimulate the growing of pre-osteoblastics cells and promote the mineralization of bone extracellular matrix by increasing the immunolabeling of osteoblastogenesis-related proteins and improving quality of bone tissue in an experimental model of osteoporosis.
related proteins, such as WNT/B-catenin canonical pathway and RUNX-2. Furthermore, raloxifene increases the expression of osteocalcin, related with bone mineralization. RLX group also demonstrated to be able to enhance the value of bone volume while reduces the bone porosity. These findings provided relevant clinical impact regarding implant rehabilitation in patients with osteoporosis treated with anti-resorptives drugs.
Attempting to optimize osteoporosis treatment, Ettinger, et al.7 (1999) conducted a randomized clinical trial (Multiple Outcomes Raloxifene Evaluation – MORE trial) that evaluated 7,705 raloxifene-treated postmenopausal women who met the World Health Organization criteria for having osteoporosis. It was observed that raloxifene was able to prevent bone loss and reduce the risk of vertebral fractures by 30–50%, but there was no significant reduction in non-vertebral fractures. However, a significant reduction in non-vertebral fractures was later found in women presenting baseline severe vertebral fractures with a risk of subsequent fractures5.
Experimental studies showed that raloxifene was able to optimize wound healing in rats with induced osteoporosis, relative to both hormone replacement therapy13-15,17 and alendronate therapy16,18. Recently, the importance of canonical Wnt/β-catenin signaling in the pathogenesis of bone tissue was highlighted due to the discovery of mutations which caused a loss of function in genes related to lipoprotein receptor-related proteins (LRPs) 5/6, reducing osteoblast numbers and favoring osteoporosis onset11.
Some researchers believe that β-catenin accumulation in the cell nucleus may interfere in the RANK/RANK ligand/osteoprotegerin (OPG) pathway by inducing OPG expression through activation of TCF/LEF transcription factors, and thus promoting osteogenesis and inhibiting osteoclastogenesis6.
Another important signaling protein in this pathway is SOST, which presents itself as a Wnt inhibitor28,30. SOST negatively modulates Wnt by competing with it for the FZD and LRP5/6 receptors, preventing
Figure 3- (A) Photomicrographs in a higher original objective (x40) of the different groups (SHAM, OVX, and RLX) and periods (14 and 42 days), in which is possible to observe an increased area of diaminobenzidine-stained cells (brown areas) around the peri-implant bone where the biomarker RUNX-2 were intense, represented by black arrow, denoting a greater active of the osteoblastogenesis; (B) The chart shows the scores submitted to the Kappa test, in which the index was adjusted to >0.8, representing the expression of RUNX-2 among the groups and in both periods; (C and D) Photomicrographs in a higher original objective (x100) about the 14 and 42 days of peri-implant bone healing from RLX group showing a moderate labeling for 14 days and middle labeling for 42 days of the biomarker RUNX-2 represented by red arrows.
YOGUI FC, MOMESSO GAC, FAVERANI LP, POLO TOB, RAMALHO-FERREIRA G, HASSUM JS, ROSSI AC, FREIRE AR, PRADO FB, OKAMOTO R
the formation of the Wnt-FZD-LRP5/6 complex, and consequently inhibiting bone formation6.
This study analyzed the effect of raloxifene on peri-implant healing in ovariectomized young rats and showed an intense staining of Wnt protein in the RLX group at 42 days of peri-implant repair and moderate to intense staining after 14 days. Regarding the β-catenin expression, we observed that this protein was moderately expressed at 14 days, and presented mild to moderate levels at 42 days. Thus, a possible explanation for the increased bone formation around the tibial implants in raloxifene-treated animals is that β-catenin is accumulating in osteoblastic cell nuclei, providing greater expression of OPG. These findings contrast with what was observed in the OVX group, where mild β-catenin expression and moderate Wnt expression were present at both time-points.
In an experimental study, Lin, et al.12 (2011) evaluated the peri-implant repair process in rat jaws by examining gene expression levels of the RUNX2 transcription factor after 3, 7, 10, and 14 days, and demonstrated that peak protein expression occurred at 14 days of repair. In addition, Stringhetta-Garcia, et al.23 (2016) found that raloxifene treatment for 120 days caused an increase in RUNX2 immunostaining in the tibiae of post-menopausal female rats. Accordingly, our study found an increasing immunostaining of the RUNX2 transcription factor after 14 days of peri-implant repair in the RLX group. However, at 42 days, it decreases the expression of this protein. In contrast, the OVX group showed low expression of RUNX2 at both study time-points. This finding may be explained by the fact that RUNX2 acts at the start of osteoblast differentiation, with a peak at 14 days. However, Wnt/β-catenin levels showed that raloxifene treatment stimulated the osteoblastic differentiation process, and consequently bone formation, around the tibial implants, compared to the ovariectomized animals that received no treatment, which showed low osteoblastic activity.
Despite the benefits of the drug regarding osteoblastic activity, it is important that the neo-formed...
bone have quality to have success in oral rehabilitation. Thus, it was evaluated the expression of osteocalcin and osteopontin as bone mineralization markers synthesized by osteoblasts, since the low expression of these proteins is associated with an increased vulnerability and fragility for long bone fractures, independent mineral density, bone volume, or porosity of the matrix. Osteocalcin acts as a growth regulator of hydroxyapatite crystals, controlling the growth of the size of these crystals without prejudice to reabsorption or bone mineralization. Osteopontin became more important in bone-related biomechanical functions.
Figure 5- (A) Photomicrographs in a higher original objective (x40) of the different groups (SHAM, OVX, and RLX) and periods (14 and 42 days), in which is possible to observe an increased area of diaminobenzidine-stained cells (brown areas) around the peri-implant bone where the biomarker osteocalcin were intense, represented by black arrows, denoting an improvement in the bone mineralization; (B) The chart shows the scores submitted to the Kappa test, in which the index was adjusted to >0.8, representing the expression of osteocalcin among the groups and in both periods; (C and D) Photomicrographs in a higher original objective (x100) about the 14 and 42 days of peri-implant bone healing from RLX group showing a moderate labeling of the biomarker osteocalcin represented by red arrows.
Figure 6- (A-D) Chart showing the highest values for RLX group regarding gene expression of osteoblastogenesis-related proteins (OC, ALP, BSP, RUNX2)
This study showed that there was an increasing labeling of osteocalcin and osteopontin in the RLX group both at 14 and at 42 days, in contrast to the OVX group, which showed mild expression in both periods. Osteopontin levels were found to be balanced across all groups at all time points. The positive effect of the drug is even more evident when associating immunohistochemical findings to data obtained by micro-CT, which uncovered increased bone volume in the RLX group compared to the OVX group. This is corroborated by previous studies in animals\textsuperscript{24}, and although there was no statistically significant difference, the results allow us to state that the drug provided fundamental characteristics for the success of peri-implant repair.
Other proteins related to mineralization of bone metabolism, such as BSP and ALP, showed greater gene expression for RLX and SHAM groups compared to OVX groups. Thus, it was clear that the biological behavior of bone healing in osteoporotic rats treated with RLX was very similar to the healthy rats (SHAM). This drug was able to recover some poor quality of bone tissue observed in OVX rats with no treatment.
The amount of porosity and trabeculae geometry was analyzed in this study and demonstrates the quality of bone tissue microarchitecture. In this way, an increase of porosity parameters shows a decreasing of bone quality\textsuperscript{1}. SMI values near to zero show the bone trabeculae like parallel plates, therefore, promoting higher bone density\textsuperscript{1}. Thus, the results related to SMI in the RLX groups indicated improvement of quality of bone tissue. Micro-CT studies also found a decrease in bone porosity in the RLX group, whereas porosity increased in the OVX group\textsuperscript{20}, demonstrating that treatment with alendronate was able to reduce the porosity of the cortical bone in post-menopausal women, and the positive effects of alendronate in preventing vertebral and non-vertebral fractures and increasing bone mineral density in osteoporosis was undeniable\textsuperscript{2,29}. However, while alendronate is the most widely used drug in the world for this purpose, its prolonged use may impair bone turnover, triggering delayed bone repair and associated with oral surgeries, such as implants placement or simple teeth extractions, is closely related to development of medication-associated osteonecrosis of the jaw (MRONJ)\textsuperscript{21}.
Raloxifene has exerted similar benefits to those of alendronate, but it was still possible to observe the positive effects of raloxifene on peri-implant repair in ovariectomized rats, in contrast to what alendronate has shown in the long-term. Other studies regarding this phenomenon must be conducted. Although there is substantial increasingly cases of MRONJ associated with dental implants, the treatment of this condition remains unclear, being necessary to rethink if that is a good choice for osteoporosis treatment in patients who need dental implants rehabilitation. Furthermore, information on the mechanism of action of raloxifene must be clarified, since little is known about how this drug enhances the osteoblastogenesis.
The analysis periods elected for this study were based, firstly, considering the cellular expression evaluated by immunohistochemistry and PCR analysis, which are higher at 14 and 42 days postoperatively. The biomarkers WNT, β-catenin, and RUNX-2, related to osteoblastogenesis cells, are more expressive in earlier periods, such as 14 days, and the biomarkers osteopontin and osteocalcin, related to cellular mineralization, are more expressive in later periods, such as 42 days. However, at 60 days, there is no relevant cellular expression due to bone maturation. Thus, we opted to analyze the bone microstructure parameters in this period (60 days), such as bone volume and porosity, verifying if that bone would be able to receive the implants to rehabilitation.
A very important analysis to provide the safety use of the drugs would be to investigate the adverse effects. In this study, we did not perform any analysis about the systemic effect of raloxifene, such as metabolizin organs evaluation (heart, liver, brain), to show some adverse effects of this drug. Although there was no observed clinical change in the animals during the therapy with raloxifene, due to the reestablishment of metabolism induced by drug therapy, it was observed...
a weight gain in the animals that received raloxifene. However, further studies of our team are being performed, aiming to show not only the local effect of osteoporosis drugs (raloxifene, strontium ranelate, PTH), but the systemic effect of these drugs and whether they show any adverse effect.
Conclusions
Regarding these findings, and despite all limitations of this study, it is possible to conclude that raloxifene treatment in ovariectomized rats provided a positive effect on tibial peri-implant repair by stimulating
osteoblast differentiation concomitant to its anti-resorption effect, resulting in increased bone formation. We also demonstrated that, by investigating bone matrix mineralization and microarchitecture characteristics, this newly formed bone is of high quality. We therefore believe that raloxifene must be considered in the treatment of osteoporosis, not only for its benefits in preventing fractures, but also as an adjunct in the dental implant rehabilitation process.
Acknowledgments
The authors would like to express their gratitude to FAPESP (#2013/11277-3 and 2012/15912-2) for the financial support.
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Regulation and Directing Stem Cell Fate by Tissue Engineering Functional Microenvironments: Scaffold Physical and Chemical Cues
Fei Xing,1 Lang Li,2 Changchun Zhou3, Cheng Long,1 Lina Wu,3 Haoyuan Lei,3 Qingquan Kong,1 Yuijiang Fan3, Zhou Xiang2,1 and Xingdong Zhang3
1Department of Orthopaedics, West China Hospital, Sichuan University, No. 37 Guoxue Lane, Chengdu, 610041 Sichuan, China
2Department of Pediatric Surgery, West China Hospital, Sichuan University, No. 37 Guoxue Lane, Chengdu, 610041 Sichuan, China
3National Engineering Research Center for Biomaterials, Sichuan University, 610064 Chengdu, Sichuan, China
Correspondence should be addressed to Changchun Zhou; [email protected]
Received 15 October 2019; Accepted 5 December 2019; Published 27 December 2019
It is well known that stem cells reside within tissue engineering functional microenvironments that physically localize them and direct their stem cell fate. Recent efforts in the development of more complex and engineered scaffold technologies, together with new understanding of stem cell behavior in vitro, have provided a new impetus to study regulation and directing stem cell fate. A variety of tissue engineering technologies have been developed to regulate the fate of stem cells. Traditional methods to change the fate of stem cells are adding growth factors or some signaling pathways. In recent years, many studies have revealed that the geometrical microenvironment played an essential role in regulating the fate of stem cells, and the physical factors of scaffolds including mechanical properties, pore sizes, porosity, surface stiffness, three-dimensional structures, and mechanical stimulation may affect the fate of stem cells. Chemical factors such as cell-adhesive ligands and exogenous growth factors would also regulate the fate of stem cells. Understanding how these physical and chemical cues affect the fate of stem cells is essential for building more complex and controlled scaffolds for directing stem cell fate.
1. Introduction
Stem cells have the ability of self-renewal and differentiation; they can be used to repair the bone, cartilage, and skin and play an important role in regenerative medicine [1, 2]. Stem cells are generally classified into embryonic stem cells and adult stem cells. Embryonic stem cells are more primitive, but some studies have shown that they may turn into tumor cells, which dramatically limits their application. At present, adult stem cells, such as bone marrow-derived mesenchymal stem cells (BMMSCs), adipose-derived stromal cells (ASCs), umbilical cord-derived mesenchymal stem cells (UC-MSCs), and even urine-derived mesenchymal stem cells (U-MSCs), have attracted more and more attention and are widely used in the field of regenerative medicine [3]. In the field of tissue engineering regeneration, regulating the proliferation and differentiation of stem cells has been an important research direction for stem cells [4, 5].
The fate of stem cells includes cell proliferation, differentiation, migration, and adhesion. Proliferation and differentiation of stem cells are influenced by the surface of scaffold materials, which have been studied by many researchers in the past decades. Ideal scaffolds for cell survival have the following specific characteristics: firstly, the materials show good biocompatibility; secondly, the materials could be degradable in vivo; thirdly, the fundamental characteristics of materials could mimic the extracellular matrix (ECM) as much as possible [6, 7].
Previous researchers suggested that the scaffold surface microenvironment influenced the fate of stem cells. And the surface microenvironments mainly include physical and biochemical factors [8, 9]. For example, scaffolds with different pore sizes and porosity would lead to different
properties and affect the fate of stem cells. Previous studies have shown that scaffolds with pore sizes of 370-400 μm are more conducive to promote the chondrogenic differentiation for ASCs [10, 11]. Also, scaffolds with different materials also affect the fate of stem cells, including cell proliferation, differentiation, and adhesion [12]. It is essential to have a comprehensive understanding of the regulation of the fate of stem cells by physical, biochemical, and other factors, so that we can better design scaffolds with specific microenvironment characteristics to regulate cells for promoting tissue regeneration.
This review summarizes the factors affecting the fate of stem cells which are mainly discussed in terms of physical and chemical aspects: the material stiffness, surface topography, three-dimensional space, mechanical stimulation, and adhesion proteins, growth factors, and substances secreted by cells on the surface of materials. This review is aimed at highlighting the effects of the surface microenvironment of biomaterials in directing stem cell fate.
2. Advanced Technology for the Manufacturing of Biomimetic Biomaterials
2.1. 3D Printing of Porous Biomimetic Scaffolds. The ideal biomimetic scaffold for tissue reconstruction should resemble natural tissue in both material composition and geometrical properties. For bone tissue biomimetic scaffold, the three-dimensional (3D) porous structure plays a crucial role for bone regeneration [13–16] (Figure 1). This biomimetic porous structure contains interconnected and micro pores and provides a temporary support for cell proliferation and tissue infiltration, as well as a microenvironment for transportation of nutrients and waste products which can function well [17–20]. At the same time, the surface topography of scaffolds also plays an important role in bone tissue regeneration and regulation of cell behaviors. Numerous methods, such as solvent casting/particle leaching [21, 22], phase separation [23, 24], emulsion freeze drying [25], chemical foaming, electrospun, 3D printing, and micropattern techniques [26–29], have been developed to fabricate different porous scaffolds for tissue engineering.
Advances in computational design and 3D printing (3DP) have resulted in quick and accurate fabrication of 3D porous scaffolds with well-controlled geometrical architectures [30–33]. 3DP can fabricate scaffolds with complex internal and external structures in various materials [34–36]. 3DP produces complex scaffolds from a 3D design file by decomposing an object's structures into a series of parallel slices. Internal 3D structures are then fabricated by reproducing these slices one layer at a time by using a sized nozzle (direct extrusion printing) or a programmed selective sintering laser (selective laser melting, SLM), electron beam melting (EBM), or a specific curing light (stereo lithography apparatus, SLA). So far, 3D printing technology has successfully printed various bioceramics, polymers, metal materials, and other biocompatible materials for bone tissue engineering scaffolds [37–39]. These printed scaffolds have highly complicated geometrical architectures with personal-customized shape for different patients in accordance with their CT data. However, the printing capability is limited. For most 3D printing technologies, objects with an accurate porosity of less than 10 μm are difficult to fabricate due to printing accuracy and printing efficiency [40–42].
2.2. Electrospinning of Biomimetic Biomaterials. Electrospinning is curing nanofibers by high-voltage electrostatic force (5-30 kV), which has the advantages of rapid and efficient preparation. In recent years, it has received great attention in the field of tissue engineering. Electrospinning could change the properties by regulating the voltage, conductivity of the solution, distance between the injector and the collector, temperature, and humidity [43]. Common electrospinning materials, including PCL, PLGA, and PLA, have been widely used for tissue regeneration [44–46] (Figure 2). In tendon repairing, orderly arrangement of electrospun nanofibers can guide the arrangement of cells, improve the deposition for ECM, and promote the differentiation of stem cells to regenerate tendon [47]. In addition, electrospun nanofibers could be a suitable carrier, and stem cell could have myogenic differentiation after adding the platelet-derived growth factor (PDGF) [48]. And the arrangement of electrospun nanofibers could be regulated according to requirements. Compared with the random arrangement, the orderly and aligned arrangement of scaffolds showed advantages in neural differentiation of stem cells and migration of neural cell in a rat T9 dorsal hemisection spinal cord injury model, which provided great promise for biomaterial design for applications in nerve regeneration [49].
2.3. Micropattern of Biomaterial Surface Topography. As important factors, the physical and topographical surface of the scaffold could regulate the cell behaviors and control cell function [53, 54]. In addition, a previous study found that the different shapes and sizes of cell could play a role in directing the fates of stem cells [55]. Round cells promoted adipogenesis while cells with high spreading preferred an osteoblast fate by activating MAP kinase pathways and Wnt signaling [53]. In addition, the increased myosin contractility enhances osteogenesis of stem cells. Therefore, the micropatterns of scaffolds could affect the cell behavior by altering the shapes of stem cells [56]. However, these microscopic structures are difficult to fabricate by conventional methods. Literatures reported that the combined uniaxial pressing method and templates may fabricate HA ceramics with regular concaves [57, 58] and grooves [59]. In that work, HA powders were compacted into disc-shaped pellets via uniaxial pressing and polystyrene resin microspheres of different sizes were used as poroshifters to form patterned surfaces with a series of regular concaves; the circular holes with diameters of about 50, 200, and 500 μm were patterned uniformly as shown in (Figure 3(a)). In vitro studies found that HA bioceramics with 50 μm concaves showed the strongest ability to induce osteogenic differentiation of human osteosarcoma MG-63 cells, as evidenced by the highest alkaline phosphatase (ALP) activity and Cbfa-1 gene expression [57]. Wang et al. reported that HA disc-shaped pellets with micropatterned grooves of ~20, 40, and 60 μm in width were patterned by transferring patterns from different aluminum
alloy templates (Figure 3(b)). The HA ceramics with micro-grooved patterns showed increased water wettability with decrease of groove width. The microgrooves evidently affected cell elongation, as MC3T3-E1 preosteoblasts were oriented along the direction of grooves, and the cell orientation angles were decreased by decreasing groove width [59].
Zhao et al. [60] fabricated HA ceramics that exhibited micro-patterned structured surfaces with square convexes of different sizes via uniaxial pressing method by using ordered micropatterned nylon sieves as templates (Figure 3(c)). Compared to the flat one, the micropatterned surface could enhance the adhesion, proliferation, and osteogenic differentiation of rat BMSCs. These studies indicated that bioceramics with regular micropattern of size close to cell size (20-50 μm) showed the best stimulation of cell response.
Furthermore, Wang and Hu [61] created ordered HA patterns with spherical (Figure 3(d)) and hexagonal (Figure 3(e)) shapes on Si and Ti substrates via electrophoretic deposition technique. Teshima et al. [62] prepared aligned CaP microstructured patterns with HA nanocrystals by using a hydrophilic/hydrophobic Si-based template photochemically made by VUV light irradiation to provide micro reaction cells for HA crystal growth. Tseng et al. [63] fabricated uniform single-crystal HA nanorods onto specific
sites of grid-shaped substrate patterned by hexagonal microcontact printing (Figure 3(f)). However, clear cell behaviors or regulation mechanism of these micropatterned scaffolds remains unidentified, but almost all of the highly ordered patterns close to the diameter of the cells show effective regulation of cell fate.
Surface micropatterning has been widely studied in the preparation of biological functional materials. The patterning methods include photolithography [64], electron beam etching [65], and microcontact transfer method [66, 67]. Traditional methods are usually complicated process and cost high, which limit its application in large-area patterning. The inkjet printing technology is easy to realize direct writing of large-area complex patterns and composite functional materials, which makes it to be a promising method of patterning [68, 69].
3. Regulation and Directing of Stem Cell Fate
3.1. Scaffold Physical Cues
3.1.1. Pore Size and Porosity Effects. The pore diameter is an essential parameter of the physical structure for porous scaffolds. Pores may determine the nutrition exchange inside of scaffolds, affect the skeletal tension of cell proliferation process, and regulate the fate of stem cells (Table 1). Cells can recognize micropores of 5 nm in the scaffolds. If the pore size is much larger than the cell diameter, the growth situation of the cells will be similar to that on the plate [70]. The pore diameter will affect the adhesion and migration of cells. It is generally believed that scaffolds with a small pore diameter were facilitating the adhesion of cells, while scaffolds with a large pore diameter are more conducive to the migration of cells from the outer layer of scaffolds to the inner layer of scaffolds. In the experiments of osteogenic differentiation of stem cells, it is generally believed that the diameter of 100-300 μm is more conducive to the osteogenic differentiation of bone marrow-derived mesenchymal stem cells [71]. Some scholars have proposed that the pore size of 200 μm is the optimal condition for the osteogenic differentiation of cells [72]. However, 350 μm is considered to be the optimal condition for cell proliferation [73]. When the diameter is larger than 500 μm, cell adhesion will be reduced, which is not conducive to cell proliferation [11]. In terms of cartilage formation, scholars believe that when the diameter is close to 400 μm, it is conducive to cartilage repairing [74]. As for the differentiation of hematopoietic stem cells, it is believed that less than 150 μm is more conducive to the differentiation of stem cells into hematopoietic stem cells [75]. In addition, high porosity could promote the transport of nutrition and oxygen, making it easier for cells to grow inward. However, due to a large number of pores, the mechanical properties of scaffolds will be decreased [76]. The optimal porosity has not been determined, and many studies have shown that scaffolds with high porosity (96.7%) can promote cell proliferation, which may be due to high porosity to promote the transport of nutrients. Some studies showed that when porosity was 86%, cell proliferation was better, which may
Figure 3: Typical orderly micropatterned scaffold surface. HA bioceramic micropatterned surface with regular small concaves (a) and larger concaves (b) [57]. HA ceramics with spherical array (c) [61]. Micropatterned vertical grooves (d) and inclined grooves (e) [59]. Ordered hexagonal-shape patterns (f) [61]. Quadrate convexes with smaller space (g) and larger space (h) [60]. Grid-shaped patterns (i) [63].
be because different scaffold materials have different effects on different cells [77].
3.1.2. Stiffness Effects. The fate of cells is also affected by the stiffness of the surface microenvironment. Firstly, studies have shown that the stiffness of matrix could affect the differentiation spectrum of stem cell (Figure 4). Stem cells differentiate into muscle cells on soft substrates and osteoblasts on harder substrates [86, 87]. Another study supported this finding, and stem cell on soft materials when stiffness is less than 0.05 kPa could promote neural differentiation effectively, while hard stiffness materials (>40 kPa) promoted osteogenic differentiation effectively [88, 89], which could be related to the Wnt signal pathway [90]. However, there is no agreement on the optimal stiffness for stem cells to differentiate into neurons, muscle cells, cartilage cells, and osteoblasts [86, 91]. Secondly, the stiffness of the material also affects stem cell migration. Stem cells tend to migrate to harder matrix [92]. However, the specific matrix of stem cell migration to the high stiffness matrix is unknown and may be associated with contractility of stem cells [93]. Moreover, the surface stiffness also affects the proliferation of stem cells [94]; a previous study has shown that hydrogels with very soft modulus (~10 Pa) decreased cell proliferation and differentiation [95]. In addition, stiffness is an important factor to maintain the survival rate for stem cells; studies have shown that stem cell on the matrix with a stiffness of 200 Pa survived more than 90% compared to 80% in cultures (100 Pa) [96]. Another study showed that the hardness of 2.5 MPa increased pluripotency [97]. However, the optimal stiffness to maintain pluripotency of stem cells has not been determined, which may be related to different stem cells and material properties from different sources.
3.1.3. Topography Effects. Surface topography plays a vital role in regulating stem cell behavior. In vivo, the topography of the extracellular matrix (ECM) is the basis for cell survival and affects stem cell behavior [99]. In vitro, the surface topography of scaffolds influences the fate of stem cells, including gene expression, cell adhesion, cell proliferation, and extracellular matrix secretion. The scaffold is the cornerstone and directly contacts with stem cell, so the effect of surface topography on stem cells has been widely studied. Surface topography such as roughness and texture is very important in regulating cell response and determining cell fate.
The roughness of the material’s surface also plays a role in the fate of stem cells, with a rougher surface reducing the proliferation rate of stem cell compared to a smooth surface. On rough surfaces, cells are more likely to form composite layers, so stem cells are more likely to accumulate in grooves, holes, canyons, and crackers, forming bone nodules and ultimately osteogenic differentiation. In the study of Graziano et al., stem cells differentiated faster on concave surfaces and showed nuclear polarity and a high expression of bone-specific proteins, and the interaction between cells and scaffolds is better. However, when cultured on the convex surface, the proliferation activity of stem cells was low, and the extracellular matrix secretion was reduced [100]. Some studies have found that topography can also affect the differentiation lineages of cells. Several lineages including chondrogenic differentiation, osteogenic differentiation, and neuronal differentiation have been studied [101–103].
In the past decades, the rapid development of nanotechnology has promoted the development of material surface topography modification [104]. Different surface topographies have been reported, such as porous silicon, TiO₂ nanotube, binary colloidal crystal, colloidal lithography, nanopillars, and nanoparticle topographies [105–107] (Figure 5). Nanoscale surface topographies can be constructed by means of electrochemical etching [108, 109], lithography [110, 111], sputtering [112], and colloidal lithography [105, 113, 114]. Each of these methods has advantages and limitations. According to topography forms, nanotech surface topographies could be divided into nanopits, nanocolumns, nanogrooves, and nanotubes. Previous studies have found that ordered nanopits can reduce cell adhesion [115]. However, disordered nanopits can better promote the osteogenic differentiation of embryonic stem cells [116]. Previous studies have found that the height of nanoliths has a great impact on the osteogenic differentiation of stem cells. The height of nanoliths less than 50 nm can stimulate the adhesion of stem cells and improve the osteogenic differentiation, while nanoliths with height of 95 nm were not good for adhesion of stem cells.
| Material | Optimal pore size (μm) | Optimal porosity (%) | Target stem cell(s) | Potential application(s) | Reference |
|----------------------------------|------------------------|----------------------|---------------------|--------------------------|-----------|
| β-Tricalcium phosphate | 200-600 | 65 | BMMSCs | Osteogenic | [78] |
| Sintered titanium fiber mesh | 250 | 86 | BMMSCs | Osteogenic | [79] |
| PCL | 200 | | ASCs | Proliferation | [74] |
| PCL | 400 | | ASCs | Chondrogenic | [74] |
| Poly(lactic-glycolic acid) | 370–400 | 80–97 | BMMSCs | Chondrogenic | [74] |
| Poly(lactic-glycolic acid) | 120–200 | 50 | ASCs | Hepatogenesis | [80] |
| Poly(lactic-glycolic acid) | 50–200 | | BMMSCs | Myogenic | [81] |
| Coralline hydroxyapatite | 200 | 75 | BMMSCs | Osteogenic | [82] |
| β-Tricalcium phosphate | 400–500 | 70 | BMMSCs | Osteogenic | [83] |
| ZrO₂ ceramic | 600 | 80–89 | ASCs | Osteogenic | [84] |
| Polycaprolactone | 100–150 | | BMMSCs | Chondrogenic | [85] |
Table 1: Proposed optimal pore sizes and porosities affecting the fate of stem cell.
Nanogrooves are the most common nanoscaffold material, which could promote cell extension or migration, fix cell arrangement, and affect cell differentiation. The arrangement of nanoscale grooves also has an effect on cell fate, and compared with the parallel groove, vertical groove retracted faster [117]. In nanoscale grooves, the ratio of grooves to ridges also influences cell differentiation, and grooves : ridges = 3 : 1 could promote stem cell osteogenesis [118]. In addition, some scholars have discussed the width of groove, and the width of the groove may have an effect on the differentiation spectrum of stem cells, but there is no unified conclusion [116, 119]. As for the limiting sensitivity to grooves, studies have shown that stem cell is sensitive to grooves in 8 nm [120]. However, because of the complexity of manipulating and evaluating cell fate, it is difficult to construct nanoscale materials systematically, and its clinical application is still limited.
In addition, hydrophobicity and chemical moieties are also important factors influencing stem cell behavior. Hydrophilic biomaterial is more conducive to protein adsorption, promoting the transport and excretion of nutrients. Therefore, it is more conducive to tissue regeneration [121, 122]. The chemical composition of the material is similar to that of the host tissue, which is more conducive to the integration of the tissue. For example, calcium phosphate ceramics are chemically similar to natural bone tissue, so they are widely used in the field of tissue engineering.
used in bone repair. It was found that this calcium phosphate material could integrate well with bone tissue [16, 37].
3.1.4. Spatial and Dimensional Influences. Cells cultured by a two-dimensional (2D) culture lose their original characteristics in vivo gradually. However, 3D culture could better simulate the living environment of cells in vivo. The cells obtained from a 3D culture were significantly different from those obtained from the 2D culture in terms of morphological structure, proliferation and differentiation, gene expression, and cell function [128]. The 3D cell culture can not only retain the material structure foundation of natural cell microenvironment but also simulate the microenvironment of cell growth in vivo (Figure 6), which overcomes the defects of the previous two methods and provides a simpler, safer, and more reliable method for cell research. More and more researches adopt 3D scaffolds for stem cell culture. Some studies have shown that the proliferation and differentiation potential of ASCs is significantly stronger than that in 2D environment when cultured about 21 days [129, 130]. 3D environment prevented the reduction of osteogenic differentiation efficiency of stem cells caused by aging or passage [130]. In the field of tissue engineering, 3D culture could promote the differentiation of stem cells into bone and cartilage compared with 2D culture, which is widely used in the osteochondral tissue engineering [16, 30]. 3D culture also provides a good scaffold for neuron growth, in which neurons could grow in all directions and form a neural network, providing a better method for neuron regeneration [131, 132]. 3D culture can also improve survival of stem cells, as shown in a study by Lee et al., which also found that 3D culture has the advantage of maintaining genomic stability [133]. In the study of Adil et al., 3D culture could generate more neurons with electrophysiological activity, increase cell activity, and integrate well with host tissues after implantation [134].
3.2. Scaffold Chemical Cues
3.2.1. Phytochemical Cue Stimulation. The chemical signal of the cell microenvironment can regulate the fate of stem cells. The chemical properties of the surface of the material, such as the characteristics of the material itself, cell coculture, and adhesion between cells could affect the proliferation and differentiation behavior of the cells. For example, many studies have reported that hydroxyapatite itself could promote osteogenic differentiation of stem cells [59]. Some growth factors such as VEGF could promote the differentiation of stem cells into vascular endothelial cells [136]. In our previous study, we have shown that cell coculture could affect the fate of stem cells [137]. Another study showed that coinjection of MSCs and VEGF could affect the fate of stem cell and improve cell implantation myocardial infarction [136, 138].
A large number of studies have been conducted on the effects of phytochemicals on the fate of stem cells. Currently, the phytochemicals studied mainly fall into the following categories: icariin [139], resveratrol [140], quercetin [141], and curcumin [142] (Table 2). Icariin is extracted from the plant herba epimedii and helps improve male fertility [143]. Icariin is associated with phosphorylation of ERK and p38 and activates the ERK and p38 MAPK signaling pathways, leading to the upregulation of MAPK target downstream transcription factors Elk1 and C-MYC, promoting the proliferation of rat BMMSCs. In addition, the optimal concentration of icariin in medium for the proliferation of BMMSCs is 320 μg/L. However, these findings need to be further confirmed in vivo [143]. As a phytoestrogen, resveratrol is a naturally occurring polyphenolic compound in red wine and numerous plants. In addition, resveratrol could activate estrogen receptor signaling selectively. For human mesenchymal stem cells, resveratrol upregulated the expression of osteolineage genes RUNX2 and osteocalcin while suppressing adipolineage genes PPARγ2 and LEPTIN in adipogenic medium, which was mediated mainly through the SIRT1/FOXO3A axis with a smaller contribution from the estrogenic pathway [144]. As an inflammatory demyelinating disease, experimental autoimmune encephalitis is a useful model providing considerable insights into the pathogenesis of multiple sclerosis. The combination of resveratrol and BMMSCs could effectively alleviate the symptoms of autoimmune encephalitis, which is associated with its immunomodulatory effects. The combination of resveratrol and BMMSCs could effectively suppress proinflammatory cytokines (IFN-γ, TNF-α) and increase anti-inflammatory cytokines (IL-4, IL-10) [145]. Quercetin is one of the most ubiquitous bioflavonoids, widely found in many kinds of plants [141]. Quercetin has a positive pharmacological effect on bone metabolism, which could play a leading role in the quercetin-promoted osteogenic proliferation and differentiation of MSCs by activating the ERK1/2 and JNK signaling pathways [146]. Curcumin is a natural phenolic component of yellow curry spice, which is used in some cultures for the treatment of diseases associated with oxidative stress and inflammation. In addition, curcumin could prevent the death of neurons in animal models of neurodegenerative disorders [142]. Kim et al. conducted a research to investigate the effects of curcumin on mouse multipotent neural progenitor cells and adult hippocampal neurogenesis. The results showed that curcumin could promote the proliferation and neural differentiation of hippocampal embryonic stem cells at low concentrations and be cytotoxic at high concentrations. In addition, curcumin could activate cellular signal transduction pathways, including ERK and p38MAPK pathways, which could regulate neuronal plasticity and stress responses [147]. In conclusion, phytochemical stimulation regulates the fate of stem cells by regulating signal pathways such as Wnt, protein kinase, and PI3K/Akt signaling pathways.
3.2.2. Cell-Adhesive Ligand Effects. The adhesion of cells and their surroundings is very important to the fate of stem cells, which can regulate the apoptosis, migration, and differentiation of stem cells [158]. This cellular adhesion to the microenvironment is mediated by transmembrane matrix receptors (Figure 7). Integrin is an important transmembrane receptor that plays an important role in signal transduction by mediating the main link between cells and ECM [159]. Integrin is a heterodimer transmembrane molecule...
composed of different alpha and beta subunits that binds directly to ECM proteins such as collagen, laminin, and fibronectin. Integrins bind to adhesion molecules (CD54 or ICAM1) on the cell surface and adhesion molecules (CD106 or VCAM1) which are present in stem cells. However, in in vitro culture, the expression of integrin is different due to different cell sources and culture methods. RGD is an integrin-binding ligand, which could be used to explore the interaction between cells and ECM [160]. Studies have shown that changing the coupling strength of RGD peptide on substrates could regulate the adhesion, diffusion, and differentiation of MSCs [161]. By adding RGD-related polypeptide into hydrogel, cell adhesion and diffusion could be promoted while high concentrations of RGD also inhibit cell detachment [162]. Due to the importance of adhesion between cells and matrix, strategies for adding binding ligands to hydrogels have been studied. Luo et al. discovered an agarose hydrogel which could react with RGD peptides by exposure to light [163]. In addition to RGD, other adhesion peptides, such as YIGSR and IKVAV, could also influence the fate of stem cell [164, 165]. Integrin, adaptor, and signal proteins together form the adhesive plaque complex, which contains more than 100 proteins which connect actomyosin and ECM and form the signaling pathway [166, 167]. In addition to integrins, cadherins are important receptors on cell surfaces and are involved in stem cell migration and homing [168]. Cadherins play an important role in stem cell early adhesion and self-renewal [169]. The study of cadherins is limited now, and more researchers are needed in the future.
### Table 2: The applications of phytochemicals for stem cell.
| Phytochemical | Affecting signal transduction pathway | Target stem cell(s) | Potential application(s) | Reference |
|---------------|--------------------------------------|---------------------|--------------------------|-----------|
| PI3K/Akt and STAT3 | SDF-1alpha/HIF-1alpha/CXCR4 | ASCs | Diabetes-associated erectile dysfunction | [148] |
| Icariin | SDF-1alpha/HIF-1alpha/CXCR4 | BMMSCs | Proliferation | [143] |
| | SDF-1alpha/HIF-1alpha/CXCR4 | BMMSCs | Migration | [139] |
| | PI3K and ERK1/2 | BMMSCs | Angiogenesis and neurogenesis | [149] |
| | SIRT1/FOXO3A | Human embryonic stem cells | Osteoblastic differentiation | [144] |
| Resveratrol | AMPK | BMMSCs | Osteogenic differentiation | [140] |
| | AMPK/Ulk1 | Embryonic stem cells | Pluripotency | [150] |
| | SIRT1 | Umbilical cord-derived mesenchymal stem cells | Neural repair of Alzheimer’s disease | [151] |
| Quercetin | p38 MAPK, ERK1/2, and JNK | BMMSCs | Osteogenesis | [141] |
| | TNF-alpha | BMMSCs | Osteogenesis | [152] |
| | BMP2, Smad1, Smad4, RUNX2, OSX, and OPN expression and Smad1 phosphorylation | BMMSCs | Differentiation | [153] |
| | Self-renewal genes, Notch1 and Hes1 | Neural stem cells | Proliferation | [154] |
| | Caveolin-1 | Epidermal stem cells | Proliferation | [155] |
| | Glucocorticoid receptor and STAT3 | Embryonic neural stem cells | Proliferation | [156] |
| Curcumin | TERT gene | ASCs | Improve lifespan | [157] |
**Figure 6:** Compared with 2D environment, 3D environment could carry growth factors, maintain stiffness, and promote stem cell differentiation [135].
**Table 2:** The applications of phytochemicals for stem cell.
receptors are also considered important for stem-niche interactions, including EGF, Notch, c-kit, CD44, and VCAM1 [170].
3.2.3. Growth Factor Effects. The development and differentiation of stem cells are affected by various internal mechanisms and microenvironmental factors, and growth factors are often used as inducers of differentiation (Figure 7). Therefore, it is very important to clarify their role in the survival or differentiation of stem cells. There are also growth factors that mobilize stem cells to return home for tissue repair. The most common growth factor includes platelet-derived growth factor, insulin-like growth factor-1, hepatocyte growth factor (HGF), EGF, and angiopoietin [172–176]. Currently, growth factor is widely used in the field of regeneration, such as bone regeneration and cartilage regeneration. There are many cytokines that promote bone formation, such as BMP, PDGF, TGF-beta, FGF, and IGF [177]. Among them, BMP is the most widely used osteogenic factor. BMP could induce MSC proliferation and differentiation into chondrocytes and osteoblasts [178]. In terms of heart repair, literatures reported that coinjection of MSCs and VEGF into the heart with myocardial infarction increased cell implantation and resulted in better cardiac function than either VEGF or MSC alone [136, 179]. Mesenchymal stem cells with IGF-1 overexpression promote bone marrow stem cell mobilization through paracrine activation of SDF-1alpha/CXCR4 signaling so as to promote cardiac repair [138]. The combination of laminin and platelet-derived growth factor could promote neuronal differentiation of U-MSCs [180]. Hepatocyte growth factor could promote the differentiation of stem cells, which may be associated with the activation of Wnt signaling [181]. Another study found that this hepatocyte growth factor significantly promotes the viability of embryo-derived mesenchymal stem cells and prevents its senescence, which is associated with transcription of RAD51 [182]. All of the above growth factors have an impact on the proliferation and differentiation of stem cells. Loading growth factors onto the scaffold material could affect the growth of stem cells, which could be the direction of tissue engineering research. Local sustained release is an important part of how to use growth factors efficiently.
4. Conclusion and Future Perspective
The fate of stem cells in the body is complicated and much remains unknown. The fate of stem cells is regulated not only by the genetic material but also by the microenvironment. The ideal microenvironment is a combination of various conditions to simulate the extracellular matrix as much as possible, to construct the physicochemical conditions suitable for the growth of stem cells, and to meet the requirements of proliferation, differentiation, adhesion, and other aspects of stem cells. Ideal microenvironments include a proper mechanical stiffness, porosity, aperture, topography, 3D environment, proper mechanical stimulation, and orderly/disordered arrangement. It is generally believed that scaffolds with a pore diameter of 100-300 μm are more conducive to the osteogenic differentiation of bone marrow-derived mesenchymal stem cells. When the diameter is larger than 500 μm, cell adhesion will be reduced, which is not conducive to cell proliferation. In terms of cartilage formation, it is generally accepted that when the diameter is close to 400 μm, it is conducive to cartilage repairing. Stiffness is an important factor to maintain the survival rate for stem cells. Stem cells tend to migrate to harder matrix. Different substrates with varied stiffness would affect stem cell
differentiation. In addition, exogenous phytochemicals, peptides, and growth factors will stimulate stem cells through a series of complex signaling pathways, affecting the fate of stem cells. Changing the microenvironment to guide stem cell behavior is challenging because of the complex structure of cells and some unknown signaling pathways, which require greater efforts in the future. With the development of fabrication techniques, there are many advance fabrication methods, such as 3D printing, electrospinning, and micro-patterning, which were successfully applied to design and fabricate scaffolds with specific microenvironment [183].
At present, many researchers have promoted stem cell differentiation and tissue regeneration by adding growth factors. However, studies have shown that matrix characteristics may be more important than exogenous addition of growth or differentiation factors, which may provide a direction for future research [86]. This review highlights the contribution of physical and chemical cues that influence stem cell fate. Most of the current studies are preclinical, and their progress in clinical applications requires additional testing to demonstrate safety and efficacy. In addition, it was found that the same materials have different effects on the fate of stem cells from different sources. Proper stem cell and matched surface microenvironment remain the focus of future research. By combining these strategies with existing material properties to guide cell fate, stem cells could be an important option in tissue engineering. Although there are many factors and cues that can regulate the release of growth factors, they have advantages and disadvantages and need to be selected according to the specific situation.
Conflicts of Interest
The authors declare that they have no conflicts of interest.
Authors’ Contributions
Fei Xing and Lang Li contributed equally to this work.
Acknowledgments
This work was supported by the National Key Research and Development Program of China (Nos. 2018YFC1106800 and 2018YFB1105600), the National Natural Science Foundation of China (31971251), the Sichuan Province Science & Technology Department Projects (2019YFH0079, 2016CZYD0004, and 2017SZ0001, 2018GZ0142, and 2019JTD0008), and the “111” Project (No. B16033).
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Abstract. The aim of the present study was to determine the impact of microRNA (miRNA/miR)-633 on the biological properties of malignant melanoma cells. Kang-Ai 1 (KAI1), also known as cluster of differentiation 82, is an important transcriptional regulator and tumor suppressor gene present in different types of tumors. miRNAs that potentially bind with KAI1 were predicted via bioinformatics analyses. In total, six putative miRNA regulators of KAI1 were identified in the present analysis, among which miR-633 was upregulated the most in melanoma tissues compared with the control group. The expression levels of miR-633 and KAI1 in melanoma tissues compared with adjacent normal tissues were then assessed. It was found that miR-633 was significantly upregulated in melanoma cells compared with the control group, whereas the expression levels of KAI1 showed the opposite results. miR-633 was predicted to target the 3'-untranslated region of KAI1 using predictive online tools, and results from luciferase reporter assays confirmed the direct regulation of KAI1 promoter activity by miR-633. Furthermore, miR-633 mimics overexpression was shown to suppress both mRNA and protein expression of KAI1, while miR-633 inhibition resulted in decreased viability and migration in melanoma cells in vitro. Taken together, the present study demonstrated, to the best of the authors’ knowledge for the first time, that miR-633 exerts an important role in melanoma through targeting KAI1.
Introduction
Melanoma is one of the most commonly occurring forms of cancer, and malignant melanoma is the third most common skin malignancy (1-6). For most patients with melanoma, immunotherapy, chemotherapy, or small-molecule inhibitor administration are not effective therapies (7). Furthermore, the outcomes of patients with advanced-stage disease remain poor (8,9).
MicroRNAs (miRNAs/miRs) are short RNAs (~22 nucleotides in length) that do not encode protein, and yet are important regulators of oncogenesis (10,11). By binding to complementary sequences in the 3'-untranslated region (3'-UTR) of target mRNAs, miRNAs can alter the stability and translation of these transcripts, thereby influencing phenotypic outcomes within cells. A single miRNA can target multiple different mRNAs, giving rise to complex regulatory networks that control diverse pathological and physiological biological activities (12,13). The dysregulation of miRNAs is a common hallmark of oncogenesis and tumor progression (14,15). By evaluating patterns of miRNA expression, it may be possible to better diagnose or monitor specific types of cancer. For example, miR-144 and miR-92a have been shown to serve as valuable and specific diagnostic biomarkers that can guide the detection of specific subtypes of colorectal cancer (16). Additionally, miR-221 can suppress the expression of PHD finger protein 2, thereby influencing liver cancer invasion, leading researchers to highlight this signaling axis as a potential target for therapeutic intervention (17). Efforts have also been made to successfully identify patterns of miRNA dysregulation associated with melanoma (18). Given their essential roles as regulators of cancer onset and progression, further analyses of miRNAs in these oncogenic contexts are warranted.
Tetraspanin cluster of differentiation 82 (CD82), also known as Kang-Ai 1 (KAI1), is an important tumor suppressor gene that was first detected based upon analyses of human metastatic prostate cancer samples (19). There is robust evidence linking KAI1 downregulation with the invasive and metastatic activities of various tumors based upon histopathological and molecular analyses (20). KAI1 mutations and associated loss-of-function are evident in a range of tumor types, reaffirming the role of this gene as a tumor suppressor (21-23). KAI1 expression in melanoma has been shown to be associated with tumor grade and patient prognosis, and it has been validated as a risk factor for disease progression (24,25). However, the association between miR-633 and malignant melanoma has not been elucidated to date. The present study investigated the role of miR-633 in the proliferation and migration of melanoma cells. Furthermore, the potential role of miR-633 in regulating KAI1 expression in melanoma cells was explored.
MicroRNA-633 enhances melanoma cell proliferation and migration by suppressing KAI1
ZHENGXIANG WANG1 and YALING LIU2
1Department of Dermatology, Hebei Medical University, Shijiazhuang, Hebei 050030;
2Department of Dermatology, The Third Hospital of Hebei Medical University, Shijiazhuang, Hebei 050031, P.R. China
Received July 24, 2020; Accepted November 17, 2020
DOI: 10.3892/ol.2020.12349
Correspondence to: Professor Yaling Liu, Department of Dermatology, The Third Hospital of Hebei Medical University, 139 Ziqiang Road, Shijiazhuang, Hebei 050031, P.R. China
E-mail: [email protected]
Key words: melanoma, CD82 antigen, microRNA-633, bioinformatics, migration
Materials and methods
Prediction of the candidate miRNA associated with KAI1. The online target gene prediction databases TargetScan (http://www.targetscan.org/vert_72), StarBase (http://starbase.sysu.edu.cn) and miRanda (http://www.microrna.org/microrna) were used to identify miRNAs that could be associated with KAI1, and to predict the binding region of miRNA-633 to the 3'‑UTR of KAI1.
Sample collection. All cancer tissues (n=11) and paracancerous tissues (n=10) used in the present study were collected via surgical resection from patients with melanoma at Cangzhou Central Hospital (Table I). No patients received any treatment, including chemotherapy or radiation therapy, prior to surgery. According to the melanoma treatment guidelines, the resection range was determined based on the different stage, and the paracancerous tissues were taken as close to the outer edge as possible to ensure that it was the adjacent normal tissue. Resected samples were subjected to pathological confirmation, after which they were snap-frozen with liquid nitrogen and stored at -80°C. However, tumor cells were present at the outer edge in one of the patients, so 11 cancer tissues and 10 paracancerous tissues were used in the present study. Patients and their families were informed of all study protocols and were asked to sign informed consent forms. The Ethics Committee of Cangzhou Central Hospital approved the present study.
Cell culture and transfection. Normal human primary epidermal melanocytes (HeMn); (The Cell Bank of Type Culture Collection of Chinese Academy of Sciences) were maintained in F-12K medium(Gibco; Thermo Fisher Scientific, Inc.) supplemented with 10% FBS (Gibco; Thermo Fisher Scientific, Inc.). A375, A2058, B16, MEL-RM and M21 melanoma cell lines(The Cell Bank of Type Culture Collection of Chinese Academy of Sciences) were maintained in RPMI-1640 media supplemented with 10% fetal bovine serum (both purchased from Gibco; Thermo Fisher Scientific, Inc.). All cells were grown in humidified 5% CO$_2$ incubators at 37°C. A375 and B16 cells were co-transfected with KAI1 wild-type (WT) or KAI1 mutant (MUT), and/or with miR-633 inhibitors or inhibitor-negative control (NC) and miR-633 mimics or mimic-NC. The transfection of cells was performed with the plasmids (Promega Corporation) using Lipofectamine 3000 (Invitrogen; Thermo Fisher Scientific Co., Ltd.) in accordance with the manufacturer's protocol, with thermocycling conditions as follows: 95°C for 30 sec, followed by 40 cycles of 92°C for 5 sec and 60°C for 30 sec, dissociation at 60°C for 1 min and 95°C for 1 sec.
Reverse transcription-quantitative PCR (RT-qPCR). TRIzol® reagent (Invitrogen; Thermo Fisher Scientific, Inc.) was used to extract total RNA from the cells and tissues, after which reverse transcription was performed with a PrimeScript RT reagent kit (Takara Biotechnology Co., Ltd.). After the cDNA concentrations were quantified, qPCR was conducted with SYBR®
| Characteristic | Number of patients, n |
|---------------|-----------------------|
| Total | 10 |
| Age, years | |
| <45 | 2 |
| ≥45 | 8 |
| Sex | |
| Male | 7 |
| Female | 3 |
| TNM classification | |
| I+II | 7 |
| III+IV | 3 |
| Distant metastasis | |
| No | 9 |
| Yes | 1 |
| TNM, tumor-metastasis-node. | |
Premix Ex Taq (Takara Biotechnology Co., Ltd.) following the manufacturer's instructions. GAPDH and U6 were utilized as normalization controls for mRNA and miRNA levels, respectively. Relative fold changes in expression levels were calculated using the 2$^{{-\Delta\Delta Cq}}$ method (26). Primers used were as follows: KAI1, forward 5'-ATCCGATATCCCGACATGATGAGATGTTGAT-3' and reverse 5'-CTAGGGCGAGTATGACAAAA-3'; GAPDH, forward 5'-ATCCGATTACCAGATACTAGACCTACATG-3' and reverse 5'-ATGGACTATATCCGGACGTTTT-3'; AG-633, forward 5'-CCGATACTAGTAGAGAAAA-3' and reverse 5'-GGACAGAATGTACTTTAAAG-3'; GCTAGA-3'; and U6, forward 5'-TGGCTTCCCTTGTCTAC-3' and reverse, 5'-AACGGTTTCAC-3'. The thermocycling conditions were as follows: 95°C for 30 sec, followed by 40 cycles of 92°C for 5 sec and 60°C for 30 sec, dissociation at 60°C for 1 min and 95°C for 1 sec.
Dual-luciferase reporter assay. Cells were transfected with KAI1WT or KAI1MUT luciferase reporter plasmids (Promega Corporation), along with miR-633 mimics or control constructs for 24 h at 37°C using Lipofectamine®3000 reagent (Invitrogen; Thermo Fisher Scientific, Inc.) in accordance with the manufacturer's protocol. Then, a dual-luciferase reporter assay system (Promega Corporation) was utilized to quantify luciferase activity. Renilla luciferase activity was used as the internal control, and data are presented as the ratio of firefly to Renilla luciferase activities.
Cell Counting Kit-8 (CCK-8) assay. Cells were added to 96-well plates (2x10^3 cells/well). At the indicated time points, 10 μl CCK-8 solution (Dojindo Molecular Technologies, Inc.) was added per well, and absorbance at 450 nm was assessed using a microplate reader (Bio-Rad Laboratories, Inc.).
Wound healing assay. Transfected cells were seeded into 6-well plates at a density of 5x10^5 cells/well and cultured to
Table I. Clinicopathological characteristics of patients with melanoma (n=10).
| Characteristic | Number of patients, n |
|-------------------|-----------------------|
| Total | 10 |
| Age, years | |
| <45 | 2 |
| ≥45 | 8 |
| Sex | |
| Male | 7 |
| Female | 3 |
| TNM classification | |
| I+II | 7 |
| III+IV | 3 |
| Distant metastasis| |
| No | 9 |
| Yes | 1 |
| TNM, tumor-metastasis-node. | |
confluency in RPMI-1640 medium with 15% FBS at 37°C with 5% CO\textsubscript{2}. A linear wound was made using a10 µl sterile pipette tip across the confluent cell layer, and the plates were washed twice to remove detached cells and debris. The cells were cultured in RPMI-1640 medium with 2.5% FBS, 24 h after the wound scraping. Then, the size of the wounds was observed and measured at 0 and 24 h under a light microscope (magnification, x20).
**Invasion assay.** To assess cell invasion, 3x10\textsuperscript{4} cells were resuspended in serum-free RPMI-1640 medium (Gibco; Thermo Fisher Scientific, Inc.) and added to the upper portion of a Transwell chamber (Corning Inc.) that had been coated with Matrigel\textsuperscript{TM}. At total of 600 µl media containing 20% FBS was added to the lower chamber, and plates were subsequently incubated for 24 h. Cells that had invaded through the matrix to the lower chamber were subsequently fixed for 20 min using 4% paraformaldehyde, after which they were stained for 20 min with crystal violet. The cells were then observed using optical light microscopy (Olympus Corporation). The numbers of invaded cells in five random fields of view were subsequently quantified for each sample.
**Western blotting.** RIPA buffer (Beyotime Institute of Biotechnology) was used to lyse cells, after which a BCA kit (Beyotime Institute of Biotechnology) was used to quantify protein levels in the lysates. Protein (40 µg/lane) was subsequently subjected to electrophoretic separation (12% SDS-PAGE), transferred to PVDF membranes (EMD Millipore), and blocked with 5% non-fat milk at room temperature for 2 h. The membranes were then incubated overnight with primary antibodies (cat. no. 10205-2-A; 1:1,000; ProteinTech Group, Inc.) at 4°C. Blots were subsequently incubated at room temperature for 2 h with HRP-conjugated secondary antibodies (cat. no. KC-4G3; 1:20,000; Kang Chen Biotech, Inc.), after which ECL (Pierce; Thermo Fisher Scientific, Inc.) was used to detect the protein bands. Image J software (1.48u version; National Institutes of Health) was used for densitometric analyses.
**Statistical analysis.** All statistical analyses were performed using SPSS 21.0 (IBM Corp.) and GraphPad Prism 7.0 (GraphPad Software, Inc.). Data are expressed as the mean ± SD. Multiple group comparisons were analyzed using one-way analysis of variance and Tukey's post hoc test. Independent-samples t-tests were used to analyze the significance of mRNA levels in tumor tissues and adjacent normal tissues. Associations between the expression of pairs of genes were evaluated using Spearman's rank correlation analyses. Independent-samples t-tests were used to analyze the significance of cell proliferation, wound healing/migration and Transwell invasion assay results. All comparisons were two-tailed. P<0.05 was considered to indicate a statistically significant difference.
**Results**
**Identification of miRNAs that potentially target KAI1 in melanoma via bioinformatics prediction analyses.** The potential upstream miRNAs that may target KAI1 were selected using the TargetScan, miRanda and StarBase online tools (27). In total, 6 putative regulators of KAI1 (miR-633, miR-362, miR-338, miR-622, miR-203 and miR-197) were identified using this approach (Fig. 1A). The expression levels of these miRNAs were subsequently measured in tumors from patients with melanoma and their matched adjacent normal tissue samples (Fig. 1B). Among the six miRNA candidates, miR-633 was found to be upregulated the most in melanoma tissues compared with adjacent normal tissues.
**miR-633 is upregulated in melanoma and is negatively correlated with KAI1 expression.** miR-633 was found to be expressed at higher levels in melanoma cells compared with HeMn control cells (Fig. 2A). Similarly, it was found that miR-633 was upregulated in melanoma tumor tissues compared with adjacent normal tissues, the results were re-plotted in Fig. 2B for ease of reference (Fig. 2B). When the mRNA expression levels for the KAI1 gene were examined in the same samples, the results exhibited an opposite pattern,
miR-633 enhances melanoma cell proliferation and migration. Finally, the biological importance of miR-633 was assessed in melanoma. Using a CCK-8 assay, it was found that transfection with the miR-633 inhibitor significantly suppressed the numbers of melanoma cells over time compared with cells transfected with NC (Fig. 4A and B), suggesting a role for this miRNA in the proliferation of melanoma cells. In addition, miR-633 inhibitor transfection into both the A375 and B16 melanoma cell lines decreased migration rates in wound healing assays (Fig. 4C) and cell invasion in Transwell assays (Fig. 4D). Collectively, these findings demonstrated that miR-633 was able to promote the migration and proliferation of melanoma cells.
Discussion
In the present study, it was demonstrated that miR-633 was significantly upregulated in melanoma tissue compared with adjacent normal tissue from 11 patients with melanoma. In addition, a series of melanoma cell lines exhibited a significantly higher level of miR-633 expression compared with HeMn cells. In previous studies, miR-633 was shown to be a functionally important tumor-associated miRNA in lung and brain cancer (28, 29). Its functional importance in melanoma, however, had yet to be properly elucidated. The present study used the TargetScan, StarBase and miRanda algorithms to predict 6 candidate miRNAs that specifically targeted KAI1. KAI1 was shown to have one potential complementary miR-633-binding site within its 3′-UTR. Experimental results demonstrated that over expression of miR-633 led to a significant reduction in the levels of KAI1 protein, and deregulated expression of miR-633 significantly altered the proliferation, migration and invasion of A375 and B16 melanoma cells. Taken together, the findings of the present study have provided, to the best of the authors' knowledge, the first
evidence that miR-633 may function as a tumor promoter in human melanoma, mediated partly through targeting KAI1 expression.
A total of 3,657 mature human miRNAs have been identified to date (miRBase, 2019, http://www.mirbase.org). In prior studies, miRNAs identified from the integumentary system were successfully used as diagnostic and prognostic biomarkers in patients with melanoma (30,31). For example, miR-213 is a suppressor of malignant melanoma progression, thereby indicating that it may be a potentially viable therapeutic target or diagnostic biomarker in patients with this form of cancer (32). Previous studies indicated that deregulation of miR-21 was associated with pro-apoptotic effects in pancreatic and breast cancer cell lines (33). In melanoma, a previous study revealed that miR-205, miR-200 and members of the let-7 family (-125b, -146a, -155, -21, -25, -23a and -29b) were deregulated (34). Previous studies also suggested that abnormal miR-633 expression...
WA NG and LIU: miR-633 ENHANCES MELANOMA CELL PROLIFERATION AND MIGRATION BY SUPPRESSING KAI1
was associated with the prednisone response early in childhood acute lymphoblastic leukemia relapse (35). However, abnormal miR-633 expression has only been definitively identified in few types of tumors to date. The association between miR-633 and malignant melanoma has not been previously elucidated. The present study demonstrated that the expression levels of miR-633 were upregulated in melanoma tissues and cell lines compared with normal tissues and cells, respectively. Furthermore, the results obtained revealed that deregulation of miR-633 significantly altered the proliferation and migration of A375 and B16 melanoma cells. Therefore, miR-633 may serve as a novel biomarker for melanoma in the future.
KAI1, also known as CD82, is an important transcriptional regulator and tumor suppressor gene, and KAI1 mutations are commonly encountered in a range of tumor types (36). KAI1 regulates chromatin accessibility, in part via the E-cadherin pathway (37), and prior bioinformatics analyses have suggested that KAI1 mutations are associated with lung, bone and brain cancer prognoses, underscoring the relevance of this gene in oncogenic contexts (38). KAI1 may attenuate signaling to shut down metastatic colonization through attenuation of epidermal growth factor receptor signaling and inhibition of the Wnt signaling pathway. You et al (39) suggested that the KAI1 promoter may be regulated by the p53 and NME/NM23 nucleoside diphosphate kinase 1 genes. In pancreatic carcinoma, over expressing KAI1 attenuated the phosphorylation of SRC and STAT3, thereby inhibiting the expression of vascular endothelial growth factor C and limiting the activity of pancreatic carcinoma cells (40). KAI1 has also been shown to serve as a mediator of metabolic reprogramming in tumor cells. For example, KAI1 can suppress the progression of cancers of the digestive system via influencing invasion-associated protein metabolism (41). It also serves as an important tumor suppressor gene in the context of integumental tumors, with KAI1 inactivating mutations being a common feature in human melanoma (42). The ability of KAI1 to suppress oncogenesis is linked to its ability to inhibit the expression of AP-1, JUNB, poly (ADP-ribose) polymerase (PARP) and other oncogenes (43). Khan et al (44) reported that KAI1 is a key regulator of Toll-like receptor 9 (TLR9) trafficking and signaling. KAI1 modulates TLR9-dependent NF-kB nuclear translocation, which is critical for inflammatory cytokine production. A recent study demonstrated that KAI1 was significantly associated with poor survival and could act as
Figure 4. miR-633 regulates melanoma cell proliferation and migration. (A) The viability of B16 and (B) A375 cells was assessed following miR-633 inhibitor or NC transfection. (C) Wound healing activity was assessed for A375 and B16 cells following transfection with miR-633 inhibitor or NC (magnification, x20). (D) Transwell invasion activity was evaluated in A375 and B16 cells following miR-633 inhibitor or NC transfection (magnification, x20). *P<0.05 vs. NC. miR, microRNA; OD, optical density; NC, negative control.
an independent prognostic factor in human melanoma for both 5-year and 10-year survival rates (45). KAI1 deregulation has been observed in melanoma cell lines and tumor samples, and the over expression of this protein may significantly reduce melanoma progression (46). Furthermore, miR-203 inhibited frizzled-2 expression via KAI1 expression in human lung carcinoma cells, and KAI1 expression may be a useful marker for metastatic, invasive cancer, and prognostic factor in tumors, such as lung cancer (47). However, the specific mechanisms governing KAI1 downregulation in the context of melanoma had yet to be clarified.
The present study aimed to investigate the role of miR-633 in melanoma through its potential interaction with KAI1, revealing that miR-633 may be an important regulator of malignant melanoma. The results showed that miR-633 was upregulated in melanoma cells and tumor tissue samples compared with their controls. In addition, miR-633 inhibition resulted in impaired migration and proliferation of A375 and B16 melanoma cells in vitro. Notably, the results of the dual-luciferase reporter assay demonstrated that miR-633 directly regulated the expression of KAI1. Therefore, the data obtained in the present study have provided important insights into the regulation of KAI1 by miRNAs in cancer cells. miR-633 may serve as a potential candidate for the diagnosis and treatment of human melanoma.
In conclusion, the present study has provided novel evidence to show that inhibition of miR-633 suppresses the proliferation and migration of the malignant melanoma cell lines A375 and B16, partly via regulation of KAI1.
Acknowledgements
Not applicable.
Funding
No funding was received.
Availability of data and materials
All data generated or analyzed during the present study are included in this published article.
Authors' contributions
YL and ZW made substantial contributions to the conception and design of the study. Both authors collected the samples and clinical data, and contributed significantly to data analysis. ZW performed the experiments and drafted the initial manuscript. YL gave final approval of the version to be published. Both authors agreed to be accountable for all aspects of the work in ensuring that questions related to the accuracy and integrity of any part of the work were appropriately investigated and resolved. Both authors have read and approved the final manuscript.
Ethics approval and consent to participate
The present study was approved by the Ethics Committee of Cangzhou Central Hospital (Cangzhou, China; approval no. 201903501). Written informed consent was provided by patients and their families prior to the study start.
Patient consent for publication
Not applicable.
Competing interests
The authors declare that they have no competing interests.
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This work is licensed under a Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International (CC BY-NC-ND 4.0) License.
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Delimiting a species’ geographic range using posterior sampling and computational geometry
Jonathan M. Keith 1, Daniel Spring 2 & Tom Kompas 3
Accurate delimitation of the geographic range of a species is important for control of biological invasions, conservation of threatened species, and understanding species range dynamics under environmental change. However, estimating range boundaries is challenging because monitoring methods are imperfect, the area that might contain individuals is often incompletely surveyed, and species may have patchy distributions. In these circumstances, large areas can be surveyed without finding individuals despite occupancy extending beyond surveyed areas, resulting in underestimation of range limits. We developed a delimitation method that can be applied with imperfect survey data and patchy distributions. The approach is to construct polygons indicative of the geographic range of a species. Each polygon is associated with a specific probability such that each interior point of the polygon has at least that posterior probability of being interior to the true boundary according to a Bayesian model. The method uses the posterior distribution of latent quantities derived from an agent-based Bayesian model and calculates the posterior distribution of the range as a derived quantity from Markov chain Monte Carlo samples. An application of this method described here informed the Australian campaign to eradicate red imported fire ants (Solenopsis invicta).
Many of the questions arising in the management of threatened and invasive species require empirical estimation of geographic range limits and shifts in range limits over time. Delimiting surveys are routinely carried out as part of initial response to the discovery of an introduced species 1–3 and to facilitate conservation efforts 4,5, with management efforts focused within the delimited range. The effectiveness of programs to slow the spread of biological invasion depends upon accurate estimation of species range limits to avoid uncontrolled expansion of the invasion edge 6,7. Accurate estimation of geographic range limits is also required for effective management of threatened species to ensure conservation efforts are applied to all locations where the species are present and to avoid costly actions being applied to unoccupied locations. The capacity to accurately estimate geographic range limits is also of central importance in understanding and predicting range shifts under environmental change to mitigate adverse impacts 8.
Two related problems arise: design of efficient surveys and inference of boundaries. These problems are solved iteratively, in part because a species distribution evolves over time and in part because an inferred boundary informs subsequent monitoring efforts 9,10. Here we focus on the inference problem, and present a new method that is applicable to a range of survey designs.
Yalcin and Leroux 7 identify six methods for inferring a species’ range: observational study, grid-based mapping, convex hull, kriging, species distribution models and hybrid methods. They define an observational study somewhat idiosyncratically as a method that estimates a characteristic of a species range, such as the maximum elevation where a species can occur. Grid-based mapping and convex hull are methods for inferring a spatial distribution from a collection of point observations, and kriging is a method for interpolating spatial variables based on point observations and potentially also environmental covariates. Species distribution models estimate ranges based on correlations between species occurrence or abundance and environmental variables. Hybrid methods, as the name suggests, combine features of multiple types, for example pairing species distribution models with mechanistic modelling of spread processes.
1School of Mathematics, Monash University, Clayton, Victoria, 3800, Australia. 2School of Ecosystem and Forest Sciences, The University of Melbourne, Melbourne, 3010, Australia. 3Centre of Excellence for Biosecurity Risk Analysis, The University of Melbourne, Melbourne, 3010, Australia. Correspondence and requests for materials should be addressed to J.M.K. (email: [email protected])
For our present purpose we propose an alternative classification comprising four types of method: utilization methods, which characterize a species’ use of spatial resources based on detected individuals; monitory methods, which use records of survey actions (including those that did not result in detections) to delimit range; correlative methods, which identify correlations between environmental variables and occupancy or abundance of a species, and use these to infer where individuals may be present even if not observed; and mechanistic methods, which explicitly model spatial population dynamics and/or detection processes to identify plausible range distributions. These distinctions are primarily conceptual – advanced methods incorporate features from all of these categories.
Utilization methods. One approach to range modelling involves utilization distributions. These provide a probabilistic representation of the use of spatial resources by an individual or species, across its range. Fleming et al. identify two distinct types: range and occurrence distributions. The range distribution “addresses the long-term area requirements of an animal, assuming its movement behaviors do not significantly change” whereas the occurrence distribution addresses the question of where the animal was located during the observation period. These definitions are framed in terms of an individual animal, but one can rephrase them for species in a straightforward manner. Methods for estimating range distributions include minimum convex polygon, kernel density estimation, mechanistic home range analysis, autocorrelated Gaussian density estimation, and local convex hull. Occurrence distributions can be estimated using the Brownian bridge density estimator. Utilization methods model the internal structure of a spatial distribution. Here we focus on delimitation, that is, determining the limit of a species’ range and quantifying uncertainty in that limit. This is a challenging inference problem, and one that utilization distributions and their associated methods are not ideally suited to address. A common practice is to find a contour of the utilization distribution that encloses 95% of the observations, but this, by definition, underestimates the extent of the range. The amount by which it underestimates is not apparent, and varies from one dataset to another.
Another problem for utilization methods is that available observations may not adequately represent the species’ range, for example due to a lack of sufficient monitoring resources, or imperfect detectability. Consequently, even enclosing 100% of observations may exclude parts of the range where no observations were made. Prior to delimitation, it is typically not clear where monitoring is required. Moreover, there may be spatial variation in detection probability, due to environmental factors or to the use of multiple monitoring methods with different detection probabilities. To overcome this problem, it is necessary to model likely locations of undetected individuals, taking into account spatial variations in detection probability.
It may be possible to repurpose the delimitation method we present below to construct utilization distributions. However, we stress that utilization distributions are intended to characterize the observed use of spatial resources; they are not designed to represent the likely locations of unobserved individuals.
Monitory methods. Monitory methods consider the history of survey actions undertaken during the management of a species, and combine detections, non-detections, and an assessment of detection probability to infer range limits, often by first constructing maps of probability of occupancy or expected abundance. For example, the method of Hauser et al. uses such records to construct a map of occupancy probabilities for an invasive plant species and prioritise subsequent survey actions.
Spatial variation in detection probability remains a problem for monitory methods, although in principle this spatial variation can be incorporated into the inference. An additional problem is that heat maps of probability of occupancy or expected abundance reflect both the geographic distribution of the species and uncertainty about the locations of undetected individuals. Consequently, a temporal sequence of such heat maps can create an illusion of range expansion merely due to increasing uncertainty regarding the locations of undetected individuals, potentially even when the range within which detections occur is contracting. Boundary curves or polygons can be constructed by finding isoliths of such heat maps, but for any chosen threshold value, the resulting isolith likewise reflects both the extent of the species’ range and the precision with which the available data delimit that range.
Correlative methods. Correlative methods, known as Species Distribution Models (SDMs) involve regressing species occurrence or abundance against climatic or other environmental covariates, and then using maps of these covariates to predict the likely spatial distribution of undetected individuals. These methods work well when species are in equilibrium with their environment. However, this is unlikely to be true in many circumstances of management interest, because pest control programs typically are applied when species ranges are expanding, and threatened species programs often are applied when ranges are contracting. Moreover, SDMs typically do not take into account non-environmental biotic factors such as the presence or absence of diseases and predators.
Ecological niche models are also relevant to correlative methods. These characterize the distribution of a species in environmental space (also known as ecological space), in which points correspond to the values of a (potentially large) number of environmental or ecological variables. In contrast, geographic space is comprised of two-dimensional spatial locations. Typically, points in geographic space can be mapped to unique points in environmental space to assess whether they are suitable for a species, but this may be of little use if suitable habitats are unoccupied, as is often the case in invasion and conservation biology.
Mechanistic methods. Another way to account for undetected individuals is to incorporate models of population dynamics into the inference procedure. In an invasive species context, the Bayesian approach developed by Mangel et al., estimates the probability of pest occupancy at different distances from the presumed invasion epicentre assuming the population expands smoothly, producing a bell-shaped spatial distribution. The
An agent-based approach. In previous work, we developed an agent-based model to reconstruct a history of the Brisbane fire ant invasion, or more precisely to sample multiple plausible histories from a posterior distribution using a Markov chain Monte Carlo (MCMC) technique. This approach combined features of all of the above methods. The available data included: extensive records of individual nest detection points, as in utilization methods; records of search actions and estimates of detection probabilities by targeted search and by public reporting in urban and rural environments, as in monitory methods; environmental variables in the form of a habitat suitability map, as in correlative methods; and a detailed model of population dynamics, including a distribution of founding distances, reproductive rate and a complete phylogenetic tree for all detected and putative undetected nests, as in mechanistic methods. While it is not possible to infer the exact number, locations or lifespans of undetected individuals, our method does simulate multiple plausible invasion histories at that level of detail. We typically sample 10000 such histories to explore the space of plausible histories consistent with the data. For the reader’s convenience, we provide a more detailed summary of the data and model parameters in Appendix 1. Full details of the model and the Markov chain Monte Carlo technique we used to sample from it are provided in Keith and Spring, primarily in the Supplementary Information.
Our approach addressed many of the limitations identified above. In particular, it can be applied in circumstances where complex spatio-temporal dynamic processes create substantial gaps in occupied regions and irregular boundary shifts over time, using data obtained with imperfect and incomplete survey methods. However, one of our outputs involved processing the 10000 sampled histories to produce a time series of heat maps showing the expected areal abundance of fire ant nests. As we point out in our discussion of monitory methods above (and in our earlier paper), a time sequence of such heat maps can create an illusion of expansion due to increasing uncertainty regarding the location of undetected nests.
Scope of this paper. Our goal in this paper is to provide a method for inferring and visualizing a species’ range limits given posterior sampled point sets, in such a way that the contribution of uncertainty to the apparent range is appropriately quantified. Each sampled point set includes known locations of detected individuals and putative locations of undetected individuals. In practice, we generate such point sets using our published agent-based method. Next, we construct a polygon enclosing each point set, then identify map coordinates contained in the interior of at least a proportion \( \alpha \) of these polygons. We provide boundaries for multiple values of \( \alpha \) to indicate the degree of uncertainty in the inferred range.
The polygons are selected from a polygon family, thus constraining the polygons to have properties deemed desirable for a specific application, such as convexity or connectedness. In our examples we use \textit{chi-shapes} - simple polygons constructed using an algorithm of Duckham et al. or modified chi-shapes (newly proposed here) to allow for multiple disjoint polygons, as described in the section on Inferring Polygons below. Alternative polygon families could be used, for example to allow polygons with holes. To illustrate the new method we estimated the boundary of an invasive species that is subject to an eradication program. The method can be also readily applied to estimate boundaries of native species that are contracting or shifting due to environmental change, harvesting pressure or demographic variability. The program we consider is aimed at eradicating a fire ant invasion in South East Queensland, Australia. We estimated the boundary of the invasion at the end of April 2015, to inform a decision on whether to continue program funding, based on historical data regarding where fire ants were detected and where efforts were made to remove them. We compared our most conservative estimate to the operational boundaries in use by the eradication program at that time. We found that the outer operational boundary at the end of April 2015 (that is, the outer limits of the region monitored by remote sensing) corresponded over most of its length to our most conservative inferred boundary. On this basis, we concluded that the invasion had been successfully delimited, subject to modest extensions being made to the operational boundary in a few identified locations.
Methods
The method takes as input multiple sets of points (that is, map locations) in a two-dimensional landscape, representing the locations of both detected and undetected individuals. These points may represent habitats, or alternatively the notional centre of range for each individual. Note that undetected individuals do not have known locations, and even the number of undetected individuals is unknown. Plausible locations for undetected individuals must therefore be imputed via some algorithm. We assume that multiple alternative sets of points are available, each containing locations of all detected individuals, but differing in the number and locations of imputed undetected individuals.
In principle, such sets of points do not have to be generated within a Bayesian framework: any algorithm capable of imputing missing data will suffice. However, the probabilistic interpretation that we give to the polygons constructed here assumes that the multiple sets of points have been sampled from a posterior distribution. In the examples presented below we use an MCMC algorithm that we developed to sample from a posterior distribution over plausible histories of a biological invasion.
**Input to the method.** The input consists of the following items:
1. Point sets $P_1, P_2, \ldots, P_N$, where each $P_i$ contains $n_i$ two-dimensional points.
2. A set $Q$ of reference points distributed throughout the region of interest.
3. A value $\alpha$, such that the polygon to be constructed will contain all reference points interior to at least a proportion $\alpha$ of the $N$ polygons constructed for the $N$ point sets (see Step 1 in the next section).
4. A family of polygons $\mathcal{F}$ and a map $\varphi$ such that any set of points $P$ maps to a unique polygon $\varphi(P) \in \mathcal{F}$. In this paper, all polygons are chi-shapes (defined below) or modified chi-shapes.
Each of the point sets $P_i, P_2, \ldots, P_N$ includes a subset of observations common to them all, representing known locations of individuals. The point sets differ in the number and locations of undetected individuals, imputed by some appropriate method. Here we use the posterior sampling method of Keith and Spring.
The set $Q$ of reference points provides a convenient discretization of the geographic region of interest. In principle it can be any collection of points scattered throughout the region, but in this paper we use the centres of cells in a square tiling. In that case, the locations of all reference points can be determined by supplying map coordinates of a reference point (in some specified coordinate system aligned to the tiling) and the side length of the tiling.
The value $\alpha$ controls how confident we can be that the polygon we ultimately report contains the entire range of the species. We stress that neither $\alpha$ nor $1 - \alpha$ should be interpreted as a proportion of the range of the species. Whatever value of $\alpha$ is used, the resulting polygon will contain all known locations of individuals, since these are common to all point sets, and thus contains the entire observed range of the species. But our goal is to construct a polygon that also contains all unobserved members of the species, and $\alpha$ reflects how conservative we want to be in constructing such a polygon.
Various options are available for the family of polygons $\mathcal{F}$. One simple choice is the family of convex polygons, in which case $\varphi(P)$ would be the convex hull of a set of points $P$. However, convex polygons have the disadvantage of resulting in potentially substantial overestimation of the species boundary when actual boundaries are nonconvex. Nonconvex boundaries are likely in many circumstances, including where unsuitable habitat prevents areas being occupied and where long-distance movements cause the boundary to “bulge outwards” in the vicinity of satellite populations.
*Chi-shapes* are a family of simple polygons (‘simple’ in the geometric sense that sides intersect only at corners, and form a closed path). This family includes all convex polygons, but chi-shapes may also be non-convex. A chi-shape $\varphi(P)$ is constructed for a set of points $P$ by starting with the Delaunay triangulation of $P$, then identifying all external edges that satisfy two criteria: (1) the edge is longer than a given length $L$; and (2) if the edge is removed, the external edges of the remaining triangles still form a simple polygon. Only the longest such edge is removed, necessarily creating two new external edges and one new external vertex. This process is iterated until no external edges satisfying these criteria remain (see Fig. 1).
In this paper, all polygons are either chi-shapes or modified chi-shapes in which we relax criterion (2). We proceed as in the preceding paragraph, except that we replace criterion (2) with the requirement: (2’) if the edge is removed, along with any other external edges in the same triangle, the remaining triangles still include all vertices (see Fig. 2). The properties of this algorithm should be analysed in future work; here we merely note that by removing the other external edges in the same triangle, it becomes possible to form disjoint polygons.
Numerous other polygon families are available, for example, the families of polygons produced by LoCoH or by parametric kernel density estimation. We do not claim that chi-shapes or modified chi-shapes are preferable to these alternatives; a comparison is a potential direction for future research.
**Inferring boundaries.** Our proposed method consists of the following steps:
1. Construct a polygon $\varphi = \varphi(P) \in \mathcal{F}$ for each point set $P_i$.
2. For each reference point, count the number of point sets for which the polygons constructed in Step 1 contain that reference point in their interior or on their edge.
3. Identify the set of reference points $Q_\alpha \subset Q$ for which the counts determined in Step 2 exceed a proportion $\alpha$ of the total number of point sets $N$.
4. Construct a polygon $\varphi = \varphi(Q_\alpha) \in \mathcal{F}$ using the reference points identified in Step 3.
If a high resolution is desired, the number of reference points may be large. In that case, Step 4 can be computationally intensive. The computational efficiency of Step 4 can be improved if the reference points are centres of cells in a square tiling, as in all our examples below. In that case, we can first identify boundary reference points. A reference point in a square tiling is said to be on the boundary if any of the four reference points immediately above, below, to the left or to the right of the point is contained in fewer than a proportion $\alpha$ of the polygons constructed in Step 2. Step 4 then consists of constructing a polygon only for these boundary reference points. If the polygons are chi-shapes or modified chi-shapes, and the length $L$ used in their construction is sufficiently...
large relative to the spacing between reference points, the polygon will be the same as if all of the reference points identified at Step 3 had been used.
Using the centres of a square tiling as reference points also facilitates an alternative visualization. The counts obtained at Step 2 (or alternatively the proportions obtained by dividing these counts by $N$) form a data matrix that can be visualized using a heat map. This heat map is of interest in its own right, and we present an example below (Fig. 3). One can also replace Steps 3 and 4 above with an algorithm for tracing an isopleth of the heat map, that is, the level set corresponding to the level $\alpha$. However, in that case the resulting polygon may not belong to the desired polygon family $\mathcal{F}$.
The proposed method can be interpreted as averaging classifiers built from multiple point sets. That is, one can interpret the polygons built at Step 1 as classifying space into infested regions (interior) and non-infested regions (exterior), with the above-mentioned heat map being essentially an average of these classifiers. In this respect,
our method resembles range bagging\(^8\). The resemblance is somewhat superficial however, as range bagging is primarily a computational technique for building classifiers in high-dimensional environmental space by averaging over classifiers in one or two dimensions. Moreover, range-bagging generates multiple point sets via sub-sampling observations rather than by imputing locations to undetected individuals.
For the analysis presented below, we experiment with square tilings having spacings of 50 m and 100 m. We also experiment with setting the minimum length of edges to be removed in the construction of chi-shapes and modified chi-shapes to be \(L = 5\) km, 10 km and 20 km.
**Results**
**Simulation study.** To test the capacity of the method to infer the geographic range of a species, and in particular to quantify the likely locations of undetected individuals, we used a simulated data set that we had previously generated to mimic a biological invasion and eradication program\(^7\). The simulation involved constructing an entire detailed history of a hypothetical invasion, starting with an initial introduction, recording individual founding events, including time of founding and location of all individuals, and also simulating management efforts to identify which individuals were detected and thus available for inference, and which nests were killed by treatment. Further details of the simulated invasion and our reconstruction of it are provided in Keith and Spring\(^7\) and are summarised in Appendix 2 below for the reader’s convenience. Here the relevant points are the following:
1) We sampled 10000 plausible histories of the invasion from a posterior distribution. From each of these we extracted the known (for detected nests) and imputed (for undetected nests) locations of all individuals alive during the second last month of the modeled period. We chose the second last month so that the imputed locations of undetected individuals would be informed by detections made in the final month. This produced 10000 point sets.
2) Because the data is simulated, we also know the true history of the invasion, including the precise location and lifespan of all detected and undetected individuals. From this we extracted the true locations of all individuals alive during the second last month of the modeled period.
Figure 4 shows inferred boundaries for \(1 - \alpha = 0.5, 0.75, 0.975, 0.99\) and 0.999 (innermost to outermost). Note that here and in the rest of the paper we specify values of \(1 - \alpha\), rather than \(\alpha\), purely for the aesthetic reason that the area enclosed increases as \(1 - \alpha\) increases.
Figure 4 also shows the true locations of all individuals that were alive in the second last month of the period modeled, and the locations of detections that occurred during that month. Note that all of the detections are inside the 0.5 boundary. Indeed, they must be contained in the boundary inferred for any value of \(\alpha\), since they are contained in all 10000 point sets.
**Case study: fire ants in brisbane.** The method presented here was developed for the National Fire Ant Eradication Program (NFAEP) to eradicate the Red Imported Fire Ant (RIFA) from the vicinity of Brisbane, Australia. As the history of this eradication program underscores the importance of accurately delimiting an invasion, we provide the following summary.
During the early years of the NFAEP, control efforts were focused primarily on known infestations and nearby areas, with relatively little surveillance around those areas. This strategy can be slow in achieving delimitation when infestations exist well beyond the boundary of the managed area. Infestations that were accurately delimited in the early years of the program, such as the Fisherman’s Island infestation, were successfully eradicated\(^31\), while infestations that were not accurately delimited have continued to spread. In June 2007, RIFA colonies were detected at Amberley in Brisbane’s southwest, outside the operational area at that time. It was subsequently
determined that an invasion had been spreading undetected from a point in or near Amberley for an extended period. This realization was a major setback for the eradication program, which had been operating with apparent success since 2001. In previous modeling, we estimated that eradication was close to being achieved by 2004, but that the population subsequently recovered, in large part due to delimitation failure. Our results indicated that Amberley was not the only delimitation failure – there were undetected areas of spread in the eastern part of the invasion at around the same time, and these contributed to the recovery after 2004.
Due to continuing spread of the Australian fire ant invasion, the eradication program’s funding and methods were reviewed. It was decided that continued funding of the program beyond June 2013 would depend partly on the invasion being successfully delimited by 30 June 2015. To increase confidence that delimitation had been achieved, the NFAEP surveyed a large area near the invasion’s estimated boundary in 2013 and 2014. To undertake this task, low cost monitoring methods involving remote sensing and citizen monitoring were applied. These methods have substantially lower detection probabilities than conventional surveillance methods, including ground surveillance with trained personnel, but enable large areas to be rapidly surveyed at affordable cost. This reliance on a surveillance method with detection probability substantially less than 1 highlights the importance of accounting for this source of observational error in estimating the invasion’s boundary.
At the time this analysis was performed, we had data on detections and interventions to the end of May 2015. We decided to assess whether the invasion had successfully been delimited by the end of April 2015, so that the inference would be informed by one month of subsequent detections. We first inferred a complete history of the invasion using a Bayesian agent-based model previously developed for reconstructing the Brisbane RIFA invasion and summarized in Appendix 1.
The remote sensing efficacy (i.e., probability of a nest being detected by aerial survey) and the founding rate (i.e., average number of nests founded per nest per month) were held fixed rather than inferred, but we investigated the impact of alternative fixed values on inferred boundaries. We therefore performed five separate MCMC runs with:
1. Remote sensing efficacy 0.2, founding rate 0.25 nests founded per nest per month.
2. Remote sensing efficacy 0.3, founding rate 0.25 nests founded per nest per month.
3. Remote sensing efficacy 0.4, founding rate 0.25 nests founded per nest per month.
4. Remote sensing efficacy 0.3, founding rate 0.15 nests founded per nest per month.
5. Remote sensing efficacy 0.3, founding rate 0.35 nests founded per nest per month.
The values of remote sensing efficacy and founding rate selected for these runs reflect ranges of plausible values for these parameters, according to advice received from Biosecurity Queensland.
Each run was continued until at least 40000 MCMC reconstructed histories were produced, with the first 20000 discarded as burn-in. Convergence was assessed visually using time-series plots of log-likelihood. For each of the reconstructed histories, we extracted the map coordinates of nests living at the end of April 2015. Thus each of our inferred boundaries was based on at least 20000 point sets.
Figure 5 (left) illustrates the 0.5 (inner group) and 0.999 (outer group) boundaries for the three runs with assumed remote sensing efficacy 0.3, and founding rates 0.15, 0.25 and 0.35 nests per nest per month. As expected, the inferred geographic extent increases with the founding rate. However, the difference is negligible for the 0.5 boundaries, and not large even for the 0.999 boundaries. We will therefore ignore the influence of founding rate
and use the middle founding rate of 0.25 nests per nest per month (that is, 3 nests per nest per year) in the analyses that follow.
Figure 5 (right) shows the 0.5 (inner group) and 0.999 (outer group) boundaries for the three runs with assumed founding rate of 0.25 nests per nest per month, and remote sensing efficacies of 0.2, 0.3 and 0.4. As expected, the inferred geographic extent increases as the assumed remote sensing efficacy decreases, but again the difference is negligible, and we will use the middle remote sensing efficacy of 0.3 in the remaining analysis. It should be noted that finding that the value we assume for remote sensing efficacy has little effect on the inference is completely different to saying the success of the program does not depend on the actual value. This is because the inference is informed by multiple data types, so that the past can be accurately reconstructed even without a precise estimate of remote sensing efficacy. Nevertheless, the eventual success of the program may depend crucially on rapid detection of relatively rare long-distance dispersal events by remote sensing.
Figure 6 presents our main result – inferred 0.5, 0.75, 0.975, 0.99 and 0.999 boundaries at the end of April 2015 assuming a founding rate of 0.25 nests per nest per month and remote sensing efficacy of 0.3. This figure also shows the operational boundaries in place at that time. These included a region designated the remote sensing scope, and low- and high-risk restricted areas. The remote sensing scope is a region that is monitored by airborne cameras. However, only a small part of this area is searched in any one month. The restricted areas have various management strategies in place to limit human-assisted movement of RIFA and to eradicate existing infestations.
Delimitation in time-series. One reason for proposing the delimitation method presented here was dissatisfaction with using our earlier abundance heat map to delimit boundaries, given its tendency to exaggerate apparent spatial extent due to uncertainty regarding the location of undetected individuals. This effect is most apparent when visualizing changes in boundaries over time, since uncertainty about the location of undetected nests tends to increase towards the end of the data collection period. Figure 7 shows the 0.5 (inner) and 0.999 (outer) inferred boundaries in December 2000–2014, using chi-shapes with \( L = 10 \) km and a square tiling with cells of 100 m by 100 m. Also shown are all detections that occurred January–December of each year (some of which are outside the December boundaries, due to clearing the pest from those areas earlier in the year).
We propose that the series of 0.5 polygons gives the best visual representation of temporal change in boundary location, since these polygons are somewhat analogous to medians, and thus less affected by increasing uncertainty. On the other hand, if one wants to identify a region that contains the entire infestation with high probability, we recommend the 0.999 polygon. The gap between these two polygons gives an indication of the degree of uncertainty in boundary location, and spatial variation in that uncertainty. Note this gap is wider in the December 2014 plot than at earlier times, but otherwise fairly constant.
The December 2000 subplot illustrates one of the advantages of our approach: it shows the inferred extent of the infestation prior to the first detections in 2001. This is possible because our sampling algorithm imputes plausible histories, including time of founding, for all nests. Similarly, the infestation centred on Amberley is visible in the west in December 2004 and 2005, even though no detections occurred there in those years.
To investigate the effect of changing the spacing between reference points, we also produced results using 50 m by 50 m cells. The results (not shown) were visually indistinguishable from Fig. 7. We concluded that our method is not much affected by cell size, at least when the side length of cells is small compared to the parameter \( L \).
Modified chi-shapes. Figure 8 shows similar results using modified chi-shapes, with all other settings the same. The advantage is that inferred boundaries can separate into disjoint polygons. This occurred for some of the
0.5 polygons, but none of the 0.999 polygons. In particular, one can see that there were two disjoint infestations in 2000, consistent with two separate introductions. The Amberley infestation can also be seen spreading separately from the main infestation between 2003 and 2006.
To investigate the effect of varying the parameter $L$ used in the construction of chi-shapes and modified chi-shapes, we repeated the analysis with $L = 5$ km and $L = 20$ km (Figs 9 and 10). The shape of the 0.5 polygons is substantially affected by the choice of $L$: with $L = 5$ km these polygons fragment into multiple disjoint components, whereas with $L = 20$ km only a single connected polygon is produced. The 0.999 polygons are much less affected by this parameter: all 0.999 polygons remained connected for all three values of $L$, although they do become increasingly “rough” as $L$ decreases.
Changing the parameter $L$ has a less dramatic effect on the 0.5 polygons when chi-shapes are used instead of our modified chi-shapes, because chi-shapes are constrained to be simple polygons.
For management actions that rely on containing the infestation with high probability, such as setting the limits of aerial searches, the 0.999 polygons will be of more interest than the 0.5 polygons. In that case, the appropriate choice of $L$ is a less pressing concern. However, efficient allocation of resources within the boundary may be better guided using an abundance or occupancy heat map, given the sensitivity of the 0.5 polygons to the choice of $L$.
Figure 6. (Top) Inferred 50%, 75%, 97.5%, 99% and 99.9% boundaries at the end of April 2015. Remote sensing detection probability was set to 0.3 and founding rate was set to 0.25 nests per nest per month. (Bottom) Low-risk restricted areas (in yellow), high-risk restricted areas (pink) and remote sensing scope (purple). Also shown in both maps are crosses marking previous detection points as at 8 July 2015, colour coded by time of detection, with the most recent detections in red and the oldest in pale brown. (Figure created with the assistance of Bob Bell of Biosecurity Queensland using ArcMap 10: www.esri.com)
Comparison to utilization methods. The method for estimating range limits described in this paper is unique in basing the inference on multiple sets of imputed coordinates representing locations of undetected individuals. It thus addresses a fundamentally different problem than utilization approaches. Both approaches identify spatial distributions, but those produced by utilization approaches represent a species' observed use of
spatial resources, whereas those produced by the new method represent posterior uncertainty in the location of range limits, accounting for undetected individuals. Nevertheless, it is interesting to compare our results to utilization approaches.
We constructed polygons using detections made in each of the years 2001–2014, using two approaches: convex hull (Fig. 11) and the r-LoCoH method\(^3\) with \(r = 10\) km (Fig. 12). The parameter \(r\) is the maximum distance of neighbors used to construct a local convex hull around each detection.
Note that we used only detections, not imputed locations of undetected nests, in this analysis, to highlight the advantage of using posterior sampling to impute locations of undetected nests. As noted above, it would also be possible to use LoCoH polygons in place of chi-shapes at Steps 1 and 4 of our algorithm, but we have not explored this possibility.
Figure 11. The 15 sub-plots represent the geographic extent of the Brisbane fire ant invasion in 2000–2014. Note each sub-plot represents an entire year, not the month of December as in Figs 7–10. Polygons are convex hulls for all nests detected in the corresponding year. Detected nests are shown as small points.
Figure 12. The 15 sub-plots represent the same observations as Fig. 11, but with polygons constructed using the r-LoCoH method instead of convex hull.
The first subplots of Figs 11 and 12 are blank because there were no detections in 2000, which in itself highlights an advantage of posterior sampling of unknown locations and founding times: inferences can be made about species distribution at times prior to the first detection. In the subplots for later years, polygons constructed using only detections do not identify several large infested regions inferred using our method. For example, compare the western infestations shown in the 2004 and 2005 sub-plots of Fig. 7 to the corresponding sub-plots in Figs 11 and 12. These regions are not apparent using either convex hull or r-LoCoH, mainly because large infested areas went undetected in those years. Our inference for those years is informed by detections made prior to 2004 and subsequent to 2005, and by models of unobserved spread. The convex hull approach also demonstrates the opposite problem – the convexity of the polygons forces inclusion of large regions that are clearly not infested. For example, compare subplots for the years 2006−2009: a large concave region is apparent in the south in Fig. 7, but not in Fig. 11. Also note that the polygons shown in Figs 11 and 12 enclose all detections from the corresponding year; had we used only the detections made in December of each year, these polygons would have been much smaller and would have failed to enclose large infested regions. Thus the temporal resolution possible with our method is much higher.
Another advantage of our method is that by constructing polygons for multiple values of \( \alpha \), one can visualize the uncertainty regarding boundary location, and spatial variation in that uncertainty. While it would also be possible to construct multiple polygons enclosing different proportions of the detections, these would reflect relative utilization of regions internal to the boundary, not uncertainty regarding the boundary location.
**Discussion**
The method presented here constructs simple connected polygons representing the boundary of a species’ geographic range. The simulation results shown in Fig. 4 demonstrate that boundaries constructed using the proposed method do not reflect the location of actual nests, including undetected nests. Note that the detections made in the month for which these boundaries were constructed do not provide a good indication of the actual range of the species: if only these detections were used to infer the boundary the range would be severely underestimated. Also note that by constructing boundaries for different values of \( \alpha \), a realistic indication of the uncertainty in the location of the boundary can be obtained. Most living individuals are contained within the 0.5 boundary, and all but one of the undetected individuals are contained within the 0.975 boundary, with the remaining individual between the 0.99 and 0.999 boundaries.
The meaning of the value \( 1 - \alpha \) requires some clarification. Strictly speaking, for each reference point contained within the \( 1 - \alpha \) boundary, \( \alpha \) is the proportion of point sets for which the corresponding polygon contains that reference point. If the point sets are sampled from a posterior distribution, and the shape of the species’ range is well approximated by a member of the polygon family, the \( 1 - \alpha \) boundary can be interpreted as containing all points with a posterior probability at least \( \alpha \) of being within the geographic range of the species.
Importantly, the polygons constructed by this method are not required to be convex, giving the method greater generality and flexibility than previously applied convex polygon methods\(^{44}\). Figure 6 illustrates that boundaries of real species distributions can be concave, and would not be well approximated if the polygon were constrained to be convex. This is most noticeable along the northern boundary, where use of a convex polygon would unnecessarily include a large geographical area within the inferred range. This demonstrates the risk of overestimating the boundary when convex polygon methods are used. Species often have nonconvex distributions resulting from spatial variation in habitat suitability and long-distance dispersal events that create outlier populations in remote locations.
For the fire ant data, we found that the extent of the invasion was likely to be within operational boundaries at the end of April 2015, with the outer edge of the area remotely sensed corresponding over most of its length to the outer edge of the 0.999 inferred boundary. On this basis, we concluded that the invasion had been accurately delimited by the end of April 2015, subject to small extensions to operational boundaries in the southeast, far west and north of the Brisbane River, near the coast. Founding events rarely occur across large bodies of water. This behaviour is not incorporated into our model, so our methods may overestimate expansion north of the river. While this does not guarantee that eradication will ultimately be achieved, or that delimitation failure will not recur at some time in the future, establishing that the invasion has been delimited is an essential prerequisite to the ultimate success of the program.
The approach developed here is well suited to practical applications for assisting managers of biological invasions and threatened species. Invasion management effectiveness can benefit from the capacity to regularly update estimates of the invasion boundary whenever new information is obtained during the course of an eradication or containment program. Such information is vital to determine whether management efforts are succeeding in contracting the invasion or slowing its spread. Regular updating of range limits also is required to assess whether threatened species populations that are subject to management are expanding or not contracting.
Our method of constructing polygons is not limited to posterior samples obtained using MCMC. For example, it could alternatively be used with posterior samples obtained using Approximate Bayesian Computation (ABC – see the seminal paper of Beaumont *et al.*,\(^{35}\) for a description). Our method requires multiple alternative point sets representing plausible locations of individual entities, but these need not even be generated via posterior sampling if alternative means of imputing missing locations are devised.
Although in this paper we have focused on the computational geometry aspects of the method, the usefulness of the resulting polygons depends crucially on the posterior sampled point sets, which we generated using our earlier agent-based Bayesian approach\(^7\). The agent based approach draws together components of utilization, monitory, correlative and mechanistic approaches, and takes into account the species’ life cycle, environmental variables and human interventions. It is a highly flexible approach that can potentially be modified for a wide variety of species, and could also incorporate genetic information, thus refining estimates of population dynamic processes and increasing the accuracy of estimated range limits.
The wide range of potential application of our approach will allow it to make substantial contributions to the problems posed by biological invasions and conservation of threatened species.
An R package *pts2polys* implementing the method described herein is available from CRAN. Currently this package uses chi-shapes, but not the modified chi-shapes we introduced above. C code implementing the method for modified chi-shapes is available from https://github.com/jonathanmkeith/posterior_polygons/releases/tag/v1.0.
**Data Availability**
Data and code used in this paper are available on request to the corresponding author.
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**Acknowledgements**
The authors are grateful to Dr. Ross Wylie from Biosecurity Queensland for data and advice, and to Bob Bell (also from Biosecurity Queensland) for generous assistance with spatial data support. The authors are grateful to the Australian Research Council Centre of Excellence for Mathematical and Statistical Frontiers for their support of this project (CE140100049).
Author Contributions
J.M.K. developed the methods and software and wrote the manuscript. D.S. proposed the project, provided data and co-wrote the manuscript. T.K. reviewed the manuscript.
Additional Information
Supplementary information accompanies this paper at https://doi.org/10.1038/s41598-019-45318-5.
Competing Interests: The authors declare no competing interests.
Publisher's note: Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.
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© The Author(s) 2019
Author/s: Keith, JM; Spring, D; Kompas, T
Title: Delimiting a species' geographic range using posterior sampling and computational geometry
Date: 2019-06-20
Citation: Keith, JM; Spring, D; Kompas, T, Delimiting a species' geographic range using posterior sampling and computational geometry, SCIENTIFIC REPORTS, 2019, 9
Persistent Link: http://hdl.handle.net/11343/225650
File Description: Published version
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Study on magnetic force of electromagnetic levitation circular knitting machine
X G Wu¹,², C Zhang¹, X S Xu¹, J G Zhang¹, N Yan¹ and G Z Zhang¹
¹School of mechanical engineering and automation, Wuhan Textile University, Wuhan, Hubei 430073, China
E-mail: [email protected]
Abstract. The structure of the driving coil and the electromagnetic force of the test prototype of electromagnetic-levitation (EL) circular knitting machine are studied. In this paper, the driving coil’s structure and working principle of the EL circular knitting machine are firstly introduced, then the mathematical modelling analysis of the driving electromagnetic force is carried out, and through the Ansoft Maxwell finite element simulation software the coil’s magnetic induction intensity and the needle’s electromagnetic force is simulated, finally an experimental platform is built to measure the coil’s magnetic induction intensity and the needle’s electromagnetic force. The results show that the theoretical analysis, the simulation analysis and the results of the test are very close, which proves the correctness of the proposed model.
1. Introduction
With the successful application of EL technology in train, more and more areas are exploring how to introduce the high-tech, maglev knitting technology is one of them [1], the so-called maglev knitting technology using electromagnetic force to drive the needle up and down movement to replace the traditional mechanical connecting rod drive. The driving mechanism of the EL circular knitting machine adopts hybrid drive (EPMH) mode of electromagnetic and permanent-magnet (PM), the electromagnetic field excited by the driving coil, PM and needles are fixed together. In the working process, the control card gives the driving coil electricity in a certain phase sequence, thus the drive coil produces a certain sequence of magnetic field, so the PM and the needle can do regular movement to knit in the magnetic field. By using the electromagnetic drive technology, the EL circular knitting machine can eliminate the middle part of the complex mechanical transmission and realize zero transmission of the needle selecting process compared with the traditional circular knitting machine’s drive mechanism of the mechanical triangle cam (A triangular shaped cam that drives the needle motion in a certain phase sequence), the direct drive mode will not produce rigid impact and shortcomings the friction and wear, energy loss and noise, which greatly improves the knitting efficiency of circular machine.
2. Knitting part and working principle
As shown in figure 1, the knitting part of the EL circular knitting machine includes needle, drive coil, sinker, cam, gear, a base and a support member, which are arranged on the corresponding position of the base. In the process of work, the coils drive the needle up and down when the coils are energized, at the same time, the gear drives cam rotation, the rotation of the cam push sinker to do reciprocating
motion of front and back (the sinker is installed in the groove of the fixed disc and forms a cam with the cam, so when the cam rotates, the sinker is driven to reciprocate), the combination of the two movements completes the knitting process.
**Figure 1.** Knitting part of Magnetic levitation knitting circular
**Figure 2.** Working principle of Magnetic levitation knitting
Magnetic drive knitting device core component comprises drive coil, PM, coil frame, needle, sensor and controller, the principle of its specific structure is shown in figure 2. From figure 2 we know that as long as the fixed drive electromagnetic coil is electrified, a certain direction of magnetic field will be produced in the vertical direction of the centre, the magnetic field will produce an interaction with the PM magnetic field, thus PM and the needle will be driven up and down. This is an open loop system, which can’t control the time and size of the electricity, so adding a sensor and controller to form a closed loop system, the displacement sensor to detect changes in needle, needle position feedback to the controller, the controller will change the size and direction of the coil current, the size and direction of the coil current will directly reflect the change of the magnetic force and the direction of the magnetic force, the change of the magnetic force of the PM will change the direction of up and down movement of the needle and speed, therefore, precise weaving action will be completed through the needle reciprocating motion.
3. Theoretical model of electromagnetic force
3.1. PM magnetic field
As shown in figure 2, the force of the conducting wire is equal to the one of the PM in the opposite direction when the PM moves during the knitting process in EPMH mode (Newton’s 3rd law) and the force will be equal to the force of the PM in the opposite direction, therefore, in the process of calculating the magnetic force, the force of the conducting wire in the magnetic field can be obtained by the theory of ampere force, so that the form and size of the force during the movement of the PM can be obtained. According to the Ampere molecular circulation hypothesis: the smallest unit that makes up a magnet is a ring current, and if these molecules are oriented in a circular arrangement, they will show N and S poles macroscopically [2].
Expanding a single energized ring into space can create a PM field mathematical model. Let a cylindrical PM radius a, high h, magnet bottom surface centre of the circle as the origin of coordinates, the bottom surface of the xoy plane, z-axis positive direction for the magnetization, the establishment of geometric model shown in figure 3.
If the magnet material and magnetization direction unchanged, and saturation magnetization, the magnetization density $J_s$ can be regarded as a constant. Calculate the magnetic field strength of any point $P(r \cos(\theta), r \sin(\theta), z - z_0)$ in the space, where $r$ and $\theta$ are the polar coordinates of the point $Q$ of $P$ on the $xoy$ plane. Select the arbitrary thickness of the PM $dz_0$ thin layer circulation, the $z$-axis axial height of $z_0$. While $a$ and $\alpha$ are the polar coordinates of the current element $dl$ in the plane of $dz_0$, and $R$ is the radius vector of the current element $dl$ to the point $P$.
According to the superposition characteristics of the magnetic field, the total magnetic field strength at any point $P$ in the space of the PM can be given by the following equation (1).
$$B = \int_0^h dB = \frac{\mu_0 J_s a}{4\pi} \int_0^h \oint \frac{dl \times R}{R^3}$$
$$= \frac{\mu_0 J_s a}{4\pi} \int_0^h \int_0^{2\pi} \begin{vmatrix} i & j & k \\ -\sin(\alpha) & \cos(\alpha) & 0 \\ r\cos(\theta) - \cos(\alpha) & r\sin(\theta) - \sin(\alpha) & z - z_0 \end{vmatrix} dz_0$$
$$R = AP - a = (r\cos(\theta) - \cos(\alpha), r\sin(\theta) - \sin(\alpha), z - z_0)$$
In the equation (1), $\mu_0$ the vacuum permeability.
3.2. Electromagnetic force model
A single coil energized wire in the magnetic field force model as shown in figure 4 above. From the Ampere formula, the electric current $Idl$ receives the electromagnetic force is the following equation (2).
$$dF = Idl \times B$$
Assuming the current direction of the coil is as shown in the figure, the direction of any point in the coil can be judged by the left-hand rule. The decomposition force $F$ is along the $z$-axis direction $F_z$ and along the coil radial direction $F_r$. As the strength of the magnetic field at the concentric ring is equal in magnitude and different in direction, so the $F_z$ is equal in size and direction, the $F_r$ points the same point to the centre of the circle and its size is equal. Further analysis shows that $F_z$ is provided by $B_z$ and $B_{\theta}$, and $F_r$ is provided by $B_r$. Axial force only needs to be known during needle movement. Therefore, it is only necessary to study the effect of $B_z$ and $B_{\theta}$ on the conducting wire.
The electromagnetic force of the single coil current element obtained by substituting the equation (1) into the equation (2), which is represented by the following equation (3).
\[
\begin{align*}
\mathbf{dF} &= \frac{\mu_0 I_s d \mathbf{l}}{4\pi} \int_0^h \int_0^{2\pi} \begin{vmatrix}
i & j & k \\
-r\sin(\theta) & r\cos(\theta) & 0 \\
\cos(\alpha) & \sin(\alpha) & \sin(\alpha) + \cos(\alpha) & \cos(\alpha) \\
\end{vmatrix} \rho(z) d\alpha dz d\theta
\end{align*}
\]
\[dl = (-r\sin(\theta), r\cos(\theta), 0) d\theta\] in the equation (3), substitute it into equation (3) and integrate \(d\theta\) to obtain the electromagnetic force on the whole single coil, which is represented by the following equation (4).
\[
\mathbf{F} = \frac{\mu_0 I_s d \mathbf{l}}{4\pi} \int_0^h \int_0^{2\pi} \frac{D}{r^3} d\alpha dz_0 d\theta
\]
Which \(D\) is as follows equation (5).
\[
D = \begin{vmatrix}
i & j & k \\
-r\sin(\theta) & r\cos(\theta) & 0 \\
\cos(\alpha)(z - z_0) & \sin(\alpha)(z - z_0) & a^2 - ar(\sin(\theta)\sin(\alpha) + \cos(\theta)\cos(\alpha)) \\
\end{vmatrix}
\]
As mentioned earlier, there is only need to calculate the axial force for the PM, so the \(z\) axial force \(F_{sz}\) is shown in the following equation (6).
\[
F_{sz} = -\frac{\mu_0 I_s a l}{4\pi} \int_0^h \int_0^{2\pi} \frac{2\pi a r(\cos(\theta)\cos(\alpha) + \sin(\theta)\sin(\alpha))}{r^3} d\alpha dz_0 d\theta
\]
This is a single-coil force model in the magnetic field, for any multi-turn coil, the force can be calculated by the force can be superimposed features. Assume that the inner diameter of the coil is \(r\), the outer diameter is \(f(z)\) and \(f(z)\) is the function of the outer diameter with respect to the \(z\) axis, the coordinates of the coil in the axial direction are \(z_1\) and \(z_2\). Also consider the existence of gaps between the coils, the axial density \(\rho_z\) and radial density \(\rho_r\) is introduced. In turn, the axial force and the radial force of the single coil are integrated. Finally, the total force of the coil in the \(z\) axis of any shape can be expressed as the following equation (7).
\[
F_z = \rho_z \rho_r \int_{z_1}^{f(z)} \int_{z_1}^{z_2} F_{sz} dz dr
\]
If any certain force \(F_z\) is given, the shape of the corresponding coil can be calculated.
4. Simulation and measurement of magnetic field and electromagnetic force
4.1. Simulation of magnetic field and electromagnetic force
According to the previous experimental study [3], knitting, the needle can smoothly hook yarn to provide conditions for the electromagnetic force is about 85mN in the process of weaving needle, the presupposition condition into equation (7) obtained a curved coil as shown in figure 5. In order to increase the needle stroke, the coil bipolar symmetrical layout, the opposite direction, through 12 V DC. Through the Ansoft Maxwell magnetic field finite element simulation software, the magnetic induction intensity simulation cloud chart under the actual working condition is shown in figure 6.
At the same time, the electromagnetic force of the PM and the needle during the movement is simulated, the simulation model is shown in figure 7, where Region is the boundary solution area and Band is the movement area. The electromagnetic force simulation curve of the PM during the movement is as shown in figure 8.
4.2. Measurement of magnetic field and electromagnetic force
Under the same power-on condition, the magnetic field induction strength of the drive coil and the magnetic force of the needle in the working stroke were measured with a Gauss meter and a dynamometer, respectively. The measurement interval is 1 mm, and the magnetic field strength curve and the magnetic force curve in the working stroke are shown in figures 9 and 10 respectively.
Figure 5. Coil structure model
Figure 6. Simulation of magnetic field strength of coil
Figure 7. Magnetic force simulation model
Figure 8. Simulation magnetic force diagram
Figure 9. Magnetic induction intensity of measurement
Figure 10. Magnetic force of measurement
Comparing figures 9 and 6, the simulation results of the magnetic induction intensity of the bipolar symmetric driving coil are in good agreement with the measured results, the magnetic fields of the two coils arranged symmetrically in the up and down direction are opposite and mainly concentrate in the middle of the coil with an average of 14 mT. Comparing figure 10 with figure 8, we can see that the electromagnetic force simulation result and the measurement result are similar, and the electromagnetic force is stable within the working stroke (position from 10 mm to 25 mm), about 95 mN, which meets the driving requirement.
5. Summary
This paper introduces a direct-drive circular knitting machine based on electromagnetic drive. Based on the basic law of electromagnetic field, a theoretical model of electromagnetic force is established and a kind of curved coil is determined. Ansoft Maxwell software was used to simulate the magnetic field and magnetic force of the established coil, the magnetic field and magnetic force were also measured. The results show that the simulation results of the magnetic field and magnetic force of the coil are in good agreement with the measured results, which can meet the demand of stable and accurate drive motion for knitting.
Acknowledgments
This research is a Textile Industry Federation guidance project and was financially supported by the National Science Foundation of China (51175384) and the Key Laboratory of Digital Textile Equipment Foundation of Hubei Province (DTL2017003 and DTL2017002).
References
[1] Wan D Y, Wu X G and Zhang C 2017 Study on needle electromagnetic force and coil profile optimization of magnetic suspension drive J. Knitting industry 8 9-12
[2] Zhao K H and Chen X M 2003 Electromagnetics (Beijing: Higher Education Press) pp 85-137
[3] Wu X G, Zhang C and Yuan B 2017 Research on magnetic force coupling and magnetic force coupling of magnetic suspension driven needles J. Knitting industry 1 13-7
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Endohedral Fullerene Fe@C_{28} Adsorbed on Au(111) Surface as a High-Efficiency Spin Filter: A Theoretical Study
Ke Xu 1,†, Tie Yang 2,†, Yu Feng 3, Xin Ruan 3, Zhenyan Liu 3, Guijie Liang 1,* and Xiaotian Wang 2,*
1 Hubei Key Laboratory of Low Dimensional Optoelectronic Materials and Devices, Hubei University of Arts and Science, Xiangyang 441053, China
2 School of Physical Science and Technology, Southwest University, Chongqing 400715, China
3 School of Physics and Electronic Engineering, Jiangsu Normal University, Xuzhou 221116, China
* Correspondence: [email protected] (G.L.); [email protected] (X.W.);
† These authors contributed equally to this work.
Received: 24 June 2019; Accepted: 23 July 2019; Published: 25 July 2019
Abstract: We present a theoretical study on the adsorption and spin transport properties of magnetic Fe@C_{28} using Ab initio calculations based on spin density functional theory and non-equilibrium Green’s function techniques. Fe@C_{28} tends to adsorb on the bridge sites in the manner of C–C bonds, and the spin-resolved transmission spectra of Fe@C_{28} molecular junctions exhibit robust transport spin polarization (TSP). Under small bias voltage, the transport properties of Fe@C_{28} are mainly determined by the spin-down channel and exhibit a large spin polarization. When compressing the right electrode, the TSP is decreased, but high spin filter efficiency (SFE) is still maintained. These theoretical results indicate that Fe@C_{28} with a large magnetic moment has potential applications in molecular spintronics.
Keywords: molecular spintronics; C_{28} endohedral fullerene; spin transport properties; spin filter
1. Introduction
Molecular spintronics has attracted tremendous attentions due to its promising applications in nanoelectronics in the past few years [1–6]. The conductance can be directly controlled by the spin degrees of freedom in a single molecule. Compared with traditional semiconductor spintronic devices, the spin–orbital coupling and hyperfine interactions in the molecule are weak [7]; therefore, the molecular building blocks in spintronics are a very promising candidate for the new generation of molecular devices that can improve performance and enhance functionality, especially in magnetic storage and quantum information processing [8,9].
One of the central issues in molecular spintronics is how to manipulate the spin freedom in a molecular junction. A common approach is having the magnetic molecule sandwiched between the source and drain metallic electrodes [10]. Among all possible candidates, magnetic (endohedral) fullerenes form an attractive family of clusters due to their peculiar structures and remarkable properties. Recently, various fullerenes that include C_{60} [11–15], C_{70} [11–13,16], and B_{40} [17,18] have been extensively studied and can be suggested as magnetoresistance devices [11,13–15] or spin filters [16,17]. In the fullerene family, it is worth noting that the small fullerene C_{28} has inherent magnetic moment [19].
Up to now, C_{28} has been extensively studied both in terms of experimental and theoretical aspects [20–28]. C_{28} adopts a Td point group, with four unpaired C atoms located at the apex of
a tetrahedron, which leads to large magnetic moment (4.0 $\mu_B$). However, the delocalized magnetic moment is unstable and easy to quench in C$_{28}$ [19], which limits its application in molecular spintronics. Fortunately, encapsulated 3d or lanthanide transition metal (TM) atoms can stabilize the structure, and the magnetic moment can also be localized in the TM atoms [20,22–24]. Previous studies mainly focused on stability [20,21,23,24], magnetic properties [20,26,28], and vibrational properties [25]. Nevertheless, the spin transport properties of the magnetic TM@C$_{28}$ have not been reported so far and thus require examination. Considering the stability and magnitude of the magnetic moment of 3d TM@C$_{28}$ [20], Fe@C$_{28}$ is very promising for molecular spintronics. Thus, two key questions should be addressed: can Fe@C$_{28}$ be adsorbed on an Au(111) surface?; and does Fe@C$_{28}$ junction have a high-performance for molecular spintronic devices? The answers to these questions may broaden the opportunities for designing novel fullerene devices.
In this research, the electronic structure of Fe@C$_{28}$ was studied first. Then, we considered all possible adsorption configurations of Fe@C$_{28}$ adsorbed on the Au(111) surface and identified the most stable configuration after structure relaxation. Finally, the spin transport properties of a scanning tunneling microscopy (STM)-type Au-Fe@C$_{28}$-Au junction at the molecular scale were explored. The Fe@C$_{28}$ junction can act as a high-efficiency spin filter, and the conductance can be effectively modulated by means of pushing forward or pulling back the Au tip.
2. Materials and Methods
In these calculations, electronic structures and geometry relaxations were performed using the SIESTA package [29]. The exchange-correlation energy functional was described by the Perdew-Burke-Ernzerhof (PBE) generalized gradient approximation (GGA) form [30]. An energy cutoff was set to be 400 Ry for the real-space mesh size. For the relaxation of structures, the Hellmann-Feynman (HF) forces on each atom was less than 0.01 eV/Å to find a local minimum.
The spin-dependent transport properties studied are based on a state-of-the-art technique where the density functional theory (DFT) is combined with the Keldysh nonequilibrium Green’s function (NEGF) theory, implemented in the NanoDcal package [31,32]. The spin-dependent current–voltage (I-V) curves and transmission functions were obtained by using the Landauer-Büttiker formula as the following equations (1) and (2):
$$I_{\sigma}(V) = \frac{e}{h} \int \frac{T_{\sigma}(E,V)[f(E-\mu_L)-f(E-\mu_R)]dE}{1} \quad (1)$$
$$T_{\sigma}(E,V) = \text{Tr}\left[\Gamma_L(E,V)G_{\sigma}(E,V)\Gamma_R(E,V)G_\sigma^\dagger(E,V)\right] \quad (2)$$
Here, $I_{\sigma}(V)$ is the current through the device under the external bias voltage $V$; $T_{\sigma}(E,V)$ is the transmission function of the junction, indicating the rate at which electrons are transmitted from the left to the right electrodes by propagating through the device; $G_{\sigma}(E,V)$ is the retarded Green’s function of the central region ($\sigma = \uparrow/\downarrow$); $\Gamma_{L,R}(E,V)$ is the left/right electrode and central region coupling matrix; $\mu_L/R$ is the chemical potential; and $f(E-\mu_{L/R})$ is the Fermi-Dirac distribution function. In our transport calculations, the model of the Fe@C$_{28}$ junction was periodic along the $x$ and $y$ directions, and the transport direction was along $z$. A mesh cutoff energy was set to be 150 Ry, and the Monkhorst-Pack ($1 \times 1$) K-point grid was adopted to sample the 2D Brillouin zone. Test calculations with a larger basis set, larger cutoff energy, and denser K-point (i.e., $3 \times 3$) provide similar results.
3. Results
3.1. Electronic Structure of Fe@C$_{28}$
First, we will discuss the electronic properties of Fe@C$_{28}$. The fully relaxed structure of Fe@C$_{28}$ fullerene adopts a C$_{2v}$ point group (Figure 1A). The Fe atom deviates from the cage center with a 0.454-Å displacement and reduces the Td symmetry to C$_{2v}$. The Fe atom is above the middle of
two pentagons sharing an edge and forms two identical Fe–C bonds, with a corresponding bond length of \( \sim 2.052 \) Å. According to symmetry classification, there are 10 types of inequivalent C atoms, 13 inequivalent C–C bonds, and 6 inequivalent rings that include 4 inequivalent pentagons and 2 hexagons, respectively. The optimized C–C bond lengths are changed from 1.430 to 1.541 Å [20]. The binding energy of Fe@C\(_{28}\) is defined as \( E_{\text{Fe@C}_{28}} - E_{C_{28}} - E_{\text{Fe}} = -1.312 \) eV, indicating that the C\(_{28}\)-encapsulated Fe atom makes the Fe@C\(_{28}\) much more stable.
Figure 1B shows that the isosurface of spin density is mainly localized on Fe atoms, which is a remarkable difference in the C\(_{28}\) case [12]. The calculated magnetic moment is mainly distributed on the Fe atom, which is about 3.270 \( \mu_B \), and the total magnetic moment of Fe@C\(_{28}\) is expected to be 4.0 \( \mu_B \).
In addition, we also examined the electronic structure of Fe@C\(_{28}\) with Td symmetry. By adopting the DFT calculations, the Td-symmetry Fe@C\(_{28}\) has a larger magnetic moment of 6.0 \( \mu_B \), but its energy is 1.054 eV higher than that of the C2v configuration. Figure 1C–E shows the spin-resolved frontier orbitals, average density of states (DOS) of C, and Fe’s 3d orbitals of Fe@C\(_{28}\). It is obvious that there are no degenerate orbitals in Fe@C\(_{28}\), since the C2v point group only has one-dimensional representations. Clearly, the energies of spin-resolved frontier molecular orbitals is significantly different from one another. The spin-up HOMO (3d\(_{xz}\) dominated in Fe) and LUMO two frontier orbitals locate at \(-0.163\) and 0.162 eV, while the spin-down HOMO and LUMO (3d\(_{x^2-y^2}\) dominated in Fe) locate at \(-0.571\) and 0.914 eV. Then, the spin-up and spin-down electrons of the HOMO–LUMO gaps are 0.325 and 1.485 eV, respectively. Since the electronic structure of the spin-up and spin-down electrons is significantly different, Fe@C\(_{28}\) could be a potential candidate in molecular spintronics.
**Figure 1.** (A) Optimized structure of Fe@C\(_{28}\) fullerene with C2v symmetry. There are 10 inequivalent C atoms, 13 inequivalent C–C bonds, and 6 inequivalent rings, with the inequivalent atoms labeled by different colors. (B) Spin density of Fe@C\(_{28}\). (C) Spin-resolved frontier orbitals of Fe@C\(_{28}\). Isovalue is set to \( \pm 0.01 \) e/Å\(^3\). (D) Average spin-resolved density of states (DOS) projected to C\(_{28}\) of the Fe@C\(_{28}\) with the energy window from \(-1.0\) to 1.5 eV. (E) Spin-resolved DOS projected to the five 3d orbitals of Fe atom.
### 3.2. Adsorption Properties
Before the spin transport calculation, we studied the adsorption properties of Fe@C\(_{28}\) on the Au(111) surface and first identified the most stable adsorption configuration. Symmetry analysis
showed that the free Fe@C\textsubscript{28} with a C\textsubscript{2v} point group has a total of 29 inequivalent sites, which include 10 types of inequivalent C atoms (named point), 13 types of inequivalent C–C bonds (named line), and 6 types of inequivalent rings, respectively. Then, three special adsorption sites at the Au(111) surface were considered, namely hollow, bridge, and top sites. Therefore, there are a total of 87 adsorption configurations. To find the most stable adsorption configuration, we relaxed all the initial structures. A 4 × 4 × 3 supercell for the Au(111) surface and 11.54 × 11.54 × 30 Å\textsuperscript{3} were adopted to mimic the adsorption unit cell. The Monkhorst-Pack (5 × 5 × 1) K-point used to sample the Brillouin zone ensures accurate results. In this calculation, we fixed the Au substrate and only relaxed the Fe@C\textsubscript{28}.
The lowest energy configuration is shown in Figure 2A,B. After adsorption, C\textsubscript{28} cage has a slight distortion, while the Fe atom has an obvious displacement. The Fe atom has a total displacement of 0.174 Å with respect to the undistorted Fe@C\textsubscript{28}, and forms a Fe–C bond of about 2.122 Å in length. The Fe@C\textsubscript{28} tends to adsorb on the bridge site of the Au(111) surface via a C–C bond. The adsorbed C–C bond is nearly parallel to the Au–Au bond (Figure 2B), and the bond length is slightly elongated from 1.435 to 1.536 Å. Two Au–C bond lengths are 2.232 and 2.354 Å after adsorption, implying effective bonding between Fe@C\textsubscript{28} and the Au(111) surface. We obtained the adsorption energy as follows: \( \Delta E = E_{\text{Fe@C}28+\text{Au} \text{sub}} - E_{\text{Fe@C}28} - E_{\text{Au} \text{sub}} \), and forms a Fe–C bond of about 2.122 Å in length.
The large adsorption energy indicates that Fe@C\textsubscript{28} on Au(111) has a strong chemical adsorption.
**Figure 2.** Most stable adsorption configuration. (A) Top view. (B) Side view. Fe@C\textsubscript{28} is favored and adsorbed on the bridge site of the Au(111) surface via a C–C bond. (C) Density of states (DOS) of Fe@C\textsubscript{28} after being adsorbed on the Au(111) surface within an energy window from −1.0 to 1.5 eV.
To understand the changes in electronic structure of Fe@C\textsubscript{28} before and after adsorption, a projected density of states (PDOS) analysis was performed (Figure 2C). Fe d orbital is around 1.3 eV above the Fermi level, which is similar to the free Fe@C\textsubscript{28}. However, due to the strong Au–C chemical bonding and charge transfer, the original sharp peaks in freestanding C\textsubscript{28} are broadened and mixed together. Mülliken population analysis showed that 0.26 e are transferred from Au(111) to Fe@C\textsubscript{28}, and the Fe atom loses 0.16 e. On the one hand, the charge transfer makes the LUMO occupied and the peak disappear (Figure 2C). On the other hand, the magnetic moment of the Fe atom is...
slightly increased by 0.17 μB. In order to see the charge transfer more clearly, we plotted the real space differential charge density distribution and average along the z direction, which is presented in Figure 3. It is clear that the charge transfer mainly occurs at the surface between Fe@C$_{28}$ and the Au substrate. Furthermore, because the Fe atom is bonded with the C that is shared by the three pentagons, a significant charge transfer was also expected. In conclusion, because the magnetic moment is hardly affected by adsorption, this robust magnetic moment provides a prerequisite for molecular spintronics applications.
**Figure 3.** The xy-plane-averaged differential charge density is along the z direction. For simplicity, the z direction coordinates of the bottom Au layer are set to zero. Insert: differential charge density of the Fe@C$_{28}$-Au adsorption configuration. The isovalue is set to ±0.008 e/Å$^3$.
3.3. Transport Properties
We designed a STM-type junction of Fe@C$_{28}$ and studied the voltammetric properties. The central region of the STM-type junction can be divided into two parts: the upper part is modeled as an Au adatom adsorbing on a 4 × 4 × 2 Au(111) hollow site, and the lower part is the most stable Fe@C$_{28}$-Au(111) adsorption configuration discussed above. The central region is shown in Figure 4A. This Au-Fe@C$_{28}$-Au junction is reasonable in experiments, and the current is easily to measure. It is well known that the contact configuration of molecules and electrodes is a key factor affecting the transport properties [33–37]. When pulling back and pushing forward the Au STM tip, the corresponding Au–C bond will be broken or formed. Therefore, the conductance of the junction can be modulated by controlling the distance between the Au tip and Fe@C$_{28}$.
The non-bonding configuration was considered first: the nearest Au–C distance was ~3.12 Å. The calculated spin-resolved I-V curves within the bias region from −1.0 to 1.0 V are shown in Figure 4B. Due to the asymmetric coupling between Fe@C$_{28}$ and the left and right Au(111) surface, the currents under the positive and negative bias are not symmetric. We found the spin-down current to be always larger than that of the spin-up current within the examined bias range. The spin-up (down) current at ±1.0 V bias of the Fe@C$_{28}$ junction is 8.26 (14.75) and −7.67 (−20.92) μA, respectively. To determine the difference between the spin-up and spin-down current, we defined the bias voltage-dependent quantity as $R(V) = |I_{\text{down}}(V)/I_{\text{up}}(V)|$. The calculated R from 2.52 to 12.05 shows effective spin polarization within the examined bias range. Furthermore, the current under the negative bias voltage is significantly larger than that of the positive bias voltage, which indicates a moderate rectification. Our results suggest that the Fe@C$_{28}$ junction is a high-efficiency spin injector under small bias voltage.
We subsequently studied the spin transport properties of the Fe@C$_{28}$ junction in equilibrium. The spin-resolved transmission spectra of the Fe@C$_{28}$ junction is plotted in Figure 5A, which shows a significant difference between the spin-up and spin-down channels nearby the Fermi level. The transmission spectra do not behave as several discrete and sharp transmission peaks but as a continuous broadening platform-like peaks for both the up and down channels, which indicates a strong molecule–electrodes coupling. For the spin-up channel, there are two 0.5-eV width platforms of transmission spectra that are located at regions from $-1.0$ to $-0.5$ eV and from 0.5 to 1.0 eV, respectively. As the transmission coefficients tend to zero nearby the Fermi level, a very small conductance is expected. However, for the spin-down channel, there is a very wide transmission peak starting at $-0.2$ eV and through the Fermi level, which gives rise to larger conductance than that of the spin-up channel. In addition, the spin-resolved current under bias V can be obtained by integrating the transmission spectra in the interval $-eV/2$ and $eV/2$, which is an intuitive explanation of why the spin-down current is much larger than the spin-up current.
To quantitatively describe the spin injection efficiency, the spin filter efficiency (SFE) under the zero bias is defined as follows: $\text{SFE} = \frac{|T_{\text{up}}(E_F) - T_{\text{down}}(E_F)|}{|T_{\text{up}}(E_F) + T_{\text{down}}(E_F)|}$. Here, $T_{\text{up}}(E_F)$ and $T_{\text{down}}(E_F)$ are the transmission coefficients of the spin-up and spin-down electrons at the Fermi level, respectively. A positive or negative value of the SFE indicates conductance dominated by the spin-up or spin-down electrons. The $T_{\text{up}}(E_F)$ and $T_{\text{down}}(E_F)$ through the junction are about $2.20 \times 10^{-2}$ and 0.27 $G_0$ ($G_0$ is the quantum conductance, and its value is $e^2/h$), respectively; the SFE is predicted to be $-84.7 \%$, indicating that spin-down electrons dominated. In fact, the real space local density of states (LDOS) of the spin-up and spin-down electrons are responsible for the different transport behaviors of two spin channels, as shown in Figure 5B. The delocalization of the LDOS for the spin-down electrons which can provides an effective transport channel at the Fermi level. While for the spin-up electrons, the LDOS do not distribute over all the scattering region, and then the transport channel is blocked at the Fermi level. Moreover, the DOS (Figure 6) also confirms that the transport channel of the spin-down electrons is more efficient. The spin-resolved DOS contributes to two C atoms that are nearest to the Au tip, a C–C bond adsorbed on the left electrode, and the Fe atom, respectively. As for the spin-up electrons, the magnitude of the DOS is very flat and tends to zero near the Fermi level. However, for the spin-down electrons, the magnitude of DOS is much larger than that of the spin-up electrons. We noticed that the DOS of the Fe has a significant contribution around the Fermi level, suggesting that the Fe atom plays a key role in the conduction of the spin-down electrons. The results of the real space LDOS and DOS are consistent, which explains the difference in conductance between the two spin channels.
Figure 5. Transport properties of the Fe@C_{28} junction. Au tip and Fe@C_{28} are non-bonding. (A) Spin-resolved transmission spectra of the Fe@C_{28} junction. (B) Spin-resolved DOS projected on two C atoms that are nearest to the Au tip, a C–C bond adsorbed on the Au(111), and endohedral Fe, respectively. Black line: total DOS; dot: Fe; virtual line: C. (C) Profile of the spin-resolved local DOS at the Fermi level, which suggests that the spin-down electrons can offer an effective conductance channel at E_F.
At last, we examined the case of the Au tip bonding with Fe@C_{28}. Pushing forward the STM tip about 1.30 Å, the Au–C bond is formed. Here, the molecule–electrodes coupling was stronger than that in the non-bonding case; therefore, the transmission peaks became higher and wider (Figure 6). The T_{up}(E_F) and T_{down}(E_F) are 9.17×10^{-2} and 0.53 G_0, respectively. The SFE is predicted to be −70.4%, indicating that the conductance and SFE can be effectively modulated by the Au–C bond forming or breaking. All in all, our findings show that the Fe@C_{28} junction can be seen as a possible candidate for a high-efficiency spin filter, spin injector, and moderate rectifier under small bias voltage, which offers promising applications in nanoelectronic devices.
Figure 6. Spin-resolved transmission spectra of the molecular junction of Au tip bonding with Fe@C\textsubscript{28}. Insert: bonded Fe@C\textsubscript{28} junction. The bonding area is denoted by the red dotted circle.
4. Conclusions
In summary, we investigated the Fe@C\textsubscript{28} absorption properties on an Au(111) surface and transport properties by first principle DFT calculations and NEGF techniques. The free Fe@C\textsubscript{28} has a localized 4.0-\(\mu\)B magnetic moment, and the cage tends to adsorb on the bridge sites of the Au(111) surface in the manner of a C–C bond. Our calculations show that the conductance-controllable Fe@C\textsubscript{28} junction can act as a high-efficiency spin filter and as an effective spin injector under small bias voltage. A pure spin current can be generated by the Fe@C\textsubscript{28} junction, which can be used as a spin source in a device, quantum computing, hard disk drive (HDD), etc. [8,9]. Moreover, when the magnetic moment of Fe@C\textsubscript{28} is flipped by the external magnetic field, the spin signal is also reversed. Thus, the proposed Fe@C\textsubscript{28} junction can also be used as a magnetic field sensor to detect the magnetic field [38]. All of the results suggest that Fe@C\textsubscript{28} not only can be seen as a promising candidate for molecular spintronics but also will be helpful for designing novel fullerene-based spin filter devices.
Author Contributions: The study was proposed and planned by K.X., Y.T., and X.W. The calculations were carried out by K.X. and Y.T. All authors discussed the results and wrote the manuscript.
Funding: This work was partially supported by the NSFC 11404109, Hubei Superior and Distinctive Discipline Group of “Mechatronics and Automobiles.”
Acknowledgments: We sincerely express our thanks to Wei Hu and Jie Li for their useful discussions.
Conflicts of Interest: The authors declare no conflict of interest.
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© 2019 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/).
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Using health action process approach to determine diet adherence among patients with Type 2 diabetes
Soheila Ranjbaran, Davoud Shojaeizadeh, Tahereh Dehdari, Mehdi Yaseri, Elham Shakibazadeh
Abstract:
INTRODUCTION: Diet adherence may cause diabetes complications to be diminished.
OBJECTIVES: This study aimed at identifying determinants of diet adherence among patients with Type 2 diabetes based on the health action process approach (HAPA).
METHODS: In this cross-sectional study, 734 patients with Type 2 diabetes, attending to South Tehran health centers, were recruited during June–December 2018. The dietary regimen scale (nine items) and a researcher-designed questionnaire consisting of HAPA constructs were used to gather the data. Data were analyzed using the Mann–Whitney test, Pearson Chi-squared test, Fisher’s exact test, and linear regression test. All statistical tests were assessed using SPSS (IBM Corp. Released 2017. IBM SPSS Statistics for Windows, Version 25.0. Armonk, NY, USA: IBM Corp.).
RESULTS: The level of nonadherence to diet was 91.1%. Diet adherence was significantly associated with family income ($P = 0.005$), level of education ($P < 0.001$), and age ($P = 0.009$). The linear regression showed that 55% of the variance of diet adherence was determined by HAPA variables. Diet adherence was associated with intention ($P < 0.001$), action planning ($P = 0.005$), and barriers ($P = 0.003$).
CONCLUSION: Most of the patients did not adhere to their diet. Appropriate programs should be designed to promote diet adherence among the patients, especially those with low literacy and patients living in poor communities.
Keywords:
Barriers, determinants, diet adherence, health action process approach, Type 2 diabetes
Introduction
About 422 million people worldwide have diabetes, and it has been estimated that more than 690 million will be afflicted by 2045. In Iran, the prevalence of Type 2 diabetes among adults was rapidly growing from 5.75% in 2010 to 8.7% in 2018. Diabetes, characterized by elevated levels of blood glucose, can potentially lead to serious damages to heart, blood vessels, eyes, kidneys, and nerves over time, if not controlled.
People with diabetes can live longer and healthier when their diabetes is early diagnosed and well managed. The risk of Type 2 diabetes is decreased by healthy eating. One of the main goals in diabetes care is to reduce diabetes complications and to reach glycemic control is healthy eating. Adherence to healthy diet is the main approach in the management of diabetes. Higher and strong adherence to plant-based dietary patterns and lifestyle recommendations has been reported as successful in lowering the risk of Type 2 diabetes. However, diet adherence is a challenge for most of the patients. Diet
adherence has been reported to be in a range of 44%–74% among patients with Type 2 diabetes.\cite{8-11}
Barriers to diet adherence among patients include cost, lack of support and family issues, low quality of life, urbanization, lack of knowledge, social pressure on eating out, eating problems and negative perspective on diabetes, good support and dyadic adjustment, assessed by partners, poor self-discipline, financial restriction, lack of disease acceptance, and lack of regular blood glucose testing.\cite{8,11-15} Diet regimens are different from patient to patient.\cite{16} Hence, it is essential to consider theories and/or models to best fit the issue. To adhere to the recommendations, one has to become motivated. Motivation guides the self-regulatory process in order to translate a dietary goal into action.\cite{17}
The health action process approach (HAPA) offers that the adoption, initiation, and maintenance of health behaviors should be understood as a structured process including a motivation phase and a volition phase.\cite{18} This model explains that once an intention to change a health behavior is formed, the change should be planned, initiated, and maintained, and relapses have to be managed. After an intention to change or adoption of a particular health behavior has been shaped, the intention has to be transformed into detailed action plans of when, where, and how to perform the desired action.\cite{19}
The HAPA-based studies carried out in Iran have shown seven constructs of HAPA being effective in determining healthful diet for patients with Type 2 diabetes. It explained 81.1% of the total variance.\cite{20} In Australia, MacPhail et al. reported that HAPA was effective in predicting health outcomes in patients with Type 2 diabetes; however, it was not effective in improving healthy eating.\cite{21} We aimed to identify determinants of diet adherence based on HAPA, as a conceptual model, among patients with Type 2 diabetes attending to the South Tehran health centers.
**Methods**
**Research design and participants**
This cross-sectional study was carried out among 734 patients with Type 2 diabetes referring to the South Tehran health centers from June to December 2018. The inclusion criteria were being diagnosed with Type 2 diabetes for more than 6 months and the absence of any mental, visual, and learning disabilities (according to the clinical diagnosis by a physician) and having consent to participate in the study. The exclusion criteria were a diagnosis of Type 1 or gestational diabetes (not Type 2 diabetes).
**Measures**
A HAPA questionnaire consisting of 8 sections and 38 items was developed based on the guidelines “Risk and Health Behaviors: Documentation of the Scales of the Research Project” and previous studies.\cite{19,21-25} Intention to diet adherence was assessed using seven-interval Likert scales, ranging from 1 (strongly disagree) to 7 (strongly agree) with higher scores indicating high level of intention (two items). Task self-efficacy of diabetes diet adherence was assessed using a four-point scale ranging from 1 (not at all true) to 4 (exactly true) (six items). Coping self-efficacy (seven items), scored for benefits item ranging from 1 (not at all true) to 4 (exactly true), with higher scores determining better condition. Recovery self-efficacy (three items) was rated on a four-point scale ranging from 1 (not at all true) to 4 (exactly true). Aaction planning (two items) and coping planning (six items) were rated on a four-point scale ranging from 1 (not at all true) to 4 (exactly true); scores were recoded to show a better condition. Barriers to adherence (nine items) and resources (three items) were assessed using items ranged from 1 (strongly disagree) to 7 (strongly agree), higher scores represented a high level of barriers and resources. Content validity ratio (CVR) and content validity index (CVI) have been measured by means of a quantitative method in accordance to the Lawshe table.\cite{26} The stability of the items was calculated by intraclass correlation coefficient (ICC). The ICC of 0.4 and above was considered as satisfactory.\cite{27} The CVI >0.9 and CVR >0.9 were accepted. The internal consistency of the HAPA-based questionnaire was high (Cronbach’s α ≥ 0.83). The ICC was satisfactory (0 > 0.6).
A reliable and valid nine-item scale was applied to measure patients’ adherence to diet.\cite{28} The total score ranged 0–9, with higher scores indicating greater adherence. The first seven items ranged from 0 (never), 0.33 (rarely), 0.66 (sometimes) to 1 (always). The last two items included: “How many days in the last week you could adhere to the prescribed diet?” and “Did you adhere to the prescribed diabetic dietary regimen yesterday?” For scoring, the reported days in the first question were divided into seven. In the second question, positive answer was scored as 1 and negative answer was scored as 0.
The Ethics Committee of Tehran University of Medical Sciences (code: IR.TUMS.SPH.REC.1396.4200) approved the study. Before completing the questionnaires, participants received a complete explanation of the plan and objectives of the study and those willing to participate provided written informed consent.
**Statistical analysis**
The associations between HAPA constructs and diet adherence were analyzed using the linear regression test. To assess the association between diet adherences with
demographic variables, the Chi-squared test, Fisher’s exact test, and Mann–Whitney test were used. $P < 0.05$ was considered statistically significant. All statistical tests were assessed using SPSS (IBM Corp., Released 2017. IBM SPSS Statistics for Windows, Version 25.0. Armonk, NY, USA: IBM Corp).
Based on the mean ± standard deviation of action self-efficacy (14.85 ± 4.91) in a previous study\[19\] with Type I error ($\alpha$) 5%, the sample size was calculated 740 individuals by the following formula (D: design effect = 2, $d = 10% S = 0.5, Z_{1−α/2} = 1.96$).
$$n = \frac{Z_{1−α/2}^2 \cdot \alpha}{d^2} \times D$$
**Results**
**Demographic characteristics**
In total, 734 participants met the criteria for inclusion. Table 1 describes the demographic characteristics of the participants. Most of the participants (91.1%) were nonadherent. The mean age of study participants was 61.6 ± 9.7, and 36.9% had primary education. There were significant associations between the diet adherence with the level of education ($P < 0.001$), age ($P = 0.009$), and income status ($P = 0.005$) [Table 1].
**Association between diet adherence and the health action process approach constructs**
To predict the patients’ diet adherence, a linear regression test was used. As shown in Table 2, significant associations were observed between the diet adherence with some HAPA constructs including intention, action planning, and barriers to adherence. Linear regression showed that HAPA constructs could predict 55% of the variance of participants’ diet adherence. Behavioral intention ($\beta = 0.32, P < 0.001$), action planning ($\beta = 0.17, P = 0.005$), and barriers to adherence ($\beta = -0.131, P = 0.003$) were predictors of diet adherence in patients with Type 2 diabetes.
**Perceived barriers influencing adherence to diet behavior**
Table 3 presents the frequency of perceived barriers influencing adherence to diet behavior. According to the results, the main barrier to diet adherence among the patients with Type 2 diabetes was difficult to abandon favorite foods and food habits (76%). The highest percentage was obtained for the first question, “It is difficult for me to avoid banned foods” (69.6%).
**Discussion**
This study was conducted aiming at identifying the determinants of diet adherence among patients with Type 2 diabetes using HAPA in Tehran, Iran. Our study showed that a significant number of patients (91.1%) were nonadherent to diet. Nonadherence to diet is the main issue among patients with Type 2 diabetes that this may be due to the complexity of diet regimen. Other studies showed a nonadherence to diet range from 74.3%\[29\] to 87.5%\[30\]. Diet adherence education in patients with diabetes needs to improve different aspect of diet recommendations and patterns for the management of diabetes. In a study conducted in Denmark, adherence to dietary recommendations (e.g., fiber, saturated fat, vegetables, fruit, and fish) was low in patients with Type 1 and Type 2 diabetes.\[31\]
Individuals with low income, individuals with low levels of education, and older patients were more nonadherent to diet. In a study conducted by Ayele \textit{et al}., low levels of education and low income were associated with nonadherence to diet among patients with Type 2 diabetes.\[29\] Evidence shows inconsistency between the studies reporting the relationship between age and adherence. In studies conducted by Yeh \textit{et al}., and Renner \textit{et al}., patient age was associated with diet adherence and older individuals have higher intentions to adhere to healthy diet.\[32,33\] Aging is related to more experience in managing daily activities as well as initiating behavior changes despite various barriers.\[33\] While, in a study by Parajuli \textit{et al}., in Nepalese, by increasing age, adherence to diet decreased.\[30\] This inconsistent finding seems to be due to different contexts of the studies. Therefore, in educational interventions, it is better to focus on messages for different age groups.
Our study showed that among HAPA constructs, intention, action planning, and barriers to adherence were predictors of the diet adherence. Patients with higher intention and action planning and fewer barriers were more adherent to their diet. People who have planned in detail “how,” “when,” and “how” to adhere to dietary recommendations are more likely to follow their diet. This result is consistent with those conducted by Rohani \textit{et al}.,\[19\] In their study, behavioral intention, action and coping planning, and recovery self-efficacy correlated with healthful diet in patients with Type 2 diabetes.\[19\] Considering the fact that most of the patients had elementary education or were illiterate, it seems difficult for them to plan their diet adherence. Educational materials and protocols available for patients with diabetes in clinics are the same for individuals with different levels of education. Providing education to patients according to their level of education seems to be helpful in improving their diet adherence.
Determining these predictors helps health educators to design targeted interventions and empower patients to deal with barriers. Behavioral intentions are not sufficient
Table 1: Comparison of diet adherence by demographic characteristics (n=734)
| Patients’ characteristics | Adherent to diet, n (%) | Nonadherent to diet, n (%) | P |
|---------------------------|-------------------------|----------------------------|----|
| **Level of education** | | | |
| Illiterate | 15 (5.6) | 254 (94.4) | 0<001\textsuperscript{a} |
| Elementary | 18 (6.6) | 253 (93.4) | |
| Middle school | 13 (13.7) | 82 (86.3) | |
| High school | 15 (18.3) | 67 (81.7) | |
| University degree | 4 (23.5) | 13 (76.5) | |
| **Age** | | | |
| ≤45 | 11 (25.6) | 32 (74.4) | 0.009\textsuperscript{a} |
| 46-55 | 19 (12.3) | 135 (87.7) | |
| 56-65 | 15 (5.1) | 280 (94.9) | |
| 66-75 | 17 (8.9) | 173 (91.1) | |
| 76+ | 3 (5.8) | 49 (94.2) | |
| **Gender** | | | 0.322\textsuperscript{b} |
| Female | 48 (9.6) | 454 (90.4) | |
| Male | 17 (7.3) | 215 (92.7) | |
| **Marital status** | | | 0.522\textsuperscript{b} |
| Married | 53 (8.9) | 545 (91.1) | |
| Single | 2 (18.2) | 9 (81.8) | |
| Died | 10 (8) | 115 (92) | |
| **Job** | | | 0.298\textsuperscript{c} |
| Unemployment | 0 | 8 (100) | |
| Retired | 16 (9.2) | 158 (90.8) | |
| Clerk | 3 (13) | 20 (87) | |
| Free job | 2 (2.9) | 68 (97.1) | |
| Housewife | 44 (9.6) | 415 (90.4) | |
| **Family income in month (RLs)** | | | 0.005\textsuperscript{a} |
| <500,000 | 1 (1.5) | 65 (98.5) | |
| 500,000-1,000,000 | 7 (6.7) | 98 (93.3) | |
| 1,000,000-2,000,000 | 52 (9.6) | 488 (90.4) | |
| >2,000,000 | 5 (21.7) | 18 (78.3) | |
| **Duration of diabetes (years)** | | | 0.156\textsuperscript{a} |
| ≤5 | 17 (7) | 227 (93) | |
| 5.01-10 | 16 (8) | 184 (92) | |
| 10.01-15 | 17 (14.4) | 101 (85.6) | |
| 15.01-20 | 7 (6.2) | 106 (93.8) | |
| 20.01+ | 8 (13.6) | 51 (86.4) | |
| **Medications** | | | 0.097\textsuperscript{c} |
| OHA | 37 (7.5) | 455 (92.5) | |
| Insulin | 15 (10.1) | 134 (89.9) | |
| OHA and insulin | 13 (14.3) | 78 (85.7) | |
\textsuperscript{a}Mann-Whitney test, \textsuperscript{b}Pearson’s Chi-square test, \textsuperscript{c}Fisher’s exact test. OHA=Oral hypoglycemic agents
Table 2: Linear regression analysis to predict diet adherence among participants
| Variable | R² | B | SE | P | Standardized coefficients β | 95% CI |
|---------------------------|-----|------|-----|-----|-------------------------------|-----------------|
| **Constant** | 0.55| 21.29| 4.64| 0<001| 0.431 | 0.27 - 0.386 |
| Intention | | 0.328| 0.02| 0<001| 0.8 | -0.125 - 0.162 |
| Task self-efficacy | | 0.018| 0.07| 0.8 | 0.016 | -0.033 - 0.022 |
| Coping self-efficacy | | 0.122| 0.07| 0.08 | 0.112 | -0.105 - 0.259 |
| Recovery self-efficacy | | -0.033| 0.05| 0.559| -0.033 | -0.144 - 0.298 |
| Action planning | | 0.176| 0.06| 0.005| 0.174 | 0.055 - 0.298 |
| Coping planning | | -0.002| 0.07| 0.978| -0.002 | -0.142 - 0.139 |
| Barriers to adherence | | -0.131| 0.04| 0.003| -0.102 | -0.217 - 0.044 |
| Resources | | 0.04 | 0.03| 0.256| 0.034 | -0.029 - 0.109 |
R²=0.55, F=100.85, P<0.05. SE=Standard error, CI=Confidence interval
to explain behavior and postintentional processes such as planning; so it should be incorporated to explain how people change their behavior.\cite{34,35}
In the present study, 76% of the participants strongly agreed that abandoning their favorite foods and eating habits was difficult. Changing in eating habits is one of the most important lifestyle changes and challenges for patients with diabetes.\cite{36} Eating habits of much delicious foods increase to the reinforcement of craving for these eaten foods.\cite{37} This meant that they have no perceived capability of quitting eating habits and following the diet. It is necessary to increase diet-related self-efficacy in patients with Type 2 diabetes. Another important reason reported by 69.6% of the participants strongly avoiding of prohibited foods was hard. Food cravings can be important barriers to diet adherence in these patients. It shows the importance of focusing on food cravings in designing diet adherence interventions. There are lots of food cues and opportunities to eat in the modern food environment that it can reinforce the impact of food cravings on diet adherence.\cite{38} Hence, improving the perceived capabilities of patients to adherent to diet seems to be necessary. The third reason for nonadherence to diet was difficult to prepare more than one type of food by the family and being forced to eat the same food that the family eats. About 47.4 of the patients reported that they could not buy recommended foods, and patients with low income were nonadherence to diet. Our findings were consistent with the findings of previous studies.\cite{29} A study by Jazayeri and Pipelzadeh among Iranian patients with diabetes found cost as the most frequently cited barrier to diet self-care. The duration of diabetes was a predictor of barriers to diet self-care, as well.\cite{39} It may be useful to provide sufficient information regarding nonexpensive and healthy food alternatives among low-income patients.
In a similar study, Vijan et al. reported expense of the diet, portion size, quality of life, and family support as barriers to the following dietary recommendations in Type 2 diabetes patients in both urban and suburban areas.\cite{12} These results show that reasons for nonadherent to diet in patients with Type 2 diabetes are varied and identifying these reasons is essential.
For 58.3% of the patients, it was difficult to adhere to diet while partying and traveling. Patients may be adherent in some conditions (e.g., when at home) but nonadherent in others (e.g., when traveling). Hence, adherence should be viewed as a dynamic phenomenon.\cite{40} It seems that people do not behave according to their intentions and their planning. Food cravings may present an important barrier to implementing a diet plan. Further studies on the food cravings of patients with Type 2 diabetes and training in mindfulness regarding diet adherence are also recommended. In a study conducted by Dalton et al., food cravings were the most commonly mentioned reason for nonadherent to diet.\cite{41} The mindful eating intervention can affect diet adherence in patients with Type 2 diabetes.\cite{42} The study of Craddock et al. showed that changing or controlling dietary environmental agents were more than twice as effective in reducing hemoglobin A1c than diets using behavioral change interventions in patients with Type 2 diabetes.\cite{43}
Health-care providers can improve intention, action planning, and barriers among patients with Type 2 diabetes through theory-based interventions to help them promote their diet adherence, which, in turn, reduces hospitalization and physician services and health-care costs in the long time.
In this study, we identified a series of cognitive factors that can predict medication adherence. These cognitive
### Table 3: Perceived barriers influencing adherence to diet (n=734)
| Barriers | Strongly disagree, n (%) | Very disagree, n (%) | Disagree, n (%) | No idea, n (%) | Agree, n (%) | Very agree, n (%) | Strongly agree, n (%) |
|-------------------------------------------------------------------------|--------------------------|----------------------|-----------------|---------------|--------------|-------------------|----------------------|
| It is difficult for me to avoid banned foods | 10 (1.4) | 12 (1.6) | 18 (2.5) | 26 (3.5) | 59 (8) | 98 (13.4) | 511 (69.6) |
| Buying recommended foods (fresh fruits and vegetables, fish, wholegrain bread, brown rice, etc.) costs me a lot | 29 (4) | 18 (2.5) | 35 (4.8) | 87 (11.9) | 102 (13.9) | 115 (15.7) | 348 (47.4) |
| The oversensitivity of my family to my diet makes me uncomfortable and disrespectful | 254 (34.6) | 119 (16.2) | 112 (15.3) | 94 (12.8) | 68 (9.3) | 29 (4) | 58 (7.9) |
| The doctor or health-care provider does not have enough time to consult my diet and answer my questions | 289 (39.4) | 168 (22.9) | 95 (12.9) | 59 (8) | 47 (6.4) | 43 (5.9) | 33 (4.5) |
| It is difficult to get more than one type of food for the family and I have to eat the same food that the family eats | 12 (1.6) | 15 (2) | 23 (3.1) | 35 (4.8) | 64 (8.7) | 120 (16.3) | 465 (63.4) |
| It is difficult for me to adhere to diet at partying and traveling | 12 (1.6) | 12 (1.6) | 16 (2.2) | 37 (5) | 75 (10.2) | 154 (21) | 428 (58.3) |
| When I get busy at work and/or at home, I forget to follow the diet | 17 (2.3) | 20 (2.7) | 28 (3.8) | 54 (7.4) | 105 (14.3) | 164 (22.3) | 346 (47.1) |
| Diet foods are not delicious | 13 (1.8) | 28 (3.8) | 68 (9.3) | 106 (14.4) | 128 (17.4) | 121 (16.5) | 270 (36.8) |
| It is difficult for me to abandon my favorite foods and food habits | 7 (1) | 12 (1.6) | 8 (1.1) | 20 (2.7) | 44 (6) | 85 (11.6) | 558 (76) |
factors that facilitate or hinder diet adherence behavior and should be considered by the diabetes program planners.
In this study, factors influencing diet adherence among patients with Type 2 diabetes according to the HAPA were identified. Data were collected using face-to-face interview, which was helped to gather valid data from low literate patients. Most available studies have worked on health behavior changes at the same time, regarding the health behavior models and/or theories. This study identified the constructs of HAPA that can help health program planners to develop interventions that may be more effective in maintaining the interventions effects. Our study had some limitations. First, measuring diet adherence based on self-report questionnaires may cause recall bias and overestimate patients’ diet adherence rate. Second, it should be careful about interpreting the associations and direction of associations from a cross-sectional survey. Another limitation of this study is that the results of our study are only relevant to the south parts of Tehran, and there are no accurate statistics on patients’ diet adherence status in the north parts of Tehran.
Conclusion
Our study showed that nonadherence to diet among patients with Type 2 diabetes was extremely high. We found intention, action planning, and barriers to adherence as the most important determinants related to the diet adherence among patients with Type 2 diabetes. Adherence to diet was associated with age, educational level, and income in patients. Designing interventional programs aiming at promoting diet adherence level considering these determinants are promising. Diabetes educators should have a specific focus on patients’ intention, action planning, and barriers of diet adherence while designing such interventions.
Acknowledgments
This study was part of a PhD thesis supported by the Tehran University of Medical Sciences (Grant number 9321108001). We appreciate the staff of South Tehran health centers and patients participated in the study.
Financial support and sponsorship
This study was supported by the Deputy Research at Tehran University of Medical Sciences.
Conflicts of interest
There are no conflicts of interest.
References
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Chronic graft-versus-host disease (cGVHD) is a major complication of allogeneic hematopoietic stem cell transplantation (allo-HCT) that is related to higher mortality and morbidity [1, 2]. Glucocorticoids has been the mainstay of the treatment for cGVHD, while it also has been widely used to treat the variety of autoimmune diseases as the combination with other immunosuppressive agents including azathioprine (AZP) to reduce long-term complications of glucocorticoids such as diabetes mellitus, iatrogenic Cushing’s syndrome, avascular necrosis of joints and osteoporosis, etc. [3–6].
Although a previous clinical trial suggested that prednisone (PRD) based regimen plus AZP (PRD + AZP) resulted in worse survival than PRD-based regimen in a standard risk group of cGVHD patients due to higher non-relapse (infection-related) mortality (NRM) [7], the therapeutic efficacy of AZP might deserve to be looked at again because there have been advances in the allo-HCT field for over the last decades, including significant improvement in supportive care such as infectious prophylaxis and treatment, as well as in evaluating cGVHD systematically. The National Institutes of Health (NIH) first proposed consensus criteria for the diagnosis of cGVHD, and tools for scoring cGVHD organ involvement and assessing overall severity in 2005, which are now widely used in clinical practice [8, 9]. In addition, a new statistical endpoint for evaluating the efficacy of cGVHD treatment, i.e. failure free survival (FFS), has been introduced and suggested to be a potential surrogate of overall survival (OS) for cGVHD treatment [10, 11]. Therefore, we retrospectively reviewed 668 consecutive patients who underwent allo-HCT between 2004 and 2012 at Princess Margaret Cancer Centre, Toronto, Canada in order to compare the efficacy of PRD + AZP and PRD-based regimens with respect to FFS as well as OS, NRM, and the incidence of relapse.
Chronic GVHD was defined, reclassified and graded by the NIH consensus criteria [8]. Among 313 patients with redefined cGVHD, we then identified 240 patients who received PRD or PRD + AZP as first line treatment for cGVHD. Late onset acute GVHD was excluded from the analysis.
The FFS was defined as time from the initiation of frontline treatment for cGVHD to treatment failure (TF), NRM or relapse of disease. TF was defined as initiation of the next line of IST for cGVHD [11] or an escalation of the dose of PRD to ≥1 mg/kg/day regardless of the target organ. OS and FFS were calculated by the Kaplan–Meier method and compared using the log rank test. The cumulative incidences of NRM, disease relapse, and the TF rate (TFR) for front line cGVHD treatment were estimated considering competing risks, with disease relapse, NRM and TFR considered as mutually-competing risks.
The transplant-related characteristics were analyzed to compare the PRD and PRD + AZP groups using Pearson’s $X^2$ or Fisher’s exact test. The univariate and multivariate analyses performed to compare OS, NRM, relapse incidence, and FFS between two treatment groups. OS and FFS were compared using the log rank test. Univariate analyses for incidence with competing risks were performed by Gray’s method. Cox proportional hazard regression model was used for multivariate analysis of survivals.
Since the characteristics of cGVHD of two treatment groups were imbalanced (Table 1), we performed a propensity score matching (PSM) analysis as a case-control study in order to adjust the potential confounding effects of the clinical features of cGVHD on treatment outcome. The
| | Whole cohort | Propensity score matching analysis cohort |
|----------------------------|--------------|------------------------------------------|
| | All, n = 240 | Prednisone alone, n = 142 | Prednisone and Azathioprine, n = 98 | p-value | All, n = 148 | Prednisone alone, n = 74 | Prednisone and Azathioprine, n = 74 | p-value |
| Median age at transplant, year (range) | 50 (19–70) | 50 (19–68) | 51 (19–70) | 52 (20–70) | 52 (21–69) | 52 (20–70) | 0.868 |
| Gender, no. (%) | | | | | | | |
| Male | 137 (57.1) | 79 (55.6) | 58 (59.2) | 0.598 | 83 (56) | 41 (55) | 42 (57) | 0.868 |
| Female | 103 (42.9) | 63 (44.4) | 40 (40.8) | | 65 (44) | 33 (46) | 32 (43) | |
| Gender mismatch, no. (%) | | | | | | | |
| Female to male | 53 (22.1) | 31 (21.8) | 22 (22.4) | 1.000 | 31 (21) | 14 (19) | 17 (23) | 0.545 |
| Other | 187 (77.9) | 111 (78.2) | 76 (77.6) | | 117 (79) | 60 (81) | 57 (77) | |
| Disease, no. (%) | | | | | | | |
| AML | 104 (43.3) | 60 (42.3) | 44 (44.9) | 0.760 | 64 (43) | 33 (45) | 31 (42) | 0.791 |
| ALL | 22 (9.1) | 11 (7.7) | 11 (11.2) | | 13 (9) | 8 (11) | 5 (7) | |
| MDS | 23 (9.6) | 13 (9.2) | 10 (10.2) | | 16 (11) | 7 (10) | 9 (12) | |
| CML | 17 (7.1) | 13 (9.2) | 4 (4.1) | | 9 (6) | 6 (8) | 3 (4) | |
| CLL | 21 (8.8) | 14 (9.9) | 7 (7.1) | | 14 (10) | 7 (10) | 7 (10) | |
| MF/MPD | 21 (8.7) | 12 (8.5) | 9 (9.2) | | 11 (7) | 4 (5) | 7 (10) | |
| Malignant lymphoma | 27 (11.3) | 15 (10.6) | 12 (12.2) | | 20 (14) | 9 (12) | 11 (15) | |
| AA | 4 (1.7) | 3 (2.1) | 1 (1.0) | | 1 (1) | 0 (0) | 1 (1) | |
| MM | 1 (0.4) | 1 (0.7) | 0 (0) | | 0 (0) | 0 (0) | 0 (0) | |
| Intensity of conditioning regimen, no. (%) | | | | | | | | |
| Myeloablative | 154 (64.2) | 93 (65.5) | 61 (62.2) | 0.681 | 90 (61) | 47 (64) | 43 (58) | 0.501 |
| Non-myeloablative | 86 (35.8) | 49 (34.5) | 37 (37.8) | | 58 (39) | 27 (37) | 31 (42) | |
| HLA and donor type, no. (%)| | | | | | | |
| Related | 146 (60.8) | 84 (59.1) | 62 (62.2) | 0.489 | 96 (65) | 46 (62) | 50 (68) | 0.591 |
| Unrelated | 86 (35.8) | 54 (38) | 32 (32.7) | | 46 (31) | 25 (34) | 21 (28) | |
| Missing | 8 (3.3) | 4 (2.8) | 4 (4.1) | | 6 (4) | 3 (4) | 3 (4) | |
| Stem cell source, no. (%) | | | | | | | |
| Bone marrow | 19 (7.9) | 12 (8.5) | 7 (7.1) | 0.811 | 8 (5) | 4 (5) | 4 (5) | 1 |
| Peripheral blood | 221 (92.1) | 130 (91.5) | 91 (92.9) | | 140 (95) | 70 (95) | 70 (95) | |
| T-cell depletion, no. (%) | 46 (19.2) | 33 (23.2) | 13 (13.3) | 0.054 | 24 (16) | 16 (22) | 8 (11) | 0.074 |
| Any grade of acute GVHD | 181 (78.9) | 113 (81.9) | 68 (73.9) | 0.148 | 106 (72) | 57 (77) | 49 (66) | 0.149 |
| Median onset of cGVHD, Day (95% CI) | 140 (131–149) | 132 (123–141) | 160 (140–180) | <0.001 | 140 (128–151) | 140 (130–149) | 152 (127–176) | 0.863 |
| Classification of NIH cGVHD | | | | | | | |
| Classical | 87 (36.2) | 48 (33.8) | 39 (39.8) | 0.418 | 51 (34.5) | 26 (35.1) | 25 (33.8) | 0.863 |
| Overlap syndrome | 153 (63.8) | 94 (66.2) | 59 (60.2) | | 97 (65.5) | 48 (64.9) | 49 (65.5) | |
| Global score of cGVHD at treatment | | | | | | | |
| Mild | 24 (10.0) | 16 (11.3) | 8 (8.2) | <0.001 | 14 (9.5) | 6 (8.1) | 8 (10.8) | 0.319 |
| Moderate | 173 (72.1) | 89 (62.7) | 84 (85.7) | | 122 (82.5) | 59 (79.7) | 62 (83.8) | |
| Severe | 43 (17.9) | 37 (26.1) | 6 (6.1) | 12 (8.1) | 9 (12.2) | 4 (5.4) | | |
| Organs involved in cGVHD | | | | | | | |
| Skin | 155 (64.6) | 88 (62.0) | 67 (68.4) | 0.108 | 101 (68) | 54 (73) | 47 (64) | 0.219 |
| Mouth | 116 (48.3) | 66 (46.5) | 50 (51.0) | 0.359 | 72 (49) | 33 (45) | 39 (53) | 0.341 |
| Eyes | 77 (32.1) | 45 (31.7) | 32 (32.7) | 0.889 | 46 (31) | 21 (28) | 25 (34) | 0.477 |
| Gastrointestinal tract | 50 (20.8) | 36 (25.4) | 14 (14.3) | 0.052 | 22 (15) | 12 (16) | 10 (14) | 0.644 |
clinical variables included in the propensity score calculations were global score (GS) by the NIH consensus criteria, the classification of the cGVHD (classical or overlap syndrome), age, gender, duration from allo-HCT to initiation of cGVHD treatment, performance status (PS), progressive type onset (PTO) of cGVHD, thrombocytopenia and organs involvement cGVHD per skin, gastrointestinal track, liver, lung, and musculoskeletal system. A total of 74 case-control pairs were identified with <0.1 of a difference in propensity score.
Of the 240 patients included in the analysis, 154 (64.2%) received myeloablative conditioning (MAC) and 86 (35.8%) reduced-intensity conditioning (RIC) (Table 1). There were no significant differences in pretransplant characteristics between the PRD and PRD + AZP groups except for T-cell depletion (TCD); 33 patients (23.2%) in the PRD group and 13 (13.3%) in the PRD + AZP group underwent T-cell depletion (*p* = 0.054). The imbalanced characteristics of cGVHD were observed between the 2 groups, including longer duration from HCT to diagnosis of cGVHD (*p* < 0.001) in the PRD + AZP group; also fewer patients with severe cGVHD (*p* < 0.001), fewer with PTO (p = 0.002), fewer with thrombocytopenia (*p* = 0.008) and better PS (*p* = 0.008).
With a follow-up duration of 43.6 months among survivors, 2-year FFS, TFR, NRM, and relapse incidence were 24.7% (95% confidence interval (CI), 19.1–30.8%), 57.5% (50.8–64.0%), 7.5% (4.5–11.5%), and 10.1% (6.5–14.5%), respectively. The PRD + AZP group had a higher FFS rate at 2 years (36.4% [26.2–46.6%]) than the PRD group (16.8% [10.8–23.9%], *p* < 0.001) (Fig. 1a) and a lower incidence of TFR at 2 years (52% [40.8–62.0%]) versus 61.5% [52.5–69.3%], *p* = 0.050). In addition, it had a lower NRM rate at 2 years (3.4% [0.9–8.85] versus 10.5% [6–16.5%], *p* = 0.050). There was no difference between the groups in the cumulative incidence of relapse at 2 years; 8.3% (3.6–15.5%, *p* = 0.507) in PRD + AZP group and 11.3% (6.5–17.4%) in PRD group.
Severity by the NIH consensus criteria was well-correlated with FFS. The FFS rate at 2 years was 62.2% (39.9–78.3%) in mild, 20.5% (14.2–27.7%) in moderate, and 16.9% (7.5–29.6%) in severe cGVHD (*p* < 0.001). Patients with mild cGVHD had a lower TFR (29.2% [12.6–48.1%]) at 2 years than those with moderate/severe cGVHD (61.4% [54–68%], *p* = 0.008). Severity by the
### Table 1 (continued)
| | Whole cohort | Propensity score matching analysis cohort |
|---------------------------|--------------|------------------------------------------|
| | All | Prednisone alone | Prednisone and Azathioprine | All | Prednisone alone | Prednisone and Azathioprine |
| | (%, n = 240) | (%, n = 142) | (%, n = 98) | (%, n = 148) | (%, n = 74) | (%, n = 74) |
| Liver | 166 (69.2) | 94 (66.2) | 72 (73.5) | 0.202 | 109 (74) | 55 (74) | 0.604 |
| Lung | 21 (8.8) | 18 (12.7) | 3 (3.1) | 0.010 | 5 (3) | 2 (3) | 0.649 |
| Musculoskeletal system | 13 (5.4) | 6 (4.2) | 7 (7.1) | 0.326 | 7 (5) | 4 (5) | 0.699 |
| Others | 7 (2.9) | 4 (2.8) | 3 (3.1) | 0.912 | 5 (3) | 3 (4) | 0.649 |
| No. of organs involved | | | | | | |
| 1–2 | 122 (50.8) | 76 (53.5) | 46 (46.9) | 0.523 | 79 (53.4) | 41 (55.4) | 0.789 |
| 3 | 74 (30.8) | 40 (28.2) | 34 (34.7) | 0.444 | 22 (29.7) | 22 (29.7) | |
| 4 or more | 44 (18.3) | 26 (18.3) | 18 (18.4) | 0.250 | 14 (19.9) | 14 (18.9) | |
| Progressive type onset | 25 (10.5) | 22 (15.5) | 3 (3.1) | 0.002 | 7 (4.7) | 4 (5.4) | 1 |
| Extensive skin involvement| 84 (35.4) | 51 (35.9) | 33 (34.7) | 0.468 | 59 (41) | 31 (42) | 0.576 |
| ECOG performance status | | | | | | |
| 0–1 | 185 (77.1) | 101 (71.1) | 84 (85.7) | 0.008 | 129 (87.2) | 65 (87.8) | 0.806 |
| 2 or higher | 55 (22.9) | 41 (28.9) | 14 (14.2) | 0.010 | 19 (12.8) | 9 (12.2) | 0.103 |
| Thrombocytopenia | 67 (27.9) | 49 (34.5) | 18 (18.4) | 0.008 | 34 (23.0) | 18 (24.3) | 0.696 |
| Eosinophilia | 86 (35.8) | 49 (34.5) | 18 (18.4) | 0.020 | 32 (42) | 31 (42) | 1.000 |
| Lymphopenia | 153 (64.0) | 98 (68.5) | 55 (56.1) | 0.021 | 89 (61) | 45 (62) | 0.613 |
| Calcinurin inhibitors in | 149 (62.1) | 99 (69.7) | 50 (56.1) | 0.003 | 87 (58.8) | 45 (60.8) | 0.616 |
AML acute myeloid leukemia, ALL acute lymphoblastic leukemia, MDS myelodysplastic syndrome, CML chronic myelogenous leukemia, MF myelofibrosis, MPD myeloproliferative disorder, CLL chronic lymphocytic leukemia, AA aplastic anemia, MM multiple myeloma, HLA human leukocyte antigen, GVHD graft-versus-host disease, cGVHD chronic GVHD, 95% CI 95% confidence interval
balanced in the two groups (Table 1). The PSM analysis factors for worse FFS.
After PSM, the characteristics of cGVHD were well-balanced in the two groups (Table 1). The PSM analysis confirmed the findings of superior outcomes in the PRD + AZP group. Two-year FFS was significantly better in the PRD + AZP (36.4%) than the PRD group (16.8%, \( p < 0.001 \)). The cumulative incidence of TFR for frontline treatment at 2 years was also lower in the PRD + AZP group (52.4% versus 70.1%, \( p = 0.013 \)). There were no significant differences in NRM or relapse rate at 2 years, but a trend towards longer OS was again observed in the PRD + AZP group of the PSM cohort (85.3% [72.6–92.4%] at 2 years in PRD + AZP group versus 75.9% [63.1–84.8%] in PRD group, \( p = 0.066 \)).
When confined to the same severity level according to the NIH consensus criteria, there was also a trend towards longer FFS in the PRD + AZP group; the favorable effect of PRD + AZP was statistically significant in the subgroup with moderate grade of cGVHD [FFS at 2 years (%); 30.5 versus 9.1, \( p = 0.001 \)], but not in the mild and severe grades. Similar results were obtained for the cumulative incidence of TFR of frontline treatment at 2 years among the patients with moderate cGVHD; 56.2% (41.6–68.6%) in the PRD + AZP group and 71.4% (46.8–81.7%) in the PRD group (\( p = 0.035 \)).
In addition, it was found that tapering of PRD dose < 0.5 mg/kg/day was more successful in the PRD + AZP group than in the PRD group: the cumulative incidence of PRD < 0.5 mg/kg/day at 6 months was 90.5% in the PRD group and 71.4% in the PRD + AZP group (\( p = 0.018 \)).
Although PSM analysis performed to overcome and control the imbalance of patients’ characteristics between PRD and PRD + AZP groups, the results of this study should be interpreted with caution given the nature of the retrospective analysis of this study, which would be weak evidence to support the role of AZP in cGVHD treatment compared the previous trial [7]. However, AZP added to a PRD-based regimen as the first-line treatment for cGVHD seems to improve FFS and may have a role as a steroid-sparing agent in the modern allo-HCT era. Since two thirds of the patients who required PRD-based treatment for cGVHD experienced the TF at 2 years, a better treatment...
strategy would be required. AZP could be worth reconsidered as a relevant option for a steroid sparing agent in cGVHD treatment.
Acknowledgements This study was presented in abstract form at the 56th annual meeting of the American Society of Hematology, Orlando, FL, December 6, 2015. Abstract 3126.
Compliance with ethical standards
Conflict of interest The authors declare that they have no competing interests.
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 license, and indicate if changes were made. The images or other third party material in this article are included in the article’s Creative Commons license, unless indicated otherwise in a credit line to the material. If material is not included in the article’s Creative Commons license 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 license, visit http://creativecommons.org/licenses/by/4.0/.
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Site-Controlled Telecom Single-Photon Emitters in Atomically-thin MoTe$_2$
Huan Zhao
Center for Integrated Nanotechnologies, Materials Physics and Application Division, Los Alamos National Laboratory
Micahel Pettes
Center for Integrated Nanotechnologies, Materials Physics and Application Division, Los Alamos National Laboratory
Yu Zheng
Center for Integrated Nanotechnologies, Materials Physics and Application Division, Los Alamos National Laboratory
Han Htoon (mailto: [email protected])
Center for Integrated Nanotechnologies, Materials Physics and Application Division, Los Alamos National Laboratory
https://orcid.org/0000-0003-3696-2896
Letter
Keywords: quantum emitters (QEs), MoTe2, quantum communication, transduction research
Posted Date: July 23rd, 2021
DOI: https://doi.org/10.21203/rs.3.rs-452814/v2
License: ☺️ This work is licensed under a Creative Commons Attribution 4.0 International License. Read Full License
Version of Record: A version of this preprint was published at Nature Communications on November 19th, 2021. See the published version at https://doi.org/10.1038/s41467-021-27033-w.
Abstract
Quantum emitters (QEs) in two-dimensional transition metal dichalcogenides (2D TMDCs) have advanced to the forefront of quantum communication and transduction research. To date, QEs capable of operating in O-C telecommunication bands have not been demonstrated in TMDCs. Here we report a deterministic creation of such telecom QEs emitting over the 1080 to 1550 nm wavelength range via coupling of 2D molybdenum ditelluride (MoTe2) to strain inducing nano-pillar arrays. Our Hanbury Brown and Twiss experiment conducted at 10 K reveals clear photon antibunching with 90% single photon purity. The photon antibunching can be observed up to liquid nitrogen temperature (77 K). Polarization analysis further reveals that while some QEs display cross-linearly polarized doublets with ~1 meV splitting resulting from the strain induced anisotropic exchange interaction, valley degeneracy is preserved in other QEs. Valley Zeeman splitting as well as restoring of valley symmetry in cross-polarized doublets are observed under 8T magnetic field.
Main Text
Quantum emitters (QEs) that emit one photon at a time are key building blocks for numerous quantum technology protocols such as quantum communications, quantum information processing, and quantum key distribution. In particular, QEs operating in the telecom bands (1.25–1.55 mm) are highly desired for implementation of quantum technologies through existing fiber-based optical communication networks. Currently, telecom-compatible QEs have been demonstrated in various III-V semiconductor quantum dots and recently in functionalized carbon nanotubes. However, several challenges such as accurate site positioning and efficient polarization control still remain for these QEs. Over the past decade, two-dimensional (2D) semiconductors have emerged as a novel platform for both fundamental research and technological applications. Leveraged by the unique membrane-like geometry, 2D semiconductors are promising for QEs as they offer high photon extraction efficiency, easy coupling to external fields, and convenient integration with photonic circuits. In addition, strain engineering can be readily applied to accurately position the emission sites. Most importantly, 2D transition metal dichalcogenides (TMDCs) have a valley degree of freedom that can be manipulated and accessed through circularly polarized excitonic optical transitions and efficiently tuned via a magnetic field, bringing new quantum functionalities to embedded QEs. Recently, 2D QEs have been demonstrated in WSe2 and hexagonal boron nitride, covering a broad emission spectrum range from ~500–800 nm. However, Single-Photon emitter (SPE) in the most desirable spectral range – the telecom bands – has never been explored in 2D systems. While most 2D semiconductors have inherent electronic band structures that limit the operating wavelength to the visible range, alpha-phase 2H-MoTe2 has a layer-dependent bandgap in the NIR regime, holding promise for telecom-compatible single photon emission.
We demonstrate the first observation of telecom single-photon emission in MoTe2 mono- and few-layers. We transferred mechanically exfoliated MoTe2 thin flakes onto nanopillar arrays to introduce strain-induced exciton localization potential (see Methods and Supplementary Section S1). We observed QEs in
both monolayer and relatively thick (>10 layers) MoTe₂ flakes. **Figure 1a** is an optical image of a MoTe₂ monolayer on nanopillar arrays. The corresponding wide-field photoluminescence (PL) image, **Figure 1b**, shows significantly brighter PL emission in strained region. Unstrained monolayer MoTe₂ features two dominant emission peaks at cryogenic temperature: exciton (X⁰) emission at around 1050 nm and trion (X⁻) emission at around 1070 nm (**Figure 1c**). With localized strain, a series of narrow PL peaks covering a broad spectral range of 1080 – 1150 nm emerges from the lower energy side of the spectrum (**Figure s3**). We attribute these PL peaks to the localized exciton states arising from strain induced hybridization of dark exciton and the defect states. The linewidths of the QE PL emission range from a few meV to sub-meV at 10 K temperature, which are nearly an order of magnitude narrower than the linewidths of the 2D exciton PL peaks (~ 10 meV). The narrow near-band-edge emission lines are also frequently observed in 2–4 layerd samples but are not seen in much thicker flakes. **Figure 1d** shows a typical narrow PL peaks from a QE that displays a linewidth (full width at half maximum, FWHM) of 920 meV. The peak is accompanied by a weak shoulder peak at ~ 2.5 meV higher energy side. Both the width and shape of this PL peak remain essentially unchanged over nearly 3 order of magnitude change in pump power. The PL intensity also vary linearly with pump power and only shows a weak saturation at powers >300 nW (**Figure 1e**).
To access the single photon emission characteristics of the QEs, we performed time-tagged, time-correlated single photon counting and Hanbury Brown-Twiss (HBT) experiments. The PL intensity time trace, PL decay curve and second-order correlation at zero time delay, or g²(0), was extracted from the photon stream. **Figure 2a** displays the PL spectrum of a strain-induced localized emitter, of which the measurement results are presented in **Figure 2b-d**. The PL decay curve (**Figure 2b**) shows a near-perfect single-exponential decay with a lifetime t = 22.2±0.1 ns that is four orders of magnitude longer than that in pristine MoTe₂ (~2 ps). This long lifetime provides a clear indication that localization of the exciton in a strain induced potential trap suppress non-radiative recombination through defects states that dominate the decay of 2D band-edge excitons.
Quantum-dot-like solid-state QEs typically have instability issues such as photon bleaching, blinking, and spectral diffusion, which hinders applications. We monitored the time-dependent PL emission under both pulse and CW laser excitation (**Figure 2b, inset, Figure s4a**), revealing a stable emission at average count rates of 1.2 kHz for pulse (9 kHz for CW) excitation without detectable photo-bleaching or blinking over the timescales presented. A time series of PL spectra also show no spectral diffusion (**Figure s6**). **Figure 2c and 2d** present the photon correlation under pulsed [g²(0) = 0.058±0.003] and CW [g²(0) = 0.181±0.030] excitation, respectively. Both values are well below the photon antibunching threshold of g²(0) = 0.5, which unequivocally reveals that the strain-induced MoTe₂ localized emitter is indeed a QE. HBT experiment conducted on a different emitter at 40 K and 77 K have further evinced that the single photon emission behavior can survive up to liquid nitrogen temperature, although the PL emission decreases significantly (**Figure s5**). Normalizing the measured count rates of QE of Figure 2 with the overall collection efficiency of our microPL system at 1108 nm (0.035%) (**Supplementary Section S3**), we
estimate the corrected emission rate of the QE to be 3.4 MHz for pulse (25.6 MHz for CW) excitation. Assuming that an exciton is localized into the QE in every excitation cycle, we can further deuce the radiative recombination efficiency of the QE to be \~7% from the ratio between the corrected emission rate under pulse excitation and the 48.5 MHz pulse excitation rate.\textsuperscript{14,25,26} This low efficiency could result from thermal hopping of excitons out of the shallow trapping potential. The efficiency increases significantly when the QE is isolated in energy from the band-edge (see below).
Obtaining telecom-compatible QEs that emit at around 1.3 mm (O-band, “original band”) and 1.55 mm (C-band, “conventional band”) are required for fiber-based quantum communications. When increasing the MoTe\textsubscript{2} layer numbers from monolayer to bulk, the bandgap of MoTe\textsubscript{2} decreases from 1.18 eV (1050 nm) to 0.95 eV (1300 nm) monotonically.\textsuperscript{20} The PL intensity also decreases orders of magnitude due to a direct-to-indirect bandgap transition commonly observed in 2D TMDCs. In our experiment, we observe bright localized telecom-band emissions from strained few-layer MoTe\textsubscript{2} although we have occasionally found such emissions in mono- and bilayer samples (Supplementary Section S6- S8). Figure 3a and Figure s7a,b present PL spectra of telecom-wavelength emitters. We typically observe such highly red-shifted bright emissions spanning 1.25–1.55 mm, covering the full telecom window. Figure s8 shows that such QEs, emitting at wavelength longer than 1300 nm are created in a 5-6 layer thick MoTe\textsubscript{2} at almost all the nano-pillar sites. In contrast to near-band-edge QEs, these are characterized by relatively broad linewidths (FWHM 7–30 meV). Figure 3b is the PL spectrum of a telecom QE, of which PL dynamics and photon correlation results are presented in Figure 3c-3f, respectively. We observed an initial PL decay with a lifetime of 163 ± 3 ns, followed by an ultra-long lifetime of 1.13 ± 0.01 ms. This ultra-long lifetime is attributed to the dominant PL peak at lower energy, confirmed by comparing the integrated PL counts from the TRPL curve with the PL counts in spectrum (details given in Supplementary Section S9). The measured lifetime is 6 orders of magnitude longer than that of the MoTe\textsubscript{2} band-edge emission and is of 2–3 orders larger than that of the near-band-edge QEs. Based on this long lifetime and the fact that these telecom-QEs are observed more on multilayer thick MoTe\textsubscript{2}, we tentatively attribute the telecom-QEs to indirect excitonic transitions, which are activated by strain induced quantum confinement potentials. Figure 3d show that this telecom-QE is also free from blinking or photon bleaching over 5000 s experiment time. The HBT experiment under pulsed excitation for the spectral window shown in Figure 3b yield a \(g^{2}(0) = 0.48\pm0.03\) (Figure 3e). Since this measurement includes contribution from a high-energy shoulder that exhibits shorter PL decay, we employed a time gated \(g^{(2)}\) experiment\textsuperscript{27} (Supplementary Section S10), in which only the photons arriving after the decay of the higher energy shoulder (i.e. after 200 ns delay) were analyzed for the \(g^{(2)}\) trace. The time gated \(g^{(2)}\) in Figure 3f shows \(g^{2}(0) = 0.155\pm0.009\) clearly proving the antibunching nature of the 1540 nm telecom emitter. Our result is the first ever demonstration of a 2D, telecom C-band QE. HBT experiments of other two QEs emitting at 1340 (O-band) and 1200 nm yielding \(g^{2}(0)\) of 0.28 ± 0.02 and 0.26 ± 0.02 respectively are also shown in Figure s9. Using overall collection efficiency of the our micro PL system at 1550 nm (0.31%) (Supplementary Section S3) and 303 kHz pulse excitation rate, we can estimate the absolute emission rate and radiative recombination efficiency of the QE of Fig. 3 to be 258 kHz and 85%,
respectively. The radiative efficiency of the telecom QEs is significantly higher than that of the near-band-edge QEs because the deep trapping potential of the telecom QEs could strongly suppress thermal detrapping of exciton which is believed to be responsible for low radiative efficiency of band edge QEs. This fact is also consistent with the extra-long PL lifetime of the telecom QEs. While this long PL lifetime is not favorable for SPE applications, it can be improved through plasmonic enhancement.
To investigate the valley physics of QEs in MoTe₂, we conducted polarization-resolved magneto-PL spectroscopy with a field normal to the sample surface (Faraday geometry). Figure 4a presents a helicity-resolved PL of a MoTe₂ QE. The spectra was taken with s + excitation and analyzed for both s + and s – helicities. The valley Zeeman splitting was not observed in the absence of a magnetic field but rose with increasing field, indicating a lifting of valley degeneracy. Using the relation between the energy splitting $\Delta E$ and the magnetic field $B$, $\Delta E = -g \mu_B B$, where $\mu_B$ is the Bohr magneton, we extracted a Landé $g$-factor of -3.61±0.02 for the QE (Supplementary Section S11), which is comparable with $g$-factors reported in other work. At zero field, the degree of circular polarization, $P_C = (I_{\sigma+} - I_{\sigma-})/(I_{\sigma+} + I_{\sigma-})$ was 13% as a result of the valley-selective-pumping effect. Significant valley polarization was observed with an applied magnetic field, reaching 52% at 8 T, which is more pronounced compared to the 30% polarization reported in magnetic-field induced valley polarization of intrinsic MoTe₂ excitons. These results indicate a vanishing fine structure splitting of the QE at zero field, which could be exploited for entangled photon generation through the biexciton/exciton cascade.
We also observed emission pairs in some of the QEs, which were found to be cross-linearly polarized doublets with sizeable zero-field energy splitting (1-3.7 meV) (Figure 4b and Supplementary Section S12). The two peaks from the doublet have a zero-field splitting of 1.09 meV and reach their maximal PL intensities in opposite linear polarization directions (horizontal/vertical), indicating the presence of fine structure. The observed cross-polarization and zero-field energy splitting have also been reported in III-V quantum dots and recently in WSe₂ QEs. Following prior studies, we attribute this fine-structure splitting to hybridization of K and K' valley polarized excitons by an asymmetric potential landscape defined by the localized strain as illustrated in Figure 4d. When the magnetic field is strong enough to overcome the anisotropic Coulomb potential (i.e. $\Delta E_{ZS} > \Delta E_0$), the linearly polarized states vanish and circularly polarized states are recovered. This restoration of valley symmetry is achieved in our QE under an 8 T magnetic field (Figure 4c).
**Methods**
**Sample Preparation.** MoTe₂ flakes were mechanically exfoliated from a flux-grown bulk crystal before they were transferred onto pre-patterned substrates. Thin layers (that is, flakes that look greenish and translucent under an optical microscope) were selected for further optical characterizations. 1-4 layer flakes can be easily distinguished by analyzing the band-edge emission wavelength and PL intensity. Flakes thicker than four layers do not have a detectable band-edge emission using mW level pump power. To prepare the strained substrates, a 50 nm Au layer was deposited on top of a Si/SiO₂ substrate to block
silicon emission, followed by the spin-coating of a 50 nm polyvinyl alcohol (PVA) dielectric layer to avoid quenching effects. Then, a ~120 nm polymethyl methacrylate (PMMA) layer was spin-coated on top of the PVA layer and patterned by electron beam lithography into PMMA nanopillar arrays with a 3 mm pitch width. A 90°C vacuum annealing was applied to enhance the contact between the 2D flakes and the nanopillars. Each pillar had a ~100 nm pillar height and a ~150 nm diameter. Note: later we found the PVA spacer layer was not necessary as the ~100 nm PMMA pillars were sufficient to separate the MoTe₂ dots from the gold layer and maintain efficient PL emission.
**Optical Characterization.** A diagram of our optical measurement setup is presented in Supplementary Section S13. Micro-PL measurements of MoTe₂ QEs were performed on a home-built confocal microscope with excitation of either an 850 nm CW Ti:sapphire laser or an 850 nm supercontinuum pulsed laser. The excitation power was typically a few mW. Samples were mounted in a continuous flow cryostat and cooled to 10–13 °K using liquid helium. The emitted light was collected through a 50x infrared objective lens (Olympus, 0.65 NA) and spectrally filtered before entering a 2D InGaAs array detector (NIRvana 640LN, Princeton Instruments). We used 150 and 300 gr/mm gratings to resolve the spectra. For TRPL and HBT experiments, the emission signal was spectrally filtered before coupled into a 50:50 optical fiber beamsplitter, which equivalently split the signal into two beams and sent them into two channels of a superconducting nanowire single-photon detector (Quantum Opus). PL intensity time trace, PL decay curves and $g^2(t)$ traces were obtained from photon detection events recorded by a PicoQuant HydraHarp 400 time-correlated single photon-counting module. We applied a bi-exponential decay model to determine the CW $g^2(0)$ value and error level. For pulsed auto-correlation measurements, $g^2(0)$ was extracted by comparing the integrated photon coincidence counts at the zero-time delay peak with the averaged integrated photon coincidence counts at 30 adjacent peaks. The error level of pulsed $g^2(0)$ was defined by the standard deviation of the integrated photon coincidence counts in the adjacent peaks. For the pulsed $g^2(0)$ measurement of the 1540 nm peak, a time gate of 200 ns was applied to significantly reduce the contribution from the undesired emissions that could not be fully removed by optical filters.
For magneto spectroscopy and polarization-resolved PL measurements, the sample was placed inside the room temperature bore of an 8.5 T liquid-helium cooled superconducting magnet. For linear polarization analysis, the excitation beam was fully depolarized using a laser depolarizer to eliminate the polarization memory effect. A half-wave plate (HWP) was inserted into the collection channel to rotate the polarization direction. A Wollaston prism was placed between the HWP and the InGaAs detector to spatially split the emission into horizontal and vertical components, followed by a depolarizer to avoid effects arising from the linear polarization dependence of the gratings. For circular polarization analysis, a quarter-wave plate (QWP) was inserted into the shared path of the excitation and the emission beams. As a result, the QWP turns the linearly polarized laser into a circularly polarized excitation source and converts the circularly polarized PL signals into linearly polarized beams. A HWP and a Wollaston prism were installed in the collection beam to spatially split the $s^+$ and $s^-$ emissions into two different areas on the 2D InGaAs array.
Declarations
Acknowledgement
The authors would like to acknowledge the helpful discussion and technical support from Dr. Christopher Lane, Dr. Jianxin Zhu, Dr. Andrew Jones and Mr. John Kevin Scott Baldwin. This work was performed at the Center for Integrated Nanotechnologies, an Office of Science User Facility operated for the U.S. Department of Energy (DOE) Office of Science. Los Alamos National Laboratory (LANL), an affirmative action equal opportunity employer, is managed by Triad National Security, LLC for the U.S. Department of Energy's NNSA, under contract 89233218CNA000001. Deterministic quantum emitter creation capability was developed under the support of DOE BES, QIS Infrastructure Development Program BES LANL22. HZ, YZ and HH acknowledge partial support form Laboratory Directed Research and Development (LDRD) program 20200104DR. HH is also partially supported by Quantum Science Center. MTP is supported by LDRD 20190516ECR. HZ also acknowledge a partial support from LANL Director’s Postdoctoral Fellow Award.
Author contributions
HZ and HH conceived the experiment. HZ, under the supervision of HH, primarily developed deterministic QE creation approach, designed and conduct the experiment, analyzed the data and composed the paper. YZ assisted in the experiment. MTP assisted in the design of the nanopillar samples and paper preparation.
Competing financial interests
The authors declare no competing financial interests.
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29. Gammon, D., Snow, E., Shanabrook, B., Katzer, D. & Park, D. Fine structure splitting in the optical spectra of single GaAs quantum dots. *Phys. Rev. Lett.* **76**, 3005 (1996).
30. Gammon, D., Snow, E., Shanabrook, B., Katzer, D. & Park, D. Homogeneous linewidths in the optical spectrum of a single gallium arsenide quantum dot. *Science* **273**, 87-90 (1996).
**Figures**
Figure 1
a, Optical image of a monolayer MoTe2 flake (with a tiny folded bilayer region outlined in black) on nanopillar arrays. The MoTe2 flake is outlined by yellow dashed lines. Scale bar: 5 mm. Inset: SEM image of a nanopillar coated with monolayer MoTe2, displaying a tent-shaped strain profile. Scale bar of the inset: 500 nm. b, Wide-field PL image of the same flake. The brighter areas, indicating stronger emission, are consistent with the pillar locations in a. Scale bar: 5 mm. c, PL spectrum of a MoTe2 monolayer on flat PMMA (lower panel) and the PL spectrum of a MoTe2 monolayer sitting on a nanopillar (upper panel) acquired at laser excitation power of 0.8 mW and 30s integration time. The MoTe2 exciton and trion peaks are identified. d, PL spectra of a representative localized MoTe2 emitter acquired at 3.3 mW and 5.5 nW pump power showing invariant shape and width (920 µeV at FWHM) of the spectral line. e, Pump-power-dependent emission intensity of the PL peak presented in Figure 1d shows near-perfect linear scaling with pump power. The red dash line is to guide the eye. All experimental data were taken at 11 K temperature.
Figure 2
a, PL spectrum of a localized MoTe2 emitter. The data of b, c, d are taken from this dot with a band pass filter that allows the shadowed region to be detected. b, the PL decay curve (red) and a single exponential decay fit (green) with a $22.2 \pm 0.1$ ns extracted lifetime. Inset plots the PL intensity as a function of experiment time showing stability of the single photon emission rate over 1 hour time. The modulation observed over the long time scale (~100 s) is mainly due to sample drift relative to the laser excitation spot. c, Second-order correlation measurement under a 850 nm pulse excitation with a 2.1 MHz repetition rate, from which a $g^2(0) = 0.058 \pm 0.003$ is extracted. d, Second-order correlation measurement under a 850 nm CW laser excitation. The red curve is a fit to the data using a bi-exponential decay function. The extracted $g^2(0) = 0.181 \pm 0.030$. All the experimental data were taken at 11 K temperature.
Figure 3
a, “O-band” and “C-band” telecom PL emissions from two multilayer MoTe2 localized emitters. b, MoTe2 quantum dot with a 1540 nm telecom emission peak and a small shoulder peak at 1510 nm. The blue and red lines are Gaussian fits to the 1540 and 1510 nm peaks, respectively. The data of c-f are taken from this dot with a band pass filter that allows the shadowed region to be detected. c, PL decay curve (red) and a bi-exponential decay fit (green) reveal the lifetime of the 1540 nm peak is $1.13 \pm 0.01$ ms. d, Time-dependent PL counts showing a stable emission over 5000 seconds. Data is recorded every 500 ms. e, Second-order correlation measurement under a 850 nm pulsed excitation with a 330 kHz repetition rate, from which $g^2(0) = 0.48 \pm 0.03$ is extracted. f, Time-gated $g(2)$ experiment shows $g^2(0) = 0.155 \pm 0.009$ under a 200 ns time gate. All experimental data were taken at 13 K temperature.
Figure 4
a, Helicity-resolved magneto-PL data of a MoTe2 localized emitter. The emitter was excited using a s+ polarized laser. b, The PL spectrum of a linearly cross-polarized doublet measured at zero field, showing a fine-structure energy splitting of ~1.1 meV. H and V denote horizontal and vertical polarization detection directions, respectively. c, Spectrum of the same doublet under an 8 T magnetic field, showing the doublet is converted to a circular cross-polarized pair. The excitation is a s+ polarized laser. The lines in a-c are Gaussian peak fits to the PL data. d, Energy diagram of the doublet as a function of the external magnetic field. The linearly-polarized states are converted into s+ and s− circularly polarized states once the Zeeman energy ($\Delta E_{ZS}$) exceeds the zero-field fine-structure splitting energy ($\Delta E_0$). The ground state is denoted as $|0\rangle$. All experimental data were taken at 11 K temperature.
Supplementary Files
This is a list of supplementary files associated with this preprint. Click to download.
- MoTe2SPESuppInfoNatPHotonsubmit.docx
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Changes in Nuclear Orientation Patterns of Chromosome 11 during Mouse Plasmacytoma Development
Abstract
Studying changes in nuclear architecture is a unique approach toward the understanding of nuclear remodeling during tumor development. One aspect of nuclear architecture is the orientation of chromosomes in the three-dimensional nuclear space. We studied mouse chromosome 11 in lymphocytes of [T38HxBALB/c]N mice with a reciprocal translocation between chromosome X and 11 (T38HT(X;11)) exhibiting a long chromosome T(11;X) and a short chromosome T(X;11) and in fast-onset plasmacytomas (PCTs) induced in the same strain. We determined the three-dimensional orientation of chromosome 11 using a mouse chromosome 11 specific multicolor banding probe. We also examined the nuclear position of the small translocation chromosome T(X;11) which contains cytoband 11E2 and parts of E1. Chromosomes can point either with their centromeric or with their telomeric end toward the nuclear center or periphery, or their position is found in parallel to the nuclear border. In T38HT(X;11) nuclei, the most frequently observed orientation pattern was with both chromosomes 11 in parallel to the nuclear border (“PP”). PCT cells showed nuclei with two or more copies of chromosome 11. In PCTs, the most frequent orientation pattern was with one chromosome in parallel and the other pointing with its centromeric end toward the nuclear periphery (“CP”). There is a significant difference between the orientation patterns observed in T38HT(X;11) and in PCT nuclei (\( P < .0001 \)).
Introduction
Chromosomes are organized in evolutionary conserved chromosome territories [1]. Their nonrandom three-dimensional (3D) positions were previously described [2], e.g., the localization of the active and inactive chromosome X and their respective genes [3,4]. Euchromatin of rod photoreceptor cells in nocturnal mammals is found in the periphery, whereas it is found in the center in diurnal mammals [5]. Not only chromosome territories are in the focus of research but also the localization of telomeric regions [6,7].
Tumor development is greatly influenced by genomic instability [8], and telomere dysfunction plays an important role in genomic instability [9]. Therefore, it is essential to study nuclear architecture in normal and tumor cells. Movement of telomeric regions during the cell cycle was observed in living ECV-TRF1 and -TRF2 cells [10] and in human osteosarcoma U2OS cells [11]. Chromosomes of primary human fibroblasts alter their positions within 15 minutes after they are made quiescent due to a removal of serum from the culture medium. This repositioning is probably dependent on nuclear myosin 1B [12]. Further changes of chromosome positions can be found during adipocyte differentiation [13] or T-cell differentiation [14].
Telomere lengthening is a method to prevent genomic instability of rapidly dividing cells [15]. This can occur due to telomerase [16] or due to cycles of homologous recombination during the process of...
alternative telomere lengthening [17]. In fast-onset plasmacytomas (PCTs), the telomere length is significantly increased for the translocation chromosome T(X;11) carrying 11E2 [18].
In the current study, we used a [T38HxBALB/c]N congenic mouse model with a reciprocal translocation between chromosomes X and 11 (rcpT(X;11)). This unique mouse model exhibits a long chromosome T(11;X) and a short chromosome T(X;11). The short chromosome T(X;11) contains cytoband 11E2 and parts of cytoband E1 (Figure 1) [19]. To determine the chromosome orientation in cancer cells and in the same cell lineage, we studied mouse PCT cells and [T38HxBALB/c]N rcpT(X;11) lymphocytes. There was a significant difference noted with respect to their chromosome 11 orientation (P < .0001). The nuclear position of the small translocation T(X;11) was also studied visually. It was most frequently found in the intermediate region of the nucleus. There was no significant change in position of T(X;11) detected between the two cell types (P = .06).
**Material and Methods**
**Cell Harvest**
Primary lymphocytes were harvested from spleens of 6- to 8-week-old congenic [T38HxBALB/c]N rcpT(X;11) mice [19]. PCT cells were harvested from the ascites of fast-onset PCT mice. The [T38HxBALB/c]N rcpT(X;11) mice were pretreated with pristane intraperitoneally and after 5 days infected with a v-abl/myc virus also administered intraperitoneally. The mean latency of fast-onset PCTs is 45 days [19,21]. Procedures were performed in accordance to Animal Protocol 11-019 approved by Central Animal Care Services, University of Manitoba (Winnipeg, MB, Canada).
**3D Nuclear Hybridizations**
For 3D nuclei fixation, lymphocytes were centrifuged at 1000 rpm for 10 minutes. After resuspension of the pellet, cells were carefully placed onto slides and fixed with 3.7% formaldehyde/1× PBS for 20 minutes at room temperature. Next, the slides underwent washing steps in 1× PBS shaking. Subsequently, the slides were washed in 0.5% Triton-X-100 for 10 minutes. The slides were incubated for 1 to 2 hours in 20% glycerol and were then subjected to four freeze-thaw cycles in liquid nitrogen afterward. Next, the slides were washed 3× in 1× PBS and then incubated in fresh 0.1 M HCl for 5 minutes. After washing the slides in 1× PBS, they were placed for at least 1 hour in 70% formamide/2× SSC.
**Multicolor Banding**
The mBANDing probe for mouse chromosome 11 (Metasystems, Altusheim, Germany) was developed by Benedek et al. (2004) [29]. The slides were equilibrated in 2× SSC, treated with RNAase A (100 μg/ml) in 2× SSC at 37°C for 1 hour, and then incubated in freshly prepared 0.01 M HCl with 100 μg/ml pepsin for 2 minutes. After washing the slides in 1× PBS, they were pretreated in 1% formaldehyde in 1× PBS/50 mM MgCl2, followed by washing in 1× PBS. Next, the slides were incubated in 0.1× SSC and then
transferred into 2× SSC at 70°C for 30 minutes for denaturation. After cooling the solution to 37°C, the slides were transferred to 0.1× SSC and then subjected to 0.07 M NaOH at room temperature for 1 minute. Afterward, the slides were placed in 0.1× SSC and then 2× SSC at 4°C followed by dehydration in ethanol (30%, 50%, 70%, and 90%). Next, the mBANDing probe was applied. The slides were sealed with rubber cement and incubated for 2 days at 37°C. After hybridization, the slides were washed in 1× SSC at 75°C and in 4× SSC/0.05% Tween20. The cells were counterstained with 4′,6-diamidino-2-phenylindole and mounted with ProLong Gold antifade (Invitrogen/Gibco, Burlington, ON, Canada).
**Image Acquisition**
For the two-dimensional image acquisition, an Axioplan 2 microscope (Carl Zeiss Ltd., Toronto, ON, Canada) with a 63×/1.4 oil objective lens (Carl Zeiss Ltd., Toronto, ON, Canada) and the ISIS-FISH imaging system 5.0 SR 3 (Metasystems Group Inc., Boston, MA) were used. The chromosomal counterstain was visualized with the help of a 4′,6-diamidino-2-phenylindole filter. To detect the four regions of chromosome 11 that were labeled with different fluorochromes (DEAC, FITC, Gold, and Texas Red), narrow band-pass filters were used (Chroma Technologies) as described by our group previously.
3D image acquisition was conducted using an AxioImager Z2 microscope (Carl Zeiss Inc. Canada) equipped with the same filters and an AxioCam MRm (Carl Zeiss Inc. Canada), combined with the Axiovision Release 4.8 software (Carl Zeiss Inc. Canada). Z-stacks of 80 slices, with 200-nm axial distance and 102-nm lateral pixel size, were acquired to reconstruct a 3D image. Using Axiovision Release 4.8 software (Carl Zeiss Inc. Canada), deconvolution was conducted with the constrained iterative algorithm (Schaefer et al., 2001).
**Image Analysis**
The results presented in this paper were analyzed by visual inspection. The chromosome 11 mBAND probe is composed of four different fluorochromes labeling four different overlapping regions of
---
**Table 1. Orientation Patterns of Chromosome 11 and Their Frequency in Diploid Cells of Congenic [T38HxBALB/c]N Mice Showing T(X;11) and in PCTs**
| T38H | Diploid PCTs | Triploid PCTs | Tetraploid PCTs | All PCTs |
|------|--------------|---------------|-----------------|----------|
| T[X;11] |
| Both homologs in parallel to the nuclear border (PP) | 90 | 24 | 24 |
| One copy points with telomeric end to the nuclear center; the other copy is in parallel (PT) | 35 | 19 | 19 |
| Both homologs point with their telomeric end to the nuclear periphery (TT) | 8 | 7 | 7 |
| One copy points with its telomeric end and the other copy with its centromeric end to the nuclear periphery (CT) | 15 | 7 | 7 |
| Both copies point with their centromeric ends to the nuclear periphery (CC) | 48 | 13 | 13 |
| One homolog points with its centromere to the nuclear periphery; the other is parallel to the nuclear border (CP) | 61 | 30 | 30 |
| CCC | 1 | 1 |
| CCP | 8 | 8 |
| CPP | 12 | 12 |
| CPT | 19 | 19 |
| CCT | 9 | 9 |
| CTT | 2 | 2 |
| TTT | 2 | 2 |
| PTT | 7 | 7 |
| PPT | 15 | 15 |
| PPP | 17 | 17 |
| CCCP | 1 | 1 |
| CCP | 4 | 4 |
| CPP | 4 | 4 |
| PPP | 5 | 5 |
| CPT | 3 | 3 |
| CPTT | 3 | 3 |
| CCPT | 3 | 3 |
| PPPT | 5 | 5 |
| PPTT | 1 | 1 |
The table shows the orientation patterns observed in the diploid T38HT[X;11] cells and in PCTs with two, three, or four copies of chromosome 11. The last column lists the orientation patterns in all PCT cells together (C = centromere points to periphery, T = telomere points to periphery, P = chromosome is parallel to nuclear periphery).
the whole chromosome 11. The telomeric end is labeled with FITC (green), the centromeric end with Texas Red (magenta), and the intermediate bands with DEAC (cyan blue) and Gold (red) (Figure 2). DEAC was not always detectable. The mBAND paint made it possible for the visual observer to determine the orientation of chromosome 11. To analyze the position of the small translocation chromosome T(X;11) labeled only with FITC (green), we divided the nucleus visually into three regions: periphery, intermediate, and center.
In addition, we used novel automated software to confirm our visual results [30]. In short, the nucleus was segmented first with an isodata threshold after some smoothing and out-of-focus blur subtraction. The chromosome bands were then segmented after the recorded images were blurred based on the band sizes. These bands were then linked together to chromosome territories based on a utility function determined by overlap and distance between the segmented bands. The orientation of each CT was then determined by calculating the eigenvectors of the inertia tensor; the orientation is indicated by the more outlying band. Consequently, the chromosome is pointing either with its telomeric end or with its centromeric end toward the nuclear periphery. Because an exact measurement is performed, no parallel orientation category is needed anymore.
The automatic analysis was only performed for the diploid cells. Automation of chromosome orientation by this program was not implemented for tri- and tetraploid cells. Therefore, we present the results assessed by visual inspection. Over 300 nuclei per cell type were acquired, and we were able to determine the orientation pattern in 224 PCT and 257 T38HT(X;11) nuclei.
### Statistical Analysis
The visually assessed orientation patterns were analyzed by chi-square, likelihood ratio chi-square, and Mantel-Haenszel chi-square tests. The nuclear positions of T(X;11) were compared by the same tests. They all led to the same result; only chi-square is shown in the paper.
The automatically measured orientation distributions were compared to each other with two-sample, two-sided Kolmogorov-Smirnov test. The two cell types that display each of the observed orientation patterns were compared using chi-square, likelihood ratio chi-square and Mantel-Haenszel chi-square tests. They yielded the same results.
### Results
In this study, we analyzed chromosome 11 orientation patterns in lymphocytes of PCTs and of T38HxBALB/cN repT(X;11) mice. We performed mBANDing and analysis on more than 300 nuclei of each cell type. The mouse chromosome 11 mBAND probe labels four overlapping segments with four fluorescing colors. The telomeric end is labeled with FITC Green, the centromeric end with Texas Red, and
the regions in between with Gold and DEAC (Figure 2). The segment labeled with DEAC was not always detectable. The mBANDed nuclei were imaged using Axiovision 4.8 Software (Carl Zeiss Inc. Canada) and deconvolved with a constrained iterative algorithm [31]. By visual inspection, we analyzed the orientation of chromosome 11 of the respective cell types and subsequently determined orientation patterns. Nuclei of T38HT(X;11) lymphocytes consistently showed a diploid chromosome constitution, whereas nuclei of PCTs either were diploid or showed an increase in chromosome 11 copy numbers. Moreover, we identified the position of the small translocation chromosome T(X;11) in all nuclei of T38HT(X;11) and PCT.
By visual inspection, we observed three different orientations in nuclei of T38HT(X;11) and PCTs: 1) chromosome 11 points with its telomeric end to the nuclear periphery and with its centromeric end to the nuclear center ("T"); 2) it points with its centromeric end to the nuclear periphery and with its telomeric end to the center ("C"); and 3) chromosome 11 is in parallel to the nuclear border ("P"). Combining the observed orientations of all chromosomes in one nucleus, we determined an orientation pattern. All observed orientation patterns are shown in Table 1. The most frequently observed orientation pattern in T38HT(X;11) was with both chromosomes located in parallel to the nuclear border ("PP") (35.0%). In all PCTs, "PP" was only observed in 10.7% (P < .01). The orientation pattern "CP" with one homolog pointing with its centromeric end toward the nuclear periphery and the other homolog being in parallel was found most frequently in PCTs (13.4% of all PCTs) and in 23.7% of T38HT(X;11) (P = .83). Both chromosomes
pointing with their centromeric ends toward the periphery ("CC") was observed in 18.7% of T38HT(X;11) and in 8.5% of all PCTs (P = .0001). The third most common orientation pattern in PCTs is "PT," with one homolog in parallel and the other pointing with its telomeric end to the periphery (8.5%). This orientation pattern was found in 13.6% of T38HT(X;11) (P < .01). Representative images of diploid PCT and T38HT(X;11) nuclei analyzed visually and automatically are illustrated in Figure 3.
Ninety-two of 224 (41.1%) PCT nuclei showed three copies of chromosome 11 (Table 1). The orientation pattern "CPT," with one copy pointing with its telomeric end and another copy with its centromeric end toward the nuclear periphery and one copy located in parallel, was also observed in 8.5% of all PCTs. The second most frequently orientation pattern in PCTs with three copies of chromosome 11 is "PPP," with all homologs located in parallel (7.6%).
Twenty-three of 224 (10.3%) PCT nuclei showed four copies of chromosome 11 (Table 1). Images of PCT nuclei with more than two copies of chromosome 11 can be seen in Figure 4.
When comparing T38HT(X;11) nuclei to all PCT nuclei with respect to their orientation patterns, a significant difference was noted (P < .0001). Regarding only diploid cells of PCTs and T38HT(X;11), there was no significant difference (P = .10). However, comparing diploid PCTs to PCTs with three or four copies of chromosome 11, a significant difference was noted (P < .0001).
For unknown reasons, the small translocation chromosome T(X;11) carrying cytoband 11E2 was only detected in 31.3% of all 224 mBANDed PCT nuclei and in 34.6% of the 257 mBANDed T38HT(X;11) nuclei. The most frequently observed position was in the intermediate region of the nucleus (61.8% of T38HT(X;11) and 74.3% of PCTs, respectively; P = .10) (Table 2). There is no significant difference between the two cell types regarding the position of T(X;11) (P = .0612). An image showing T(X;11) is demonstrated in Figure 4.
**Discussion**
We used mBANDing to determine the orientation of chromosome 11 in PCTs and lymphocytes of [T38HxBALB/c]N mice showing T(X;11) and in diploid, triploid, and tetraploid PCTs.
**Table 2. Nuclear Position of the Small Translocation Chromosome T(X;11) in Cells of Congenic [T38HxBALB/c]N Mice Showing T(X;11) and in Diploid, Triploid, and Tetraploid PCTs**
| Nuclear Position | T38H T[X;11] | All PCTs | Chi-Square |
|-----------------|-------------|----------|------------|
| Periphery | 14 (15.7%) | 12 (17.1%)| .81 |
| Intermediate | 55 (61.8%) | 52 (74.3%)| .10 |
| Central | 20 (22.5%) | 6 (8.6%) | .02 |
The nuclear positions of T(X;11) were compared by chi-square analysis. There is no significant difference between the two cell types regarding the nuclear position of T(X;11) (P = .06). A chi-square value of P > .05 indicates that the frequency of the T(X;11) position is similar between the two cell types.
We used mBANDing to determine the orientation of chromosome 11, a significant difference was noted (P < .0001). The third most common orientation pattern in PCTs with three or four copies of chromosome 11, we found various orientation patterns (Table 1), e.g., the orientation pattern “CPT” (one homolog is pointing with its centromeric end and another with its telomeric end toward the nuclear center, and a third is in parallel) in 8.5% of all PCTs. When comparing PCT nuclei with three or four chromosome 11 copies to diploid PCT nuclei, a significant difference was noted (P < .0001). Furthermore, when comparing T38HT(X;11) to all PCT nuclei, we identified different orientation patterns (P < .0001).
The small translocation chromosome T(X;11) was analyzed visually and found in the intermediate region of the nucleus in 74.3% of the PCTs and in 61.8% of T38HT(X;11) (P = .10) (Table 2).
In our previous paper, we presented nonrandom orientation patterns for chromosome 11 in 3D nuclei of PreB lymphocytes of BALB/c origin and of [T38HxBALB/c]N wild-type mice [26]. There was a distinct difference between the frequency of the observed orientation patterns, and this was found in both cell types. The orientation pattern most frequently observed was with both chromosomes 11 in parallel to the nuclear periphery ("PP"). The second most common pattern was with one homolog in parallel and the other homolog pointed with its centromeric end toward the nuclear periphery ("CP").
The focus of the current study is the 3D nuclear orientation of chromosome 11 in mouse PCTs. We investigated changes in the nuclear orientation during the process of PCT development.
Nuclear architecture is important for nuclear function [5,9]. It is known that telomere dysfunction leads to genomic instability and therefore to tumorigenesis. Key factors of telomere dysfunction are the shortening of telomeres, breakage-bridge-fusion cycles, and the formation of telomeric aggregates (TAs) [32–34]. A trigger for TA formation is c-Myc deregulation [35]. Louis et al. (2005) described not only that c-Myc deregulation leads to TA formation resulting in breakage-bridge-fusion cycles but also that changes of nuclear positions lead to closer proximity of telomeres, resulting in chromosomal rearrangements [35]. Changes in chromosome orientation may also lead to closer proximity of telomeres and could therefore be linked to telomere aggregation.
Rotation is a way of movement and a possible way to change nuclear positions. The mechanisms of a possible rotation are currently unknown. One may hypothesize that chromosomes rotate to access transcription factories. The transcription of genes within the telomeric end 11E2 might be enhanced due to telomeric orientation toward the nuclear center. Future studies will elucidate these questions.
In conclusion, we found distinct 3D orientation patterns of mouse chromosome 11 in diploid lymphocytes of [T38HxBALB/c]N recP(X;11) mice and of PCTs. How and whether the changes of the orientation patterns in PCT nuclei with three or four chromosomes 11 impact on tumor progression will be the focus of future studies.
**Acknowledgements**
This study was supported by the Canadian Institutes of Health Research. A. K. S. received a travel award from Bayer. We thank Mary Cheang for statistical analysis. The authors declare that they have no competing interests.
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Predicted Composite Signed-Distance Fields for Real-Time Motion Planning in Dynamic Environments
Mark Nicholas Finean, Wolfgang Merkt, and Ioannis Havoutis
Oxford Robotics Institute, University of Oxford
{mfinean, wolfgang, ioannis}@robots.ox.ac.uk
Abstract
We present a novel framework for motion planning in dynamic environments that accounts for the predicted trajectories of moving objects. We explore the use of composite signed-distance fields in motion planning and detail how they can be used to generate signed-distance fields (SDFs) in real-time to incorporate predicted obstacle motions; to achieve this, we introduce the concept of predicted signed-distance fields. We benchmark our approach of using composite SDFs against performing exact SDF calculations on the workspace occupancy grid. Our proposed technique generates predictions substantially faster and typically exhibits an 81–97% reduction in time for subsequent predictions. We integrate our framework with GPMP2 to demonstrate a full implementation of our approach in real-time, enabling a 7-DoF Panda manipulator to smoothly avoid a moving obstacle in simulation and hardware experiments.
1 Introduction
To integrate autonomous systems into our daily lives, we need to ensure that they operate safely in the dynamic world around them. We must, therefore, develop robots that can adapt their movements as necessary to avoid moving obstacles. This holds whether we consider robots in a household environment avoiding humans and pets, autonomous vehicles on a road avoiding other cars and pedestrians, or robots operating in a dynamic industrial setting.
There has been significant research into motion planning; however, the current ability of robots to react in dynamic environments, with moving obstacles, is still lacking. Many approaches rely on fast re-optimisation to account for changes in the environment, yet do not account for the predicted motions of the obstacles. By neglecting predicted motions, robots encounter failure cases, as depicted in Figure 2, where depending on the speed of the obstacle, the robot repeatedly plans to move in front of the moving obstacle. This scenario occurs because the optimisation can become trapped in a local minimum from which it cannot escape since it does not have full information of the obstacle trajectory during the early iterations. The resultant trajectory is both sub-optimal and potentially dangerous. In this paper, we show that the solution to this is to incorporate predicted obstacle motions into the planning problem.
Motion planners that would otherwise use signed-distance fields are forced to adopt alternative methods, such as binary collision costs (Park, Pan, and Manocha 2012), to incorporate predictions. This is because the computation time for calculating SDFs prohibits real-time usage—i.e., the ability to generate predictions at a much higher frequency than environment observations are made, typically 30 Hz. Our results motivate using predictions and show that we can generate real-time predictions for signed-distance fields by using composite signed-distance fields.
We integrate our method of composite SDF predictions into our novel framework which uses the GPMP2 motion planner (Mukadam et al. 2018) to solve for collision-free trajectories in environments with moving obstacles.
The key contributions of this paper are:
1. Introduction of predicted signed-distance fields for mo-
tion planning in the presence of moving obstacles.
2. Extension of GPMP2 to plan using predicted obstacle trajectories.
3. A novel framework for motion planning in dynamic environments using composite signed-distance fields.
2 Related Work
Motion planning in the presence of moving obstacles is an open problem, while solutions generally fall into two categories. The first is to assume full prior knowledge of the moving obstacle trajectories in the scene (Menon, Cohen, and Likhachev 2014; Hsu et al. 2002; Merkt, Ivan, and Vijayakumar 2019). The second approach is ‘continuous re-planning’ in which the motion planner either re-optimises and adapts the current planned trajectory, or considers multiple trajectory modes at any one time, such as in ITOMP (Park, Pan, and Manocha 2012), and smoothly switches between them as new information is provided (Kolur et al. 2019; Zucker et al. 2013). However, there have been few works that incorporate predicted obstacle motions into the motion planning of articulated systems.
Nam et al. model obstacle motions as a random walk process and assign an artificial potential based on the probability density function of their predicted positions (Yun Seok Nam, Bum Hee Lee, and Moon Sang Kim 1996). Park et al. proposed IAMP which integrates ITOMP with human motion prediction based on supervised learning (Park, Park, and Manocha 2019). Li and Shah implement a probabilistic roadmap approach in which the roadmap is constructed using an obstacle motion prediction, essentially assuming a prior knowledge of the trajectory (Li and Shah 2019).
To further explore this problem, we first consider the environment representations used in motion planners.
Binary occupancy information enables search-based methods such as A* and D*-Lite, as well as sampling-based methods like Probabilistic Road Maps (PRMs) and Rapidly-exploring Random Trees (RRTs), to perform collision avoidance (Hart, Nilsson, and Raphael 1968; Koenig and Likhachev 2002; Kavraki et al. 1996; Kavraki, Kolountzakis, and Latombe 1998; LaValle 1998; Kuffner and LaValle 2000). In contrast, continuous optimisation-based approaches additionally require gradients so commonly use a Euclidean distance transform (EDT), or Euclidean signed-distance field (ESDF), to represent the environment.
When planning in 3D space, the environment is most often split into an array of discrete volume elements. We define a ‘voxel’ to represent a single discrete volume in space. An ESDF is a 3D voxelgrid in which each cell contains the signed-distance to the closest obstacle surface. The sign denotes whether the cell is within or outside the surface boundary. In addition to providing distance information which can be used to assign collisions costs, tri-linear interpolation enables us to obtain gradients.
Motion planners such as CHOMP, TrajOpt, and GPMP2 use ESDFs to represent the environment and demonstrate them to be very effective in enabling fast planning in static environments (Ratliff et al. 2009; Schulman et al. 2014; Mukadam et al. 2018). However, the limitations of SDFs become apparent when we look to apply them in dynamic environments.
ITOMP considered obstacle trajectory prediction for use in dynamic environments. However, in contrast to their general approach for static collision costs, which uses EDTs, they implement a simple occupancy cost for predicted motions based on “geometric collision detection between the robot and moving obstacles” (Park, Pan, and Manocha 2012). At each time-step in the optimisation a binary cost is allocated for every moving obstacle that is in collision. The reason for their approach is that EDTs are commonly considered to have CPU compute times that are not fast enough for real-time performance, thus are pre-computed and assumed to be static.
Various methods have been proposed to reduce the compute time for exact EDTs. Maurer et al. show that an exact distance transform can be calculated in linear time (Maurer, Qi, and Raghavan 2003). Approximate methods, such as the Chamfer Distance Transform (CDT) and Fast Marching Method (FMM), have also been proposed (Jones, Barron, and Sramek 2006) to achieve fast approximations. In robotics, we often accumulate information over time; this is in contrast to areas such as medical image processing, where an ESDF will be constructed from all of the information available. This has lead to significant work being conducted into faster integration of new occupancy information into signed-distance fields. Oleynikova et al. found that Truncated Signed-Distance Fields (TSDFs) are faster to construct than Octomaps, a widely used package that maps the environment using octrees (Hornung et al. 2013), and proposed, VoxBlox, a method to build an ESDF from projective TSDFs incrementally (Oleynikova et al. 2017). In contrast to ESDFs, TSDFs use a ‘projected distance’ metric and consider distances only within a truncated radius of surface boundaries. TSDFs are commonly used in vision for surface reconstruction (Newcombe et al. 2011; Whelan, Kaess, and...
Fallon 2012).
Despite the speed-ups achieved by state-of-the-art methods, they are not able to calculate SDFs fast enough for use in a real-time motion planner that uses what we term ‘predicted signed-distance fields’—predictions of what the ESDF of the workspace will be for future times based on estimates of obstacle geometry, velocity, and direction. We propose using composite signed-distance fields to generate predicted signed-distance fields in real-time.
Zucker et al. first mentioned the concept of composite SDFs, noting that distance fields are compositional under the \( \min \) operation (Zucker et al. 2013). Thus the distance field computation can be reduced to a minimisation across a set of pre-computed distance field primitives. In the computer graphics community, composition of object-centric SDFs is used to unionise objects in ‘Constructive Solid Geometry’ as well as to combine the SDFs of individual objects into a single SDF of the scene for ray-marching (Reiner, Mückl, and Dachschafter 2011).
Zucker et al. use composite SDFs in ‘CHOMP-R’ to quickly update their environment representation in response to a changing environment. However, to our knowledge, they have not been used in a predictive manner. We provide further analysis of this technique and leverage it in our novel framework which extends it to the domain of integrating predicted object trajectories into motion planning.
To demonstrate our framework, we integrate it with GPMP2 which formulates motion planning as probabilistic inference on a factor graph and uses Gaussian Processes (GPs) to represent continuous-time trajectories with a small number of states (Mukadam et al. 2018). Trajectories are found by using the GTSAM framework (Dellaert 2012) to exploit sparsity in the problem and perform fast probabilistic inference on factor graphs. Collision avoidance is applied via the use of ‘obstacle factors’, which evaluate the collision-free likelihood, using a hinge-loss obstacle cost for each time-step. The hinge-loss is calculated, in both CHOMP and GPMP2, by using an approximate robot model, comprised of spheres, to query the signed-distance field (Ratliff et al. 2009; Mukadam et al. 2018). However, Mukadam et al. use a single pre-computed SDF of the surrounding environment that is shared by all of the obstacle factors (Mukadam et al. 2018) and so does not incorporate the dynamics of moving obstacles. Kolur et al. consider dynamic environments but update all of the obstacle factors to use the same updated SDF and then re-optimise to solve for an updated trajectory plan (Kolur et al. 2019).
3 Methods
Part 3.1 describes our method of predicting trajectories for dynamic obstacles. Part 3.2 details our novel framework for predicting environment representations, using composite signed-distance fields, and then outlines how they can be integrated with a motion planner. We describe an experiment to examine the speed-up attained by using composite signed-distance fields in contrast to exact computations. In Part 3.3, we describe how we adapted the GPMP2 motion planner to react in dynamic environments as well as an experiment which demonstrates its applicability. In Parts 3.4 and 3.5, we demonstrate our fully integrated framework in simulation and on hardware, respectively. In both, a 7-DoF Panda manipulator successfully avoids a moving obstacle.
3.1 Obstacle Trajectory Prediction
To demonstrate that our approach enables the incorporation of obstacle trajectory predictions, we consider a simple prediction strategy for the occupancy of the workspace. Consider a 3D workspace, \( W \), which comprises of a set of \( i = 1, \ldots, n \) stationary objects, \( O_i \), and \( j = 1, \ldots, m \) moving (dynamic) objects, \( O_j^d \). At a given time, \( t \), a moving object with a centroid position, \( v_j(t) \), will travel at velocity \( v_j(t) \). We write the collection of discretised positions and velocities as \( X(t) = [x_1(t), x_2(t), \ldots, x_m(t)]^T \) and \( V(t) = [v_1(t), v_2(t), \ldots, v_m(t)]^T \).
In our simulated experiments, we assume noiseless sensor data and subsequently an accurate occupancy grid of the workspace, \( G(t) \), at each time-step. At any given time, we can identify and isolate occupied regions of the workspace. From these regions, we calculate the centroid and list of voxels associated with each object. By comparing two successive frames, at times \( t \) and \( t + \delta t \), we identify which objects are moving and estimate their respective velocities from the motion of each centroid—this enables us to identify occupancy grids associated with the static scene, \( G_{static} \), and the moving obstacles, \( G_{moving}(t) \).
With centroid and velocity information, we propagate each object using a constant-velocity model to produce a predicted trajectory of the centroid. This method inherently gives accurate trajectory predictions when an object is moving in a straight line with constant-velocity. However, we emphasise that the prediction model is fully replaceable and that a more sophisticated object tracking and trajectory prediction can be implemented within our framework, e.g. a KLT tracker or Unscented Kalman Filter (Jianbo Shi and Tomasi 1994; Raj et al. 2016).
3.2 Composite Signed-Distance Field Generation
Building on the previous description of how to identify the static and moving parts of the scene, we use \( G_{static} \) to calculate the static SDF \( S_{static} \). Next, we consider an occupancy box, \( B_j \), around each of the \( m \) moving objects, \( O_j^d \), that we have identified in \( G_{moving} \). Each occupancy box is chosen to be of equal size to \( O_j^d \), plus an additional \( \epsilon \) in all directions. For each \( B_j \), we calculate the corresponding object SDF, \( S_j \).
The resultant SDF is the smallest cuboid which encloses all voxels in 3D space with signed-distance values equal to or less than a distance \( \epsilon \) away from the surface of the object. We introduce \( \epsilon \) as a safety margin desired to be penalised in collision avoidance. When this method is integrated with a motion planner, \( \epsilon \) should equal the desired safety margin around objects to be penalised plus the size of the largest collision sphere associated with the approximate robot model.
Similar to \( X(t) \) and \( V(t) \), we denote the stacked vector of moving SDFs at a given time as \( S(t) \). In practice, we may accumulate more information about the shape of each moving object, hence \( S(t) \) is a function of time. However, for demonstration, our simulations assume noiseless sensor
Figure 3: 3a, 3b and 3c depict a toy example of three moving spheres entering the workspace in which a static obstacle (large central sphere) is present. White regions in the workspace represent free space, while black regions are occupied. 3d shows an SDF of the static environment, with the tracked objects in 3b overlaid for illustration purposes. For each of the tracked objects in the scene, an SDF is calculated and associated with them. By tracking the positions of the moving objects, we infer their velocities in order to make predictions of their future positions. At these future positions, we can superpose the object SDFs onto the static SDF using a min operation—the result is a composite SDF. 3e shows a composite SDF for $t_2$. For comparison, 3f shows the corresponding exact SDF. Critically for motion planning, the two are identical for distances up to $\epsilon$ away from the obstacle surface boundaries, as indicated by the red dashed line.
Algorithm 1 Real-time Update Loop
**Usage:** Continuously updates the motion planner
**Initialisation:**
1: $S = \text{getObjectSDFs}()$
2: $S_{\text{static}} = \text{getStaticSDF}()$
**Execution:**
3: while not shutdown do
4: $S = \text{updateObjectSDFs}()$
5: $X = \text{updateObjectPositions}()$
6: $V = \text{updateObjectVelocities}()$
7: for $t$ in times_to_predict do
8: $X_{\text{predicted}} = \text{calcFutureObjPositions}(t)$
9: $S_{\text{predicted}} = \text{predictSDF}(t, X, V, S, S_{\text{static}})$
10: $\text{updateMotionPlanner}(t, S_{\text{predicted}})$
11: end for
12: $\text{reoptimiseAndSendTrajectory}()$
13: end while
For any future time, $t_f$, we can predict the occupancy of the workspace by propagating the current position $x_j(t_n)$ of each moving obstacle SDF $S_j$ to its predicted position using velocity $v_j(t_n)$. Similar to considering an occupancy grid as the superposition of all occupied regions, we consider the workspace SDF as the superposition of all object SDFs in the scene—this forms the basis of a composite SDF.
To calculate the resultant composite SDF for a given time, we take the minimum voxel value (i.e., signed-distance) of all overlapping scene and object SDFs. By construction, the composite SDF is guaranteed to be accurate up to the distance $\epsilon$. We illustrate this process in Figure 3.
Algorithms 1 and 2 describe how we use this method in an update loop for motion planning with SDF predictions generated in real-time. While obstacle prediction in motion planning is not novel, to our knowledge this has not been performed by predicting the SDF of the environment for different time-steps to solve for a trajectory. Our approach thus relates to time-configuration space planning, explicitly encoding the state of the environment at different points in time (Merkt, Ivan, and Vijayakumar 2019).
To evaluate the speed-up achieved using composite SDFs, we constructed a set of four dynamic datasets modelled on the ‘table and cabinet’ setup presented in (Mukadam, Yan, and Boots 2016). Each of the environments contains a table and cabinet with the addition of: a) one small moving box, b) two small moving boxes, c) one moving pillar, d) two moving pillars. Figure 4 shows aerial and three-quarter perspective views of the ‘single moving pillar’ setup. We also include a simpler environment consisting of an empty workspace with a large moving block.
For each dynamic environment, we simulate 31 different time-steps in a $96 \times 96 \times 96$ workspace with 4 cm resolution. At each time-step, we produce composite SDF predictions for the remaining time-steps. We perform the same simulation and benchmark against the exact SDF computations as calculated in GPMP2, using MATLAB’s bwdist function, on the predicted occupancy grids.
3.3 Dynamic GPMP2
We adapt the original GPMP2 implementation to enable rapid updates of the SDF associated with each obstacle factor independently. The process of quickly updating obstacle factors facilitates a motion planner that can re-optimise and adapt planned trajectories to a changing environment.
To examine the effect of using independent SDFs for each obstacle factor, and to assess the importance of incorporat-
ing obstacle dynamics, we considered and compared three different scenarios in dynamic environments. Each scenario considers a different degree of perception; they are as follows:
1. **Static**: Assumes a static workspace and all obstacle factors remain unchanged throughout the execution of the trajectory. The factor graph is thus optimised only once.
2. **Execute-and-update**: Obstacles factors are initialised with the initial SDF of the scene. During execution, at each time-step, all obstacle factors with a time-index greater than or equal to the current time are updated to use the current observation of the workspace. The trajectory is re-optimised and executed at each time-step in an iterative process.
3. **Full prior knowledge**: Each obstacle factor is provided with the known SDF of the environment at the associated time. The factor graph has maximum knowledge of the environment evolution and is thus only optimised once.
The factor graphs associated with each of the perception scenarios are illustrated in Figure 5.
To test each scenario, we used a 7-DoF WAM robot arm in simulation to plan trajectories in the ‘single moving pillar’ setup shown in Figure 4. Plans were conducted over seven different combinations of start and goal configurations, and a range of moving obstacle speeds, 0.1 m/s to 1.0 m/s. We recorded the resultant smoothness (GP) cost associated with each trajectory and the number of collisions that the robot made with the environment.
To formalise the task, we constructed a factor graph comprising of 31 time-indexed variable nodes, separated by 0.1 s intervals, to form a 3 s time horizon. Prior factors were added to specify the start and goal configurations, and Gaussian priors used to connect variable nodes, as in (Mukadam et al. 2018). We assigned an obstacle factor to each variable node and interpolated obstacle factors between pairs of variable nodes with a discretisation of $\tau = 5 \text{ ms} (n_{\text{int}} = 19)$ to provide dense collision checking along the trajectory. Further parameters used were $\tau = 0.2 \text{ m}$ to encourage safe clearance of obstacles, as well as $\sigma_{\text{cost}} = 0.2$, as a result of tuning, to weight the relative costs of trajectory smoothness and collision avoidance. The environment was discretised at 4 cm resolution in a $96 \times 96 \times 96$ voxel workspace.
We performed another similar experiment on the experimental setup shown in Figure 1, in which a Franka Emika Panda 7-DoF robotic arm was tasked with reaching across the gap between two tables to achieve a ‘pick-up’ goal configuration. During execution, a Toyota HSR traverses the walkway between the tables, acting as a moving obstacle. For this setup, we used 42 different combinations of start and goal configuration. The moving obstacle speed was chosen to be in the range of 1.0 m/s to 2.0 m/s, most closely resembling walking speeds of a human. We chose $\tau = 0.05 \text{ s} (n_{\text{int}} = 1)$ to save compute time and because the time interval between variable nodes was already small. Other parameters used were $\sigma_{\text{cost}} = 0.05$ and $\epsilon = 0.3 \text{ m}$ based on cost tuning. As before, the environment was discretised at 4 cm resolution in a $96 \times 96 \times 96$ voxel workspace.
### 3.4 Closed-loop Implementation
We combined our predictive framework using composite signed-distance fields with our dynamic approach, applied within GPMP2, to solve planning problems in dynamic environments. The control loop is shown in Algorithm 1. In each iteration of the control loop, we observe the environment and update the workspace occupancy grid. We populate the occupancy grid by tracking the position of model states in the Gazebo simulation and inserting occupied regions into the occupancy grid at corresponding locations.
Using the methods discussed in Section 3.1, we segment and track obstacles online. A constant-velocity model is applied to each of the segmented moving objects, enabling us to predict the future locations of each object and generate composite SDFs for all obstacle factors with time-index equal to or greater than the current time. To our knowledge, this is the first work to implement and update different SDFs.
---
**Figure 4**: ‘Single moving pillar’ environment - Aerial and three-quarter perspective views of an example environment in which a tall pillar traverses the floor. Example start and goal configurations are illustrated in Figure 5. Plans were conducted over seven intervals, to form a surprising of 31 time-indexed variable nodes, separated by 2018). We assigned an obstacle factor to each variable node with the known SDF of the environment at the associated goal configuration. During execution, a Toyota HSR traverses the gap between two tables to achieve a ‘pick-up’ goal configuration. During execution, a Toyota HSR traverses the gap between two tables to achieve a ‘pick-up’ goal configuration. Further parameters used were $\tau = 0.2 \text{ m}$ to encourage safe clearance of obstacles, as well as $\sigma_{\text{cost}} = 0.2$, as a result of tuning, to weight the relative costs of trajectory smoothness and collision avoidance. The environment was discretised at 4 cm resolution in a $96 \times 96 \times 96$ voxel workspace.
**Figure 5**: Factor graphs associated with three different feedback scenarios. Variable nodes are shown in white, prior factors in black, and coloured obstacle factors. Top - the obstacle factors share the same SDF and remain unchanged during execution. Middle - as the trajectory is executed, the current and all future obstacle factors are replaced with the latest SDF. Bottom - as the trajectory is executed, the current obstacle factor is updated to the latest observed SDF while all future obstacle factors receive updated SDF predictions.
for each time-step as in time-configuration space planning. A prior factor is also added for the current time-index to set the current configuration of the robot. The factor graph is then re-optimised and the new trajectory is merged with the current trajectory being executed on the robot.
We demonstrate our closed-loop implementation of the proposed framework on a Panda 7-DoF robotic arm in Gazebo, using the same task as described previously in which the Panda reaches across a gap to place the end-effector over a table, as in a pick-and-place task. We set the HSR base movement speed at 1.4 m/s to test against a speed comparable with the average walking pace (Hermansson et al. 1994; Nolan et al. 2018; Wang et al. 2019).
3.5 Hardware Experiments
We validate our dynamic GPMP2 approach in the presence of uncertainty in the execution of the trajectory, as well as the pose of the dynamic obstacle, in hardware experiments. We use a Franka Emika Panda arm in conjunction with a Realsense D435i RGB-D camera for object tracking and detection. We used apriltag_ros (Malyuta et al. 2019) to identify the pose of an AprilTag (Wang and Olson 2016) fiducial marker affixed to a dynamic obstacle (box). For safety purposes, we used a longer time-horizon of 5 s and an epsilon value of 0.4 m to encourage both lower joint speeds and comfortable collision avoidance. The robot was positioned on a single table and tasked with a variety of motions, including the same motion as in the previous experiment, and avoiding the box as moved by the operator.
4 Evaluation
We conducted experiments using an 8-core Intel Core i7-9700 CPU @ 4.50 GHz and 2133 MHz DDR4 RAM. Signed-distance field computations were performed in series, as in the original GPMP2 implementation, using the bwdist function in MATLAB. GTSAM was configured to use multi-threading enabled for linearising the factor graph.
4.1 Composite SDF Prediction
Computation times for composite signed-distance fields and full computation from 96 × 96 × 96 occupancy grids are shown in Table 1.
The composite initialisation time, highlighted in grey, comprises of the time to calculate the SDFs associated with the static workspace, S_{static}, and each of the moving obstacles in the scene, S. This initial time penalty must be paid at the start up of the experiment or any subsequent time you wish to update the object and static environment SDFs. However, our results show that beyond this initialisation penalty, it is significantly faster to generate predicted composite SDFs than to perform full SDF calculations; we see a 7.9x to 28.0x speed-up for subsequent predictions depending on the discretisation of the workspace. This has a significant impact on enabling SDF predictions to be generated in real-time—conducting our experiment for a 96 × 96 × 96 discretisation of the workspace, as in our closed-loop implementation, gives a mean SDF generation rate of 540 Hz, compared with 36 Hz for the benchmark.
4.2 Dynamic GPMP2
The performance of the three scenarios described in Section 3.3, on the ‘single moving pillar’ dataset, are presented in Figure 6. The figure shows an absence of data for the obstacle speed of 0.5 m/s; at 0.5 m/s, the obstacle intersects the goal configurations at the end of the 3 s time horizon, resulting in inevitable collisions. Therefore, we exclude results for 0.5 m/s from our analysis. Of 69 planning results, we exclude three for which none of the planning scenarios found a collision-free trajectory.
Our results strongly support the incorporation of future obstacle motions into motion planning. Figure 6 shows that in most cases, including the obstacle trajectory motion into the planning significantly increases the likelihood of both finding a collision-free trajectory and reducing the jerk associated with the trajectory. Furthermore, the results motivate the use of our proposed framework in which we generate predicted ESDFs in real-time.
We note here that our implementation of a dynamic obstacle factor in GPMP2 incurs a cost of ≈2 ms to be replaced by an obstacle factor with a different SDF.
4.3 Closed-Loop Implementation
Our closed-loop implementation was successful in providing re-optimised trajectories fast enough for a Panda arm to avoid a moving HSR robot while reaching across a gap between two tables. Figure 1 illustrates the trajectory taken in each of the three cases. The ‘static’ case would result in a collision and the ‘execute and update’ would exhibit erratic movements. Figure 7 shows a comparison of the resultant joint position trajectories for the ‘execute and update’ against our composite prediction method. The results lend further support that by including predicted SDFs into motion planning, we can obtain smoother robot trajectories.
This experiment was conducted using a 96 × 96 × 96 workspace with 4 cm resolution. The parameters for the motion planner were \( \rho_{int} = 1 \), \( \sigma_{obs} = 0.05 \), \( \varepsilon = 0.3 \) m. A time horizon of 3 s was given, with variable factors time-indexed in steps of \( \delta_t = 0.1 \) s, resulting in 31 support states. The first iteration of the control loop results in the slowest update frequency because more future factors need to be updated and more predictions are generated. Averaged over 100 runs, our implementation runs at 3.4 Hz in the early iterations, with a standard deviation of 0.1 Hz. In the later iterations, we achieve an update frequency of \( \approx 10 \) Hz. We demonstrate the resultant trajectories for each of the three cases in the accompanying video. 1
4.4 Hardware Experiments
Our implementation performed well on the real robot arm, producing re-planned trajectories which successfully avoided the dynamic object in many cases. An example comparison against using composite SDFs but without prediction is shown in Figure 8. By accounting for the predicted motion of the obstacle, the manipulator is able to avoid the obstacle by following a much smoother trajectory.
---
1 https://youtu.be/vJH8qBRMedw
Figure 6: Results for experiments conducted on the WAM arm in the ‘single moving pillar’ setup are shown in Figures 6a and 6b. Results for the Panda arm avoiding a moving HSR are shown in 6c and 6d. We see that in all cases, using full knowledge of obstacle trajectories provides at least an equal chance of finding a collision-free trajectory using GPMP2; for most obstacle speeds, the improvement is significant.
Figure 7: Example trajectories for joint position and velocity. Our results highlight that the inclusion of environment prediction in motion planning can lead to smoother trajectories which exhibit less erratic movements.
Figure 8: Top row - online motion planning using our approach of composite signed distance fields and prediction. Bottom row - using composite signed distance fields but without prediction. From left to right, the images show the planned trajectory for times $t = 0\,\text{s}$, $t = 2.5\,\text{s}$ and $t = 5.0\,\text{s}$ (resultant trajectory). The blue highlight indicates the configuration of the robot at the current time-step while the purple line show the planned end-effector trajectory. The predictive component of our framework enables a smoother resultant trajectory, as shown in Figure 8c.
We found that while neglecting to predict the obstacle motion was also effective at avoiding obstacles due to the high re-plan frequency, the robot would exhibit erratic behaviours, in particular when the obstacle position coincided with the desired arm goal state.
5 Discussion
Our proposed framework gives compelling results in support of incorporating predicted obstacle trajectories into motion planning in time-configuration space. While we implemented a constant-velocity model to demonstrate our framework’s novel ability to include obstacle trajectory predictions directly into SDF-based based motion planning, one can replace this with a more complex model that takes into account any prior information we have on the obstacle’s trajectory, including its history. Exploring different prediction models for obstacle motion was beyond the scope of this work and as such we did not explore the avoidance of obstacles that follow complex motions, such as curved trajectories; we leave this for future work. Without using a more complex model, our current implementation is likely to fail in circumstances where the obstacle suddenly changes direction or stops.
A limitation of the proposed method is the potentially large memory requirements associated with assigning and storing different signed-distance fields for different time-indexed obstacle factors. For example, if a $300 \times 300 \times 300$ discretisation of the workspace is required for an application, our previous problem of a 3 s time horizon, discretised into 31 time-steps, will require ≈6.24 GB RAM.\footnote{A double is stored using 8 bytes, $300^3 \times 8 = 2.16 \times 10^8$ bytes = 206 MB, 31 × 206≈6.24 GB} We thus encounter a trade-off; minimising the workspace size results in quicker computation and lower memory requirements, however, to monitor a larger workspace requires the resolution to be decreased. We believe that this method could be adapted in future work to perform the superposition on a query basis, rather than computing the composite signed-distance field for the entire workspace.
Generating composite predictions for each time-step, as well as the updating of the obstacle factors, are operations which seem suitable for parallelisation. By updating factors in parallel, we believe that significantly higher update rates could be achieved allowing for more interactive and responsive behaviour.
We have demonstrated benefits of predicted composite SDFs that are independent of state-of-the-art SDF computing techniques. In our future work, we will evaluate different methods that can leverage our technique and framework, particularly parallel implementations. We also note that while pre-computing a static scene is acceptable for a fixed-base robot arm, it is less useful in the context of a mobile robot performing tasks in an unmapped region of space. To address this, we are working on integrating our approach with ESDFs that are updated from live point-cloud data.
6 Conclusion
This paper explored the application of composite signed-distance fields to motion planning in dynamic environments. We first exploited the speed of the min operation for composition of SDFs, and secondly, that signed-distance field representations must only be accurate up to a specified $\epsilon$ for motion planning problems. We show that composite SDFs can be used to provide significant speed-up for generating SDFs when accounting for moving obstacles. We investigated motion planning with a GPMP2 implementation which uses dynamic obstacles factors, enabling the planner to account for moving obstacles. Over a range of tasks and two different robot platforms, our results show that by incorporating predicted obstacle trajectories, we can significantly reduce the smoothness cost of trajectories and the rate of collisions. We leveraged composite SDFs and a dynamic GPMP2 implementation to present a novel framework which exploits the sparsity of the workspace and the compositional nature of signed-distance fields to generate real-time predictions of the workspace SDF, predicted signed-distance fields. We verified our approach on a real 7-DoF Panda arm with obstacle tracking performed using fiducial sensing, demonstrating that it can plan trajectories in dynamic environments and successfully avoid moving obstacles.
Acknowledgments
This research was supported by (1) the UK Engineering and Physical Sciences Research Council (EPSRC) through the University of Oxford Centre for Doctoral Training, Autonomous Intelligent Machines and Systems (AIMS, grant references EP/L015897/1 and EP/R512333/1), the UK RAI Hub for Offshore Robotics for Certification of Assets (ORCA, grant reference EP/R026173/1), and the EPSRC grant Robust Legged Locomotion (EP/S002383/1), as well as (2) the European Commission under the Horizon 2020 project Memory of Motion (MEMMO, project ID: 780684).
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The Effects of the COVID-19 Pandemic on the Mass Market Retailing of Wine in Italy
Francesca Gerini, Andrea Dominici * and Leonardo Casini
Department of Agriculture, Food, Environment and Forestry, University of Florence, P.le delle Cascine 18, 50144 Firenze, Italy; [email protected] (F.G.); [email protected] (L.C.)
* Correspondence: [email protected]
Abstract: The purpose of this study was to provide a detailed framework of wine purchases in supermarkets during the COVID-19 pandemic. The unexpected diffusion of the virus and the restrictions imposed in Italy to prevent its spread have significantly affected the food purchasing habits of consumers. By analyzing the scanner data of the wine sales in the Italian mass market retail channel, this study was intended to show whether and how the dynamics triggered by the pandemic have modified the overall value and type of wine purchases, focusing on prices, formats, and promotional sales. In particular, this study explores sales in two separate periods, namely March–April (the “lockdown”, with general compulsory closing and severe restrictions) and June–July 2020 (the “post-lockdown”, in which some limitations were no longer effective). The analysis of wine sales during lockdown and post-lockdown and the study of the variations compared to the sales of the previous years showed some significant changes in purchase behavior. The results could provide managers, researchers, and policy makers with extensive insights into the purchasing patterns of consumers during this unprecedented time and reveal trends that may characterize the structure of the future wine demand.
Keywords: coronavirus; scanner data; wine consumer; lockdown; supermarkets
1. Introduction
In December 2019, various cases of pneumonia began to crop up in China [1]. Later identified as the new SARS-CoV-2 coronavirus (also called COVID-19), the disease rapidly spread all over the world, affecting more than 90 million people, and causing almost two million deaths in a year [2]. In Italy, after verifying the first two cases of COVID-19 on 30 January 2020, various restrictive measures were adopted, some of which were very rigid, in view of fighting the pandemic. Lockdowns, closing restaurants and bars, travel restrictions, and working from home were just a part of these limitations that have significantly affected food habits, the purchasing channels of food products, and even the contents of the shopping cart [3–5]. For example, in the period between 17 February and 3 May 2020, the value of sales in mass market retailing (MMR) observed by Nielsen, recorded a growth of +4.2% compared to the same period from the previous year [5].
The unexpected pandemic caused an unprecedented global crisis and disrupted food systems, changing regular food choices and habits, and making food even more central in customers’ lives [6–9]. The impact of the pandemic may have influenced wine purchase behavior, shifting the sales channel and changing the typology and characteristics of the wine that was bought, and therefore misaligning sales from the trends forecasted by previous studies. A study by Wittwer and Anderson [10] projected for 2020 a reduction of 14% in the value of the domestic consumption of wine in Western Europe due to COVID-19. In particular, within wine groups, they predicted –8% for wine with a price less than 2.5 USD/liter, –11% for wine in the range of 2.5–7.5 USD/liter, and –7% for wine priced over 7.5 USD/liter. The first report conducted in Italy by IRI [11] pointed out an increase
Foods 2021, 10, 2674
This situation elicited the need to explore in depth the wine sales observed during the pandemic in the MMR channel. Did they increase compared to the past? In which price range did consumers purchase the most wine? What was the most purchased format during the pandemic? Have the wine promotion sales grown? Was there an increase in the prices of wine bottles? The purpose of this study was to answer these questions, providing a detailed framework for the different formats and price ranges chosen by customers during two different periods of the COVID-19 pandemic. Since the pandemic began, an initial period of compulsory closing called a “lockdown” (March–May 2020) was followed by a period in which limitations were no longer effective, and in Italy people returned to a general resumption of economic activities and free circulation among regions. Our analysis thus investigated the wine sales in these two different periods, namely, March–April (lockdown) and June–July 2020 (post-lockdown). The analysis applied in these two different timeframes provided several conclusions. Firstly, we compared the trend of total wine sales in March–April 2020 with the sales of the same two months in previous years. This examination allowed us to verify whether the unexpected lockdown caused a change in the consumer wine purchasing patterns. Moreover, the analysis was expanded to examine the data for the June–July 2020 period. The results of this period enabled us to explore the evolutions in wine purchases, namely, whether the sales trends taken on during the lockdown were maintained afterwards, and to observe if these trends showed variations compared to the same two-month period for previous years.
Although several previous studies have explored the changing trends in food purchases during the pandemic, analyzing the variations of sales compared to 2019 [14–17], there is a lack of information regarding wine purchases. In addition to representing a traditional element in food expenditures of Italians, wine is a suitable product to identify market trends in a period of crisis. In fact, not being an essential good, wine is characterized by a demand that is more sensitive to the socio-economic dynamics [18], such as that underway during this unprecedented pandemic. The sales of wine in Italy are traditionally pulled by the MMR, which represents the main distribution channel. In fact, according to a survey conducted by Mediobanca [19], in 2019, 36% of national sales of the principal wine-growing companies were made on the MMR channel. The second distribution channel was that of wholesalers/brokers (19.6%), followed by the hotel, restaurant, and catering (HoReCa) sector with 16.8%. Wine sales in wine shops and wine bars totalled 6.9%, whereas direct sales accounted for 11.6%. Direct sales also included online trading, which represented 1.1% on average. The rest of the wine sales were included in the category of “other” distribution channels. Despite the relevant role of MMR in the wine market, no prior studies have provided detailed insights into wine consumers’ purchases by considering the wine sales in this channel during the pandemic. Using store scanner data, this study explored whether the market for wine in supermarkets changed in two particular periods of the pandemic, characterized by different restrictions. Furthermore, the analysis of real wine sales data allowed us to verify whether the results reported by previous empirical studies are confirmed by real sales data.
The analysis of wine sales in MMR during the pandemic contributes to the literature by shedding light on how consumers change their purchasing patterns during an emergency crisis, which is unique in several aspects. In fact, though the crisis caused by COVID-19 may share some similarities with previous economic and financial crises, no previous pandemic has affected so many countries in such a short period of time or has caused a
sudden global stop in economic activity induced by containment measures [20,21]. In this sense, the purchase behavior acquired during this period could have also long-term effects that may characterize the structure of the final demand for wine on the MMR channel even after the pandemic.
2. Study Overview and Research Questions
After the first two cases of COVID-19 on 30 January 2020, the Italian government started to take strong containment measures to prevent the spread of the pandemic. Following the first closings, localized in several areas of the country by the end of the month of February, a DPCM (Decree of the Prime Minister’s Office), dated 9 March, established several restrictions over the entire national territory. In addition to prohibiting travel (except for when motivated by self-certified reasons of work, situations of necessity, or health reasons) and all forms of assembly of people in public places, the decree also provided for the closing of schools, museums, theatres, and movie theatres, as well as prohibiting civil and religious ceremonies. Furthermore, in order to reduce the chance of contact between people, the DPCM provided for the closing of bars and restaurants at 6 pm, thereby preventing the possibility of on-premises dining. These measures were further reinforced by a new DPCM that entered into effect on 12 March, which suspended all retail sales activities, except for stores dealing in foodstuffs, basic requirements, and pharmacies. These restrictive measures were then followed by the closing of all public food-service establishments, including bars, restaurants, pubs, pizzerias, and catering. The DPCM, however, allowed the possibility for food service providers to make home deliveries. These adopted measures remained valid for about two months, that is, until the second half of the month of May.
The first let-ups on restrictions were permitted by the DPCM that entered effect as of 4 May, which authorized food services on a take-away basis, prohibiting the consumption of products on the premises and parking in the immediate vicinity. The resumption of food service activities was permitted as of 18 May, limiting admission to a small number of customers, and adopting social distancing amongst them. As of the 3 June, travel was authorized between the regions of Italy and abroad. Figure 1 shows these data on a timeline.
The spread of the pandemic and the consequent restrictive measures adopted could have modified the market sales of wine. In Italy, MMR represents the first distribution
channel for wine in terms of value and volume. Table 1 reports an overall picture of the Italian wine market for this distribution channel.
| Year | Sales in value (Millions of EUR) | Sales in volume (Millions of liters) | Price (EUR/liter) | Sales by format (Millions of EUR) |
|------|---------------------------------|-------------------------------------|------------------|----------------------------------|
| 2014 | 1505.4 | 505.1 | 2.98 | Glass up to 0.75 liters |
| 2015 | 1540.3 | 511.3 | 3.01 | 1065.5 |
| 2016 | 1556.7 | 506.0 | 3.08 | 1116.5 |
| 2017 | 1603.1 | 508.7 | 3.15 | 1163.1 |
| 2018 | 1644.3 | 483.7 | 3.40 | 1216.6 |
| 2019 | 1669.0 | 485.7 | 3.44 | 1247.8 |
| 2020 | 1793.5 | 509.1 | 3.52 | 1289.0 |
Source: Unione Italiana Vini [22] on IRI data.
In general, the data in Table 1 show a general increase in the whole wine sales in MMR for 2020. Considering also that the sale of foodstuffs via MMR increased in the lockdown period [5], we intend to explore whether and how this change in purchase patterns also affected wine sales in the considered period. Hence, the first underlying research questions of this study are:
**Q1:** During the lockdown, how much were the wine sales in terms of value and volume on the MMR channel? Did these wine sales change compared to the past?
For one segment of the population, the pandemic brought some economic difficulties. Compared to the same periods in 2019, the authorized unemployment benefits paid out were 16 times higher in March–April 2020 and 12 times higher in June–July 2020 [23]. In the second trimester of 2020, Italy recorded a decline in the number of employed people (−3.6%) compared to the same period of 2019 [24]. Economic difficulties may therefore have influenced food habits, especially regarding an increase in the sales of low-cost products. In a study on the changes in the food consumption patterns of Greek households due to the economic crisis, Duquenne and Vlontzos [25] showed that consumers preferred less expensive products, characterized by low prices. The non-premium wines or basic wines, which is to say wines with an average price of less than 3 EUR/liter [26], represented a preferred sales channel in the modern distribution [27]. According to Casini et al. [28], in 2017 basic wine represented 33.0% of wine sales in value. Although the consumption of basic wine was correlated with lower income consumers [27], the economic difficulties caused by the pandemic could have caused a decline in the purchasing power of families and a consequent increase in the sales of these wines. Furthermore, the period of lockdown saw an increase in home consumption, owing to the closing of most economic activities, in addition to the introduction of remote working [7]. This shift in consumption could have given rise to an increase in purchases of wine for daily consumption on the MMR channel and, therefore, of basic wine.
**Q2:** During the lockdown, in which price range did consumers purchase the most wine? What price ranges showed noticeable changes compared to the previous years?
The range of basic wines is complex and characterized by marked heterogeneity [27]. In fact, the basic wine category includes wines in bottles or other packaging, such as plastic, carton (in Italy known as brik), bag-in-box, and demijohn packaging. Some of these formats may have recorded substantial increases in sales during this period for several reasons. On one hand, the limitations of movement imposed during the lockdown and the period immediately following it forced people to purchase large amounts of wine at neighbourhood supermarkets, such as the bag-in-box or demijohn, which previously were traditionally purchased directly from the winegrower or from wine retailers who were no longer accessible due to restrictions. Moreover, in order to avoid long queues to
enter supermarkets and limit to possible opportunities of infection, the general trend of consumers was to reduce the number of times they went to the supermarket, preferring the purchase of foods and beverages in large amounts and with long best-before selling dates [29]. In this sense, the bag-in-box is a convenient packaging alternative. In addition to containing a large quantity and lasting longer, it maintains the wine’s sensory qualities longer than a glass bottle once it has been opened. Moreover, at the same volume, the bag-in-box packaging format or plastic prove to be more practical and easier to transport compared to glass bottles, which are at risk of breaking [30]. Therefore, our research questions are the following:
**Q3:** In the basic wine category, which were the most purchased wine formats? Which format showed the best performance compared to the past? Which format the worst?
In Italian MMR, most of the sales in value are made in the 0.75 liter bottle format. In 2017, bottles sales accounted for EUR 1205.1 million and represented 75% of the total sales in value [28]. However, in MMR we can find bottles of wine with different prices and of different types. In fact, we can find bottles of *basic wine* priced under EUR 3/liter, and *premium* bottles priced over EUR 3/liter. The latter category is vast and includes even very expensive wines. We can imagine that the sale of wines belonging to different price ranges showed different trends during the lockdown. For example, the economic difficulties that emerged for several consumers and the trend towards saving could have driven the purchases of some consumers towards bottles in the *basic* range. At the same time, closing restaurants and wine bars prevented the customers of these establishments from consuming high-quality wine, in a higher price range, and often marked with indications of origin.
Although in 2019 the HoReCa sector represented less than one-fifth of the overall wine market, wines that sold at more than EUR 25 reached 33.5% of the total sales [19]. This type of product that was previously consumed in restaurants could have entered homes more often during the lockdown. Moreover, the impossibility of celebrating special occasions with friends and relatives could have led to a reduction in the sales of the expensive wines [31–33]. For these occasions, the choice of wine often involved a bottle that also served to impress others [34]. In this sense, one could opt for a *great wine*, one that cost more than EUR 25 [35].
The pandemic could have influenced not only bottle prices, but also promotion policies. For food in general, Altroconsumo [36] has registered a general negative trend of promotional sales in Italian MMR. The large turnout of customers in supermarkets during the lockdown may have diminished the necessity of attracting consumers with promotional activities. At the same time, some supermarket chains could have decided not to change their promotional policies for ethical reasons.
Finally, the assortments of bottles available on the shelves of MMRs may have changed. Several wine producers, due to the closing of HoReCa and difficulties in exportation, entered new sales channels such as supermarkets [16,37,38]. Meanwhile, provision difficulties occurring during lockdown may have given rise to problems of widespread availability. These issues could have involved a change in the number of single items purchased by consumers. This number can be obtained by means of the EAN (European Article Number) code, that is, the barcode connected to every single item.
To explore the overall sales of wine bottles, our research question was the following:
**Q4:** During lockdown, what was the performance of the 0.75 liter glass bottles, exploring the total sales value, prices, promotion sales, and the number of EAN codes purchased?
All the above research questions concern the purchasing behavior of wine consumers in the March–April 2020 period and its evolution compared to the same period in previous years. However, with the progressive reopening of commercial activities in mid-May, consumers may have changed their behavior again. In this sense, wine purchases made in June and July 2020 may have followed the trends observed during the lockdown or may have confirmed the trends of the years prior to the pandemic. We therefore asked:
Q5: In the post-lockdown period, which trends in the sales of various types of wine were in line with those of the lockdown? Which sales followed the evolution trend of previous years?
3. Materials and Methods
In order to explore wine sales in depth and answer the proposed research questions, we used the IRI Infoscan database, which reports the scanner data of the sales of still and semi-sparkling wines (wines with an excess pressure, due to carbon dioxide in solution, of not less than 3 bar when kept at a temperature of 20 °C in closed containers) throughout Italy for the MMR channel, including superstores (hypermarts), supermarkets, self-service stores (superettes + minimarkets), and discount stores. Scanner data has been widely used in the literature to investigate the demand for food products [14, 38–44] and wine [27, 45]. The advantage of using this type of revealed preference data is that it refers to consumers’ actual purchases, resulting in a more reliable and useful analysis of market trends [40, 41].
Store scanner data are collected at cash registers and identify the products, quantities sold, and prices paid. Each product sold is defined by an EAN code. These data thus supply the sum of the monthly sales in terms of value, volume, and unit, both at discounted and base prices. Furthermore, for each EAN code, the database reports additional information, such as year and month of sales, denomination (if available), brand, winegrower, colour (red, white, or rosé), geographical indication, type of format (e.g., plastic, bag-in-box, carton), volume of format (e.g., 0.75 liters, 1 liter, 1.5 liters), and grape variety.
The collected data were extracted for the wine sales recorded in March–April (termed b1) and June–July (termed b2) of 2020, the year of the pandemic’s appearance, and the total sales of the same periods of the single years from 2015 to 2019. These selected data were deeply analyzed to observe annual variations, following the methodology applied in the literature for exploring consumption trends during the COVID-19 pandemic. In fact, several scholars have analyzed purchasing patterns using secondary data (such as IRI data), exploring variations with respect to the previous year and consequently drawing inferences. Arellana et al. [46] studied the impacts on transport systems (focusing on air, freight, and urban transport demand) due to the COVID-19 outbreak in Colombia. Coluccia et al. [16] offered an analysis on the status of the agri-food sector during the pandemic, with an exploration of consumers’ demands by analyzing retail sales value and the consumer food price index. Cavallo et al. [15] presented an overview of the main changes in food habits during the lockdown, analyzing purchases of different food products compared to 2019. Using food purchase data, Del Pozo de la Calle et al. [17] described the nutritional quality of diets in Spanish households during the first COVID-19 epidemic wave and detected variations with respect to the same period of 2019. Bracale and Vaccaro [14] analyzed IRI data of 30 categories of food products during the first period of the pandemic (from 23 February to 29 March 2020) and explored the differences with sales from the same period of 2019. This established methodology represents a useful tool for implementing early analyses and evidencing changing trends on purchasing food habits caused by this unprecedented pandemic that the world is currently experiencing. At the same time, these first contributions have paved the way for further research on the food market. In contrast with the previously mentioned literature, instead of considering only data from 2019 (the year immediately preceding the pandemic), we have expanded our analyses to 2015, in order to draw precise conclusions on purchasing trends and to underline the presence of trends. Specifically, we compared the sales of 2020 b1, in the lockdown period, with the sales of b1 of the respective previous years. To study the situation of the post-lockdown period, a twofold comparison was made: the first between the 2020 b2 data and the data of b1 of the same year; the second between the 2020 b2 data and the b2 data of the previous years. This twofold examination made it possible to verify whether, after lockdown, the wine sales in MMR maintained the trends verified during the lockdown, or whether they instead fell back in line with the trends of previous years.
4. Results
4.1. Wine Purchases during Lockdown
To explore the wine purchases during the lockdown period and answer research questions Q1–Q4, we examined the sales trends of wine from 2015 to 2020 in the March–April (b1) period.
Considering Q1, the total sales in the 2020 b1 period showed an increase in sales in terms of both value and volume, with different performances compared to the previous years (Figure 2).
In fact, even though from 2016 the sales in terms of value showed a constant increase, 3.5% annually on average, in 2020 they nosed up to EUR 316.32 Million, thus recording +20.8% compared to 2015 b1 and +9.98% compared to 2019 b1 (more than double the food sales [47]). The performance of sales in terms of volume in 2020 was even more surprising. After a seesaw trend in 2015–2017, the sold volumes diminished, in 2019 reaching 83.98 million liters. The lockdown reversed this trend, with an increase in sales in terms of volume of 11.2% over the previous year, and reaching a total of 93.35 million liters. In particular, the rate of increase for the sales in volume in 2020 b1 was similar to that of the sales in value.
To answer Q2, we analyzed the trends in wine sales by price range (Table 2).
Table 2. Sales in the value of wine by price ranges (Millions of EUR).
| Price Ranges | 2015 b1 | 2016 b1 | 2017 b1 | 2018 b1 | 2019 b1 | 2020 b1 | Var. 2019 b1/2020 b1 |
|---------------|---------|---------|---------|---------|---------|---------|----------------------|
| 0–3 EUR/liter | 101.1 | 95.1 | 92.8 | 90.7 | 88.6 | 99.6 | +12.5% |
| 3–6 EUR/liter | 97.1 | 92.9 | 100.5 | 107.4 | 108.1 | 115.7 | +7.1% |
| 6–14 EUR/liter| 56.3 | 63.2 | 68.9 | 72.3 | 77.9 | 89.1 | +14.3% |
| 14–25 EUR/liter| 5.4 | 6.5 | 7.6 | 9.3 | 9.7 | 9.0 | −7.7% |
| >25 EUR/liter | 2.1 | 2.2 | 2.8 | 2.9 | 3.6 | 2.9 | −19.0% |
The greatest percentage increase in terms of sales in value occurred for the wines priced between 6 and 14 EUR/liter (+14.3% compared to 2019 b1). However, in 2020, the basic wines (0–3 EUR/liter) seemed to show the most surprising result. Although in fact they represent the second largest percentage increase in absolute value (+12.5% compared to 2019 b1), this increase is also accompanied by a reversal of trends compared to the sales
of the previous years. The sales in value of basic wine were in fact constantly declining, turning around only in 2020 until they reached EUR 99,600,000. The data that emerged in this analysis showed interesting trends also for products that fell within other price ranges. Wines priced between 3–14 EUR/liter confirmed the positive trend of the previous years, though with different increase rates. Although the 3–6 EUR/liter range, following the stagnation of 2019 (+0.7% compared to 2018 b1) returned to a growth in the percentage value similar to that of previous years (+7.1% compared to 2019 b1), the 6–14 EUR/liter range in 2020 showed the greatest growth rate compared to previous years. A change in the trend occurred, however, for the wines priced over 14 EUR/liter which, after positive variations though with different magnitudes, recorded a reduction in sales in 2020 b1. In particular, the wines priced between EUR 14 and EUR 25 per liter scored −7.7% compared to 2019 b1, whereas those priced over EUR 25 decreased by 19.0%.
Regarding Q3, we explored the sales of various formats of wine in the 0–3 EUR/liter range and their evolution from 2015 (Table 3).
| Formats | 2015 b1 | 2016 b1 | 2017 b1 | 2018 b1 | 2019 b1 | 2020 b1 | Var. 2019 b1/2020 b1 |
|------------------------------|---------|---------|---------|---------|---------|---------|---------------------|
| Bag-in-box | 2.84 | 3.17 | 3.43 | 4.46 | 4.59 | 6.97 | +52.0% |
| Carton | 37.92 | 35.22 | 35.45 | 36.50 | 35.97 | 39.76 | +10.5% |
| Plastic | 3.96 | 3.63 | 3.64 | 3.90 | 3.64 | 4.91 | +34.9% |
| Glass more than 2 liters | 7.01 | 5.80 | 5.56 | 5.18 | 4.84 | 6.68 | +38.1% |
| Glass from 0.76 to 2 liters | 19.05 | 17.09 | 16.01 | 15.52 | 13.83 | 16.87 | +22.0% |
| Glass up to 0.75 liter | 30.30 | 30.24 | 28.74 | 25.18 | 25.69 | 24.43 | −4.9% |
Although it was the most sold format in this range, the carton was the format that exhibited the lowest rate of increase in sales. In fact, after a strong decline in 2016, followed by a seesaw trend in the years following, in 2020 b1 it recorded an increase of +10.5%, reaching EUR 39.76 million. However, the major increases in terms of sales in value were recorded for the large formats, that is, those of two liters or more. In this sense, in 2020 b1 the bag-in-box format showed surprising results. In fact, even though in previous years the trend had always been positive, despite different annual variations, indicating the consumer’s greater appreciation of this product, 2020 b1 recorded an increase of 52% compared to 2019 b1 with EUR 6.97 million in sales. Wine in plastic containers, sold especially in the three- and five-liter formats, marked an increase of +34.9% over 2019 b1. Wine in glass containers with a higher capacity than 0.75 liters, that is, the two types of “glass from 0.76 to 2 liters” and “glass more than 2 liters” (type mainly formed by five-liter demijohns), in 2020 b1 recorded a net sales increase (+22.0% and +38.1% respectively compared to 2019 b1), reversing the declining trend of the previous years. The category “glass up to 0.75 liters” (where 0.75 liter bottles constitute 99% of the total sales of this format) is the only one that recorded a reduction in 2020 b1 (−4.9% compared to 2019 b1). Even though this category showed an increment in 2019 b1, the reduction in 2020 b1 followed the general decrement that had characterized this format on the market since 2015. This result draws particular interest in a sales framework, where all the formats exhibited positive performances.
To explore the 0.75 liter glass bottle format and answer Q4, we first analyzed the trends of total wine purchases in 0.75 liter glass bottles and by price range (Table 4).
The value of the total sales of this format grew in 2020, rising to EUR 234.11 million. However, the growth rate with respect to the previous year (+6.8%) was similar to that of the entire wine sector. It is interesting to note, however, the different trends depending on the price range. The bottles belonging to the *ultra-premium category* (with prices higher than 14 EUR/liter) underwent a reduction of sales in value. This reduction was unexpected: after a constant growth in the previous period, in 2020 the bottles priced between 14 and 25 EUR/liter took up position at −7.4%, and those of the *great wines* (>25 EUR/liter), at −19.6% with respect to 2019. Table 4 also provides interesting results concerning the intermediate ranges of 3–6 and 6–14 EUR/liter. The sales confirm the positive trend assumed in the previous years and show a steady increase in the two months of lockdown compared to 2019, respectively of +6.1% and +14.8%.
Concerning the promotional sales in value of the 0.75 liter bottles (Table 5), in 2020 the data showed a 17% reduction of sales in promotion compared to the previous year.
### Table 4. Wine sales in value of 0.75 liter bottles by price range (millions of EUR).
| Price Range | 2015 b1 | 2016 b1 | 2017 b1 | 2018 b1 | 2019 b1 | 2020 b1 | Var. 2019 b1/2020 b1 |
|---------------|---------|---------|---------|---------|---------|---------|---------------------|
| 0–3 EUR/liter | 30.30 | 30.24 | 28.74 | 25.18 | 25.69 | 24.43 | −4.9% |
| 3–6 EUR/liter | 93.66 | 89.88 | 97.36 | 103.84 | 104.24 | 110.63 | +6.1% |
| 6–14 EUR/liter| 55.08 | 61.60 | 67.27 | 70.67 | 76.19 | 87.46 | +14.8% |
| 14–25 EUR/liter| 5.22 | 6.30 | 7.34 | 9.07 | 9.50 | 8.80 | −7.4% |
| >25 EUR/liter | 1.97 | 2.08 | 2.74 | 2.84 | 3.48 | 2.80 | −19.6% |
| **Total** | 186.23 | 190.10 | 203.45 | 211.59 | 219.10 | 234.11 | +6.8% |
For exploring whether purchases of 0.75 liter bottles of wine increased in terms of EAN codes, we conducted an analysis, of which the results are presented in Figure 3. As of 2016, we witnessed an increase in the number of different labels purchased by consumers, but the year 2020 recorded a halt, with a 6.0% decrease over the previous year.
### Table 5. Sales in value in promotion of wine in 0.75 liter bottles (millions of EUR).
| | 2015 b1 | 2016 b1 | 2017 b1 | 2018 b1 | 2019 b1 | 2020 b1 | Var. 2019 b1/2020 b1 |
|-------|---------|---------|---------|---------|---------|---------|---------------------|
| **Total** | 82.56 | 84.36 | 87.71 | 87.17 | 93.64 | 77.78 | −17.0% |
The trend of average prices for bottled sales was also analyzed (Table 6). The price trends since 2015 have always exhibited positive signs, settling on 4.91 EUR/liter in 2019 (+2.2% with respect to 2018) and 4.99 EUR/liter in 2020. This increase (+1.7%) during lockdown seems to follow the trend of the previous years.
Table 6. Average price of wine in a 0.75 liter bottle (EUR/liter).
| | 2015 b1 | 2016 b1 | 2017 b1 | 2018 b1 | 2019 b1 | 2020 b1 | Var. 2019 b1/2020 b1 |
|--------|---------|---------|---------|---------|---------|---------|---------------------|
| Total | 4.37 | 4.46 | 4.57 | 4.81 | 4.91 | 4.99 | +1.7% |
4.2. Wine Purchases in the Post-Lockdown Period
The final research questions (Q5) explored the possible changes in purchasing trends in June–July 2020 (b2) compared to the lockdown period (2020 b1) and the same period of previous years. The first significant result we wish to stress concerns the sales in value (Figure 4).
Figure 4. Wine sales trend in value on the Italian MMR (millions of EUR).
In 2020 b2, the post-lockdown two-month period, we noted a more marked increase in wine sales compared to previous years. Although in fact, as of 2016 b2, we had recorded average annual increases of 2.0% compared to the b2 of the previous year, in the post-lockdown 2-month period, sales showed an increase of +5.9%. This result seems particularly significant, despite sales having suffered the usual decrease compared to the sales of b1, owing to the season. In fact, as pointed out by Contini et al. [18], with the arrival of summer, wine sales recorded a decline compared to the first four-month period of the same year. These performances indicate that, in spite of the lifting of restrictions, the Italians maintained high wine purchases in MMR, though attenuated by the arrival of summer.
Analyzing trends by price range (Figure 5 and Table 7), it emerges that in the post-lockdown period, the sales in the value of wines priced up to 3 EUR/liter increased over the previous year (+2.6%), despite the seasonal decline compared to b1, after years of a negative trend (−3% on the average).
In 2020 b2, the post-lockdown two-month period, we noted a more marked increase in wine sales compared to previous years. Although in fact, as of 2016 b2, we had recorded average annual increases of 2.0% compared to the b2 of the previous year, in the post-lockdown period, sales showed an increase of +5.9%. This result seems particularly significant, despite sales having suffered the usual decrease compared to the sales of the lockdown 2-month period, sales showed an increase of +5.9%. This result underlines that the purchases of basic wine, although decreased compared to the lockdown, grew +2.6% with respect to 2019 b2. Taking a closer look at the trends between sales by price range, we must also stress the performance of the 3–6 EUR/liter category, which is to say the category that as of 2017 comprised most of the sales in value.
Analyzing trends by price range (Figure 5 and Table 7), it emerges that in the post-lockdown period, the sales in the value of wines priced up to 3 EUR/liter increased over the previous year (+2.6%), despite the seasonal decline compared to b1, after years of a lockdown period, the sales in the value of wines priced up to 3 EUR/liter increased over the previous year. These performances indicate that, in spite of the lifting of restrictions, the Italianians maintained high wine purchases in MMR, though attenuated by the arrival of summer, wine sales recorded a decline compared to the first four-month period of the previous year, (+9.6%) compared to b2 of the previous year. Although in fact, as of 2016 b2, we had recorded average annual increases of 2.0% compared to the b2 of the previous year, in the post-lockdown period, sales showed an increase of +5.9%. This result seems particularly significant, despite sales having suffered the usual decrease compared to the sales of the lockdown 2-month period, sales showed an increase of +5.9%. This result underlines that the purchases of basic wine, although decreased compared to the lockdown, grew +2.6% with respect to 2019 b2. Taking a closer look at the trends between sales by price range, we must also stress the performance of the 3–6 EUR/liter category, which is to say the category that as of 2017 comprised most of the sales in value.
Analyzing trends by price range (Figure 5 and Table 7), it emerges that in the post-lockdown period, the sales in the value of wines priced up to 3 EUR/liter increased over the previous year (+2.6%), despite the seasonal decline compared to b1, after years of a lockdown period, the sales in the value of wines priced up to 3 EUR/liter increased over the previous year. These performances indicate that, in spite of the lifting of restrictions, the Italianians maintained high wine purchases in MMR, though attenuated by the arrival of summer, wine sales recorded a decline compared to the first four-month period of the previous year, (+9.6%) compared to b2 of the previous year. Although in fact, as of 2016 b2, we had recorded average annual increases of 2.0% compared to the b2 of the previous year, in the post-lockdown period, sales showed an increase of +5.9%. This result underlines that the purchases of basic wine, although decreased compared to the lockdown, grew +2.6% with respect to 2019 b2. Taking a closer look at the trends between sales by price range, we must also stress the performance of the 3–6 EUR/liter category, which is to say the category that as of 2017 comprised most of the sales in value.
This result underlines that the purchases of basic wine, although decreased compared to the lockdown, grew +2.6% with respect to 2019 b2. Taking a closer look at the trends between sales by price range, we must also stress the performance of the 3–6 EUR/liter category, which is to say the category that as of 2017 comprised most of the sales in value. Following the decrease in sales recorded in 2019 b2 (−1.3%) compared to b2 of the previous year, the sales of this price range changed direction during the post-lockdown period, also recording a higher percentage increase (+11.2%).
Figure 6 and Table 8 shows the values and the trends of the bag-in-box and plastic formats in the 0–3 EUR/liter range in the post-lockdown period. Despite the marked decrease in sales compared to 2020 b1, owing to the seasonality and the fact that during lockdown they had seen a strong increase of sales compared to the past, these formats recorded marked sales increases compared to 2019 b2, respectively of +21.7% for the bag-in-box, and + 8.8% for the plastic container. Therefore, even after lockdown, consumers maintained the habit of purchasing wine in the basic price range in the bag-in-box and plastic formats.
The analysis of the sales of wine in 0.75 liter glass bottles shows that the average prices per liter did not present significant variations (+0.5%) in 2020 b2 compared to 2019 b2. The 2020 b2 results indicate for great wines (Table 9) a substantial drop in sales value (−13.6% compared to 2019 b2). This fact contrasts with the past trends, in which, in the 2016–2019 b2 period, we always witnessed an increase in sales compared to the previous years (13.9% on average). In fact, in the summer months, consumers are used to purchasing more expensive wines. The results demonstrated that in 2020 b2 consumers opted for lower ranges, of which the trends were positive (for example, wines 3–6 EUR/liter, +11.3% compared to 2019 b2). We note, however, an increase in sales for great wines compared to lockdown, which is coherent with the seasonal positive trend for this price range.
Table 10 shows the trends of promotional sales of 0.75 liter bottles. Compared to 2019 b2, 2020 b2 recorded an increase in sales under promotion (+10.8%), confirming the positive trend encountered in the past. It is interesting to note, however, the increase with respect to the lockdown period. The usual decline in promotional sales of the summer season with respect to the spring months, which had always occurred in previous years, was reversed in 2020 with an increase of +7.7%.
Therefore, several purchasing trends encountered in 2020 b2 changed compared to the b2 period in the previous years. This is shown, in particular, by the increase in overall wine sales, the increase in wines priced below 3 EUR/liter and bottles priced between 3 and 6 EUR/liter, the boom of wine sales in the bag-in-box and plastic formats, and the drop in sales of bottles priced above 25 EUR/liter. These trends examined in the post-lockdown followed the purchasing habits acquired by consumers during the lockdown.
Figure 6. Wine sales in value (million EUR) of bag-in-box and plastic in the 0–3 EUR/liter price range.
Table 8. Percentage change of wine sales in value by format in the 0–3 EUR/liter price range compared to the previous period: for each year, (i) the variation of b2 compared to b1, and (ii) the variation of b2 compared to b2 of the previous year.
| Format | 2015 | 2016 | 2017 | 2018 | 2019 | 2020 |
|----------|-------|-------|-------|-------|-------|-------|
| Bag-in-box | | | | | | |
| i | +7.2% | +6.2% | +7.2% | +2.2% | −2.3% | −21.8%|
| ii | − | +11.0%| +9.1% | +23.7%| −1.5% | +21.7%|
| Plastic | | | | | | |
| i | −2.3% | −3.5% | +0.6% | −3.4% | −3.5% | −22.2%|
| ii | − | −9.4% | +4.5% | +3.0% | −6.7% | +8.8% |
Table 9. Percentage change of wine sales in value in 0.75 liter bottles by price range compared to the previous period: for each year, (i) the variation of b2 compared to b1, and (ii) the variation of b2 compared to b2 of the previous year.
| Price Range | 2015 | 2016 | 2017 | 2018 | 2019 | 2020 |
|-------------|------|------|------|------|------|------|
| 0–3 EUR/liter | $i$ | -8.8% | -4.3% | -6.4% | -6.0% | -4.9% | 1.5% |
| $ii$ | +4.7% | 7.0% | 12.0% | 3.2% | 1.4% |
| 3–6 EUR/liter | $i$ | -11.5% | -7.3% | -9.5% | -13.2% | -14.6% | -10.4% |
| $ii$ | 0.5% | 5.8% | 2.3% | -1.3% | 11.3% |
| 6–14 EUR/liter | $i$ | -1.7% | -2.0% | -5.0% | -1.1% | -3.9% | -12.6% |
| $ii$ | 11.4% | 6.0% | 9.3% | 4.7% | 4.4% |
| 14–25 EUR/liter | $i$ | -13.1% | -13.1% | -13.7% | -17.2% | -12.9% | 0.4% |
| $ii$ | 20.6% | 15.7% | 18.5% | 10.3% | 6.8% |
| >25 EUR/liter | $i$ | 6.0% | 9.5% | 1.8% | 11.5% | 0.8% | 8.3% |
| $ii$ | 9.2% | 22.1% | 13.4% | 10.9% | -13.6% |
Table 10. Percentage change in wine sales in value in 0.75 liter bottles under promotion compared to the previous period: for each year, (i) the variation of b2 compared to b1, and (ii) the variation of b2 compared to b2 of the previous year.
| Bottle | 2015 | 2016 | 2017 | 2018 | 2019 | 2020 |
|--------|------|------|------|------|------|------|
| 0.75 liter | $i$ | -16.7% | -17.5% | -16.8% | -17.0% | -19.2% | 7.7% |
| $ii$ | -1.2% | 4.8% | 0.9% | 4.6% | 10.8% |
5. Discussions
This study provided evidence on different consumers’ purchasing patterns for wine compared to the previous years. Similar to other foodstuffs [15], the dynamics set off by the pandemic have modified the value and type of wine purchases. Even if wine has lost that essential role in the Italian meal that it played in the past, it still remains an important component of Italian food expenditure [48]. During the lockdown, wine purchased on the MMR channel increased by 11.2% in volume and 9.9% in value, more than double the value of the total food sales observed by Nielsen [47]. The closing of bars and restaurants could have had a role in the increasing performance of wine sales on the MMR channel, as could the increased number of people working remotely from home during lockdown [7]. In fact, remote workers have shown the highest increase in the consumption frequency of wine (+17.9%) [49]. This eating pattern established is also related to the increase in the purchase of comfort foods, types of food that give psychological comfort in periods of stressful events and are therefore purchased under an emotional impulse, rather than as a real necessity [15]. However, our results may be in part attenuated by the increment in wine sales from different channels, i.e., small grocery stores and e-commerce, as evidenced by IRI [11].
We witnessed an increase in sales for wines priced below 3 EUR/liter (+12.5%), a boom of wine sales in the bag-in-box and plastic formats (respectively, +52.0% and +34.9%), and a reduction in the sales of bottles belonging to the ultra-premium category (priced over 14 EUR/liter). The increase in sales of low-priced wines such as the reduction of wine priced over 14 EUR/liter may find an explanation in the economic difficulties that emerged with the pandemic. The economic shocks due to COVID-19 and the sharp increase in unemployment have probably led some consumers to place more importance on price in food sales compared to other factors [50]. Wine, not being an essential good, is characterized by a demand that is more sensitive to socio-economic dynamics [18], and the price results in being the most important attribute in the purchasing act during an economic crisis [51]. Together with the financial crisis, the government has imposed some restrictions during the lockdown by forbidding celebrations or meetings with relatives. Since for special
occasions consumers are willing to pay higher prices for a bottle of wine [52,53], these social limitations contribute to the decline in wine sales in the super-premium and great categories, as also emerged in a study by Vergamini et al. [54]. The negative trend of great wines persisted even in the period after lockdown, with a lower sales value compared to the levels of the previous years.
Differently from the general trends analyzed for wine, the 0.75 liter glass bottles priced under 3 EUR/liter record a reduction in their sales during the lockdown. Albeit with the necessary caution, on the basis of the results, the decline of bottled wine sales in the under 3 EUR/liter price range could be due to the fact that, during the lockdown, when oriented towards a basic wine, the consumer preferred other formats such as carton or bag-in-box. In fact, further analyses on the sales volume data confirmed this trend in sales value. Although wine bottles showed a decrease in sales in volume equal to −6.0%, bag-in-box and plastic exhibited a growth, respectively, of +42.6% and +32.2%. The explosion of sales in MMR of large formats such as bag-in-box and plastic is one of the most surprising trends of consumption acquired during the two-month periods. The forced change in the consumers’ daily eating habits during the lockdown, characterized by an increase in the number of meals eaten at home, may have promoted the growth of the purchases of “daily consumption wine”, as these formats are traditionally considered [55]. In addition, in other countries researchers have observed an orientation towards large formats during the pandemic, namely, consumers bought larger-sized alcoholic beverages in consequence of the less frequent shopping trips due to concern of contagion and restrictions [29]. The literature seems to confirm that, at the supermarket, the consumer opted for easily transportable wine containers that, at the same time, ensured good product preservability. Although in the past, particularly the bag-in-box format was the target of prejudice and considered with contempt as a metallized plastic bag in a cardboard box, the lockdown has caused its sales to skyrocket thanks to its capability to respond to consumers’ temporary demands in terms of practicality, convenience, and the need to stock up on the product. Not only is this format a good buy for money, but it also makes it possible to preserve the wine well for days after opening, thanks to the absence of light and contact with the air [56]. Moreover, bag-in-box packaging is often related to the concept of sustainability, biodegradability, and the use of recyclable materials. These qualities, which Italian consumers are increasingly more interested in [57–59], could further boost their loyalty and attract new customers. The appreciation for bag-in-box formats is also confirmed by the sales of the post-lockdown period. If this format did not find general support among consumers before the pandemic, their purchases due to the contingent situation and their satisfaction with the taste could have modified the consumers’ opinion on the bag-in-box format, convincing them to buy it again.
Despite reopenings in the restaurant sector, in the post-lockdown period the value of wine sales on the MMR channel, as well as the market share of low-priced wines and large formats, was higher compared to the same period in previous years, confirming the sales trend evidenced in the lockdown.
The negative trend of promotional sales in value of the 0.75 liter bottles (−17%) is worthy of particular attention. We can trace this outcome back to the general negative trend of all food promotional sales in the Italian MMR [36]. In an investigation into the possible causes of this phenomenon conducted during the lockdown, different reasons were given by the directors of supermarket chains [60]. According to some of these directors, the decrease in food promotion purchases were due to the change in the purchasing habits of consumers who shopped quickly, paying more attention to safety than promotions and focusing on essential products that were not subject to promotions. Instead, another group of supermarkets directors has stated that promotions were modulated according to the availability of the industry that could not cope with the required volumes, because in March food purchases increased by a quarter [60]. If in MMR during the lockdown the value of the purchases of wine bottles under promotion decreased, the following period did not confirm this trend. In fact, in the b2 2020 period, promotional wine sales increased,
contradicting the usual seasonal decline for the months of June and July traditionally observed in the previous years and evidenced by the literature.
6. Conclusions
Our study provides a detailed analysis of wine sales during the COVID-19 pandemic on the MMR channel throughout Italy. Since MMR traditionally represents the main distribution channel for wine and the HoReCa sector was closed due to the restrictive measures during the lockdown, this study provides insights on a very relevant part of the wine market in this pandemic period. In particular, the analysis of the sales in the period of the lockdown (March–April 2020) and post-lockdown (June–July 2020) enabled us to outline a detailed and effective evolution framework of this sector, compared to the previous years. The scenario depicted shows the effects on wine sales of a global crisis that is unprecedented and not fully comparable with previous economic or health crises. To our knowledge, no previous studies have so thoroughly explored the total wine sales of this market channel during this unique period. We believe that such an analysis of the dynamics of wine purchases made during the pandemic could shape our expectations for the evolution of the future wine market.
Even though the COVID-19 virus is increasingly under control, it has still not been overcome. The persisting outbreak and the restrictions that are frequently reintroduced (although less severe compared to the lockdown period) mean these new purchasing patterns acquired with the pandemic could be assimilated as new everyday habits. The transformed structure of wine demand provides marketers with some indications on the strategies for facing these new shopping paradigms. In the case of bag-in-box wines, producers are encouraged to organize testing sessions or offer free samples in supermarkets to try the product and acquire consumers’ loyalty. Considering the increasing consumer agreement with bag-in-box wine, winegrowers could resort to this type of packaging more often, characterizing the product with aspects aimed at supply chain traceability and environmental sustainability in the packaging. Moreover, producers of premium wines could think about expanding their supply and introduce the bag-in-box format on the market with a higher-priced wine, according to the regulations of denominations of origin. As far as retailers are concerned, the growing interest of consumers in this type of wine can be used as a potential lever to boost customer loyalty and attract new customers, also publicized by means of promotional campaigns. Alternative package formats and materials, such as bag-in-box packaging, are also particularly appreciated by millennials [61].
The framework on wine sales and the changing trends during the pandemic evidenced in this study represent an early contribution on the evolution of the wine market and can constitute a point of departure for further studies undertaking more thorough analyses using other methodologies. Our study focused on the first period of the pandemic, exploring the wine sales until July. It would be useful to expand the analysis by including the data for the same period of 2021, in which the mass vaccination campaign against COVID-19 allowed a gradual return to a normal way of life. These longer time series could allow a better comprehension of the evolution of consumers’ purchasing patterns.
Our outcomes suggest to researchers the need to implement studies with testing sessions or free samples to elicit consumers’ preferences and willingness to pay, especially for products with alternative packaging, such as bag-in-box wines, or other types of food which meet with widespread scepticism. In fact, the evidence that emerged from hypothetical studies could be reversed by experimental studies involving a real experience with the product and that allow respondents to value the characteristics of the food considered in the study. The methodology used in this study could also provide the starting point for a more complete analysis of the food market. Indeed, the changes in sales that emerged for wine during the pandemic may have affected other food products as well. An example is beer, which is increasingly appreciated by consumers and can be subject to a substitution effect with wine. These analyses should be conducted considering the temporal evolution of the pandemic to provide better evidence on the emerging trends. To complete the picture of the
wine market during the pandemic, future studies should integrate sales data considering segmentation variables such as economic conditions, working habits during the lockdown, and psychographic characteristics.
Our exploratory study has some limitations that should be recognized. The main limitation of this study was the use of a secondary data source, which was context-specific and not generalizable to other countries, characterized by different restrictions imposed and consumer characteristics. In fact, given the different spread of the pandemic in the various countries over time, each government has adopted restrictive measures and limitations according to its own sanitary situation. In Italy, which was the first Western country to establish the lockdown, the restrictive measures may have lasted longer or been stricter, affecting purchasing habits in a different way than in other countries. Concerning our data, the database used did not include the data on the sales related to sparkling wines. This therefore prevented us from further investigating this type of wine, which represents a part of wine sales at supermarkets, and which is traditionally purchased for special occasions such as meetings with friends and relatives. Among the limits of this study, we wish to include the impossibility of conducting analyses of socio-economic categories of consumers. Although store scanner data, referring to sales aggregated on the territory by product, make it possible to survey general trends, they do not allow us to conduct analyses on the socio-economic characteristics of purchasers. For this reason, in this study it was not possible to exploit the traits of the buyers and the motivations that led to the choice of certain types of wine.
Author Contributions: F.G., A.D. and L.C. contributed equally to this project. 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: Not applicable.
Conflicts of Interest: The authors declare no conflict of interest.
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Revisiting Supertagging and Parsing: How to Use Supertags in Transition-Based Parsing
Wonchang Chung
Dept. of Computer Science
Columbia University
New York, NY, USA
[email protected]
Siddhesh Suhas Mhatre
Dept. of Computer Science
Columbia University
New York, NY, USA
[email protected]
Alexis Nasr
LIF
Université Aix Marseille
Marseille, France
[email protected]
Owen Rambow
CCLS
Columbia University
New York, NY, USA
[email protected]
Srinivas Bangalore
Interactions, Inc.
New Providence, NJ, USA
[email protected]
Abstract
We discuss the use of supertags derived from a TAG in transition-based parsing. We show some initial experimental results which suggest that using a representation of a supertag in terms of its structural and linguistic dimensions outperforms the use of atomic supertags.
1 Introduction
The notion of supertagging was introduced by Bangalore and Joshi (1999). A supertag is the name of an elementary tree assigned to a word in a TAG derivation of the sentence. A supertag therefore encodes not only the part of speech, but also the syntactic properties of the word. They proposed a two-step approach to parsing: a supertagger determines the supertag for each word in a sentence, and a deterministic and rule-based “lightweight dependency analyzer” then derives the structure from the supertags.
The MICA parser (Bangalore et al., 2009) uses a supertagger and a subsequent chart parser which takes the 10-best supertags for each word as input. MICA uses a probabilistic context free grammar which is lexicalized on the supertags, but not on words. The MICA parser is fast, and has good performance. Nasr and Rambow (2006) showed that the MICA approach outperforms the lightweight dependency analyzer of Bangalore and Joshi (1999). To our knowledge, MICA is the only TAG parser trained on the Penn Treebank that uses supertagging; it is freely available.1
The MICA parser has several drawbacks: while it is fast, the time complexity is \(O(n^3)\). Furthermore, the system is complex as the chart parser itself is compiled using the SYNTAX system (Boullier and Deschamp, 1988), making further development difficult. Finally, it is unclear how to include recent advances in lexical representation (word embeddings) and machine learning (deep learning).
This paper presents a new parser based on TAG, which uses supertagging and a distinct parsing step. Unlike MICA, the parsing is based on the transition-based parser of Nivre et al. (2004). While there has been some work using supertags with transition-based parsing (Ouchi et al., 2014), this is the only work (to our knowledge) which specifically refers to TAG grammar.
Bangalore et al. (2009) train a version of MAL T with gold and predicted supertags. MAL T can exploit the gold supertags, but not the predicted supertags (they do not improve over not using them). The problem with using supertags in transition-based parsing is that exploiting n-best supertag input is difficult, and given the large number of supertags, supertagging is hard and the 1-best supertag is not good enough to allow for a good parse to be constructed. In this paper, we present initial investigations to address this problem. We decompose the supertag into linguistic dimensions, which provides for a generalization of the notion of supertag.
2 Corpus and Grammar
We use the grammar and the corpus extracted by Chen (2001). This grammar was engineered in such a way that the derivation trees are meaningful deep-syntactic representations. This grammar was also used in the MICA parser (Bangalore et al., 2009). It has 4725 elementary trees extracted from
1urlhttp://mica.lif.univ-mrs.fr
the training set of the WSJ portion of the Penn Treebank (Sections 01-22). Every sentence in the corpus is given a derivation. Sentences in the development set (Section 00) and the test set (Section 23) may contain elementary trees that have not been seen in the training corpus.
We automatically analyzed the elementary trees that make up the extracted TAG, assigning each tree a vector of 20 dimensions. These dimensions fall into three categories:
- Dimensions that describe the phrase structure of the elementary tree. We concentrate on aspects that we think will be important for parsing.
- Interpretations of the tree. These are linguistic dimensions which abstract from the phrase structure of the tree.
- Linguistic transformations on the tree. These are syntactic variations that the tree encodes, such as wh-movement.
This approach of breaking down a supertag into components is inspired by the hypertags of Kinyon (2000). Our set of dimensions is shown in Figure 1.
3 Supertagging
The supertagger architecture is very simple: supertags are predicted independently of each other. The prediction is performed using an online passive-aggressive algorithm (Crammer et al., 2006). We used the implementation of the Python Scikit-Learn library.²
The classifier uses a total of 26 features: the word to be supertagged, its part-of-speech tag as well as the 6 preceding and following words and part-of-speech tags. To vectorize the feature data, the one-hot encoding method was used.
Training was performed on the training set of the WSJ portion of the Penn Treebank (950,028 tokens) and the evaluation on the development set (40,461 tokens). In order to reduce the amount of memory used for training, the sparse matrix constructor was used. The peak amount of memory used for training task was less than 50GB, and the processing time was less than 1 hour in wall-clock time on our machines.
2http://scikit-learn.org/stable/modules/generated/sklearn.linear_model.PassiveAggressiveClassifier.html
4 Parsing
4.1 Background
The parser used in this study, named SuTRA (for Supertag- and Transition-based Parser), is a standard transition based parser (Nivre et al., 2004). Giving a thorough descriptions of transition based parsers is not the aim of this paper; we will just briefly describe below the basic ideas behind transition based parsing to allow the reader to follow the rest of the paper.
Transition-based parsers are based on two fundamental objects: configurations and transitions
A configuration \((s, b, D)\) describes the state of the parsing process at a given time. \(b\) is a buffer that contains the words of the sentence to parse not yet processed. The leftmost word of the buffer is noted \(b_0\). \(b_0\) can be taken from the buffer and pushed on the stack \(s\). \(D\) is a set containing dependencies that have been built to this point by the parser. The parser tries to build a dependency between the word that is on the top of the stack \(s_0\) and the next word in the buffer \(b_0\). Two types of attachements are considered, left attachements that have as a governor word \(b_0\) and as a dependent \(s_0\) and right attachements that have \(s_0\) as governor and \(b_0\) as dependent. The initial configuration of the parser is \(([], [w_1 \ldots w_n], \emptyset)\): the stack is empty, the buffer contains all the words of the sentence to parse and the dependency set is empty. A fi-
Figure 2: Learning curve of the supertagger
The supertagger accuracy is 87.88% on the development set, a bit lower than the results obtained on this data by Bangalore et al. (2005), which was 88.53%. The learning curve is shown in Figure 2.
A transition operates on a configuration $c_i$ to produce a configuration $c_{i+1}$. In our implementation, three types of transitions are defined:
**Left Arc** builds a dependency $(b_0, l, s_0)$ (a transition that has $b_0$ as a governor, $s_0$ as a dependent and $l$ as a label). This transition adds the new dependency to $D$ and pops the stack.
**Right Arc** builds a dependency $(s_0, l, b_0)$. This transition adds the new dependency to $D$ and replaces $b_0$ with $s_0$.
**Shift** does not create a new dependency, it just remove $b_0$ from the buffer and pushes it on the stack.
The parser is a greedy deterministic parser. Given a configuration, it predicts the most likely transition to make. A new configuration is produced and the process iterates until a final configuration is reached. The dependency structure produced is the set $D$.
The heart of the parser is the classifier that predicts which transition to make given a configuration. The number of possible configurations being very large, we decompose a configuration into a feature vector. During training, the classifier associates a score to each feature. At decoding time, the classifier adds the scores of the features corresponding to the current configuration in order to select the most likely transition. The classifier used in this work is a simple averaged percep-
tron (Freund and Schapire, 1999).
The feature templates used by the classifier are of three sorts:
**Word features** describe different aspects of the words that are present either on the stack of the parser or in the buffer. They are of the form \((s|b)(0|1|2|3)(f|l|c|p|m)\) where:
- \(s|b\) indicates whether the word described is in the stack or the buffer
- \(0|1|2|3\) indicates the position of the word in the stack or the buffer \((s0\) is the top stack word and \(b0\) is the first word in the buffer).
- \(f|l|c|p|m\) indicates whether we are referring to the form of the word \((f)\), its lemma \((l)\), its coarse part of speech \((c)\), its part of speech \((p)\) or its morphological features \((m)\).
**Distance features** indicate the distance in the string between two words. They are of the form \(d_{X,Y}\) where \(X\) and \(Y\) correspond to words either on the stack or in the buffer. The only feature of this category that is used is \(d_{s0,b0}\).
**Structural features** describe some aspects of the dependency structure built so far by the parser. They are of three sorts:
- \(l_X\) which indicate the syntactic function (role label) of the leftmost dependent (if any) of word \(X\). Two features of this category are defined: \(r_{s0r}\) and \(r_{b0r}\).
- \(r_X\) which indicate the syntactic function (role label) of the rightmost dependent (if any) of word \(X\). Two features of this category are defined: \(l_{s0r}\) and \(l_{b0r}\).
- \(n_X\) which indicate the number of dependents of word \(X\). Two features of this category are defined: \(n_{s0}\) and \(n_{b0}\).
**Configuration features** describe some aspects of the current configuration of the parser. They are of four sorts:
- \(sh\) indicates the height of the stack
- \(bh\) indicates the number of elements in the buffer
- \(dh\) indicates the number of dependencies built so far
- \(tn\) with \(n=1,2,3,4\), indicates the \(n^{th}\) preceding transition that led to the current configuration
Each feature template can be used independently or in combination with others, in which case a weight is computed for a combination of their values.
### 4.2 Parser 1: Baseline Parser without Supertags
We start by describing our baseline parser, which is S UT RA without any supertag features at all.
Table 4 shows the set of feature templates (called a feature model) used for our baseline parser. (All of the tables related to the machine learning features are at the end of the paper.) Feature templates 1 to 18 are simple feature templates, those ranging from 19 to 29 are combination of two simple feature templates.
The performance of the baseline parser is shown in Table 1 in the first row, with separate results for labeled attachment score (LAS) and unlabeled attachment score (UAS). Since we are not using supertags in this experiment, the results are the same for gold and predicted supertags.
For the sake of comparison, we also give results for a MALT parser trained on our corpus (2nd line in Table 1; the results are taken from (Bangalore et al., 2009)). Our baseline results are directly comparable to those for MALT without supertags, as both are transition-based parsers which do not use supertags. We see that our results are a little worse, which we attribute to differences in the machine learning, and differences in the feature set used. However, for the sake of the experiments in this paper, we take our results as meaning that we have replicated the previous results.
### 4.3 Parser 2: Using Supertags
We now use supertags. In the first experiment, we simply add the supertags as labels in our parser by means of the following word feature templates: \((s|b)(0|1|2|3)(s)\), where the first two components of the templates \((s|b)\) and \((0|1|2|3)\) keep the same meaning as before and \(s\) refers to the supertag of the word. The feature model of Parser 2 adds to the feature model of the baseline Parser the feature templates shown in Table 5. These templates correspond to templates of the baseline parser in which part of speech tags are remplaced by supertag tags.
The results of P2 are displayed in Table 1 in row 3. As one can see, when feeding the parser with gold supertags, the results accuracy of the parser jumps to 96.97 UAS and 95.99 LAS. Supertags carry much more syntactic information than just POS tags that the parser can make use of in order to predict the syntactic structure of the sentence. When supertags are predicted with the supertagger of section 3, the accuracy dips to 89.86 UAS and 87.75 LAS, respectively. This represents an absolute increase of 2.24 points of UAS and 2.52 points of LAS with respect to the baseline parser. We also compare P2 to MALT using supertags, shown in row 4. We see that our parser outperforms MALT with stags by a small margin when using predicted supertags (not gold supertags). Part of the difference in the predicted supertags is due to the use of gold POS tags in our experiments, so we conclude that we are again replicating the previous result.
We also provide the results for MICA (row 5). We see that for gold supertags, MICA provides the best overall results, but not for predicted supertags. This is because MICA in fact only uses supertags.
### 4.4 Parser 3: Using Dimensions of Supertags
We now perform experiments to see whether the individual dimensions of the supertags can help in parsing. The motivation is that if a supertag is incorrectly predicted, some of the dimensions may still be correct (for example, the predicted supertag has a transitive verb instead of an intransitive verb, but the subject is empty in both supertags).
In order to be able to exploit the supertag dimensions in the parser, we add the following word feature templates: \((s|b)\) \((0|1|2|3)\) \((A|B|\ldots|T|U)\) where, as before, the first two components of the templates \((s|b)\) and \((0|1|2|3)\) keep the same signification and the letters A to U refer to one dimension of the vector representation of supertags. The correspondence is given in Table 3. The feature model of parser 3 is the union of the feature model of P2 and the features of Table 6.
We observe that we cannot use all dimensions of the linguistic vector representation of the supertag, because the combinations would result in a combinatorial explosion in the number of features for machine learning. In order to gain a better understanding of which dimensions of the decomposed supertags are useful for parsing, we performed ablation studies, first on the dimensions, and then on the machine learning features. We discuss them in turn.
In the first study we removed each dimension of the supertag (eg. dsubcat, ssubcat, …) in turn and computed the parsing accuracy. For this ablation study, we use a feature model that comprises simple features derived from supertags and non-supertags. Specifically, this model comprises the following features: features 1 through 18 from Table 4, plus \(s0x\), \(s1x\), \(b0x\), and \(b1x\), where \(x\) is a variable denoting the dimensions (represented as in Table 3). We use this model because it is a simple model. The results are shown for gold and predicted stags in Table 2.
For the gold experiments (first two columns), we see that mainly the dimensions that describe the phrase structure are useful for parsing: all of these dimensions except for coanc help, and all the most useful dimensions are of this type. This is because in a TAG grammar, the phrase structure encodes exactly how trees can combine in the parse, so that this is the information needed for a correct parse. In addition, we have several of the dimensions relating to transformations that help a bit. When we look at the predicted supertags, we
| Parser | Gold Stags | Predicted Stags |
|-------------|------------|-----------------|
| | UAS | LAS | Stag acc. | UAS | LAS |
| Baseline | — | — | — | 87.65 | 85.23 |
| MALT | — | — | — | 88.9 | 86.9 |
| P2 | 97.02 | 96.00 | 87.88 | 89.83 | 87.75 |
| MALT-Stag | 97.20 | 96.90 | 88.52 | 88.50 | 86.80 |
| MICA | 97.60 | 97.30 | 88.52 | 87.60 | 85.80 |
| P3 | 97.46 | 96.51 | 87.88 | 89.96 | 87.86 |
Table 1: Results for different configurations.
see that seven of the eleven dimensions that are useful for the gold condition are still useful, most of them structural. However, we also expect to see a shift, as some dimensions are harder to predict with sufficient accuracy. In particular, we see that rfront no longer helps. We hypothesize that this is because there is a large number of possible values for this dimension (more than for lfront, because of the syntax of English), and that an error immediately reduces the usefulness of this dimension. Perhaps as a result, the dsubcat dimension is useful in the predicted condition. The dsubcat dimension abstracts over actual phrase structure, and therefore has a smaller set of possible values, while still providing some of the same information that the dsubcat dimension provides (what depends this head expects).
Now we turn to the second ablation study, in which we concentrate on specific features rather than dimensions. To pick out those individual features (e.g. s0A, s1B, …) in the feature model of the remaining supertag dimensions (e.g. dsubcat, ssubcat, …) that cause a decrease in performance, we performed another level of feature ablation. We use the same feature model we used in the first ablation study. For each supertag dimension that remained after the first ablation study, we removed each corresponding machine learning feature one by one in and computed the parsing accuracy. For example, if we consider supertag dimension dsubcat (represented as A), then we performed experiments where we removed the feature s0A in the feature model, followed by s1A and so on, every time observing the effects on the parsing accuracy. This was done for every remaining supertag dimension. Again, at the end of this set of experiments we eliminated those features from our feature model that cause a decrease in parsing performance when included. Because of the large number of results, we do not present them in detail.
Till now we had considered only the supertag dimensions in our model independently. Our last set of experiments comprises combining some of these features from the feature model. Here, we used our intuition to propose certain combinations. One set of features we combined were the ones corresponding to the dimensions ‘lfront’ and ‘rfront’. These correspond to ordered list of frontier nodes to the left and right of the main lexical anchor respectively. We merge both lfront or rfront with the root of the elements on top of the stack and buffer. These features were then combined with the ‘dir’ dimension which gave encouraging results. We tried 8 different combinations in this manner and got the best results for the following feature model which is shown in Table 6. This set of features also includes those features that correspond to non-supertag features that gave us the best performance.
The results of P3 are displayed in the last line of Table 1. As one can see the decomposed representation of the supertag has a beneficial impact for both the gold and predicted supertag conditions. The error reduction for gold supertags (UAS) is 15%; for predicted, the error reduction is much smaller (1%). We think this smaller error reduction may be due to the fact that in our feature engineering, which was guided by our intuition, we did not take into account the accuracy of different dimensions, assuming implicitly the case in which the dimensions are correctly predicted. Our new results are better than the best published parsing results so far on this corpus, as far as we know.
5 Conclusion
We have presented work in progress, that shows that supertagging can be useful for transition-based parsing. Our initial experiments suggest that considering the dimensions of the supertag can help further.
A major problem is devising machine learning features for the parser from the dimensions, given the very large number of possibilities due to the combinatorics of the combined features. In future work, we plan to use deep learning to obviate the need for feature engineering. This will also entail using word embeddings, which we will also use for supertagging. We will look to the rich literature on supertagging and parsing in CCG for guidance. In addition, we will also start using predicted POS tags in our experiments.
References
Srinivas Bangalore and Aravind Joshi. 1999. Supertagging: An approach to almost parsing. *Computational Linguistics, 25*(2):237–266.
Srinivas Bangalore, Patrick Haffner, and Gaël Emami. 2005. Factoring global inference by enriching local representations. Technical report, AT&T Labs – Research.
Table 2: Ablation study for supertag linguistic features, with gold standard supertags and predicted supertags. Each row lists one feature which was removed in turn. The resulting difference in performance is shown (labeled and unlabeled dependency accuracy without punctuation), first for gold supertags, then for predicted supertags. If a result gets worse upon removal of a feature (negative value), then that dimension is important. We show the retained dimensions by boldfacing their resulting change in accuracy.
| Feature | Gold LAS | Gold UAS | Predicted LAS | Predicted UAS |
|-----------|---------|---------|---------------|---------------|
| predaux | +.07 | +.05 | +.04 | 0 |
| rel | +.07 | +.06 | -.06 | -0.05 |
| particle | +.05 | +.05 | 0 | -.05 |
| coanc | +.04 | +.02 | 0 | -.07 |
| ssbbcat | +.04 | +.03 | 0 | -.01 |
| wh | +.02 | +.02 | +.05 | +.02 |
| comp | +.01 | +.01 | -.01 | -.05 |
| dssbbcat | +.01 | +.02 | -.07 | -.09 |
| pred | 0 | 0 | +.06 | +.03 |
| Feature | Gold LAS | Gold UAS | Predicted LAS | Predicted UAS |
|-----------|---------|---------|---------------|---------------|
| datshift | -.01 | -.01 | +.07 | +.03 |
| voice | -.02 | -.02 | -.03 | -.07 |
| esubj | -.03 | -.02 | -.03 | -.06 |
| appo | -.04 | -.04 | +.02 | 0 |
| substnodes| -.04 | -.02 | 0 | -.01 |
| adnodes | -.04 | -.04 | -.17 | -.19 |
| modif | -.07 | -.10 | -.09 | -.11 |
| lfront | -.07 | -.06 | -.05 | -.07 |
| rfront | -.16 | -.15 | +.02 | -.02 |
| root | -.32 | -.32 | -.09 | -.12 |
| dir | -.90 | -.88 | -.40 | -.43 |
Yoav Freund and Robert E Schapire. 1999. Large margin classification using the perceptron algorithm. *Machine learning*, 37(3):277–296.
Alexandra Kinyon. 2000. Hypertags. In *Proceedings of the 18th International Conference on Computational Linguistics (COLING 2000)*.
Alexis Nasr and Owen Rambow. 2006. Parsing with lexicalized probabilistic recursive transition networks. In *Finite-State Methods and Natural Language Processing*, Springer Verlag Lecture Notes in Computer Science.
Joakim Nivre, Johan Hall, and Jens Nilsson. 2004. Memory-based dependency parsing. In *HLT-NAACL 2004 Workshop: Eighth Conference on Computational Natural Language Learning (CoNLL-2004)*, pages 49–56, Boston, Massachusetts, USA.
Hiroki Ouchi, Kevin Duh, and Yuji Matsumoto. 2014. Improving dependency parsers with supertags. In *Proceedings of the 14th Conference of the European Chapter of the Association for Computational Linguistics, volume 2: Short Papers*, pages 154–158, Gothenburg, Sweden, April. Association for Computational Linguistics.
Srinivas Bangalore, Pierre Boullier, Alexis Nasr, Owen Rambow, and Benoît Sagot. 2009. MICA: A probabilistic dependency parser based on tree insertion grammars. In *NAACL HLT 2009 (Short Papers)*.
Pierre Boullier and Philippe Deschamp. 1988. Le système SYNTAX™ – manuel d’utilisation et de mise en œuvre sous UNIX™. http://syntax.gforge.inria.fr/syntax3.8-manual.pdf.
John Chen. 2001. *Towards Efficient Statistical Parsing Using Lexicalized Grammatical Information*. Ph.D. thesis, University of Delaware.
Koby Crammer, Ofer Dekel, Joseph Keshet, Shai Shalev-Shwartz, and Yoram Singer. 2006. On-line Passive-Aggressive Algorithms. *Journal of Machine Learning Research*, 7:551–585.
Table 3: List of supertag dimensions used, with short name used in the tables of machine learning features
| A | dsubcat | B | ssubcat | C | voice |
|---|---------|---|---------|---|-------|
| D | comp | E | datshift | F | root |
| G | lfront | H | rfront |
| J | adjnodes | K | substnodes | L | rel |
| M | particle | N | coane | O | modif |
| P | dir | Q | pred | R | esubj |
| S | wh | T | appo | U | predaux |
Table 4: Baseline feature model
Table 5: Parser 2 feature model (in addition to the features shown in Table 4).
Table 6: Parser 3 feature model (in addition to the features shown in Table 4 and Table 5).
| 2025-03-06T00:00:00 |
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BEING VAN KAMPEN IS A UNIVERSAL PROPERTY∗
TOBIAS HEINDELA, AND PAWEŁ SOBOCIŃSKIB
a Laboratoire d’Informatique de Paris-Nord, Université de Paris, France
e-mail address: [email protected]
b DSSE, Electronics and Computer Science, University of Southampton, United Kingdom
e-mail address: [email protected]
ABSTRACT. Colimits that satisfy the Van Kampen condition have interesting exactness properties. We show that the elementary presentation of the Van Kampen condition is actually a characterisation of a universal property in the associated bicategory of spans. The main theorem states that Van Kampen cocones are precisely those diagrams in a category that induce bicolimit diagrams in its associated bicategory of spans, provided that the category has pullbacks and enough colimits.
INTRODUCTION
Exactness, or in other words, the relationship between limits and colimits in various categories of interest is a research topic with several applications in theoretical computer science, including the solution of recursive domain equations [35], semantics of concurrent programming languages [37] and the study of formal grammars and transformation systems [10]. Researchers have identified several classes of categories in which certain limits and colimits relate to each other in useful ways; extensive categories [7, 31] and adhesive categories [29] are two relatively recent examples. Going further back, research on toposes and quasitoposes involved elaborate study of their exactness properties [20, 38].
Extensive categories [7] have coproducts that are “well-behaved” with respect to pullbacks; more concretely, they are disjoint and stable under pullback. Extensivity has been used by mathematicians [6] and computer scientists [33] alike. In the presence of products, extensive categories are distributive [7] and thus can be used, for instance, to model circuits [36] or to give models of specifications [13]. Sets and topological spaces inhabit extensive categories while quasitoposes are not, in general, extensive [21].
Adhesive categories [28, 29] have pushouts along monos that are similarly “well-behaved” with respect to pullbacks—they are instances of Van Kampen squares. Adhesivity has been used as a categorical foundation for double-pushout graph transformation [28, 11] and has
∗ This paper is an extended version of the CALCO ’09 paper “Van Kampen colimits as bicolimits in Span” [17].
found several related applications [12, 34]. Toposes are adhesive [30] but quasitoposes, in general, are not [22].
The elementary characterisation of coproducts in extensive categories and pushouts along monos in adhesive categories can be seen as specific instances of a general condition that can be expressed for any colimit. Cockett and Guo dubbed the colimits that satisfy this condition Van Kampen (vk) colimits [9], generalising the Van Kampen squares of [28]. Indeed, examples of vk-colimits include coproducts in extensive categories and pushouts along monos in adhesive categories; the simplest example is a strict initial object.
The definition of vk-colimits relies only on elementary notions of category theory. This feature, while attractive because of the implied simplicity, obscures relationships with other categorical concepts; the mathematical meaning of vk-colimits, so to speak. More abstract characterisations exist for extensive and adhesive categories. For instance, a category C is extensive if and only if the functor +: C ↓ A × C ↓ B → C ↓ A + B is an equivalence for any A, B ∈ C [31, 7]; adhesive categories can be characterised in a similar manner [29]. Our definition of vk-cocone is of the latter kind, i.e. in terms of an equivalence of categories. We also provide an elementary characterisation in the spirit of Cockett and Guo.
This paper contains one central theorem: vk-cocones are those diagrams that are bicolimit diagrams when embedded in the associated bicategory of spans. Bicolimits are the canonical notion of colimit in a bicategory. This characterises “being Van Kampen” as a universal property. We believe that this insight captures and explains the essence of the various aforementioned well-behaved colimits studied in the literature.
Structure of the paper. In Section 1 we examine the category of spans and its applications. In Section 2 we exhibit the relationship between coproducts in extensive categories and coproducts in their associated categories of spans, and explain why it is necessary to consider bicategories of spans in order to extend this relationship to arbitrary colimits. In Section 3 we isolate the relevant class of bicategories and recall the related notions. In Section 4 we give a definition of vk-cocones together with an elementary characterisation and several examples. In Section 5 we recall the definition of bicolimits and prove several technical lemmas that allow us to pass between related concepts in a category and its associated bicategory of spans. The main theorem is proved in Section 6.
1. Spans and generalised relations
There are several concepts in category theory that generalise relations between sets. The set theoretical concept of multirelation from C to D is a span of functions C ← l→ X →− r→ D, which we will denote (l, X, r): C → D, or simply (l, r). The set X is sometimes referred to as the carrier. Roughly, a pair of elements (c, d) ∈ C × D can be related in a number of ways; concretely this is determined by the size of the preimage at (c, d) of the function (l, r): X → C × D, i.e. (l, r)−1(c, d). Two such spans (l, X, r) and (l′, X′, r′) would normally be considered equivalent if there is a bijection ϕ: X → X′ that satisfies l′ϕ = l and r′ϕ = r. The existence of such a bijection yields an equivalence relation; quotienting by this gives what we shall refer to as an abstract span. Sometimes, for emphasis, we shall refer to ordinary spans as concrete spans. A multirelation is thus an abstract span in the category of sets and functions. Ordinary relations are captured by those abstract spans in which (l, r) is injective.
The concept of a span of morphisms makes sense in any category $\mathbf{C}$, not only $\mathbf{Set}$; indeed we shall make use of the notation introduced in the previous paragraph generally. Extra structure is needed in order to compose spans, hence from this point onwards we assume that $\mathbf{C}$ has pullbacks. Below we give an overview of the category of $\mathbf{C}$-spans, denoted by $\text{Sp}(\mathbf{C})$. Figure 1 accounts for its morphisms, identities and composition. More explicitly,
$$\text{Sp}(\mathbf{C})$$
has the same objects as $\mathbf{C}$ and a morphism from $\mathbf{C}$ to $\mathbf{D}$ is an equivalence class of spans $\mathbf{C} \xleftarrow{X} \mathbf{X} \xrightarrow{r} \mathbf{D}$. The identity on an object $\mathbf{C}$ is a span of identities in $\mathbf{C}$; composition is obtained via pullback as illustrated in Figure 1 on the right. It is not difficult to check that these definitions yield a category. Moreover, when $\mathbf{C} = \mathbf{Set}$ this yields the expected composition of multirelations. Moreover, $\mathbf{C}$ has a standard embedding $\Gamma: \mathbf{C} \rightarrow \text{Sp}(\mathbf{C})$ into the span category. This inclusion acts as the identity on objects and maps each morphism $f: \mathbf{A} \rightarrow \mathbf{B}$ in $\mathbf{C}$ to its graph $\Gamma(f): \mathbf{A} \rightarrow \mathbf{B} = (\text{id}_A, f)$; hence this embedding is also referred to as the graphing functor [14].
Remark 1.1. Another way of generalising the concept of relation between sets to “relations” between categories is via the notion of profunctor from $\mathbf{C}$ to $\mathbf{D}$: it is an ordinary functor $F: \mathbf{C} \times \mathbf{D}^{\text{op}} \rightarrow \mathbf{Set}$ (here $\mathbf{Set}$ could be replaced by another suitable monoidal category $\mathbf{V}$). Composition is via the left Kan extension along the Yoneda embedding [5]. The resulting structure is not a category but a bicategory. Multirelations from $\mathbf{C}$ to $\mathbf{D}$ can be seen as profunctors where $\mathbf{C}$ and $\mathbf{D}$ are considered as discrete categories. Formalising this observation yields a biequivalence from $\text{Span}(\mathbf{Set})$ to the bicategory of profunctors between discrete categories [27]. This fact relies on a special property of $\mathbf{Set}$, namely the equivalence of categories $\mathbf{Set} \downarrow \mathbf{C} \cong [\mathbf{C}, \mathbf{Set}]$, and therefore does not generalise readily.
Spans occur in very different contexts and often allow succinct characterisations of various concepts. For example: Katis, Sabadini and Walters [24] use spans to model systems with boundary (see also [15]); bisimulation has been captured as a span of open maps [23] as well as a span of coalgebra morphisms [2]; an internal category is a monad in the bicategory of spans [4]; interaction categories [1] can be seen as examples of process categories [8], which are certain quotients of span bicategories; Mackey functors are coproduct preserving functors from the span-category [32].
2. Colimits in the span category
We have seen that $\mathbf{C}$ embeds into $\text{Sp}(\mathbf{C})$ and spans can be thought of as generalised relations. It is well-known (see, for example, [14, 1.911]) that in toposes colimits are preserved into the associated category of relations via the standard embedding. A natural question then is what conditions of $\mathbf{C}$ colimits are necessary and sufficient for them to be preserved by the
embedding into $\text{Sp}(C)$. We begin our investigation with the concrete case of coproducts. It turns out that this problem is closely related with the notion of extensive categories, where coproducts interact well with pullbacks.
The following, elementary definition of extensive categories makes this explicit [7].
\textbf{Definition 2.1.} A category is extensive when
1. it has finite coproducts;
2. it has pullbacks along coproduct injections;
3. given a diagram on the left of Figure 2 with the bottom row a coproduct diagram, the top row is a coproduct diagram if only if the two squares are pullbacks.
The relevant observation about coproducts in extensive categories is that the universal property of coproducts does not only apply to morphisms of the category itself but actually extends to spans. More precisely, given an ordinary coproduct $A \to_{i_1} A + B \leftarrow_{i_2} B$ and a pair of morphisms $f: A \to C$ and $g: B \to C$ there exists unique mediating morphism $[f,g]: A + B \to C$; given a coproduct in an extensive category and a pair of spans $A \to (x,h) \to C$ and $B \to (y,k) \to C$ there exists a unique mediating span $A + B \to (x+y,[h,k]) \to C$. This was already noticed by Lindner [32].
More can be said: it turns out that if a coproduct in $C$ is also a coproduct in $\text{Sp}(C)$ then it satisfies the extensivity condition of Figure 2. Hence, the extensivity condition characterises the universal property of coproducts in the “larger universe” of spans. Summarizing, a coproduct in $C$ satisfies the extensivity condition if and only if it is a coproduct in $\text{Sp}(C)$.
\textbf{Proposition 2.2.} Let $C$ be a category with coproducts and pullbacks. Then $C$ is extensive if and only if the graphing functor $\Gamma: C \to \text{Sp}(C)$ preserves coproducts.
\textit{Proof.} The fact that $\Gamma$ preserves coproducts when $C$ is extensive was shown by Lindner [32 Lemma 3].
For the converse, assume that $\Gamma: C \to \text{Sp}(C)$ preserves coproducts. First we shall show that coproducts in $C$ are stable under pullback. Let $A \to_{i_A} A + B \leftarrow_{i_B} B$ be a coproduct diagram and $z: Z \to A + B$. Consider the diagram below.
First assume that $A \leftarrow x - i \rightarrow Z$ and $Z \leftarrow j - y \rightarrow B$ are pullbacks of $A - i_A \rightarrow A + B \leftarrow z - Z$ and $Z \leftarrow i - A + B \leftarrow i_B - B$, respectively. The existence of $k: Z \rightarrow X + Y$ with $ki = i_X$ and $kj = i_Y$ follows from the fact that $(i_A, i_B)$ is a coproduct diagram in $\text{Sp}(C)$. The universal property of $X + Y$ in $C$ implies that $k[i, j] = \text{id}_{X+Y}$ (**). The universal property of $A + B$ in $\text{Sp}(C)$ implies that $(z, \text{id}) = (z, [i, j]k)$ in $\text{Sp}(C)$, which implies the existence of an isomorphism $\varphi: Z \rightarrow Z$ with $[i, j]k = \varphi$ (**). It now follows from (***) that $k$ is split epi and from (****) that it is mono; thus $k$ is an isomorphism.
To verify the second part of the extensivity condition, consider the boundary of the diagram above. We need to show that $A \leftarrow x - X \leftarrow iX - X + Y$ and $X + Y \leftarrow iY - Y \leftarrow yB$ are pullbacks of $A - iA \rightarrow A + B \leftarrow x + y - X + Y$ and $X + Y \leftarrow x + y - A + B \leftarrow iB - B$. Now since $A + B$ is a coproduct in $\text{Sp}(C)$ we get the existence of the interior part of the diagram, with the two squares pullbacks. By the argument in the previous paragraph $Z$ is the coproduct of $X$ and $Y$ and so $k$ is an isomorphism.
The main insight that can be gained by inspection of this proof is a correspondence between existence and uniqueness of mediating spans on the one hand and the two directions of the bi-implication of the Extensivity Condition in Figure 2 on the other hand. An analogous correspondence will recur later in the development of the main result in the bicategory of spans. The necessity of the bicategorical setting when considering arbitrary colimits is the topic of the remainder of this section.
### 2.1. The abstract span category is not enough.
Proposition 2.2 could tempt one to try a generalisation to pushouts in the sense that a pushout is “well-behaved” in $C$ if and only if it is preserved by $\Gamma$ as a pushout in $\text{Sp}(C)$.
A good candidate for a “well-behaved” pushout is given by the notion of Van Kampen squares, which appeared as part of the definition of adhesive categories [28]; indeed this definition was partly motivated by the extensivity condition of coproducts.
**Figure 3. Van Kampen square**
**Definition 2.3** (Van Kampen square). A commutative square $B \leftarrow f - A - m \rightarrow C$, $B - n \rightarrow D \leftarrow g - C$ is Van Kampen when for each commutative cube as illustrated in Figure 3 on the left that has pullback squares as rear faces, its top face is a pushout square if and only if its front faces are pullback squares (see Figure 3).
A category is adhesive when it has pushouts along monomorphisms and these are Van Kampen squares.
Differently from coproducts in extensive categories, Van Kampen squares do not induce pushouts via inclusion into the span category. Roughly, the reason for this is that for every
pair of concrete \( C \)-spans \( C \leftarrow X \rightarrow D \) and \( C \leftarrow X' \rightarrow D \), there may be several different isomorphisms \( \varphi_1, \varphi_2, \ldots : X \to X' \) which witness that \( (l, r): C \to D \) and \( (l', r'): A \to B \) are the same arrow in \( \text{Sp}(C) \).
Figure 4. Van Kampen square in \( C = [\cdot \to \cdot, \text{Set}] \) and a cocone of spans
Our counterexample is a pushout in the category \( \text{Set} \)-arrows, i.e. the functor category \( [\cdot \to \cdot, \text{Set}] \), which is adhesive \([29]\). The objects of this category are functions. They will be depicted as gray boxes in which all input-output pairs are connected by arrows of the form ‘\( \mapsto \)’ (see Figure 4); each element of the domain is rendered as a small circle ‘\( \circ \)’, while each element of the codomain is represented by a star ‘\( \star \)’.
Now Figure 4(A) is a pushout of a pair of monomorphisms and hence a Van Kampen square. Consider the cocone for the “same” span of morphisms in \( \text{Sp}(C) \) described in Figure 4(B); in the latter figure the gray arrows belong to \( C \) while the arrows \( s \) and \( t \) belong to \( \text{Sp}(C) \). Figure 4(C) shows the diagonal span \( d \) of this square. Observe that any concrete representative of the diagonal span \( d \) actually has a non-trivial symmetry group which consists of one non-identity automorphism as well as the identity.
As illustrated in Figure 5 each of the mediating spans can be constructed in the category \( C \) by means of the Van Kampen square property. The cocone from Figure 4(B) consisting of \( s \) and \( t \) is now pointing to the top. Commutativity of the cocone in \( \text{Sp}(C) \) gives a pair of \( C \)-pullbacks in the back of each of the diagrams in Figure 5. Depending on choices of pullbacks and witnesses for the abstract equality of the composite spans, we obtain two different diagrams over which we can take a pushout. (In Figure 5 we tried to express this fact by “switching” of the two stars in the carrier of right span of the cocone.) These two diagrams on top of a cube yield two different mediating arrows in the category of spans by taking the pushout in \( C \). In the end, we obtain two different mediating spans to the same cocone in \( \text{Sp}(C) \), and thus \( \cdot \leftarrow \Gamma(n') \rightarrow \cdot \leftarrow \Gamma(m') \rightarrow \cdot \) cannot be a pushout of \( \cdot \leftarrow \Gamma(m) \rightarrow \cdot \leftarrow \Gamma(n) \rightarrow \cdot \).
Remark 2.4. To solve the problem of non-trivial symmetry groups of spans one could try to restrict to partial map spans, i.e. those spans with a monomorphisms from the carrier into the domain. This however would yield a (properly) weaker notion, which one could call partial Van Kampen square \([16]\). In fact, in the category of sets and, more generally, any
elementary topos, all colimits are partial Van Kampen colimits while there are examples of pushouts in Set, which are not Van Kampen [29].
The only canonical way to “tame” the non-trivial symmetry groups of spans is to keep track of the involved isomorphisms, i.e. we have to work in a bicategory $\text{Span}(C)$ of (concrete) spans in $C$.
It turns out that by moving to the setting of bicategories (recalled in the proceeding section) we obtain not only that Van Kampen squares characterise those pushouts that are preserved by $\Gamma$ but that a general Van Kampen condition (introduced in Section 4) characterises those colimits that satisfy the bicategorical universal property of colimits.
3. Bicategories
Here we introduce background on bicategories [4, 5, 27] and some notational conventions. Our focus is the bicategory of spans over a category $C$ with a choice of pullbacks (see Example 3.3). This allows us to avoid unnecessary book-keeping by considering only those bicategories that satisfy the identity axioms strictly. It is only a cosmetic choice, the development can be easily adapted to the standard setting of bicategories.
**Definition 3.1** (Strictly unitary bicategories). A strictly unitary (su) bicategory $\mathcal{B}$ consists of:
- a collection $\text{ob} \mathcal{B}$ of objects;
- for $A, B \in \text{ob} \mathcal{B}$ a category $\mathcal{B}(A, B)$, the objects and arrows of which are called, respectively, the arrows and the 2-cells of $\mathcal{B}$. Composition is denoted by $\circ$ and referred to as vertical composition. Given $(f : A \to B) \in \mathcal{B}(A, B)$, its identity 2-cell will be denoted $\iota_f : f \to f$. Each $\mathcal{B}(A, A)$ contains a special object $\text{id}_A : A \to A$, called the identity arrow;
• for $A, B, C \in \text{ob } B$, a functor $c_{A,B,C} : B(A, B) \times B(B, C) \to B(A, C)$ called horizontal composition. On objects, $c_{A,B,C}(f, g)$ is written $g \circ f$, while on arrows $c_{A,B,C}(\gamma, \delta)$ it is $\delta \circ \gamma$. For any $f : A \to B$ we have $\text{id}_B \circ f = f \circ \text{id}_A$;
• for $A, B, C, D \in \text{ob } B$, arrows $f : A \to B$, $g : B \to C$ and $h : C \to D$ an associativity natural isomorphism $\alpha_{A,B,C,D}(f, g, h) : h \circ (g \circ f) \to (h \circ g) \circ f$. It satisfies the coherence axioms: for any composable $f, g, h, k$, we have $\alpha_{f, \text{id}, g} = \text{id}_{g}$ and also that the following 2-cells are equal:
\[
\begin{array}{c}
\begin{array}{c}
E \\
\downarrow^k
\end{array}
\begin{array}{c}
D \\
\downarrow^h
\end{array}
\begin{array}{c}
C \\
\downarrow^\alpha
\end{array}
\begin{array}{c}
B \\
\downarrow^{g \circ f}
\end{array}
\begin{array}{c}
A \\
\end{array}
\end{array}
\]
\[
\begin{array}{c}
\begin{array}{c}
E \\
\downarrow^k
\end{array}
\begin{array}{c}
D \\
\downarrow^h
\end{array}
\begin{array}{c}
C \\
\downarrow^{\text{ho}(g \circ f)}
\end{array}
\begin{array}{c}
B \\
\downarrow^{(h \circ g) \circ f}
\end{array}
\begin{array}{c}
A \\
\end{array}
\end{array}
\]
\[E, D, C, B, A \]
Example 3.2. Any (ordinary) category $C$ is a (su-)bicategory with trivial 2-cells.
As we have seen, composition in the category $\text{Sp}(C)$ is obtained via pullback. Because of the universal property of pullbacks and the fact that the arrows of $\text{Sp}(C)$ are abstract spans, composition defined in this fashion is well-defined. Instead, in order to compose concrete spans we shall need to assume some choice of pullback in $C$; this means that for any cospan $X \leftarrow f \rightarrow Z \leftarrow g \rightarrow Y$ there is a chosen object $X \times_Z Y$ and span $X \leftarrow \pi_1 - X \times_Z Y \rightarrow \pi_2 \rightarrow Y$ that together with $f$ and $g$ forms a pullback square. Moreover we assume that the choice preserves identities: if $f$ is $\text{id}_X$ then $X \times_Z Y = Y$ and $\pi_1 = \text{id}_Y$, and analogously for $g$. This is a completely harmless assumption since the identity of the chosen pullback diagram for any cospan is insignificant: any two choices are equivalent.
Example 3.3 (Span bicategory [4]). Assume that $C$ has a choice of pullbacks that preserves identities. $\text{Span}(C)$ has:
• as objects, the objects of $C$, i.e. $\text{ob } \text{Span}(C) = \text{ob } C$;
• as arrows from $C$ to $D$, the $C$-spans $C \leftarrow l \rightarrow X \rightarrow r \rightarrow D$. The composition with another span $D \leftarrow l' \rightarrow Y \rightarrow r' \rightarrow E$ is obtained via the chosen pullback as illustrated below; however this composition is only associative up to canonical isomorphism. The identity on an object $C$ is the span $C \leftarrow \text{id} \rightarrow C \rightarrow \text{id} \rightarrow C$.
\[
\begin{array}{c}
\begin{array}{c}
C \\
\downarrow^l
\end{array}
\begin{array}{c}
X \\
\downarrow^r
\end{array}
\begin{array}{c}
Y \\
\downarrow^{r'}
\end{array}
\begin{array}{c}
E \\
\end{array}
\end{array}
\]
\[
\begin{array}{c}
\begin{array}{c}
C \\
\downarrow^l
\end{array}
\begin{array}{c}
D \\
\downarrow^{l'}
\end{array}
\begin{array}{c}
E \\
\end{array}
\end{array}
\]
• its 2-cells $\xi : (l, r) \rightarrow (l', r')$ are $C$-arrows $\xi : X \rightarrow X'$ between the respective carriers such that $l' \circ \xi = l$ and $r' \circ \xi = r$.
For our purposes it suffices to consider strict homomorphisms between su-bicategories.
Definition 3.4 (Strict homomorphisms [4]). Let $\mathcal{A}$ and $\mathcal{B}$ be su-bicategories. A strict homomorphism $\mathcal{F} : \mathcal{A} \rightarrow \mathcal{B}$ consists of a function $\mathcal{F} : \text{ob } \mathcal{A} \rightarrow \text{ob } \mathcal{B}$ and a family of functors $\mathcal{F}(A, B) : \mathcal{A}(A, B) \rightarrow \mathcal{B}(FA, FB)$ such that:
(i) for all $A \in \mathcal{A}$, $\mathcal{F}(\text{id}_A) = \text{id}_{\mathcal{F}A}$;
(ii) for all $f: A \to B$, $g: B \to C$ in $\mathcal{A}$, $\mathcal{F}(g \circ f) = \mathcal{F}(g) \circ \mathcal{F}(f)$;
(iii) $\mathcal{F}\alpha_{A,B,C,D} = \alpha_{\mathcal{F}A, \mathcal{F}B, \mathcal{F}C, \mathcal{F}D}$.
Example 3.5. The following strict homomorphisms will be of interest to us:
- the covariant embedding $\Gamma: \mathcal{C} \to \text{Span}(\mathcal{C})$ which acts as the identity on objects and takes an arrow $f: C \to D$ to its graph $(\text{id}, f): C \to D$. It allows to consider the objects and morphisms in the “universe” $\mathcal{C}$ in the “larger universe” Span($\mathcal{C}$);
- $\Gamma F: \mathcal{J} \to \text{Span}(\mathcal{C})$ where $F: \mathcal{J} \to \mathcal{C}$ is a functor. It allows to lift every diagram in $\mathcal{C}$ to a diagram in Span($\mathcal{C}$);
- given a su-bicategory $\mathcal{B}$ and $B \in \text{ob}\mathcal{B}$, we shall abuse notation and denote the strict homomorphism from $\mathcal{J}$ to $\mathcal{B}$ which is constant at $B$ by $\Delta_B$. It is used to define conical bi-colimits for diagrams. Note that in the case of $\mathcal{B} = \text{Span}(\mathcal{C})$, "$\Delta = \Gamma\Delta$".
Definition 3.6 (Lax transformations). Given strict homomorphisms $F, G: \mathcal{A} \to \mathcal{B}$ between su-bicategories, a (lax) transformation consists of arrows $\kappa_A: F_A \to G_A$ for all $A \in \mathcal{A}$ and 2-cells $\kappa_f: Gf \circ \kappa_A \Rightarrow \kappa_B \circ Ff$ for all $f: A \to B$ in $\mathcal{A}$ (illustrated below)
\[
\begin{array}{c}
\xymatrix{ FA \ar[rr]^{Ff} \ar[dr]_{\kappa_A} & & FB \\
& G_A \ar[ur]_{\kappa_B} \ar[dr]_{\kappa_f} & \\
& GB & GC }
\end{array}
\]
such that:
(i) $\kappa_{\text{id}_A} = \iota_{\kappa_A}$ for each $A \in \mathcal{A}$;
(ii) for any $f: A \to B$, $g: B \to C$ in $\mathcal{A}$, the following 2-cells are equal:
\[
\begin{array}{c}
\xymatrix{ FA \ar[rr]^{Ff} \ar[dr]_{\kappa_A} & & FB \ar[rr]^{Fg} \ar[dr]_{\kappa_B} & & FC \\
& G_A \ar[ur]_{\kappa_B \circ Ff} \ar[dr]_{\kappa_f} & & GB \ar[ur]_{\alpha} \ar[dr]_{\kappa_B \circ Ff} & & GC \\
& G_A \ar[ur]_{G_g \circ \kappa_B} & & GB \ar[ur]_{\alpha} & & GC }
\end{array}
\]
A transformation is said to be strong when all the $\kappa_f$ are invertible 2-cells. Given $B \in \mathcal{B}$ and a homomorphism $\mathcal{M}: \mathcal{J} \to \mathcal{B}$, a pseudo-cocone $\lambda: \mathcal{M} \to \Delta B$ is a synonym for a strong transformation $\lambda: \mathcal{M} \to \Delta B$.
Because bicategories have 2-cells, there are morphisms between transformations. They are called modifications and are defined as follows.
Definition 3.7 (Modifications [4, 26]). Given natural transformations $\kappa, \lambda$ from $\mathcal{F}$ to $\mathcal{G}$, a modification $\Xi: \kappa \to \lambda$ consists of 2-cells $\Xi_A: \kappa_A \to \lambda_A$ for $A \in \mathcal{A}$ such that, for all
Composition is componentwise, the identity modification on \( \kappa \) is
\[
I_\kappa = \{ i_{\kappa_A} \}_{A \in \mathcal{A}}.
\]
Given \( \mathcal{SU} \)-bicategories \( \mathcal{A} \) and \( \mathcal{B} \), let \( \text{Hom}_l[\mathcal{A}, \mathcal{B}] \) denote the \( \mathcal{SU} \)-bicategory of homomorphisms, lax transformations and modifications. Let \( \text{Hom}_s[\mathcal{A}, \mathcal{B}] \) denote the corresponding \( \mathcal{SU} \)-bicategory with arrows the strong transformations.
4. Van Kampen cocones
The extensivity condition for coproducts and the notion of Van Kampen condition for pushouts are both examples (for particular colimits) of a more general condition. Colimit diagrams that satisfy it are called Van Kampen cocones. Here we give this definition together with an elementary characterisation.
Let us consider coproducts as a motivating example. A coproduct diagram
\[
A \rightarrow i_1 A + B \leftarrow i_2 B
\]
in a category \( \mathcal{C} \) is a cocone of the two-object diagram \( \langle A, B \rangle \). If \( \mathcal{C} \) has chosen pullbacks (along coproduct injections) then \( i_1 \) yields a functor \( i_1^*: \mathcal{C} \downarrow (A + B) \rightarrow \mathcal{C} \downarrow A \) that takes an arrow \( x: X \rightarrow A + B \) to its pullback \( i_1^*x: i_1^*X \rightarrow A \) along \( i_1 \) — similarly for \( i_2 \). Then \( x \mapsto \langle i_1^*x, i_2^*x \rangle \) defines the functor \( \langle i_1^*, i_2^*\rangle: (\mathcal{C} \downarrow A + B) \rightarrow (\mathcal{C} \downarrow A \times \mathcal{C} \downarrow B) \) on objects. The coproduct \( A + B \) satisfies the extensivity condition exactly when this functor is an equivalence of categories (see [7]).
The situation readily generalises as follows: replace \( \langle i_1, i_2 \rangle \) by any cocone \( \kappa: \mathcal{D} \rightarrow \Delta A \) from a functor \( \mathcal{D}: \mathcal{J} \rightarrow \mathcal{C} \) to an object \( A \) in a category \( \mathcal{C} \) with (enough) pullbacks. Any arrow \( x: X \rightarrow A \) induces a natural transformation \( \Delta x: \Delta X \rightarrow \Delta A \) in the obvious way. Since also \( \kappa: \mathcal{D} \rightarrow \Delta A \) is a natural transformation, \( \Delta x \) can be pulled back along \( \kappa \) in the functor category \( [\mathcal{J}, \mathcal{C}] \) yielding a natural transformation \( \kappa^*(\Delta x): \kappa^*(\Delta X) \rightarrow \mathcal{D} \).
\[
\begin{array}{ccc}
X & \xrightarrow{\Delta x} & \kappa^*(\Delta X) \\
\downarrow & \kappa^*(\Delta x) & \\
A & \kappa \downarrow & \mathcal{D}
\end{array}
\]
The described operation extends to a functor \( \kappa^*(\Delta \omega) \) from \( \mathcal{C} \downarrow A \) to (a full subcategory of) \( [\mathcal{J}, \mathcal{C}] \downarrow \mathcal{D} \) using the universal property of pullbacks; it takes morphisms with codomain \( A \) to cartesian transformations with codomain \( \mathcal{D} \).
**Definition 4.1 (Cartesian transformations).** Let \( \mathcal{E}, \mathcal{D} \in [\mathcal{J}, \mathcal{C}] \) be functors and let \( \tau: \mathcal{E} \rightarrow \mathcal{D} \) be a natural transformation. Then \( \tau \) is cartesian when all the naturality squares are pullback
squares, i.e. if the pair $E_i \leftarrow \tau_i - D_i \rightarrow D_j$ is a pullback of $E_i - \xi_u \rightarrow E_j \leftarrow \tau_j - D_j$ for all $u: i \rightarrow j$ in $J$.
Let $[J, C]\downarrow D$ be the slice category over $D$, which has natural transformations with codomain $D$ as objects. Let $[J, C]\downarrow \downarrow D$ denote the full subcategory of $[J, C]\downarrow D$ with the cartesian transformations as objects.
**Definition 4.2** (Van Kampen cocones). Let $D: J \rightarrow C$ be a functor, and let $\kappa: D \rightarrow \Delta A$ be a cocone such that pullbacks along each $\kappa_i$ exist ($i \in J$). Then $\kappa$ is Van Kampen (VK) if the functor $\kappa^*(\Delta A): C \downarrow A \rightarrow [J, C]\downarrow D$ is an equivalence of categories.
**Proposition 4.3** (Elementary VK characterisation). Suppose that $C$ has pullbacks and $J$-colimits, $D: J \rightarrow C$ is a functor and $\kappa: D \rightarrow \Delta A$ a cocone such that $C$ has pullbacks along $\kappa_i$ ($i \in J$). Then $\kappa: D \rightarrow \Delta A$ is Van Kampen iff for every cartesian transformation $\tau: E \rightarrow D$, arrow $x: X \rightarrow A$ and cocone $\beta: E \rightarrow \Delta X$ such that $\kappa \circ \tau = \Delta x \circ \beta$, the following are equivalent:
(i) $\beta: E \rightarrow \Delta X$ is a $C$-colimit;
(ii) $D_i \leftarrow \tau_i - E_i - \beta_i \rightarrow X$ is a pullback of $D_i - \kappa_i \rightarrow A \leftarrow x - X$ for all $i \in J$.
**Proof.** The proof is a straightforward generalisation of the corresponding characterisation of Van Kampen squares [29, Proposition 2.6]. Assume (i)$\Leftrightarrow$(ii) as well as existence of $J$-colimits. Essential surjectivity of $\kappa^*$ follows easily from (i)$\Rightarrow$(ii). The fact that $\kappa^*$ is faithful follows from (ii)$\Rightarrow$(i) and it is full because of existence of $J$-colimits.
Conversely, in the presence of $J$-colimits, $\kappa^*$ has a left adjoint defined in the obvious way by taking the appropriate colimits. Then if $\kappa^*$ is an equivalence, it follows that the unit and counit of this adjunction are isomorphisms. Now (i)$\Rightarrow$(ii) is implied by the fact that the unit is an isomorphism and (ii)$\Rightarrow$(i) is a consequence of the counit being an isomorphism. □
Cockett and Guo’s [9] definition of Van Kampen colimits is the equivalence of (i) and (ii) in our Proposition 4.3. If the relevant pullbacks and colimits exist then clearly the two definitions are equivalent.
**Remark 4.4.** With the assumptions of Proposition 4.3, any Van Kampen cocone $\kappa: D \rightarrow \Delta A$ is a colimit diagram of $D$ in $C$ (take $\tau = \text{id}_D$ and $x = \text{id}_A$).
**Example 4.5.** The following well-known concepts are examples of VK-cocones:
(i) a strict initial object is a VK-cocone for the functor from the empty category;
(ii) a coproduct diagram in an extensive category \([7]\) is a \(\text{VK}\)-cocone for a functor from the discrete two object category;
(iii) a regular epimorphism \(p : E \to B\) in a regular category is the Van Kampen cocone of its kernel pair \([1] r, s : P \rightrightarrows E\), i.e. in any commuting diagram of the following form
\[
\begin{array}{c}
Q \xrightarrow{u} F \\
\downarrow v \quad \downarrow q \\
P \xrightarrow{r} E \xrightarrow{p} B
\end{array}
\]
in which \(u, v : Q \rightrightarrows F\) is a kernel pair (of some morphism) and the squares on the left are pullbacks, the morphism \(q\) is the coequaliser of \(u, v : Q \rightrightarrows F\) if and only if the right square is a pullback. This is a direct consequence of a result of Barr and Kock \([3, \text{Example 6.10}]\). Notice that in this case the colimits in question are coequalisers of kernel pairs; this means that we implicitly restrict the category on the right hand side of the equivalence in Definition \([4,2]\) to the full subcategory with objects the kernel pairs.
A \(\text{VK}\)-cocone from a span is a Van Kampen square (see Definition \([2,3]\)). In the left hand diagram in Figure \(3\) the two arrows \(B \xleftarrow{f} A \xrightarrow{m} C\) describe a diagram from the three object category \(\cdot \leftarrow \cdot \to \cdot\), and the cospan \(B \xrightarrow{n} D \xleftarrow{g} C\) gives a cocone for this diagram. That the back faces are pullback squares means that we have a cartesian transformation from \(B' \xleftarrow{f'} A' \xrightarrow{m'} C\) to \(B \xleftarrow{f} A \xrightarrow{m} C\). Adhesive categories are thus precisely categories with pullbacks along monomorphisms exist and are \(\text{VK}\)-cocones.
5. Colimits in the span bicategory
In Section \([2]\) we showed that coproducts that satisfy the extensivity condition are precisely those that are preserved into the span category (Proposition \([2,2]\) when the latter is well-defined, i.e. if all pullbacks exist. This correspondence failed when we considered pushouts which are Van Kampen squares—a condition for pushouts analogous to the extensivity condition for coproducts. The main result of this paper, Theorem \([6,3]\) asserts that the correspondence holds not only for pushouts but for general Van Kampen cocones when considering the canonical embedding into the span bicategory providing that it exists, i.e. the ambient category has all pullbacks. In order to show this we shall need to recall the canonical notion of colimit in bicategories in general and in bicategories of spans in particular.
To give the flavour of the correspondence between \(\text{VK}\)-cocones in \(C\) and colimits in \(\text{Span}(C)\) we outline how Van Kampen squares induce (bi)pushout squares via the embedding \(\Gamma\). An illustration of this is given in Figure \(6\).
At the base of Figure \(F(A)\) is (the image of) a \(C\)-span \(B \xleftarrow{f} A \xrightarrow{m} C\) in \(\text{Span}(C)\). Further, if \((b, b') : B \to E\) and \((c, c') : C \to E\) are a pseudo-cocone for \(B \xleftarrow{\Gamma f} A \xrightarrow{\Gamma m} C\) in \(\text{Span}(C)\) then taking pullbacks of \(b\) along \(f\) and \(c\) along \(m\) (in \(C\)) yields isomorphic objects over \(A\), say \(a_0\) and \(a_c\); as a result we obtain two pullback squares that will be the back faces of a commutative cube.
\(^1\)The kernel pair of a morphism is obtained by pulling it back along itself.
Next, let the bottom of Figure 6 (b) be (the image of) a commuting $C$-square, thus yielding another pseudo-cocone of $B \leftarrow f - A - m \rightarrow C$, namely $B - \Gamma f - A - \Gamma m - \rightarrow C$. If there is a mediating morphism $(d, d')$: $D \rightarrow E$ to $B - (b, b') \leftarrow E - (c, c') - \rightarrow E$ of Figure 6 (a) then pulling back $d$ along $n$ and $g$ results in morphisms $d_n$ and $d_g$, which are isomorphic to $b$ and $c$; the resulting pullback squares provide the front faces of a cube.
Now, if $B - n \rightarrow D - g - C$ is a $vk$-cocone of $B - f - A - m \rightarrow C$ then such a mediating morphism can be constructed by taking $D'$ as the pushout of $B'$ and $C'$ over either one of $A'$ or $A''$. The morphisms $d: D' \rightarrow E$ and $d': D' \rightarrow D$ arise from the universal property of pushouts, everything commutes and the front faces are pullback squares because of the $vk$-property. Further this mediating morphism is essentially unique, which means that given any other span $(e, e')$: $D \rightarrow E$ such that both $(b, b') \cong (e, e') \circ \Gamma n$ and $(c, c') \cong (e, e') \circ \Gamma g$ hold, the two spans $(e, e')$ and $(d, d')$ are isomorphic via a unique isomorphism.
Though this sketch lacks relevant technical details, it gives a good indication of the diagrams that are involved in the proof of the fact that Van Kampen squares in $C$ induce bipushouts in Span($C$). Moreover, also the converse holds, i.e. if the image of a pushout is a bipushout in Span($C$) then it is a Van Kampen square.
5.1. **Span bicolimits.** Clearly any diagram in Span($C$) can be “decomposed” into a diagram in $C$: each arrow in Span($C$) gives two $C$-arrows from a carrier object; moreover a 2-cell is a compatible $C$-arrow between the carriers.
We shall start with further observations along these lines. Roughly we are able to “drop a dimension” in the following sense. First, it is easy to see that $[J, C]$ inherits a choice of pullbacks from $C$. In particular, it follows that Span($[J, C]$) is a su-bicategory. Now, given $F, G \in [J, C]$ we note that:
- spans of natural transformations from $F$ to $G$ correspond to lax transformations from $\Gamma F$ to $\Gamma G$; and
- morphisms of such spans are the counterpart of modifications.
The following lemma makes this precise.
Lemma 5.1. There is a strict homomorphism
\[ \Gamma: \text{Span}([J, C]) \to \text{Hom}_J [J, \text{Span}(C)] \]
that takes \( F \in [J, C] \) to \( \Gamma F \) and is full and faithful on both arrows and 2-cells.
Proof. A span of natural transformations \( (\varphi, \psi): F \to G \) with carrier \( H \) is mapped to a lax transformation from \( \Gamma F \) to \( \Gamma G \) as follows: for each \( i \in J \), we put \( \kappa_i := (\varphi_i, \psi_i): F_i \to G_i \), and for each morphism \( u: i \to j \) in \( J \), we define a 2-cell \( \kappa_u: \Gamma G_u \circ \kappa_i \to \kappa_j \circ \Gamma F_u \) as sketched below. More explicitly, by naturality of \( \varphi \) we have that \( F_u \circ \varphi_i = \varphi_j \circ H_u \) and so the arrow \( \kappa_u: H_i \to F_i \times F_j \overset{\pi_2}{\rightarrow} H_j \) is the unique one satisfying \( \varphi_i = \pi_1 \circ \kappa_u \) and \( H_u = \pi_2 \circ \kappa_u \). To check that \( \kappa_u \) is a 2-cell it remains verify that \( \psi_j \circ \pi_2 \circ \kappa_u = \psi_j \circ H_u = G_u \circ \psi_i \), which follows by the naturality of \( \psi \).
Further, a 2-cell between spans \( (\varphi, \psi), (\varphi', \psi'): F \to G \) with respective carriers \( H, H' \) is a natural transformation \( \xi: H \to H' \) satisfying both \( \varphi' \circ \xi = \varphi \) and \( \psi' \circ \xi = \psi \). This induces a modification \( \{ \xi_i \}_{i \in J}: \Gamma(\varphi, \psi) \to \Gamma(\varphi', \psi') \).
It follows from the definition that \( \kappa_{\varphi_1} = \iota_H \). To check the second requirement of lax transformations (see Definition 3.10), consider two arrows \( u: i \to j \) and \( v: j \to k \) in \( J \). Since \( \alpha_{F_u \circ F_j, G_v} \) and \( \alpha_{G_v \circ G_k} \) are identities, one merely has to show \( \alpha \circ \kappa_{\varphi_1} = \kappa_v \circ \iota_{F_u} \circ \iota_{G_v} \circ \kappa_u \).
Faithfulness on arrows is immediate. Conversely, given a lax transformation \( \kappa: \Gamma F \to \Gamma G \), we construct a functor \( H \) and natural transformations \( \varphi: H \to F, \psi: H \to G \) such that \( \Gamma(\varphi, \psi) = \kappa \) as follows: let \( H_i \) be the carrier of the span \( \kappa_i \) and \( H_u := \pi_2 \circ \kappa_u \), and further \( \varphi_i \) and \( \psi_i \) are the left and right component of span \( \kappa_i \), respectively. Functoriality follows directly from the commutativity of the diagram above; naturality of \( \varphi \) and \( \psi \) follows from the fact that each \( \kappa_u \) is a 2-cell.
Finally, a 2-cell between spans \( (\varphi, \psi), (\varphi', \psi'): F \to G \) with respective carriers \( H, H' \), is a natural transformation \( \xi: H \to H' \) satisfying both \( \varphi' \circ \xi = \varphi \) and \( \psi' \circ \xi = \psi \). To prove that such a 2-cell induces a modification \( \{ \xi_i \}_{i \in J}: \Gamma(\varphi, \psi) \to \Gamma(\varphi', \psi') \) one needs to verify the equality \( \kappa'_u \circ \xi_i = \xi_j \circ \kappa_u \); this amounts to the commutativity of the diagram below. To see why the diagram commutes, consider the two projections \( F_i \to F_i \times F_j \overset{\pi_2}{\rightarrow} H_j \to H'_j \).
now one has \( \pi_1 \circ \kappa'_u \circ \xi_i = \varphi_i = \pi_1 \circ (F_i \times F_j \xi_j) \circ \kappa_u \) because of \( \varphi = \varphi' \circ \xi \) and \( \pi_2 \circ \kappa'_u \circ \xi_i = \mathcal{H}'_u \circ \xi_i = \xi_j \circ \mathcal{H}_u = \pi_2 \circ (F_i \times F_j \xi_j) \circ \kappa_u \) by naturality of \( \xi : \mathcal{H} \to \mathcal{H}' \).
![Diagram]
Conversely, any modification \( \Xi : \kappa \to \kappa' \) is a natural transformation \( \{ \Xi_i \}_{i \in I} : \mathcal{H} \to \mathcal{H}' \) where \( \mathcal{H} \) and \( \mathcal{H}' \) are the respective carrier functors—naturality follows directly from the commutativity of the diagram above (taking \( \xi_i = \Xi_i \) and \( u = \text{id}_i \)).
**Corollary 5.2.** For any functor \( F \in [J, C] \), the strict homomorphism \( \Gamma \) defines a natural isomorphism between the following two functors of type \([J, C] \to \text{Cat}: [\text{Span}(\mathcal{C})]((F, \omega) \cong \text{Hom}[J, \text{Span}(\mathcal{C})](\Gamma F, \Gamma \omega). \]
The above lemma and corollary can be adapted for strong transformations instead of lax ones (this will recur when we discuss bicolimits formally). The restriction to strong transformations has a counterpart on the other side of the isomorphism of Corollary 5.2: we need to restrict to those spans in \([\text{Span}(\mathcal{C})]((F, G)\) that have a cartesian transformation from the carrier to \( F \).
Recall that a cartesian transformation between functors is a natural transformation with all naturality squares pullbacks (see Definition 4.1). It is an easy exercise to show that cartesian transformations include all natural isomorphisms and are closed under pullback. Hence—similarly to how one restricts the arrows of a span bicategory to partial maps i.e. those spans with the left component mono—we let \( \text{Span}^{\text{cart}}_{[J, C]} \) be the (non-full) sub-bicategory of \([\text{Span}(\mathcal{C})]((F, G)\) that has as arrows from \( F \) to \( G \) those spans in which the left component is cartesian. Adapting the proof of Lemma 5.1, one obtains the following.
**Proposition 5.3.** There is a strict homomorphism \( \Gamma : \text{Span}^{\text{cart}}_{[J, C]} \to \text{Hom}[J, \text{Span}(\mathcal{C})][J, \text{Span}(\mathcal{C})]((\Gamma F, \Gamma \omega) \cong \text{Hom}[J, \text{Span}(\mathcal{C})][J, \text{Span}(\mathcal{C})]((\Gamma F, \Gamma \omega).
The above lets us pass between diagrams in \( \text{Span}(\mathcal{C}) \) and \( \mathcal{C} \): for example the strong transformations of homomorphisms to \( \text{Span}(\mathcal{C}) \) are those spans of natural transformations of functors to \( \mathcal{C} \) that have a cartesian first component; the modifications of the former are the morphisms of spans of the latter. This observation will be useful when relating the notion of bicolimit in \( \text{Span}(\mathcal{C}) \) with the notion of \( \text{vk}-\text{cocone} \) in \( \mathcal{C} \).
For our purposes we need to recall only the definition of (conical) bicolimits for functors with domain an (ordinary) small category \( J \). Given a homomorphism \( M : J \to \mathcal{B} \), a bicolimit of \( M \) is an object \( \text{bicol } M \in \mathcal{B} \) together with a pseudo-cocone \( \kappa : M \to \Delta(\text{bicol } M) \) such that “pre-composition” with \( \kappa \) gives an equivalence of categories
\[
\mathcal{B}(\text{bicol } M, X) \cong \text{Hom}[J, \mathcal{B}](M, \Delta X)
\]
that is natural in $X$ (i.e. the right hand side is essentially representable as a functor \( \lambda X. \text{Hom} [J, B] (M, \Delta X) : \mathcal{B} \to \textbf{Cat} \)); the pair \((\text{bicol} M, \kappa)\) is referred to as the bicolimit of \(M\). We will often speak of \(\kappa : M \to \Delta \text{bicol} M\) as a bicolimit without mentioning the pair \(\langle \text{bicol} M, \kappa \rangle\) explicitly.
To make the connection with the elementary characterisation of Van Kampen cocones in Proposition 4.3, we use the fact that equivalences of categories can be characterised as full, faithful functors that are essentially surjective on objects to derive the following equivalent, elementary definition.
**Definition 5.4 (Bicolimits).** Given an su-bicategory \(\mathcal{B}\), a category \(J\) and a strict homomorphism \(M : J \to \mathcal{B}\), a bicolimit for \(M\) consists of:
- an object \(\text{bicol} M \in \mathcal{B}\);
- a pseudo-cocone \(\kappa : M \to \Delta \text{bicol} M\): for each \(i \in J\) an arrow \(\kappa_i : M_i \to \text{bicol} M\), and for each \(u : i \to j\) in \(J\) an invertible 2-cell \(\kappa_u : \kappa_i \to \kappa_j \circ M_u\) satisfying the axioms required for \(\kappa\) to be a strong transformation.
The bicolimit satisfies the following universal properties.
(i) **essential surjectivity:**
for any pseudo-cocone \(\lambda : M \to \Delta X\), there exists \(h : \text{bicol} M \to X\) in \(\mathcal{B}\) and an invertible modification \(\Theta : \lambda \to \Delta h \circ \kappa\). The pair \(\langle h, \Theta \rangle\) is called a mediating cell from \(\kappa\) to \(\lambda\).
(ii) **fullness and faithfulness:**
for any \(h, h' : \text{bicol} M \to X\) in \(\mathcal{B}\) and each modification \(\Xi : \Delta h \circ \kappa \to \Delta h' \circ \kappa\), there is a unique 2-cell \(\xi : h \to h'\) satisfying \(\Xi = \Delta \xi \circ I\kappa\) (and hence \(\xi\) is invertible iff \(\Xi\) is).
Condition (ii) of this definition implies that mediating cells from a bicolimit to a pseudo-cocone are **essentially unique:** any two such mediating cells \(\langle h, \Theta \rangle\) and \(\langle h', \Theta' \rangle\) are isomorphic since \(\Theta' \circ \Theta^{-1} : \Delta h \circ \kappa \to \Delta h' \circ \kappa\) corresponds to a unique invertible 2-cell \(\zeta : h \to h'\) such that \(\Theta' \circ \Theta^{-1} = \Delta \zeta \circ I\kappa\).
To facilitate the exposition of the relationship between the bicolimits in \(\text{Span}(\mathcal{C})\) and \(\text{vk}-\text{cocones}\) in \(\mathcal{C}\) we shall first reformulate the above elementary definition of bicolimits. Given a pseudo-cocone \(\kappa : M \to \Delta C\), a morphism \(h : C \to D\) will be called **universal for \(\kappa\)** or \(\kappa\)-**universal** if, given any other morphism \(h' : C \to D\) with a modification \(\Xi : \Delta h \circ \kappa \to \Delta h' \circ \kappa\),
there exists a unique 2-cell $\xi: h \to h'$ satisfying $\Xi = \Delta \xi * I_\kappa$; further, a mediating cell $\langle h, \Theta \rangle$ is called universal, if the morphism $h$ is universal. The motivation behind this terminology and the slightly redundant statement of the following proposition will become apparent in Section 6; its proof is straightforward.
**Proposition 5.5.** A pseudo-cocone $\kappa: M \to \Delta C$ from a diagram $M$ to $C$ is a bicolimit iff both of the following hold:
(i) for any pseudo cocone $\lambda: M \to \Delta D$ there is a universal mediating cell $\langle h: C \to D, \Theta \rangle$ from $\kappa$ to $\lambda$;
(ii) all arrows $h: C \to D$ are universal for $\kappa$.
We are interested in bicolimits of strict homomorphisms of the form $\Gamma F$ where $F: J \to C$ is a functor and $\Gamma: C \to \text{Span}(C)$ is the covariant embedding of $C$. The defining equivalence of bicolimits in (5.1) specialises as follows:
$$\text{Span}(C)(\text{bicol } \Gamma F, X) \simeq \text{Hom}_{\text{Span}(C)}(\Gamma F, \Delta X).$$
Using Proposition 5.3, this is equivalent to:
$$\text{Span}(C)(\text{bicol } \Gamma F, X) \simeq \text{Span}_{[J,C]}(\Gamma F, \Delta X).$$
We shall exploit working in $\text{Span}_{[J,C]}$ in the following lemma which relates the concepts involved in the elementary definition of bicolimits with diagrams in $C$. It will serve as the technical backbone of our main theorem.
**Lemma 5.6 (Mediating cells and universality for spans).** Let $\kappa: F \to \Delta C$ be a cocone in $C$ of a diagram $F \in [J,C]$, and let $\lambda: \Gamma F \to \Delta D$ be a pseudo-cocone in $\text{Span}(C)$ where $\lambda_i = (\varphi_i, \psi_i)$ for all $i \in J$:
(i) to give a mediating cell
$$\langle C \xrightarrow{h_1} H \xrightarrow{h_2} D, \Theta: \lambda \to \Delta (h_1, h_2) \circ \Gamma \kappa \rangle$$
from $\Gamma \kappa$ to $\lambda$ is to give a cocone $\vartheta: \mathcal{H} \to \Delta H$ where $\mathcal{H}$ is the carrier functor of the image of $\lambda$ in $\text{Span}_{[J,C]}(\Gamma F, \Delta D)$ (see Proposition 5.3) such that the resulting three-dimensional diagram (†) in $C$ (below) commutes and its lateral faces $\vartheta_1 \vartheta_2 \vartheta_C$ are pull-backs;
(ii) to give a modification \( \Xi: \Delta(h_1, h_2) \circ \Gamma \kappa \to \Delta(h'_1, h'_2) \circ \Gamma \kappa \) for a pair of spans
\[(h_1, h_2), (h'_1, h'_2): C \to D\]
is to give a cartesian transformation \( \Xi: F \times_{\Delta C} \Delta H \to F \times_{\Delta C} \Delta H' \) such that the two equations \( \pi'_1 \circ \Xi = \pi_1 \) and \( (\Delta h'_2) \circ \pi'_2 \circ \Xi = (\Delta h_2) \circ \pi_2 \) hold.
Here \( F \leftarrow_{\pi_1} F \times_{\Delta C} \Delta H \leftarrow_{\pi_2} \Delta H \) is the pullback of \( F \leftarrow_{\kappa} \Delta C \leftarrow_{\pi_1} \Delta H \) as sketched in (\( \ddagger \)) above and similarly for \( h'_1: H' \to C \). Further, to give a cell \( \xi: (h_1, h_2) \to (h'_1, h'_2) \) that satisfies \( \Delta \xi \ast I_{\Gamma \kappa} = \Xi \) is to give a \( C \)-arrow \( \xi: H \to H' \) which satisfies the three equations \( h'_1 \circ \xi = h_1, h'_2 \circ \xi = h_2 \) and \( \Delta \xi \circ \pi_2 = \pi'_2 \circ \Xi \);
\[
\begin{array}{c}
F_i \times_C H
\end{array}
\]
\[
\begin{array}{c}
\Xi_i \rightarrow F_i \times_C H'
\end{array}
\]
(iii) given a span \( (h_1, h_2): C \to D \), if the pullback of \( \kappa \) along \( h_1 \) is a colimit, i.e. if \( \pi_2: F \times_{\Delta C} \Delta H \to \Delta H \) is a colimit, then \( (h_1, h_2) \) is universal for \( \Gamma \kappa \);
(iv) conversely, if \( (h_1, h_2) \) is universal for \( \Gamma \kappa \), then \( \pi_2: F \times_{\Delta C} \Delta H \to \Delta H \) is a colimit—provided that some colimit of \( F \times_{\Delta C} \Delta H \) exists in \( C \).
Proof. Both (iii) and (iv) are immediate consequences of Proposition 5.3.
As for (iii), we need to show that every modification \( \Xi: \Delta(h_1, h_2) \circ \Gamma \kappa \to \Delta(h'_1, h'_2) \circ \Gamma \kappa \) is equal to \( \Delta \xi \ast I_{\Gamma \kappa} \) for a unique \( \xi: (h_1, h_2) \to (h'_1, h'_2) \). By (iii), \( \Xi \) is a natural transformation \( \Xi: F \times_{\Delta C} \Delta H \to F \times_{\Delta C} \Delta H' \). Then, by naturality of \( \Xi \), we have that \( \pi'_2 \circ \Xi \circ (F_u \circ_{\Delta C} \Delta H) = \pi'_2 \circ \Xi \) for all \( u: i \to j \) in \( J \), and since \( \pi_2 \) is a colimit we have a unique \( \xi: H \to H' \) satisfying \( \xi \circ \pi_2 = \pi'_2 \circ \Xi \) for all \( i \in J \). The equations \( h_i = h'_i \circ \xi \) follow from the universal property of \( \pi_2 \) (and the properties of \( \Xi \)). To show uniqueness of \( \xi \), let \( \zeta: (h_1, h_2) \to (h'_1, h'_2) \) be a 2-cell such that \( \Xi = \Delta \zeta \ast I_{\Gamma \kappa} \); then using the second statement of Lemma 5.3, \( \Delta \zeta \circ \pi_2 = \pi'_2 \circ \Xi \); hence \( \zeta = \xi \) follows since \( \pi_2 \) is a colimit. In summary, \( (h_1, h_2) \) is universal for \( \Gamma \kappa \).
To show (iv), let \( \langle H', \vartheta \rangle \) be a colimit of \( F \times_{\Delta C} \Delta H \). Now, it suffices to show that there is a \( C \)-morphism \( \xi: H \to H' \) such that \( \vartheta = \Delta \xi \circ \pi_2 \).
By the universal property of \( \vartheta \), we obtain unique \( C \)-arrows \( h'_1: H' \to C \) and \( h'_2: H' \to D \) such that \( h'_1 \circ \vartheta = \kappa \circ \pi_1 \) and \( h'_2 \circ \vartheta = \Delta h_2 \circ \pi_2 \). It also follows that the two equations \( h_1 \circ k = h'_1 \) and \( h_2 \circ k = h'_2 \) hold. Pulling back \( \kappa \) along \( h'_1 \) yields a span \( F \leftarrow_{\pi'_1} F \times_{\Delta C} \Delta H' \leftarrow_{\pi'_2} \Delta H' \); we then obtain a natural transformation \( \Xi: F \times_{\Delta C} \Delta H \to F \times_{\Delta C} \Delta H' \) which satisfies \( \pi_1 = \pi'_1 \circ \Xi \) and \( \vartheta = \pi'_2 \circ \Xi \).
The reason is that once such a \( \xi \) is provided, there is a unique \( k: H' \to H \) satisfying \( \Delta k \circ \vartheta = \pi_2 \), and thus \( \xi \circ k = \text{id}_{H'} \) by the universal property of colimits; moreover \( k \circ \xi = \text{id}_H \) must hold since \( (h_1, h_2) \) is universal for \( \Gamma \kappa \).
and hence also $\Delta h_2 \circ \pi_2 = \Delta h'_2 \circ \vartheta = \Delta h'_2 \circ \pi'_2 \circ \Xi$. By (ii), this defines a modification $\Xi: \Delta(h_1, h_2) \circ \Gamma \kappa \to \Delta(h'_1, h'_2) \circ \kappa$. Using universality, we get a unique $\xi: H \to H'$ such that $h'_1 \circ \xi = h_1$, $h'_2 \circ \xi = h_2$ and $\Delta \circ \pi_2 = \pi'_2 \circ \Xi = \vartheta$.
\[ \square \]
6. Van Kampen cocones as span bicolimits
Here we prove the main result of this paper, Theorem 6.3. Roughly speaking, the conclusion is that (under natural assumptions—existence of pullbacks and enough colimits in C) to be $\forall K$ in C is to be a bicolimit in $\text{Span}(C)$. The consequence is that “being $\forall K$” is a universal property—in $\text{Span}(C)$ rather than in C.
The proof relies on a correspondence between the elementary characterisation of Van Kampen cocones in C of Proposition 5.3 and the universal properties of pseudo-cocones in $\text{Span}(C)$ of Proposition 5.5. More precisely, given a colimit $\kappa: M \to \Delta C$ in C, we shall show that:
- $\Gamma\kappa$-universality of all spans $(h_1, h_2): C \to D$ corresponds to the implication (ii) $\Rightarrow$ (i) of Proposition 5.3, which is also known as pullback-stability or universality of the colimit $\kappa$;
- existence of some universal mediating cell from $\Gamma \kappa$ to any $\lambda: \Gamma F \to \Delta D$ is the counterpart of the implication (i) $\Rightarrow$ (ii) of Proposition 5.3 which—for want of a better name—we here refer to as “converse universality” of $\kappa$;
- thus, $\Gamma \kappa$ is a bicolimit in $\text{Span}(C)$ if and only if the colimit $\kappa$ is Van Kampen.
The first two points are made precise by the statements of the following two lemmas. The third point is the statement of the main theorem.
Lemma 6.1 (Converse universality). Let $F \in [J, C]$ where $C$ has pullbacks and for all $(\tau: E \to F) \in [J, C] \downarrow F$ a colimit of $E$ exists. Then $\kappa: F \to \Delta C$ satisfies “converse universality” iff given any pseudo-cocone $\lambda: \Gamma F \to \Delta D$, there exists a universal mediating cell $\langle (h_1, h_2), \Theta \rangle$ from $\Gamma \kappa$ to $\lambda$ in $\text{Span}(C)$.
Proof. ($\Rightarrow$) Suppose that $\lambda: \Gamma F \to \Delta D$ is a pseudo-cocone in $\text{Span}(C)$.
For $u: i \to j$ in J, we obtain a commutative diagram, as illustrated (see Proposition 5.3). Let $\vartheta: H \to \Delta H$ be the colimit of $H$; thus we obtain $h_1: H \to C$ and $h_2: H \to D$ making diagram (†) commute. By converse universality, the side faces $\frac{\xi_1 \circ \pi_1}{\tau_1 : \xi_1 : F_1 \to C}$ are pullback squares; using Lemma 5.6(iii) we get an invertible modification $\Theta: \lambda \to \Delta(h_1, h_2) \circ \kappa$. That $(h_1, h_2)$ is universal follows from Lemma 5.6(iii) since $\vartheta$ is a colimit.
(⇐) If in diagram (†) $D = \text{col} H$ and $(D, \psi)$ is the corresponding colimit, we first use the assumption to obtain a universal mediating cell $\langle (h_1, h_2), \Theta \rangle$ from $\Gamma \kappa$ to $\lambda^{(\varphi, \psi)}$ where $\lambda^{(\varphi, \psi)}$ is the pseudo-cocone corresponding to the cartesian transformations $\varphi: H \to F$
and \( \psi : \mathcal{H} \to \Delta D \) such that \( \Lambda^{(\varphi, \psi)} = (\varphi_i, \psi_i) \) as in Lemma 5.6(i); the latter also provides \( \vartheta : \mathcal{H} \to \Delta H \) such that \( h_2 \circ \vartheta_i = \psi_i \) and all \( \mathcal{F}_{\alpha} \uparrow_{\varphi_i} \mathcal{F}_i \uparrow_{\psi_i} \mathcal{H} \) are pullback squares.
\[
\begin{array}{c}
\mathcal{H}_i \\
\downarrow \varphi_i \\
\mathcal{F}_i \\
\downarrow \kappa_i \\
C \\
\end{array}
\quad
\begin{array}{c}
\mathcal{H}_j \\
\downarrow \varphi_j \\
\mathcal{F}_j \\
\downarrow \kappa_j \\
C \\
\end{array}
\quad
\begin{array}{c}
\mathcal{H}_u \\
\downarrow \psi_i \\
\mathcal{F}_u \\
\downarrow \kappa_i \\
C \\
\end{array}
\quad
\begin{array}{c}
H \\
\downarrow h_2 \\
H \\
\downarrow h_1 \\
C \\
\end{array}
\quad
\begin{array}{c}
D \\
\end{array}
\]
(†)
It suffices to show that \( h_2 = \text{id}_H \). However, by the universal property of the colimit \( \langle D, \psi \rangle \), there is an arrow \( k : D \to h \) such that \( k \circ \psi_i = \vartheta_i \). The equation \( h_2 \circ k = \text{id}_D \) holds because \( \langle D, \psi \rangle \) is a colimit in \( C \), and \( k \circ h_2 = \text{id}_H \) follows since \( (h_1, h_2) \) is universal for \( \Gamma \kappa \).
**Lemma 6.2 (Universality).** Consider \( \mathcal{F} \in [J, C] \) where \( C \) has pullbacks such that for all \( (\tau : \mathcal{E} \to \mathcal{F}) \in [J, C] \downarrow \mathcal{F} \), a colimit of \( \mathcal{E} \) exists. Then \( \kappa : \mathcal{F} \to \Delta C \) satisfies universality iff every morphism \( (h_1, h_2) : C \rightrightarrows D \) in \( \text{Span}(C) \) is universal for \( \Gamma \kappa \).
**Proof.** (⇒) Any morphism \( (h_1, h_2) \) leads to a diagram (†) where all the side-faces are pullbacks. By universality of \( \kappa \), the cocone \( \pi_2 \) of the top face is a colimit; thus \( (h_1, h_2) \) is universal for \( \Gamma \kappa \) by Lemma 5.6(iii).
(⇐) Suppose that in diagram (†) the side faces are all pullbacks. By assumption \( (h_1, h_2) \) is universal for \( \Gamma \kappa \), thus \( \langle H, \pi_2 : \mathcal{F} \times_{\Delta C} \Delta H \to \Delta H \rangle \) is a colimit by Lemma 5.6(iv).
Finally, these two lemmas together with Proposition 5.5 imply our main result.
**Theorem 6.3.** Let \( \mathcal{F} \in [J, C] \) where \( C \) has pullbacks and for all cartesian transformations \( \tau : \mathcal{E} \to \mathcal{F} \), a colimit of \( \mathcal{E} \) exists. Then a cocone \( \kappa : \mathcal{F} \to \Delta C \) is Van Kampen iff \( \Gamma \kappa : \Gamma \mathcal{F} \to \Delta C \) is a bicolimit in \( \text{Span}(C) \).
### 7. Conclusion, related work and future work
We gave a general definition of Van Kampen cocone that captures several previously studied notions in computer science, topology, and related areas, showing that they are instances of the same concept. Moreover, we have provided two alternative characterisations: the first one is elementary, and involves only basic category theoretic notions; the second one exhibits it as a *universal property*: Van Kampen cocones are just those colimits that are preserved by the canonical covariant embedding into the span bicategory.
There is some interesting related recent work. Milius [33] showed that coproducts are preserved (as a lax-adjoint-cooplimit) in the 2-category of relations over an extensive category \( C \). Cockett and Guo [9] have investigated the general conditions under which partial map categories are join-restriction categories: roughly, certain colimits in the underlying category are required to be \( \text{vk} \)-cocones.
Finally, the definition of Van Kampen cocone allows for several natural variations. For example, one may replace the slice category over the object at the “tip” of cocones by a (full) subcategory of it; this is exactly the step from global descent to \( \mathcal{E} \)-descent [19] and is closely related to the proposals in [11, 13] for a weakening of the notion of adhesivity.
Alternatively, one may start with cocones or diagrams of a particular form. In this way quasi-adhesive categories \cite{29} arise as in the latter only pushouts along regular monos are required to be \( \text{VK} \); another example is the work of Cockett and Guo \cite{9}, where Van Kampen cocones exist for a class of diagrams that naturally arises in their study of join restriction categories. Thus, possibly combining the latter two ideas, several new forms of Van Kampen cocones and diagrams arise as the subject for future research.
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Floquet driven frictional effects
Valid Mosallanejad,1,2,∗ Jingqi Chen,1,2 and Wenjie Dou1,3,2,†
1|Department of Chemistry, School of Science, Westlake University, Hangzhou, Zhejiang 310024, China
2|Institute of Natural Sciences, Westlake Institute for Advanced Study, Hangzhou, Zhejiang 310024, China
3|Department of Physics, School of Science, Westlake University, Hangzhou, Zhejiang 310024, China
When the coupled electron-nuclear dynamics are subjected to strong Floquet driving, there is a strong breakdown of the Born-Oppenheimer approximation. In this article, we derive a Fokker-Planck equation to describe non-adiabatic molecular dynamics with electronic friction for Floquet driven systems. We first provide a new derivation of the Floquet quantum-classical Liouville equation (QCLE) for driven electron-nuclear dynamics. We then transform the Floquet QCLE into a Fokker-Planck equation with explicit forms of frictional force and random force. We recast the electronic friction in terms of Floquet Green’s functions such that we can evaluate the electronic friction explicitly. We show that the Floquet electronic friction tensor exhibits antisymmetric terms even at equilibrium for real-valued Hamiltonian, suggesting that there is a Lorentz-like force in Floquet driven non-Born Oppenheimer dynamics even without any spin-orbit couplings.
Introduction. – The molecular dynamics near metallic surfaces can be non-adiabatic in nature and hence Born-Oppenheimer (BO) approximation is not necessary correct [1–3]. The electronic friction approach is considered as the first order correction to the BO approximation [4], which can be understood as quantum mechanical damping force of a manifold of fast relaxing electronic on classical nuclear motion. Electronic friction approaches were successful in explaining many experimental results such as molecular beam experiments [5–7], electrochemistry [8], charge/spin transport phenomena [9, 10]. Quantitatively, electronic friction is a tensor which appears on the generalized Langevin equation [11]. One of the first notable quantum mechanical derivations of the electronic friction tensor is given by Head-Gordon and Tully [12]. Later, more rigorous expressions are derived from Keldysh Green’s function [13, 14], path integral [15, 16], quantum classical Liouville equation (QCLE) [17], exact factorization [18]. It has been shown that there is only one universal electronic friction tensor in the Markovian limit [19, 20]. Furthermore, study shows that the friction tensor can exhibit antisymmetric terms even at equilibrium when spin-orbit couplings are involved. [21]
Now, there are increasing interests in understanding of the dynamics of molecular systems with strong light-matter interactions, which is helpful for interpreting photochemistry and spectroscopy [22, 23]. In particular, people are interested in how to use light/photon to manipulate chemical reactions where the dynamical interplay between light and electronic non-adiabatic transitions plays a significant role. At the same time, active research is currently ongoing to understand the response of quantum systems to a periodic driving force, or so called “Floquet driven” systems [24–26]. Floquet theorem provides a powerful method for the analysis of quantum systems subjected to periodic external drivings. Effects, such as phase transitions and pump-probe photoemission can be explained by applying Floquet theorem in solving quantum mechanical problems [27–29]. The coupled electron-nuclear dynamics with strong light-matter interactions can be described by the Floquet quantum classical Liouville equation (QCLE) successfully. [30–32]. In this article, we offer a new derivation for the Floquet QCLE starting from Floquet Liouville equation. Moreover, we map the Floquet QCLE into a Langevin equation with all non-adiabatic correction being incorporated into frictional effects. Furthermore, we demonstrate that the Floquet electronic friction tensor exhibits antisymmetric terms even at equilibrium for real-valued Hamiltonian.
Liouville-von Neumann equation in the Floquet representation. – For the coupled electron-nuclear motion, we consider a general Hamiltonian $\hat{H}$ that can be divided into the electronic Hamiltonian $\hat{H}_e$ and the nuclear kinetic energy:
$$\hat{H} = \hat{H}_e(\mathbf{R}, t) + \sum_{\alpha} \frac{\hat{P}_{\alpha}^2}{2M_{\alpha}}$$ \hspace{1cm} (1)
Here $\mathbf{R} = \{R_{\alpha}\}$ and $\hat{\mathbf{P}} = \{\hat{P}_{\alpha}\}$ are position and momentum operators for the nuclei respectively. We use $\alpha$ to denote nuclear degrees of freedom. Note that, the electronic Hamiltonian $\hat{H}_e(\mathbf{R}, t)$ is considered to be an explicit function of $\mathbf{R}$ and time $t$. Below, we will consider the case that the system is subjected to periodic driving, such that $\hat{H}_e(\mathbf{R}, t + T) = \hat{H}_e(\mathbf{R}, t)$. $T$ is the period of the driving frequency.
The equation of motion for the density operator follows Liouville-von Neumann (LvN): $\frac{d\hat{\rho}(t)}{dt} = -\frac{i}{\hbar}[\hat{H}(t), \hat{\rho}(t)]$. For the periodic driving system, we can derive a Floquet Liouville-von Neumann (LvN) equation describe the time evolution of the density operator in Floquet representation. To do so, two transformations are needed to derive Floquet representation of LvN: (I) Transformation of LvN into the Fourier representation and (II) transformation from the Fourier representation to the Floquet representation. The details of part (I) is given in the Supplementary Information S1. Fourier representation
Here, the Fourier representations of Hamiltonian and density operators \([\hat{H}^f(t)\) and \(\hat{\rho}^f(t)\)] are given by
\[
\hat{H}^f(t) = \sum_n \hat{H}^{(n)} \hat{L}_n e^{i n \omega t}, \quad \hat{\rho}^f(t) = \sum_n \hat{\rho}^{(n)}(t) \hat{L}_n e^{i n \omega t}. \tag{3}
\]
The operator \(\hat{L}_n\) denotes the nth ladder operator in Fourier space (see SI for detailed definition). The Fourier expansion coefficients of the Hamiltonian is given by \(\hat{H}^{(n)} = 1/T \int_0^T \hat{H}(t)e^{-i n \omega t} dt\). Indeed, Eqs. (3) are Fourier expansions modified by adding the ladder operator \(\hat{L}_n\). We stress that, the ladder operator turns the vector-like Fourier expansion into a matrix-like representation. We then transform the density operator from the Fourier representation to the Floquet representation as
\[
\hat{\rho}_F(t) = e^{-i N \omega t} \hat{\rho}^f(t) e^{i N \omega t} = \sum_n \hat{\rho}^{(n)}(t) \hat{L}_n, \tag{4}
\]
where \(N\) is the number operator in Floquet representation (see SI for detailed definition). Employing such a definition, the equation of motion for \(\hat{\rho}_F(t)\) now reads
\[
\frac{d}{dt} \hat{\rho}_F(t) = -\frac{i}{\hbar} \left[ \hat{H}_F, \hat{\rho}_F(t) \right], \tag{5}
\]
where we have defined the following Floquet representation for the Hamiltonian as
\[
\hat{H}_F = \sum_n \hat{H}^{(n)} \hat{L}_n + N \hbar \omega. \tag{6}
\]
We have used the commutation relations between the ladder and number operators, \([\hat{N}, \hat{L}_n] = n \hat{L}_n\) and \(e^{-i N \omega t} \hat{L}_n e^{i N \omega t} = \hat{L}_n e^{-i n \omega t}\) to derive the above equations. We note that the Floquet LvN equation have the same structure as the traditional LvN. The advantage of the Floquet LvN is to allow us to program the dynamics using the time independent Hamiltonian, Floquet QCLE. – To derive the Floquet QCLE, we perform the partial Wigner transformation with respect to the nuclear degrees of freedom on the Floquet LvN equation, Eq. (1), as
\[
\frac{d}{dt} \left( \hat{\rho}_W(t) \right) = -\frac{i}{\hbar} \left( \hat{H}_W \hat{\rho}_W(t) - \hat{\rho}_W \hat{H}_W \right). \tag{7}
\]
We have used subscript \(W\) to denote the Wigner transformation. The Wigner transformation is given by
\[
\hat{O}_W (\mathbf{R}, \mathbf{P}, t) = \int \mathcal{D}\mathbf{y} e^{-i \frac{\mathbf{y} \cdot \mathbf{R}}{2}} \frac{1}{2} \mathcal{O}(t) |\mathbf{R} + \frac{\mathbf{y}}{2} \rangle \langle \mathbf{R} - \frac{\mathbf{y}}{2}|, \tag{8}
\]
where \(\mathcal{O}(t)\) is an arbitrary operator and \(|\mathbf{R}\rangle\) is the real space representation of the nuclear degree of freedom.
As a result of this transformation, \(\mathbf{R}\) and \(\mathbf{P}\) can be interpreted as position and momentum variables in the classical limit. Note that, the Wigner-Moyal operator can be used to express the partial Wigner transform of the product of operator \(A\) and \(B\):
\[
(\hat{A}\hat{B})_W (\mathbf{R}, \mathbf{P}) = \hat{A}_W (\mathbf{R}, \mathbf{P}) e^{-i \hbar \hat{A}/2} \hat{B}_W (\mathbf{R}, \mathbf{P}),
\]
\[
\hat{A} = \sum \frac{\partial}{\partial P^\alpha} \frac{\partial}{\partial R^\alpha} - \frac{\partial}{\partial R^\alpha} \frac{\partial}{\partial P^\alpha}. \tag{9}
\]
When truncating the Wigner-Moyal operator to the first order in the Taylor expansion, \(e^{-i \hbar \hat{A}/2} \approx (1 - i \hbar \hat{A}/2)\), we arrive at the Floquet QCLE as
\[
\frac{d}{dt} \hat{\rho}_W(t) = \frac{1}{2} \left( \hat{H}_W \hat{\rho}_W - \hat{\rho}_W \hat{H}_W \right). \tag{10}
\]
Here, we have denoted \((\hat{O}_F)_W (\mathbf{R}, \mathbf{P}) = \hat{O}_W (\mathbf{R}, \mathbf{P})\). The subscript \(WF\) indicates that the Wigner transformation performed after the Floquet transformation. For the coupled electron-nuclear Hamiltonian in Eq. (1), we can rewrite the Floquet QCLE as follows
\[
\frac{\partial}{\partial t} \hat{\rho}_W(t) = -\frac{\hat{L}}{\hbar} \hat{\rho}_W(t) - \sum_{\alpha} \frac{P_{\alpha}}{M_{\alpha}} \frac{\partial \hat{\rho}_W(t)}{\partial R_{\alpha}} + \frac{1}{2} \sum_{\alpha} \left( \frac{\partial^2 \hat{\rho}_W(t)}{\partial R_{\alpha} \partial P_{\alpha}} \right), \tag{11}
\]
Here \(\hat{L}_W(t) = i/\hbar[\hat{H}_W, \hat{\rho}_W(t)]\). \(\hat{H}_W\) is the Floquet-Wigner transformed electronic Hamiltonian \(H_e\). We have also denoted the anti-commutator as \([A, B] = AB - BA\). This Floquet QCLE is consistent with the recently published work (see Eq. 14 in Ref. [33]). Such a Floquet QCLE represents the non-adiabatic dynamics of the coupled electron-nuclear system subjected to periodic driving. The Fokker-Planck equation. – In the limit when the nuclear motion is slow as compared to electronic motion as well as the driving speed, we can trace out all electronic degrees of freedom and Floquet levels, such that we are left with the pure nuclear density. To be more explicit, \(\mathcal{A}(\mathbf{R}, \mathbf{P}, t) = T_{r_e, F} \hat{\rho}_W(t)\). Here, \(T_{r_e, F}\) denotes trace over both many-body electronic states and Fourier space. To the first order in the correction to the BO approximation, we arrive at a Fokker-Planck equation for the pure nuclear density \(A\):
\[
\frac{\partial}{\partial t} A = -\sum_{\alpha} \frac{P_{\alpha}}{m_{\alpha}} \frac{\partial A}{\partial R_{\alpha}} - \sum_{\alpha} F_{\alpha} \frac{\partial A}{\partial P_{\alpha}} + \sum_{\alpha \beta} \gamma_{\alpha \beta} \frac{\partial^2 A}{\partial P_{\alpha} \partial P_{\beta}}. \tag{12}
\]
The detailed derivation can be found in the SM. Here \(F_{\alpha} = T_{r_e, F}(\partial \hat{H}_F/\partial R_{\alpha} \hat{\rho}_{ssF})\) is the mean force. \(\hat{\rho}_{ssF}\) is
the steady state Floquet electronic density. The Fokker-Planck equation is equivalent to the Langevin equation
\[ m_\alpha \dot{R}_\alpha = F_\alpha - \sum_\beta \gamma_{\alpha\beta} \dot{R}_\beta + \delta F_\alpha. \]
Here \( \delta F_\alpha \) is the random force, which satisfies
\[ \frac{1}{2} \left( \delta F_\alpha(0) \delta F_\beta(t) + \delta F_\beta(0) \delta F_\alpha(t) \right) = \overline{D_{\alpha\beta}^R} \delta(t). \]
\( \overline{D_{\alpha\beta}^R} \) is the correlation function of the random force. \( \gamma_{\alpha\beta} \) is the friction coefficient.
\[ \gamma_{\alpha\beta} = -\int_0^\infty dt T_{\text{r},F} \left( \frac{\partial \hat{H}_F^\alpha}{\partial \hat{R}_\alpha} e^{-i\int_0^t dt' \frac{\partial \hat{H}_F}{\partial R_\beta} e^{i\int_0^{t'} dt'' \frac{\partial \hat{H}_F}{\partial R_\beta}}} \right). \]
\[ \langle \hat{H}_F^\alpha(0) \hat{H}_F^\beta(t) \rangle = \overline{D_{\alpha\beta}^R} \delta(t). \]
Up to now, we have successfully transformed the coupled electron-nuclear motion subjected to periodic driving into a Langevin equation for the pure nuclear motion with all electronic motion and Floquet driving being incorporated into frictional force and random force. We now proceed to evaluate the frictional force in terms of Green’s function.
**Quadratic electronic Hamiltonian.** Our derivation above is general as long as the nuclear motion is slow as compared to electronic motion and Floquet driving. We now consider quadratic electronic Hamiltonian,
\[ \hat{H}_e(R, t) = \sum_{ab} H_{ab}(R, t) b_a^\dagger b_b. \]
One can then transform the Floquet electronic friction into the single particle representation as
\[ \gamma_{\alpha\beta} = -\hbar \int_{-\infty}^{\infty} \frac{d\epsilon}{2\pi} T_{\text{r},F} \left( \frac{\partial \hat{H}_F^R}{\partial \hat{R}_\alpha} \frac{\partial \sigma_{s,F}}{\partial \hat{R}_\beta} \frac{\partial \hat{G}_F^s}{\partial \hat{R}_\beta} \right). \]
where \( T_{\text{r},F} \) denotes the trace over both single particle electronic DoFs and Fourier space. We have defined the Floquet Retarded and Advance Green’s function:
\[ G_F^{R/A} = (\epsilon \pm i\eta - \hat{H}_F)^{-1}, \eta \rightarrow 0^+. \]
Here, \( \hat{H}_F \) is the Floquet single particle electronic Hamiltonian, and \( \sigma_{s,F} \) denotes the Floquet single-particle density matrix, which is defined as \( \sigma_{s,F} = T_{\text{r},F} (b_a^\dagger b_a) \). The Floquet single-particle density matrix can be further expressed in terms of Floquet lesser Green’s function, such that the final expression for the Floquet electronic friction is given by:
\[ \gamma_{\alpha\beta} = \hbar \int_{-\infty}^{\infty} \frac{d\epsilon}{2\pi} T_{\text{r},F} \left( \frac{\partial \hat{H}_F^R}{\partial \hat{R}_\alpha} \frac{\partial \hat{H}_F^R}{\partial \hat{R}_\beta} \frac{\partial \hat{G}_F^s}{\partial \hat{R}_\beta} \right) + \text{h.c.} \]
See the Supplementary Information for the details of derivation. \( G_F^- \) is the lesser Floquet Green’s function. Note that the Floquet electronic friction is the same as non-Floquet electronic friction, except Green’s functions are now the Floquet version of the corresponding Green’s function. **Dot-lead separation.** We now consider a specific model, such that we can calculate the Floquet electronic friction explicitly. We will demonstrate that the Floquet driving electronic friction exhibits antisymmetric terms for real Hamiltonian even without any current. To be more specific, we consider a Hamiltonian with dot-lead separation:
\[ \hat{H}_s = \hat{H}_s + \hat{H}_b + \hat{H}_v \]
\[ \hat{H}_b = \sum_{\zeta k} \epsilon_{\zeta k} c_{\zeta k}^\dagger c_{\zeta k} \]
\[ \hat{H}_v = \sum_{\zeta k,i} V_{\zeta k,i} (c_{\zeta k}^\dagger d_i + d_i^\dagger c_{\zeta k}). \]
Here, \( \hat{H}_s \) is the dot Hamiltonian. The bath Hamiltonian consists of the left and right (\( \zeta = L, R \)) leads. \( \hat{H}_v \) describes the system-bath couplings. \( U(R) \) is the potential for the nuclei.
For such a model, we can calculate Floquet Green’s function exactly. In particular, the Retarded Green’s function for the system is given by:
\[ G_{s,F}^R(\epsilon) = (\epsilon - \Sigma_{s,F}^{R}(\epsilon) - \hbar^2 \gamma)^{-1}, \]
\[ \Sigma_{s,F}^{R}(\epsilon) = \sum_{\zeta = L,R} \Sigma_{s,F}^{R}(\epsilon) \]
\[ \Sigma_{s,F}^{L,R}(\epsilon) = \sum_{k} V_{\zeta k,i} g_{F,\zeta k}^L(\epsilon)V_{\zeta j,k}^R. \]
\[ g_{F,\zeta k}^L(\epsilon) = \frac{i}{\hbar} f(\epsilon - \hbar \omega - \mu_\zeta) \delta(\epsilon - \epsilon_{\zeta k} - \hbar \omega). \]
The lesser Green’s function for the system is then given by
\[ G_{s,F}^<(\epsilon) \]
\[ = \sum_{\zeta = L,R} \Sigma_{s,F}^>(\epsilon) \]
\[ + \sum_{\epsilon} G_{s,F}^>(\epsilon) \Sigma_{s,F}^<(\epsilon) G_{s,F}^>(\epsilon). \]
Here, \( \Sigma_{s,F}^>(\epsilon) \) is the lesser Green’s function for the \( \zeta \) lead. \( g_{F,\zeta k}^<(\epsilon) \) is the lesser Green’s function for the \( \zeta \) lead. \( f(\epsilon - \hbar \omega - \mu_\zeta) \) where \( f \) is the Fermi function. In what following, we will invoke the wide band approximation, such that \( |\Sigma_{s,F}^>(\epsilon)| \approx \frac{1}{2} \Gamma_{ij} \), and \( |\Sigma_{s,F}^<(\epsilon)| \approx i\Gamma_{ij} f(\epsilon - \hbar \omega). \]
We can then proceed to calculate Floquet electronic friction using these Green’s functions.
**Results and Discussion.** We will now consider a two-level and two nuclear DoFs model:
\[ [h^s](x,y,t) = \begin{pmatrix} x + \Delta & A_y + B \cos(\omega t) \\ A_y + B \cos(\omega t) & -x - \Delta \end{pmatrix}. \]
The nuclear potential \( U(R) \) is taken to be harmonic oscillators in both \( x \) and \( y \) dimensions. The diagonal terms of Hamiltonian represent two shifted parabolas in \( x \) direction with a driving force of \( 2\Delta \). The off-diagonal couplings depend on displacement in \( y \) direction as well as external time-periodic driving \( B \cos(\omega t) \) from a monochromatic light source. \( B \) represents the strength of the external driving (e.g., the intensity of light) and \( \omega \).
is the frequency of the time-periodic driving. Below, we consider the case where the first level couples to the left lead and the second level couples to the right lead, and we set $\Gamma_{11} = \Gamma_{22} = \Gamma$. In the equilibrium case (where $\mu_L = \mu_R$) and without any driving, the electronic friction is shown to be symmetric along nuclear DoFs provided the Hamiltonian is real [21]. In Fig. 1, we plot the friction tensor as a function of the nuclear coordinates $(x, y)$. In particular, we define the symmetric and antisymmetric components $\gamma_{xy}^S = (\gamma_{xy} + \gamma_{yx})/2, \gamma_{xy}^A = (\gamma_{xy} - \gamma_{yx})/2$ of the friction tensor. In the absence of external driving ($B = 0$), the antisymmetric component is indeed vanished (as predicted). The frictions tensors $\gamma_{xx}$ and $\gamma_{yy}$ consists of two Gaussian curves which are merged along the orientations of the nuclear coordinate. This results agree with previous findings for real Hamiltonian without any driving [21]. We now turn on time-periodic off-diagonal coupling by setting $B = 1$. As shown in Fig. 2, the antisymmetric term $\gamma_{xy}^A$ is no longer zero when Floquet driving is turning on. Moreover, the distributions of $\gamma_{xx}, \gamma_{yy}$, and $\gamma_{xy}^S$ in the real space is enlarged as compared to the non-Floquet case. The magnitude of $\gamma_{xx}$ and $\gamma_{xy}^S$ are also increased by almost factor of 2. Finally, in Fig. 3 we plot the frictional terms for the increased driving frequency ($\omega = 1$). In such a case, the magnitude of the antisymmetric terms (the Lorentz force) is notably increased, whereas the magnitudes of the other terms do not change significantly. Interestingly, the shape of $\gamma_{xx}$ is composed of two large ellipses and two small ones. The central distance between the larger ellipse and the smaller one in $x$ axis is about $\omega$. This is consistent with the picture of Floquet replica of the potential surfaces separated by $\omega$. Finally, note that all friction terms have mirror symmetry around the avoided crossing point $(x = -\Delta$ and $y = 0)$ and magnitudes of $\gamma_{xy}^A$ and $\gamma_{xy}^S$ are always maximized far from the avoided crossing. Conclusion. We have formulated quantum-classical Liouville equation in Floquet representation to describe non-adiabatic dynamics with light-matter interactions. We have further mapped the Floquet QCLE into a Langevin dynamics where all electronic DoFs and light-matter interactions are incorporated into a friction tensor. We then recast the friction tensor into the form of Floquet Green’s functions such that we can evaluate the friction tensor explicitly. We show that the light-matter interactions can introduce anti-symmetric friction tensor even at equilibrium without any spin-orbit couplings. Future work must explore how the Lorentz-like force affects the dynamics in a realistic situation. We acknowledge the startup funding from Westlake University.
**FIG. 1:** Floquet friction tensors in absence of external driving $B = 0$: $\gamma_{xx}$ (top left), $\gamma_{xy}^S$ (top right), $\gamma_{xy}^A$ (bottom left) and $\gamma_{yy}$ (bottom right). Parameters: $\Gamma = 1$, $\mu_{R,L} = 0$, $\beta = 2$, $A = 1$, $\Delta = 3$, $\omega = 0.5$, $B = 1$, $N = 5$.
**FIG. 2:** Floquet friction tensors in presence of external driving: $\gamma_{xx}$ (top left), $\gamma_{xy}^S$ (top right), $\gamma_{xy}^A$ (bottom left) and $\gamma_{yy}$ (bottom right). Parameters: $\Gamma = 1$, $\mu_{R,L} = 0$, $\beta = 2$, $A = 1$, $\Delta = 3$, $\omega = 0.5$, $B = 1$, $N = 5$.
\*[email protected]
\[email protected]
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FIG. 3: Floquet Friction tensors in presence of external driving with a larger frequency: $\gamma_{xx}$ (top left), $\gamma_{xy}$ (top right), $\gamma^A_{xy}$ (bottom left) and $\gamma_{yy}$ (bottom right). Parameters: $\Gamma=1$, $\mu_{R,L}=0$, $\beta=2$, $A=1$, $\Delta=3$, $\omega=1$, $B=1$, $N=5$.
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Supplementary Information for Floquet driven frictional effects
Vahid Mosallanejad,1, 2, * Jingqi Chen, 1, 2 and Wenjie Dou1,3, 2, †
1 Department of Chemistry, School of Science, Westlake University, Hangzhou, Zhejiang 310024, China
2 Institute of Natural Sciences, Westlake Institute for Advanced Study, Hangzhou, Zhejiang 310024, China
3 Department of Physics, School of Science, Westlake University, Hangzhou, Zhejiang 310024, China
PACS numbers:
DRIVATION OF LIOUVILLE-VON NEUMANN EQUATION IN THE FOURIER REPRESENTATION
In what follows we show that Liouville-von Neumann (LvN) equation of motion in the Fourier representation keeps the same form as the non-Fourier one as: \( d\hat{\rho}^f(t)/dt = -i/\hbar[\hat{H}^f(t), \hat{\rho}^f(t)] \) where \( \hat{\rho}^f \) and \( \hat{H}^f \) denote the density and Hamiltonian operators in the Fourier representation [S1]. The procedure has two parts; 1) Discreet expansion of the LvN in the Fourier space and 2) transferring from Fourier expansion to the Fourier representation. Part one begins by employing discreet Fourier expansions for both the time dependent Hamiltonian and density operators as
\[
\hat{H}(t) = \sum_n \hat{H}^{(n)} e^{in\omega t}, \quad \hat{\rho}(t) = \sum_n \hat{\rho}^{(n)}(t) e^{in\omega t}. \tag{S1}
\]
Note that the coefficients \( \hat{\rho}^{(n)} \) is time-dependent whereas the \( \hat{H}^{(n)} \) is not. We then substitute above expansions on the LvN equation, \( d\hat{\rho}(t)/dt = -i/\hbar[\hat{H}(t), \hat{\rho}(t)] \), as
\[
\sum_n \left( \frac{d\hat{\rho}^{(n)}(t)}{dt} e^{in\omega t} + in\omega \hat{\rho}^{(n)}(t) e^{in\omega t} \right) = -\frac{i}{\hbar} \sum_{k,m} \left[ \hat{H}^{(k)}, \hat{\rho}^{(m)}(t) \right] e^{i(k+m)\omega t} = -\frac{i}{\hbar} \sum_{n,m} \left[ \hat{H}^{(n-m)}, \hat{\rho}^{(m)}(t) \right] e^{in\omega t}. \tag{S2}
\]
Next, we introduce the Floquet Number and Floquet Ladder operators as
\[
\hat{N}|n\rangle = n|n\rangle, \quad \hat{L}_n|m\rangle = |n+m\rangle. \tag{S3}
\]
In the matrix form, \( \hat{N} \) can be understood as a matrix with integer numbers on its diagonal and \( \hat{L}_n \) is an off-diagonal identity matrix shifted by \( n \). Following relations are hold for these two operators
\[
[\hat{N}, \hat{L}_n] = n\hat{L}_n, \quad [\hat{L}_n, \hat{L}_m] = 0, \quad \hat{L}_n\hat{L}_m = \hat{L}_m\hat{L}_n = \hat{L}_{n+m}. \tag{S4}
\]
Next, we introduce Fourier representations as
\[
\hat{H}^f(t) = \sum_n \hat{H}^{(n)} \hat{L}_n e^{in\omega t}, \quad \hat{\rho}^f(t) = \sum_n \hat{\rho}^{(n)}(t) \hat{L}_n e^{in\omega t}, \tag{S5}
\]
where we have modified Fourier expansions by adding the ladder operator \( \hat{L}_n \). We also introduce the Fourier representation of the LvN equation as
\[
\frac{d\hat{\rho}^f(t)}{dt} = -\frac{i}{\hbar} [\hat{H}^f(t), \hat{\rho}^f(t)]. \tag{S6}
\]
Afterward, we substitute Fourier representations of \( \hat{H} \) and \( \hat{\rho} \) [Eqs. (S5)] into above relation as
\[
\sum_n \left( \frac{d\hat{\rho}^{(n)}(t)}{dt} \hat{L}_n e^{in\omega t} + in\omega \hat{\rho}^{(n)}(t) \hat{L}_n e^{in\omega t} \right) = -\frac{i}{\hbar} \sum_{k,m} \left[ \hat{H}^{(k)}, \hat{\rho}^{(m)}(t) \hat{L}_m \right] e^{i(k+m)\omega t} = -\frac{i}{\hbar} \sum_{n,m} \left[ \hat{H}^{(n-m)}, \hat{\rho}^{(m)}(t) \right] \hat{L}_n e^{in\omega t}, \tag{S7}
\]
where we have used \( [\hat{L}_n\hat{L}_m, \hat{L}_m] = 0 \) and \( \hat{L}_n\hat{L}_m = \hat{L}_m\hat{L}_n = \hat{L}_{n+m} \) in the last line. Since for each \( n \), two sides of Eq. (S2) and Eq. (S7) are equivalent then we have proven that the LvN equation in Fourier representations keeps the original form and hence Eq. (S6) is valid.
DERIVATION OF FOKKER-PLANCK EQUATION
To derive an EOM for the nuclei, we take into account the following weak approximation for the mixed nuclear-electron Floquet density operator $\hat{\rho}_{WF}(\mathbf{R}, \mathbf{P}, t)$ as
$$\dot{\hat{\rho}}_{WF}(\mathbf{R}, \mathbf{P}, t) = \mathcal{A}(\mathbf{R}, \mathbf{P}, t)\hat{\rho}_{ssF}(\mathbf{R}) + \hat{\mathcal{B}}(\mathbf{R}, \mathbf{P}, t), \tag{S8}$$
where the nuclear phase space density is denoted by $\mathcal{A}(\mathbf{R}, \mathbf{P}, t)$. The Floquet steady-state electronic density operator is denoted by $\hat{\rho}_{ssF}(\mathbf{R})$ and the difference operator is denoted by $\hat{\mathcal{B}}(\mathbf{R}, \mathbf{P}, t)$. Note that $\hat{\mathcal{L}}_{WF}(\hat{\rho}_{ssF}(\mathbf{R})) = 0$ and $\hat{\rho}_{ssF}(\mathbf{R})$ is normalized on the electronic part at all $\mathbf{R}$ such that $Tr_{e,F}(\hat{\rho}_{ssF}(\mathbf{R})) = N$, where $N$ is the Fourier space dimension. For further simplicity, we write a compact form of Eq. (10), the Floquet QCLE, as the following
$$\frac{d}{dt}\hat{\rho}_{WF}(t) = -\hat{\mathcal{L}}_{WF}(\hat{\rho}_{WF}(t)) + \left\{ \hat{H}_{WF}, \hat{\rho}_{WF} \right\}_a, \tag{S9}$$
where $\hat{\mathcal{L}}_{WF}(\hat{\rho}_{WF}(t)) \equiv i/\hbar [\hat{H}_{WF}, \hat{\rho}_{WF}(t)]$ and $\left\{ \hat{A}, \hat{B} \right\}_a \equiv -1/2(\hat{A} \hat{B} \hat{A} - \hat{B} \hat{A} \hat{A})$. After substitution of Eq. (S8) in Eq. (S9), and taking the trace over the electronic bath and Fourier space as
$$\frac{\partial}{\partial t} Tr_{e,F} \left( \mathcal{A}(t)\hat{\rho}_{ssF} + \hat{\mathcal{B}} \right) = Tr_{e,F} \left\{ \hat{H}_{WF}, \mathcal{A}(t)\hat{\rho}_{ssF} \right\}_a + Tr_{e,F} \left\{ \hat{H}_{WF}, \hat{\mathcal{B}} \right\}_a, \tag{S10}$$
we arrive to
$$\frac{\partial}{\partial t} \mathcal{A}(t) = -\sum \left( \frac{P_\alpha}{M_\alpha} \right) \frac{\partial \mathcal{A}(t)}{\partial R_\alpha} + \sum \frac{1}{2} Tr_{e,F} \left( \frac{\partial \hat{H}_{WF}}{\partial P_\alpha} \frac{\partial \mathcal{A}(t)\hat{\rho}_{ssF}}{\partial P_\alpha} + \frac{\partial \mathcal{A}(t)\hat{\rho}_{ssF}}{\partial P_\alpha} \frac{\partial \hat{H}_{WF}}{\partial P_\alpha} \right) +$$
$$\sum \frac{1}{2} \frac{1}{2} Tr_{e,F} \left( \frac{\partial \hat{H}_{WF}}{\partial P_\alpha} \frac{\partial \hat{B}}{\partial P_\alpha} + \frac{\partial \hat{B}}{\partial P_\alpha} \frac{\partial \hat{H}_{WF}}{\partial P_\alpha} \right). \tag{S11}$$
Note that, $Tr_{e,F} \hat{\mathcal{L}}_{WF} \left( \mathcal{A}(t)\hat{\rho}_{ssF} + \hat{\mathcal{B}} \right) = Tr_{e,F} \hat{\mathcal{L}}_{WF} \left( \hat{\mathcal{B}} \right) = 0$ and $Tr_{e,F}(\partial \mathcal{B}/\partial R^\alpha) = 0$. Since $\hat{\rho}_{ssF}$ does not depends in $P_\alpha$, we can further simplify the above relation as
$$\frac{\partial}{\partial t} \mathcal{A}(t) = -\sum \left( \frac{P_\alpha}{M_\alpha} \right) \frac{\partial \mathcal{A}(t)}{\partial R_\alpha} + \sum Tr_{e,F} \left( \frac{\partial \hat{H}_{WF}}{\partial R_\alpha} \frac{\partial \mathcal{A}(t)\hat{\rho}_{ssF}}{\partial P_\alpha} + \frac{\partial \mathcal{A}(t)\hat{\rho}_{ssF}}{\partial P_\alpha} \frac{\partial \hat{H}_{WF}}{\partial R_\alpha} \right). \tag{S12}$$
In above relation, we have also use the fact that $Tr[AB] = Tr[BA]$. At this point, one needs to express $\hat{\mathcal{B}}$ in terms of $\hat{\mathcal{A}}$. To proceed, we can first have a relation for $\partial \mathcal{B}/\partial t$ as:
$$\frac{\partial}{\partial t} \mathcal{B} = -\hat{\rho}_{ssF} \frac{\partial}{\partial t} \mathcal{A}(t) + \left\{ \hat{H}_{WF}, \mathcal{A}(t) \right\}_a \hat{\rho}_{ssF} + \left\{ \hat{H}_{WF}, \mathcal{B} \right\}_a - \hat{\mathcal{L}}_{WF}(\mathcal{B})$$
$$= \left\{ \hat{H}_{WF}, \mathcal{B} \right\}_a - \hat{\rho}_{ssF} Tr_{e,F} \left\{ \hat{H}_{WF}, \mathcal{B} \right\}_a$$
$$= \hat{\rho}_{ssF} Tr_{e,F} \left\{ \hat{H}_{WF}, \mathcal{A}(t)\hat{\rho}_{ssF} \right\}_a + \left\{ \hat{H}_{WF}, \mathcal{A}(t)\hat{\rho}_{ssF} \right\}_a - \hat{\mathcal{L}}_{WF}(\mathcal{B}). \tag{S13}$$
Next, we assume that nuclei move much slower than electrons. With that assumption, only the last three terms of the above relation will survive as
$$\hat{\mathcal{L}}_{WF}(\mathcal{B}) = -\hat{\rho}_{ssF} Tr_{e,F} \left\{ \hat{H}_{WF}, \mathcal{A}(t)\hat{\rho}_{ssF} \right\}_a + \left\{ \hat{H}_{WF}, \mathcal{A}(t)\hat{\rho}_{ssF} \right\}_a =$$
$$= \hat{\rho}_{ssF} \left( -\sum \left( \frac{P_\alpha}{M_\alpha} \right) \frac{\partial \mathcal{A}(t)}{\partial R_\alpha} + \sum Tr_{e,F} \left( \frac{\partial \hat{H}_{WF}}{\partial R_\alpha} \frac{\partial \mathcal{A}(t)\hat{\rho}_{ssF}}{\partial P_\alpha} \right) \frac{\partial \mathcal{A}(t)\hat{\rho}_{ssF}}{\partial P_\alpha} \frac{\partial \hat{H}_{WF}}{\partial R_\alpha} \right)$$
$$= \sum \left( \frac{P_\beta}{M_\beta} \right) \frac{\partial \mathcal{A}(t)}{\partial R_\beta} \frac{\partial \hat{\rho}_{ssF}}{\partial R_\beta} \frac{\partial \hat{\rho}_{ssF}}{\partial P_\beta} + \frac{\partial \hat{\rho}_{ssF}}{\partial P_\beta} \frac{\partial \mathcal{A}(t)}{\partial P_\beta}$$
$$= \frac{1}{2} \sum \left( \frac{\partial \hat{H}_{WF}}{\partial R_\beta} \frac{\partial \hat{\rho}_{ssF}}{\partial R_\beta} + \frac{\partial \hat{H}_{WF}}{\partial P_\beta} \frac{\partial \hat{\rho}_{ssF}}{\partial P_\beta} \right) \frac{\partial \mathcal{A}(t)}{\partial P_\beta}. \tag{S14}$$
Formal solution for $\hat{B}$ is given by
$$\hat{B} = -\sum_\beta \hat{L}_{WF}^{-1} \frac{\partial \hat{\rho}_{ssF}}{\partial R_\beta} \left( \frac{P_\beta}{M_\beta} \right) A(t)$$
$$- \sum_\beta \hat{L}_{WF}^{-1} \hat{\rho}_{ssF} T_{r_e,F} \left( \frac{\partial \hat{H}_{WF}^c}{\partial R_\beta} \partial \hat{\rho}_{ssF} \right) \frac{\partial A(t)}{\partial P_\alpha}$$
$$+ \frac{1}{2} \sum_\beta \hat{L}_{WF}^{-1} \left( \frac{\partial \hat{H}_{WF}^c}{\partial R_\beta} \hat{\rho}_{ssF} + \hat{\rho}_{ssF} \frac{\partial \hat{H}_{WF}^c}{\partial R_\beta} \right) \frac{\partial A(t)}{\partial P_\alpha} \frac{\partial A(t)}{\partial P_\beta}.$$ (S15)
Note that the first and third terms of Eq. (S14) cancel each other out. The above relation should be rearranged such that $\partial \hat{B}/\partial P_\alpha$ is given by
$$\frac{\partial \hat{B}}{\partial P_\alpha} = -\sum_\beta \hat{L}_{WF}^{-1} \frac{\partial \hat{\rho}_{ssF}}{\partial R_\beta} \left( \frac{P_\beta}{M_\beta} \right) A(t)$$
$$+ \frac{1}{2} \sum_\beta \hat{L}_{WF}^{-1} \left( -\hat{\rho}_{ssF} 2T_{r_e,F} \left( \frac{\partial \hat{H}_{WF}^c}{\partial R_\beta} \hat{\rho}_{ssF} \right) + \left( \frac{\partial \hat{H}_{WF}^c}{\partial R_\beta} \hat{\rho}_{ssF} + \hat{\rho}_{ssF} \frac{\partial \hat{H}_{WF}^c}{\partial R_\beta} \right) \right) \frac{\partial A(t)}{\partial P_\alpha} \frac{\partial A(t)}{\partial P_\beta}. \quad (S16)$$
Substitution of $\partial \hat{B}/\partial P_\alpha$ in Eq. (S12) give a rise to
$$\frac{\partial}{\partial t} A(t) = -\sum_\alpha \left( \frac{P_\alpha}{M_\alpha} \right) \frac{\partial A(t)}{\partial P_\alpha} \frac{\partial A(t)}{\partial P_\alpha}$$
$$+ \sum_\alpha -T_{r_e,F} \left( \frac{\partial \hat{H}_{WF}^c}{\partial R_\alpha} \hat{L}_{WF}^{-1} \frac{\partial \hat{\rho}_{ssF}}{\partial R_\beta} \right) \frac{\partial A(t)}{\partial P_\alpha} \left( \frac{P_\beta}{M_\beta} \right) A(t)$$
$$+ \sum_\alpha \frac{1}{2} T_{r_e,F} \left( \frac{\partial \hat{H}_{WF}^c}{\partial R_\alpha} \hat{L}_{WF}^{-1} \left( -\hat{\rho}_{ssF} 2T_{r_e,F} \left( \frac{\partial \hat{H}_{WF}^c}{\partial R_\beta} \hat{\rho}_{ssF} \right) + \left( \frac{\partial \hat{H}_{WF}^c}{\partial R_\beta} \hat{\rho}_{ssF} + \hat{\rho}_{ssF} \frac{\partial \hat{H}_{WF}^c}{\partial R_\beta} \right) \right) \right) \frac{\partial A(t)}{\partial P_\alpha} \frac{\partial A(t)}{\partial P_\beta}. \quad (S17)$$
With that, we already derived the Floquet forms of mean force, $F$, friction, $\gamma_{\alpha\beta}$, and the correlation function of the random force, $D_{\alpha\beta}$, by comparing the above relation with the Fokker-Planck equation, Eq. (12), mentioned in the main context [S2]. Comparing the new results with previously derived electronic friction, one can conclude that the Floquet version of electronic friction keeps similar form as the non-Floquet version. However, constituents should be transformed into their Floquet representations.
In the followings, we turn our attention toward further simplifications of the friction tensor. At this point, we employ the identity $\hat{L}_{WF}^{-1} = \lim_{n \to 0^+} \int_0^\infty dt e^{-\hat{L}_{WF} t} e^{-\hat{L}_{WF} t - i\eta} e^{i\hat{L}_{WF} t} e^{i\hat{L}_{WF} t + i\eta}$. With that, the Floquet friction tensor can be given by
$$\gamma_{\alpha\beta} = -\int_0^\infty dt T_{r_e,F} \left( \frac{\partial \hat{H}_{WF}^c}{\partial R_\alpha} e^{-i(\hat{H}_{WF} t - i\eta)t/h} \frac{\partial \hat{\rho}_{ssF}}{\partial R_\beta} e^{i(\hat{H}_{WF} t + i\eta)t/h} \right). \quad (S18)$$
In what follows, $\gamma_{\alpha\beta}$ denotes the Floquet friction tensor without an extra indicator. In fact the above friction relation is expressed in the many-body representation but it holds in the single-particle basis as well. It has been shown previously that if a non-interacting quadratic electronic Hamiltonians of the form $\sum_{\alpha \beta} H_{ab}(R,t) \hat{b}_a^\dagger \hat{b}_b + U(R)$ is considered, then friction relation in the single-particle basis keeps the same format as many-body one [S3]. Similar argument can be repeated to derive the following single-particle alternative of the Floquet friction as
$$\gamma_{\alpha\beta} = -\int_0^\infty dt T_{r_{m,F}} \left( \frac{\partial H_{F}}{\partial R_\alpha} e^{-i(H_{F} t - i\eta)t/h} \frac{\partial \sigma_{ssF}}{\partial R_\beta} e^{i(H_{F} t + i\eta)t/h} \right). \quad (S19)$$
In above relation, $H_{F}$ is the Floquet single particle electronic Hamiltonian, and $T_{r_{m,F}}$ represents the trace over single-particle orbitals and also the trace over Fourier space. Here, we have defined $[\sigma_{ssF}]_{ab} = T_{r_e} \left( \hat{b}_a^\dagger \hat{b}_b \hat{\rho}_{ssF} \right)$. Note that $U(R)$ does not contribute to the friction.
FRICTION IN FLOQUET GREEN’S FUNCTION REPRESENTATION
Furthermore, one can recast the Floquet friction tensor into the energy domain as
$$
\gamma_{\alpha \beta} = -\int_0^\infty dt \int_0^\infty dt' T_{m,F} \left( \frac{\partial H}{\partial R_\alpha} e^{-i(H_F-i\eta)t'}/h \frac{\partial \sigma_{ssF}}{\partial R_\beta} e^{i(H_F+i\eta)t'/h} \right) \delta(t-t')
$$
$$
= -\int_{-\infty}^\infty \frac{de}{2\pi} \int_0^\infty dt \int_0^\infty dt' T_{m,F} \left( \frac{\partial H}{\partial R_\alpha} e^{-i(H_F-i\eta)t'/h} \frac{\partial \sigma_{ssF}}{\partial R_\beta} e^{i(H_F+i\eta)t}/h \right) e^{i(t-t')/h}
$$
$$
= -\hbar \int_{-\infty}^\infty \frac{de}{2\pi} T_{m,F} \left( \frac{\partial H}{\partial R_\alpha} \frac{1}{\epsilon + i\eta - H_F} \frac{\partial \sigma_{ssF}}{\partial R_\beta} \frac{1}{\epsilon - i\eta - H_F} \right).
$$
Hence, we have redefined the \( \gamma_{\alpha \beta} \), partially, in terms of the Floquet Retarded and Advanced Green’s functions, \( G_F^{R/A} = (\epsilon \pm i\eta - H_F)^{-1} \), as
$$
\gamma_{\alpha \beta} = -\hbar \int_{-\infty}^\infty \frac{de}{2\pi} T_{m,F} \left( \frac{\partial H}{\partial R_\alpha} G_F^R \frac{\partial \sigma_{ssF}}{\partial R_\beta} G_F^A \right).
$$
(S21)
For a practical calculation of electronic friction tensors, one needs to express the derivative \( \partial \sigma_{ssF}/\partial R_\beta \) in terms of the Floquet lesser Green’s function denoted by \( G_F^- \). The \( \sigma_{ssF} \) relates to the \( G_F^- \) by
$$
\sigma_{ssF} = \int \frac{de'}{2\pi i} G_F^- (\epsilon') = \int \frac{de'}{2\pi i} G_F^R (\epsilon') \Sigma_F^- (\epsilon') G_F^A (\epsilon'),
$$
(S22)
where \( \Sigma_F^- \) is the total lead’s Floquet lesser self-energy[S4]. Here, we have adopted a dot-lead (system-bath) separation. Furthermore, we have assumed that \( \Sigma_F^- \) neither depends on the energy \( \epsilon' \) (so-called wide-band approximation) nor on the position \( R \) (so-called Condon approximation). Note that the wide-band approximation allows us to express the lesser green’s function in the Floquet representation as \( G_F^- (\epsilon') = G_F^R (\epsilon') \Sigma_F^- G_F^A (\epsilon') \). With Condon approximation, one can easily derive the following identity
$$
\frac{\partial G_F^-}{\partial R_\beta} = G_F^R \frac{\partial H}{\partial R_\alpha} G_F^- + G_F^- \frac{\partial H}{\partial R_\alpha} G_F^A.
$$
(S23)
It is important to note that we cannot directly substitute \( \partial \sigma_{ssF}/\partial R_\beta \) of Eq. (S22) into Eq. (S21) due to extra integration over \( \epsilon' \). To proceed further, we can replace the \( T_{m,F}(...) \) with \( \sum_n \langle n | ... | n \rangle \) in the last line of Eq. (S20) and use the eigenbasis of the Floquet electronic Hamiltonian, \( H_F | n \rangle = \epsilon_n | n \rangle \), as
$$
\gamma_{\alpha \beta} = -\hbar \sum_n \int_{-\infty}^\infty \frac{de}{2\pi} \langle n | \frac{\partial H}{\partial R_\alpha} \frac{1}{\epsilon + i\eta - H_F} \frac{\partial \sigma_{ssF}}{\partial R_\beta} | n \rangle \frac{1}{\epsilon - i\eta - \epsilon_n}.
$$
(S24)
Next, we will use the Floquet identity operator \( \sum_m \langle m | m \rangle \) as
$$
\gamma_{\alpha \beta} = -\hbar \sum_{n,m} \int_{-\infty}^\infty \frac{de}{2\pi} \langle n | \frac{\partial H}{\partial R_\alpha} | m \rangle \frac{1}{\epsilon + i\eta - \epsilon_m} \langle m | \frac{\partial \sigma_{ssF}}{\partial R_\beta} | n \rangle \frac{1}{\epsilon - i\eta - \epsilon_n}.
$$
(S25)
Taking the singularity point at \( \epsilon = i\eta + \epsilon_n \) and using the residue theorem for contour integration leads to
$$
\gamma_{\alpha \beta} = -\hbar \sum_{n,m} \langle n | \frac{\partial H}{\partial R_\alpha} | m \rangle \frac{1}{\epsilon_n - \epsilon_m + i2\eta} \langle m | \frac{\partial \sigma_{ssF}}{\partial R_\beta} | n \rangle.
$$
(S26)
At this point, we will evaluate the last term of above expression as: \( \langle m | \frac{\partial \sigma_{ssF}}{\partial R_\beta} | n \rangle \). According to Eqs. (S22) and (S23), this term has two parts as
$$
\langle m | \frac{\partial \sigma_{ssF}}{\partial R_\beta} | n \rangle = \int \frac{de'}{2\pi i} \langle m | G_F^R (\epsilon') \frac{\partial H}{\partial R_\alpha} G_F^- (\epsilon') \Sigma_F^- G_F^A (\epsilon') | n \rangle + \langle m | G_F^R (\epsilon') \Sigma_F^- G_F^A (\epsilon') \frac{\partial H}{\partial R_\alpha} G_F^- (\epsilon') | n \rangle.
$$
(S27)
The integration over $\epsilon'$ can be accomplished by using the eigenbasis of the Floquet electronic Hamiltonian and employing the identity operator $\sum_{m'} |m'\rangle\langle m'|$. The first part is given by
$$\sum_{m'} \int \frac{d\epsilon'}{2\pi i} \frac{1}{\epsilon' + i\eta - \epsilon_{mF}} \langle m| \frac{\partial H_F}{\partial R_\beta} |m'\rangle \frac{1}{\epsilon' + i\eta - \epsilon_{m'F}} \langle m'| \Sigma^\beta_F |n\rangle \frac{1}{\epsilon' + i\eta - \epsilon_{nF}}.$$
(S28)
Similarly (by taking the singularity point at $\epsilon' = -i\eta + \epsilon_{mF}$), the second part reduces to
$$\sum_{m'} \langle m| \Sigma^\beta_F |m'\rangle \frac{1}{\epsilon_{mF} - \epsilon_{m'F} + i2\eta} \langle m'| \frac{\partial H_F}{\partial R_\beta} |n\rangle \frac{1}{\epsilon_{mF} - \epsilon_{m'F} + i2\eta}.$$
(S29)
A relation for $\gamma_{\alpha\beta}$ can be derived by substitution of these two parts in the Eq. (S25) as
$$\gamma_{\alpha\beta} = -i\hbar \sum_{n,m,m'} \langle n| \frac{\partial H_F}{\partial R_\alpha} |m\rangle \frac{1}{\epsilon_{nF} - \epsilon_{mF} + i2\eta} \left( \frac{1}{\epsilon_{nF} - \epsilon_{mF} + i2\eta} \langle m| \frac{\partial H_F}{\partial R_\beta} |m'\rangle \frac{1}{\epsilon_{mF} - \epsilon_{m'F} + i2\eta} \langle m'| \Sigma^\beta_F |n\rangle \right)$$
(S30)
$$+ \langle m| \Sigma^\beta_F |m'\rangle \frac{1}{\epsilon_{mF} - \epsilon_{m'F} + i2\eta} \langle m'| \frac{\partial H_F}{\partial R_\beta} |n\rangle \frac{1}{\epsilon_{mF} - \epsilon_{m'F} + i2\eta}.$$
Taking similar procedures (replacing $Tr_{m,F}(...) \sum_n \langle n| |n\rangle$, using the eigenbasis of the Floquet electronic Hamiltonian and employing the identity operators) one can conclude the following general single integration formula
$$\gamma_{\alpha\beta} = \hbar \int_{-\infty}^{\infty} \frac{d\epsilon}{2\pi} Tr_{m,F} \left( \frac{\partial H_F}{\partial R_\alpha} \frac{\partial G^{R,A}_F}{\partial \epsilon} \frac{\partial H_F}{\partial R_\beta} \frac{\partial G^{A,R}_F}{\partial \epsilon} - \frac{\partial H_F}{\partial R_\alpha} G^{R,A}_F \frac{\partial H_F}{\partial R_\beta} \frac{\partial G^{A,R}_F}{\partial \epsilon} \right).$$
(S31)
delivers a similar output as Eq. (S30). Note that, we have used the identity $\frac{\partial G^{R,A}_F}{\partial \epsilon} = -G^{R,A}_F \frac{\partial G^{A,R}_F}{\partial \epsilon}$. [S2]. This relation is a practical formula for evaluation of $\gamma_{\alpha\beta}$. The second term in Eq. (S30) is also the hermitian conjugate of the first part. Since the trace in any basis set is the same, Eq. (S31) represents a general form for Floquet electronic friction.
* Electronic address: [email protected]
1 Electronic address: [email protected]
[S1] K. L. Ivanov, K. R. Mote, M. Ernst, A. Equbal, and P. K. Madhu, Progress in Nuclear Magnetic Resonance Spectroscopy 126, 17 (2021).
[S2] W. Dou, G. Miao, and J. E. Subotnik, Physical review letters 119, 046001 (2017).
[S3] W. Dou and J. E. Subotnik, Physical Review B 97, 064303 (2018).
[S4] H. H. Yap, L. Zhou, J.-S. Wang, and J. Gong, Physical Review B 96, 165443 (2017).
| 2025-03-04T00:00:00 |
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Biosorption: An Interplay between Marine Algae and Potentially Toxic Elements—A Review
Muhammad Bilal 1, Tahir Rasheed 2, Juan Eduardo Sosa-Hernández 3, Ali Raza 4, Faran Nabeel 2 and Hafiz M. N. Iqbal 3,*
1 State Key Laboratory of Microbial Metabolism, School of Life Sciences and Biotechnology, Shanghai Jiao Tong University, Shanghai 200240, China; [email protected]
2 State Key Laboratory of Metal Matrix Composites, The School of Chemistry & Chemical Engineering, Shanghai Jiao Tong University, Shanghai 200240, China; [email protected] (T.R.); [email protected] (F.N.)
3 Tecnologico de Monterrey, School of Engineering and Sciences, Campus Monterrey, Ave. Eugenio Garza Sada 2501, Monterrey, N.L., CP 64849, Mexico; [email protected]
4 School of Biomedical Engineering, Shanghai Jiao Tong University, Shanghai 200240, China; [email protected]
*
Correspondence: [email protected] or [email protected]; Tel.: +528183582000 (ext. 5679)
Received: 22 January 2018; Accepted: 16 February 2018; Published: 19 February 2018
Abstract: In recent decades, environmental pollution has emerged as a core issue, around the globe, rendering it of fundamental concern to eco-toxicologists, environmental biologists, eco-chemists, pathologists, and researchers from other fields. The dissolution of polluting agents is a leading cause of environmental pollution of all key spheres including the hydrosphere, lithosphere, and biosphere, among others. The widespread occurrence of various pollutants including toxic heavy metals and other emerging hazardous contaminants is a serious concern. With increasing scientific knowledge, socioeconomic awareness, human health problems, and ecological apprehensions, people are more concerned about adverse health outcomes. Against this background, several removal methods have been proposed and implemented with the aim of addressing environmental pollution and sustainable and eco-friendly development. Among them, the biosorption of pollutants using naturally inspired sources, e.g., marine algae, has considerable advantages. In the past few years, marine algae have been extensively studied due to their natural origin, overall cost-effective ratio, and effectiveness against a broader pollutant range; thus, they are considered a potential alternative to the conventional methods used for environmental decontamination. Herein, an effort has been made to highlight the importance of marine algae as naturally inspired biosorbents and their role in biosorption. Biosorption mechanisms and factors affecting biosorption activities are also discussed in this review. The utilization of marine algae as a biosorbent for the removal of numerous potentially toxic elements has also been reviewed.
Keywords: biosorption; biosorbent; marine algae; toxic elements; environmental pollution
1. Introduction
Increasing pollution is one of the major problems that our ecosystem is facing both at the aquatic and the terrestrial level. Some of the sources of polluting agents include chemical byproducts, herbicides, pesticides, pharmaceuticals, cosmeceuticals, leather, textiles, the plastic industry, pigments, electroplating, storage batteries, mining, smelting, metallurgical processes, nanoparticles, etc. [1,2]. However, besides their technological importance, the abovementioned contaminants are included in the category of persistent and/or emerging environmental pollutants, because they cannot be destroyed or degraded [1,3,4]. Also, these polluting agents are a leading cause of environmental pollution in almost all the key spheres, including the hydrosphere, lithosphere, and biosphere [2,5].
In recent decades, environmental pollution has emerged as a core issue around the globe, rendering it of fundamental concern to eco-toxicologists, environmental biologists, eco-chemists, pathologists, and researchers from other fields. Owing to rapid industrial expansion and the continued growth of the human population, the consequences of environmental pollution are worse than ever. Therefore, advanced methods with unique redefining approaches are required to meet the demands of the growing world population. Such strategies of the so-called “green agenda” are nowadays equally important for the sustainable development of all modern societies.
So far, numerous detection and removal methods have been proposed and implemented with the aim of addressing environmental pollution and sustainable and eco-friendly development. Among them, fluorescent-based sensors and electrochemical sensors for detection purposes, immobilized enzyme-based catalytic systems and photocatalytic systems for degradation purposes, along with other physiochemical-based process, etc. are the most widely used, though each have certain advantages and disadvantages [1,4–20]. Therefore, advanced methods with unique redefining approaches are required to remove potentially toxic elements and other hazardous pollutants from aqueous environments. Considering the adverse health outcomes, a clean and sustainable environment is of great importance.
The recovery of potentially toxic elements such as silver, gold, and uranium from chemically treated aqueous solutions is cost-effective [21]. However, the treatment of potentially toxic elements in wastewater is a challenge not only from an economic point of view but also from an environmental one. In order to remove potentially toxic elements, various physiochemical techniques such as ion exchange [22], chemical precipitation [23], electrokinetics [24], adsorption [25], and membrane processing [26] have been employed. Physiochemical processes pose high costs due to the expensive chemicals required for treatment of potentially toxic elements. Incomplete removal of potentially toxic elements is another factor involved in physiochemical processes. Furthermore, stringent conditions placed by regulating authorities on effluents also demand alternative methods. Potentially toxic elements can be removed from wastewater through biosorption from algae, which is an efficient, safe, and more economical method. Algae are also used for sorption of heavy radionuclides [27] and can recover metal ions such as gold and silver [28]. However, removal of potentially toxic elements can be attained by acquiring knowledge of algae. Biosorption mechanisms for potentially toxic element removal include ion exchange and complex formation, whereas electrostatic interaction proceeds at the micro-level. For the biosorption of metals, ion exchange is an important mechanism [29,30].
In this context, naturally inspired sources/materials, e.g., the biosorbent potentialities of marine algae and algae-based compounds, have appeared as an alternative technology with special reference to biosorption (Figure 1). Natural sources are now considered ecologically safer, cheaper, and more efficient for removing toxic metal ions and other hazardous pollutants from aqueous environments, e.g., industrial wastewater [15]. As compared to other methods, biosorption is rapid, reversible, economical, and eco-friendly. Owing to its range of novel aspects, as mentioned above, biosorption can be used in several ways under numerous conditions to reduce environmental pollution. Naturally inspired biosorbents, e.g., marine algae, offer several advantages such as (1) diverse multifunctional groups on their surface, (2) relatively small and uniform distribution of binding sites on the surface, (3) requires minimal preparatory steps, (4) no or less consumption of harsh chemicals, (5) naturally renewable, recyclable, and easily available all year round, (6) excellent retention capacity, and so on. Based on the literature, the utilization of marine algae as biosorbents has been successfully tested for several biotechnological and industrial applications including the removal of various potentially toxic elements [15,31–37].
2. Marine Algae: Sources, Production Strategies, and Applied Perspectives
Marine life is full of biodiversity but little explained in terms of total species. Indeed, there exists a range of exceptional sources of microorganisms including plants and animals that show particular features. Algae are one such group and cover about 30,000 species from various phylogenetic groups. Broadly, algae can be categorized into two groups: (1) macroalgae (multicellular); and (2) microalgae (unicellular). However, algae are heterogeneous from an evolutionary point of view [39]. Coastal area algae are mostly macroalgae and classified into three types: Chlorophyta (green), Rhodophyta (red), and Phaeophyta (brown) algae [34,35,37,40,41]. Microalgae are found as phytoplankton throughout the oceanic ecosystem [40]. Microalgae consist of varied species and present biochemical properties, particularly undertaking oxygen-mediated photosynthesis [42]. They can survive under less favorable conditions such as high salinity, heat, cold, varied light sources, osmotic pressure, and anaerobiosis. Microalgae are the main food producers for animals because of fatty acid, sterol, carbohydrate, mineral, vitamin, protein, tocopherols antioxidant, chlorophyll, and carotenoid production [43].
During photosynthesis, algae cells convert solar energy to chemical energy, which generates chemical compounds of biological activities known as bioactive compounds. Production of these bioactive compounds could be associated with microbial and algal growth [44]. The Dictionary of Marine Natural Products is a key data source, listing more than 30,000 bioactive compounds from algae, and that number is gradually increasing every year [45].
Production of photosynthetic microorganisms by autotrophic cultivation is increasing, mainly for to get useful biomolecules. Various methods have been developed for microalgae cultivation such as open pond cultivation and photobioreactor cultivation, including membrane, flat-plate, helicoidal, horizontal, and vertical photobioreactors [46]. For improved biomass composition, tubular reactors using airlift systems are most common. Heterotrophic conditions could also produce microalgae with sufficient nutrients, whereas in mesotrophic environments and the non-availability of light, nutrients are achieved heterotrophically as well as autotrophically [47].
Macroalgae, also known as seaweeds, are used for the production of phycocolloids such as agar and alginates [48]. Some macroalgae like brown and red algae are employed in cosmetics because of their sugar, mineral, lipid, vitamin, and amino acid contents, as well as some other biological compounds [48]. Algae have become a sustainable resource due to the growing demand for bioprocessing to obtain environmentally friendly products [49]. Recently, bioactive compounds from algae [37,48], have become important and are being utilized in various environment-related applications like biofuel production, CO₂ sequestration, wastewater treatment, oxygen discharge to the environment, and reducing the effects of greenhouse gases [40,50].
3. Biosorption and Its Mechanisms
Different mechanisms have been reported for the removal of potentially toxic elements through biosorption. Previously, biosorption was categorized into metabolism-dependent or metabolism-independent biosorption [51]. However, later on, metabolism-dependent processes were termed bioaccumulation, and metabolic-independent processes were termed biosorption [52,53]. Bioaccumulation, also termed active biosorption, involves two processes: the first is similar to biosorption, involving attachment of potentially toxic elements to the surface; and in the second step active transportation of metal ions into cells occurs [54]. Biosorption is a passive process that occurs at a faster rate than bioaccumulation. Adsorption, chelation/complexation, ion exchange, and surface precipitation are different processes reportedly involved in biosorption (Figure 2) [55,56]. Among them, ion exchange is considered the principle mechanism of biosorption, which occurred through different functional groups present on the surface of biomass [53,57]. The mechanism of biosorption usually depends upon the biomass that is going to be used for the removal of potentially toxic elements [53]. For instance, the composition of the cell wall is different in bacteria (peptidoglycan), fungi (chitin), and algae (alginate, sulfonated polysaccharides); therefore, variation in the presence of functional groups on the surface of the cell wall is responsible for the difference in mechanisms [55,58]. Apart from the cell wall, extracellular polymer substances secreted by microorganisms are also found to play an important role in biosorption [59]. Verma et al. [60] reported ion exchange as a principle mechanism for the biosorption of potentially toxic elements by dry biomass of macrophytes. They presumed that aquatic macrophytes served as natural ion exchangers. Monovalent ions (H\(^+\), Na\(^+\)/K\(^+\)) were reported to be involved in the ion exchange process due to a weak attachment with biomass as compared to divalent ions [60]. Very recently, Ahmad et al. [61] reported that sulfate, carboxyl, and hydroxyl groups are involved in biosorption by microalgae. Changing of the morphological structure observed by scanning electron microscope (SEM) and/or energy dispersive X-ray (EDX) after biosorption also indicated the facilitation of sorption of metal ions by pores present on the surface [61]. However, in general, the mechanism of metal ion absorption by biomass is complicated and involves different processes.
Figure 2. A schematic representation of the mechanisms involved in the biosorption of potentially toxic elements, e.g., heavy metal ions.
4. Factors Affecting Biosorption
Different factors can influence biosorption processes such as pH, temperature, initial metallic concentration, contact time, competing ions/co-ions, and biosorbent dosage [38,61,62]. Among these factors, pH is the most important factor. Increase in pH also increases the biosorption of metal ions, however; too great an increase in pH can cause precipitation, which should be avoided [62]. Optimum
pH varied for different biosorption systems. An increase in pH up to 5 caused an increase in biosorption capacity (98%), but a further increase in pH led to reduced capacity. Protonation and deprotonation of functional groups is controlled by the pH of the medium, which affects the biosorption capacity: at low pH, carboxylic groups, being acidic, exist in a protonated state due to the presence of excess H$^+$ and H$_3$O$^+$; therefore, repulsive forces of these protonated groups with positively charged heavy metal ions are responsible for the lower biosorption capacity at low pH [61,63]. With the increase in pH, functional groups such as amine, carboxyl, and hydroxyl groups are exposed by deprotonation, which enhances electrostatic attraction with heavy metal ions due to a negative charge. The high increase in pH leads to the formation of hydroxide anionic complexes and precipitation is a reported reason for the low biosorption capacity [61,63–65].
Temperature is also an important parameter influencing the sorption process [55]. Change in temperature alters thermodynamic parameters, resulting in variation in sorption capacity [38]. The influence of temperature on the sorption process depends upon its nature. In endothermic sorption processes, an increase in temperature leads to an increase in biosorption; on the other hand, an increase in temperature decreases biosorption in the case of exothermic sorption processes [38]. For instance, the biosorption of Pb(II) by algae was found to increase with an increase in temperature [66]. The biosorption of Pb(II), Cd(II), and Co(II), from an aqueous solution on green algae waste biomass has also been reported [16]. In another report, Ahmad et al. [61] found a reduction in biosorption of Fe(II), Mn(II), and Zn(II) by freely suspended and Ca–alginate immobilized with Chlorella vulgaris with an increase in temperature (25–45 °C) due to the exothermic nature of the biosorption process. A very high temperature can also denature the biomass structure [61].
The contact time of biosorbent influences total biosorption. An increase in contact time up to the optimum contact time increases biosorption; afterwards it becomes relatively constant. Occupancy of all active sites causes saturation of biomass, leading to an equilibrium state [63,67]. The optimum time is different for different types of biosorbents such as 60 min for red macroalgae [63] and 300 min for immobilized algal mass (240 min for free suspended mass) [61]. The initial metal ionic strength also affects biosorption. A high initial metallic concentration exhibits high biosorption capacity due to the availability of free active sites [68]. A similar trend was also reported by changing the adsorbent dose, i.e., initial increase and then equilibrium state [69,70].
5. Potential Biosorbents
For biosorption purposes, different living and non-living biomasses have been reported such as algal biomass, fungi, bacteria, agricultural waste, etc. [71]. Typically, an ideal biosorbent should possess features like availability, non-toxicity, high metal binding capacity, large-scale usability, and regeneration/re-usability [21]. Algal biomass is the most employed biosorbent compared to any other material. As no treatment is required for algae, it is considered a low-cost biosorbent, and its cell wall characteristics endow it with high metal ion binding capacity [72]. Non-living algal mass has been reported to be more promising as compared to living algae because of the higher metal ions sorption capacity at a higher rate, and it does not require nutrients grown in a medium [38]. Moreover, adsorbed heavy metal ions on dead algal mass can be removed using de-ionized water or desorption agents [38]. Different types of algae have been reported as biosorbents such as marine algae, marine red macroalgae, marine brown macroalgae, and freshwater green macroalgae. Brown algae are reported to have good biosorption capacity due to the presence of alginates in their cell walls [73].
6. Potentially Toxic Elements—Heavy Metals
Heavy metals exist naturally in the earth’s crust and are distributed in the soil. While there is no clear definition for heavy metals, density is the defining element in most situations. Conventionally, on the periodic table, heavy metals are those with an atomic number greater than 20 [65]. Considering their atomic density higher than 4 g cm$^{-3}$ (5 times higher than water), they form a group of about 53, including metals and elements with metallic properties [74]. Heavy metals are referred to as
high-density elements and cause toxicity at low strengths. Nevertheless, from an ecological point of view, any metal or related metalloid that is not biodegradable and produces environmental pollution can be taken as a heavy metal [74]. Some heavy metals (e.g., Cu, Zn, Ni, Cu, Mn, and Co) are essential for plant life, whereas some do not have any biological role and have toxic effects (e.g., Pb, Hg, and Cd) [75]. Therefore, any metal or metalloid that causes a harmful effect on the environment, does not play a vital role in biological functions, shows toxicity at low strengths (e.g., Pb and Hg), or plays a vital role in biological functions but produces harmful effects if present in a high concentration (e.g., Cu and Mo) [74]. Wang and Chen [21] classified harmful heavy metals into three divisions: toxic metals (Pb, Hg, Zn, Cr, Ni, Co Cd, Cu, Sn, As, etc.), radionuclides (U, Th, Am, Ra, etc.), and precious metals (Au, Ag, Pt, Ru, etc.).
Urbanization, industrialization, population growth, and continuous cultivation have damaged the global environment. The toxic effects and major mechanisms of toxicity of different heavy metals are summarized in Table 1. Human activities and industrial applications of heavy metals have increased toxicity levels and pose harmful effects to the environment [74,76]. Several reports report the varied use of heavy metals [77] in different industrial [21] and agrarian practices [78], in addition to indiscriminate disposal [79]. Among the other harmful effects of heavy metals, water pollution is one of the serious issues worldwide [80]. Several heavy metals released into the environment by different activities undergo transformations, are dispersed and accumulated in the food chain, and cause serious health concerns [81]. In short, removal of heavy metals is a challenge as they are not biodegradable and hence hinder the self-purification capability of marine life when discharged to the aquatic environment [82].
### Table 1. Toxic effects and major mechanisms of toxicity of different heavy metals.
| Heavy Metal | Major Uses/Sources | Toxic Effects | Mechanism of Toxicity | References |
|-------------|--------------------|--------------|-----------------------|------------|
| Lead (Pb) | Lead batteries, lead paint, devices to shield from X-rays. | Nervous system, male reproductive system, microvascular endothelium, immune system, impairs mammalian spermatogenesis and sperm quality in vivo, inhibits sperm functions in vitro. | Lead has no biological functions. Oxidative stress (reactive oxygen species, ROS), with a reduction in the effects of antioxidants, is the principal mechanism. Lead ions also replace other ions such as Ca²⁺, Mg²⁺, and Na⁺ and disturb normal cell functions such as cellular adhesion, apoptosis, and neurotransmitter release. | [83–88] |
| Arsenic (Ar) | Agricultural chemicals (pesticides, fungicides, herbicides). | Cardiovascular/peripheral vascular disease, developmental abnormalities, immunological, and neurological disorders, carcinogenesis, diabetes, portal fibrosis. | Oxidative stress, genotoxicity, alteration in DNA repair, and p53 suppression (major contributor to carcinogenesis). | [89–93] |
| Cadmium (Cd) | Metal industry, paint pigments, fertilizers, cigarette smoke, food. | Pulmonary and gastrointestinal irritation, carcinogenesis (development of adenocarcinomas), Kidneys, liver and bones are also effected by cadmium exposure. | Competition with other ions (zinc, iron, copper), genotoxicity, lipid peroxidation, oxidative stress. | [94–97] |
| Chromium | Anticorrosive, industrial welding, chrome plating, leather industry, wood preservation. | Carcinogenic, gastric and intestinal ulcers, sperm damage, male reproductive system problems, anemia. | Cr (VI) is more potent than Cr (III); Oxidative stress, genotoxicity, alteration in cellular signaling pathway | [94,98] |
Table 1. Toxic effects and major mechanisms of toxicity of different heavy metals.
| Heavy Metal | Major Uses/Sources | Toxic Effects | Mechanism of Toxicity | References |
|-------------|-------------------|---------------|-----------------------|------------|
| Mercury (Hg) | Natural processes involved oceanic emissions and biomass burning. Anthropogenic sources included power plants, metal industry and gold mining. | Alzheimer’s disease, Parkinsonism, respiratory depression | Binding of mercury with sulfhydryl (–SH) groups disrupts normal cellular enzymatic processes. Increase in free radical concentration due to blockage of GSH by Hg is responsible for cell-damaging effects. | [94,95,97] |
| Copper (Cu) | Agriculture (fertilizers), leather industry (tanning), and photo-voltaic cells. | Carcinogenic, neurodegenerative disorders, responsible for complications in diabetes, promotes atherosclerosis. | Oxidative stress, enzyme inhibition, replaces normal ions of the body. | [94,99–101] |
| Zinc (Zn) | Oil refinery, mining, brass manufacturing, plumbing. | Ataxia, depression, gastrointestinal irritation, hematuria, icterus, impotence, kidney and liver failure, lethargy, macular degeneration, metal fume fever, prostate cancer, seizures, vomiting. | | [94,102] |
7. Biosorption of Potentially Toxic Elements
Potentially toxic elements are removed from wastewater by algae, mostly through inactive biomass and non-living algae. Fewer data are available on using live algae for potentially toxic element removal [103], as toxic elements poison the algae. Although sorption largely depends on the stage of the algae growth, there are several factors that affect the biosorption of metal ions. The process of biosorption is more complicated in living algae as compared to non-living algae as biosorption occurs in the growth stage and the intracellular consumption of potentially toxic elements mostly takes place at this stage. The cells of non-living algae absorb potentially toxic elements at the cell membrane surface. Therefore, the process is known as an extracellular process [104]. Non-living algal biomass includes polymers such as sugars, glycoproteins, cellulose, pectins, etc., which effectively bind and adsorb potentially toxic elements from wastewater [105]. Two stages are involved in the accumulation of potentially toxic elements through microorganisms [106]. During the first stage, fast inactive biosorption proceeds at the cell surface with no cellular metabolism involved, whereas active sorption occurs during the second stage, which involves the cell cytoplasm. The second stage is considered intracellular ion accumulation since it involves cell metabolism. Intercellular ion accumulation plays a vital role in the biosorption detoxification of potentially toxic elements [107].
The biosorption ability of algae cell surface is designated by the availability of the binding moiety, i.e., carboxyl, hydroxyl, amine, phosphoryl, sulphuryl, sulfate, carbohydrate, imidazole, phosphate, etc. [108]. The presence of the binding site on the algae cell for potentially toxic elements accumulation is analyzed by Fourier-transform infrared spectroscopy (FTIR) spectroscopy [109]. Accumulation of the potentially toxic elements on the algae cell depends on various factors such as the number of functional moieties, the approachability of binding sites, binding constants, and the chemical state of the moieties. Most binding moieties make the cell surface negatively charged overall as a result of carboxyl and phosphate deprotonation [110]. Biosorption of the metal ions starts from the algae cell wall. Various binding groups, for example OH\(^-\), COO\(^-\), NO\(^3^-\), RS\(^-\), SH\(^-\), PO\(^4^3^-\), RNH\(^2^-\) and RO\(^-\) encourage adsorption of the metal ions. These groups exist outside (cell surface) and inside (cytoplasm and vacuoles) the cell wall. The biosorption mechanism of metal ions across the cell walls could be supported by cytosolic protein-mediated metal ions transfer [111]. Vacuoles, therefore, accumulate metal ions and are considered metal ion organelles. The data based on the affinity for various metal ions...
and the corresponding cellular ligands are illustrated in Figure 3. Ligands with R present alkyl groups, for example propyl and metal ions categorized into A, B, and borderline subcategories. Category I shows the connection of ligands with metal ions of Class A through an oxygen atom. Metal ions from Class B can be connected with ligands of category II and III, whereas borderline cations can be associated with various atoms from categories I, II, and III [52]. The categorization is well defined, but it would be more convenient if the classification is based on metal complexation constants from a chemistry viewpoint. This can be more helpful for scientists trying to decide on the biosorption ability of a particular metal among competing ions.
Figure 3. A schematic representation of three classes of metals based on ligands present in biological systems. LCI, ligand class I; LCII, ligand class II; and LCIII, ligand class III.
The cell wall in algae cells is an initial hindrance to the biosorption of potentially toxic elements. Most of the binding sites present in algae cells are due to polysaccharides and proteins [112]. Different algal strains have different cell wall compositions and varying capacity of biosorption of potentially toxic elements. Romera et al. [113] studied different algae strains for the biosorption of potentially toxic elements and proposed brown algae as a good contender. Brown algae have a high affinity for the biosorption of lead because of the presence of alginate in the cell walls and the capacity of biosorption depends on the binding sites available on the alginate [32,113]. Several factors such as metal ion concentration, competing for metal ions, temperature, and pH affect the biosorption of potentially toxic elements in addition to available binding sites on the algae cell.
7.1. Biosorption of Cadmium
Cadmium is found in nature in the form of deposits with other elements. The toxic metal is discharged in industrial effluents from phosphate fertilizers, plating, stabilizers, and cadmium–nickel alloy batteries. Low concentrations of cadmium can accumulate and become harmful to the ecosystem. Cadmium can cause “Itai-itai” bone softening and fractures in humans [114]. Other effects of cadmium on human health include lung cancer, kidney failure, and damage to respiratory and reproductive
systems [115,116]. Therefore, efficient, reliable, and economical removal of cadmium from water is required. Biosorption of cadmium using marine algae is a safe, useful, and eco-friendly solution to wastewater treatment. Table 2 presents various algae’s capacity to remove potentially toxic elements.
The table comprises Cd\(^{2+}\) removal in the pH range from 4 to 8. It has been found that algae *C. reinhardtii*, *Scenedesmus* spp., *S. platensis*, *Chlorella* spp. as well as *Tetraselmis* spp. efficiently remove Cd\(^{2+}\), whereas the uptake of Cd\(^{2+}\) from *Planothidium lanceolatum* live cells is significant, i.e. 275.51 mg g\(^{-1}\) [117].
Table 2. Biosorption potentialities of various marine algae to remove potentially toxic elements from aqueous solutions.
| Potentially Toxic Elements | Algae Used | Adsorption Capacity | References |
|----------------------------|----------------------|---------------------|------------|
| Zn(II) | Ulva sp. | 29.63 mg/g | [118] |
| Cd(II) | Chlorella vulgaris (dead) | 96.8% | [119] |
| Cd(II) | Chlorella vulgaris (live) | 95.2% | [119] |
| Cd | Scenedesmus quadricauda | 66% | [120] |
| Pb | Scenedesmus quadricauda | 82% | [120] |
| Cd(II) | Ulva lactuca | 85% | [121] |
| Cd(II) | Ulva lactuca | 29.2 mg/g | [122] |
| Pb(II) | Ulva lactuca | 34.7 mg/g | [122] |
| Cd(II) | Ceramium virgatum | 39.7 mg/g | [123] |
| Cu(II) | Ulva fasciata | 73.5 mg/g | [124] |
| Cu(II) | Sarqassum sp. | 72.5 mg/g | [124] |
| Hg(II) | Chlamydomonas reinhardtii | 89.5 mg/g | [125] |
| Cd(II) | Chlamydomonas reinhardtii | 66.5 mg/g | [125] |
| Pb(II) | Chlamydomonas reinhardtii | 253.6 mg/g | [125] |
| Cr(VI) | Spirulina sp. | 14.7 × 10\(^{3}\) mg metal/kg | [126] |
| Cd(II) | Padina sp. | 90% | [127] |
| Cd(II) | Durvillaea potatorum | 90% | [128] |
7.2. Biosorption of Chromium
Chromium is the seventh most prevalent metal on earth and is found in ores with other metals like chromite (FeCr\(_2\)O\(_3\)), chrome ochre (Cr\(_2\)O\(_3\)), and crocoite (PbCrO\(_3\)). The foremost industrial sources of chromium are the leather, tanning, textile, and electroplating industries. Industry waste has hexavalent and trivalent ions of chromium, i.e., Cr\(^{6+}\) and Cr\(^{3+}\) [129]. Cr\(^{3+}\) is less toxic to living organisms than Cr\(^{6+}\) [116,130]. Cr\(^{3+}\) is helpful in sugar and fat metabolism, and Cr\(^{6+}\) is used in industry for salt production [129,131]. Both states of chromium metals are used for chrome plating, pigment fabrication, in the glass industry, in the leather industry as a tanning agent, etc. [132]. They damage organs such as the liver, kidneys, and skin and can cause ulcers, pulmonary congestion, and vomiting [132,133]. In order to reduce the effects of chromium, it needs to be modified to a less toxic state and treated before release into the environment.
7.3. Biosorption of Lead
Lead is also a toxic metal that can easily accumulate in plants, the human body, and other living organisms. It is found in nature in the state of sulfide, cerussite (PbCl\(_2\)) ore, and galena [134]. Wastewater from industries such as electrical, steel, electroplating, explosives, etc. is the main source of lead pollution. Its function is to produce DNA, protein, and replication of the cell [134]. It is harmful to the nervous system, kidneys, and mental health and causes cancer in humans [135,136]. Lead is also toxic to plants and animals. Therefore, the latest techniques are required to remove lead from water. Biosorption through algae is an innovative technique for the removal of lead from the ecosystem. As mentioned in Table 2, *Spirulina* as well as *Chlorella* spp. algae show potential for Pb\(^{2+}\) removal capacity. Also, significant results have been achieved for lead removal with immobilized cells, i.e., *C. reinhardtii* [125].
7.4. Biosorption of Zinc
Zinc is helpful in various biochemical processes and controls physiological mechanisms in living tissues. With other metals (such as steel alloys), it works as a protective layer to control corrosion. Other forms of zinc are used in industrial processes like steel, mining, and coal combustion [137]. Although a trace amount of zinc is required by the body, if present in excess amounts it can upset normal health. It can cause fever, pain, skin inflammation, vomiting, and anemia [137]. Sources of zinc pollution in the ecosystem are the paper, steel, electroplating, and brass industries. Given the effects of zinc metals, it becomes important to treat wastewater effectively before releasing it into the environment. Zinc has been studied for biosorption in the pH range from 5 to 7.5 (Table 2). *P. lanceolatum* algae are a potential contender to remove zinc metal up to 118.66 mg g\(^{-1}\) [117].
8. Concluding Remarks and Future Considerations
In conclusion, the above data suggest that the effective removal of potentially toxic elements from aqueous media can be achieved by biosorption using marine algae biomass as a biosorbent. Naturally inspired biosorbents, e.g., marine algae, offer several advantages such as (1) diverse multifunctional groups on their surface, (2) relatively small and uniform distribution of binding sites on the surface, (3) requiring minimal preparatory steps, (4) no or less consumption of harsh chemicals, (5) being naturally renewable, recyclable, and easily available all year round, (6) excellent retention capacity, and so on.
Despite the modern expansion of the biotechnological and industrial arena, along with the plethora of information available on various types of bioremediation processes, numerous challenges still need to be addressed. For example, the emergence of new pollutants, potentially toxic elements’ dissemination profiles, eco-friendly detection, removal fate, and reliable and consistent monitoring are research gaps that need to be addressed in future studies. In this context, proper management and strategies should be adapted to maintain aquatic and terrestrial environmental health and protect from further deterioration.
Furthermore, many other unsolved questions must be tackled. For example, insufficient detection methods, malpractice, and limitations within practice technologies greatly affect the detection fate and removal behavior of potentially toxic elements. The role of low-risk contaminants in the emergence of new pollutants should also be addressed in future studies. It could be useful to involve multidisciplinary scientists, policymakers, and stakeholders to strengthen the detection and removal/degradation of life-threatening pollutants at a global level.
Acknowledgments: The literature facilities provided by Shanghai Jiao Tong University, Shanghai 200240, China and Tecnologico de Monterrey, Mexico are thankfully acknowledged.
Author Contributions: Muhammad Bilal and Hafiz M. N. Iqbal designed the review contents; Tahir Rasheed, Ali Raza, and Faran Nabeel reviewed the literature; Juan Eduardo Sosa-Hernández and Ali Raza designed the figures and tables; Muhammad Bilal and Hafiz M. N. Iqbal critically reviewed and revised the paper. All authors read and approved the final manuscript.
Conflicts of Interest: The authors report no conflicting interest in any capacity, competing or financial.
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Comparing low-pass sequencing and genotyping for trait mapping in pharmacogenetics
Kaja Wasik¹, Tomaz Berisa¹, Joseph K. Pickrell¹, Jeremiah H. Li¹*, Dana J. Fraser², Karen King² and Charles Cox³
Abstract
Background: Low pass sequencing has been proposed as a cost-effective alternative to genotyping arrays to identify genetic variants that influence multifactorial traits in humans. For common diseases this typically has required both large sample sizes and comprehensive variant discovery. Genotyping arrays are also routinely used to perform pharmacogenetic (PGx) experiments where sample sizes are likely to be significantly smaller, but clinically relevant effect sizes likely to be larger.
Results: To assess how low pass sequencing would compare to array based genotyping for PGx we compared a low-pass assay (in which 1x coverage or less of a target genome is sequenced) along with software for genotype imputation to standard approaches. We sequenced 79 individuals to 1x genome coverage and genotyped the same samples on the Affymetrix Axiom Biobank Precision Medicine Research Array (PMRA). We then down-sampled the sequencing data to 0.8x, 0.6x, and 0.4x coverage, and performed imputation. Both the genotype data and the sequencing data were further used to impute human leukocyte antigen (HLA) genotypes for all samples. We compared the sequencing data and the genotyping array data in terms of four metrics: overall concordance, concordance at single nucleotide polymorphisms in pharmacogenetics-related genes, concordance in imputed HLA genotypes, and imputation r². Overall concordance between the two assays ranged from 98.2% (for 0.4x coverage sequencing) to 99.2% (for 1x coverage sequencing), with qualitatively similar numbers for the subsets of variants most important in pharmacogenetics. At common single nucleotide polymorphisms (SNPs), the mean imputation r² from the genotyping array was 0.90, which was comparable to the imputation r² from 0.4x coverage sequencing, while the mean imputation r² from 1x sequencing data was 0.96.
Conclusions: These results indicate that low-pass sequencing to a depth above 0.4x coverage attains higher power for association studies when compared to the PMRA and should be considered as a competitive alternative to genotyping arrays for trait mapping in pharmacogenetics.
Keywords: Trait mapping, Low-pass sequencing, Pharmacogenetics, Genotype imputation
Background
Research in human genetics relies on efficiently profiling the genome of large numbers of individuals. A number of approaches can be used for this, usually trading off comprehensiveness (i.e. the fraction of the genome that is measured) with cost. By far the most commonly-used approach is the genotyping array, in which a set of known polymorphisms (usually around 500,000-2,000,000) is measured. This technology is inexpensive (currently on the order of tens to hundreds of dollars), but the set of genetic variants profiled is a small number of all known variants, and the technology does not allow for the detection of new (for example rare or population-specific) genetic variants. Genotyping arrays are commonly used for pharmacogenetics (PGx) studies where typically sample numbers are more limited, but inclusion of PGx focused variants on the arrays makes them suitable tools for screening the genome for markers associated with efficacy and adverse events [3, 15, 16].
The technological alternative to genotyping technology is sequencing technology, in which specific polymorphisms are not targeted for analysis, but rather the entire genome is sampled with some average depth of coverage. As sequencing costs have dropped, low-pass sequencing (for our purposes, which we will define as sequencing in which the average coverage of the genome is equal to or lower than 1x) becomes an appealing alternative to genotyping [4, 6, 14]. As an intuition for why this approach is useful, note that a human sample sequenced at 0.4x coverage is expected to have a single sequencing read covering each of around 28 million of the 84.7 million genetic variants identified in the 1000 Genomes Project [1], while a genotyping array obtains measurements (albeit somewhat less noisy measurements) at two orders of magnitude fewer sites.
In this paper, we directly compare genotyping results from low-pass sequencing to a commonly used genotyping array, the Affymetrix Axiom Biobank Precision Medicine Research Array (PMRA). Two types of metrics are relevant for this comparison. One is simply the genome-wide coverage of the assay, which we measure using average imputation quality. The other is genotyping quality at particular genetic variants of interest. We were particularly interested in applications to PGx—the identification of genetic variants that influence drug response. In this application, genetic variants in the major histocompatibility complex (MHC) and genes involved in drug metabolism (so-called “ADME” genes, for absorption, distribution, metabolism, and excretion) are known to be particularly relevant. We thus considered these separately.
Results
We selected 79 individuals to be both genotyped and sequenced. These individuals derive from a pool of volunteers based out of Cambridge, UK for which prior consent was obtained. Each individual was genotyped on the Affymetrix Axiom Biobank PMRA, and sequenced by Gencove, Inc. to an average of 1x coverage using the Illumina HiSeq 4000 platform with paired-end 150 base pair reads. Sequencing reads were then sampled at random to obtain an average of 0.8x, 0.6x, and 0.4x coverage of the genome (Methods).
We then performed genotyped imputation of genetic variants in the 1000 Genomes Phase 3 release. This imputation was performed using minimac2 (for the genotyping array data) or Gencove’s lo imposte software v0.18 (for the low-pass sequencing data, see Methods for details). Both the unimputed PMRA data and the imputed low-pass sequencing data were then used to impute HLA genotypes using HIBAG [18].
The relevant metrics to use when comparing the two technologies depend on the downstream use cases. Specifically, if an investigator is interested in identifying genetic variants associated with a trait but has no a priori knowledge of where in the genome such variants are likely to be located, then the relevant metric is the average correlation between imputed genotype calls and true genotypes. On the other hand, if the investigator knows that specific variants are most likely to be relevant to the trait of interest, then the relevant metric is the concordance between the technologies at those specific sites. Since in PGx applications there are some specific genes and variants of interest, we computed metrics in both of these classes.
Overall genotype concordance
We first examined the overall concordance between the genotyping arrays and imputed sequences at different depths. To do this, we removed genotypes imputed with low confidence (with less than 90% posterior probability on a single genotype), and assessed the concordance between the two platforms, averaging across individuals, using metrics from the draft guidance of the United States Food and Drug Administration [19]. These metrics measure concordance for variants present and absent in a reference genome—a “positive percent agreement” (PPA) for variants that are different from the reference and a “negative percent agreement” (NPA) for variants that match a reference genome. For our purposes we considered the genotypes from the PMRA as “truth”; in this case the PPA ranged from 98.2% for 0.4x coverage sequencing to 99.2% for 1x coverage sequencing, while the NPA ranged from 99.8% for 0.4x coverage to 99.9% for 1x coverage (Table 1).
Genotype concordance at ADME genes
We then specifically compared the concordance between the genotypes at variants in ADME genes as defined by
There were 216 such variants that were directly genotyped on the PMRA. We thus computed the same concordance metrics specifically at these 216 variants. For these analyses we excluded low-confidence genotype calls from the low-pass sequencing data; the percentage of excluded calls range from 1.6% of genotype calls in the 0.4x data down to 0.8% of genotype calls in the 1x data.
Concordance results are presented in Fig. 1a. At common variants (where the minor allele is present in more than five copies in the sample, corresponding to a minor allele frequency over 3%), PPA ranged from 98.5% (for 0.4x coverage) up to 99.4% (for 1x coverage). The lowest concordance metric was the PPA at rarer variants, which ranged from 82.1% (for 0.4x coverage) to 95.2% (for 1x coverage).
**Genotype concordance at HLA**
Apart from ADME genes, another important locus in PGx is the MHC region. We imputed four digit HLA alleles from both the PMRA and sequencing data using HIBAG [18], and assessed the concordance across the two platforms at each of the seven HLA genes assessed by HIBAG. (Fig. 1b). There was little variation in imputed genotype concordance across levels of sequencing coverage, and with the exception of the gene DPB1, concordance was above 95%.
For samples where we saw consistent discordance for a given gene between the platforms, we then generated gold standard HLA genotype calls (Methods). A total of 15 HLA genotype calls in 12 samples were retested in this manner. The correct calls were obtained at 7/15 genotypes from the PMRA, and 6, 7, 7, and 8/16 genotypes after imputation from 0.4x, 0.6x, 0.8x, and 1x sequencing, respectively.
**Imputation quality and comparison**
Finally, an important metric of how well a technology assays known polymorphisms in the genome is the squared correlation between imputed genotype dosages and the true genotypes (known as “imputation r\(^2\)”.
Intuitively, if the researcher has a flat prior on where in the genome to look for an association between a genetic variant and a trait, the average squared correlation is a measure of the power of the study.
### Table 1 Genotype concordance between genotyping and sequencing platforms
| Comparison | PPA (%) | NPA (%) | No Calls (Average) |
|---------------|---------|---------|--------------------|
| Accuracy, 0.4x vs PMRA | 98.22% | 99.82% | 2535 |
| Accuracy, 0.6x vs PMRA | 98.76% | 99.85% | 1848 |
| Accuracy, 0.8x vs PMRA | 99.01% | 99.86% | 1508 |
| Accuracy, 1x vs PMRA | 99.19% | 99.88% | 1251 |
In all cases the genotyping array was treated as ‘Truth’. Positive % Agreement (PPA) – The percent of non-reference calls in the Truth dataset detected by Test, ignoring no calls in Test. (True Positives / True Positives + False Negatives). Negative % Agreement (NPA) – The percent of reference calls in the Truth dataset detected by Test, ignoring no calls in Test. (True Negatives / True Negatives + False Positives). No Calls – Count of No Calls in test that were variant in Truth. No calls are averaged across all 79 individuals. The total number of overlapping variants between the PMRA and the imputed sequence data is ~423 k
Hoverlson et al. [7]. There were 216 such variants that were directly genotyped on the PMRA. We thus computed the same concordance metrics specifically at these 216 variants. For these analyses we excluded low-confidence genotype calls from the low-pass sequencing data; the percentage of excluded calls range from 1.6% of genotype calls in the 0.4x data down to 0.8% of genotype calls in the 1x data.
Concordance results are presented in Fig. 1a. At common variants (where the minor allele is present in more than five copies in the sample, corresponding to a minor allele frequency over 3%), PPA ranged from 98.5% (for 0.4x coverage) up to 99.4% (for 1x coverage). The lowest concordance metric was the PPA at rarer variants, which ranged from 82.1% (for 0.4x coverage) to 95.2% (for 1x coverage).
**Genotype concordance at HLA**
Apart from ADME genes, another important locus in PGx is the MHC region. We imputed four digit HLA alleles from both the PMRA and sequencing data using HIBAG [18], and assessed the concordance across the two platforms at each of the seven HLA genes assessed by HIBAG. (Fig. 1b). There was little variation in imputed genotype concordance across levels of sequencing coverage, and with the exception of the gene DPB1, concordance was above 95%.
For samples where we saw consistent discordance for a given gene between the platforms, we then generated gold standard HLA genotype calls (Methods). A total of 15 HLA genotype calls in 12 samples were retested in this manner. The correct calls were obtained at 7/15 genotypes from the PMRA, and 6, 7, 7, and 8/16 genotypes after imputation from 0.4x, 0.6x, 0.8x, and 1x sequencing, respectively.
**Imputation quality and comparison**
Finally, an important metric of how well a technology assays known polymorphisms in the genome is the squared correlation between imputed genotype dosages and the true genotypes (known as “imputation r\(^2\)”.
Intuitively, if the researcher has a flat prior on where in the genome to look for an association between a genetic variant and a trait, the average squared correlation is a measure of the power of the study.
We computed this metric for different levels of sequencing coverage by correlating the imputed allelic dosages with directly genotyped sites. We computed this same metric for the genotype data by using the leave-one-out $r^2$ at genotyped sites computed by minimac2. At common variants (allele frequency > 5% in the cohort), the average $r^2$ obtained from the genotyping array was 0.9 (Fig. 2), consistent with previous reports from a European population [13]. For the sequencing data, this metric varied from 0.91 (for 0.4x coverage) to 0.96 (for 1x coverage). When all variants across the frequency spectrum were considered, the difference in average $r^2$ between assays was even more pronounced, with the average $r^2$ for the genotyping array being 0.85 and the average $r^2$ for the sequencing data ranging from 0.88 (for 0.4x coverage) to 0.93 (for 1x coverage).
To investigate the effect of the choice of imputation reference panel on imputation performance on the sequencing data, we performed a head-to-head comparison between using the 1000 Genomes and a subset of the Haplotype Reference Consortium (HRC) haplotypes [12] as reference panels using the above methodology (i.e., by treating the array data as “truth” and comparing overlapping sites between the reference panel and the array sites). Using the HRC dataset as the imputation reference panel yielded marginal increases in average $r^2$ values in all minor allele frequency (MAF) bins but the lowest, where it suffered a decrease of about 0.036 as compared to the 1000 Genomes imputed sites in the same bin (Supp. Tables S1, S2). The exact details and further discussion on this particular comparison can be found in the accompanying Supplementary Materials (Supp. Figs. S1, S2).
**Discussion**
In this paper, we performed a direct comparison between low-pass sequencing (combined with imputation) and a commonly-used genotyping array for the purposes of trait mapping in pharmacogenetics.
We observed that overall, genotype calls across the two platforms were highly concordant, with a positive percent agreement (PPA) of the imputed sequence data to the genotyping array calls ranging from 98.22% at 0.4x to 99.19% at 1x coverage.
At ADME genes, we observed qualitatively similar results, with a PPA ranging from 98.5 to 99.4% at sites of common variation (> 3% minor allele frequency in this cohort) and a PPA ranging from 82.1 to 95.2% at rarer variants (< 3%).
Four-digit HLA alleles in the MHC region imputed from sequencing data had high concordance with those imputed from the PMRA, with all concordances across the range of sequencing coverage observed to be above 95% with the exception of those in the DPB1 gene; further validation using a gold-standard assay of the HLA genotype calls resulted in similar concordance results between the imputed sequence or PMRA data and the resulting gold standards.
For the purposes of trait mapping, low-pass sequencing above a sequencing coverage of 0.4x had higher overall imputation accuracy as measured by imputation $r^2$ than the genotyping array, indicating a corresponding increase in power.
Beyond simply comparing concordance between assays, it is important to consider other, orthogonal considerations when deciding between low-pass sequencing and genotyping arrays for PGx purposes. For instance, due to the sheer number of measurements (reads) made during a sequencing run (even at very low coverages), sequence data allows far more sensitive detection of copy number and structural variation [5, 20]. As intuition, consider that sequencing a human genome at a depth of 0.1x using 150 bp reads yields 2.2 million reads corresponding to measurements at 330Mbp, compared to a typical genotyping array which generates point measurements at only a few hundreds of thousands to a couple million sites.
Similarly, sequencing affords the capability to perform metagenomic profiling and analysis of the microbiome via analysis of non-human sequencing reads deriving from a DNA sample, as well as analysis of mitochondrial count [2, 17].
Logistical and budgetary considerations are also essential in real-world project planning. In a number of scenarios with different outcomes and study designs, low-pass sequencing has been shown to increase performance, for example by increasing the effective sample size of a genome-wide association study [14] or increasing the accuracy of polygenic risk scoring [10].
One of the drawbacks of low-pass sequencing compared to genotyping arrays is that while the average performance over the entire genome is consistently higher with sequencing, there may occasionally be a subset of specific SNPs or genes that, for a given study design, must be assayed with a level of accuracy and precision which low-coverage sequencing is simply unable to provide. In order to address this, it may be useful to develop an assay which combines low-pass whole genome sequencing with higher-depth coverage of pre-selected target regions on the genome, such that a single sequencing run simultaneously yields low-coverage sequence data across the genome at the same time as assaying specific SNPs, variants, or genes of interest with clinical grade accuracy.
**Conclusion**
As research into the effects of genetics on drug response continues to accelerate, it will become increasingly important for assays used in pharmacogenetics to provide reliable measurements both across the entire genome and at specific PGx focused variants. Our results demonstrate that low-pass sequencing and imputation provide a competitive alternative to genotyping arrays in both of these applications.
It is worth noting that the cost of sequencing is declining rapidly; if sequencing a human genome to 30x coverage costs $1000, then the cost of sequencing a human sample to 0.4x coverage is around $13. The key components of cost in a low-pass sequencing assay then become sequencing library preparation and analysis. As the costs of sequencing continue to drop, the importance of these latter costs will continue to grow.
**Methods**
**Genotyping**
Samples were from study TMT109167: A study to collect blood samples from members of the Clinical Unit Cambridge, UK (CUC) volunteer panel for DNA extraction and storage, for investigation of prospective genotype-phenotype relationships and stratification of subjects for recruitment into future clinical trials.
DNA samples were genotyped by BioStorage Technologies/Bioprocessing Solutions Alliance, Brooks Life Sciences (Piscataway, NJ, USA) using the Affymetrix Axiom PMRA.
Prior to genotype imputation, variants in each GWAS dataset were excluded using standard Affymetrix QC thresholds for the PMRA, if there were deviations from Hardy-Weinberg proportions within subgroups of any given ancestry or showed gross and irreconcilable differences in alleles or allele frequency with reference panel genotypes from the HapMap or 1000 Genome projects. Standard Affymetrix array QC sample level thresholds were also applied prior to imputation.
[http://www.affymetrix.com/support/downloads/manuals/axiom_genotyping_solution_analysis_guide.pdf](http://www.affymetrix.com/support/downloads/manuals/axiom_genotyping_solution_analysis_guide.pdf)
**Imputation of PMRA data**
Genotype imputation for genetic variants that were not directly genotyped (“untyped variants”) was performed using a cosmopolitan haplotype reference panel from the 1000 Genomes Project [The 1000 Genomes Project Consortium, 2015], and using Hidden Markov Model methods as implemented in MaCH and minimac [8, 9].
**HLA genotyping**
High resolution HLA genotyping was performed at BioStorage Technologies/Bioprocessing Solutions Alliance, Brooks Life Sciences (Piscataway, NJ, USA) using the Thermo Fisher AllSet+ Gold SSP High-Resolution HLA kit for HLA-A, HLA-B, HLA-DRB1, HLA-DQB1 and HLA-DPB1 following the manufacturer’s instructions.
**Sequencing**
Sequencing libraries were prepared from DNA using the KAPA Library Preparation Kit by Roche and sequenced on an Illumina HiSeq 4000 instrument. Sequencing reads for each sample were aligned to the genome using bwa mem [9], and sequencing reads were randomly sampled to obtain different levels of sequencing coverage. Imputation of genotypes from sequencing data was done using loimpute v. 0.18 by Gencove, Inc. (New York, NY) to a reference panel comprising a subset of the 1000 Genomes Phase 3 (described in more detail in the Supplementary Materials).
**Imputation of sequencing data**
Imputation was performed using an implementation of the Li and Stephens model [11], described in more detail in the Supplementary Note.
**Abbreviations**
PGx: Pharmacogenetics; PMRA: Precision Medicine Research Array; HLA: Human leukocyte antigen; ADME: Absorption, distribution, metabolism, and excretion; SNP: Single nucleotide polymorphism; MHC: Major histocompatibility complex; PPA: Positive percent agreement; NPA: Negative percent agreement; MAF: Minor allele frequency; HRC: Haplotype Reference Consortium
Supplementary Information
The online version contains supplementary material available at https://doi.org/10.1186/s12864-021-07508-2.
Additional file 1: Supplementary note. Details of the model underlying lofreq, the software used to impute the low-pass sequencing data analysed in this study.
Additional file 2: Additional materials. Description of imputation performance using the HRC as a haplotype reference panel rather than the 1000 Genomes Phase 3 release. Figure S1. Comparison of imputation $r^2$ across allele frequency bins for the 1000 Genomes panel.
Figure S2. Comparison of imputation $r^2$ across allele frequency bins for the HRC panel.
Acknowledgements
The abstract from an early version of this study was presented at the 51st European Society of Human Genetics Conference (see https://www.nature.com/articles/s41431-019-0407-4#Sec270).
Authors’ contributions
KW, TB, JKP, and CC designed the study. KW, DJF, and KK performed the experiments. TB, JKP, JHL, DJF, KK, and CC analyzed the data. All authors reviewed the manuscript. The authors thank and approved the final manuscript.
Funding
Not applicable.
Availability of data and materials
The datasets generated and/or analysed during the current study are proprietary and are therefore not publicly available. The data were not consented for use outside the scope of the present study, and as such, dataset access cannot be applied for. Details on the 1000 Genomes Phase 3 release dataset and instructions on how to download the data can be found at the following URL: https://www.internationalgenome.org/category/phase-3/
Details on the Haplotype Reference Consortium datasets and instructions on how to apply for and access the data can be found at the following URL: http://www.haplotype-reference-consortium.org/data-access
Declarations
Ethics approval and consent to participate
Ethical approval (URC ref.: 08/H0302/100, UK) and written informed consent were obtained prior to conducting this study. Namely, ethics approval was granted by National Research Ethics Service, Cambridgeshire 2 Research Ethics Committee, Victoria House, Capital Park, Fulbourn, Cambridge. CB21 5XH on 2nd Dec. 2008. They are part of The Research Ethics Service (RES) affiliated with the Health Research Authority (HRA), based in the UK.
Consent for publication
Not applicable.
Competing interests
K. W., T.B., J.K.P., and J.H.L were employees of Gencove, Inc at the time of writing.
Author details
1Gencove, Inc., New York, NY 10016, USA. 2PAREXEL Genomic Medicine, Durham, NC 27713, USA. 3GiloSmithKline, Stevenage, UK.
Received: 6 May 2020 Accepted: 5 March 2021
Published online: 20 March 2021
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Elastic and inelastic transmission in guided atom lasers: a truncated Wigner approach
Julien Dujardin,‡ Arturo Argüelles, and Peter Schlagheck
Département de Physique, University of Liège, 4000 Liège, Belgium
We study the transport properties of an ultracold gas of Bose-Einstein condensate that is coupled from a magnetic trap into a one-dimensional waveguide. Our theoretical approach to tackle this problem is based on the truncated Wigner method for which we assume the system to consist of two semi-infinite non-interacting leads and a finite interacting scattering region with two constrictions modelling an atomic quantum dot. The transmission is computed in the steady-state regime and we find a good agreement between truncated Wigner and Matrix-Product State calculations. We also identify clear signatures of inelastic resonant scattering by analyzing the distribution of energy in the transmitted atomic matter wave beam.
PACS numbers: 67.85.De, 03.75.Pp, 67.10.Jn, 03.65.Sq
I. INTRODUCTION
The progress of the last two decades in the field of ultracold atoms has opened the possibility of investigating mesoscopic transport properties of interacting matter waves. A very important step in this context is the realization of atom lasers [1–4] permitting to create a beam of atoms by coherently outcoupling a trapped Bose–Einstein condensate (BEC) into an optical waveguide at a well-defined energy and flux [3–11]. This research is particularly interesting in view of the perspective to realize bosonic atomtronic devices [12–15] and to study analogies with their fermionic counterpart [16–18].
A typical configuration of such a device is an atomic quantum dot that features resonant transport [19] and atom blockade [18, 20]. These features can be used as building blocks for atomic transistors [12, 14, 15].
A theoretical modeling of such scattering processes within guided atom lasers faces the challenge of dealing with interactions between atoms. A full many-body treatment of such an open system is very complex and impossible to solve exactly in practice. During last years, these scattering processes have been studied in the mean-field approximation described by a nonlinear Gross–Pitaevskii (GP) equation [21–23]. While this description gives satisfactory results for a weak nonlinearity, the question of validity arises rapidly in the case of strong nonlinear dynamics [24] where dynamical instabilities occur. It has also been pointed out that in the presence of disordered potentials, even a weak atom-atom interaction strength can lead to inelastic scattering processes [24, 25], which can not be accounted for in the framework of the mean-field GP approximation.
The main focus of this work is to study such inelastic scattering processes in an atom laser context. We employ the truncated Wigner method (tW) [26–28] for this purpose. The latter amounts to sampling the initial quantum state by classical fields and to propagating them according to a slightly modified GP equation. This method has been used to study the reflection of a BEC on abrupt potential barriers at zero temperature [29] and at finite temperature [30]. It can also be used to study the dynamics of a trapped BEC [31] when an optical lattice is adiabatically superimposed to the trapping potential. It has also been used to study the many-body Landau-Zener effect [32] as well as far from equilibrium dynamics (in particular non-thermal fixed-points) of many-body systems [33]. Finally, the tW method can also take into account a continuous measurement process [34] during the evolution of the system.
We specifically apply the tW method to study the transmission of a one-dimensional guided atom laser beam across a double barrier potential forming an atomic quantum dot as described in Sec. III. In this scenario, we are particularly interested in resonant transport. To this end, we suppose a finite extent of the interacting region and discretize the one-dimensional space according to a finite-difference scheme. We generalize, in Sec. IV, the tW method to open systems using Smooth Exterior Complex Scaling [35–39]. We then study numerically, in Sec. V, the transmission properties through the quantum dot model described in Sec. III. The obtained results are then confronted, in Sec. V A, to the predictions provided by the mean-field approximation and to Matrix-Product State (MPS) calculations. In Secs. V B–D, we analyze the energy distribution of the transmitted beam using the tW method and develop a Bogoliubov approach to understand the physical origin of the inelastic peaks that appear in the energy distribution.
II. SCATTERING CONFIGURATION
We consider a guided atom laser experiment such as the one represented in Ref. [5], where a magnetically trapped BEC plays the role of a coherent source of atoms. In this particular experiment, the atoms are outcoupled by a rf-knife rendering the final state insensitive to the magnetic field, but sensitive to the optical potential formed by an elongated far off-resonance optical beam constituting an atomic waveguide. Ideally, the propagation of the atoms at well defined energy is quasi-
‡ [email protected]
one-dimensional (1D) along the waveguide. It is then possible to engineer an atomic quantum dot geometry by focusing two far-detuned laser beams perpendicular to the waveguide. In this paper, we specifically consider a waveguide configuration in which spatial inhomogeneities and atom-atom interactions are non-vanishing only in a finite region of space. Such a system is represented in Fig. II(a).
In order to properly implement the tW method, we discretize the 1D space by a series of points or sites separated by a constant distance \( \Delta \), thereby forming a spatial grid. The wavefunction is then defined on these points. The sites are labeled with an index \( l \in \mathbb{Z} \). One additional site \( S \) is introduced in order to represent the source of atoms. This additional site \( S \) is connected to the waveguide at site \( l_S \) as illustrated in Fig. II(b).
We treat the spatial derivatives with a finite-difference approximation. The Hamiltonian is then given by
\[
\hat{H} = \sum_{l=-\infty}^{+\infty} \left[ -J (\hat{a}_{l+1}^{\dagger} \hat{a}_l + \hat{a}_l^{\dagger} \hat{a}_{l+1}) + \frac{g_l}{2} \hat{n}_l (\hat{n}_l - 1) + V_l \hat{n}_l \right] + \kappa^* (t) \hat{b}^{\dagger} \hat{a}_{l_s} + \kappa (t) \hat{a}_{l_s}^{\dagger} \hat{b} + \mu \hat{b}^{\dagger} \hat{b},
\]
(1)
Here \( \hat{b} \) and \( \hat{b}^{\dagger} \) are the annihilation and creation operator of the reservoir, respectively, \( \mu \) is its chemical potential defined relative to the center of the band, and \( \hat{a}_l \) and \( \hat{a}_l^{\dagger} \) are the annihilation and creation operators, respectively, on the site \( l \) of the chain. The hopping strength to the nearest neighbors is given by \( J = \hbar^2 / 2m \Delta^2 \), the on-site interaction strength is \( g_l \), and the on-site potential is \( V_l \). The coupling strength \( \kappa (t) \) is related to the out-coupling process of atoms from the reservoir and can be controlled in a time-dependent manner (e.g. through the variation of the intensity of a radio-frequency field in the case of Refs. [3, 6]). We suppose that the source is adiabatically switched on from zero to a maximal value of \( \kappa \), i.e.
\[
\lim_{t \to \infty} \kappa (t) = \kappa.
\]
(2)
This Hamiltonian is similar to a Bose-Hubbard (BH) system describing an optical lattice in which only the lowest band in the Brillouin zone is considered. For the case where the on-site potential and interaction strength vanish, the dispersion relation is identical to the one of the free lattice and is given by
\[
E(k) = -2J \cos (k),
\]
(3)
with a wavenumber \( k / \Delta \). In the limit \( k \ll 1 \), we have \( E(k) = -2J + Jk^2 \) which, apart from a constant shift, corresponds to the dispersion relation of a free atom.
The scattering configuration of an atomic quantum dot is modeled by two sites with non-zero on-site potential. Between these two sites, we allow atoms to interact as depicted in Fig. II(b). This can be justified if, for instance, the waist of the elongated optical beam is particularly narrow at the position where the quantum dot is located. The perpendicular confinement is then rather strong and it is likely that collisions occur between atoms. Formally, this model can be encoded as
\[
V_l = V (\delta_{l,l_0} + \delta_{l,l_0+L_D}),
\]
(4a)
\[
g_l = g \sum_{j=1}^{L_D-1} \delta_{l,l_0+j},
\]
(4b)
where \( l_0 \in \mathbb{Z} \) is arbitrary and \( L_D \) is the length of the quantum dot. We set \( L_D = 6 \) in the rest of the paper.
![FIG. 1. (color online) (a) A trapped BEC depicted by a (green) circle is loaded into a waveguide with two constrictions modeling an atomic quantum dot. The bold (black) lines represent the isopotentials of the waveguide. (b) One dimensional infinite Bose-Hubbard (BH) chain for the quantum dot model (see Eqs. I). The condensate is prepared within a trap represented by the green circle (S) and coupled to the infinite BH chain (dashed green line). The big (red) circles represent a non-vanishing on-site atom-atom interaction. The two displaced sites enclosing the interaction region represent two sites where the on-site potential is nonzero.
III. TRUNCATED WIGNER METHOD FOR OPEN BH SYSTEMS
Phase-space methods were introduced by Wigner [26] and Moyal [28] and their development started in the 60's with successful applications in quantum optics by Glauber [30] and Sudarshan [31]. These methods allow to go beyond the mean-field GP description by, essentially, sampling the initial quantum state by classical fields. The prescription to sample the initial state and the equation of motion are not unique. In this paper we choose the truncated Wigner method (tW). The evolution of the system is then given by a classical equation of motion similar to the GP equation. In particular, the tW method maps the density matrix of the system onto a quasi-distribution function fulfilling a Fokker–Planck equation. It is then possible to replace this equation with a system of Langevin equations that can be numerically solved by a Monte-Carlo method. This section is devoted to generalize the tW method to open systems.
A. Truncated Wigner Method for BH systems
Let us consider a general Bose-Hubbard (BH) system with on-site two-body interaction. Denoting by $A = \{S, 0, \pm 1, \pm 2, \ldots \}$ the ensemble of sites of the BH system, the many-body Hamiltonian of the system can be written as
$$\mathcal{H} = \sum_{\alpha \in A} \sum_{\alpha' \in A} h_{\alpha \alpha'} \hat{a}^\dagger_\alpha \hat{a}_{\alpha'} + \frac{g_0}{2} \hat{n}_\alpha (\hat{n}_\alpha - 1),$$ \hspace{1cm} (5)
where we defined by $\hat{n}_\alpha$ and $\hat{a}_\alpha^\dagger$ the annihilation and creation operators, respectively, on the site $\alpha$ of the chain, and by $\hat{a}_{\alpha'} = \hat{a}^\dagger_{\alpha'} \hat{a}_{\alpha'}$ the corresponding number operator. The matrix elements $h_{\alpha \alpha'}$ represent on-site energies as well as possible hoppings between the sites. We impose $h_{\alpha \alpha'} = h_{\alpha' \alpha}$ to ensure that the Hamiltonian remains hermitian. This general form makes our description also valid for more involved connections between different sites of the grid, such as small-world networks.
The general idea of the Wigner approach is to map the evolution of the density matrix prescribed by the von Neumann equation
$$i\hbar \frac{\partial \hat{\rho}(t)}{\partial t} = [\mathcal{H}, \hat{\rho}(t)]$$ \hspace{1cm} (6)
to the evolution of the Wigner function $W \equiv \mathcal{W}(\{\psi_\alpha, \psi_\alpha^*\}, t)$ that is defined in the phase space spanned by the classical amplitudes $\psi_\alpha$ associated with each site $\alpha$. The Wigner function represents a quantum quasi-probability distribution and is defined as
$$\mathcal{W}(\{\psi_\alpha, \psi_\alpha^*\}, t) = \prod_{\alpha \in A} \frac{1}{\pi^2} \int d\lambda_\alpha d\lambda_\alpha^* e^{-\lambda_\alpha \psi_\alpha^* + \lambda_\alpha^* \psi_\alpha} \times \chi_{\mathcal{W}}(\{\lambda_\alpha, \lambda_\alpha^*\}, t),$$ \hspace{1cm} (7)
which is the Fourier transform of the characteristic function $\chi_{\mathcal{W}}$
$$\chi_{\mathcal{W}}(\{\lambda_\alpha, \lambda_\alpha^*\}, t) = \text{Tr} \left[ \hat{\rho}(t) \prod_{\alpha \in A} e^{\lambda_\alpha \hat{a}_\alpha^\dagger - \lambda_\alpha^* \hat{a}_\alpha^\dagger} \right].$$ \hspace{1cm} (8)
The classical amplitudes $\psi_\alpha$ and $\psi_\alpha^*$ are complex canonical variables representing coherent states in phase space. The evolution of the Wigner function is then given by
$$i\hbar \frac{\partial \mathcal{W}}{\partial t} = \sum_{\alpha \in A} \left[ - \sum_{\alpha' \in A} \left( h_{\alpha \alpha'} \frac{\partial}{\partial \psi^*_\alpha} \psi_\alpha - h_{\alpha' \alpha}^* \frac{\partial}{\partial \psi^*_\alpha} \psi^*_{\alpha'} \right)
- g_0 \left( \frac{\partial}{\partial \psi_\alpha} \psi_\alpha - \frac{\partial}{\partial \psi^*_\alpha} \psi^*_{\alpha} \right) |\psi_\alpha|^2 - 1
+ g_0 \left( \frac{\partial^2}{\partial \psi^2_\alpha} \frac{\partial}{\partial \psi^*_\alpha} \psi_\alpha - \frac{\partial^2}{\partial \psi_\alpha^2} \frac{\partial}{\partial \psi^*_\alpha} \psi^*_{\alpha} \right) \right] \mathcal{W}.$$ \hspace{1cm} (9)
Numerical integration of this equation is practically impossible since the dimension of the phase space is very large.
The so-called truncated Wigner approximation consists in neglecting the third order derivatives in Eq. (9). The resulting equation is commonly called the truncated Wigner equation and corresponds to a Fokker-Planck equation with only a drift term. It can be shown that this approximation is valid if there is locally a large number of atoms in the waveguide. The evolution of the Wigner function can be mapped to a set of coupled Langlevin equations where the canonical variables $\psi_\alpha \equiv \psi_\alpha(t)$ and $\psi^*_\alpha \equiv \psi^*_\alpha(t)$ are now time-dependent. They satisfy
$$i\hbar \frac{\partial \psi_\alpha}{\partial t} = \sum_{\alpha' \in A} h_{\alpha \alpha'} \psi_{\alpha'} + g_0 (|\psi_\alpha|^2 - 1) \psi_\alpha.$$ \hspace{1cm} (10)
The mapping gives another set of equations for the evolution of $\psi^*_{\alpha}$ which correspond to the complex conjugate of Eq. (10).
For the specific case of our guided atom-laser configuration, we can now write the final set of equations of motion for the sites representing the waveguide and the site corresponding to the source as
$$i\hbar \frac{\partial \psi_l}{\partial t} = (V_l - \mu) \psi_l - J (\psi_{l+1} + \psi_{l-1}) + g_l (|\psi_l|^2 - 1) \psi_l + \kappa(t) \psi_S \delta_{l, l_S},$$ \hspace{1cm} (11a)
$$i\hbar \frac{\partial \psi_S}{\partial t} = \kappa^* (t) \psi_{l_S}.$$ \hspace{1cm} (11b)
It is nearly identical to a discrete GP equation except for a slightly different interaction term.
B. The initial state
The initial Wigner function $\mathcal{W}(\{\psi_\alpha, \psi_\alpha^*\}, t_0)$ represents the initial quantum state of the system and has to be sampled by the classical fields $\psi_\alpha$. The latter can, for instance, represent coherent, thermal, squeezed or Fock states and its time evolution is governed by classical trajectories evolving according to Eqs. (11). We consider that initially, at $t = t_0$, the waveguide is empty and the ground state of the reservoir trap is macroscopically populated with a large number $N$ of atoms at zero temperature. The Wigner function can then be written as
$$\mathcal{W} = \mathcal{W}_G(\{\psi_l, \psi^*_l\}, t_0) \times \mathcal{W}_S(\psi_S, \psi^*_S, t_0),$$ \hspace{1cm} (12)
at time $t = t_0$, where $\mathcal{W}_G(\{\psi_l, \psi^*_l\}, t_0)$ and $\mathcal{W}_G(\{\psi_l, \psi^*_l\}, t_0)$ correspond to the Wigner function of the source of atoms and the waveguide, respectively.
Since the waveguide is initially empty, the corresponding Wigner function has the form
$$\mathcal{W}_G(\{\psi_l, \psi^*_l\}, t_0) = \prod_{l \in \mathbb{Z}} \left( \frac{2}{\pi} \right) \exp(-2|\psi_l|^2).$$ \hspace{1cm} (13)
We can therefore sample the initial state with complex Gaussian random variables. More precisely, the initial values of the amplitudes $\psi_l$ can be written as
$$\psi(t = t_0) = \frac{1}{2} (A_l + iB_l),$$
where $A_l$ and $B_l$ are real, independent Gaussian random variables with unit variance and zero mean, i.e. for each $l, l' \in \mathbb{Z}$ we have
$$A_l = \overline{B_l} = 0,$$
$$A_r A_l = \overline{B_r B_l} = \delta_{l,v},$$
$$\overline{A_l B_l} = 0,$$
where the overline denotes the average of the random variables. As a consequence, each site $l$ of the grid representing the empty waveguide has the average atom density $\langle |\psi_l(t_0)|^2 \rangle = 1/2$.
We are now considering the source part which represent a BEC with a high number $N$ of atoms such that it can be safely described by a coherent state $\langle \psi_S^0 \rangle$. The initial Wigner function $W_S(\psi_S, \psi_S^*, t_0)$ therefore reads
$$W_S(\psi_S, \psi_S^*, t_0) = \left( \frac{2}{\pi} \right)^{N/2} \exp(-2|\psi_S - \psi_S^0|^2).$$
As $N$ is very large, the relative uncertainty of both the amplitude $|\psi_S^0| = \sqrt{N}$ and the associated phase of the source are negligibly small. We therefore treat the source term completely classically, i.e. we set $\psi_S^0 = \sqrt{N}$.
Supposing, in addition, that the coupling $\kappa(t)$ tends to zero such that $N |\kappa(t)|^2$ remains finite, we can safely neglect the depletion of the source or any back-action of the waveguide to the source since $\psi_S(t) = \sqrt{N} (1 + \mathcal{O}(|\kappa|^2))$ at any finite time $t > t_0$. This allows us to solely focus on the evolution of the field in the chain. The equation to solve reads
$$ih \frac{\partial \psi_l}{\partial t} = \left( V_l - \mu \right) \psi_l - J \left( \psi_{l+1} + \psi_{l-1} \right) + g_l (|\psi_l|^2 - 1) \psi_l + \kappa(t) \sqrt{N} \delta_{l,t_S}. $$
One can notice that if $|\psi_l|^2$ is very large, we recover the discrete GP equation.
### C. Observables
It can be shown \cite{45} that the time-dependent expectation value of the symmetrically ordered product of the operator $\hat{a}_l$ and $\hat{a}_l^\dagger$ is of the form
$$\left\langle \prod_{l \in \mathbb{Z}} \left( \hat{a}_l^\dagger \right)^{\tau_l} \hat{a}_l^\tau_l \right\rangle_{sym} = \prod_{l \in \mathbb{Z}} \int d\psi_l d\psi^*_l \left( \psi^*_l \right)^{\tau_l} \psi^{\tau_l}_l$$
$$\times \mathcal{W}\{\psi_l, \psi^*_l\}, t\rangle ,$$
where $\left\langle \prod_{l \in \mathbb{Z}} \left( \hat{a}_l^\dagger \right)^{\tau_l} \hat{a}_l^\tau_l \right\rangle_{sym}$. denotes the symmetrically ordered product i.e. the average of $(r_1 + s_1)!/(r_1!s_1!)$ possible orderings of $r_1$ creation operators and $s_1$ annihilation operators. For instance, setting $r_1 = 2$ and $s_1 = 1$ we have
$$\left\langle \left( \hat{a}_l^\dagger \right)^2 \hat{a}_l \right\rangle = \frac{1}{3} \left[ \left( \hat{a}_l^\dagger \right)^2 \hat{a}_l + \hat{a}_l^\dagger \hat{a}_l^\dagger + \hat{a}_l^\dagger \hat{a}_l \right].$$
This equation allows us to calculate the expectation value of observables on a particular site. Specifically, the expectation value of the total density $n_t(t)$ and the current $j_t(t)$ on a site $l$ are given by
$$n_t(t) = \langle \hat{n}_t(t) \rangle = \langle \hat{a}_l^\dagger(t) \hat{a}_l(t) \rangle = |\psi_l(t)|^2 - 0.5,$$
$$j_t(t) = \langle \hat{j}_t(t) \rangle = \frac{i}{\hbar} \left( \langle \hat{a}_{l+1}^\dagger(t) \hat{a}_l(t) - \hat{a}_l^\dagger(t) \hat{a}_{l+1}(t) \rangle \right)$$
$$= \frac{i}{\hbar} \left( \psi_{l+1}^* \psi_l(t) - \psi_l^* \psi_{l+1}(t) \right),$$
where the overline denotes the statistical average over all classical initial states. In addition, we can determine the coherent part of the density $n_t^{coh}(t)$ as well as the coherent part of the current $j_t^{coh}(t)$ through
$$n_t^{coh}(t) = |\langle \hat{a}_l(t) \rangle|^2 = |\psi_l(t)|^2,$$
$$j_t^{coh}(t) = \frac{i}{\hbar} \left( \psi_{l+1}^* \psi_l(t) - \psi_l^* \psi_{l+1}(t) \right).$$
In the mean-field limit, the coherent part of the density and the current correspond to the usual GP density and current. We can also identify the incoherent part as the difference of the total and coherent parts of the density and the current:
$$n_t^{inc}(t) = n_t(t) - n_t^{coh}(t),$$
$$j_t^{inc}(t) = j_t(t) - j_t^{coh}(t).$$
The situation evidently simplifies in the special case of a waveguide without any on-site potential or interaction between the atoms. In this case, the GP as well as the tW evolution equations reduce to the standard one-body Schrödinger equation and hence the coherent and total densities in the waveguide are identical. The stationary density $n_\infty$ is given by
$$n_\infty = \lim_{t \to \infty} |\psi(t)|^2 = \lim_{t \to \infty} |\psi(t)|^2 - 0.5$$
$$= \frac{N |\kappa|^2}{4J^2 - \mu^2},$$
and the stationary current $j_\infty$ is given by
$$j_\infty = \frac{N |\kappa|^2}{\sqrt{2J(4J^2 - \mu^2)}}.$$
### D. Truncated Wigner for open systems
We are able to represent the infinite chain in terms of a finite open system if we assume that the on-site potential
and the contact interaction are non-vanishing only in a finite region of space. This finite region will be named the scattering region and the regions on the left and the right hand side of it are called the left and right leads, in close analogy to electronic mesoscopic physics. Without loss of generality, we shall assume that the scattering region is defined in the interval \( l \in \{1, \cdots, L\} \) on the grid. The dynamics in the leads is linear and can therefore be solved analytically. We then find that the evolution equation can be written as
\[
i\hbar \frac{\partial \psi_l}{\partial t} = (V_l - \mu_l)\psi_l + g_l |\psi_l|^2 \psi_l + \kappa(t) \sqrt{\delta_{l,t,L}}
\]
\[
- J [\psi_{l-1}(1 - \delta_{l,1}) + \psi_{l+1}(1 - \delta_{l,L})] - \frac{2i}{\hbar} (\delta_{l,1} + \delta_{l,L}) J^2 \int_0^t dt' \mathcal{M}_l (t - t') \psi_l (t')
\]
\[
+ \delta_{l,1} \chi_1 (t) + \delta_{l,L} \chi_L (t),
\]
for the site \( l \) within the scattering region \( (l = 1, \cdots, L) \) with
\[
\chi_1 (t) = 2J \sum_{\nu = -\infty}^0 \mathcal{M}_{\nu - 1} (t - t_0) \psi_\nu (t_0),
\]
\[
\chi_L (t) = -2J \sum_{\nu = L + 1}^\infty \mathcal{M}_{\nu - L} (t - t_0) \psi_\nu (t_0),
\]
and
\[
\mathcal{M}_l (\tau) = \frac{i\hbar}{2} \left[ J_{l-1} \left( \frac{2J \tau}{\hbar} \right) + J_{l+1} \left( \frac{2J \tau}{\hbar} \right) \right] e^{i\mu \tau / \hbar}
\]
where \( J_l \) is the Bessel functions of the first kind of the order \( l \).
As no approximation has yet been made, Eq. (28) reproduces the true evolution of the infinite nonlinear system under consideration described by Eq. (17). The integral term in the third line of Eq. (28) exactly describes the decay into the left and right leads and therefore yields a perfectly transparent boundary condition that is defined on the first and last site of the scattering region. The terms \( \chi_1 (t) \) and \( \chi_L (t) \) in Eq. (28) account for the propagation of the initial quantum fluctuations that arise in the framework of the tW approximation and that eventually, during the time propagation, enter the scattering region. These terms \( \chi_1 (t) \) and \( \chi_L (t) \), considering the initial emptiness of the leads in the tW prescription (see Eqs. (14)), take the form of quantum noise entering the system. The autocorrelation functions related to these noise terms are given by
\[
\chi_1^2 (t) \chi_1 (t + \tau) = \chi_L^2 (t) \chi_L (t + \tau) = -i \mathcal{M}_1 (\tau).
\]
The integral term in Eq. (28) renders the numerical simulation rapidly inefficient because the whole integral has to be recomputed at every time step. The most efficient way to avoid this problem in the numerical computations \( [39] \) is to remove this integral term and replace it by Smooth Exterior Complex Scaling \( [35, 57, 16, 50] \).
The evolution of the finite open system is now governed by the following equation
\[
i\hbar \frac{\partial \psi_l}{\partial t} = (V_l - \mu_l) \psi_l + g_l |\psi_l|^2 \psi_l + \kappa(t) \sqrt{\delta_{l,t,L}} + 2J(q_l + q_l^{-1}) \psi_l
\]
\[
+ \frac{1}{q_{l+1}} + \frac{1}{q_{l+1}^2} \psi_{l+1}
\]
\[
- J \left[ \frac{1}{q_{l-1}} - \frac{1}{q_{l-1}^2} \right] \psi_{l-1}
\]
\[
+ \delta_{l,1} \chi_1 (t) + \delta_{l,L} \chi_L (t),
\]
where \( q_l \) is a smooth function of the site index \( l \). In the scattering region \( (1 \leq l \leq L) \) we impose \( q_l = 1 \), while \( q_l \) is smoothly ramped to \( e^{i \theta} \) within the left \( (l < 1) \) and the right \( (l > L) \) leads where \( \theta \) is an arbitrary positive angle. The function \( q_l \) represents the discrete derivative of \( q_l \) with respect to \( l \). If \( q_l \neq 1 \), the Hamiltonian is not hermitian any longer and the outgoing atoms are absorbed without reflection, provided that the discrete function \( q_l \) is sufficiently smooth \( (i.e., q_{l+1} - q_l \approx q_l^2 \approx q_l) \). This approach was successfully tested in Ref. [39] for the case of a linear and a nonlinear Schrödinger equation with or without quantum fluctuations as described in Eqs. (16) and Eqs. (20).
### IV. TRANSMISSION ACROSS A QUANTUM DOT
#### A. Transmission spectrum
We now study transport across a symmetric double barrier potential that can be seen as a resonator. Hence, in absence of interaction, we know that the transmission spectrum will give rise to a series of Fabry-Pérot or Breit-Wigner peaks at resonances. As explained in Ref. [21], the presence of atom-atom contact interaction bends these peaks. Depending on the strength of the nonlinearity within the resonator, bistability can occur as seen in Fig. 1. This bistability can be seen as an artifact of the mean-field approximation since many-body quantum scattering processes are linear from a microscopic point of view and, as a consequence, we expect a unique many-body scattering state to establish.
We now discuss the effects of the interaction on the Fabry-Pérot peaks beyond the mean-field GP description. We fix the maximal coupling strength between the source and the waveguide to \( N|\kappa|^2 = J^2 \). In Fig. 2, we plot the transmission across the quantum dot against the chemical potential with an interaction strength \( g = 0.2J \) and an on-site potential \( V = J \). The total transmission \( T \) is determined by comparing the total current in the downstream region to the stationary current \( [27] \) obtained in the case of a perfectly homogeneous and interaction-free waveguide:
\[
T = \lim_{t \to \infty} j(t) / j^{\infty}.
\]
[35] Smith et al., Phys. Rev. Lett. 100, 210407 (2008).
It can be decomposed into its coherent $T^{\text{coh}}$ and incoherent $T^{\text{incoh}}$ part by respectively comparing the coherent and incoherent current to the free current [27]:
$$T^{\text{coh}} = \lim_{t \to \infty} j^{\text{coh}}(t)/J, \quad (34a)$$
$$T^{\text{incoh}} = \lim_{t \to \infty} j^{\text{incoh}}(t)/J. \quad (34b)$$
In the mean-field description, we observe that the GP curve is bent and features bistability as it was shown by Paul et. al. [21]. This curve has been obtained by solving the stationary GP equation in the same way as it was done in Ref. [22]. The dashed black curves correspond to solutions of the stationary GP equation that are unstable (middle branch of the resonance peak) and inaccessible through a time-dependent loading of the waveguide at constant chemical potential (upper branch of the resonance peak).
In order to benchmark our tW calculations, we compare the total transmission given by Eq. (33) to the one obtained by a genuinely quantum simulation using Matrix-Product State (MPS) [51–53] calculations. This method is based on the Density-Matrix Renormalization Group [54] (DMRG) which uses renormalization techniques to express in an optimized way the density matrix of a block within the system under consideration. The states produced by this process belong to the class of matrix-product states [51–53], which offer a highly optimized way of treating the full problem as long as no highly entangled states are present. When the number of matrix is quite low and the system is very small, the agreement between the tW and MPS methods. Both methods clearly show that the transmission is not perfect at resonance, meaning that full resonant transmission is prohibited. The orange dotted curve in Fig. 2 displays the incoherent part of the transmission. We can see that about ten to twenty percent of the transmission comes from incoherent atoms at the resonances, which appears to be a consequence of the enhanced atomic density within the quantum dot at resonance. Indeed, in contrast to the coherent part of the transmitted beam, the incoherent atoms may exit the quantum dot to either one of the leads. They thereby inhibit perfect transmission of the atomic beam at resonance.
### B. Energy distribution of the transmitted atoms
We are now interested in signatures of inelastic scattering in the transmitted beam. To this end, we take a large but finite number of sites $L_R = 1000$ in the transmitted region and define $\hat{a}(k)$ as
$$\hat{a}(k) = \frac{1}{\sqrt{L_R}} \sum_{l=L_D+2}^{L_D+2+L_R} \hat{a}_l e^{-ikl}, \quad (35)$$
corresponding to the annihilation operator associated with the momentum eigenstate $e^{ikl}$ within the right lead. Noting that $[\hat{a}(k), \hat{a}^\dagger(k)] = 1$ from this definition and following the procedure explained in the section III C we can calculate the steady-state average total and coherent number of atoms moving with a wavenumber $k$ through
$$n(k) = \langle \hat{a}(k) \rangle = \langle \hat{a}^\dagger(k) \hat{a}(k) \rangle = |\psi(k)|^2 - 0.5, \quad (36a)$$
$$n^{\text{coh}}(k) = |\langle \hat{a}(k) \rangle|^2 = |\psi(k)|^2, \quad (36b)$$
with
$$\psi(k) = \frac{1}{\sqrt{L_R}} \sum_{l=L_D+2}^{L_D+2+L_R} \psi_l e^{-ikl}. \quad (37)$$
Since all the transmitted atoms have $k > 0$, we define the total $n_E$ and coherent $n_E^{\text{coh}}$ average number of transmitted atoms moving with energy $E$ by
$$n_E \equiv n(k_E), \quad (38a)$$
$$n_E^{\text{coh}} \equiv n^{\text{coh}}(k_E), \quad (38b)$$
where $k_E$ is obtained by inverting the dispersion relation [30]:
$$k_E = \arccos(-E/2J). \quad (39)$$
The visibility of the peaks is enhanced, which corresponds to the coherent beam atoms coming from the source. In Fig. 3 (b,c,e–g) we can identify the appearance of two types of peaks (designated by arrows of different colors). As first type, we have two side peaks on the left- and right-hand side of the main peak at the incident beam energy, as seen for example in Fig. 3 (b,g) (black arrows). This will be further discussed in Sec. IV C. The second type of peaks correspond to inelastic scattering processes of atoms that thereby undergo a transition between different single-particle levels within the atomic quantum dot. They can be seen in Fig. 3 (c–f) (blue arrows) and will be discussed in Sec. IV D.
C. Collective oscillations
To understand the appearance of the two side peaks in the immediate vicinity of the incident beam energy, we study a leaky and driven single-level model with energy $E_0$ and two-body interaction between atoms with an interaction strength $g$. In the Heisenberg picture, the evolution equation of the field operator $\hat{a} \equiv \hat{a}(t)$ related to the level reads
$$i\hbar \frac{\partial \hat{a}}{\partial t} = (E_0 - i\gamma/2)\hat{a} + g\hat{a}^\dagger\hat{a} + [\kappa\hat{b} + \hat{\xi}(t)]e^{-i\mu t/\hbar},$$
where $\hat{b}$ correspond to the annihilation operator of the source which is coupled to the level with a coupling strength $\kappa$. The use of an imaginary leaky term $i\gamma/2$ implies that the losses are Markovian, which is justified in the limit of weak coupling between the single-level system and the leads. As was discussed in Sec. III D reducing the infinite waveguide to a finite open system introduces additional noise terms emerging from the initial vacuum fluctuations outside the quantum dot. Theses noise terms are accounted for by a time-dependent noise operator $\hat{\xi}(t)$ satisfying
$$[\xi(t), \xi(t')] = \xi_0^2 \delta(t-t'),$$
for some $\xi_0 \in \mathbb{R}$. For the sake of simplicity we consider here a white noise. The commutation relations for the bosonic field operators are given by
$$[\hat{a}(0), \hat{a}^\dagger(0)] = 1,$$ \hspace{1cm} (42a)
$$[\hat{b}, \hat{b}'] = 1.\hspace{1cm} (42b)$$
This model has the same ingredients as the atomic quantum dot system but offers the advantages to allow for analytical results.
For this particular system, we are interested in the appearance of side peaks near the resonance for a weak atom-atom interaction and large population of the single-particle level. As a consequence, the truncated Wigner evolution equation of the wavefunction $\psi \equiv \psi(t)$ can be written as
$$i\hbar \frac{\partial \psi}{\partial t} = (E_0 + g|\psi|^2 - i\gamma/2)\psi + [\kappa\sqrt{N} + \xi(t)]e^{-i\mu t/\hbar},$$
where $\psi$ is written as
$$\psi = \sum_{n=0}^{\infty} \sqrt{n} a_n(t) \phi_n,$$
and $a_n(t)$ is the annihilation operator of the $n$th level. $\phi_n$ are the eigenstates of the unperturbed system. The time-dependent matrix elements of the truncated Wigner function can then be calculated in the basis of the eigenstates of the unperturbed system. The results are presented in Figs. 4 (a,b) for $g=0.05J$, 0.07J, 0.09J and $J=0.1J$. The peaks designated by blue arrows arise from atoms that have undergone a transition between two single-particle levels of the atomic quantum dot.
In Fig. 3 (a) we plot the transmission versus the normalized chemical potential of the incoming atoms with $V = 4J$, $g = 0.02J$ and $N|\kappa|^2 = J^2$. We can see the appearance of well-resolved resonance peaks. Compared to Fig. 2 the visibility of the peaks is enhanced, which is expected as the enhancement of the potential barrier forming the quantum dot leads to a greater lifetime of the corresponding quasi-bound states. In Figs. 3 (b–g), we plot the energy distribution of the transmitted atoms. We can see the appearance of additional peaks depending on the value of the chemical potential. For Fig. 3 (d), where the chemical potential $\mu/2J = -0.37$ is far away from any resonance, we can only observe one peak corresponding to the coherent beam atoms coming from the source. In Fig. 3 (b,c,e–g) we can identify the appearance of two types of peaks (designated by arrows of different colors). As first type, we have two side peaks on the left- and right-hand side of the main peak at the incident beam energy, as seen for example in Fig. 3 (b,g) (black arrows). This will be further discussed in Sec. IV C. The second type of peaks correspond to inelastic scattering processes of atoms that thereby undergo a transition between different single-particle levels within the atomic quantum dot. They can be seen in Fig. 3 (c–f) (blue arrows) and will be discussed in Sec. IV D.
C. Collective oscillations
To understand the appearance of the two side peaks in the immediate vicinity of the incident beam energy, we study a leaky and driven single-level model with energy $E_0$ and two-body interaction between atoms with an interaction strength $g$. In the Heisenberg picture, the evolution equation of the field operator $\hat{a} \equiv \hat{a}(t)$ related to the level reads
$$i\hbar \frac{\partial \hat{a}}{\partial t} = (E_0 - i\gamma/2)\hat{a} + g\hat{a}^\dagger\hat{a} + [\kappa\hat{b} + \hat{\xi}(t)]e^{-i\mu t/\hbar},$$
where $\hat{b}$ correspond to the annihilation operator of the source which is coupled to the level with a coupling strength $\kappa$. The use of an imaginary leaky term $i\gamma/2$ implies that the losses are Markovian, which is justified in the limit of weak coupling between the single-level system and the leads. As was discussed in Sec. III D reducing the infinite waveguide to a finite open system introduces additional noise terms emerging from the initial vacuum fluctuations outside the quantum dot. Theses noise terms are accounted for by a time-dependent noise operator $\hat{\xi}(t)$ satisfying
$$[\xi(t), \xi(t')] = \xi_0^2 \delta(t-t'),$$
for some $\xi_0 \in \mathbb{R}$. For the sake of simplicity we consider here a white noise. The commutation relations for the bosonic field operators are given by
$$[\hat{a}(0), \hat{a}^\dagger(0)] = 1,$$ \hspace{1cm} (42a)
$$[\hat{b}, \hat{b}'] = 1.\hspace{1cm} (42b)$$
This model has the same ingredients as the atomic quantum dot system but offers the advantages to allow for analytical results.
For this particular system, we are interested in the appearance of side peaks near the resonance for a weak atom-atom interaction and large population of the single-particle level. As a consequence, the truncated Wigner evolution equation of the wavefunction $\psi \equiv \psi(t)$ can be written as
$$i\hbar \frac{\partial \psi}{\partial t} = (E_0 + g|\psi|^2 - i\gamma/2)\psi + [\kappa\sqrt{N} + \xi(t)]e^{-i\mu t/\hbar},$$
where $\psi$ is written as
$$\psi = \sum_{n=0}^{\infty} \sqrt{n} a_n(t) \phi_n,$$
and $a_n(t)$ is the annihilation operator of the $n$th level. $\phi_n$ are the eigenstates of the unperturbed system. The time-dependent matrix elements of the truncated Wigner function can then be calculated in the basis of the eigenstates of the unperturbed system. The results are presented in Figs. 4 (a,b) for $g=0.05J$, 0.07J, 0.09J and $J=0.1J$. The peaks designated by blue arrows arise from atoms that have undergone a transition between two single-particle levels of the atomic quantum dot.
In Fig. 3 (a) we plot the transmission versus the normalized chemical potential of the incoming atoms with $V = 4J$, $g = 0.05J$, $N|\kappa|^2 = J^2$ computed by the GP (black line, following the same color convention as in Fig. 2) and the tW prescription (red line for the total transmission and orange line for the incoherent part of the transmission). The panels below show the energy distribution of the outgoing flux according to the tW calculation for an incident beam energy of $\mu/2J = -0.86$ for (b), $\mu/2J = -0.52$ for (c), $\mu/2J = -0.37$ for (d), $\mu/2J = -0.04$ for (e), $\mu/2J = 0.47$ for (f), $\mu/2J = 0.87$ for (g). The black lines correspond to the coherent and the red lines to the total part of outgoing atoms. The peaks designated by a black arrow arise from collective oscillations about a single resonance as discussed in Sec. IV C. The peaks designated by blue arrows arise from atoms that have undergone a transition between two single-particle levels of the atomic quantum dot.
FIG. 3. (color online) (a) Transmission spectrum of the quantum dot geometry with $V = 4J$, $g = 0.05J$, $N|\kappa|^2 = J^2$ computed by the GP (black line, following the same color convention as in Fig. 2) and the tW prescription (red line for the total transmission and orange line for the incoherent part of the transmission). The panels below show the energy distribution of the outgoing flux according to the tW calculation for an incident beam energy of $\mu/2J = -0.86$ for (b), $\mu/2J = -0.52$ for (c), $\mu/2J = -0.37$ for (d), $\mu/2J = -0.04$ for (e), $\mu/2J = 0.47$ for (f), $\mu/2J = 0.87$ for (g). The black lines correspond to the coherent and the red lines to the total part of outgoing atoms. The peaks designated by a black arrow arise from collective oscillations about a single resonance as discussed in Sec. IV C. The peaks designated by blue arrows arise from atoms that have undergone a transition between two single-particle levels of the atomic quantum dot.
where $N$ is the number of atoms in the source and the term $|\psi|^2 - 1$ is well approximated by $|\psi|^2$. The classical equivalent $\xi(t)$ of the quantum noise $\dot{\xi}(t)$ has following properties
\begin{align}
\overline{\xi(t)} &= 0, \\
\overline{\xi(t)\xi(t')} &= \frac{\xi_0^2}{2} \delta(t-t'),
\end{align}
in perfect analogy with the truncated Wigner prescription to sample the initial quantum state with classical fields.
Instead of determining the number of atoms at energy $E$ by means of a spatial Fourier transform in the transmitted beam, we define it through a temporal Laplace transform of the amplitude on the level under consideration. We define the Laplace transform as
$$\tilde{\psi}(E) = \frac{1}{\sqrt{\hbar T}} \int_0^\infty \psi(t) \exp \left( \frac{1}{T} - \frac{E}{\hbar} \right) t \, dt,$$
for a fixed (and ideally very large) observation time $T$. The number of atoms at energy $E$ is calculated according to Eq. (45) and reads
$$\langle n_E \rangle = |\psi(E)|^2 - \frac{1}{2} \langle \hat{a}(E), \hat{a}^\dagger(E) \rangle.$$
We are interested in collective oscillations of the condensate. For that purpose, we assume that we are close to a stationary state $\phi_0$ defined as the solution of the stationary GP equation
$$(E_0 - \mu - i\gamma/2 + 2g|\phi_0|^2)\phi_0 + \kappa \sqrt{N} = 0. \quad (47)$$
We then decompose the wavefunction $\psi(t)$ as $\psi(t) = (\phi_0 + \delta\psi(t)) e^{-i\mu t/\hbar}$ and linearize the resulting evolution equation for $\delta\psi(t)$. We thereby obtain the Bogoliubov equations associated with Eq. (43) which read
\begin{align}
\begin{pmatrix} \Sigma - E & 2g\phi_0^* \\ -2g\phi_0 & -(\Sigma^* + E) \end{pmatrix} \begin{pmatrix} \delta\psi(E) \\ \delta\psi^*(-E) \end{pmatrix} = (-\xi(E) \xi^*(-E)) \begin{pmatrix} \Sigma - E & 2g\phi_0^* \\ -2g\phi_0 & -(\Sigma^* + E) \end{pmatrix},
\end{align}
after applying a Laplace transform according to Eq. (45), with
$$\Sigma = E_0 - \mu + 2g|\phi_0|^2 - i \left( \frac{\gamma}{2} - \frac{\hbar}{T} \right).$$
Solving the system of equations (48), we find
\begin{align}
|\delta\psi(E)|^2 &= \frac{|(\Sigma + E|^2 + g^2|\phi_0|^4)\xi_0^2/4\hbar}{|\Sigma - E||\Sigma^* + E| - g^2|\phi_0|^4|2^2},
\end{align}
which yields
\begin{align}
|\psi(E)|^2 &= \frac{1}{\hbar T} T^{-2} (E - \mu)^2/\hbar^2 + |\delta\psi(E - \mu)|^2.
\end{align}
Following the same steps as in the previous lines, and supposing that $N \to \infty$, $\kappa \to 0$ in such a way that $N|\kappa|^2$ remains constant, we can compute the commutator of Eq. (46), which is given by
$$[\hat{a}(E), \hat{a}^\dagger(E)] = \frac{|(\Sigma + E|^2 + g^2|\phi_0|^4)\xi_0^2/4\hbar}{|\Sigma - E||\Sigma^* + E| - g^2|\phi_0|^4|2^2}.$$
The total number of atoms at energy $E$ finally reads
$$\langle n_E \rangle = \frac{1}{\hbar T} T^{-2} + (E - \mu)^2/\hbar^2 + \frac{g^2|\phi_0|^4\xi_0^2/4\hbar}{|\Sigma - E||\Sigma^* + E| - g^2|\phi_0|^4|2^2}.$$
In Fig. 4 we plot $\langle n_E \rangle$ for $\mu/E_0 = 1.08$ for an observation time $E_0 T = 500\hbar$ and $\xi_0/E_0 = 0.5$. The interaction strength is set to $g/E_0 = 0.02$, the leak rate to $\gamma/E_0 = 0.001$ and the source of atom to $\sqrt{\kappa}/E_0 = 0.05$. We directly see the spectral signature of collective oscillations for $\mu/E_0 = 1.08$ which is close to the nonlinear resonance (i.e., the population of the single-level system is high). This is in accordance with our previous findings for the quantum dot where collective oscillations appear near the resonances (see Fig. 5 a)). The occurrence of these side-peaks is, furthermore, in perfect qualitative agreement with the atom blockade study of Carnusso in Ref. 19.
**FIG. 4.** (color online) Average number of atoms $\langle n_E \rangle$ at energy $E$ for $g/E_0 = 0.02$, $\gamma/E_0 = 0.001$, $\sqrt{\kappa}/E_0 = 0.05$, $E_0 T = 500\hbar$ and $\xi_0/E_0 = 0.5$. The presence of collective oscillations is clearly manifested in form of two side peaks appearing at $E - \mu \approx \pm 0.36 E_0$. The (red) dots show the results obtained by numerically integrating Eq. (49) and applying a Laplace transform according to Eq. (45). They are in perfect agreement with the theoretical prediction (black line) of Eq. (50).
**D. Bogoliubov excitations in the quantum dot**
We are now interested in the Bogoliubov modes within the multi-mode quantum dot configuration that we focus on in this paper. To this end, we numerically solve the Bogoliubov equations defined with respect to the stationary solution of the effective GP-like equation (32). The stationary wavefunction of Eq. (32) defined on the grid is given by $\phi_{0,l}$ on site $l$. We can solve the Bogoliubov equations
$$\mathcal{T}_N^{(n)} = \epsilon_n \mathcal{Y}^{(n)},$$
where $N$ is the number of atoms in the source and the term $|\psi|^2 - 1$ is well approximated by $|\psi|^2$. The classical equivalent $\xi(t)$ of the quantum noise $\dot{\xi}(t)$ has following properties
\begin{align}
\overline{\xi(t)} &= 0, \\
\overline{\xi(t)\xi(t')} &= \frac{\xi_0^2}{2} \delta(t-t'),
\end{align}
in perfect analogy with the truncated Wigner prescription to sample the initial quantum state with classical fields.
Instead of determining the number of atoms at energy $E$ by means of a spatial Fourier transform in the transmitted beam, we define it through a temporal Laplace transform of the amplitude on the level under consideration. We define the Laplace transform as
$$\tilde{\psi}(E) = \frac{1}{\sqrt{\hbar T}} \int_0^\infty \psi(t) \exp \left( \frac{1}{T} - \frac{E}{\hbar} \right) t \, dt,$$
where $\epsilon_n$ is the $n^{th}$ eigenvalue and $y^{(n)}$ the related eigenvector. The matrix $\mathcal{T}$ is defined as
$$\mathcal{T} = \begin{pmatrix} \mathcal{L} & \mathcal{C} \\ -\mathcal{C}^* & -\mathcal{L}^* \end{pmatrix},$$
(55)
with the matrix elements of $\mathcal{L}$ and $\mathcal{C}$ defined by
$$\mathcal{L}_{ll'} = (V_l - \mu q_l + 2g_l|\phi_{0,l}|^2)\delta_{l,l'},$$
(56)
$$-J_l(\delta_{l+1,l'} + \delta_{l-1,l'}),$$
(57)
$$\mathcal{C}_{ll'} = g^2_l\delta_{l,l'},$$
(58)
with $l,l' = 0,1,\ldots,L$ and
$$J_l = J\left[\frac{1}{q_l} - \frac{1}{q_{l'}}\right],$$
(59)
in the presence of SECS, see Eq. (52). Clearly, $\mathcal{T}$ is not hermitian. Hence, the corresponding eigenvalues $\epsilon_n$ are complex, and their imaginary part is related to the width of the corresponding resonance peak.
The numerically computed results are plotted for two different values of $\mu$ in Fig. 5. The vertical black lines correspond to the expected Bogoliubov eigenenergies $\Re(\epsilon_n)$ and the grey zones correspond to the expected width of the peaks given by $2\Im(\epsilon_n)$. The upper panel shows the results for $\mu/2J = -0.86$ and we can see that collective oscillations appear within the quantum dot in agreement with the Bogoliubov theory. The lower panel corresponds to a chemical potential $\mu/2J = -0.04$ that is close to the energy corresponding to the 3rd resonance. It shows a richer structure of peaks arising from the superposition of collective oscillations and inelastic scattering. Indeed, two colliding atoms at the incident energy $\mu/2J = -0.04$ can exchange energy through a collision process. After the collision, the first atom can end up on the 4th energy level and the second can end up on the 2nd energy level as depicted in Fig. 5. The results given in the tW calculation are in very good agreement with the Bogoliubov theory.
The truncated Wigner method appears to be a very convenient tool to study transport of interacting Bose–Einstein condensates across more involved scattering configurations such as one–dimensional disordered potentials. This shall be discussed in a forthcoming publication [57]. The approach presented in this paper can, furthermore, be extended to account for a more realistic description of the experimental configurations at hand involving, for instance, two reservoirs of $N$ atoms at ultralow but finite temperatures. This extension will then allow to simulate source-drain transport processes across quantum dot like configurations, paving the way to a realistic theoretical study of atomtronics devices or atomic transistors.
V. CONCLUSIONS
In the present work, we studied one-dimensional resonant transport of Bose–Einstein condensates within a guided atom laser configuration. For this purpose, we introduced a generalization of the truncated Wigner method to open systems. The reduction from an infinite system to a finite scattering region introduces an additional term accounting for quantum fluctuation which takes the form of a quantum noise. We made use of smooth exterior complex scaling to absorb the outgoing flux of atoms. This allowed us to study resonant and non-resonant transport across a one-dimensional atomic quantum dot beyond the mean–field Gross–Pitaevskii description.
The truncated Wigner method was used to compute the transmission across a quantum dot configuration. We observed that perfect resonant transmission is inhibited due to incoherent atoms creating a transmission blockade. This effect is in quantitative agreement with a Matrix-Product State calculation. The incoherent atoms originate from two different physical processes. The first one is the creation of collective oscillations on an individual single-particle level within the quantum dot leading to two side peaks in the direct vicinity of the incident beam energy. The second one is related to inelastic collisions of atoms where atoms are transferred to other energy levels within the quantum dot.
FIG. 5. (color online) Energy distribution of the transmitted beam for two different values of the chemical potential: $\mu/2J = -0.86$ for the upper panel and $\mu/2J = -0.04$ for the lower panel. The black vertical lines correspond to the expected Bogoliubov energies. They are in good agreement with the tW calculations. The grey zones correspond to the expected width of the peaks given by $2\Im(\epsilon_n)$. The upper panel shows two side peaks around the chemical potential creating a collective oscillation inside the quantum dot. For the lower panel, we observe that, on top of the collective oscillation, inelastic collisions occur transferring atoms in the 2nd or 4th energy level as depicted in the sketch on the top right side. The tW results are well reproduced by the Bogoliubov theory.
ACKNOWLEDGMENTS
The authors want to thank Boris Nowak for fruitful discussions. Computational resources have been provided by the Consortium des Equipements de Calcul Intensif (CECI), funded by the Fonds de la Recherche Scientifique de Belgique (F.R.S.-FNRS) under Grant No. 2.5020.11.
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Numerical simulation on the deformation and failure of the goaf surrounding rock in Heiwang mine
Yandong Shang\textsuperscript{1,2}, Yanpei Guo\textsuperscript{1,2,3} and Wenquan Zhang\textsuperscript{3}
\textsuperscript{1} Taian compus, Shangdong University of Science and Technology, Taian 271019, China;
\textsuperscript{2} State Key Laboratory of Mining Disaster Prevention and Control, Qingdao 266590, China.
\textsuperscript{3} [email protected]
Abstract: The stability of overlying rock mass of mined-out area was simulated using finite difference software FLAC3D according to the gob distribution of Heiwang iron mine. The deformation, failure characteristics of surrounding rock was obtained. The subsidence of strata above the middle mined-out area was the biggest. The maximum subsidence of ground surface was 12.4mm. The farther away from the central goaf was, the smaller the vertical subsidence value was. There was almost no subsidence on the two lateral surrounding rock near mined-out area. There exists the potential danger when cutting along the boundary of goaf. The tensile stress appeared at the top and bottom of the mined-out area. The maximum of tensile stress was 34.7kPa. There was the compressive stress concentration phenomenon in the lateral boundary of mined-out area. The stress concentration coefficient was about 1.5 on both sides of gob. The upper section of the middle goaf was subjected to the tensile failure, and the upper rock mass of both sides was mainly subjected to the tensile-shear failure. The ore pillars on the inner side of the goaf were mainly subjected to the shear failure. When the overlying strata were complete, the possibility of sudden instability of the ore pillar and the sudden subsidence of the ground surface could not occur. The achievements can provide theoretical basis for the processing of the goaf.
1. Introduction
The processing of goaf was a technical problem of mining safety production in China. So far, the existing method on empty area treatment was hard to widely practice for its expensive costs. So, the study on the stability of the surrounding rock was very important. The influence of coal mining on the surface stability was studied by analytic method\cite{1}. A similar simulation experiment was conducted to study the horizontal and vertical deformations of strata in the coal mine\cite{2}. The numerical simulation of the stability of the goaf was carried out using three-dimensional finite element method\cite{3}. Based on fuzzy matter-element theory, the fuzzy matter-element evaluation model was constructed based on fuzzy matter-element theory. The deformation monitoring scheme in the area of going-out area was discussed\cite{4}. Other scholars had done some other researches on going-away areas\cite{5-9}. In this paper, the stability of overlying rock mass of mined-out area was simulated using finite difference software FLAC3D according to the gob distribution of Heiwang iron mine. The deformation and plastic zone of surrounding rock was obtained. The achievements can provide theoretical basis for the processing of the goaf.
2. Geological situation of construction
Heiwang iron mine was located in the middle of Zi river fault zone. The ground layer was dominated by the middle orдовикian system. The bottom part was the cold system. The fracture structure was quite developed. There was almost no alienation. The deposit was controlled by fracture structure. Since Heiwang iron mine was closed, the illegal mining and beneficiation activities were very serious. There left a large number of non-standard underground mined-out area with different sizes and shapes. And this kind of situation had a tendency to spread. Most of the empty area was not handled in time. The ore had been deformed and destroyed owing to the pressure, weathering and the influence of blasting vibration. Their location, size, shape was changed. It was easy to produce the ground collapse suddenly. This is likely to cause serious harm to the lives and property of the local people, so it was urgent to solve this problem.
3. Numerical simulation of surrounding rock stability of mined-out area
3.1. The model and parameters
The three-dimensional numerical calculation model was established according to the actual formation, it was with the length of 120m, the height of 50m, and the width of 60m. The upper boundary of the model was the free boundary, the bottom boundary was fixed, and the lateral boundary was the lateral displacement constraint. There were three mining areas in the model. The buried depth of deposits was 10m. The goaf were with the width of 4m and the height of 14m, and the width of the pillar was 8m. The 3D numerical calculation model and the size of the deposit mining were shown in Figure 1. Elastic-plastic is the most basic property of rock. In numerical simulation, the properties of almost all rock materials can be exhibited by an elastic-plastic model. So, the deposit was described by elastic-plastic model that obeys the mohr-coulomb yield criterion. The physical and mechanical parameters of rock mass were shown in Table 1.
**Figure 1.** The 3D numerical calculation model and the size of the deposit mining.
| Rock layer | weight (kN/m³) | Bulk modulus (MPa) | Shear modulus (MPa) | Cohesion (kPa) | Internal friction Angle (°) | Poisson's ratio |
|------------|----------------|--------------------|--------------------|---------------|-----------------------------|----------------|
| Limestone | 25.1 | 10320 | 5040 | 90 | 27 | 0.26 |
3.2. The analysis of numerical simulation results
3.2.1 The analysis of vertical displacement of strata The vertical displacement of stratum and surface after mining was shown in Figure 2 and Figure 3. From the two figures, the subsidence of strata above
the middle mined-out area was the biggest, and the maximum subsidence of ground surface was 12.4 mm. The farther away from the central goaf was, the smaller the vertical subsidence value was. There was almost no subsidence on the two lateral surrounding rock near mined-out area. But there exists the potential danger when cutting along the boundary of goaf. There was heave phenomenon at the bottom of the pillar. The closer from the middle of goaf was, the larger the heave was. The maximum heave value was 0.36 mm.
**Figure 2.** The vertical displacement of strata after mining.
3.2.2 **The analysis of vertical stress of stratum**
The vertical stress of strata after mining was shown in Figure 4. From Figure 4, the tensile stress appeared at the top and bottom of the mined-out area. The maximum of tensile stress was 34.7 kPa. There was compressive stress concentration phenomenon in the lateral boundary of mined-out area. The stress concentration coefficient was about 1.5 on both sides of gob.
**Figure 3.** The vertical displacement of surface after mining.
3.2.3 The analysis of plastic zone of surrounding rock
The distribution of plastic zone of surrounding rock after mining was shown in Figure 5. From Figure 5, the upper section of the middle goaf was subjected to the tensile failure, and the upper rock mass of both sides was mainly subjected to the tensile-shear failure. The ore pillars on the inner side of the goaf were mainly subjected to the shear failure, and the same, the lateral rock mass near the goaf mainly the shear failure.
4. Conclusions
The stability of overlying rock mass of mined-out area was simulated using finite difference software FLAC3D according to the gob distribution of Heiwang iron mine. The deformation and plastic zone of surrounding rock was obtained. The subsidence of strata above the middle mined-out area was the biggest. The maximum subsidence of ground surface was 12.4mm. The farther away from the central goaf was, the smaller the vertical subsidence value was. There was almost no subsidence on the two lateral surrounding rock near mined-out area. There exists the potential danger when cutting along the boundary of goaf. The tensile stress appeared at the top and bottom of the mined-out area. The maximum of tensile stress was 34.7kPa. There was the compressive stress concentration phenomenon in the lateral boundary of mined-out area. The stress concentration coefficient was about 1.5 on both sides of gob. The upper section of the middle goaf was subjected to the tensile failure, and the upper...
rock mass of both sides was mainly subjected to the tensile-shear failure. The ore pillars on the inner side of the goaf were mainly subjected to the shear failure. When the overlying strata were complete, the possibility of sudden instability of the ore pillar and the sudden subsidence of the ground surface could not occur.
Acknowledgment
The author would like to thank the financial support by the National Natural Science Foundation of China (Grant No. 41472281) and National science Foundation of liaoning province (No.20170540143).
References
[1] DUAN Weiqiang 2015 Analysis and Study on Influence of Coal Mine Gob Area upon Surfance Stability[J] Mining Safety and Environmental Protection 42(3) 81-85
[2] FENG Guorui, REN Yafeng, WANG Xianxia, LI Jizu, KANG Lixun 2011 Experiment Study on the Movement and Deformation of Rock Strata Between Coal Seams in the Coal Mining Above Gob Area[J] Mining Safety and Environmental Protection 28(3) 430-435
[3] CHEN Zancheng, HOU Kepeng, YANG Bajiu 2010 3D Finite Element Numerical Simulation on Gob Stability of Some Mine[J] Non Ferrous Metal 62 (3) 142-145
[4] TANG Shuo, LUO Zhou-quan, XU Hai 2012 Evaluation of stability of goaf based on fuzzy matter-element theory[J] China Safety Science Journal 22(7) 24-30
[5] LI Yongxin 2010 Discussion on Defornation Monitoring Scheme of Goaf in Yuzhou[J], Resources Environment and Engineering 24 (5) 531-534
[6] TAN Zhihong, JIA Tianrang, HAN Zhenglin, YAN Jiangwei 2011 Numerical Simulation Study on Influence of Surrounding Rock's Uniformity upon Stability of Roadway near Gob Area[J] Mining Safety and Environmental Protection 38 (3) 23-25
[7] SHANG Zhenhua, TANG Shaohui, JIAO Wenyu, LIU Chang 2014 Failure Probability of Goaf in Large-scale Based on Simulation of FLAC3D[J] Rock and Soil Mechanics 10 3000-3006.
[8] WEN Zhijie, TAN Yunliang, HAN Zuozhen, MENG Fanbao 2016 Construction of Time-Space Structure Model of Deep Stope and Stability Analysis[J] Polish Journal of Environmental Studies 25(06) 2633-2639
[9] WEN Zhijie, RINNE Mikael, HAN Zuozhen, SONG Zhen, SHI Yongkui 2014 Structure Model of Roadway with Large Deformation and Its Basic Research into Engineering Theories[J] Tehnički vjesnik–Technical Gazette 5(21) 1065-1071
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Usefulness of the delta neutrophil index in predicting surgery in patients with foot and ankle infection
Ji eun Shin¹, Kyung Deok Seo², Hyun Jae Cha³, Jong Wook Lee³, Youn Moo Heo², Kwang Kyoun Kim², Tae Gyun Kim³, Chan Kang⁴, Gi Soo Lee⁴, Jae Hwang Song.²*
¹Department of Biomedical Informatics, College of Medicine, Konyang University, Daejeon, Republic of Korea, ²Department of Orthopedic Surgery, Konyang University Hospital, Daejeon, Republic of Korea, ³Department of Laboratory Medicine, Konyang University Hospital, Daejeon, Republic of Korea, ⁴Department of Orthopedic Surgery, Chungnam National University Hospital, Daejeon, Republic of Korea
* [email protected]
Abstract
Background
In foot and ankle infections, cases with apparent soft-tissue necrosis or purulent fluid collections definitely require surgical treatments. However, clinicians often have difficulty in determining whether to perform surgery in ambiguous cases without these findings. This study aimed to investigate the impact of the delta neutrophil index as a predictor of surgical treatment in patients with foot and ankle infections.
Methods
In total, 66 patients diagnosed with foot and ankle infections who underwent the delta neutrophil index test were retrospectively investigated. Medical records, including data on diabetes mellitus status, delta neutrophil index values, white blood cell count, polymorphonuclear leukocyte count, erythrocyte sedimentation rate, and C-reactive protein level, were retrospectively investigated. Logistic regression models were analyzed for the correlation between biomarkers, such as the delta neutrophil index and surgical treatment. The area under the curve was investigated to evaluate the cut-off value of the logistic model in predicting surgery.
Results
The relationship between the delta neutrophil index and surgical treatment was analyzed. The delta neutrophil index, adjusted for diabetes mellitus, was the best predictor of future surgical intervention. Based on the Youden index, the cutoff point (the equation’s adjusted by diabetes mellitus) for the prediction of surgical treatment was defined as a probability of 0.3, with sensitivity and specificity of 82.4% and 77.6%, respectively.
Conclusions
Based on the present study, the delta neutrophil index can help clinicians decide the appropriate surgical treatment for foot and ankle infections at the right time.
Introduction
Foot and ankle infections are common causes of morbidity, disability, and mortality [1, 2]. Foot and ankle infections pose a difficult and challenging treatment dilemma since patients often have poor vascular status and severe wound complications, such as in patients with diabetes mellitus and peripheral arterial occlusive disease [2]. Although cases with apparent soft-tissue necrosis or purulent fluid collections definitely require surgical treatments, including irrigation, debridement, or amputation [2], clinicians often have difficulty in determining whether to perform surgery in ambiguous cases without these findings.
To evaluate the severity of infection, history taking, physical examination, and radiographic evaluation are important. During physical examination, inspection should be performed to detect signs of infection, including tenderness, heating sense, erythema, swelling, blisters, and drainage [2]. For the radiographic evaluation, simple radiographs and magnetic resonance imaging studies can be used to obtain useful information regarding infective findings of the bone and soft tissue structure [2]. However, some limitations of the aforementioned tests remain due to their limited sensitivity and specificity [3].
Laboratory markers are another essential diagnostic tool that can quantitatively predict the severity and prognosis of infections. Laboratory markers, including white blood cell (WBC) count, polymorphonuclear leukocyte (PMN) count, erythrocyte sedimentation rate (ESR), and C-reactive protein (CRP) level, have been used for the diagnostic investigation of foot and ankle infections. However, these laboratory parameters cannot appropriately reflect the severity of foot and ankle inflammation; hence, it is difficult to predict necessity for operation in the patients [3–6]. Therefore, a novel serum biomarker that determines the need for surgery is required.
During infection, immature granulocytes (IGs) reveal the increased production of granulocytes [7], and it has been demonstrated that increased IGs is a useful biomarker for predicting infection [8]. However, manual counting of IGs needs considerable effort and time. The Delta neutrophil index (DNI) is a new, innovative parameter of the circulating fraction of IGs, and is automatically estimated using a cell analyzer without manual counting [9]. Recently, several studies reported that DNI significantly correlates with IGs, and proved the usefulness of DNI as a predictor of infection [4]. An increased DNI was related not only with severity of infection, but also with bacteremia, disseminated intravascular coagulation, and mortality in sepsis [4, 10–12].
Therefore, given the strong association with the severity of other inflammatory diseases, we hypothesized that the DNI would predict patients with foot and ankle infections in need of surgery. To the best of our knowledge, no previous studies have evaluated the correlation between DNI and foot and ankle infections. Hence, the present study aimed to investigate the usefulness of the DNI as a predictor of surgical treatment in patients with foot and ankle infections.
Materials and methods
Participants and subgroup analysis
The institutional review board (IRB) of Konyang University Hospital (KYUH 2020–06–025) approved this study. Following the guidelines for the diagnosis of skin and soft tissue infections by the infectious diseases society of America [13] and referring the most commonly used diagnostic terms associated with foot and ankle infections in our hospital, patients of our orthopedic department with the word “cellulitis; erysipelas; necrotizing fasciitis; furuncle; carbuncle; abscess; diabetic foot infection; septic arthritis; osteomyelitis” in discharge codes
registered in computerized hospital records were initially considered as patients with foot and ankle infections. This study enrolled 99 of 648 patients with foot and ankle infections diagnosed at our hospital between 2002 and 2007 who underwent the DNI exam (Fig 1). We excluded patients aged < 18 years, those with infection related to trauma (i.e., sprain or fracture), peri-implant infection, benign or malignant tumors, autoimmune diseases, and hematologic disorders. Finally, a cohort of 66 patients with foot and ankle infections were enrolled in the present study.
Data were collected retrospectively by reviewing medical records by two orthopedic surgeons who were blinded to the study. The following data were extracted from medical records: sex, age, admission day, diabetes mellitus (DM) status, inflammatory markers (measured on admission date, including DNI, WBC, PMN, ESR, and CRP), and other laboratory data (measured on admission date, including hemoglobin, hematocrit, platelet, prothrombin time, activated partial thromboplastin time, glucose, blood urea nitrogen, creatinine, total protein, albumin, sodium, potassium, and chloride).
To determine the treatment methods, signs of infection including erythema, swelling, blisters, heating sensation, pain, tenderness, drainage, as well as laboratory data, were thoroughly
investigated by orthopedic surgeons who had more than 5 years of clinical experience. Initially, all patients underwent medical treatment with empirical intravenous (IV) antibiotics, such as Ampicillin-sulbactam [14] or cefazolin [15], regardless of surgical or non-surgical group. IV antibiotic treatment was maintained until the infection signs and laboratory outcomes were improved. Patients with extensive bone involvement, apparent purulent discharges, or soft tissue gangrene promptly underwent surgical treatments, including irrigation, debridement, or amputation. In ambiguous cases, the final decision regarding surgical intervention was made by the surgeon when abnormal laboratory outcomes and clinical signs persisted, despite medical treatment.
For statistical analysis, the participants were divided into two groups: the surgery and non-surgery groups. The aforementioned data obtained by reviewing the electronic medical records were compared between the two groups.
**Delta neutrophil index measurement**
DNI is measured by the difference between leukocyte subfractions estimated using a nuclear lobularity assay and a cytochemical myeloperoxidase (MPO) stain. The DNI values were calculated by a hematology analyzer (ADIVA 120, Siemens, Inc.) by performing complete blood count (CBC) without additional cost or time, and the DNI values were calculated automatically and reported with the CBC results under prescription.
**Statistical analysis**
Statistical and graphical analyses were performed using SPSS version 28.0 (IBM Corp., Armonk, NY, USA). Continuous data were compared between the two groups using Student’s t-test (parametric data) or the Mann-Whitney U test (nonparametric data). The Chi-squared or Fisher’s exact tests were used for the analysis of categorical data. Logistic regression analysis was used to calculate the predictive probability of each biomarker and combined biomarkers. To evaluate the cut-off value for predicting surgery, the receiver operating characteristic (ROC) curves and the area under the curve (AUC) were investigated. Each cut-off value was selected to maximize the sum of sensitivity and specificity. Statistical significance was set at $p < 0.05$ in all analyses.
**Results**
Participants were divided into the surgery (n = 17) (Table 1) and non-surgery groups (n = 49). None of the patients included in the non-surgery group underwent surgery within 1 year follow up, and most of them needed intravenous antibiotic treatment for about 2–3 weeks.
The mean age, admission day, and rate of DM in the surgery group were significantly higher than those in the non-surgery group (p < .001, respectively) (Table 2). In terms of inflammatory markers, DNI was the only marker that showed a significant difference between the two groups (p = .045). The mean of glucose (p < .001), blood urea nitrogen (p = .019), and potassium (p = .042) in the surgery group were significantly higher, and the mean of hemoglobin (p < .001), hematocrit (p < .001), total protein (p = .035), and albumin levels (p < .001) were significantly lower than those in the non-surgery group.
Based on the logistic regression analysis for inflammatory biomarkers, DNI was the only significant predictor of surgical intervention (Table 3); as DNI increased, the odds ratio (OR) was 1.512-fold higher (95% confidence interval [CI], 1.013–2.257, p = 0.043).
Given the strong association between DM and surgery for the treatment of foot and ankle infections, we analyzed inflammatory markers adjusted by DM modalities (Table 4). The ROC curve and AUC were investigated using the p-value estimated by logistic regression analysis of
combined DM modalities [16]. The cut-off ranges (cutofflogitP) of logitP (fitted equations) and corresponding incidence (Pcutoff) were estimated using the maximum Youden index [16]. Based on the logitP, the Pcutoff value of DNI was 0.3, and its sensitivity and specificity were 82.4% and 77.6%, respectively, with an AUC of 0.839 (95% CI, 0.742–0.937, \( p < .001 \)). As a result, the combination of DM and DNI was the most powerful method for predicting surgical interventions (Fig 2).
### Discussion
The findings of this study support our hypothesis that DNI could predict surgical treatment in patients with foot and ankle infections. The combination of DM and DNI revealed the highest predictive power for surgical treatment in these patients.
The foot and ankle have a distinctive risk of infection since they have important role in weight bearing and frequent exposure to trauma. Also their treatment is challenging since it is often affected by poor vascular supply or sensations related with diseases such as diabetes. Although many cases of foot and ankle infections can resolve with medical treatment, operative treatment is required in patients refractory to non-operative treatment. However, predicting the necessity of operation in patients with foot and ankle infections is challenging, since the clinical course varies depending on disease severity. In particular, determining surgery, such as amputation, can be a huge dilemma for surgeons and patients. However, a meaningless delay may aggravate morbidities such as gangrenous changes, or mortality. For this reason, it is important to timely determine the need of surgery in foot and ankle infections using objective diagnostic tools. To this end, researchers have sought novel markers that can be used to identify patients most likely to benefit from surgical treatment [17].
In the early period of sepsis and infection, immature neutrophils enter the circulation to compensate for the lack of active neutrophils, thereby causing a "leftshift" [18]. In this setting, the number of neutrophil bands, which indicate the amount of immature neutrophils, is
| Patient number | Sex | Age | Diabetes mellitus | Diagnosis | Operation |
|----------------|-----|-----|-------------------|-----------|-----------|
| 1 | M | 74 | + | Diabetic foot ulcer | Incision and drainage |
| 2 | F | 91 | + | Osteomyelitis | Amputation, 1st toe |
| 3 | F | 73 | + | Osteomyelitis | Amputation, 1st toe |
| 4 | M | 87 | + | Peripheral arterial occlusive disease | Disarticulation, 2nd MTPJ |
| 5 | M | 71 | + | Osteomyelitis | Disarticulation, 4th MTPJ |
| 6 | F | 91 | + | Peripheral arterial occlusive disease | Below knee amputation |
| 7 | M | 76 | + | Osteomyelitis | Disarticulation, 5th MTPJ |
| 8 | M | 84 | + | Diabetic foot ulcer. | Incision and drainage |
| 9 | M | 71 | + | Peripheral arterial occlusive disease | Amputation, 4th toe |
| 10 | M | 67 | + | Osteomyelitis | Disarticulation, 3rd MTPJ |
| 11 | F | 96 | - | Osteomyelitis | Disarticulation, 5th MTPJ |
| 12 | F | 77 | + | Diabetic foot ulcer | Incision and drainage |
| 13 | F | 59 | + | Diabetic foot ulcer | Incision and drainage |
| 14 | M | 86 | + | Peripheral arterial occlusive disease | Amputation, Lisfranc joint |
| 15 | M | 45 | + | Osteomyelitis | Disarticulation, 5th MTPJ |
| 16 | M | 50 | - | Cellulitis, ankle | Incision and drainage |
| 17 | M | 34 | - | Cellulitis, foot | Incision and drainage |
M, male; F, female; MTPJ, metatarsalophalangeal joint.
### Table 2. Baseline characteristics of participants with foot and ankle infection*.
| Variables | Total (n = 66) | Surgery group (n = 17; 25.8%) | Non-surgery group (n = 49; 74.2%) | p value |
|-------------------------|----------------|--------------------------------|-----------------------------------|---------|
| **Demographic characteristics** | | | | |
| Sex | | | | .528 |
| Male | 48 (72.7%) | 11 (64.7%) | 37 (75.5%) | |
| Female | 18 (27.3%) | 6 (35.3%) | 12 (24.5%) | |
| Age (y) | 54.7 (18–96) | 72.5 (34–96) | 48.6 (18–92) | < .001 |
| Admission day (d) | 21.5 (2–131) | 42.6 (12–131) | 14.2 (2–67) | < .001 |
| Diabetes Mellitus | 29 (43.9%) | 14 (82.4%) | 15 (30.6%) | < .001 |
| **Inflammatory markers**| | | | |
| DNI (%) | 2.0 (0–8.4) | 2.7 (0–8.4) | 1.8 (0–4.3) | .045 |
| WBC (cells/μL) | 1253.5 (4870–30710) | 12147.7 (5160–30710) | 1267 (4870–64700) | .220 |
| PMN (%) | 71.9 (46.7–87.9) | 73.7 (52.4–87.9) | 71.3 (46.7–86.1) | .153 |
| ESR (mm/h) | 34.0 (2–120) | 36.5 (2–65) | 33.2 (1–120) | .180 |
| CRP (mg/dL) | 6.9 (0.3–20.0) | 6.4 (0.3–20.0) | 7.1 (0.3–20.0) | .143 |
| **Other laboratory data**| | | | |
| Hb (g/dL) | 13.0 (9.2–16.4) | 11.5 (9.2–14.3) | 13.5 (9.9–16.4) | < .001 |
| Hct (%) | 37.2 (28.6–49.9) | 33.4 (28.6–40.1) | 38.5 (28.6–49.9) | < .001 |
| Plt (x1000/μL) | 278.9 (128–586) | 286.7 (128–586) | 276.1 (134–536) | .686 |
| PT (s) | 13.7 (11.6–17.3) | 13.7 (11.9–17.3) | 13.6 (11.6–15.7) | .481 |
| aPTT (s) | 37.8 (2.6–63.9) | 37.9 (25.6–63.9) | 37.8 (2.6–56.0) | .090 |
| Glucose (mg/dL) | 171.0 (70–517) | 267.8 (70–517) | 137.4 (79–266) | < .001 |
| BUN (mg/dL) | 16.0 (6.6–52.4) | 19.0 (6.6–52.4) | 14.9 (7.0–50.0) | .019 |
| Cr (mg/dL) | 1.1 (0.6–4.6) | 1.1 (0.7–3.3) | 1.1 (0.6–4.6) | .496 |
| Total protein (g/dL) | 6.9 (5.5–8.1) | 6.6 (5.5–7.9) | 7.1 (5.9–8.1) | .035 |
| Albumin (g/dL) | 3.8 (2.5–4.7) | 3.5 (2.5–4.3) | 4.0 (2.5–4.7) | < .001 |
| Na (mmol/L) | 137.2 (128.0–144.0) | 135.5 (128.0–143.0) | 137.8 (132.0–144.0) | .067 |
| K (mmol/L) | 4.2 (3.4–5.9) | 4.4 (3.9–5.7) | 4.2 (3.4–5.9) | .042 |
| Cl (mmol/L) | 102.6 (91.6–109.0) | 102.1 (91.6–108.0) | 102.8 (94.2–109.0) | .493 |
*Values are presented as the mean and range (min–max). Boldface indicates a statistically significant difference between the two groups (p < .05).
DNI, delta neutrophil index; WBC, white blood cell; PMN, polymorphonuclear leukocyte; ESR, erythrocyte sedimentation rate; CRP, C-reactive protein; Hb, hemoglobin; Hct, hematocrit; Plt, platelet; PT, prothrombin time; aPTT, activated partial thromboplastin time; BUN, blood urea nitrogen; Cr, creatinine; Na, sodium; K, potassium; Cl, chloride.
https://doi.org/10.1371/journal.pone.0272574.t002
### Table 3. Predictors of surgical intervention for foot and ankle infection as determined by univariate logistic regression analysis.
| Variables | OR | 95% CI | p value |
|-----------|--------|--------------|---------|
| DNI (%) | 1.512 | 1.013–2.257 | .043 |
| WBC (cells/μL) | 1.000 | 1.000–1.000 | .607 |
| PMN (%) | 1.042 | 0.971–1.118 | .255 |
| ESR (mm/h) | 1.010 | 0.981–1.039 | .511 |
| CRP (mg/dL) | 0.931 | 0.824–1.051 | .245 |
DNI, delta neutrophil index; WBC, white blood cell; PMN, polymorphonuclear leukocyte; ESR, erythrocyte sedimentation rate; CRP, C-reactive protein; OR, odds ratio; CI, confidence interval.
https://doi.org/10.1371/journal.pone.0272574.t003
increased [19]. Using IGs for evaluating infection has been recently suggested by several investigators [20]. However, counting granulocyte parameters is difficult, and methods for reliable quantification have not been established [4]. Furthermore, measuring IGs is labor-intensive and time-consuming.
On the contrary, the DNI is a measured value that reveals the ratio of IGs to the total neutrophil count [21]. The DNI is assessed by an automatic system through the nuclear lobularity.
### Table 4. Combined DM modalities of the inflammatory markers.
| Model | Cut-off logit $P$ | $P_{\text{cutoff}}$ | AUC (95% CI) | Sensitivity, % | Specificity, % | p value |
|-------------|------------------|----------------------|--------------|----------------|----------------|----------|
| DM+DNI | -0.849 | 0.300 | 0.839 (0.742–0.937) | 82.4 | 77.6 | <.001 |
| DM+WBC | -0.13 | 0.468 | 0.759 (0.630–0.887) | 82.4 | 71.4 | .002 |
| DM+PMN | -0.27 | 0.433 | 0.777 (0.645–0.909) | 82.4 | 71.4 | .001 |
| DM+ESR | -0.254 | 0.437 | 0.772 (0.620–0.923) | 82.4 | 83.7 | .001 |
| DM+CRP | -0.106 | 0.473 | 0.775 (0.616–0.934) | 70.6 | 87.8 | .001 |
DM, diabetes mellitus; DNI, delta neutrophil index; WBC, white blood cell; PMN, polymorphonuclear leukocyte; ESR, erythrocyte sedimentation rate; CRP, C-reactive protein; AUC, area under the curve; CI, confidence interval.
**https://doi.org/10.1371/journal.pone.0272574.t004**
and MPO channels [22]. By using an automatic cell analyzer, clinicians can easily obtain the DNI value which reports the index of the IGs fraction. The DNI has been reported to have a significant relationship with the severity of several infectious diseases [3]. Also, many previous studies have suggested the DNI as a useful predictor of surgical decisions [3]. Furthermore, no additional cost or time is necessary for obtaining the DNI [11]. Most importantly, the DNI has been reported to be a better predictor of infection and prognosis compared to traditional markers, including WBC count, ESR, and CRP [4–6].
The diagnosis of infection can be difficult if WBC values are in the normal or lower range because of leukopenic diseases, including tuberculosis and typhoid fever [4]. Instead, the DNI can diagnose and predict infections in patients with high accuracy, since the proportion of IGs is elevated even under the condition of normal WBC or absolute neutrophil count (ANC) [23].
ESR and CRP are commonly used biomarkers for the diagnosis and monitoring of infection. They can also provide accurate information related with inflammatory symptoms in orthopedic conditions [24]; however, there are some limitations associated with their use. Since an increase of ESR is induced by the rouleaux formation of red blood cells, ESR is rather insensitive to minor infection and its response to inflammation is quite slow [24]. Hence, ESR is currently not recommended as a screening test [25]. CRP is a preferred biomarker for acute inflammatory conditions since it shows more rapid kinetics and shorter half-life [26]. Therefore, it is useful for investigating response to treatment as well as diagnosis of infection. However, CRP levels can increase in several situations which cause tissue injury, including surgery, malignancies, and trauma [14]. In addition, CRP is not a specific parameter for infection-induced inflammation, as it can be increased in systemic autoimmune diseases, such as rheumatoid arthritis.
Procalcitonin has been used for the identification of bacterial infections [17] because of several advantages over other biomarkers, such as the wide biological range and short time of induction after bacterial infection. Thus procalcitonin has been widely used to guide the initiation and termination of antibiotics in various bacterial diseases [27]. In a systematic review and meta-analysis, the DNI’s pooled sensitivity and specificity as a predictive factor for infection were 0.67 (95% CI, 0.62–0.71) and 0.94 (95% CI, 0.94–0.95), respectively, with an AUC of 0.89 [4]; these results were comparable to those of CRP [28] and procalcitonin [29] as predictive factors for infection in previous studies. Since both CRP and procalcitonin levels elevate several hours after disease onset [30] while the DNI increases 12 h before the initiation of organ failure in patients with severe infection [31], the DNI can help diagnose and initiate treatment against infections faster [4]. Also, the DNI has much shorter life than procalcitonin, which is helpful during follow-up for therapeutic efficacy [4].
Among the inflammatory biomarkers, the DNI was the only marker that showed a significant difference between the surgery and non-surgery groups, and it was the only significant predictor of surgical intervention for foot and ankle infections. Among the baseline characteristics, DM and glucose levels differed significantly between the two groups. Given the strong association between DM and surgical intervention for the treatment of foot and ankle infections, we investigated the combined DM modalities of inflammatory markers [16]. A previous study suggested that combining ROC curve and logistic regression analyses is feasible for identifying several disease markers [16]. We found that the combination of DM and DNI exhibited the highest predictive power for operative treatment patients.
In previous studies of other diseases, the DNI was suggested as a useful biomarker that could predict surgical intervention [3, 32]. For example, Lee et al. [32] suggested that the initial DNI level can be a useful predictor for determining surgical intervention in patients with intestinal obstruction. The area under the ROC curve of the initial DNI (0.543) was higher than
that of CRP (0.460) and WBC (0.449) in these patients. Similarly, Son et al. [3] reported that
the DNI may be a good predictor for determining the necessity for operative treatment in
chronic rhinosinusitis patients. Also in that setting, the area under the ROC curve of the initial
DNI (0.782) was higher than that of WBC (0.571) and ESR (0.600). Hence, the combination of
DM and DNI in the present study can also be suggested as a useful predictor of surgical treat-
ment, considering the high AUC of the ROC curve (0.839).
To our knowledge, this is the first study to investigate the correlation between the DNI and
foot and ankle infections. We compared DNI with several other inflammatory markers,
including WBC, PMN, ESR, and CRP, which are the most commonly used laboratory tests for
the diagnosis and monitoring of foot and ankle infections.
Our study has some limitations that should be acknowledged. First, the study was limited
by its retrospective and single-center design, and its small sample size. Second, due to the
nature of the retrospective cohort study design, potential confounders may exist. However,
potential confounders such as comorbidity of peripheral arterial occlusive disease or chronic
kidney disease were not identified in the present study. Further prospective studies with a
larger number of patients that will include investigation of these confounders are therefore
required. Third, clinical and radiological evaluations, which might have been an important fac-
tor in predicting surgery, were not included in this study. Fourth, the inclusion rate of the
study was low (15%) since not all patients with foot and ankle infection underwent DNI test;
this is because some doctors (professors or residents) of the orthopedic department did not
Prescribe the DNI code at that time. Finally, the study was performed from 2002 to 2007,
because calculation of DNI was not available after that period due to a change of the auto-an-alyzer type in our hospital. However, many medical centers are still using the DNI for labora-
tory tests related to diagnosing and monitoring various infectious diseases.
Conclusions
The DNI, adjusted for DM, was the best predictor of future surgical intervention in patients
with foot and ankle infections. We suggest that the DNI can help clinicians determine the
appropriate surgical treatment for foot and ankle infections at the right time. Further prospec-
tive studies with larger number of patients are required to support our data and minimize the
limitations of this study.
Supporting information
S1 Data.
(SAV)
Author Contributions
Conceptualization: Ji eun Shin, Jong Wook Lee, Gi Soo Lee, Jae Hwang Song.
Data curation: Kyung Deok Seo, Hyun Jae Cha.
Formal analysis: Youn Moo Heo, Kwang Kyoun Kim, Tae Gyun Kim, Chan Kang.
Methodology: Ji eun Shin, Jae Hwang Song.
Supervision: Ji eun Shin, Jae Hwang Song.
Visualization: Ji eun Shin, Jae Hwang Song.
Writing – original draft: Kyung Deok Seo, Jae Hwang Song.
Writing – review & editing: Ji eun Shin, Jae Hwang Song.
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32. Lee H, Kim I-K, Ju MK (2017) Which patients with intestinal obstruction need surgery? The delta neutrophil index as an early predictive marker. Annals of Surgical Treatment and Research 93: 272–276. https://doi.org/10.4174/asstr.2017.93.5.272 PMID: 29184881
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Fracture toughness of seven resin composites evaluated by three methods of mode I fracture toughness ($K_Ic$)
Ayse MESE1, Joseph EA PALAMARA2, Rafat BAGHERI2,3, Mehdi FANI3 and Michael F. BURROW2
1 Department of Prosthodontics, School of Dentistry, Dicle University, Diyarbakir, Turkey
2 Restorative Section, Melbourne Dental School, The University of Melbourne, 720 Swanston St, Melbourne, Australia
3 Department of Dental Materials and Biomaterials Research Center, School of Dentistry, Shiraz University of Medical Sciences, Ghomabad, Ghasrodasht St, Shiraz, Iran
Corresponding author, Rafat BAGHERI; E-mail: [email protected]
This study compared the fracture toughness values of seven resin composites and analyzed the consistency of data values using three methods: compact tension, three point and four point bending for Mode I failure. Seven resin composites were selected: Estellite Sigma Quick, Esthet X HD, Filtek Supreme XTE, Heliomolar, Ice, Rok, and Vit-l-escence. For each material, 18 specimens ($n=6$ for each test) were prepared. Maximum load to failure was recorded using a universal testing machine and fracture toughness was calculated. There was a direct significant correlation among all tested methods. Rok showed the highest and Estelite the lowest $K_Ic$ values. SEM of the fractured surface of compact tension method showed propagation of the cracks from stresses concentrating at the corner of the notch and the surface of the sample. Four-point test gave the largest range in $K_Ic$ and was a simple method to discriminate between the resin composite values of $K_Ic$.
Keywords: Fracture toughness, Four-point method, Three-point method, Compact tension method, Resin composite
INTRODUCTION
Resin composites are now commonly used for all types of restoration; however, they tend to be brittle and this shortcoming relates to a sensitivity to flaws and defects that increases susceptibility to catastrophic failure3. New formulations of resin composites are continually appearing on the market with different mechanical properties.
The ability of a restoration to tolerate fracture partly lies in material composition and filler volume. A higher filler loading has been shown to result in higher fracture toughness up to a threshold value of $\sim 55$ to $57\%$ filler loading2,4. Kim et al. in their study of the effect of filler loading and morphology on the mechanical properties of resin composites (filler loading rate of 41.24 to 59.05 vol%), determined the maximum toughness at the threshold level of approximately $55\%$ filler. Ilie et al. in their study of fracture toughness of restorative materials also reported an increase in $K_Ic$ with the volume fraction of fillers until a critical volume fraction of $57\%$.
The physical and mechanical properties of resin composite critically affect the performance in the oral cavity. Due to the wide use of resin composites, they should reproduce the strength and wear limits similar to natural tooth structure being able to resist occlusal forces including tensile, compressive, and shear stresses. One of the common mechanical tests used to assess brittle restorative materials is fracture toughness.
$K_Ic$ is an important measure of a material’s properties as it indicates the largest amount of stress that a material can bear prior to failure. A variety of fracture toughness testing methods have been used to evaluate the relative fracture toughness of resin composites5. These tests include four-point bending6,7, single-edge-notched beam8, chevron notch, compact tension9,10, and the indentation hardness method11, all resulting in a range of values of $K_Ic$, even for the same material11,9. These methods require different specimen geometries related to the size and shape of the specimens, size of the crack, and loading configuration.
Due to the complexity of the forces that direct restorations are subjected to in the oral cavity, it is not easy to select a suitable method for testing fracture toughness of resin composites. Several studies attempted to establish some clinically reliable testing protocols for evaluating the fracture toughness of brittle dental materials12-15. One of the most reported reliable methods is the single edge V-notched beam (SEVNB) which has been used in the ceramics standard, ISO 687216. It has been shown that SEVNB method is a reproducible approach17. However, the reported values show a large discrepancy in the fracture toughness values obtained from this method18; this could be related to the difficulties in preparing the V-notch that may vary in size and consequently lead to different $K_Ic$ values.
This study aimed to compare fracture toughness of seven resin composites using three different methodologies to see if outcomes were similarly ranked and of the same order of magnitude. The fractographic features of the surface were evaluated using scanning electron microscopy (SEM). The null hypothesis is that fracture toughness values are not similarly ranked using three different methodologies and that the geometry of
the testing method (Mode I) has no effect on the fracture toughness value.
MATERIALS AND METHODS
Specimen preparation
1. Four-point test method
Seven resin composites of shade A2 were selected (Table 1) with the particle filler content ranging from 66.7 to 82.3 wt% (46 to 67.7 vol%). A custom-made, brass and aluminium mould with a notch centrally placed was used to prepare the specimens (Fig. 1-A). Six bar-shaped specimens of 25 mm long×2 mm thick and 5 mm width (Fig. 1-B) were prepared from each material by filling the mould and pressing between transparent plastic strips and glass plates to extrude the excess material. The materials were light cured through transparent strips according to the manufacturers’ instructions for 40 s (three exposures over equal areas) using a light-polymerizing LED unit with a wavelength range of 440–480 nm at an output of 1,500 mw/cm² (Radii plus LED, SDI, Bayswater, Vic, Australia). Each specimen was
Table 1 Materials description
| Materials | Manufacturer | Type | Resin | Filler’s type, size and % | Lot # |
|---------------|-------------------------------|--------------------|-------------------------|-----------------------------------|--------|
| Estelite Sigma Quick | Tokuyama Dental, Tokyo, Japan | Submicron filled composite | Bis-GMA, TEGDMA | SiO₂, ZrO₂ (200 nm), PFSC (average 0.2 μm); 78 wt% (63 vol% ) | E033 |
| Esthet X HD | Dentsply, Caulk, USA | Microhybrid Composites | BIS-GMA, BIS-EMA, TEGDMA | Barium, FSG (<1 μm), NFS (0.04 μm), TD (nanofiller); 60 vol% (76 wt%) (0.2 to 2.5 μm) | 1111041|
| Filtek Supreme XT | 3M ESPE St. Paul, MN, USA | Nanohybrid Composites | Bis-GMA, UDMA, TEGDMA, Bis-EMA | 63.3 vol% (78.5 wt%) SF, ZF, AZSCF (5 to 75 nm) | N395233|
| Heliomolar | Ivoclar Vivadent, Schaan, Liechtenstein | Microfilled Composite | BisGMA, UDMA, D DDDMA | 0.04–0.2 μm, 46 vol% (66.7 wt%) | N04438|
| Ice | Southern Dental Industries, Vic, Australia | Nanohybrid Composite | UDMA/BisEMA/TEGDMA | SAS, AS (0.04–1.5 μm), Average1.0 μm, 61 vol% (78 wt%) | 12096SN|
| Rok | SDI, Vic, Australia | Hybrid Composite | UDMA, TEGDMA, Bis-EMA | SAS, AS, (0.04–2.5 μm); 67.7 vol% (82.3 wt%) | 120844|
| Vit-l-escence | Ultradent Products, USA | Microhybrid Composite | Bis-GMA | Bis-GMA, Average particle size (0.7 μm); 58 vol% (75 wt%) | B56VM |
SF=Silica filler, ZF=Zirconia filler, AZSCF=Aggregated zirconia/silica cluster filler
SAS=Strontium alumino silicate, AS=amorphous silica, FSG=fluoroalumino silicate glass, NFS=Nanofiller silica, TD=Titanium Dioxide, PFSC=Prepolymerized filler of silicacomposite, DDDMA=Decandioldimethacrylate.
Fig. 1 A: Custom-made, brass and aluminium mould with a centrally placed notch, B: Bar-shaped specimen.
removed from the mould and light-cured on the opposite side for an additional 3×40 s. Before the measurement of \( K_c \), the specimens of each material were stored in distilled water at 37ºC for 24 h.
After polymerization, in order to obtain a flat surface, the edges of the specimens were ground by gentle wet grinding using 1000-grit silicon carbide paper. A new razor blade was used under hand pressure to create a sharp crack in the notch. Crack length was measured and recorded for each specimen using a stereomicroscope (LV 150 Eclipse, Nikon, Japan) at 60× magnification. The width and height of each specimen was measured using a digital calliper with accuracy of ±0.1 mm. Figure 2-A displays the specimen geometry for determination of fracture toughness by the four-point bend method. The specimens were placed in the universal testing machine (Zwick/Roll Z020, Zwick, Germany) using a four-point bend test jig, loaded at a crosshead speed of 0.5 mm/min, and calibrated using the internal calibration. The maximum load at specimen failure was recorded and the \( K_c \) (MPam\(^{0.5}\)) was calculated using the following equation:
\[
K_c = \frac{F \cdot S_{1} - S_{2}}{B \cdot w^{1.5}} \cdot Y \]
Where:
- \( F \) = fracture load,
- \( S_{x} \) = span (\( x = 1 \): outer span; \( x = 2 \): inner span),
- \( B \) = specimen width,
- \( a/w \) = notch depth,
- \( w \) = specimen height,
- \( Y \) = stress intensity shape factor
2. Three-Point test [Single-edge notched beam method (SENB)]
The same mould and method as the four-point test was used to prepare six specimens for each of the seven materials (Fig. 2-B). The specimens were placed in the universal testing machine (Zwick/Roll Z020, Zwick) using a three-point bend test jig, loaded at a crosshead speed of 0.5 mm/min, and calibrated using the internal calibration. The maximum load at specimen failure was recorded and the \( K_c \) (MPam\(^{0.5}\)) was calculated using the following equation:
\[
K_c = \frac{F}{B} \cdot \frac{S_{c}}{w^{3/2}} \cdot f(c/w)
\]
\( f(c/w) = 2.9(c/w)^{1/2} - 4.6(c/w)^{3/2} + 21.8(c/w)^{5/2} - 37.6(c/w)^{7/2} \)
\( F = \text{Maximum Load}, \ B = \text{Specimen width}, \ S = \text{Supporting span}, \ w = \text{Specimen height}, \ c = \text{notch length}, \ f(c/w) = \text{a function of } c \text{ and } w \)
3. Compact Tension (CT) test method
A custom-made, polytetrafluorethylene (PTFE) split mould was used to prepare six disk-shaped specimens for each of the seven materials. A schematic of the specimen and details of the dimensions were shown and described in previous studies\(^9,17\). A pre-crack was created in the mini-compact specimen with a razor blade, as described by Kovarik and Fairhurst\(^18\) in accordance with ASTM Designation: E399-83\(^19\). The split mould was assembled.
using guide screws. The mould was filled with the resin composite and covered by plastic matrix strips and glass plates under gentle hand pressure in order to extrude the excess material. A razor blade was used to create a sharp pre-crack in the notch during polymerization of the resin composite. The materials were cured according to the manufacturers’ recommended exposure times, using the same LED curing light as explained above.
The specimens of each material were stored in distilled water at 37°C for 24 h and then ground by gentle wet grinding using 1000-grit silicon carbide papers in order to adjust the thickness to 2 mm ±0.2 and measured using a digital calliper with accuracy of ±0.1 mm. Faulty specimens having voids or cracks were discarded.
The specimens were secured in universal testing machine (Zwick/Roll Z020, Zwick) using guide pins placed through the specimen’s holes (Fig. 3-C). Tensile loading was applied at a crosshead speed of 0.5 mm/min; the maximum load at failure was recorded and the $K_{\text{IC}}$ (MPa.m$^{0.5}$) was calculated using the following formula:
$$K_{\text{IC}} = \frac{F}{BW^{0.5}} \cdot f\left(\frac{a}{w}\right)$$
Where:
$$f\left(\frac{a}{w}\right) = \frac{(2+\frac{a}{w})[0.76+4.8\frac{a}{w}-11.58(\frac{a}{w})^2+11.43(\frac{a}{w})^3-4.08(\frac{a}{w})^4]}{(1-\frac{a}{w})^{1.5}}$$
$F$=maximum load at specimen fracture, $f(a/w)$=function of $a$ and $w$
$B$=specimen thickness, $W$=dimension from the un-notched edge of the specimen to the plane centreline of the loading holes.
**Scanning electron microscopy**
To observe the fractured surface in each testing method, two randomly selected specimens of each group were examined under an environmental scanning electron microscope (ESEM, FEI Quanta, OR, USA) with original magnification range of 100 to 2,000 times (Figs. 3a–c). Samples were sectioned parallel to the fractured surface using a diamond peripheral saw (Minimat 230CS, Struers, Copenhagen, Denmark) and stuck to a SEM stub with carbon conductive tape.
**Data analysis**
The collected data were analyzed using the SPSS package (version 18, SPSS, Chicago, IL, USA). The normality assumption was assessed using Kolomogorov-Smirnov test. The Pearson correlation coefficient was performed to evaluate the possible correlation between the three tests. Then, one-way ANOVA with post hoc Tukey’s test was used for each method to compare the fracture toughness of the seven tested materials.
**RESULTS**
The mean $K_{\text{IC}}$ values and standard deviations from all tests for the seven resin composites are presented in Table 2. The values obtained from CT test were lower than those obtained by four-point or three-point loading tests. Figures 4–6 shows force-displacement curve for representative specimens of the each material of CT, three point and four point tests respectively.
**Comparison among the three methods**
The Pearson correlation coefficient analysis showed a strong direct significant correlation between the three methods; between CT and three-point test ($p<0.004$, $r=0.509$); CT and four-point ($p<0.001$, $r=0.438$) and between four-point and three-point ($p<0.001$, $r=0.614$). The lowest values were obtained when using the compact tension method.
---
Fig. 3
(a) Compact tension fracture test of Esthet X shows “artificially introduced crack interface” (A), mirror region (B), mist region (C), hackle region (D) and voids (E),
(b) Three-point fracture of Filtek Supreme showing “artificially introduced line notch interface” (A) and voids (B),
(c) Four-point fracture of Heliomolar shows “artificially introduced line notch interface” (A) and voids along an internal line defect (B).
Table 2 Means $K_I$ (MPa.m$^{0.5}$) and SD(±) of all materials in 3 testing methods $n=6$
| Materials | Compact tension | Four-point bending | Three-point bending |
|--------------------|-----------------|--------------------|---------------------|
| Estellite Sigma Quick | 0.51 (0.15)$^a$ | 0.90 (0.17)$^a$ | 0.91 (0.17)$^p$ |
| Esthet. X HD | 0.56 (0.07)$^a$ | 1.45 (0.24)$^{bc}$| 1.34 (0.20)$^{bc}$ |
| Filtek Supreme XTE | 0.58 (0.05)$^a$ | 1.48 (0.20)$^{bc}$| 1.45 (0.13)$^{bc}$ |
| Heliomolar | 0.49 (0.06)$^a$ | 1.05 (0.19)$^{cd}$| 1.13 (0.08)$^{cd}$ |
| Ice | 0.56 (0.06)$^a$ | 1.28 (0.24)$^{cd}$| 1.16 (0.17)$^{cd}$ |
| Rok | 0.75 (0.08)$^b$ | 1.75 (0.09)$^r$ | 1.48 (0.07)$^r$ |
| Vit-l-escence | 0.53 (0.10)$^a$ | 1.17 (0.07)$^{bc}$| 1.08 (0.15)$^{bc}$ |
Different lower case letters indicate that the values are statistically significant for each column ($p<0.05$).
Fig. 4 Force-Displacement curve for representative specimens of the each material of CT test.
Fig. 5 Force-Displacement curve for representative specimens of the each material of three-point test.
Fig. 6 Force-Displacement curve for representative specimens of the each material of four-point test.
Comparisons of fracture toughness among different materials
One-way ANOVA and post hoc Tukey’s test showed a significant variation among materials for the different tests. For CT test, the differences among materials were not significant except for Rok (0.75 MPa.m$^{0.5}$) which showed a significantly higher value than all other materials. In four-point test, Rok (1.75 MPa.m$^{0.5}$), Filtek Supreme (1.48 MPa.m$^{0.5}$) and Esthet X (1.45 MPa.m$^{0.5}$) demonstrated the highest values, whilst Estellite Sigma Quick (0.90 MPa.m$^{0.5}$) and Heliomolar (1.05 MPa.m$^{0.5}$) the lowest. For three-point test, Rok, Filtek Supreme and Esthet X showed the highest values, respectively, in contrast with Estellite Sigma Quick, and Vit-l-escence which showed the lowest values.
Results of SEM examination
The SEM fractographic examination is presented in Figs. 3a–c. Figure 3-a illustrates an example of the fractured surface of CT method (in Esthet X) indicating...
flaws and characteristic crack initiation point where a mirror, mist and hackle region at the corner of the compact tension with the notch and the disk surface can be seen. Figure 3-b shows an image of the three-point fracture test of Filtek Supreme showing a line of voids just below the introduced notch (artificial crack) interface on the fractured surface. Figure 3-c shows the four-point fracture test displaying internal defects in Heliomolar and as a line defect associated with voids crossing the field of view that may account for the low fracture toughness values for this material.
**DISCUSSION**
The Mode I fracture toughness ($K_c$) is the lowest stress at which catastrophic crack propagation will occur due to its tensile opening of the crack. $K_c$ is an important material property as it represents the ability of a material to resist crack propagation from an existing flaw.
In this laboratory study, three methods of determining fracture toughness values for Mode I (tensile force) were evaluated for different types of resin composites. The results showed a strong direct significant correlation between all tested methods with the lowest values for CT method. The low value found for the CT fracture test compared to the three- and four-point tests could be due to the concentration of tensile and possibly torsional or shear stresses occurring at the edges (corners) of the line notch interface with the surface of the disk. Corner stresses developed at flaws present at the introduced crack interface of the CT samples (Fig. 3-a).
The tensile stress due to the mirror size (Fig. 3-a) can be calculated from the formula: $\sigma = \frac{\sqrt{aR}}{A}$. Where $A$ is a constant of the material; $R$ is the mist hackle radius and $\sigma$ is the stress. "A" is equal to $\sim 2.6$ MPA $\sqrt{m}$ according to Quinn for 85 wt% of filler in a Bis-GMA/TEGDMA composite. This implies that the localized tensile stress is concentrated at the notch/surface corner and not along the length of the interface. The stress value to initiate the crack was approximately 106 MPa. This is consistent with the flexural strength reported for Esthet X.
It appears that it is difficult to obtain a uniform stress along the whole line of the introduced notch and that stresses will preferentially concentrate at the corners of the disk. Consequently, this produces low fracture toughness values for this rigid CT geometry compared to the three and four-point fracture methods.
Dental composites are multipurpose materials which have grown fast since the materials were first introduced to the market. Modification of the filler types, reduction of the filler particle size but also an associated increase in size range that has allowed an increase in the filler loading are the most significant changes that have occurred since their introduction in the 1960's. In resin composite with particles ranging from 0.04 to 0.20 μm, classified as micro-filled, about 50% of the volume of the material is resin which provides excellent surface smoothness. However, their physical and mechanical properties are inferior to those of hybrid resin composites as observed in our study for Heliomolar with its low filler content.
More recently, the description “nano-hybrid” has been marketed. The distinction between micro-hybrids and nano-hybrids is not always clear, perhaps due in part to the way they are marketed. After all, even micro-hybrids contain a small fraction of nano-sized (sub 100 nanometer) particles. Manufacturers add nanoparticles to micro-hybrids to fill the resin filled gaps between the larger particles. This can result in improved esthetic quality. There is, however, a limit to the amount of nanoparticles that can be added before the handling becomes too stiff and therefore unworkable clinically.
In our study as shown in Table 2, the hybrid resin composite (Rok) with the highest filler vol% 67.7 (82.3 wt%) and the largest filler sizes (2.5 μm) showed significantly higher values in all tests compared to the nano-hybrid, micro-hybrid and microfill composites. On the other hand, when the materials were tested by compact tension method, Heliomolar with the lowest filler content of 46 vol% (66.7 wt%) showed the lowest $K_c$ value (0.49 MPam$^{0.5}$) followed by Vit-l-escence (0.53 MPam$^{0.5}$) with filler content of 58 vol% (75 wt%). Apart from Estelite, all other materials showed a direct positive relationship between $K_c$ values and filler vol% (wt%), i.e. (within the range investigated) as the filler content increased, the fracture toughness also increased. However, the four point loading method showed the greatest change in fracture toughness as a function of filler loading.
The wide distribution of particle sizes leads to a higher filler loading and therefore resultant higher fracture toughness. Improvements in resin composites have been directed at increasing the filler content in the resin matrix and reducing the filler particle size range. There is a correlation between the filler particle size and the maximum filler volume that can be incorporated in the resin matrix. Similarly, the particle morphology is believed to have an effect on the fracture toughness values so that the percentage of the filler volume is influenced by filler morphology. There was no significant difference between nano-hybrid and micro-hybrid which contain a mixture of larger particles and smaller sub-micrometre sized particles, usually amorphous or colloidal silica. Particle size on average is typically below 3 micrometre but above 0.04 micrometres.
**CONCLUSION**
Within the limitations of this study, the four-point and three-point tests gave similar $K_c$ values. Lower values were observed for the compact tension method which may be due to corner stresses generated during testing. All the methods of testing showed similar ranking order between the resin composites tested. Of the systems tested the four-point method provides a more discriminating method to determine the fracture toughness ($K_c$) value for resin composites with different percent filler content.
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Impact of two myostatin (MSTN) mutations on weight gain and lamb carcass classification in Norwegian White Sheep (Ovis aries)
Inger A Boman1,2*, Gunnar Klemetsdal1, Ola Nafstad3, Thor Blichfeldt2, Dag I Våge4
Abstract
Background: Our aim was to estimate the effect of two myostatin (MSTN) mutations in Norwegian White Sheep, one of which is close to fixation in the Texel breed.
Methods: The impact of two known MSTN mutations was examined in a field experiment with Norwegian White Sheep. The joint effect of the two MSTN mutations on live weight gain and weaning weight was studied on 644 lambs. Carcass weight gain from birth to slaughter, carcass weight, carcass conformation and carcass fat classes were calculated in a subset of 508 lambs. All analyses were carried out with a univariate linear animal model.
Results: The most significant impact of both mutations was on conformation and fat classes. The largest difference between the genotype groups was between the wild type for both mutations and the homozygotes for the c.960delG mutation. Compared to the wild types, these mutants obtained a conformation score 5.1 classes higher and a fat score 3.0 classes lower, both on a 15-point scale.
Conclusions: Both mutations reduced fatness and increased muscle mass, although the effect of the frameshift mutation (c.960delG) was more important as compared to the 3'-UTR mutation (c.2360G>A). Lambs homozygous for the c.960delG mutation grew more slowly than those with other MSTN genotypes, but had the least fat and the largest muscle mass. Only c.960delG showed dominance effects.
Background
In Norwegian White Sheep (NWS), two myostatin (MSTN) mutations affecting conformation and fat classes are segregating: the 3'-UTR mutation creating an illegitimate microRNA site (c.2360G>A) that was identified in Texel sheep [1] and a frameshift mutation explained by a deletion of one base pair in nucleotide position 960 (c.960delG), identified in NWS [2]. While c.2360G>A reduces the level of circulating myostatin to approximately one third, c.960delG generates a completely non-functional protein.
Initially, the aim of the current study was to investigate the effect of the c.960delG mutation on growth and carcass traits in NWS under ordinary commercial management conditions. NWS is a synthetic crossbreed, composed of the Dala, Rygja, Steigar and Texel breeds [3]. However, during the course of this experiment, another MSTN mutation (c.2360G>A) was published [1]. Since the Texel breed is one of the NWS founder breeds [3,4], the ongoing study was expanded in order to include this new mutation. Here we present data on how the two mutations affect weight gain and lamb carcass classification.
Methods
Genotyping
Genotyping of the two MSTN positions, c.960 and c.2360, was carried out as described by Boman et al. [2]. First, the animals were genotyped only at position c.960, and then retyped at position c.2360, after publication of the second mutation.
Experimental design
The field experiment comprised two experimental years in the Vesterålen area, in the north of Norway.
Year 1
The first year, all ewes of ten commercial NWS flocks were genotyped at the c.960 position. In essence, for each ewe homo- or heterozygous for c.960delG, an age-matched control ewe without the mutation from the same flock was also included in the study. All ewes were mated to a ram without the mutation (n = 34). Two flocks were excluded from the study due to the low numbers of ewes carrying the mutation (4 and 6, respectively). The remaining flocks were genetically well tied, since six belonged to the same ram circle, one was a former member of the circle and one had a history of rams purchased from the circle. A total of 200 ewes (100 case/control pairs) were included in the study, and each flock was represented with 18 to 28 ewes. In six flocks, ultrasound scanning to count the number of foetuses had been performed, thus only pregnant ewes were included in the experiment. The first priority was to include all homozygous ewes, thereafter the youngest heterozygous ewes within each flock. The numbers of ewes and rams per genotype are given in Table 1. The selected ewes’ lambs born this year were genotyped.
Year 2
It was decided to replace two of the flocks from year 1, by another flock. This flock was in an adjacent ram circle, having genetic ties to the original experimental flocks because common AI rams had been used and local elite rams had been exchanged. Basically, the same sampling strategy as in year 1 was followed; 100 ewes with the c.960delG mutation and 100 without were included. In both groups, ewes with a low estimated overall breeding value were sampled, since these are not relevant for producing replacements. Prediction of the breeding value, is described by Eikje et al. [5]. Each flock was represented with 20 to 30 ewes. In addition, we balanced the groups with respect to age and flock as in year 1. All ewes were artificially inseminated with frozen semen from rams heterozygous for the c.960delG mutation (n = 7). For the ewes that returned, a local ram carrying the mutation was used. The numbers of ewes and rams per genotype are given in Table 1. The selected ewes’ lambs were also genotyped in year 2.
Management and slaughter
The experiment did not interfere with normal management; for example, the farmers were allowed to move lambs to a foster mother or providing supplemental feeding. In year 1, the farmers decided if and when to slaughter the lambs, while in year 2 all experimental lambs were intended to be slaughtered.
At approximately four months of age, the lambs were gathered and transferred from the rough grazing pasture to the farm. Subsequently, the weaning weight of the lambs was measured and the farmers selected the lambs to be sent directly for slaughter, and those to be kept on rich pasture, for finishing. Live weight was used as a guide to decide when to slaughter the lambs according to common practise. Some farmers shipped lambs only twice in the season, while others shipped them more frequently, depending on management choices and flock size.
The lambs were all slaughtered in the same commercial abattoir, and carcass classification was carried out according to the EUROP classification system in Norway [6], which is on a 15-point scale, a value of 15 being the meatiest or fattiest class, respectively.
Statistical analysis
Data on growth and carcass traits were retrieved from the national sheep recording system (SRS). The data were analysed univariately for weight gain per day from birth to weaning, weaning weight, carcass weight gain per day from birth to slaughter, carcass weight, carcass conformation class and fat class (Yijklmno), with the following linear model, using DMUAI in the DMU software package [7]:
\[ Y_{ijklmno} = G_i + GD_j + S_k + R_l + AD_m + f_n + i_0 + e_{ijklmno} \]
where \( G_i \) is the fixed effect of the ith genotype class (1, ..., 6; see Table 2), \( GD_j \) is the fixed effect of the jth genotype class of the dam (1, ..., 5; as in Table 2, except the class homozygous for c.960delG), \( S_k \) is the fixed effect of the kth sex class (male or female), \( R_l \) is the fixed effect of the lth rearing class (1, 2, 3, or bottle lamb), \( AD_m \) is the fixed effect of the nth age of dam class (1, 2, 3, 4 or 5), \( f_n \) is the random effect of the nth flock-year class (1, ..., 15), \( i_0 \) is the random additive genetic effect of the oth animal and \( e_{ijklmno} \) is the random residual term. The pedigree file comprised a total of 3292 animals, a pruned subset retrieved from the SRS for the experimental animals, comprising all known ancestors in six generations.
In the statistical model, the effects of sex, rearing class and age of dam were factors that we \textit{a priori} believed to affect the traits since they are taken into account in the
### Table 1 Number of ewes and rams (local/AI) per genotype and year
| Sex | c.960 | GG | G(delG) | delG(delG) | GG | G(delG) | delG(delG) |
|-----|-------|----|---------|------------|----|---------|------------|
| | | | | | | | |
| Year 1 | 100 | 96 | 4 | 29/5 | 100| 96 | 3 |
| Year 2 | 101 | 96 | 3 | 10/7 | 101| 96 | 10/7 |
Guanine (G) is found in the mutated position (c.960) in the wild type; in year 2, a local ram serviced ewes that returned.
national prediction of breeding values for traits recorded in the autumn.
An equivalent model, analysing the same data with the same software, was used to estimate the allelic effects rather than the genotype class effects:
\[ Y_{ijklmnop} = a_{2360} x_1 + d_{2360} x_2 + a_{960} x_3 + d_{960} x_4 + \text{int} x_5 + g_{1} + r_{1} + d_{m} + f_{y} + i_{o} + e_{ijklmnop} \]
where the regression coefficients for the additive and dominant allelic effect of c.2360G>A (a2360,d 2360) and c.960delG (a960,d 960) give a weight to their interaction (int), while the x’s are indicator (dummy) variables; x1 is the number of c.2360G>A alleles (0,1,2), x2 is 1 if heterozygous in c.2360 and 0 otherwise, x3 is the number of c.960delG alleles (0,1,2), x4 is 1 if heterozygous in c.960 and 0 otherwise, x5 is 1 for compound heterozygotes and 0 otherwise, and the other terms are defined as in the model above.
To test the impact of the two MSTN-mutations in the first model, the wild type individuals (GG_GG, for cDNA position 960 and 2360, respectively) were used as reference. We also wanted to test the impact of the genotypes carrying the c.960delG-mutation, against the group GG_AA. Hypothesis testing was done by the following contrasts, using V3.1 of PEST [8], with variance components from the DMUAI run as input:
1. H0: MSTN-genotype - GG_GG (wild type) = 0, where MSTN-genotype is GG_AG, GG_AA, G(delG)_GG, G(delG)_AG or (delG)(delG)_GG against H1: MSTN-genotype - GG_GG ≠ 0.
2. H0: MSTN-genotype - GG_AA = 0, where MSTN-genotype is G(delG)_GG, G(delG)_AG or (delG)(delG)_GG, against H1: MSTN-genotype - GG_AA ≠ 0.
Hypothesis testing for the allelic effects in the second model was done by the following contrasts, using the same software and variance components:
1. H0: regression coefficient = 0, where regression coefficient is the additive, dominance and interaction terms a2360, d2360, a960, d960 and int, against H1: regression coefficient ≠ 0.
2. H0: a960 - a2360 = 0, against H1: a960 - a2360 ≠ 0.
Note that since the two models are equivalent, some of the tests are identical.
Estimation of variance components for daily carcass weight gain did not converge due to little information in the data. The heritability was therefore set to 15%.
**Results**
The number of homozygous c.960delG ewes was low (Table 1), and thus their progeny were omitted from the analysis. In the autumn, 644 lambs (50.9% females) were recorded with weaning weight (Table 2) and 508 were slaughtered. However, due to recruitment, only 41.2% of the slaughtered lambs were females. The mean age of the dams was 3.1 years, ranging from 1 to 7 years. The average number of lambs weaned was 2.3, ranging from 1 to 4. Eleven lambs were bottle fed.
None of the animals homozygous for either mutation carried the other mutation, implying that no crossover had occurred between the two mutations. The lambs could therefore be divided into six genotype groups, depending on which combination of mutations and wild type allele they carried (Table 2). Homozygous c.960delG-lambs were only produced the second year, since the rams used the first year did not carry this mutation.
The group of homozygous individuals for c.960delG was significantly different from the reference groups, both the wild type (GG_GG) and GG_AA for three of the observed traits (Table 3). The homozygous c.960delG animals had lower daily weaning weight gain (312 g per day), lower weaning weight (44.6 kg), but higher carcass weight (23.3 kg). Daily gain of slaughter weight was very similar for all groups, ranging from 134 to 143 g per day, with no significant differences.
For carcass conformation and carcass fat, both mutations increased or decreased, respectively, scores in comparison to those of the reference MSTN groups numerically (Table 3). For both traits, all genotype groups differed significantly (P < 0.05) from the wild type group (GG_GG), except GG_AG for carcass conformation. For both carcass conformation and carcass fat, the genotype G(delG)_GG was not significantly
---
| Table 2 Number of lambs per genotype group for various traits |
|-----------------------------|-----------------------------|-----------------------------|-----------------------------|-----------------------------|
| c.960 | GG | AG | AA | G(delG) | (delG)(delG) |
| c.2360 | | | | |
| Weight gain/d from birth to weaning (g) | 78 | 216 | 114 | 105 | 106 | 19 |
| Weaning weight (kg) | 78 | 219 | 114 | 107 | 107 | 19 |
| Carcass weight gain/d from birth to slaughter (g) | 59 | 165 | 84 | 92 | 89 | 15 |
| Carcass traits | 59 | 167 | 84 | 94 | 89 | 15 |
Guanine is found at the mutated position in wild types, both in the c.960 and the c.2360 position, while (delG) and adenine (A) respectively, are found when the mutations are present. Carcass traits are carcass weight, carcass conformation class and carcass fat class.
---
Boman et al. Genetics Selection Evolution 2010, 42(4) http://www.gsejournal.org/content/42/1/4 Page 3 of 7
different from the genoty pe GG-AA, while the genotypes G(delG)_AG and (delG)(delG)_GG resulted in significant (P < 0.001) effects, towards more meaty and less fatty animals. The wild type group had a carcass conformation class and fat class of 7.4 and 6.0, respectively; homozygotes for the c.2360G>A mutation had 8.1 and 5.1 respectively; and homozygotes for the c.960delG mutation showed the largest effect with 12.5 and 3.0, respectively (for illustration; see Figure 1).
The allelic effects are given in Table 4. The mutation in c.2360 showed a significant additive effect only on carcass conformation (0.3) and fat class (-0.4), and no significant effect of dominance. The mutation in c.960 significantly affected all traits, except for daily carcass weight gain. For this mutation, there were also significant dominance effects for four of these traits. For carcass conformation class, a significant interaction between the mutations was estimated.
**Discussion**
The results show that both the c.2360G>A and c.960delG mutations affect conformation and fat class in NWS lambs, yielding a carcass with less fat and increased muscle mass (Table 3 and 4). The effect of the c.960delG mutation is larger than that of the c.2360G>A mutation. This is in line with the results obtained by Boman et al. [2], who suggest this is most likely due to the different functional impact of the two mutations. The effect of the c.2360G>A mutation, as compared to the wild type, is slightly more pronounced in this experiment, compared to the material reported by Boman et al. [2]. However, in the experiment reported here, we were able to study more than one flock environment, a larger number of lambs in all MSTN-groups, and the farmers only partially decided which lambs to slaughter. In addition, the statistical model also accounted for the proper number of lambs following the ewe at weaning, rather than the number of lambs born.
There were no overlap between rams and years. It is possible that the genetic contribution from the rams and the flock-year effects may have been confounded, but this will not affect the relative size of effects of genotype classes. Also, lambs homozygous for the c.960delG mutation were only produced the second year. As the five other genotype classes were produced both years, this lack of complete cross classification should not be a problem.
Since the c.2360G>A-mutation is already segregating in NWS at a medium frequency (Table 2), we hypothesise that in the future this mutation will reach near-fixation in NWS, as in the Texel breed [1,9]. Therefore we tested the other MSTN-groups against the group homozygous for c.2360G>A, in addition to testing against the wild type.
In Norway, live weight is the most important criterion for deciding when to slaughter lambs. Thus, the higher carcass weight for the homozygous c.960delG mutation group may be explained by enlarged dressing.
Figure 1. A typical NWS lamb carcass, flanked by two carcasses homozygous for the MSTN mutation c.960delG. Carcass weight, EUROP conformation class and fat class (both on a 15 points scale), from the left: 29.5 kg, 15, 4; 18.9 kg, 8, 5, and 24.8 kg, 15, 3. Photo: Audun Flåtten, Animalia.
Table 4 Solutions ± standard errors for various traits and allelic effects
| Allelic effect | a2360 | d2360 | a960 | d960 | int. |
|--------------------------------------------------|--------|--------|--------|--------|--------|
| Weight gain/d from birth to weaning (g) | -3 ± 4 | -2 ± 5 | -2.001 ± 0.7 | 2.001 ± 8 | -7 ± 9 |
| Weaning weight (kg) | -0.6 ± 0.5 | -0.2 ± 0.6 | -2.8 ± 0.9 | 2.8 ± 1.0 | -0.5 ± 1.2 |
| Carcass weight gain/d from birth to slaughter (g) | 1 ± 2 | -2 ± 3 | 3 ± 3 | 4 ± 4 | -1 ± 5 |
| Carcass weight (kg) | 0.2 ± 0.2 | 0.3 ± 0.3 | 0.034 ± 0.4 | -0.2 ± 0.4 | 0.3 ± 0.5 |
| Carcass conformation class (scale 1-15) | 0.30001 ± 0.1 | -0.1 ± 0.2 | 2.00000 ± 0.2 | -1.00000 ± 0.3 | 0.004014 ± 0.3 |
| Carcass fat class (scale 1-15) | -0.40000 ± 0.1 | -0.2 ± 0.1 | -1.50000 ± 0.2 | 0.50000 ± 0.2 | 0.0 ± 0.3 |
Additive (a) and dominance (d) effect for mutations in position c.2360 and c.960 respectively, and the interaction effect (int), where both mutations are present. The P-value of genotype classes contrasted with the wild type (GG, GG) is presented as superscript, while the P-value for G(delG)_GG, G(delG)_AG and (delG)_GG contrasted with GG, AA is given in subscript. The P-values are given only for significant findings (P < 0.05).
percentage, indicated by the enhanced carcass conformation class for this group (Table 3). The reduced weaning weight and weaning weight gain per day (Table 3) also show that the group homozygous for c.960delG grows slowly. However, it is likely that a possibly enlarged dressing percentage, together with the fact that slaughter information was discarded for slow growing lambs in this group (Table 2), explain why the carcass weight gain per day is closer to that of other groups than expected from live weight gain.
The effects of the c.2360G>A mutation have also been examined in other studies. Before this mutation was reported, Laville et al. [10] had investigated the effect of the corresponding QTL in Belgian Texel sheep. They reported a QTL effect that increased conformation scoring and carcass weight, and reduced the fat score. Kijas et al. [9] had found that under Australian conditions, the g.+6723G>A mutation (equals the c.2360G>A mutation) had significant effects on slaughter measurements of muscle mass and fatness, but only minor impact on live weight and growth. These results correspond well with our findings.
Similarly, Hadjipavlou et al. [11] had studied the effect of the c.2360G>A mutation on Charollais lambs, and did not find any effect on live weight. With an animal model, AA animals were found to have significantly larger muscle depth than AG and GG animals, while AG and GG animals were not significantly different. None of the fat depths were significantly different. They concluded that the effect on phenotype depended on the genetic background, a point that is clearly demonstrated in our material for carcass conformation class, showing that animals heterozygous for the c.2360G>A mutation are strongly influenced by the genotype at the c.960 position.
Conclusions
In NWS, increased muscle mass and reduced carcass fat are caused by the c.960delG and the c.2360G>A mutations. The impact of c.960delG is more important compared to c.2360G>A, and displays dominance effects. In the rough grazing environment of this experiment, lambs homozygous for the c.960delG mutation experienced reduced growth rate.
Acknowledgements
We thank the producers that participated in the field experiment and Hans Vestjord for helping with collecting blood samples. Sille Karoliussen is acknowledged for excellent technical help. The project has received funding from the Research Council of Norway (project no 173923/110) and Marketing levies (paid by producers).
Author details
1Department of Animal and Aquacultural Sciences, Norwegian University of Life Sciences (UMB), PO Box 5003, N-1432 Ås, Norway. 2The Norwegian Association of Sheep and Goat Breeders, PO Box 104, N-1431 Ås, Norway. 3Animalia – Meat and Poultry Research Centre, PO Box 396 Økern, N-0513 Oslo, Norway. 4Centre for Integrative Genetics (CIGENE), Department of Animal and Aquacultural Sciences, Norwegian University of Life Sciences (UMB), PO Box 5003, N-1432 Ås, Norway.
Authors’ contributions
IAB carried out the experiment, performed the statistical analysis and drafted the manuscript. DIV was responsible for genotyping of the animals, and improved the manuscript, jointly with GK. All authors participated in planning the experiment, read and approved the final manuscript.
Competing interests
The authors have been granted a patent in the UK on the diagnostic method of gene testing for the c.960delG mutation (GB2433320).
Received: 4 March 2009 Accepted: 29 January 2010 Published: 29 January 2010
References
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2. Boman IA, Klemetsdal G, Blichfeldt T, Nafstad O, Våge DI: A frameshift mutation in the coding region of the myostatin gene (MSTN) affects carcass conformation and fatness in Norwegian White Sheep (Ovis Aries). Animal Genetics 2009, 40:418-422.
3. Elkie ED: Sauerarset. Forelesningsnotat Institutt for husdyravl, Ås-NLH 1976.
4. Maurtvedt A: Texelamma på NLH. En sprek og livat gjeng.
5. Johansen J, Aastveit AH, Egelandsdal B, Kvaal K, Roe M: Validation of the EUROP system for lamb classification in Norway: repeatability and accuracy of visual assessment and prediction of lamb carcass composition. Meat Science 2006, 74:497-509.
6. Groeneveld E: PEST user’s manual Germany, Institute of Animal Husbandry and Animal Behaviour, FAI 1990.
9. Kijas JW, McCulloch R, Edwards JEH, Oddy VH, Lee SH, Werf van der J. Evidence for multiple alleles effecting muscling and fatness at the Ovine GDF8 locus. *BMC Genetics* 2007, 8:80.
10. Laville E, Bouix J, Sayd T, Bibe B, Elsen JM, Lartuz C, Eychenne F, Marcq F, Georges M. Effects of a quantitative trait locus for muscle hypertrophy from Belgian Texel sheep on carcass conformation and muscularity. *J Anim Sci* 2004, 82:3128-3137.
11. Hadjipavlou G, Matika O, Clop A, Bishop SC. Two single nucleotide polymorphisms in the myostatin (GDF8) gene have significant association with muscle depth of commercial Charollais sheep. *Animal Genetics* 2008, 39:346-353.
doi:10.1186/1297-9686-42-4
Cite this article as: Boman et al: Impact of two myostatin (MSTN) mutations on weight gain and lamb carcass classification in Norwegian White Sheep (*Ovis aries*). *Genetics Selection Evolution* 2010 42:4.
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Shift of CO$_2$-I absorption bands in diamond: a pressure or compositional effect? A FTIR mapping study
Evgenii P. Barannik$^1$, Andrey A. Shiryaev$^{2,*}$, Thomas Hainschwang$^3$
1) Moscow Gemological Laboratory, Arbat St., 30/2, bld. 2, Moscow, Russia
2) A.N. Frumkin Institute of physical chemistry and electrochemistry, Russian Academy of Sciences, Leninsky pr. 31 korp. 4, 119071, Moscow
3) GGTL - GEMLAB Laboratory, Gnetsch, 42, LI – 9496 Balzers, Liechtenstein
* Corresponding author: Shiryaev A.A., email: [email protected] AND [email protected]
Abstract
Infra-red maps and profiles with high spatial resolution were obtained for two single crystal diamonds with pronounced CO$_2$ IR absorption peaks. Detailed examination allows unambiguous assignment of the spectral features to solid CO$_2$-I phase. It is shown that the distribution of IR band positions, intensities and widths in the sample follows regular patterns and is not chaotic as was suggested in previous works where spectra of a few individual spots were analysed. Consequently, pressure effects alone fail to explain all observed features and shifts of the CO$_2$ bands. Experimental data can be explained by presence of impurities (such as water, N$_2$, etc.) in the trapped CO$_2$. This implies that spectroscopic barometry of CO$_2$ microinclusions in diamond may be subject to poorly controlled bias. However, barometry is still possible if Davydov splitting of the CO$_2$-I $\nu_2$ band is unequivocally observed, as this indicates high purity of the CO$_2$ ice.
Keywords: diamond; CO$_2$ ice; Infra-red microscopy; barometry, impurity
1. Introduction
Carbon dioxide is an important metasomatic agent in Earth’s mantle and plays a major role in the carbon cycle. The presence of CO$_2$ in diamonds was inferred long time ago from mass-spectrometry studies (Melton et al., 1972, Melton and Giardini, 1974, 1975, 1981). Presence of carbon dioxide in some gem quality single crystal diamonds follows from IR spectroscopy (Schrauder and Navon, 1993; Chinn, 1995) and cryomicroscopy of fluid inclusions (Voznyak et al., 1992; Tomilenko et al., 1997; Smith et al., 2014). Based on the pressure-induced shift of CO$_2$ peak positions Schrauder and Navon (1993) inferred extremely high residual pressures reaching 5 GPa in one specimen, suggesting the presence of compressed solid CO$_2$. Even higher residual pressures, up to 20 GPa, were mentioned in an extensive investigation of CO$_2$-containing diamonds by Chinn (1995). In that work strong variations in the shape of the CO$_2$-related bands between different samples and even between analysis points in the same specimen were reported.
Investigation of a large set of polished diamonds with CO$_2$ IR bands (termed as “CO$_2$ diamonds”) using a beam condenser, i.e. allowing analysis of relatively small spots, revealed high variability of positions, widths, and relative intensities of CO$_2$ $\nu_3$ and $\nu_2$ bands (Hainschwang et al., 2006, 2008). These authors suggested that such a variability cannot be explained by the presence of CO$_2$ phase inclusions and tentatively proposed integration of CO$_2$-molecules in the diamond lattice. The presence of oxygen as a lattice impurity in diamond is plausible (Shiryaev et al., 2010 and references therein, Palyanov et al., 2016), but its correlation with the CO$_2$-absorption is uncertain. In this work, we report the results of a detailed investigation of diamond single crystals possessing CO$_2$ absorption bands using IR microscopy and discuss implications for diamond studies and for more general application of barometry of fluid inclusions in minerals based on spectroscopic data.
2. Samples and methods
Two CO$_2$-rich diamonds - FN7112 and FN7114 - were studied. Diamond FN7114 was described in Hainschwang et al. (2008). The samples were obtained commercially and their source is unknown. The stones were laser cut from gems and subsequently polished to make a double-sided plate. Both samples were treated at 6 GPa and 2100 °C for 10 minutes; the treatment did not influence the color and CO$_2$-related vibrations (Hainschwang et al., 2008). The sample FN7112 is 3.16 mm in diameter and 0.89 mm thick (mass 0.08 ct); the FN7114 dimensions are 2.51 mm and 1.03 mm (mass 0.06 ct), respectively. According to our previous X-ray topography study (Shiryaev et al., 2010), the samples are single crystals.
FTIR spectra were collected with a Nicolet iN10 FTIR microscope equipped with a liquid N$_2$-cooled MCT detector. The microscope and sample compartment were continuously purged with dry high-purity N$_2$ before and during spectral acquisition. Although strongly suppressed, traces of CO$_2$ gas were still observed in spectra. Assuming that this gas signal was from atmospheric contamination, a component of CO$_2$ gas (represented by the $\nu_2$ and $\nu_3$ bands) was included in the fit. The absorption of gaseous CO$_2$ for each spectrum was chosen in a way to minimize the difference between the experimental data and the model. This procedure is possible, firstly, because the shape of gaseous CO$_2$ absorption is known from independent atmospheric measurements, and secondly, because the bands of gaseous CO$_2$ and CO$_2$-I overlap only partially. All measurements were performed in transmission mode on free-standing samples at room temperature. For consistency, the microscope was focused on the upper surface of the sample. For the mapping, a square 150×150 μm$^2$ aperture and 100 μm step were used. For the profiles a 30×30 μm$^2$ aperture and 30 μm step were used. Due to high refractive index of diamond, the thickness-averaged size of the analyzing IR beam somewhat deviates from the quoted aperture size. Spectra were acquired in the 600-4000 cm$^{-1}$ spectral range. At least 64 scans per spectrum at a resolution of 2 cm$^{-1}$ were recorded.
FTIR spectra were processed using a custom Lua script for Fityk software (Wojdyr, 2010). The absorbance measurements were normalized to lattice absorption of a reference type IIa diamond sample; after the normalization, the spectrum of the type IIa reference was subtracted. Linear baseline correction was performed for each zone of interest. Most CO$_2$-related bands ($v_{2a}$, $v_{2b}$, $^{13}$CO$_2$ $v_{3b}$, $v_{3a}$) as well as carbonate and platelet bands were fitted with Gaussian distributions. Positions of relevant CO$_2$-related absorption bands are summarised in Table 1. The CO$_2$-I $v_{3b}$ band was approximated by two Gaussians with identical position. A Voigt profile was used for the peak at 3107 cm$^{-1}$ (tentatively assigned to a VN$_3$H-center, Goss et al., 2014).
Concentrations of nitrogen in A and B form were calculated after spectral decomposition in the one-phonon region and using coefficients from Boyd et al. (1994) and Kiflawi et al. (1994). Tentative identification of minerals in inclusions was made using compilation by Chukanov and Chervonnyi (2016). Plots and maps were created using Matplotlib library for Python (Hunter, 2007). All raw and processed FTIR spectra are available as Supplementary Materials.
Table 1. Assignment of the CO$_2$-related bands (Osberg and Hornig, 1952; Lu and Hofmeister 1995).
| Position (cm$^{-1}$) | Band | Assignment |
|---------------------|----------|-----------------------------------|
| 650 | $v_{2b}$ | CO$_2$-I, bending ($v_2$) mode |
| 660 | $v_{2a}$ | CO$_2$-I, bending ($v_2$) mode |
| 2299-2305 | $^{13}$CO$_2$ $v_{3b}$ | CO$_2$-I, $^{13}$CO$_2$ analog of the $v_3$ mode |
| 2369-2375 | $v_{3b}$ | CO$_2$-I, symmetric stretching ($v_3$) mode |
| 2415 | $v_{3a}$ | uncertain |
| 3615 | $v_3 + 2v_2$ | CO$_2$-I, overtone |
| 3740 | $v_3 + v_1$ | CO$_2$-I, overtone |
3. Results
3.1. The samples
Both studied diamonds are single crystals with a light greenish-brown color. Diamond FN7112 shows faint yellow fluorescence under ultraviolet light excitation, while diamond FN7114 is inert. The diamonds contain tiny inclusions of roughly hexagonal shape with dimensions of 5-10 µm and thickness of less than a micron (Fig. 1). In sample FN7112 the
inclusions are present in the whole body of the stone and are crystallographically oriented; in some regions larger plates appear to be surrounded by smaller ones, possibly indicating that decrepitation of some inclusions has occurred. In sample FN7114 the inclusions occur in clusters of up to ~10 plates. It is important to emphasize that there is no obvious correlation between abundance and distribution of these inclusions and infra-red features (including CO$_2$-related bands) described below. Similar inclusions were reported by Lang et al. (2007) and Hainschwang et al. (2020) and ascribed to graphite. Raman microscopy of the inclusions (excitation 532 and 785 nm), X-ray diffraction, X-ray fluorescence and phase tomography have not provided useful information, thus unambiguous identification of the inclusions is not yet possible. However, the hypothesis of the presence of graphite or other types of sp$^2$-carbon in the inclusions now appears to be less sound, given the high sensitivity of Raman spectroscopy with visible excitation to sp$^2$-C and the absence of any relevant features in our spectra. In addition, needle-like inclusions with length up to ~40 µm are also present (see also Hainschwang et al. 2020). The later ones clearly do not correspond to the hexagonal plates viewed edge-on as suggested by careful examination under several inclination angles and generally larger sizes of the needles.
In both samples unusual absorption features between ~900-1400 cm$^{-1}$ (one-phonon region) which cannot be ascribed to known nitrogen-related defects are observed (Fig. 2). Maxima of the bands are at 1060, 1120-1140, ~1245, ~1300 cm$^{-1}$, and a broad band with a maximum at ~1375 cm$^{-1}$ may also be related to this set of absorptions. A sharp peak at 1332 cm$^{-1}$ (Raman frequency of diamond) is always present, but its unique assignment is barely possible, since in crystals with diamond structure this vibration becomes IR-active in the presence of any defect, violating point symmetry of the matrix (Birman, 1974). These absorption bands were discussed in a previous study of CO$_2$-diamonds (Hainschwang et al., 2008). Similar features were observed in a recent study of diamonds from Chidliak, Canada (Lai et al., 2020); no microinclusions were observed microscopically in these samples (Lai, pers. comm). Broad bands, possibly related to water or OH-containing groups in inclusions, are observed in the 1450-1750 and 3200-3700 cm$^{-1}$ spectral regions for both samples (Fig. 2). Attempts to establish correlations between OH-related and carbonate bands were abandoned due to interference of broad bands with unknown origin, shapes and intensities.
Below we discuss in detail the spectral features of the studied diamonds.
**Figure 2.** Typical FTIR spectra of the studied diamonds showing analysis points with CO$_2$-related absorptions. A – the whole recorded range, B – one-phonon region. For diamond FN7114, the spectrum of the brown zone is shown. For clarity, the spectrum of the specimen FN7114 is vertically displaced by 2 cm$^{-1}$.
3.2. Diamond FN7112.
A photomicrograph of the sample is shown in Fig. 3A. The FTIR spectra of specimen FN7112 show carbonate (870 and 1430 cm$^{-1}$) and 800 cm$^{-1}$ (possibly a silicate, e.g. quartz)
bands, weak peaks at 3107 cm\(^{-1}\) and 3272 cm\(^{-1}\); maps of some of these features are shown in Fig. 3 B-D. Absorption by nitrogen-related A, B or C-centers is not detected. The bands at 650, 660 and 2370 cm\(^{-1}\) are due to CO\(_2\) \(\nu_{2a}\), \(\nu_{2b}\), and \(\nu_{3b}\) vibrations (Fig. 4 A, B); weak features at \(~3615\) and \(~3740\) cm\(^{-1}\) are \(\nu_3 + 2\nu_2\) and \(\nu_3 + \nu_1\) overtones, respectively (Fig. 4E). A very weak feature at 2300 cm\(^{-1}\) is due to \(^{13}\)CO\(_2\) \(\nu_{3b}\). The bands show no rotational splitting and are shifted from the position of gaseous carbon dioxide. We assign these bands to the CO\(_2\)-I phase, see Discussion for detail. The most intense of the bands, the \(\nu_{3b}\), appears symmetrical. In some spectra a shoulder at 2350 cm\(^{-1}\) due to residual CO\(_2\) gas in the spectrometer is visible.
The integrated area of the CO\(_2\)-I bands varies significantly across specimen FN7112 as shown by maps of \(\nu_{2b}\), \(\nu_{2a}\) and \(\nu_{3b}\) peaks (Fig. 3 E-G). The CO\(_2\) distribution is unrelated to strain observed in polarized light, but inversely correlates with intensity of the coloration: the CO\(_2\) bands are stronger in less intensely colored zone. Apparently, the number of visible hexagonal inclusions is not correlated with the intensity of CO\(_2\) absorption.
Figure 3. General view and FTIR maps of diamond FN7112. A - photomicrograph; red rectangle shows the position of the FTIR maps. Specimen diameter is 3.1 mm. Black rim is due to extinction in the crown; darkened roughly vertical fields to the right and left of the red rectangle - supporting polymer film. The FTIR maps are shown slightly larger than area marked on A to improve visibility. B - integrated area of 800 cm\(^{-1}\) band, C - integrated area of carbonate band; D - Integrated area of 3107 cm\(^{-1}\) peak. E-G - integrated areas of CO\(_2\)-related bands; H - position of \(\nu_{3b}\) band; I - residual pressure in CO\(_2\) inclusions calculated assuming absence of other factors influencing \(\nu_{3b}\) band position (see text for detail).
Figure 4. CO₂-related bands in FTIR spectra of the studied diamonds. A-D – examples of spectral decomposition for ν₂ and ν₃ regions. A, B – diamond FN7112; C, D – diamond FN7114. Experimental atmospheric spectra are shown for comparison. Residues show the difference between experimental data and the model. E - High frequency part of a diamond FN7114 spectrum.
3.3. Diamond FN7114
FN7114 is a diamond with distinct zoning; brown, yellow and (near) colorless zones are distinguished; IR-active features generally follow the zoning (Fig. 5). The colorless zone shows absorption by A, B-centers and platelets, superposed on unassigned bands (see Section 3.1). The three-phonon region possesses a complex shape between 3100-3300 cm⁻¹ with peaks at 3107, 3272 and very weak features at 3144, 3200, 3238, 3257 cm⁻¹. The ~800 cm⁻¹ band is rather uniformly distributed. Carbonates (possibly calcite) are detectable near the black feature visible in the right half of the diamond, which probably represents a healed fracture.
Figure 5. General view and FTIR maps of diamond FN7114. A - photomicrograph; red rectangle shows the position of the FTIR maps, arrow indicates direction of the profile. Specimen diameter is ~2.5 mm. Black rim is due to extinction in the crown; darkened roughly vertical fields to the left of the red rectangle – supporting polymer film. The FTIR maps are shown slightly larger than area marked on A to improve visibility. FTIR spectra of “black” mapped regions were obtained according to the standard procedure. FTIR maps: B, C, D, F – distribution of defects (see notations). E – nitrogen aggregation. Inclusions: G – integrated area of carbonate band; H – integrated area of 800 cm\(^{-1}\) band. I-O – CO\(_2\)-related bands. I - integrated area of \(\nu_{3a}\) band; J-L – integrated area, FWHM and position of \(\nu_{3b}\) band. M – residual pressure in CO\(_2\) inclusions calculated assuming absence of other factors influencing \(\nu_{3b}\) band position (see text for detail). N, O – integrated area and position of \(^{13}\)CO\(_2\) \(\nu_{3b}\) band.
It is convenient to discuss changes of the spectral features in different zones of the specimen using profile across the sample shown by vertical arrow in Fig. 5A; evolution of various features is shown in Figure 6. Peaks due to carbon dioxide vary considerably in intensity and shape between the zones (Figs. 5, 6). The colorless zone shows weak CO$_2$-I bands; the yellow zone exhibits the strongest CO$_2$-I absorption and the brown zone spectra show a weak CO$_2$-I band with an additional feature at 2415 cm$^{-1}$ (Fig. 6). Assignment of the band at 2415 cm$^{-1}$ ($\nu_{3a}$) is uncertain, but several possibilities are examined in the Discussion section. In addition, a small band at 2300 cm$^{-1}$ is observed. We assign it to the $\nu_3$ vibration of isotopically-substituted carbon dioxide molecule, i.e. $^{13}$CO$_2$ $\nu_{3b}$; the supporting evidence is given in the Discussion section.
**Figure 6.** Evolution of CO$_2$-related bands in FTIR spectra along the profile across diamond FN7114. For A-D spectra are normalized, but no other manipulations are performed. A, B – spectra of the brown zone. C, D – spectra of the yellow and colorless zone. Dashed vertical lines at 660 (A, C) and 2370 cm$^{-1}$ (B, D) are provided for visual reference. E, F – changes in band position and FWHM. Markers show band center positions; shaded regions are set to ±FWHM. The color scheme shows profile point number.
Along the profile, the CO$_2$-I $\nu_{3b}$ band broadens (FWHM increases from 20 to 55 cm$^{-1}$) and its center shifts from 2369 to 2375 cm$^{-1}$; the $^{13}$CO$_2$ $\nu_{3b}$ isotopic band behaves in a similar way (Fig. 6). The position of the $\nu_{2a}$ band does not change significantly, while its FWHM increases from 8 to 17 cm$^{-1}$. Upon broadening of the more intense $\nu_{2a}$ band, the $\nu_{2b}$ component turns into a shoulder, introducing uncertainty into its position for the zone containing nitrogen defects.
Examination of distribution of the CO$_2$-related and carbonates bands does not allow to establish a solid correlation. Whereas for diamond FN7112 these phases might be correlated, for sample FN7114 no relation is apparent. Therefore, it is unclear whether CO$_2$-carbonate correlation exists.
Figure 7A shows evolution of integrated areas of the CO$_2$-related bands and nitrogen concentration along the profile. At the transition from the brown to yellow zone (points 20-30), the absorption of CO$_2$-I rapidly increases and the $\nu_{3a}$ band disappears. Simultaneously, defect-related bands in the 900-1400 cm$^{-1}$ region undergo a complex shape change; total absorption diminishes; the peak at 1332 cm$^{-1}$ becomes more prominent. In the same time, absorption in the ranges 1450-1750 and 3200-3700 cm$^{-1}$ becomes stronger.
**Figure 7.** Evolution of CO$_2$ and N-related IR features along the profile across diamond FN7114. A — concentration of nitrogen-related defects and areas of $\nu_{3a}$ and CO$_2$-I $\nu_{3b}$ (the area of CO$_2$-I $\nu_{3b}$ band is multiplied by 0.25). B - Nitrogen aggregation plot for diamond FN7114. The activation energy and Arrhenius constant are from Taylor et al. (1990). The data are corrected for laboratory-based HPHT annealing described by Hainschwang et al. (2008). The color scheme shows profile point number.
Since the studied sample represents a laser-cut polished piece of a gem diamond, identification of the growth direction is not trivial. X-ray topography does not reveal obvious growth dislocations, partly due to the moderate degree of plastic deformation. However, examination of a plot of nitrogen concentration vs N aggregation state (Fig. 7B) might give a clue. If one assumes that the diamond growth proceeded in a gradually cooling system, the N aggregation plot suggests that the N-containing zone reflects late stages of the crystal formation. This does not necessarily imply absence of N in the growth medium; it rather indicates unfavorable conditions for incorporation of this impurity. The content of N in the form of common A and B defects gradually increases towards the end of the profile (Fig. 7A). We note, however, that any hypothesis about the N concentration in the FN7114 diamond may be somewhat simplistic, since we do not know yet whether the defects giving rise to absorbance in the one-phonon region contain nitrogen or not.
4. Discussion
4.1. Band assignment.
4.1.1. Major CO$_2$-I bands
At room temperature, CO$_2$ crystallizes into a cubic phase I between 0.6 GPa and 2 GPa (Lu and Hofmeister 1995, Olijnyk and Jephcoat, 1995); the variations in the transition pressure are ascribed to the size of the CO$_2$ droplets and, possibly, the nature of the surrounding medium. In the pressure range of ~8-13 GPa a transition into orthorhombic CO$_2$-III occurs (Lu and Hofmeister, 1995). Fundamental modes and, consequently, IR spectra of these phases differ. The IR spectrum of CO$_2$-I shows two bending bands ($\nu_{2a}$, $\nu_{2b}$) and a single asymmetric stretching band ($\nu_3$). The CO$_2$-III spectrum is characterized by splitting of the fundamental modes, showing in total three bending and two stretching bands. With increasing pressure, the stretching and bending vibrations have positive and negative shifts, respectively, in both phases I and III.
(Hanson and Jones, 1981; Lu and Hofmeister, 1995). If the \( \nu_2 \) and \( \nu_3 \) bands observed in our work indeed arise from the CO\(_2\)-I phase, a linear correlation between their areas is expected. Figure 8 shows correctness of this assumption for both samples. We emphasize that the spectra of the brown zone in diamond FN7114 show two main components in the \( \nu_3 \) region — \( \nu_{3a} \) and \( \nu_{3b} \). Only \( \nu_{3b} \) appears to correspond to the CO\(_2\)-I phase; areas of \( \nu_{3a} \) and CO\(_2\)-I bands are inversely correlated. Based on the observed number of bands, positions and \( \nu_{2b} + \nu_{2a} \) to \( \nu_{3b} \) area correlation, we can confidently assign \( \nu_{2b} \), \( \nu_{2a} \), \( \nu_{3b} \) to the CO\(_2\)-I phase.
**Figure 8.** Correlation of the integrated area of CO\(_2\) \( \nu_2 \) and \( \nu_3 \) bands for studied diamonds. A — \( \nu_{2a} + \nu_{2b} \) and \( \nu_{3b} \) bands for diamond FN7112. Datasets for both map and profile through diamond FN7112 are shown. B — \( \nu_{2a} + \nu_{2b} \) and \( \nu_{3b} \) bands for diamond FN7114.
A \( \nu_{2b} \) band centred at 650 cm\(^{-1} \) contributes up to 15\% to the \( \nu_{2a} \) (660 cm\(^{-1} \)) area. It behaves differently from that of \( \nu_{3b} \) and the 2415 cm\(^{-1} \) peak (the \( \nu_{3a} \) band, see below), transforming into a shoulder in the nitrogen-rich zone of the diamond. The \( \nu_{2a} \) and \( \nu_{2b} \) bands correspond to CO\(_2\) bending influenced by Davydov splitting. Lattice disorder markedly influences the magnitude of the Davydov splitting in molecular crystals. In particular, addition of 10\% of H\(_2\)O into CO\(_2\) ice leads to suppression of the splitting (Baratta and Palumbo, 2017). Consequently, the presence of distinct \( \nu_{2b} \) absorption may indicate purity of CO\(_2\)-ice in inclusions.
4.1.2. Isotopic $^{13}$CO$_2$-ν$_{3b}$ band
A weak band at 2300 cm$^{-1}$ (Fig. 4 B,D) is observed in the whole mapped region of sample FN7114 (Fig. 5K) and in zones with relatively high CO$_2$ absorption in diamond FN7112 (Fig. 4B). The measurement of the 2300 cm$^{-1}$ band is complicated due to its superposition on intrinsic diamond absorption bands. For the profile across the sample FN7114, the area of 2300 cm$^{-1}$ band was measured to be 0.5-1.2% of ν$_{3b}$ area. This band is redshifted 70 cm$^{-1}$ from the CO$_2$ ν$_{3b}$ peak and its position varies along the profile from 2299 to 2305 cm$^{-1}$ whereas the ν$_{3b}$ peak shifts from 2369 to 2375 cm$^{-1}$. The FWHM and spatial distribution of the ν$_{3b}$ and 2300 cm$^{-1}$ bands behave in a similar manner. In harmonic approximation, substitution with a heavy isotope should redshift absorption bands and the area of the relevant band should correspond to the isotopic fraction, i.e. ~1.1 % in the case of carbon. For crystalline CO$_2$ the ν$_{3}$ $^{13}$CO$_2$ band is located at 2283 cm$^{-1}$ and is redshifted 62 cm$^{-1}$ from ν$_{3}$ $^{12}$CO$_2$ peak at 2345 cm$^{-1}$ (Dows and Schettino, 1973). Based on the observed changes in intensity, position and width, the 2300 cm$^{-1}$ band can be assigned to the ν$_{3b}$ mode of $^{13}$CO$_2$; thus we denote the 2300 cm$^{-1}$ band as $^{13}$CO$_2$ ν$_{3b}$.
4.1.3. The 2415 cm$^{-1}$ (ν$_{3a}$) band
A band at 2415 cm$^{-1}$ denoted as ν$_{3a}$ (Chinn, 1995) is observed in spectra of FN7114, but is practically absent in spectra of diamond FN7112 (Fig. 4 B,D). This band can be enhanced by HPHT treatment of CO$_2$ diamonds (Hainschwang et al. 2008). According to our data, the ν$_{3a}$ band area can reach 70% of the ν$_{3b}$. Analyzing its behavior along the profile, one can see that this band is relatively intense in the brown part of the sample FN7114, but almost disappears closer to the N-containing zone. The gradual disappearance of this band correlates with an increase of broad features between 3200-3700 and 1450-1750 cm$^{-1}$ (possibly, OH-related) and a weak peak at 800 cm$^{-1}$. Judging from spectra with prominent 2415 cm$^{-1}$ band, its position and FWHM (~55 cm$^{-1}$) are approximately constant. The assignment of this band is uncertain, but several possibilities are discussed below.
Hainschwang et al. (2008) assigned the ν₃a band to a highly shifted ν₃. However, detailed examination shows that the ν₃a band cannot be assigned to the CO₂-I or CO₂-III macroscopic phases. The value of 2415 cm⁻¹ exceeds wavenumbers possible for CO₂-I phase as it would imply pressures outside of the CO₂-I stability field. For the CO₂-III phase an increase of pressure from 9 to 20 GPa shifts ν₃ bands from 2408 to 2436 cm⁻¹ and from 2351 to 2369 cm⁻¹ (Lu and Hofmeister, 1995). The assignment of the 2415 cm⁻¹ band to the CO₂-III phase would also imply existence of a more intense feature centered at ~2355 cm⁻¹, which is actually absent.
Secondly, the CO₂ bending mode in spectra from sample FN7114 is doubly split, showing only ν₂a and ν₂b components, excluding the CO₂-III phase. However, the ν₃b and ν₃a bands appear to be closely linked. Figure 7A shows that areas of ν₃a and ν₃b bands are inversely related by a factor of 2-3. Moreover, if the ν₃a band is assigned to a shifted ν₃, the linear dependence between the ν₂ and ν₃ area is violated for sample FN7114 (Fig. 9). If we assume that the ν₃a band is not related to the ν₃ mode of CO₂-I, the linearity is restored.
**Figure 9.** Correlation of the integrated areas of ν₂a+ν₂b and ν₃b+ν₃a bands for diamond FN7114. Presence of several segments is explained by evolution of areas of corresponding bands along the profile. Profile points between 1-20 and 20-35 are influenced by ν₃a and thus deviate from linearity.
The 2415 cm⁻¹ band could be a ν₃ LO (longitudinal optical) phonon mode, provided that the thickness of the substance is sufficiently small and/or the incident IR beam is not perpendicular to the CO₂ film surface (Berreman, 1963). At low temperatures in pure CO₂ ice.
the LO phonon is blueshifted 39 cm\(^{-1}\) from the TO (transverse optical) mode. The shape and maximum position of the LO band depends on the presence of impurities in the ice (Cooke et al., 2016). It should be noted, however, that we do not observe features unambiguously assigned to the \(v_2\) LO phonon mode.
And last but not least, the \(v_{3a}\) feature may represent hydrogen bonds in hydrogen carbonates. For example, bands with important features in the relevant spectral range are observed in CO\(_2\)·H\(_2\)O complex and carbonic acid (Zheng and Kaiser, 2007); broadly similar spectra are reported for KHCO\(_3\) single crystal (Lucazeau and Novak, 1973). Albeit it readily decomposes at ambient conditions, carbonic acid is stable at pressures of several GPa and rather high temperatures (Wang et al., 2016, Abramson et al., 2017). Of course, IR spectra of both carbonic acid and KHCO\(_3\) contain numerous bands absent in our case. Nevertheless, hydrogen bonds in protonated carbonate species are among plausible species responsible for the 2415 cm\(^{-1}\) peak, since local environment of HCO\(_3\)\(^-\) ions may lead to marked spectral variations. If this assumption is correct, behavior of this band along the profile may correspond to gradual disappearance of the protonated compounds into CO\(_2\) and aqueous solution. A related process of diamond formation by pH drop was recently proposed by Sverjensky and Huang (2015).
4.2. Shift of CO\(_2\) IR bands
Several independent mechanisms may be responsible for blueshift of CO\(_2\) \(v_3\) absorption bands and may influence their shapes: a) residual pressure; b) size, shape and eventual heterogeneous structure of CO\(_2\) precipitates; c) strong interaction of CO\(_2\) with matrix; d) presence of impurities in the CO\(_2\). These possibilities are considered in detail below.
4.2.1. Pressure effects.
In the case of CO\(_2\)-containing microinclusions in diamond, the most common explanation for the shifted CO\(_2\) absorption bands is high residual pressure (e.g., Schrauder and Navon, 1993,
Residual CO$_2$ pressure may be estimated from the pressure shift of the absorption bands using the experimental data of Hofmeister and Lu (1995) and Hanson and Jones (1981). In our work spectra with a CO$_2$ $\nu_{3b}$ area of at least 125 cm$^{-2}$, for which relatively precise peak position measurements were possible, were used for this purpose. The calculated pressures vary significantly for both samples. In sample FN7114 the values are 3.7-5.0 GPa (Fig. 5O). The observed positions of $\nu_{2a}$ and $\nu_{2b}$ also fit the expected values for ~4 GPa. However, the $\nu_{2a}$ pressure derivative is too small for meaningful calculations using the available data; precise determination of $\nu_{2b}$ position is difficult due to its transformation into a shoulder. For sample FN7112 only some points have $\nu_{3b}$ area of more than 125 cm$^{-2}$, so reported maps are incomplete. For sample FN7112 calculated pressures are 3.7-4.2 GPa (Fig. 3I).
The principal problem with the attribution of the blueshifted bands to pressure effects only lies in the peculiar spatial distribution of inferred pressures in the diamonds. This was noted already in previous works (Schrauder and Navon 1993, Chinn 1995, Hainschwang et al. 2008) and is addressed in more detail in the present work. In sample FN7112, the CO$_2$ bands with the largest shift (the highest inferred pressure) form irregular zones. In diamond FN7114, the inferred residual pressure increases upon approaching the nitrogen-containing zone. The nitrogen aggregation plot for the latter diamond indicates that temperature was most likely decreasing during crystallization of the N-containing zone, which is difficult to reconcile with increasing pressure. Note, however, that nitrogen may be contained in IR-inactive defects or in unidentified defects with unknown IR cross-section. The IR beam may eventually average over several growth horizons, although this contribution appears to be minor, since the trend on the Taylor plot does not show sharp or erratic changes.
From calculations based on elasticity theory, Anthony and Meng (1997) suggested that certain spatial distributions of microinclusions may indeed generate stresses approaching the crushing strength of diamond and lead to plastic deformation. In principle, partial release of the residual pressure by the plastic flow might be able to explain the gradual changes of CO$_2$ bands.
positions. Chinn (1995) suggested that extremely high pressures in some of diamonds are explained by partial graphitization of the inclusion walls, see Anthony (1994) for relevant calculations. However, several observations indicate that pressure alone cannot be the cause of the band behavior: a) the pressure hypothesis does not explain the observed decrease of the absorption and band broadening; b) lack of correlation between the inclusions observed microscopically and the CO$_2$ absorption peaks casts doubt on the “stress” hypothesis. X-ray topographs of these stones shows numerous small specks, which are almost certainly due to localized strain fields surrounding hexagonal inclusions. In the same time, X-ray topography, being a sensitive method, shows rather moderate degree of deformation and distribution of stress in the samples does not follow evolution of the CO$_2$-related IR bands.
4.2.2. Crystallography and structure of CO$_2$ precipitates
In thin crystals with cubic symmetry a LO phonon may appear in transmission mode IR measurements (Berreman, 1963); for thin layers of CO$_2$ ices this was well demonstrated by Escribano et al. (2013). This effect may strongly distort the “standard” spectrum and novel peaks may appear as blueshifted bands of CO$_2$. It was also shown (Signorell et al., 2006; Isenor et al., 2013) that in core-shell CO$_2$-N$_2$O and CO$_2$-H$_2$O nanoparticles the spectral envelope very strongly depends on the thickness of the layers (particle structure), shape and composition of the particles. Some of the CO$_2$-diamonds from Chinn (1995) (e.g., GC 859C, 727H, 874-C1 and C-2, 790B) show spectra remarkably similar to those modelled and measured by Isenor et al. (2013). Variations of composition and structure of the CO$_2$-containing inclusions may explain at least part of the observed complexity. We also note that, due to limited spectral resolution (2 cm$^{-1}$) of our experiment, variations in chemistry, shape, and stress state experienced by the CO$_2$-species, fine structure of the CO$_2$ absorption bands may be unresolved.
4.2.3. Matrix interaction
Hainschwang et al. (2008) used the anomalous shifts, FWHM and intensities of bands assigned to CO$_2$ to propose that in the studied diamonds those features cannot be explained by microinclusions of CO$_2$. Instead, they suggest that exsolution of oxygen impurities in the diamonds may form CO$_2$ molecules and that their interaction with the diamond lattice is responsible for the observed spectral peculiarities. This scenario is qualitatively similar to the behaviour of CO$_2$-molecules in channels present in the structure of cordierite and some other minerals (see Chukanov and Chervonnyi (2016) and references therein). For the diamond case, models resembling sub-nm voids with fullerene-like walls were considered, but correspondence between the calculations and experimental spectra is, at best, qualitative (Adjizian et al., 2009). Refinement of this model requires very detailed analysis of atomic structure of the void walls, not performed yet. Assignment of the observed regular evolution of IR bands across diamond crystals to the voids filled with pure CO$_2$ necessitates a mechanism of similar changes in the void structure.
4.2.4. Influence of impurities in CO$_2$.
A hypothesis, which, in our view, better fits experimental data, is discussed below. The presence of impurities in CO$_2$ ice may influence positions, width and splitting of IR features. For example, in mixed CO$_2$-H$_2$O ice an increase of water fraction from 22 to 75% leads to blueshift of the $\nu_3$ maximum by almost 9 cm$^{-1}$ (Cooke et al., 2016). Judging solely by the position of the $\nu_3$ maximum, such blueshift can be interpreted as an increase in pressure by ~1.5 GPa, which is obviously not the case. As already mentioned, admixture of water also leads to band broadening and a loss of $\nu_2$ Davydov splitting occurs (Cooke et al., 2016). Raman study of fluid N$_2$-CO$_2$ inclusions in natural diamonds also suggest a strong influence of chemical composition on spectral features (Smith et al., 2014). Examination of a profile across the FN7114 sample shows gradual evolution of position, FWHM and intensity of the CO$_2$-bands. In the nitrogen-rich zone
CO$_2$-I bands become weaker, broader and shifted. All those phenomena can be explained by an increase of the impurity fraction in the CO$_2$ ice.
4.3. Implications for oxygen in diamond.
Conclusive evidence for oxygen impurities in the diamond lattice remains elusive. However, there is a growing body of evidence that several spectroscopic features of diamonds could be related to this impurity: an optical absorption band with a peak at 480 nm (Hainschwang et al., 2008), a peak at 1060 cm$^{-1}$ in IR (Malogolovets and Nikityuk, 1978, Palyanov et al., 2016) and the 566 nm luminescence band (Palyanov et al., 2016). Earlier works (Hainschwang et al 2008, Schrauder and Navon, 1993) indicated that the CO$_2$ IR absorption is stronger in regions with lower concentrations of N-related defects, see also Fig. 7 A from the present study. SIMS investigation of a large set of diamonds showed the existence of a positive correlation between total N and O contents (Shiryaev et al., 2010). Since the later element is clearly present as a substitutional impurity, this correlation appears to support the hypothesis of oxygen-related defects in the diamond lattice. We stress that the proportionality coefficient between N and O in SIMS data for the CO$_2$ and pseudo-CO$_2$ diamonds differs considerably from those in samples lacking CO$_2$ IR features. It was suggested that the coexistence of these two impurities in a given volume and their interaction prevents formation and/or hinders IR manifestations of well-known N defects and at least part of the SIMS and X-ray scattering results can be explained by formation of N-O-containing inclusions.
One of the main results of the present study is that the position and intensity of the CO$_2$ peaks in diamonds are not entirely random, but, instead, gradual changes and/or domains enriched in CO$_2$ are present. In many cases, crystallographic zoning revealed by cathodoluminescence is present (Chinn, 1995, Hainschwang et al., 2008). All studies of CO$_2$-diamonds mention anticorrelation of the carbon dioxide features and IR-active N and H impurities in the diamond lattice. Our detailed FTIR mapping and profiling show that although
some amount of structural hydrogen and nitrogen is definitely present in all parts of the studied samples as manifested by the 3107 cm\(^{-1}\) peak, the CO\(_2\)-absorption bands indeed become weaker with increased concentration of common A and B defects. Interestingly, diamond synthesis in CO\(_2\)-rich alkaline systems always produces N-rich crystals (Khokhryakov et al., 2016, Palyanov et al., 2016). Incorporation of nitrogen in diamond is clearly a complex function of N speciation and abundance in the growth medium, which, in turn, depend on its composition and fO\(_2\). Therefore, the CO\(_2\)-N(H) dependencies suggest the importance of the composition of the growth medium on the prominence of the CO\(_2\)-features. Changes of fluid chemical composition will be pronounced not only in IR spectra of hydrous fluids or melts captured by diamonds (Zedgenizov et al., 2005; Weiss et al. 2013), but also in spectra of CO\(_2\)-bearing diamonds.
5. Conclusions
A detailed FTIR investigation of polished plates cut from two CO\(_2\)-rich single crystal diamonds reveals that changes of the CO\(_2\)-related IR features are not as random as it might seem from examination of bulk samples. Regular evolution of the position of the bands, FWHM and intensity is recorded for one of the samples; for the second stone, several domains with highly variable spectra are observed. Consideration of various possible mechanisms responsible for blueshift of CO\(_2\)-absorption bands suggests that the observed spectral shifts cannot be explained exclusively by the residual pressure assumption. In our view, accounting for impurities (primarily aqueous and N-containing species) in entrapped CO\(_2\) ice is necessary for consistent explanation of the data. In future works spatially resolved spectroscopic measurements are preferred over the bulk ones, otherwise strong peak overlap may occur.
An important implication of our results is that shifts of CO\(_2\)-related bands in diamonds should be employed as a barometer with great care. If unaccounted for, impurities in CO\(_2\) ice can introduce significant bias. In high purity CO\(_2\)-I the \(v_2\) band is subject to Davydov splitting. Consequently, CO\(_2\) spectroscopic barometry gives unambiguous results only in cases when
Davydov splitting of CO$_2$ v$_2$ band is clearly observed. Schrauder and Navon (1993) reported a strong asymmetry of the v$_2$ CO$_2$ band, but in their spectrum there is no obvious Davydov splitting. This may indicate the presence of impurities in CO$_2$ ice in their sample. Thus, the reported residual pressure appears to be overestimated as it was calculated solely based on the position of the CO$_2$ bands.
Our results allow to explain the nature of CO$_2$ related bands in CO$_2$-diamonds by the presence of impure CO$_2$-I in microinclusions. However, this does not exclude the possibility of the presence of oxygen as a lattice impurity in diamonds.
**Supplementary materials**
All raw and processed FTIR spectra are available as Supplementary Materials at: “FTIR maps and profiles for CO2-rich diamonds”, Mendeley Data, V2, doi: 10.17632/yjrgv5fhhm.2.
**Acknowledgments**
The study was partly supported by RFBR grant 13-05-91320-SIG-a to AAS. We thank Dr. A. Shapagin for access to FTIR microscope and Uladzislava Dabranskaya from Utrecht University for creation of the graphical abstract. We highly appreciate thorough consideration of the manuscript and highly useful comments made by two anonymous reviewers.
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Production of CRISPR/Cas9-Mediated Self-Cleaving Helper-Dependent Adenoviruses
Donna J. Palmer,1 Dustin L. Turner,1 and Philip Ng1
1Department of Molecular and Human Genetics, Baylor College of Medicine, One Baylor Plaza, Houston, TX 77030, USA
Prolonged expression of CRISPR/Cas9 raises concerns about off-target cleavage, cytotoxicity, and immune responses. To address these issues, we have developed a system to produce helper-dependent adenoviruses that express CRISPR/Cas9 to direct cleavage of the vectors’ own genome after transduction of target cells. To prevent self-cleavage during vector production, it was necessary to downregulate Cas9 mRNA as well as inhibit Cas9 protein activity. Cas9 mRNA downregulation was achieved by inserting the target sequences for the helper-virus-encoded miRNA, mivaRNAi, and producer-cell-encoded miRNAs, hsa-miR183-5p, and hsa-miR218-5p, into the 3’ UTR of the HDAd-encoded Cas9 expression cassette. Cas9 protein activity was inhibited by expressing anti-CRISPR proteins AcrIIA2 and AcrAI4 from both the producer cells and the helper virus. After purification, these helper-dependent adenoviruses will perform CRISPR/Cas9-mediated self-cleavage in the transduced target cells, thereby limiting the duration of Cas9 expression and thus represent an important platform for improving the safety of gene editing by CRISPR/Cas9.
INTRODUCTION
CRISPR/Cas9 has revolutionized genome editing because of its efficiency and ease of use. However, the prolonged expression of Cas9 in target cells raises important safety concerns regarding off-target cleavage, cytotoxicity, and immune responses.1–3 To maximize safety, Cas9 expression should be transient, ceasing after the desired DNA double-strand break has been accomplished. In this study, we have achieved this by developing a system for producing helper-dependent adenoviruses (HDAds) that express Streptococcus pyogenes CRISPR/Cas9, which directs self-cleavage of the vectors’ own genome following transduction of target cells. HDAds have no viral genes and are excellent for many gene- and cell-therapy applications because they can mediate high-efficiency transduction of many different cell types from many different species in vivo and in vitro independent of the cell cycle, they have an enormous cloning capacity of 36 kb, they do not integrate into the host genome, and they provide long-term transgene expression with reduced toxicity.4 Thus, this system can be used to improve the safety of CRISPR/Cas9 gene editing, and its utility and implications are discussed.
RESULTS
Producing a CRISPR/Cas9-mediated self-cleaving HDAd was not our original objective. Instead, we were originally interested in producing an all-in-one HDAd for homology-directed repair (HDR) by gene targeting (Figure 1). This is because we38 and others7–18 have shown that HDAds can efficiently deliver donor DNA into cells to achieve gene targeting by spontaneous homologous recombination. We hypothesized that the efficiency of gene targeting by HDAd could be further improved by incorporating CRISPR/Cas9 to introduce a recombinogenic double-strand break (DSB) at the chromosomal target (Figure 1). Thus, we constructed an all-in-one HDAd (called HD+donor+sgRNA+Cas9) that contained the donor DNA and expressed Cas9 and single-guide RNA (sgRNA) to target the chromosome (Figures 1 and 2A). To avoid self-cleavage of the all-in-one HDAd during vector production, the canonical 5′ CA 3′ protospacer adjacent motif (PAM) in the donor was mutated to 5′ TCA 3′ (Figures 1 and 3A). However, HD+donor+sgRNA+Cas9 could not be produced with our standard 116 producer cells19 and our standard helper virus AdNG163;20 multiple viral bands were present after cesium chloride (CsCl) ultracentrifugation (Figure 3C) and restriction analysis of the virion DNA (Figure 4, lane 3) revealed that it did not match the expected pattern of the plasmid from which it was derived (Figure 4, lane 4). These results indicate that the vector had undergone genomic rearrangement. Sequencing of the HD+donor+sgRNA+Cas9 virion DNA revealed site-specific Cas9 cleavage (Figure 3C) compared to the expected sequence of its parental plasmid (Figure 3B); the sequence is interpretable and as expected up to the Cas9 cleavage site, but afterward it becomes uninterpretable, and this can be attributed to the formation of insertions and deletions (indels) due to non-homologous end joining (NHEJ) as a consequence of site-specific Cas9 cleavage (Figure 3C). Together, these results indicate that during production of HD+donor+sgRNA+Cas9, CRISPR/Cas9-mediated site-specific self-cleavage occurred despite mutating the PAM in the donor from 5′ CA 3′ to 5′ TCA 3′. That CRISPR/Cas9 can cleave at sgRNA target sites without a canonical 5′ CCN 3′ PAM has been observed, albeit at much reduced efficiencies.21–23 And this is likely exacerbated during vector production because the HDAd genome containing the Cas9 expression cassette is replicated to 105 to 106 copies,24 which results in an enormous amount of Cas9 in the producer cells leading to efficient site-specific cleavage of the donor DNA, even with the 5′ CA 3′ to 5′ TCA 3′ PAM.
mutation. It was our desire to produce this all-in-one HDAd without genomic rearrangement that led to the successful development of a system to produce a CRISPR/Cas9-mediating self-cleaving HDAd as detailed below.
One possible strategy to overcome CRISPR/Cas9-mediated self-cleavage is to downregulate Cas9 mRNA during vector production by miRNA. Two such strategies have been described to downregulate transgene expression from the HDAd during its production. The first strategy makes use of two microRNAs (miRNAs), hsa-miR183-5p and hsa-miR218-5p, expressed exclusively by the HDAd producer cells. The second strategy makes use of a miRNA expressed by the helper virus called mivaRNAI. Because these miRNAs are only present during vector production, transgene expression from the HDAd is unimpeded in the transduced target cells. We utilized both strategies by inserting the target sequence for these three miRNAs in the 3′ UTR of the Cas9 expressed to create HD-donor-sgRNA-Cas9miR (Figure 2B) and attempted to produce this vector in 116 cells with AdNG163. Unfortunately, multiple viral bands were observed following CsCl ultracentrifugation, indicating vector genome rearrangement (Figure 3D).
Encouragingly, the number of virus bands was reduced compared to that observed for HD+donor+sgRNA+Cas9, suggesting the miRNA strategy reduced but did not eliminate CRISPR/Cas9-mediated self-cleavage. Restriction analysis of the HD+donor+sgRNA+Cas9miR virion DNA (Figure 4, lane 5) revealed that it did not match the expected pattern of the plasmid from which it was derived (Figure 4, lane 6). These results indicate that the vector had undergone genomic rearrangement. Sequence analyses of the HD+donor+sgRNA+Cas9miR virion DNA revealed site-specific Cas9 cleavage (Figure 3D) compared to the expected sequence of its parental plasmid (Figure 3B); the sequence is as expected up to the Cas9 cleavage site, after which it becomes uninterpretable because of indel formation due to NHEJ (Figure 3D). Again, it was encouraging that the sequence of HD+donor+sgRNA+Cas9miR was more “interpretable” than that of HD+donor+sgRNA+Cas9 (Figure 3C), again indicating that the miRNA strategy was able to reduce but not eliminate CRISPR/Cas9-mediated self-cleavage during HDAd production even with the PAM mutated from 5’ CCA 3’ to 5’ TCA 3’.
Encouragingly, production of HD+donor+sgRNA+Cas9miR in 116 cells with AdNG163Acr yielded a single virus band following CsCl ultracentrifugation (Figure 3E). Also encouraging was that restriction analysis of the HD+donor+sgRNA+Cas9miR virion DNA (Figure 4, lane 9) revealed a pattern that was indistinguishable to the plasmid from which it was derived (Figure 4, lane 10). Finally, sequence analysis of HD+donor+sgRNA+Cas9miR virion DNA revealed the expected sequence with no evidence of indel formation at the Cas9 cleavage site (Figure 3E). Taken together, these results indicate that the all-in-one HD+donor+sgRNA+Cas9miR could be successfully produced in 116 cells with AdNG163Acr.
Although the combination of miRNA and anti-CRISPR proteins expressed from the helper virus permitted for the production of HD+donor+sgRNA+Cas9miR, it should be emphasized that the CRISPR/Cas9 target in the vector contained the 5’ CCA 3’ to 5’ TCA 3’ PAM mutation. Would this same strategy permit successful production of CRISPR/Cas9-mediated self-cleaving HDAd with a bona fide 5’ CCN 3’ PAM? The significance of producing such a
vector will be addressed in the Discussion. To answer this question, we created two new HDAds designed to self-cleave their own reporter LacZ transgene, called HD+LacZ+sgRNA633+Cas9miR and HD+LacZ+sgRNA86+Cas9miR (Figures 2D and 2E), and proceeded to produce them in 116 cells with AdNG163Acr. HD+LacZ+sgRNA633+Cas9miR and HD+LacZ+sgRNA86+Cas9miR differ in the sgRNA sequence used to self-cleave the LacZ transgene, and both contain targets for mivaRNAI, hsa-miR183-5p, and hsa-miR218-5p in the 3′ UTR their Cas9 expression cassettes. As shown in Figures 5A and 5D, only a single virus band was visible following CsCl ultracentrifugation. Restriction analyses of virion DNA from both vectors (Figure 4, lane 14 for HD+LacZ+sgRNA633+Cas9miR and lane 17 for HD+LacZ+sgRNA86+Cas9miR) revealed a pattern indistinguishable from their parental plasmids (Figure 4, lanes 13 and 19, respectively), and with additional faint bands consistent with the AdNG163Acr (see Figure 4, lane 16). Sequence analyses of the virion DNA revealed indel formation precisely at the site of Cas9 cleavage for both vectors (Figures 5A and 5D). Therefore, the method that successfully produced HD+donor+sgRNA+Cas9miR (bearing 5′ CCA 3′ to 5′ TCA 3′ PAM mutation) by preventing CRISPR/Cas9-mediated self-cleavage, did not permit production of HD+LacZ+sgRNA633+Cas9miR and HD+LacZ+sgRNA86+Cas9miR, indicating that suppression of CRISPR/Cas9 by mivaRNAI, hsa-miR183-5p, and hsa-miR218-5p, and AcrIIA4 and AcrIIA2 when expressed from the helper virus, were not enough to prevent cleavage in the presence of a bona fide 5′ CCN 3′ PAM.
Therefore, we sought next to further inhibit Cas9 activity during vector production by engineering the producer cells to constitutively express AcrIIA4 and AcrIIA2. This was accomplished by stably transfecting the producer cell line 116 with the plasmid pNG191 (Figure 2F), and G418-resistant colonies were screened by their ability to amplify HD+LacZ+sgRNA633+Cas9miR using the ANG163Acr. Several G418-resistant clones were able to amplify HD+LacZ+sgRNA633+Cas9miR, and one such cell line, 116Acr3, was chosen for large-scale production of HD+LacZ+sgRNA633+Cas9miR and HD+LacZ+sgRNA86+Cas9miR using AdNG163Acr. Following CsCl ultracentrifugation, only a single virus band was visible for of HD+LacZ+sgRNA633+Cas9miR (Figure 5B) and HD+LacZ+sgRNA86+Cas9miR (Figure 5E). Restriction analyses of virion DNA from both vectors (Figure 4, lane 15 for HD+LacZ+sgRNA633+Cas9miR and lane 18 for HD+LacZ+sgRNA86+Cas9miR) revealed a pattern indistinguishable from their parental plasmids (Figure 4, lanes 13 and 19, respectively), and with additional faint bands consistent with the AdNG163Acr (see Figure 4, lane 16). Sequence analyses of HD+LacZ+sgRNA633+Cas9miR and HD+LacZ+sgRNA86+Cas9miR virion DNAs revealed the expected sequence with no evidence of indel formation at the site of Cas9 cleavage (Figures 5B and 5E, respectively). Finally, because HD+LacZ+sgRNA633+Cas9miR and HD+LacZ+sgRNA86+Cas9miR contain the reporter LacZ transgene, their infectivity (the proportion of physical viral particles that are infectious expressed as the viral particle to blue-forming unit ratio [vp:BFU]) can be determined by titration.20 HD+LacZ+sgRNA633+Cas9miR and HD+LacZ+sgRNA86+Cas9miR produced in 116Acr3 cells with AdNG163Acr without genome rearrangement (Figures 5B and 5E) had vp:BFU ratios of 24:1 and 18:1, respectively. These ratios are comparable to the parental HD28E4LacZ from which they were derived, which ranged from 12:1 to 22:1,19,20 and all of these ratios are below the FDA recommended ratio of 30:1 for clinical-grade adenoviruses.28 In contrast, HD+LacZ+sgRNA633+Cas9miR and HD+LacZ+sgRNA86+Cas9miR produced in 116Acr cells with AdNG163Acr that showed evidence of indel formation within the LacZ transgene (Figure 5A and 5C) had much higher vp:BFU ratios of 44:1 and 87:1. This higher vp:BFU was expected because a subpopulation of these vectors will have had their LacZ transgene inactivated by CRISPR/Cas9-mediated indel formation.
With a producer cell expressing AcrIIA2 and AcrIIA4 along with a helper virus expressing AcrIIA2 and AcrIIA4, we wondered if down-regulation of Cas9 mRNA by mivaRNAI, hsa-miR183-5p, and hsa-miR218-5p was still required to prevent self-cleavage during vector production. To determine this, we tried to produce HD+LacZ+sgRNA633+Cas9 (which lacks the target sites for mivaRNAI, hsa-miR183-5p, and hsa-miR218-5p; see Figure 2A) in 116Acr3 cells with AdNG163Acr. The results revealed that self-cleavage had
sgRNA633 sequence CCGACGGGTGTACTCGCTCAC
A HD+LacZ+sgRNA633+Cas9miR produced in 116 cells with AdNG163Acr
Vp:BFU = 44:1
B HD+LacZ+sgRNA633+Cas9miR produced in 116Acr3 cells with AdNG163Acr
Vp:BFU = 24:1
C HD+LacZ+sgRNA633+Cas9 produced in 116Acr3 cells with AdNG163Acr
Vp:BFU = 62:1
gRNA86 sequence CCGCAGATAGAGATTCGGATT
D HD+LacZ+sgRNA86+Cas9miR produced in 116 cells with AdNG163Acr
Vp:BFU = 87:1
E HD+LacZ+sgRNA86+Cas9miR produced in 116Acr3 cells with AdNG163Acr
Vp:BFU = 18:1
(legend on next page)
occurred during vector production; as shown in Figure 5C, more than one viral band was visible following CsCl ultracentrifugation, sequence analyses of the virion DNA reveal indel formation at the Cas9 cleavage site, and titration of the vector revealed a reduction in infectivity with a vp:BFU ratio of 62:1. These results indicate that downregulation of Cas9 mRNA by mivaRNAI, hsa-miR183-5p, and hsa-miR218-5p is necessary to prevent self-cleavage during vector production.
In summary, we were successful in producing CRISPR/Cas9-mediated self-cleavage of the HDAd even when the sgRNA target within the vector possessed a bona fide 5’ CCN 3’ PAM, by exploiting mivaRNAI, hsa-miR183-5p, and hsa-miR218-5p to downregulate Cas9 mRNA and by inhibiting Cas9 protein activity through expression of AcrIIA2 and AcrIIA4 from the producer cells and helper virus. The ability to produce a CRISPR/Cas9-mediated self-cleaving HDAd is significant because long-term Cas9 expression is undesirable due to safety concerns associated with off target cleavage, cytotoxicity, and immune responses. A CRISPR/Cas9-mediated self-cleaving HDAd would solve these problems. For example, the desired gene editing can be performed with a CRISPR/Cas9-mediated self-cleaving HDAd, which also limits the duration of CRISPR/Cas9 expression (Figure 7).
Recently, Li et al. reported toxicity following transduction of human hematopoietic stem cells with HDAd expressing CRISPR/Cas9. This CRISPR/Cas9-mediated toxicity was alleviated by transduction with a second HDAd expressing AcrIIA2 and AcrIIA4. However, the requirement for sequential co-transduction by two HDAd adds cost and complexity and reduces efficiency, and transduced cells continue to express immunogenic Cas9, AcrIIA2, and AcrIIA4. Instead, the CRISPR/Cas9-mediated self-cleaving HDAd described herein represents an improved approach able to accomplish the same objective but without the drawbacks noted. Finally, the strategies described here may be adapted to produce CRISPR/Cas9-mediated self-cleaving vectors based on other viruses.
MATERIALS AND METHODS
Adenoviruses
HD+donor+sgRNA+Cas9 was derived from HD-23.8-CFTRm-PACTk-DTA by replacing the LacZ expression cassette with a Cas9 expression and by changing the PAM in the donor from 5'CCA 3' to 5'TCA 3'. HD+donor+sgRNA+Cas9 was derived from HD+donor+sgRNA+Cas9 by inserting the target sequences for mivaRNAI, hsa-miR183-5p, and hsa-miR218-5p (shown in Figure 2) into the NotI site present in the 3' UTR of Cas9 expression cassette in HD+donor+sgRNA+Cas9. The helper virus AdNG163Acr was derived from AdNG16320 by inserting the AcrIIA4 and AcrIIA2 expression cassette into the unique ClaI sites of the stuffer sequence in the adenoviral E3 region. HD+LacZ+sgRNA663+Cas9miR was constructed by inserting the 5,896-bp AscI fragment containing the Cas9 expression cassette from HD+donor+sgRNA+Cas9 into the unique Ascl site of HDΔ28E4LacZ followed by inserting the sgRNA633 expression cassette into the unique ScI site. HD+LacZ+sgRNA86+Cas9miR was constructed the same way, except the Cas9 expression and by changing the PAM in the donor from 5'CCA 3' to 5'TCA 3'. HD+donor+sgRNA+Cas9 by inserting the target sequences for mivaRNAI, hsa-miR183-5p, and hsa-miR218-5p (shown in Figure 2) into the NotI site present in the 3' UTR of Cas9 expression cassette in HD+donor+sgRNA+Cas9. The helper virus AdNG163Acr was derived from AdNG16320 by inserting the AcrIIA4 and AcrIIA2 expression cassette into the unique ClaI sites of the stuffer sequence in the adenoviral E3 region. hd+LacZ+sgRNA663+Cas9miR was constructed by inserting the 5,896-bp AscI fragment containing the Cas9 expression cassette from HD+donor+sgRNA+Cas9 into the unique Ascl site of HDΔ28E4LacZ followed by inserting the sgRNA633 expression cassette into the unique ScI site. HD+LacZ+sgRNA86+Cas9miR was constructed the same way, except the Cas9 expression cassette in HD+donor+sgRNA+Cas9 was derived from HD-23.8-CFTRm-PACTk-DTA by replacing the LacZ expression cassette with a Cas9 expression and by changing the PAM in the donor from 5'CCA 3' to 5'TCA 3'. HD+donor+sgRNA+Cas9 was derived from HD+donor+sgRNA+Cas9 by inserting the target sequences for mivaRNAI, hsa-miR183-5p, and hsa-miR218-5p (shown in Figure 2) into the NotI site present in the 3' UTR of Cas9 expression cassette in HD+donor+sgRNA+Cas9. The helper virus AdNG163Acr was derived from AdNG16320 by inserting the AcrIIA4 and AcrIIA2 expression cassette into the unique ClaI sites of the stuffer sequence in the adenoviral E3 region. HD+LacZ+sgRNA663+Cas9miR was constructed by inserting the 5,896-bp AscI fragment containing the Cas9 expression cassette from HD+donor+sgRNA+Cas9 into the unique Ascl site of HDΔ28E4LacZ followed by inserting the sgRNA633 expression cassette into the unique ScI site. HD+LacZ+sgRNA86+Cas9miR was constructed the same way, except the Cas9 expression cassette in HD+donor+sgRNA+Cas9 was derived from HD-23.8-CFTRm-PACTk-DTA by replacing the LacZ expression cassette with a Cas9 expression and by changing the PAM in the donor from 5'CCA 3' to 5'TCA 3'. HD+donor+sgRNA+Cas9 was derived from HD+donor+sgRNA+Cas9 by inserting the target sequences for mivaRNAI, hsa-miR183-5p, and hsa-miR218-5p (shown in Figure 2) into the NotI site present in the 3' UTR of Cas9 expression cassette in HD+donor+sgRNA+Cas9. The helper virus AdNG163Acr was derived from AdNG16320 by inserting the AcrIIA4 and AcrIIA2 expression cassette into the unique ClaI sites of the stuffer sequence in the adenoviral E3 region. HD+LacZ+sgRNA663+Cas9miR was constructed by inserting the 5,896-bp AscI fragment containing the Cas9 expression cassette from HD+donor+sgRNA+Cas9 into the unique Ascl site of HDΔ28E4LacZ followed by inserting the sgRNA633 expression cassette into the unique ScI site. HD+LacZ+sgRNA86+Cas9miR was constructed the same way, except the Cas9 expression cassette in HD+donor+sgRNA+Cas9 was derived from HD-23.8-CFTRm-PACTk-DTA by replacing the LacZ expression cassette with a Cas9 expression and by changing the PAM in the donor from 5'CCA 3' to 5'TCA 3'. HD+donor+sgRNA+Cas9 was derived from HD+donor+sgRNA+Cas9 by inserting the target sequences for mivaRNAI, hsa-miR183-5p, and hsa-miR218-5p (shown in Figure 2) into the NotI site present in the 3' UTR of Cas9 expression cassette in HD+donor+sgRNA+Cas9. The helper virus AdNG163Acr was derived from AdNG16320 by inserting the AcrIIA4 and AcrIIA2 expression cassette into the unique ClaI sites of the stuffer sequence in the adenoviral E3 region.
HDAd Producer Cell
The plasmid pNG191 (Figure 2F) contains the expression AcrIIA4 and AcrIIA2 from AdNG163Acr but with a synthetic DNA sequence bearing the neomycin-resistance coding region inserted between AcrIIA2 and the polyadenylation signal. The 116Acr3 producer cell line was generated as follows: plasmid pNG191 was digested with ApaLI, and 2 µg was transfected into 60-mm dishes of 116 cells cultured in 100 µg/mL hygromycin (Sigma, St. Louis, MO, USA). Forty-eight hours later, G418 (InvivoGen, San Diego, CA, USA) was added to the culture media at a concentration of 400 µg/mL. Well-isolated drug-resistant colonies were picked and expanded to assess their ability to amplify HD+LacZ+sgRNA663+Cas9miR as described previously.19
AUTHOR CONTRIBUTIONS
D.J.P, D.L.T., and P.N. conducted the experiments. P.N. designed the experiments and wrote the paper.
ACKNOWLEDGMENTS
This work was supported by internal Baylor College of Medicine funds.
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The OpenCitations Data Model
Marilena Daquino1, Silvio Peroni1, David Shotton2, Giovanni Colavizza3, Behnam Ghavimi4, Anne Lauscher5, Philipp Mayr6, Matteo Romanello7, and Philipp Zumstein5*
1 University of Bologna {marilena.daquino2,silvio.peroni}@unibo.it
2 University of Oxford [email protected]
3 University of Amsterdam [email protected]
4 University of Bonn [email protected]
5 University of Mannheim [email protected], [email protected]
6 GESIS - Leibniz-Institute for the Social Sciences [email protected]
7 cole Polytechnique Fdrale de Lausanne [email protected]
Abstract. A variety of schemas and ontologies are currently used for the machine-readable description of bibliographic entities and citations. This diversity, and the reuse of the same ontology terms with different nuances, generates inconsistencies in data. Adoption of a single data model would facilitate data integration tasks regardless of the data supplier or context application. In this paper we present the OpenCitations Data Model (OCDM), a generic data model for describing bibliographic entities and citations, developed using Semantic Web technologies. We also evaluate the effective reusability of OCDM according to ontology evaluation practices, mention existing users of OCDM, and discuss the use and impact of OCDM in the wider open science community.
Keywords: Open citations · Scholarly data · Data model.
1 Introduction
In recent years, largely thanks to the Initiative for Open Citations (I4OC8), most major scholarly publishers have made their bibliographic reference data open, resulting, for example, in more than 700 million citations now being made
* Authors’ contributions and roles are specified according to the CrediT taxonomy. Marilena Daquino (Conceptualization, Data curation, Formal analysis, Investigation, Methodology, Software, Writing-original draft). She is responsible for section "Background" and section "Analysis of OCDM reusability"; Silvio Peroni (Conceptualization, Investigation, Methodology, Software, Data curation, Supervision, Funding acquisition, Project administration, Writing-original draft); David Shotton (Conceptualization, Investigation, Methodology, Supervision, Funding acquisition, Project administration, Writing-original draft); Giovanni Colavizza, Behnam Ghavimi, Anne Lauscher, Philipp Mayr, Matteo Romanello, Philipp Zumstein (Investigation, Resources, Validation, Writing-review and editing).
8 https://i4oc.org
openly available in COCI, the OpenCitations Index of Crossref open DOI-to-DOI citations [17]. As a consequence, scholarly database providers and bibliometric analysis software have started to integrate open citation data in their services, thereby offering an alternative to the current reliance on proprietary citation indexes.
Open bibliographic and citation metadata are beneficial because they enable anyone to perform meta-research studies on the evolution of scholarly knowledge, and allows national and international research assessment exercises characterized by transparent and reproducible processes. Within this context, bibliographic citations are essential components of scholarly discourse, since they remain the dominant measurable unit of credit in science [12]. They carry evidence of scholarly networks and of the progress of theories and methods, and are fundamental aids in tenure evaluation and recommendation systems. To perform open bibliometric research and analysis, the publications upon which the work is based should be FAIR, namely Findable, Accessible, Interoperable, and Reusable [35]. Ideally, such data should be made available without any restrictions, licensed under a Creative Commons CC0 waiver⁹, and the software for programmatically accessing and analysing them should be also released with open source licences.
However, data suppliers use a variety of licenses, technologies, and vocabularies for representing the same bibliographic information, or use ontology terms defined in the same ontologies with different nuances, thereby generating diversity in data representation. The adoption of a common, generic, open and documented data model that employs clearly defined ontological terms would ensure data consistency and facilitate integration tasks.
In this paper we present the OpenCitations Data Model (OCDM), a data model based on existing ontologies for describing information in the scholarly bibliographic domain with a particular focus on citations. OCDM has been developed by OpenCitations [29], an infrastructure organization for open scholarship dedicated to the publication of open bibliographic and citation data using Semantic Web technologies. Herein, we propose a holistic approach for evaluating the reusability of OCDM according to ontology evaluation methodologies, and we discuss its uptake, impact, and trustworthiness.
We compared OCDM to similar existing solutions and found that, to the best of our knowledge, OCDM (a) has the broadest vocabulary coverage, (b) is the best documented data model in this area, and (c) has already a significant uptake in the scholarly community. The main advantages of OCDM, in addition to the consistency of data description that it facilitates, are that it was designed from the outset to enable use by those who are not Semantic Web practitioners, that it is properly documented, and it is provided with accompanying software for managing the entire life-cycle of data created according to OCDM.
The paper is organized as follows. In Section 2 we clarify the scope and motivations for this work. In Section 3 we present the data model and its documentation, software and current adopters. In Section 4 we present the criteria
⁹ https://choosealicense.com/licenses/cc0-1.0/
we have used to evaluate OCDM reusability and we present results, further discussed in Section 5.
2 Background
The OpenCitations Data Model (OCDM) [9] was initially developed in 2016 to describe the data in the OpenCitations Corpus (OCC) [10]. In recent years OpenCitations has developed other datasets while OCDM has been adopted by external projects, and OCDM has been expanded to accommodate these changes. We have recently further expanded the OpenCitations Data Model to accommodate the extended metadata requirements of the Open Biomedical Citations in Context Corpus project (CCC). This project has developed an exemplar Linked Open Dataset that includes detailed information on citations, in-text reference pointers such as Berners-Lee et al. 2011, and identifiers of the citation contexts (e.g. sentences, paragraphs, sections) within which in-text reference pointers are located, to facilitate textual analysis of citation contexts. The citations are treated as first-class data entities [26], enriched with open bibliographic metadata released using a CC0 waiver that can be mined, stored and republished. This includes identifiers specifying the specific positions of the various in-text reference pointers within the text. However, the literal text of these contexts are not stored within the Open Biomedical Citations in Context Corpus, and regrettably in many cases the full text of the published entities cannot be mined from elsewhere in an open way, even for some (view only) Open Access articles, because of copyright, licensing and other Intellectual Property (IP) restrictions. Table 1 shows the representational requirements (hereinafter, for the sake of simplicity, also called citation properties and numbered (P1-P8) that we were interested in recording for each citation instantiated from within a single paper:
3 The OpenCitations Data Model
The OCDM permits one to record metadata about bibliographic references and their textual contexts, bibliographic entities (citing and cited publications) and the citations that link them, agents and their roles (e.g. author, editor), identifiers for the foregoing entities, provenance metadata and much more, as shown diagrammatically in Figure 1. All terms described in the OCDM are brought together in the OpenCitations Ontology (OCO, https://w3id.org/oc/ontology). OCO aggregates terms from the SPAR (Semantic Publishing and Referencing) Ontologies [28] and other well-known ontologies, such as PROV-O [4] and Web Annotation Ontology [32].
Citations are instances of the class cito:Citation defined in CiTO, the Citation Typing Ontology [11]. Subclasses (not shown in Fig. 1), relevant for P1, include
---
10 http://opencitations.net/corpus
11 http://purl.org/spar/cito
| ID | Description |
|----|-------------|
| P1 | A classification of the type of citation (e.g. self-citation). |
| P2 | The bibliographic metadata of the citing and cited bibliographic entities (e.g. type of published entity, identifiers, authors, contributors, publication date, publication venues, publication formats). |
| P3 | The bibliographic reference, typically found within the reference list of the citing bibliographic entity, that references a cited bibliographic entity. |
| P4 | The separate identifiers of all the in-text reference pointers included in the text of the citing entity, that denote bibliographic references within the reference list. |
| P5 | The co-occurrence of in-text reference pointers within each in-text reference pointer lists (e.g. [3,5,12]). |
| P6 | The identifiers of structural elements (e.g. XPath of sentences, paragraphs, captions) that specify where, in the full text, an in-text reference pointer appears. |
| P7 | The function or purpose of the citation (e.g. to cite as background, extend, or agree with the cited entity) to which each in-text reference pointer relates. |
| P8 | Provenance information of the citation extraction process (e.g. responsible agents, data sources, extraction dates). |
**Table 1.** Representational requirements of the OpenCitations Data Model
---
**Fig. 1.** Main classes and properties of the OpenCitations ontology
The OpenCitations Data Model
cito:AuthorSelfCitation, cito:JournalSelfCitation, cito:FunderSelfCitation, cito:AffiliationSelfCitation, and cito:AuthorNetworkSelfCitation. In addition, citations can be characterized with a purpose or function with respect to the related citation context, by means of the property cito:hasCitationCharacterisation and the use of one or more CiTO properties (e.g. cito:usesMethodIn) (P7).
Instances of the class fabio:Expression, defined in FaBiO, the FRBR-aligned Bibliographic Ontology \(^\text{12}\), can be linked to bibliographic metadata such as the publication date, authors, and publication venues. Instances of the class fabio:Manifestation aggregate information on specific editions and formats (P2).
Instances of the class oa:Annotations, defined in OA, the Web Annotation Ontology \(^\text{13}\) link instances of the class cito:Citation to instances of biro:BibliographicReference (P3), defined in BiRO, the Bibliographic Reference Ontology \(^\text{14}\) and individuals of c4o:InTextReferencePointer (P4), defined in C4O, the Citation Counting and Context Characterisation Ontology \(^\text{15}\). Lists of in-text reference pointers are represented by the class c4o:SingleLocationPointerList (P5).
Structural elements wherein in-text reference pointers appear are represented as individuals of deo:DiscourseElement, defined in DEO, the Discourse Element Ontology \(^\text{16}\). Elements are uniquely identified (P6) by means of instances of datacite:Identifier, defined in the DataCite Ontology \(^\text{17}\).
Finally, as summarized in Figure 2, OCDM provides guidance for describing the provenance and versioning of each entity under consideration, and also enables the specification of the main metadata related to the datasets containing such entities (P8). To this end, the OCDM reuses terms from PROV-O, the Provenance Ontology \(^\text{18}\), VoID, the Vocabulary of Interlinked Datasets \(^\text{19}\), and DCAT, the Data Catalog Vocabulary \(^\text{20}\).
Each bibliographic entity described by the OCDM is annotated with one or more provenance snapshots (i.e. instances of prov:Entity, each snapshot intended as a specialisation of the bibliographic entity via prov:specializationOf) as defined in \(^\text{21}\). In particular, each snapshot records the set of statements having the bibliographic entity as its subject at a fixed point in time, validity dates, responsible agents for either the creation or the modification of the metadata, primary data sources, and a SPARQL query summarising changes with respect to any prior snapshot.
\(^\text{12}\) http://purl.org/spar/fabio
\(^\text{13}\) https://www.w3.org/ns/oa
\(^\text{14}\) http://purl.org/spar/biro
\(^\text{15}\) http://purl.org/spar/c4o
\(^\text{16}\) http://purl.org/spar/deo
\(^\text{17}\) http://purl.org/spar/datacite
\(^\text{18}\) http://www.w3.org/ns/prov
\(^\text{19}\) http://rdfs.org/ns/void
\(^\text{20}\) http://www.w3.org/ns/dcat
Lastly, a dataset (\texttt{dcat:Dataset}) containing information about the bibliographic entities is described with cataloging information (e.g. title, description, publication and change dates, subjects, webpage, SPARQL endpoint) and distribution information (\texttt{dcat:Distribution}) which also includes the specification of licenses, dumps, media types, and data volumes.
### 3.1 OCDM documentation and resources
In order to make the OCDM understandable and reusable by both the Semantic Web community and communities with no expertise in Semantic Web technologies, support material has been produced. All materials are available at \url{http://opencitations.net/model} and include the following resources.
**Human-readable documentation.** The OCDM documentation [9] provides (1) detailed definitions of terms characterising open citation data and open bibliographic metadata, (2) naming conventions and URI patterns, and (3) real-world examples. OCDM is supplemented by two additional specifications, i.e. the definition of the Open Citation Identifier (OCI) [26] and the definition of the In-Text Reference Pointer Identifier (InTRePID) [33].
**OCDM-compliant data examples.** All the data introduced in the OCDM documentation are expressed and provided in JSON-LD to make it easily understandable both to RDF experts and other Web users. In addition, CSV templates have been adopted so as to express and share parts of the OCDM e.g. to store the citation data in COCI [17].
**Ontology development documentation.** The first version of the OCDM, released in 2016, addressed citation properties P1-P3 and P8, by directly reusing the SPAR Ontologies and other existing vocabularies [28]. Within the context of the CCC project described above, we used SAMOD [27], an agile data-driven methodology for ontology development, to extend OCO with terms relevant to P4-P7. Motivating scenarios, competency questions, and a glossary of terms of all the new entities included in the OCDM, are available for reproducibility purposes.
**Open source software leveraging the data model.** The source code of the knowledge extraction and data re-engineering pipeline for managing data ac-
The pipeline includes software originally developed for creating the data within the OpenCitations Corpus (i.e. BEE and SPACIN), new software used to create the OpenCitations Indexes (i.e. Create New Citations CNC), and a user-friendly web application called BCite [10] for creating OCDM-compliant RDF data from lists of bibliographic references. In addition, we have released tools to support the development of applications leveraging data organized according to OCDM: RAMOSE (to create RESTful APIs over SPARQL endpoints), OSCAR (to create user-friendly search interface for querying SPARQL endpoints [13]) and LUCINDA (a configurable browser for RDF data). Configuration files for setting up these three tools to work with OCDM data are available in their GitHub repositories.
**Licenses for reuse.** OCDM (both the documentation and OCO) is released under a CC-BY license. Software solutions are released under the ISC license. The OCDM-compliant data served by OpenCitations are made open under CC0.
### 3.2 OCDM adopters
To date, OCDM, central to the work of OpenCitations, has three acknowledged external early adopters. The OpenCitations datasets modelled using OCDM include: the OpenCitations Corpus (OCC), including about 13 million citation links and the OpenCitations Indexes, which include more than 702 million citations. Forthcoming datasets, that will be released during 2020, include OpenCitations Meta, which stores metadata of the citing and cited entities involved in the citations included in the Indexes, and the Open Biomedical Citations in Context Corpus (CCC), mainly derived from the Open Access corpus of biomedical articles provided by PubMed Central, that will include detailed information on in-text reference pointers denoting each reference in the reference list, and their textual contexts. The early adopters of OCDM are as follows.
The Extraction of Citations from PDF Documents (EXCITE) project [20] is run by GESIS and the University of Koblenz. The aim of EXCITE is to extract and match citations from social science publications. To date, EXCITE has extracted around 1 million citations, has converted the data to RDF according to OCDM, and has then published it by ingestion into the OCC.
The Linked Open Citation Database (LOC-DB) [21] is a project which aims to demonstrate that it is possible for academic libraries to catalogue citation relations sustainably, accurately, and cooperatively. So far, the project has stored bibliographic and citation data for about 7000 published entities. LOC-DB has used a customisation of the OCDM as the data model for defining its data, and exports data in OCDM/JSON-LD so as to be ingested into the OCC.
The Venice Scholar Index (VSI)[21] is an instance of the Scholar Index, originated from the Linked Books project [8] founded by the Swiss National Science Foundation. The citation index includes about 4 million references to publica-
tions cited in the historiography of Venice. VSI exports data into RDF data according to OCDM so as to be integrated into the OCC.
4 Analysis of OCDM reusability
A holistic approach has been used to evaluate the OCO ontology and to infer properties relevant to OCDM. We adopted seminal definitions and classifications of ontology evaluation approaches [6, 14] and we selected the following dimensions and approaches that are representative with respect to OCDM reusability.
[E1] Lexical keyword similarity. This addresses the similarity of definitions in OCO with respect to the real-world knowledge to be mapped. We adopted a data-driven evaluation [7] to map OCO definitions with terms included in a corpus of documents encoded in JATS/XML [22] which is a standard markup language for scholarly documents.
[E2] Vocabulary coverage. This addresses the coverage of concepts, instances, and facts of OCO with respect to the domain to be covered. [E2.1] We validated OCO coverage by comparing it with competing ontologies [25]. [E2.2] Secondly, we adopted an application-based approach [31] to address OCO coverage in four applications that leverage it: OpenCitations, EXCITE, LOC-DB, and ScholarIndex.
Also, we addressed aspects peculiar to OCDM reusability, namely:
[E3] Usability-profiling. This encompasses the communication context of OCDM, i.e. its pragmatics. We evaluated OCDM recognition level [13], i.e. the efficiency of access to OCDM ontologies, documentation, and software, by comparing it with competing ontologies [25].
Lastly, we addressed current uptake, potential impact, and trustworthiness of OCDM [23].
4.1 E1: Lexical keyword similarity
We created a randomized corpus of 2800 JATS documents taken from the Open Access Subset of biomedical literature hosted by Europe PubMed Central [24]. We extracted the list of XML elements used in the documents within this corpus (117 elements), and we expanded element names with definitions scraped from the online XML schema guidelines (e.g. `<p>` became Paragraph). We manually pruned non-relevant elements such as MathML markup, text style elements (e.g. `<italic>`), redundant wrapping elements (<keywordGroup>) and elements that are out of scope (e.g. `<biography>`), resulting in a refined list of 45 terms.
Secondly, we extracted definitions from OCO (118). We manually pruned terms that were not relevant (e.g. annotation properties, provenance, and distribution related terms), terms that represent hierarchy, sequences, and linguistic
aspects not available in XML (e.g. partOf, hasNext, Sentence), and terms dependent on post-processing activities (e.g. self-citation, hasCitationCharacterisation), resulting in a refined list of 77 OCO definitions.
We then used Wordnet\footnote{https://wordnet.princeton.edu/} to automatically expand both XML and ontology definitions with synonyms, and we matched synsets similarities. We used a symmetric similarity score to find best matches between the synsets. We considered two thresholds for the similarity match, 0.7 and 0.5, and we manually computed precision and recall. Table\textsuperscript{2} shows the results.
| Threshold | Matches | Precision | Recall |
|-----------|---------|-----------|--------|
| 0.7 | (25/45) 55.5\% | (24/25) 96\% | (24/45) 53.3\% |
| 0.5 | (33/45) 73.3\% | (31/33) 93.9\% | (31/45) 68.8\% |
\textbf{Table 2.} Lexical similarity between JATS/XML elements and OCO terms
The coverage of JATS terms in OCO was 55.5\% when the threshold was greater than 0.7, with high precision (96\%) and average recall (53.3\%). The coverage was 73.3\% when the threshold was greater than 0.5, with still high precision (93.3\%) and average recall (68.8\%). False negative results included acronyms (e.g. issn) that did not have a match in Wordnet, and terms of the taxonomy that were underrepresented in the corpus (e.g. book). Likewise, false positive results were due to acronyms used in XML definitions that were not correctly parsed (e.g. URI for This Same Article Online was incorrectly matched with fabio:JournalArticle).
\subsection*{4.2 E2: Vocabulary coverage}
\[E2.1\] Vocabulary coverage in existing vocabularies. Since gold standard ontologies are not available, we referred to existing data models and relevant ontologies. For the sake of completeness we addressed both open and non-open citation data providers and (semi-)open citation data providers\footnote{See the definition at \url{https://opendefinition.org/licenses/}}, and both graph data providers and others. We reviewed the vocabulary coverage with respect to P1-P8. We did not take into account discipline coverage or citation counting. The complete list of data models and references is available at \url{https://github.com/opencitations/metadata}. Table\textsuperscript{3} summarizes the comparison of vocabularies coverage, an x indicating that the source had metadata of relevance to the citations properties P1-P8 (Table\textsuperscript{1}).
Non-open citation data providers include Google Scholar, Scopus\footnote{https://wordnet.princeton.edu/}, Web of Science (WoS)\footnote{https://wordnet.princeton.edu/}, CiteSeerX\footnote{https://opendefinition.org/licenses/}, and Dimensions\footnote{https://wordnet.princeton.edu/}. Their data models cover a few aspects of bibliographic metadata (P2) and provenance data (P8). WoS, CiteSeerX, and Dimension also includes bibliographic references (P3). In addition, WoS and CiteSeerX also cover types of citations (P1), and only CiteSeerX includes citation context sentences (P6).
Table 3. Vocabulary coverage according to P1-P8
| | P1 | P2 | P3 | P4 | P5 | P6 | P7 | P8 |
|----|----|----|----|----|----|----|----|----|
| Google Scholar | x | | x | | | | | |
| Scopus | x | | | x | | | | |
| Web of Science | x | x | | | x | | | |
| CiteseerX | x | x | | | | x | | |
| Dimensions | x | | | x | | | | |
| Crossref | x | | | | x | | | |
| EPMC | x | | | | | | | x |
| Datacite | x | x | | | | | x | |
| DBLP | x | | | | | | | |
| MAKG | x | x | | | x | | | |
| GORC | x | | | | | | | x |
| SciGraph | x | | | | | | x | |
| WikiCite | x | | | | | | | |
| OpenCitations | x | x | | | x | | x | |
Open citation data providers include Crossref [18], Europe PubMed Central (EPMC), DataCite, DBLP, Microsoft Academic Knowledge Graph (MAKG) [11] (which is based on Microsoft Academic Graph [34] and which reuses the SPAR Ontologies and links to resources in Wikidata and OpenCitations), the Semantic Scholar Open Research Corpus (ORC) [3], the Semantic Scholars Graph of References in Context (GORC) [23], Springer Natures SciGraph [15] (which is based on Schema.org), WikiCite (which includes terms aligned to SPAR Ontologies and interlinking with the OpenCitations Corpus), and the OpenCitations datasets [29]. All data models cover P2, and all except MAKG also cover P8. Only OpenCitations covers P1. In addition, Crossref, Europe PMC, DataCite, MAKG, GORC, and OpenCitations cover P3. MAKG, GORC, and OpenCitations cover P6, while the latter two also includes in-text reference pointers (P4) and related lists (P5). DataCite and OpenCitations allow the tracking of citation functions (P7).
[E2.2] Vocabulary coverage in OCDM reusers. We separately analysed the vocabulary coverage in acknowledged adopters of OCDM.
EXCITE data fully covers P2, P3 and P8. Its local data model also includes information about the data quality of extracted references, which is not currently mapped to OCDM.
LOC-DB data fully covers P2, P3, and P8. The OCDM was extended in its local data model so as to cover information about its OCR activities performed on PDF scans.
Venice Scholar Index (VSI) aligned data to OCDM terms so as to fully cover P2, P3, P4, P6, and P8. In order to cover peculiar needs of the project relevant to P2, the classes fabio:Work and fabio:Expression defined in the SPAR Ontologies (and reused in OCO) were specialized so as to include the following sub-classes: fabio:ArchivalRecord, fabio:ArchivalRecordSet, fabio:ArchivalDocument, and fabio:ArchivalDocumentSet [27]
---
[27] As documented at https://github.com/SPAROntologies/fabio/issues/1
4.3 E3: Usability profiling
We compared the documentation available for existing graph data providers, namely: MAKG, Semantic Scholar, SciGraph, and WikiCite. We considered the same dimensions used to address OCDM documentation, namely: (1) human-readable documentation, (2) machine-readable data model and examples, (3) ontology development documentation, (4) open source software leveraging the model, and (5) licenses for reuse.
The MAKG data model is graphically represented in [11]. Software for creating RDF data is available, but no machine-readable data model and examples are provided. Likewise, the development of the data model is not described. Moreover, according to Frber [11], the property $c4o$::hasContext is used to annotate instances of cito::Citation, rather than $c4o$::InTextReferencePointer as prescribed in C4O, preventing it from representing consistently P3, P4, and P7 in future works, and from merging third-party data with OpenCitations. Lastly, no license is specified for the data model.
The Semantic Scholar Open Research Corpus data model is described in [3]. A machine-readable example of the data model is presented in a dedicated web page[28]. No further documentation is available. Similarly, GORC is described in [23], where an example of JSON data is presented. Both datasets are released under OCD-BY (i.e. an open license), although programmatically accessing data through their APIs requires one to subscribe to a more restrictive and non-open license (comparable to CC-BY-NC-ND). No license associated with the data model is stated.
The Schema.org main classes reused in SciGraph are described in a dedicated web page[29]. While the ontology is reused as-is, the SciGraph data model[30] is released as a JSON-LD file and machine-readable examples are available under a CC-BY license. Development documentation of the data model is not available.
Several sources address the Wikidata model used for WikiCite, including templates[31] and examples[32]. However, no dedicated documentation nor a machine-readable version of the model having citations as a scope is separately available. Data, software, and the general data model are all released under the CC0 license.
Lastly, as aforementioned, OCO (https://w3id.org/oc/ontology) and OCDM [9] are described in dedicated human-readable documentation, including machine-readable data model and examples, available under a CC-BY license. The ontology development documentation and the open source software leveraging the model are available on github (ISC licence). All materials are gathered in the official page of the OCDM data model[33].
[28] http://s2-public-api-prod.us-west-2.elasticbeanstalk.com/corpus/
[29] https://scigraph.springernature.com/explorer/datasets/ontology/
[30] https://github.com/springernature/scigraph
[31] https://www.wikidata.org/wiki/Template:Bibliographic_properties
[32] https://www.wikidata.org/wiki/Wikidata:WikiProject_Source_MetaData
[33] http://opencitations.net/model
4.4 OCDM uptake, potential impact, and trustworthiness
We can quantify current uptake of the OCDM documentation by using statistics provided by Figshare and Altmetrics, and the number of users views of the model description page in the OpenCitations website. To date (24 March 2020), the Figshare document [9] has been viewed 9520 times, downloaded 1260 times, and cited 6 times (self-citations excluded). Moreover, 101 tweets from 66 users include direct links to the document. Separately, the web page dedicated to the model (http://opencitations.net/model) has received 13,844 views from 8,202 unique users since 2018.
We can estimate the potential impact of OCDM by considering (a) different types of possible reuse of the model, (b) the number of current reusers of the data model, (c) projects and applications leveraging data created according to OCDM, and (d) the kind of users of data created according to OCDM.
In detail, OCDM can be reused as is, via alignment for interchange purposes, and as a JSON data model for non-Semantic Web users. Currently OCDM is used by OpenCitations for all its datasets, and by three acknowledged early adopters, namely: EXCITE and LOC-DB, which reuse OCDM as is, and VSI, which aligned terms to OCDM. EXCITE data have been ingested in the OpenCitations Corpus, while LOC-DB and VSI data are going to be ingested soon. VOSViewer [34], CitationGecko [35], VisualBib [36], and OAHelper [37] are applications that leverage OpenCitations data conforming to OCDM retrieved via the OpenCitations REST APIs or directly through its SPARQL endpoints. Moreover, OpenAIRE [38], MAKG, and WikiCite align data to OpenCitations. Both DBLP and Lens.org [39] use citation data from OpenCitations to enrich their bibliographic metadata records.
The main users of OpenCitations data include scholars in scientometrics, researchers in the life sciences, biomedicine, the physical sciences, and the information technology domain. OpenCitations is currently expanding its coverage to include the social science and the arts and humanities disciplines. The main users of EXCITE data are researchers in the social sciences, while those of the data held by LOC-DB and the Venice Scholar Index include librarians and researchers in the humanities.
Lastly, we address trustworthiness of OCDM. Long-term availability of ontologies is crucial for the development of the Semantic Web, and the trustworthiness of the ontology creators is important. OCDM, OCO, and the SPAR Ontologies are all maintained by OpenCitations, which has been recently selected by the Global Sustainability Coalition for Open Science Services (SCOSS [40]) as
---
34 https://www.vosviewer.com/
35 https://citationgecko.com/
36 https://visualbib.uniud.it/en/project/
37 https://www.otzberg.net/oahelper/
38 https://www.openaire.eu/
39 https://lens.org/
40 https://scoss.org/
an open infrastructure deserving of crowdfunding support from the scholarly community, thereby helping to ensure its long-term sustainability.
Along with trustworthiness, another important factor is the general interest in the community towards research topics and outputs that can leverage OCDM. So far, two OpenCitations projects dedicated to the enhancement of the Linked Open Data corpus have been funded by the Alfred P. Sloan Foundation\footnote{See \url{https://sloan.org/grant-detail/8017}} and the Wellcome Trust, as mentioned above in Section Background. Moreover, the Internet Archive and Figshare have both offered to archive backup copies of the OpenCitations datasets without charge.
5 Discussion and conclusions
First, we evaluated lexical similarity of OCO definitions over the knowledge included in data sources encoded in JATS/XML, a gold standard for academic publications [E1]. While the recall is only average, mainly due to mistakes in parsing of acronyms, for those terms that were correctly matched the lexical similarity precision is high, showing that OCO is feasible for representing data sources organized according to the gold standard. One of the known limits of data-driven evaluation methodologies is that these do not address possible changes in the domain knowledge over time. To date, early adopters of OCO continuously contribute with new scenarios to be represented in the model, which is correspondingly expanded. As a result, OCO will remain a comprehensive reference point for future developments.
Secondly, we evaluated OCO vocabulary coverage as compared with competing data models [E2.1] and in the context of early adopters [E2.2]. Only OCDM fully covers P1-P8. In particular, only one other provider covers P4 and P5 (identifiers for in-text references and groups of these), three providers cover property P6 (although they only store full-text sentences, and lack identifiers for in-text reference pointers), and only one other provider covers property P7 (citation function). Two graph-data providers reuse terms from SPAR Ontologies (either directly or by alignment) in different ways, generating heterogeneity in data.
Among early adopters, LOC-DB required extensions in order to represent special information related to the cataloguing of digital objects, and VSI required us to expand the FaBiO ontology to permit description of non-published entities. While such changes can be deemed marginal, these are relevant hints for future developments in the humanities domain and will require further analysis. Nonetheless, the OCDM vocabulary coverage is satisfying and strengthens its reusability across domains and applications.
We showed how alternative citation data providers ensure access to their data models [E3]. Peer-reviewed articles are the main access point to descriptions of those data models, with additional information scattered across various web pages and repositories. While machine-readable data models and examples are mostly available, none of the other providers referenced detailed development
documentation. Moreover, the licenses for reusing the data models are not always defined. In conclusion, OCDM appears to be the most documented and findable data model.
Again, no comparison was possible of the uptake of the alternative models in the community. We showed that OCDM has been relatively popular in community social networks, and that the documentation has been downloaded and read by many people. At the moment we cannot measure for what purpose the OCDM documentation has been reused, with the exception of the three early-adopter projects listed in this paper.
We have shown that OCDM is potentially of significant usefulness to several communities, and fosters reuse in combination with legacy technologies, and we have highlighted ongoing interest from several parties in the maintenance and ongoing development of OCDM in support of several projects.
In future works, we will (a) create SHeX shapes to facilitate reusers in mapping their data to OCDM, and (b) trace OCDM usage scenarios by asking users to fill in a form for statistical purposes.
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An exploratory study of recovery of rare-earth elements from monazite in mild conditions using statistical-mixture design
A.C.S.P. Souza, E.C. Giese
Abstract: Monazite is a phosphate mineral, considered an essential source of light rare-earth elements (REE). The present work sought to evaluate different methods of solubilization of REE through the use of different concentrations of inorganic acids (H$_2$SO$_4$, HCl, and HNO$_3$) and organic acids (citric, oxalic, and lactic) in mild conditions at room temperature. According to the results, the inorganic acid solutions favored the solubilization in order of Ce$^{3+}$, La$^{3+}$, Nd$^{3+}$, Pr$^{3+}$, and Sm$^{3+}$ elements, while organic acid solutions only favored the solubilization of Ce$^{3+}$ and La$^{3+}$. Nitric acid was the more efficient leaching agent for the first group. In the case of organic acids, lactic acid solubilized Ce$^{3+}$, while mixtures of lactic and citric acids appeared to solubilize La$^{3+}$.
Keywords: Monazite, Rare-Earth elements, Chemical leaching, Design of Experiments.
reactions with microbial metabolites [8] and immobilization of REE of liquid matrices, mainly by sorption by biomass [9-13].
The microbially mediated REE solubilization occurs mainly via acidolysis, oxidoreduction, and complexation reactions. Acidolysis, that is, the proton-induced metal ion solubilization implies the exchange and replacement of metallic elements from mineral surfaces by protons. The REE mobilization through reducing or oxidative reactions or through the action of metabolically produced complexing agents has also been described in the literature [14].
Biohydrometallurgy can be considered an emerging green technology for the recovery of metals due to its environmentally friendly, simple, and economical processing. Bioleaching consists of a hydrometallurgical process of dissolving minerals through a group of microorganisms capable of producing acids and or oxidizing agents from the constituents of the ore itself in the leaching process [15]. However, few studies seek to elucidate the biological advantage of the interaction between microorganisms and minerals with REE [16, 17].
Few researchers have studied the assistance of microbial organic acid producers in the monazite bioleaching process. Thus, the present work sought to evaluate different leaching agents for REE extraction from a Brazilian monazite sample using a mixture-design experiment.
2. Experimental
Analytical grade reagents were used in preparing acid concentrations of 100 g L⁻¹. These acids were used in chemical leaching tests that mimicked metal dissolution achieved by microorganisms under mild temperature conditions. For monazite leaching tests, about 0.5 g of monazite sample was added in 150 mL Becker glass containing 50 mL of different acid mixtures.
The effect of the mixture of two sets containing three different inorganics (H₂SO₄, HCl, HNO₃) (Table 1) or organics (citric, oxalic, lactic) (Table 2) acids on the solubilization of REE from Brazilian monazite was evaluated through a statistical mixture-design.
The experimental runs remained on a shaking table, at room temperature, under constant agitation of 100 rpm over 60 minutes. After the end of the stirring, 20 mL of the leachate was centrifuged at 4000 rpm and 25 °C for 15 minutes, and the supernatant was collected for analysis. Determination of the final concentration of metal ions in solution was performed by inductively-coupled plasma atomic emission spectrometry (ICP-OES Perkin Elmer, OPTIMA3000, USA).
| Run | H₂SO₄ | HCl | HNO₃ | Ce | La | Nd | Pr | Sm |
|-----|--------|-----|------|----|----|----|----|----|
| 1 | 0 | 0 | 1 | 1.03 | 0.52 | 0.39 | 0.11 | 0.09 |
| 2 | 1 | 0 | 0 | 2.58 | 1.21 | 0.96 | 0.26 | 0.19 |
| 3 | 0 | 1 | 0 | 3.63 | 2.00 | 1.37 | 0.37 | 0.26 |
| 4 | 0.5 | 0 | 0.5 | 1.00 | 0.48 | 0.39 | 0.10 | 0.08 |
| 5 | 0.5 | 0.5 | 0 | 3.13 | 1.61 | 1.17 | 0.31 | 0.22 |
| 6 | 0 | 0.5 | 0.5 | 1.07 | 0.67 | 0.42 | 0.11 | 0.09 |
| 7 | 0.33 | 0.33| 0.33 | 1.22 | 0.69 | 0.46 | 0.12 | 0.11 |
| Run | Citric | Oxalic | Lactic | Ce | La | Nd | Pr | Sm |
|-----|--------|--------|--------|----|----|----|----|----|
| 1 | 0 | 0 | 1 | 0.15 | 0.09 | N.D. | N.D. | N.D. |
| 2 | 1 | 0 | 0 | 0.06 | 0.06 | N.D. | N.D. | N.D. |
| 3 | 0 | 1 | 0 | 0.19 | 0.10 | N.D. | N.D. | N.D. |
| 4 | 0.5 | 0 | 0.5 | 0.04 | 0.04 | N.D. | N.D. | N.D. |
| 5 | 0.5 | 0.5 | 0 | 0.03 | 0.04 | N.D. | N.D. | N.D. |
| 6 | 0 | 0.5 | 0.5 | 0.16 | 0.09 | N.D. | N.D. | N.D. |
| 7 | 0.33 | 0.33 | 0.33 | 0.02 | 0.03 | N.D. | N.D. | N.D. |
In a mixture experiment, the sum of the component fractions must be equal to unity, and their proportions must be non-negative. The restrictions on the levels of each factor are expressed as follows:
\[ \sum_{i=1}^{q} x_i = 1 \text{ (i. e., } 100\%) \]
\[ x_i \text{ represents the proportion of the } i^{th} \text{ component in the mixture, and } q \text{ is the number of components. The independent variables in the mixture experiments for optimization of REE extraction } (Y, \text{ mg L}^{-1}) \text{ were: inorganic acid leaching set: } x_1 (\text{H}_2\text{SO}_4, \text{ mL}), x_2 (\text{HCl}, \text{ mL}), \text{ and } x_3 (\text{HNO}_3, \text{ mL}); \text{ and organic acid leaching set: } x_1 (\text{citric, mL}), x_2 (\text{oxalic, mL}), \text{ and } x_3 (\text{lactic, mL}). \]
Analysis of variance (ANOVA) and multiple regression analyses was performed using Statistica version 13.5 (StatSoft, Inc.).
3. Results and Discussion
The use of statistical methodologies such as response surface methodology (RSM) and Box-Behnken to optimize monazite ore leaching has been reported in the literature [18]. In the present work, a statistical mixture-design technique was used to study the effects of different inorganic and organic acids and their mixtures on the REE extraction from Brazilian monazite, as described in Table 1 and Table 2. An equation was obtained for the inorganic acid leaching (H$_2$SO$_4$, HCl, HNO$_3$) of Ce$^{3+}$ (Y$_1$, Equation 2), La$^{3+}$ (Y$_2$, Equation 3), Nd$^{3+}$ (Y$_3$, Equation 4), Pr$^{3+}$ (Y$_4$, Equation 5) and Sm$^{3+}$ (Y$_5$, Equation 6) through the analysis of the multiple regressions of the experimental data:
\[
Y_1 = 3.218095x_3 \\
Y_2 = 1.807048x_3 \\
Y_3 = 1.215810x_3 \\
Y_4 = 0.325143x_3 \\
Y_5 = 0.232571x_3
\]
Effect terms of the variable $x_1$ (sulfuric acid) and $x_2$ (chloridric acid) were discarded as non-significant, as shown in the variance analysis (ANOVA). According to Figure 1, the solubilization of REE had increased following the REE molecular weight, and the order of REE extractions was Ce$^{3+}$ > La$^{3+}$ > Nd$^{3+}$ > Pr$^{3+}$ > Sm$^{3+}$.
To date, sulfuric acid is the primary acid that has been used industrially for extracting REE from monazite. However, different researchers used nitric acid to dissolve monazite and other associated metals from apatites (phosphorites) containing monazite [19]. Apparently, nitric acid is more effective for leaching REE from phosphorites than sulfuric acid [20]. Monazite from East Siberia, e.g., containing 3-7% REO, was leached in HNO$_3$ [21].
Organic acids have been studied as alternative leaching reagents for REE extraction from REE-bearing ores to address those issues and provide environmentally acceptable techniques. The organic acid is an alternative chemical to replace the strong acid in the leaching process. This is because the organic acid has a low level of a hazard than the strong acid [22]. The dissolution of minerals by organic acid weathering is usually explained based on surface reaction models in which the dissolution rate is positively correlated with the concentration of protonated, deprotonated, and organic complexes on the surface of the solid phase [23]. Metabolic products from the growth of *Aspergillus terreus* and *Paecilomyces* spp. Fungal strains have leached REE from monazite to concentrations 1.7-3.8 times those of HCl solutions. Organic acids released by these microorganisms included acetic, citric, gluconic, itaconic, oxalic, and succinic acids [16].
Figure 1. Response surface contours for chemical leaching of Brazilian monazite by inorganic acid leaching. (A) Ce$^{3+}$ extraction (mg L$^{-1}$); (B) La$^{3+}$ extraction (mg L$^{-1}$); (C) Nd$^{3+}$ extraction (mg L$^{-1}$); (D) Pr$^{3+}$ extraction (mg L$^{-1}$) and (E) Sm$^{3+}$ extraction (mg L$^{-1}$).
Figure 2. Response surface contours for chemical leaching of Brazilian monazite by organic acid leaching. (A) Ce\(^{3+}\) extraction (mg L\(^{-1}\)) and (B) La\(^{3+}\) extraction (mg L\(^{-1}\)).
An equation was obtained for the organic acid leaching (citric, oxalic, lactic) of Ce\(^{3+}\) (\(Y_6\), Equation 7) and La\(^{3+}\) (\(Y_7\), Equation 8) through the analysis of the multiple regressions of the experimental data:
\[
Y_6 = 0.084286x_3 \\
Y_7 = 0.033238x_3
\]
Effect terms of the variables \(x_1\) (citric acid) and \(x_2\) (oxalic acid) were discarded as non-significant, as shown in the variance analysis (ANOVA). According to Figure 2, REE’s solubilization has increased following the REE molecular weight, and the order of REE extractions was Ce\(^{3+}\) > La\(^{3+}\).
No contents of Nd\(^{3+}\), Pr\(^{3+}\), and Sm\(^{3+}\) were detected in the leachates. Greater than 40% solubilization of Ce\(^{3+}\) and La\(^{3+}\) was obtained by Lazo et al. [24] from an oxalic acid leaching following EDTA precipitation. Analysis of the solids determined that the REE were re-precipitating as oxalate salts [25]. Also, according to Figure 2, lactic acid was able to solubilize Ce\(^{3+}\) (Figure 2A) while mixtures of lactic and citric acid seemed to be able to solubilize La\(^{3+}\) (Figure 2B). The order of strength of studied acids is oxalic (pK\(_a\) = 1.25) > citric (pK\(_a\) = 3.13) > lactic (pK\(_a\) = 3.83).
Lactic acid is an \(\alpha\)-hydroxy acid and contains a carboxyl group adjacent to a hydroxyl group. The presence of an \(\alpha\)-hydroxyl group increases the acidity compared with that of an average monobasic acid. Lactic acid leaching systems have been employed successfully in sustainable REE recovery from monazite [26]. In addition to reducing pH, which somewhat increases phosphate minerals’ solubility, some organic acids can form complexes with the cations released from phosphate minerals and thus improve overall solubilization.
4. Conclusion
The ongoing development of new advanced technologies created increasing demands for REE in the international markets, emphasizing new resources to ensure adequate supply and access. This preliminary study indicated that the mechanism of acid leaching of Brazilian monazite depends on the acid used, possibly the solubilization of Ce\(^{3+}\) and La\(^{3+}\) under organic acid leaching conditions. These studies are essential to developing bioleaching process methods for a sustainable REE extraction.
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[23] G. Furrer, & W. Stumm, The role of surface coordination in the dissolution of δ-Al₂O₃ in dilute acids, Chimia, 37 (1983) 338-341.
[24] D.E. Lazo, L.G. Dyer, R.D. Alorro & R. Browner, Treatment of monazite by organic acids I: Solution conversion of rare earths, Hydrometallurgy, 174
Acknowledgement
A.C.S.P. Souza is grateful for the scientific initiation scholarship granted by CNPq/PIBIC/CETEM
Funding
This study was not funded by any grant
Conflict of interest
None of the authors have any conflicts of interest to declare.
Author’s contribution
Ana Carolina S. P. de Souza carried out the experiments. Ellen C. Giese conceived the original idea, supervised the project and wrote the manuscript.
About the License
The text of this article is licensed under a Creative Commons Attribution 4.0 International License
Cite this Article
A.C.S.P. Souza, E.C. Giese, An exploratory study of recovery of rare-earth elements from monazite in mild conditions using statistical-mixture design, International Research Journal of Multidisciplinary Technovation, Vol 3, Iss 2 (2021) 20-25.
DOI: https://doi.org/10.34256/irjmt2124
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Long-distance singularities in multi-leg scattering amplitudes
Einan Gardi
Higgs Centre for Theoretical Physics, School of Physics and Astronomy, The University of Edinburgh, Edinburgh EH9 3FD, Scotland, UK
E-mail: [email protected]
Øyvind Almelid
Higgs Centre for Theoretical Physics, School of Physics and Astronomy, The University of Edinburgh, Edinburgh EH9 3FD, Scotland, UK
E-mail: [email protected]
Claude Duhr
CERN Theory Division, 1211 Geneva 23, Switzerland
Center for Cosmology, Particle Physics and Phenomenology (CP3), Université Catholique de Louvain, 1348 Louvain-La-Neuve, Belgium
E-mail: [email protected]
We report on the recent completion of the three-loop calculation of the soft anomalous dimension in massless gauge-theory scattering amplitudes. This brings the state-of-the-art knowledge of long-distance singularities in multi-leg QCD amplitudes with any number of massless particles to three loops. The result displays some novel features: this is the first time non-dipole corrections appear, which directly correlate the colour and kinematic degrees of freedom of four coloured partons. We find that non-dipole corrections appear at three loops also for three coloured partons, but these are independent of the kinematics. The final result is remarkably simple when expressed in terms of single-valued harmonic polylogarithms, and it satisfies several non-trivial constraints. In particular, it is consistent with the high-energy limit behaviour and it satisfies the expected factorization properties in two-particle collinear limits.
Loops and Legs in Quantum Field Theory
24-29 April 2016
Leipzig, Germany
*Preprint numbers: Edinburgh 2016/10, CERN-TH-2016-141, CP3-16-31
†Speaker.
‡On leave from the “Fonds National de la Recherche Scientifique” (FNRS), Belgium.
1. Introduction
Long-distance singularities are a central feature of gauge-theory scattering amplitudes, and a detailed understanding of their structure is key to precision collider physics [2–42]. Owing to their factorization properties, the singularities are largely independent of the hard scattering process. Furthermore, they exponentiate and can therefore be compactly summarised by the so called soft anomalous dimension.
Until recently, the soft anomalous dimension for the scattering of any number of massless coloured particles was known to two loops. To this order it admits a remarkably simple structure consisting of a sum over colour dipoles formed by any pair of external legs [8, 13, 15–17]. In this talk we report on the recent computation of the three-loop corrections to the soft anomalous dimension [1]. The calculation we performed confirmed the expectation [15–21] that three-loop corrections depart from the above dipole structure, and correlate between the kinematic and colour degrees of freedom of up to four partons. We find that a non-vanishing correction appears already for three coloured partons, but it is a constant, involving no kinematic dependence. The new three-loop result also contributes to understanding factorization properties of scattering amplitudes in the collinear and high-energy limits.
2. Factorization at fixed-angles and the soft anomalous dimension
We are interested in the infrared (IR) structure of a scattering amplitude for \(n\) massless partons. Given external legs with momenta \(p_i\), for \(i = 1..n\), where \(p_i^2 = 0\), we consider the kinematic limit of fixed-angle scattering, where all Lorentz invariants \(p_i \cdot p_j\) are taken large. Infrared singularities (both soft and collinear) can then be factorized as follows
\[
\mathcal{M}_n(\{p_i\}, \alpha_s) = Z_n(\{p_i\}, \mu, \alpha_s) \mathcal{H}_n(\{p_i\}, \mu, \alpha_s),
\]
where \(\mu\) is a factorization scale, \(\alpha_s = \alpha_s(\mu^2)\) is the renormalised \(D\)-dimensional running coupling, \(\mathcal{H}_n\) is a finite hard scattering function, and \(Z_n\) is an operator in colour space collecting all IR singularities as poles in the dimensional regularization parameter \(\varepsilon = (4 - D)/2\). These singularities originate in loop momenta becoming either soft or collinear to any of the scattered partons (see e.g. Ref. [6]). Collinear singularities depend on the spin and momentum of that particle, and decouple from the rest of the process; their contribution is known to three-loops [24, 45], and will not be discussed here in detail. In contrast, soft singularities are independent of the spin, but they depend on the relative directions of motion and the colour degrees of freedom of all scattered particles. Hence, soft singularities are sensitive to the colour flow in the entire process. Nevertheless, they are significantly simpler than finite contributions to the amplitude, opening a unique possibility to explore multi-leg gauge-theory amplitudes at the multi-loop level.
The simplification of the soft limit is apparent already at the level of the Feynmann rules: emission of a soft gluon with momentum \(k\) off an energetic particle with momentum \(p_j \gg k\), taken at leading order in the soft gluon momentum, amounts to a factor of \(g_s T^a_i \frac{p_i^\mu}{p_i^2 + i0} = g_s T^a_i \frac{p_i^\mu}{p_i^2 + i0}\), where we replaced the momentum of the emitting particle by its four-velocity, emphasising the rescaling symmetry of this Feynman rule. This symmetry is responsible for the main features of soft singularities. The soft approximation can be equivalently formulated in configuration space, as emission
from a Wilson line following the classical trajectory of the particle with momentum $p_i$ and carrying the same colour charge:
$$\Phi_\beta = \mathcal{P} \exp \left[ i g_s \int_0^\infty dt \beta_i \cdot A^\mu(t) T^\mu_i \right],$$
(2.2)
where $\mathcal{P}$ orders the colour matrices along the path. To avoid collinear singularities we perform our calculation with non-lightlike velocities $\beta^2 \neq 0$. Considering fixed-angle scattering of $n$ legs, soft singularities are fully captured by the following Wilson-line correlator, the so-called soft function,
$$S(\{ \gamma_{ij} \} ; \mu) = \langle T(\Phi_{\beta_1} \otimes \Phi_{\beta_2} \cdots \otimes \Phi_{\beta_n} \otimes \Phi_{\beta_n}) \rangle$$
(2.3)
where the kinematic dependence appears through cusp angles, $\gamma_{ij} = 2 \beta_i \cdot \beta_j / \sqrt{\beta_i^2 \beta_j^2}$, which are invariant under velocity rescaling.
The factor $Z_n$ containing all soft and collinear singularities in Eq. (2.1) can be written as a solution of a renormalization-group equation as
$$Z_n = \mathcal{P} \exp \left\{ -\frac{1}{2} \int_0^\infty \frac{d\lambda^2}{\lambda^2} \Gamma_n(\{ p_i \}, \lambda, \alpha_s(\lambda^2)) \right\},$$
(2.4)
where $\Gamma_n$ is the so-called soft anomalous dimension matrix for multi-leg scattering, and $\mathcal{P}$ stands for path-ordering of the matrices according to the order of scales $\lambda$. $\Gamma_n$ itself is finite, and IR singularities are generated in Eq. (2.4) through the dependence of $\Gamma_n$ on the $D$-dimensional coupling, which is integrated over the scale down to zero momentum. Factorization and the rescaling symmetry of the Wilson line velocities [15–17] put stringent constraints on the functional form of $\Gamma_n$, which through three loops, must take the form
$$\Gamma_n(\{ p_i \}, \lambda) = \Gamma_n^{\text{dip}}(\{ p_i \}, \lambda) + \Delta_n(\{ \rho_{ijkl} \}),$$
(2.5)
with
$$\Gamma_n^{\text{dip}}(\{ p_i \}, \lambda) = -\frac{1}{2} \hat{\gamma}_K(\alpha_s) \sum_{i<j} \log \left( \frac{-s_{ij}}{\lambda^2} \right) T_i \cdot T_j + \sum_{i=1}^n \gamma_i(\alpha_s),$$
(2.6)
where $-s_{ij} = 2 |p_i \cdot p_j|/e^{-i \pi \lambda_{ij}}$, with $\lambda_{ij} = 1$ if partons $i$ and $j$ both belong to either the initial or the final state and $\lambda_{ij} = 0$ otherwise; $T_i$ is the colour generator in the representation of parton $i$, acting on the colour indices of the amplitude as described in Ref. [7]; $\hat{\gamma}_K(\alpha_s)$ is the universal cusp anomalous dimension [2,43,44], with the quadratic Casimir of the appropriate representation scaled out; $\gamma_i$ are the anomalous dimensions of the fields associated with external particles, which govern hard collinear singularities, currently known to three loops [24,45]. Equation (2.6) is known as the dipole formula, and captures the entirety of the soft anomalous dimension up to two loops. Finally, $\Delta_n(\{ \rho_{ijkl} \})$ represents the correction going beyond the dipole formula, which starts at three loops,
$$\Delta_n(\{ \rho_{ijkl} \}) = \sum_{\ell=3}^\infty \left( \frac{\alpha_s}{4\pi} \right)^\ell \Delta_n^{(\ell)}(\{ \rho_{ijkl} \}).$$
(2.7)
1Casimir scaling of the cusp anomalous dimension holds through three loops [43]; it may be broken by quartic Casimirs starting at four loops.
and depends on the kinematics via \textit{conformally-invariant cross ratios} (CICRs),
\[
\rho_{ijkl} \equiv \frac{(-s_{ij})(-s_{kl})}{(-s_{ik})(-s_{jl})} = \frac{\gamma_{ij} \gamma_{kl}}{\gamma_{ik} \gamma_{jl}},
\]
which are invariant under a rescaling of any of the momenta. In the following we report on the calculation of the three-loop function \( \Delta_n^{(3)}(\{\rho_{ijkl}\}) \).
With the exception of hard collinear singularities (\( \gamma_{ij}(\alpha_s) \) in Eq. (2.6)), one may compute the soft anomalous dimension \( \Gamma_n(\{p_i\},\lambda) \) to any order through the renormalization of the soft function in Eq. (2.3): in dimensional regularization, loop corrections to the soft function are scaleless integrals, which vanish in the absence of a cutoff. Hence, one may directly infer the infrared poles in \( \varepsilon \) from the ultraviolet ones. This calculation strategy has marked advantages over the alternative of extracting the infrared poles from an amplitude, since one never needs to evaluate finite corrections, and one may make direct use of the known iterative structure of renormalization along with the exponentiation properties of Wilson line correlators [35–42].
We note that \( \Delta_n^{(3)} \) is independent of the details of the underlying theory and completely determined by soft gluon interactions. In particular, this implies that \( \Delta_n^{(3)} \) is the same in QCD and in \( \mathcal{N} = 4 \) Super Yang-Mills, and it is therefore expected to be a pure polylogarithmic function of weight five. Its functional form has been constrained by considering collinear limits and the Regge limit [14–22], but despite progress in understanding these limits it remained unclear whether three-loop corrections to the dipole formula are in fact present. The situation changed with the completion of the direct computation of \( \Delta_n^{(3)} \) [1] on which we report in the present talk.
3. Computing connected graphs
We set up the calculation of the soft anomalous dimension through the renormalization of a product of semi-infinite Wilson lines with four-velocities $\beta_k$, with $\beta_k^2 \neq 0$. By considering non-lightlike lines we avoid collinear singularities, and obtain kinematic dependence via cusp angles $\gamma_{ij} \equiv 2\beta_i \cdot \beta_j / \sqrt{\beta_i^2 \beta_j^2}$. We eventually extract $\Delta^{(3)}$ for massless scattering by considering the asymptotic lightlike limit $\beta_k^2 \to 0$, where the kinematic dependence reduces to CICRs as in Eq. (2.8).
Considering the set of contributing diagrams at three loops, it is clear at the outset that the diagrams that connect the maximal number of Wilson lines, that is four lines, shown in Fig. 1, have a special status: these are the only diagrams that depend on all six cusp angles $\gamma_{ij}$ with $1 \leq i < j \leq 4$. Hence these four diagrams are expected to involve non-trivial dependence on CICRs (defined in Eq. (2.8)). Importantly, this kinematic dependence remains in place upon taking the simultaneous lightlike limit, $\gamma_{ij} \to -\infty$. In contrast, all other webs reduce in this limit to a sum of products of logarithms of $\gamma_{ij}$. This applies in particular to the webs of Fig. 2: these webs connect all of the four lines, but they never involve any set of four angles that may form a cross ratio as in Eq. (2.8). It is clear that webs connecting three or two lines out of the four, as in Figs. 3 and 4,
cannot give rise to cross ratios, and so they reduce to polynomials in logarithms of $\gamma_j$ for near lightlike kinematics. Of course, cross ratios may be formed upon summing the webs of Figs. 2, 3 and 4, but these contributions are necessarily polynomial in logarithms of the CICRs.
It follows that the primary ingredient in deriving $\Delta^{(3)}_4 \left( \{ \rho_{ijkl} \} \right)$ is the computation of the four-line connected diagrams in Fig. 1. Below we briefly describe the strategy of the calculation and the result we obtain for these diagrams, before presenting the complete result for the anomalous dimension. The computation of all diagrams will be discussed in dedicated publication [46].
We set up the calculation in configuration space, with four non-lightlike Wilson lines with four-velocities $\beta_k$. The position of the three- and four-gluon vertices off the Wilson lines are integrated over in $D = 4 - 2\varepsilon$ dimensions. Following Ref. [35, 41], we introduce an infrared regulator which exponentially suppresses contributions far along the Wilson lines. This is necessary to capture the ultraviolet singularity associated with the renormalization of the vertex where the Wilson lines meet. Upon performing the integral over the overall scale, we observe that each of the diagrams in Fig. 1 has a single $1/\varepsilon$ ultraviolet pole, without any subdivergences. The contribution of each diagram to the soft anomalous dimension is the coefficient of that pole, which is finite in $D = 4$ dimensions.
Next, considering the leftmost diagram in Fig. 1, we observe that for fixed gluon-emission vertices along the Wilson lines, the integral over the position of the four-gluon vertex gives rise to a four-mass one-loop box integral in 4 dimensions; Similarly, in each of the remaining three diagrams in Fig. 1, the integrals over the positions of the two three-gluon vertices yield a four-mass diagonal-box two-loop integral. We proceed by deriving multifold Mellin-Barnes (MB) representations for each of these off-shell four-point functions.
Next we integrate over the position of the gluon emission vertices along the Wilson lines, obtaining a MB representation of each of the connected graphs for the general non-lightlike case, depending on all of the six cusp angles $\{ \gamma_j \}$. We proceed by applying standard techniques [48] to perform a simultaneous asymptotic expansion near the lightlike limit $\gamma_j \to -\infty$, where we neglect any term suppressed by powers of $1/\gamma_j$, obtaining a sum of lower-dimensional MB integrals. These are converted into parametric integrals using the methods of Ref. [49], which we then performed by means of modern analytic integration techniques [50]. The result for the leftmost diagram in Fig. 1 reads:
$$w_{Ag} = \frac{1}{\varepsilon} \left( \frac{\alpha_s}{4\pi} \right)^3 T^a_1 T^b_2 T^c_3 T^d_4 \left[ f^{abc} f^{cde} \frac{z\bar{z} - z - \bar{z}}{z - \bar{z}} + f^{ade} f^{bce} \frac{1 - z\bar{z}}{z - \bar{z}} + f^{ace} f^{bde} \frac{1 - z - \bar{z}}{z - \bar{z}} \right] g_1(z, \bar{z}, \{ \gamma_j \})$$
(3.1)
and the one for the second diagram takes the form
$$w_{(12)(34)} = \frac{1}{\varepsilon} \left( \frac{\alpha_s}{4\pi} \right)^3 T^a_1 T^b_2 T^c_3 T^d_4 f^{abc} f^{cde} \left[ g_0(z, \bar{z}, \{ \gamma_j \}) - \frac{z\bar{z} - z - \bar{z}}{z - \bar{z}} g_1(z, \bar{z}, \{ \gamma_j \}) \right],$$
(3.2)
where $g_0$ and $g_1$ are pure polylogarithmic functions of uniform weight five in the variables $z \equiv z_{ijkl}$ and $\bar{z} \equiv \bar{z}_{ijkl}$ which are related to the CICRs of Eq. (2.8) via
$$z_{ijkl} \bar{z}_{ijkl} = \rho_{ijkl} \quad \text{and} \quad (1 - z_{ijkl})(1 - \bar{z}_{ijkl}) = \rho_{ijkl}. \quad (3.3)$$
Some more details on this computation were presented in the previous Loops and legs conference [47].
The remaining two diagrams in Fig. 1 can be obtained from $w(12)(34)$ by appropriate permutations of the lines. The sum over all four connected graphs, $w_{\text{con.}} = w_{4\ell} + w(12)(34) + w(13)(24) + w(14)(23)$, displays a drastic simplification as compared to individual diagrams, namely, individual graphs are not pure functions but the sum is. Specifically, the function $g_1$, which appears in all of them, exactly cancels in the sum, and one is left with three permutations of the function $g_0$, which has no rational prefactor. This is in agreement with the expectation that (maximally helicity-violating) amplitudes in $\mathcal{N} = 4$ Super Yang-Mills are pure and have a uniform maximal weight.
The next simplification occurs upon applying the Jacobi identity to the sum of connected 4-line webs:
$$w_{\text{con.}} = \frac{1}{\varepsilon} \left( \frac{\alpha_s}{4\pi} \right)^3 T_1 T_2 T_3 T_4 \left[ f^{a b e} f^{c d e} g_1 (z, \bar{z}, \{ \gamma_j \}) + f^{a c e} f^{b d e} g_2 (z, \bar{z}, \{ \gamma_j \}) \right],$$
where $g_1 = g_0 + [g_0]_{j \leftrightarrow k}$ and $g_2 = [g_0]_{j \leftrightarrow \ell \leftrightarrow k} + [g_0]_{j \leftrightarrow k}$. Crucially, the functions $g_{1,2}(z, \bar{z}, \{ \gamma_j \})$ separate as follows:
$$g_{1,2}(z, \bar{z}, \{ \gamma_j \}) = P_{1,2}(z, \bar{z}) + Q_{1,2}(\{ \log (\gamma_j) \}),$$
where $P_{1,2}(z, \bar{z})$ is a sum of harmonic polylogarithms (of weight 5) depending exclusively of on CICRs via $z$ and $\bar{z}$, while $Q_{1,2}(\{ \log (\gamma_j) \})$ is a polynomial in the logarithms of $\gamma_j$. This split must have happened for the full result for $\Delta_n$ to be a function of CICRs: indeed $Q_{1,2}(\{ \log (\gamma_j) \})$ cancels against contributions of the remaining diagrams --- which are also polynomial in $\{ \log (\gamma_j) \}$ --- leaving behind pure CICR dependence.
4. Colour structure and colour conservation at three loops
Let us now turn to discuss the colour structure of the soft anomalous dimension for $n$ coloured lines. According to the non-Abelian exponentiation theorem [42] the colour factors in $\Delta_n$ must all correspond to connected graphs. Thus, at three loops we expect the “quadrupole” colour structures of Fig. 1, i.e., $T_i T_j T_k T_l f^{a b c} f^{d e f}$ plus permutations, where the four lines connected $(i,j,k,l)$ are any subset of four out of the $n$ lines.
The next question is then whether any other colour factor is admissible in $\Delta_n(3)$, namely ones that involve fewer than four lines. One possibility could be tripoles correcting correlating three partons, with colour factors proportional to $i f^{a b c} T_i T_j T_k$. Such tripoles appear starting from two loops for non-lightlike Wilson lines [25–35], but are excluded in the lightlike case at any order because the corresponding kinematic dependence on the three momenta is bound to violate the rescaling symmetry constraints [15–17]. While a constant correction proportional to $i f^{a b c} T_i T_j T_k$ is excluded by Bose symmetry, kinematic-independent corrections involving three lines of the form $f^{a b c} f^{d e f} \{ T_i, T_j, T_k \}$ as the first diagram on Fig. 3, are admissible and do indeed appear.
---
3One notes that the separation in (3.5), while highly constraining, is not unique: powers of logarithms of CICRs can be expressed in either way. The computation of the remaining diagrams of Figs. 2, 3 and 4, uniquely fixes the answer.
4In this context a “connected graph” is one that remains connected upon removing all Wilson lines, so for example all diagrams in Fig. 1 are connected while all those of Fig. 2 are non-connected. This does not imply that the latter do not contribute – they do, but with the colour factors of the former. For further details see Refs. [35, 38–42].
We conclude that the general form of the non-dipole correction to the soft anomalous dimension for \( n \) coloured lines is given by
\[
\Delta_n^{(3)}\left(\{\rho_{ijkl}\}\right) = 16 f_{abc} f_{cde} \left\{ -C \sum_{i=1}^{n} \sum_{j \neq k \neq l}^{n} \left[ T_{i}^{a}, T_{i}^{d} \right] T_{k}^{b} T_{l}^{c} + \sum_{1 \leq i < j < k < l \leq n} \left[ T_{i}^{a} T_{j}^{b} T_{k}^{c} T_{l}^{d} \right] \mathcal{F} \left( \rho_{ikjl}, \rho_{iklj} \right) + T_{i}^{a} T_{j}^{b} T_{k}^{c} T_{l}^{d} \mathcal{F} \left( \rho_{ijkl}, \rho_{ijlk} \right) \right\} ,
\]
where \( C \) is a constant and \( \mathcal{F} \) is a function of two CICRs. Note that the contribution proportional to the constant \( C \) is present starting from the three-line case, \( n = 3 \). Both \( C \) and \( \mathcal{F} \) are independent of the colour degrees of freedom. The terms in this sum are not all independent, because of the antisymmetry of the structure constants and the Jacobi identity. We emphasise that \( C \) and \( \mathcal{F} \) are independent of the number of legs \( n \). We can therefore determine these functions by considering the simplest case of four Wilson lines, \( \Delta_4^{(3)} \).
In organising the calculation we made use of non-Abelian exponentiation, and computed webs, namely diagrams that contribute directly to the exponent. A web can be either an individual connected diagram, as in Fig. 1, or a set of non-connected diagrams which are related by permuting the order of gluon attachments to the Wilson lines [38–42]; representative diagrams from such webs are shown in Fig. 2. In either of these cases, the contribution to \( \Delta_4^{(3)} \) is associated with fully connected colour factors. The classification of webs connecting four and three Wilson lines was done in Ref. [42].
Another important element in organising the calculation is colour conservation. The anomalous dimension \( \Gamma_n \) is an operator in colour space that acts on the hard amplitude, which is a colour singlet and must therefore satisfy [8]
\[
\left( \sum_{i=1}^{n} T_{i}^{a} \right) \mathcal{H}_n = 0 .
\]
This colour conservation constraint is implicit in Eqs. (2.6) and (4.1). When computing \( \Delta_4^{(3)} \) one may form a colour basis by systematically eliminating \( T_4 \) in favour of \( T_i \), \( 1 \leq i \leq 3 \), thereby reducing all four-line colour factors to three-line ones. This way colour conservation relates between diagrams connecting a different number of Wilson lines: the diagrams in Figs. 3 and 4, which connect three or two Wilson lines, contribute together with those connecting four lines. Let us see this explicitly. The sum of all three-loop webs connecting four lines can be cast into the Bose symmetric form
\[
G_4(1,2,3,4) = T_1^{a} T_2^{b} T_3^{c} T_4^{d} \left[ f^{a b c d e} H_4[(1,2),(3,4)] + f^{a c b d e} H_4[(1,3),(2,4)] + f^{a d b c e} H_4[(1,4),(2,3)] \right] ,
\]
where the kinematic function \( H_4 \) satisfies the following permutation properties: \( H_4[(1,2),(3,4)] = -H_4[(2,1),(3,4)] = H_4[(3,4),(1,2)] \); this function depends on logarithms of cusp angles as well as on non-trivial functions of CICRs. Using colour conservation to eliminate \( T_4 \) in favour of the
sum of the other three generators, we convert the result to a three-line colour basis:
\[
G_4(1, 2, 3, 4) = -\frac{1}{2} f^{a be} f^{c de} \sum_{(i,j,k) \in \{1,2,3\}} \left\{ T^a_i, T^b_j \right\} T^c_j T^d_k \left( H_4[(i,j),(k,4)] + H_4[(i,k),(j,4)] \right) .
\] (4.4)
Let us consider next diagrams that connect fewer Wilson lines. The sum of all two-line three-loop diagrams may be written as
\[
G_2(1, 2) = \text{dipole} - f^{a be} f^{c de} \sum_{(i,j,k) \in \{1,2,3\}} \left\{ T^a_i, T^b_j \right\} \left\{ T^c_j, T^d_k \right\} H_2(i, j, k),
\] (4.5)
where the first term represents the dipole \( T_1 \cdot T_2 \) contribution to \( \Gamma_n^{\text{dip}} \) of Eq. (2.6). In contrast, the second term involving an anti-commutator on each of the lines is relevant for the calculation of \( \Delta_n^{(3)} \); its kinematic dependence is contained in \( H_2(1, 2) = H_2(2, 1) \). Similarly, the sum of all three-line diagrams takes the form
\[
G_3(1, 2, 3) = f^{a be} f^{c de} \sum_{(i,j,k) \in \{1,2,3\}} \left\{ T^a_i, T^b_j \right\} T^c_j T^d_k H_3[i, j, k],
\] (4.6)
with \( H_3[i, j, k] = H_3[i, k, j] \). We omitted here the tripole term, proportional to \( f^{a be} T^b_i T^c_k T^e_j \), which vanishes for lightlike kinematics where \( \gamma_j \rightarrow -\infty \). Note that in this limit \( H_2 \) and \( H_3 \) are necessarily polynomials in \( \log(-\gamma_j) \).
Summing over all subsets of two and three lines out of four and using colour conservation, we have
\[
G_2(1, 2, 3, 4) + G_3(1, 2, 3, 4) = \text{dipoles} + f^{a be} f^{c de} \left[ \sum_{(i,j,k) \in \{1,2,3\}} \left\{ T^a_i, T^b_j \right\} T^c_j T^d_k U(i, j, k), 4 \right]
- \frac{1}{2} \sum_{1 \leq i \leq j \leq 3} \left\{ T^a_i, T^b_j \right\} \left\{ T^c_j, T^d_i \right\} \left( H_2[i, j, 4] + H_3[j, 4, 3] + H_3[4, j, 3] \right) \bigg] \bigg],
\] (4.7)
where
\[
U(i, j, k, 4) \equiv H_3[i, j, k] - H_3[i, k, j] - H_3[i, j, 4] - H_3[i, 4, j] - H_3[4, j, i] - H_3[4, i, j] + H_3[4, j, k] - H_3[4, k, j] \bigg] \bigg).
\] (4.8)
The three- and two-line contributions of Eq. (4.7) must be added to the contribution of the four-line diagrams in Eq. (4.4) to obtain the final, gauge-invariant result for the anomalous dimension, \( \Delta_4^{(3)} = G_4(1, 2, 3, 4) + G_3(1, 2, 3, 4) + G_2(1, 2, 3, 4) \). This may then be contrasted with the general form for \( \Delta_4^{(3)} \) in Eq. (4.1). Upon applying colour conservation to the latter, the comparison leads to the following conclusions:
- The combination multiplying the two-line colour factor in Eq. (4.7) must be proportional to the constant \( C \) in Eq. (4.1):
\[
C = \frac{1}{3} \left( H_3[i, j, k] + H_3[j, k, i] + H_3[k, i, j] \right) \bigg],
\] (4.9)
• The function $\mathcal{F}$ is obtained through the following combination of four-, three- and two-line kinematic functions $H_n$:
$$\mathcal{F}(p_{ijkl}, p_{likj}) = H_4[(i, j), (k, l)] - \frac{2}{3} \left( H_3[i, \{j, k\}] - H_3[i, \{j, l\}] - H_3[j, \{i, k\}] + H_3[j, \{i, l\}] \right)$$
$$+ H_3[k, \{i, l\}] - H_3[k, \{i, j\}] - H_3[l, \{i, k\}] + H_3[l, \{i, j\}] \right).$$
(4.10)
The above equations put strong constraints on the kinematic functions $H_n$: the function $\mathcal{F}$ depends on CICRs, while the individual functions $H_n$ on the right-hand side of Eq. (4.10) depend on logarithms of cusp angles. These must therefore conspire to combine into logarithms of CICRs. In addition, $C$ is a constant, so the kinematic dependence of the functions $H_3$ must cancel in the sum in Eq. (4.9). Our computation satisfies all these constraints, providing a strong check of the result.
5. The three-loop correction to the soft anomalous dimension
Adding up all contributing webs according to Eqs. (4.10) and (4.9), we find the following results for the function $\mathcal{F}$ and the constant $C$ of Eq. (4.1):
$$\mathcal{F}(p_{ijkl}, p_{likj}) = F(1 - z_{ijkl}) - F(z_{ijkl}),$$
$$C = \zeta_3 + 2\zeta_2 \zeta_3,$$
(5.1)
where we recall that $z = z_{ijkl}$ and $\bar{z} = \bar{z}_{ijkl}$ are related to the CICRs by Eq. (3.3) and
$$F(z) = \mathcal{L}_{10101}(z) + 2\zeta_2 [\mathcal{L}_{001}(z) + \mathcal{L}_{100}(z)],$$
(5.2)
where the functions $\mathcal{L}_w(z)$ are Brown’s single-valued harmonic polylogarithms (SVHPLs) [51] (see also Ref. [53]), where $w$ is a word made out of 0’s and 1’s. Note that we kept implicit the dependence of these functions on $\bar{z}$. SVHPLs can be expressed in terms of ordinary harmonic polylogarithms (HPLs) [52] in $z$ and $\bar{z}$. The result for $F$ in terms of HPLs is attached in computer-readable format to Ref. [1].
Let us now briefly discuss the main features of the result. First, we note that while $F(z)$ is defined everywhere in the physical parameter space, it is only single-valued in the part of the Euclidean region (the region where all invariants are spacelike, $p_i \cdot p_j < 0$) where $z$ and $\bar{z}$ are complex conjugate to each other. Single-valuedness ensures that $\Delta_n^{(3)}$ has the correct branch cut structure of a physical scattering amplitude [53, 54]: it is possible to analytically continue the function to the entire Euclidean region while the function remains real throughout [55]. Next note that if one considers $F(z)$ as a function of two independent variables $z$ and $\bar{z}$ (not a complex conjugate pair) this function has branch points for $z$ and $\bar{z}$ at 0, 1 and $\infty$. Crossing momenta from the final to the initial state is realized by taking monodromies around these points.
Making the permutation (Bose) symmetry manifest, the final answer may be written as:
\[
\Delta^{(3)}_a = 16 \sum_{1 \leq i < j < k < l \leq n} \mathbf{T}^i_j \mathbf{T}^k_l \mathbf{T}^d_l \left[ f_{abc} f_{cde} \left( F(1 - 1/\tilde{z}_{ijkl}), 1 - 1/\tilde{z}_{ijkl}) - F(1/\tilde{z}_{ijkl}, 1/\tilde{z}_{ijkl}) \right) \\
+ f_{ace} f_{bed} \left( F(1 - \tilde{z}_{ijkl}), 1 - \tilde{z}_{ijkl}) - F(\tilde{z}_{ijkl}, \tilde{z}_{ijkl}) \right) \\
+ f_{ade} f_{bce} \left( F(1/(1 - \tilde{z}_{ijkl}), 1/(1 - \tilde{z}_{ijkl})) - F(\tilde{z}_{ijkl}/(\tilde{z}_{ijkl} - 1), \tilde{z}_{ijkl}/(\tilde{z}_{ijkl} - 1)) \right) \\
- C \sum_{i=1}^n \sum_{j,k \neq i} f_{abc} f_{cde} \left( \mathbf{T}^i_j \mathbf{T}^k_l \mathbf{T}^c_j \mathbf{T}^e_k \right) \right]
\]
(5.3)
where, as in Eq. (4.1), colour conservation among the \( n \) lines is implicit. For any subset of four lines (\( i, j, k \) and \( l \)) Bose symmetry is realized on the function \( F \) by the action of the group \( S_3 \) which keeps the momentum \( p_i \) fixed and permutes the remaining three momenta. As is clear from Eq. (5.3), this group acts on the space of SVHPLs by change of arguments generated by the transformations \((z, \bar{z}) \mapsto (1 - \bar{z}, 1 - z) \) and \((z, \bar{z}) \mapsto (1/\bar{z}, 1/z) \), with \( z = z_{ijkl} \). Geometrically this corresponds to exchanging the three singularities at \( z \in \{0, 1, \infty\} \). Moreover, the space of all HPLs, and hence also SVHPLs, is closed under the action of this \( S_3 \); this gives rise to functional relations among HPLs with different arguments, making it possible to express all the terms in Eq. (5.3) through SVHPLs with argument \( z \).
An additional symmetry group \( Z_2 \) arises from the definition of \((z, \bar{z}) \) in Eq. (3.3), which is invariant under swapping the two, \( z \leftrightarrow \bar{z} \). Hence \( F(z) \) must be invariant under this transformation, i.e. \( F(\bar{z}) = F(z) \). This symmetry is realized on the space of SVHPLs by the operation of reversal of names, namely, if \( w \) is a word made out of \( 0 \)'s and \( 1 \)'s, and \( \bar{w} \) the reversed word, then we have \( \mathcal{L}_w(\bar{z}) = \mathcal{L}_w(z) + \ldots \), where the dots indicate terms proportional to multiple \( \zeta \) values. Even functions then correspond to ‘palindromic’ words (possibly up to multiple \( \zeta \) values), and indeed Eq. (5.2) is ‘palindromic’.
Finally, let us comment on the momentum conserving limit of \( \Delta^{(3)}_a \), which corresponds to two-to-two massless scattering. In this limit we have \( \bar{z} = z = s_{12} / s_{13} = -s/(s+t) \). It follows that for two-to-two massless scattering \( F(z) \) can be expressed entirely in terms of HPLs with indices \( 0 \) and \( -1 \) depending on \( s/t \), in agreement with known results for on-shell three-loop four-point integrals [34, 56, 57].
A further consistency check of the result is available upon specialising to the Regge limit\(^5\). By expanding Eq. (5.2) at large \( s/(-t) \) we find no \( \alpha_s^2 \ln^p(s/(-t)) \) for any \( p > 0 \): \( \Delta^{(3)}_a \) simply tends to a constant in this limit. This is entirely consistent with the behaviour of a two-to-two scattering amplitude in the Regge limit [19, 20, 58]; indeed, the dipole formula alone is consistent with predictions from the Regge limit through next-to-next-to-leading logarithms at three loops [58].
\(^5\)Taking the Regge limit requires analytic continuation to the physical region of \( 2 \rightarrow 2 \) scattering, to be discussed in detail in [46].
6. Two-particle collinear limits
Finally, let us comment on the behaviour of $\Delta_n^{(3)}$ in the limit where two final-state partons become collinear. A well-known property of an $n$-parton scattering amplitude is that the limit where any two coloured partons become collinear can be related to an $(n-1)$-parton amplitude:
$$\mathcal{M}_n(p_1, p_2, \{p_j\}) \xrightarrow{|P|^2 \to 0} \mathbf{Sp}(p_1, p_2) \mathcal{M}_{n-1}(P, \{p_j\}),$$
(6.1)
where one of the partons in $\mathcal{M}_{n-1}(P, \{p_j\})$ replaces the collinear pair, and has a colour charge $T = T_1 + T_2$ and momentum $P = p_1 + p_2$, while the remaining $(n-2)$ partons $\{p_j\}$ are the non-collinear ones in the original amplitude, which we refer to as ”the rest of the process” below. The splitting amplitude $\mathbf{Sp}(p_1, p_2)$ is an operator in colour space which captures the singular terms for $P^2 \to 0$. All elements in Eq. (6.1) have infrared singularities, and these must clearly be related. Furthermore, $\mathbf{Sp}$ is expected to only depend on the quantum numbers of the collinear pair [59] to all orders in perturbation theory. Hence also its soft anomalous dimension,
$$\Gamma_{\mathbf{Sp}} = (\Gamma_n - \Gamma_{n-1})|_{|P|^2} = \Gamma_{\mathbf{Sp}}^{\text{dip}} + \Delta_{\mathbf{Sp}},$$
(6.2)
must be independent of the momenta and colour degrees of freedom of the rest of the process. This property is automatically satisfied for the dipole formula, but it is highly non-trivial for it to persist when quadrupole corrections are present. Indeed, the quadrupole interaction might introduce correlations between the collinear pair and the rest of the process. In Refs. [16, 18] this property was used to constrain $\Delta_n$, but this was done under the assumption that $C$ in Eq. (4.1) vanishes. Given our result for $\Delta_n^{(3)}$, the non-dipole correction to the splitting amplitude at three loops are determined:
$$\Delta_{\mathbf{Sp}}^{(3)} = (\Delta_n^{(3)} - \Delta_{n-1}^{(3)})|_{|P|^2} = -24(\xi_3 + 2\xi_2 \xi_3) \left( f^{a b c e f d e} \left\{ T_1^a, T_1^b \right\} \left\{ T_2^c, T_2^d \right\} + \frac{1}{2} C_2^2 \mathbf{T}_1 \cdot \mathbf{T}_2 \right).$$
(6.3)
We note that $\Delta_{\mathbf{Sp}}^{(3)}$ only depends on the colour degrees of freedom of the collinear pair, and is entirely independent of the kinematics, and hence fully consistent with general expectations\footnote{We recall that strict collinear factorization is restricted to time-like kinematics with both collinear partons in the final state, but it is violated for space-like splitting [60].} [59]. We emphasise that $\Delta_{\mathbf{Sp}}^{(3)}$ is independent of the value of $n$ that was used to compute it. In particular, $\Delta_{\mathbf{Sp}}^{(3)}$ agrees with $\Delta_3^{(3)}$ for $n = 3$, in agreement with the fact that $\Delta_2^{(3)} = 0$. Indeed, the fact that the difference in Eq. (6.3) is independent of $n$ requires intricate relations between different sets of diagrams and thus provides a highly non-trivial check of the calculation.
7. Conclusions
To conclude, we computed [1, 46] all connected graphs contributing to the soft anomalous dimension in multi-parton scattering and determined the first correction going beyond the dipole formula. We find that such corrections appear at three-loops already for three coloured partons, but they only involve kinematic dependence in amplitudes with at least four coloured partons, when...
IR singularities at three-loops
Einan Gardi
conformally-invariant cross ratios can be formed. The final result is remarkably simple: it is expressed in terms of single-valued harmonic polylogarithms of uniform weight five. Finally, we recover the expected behaviour of amplitudes in both the Regge limit and in two-particle collinear limits, and make further concrete predictions in both these limits.
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On an elliptic system with symmetric potential possessing two global minima
Nicholas D. Alikakos* and Giorgio Fusco†
Abstract
We consider the system
\[ \Delta u - W_u(u) = 0, \quad \text{for } u : \mathbb{R}^2 \to \mathbb{R}^2, \quad W : \mathbb{R}^2 \to \mathbb{R}, \]
where \( W_u(u) = (W_{u_1}(u), W_{u_2}(u)) \), in an equivariant class of functions. We prove that there exists \( u \), a two-dimensional solution, which satisfies the conditions
\[ u(x_1, x_2) \to a^\pm, \quad \text{as } x_1 \to \pm \infty, \]
where \( a^+, a^- \in \mathbb{R}^2 \) are the two global minima of the potential \( W \). We also consider the problem on bounded rectangular domains with Neumann boundary conditions and also give higher-dimensional extensions. The problem above was first studied by Alama, Bronsard, and Gui in [1].
1 Introduction
We begin by describing the general context. The problem we examine is a simple but representative example. The objects of study are primarily certain entire solutions to
\[ \Delta u - W_u(u) = 0, \quad \text{for } u : \mathbb{R}^N \to \mathbb{R}^N, \quad W : \mathbb{R}^N \to \mathbb{R}. \]
Here, \( W \) is a potential that has a finite number of (global) minima, also called ‘phases’, \( M = \{a_1, \ldots, a_n\} \), with \( W(a_1) = \cdots = W(a_n) = 0 \) and \( W(u) > 0 \) otherwise. We note that (1.1) includes solutions
\[ u : \mathbb{R}^i \to \mathbb{R}^N, \quad \text{for } 1 \leq i < N, \]
by trivial extension. The entire solutions we are seeking are bounded and, in addition, they approach the minima of \( W \) in certain directions at infinity. For example, if \( i = 1 \), then (1.1) becomes a Hamiltonian system of second-order ODEs and the solutions of interest are those satisfying the ‘boundary’ conditions
\[ u(x_1) \to a^\pm, \quad \text{as } x_1 \to \pm \infty. \]
Figure 1: The potential $W$ with two minima $a^+, a^-$.
Such solutions for $i = 1$ are known as *heteroclinics*, and the corresponding problem is known as the connection problem \[19\].
Another important hypothesis on $W$ is symmetry. We assume that $W(gu) = W(u)$, for all $g \in G$,
where $G$ is a finite reflection subgroup of the orthogonal group $O(\mathbb{R}^N)$, and we seek $G$-equivariant solutions to (1.1), that is, solutions satisfying
$$u(gx) = gu(x), \text{ for all } g \in G.$$
The *fundamental region* $F$ for a finite subgroup of $O(\mathbb{R}^N)$ is a convex set, actually it is the intersection of half-spaces \[10\]. It is defined in Section 3, and it plays a role in our considerations. For the main example in this paper, $N = n = 2$, $G = \mathcal{H}_2^2$, the dihedral group with four elements $\{I, T_1, T_2, S\}$ (the two reflections with respect to the axes $u_1$ and $u_2$, the rotation by $\pi$, and the identity), while $F$ in this case is $\{(u_1, u_2) | u_1 \geq 0, u_2 \geq 0\}$ and $a^\pm = (\pm a, 0)$ for $a > 0$.
Problem \[(1.1)\] has variational structure. It is clearly the Euler-Lagrange equation corresponding to the functional
$$J(u) = \int_{\mathbb{R}^N} \left\{ \frac{1}{2} |\nabla u|^2 + W(u) \right\} \ dx.$$
An important feature of the problem and also a source of difficulty is that for the solutions we are seeking, for $N > 1$, the functional $J$ is not finite. For $N = 1$, $J$ coincides with the action; in this case, it is finite and heteroclinic solutions or connections can be obtained as minimizers of the action in the class of functions approaching $a^\pm$ at $\pm\infty$ (see \[2\] for the scalar case and \[5\] for the vector one).
The problem at hand is of interest because it is nonconvex and also a system. Moreover, the class of solutions sought are not radial. It originates from geometric evolution and phase transitions. The relevant dynamic problem $u_t = \varepsilon^2 \Delta u - W_u(u)$, on $\mathbb{R}^N$, is known as the vector Allen-Cahn equation; this is a gradient flow of the functional
$$\int_{\mathbb{R}^N} \left\{ \frac{1}{2} |\varepsilon \nabla u|^2 + W(u) \right\} \ dx.$$
For small positive $\varepsilon$, one expects that typical initial data will evolve quickly, at an $O(1)$ timescale, towards the set $M$ of wells, so that the domain is partitioned into *phase regions*, in each
one of which \( u \) is approximately constant \((u \simeq a_i)\). These regions are separated by thin zones, the \textit{diffused interfaces}, that evolve approximately by the geometric law \( V = \varepsilon^2 H \). Here, \( V \) is the normal velocity and \( H \) the mean curvature of the interface. The profile of the solution near the interfaces is a rescaled connection. At a \textit{junction}, the meeting point of the interfaces, the angles attain certain values (the \textit{Plateau conditions}) that remain fixed as long as the junction exists. For example, for \( N = 2 \) and a triple-well potential, typically, triple-junctions are formed. The structure of \( u \) near the interface and away from the triple-junction is essentially one-dimensional, depending only on the distance from the interface, with a profile close to a scaled version of a solution to \((1.1)\) with \( i = 1, N = 2 \). This is plausible since at the interface the Laplacian and the free term balance each other, to principal order in \( \varepsilon \), and thus \((1.1)\) is satisfied approximately. The angle conditions are determined by the transition energies connecting the states on each side of the interface. On the other hand, at the junction the structure is two-dimensional and is close to a scaled solution of \((1.1)\) with \( i = 2, N = 2 \). We refer to \([8]\) for formal and rigorous evidence supporting these scenarios. The rigorous analysis of the PDE solution at the junction was done subsequently in \([7]\) for a potential respecting the symmetries of the equilateral triangle.
The main example of the present paper is also motivated from the dynamics of interfaces. As was established in \([3]\), there are multiple-well potentials \( W \) for which the connection problem between two phases admits two (or more) distinct solutions. To be specific, assume that there exist precisely two connections \( e_{\pm} \) connecting two of the wells of the potential. As a result, the interface separating these two phases is made up of two types of pieces (see Figure 1 in \([3]\)). Simulations show that a wave is generated on the interface itself, which propagates and converts the interface into the type with lesser action. The structure of the solution at the boundary between these pieces is two-dimensional, and well approximated by a rescaled solution to
\[
\begin{align*}
\Delta u - W_u(u) &= -c \frac{\partial u}{\partial x_2}, \quad \text{for } u : \mathbb{R}^2 \to \mathbb{R}^2, \\
u(x_1, x_2) &= a^\pm, \quad \text{as } x_1 \to \pm \infty, \\
u(x_1, x_2) &= e^{\pm}(x_1), \quad \text{as } x_2 \to \pm \infty.
\end{align*}
\]
Problem \((1.2)\) is a travelling-wave problem with speed \( c \). If \( e_+ \) and \( e_- \) have equal actions, then \( c = 0 \) and the speed of the wave, to principal order, is zero. In simulations we observe propagation also in this case but now slower and with a speed apparently determined by geometric effects. In the present paper we study \((1.2)\) with \( c = 0 \). Problem \((1.2)\) for \( c \neq 0 \) is, to our knowledge, still open \([9]\).
Returning back to the discussion of triple-junctions on the plane, we note that there is an analog in three dimensions. \( W \) now has to be a quadruple-well potential \((n = 4)\). The interfaces become surfaces and their meeting point is a quadruple-junction where the four phases coexist. At the junction, the solution is approximated by a rescaled solution to \((1.1)\) with \( N = 3 \). This has been established at the level of formal asymptotics in \([4]\); the rigorous analysis has appeared very recently in \([11]\).
The discussion above suggests that there are three important numbers in the study of \((1.1)\) that can be singled out.
- The \textit{number of phases}, which equals the number of wells, that is, the number of minima.
• The minimal dimension in the $u$-space that allows coexistence of a given number of phases. For example, for coexistence of three phases, $u$ has to be two-dimensional.
• The genuine dimension of the solution to (1.1), that is, the minimal $i$ in (1.1) that describes the solution.
We now come to the statement of our main results. We begin with the hypotheses.
(h1) The potential $W$ is $C^2$, $W : \mathbb{R}^2 \to \mathbb{R}_+ \cup \{0\}$, and has exactly two nondegenerate global minima $a^\pm$, where $a^+ = (a, 0)$, $a^- = (-a, 0)$, for $a > 0$. Also, $\partial^2 W(u) \geq c^2 \text{Id}$, for $|u - a^\pm| < r_0$.
(h2) $W$ has the symmetry of the dihedral group $\mathcal{H}^2_2$. Thus $W(gu) = W(u)$, $g \in \mathcal{H}^2_2$. The solution $u$ is $\mathcal{H}^2_2$-equivariant, that is, $u(g(x)) = g(u(x))$, $g \in \mathcal{H}^2_2$. Finally, we assume that $W(u) \geq \max_{\partial C_0} W$, for $u$ outside a certain bounded, $\mathcal{H}^2_2$-symmetric, convex set $C_0$.
(h3) We set $D := \{(u_1, u_2) \mid u_1 \geq 0\}$. We assume that there exists a $C^2$ function $Q : D \setminus \{a^+\} \to \mathbb{R}_+ \cup \{0\}$, convex, with $Q(u) > 0$ for $u \in D \setminus \{a^+\}$, $Q(u) = |u - a^+|$ for $|u - a^+| < r_0$, satisfying the relation
$$W_u(u) \cdot Q_u(u) \geq 0,$$
for $u \in D$.
(h4) The ‘scalar’ trajectory $e_0$ which always exists by symmetry and as a curve lies on the $u_1$ axis and connects $a^+$, $a^-$, is assumed not to be a global minimum of the action
$$E(U) = \int_{\mathbb{R}} \left\{ \frac{1}{2} |U_x|^2 + W(U) \right\} dx$$
among the trajectories connecting $a^-$ and $a^+$. It follows by [5] that there exists at least one pair of connecting trajectories $e_{\pm}$ which globally minimize the action in the class of trajectories that connect $a^\pm$ and with action strictly less than that of the scalar trajectory, $E(e_{\pm}) < E(e_0)$. We denote the set of minimizing connections of the action by $A$.
Under the hypotheses above, we establish the following
**Theorem 1.1.** There exists a solution $u$ to
$$\Delta u - W_u(u) = 0,$$
for $u : \mathbb{R}^2 \to \mathbb{R}^2$,
which is $\mathcal{H}^2_2$-equivariant and satisfies the estimate
$$|u(x) - a^+| < Me^{-c|x_1|}, \text{ for } x_1 \geq 0,$$
\footnote{The symmetry of $W$ assumed in (h2) implies that $W_{u_2}(u_1, 0) = 0$. Consequently, the solution of the scalar equation $e_{x_1}^2 - W_{u_1}(e, 0) = 0$, $e(\pm \infty) = \pm a$, extends trivially to a solution of (1.1) by setting $e_0(x_1) = (e(x_1), 0)$. We normalize it by taking $e(0) = 0$.}
where $M$ is a constant depending only on $W$ and $c$ is as in (h$_1$), which in particular implies that
\begin{equation}
(1.3) \quad u(x) \neq 0.
\end{equation}
Also,
\begin{equation}
(1.4) \quad u(x) \neq e_0(x_1), \quad (e_0(0) = 0)
\end{equation}
where $e_0(x_1)$ is the scalar connection introduced in (h$_4$).
Moreover the solution is genuinely two-dimensional\footnote{See the discussion following (1.1); $u$ cannot be described by a function with $i = 1.$} there exists a sequence $x_2^n \to \infty$, such that
\begin{equation}
(1.5) \quad u(x_1, x_2^n) \to \tilde{e}_+(x_1) \quad \text{and} \quad u(x_1, -x_2^n) \to \tilde{e}_-(x_1),
\end{equation}
where $\tilde{e}_\pm$ are connecting orbits of $a^+, a^-$, symmetric to each other, with $\tilde{e}_\pm(0) = 0$, and distinct from the scalar $e_0$.
The theorem above is modeled after a similar result in Alama, Bronsard, and Gui [1]. In spite of the many similarities between the two results, there are also significant differences that stem mainly from the hypotheses and the methods of proof. In [1], the authors consider an expanding sequence of infinite horizontal strips and impose Dirichlet conditions that effectively tie the solution to a given pair of connections in the $x_2$-direction and to the two minima in the $x_1$-direction. We instead consider a unilateral constraint only in the $x_1$-direction that forces the solution to be close to the minima at $\pm \infty$ and otherwise minimize freely, thus solving a Neumann problem on each strip. We derive information in the $x_2$-direction \textit{a posteriori}, and at the very end. As a result, for example, contrary to [1], we do not need to assume uniqueness of the pair of connections $e_\pm$ (see Example 2 below) and thus allow, in principle, the existence of multiple solutions.
Easy estimates allow the passage to a limiting $u$ that satisfies the equation in the whole plane. The task then is to show that $u$ is not trivial. Equivariance excludes the zero-dimensional solutions $u \equiv a^\pm$ and also excludes one-dimensional solutions like $e_\pm$. For excluding the possibility $u \equiv 0$, we utilize a uniform (with respect of the expanding domains) exponential estimate which is among the main tools in our work. Here we invoke (h$_3$), the $Q$-monotonicity of $W$. For excluding the scalar connection $e_0$, we utilize (h$_4$).
The other major point is a positivity result that underlies the whole procedure: we show that the minimizers of the constrained problems leave the fundamental region invariant.
In passing to the limit, we follow an idea from [1] that gives tight upper and lower bounds (see Steps 1, 2 and 3 in the proof of Theorem 7.1). We note that [1] follows closely the methodology of [7]. The limiting procedure along strips can be found in [15], [16].
Our next theorem concerns the bounded-domain problem on large rectangles.
\textbf{Theorem 1.2.} Suppose that $W$ satisfies hypotheses (h$_1$), (h$_2$). Then, we can determine $R_0 \geq 1$ and $\mu_0 \geq 1$, so that for $R > R_0$ and $\mu \geq \mu_0$, there exists an equivariant minimizer of
the functional \( J_{R,\mu}(u) = \int_{\Omega_{R,\mu}} \left\{ \frac{1}{2} |\nabla u|^2 + W(u) \right\} \, dx \) that satisfies, weakly in \( W^{1,2}(\Omega_{R,\mu}) \), the problem
\[
\begin{align*}
\Delta u - W_u(u) &= 0, & \text{in } \Omega_{R,\mu}, \\
\frac{\partial u}{\partial n} &= 0, & \text{on } \partial \Omega_{R,\mu}.
\end{align*}
\]
Moreover, if in addition \((h3), (h4)\) are satisfied, then the solution tends, as \( R \to \infty \), to a solution as described in (1.5) in Theorem 1.1. Here, \( \Omega_{R,\mu} = \{(x_1, x_2) \mid |x_1| < \mu R, |x_2| < R\} \).
Thus, it is genuinely two-dimensional.
The paper is organized as follows. In Section 1 we give two examples that fit in the framework of Theorems 1.1 and 1.2, and two higher-dimensional extensions of these theorems. The first extension is a three-dimensional result whose purpose is to bring out the hierarchy of the solutions that can exist in the same problem. Such hierarchies have been found already in \([\text{III}]\). The second extension is an \( N \)-dimensional result closer in spirit to Theorem 1.1, together with an application to a system that possesses an entire radial solution. In the rest of the paper we give the proofs. Specifically, in Section 3 we introduce and solve the constrained problem, in Section 4 we establish the positivity property, and in Section 5 we establish half of the bounded-domain theorem (existence) by showing that the constraint is not realized for large domains. In Section 6 we establish the exponential estimate by an iteration argument and finally, in Section 7 we take the limit and establish Theorem 1.1 from which the remaining of Theorem 1.2 (genuine two-dimensionality) follows. In Section 8 we give the proofs of the higher-dimensional extensions.
An important question is to what extent the approach followed here and consists of the constrained problem, the positivity property (establishes low complexity of the minimizer), and the exponential estimate, is capable of generalization to the general finite reflection group. The exponential estimate is technically easy in the present setup because of the simplicity of the geometry. In \([\text{II}]\), we have been able to obtain the exponential estimate in a general setup under \((h3)\). The positivity property appears hard to extend to the general case. However, the symmetries of the group impose boundary conditions on the fundamental domain. By utilizing the parabolic flow, we have been able to show that there is a minimizer in the class of the positive maps \([\text{I}]\) that does not realize the constraint. Thus, overall, the approach appears general.
2 Observations, examples, and higher-dimensional extensions
**Example 1.** Consider the potential
\[
W_1(z) = \left| \frac{z^2 - 1}{z^2 + \varepsilon^2} \right|^2, \quad \text{for } 0 < \varepsilon < \infty, \quad z = u_1 + iu_2, \quad u = (u_1, u_2).
\]
\(W_1\) has two global minima at \( a^\pm = (\pm 1, 0) \) and obviously has the symmetry \((h2)\). It has been shown in \([\text{III}]\) that there exist exactly three trajectories connecting \(-1\) with \( e^\varepsilon_+, e^\varepsilon_- \), and \( e_0^\varepsilon \), with \( e_+^\varepsilon, e_-^\varepsilon \) reflections of each other with respect to the \( u_1 \)-axis and with \( e_0^\varepsilon \) lying
Figure 2: The figure on the left shows a computation of the trajectories $e^\pm_\varepsilon$ for the potential $W_1$, for $0 < \varepsilon < \infty$. We note that $e^\pm_\varepsilon$ tend to the unit circle as $\varepsilon \to 0$ while their envelope, as $\varepsilon \to \infty$, is given by $u_1^2 = u_2^2/3 + 1$. The disc-like boundary shown in the figure corresponds to $\varepsilon = \sqrt{3}/6 < \varepsilon^* = 0.4416\ldots$
The region bounded by $e^\pm_\varepsilon$ ceases to be convex for $\varepsilon = \sqrt{3}/6 < \varepsilon^* = 0.4416\ldots$ The existence of a $Q$ such that $Q_u \cdot W_u \geq 0$ in $D$ is geometrically evident [14]. On the right are the level sets of $W_1(z)$ for $\varepsilon = \sqrt{3}/6 < \varepsilon^* = 0.4416\ldots$
Example 2. Consider the potential
\begin{equation}
W_2(z) = \left| \frac{z^2 - 1}{z^2 + \varepsilon_1^2} \right|^2 \left| \frac{z^2 - 1}{z^2 + \varepsilon_2^2} \right|^2, \quad \text{for } 0 \leq \varepsilon_1 \leq \varepsilon_2 < \infty, \; z = u_1 + iu_2, \; u = (u_1, u_2).
\end{equation}
In addition, by applying [3], the action of each orbit can be calculated explicitly.
\[ W_2 \text{ has global minima at } a^\pm = (\pm 1, 0) \text{ and obviously satisfies } \text{(h2). Applying the theory in } [3], \text{ we get that for } \varepsilon_1 > 0 \text{ there exist precisely five connecting orbits between } a^+ \text{ and } a^-, \text{ which we denote by } e_{1,\pm}(\varepsilon_1, \varepsilon_2), e_{2,\pm}(\varepsilon_1, \varepsilon_2), \text{ and } e_0(\varepsilon_1, \varepsilon_2). \text{ We denote by } e_0 \text{ the ‘scalar’ connection mentioned in } (h4) \text{ that lies on the } u_1\text{-axis while the rest of the connections are symmetric in pairs with respect to the reflection } u_2 \mapsto -u_2 \text{ (see Figure 3a)} \text{ and are determined by the equation}
\[ u_2 - \frac{(\varepsilon_1^2 + 1)^2}{4\varepsilon_1(\varepsilon_2 - \varepsilon_1^2)} \ln \left( \frac{(\varepsilon_1 - u_2)^2 + u_1^2}{(u_2 + \varepsilon_1)^2 + u_1^2} \right) + \frac{(\varepsilon_1^2 + 1)^2}{4\varepsilon_2(\varepsilon_2 - \varepsilon_1^2)} \ln \left( \frac{(\varepsilon_2 - u_2)^2 + u_1^2}{(u_2 + \varepsilon_2)^2 + u_1^2} \right) = 0. \]
In addition, by applying [3], the action of each orbit can be calculated explicitly.
\[ E_0 := E(e_0) = \frac{1}{\sqrt{2}} \left| 2 - \frac{(\varepsilon_1^2 + 1)^2}{\varepsilon_1(\varepsilon_2^2 - \varepsilon_1^2)} \arctan \varepsilon_1 + \frac{(\varepsilon_2^2 + 1)^2}{\varepsilon_2(\varepsilon_2^2 - \varepsilon_1^2)} \arctan \varepsilon_2 + \frac{(\varepsilon_1^2 + 1)^2}{\varepsilon_1(\varepsilon_2^2 - \varepsilon_1^2)} \right|, \]
\[ E_1 := E(e_{1,\pm}) = \frac{1}{\sqrt{2}} \left| 2 - \frac{(\varepsilon_2^2 + 1)^2}{\varepsilon_2(\varepsilon_2^2 - \varepsilon_1^2)} \arctan \varepsilon_2 + \frac{(\varepsilon_1^2 + 1)^2}{\varepsilon_1(\varepsilon_2^2 - \varepsilon_1^2)} \arctan \varepsilon_1 + \frac{(\varepsilon_2^2 + 1)^2}{2\varepsilon_2(\varepsilon_2^2 - \varepsilon_1^2)} \right|, \]
\[ E_{II} := E(e_{2,\pm}) = \frac{1}{\sqrt{2}} \left| 2 + \frac{(\varepsilon_2^2 + 1)^2}{\varepsilon_2(\varepsilon_2^2 - \varepsilon_1^2)} \arctan \varepsilon_2 - \frac{(\varepsilon_1^2 + 1)^2}{\varepsilon_1(\varepsilon_2^2 - \varepsilon_1^2)} \arctan \varepsilon_1 \right|. \]
We observe that \( e_2^- \cup e_1^- \) form the boundary of a region which increases unboundedly as \( \varepsilon_2 \to \infty \) but approaches a limiting region as \( \varepsilon_2 \to 0 \), always enclosing all poles \( (0, \pm \varepsilon_k i), \) \( k = 1, 2 \). On the other hand, \( e_1^+ \cup e_2^+ \) form the boundary of an interior region, containing only one pair of poles, that approaches limiting regions as \( \varepsilon_2 \to 0, \varepsilon_2 \to \infty \).
We note that
\[ E_0(\varepsilon_1, \varepsilon_2) \rightarrow \begin{cases}
\infty, & \text{as } \varepsilon_1 \rightarrow 0, \\
\text{finite limits as } \varepsilon_1, \varepsilon_2 \rightarrow \varepsilon^* \neq 0 & \text{and also as } \varepsilon_1 \rightarrow \infty \text{ or } \varepsilon_2 \rightarrow \infty.
\end{cases} \]
\[ E_1(\varepsilon_1, \varepsilon_2) \rightarrow \begin{cases}
\infty, & \text{as } \varepsilon_2 - \varepsilon_1 \rightarrow 0 \\
\text{finite limits, as } \varepsilon_1 \rightarrow 0, \ \varepsilon_2 \rightarrow \infty.
\end{cases} \]
\[ E_{II}(\varepsilon_1, \varepsilon_2) \rightarrow \begin{cases}
\text{finite limit, as } \varepsilon_2 \rightarrow 0, \\
\infty, & \text{as } \varepsilon_2 \rightarrow \infty.
\end{cases} \]
From the previous relations, we get that
\[ E_I > E_{II}, \text{ as } \varepsilon_2 \rightarrow 0 \text{ (with } \varepsilon_1 \text{ held constant)}, \]
\[ E_I < E_{II}, \text{ as } \varepsilon_2 \rightarrow \infty \text{ (with } \varepsilon_1 \text{ held constant)}. \]
It then follows easily that there exists a continuous function \( \varepsilon_1 \mapsto \sigma^*(\varepsilon_1) \) and \( \varepsilon_1^* > 0 \) such that
\[ (2.3) \quad E_{II}(\varepsilon_1, \sigma^*(\varepsilon_1)) = E_I(\varepsilon_1, \sigma^*(\varepsilon_1)) < E_0(\varepsilon_1, \sigma^*(\varepsilon_1)), \]
for \( 0 \leq \varepsilon_1 < \varepsilon_1^* \).
Theorem 7.1 applies to \( C^\infty \) mollifications of \( W_2 \) with \( \varepsilon_2 = \sigma^*(\varepsilon_1), 0 \leq \varepsilon_1 < \varepsilon_1^* \), and produces an \( \mathcal{H}_2^2 \) equivariant solution, apparently not unique (in contrast to the previous example), which has the property that for some sequence \( x_2^n \rightarrow \infty \), as \( n \rightarrow \infty \),
\[ u(x_1, x_2^n) \rightarrow e_+^i(x_1), \quad u(x_1, -x_2^n) \rightarrow e_-^i(x_1), \]
where \( i \in \{1, 2\} \) but not known otherwise. We believe that for the example at hand it should be possible to prove that there exist two distinct solutions \( u^i \) satisfying
\[ \lim_{x_2 \rightarrow \pm \infty} u^i(x_1, x_2) = e_\pm^i(x_1), \text{ for } i = 1, 2, \]
each mapping the plane \( \mathbb{R}^2 \) diffeomorphically to the corresponding region bounded by the connections. These are difficult questions; see [12] and the counterexample in [13] for related work.
Next we come to the higher-dimensional extensions that are studied in Section 8.
**Extension 1.** We consider the problem
\[ (2.4) \quad \begin{cases}
\Delta u - W_u(u) = 0, & \text{for } u : \mathbb{R}^3 \rightarrow \mathbb{R}^3, \\
\lim_{x_1 \rightarrow \pm \infty} u(x_1, x_2, x_3) = (\pm a, 0, 0).
\end{cases} \]
with hypotheses
(hₐ) (Minima) The potential $W$ is $C^2$, $W : \mathbb{R}^3 \to \mathbb{R}_+ \cap \{0\}$ with precisely two nondegenerate minima $a^+$ and $a^-$, where $a^+ = (a, 0, 0)$, $a^- = (-a, 0, 0)$, for $a > 0$, and $\partial^2 W(u) \geq c^2 \text{Id}$, for $|u - a^+| < r_0$. Also, $W_u(u) \cdot u > 0$ for $u$ outside a ball centered at the origin and containing the minima.
(hₐ) (Symmetries) We assume that $W$ is invariant under the symmetry group generated by the reflections with respect to the planes $u_1 = 0$, $u_2 = 0$, $u_3 = 0$, $u_2 = \pm u_3$. This group has eight elements and is isomorphic to the dihedral group $H^4_2$ in the $(u_2, u_3)$-plane (symmetries of the square). We denote it by $H^3_3$.
We thus assume
$$W(gu) = W(u), \text{ for } g \in H^3_3$$
(hₐ) (Connections) We assume, besides $e_0$, the existence of precisely one pair of connecting orbits between $a^+$ and $a^-$ on each of the planes $u_3 = 0$, $u_2 = u_3$, $u_2 = -u_3$, denoted by $e^1_+, e^1_-$, $e^2_+, e^2_-$, $e^3_+, e^3_-$, and $e^4_+,$ $e^4_-$ respectively. Symmetry implies
$$E_I := E(e^1_+) = E(e^1_-),$$
$$E_{II} := E(e^2_+) = E(e^2_-).$$
Consequently, in total we have nine connecting orbits between $a^+$ and $a^-$ (see Figure 4). We assume that
$$E(e_0) > E_I > E_{II}$$
Thus,
- $E_{II}$ is the minimum value of the action among all curves connecting $a^+$ and $a^-$.
- $E_I$ is the minimum value of the action among curves connecting $a^+$ and $a^-$, and lying entirely on either of the planes $u_3 = 0$, $u_2 = 0$.
(hₐ) (Q-monotonicity) Let $D = \{(u_1, u_2, u_3) \mid u_1 \geq 0\}$. We assume that there exists a $C^2$ convex function $Q : D \setminus \{a^+\} \to \mathbb{R}_+ \cup \{0\}$ with $Q(u) > 0$ for $u \neq a^+$ and $Q(u) = |u - a^+|$ for $|u - a^+| < r_0$, satisfying the relation
$$W_u(u) \cdot Q_u(u) \geq 0, \text{ for } u \in D.$$
We study the problem in the class of $H^3_3$-equivariant vector fields. Note that we impose more symmetry on the potential than required for the solution. Under the hypotheses (hₐ)–(hₐ), we establish in Theorem 8.1 the existence of a genuine three-dimensional, $H^3_3$-equivariant, bounded solution to (2.4). In fact, we exhibit in this example a full hierarchy of solutions: a three-dimensional solution, which approaches in the $x_1$-direction the critical points $a^\pm$ (zero-dimensional solutions), while in the $x_2$- and $x_3$-directions, approaches distinct two-dimensional solutions, which themselves have boundaries made up of one-dimensional connections. The ideas are as follows. The existence of the nonequivariant connecting orbits $e_\pm$ in Example 1 above, with action less than that of $e_0$, exclude $e_0$ as a candidate for a (trivial) two-dimensional minimizer and imply the existence of a genuine two-dimensional solution. In the
present example, in addition to $e_0$, we have two two-dimensional $\mathcal{H}_3^-$-equivariant solutions. The $\mathcal{H}_3^2$ symmetry together with the hypothesis $E_1 > E_{11}$ implies the existence of non-$\mathcal{H}_3^2$-equivariant two-dimensional solutions which play an role analogous to $e_\pm$ in the exclusion of the $\mathcal{H}_3^2$-equivariant two-dimensional solutions as candidates for (trivial) three-dimensional minimizers and thus implying the existence of an $\mathcal{H}_3^2$-equivariant genuine three-dimensional solution.
**Extension 2.** We conclude Section 2 with an $n$-dimensional extension of Theorem 1.1 which we now describe. Let $u = (u_1, \ldots, u_n)$ be the typical element of $\mathbb{R}^n$; we write $u = (u_1, u')$ with $u' = (u_2, \ldots, u_n) \in \mathbb{R}^{n-1}$. We denote by $T_j : \mathbb{R}^n \to \mathbb{R}^n$ the reflection with respect to the plane $u_j = 0$, that is, the map defined by
$$T_j(u_1, \ldots, u_j, \ldots, u_n) := (u_1, \ldots, -u_j, \ldots, u_n).$$
We let $G$ be the reflection group generated by $T_j$, $j = 1, \ldots, n$, and $G'$ the reflection group generated by $T_j$, $j = 2, \ldots, n$. If $G$ is a group, we denote by $|G|$ the order of $G$, that is, the number of elements of $G$. Note that $|G| = 2^n$, $|G'| = 2^{n-1}$. We denote by $F$, $F'$, $F' \cap F \neq \emptyset$, convex (open) fundamental regions defined in $\mathbb{R}^n$ by the reflection groups $G$, $G'$ (see Section 3).
In this case, the hypotheses are as follows.
(hi) (Minima) Assume $W : \mathbb{R}^n \to \mathbb{R}$ is a $C^2$ function such that there exists an $\alpha > 0$ with $W(\pm \alpha, 0') = 0$, $W(u) > 0$, for all $u \neq (\pm \alpha, 0')$ and $(\pm \alpha, 0')$ are nondegenerate zeros of $W$, as in (h1).
(hii) (Symmetries) \( W \) is equivariant with respect to \( G \), that is, \( W(gu) = W(u) \), for all \( g \in G \). Also we assume that \( W(u) \geq \max_{\partial C_0}[W] \) for \( u \) outside a certain bounded, \( G \)-symmetric, convex set \( C_0 \), as in (h2).
(hiii) (Q-monotonicity) We assume that there exists a \( C^2 \) function \( Q : D \setminus \{a^+\} \to \mathbb{R}_+ \cup \{0\} \), convex, with \( Q(u) > 0 \) for \( u \in D \) and \( Q(u) = |u - a^+| \) for \( |u - a^+| < r_0 \), satisfying the relation
\[
W_u(u) \cdot Q_u(u) \geq 0, \text{ for } u \in D.
\]
(hiv) (Connections) For each \( e \neq e_0 \in A \subset W^{1,2}(\mathbb{R}) \), (the analogue of (h3)), the set of minimizers of the connection problem, we have
\[
\# \tilde{e} = |G'|, \text{ for } e \in A
\]
where \( \# \tilde{e} \) denotes the cardinality of the set \( \tilde{e}, \tilde{e} := \{ge \mid g \in G'\} \).
Under these hypotheses, we establish in Theorem 8.3 the existence of a genuinely \( n \)-dimensional, \( G \)-equivariant solution to
\[
\Delta u - W_u(u) = 0,
\]
\[
\lim_{x_1 \to \pm \infty} u(x_1, x') = (\pm \alpha, 0').
\]
In the following, the square brackets on the side of sections, theorems etc. indicate which of the hypotheses are needed for the developments there.
3 The constrained problem [h1]
Let \( \Omega_{R,\mu} = \{(x_1, x_2) \mid |x_1| < \mu R, |x_2| < R\} \) and \( C^+_{R,\mu,\eta} = \{(x_1, x_2) \in \Omega_{R,\mu} \mid \eta R \leq x_1 \leq \mu R\} \), where \( R \in [1, \infty), \mu \in [1, +\infty), \frac{1}{2} < \eta < \mu \), and \( C^-_{R,\mu,\eta} = \{(x_1, x_2) \in \Omega_{R,\mu} \mid -\mu R \leq x_1 \leq -\eta R\} \). Finally, the domain \( \Omega_{R,\infty} \), for \( \mu = \infty \), is the strip \( |x_2| < R \). Consider the equivariant Sobolev space \( W^{1,2}_E(\Omega_{R,\mu}) = \{u : \Omega_{R,\mu} \to \mathbb{R}^2 \mid u \in W^{1,2}(\Omega_{R,\mu}), u H^2_\omega \text{-equivariant}\} \). We consider, for \( r < r_0 \) fixed, the set
\[
U_{R,\mu}^r := \{u \in W^{1,2}_E(\Omega_{R,\mu}) \mid |u(x) - a^\pm| \leq r, \text{ a.e. } x \in C^\pm_{R,\mu,\eta}\}
\]
and the functional
\[
J_{R,\mu}(u) = \int_{\Omega_{R,\mu}} \left\{ \frac{1}{2} |\nabla u|^2 + W(u) \right\} \, dx
\]
which we denote by \( J \) whenever there is no risk of confusion.
**Proposition 3.1.** Let \( 1 \leq R < \infty, 1 \leq \mu \leq \infty, \frac{1}{2} < \eta \leq \mu \) and \( r < r_0 \) fixed, where \( r_0 \) as in (h1). Then, the problem
\[
\min_{U_{R,\mu}^r} \int_{\Omega_{R,\mu}} \left\{ \frac{1}{2} |\nabla u|^2 + W(u) \right\} \, dx
\]
has a solution \( u_{R,\mu} \in W^{1,2}_E(\Omega_{R,\mu}) \) for \( \mu < \infty \) and \( u_{R,\infty} \in (W^{1,2}_E)_{loc}(\Omega_{R,\infty}) \) to
\[
J(u_{R,\mu}) = \inf_{U_{R,\mu}^r} [J]
\]
Proof. For $\mu < \infty$, we fix $R$ and $\mu$, and define the linear function $u_{aff} : \Omega_{R,\mu} \to \mathbb{R}^2$, such that
$$u_{aff}(x) := \begin{cases} a^-, & \text{for } x_1 \in [-\mu R, -1], \\
\frac{1-x_1}{2}a^- + \frac{1+x_1}{2}a^+, & \text{for } x_1 \in [-1, 1], \\
a^+, & \text{for } x_1 \in [1, \mu R]. \end{cases}$$
(3.4)
$u_{aff}$ belongs to $U_{c,R,\mu}$ for every $R \geq 1$, $\mu \geq \eta$ and satisfies the estimate
$$J(u_{aff}) < CR.$$
(3.5)
Since $W \geq 0$, it follows that $0 \leq \inf_{U_{c,R,\mu}} J < J(u_{aff}) < CR$ where without loss of generality we assumed the middle inequality to be strict. Let $\{u_n\}$ be a minimizing sequence of $J$, that is, $J(u_n) \to \inf_{U_{c,R,\mu}} [J]$. For the sequence $\{u_n\}$ we have the following estimates
$$\begin{cases} (i) \int_{\Omega_{R,\mu}} \frac{1}{2} |\nabla u_n|^2 \, dx < J(u_{aff}) < CR, \\
(ii) \int_{\Omega_{R,\mu}} |u_n|^2 \, dx < C(R, \mu). \end{cases}$$
(3.6)
where in (3.6)(ii), $C(R, \mu)$ denotes a constant depending on $R, \mu$. Then, there exists a subsequence, by weak compactness, which we still denote by $\{u_n\}$, such that
$$u_n \rightharpoonup u, \text{ weakly in } W^{1,2}_E(\Omega_{R,\mu}).$$
By lower semicontinuity in $L^2_E(\Omega_{R,\mu})$, it follows that
$$\liminf_{n \to \infty} \int_{\Omega_{R,\mu}} |\nabla u_n|^2 \, dx \geq \int_{\Omega_{R,\mu}} |\nabla u|^2 \, dx$$
(3.7)
and by the compactness of the embedding $W^{1,2}_E(\Omega_{R,\mu}) \subset L^2_E(\Omega_{R,\mu})$ and the lemma of Fatou we have
$$\liminf_{n \to \infty} \int_{\Omega_{R,\mu}} W(u_n) \, dx \geq \int_{\Omega_{R,\mu}} W(u) \, dx,$$
(3.8)
and thus the proposition holds.
For \( \mu = \infty \), let now \( \Omega_{R,\infty} \) stand for the infinite strip \( \{(x_1, x_2) | |x_2| < R\} \). We consider the Fréchet space \( W^{1,2}_{\text{loc}}(\Omega_{R,\infty}) \) whose topology is defined by the seminorms of \( W^{1,2}_m := W^{1,2}_m([-m, m] \times [-R, R]) \). We assume now that \( \{u_n\} \) is bounded in the locally convex sense in \( W^{1,2}_{\text{loc}}(\Omega_{R,\infty}) \). Utilizing a standard diagonal argument and the representation of functionals in \( (W^{1,2}_m)^* \) induced by the embedding \( W^{1,2}_m \hookrightarrow L^2_m \times (L^2_m)^2 \), it follows that \( \{u_n\} \) is weakly precompact in the topology of \( W^{1,2}_{\text{loc}}(\Omega_{R,\infty}) \) generated by the duals \( (W^{1,2}_m)^* \), that is, there exist a subsequence \( \{u_{n_k}\} \) denoted again by \( \{u_n\} \), and a \( u \in W^{1,2}_{\text{loc}}(\Omega_{R,\infty}) \), such that, for every \( m = 1, 2, \ldots \)
\[ u_n \rightharpoonup u \text{ weakly in } W^{1,2}_m, \text{ as } n \to \infty. \]
By the estimate (3.6)(i) and the local version of (3.6)(ii), we may assume that, up to a further subsequence, \( u_n \to u \) a.e. on \( \Omega_{R,\mu} \), due to the embedding \( W^{1,2}_{\text{loc}}(\Omega_{R,\mu}) \Subset L^2(\Omega_{R,\mu}) \). This validates (3.7) and (3.8) above and finishes the proof.
4 The positivity property
Let \( V \) be a real Euclidean vector space, and let \( O(V) \) stand for the orthogonal group. For every finite subgroup \( G \) of \( O(V) \) a fundamental region is defined as a set \( F \) with the following properties.
(i) \( F \) is open in \( V \),
(ii) \( F \cap TF = \emptyset \) if \( I \neq T \in G \),
(iii) \( V = \cup \{(TF)^- | T \in G\} \),
where with \( ( \ )^{-} \) we denote the closure of the set. The fundamental region \( F \) can be chosen to be convex, actually a simplex (see [10]). More generally, if \( X \) is a subset of \( V \), invariant under \( G \), then a subset \( D \) is a fundamental domain if it is of the form
\[ D = X \cap F. \]
If \( G=H^2_2 \), a fundamental region is \( F = \{(u_1, u_2) | u_1 \geq 0, u_2 \geq 0\} \). For \( X = \Omega_{R,\mu} \), we take as fundamental domain the set \( \Omega^1_{R,\mu} = \Omega_{R,\mu} \cap F. \)
Proposition 4.1. [b2] Let \( u_{R,\mu} \), for \( R, \mu \in [1, \infty) \), be the minimizing function of the constrained problem (3.2). Then, there exist \( u^*_{R,\mu} \in U^c_{R,\mu} \) with the properties
\[
\begin{align*}
J(u^*_{R,\mu}) & \leq J(u_{R,\mu}) \\
u^*_{R,\mu}(\Omega_{R,\mu}) & \subset F^-
\end{align*}
\]
\[ \text{We owe this argument to N. Katzourakis} \]
14
Figure 6: The fundamental region $F$ of $\mathcal{H}^2_2$ and the fundamental domain $\Omega^1_{R,\mu} = \Omega_{R,\mu} \cap F$.
Proof. Set
\begin{equation}
Au := \begin{cases}
u, & u \in F \\
T_1^{-1} u, & u \in T_1(F) \\
(T_2T_1)^{-1} u, & u \in T_2T_1(F) = S(F) \\
T_2^{-1} u, & u \in T_2(F)
\end{cases}
\end{equation}
Clearly, $\Lambda$ maps $\mathbb{R}^2$ into $F$. Also, it can be checked that
\begin{equation}
|\Lambda(u_A) - \Lambda(u_B)| \leq |u_A - u_B|,
\end{equation}
where $|\cdot|$ is the Euclidean norm.
Next, we define the operator
\begin{equation}
(Lu)(x) := \Lambda u(x), \text{ for } x \in \Omega^1_{R,\mu},
\end{equation}
and extend by equivariance on $\Omega_{R,\mu}$. We will show that
\begin{equation}
L : U^c_{R,\mu} \to U^c_{R,\mu},
\end{equation}
which means that $L$ preserves Sobolev equivariance and the constraint.
We begin by verifying that $L$ preserves Sobolev equivariance. By standard approximation arguments, the only source of difficulty is the possible loss of continuity along the symmetry lines where the gluing in the definition of $L$ takes place. We check two cases and leave the rest to the reader.
We consider $x^+, \bar{x}, x^-$ as in Figure 7 with $T_1 x^+ = x^-$ and $|x^+ - x^-|$ small, and $T_1 \bar{x} = \bar{x}$. We would like to show that $|(Lu)(x^+) - (Lu)(x^-)|$ is small for $|u(x^+) - u(x^-)|$ small. By equivariance, $T_1(u(\bar{x})) = u(T_1 \bar{x}) = u(\bar{x})$ and therefore, $u(\bar{x})$ lies on the $u_2$-axis. We assume
that \( u(x^-), u(\bar{x}), u(x^+) \) are as in Figure 7. Then,
(i) \[ Lu(x^-) = \Lambda u(x^-) = T_2 u(x^-), \]
\[ Lu(x^+) = T_1 \Lambda u(T_1^{-1} x^+) = T_1 \Lambda u(x^-) = T_1 T_2 u(x^-) = T_2 u(x^+), \]
(ii) \[ Lu(x^-) = \Lambda u(x^-) = T_1 T_2 u(x^-) = T_2 u(x^-), \]
\[ Lu(x^+) = T_1 \Lambda u(T_1^{-1} x^+) = T_1 \Lambda u(x^-) = T_1 T_1 T_2 u(x^-) = T_2 u(x^-). \]
consequently, continuity is verified in these cases. The verification of the constraint is straightforward. Finally, we define
\[ u^*_{R,\mu} := Lu_{R,\mu} \]
and verify that \( u^*_{R,\mu} \) does not increase the functional \( J \). Indeed,
\[ W((Lu)(x)) = W(g \Lambda u(g^{-1} x)) = W(\Lambda u(g^{-1} x)) = W(u(g^{-1} x)) \]
and consequently, the term \( W \) of the functional \( J \) does not change since \( T_i \) is an isometry. On the other hand, the term \( \int_{\Omega_{R,\mu}} |\nabla u|^2 \, dx \) does not increase by (4.3). \( \square \)
**Corollary 4.1.** \([h_1, h_2]\) Without loss of generality, we may assume that the minimizer \( u_{R,\mu} \) of the constrained problem satisfies
\[ u_{R,\mu}(\Omega^1_{R,\mu}) \subseteq F^- \]
Next we need an a priori bound.
**Lemma 4.1.** There is an \( M > 0 \), independent of \( R, \mu, \eta \), such that
\[ |u_{R,\mu}(x)| < M, \text{ for } x \in \Omega_{R,\mu}. \]
**Proof.** For the convex set \( C_0 \) introduced in \((h_1)\), we consider the mapping \( \Lambda : \mathbb{R}^2 \rightarrow C_0, \)
\[ \Lambda u := \begin{cases} Pu, & \text{if } u \notin C_0, \\ u, & \text{if } u \in C_0, \end{cases} \]
where \( Pu \) is the projection of \( u \) on \( \partial C_0 \). By \((h_1)\), \( W(\Lambda u) \leq W(u) \). Also, the mapping \( \Lambda \) is nonexpansive in the Euclidean norm. We set \((Lu)(x) := \Lambda u(x)\) and notice that \( L \) preserves equivariance, honors the constraint, and reduces \( J_{R,\mu} \). It follows that the minimizer \( u_{R,\mu} \) of the constrained problem takes values in \( C_0 \). Thus (4.7) holds. \( \square \)
5 Removing the constraint—the case of the bounded domain
Given \( u : x \in \mathbb{R}^2 \rightarrow \mathbb{R}^2 \), we write \( u(x) - a^\pm \) in polar form,
\[
\rho(x) = |u(x) - a^\pm| = \rho^+(x)n^+(x),
\]
where \( \rho^+: x \in \mathbb{R}^2 \rightarrow \mathbb{R}^+ \) and \( n^+: x \in \mathbb{R}^2 \rightarrow S^1 \). So, if \( u \in U_{\mathbb{R},\mu}^c \), we have
\[
u(x) = a^+ + \rho^+(x)n^+(x), \text{ with } \rho^+(x) \leq r \text{ for } x \in C_{\mathbb{R},\mu,\eta}^+\]
and similarly for \( x \in C_{\mathbb{R},\mu,\eta}^- \). We notice that the polar form is well defined for \( \rho(x) \neq 0 \).
For \( u \in W_{\text{loc}}^{1,2} \), it follows that \( \rho, n \in W_{\text{loc}}^{1,2} \) and moreover, \( |\nabla u|^2 = |\nabla \rho|^2 + \rho^2|\nabla n|^2 \). On the other hand, on the set \( \{u = a\} \), we have \( |\nabla u| = 0 \text{ a.e.} \). Therefore, for any measurable set \( S \), we have
\[
\int_S |\nabla u|^2 \, dx = \int_{S \cap \{\rho > 0\}} \{|\nabla \rho(x)|^2 + \rho^2(x)|\nabla n(x)|^2\} \, dx.
\]
Lemma 5.1. \( \text{[h1]} \) Suppose \( u_{\mathbb{R},\mu} \) is a minimizer of the constrained problem \( (3.2) \). Then, the following estimate holds.
\[
\rho_{\mathbb{R},\mu}^+(x) \leq r \frac{\cosh \left(c(R\mu - x_1)\right)}{\cosh \left(c(\mu - \eta)R\right)}, \text{ a.e. } x \in C_{\mathbb{R},\mu,\eta}^+\]
where \( c \) as in \( \text{[h1]} \), with an analogous estimate for \( x \in C_{\mathbb{R},\mu,\eta}^- \). Here, \( 1 \leq R < \infty, 1 \leq \mu \leq \infty, \) and \( \frac{1}{2} < \eta < \mu \), for \( r < r_0 \).
Note that an important consequence of the corollary is that the constraint is realized, if at all, on the line \( \{x_1 = \eta R\} \).
Proof. Suppose that
\[
\begin{cases}
\Delta w - c^2 w \geq 0, \\
Bw \leq 0,
\end{cases}
\]
weakly in the space \( W_{\#}^{1,2}(C_{\mathbb{R},\mu,\eta}^+) \), the latter defined as the completion in the \( W^{1,2} \) norm of the space
\[
\{ f \in C^\infty(C_{\mathbb{R},\mu,\eta}^+) \cap W^{1,2}(C_{\mathbb{R},\mu,\eta}^+) \mid f^+ = 0 \text{ on } \{x_1 = \eta R\}\},
\]
where
\[
Bw := \begin{cases}
w, & \text{on } x_1 = \eta R, \\
\frac{\partial w}{\partial n}, & \text{on } \partial L C_{\mathbb{R},\mu,\eta}^+ (:= \partial C_{\mathbb{R},\mu,\eta}^+ \setminus \{x_1 = \eta R\}),
\end{cases}
\]
and (5.2) is meant in the sense
\[
\int_{C_{\mathbb{R},\mu,\eta}^+} \{\nabla w \nabla \phi + c^2 w \phi\} \, dx \leq 0,
\]
and (5.2) is meant in the sense
\[
\int_{C_{\mathbb{R},\mu,\eta}^+} \{\nabla w \nabla \phi + c^2 w \phi\} \, dx \leq 0,
\]
for \( w, \phi \in W^{1,2}_\#(C^+_R, \mu, \eta) \) with \( \phi \geq 0 \) a.e. Then, we claim that
\[
(5.4) \quad w \leq 0, \text{ a.e. in } C^+_R, \mu, \eta.
\]
To prove the claim, by density we can take \( \phi := w^+ \) in (5.3) and so we can conclude that
\[
0 \geq \int_{C^+_R, \mu, \eta} \left\{ \nabla w \nabla w^+ + c^2 w^+ w^+ \right\} dx = \int_{C^+_R, \mu, \eta} \left\{ |\nabla w^+|^2 + c^2 |w^+|^2 \right\} dx = 0,
\]
thus, \( w^+ = 0 \) in \( C^+_R, \mu, \eta \). Next we will show that
\[
(5.5) \quad \Delta \rho_R, \mu \geq \rho_R, \mu c^2 \text{ weakly in } W^{1,2}_\#(C^+_R, \mu, \eta).
\]
For showing (5.5), we consider \( u_\varepsilon(x) = u_{R, \mu}(x) + \varepsilon \hat{p}(x) n(x) \) with \( \hat{p}(x) \leq 0 \) in \( C^+_R, \mu, \eta \), \( \hat{p} \in C^\infty_0(C^+_R, \mu, \eta) \). We notice that
\[
|u_\varepsilon(x) - a^\pm| = |\rho_{R, \mu}(x) + \varepsilon \hat{p}(x)| \leq r \text{ in } C^+_R, \mu, \eta.
\]
Then,
\[
\frac{d}{d\varepsilon} \bigg|_{\varepsilon=0} J(u_\varepsilon) \geq 0 \iff \frac{d}{d\varepsilon} \bigg|_{\varepsilon=0} \int_{C^+_R, \mu, \eta} \left\{ \frac{1}{2} |\nabla u_\varepsilon|^2 + W(u_\varepsilon) \right\} dx \geq 0
\]
\[
\iff \int_{C^+_R, \mu, \eta} \left\{ \nabla \rho_{R, \mu} \nabla \hat{p} + (\rho_{R, \mu} \hat{p}) |\nabla n(x)|^2 + \hat{p} W_u(u_{R, \mu}) n(x) \right\} dx \geq 0
\]
from which it follows that
\[
\int_{C^+_R, \mu} \left\{ \nabla \rho_{R, \mu} \nabla \hat{p} + \hat{p} W_u(u_{R, \mu}) n(x) \right\} dx \geq 0.
\]
Utilizing (h1) we obtain from this
\[
\int_{C^+_R, \mu} \left\{ \nabla \rho_{R, \mu} \nabla \hat{p} + c^2 \hat{p} \rho_{R, \mu} \right\} dx \geq 0,
\]
and therefore (5.5) has been established.
Next we will show that \( \rho_{R, \mu} < r \) a.e. in the interior of \( C^+_R, \mu, \eta \) from which it will follow, up to a modification on a null set, that \( u_{R, \mu} \) is a classical solution of
\[
(5.6) \quad \Delta u_{R, \mu} - W_u(u_{R, \mu}) = 0, \text{ in the interior of } C^+_R, \mu, \eta.
\]
Suppose now for the sake of contradiction that \( \rho_{R, \mu} = r \) on a set \( A \) of positive measure. However, this is in conflict with \( \Delta \rho_{R, \mu} \geq c^2 \rho_{R, \mu} \) in \( W^{1,2}_\#(C^+_R, \mu) \) since \( \nabla \rho_{R, \mu} = 0 \) a.e. on this set \( A \). Therefore, \( \rho_{R, \mu} < r \) a.e. in \( C^+_R, \mu, \eta \) as required.
In the following we show that
\[
(5.7) \quad \frac{\partial \rho_{R, \eta}}{\partial n} = 0 \text{ on } \partial L C^+_R, \mu, \eta \setminus \{A, B\},
\]
where \( A, B \) are the corners. For \( x^* \) in a subset of points \( \partial L C^+_R \setminus \{A, B\} \) such that \( \rho_{R, \mu}(x^*) < r \) a.e. on it, the natural boundary conditions hold classically and so (5.7) is valid. Therefore, the case of interest is when \( \rho_{R, \mu}(x^*) = r \). We notice that in the interior of \( C^+_R, \mu, \eta \), (5.6) is satisfied.
classically and that $u_{R,\mu}$ is regular. From the bound $|u_{R,\mu}| < \text{const}$, which holds uniformly in the interior of $C_{R,\mu,\eta}$, we obtain by elliptic regularity that $|\nabla \rho_{R,\mu}| < \text{const}$, on the boundary with a similar estimate on the second-order derivatives. Consequently, $\rho_{R,\mu}(x)$ is continuous at $x^*$ and the outer normal derivative $\partial \rho_{R,\mu}/\partial n$ exists at $x^*$. We know that $\Delta \rho_{R,\mu} \geq c^2 \rho_{R,\mu}$ classically in the interior of $C_{R,\mu}$ and by the preceding argument, $\rho_{R,\mu}$ is continuous at $x = x^*$ and $\partial \rho_{R,\mu}/\partial n (x^*)$ exists. Applying the Hopf lemma, we obtain
$$\frac{\partial \rho_{R,\mu}}{\partial n} (x^*) > 0.$$
We now set $u_\varepsilon(x) = u_{R,\mu} + \varepsilon \hat{p}(x)n$, $\hat{p} \leq 0$ smooth with $\text{supp}(\hat{p}) \subseteq B(x^*; \delta) \cap C_{R,\mu,\eta}$, $0 < \delta \ll 1$. Then, $u_\varepsilon \in U_{R,\mu}^c$ and
$$0 \leq \frac{d}{d\varepsilon} \bigg|_{\varepsilon=0} \int_{\Omega_{R,\mu}} \left\{ \frac{1}{2} |\nabla u_\varepsilon|^2 + W(u_\varepsilon) \right\}^2 \ dx \int_{\partial \Omega_{R,\mu}} \frac{\partial \rho_{R,\mu}}{\partial n} \hat{p} \ dS,$$
which however is in contradiction to (5.8). Therefore, $\rho_{R,\mu}(x^*) = r$ cannot possibly hold and so (5.7) is valid.
To conclude, we set $v := \rho_{R,\mu}^+(x) - r \cosh \left( c(R\mu - x_1) \right) / \cosh \left( c(\mu - \eta)R \right)$. We will show that $v$ satisfies (5.2). By the preceding argument, it follows that $\Delta v - c^2 v \geq 0$ classically in the interior of $C_{R,\mu,\eta}^+$. Thus, given $\phi$ as in the definition of (5.5), we have
$$0 \leq \int_{C_{R,\mu}^+} \left\{ \Delta v - c^2 v \right\} \phi \ dx = \int_{C_{R,\mu}^+} \left\{ -\nabla v \nabla \phi - c^2 v \phi \right\} \ dx + \int_{\partial L_{C_{R,\mu,\eta}}} \frac{\partial v}{\partial n} \phi \ dS$$
$$\int_{C_{R,\mu}^+} \left\{ -\nabla v \nabla \phi - c^2 v \phi \right\} \ dx.$$
Finally we note that the points $A, B$ are negligible in the boundary integral since $|\nabla v| < \text{const}$, up to the boundary. The proof of Lemma 5.1 is complete.
**Corollary 5.1.** [h1] Suppose $u_{R,\mu}$ is the minimizer of the constrained problem (3.2). Then the following estimate is true.
$$\rho_{R,\mu}^+(x) \leq 2re^{-c(x_1-\eta R)}, \ a.e. \ x \in C_{R,\mu,\eta}^+,$$
where $1 \leq R < \infty$, $\frac{1}{2} < \eta < \mu$, and fixed $r < r_0$, with an analogous result for $x \in C_{R,\mu,\eta}^-$. We begin with a result that is of some independent interest, to be utilized later.
**Lemma 5.2** (Chop-off Lemma, cf. [5]; requires only the monotonicity of $\lambda \mapsto W(a + \lambda w)$, $|w| = 1, \lambda < r_0$). Suppose $A$ is an open set in $\mathbb{R}^2$ and $u$ a global minimizer of
$$\min_{\rho \mid \mid} \int_A \left\{ \frac{1}{2} |\nabla u|^2 + W(u) \right\} \ dx < \infty$$
subject to a unilateral constraint $|\rho^+| \leq M$ on an open subset $A' \subseteq A$. We employ the representation $u(x) = a^+ + \rho^+(x)n^+(x)$, $2r < r_0$, and $\Gamma \subset \partial A$ and possibly empty. Then the following estimate holds.
(5.11) $\rho^+(x) \leq r \text{ a.e. on } A$.
Proof. We first establish the estimate
(5.12) $\rho^+(x) \leq 2r$, a.e. on $A$.
We begin by proving it under the hypothesis $\rho^+(x) > r$ on $A$. For $r_0 > \hat{r} > 2r$, we consider the sets
$$A^+ = \{ x \in A \mid \rho^+(x) > \hat{r} \}, \quad A^- = \{ x \in A \mid \rho^+(x) \leq \hat{r} \},$$
and define the function
$$\theta(\tau) := \begin{cases} 1, & \tau \leq r, \\ \frac{\hat{r} - \tau}{\hat{r} - \hat{r}}, & \hat{r} < \tau < \hat{r}, \\ 0, & \tau \geq \hat{r}. \end{cases}$$
We also define $\hat{u}(x) := a + r\theta(\rho^+(x))n^+(x)$ and $|\hat{u}(x) - a| = r\theta(\rho^+(x)) =: \hat{p}(x)$. We will establish the validity of the following estimate.
$$|\nabla \hat{u}(x)| \leq |\nabla u(x)|.$$
We recall that $|\nabla u|^2 = |\nabla \rho^+|^2 + (\rho^+)^2|\nabla n^+|^2$, thus,
$$|\nabla \hat{u}(x)|^2 = |\nabla \hat{p}(x)|^2 + \hat{p}^2(x)|\nabla n^+|^2,$$
with
$$|\nabla \hat{p}(x)|^2 = r^2|\nabla \theta(\rho^+(x))|^2 = r^2(\theta')^2|\nabla \rho^+(x)|^2 \leq \frac{r^2}{(\hat{r} - r)^2}|\nabla \rho^+(x)|^2 \leq |\nabla \rho^+(x)|^2,$$
where we have used the assumption $\hat{r} > 2r$. Thus, in $A$ and for $\hat{r} > 2r$ we have
$$|\nabla \hat{u}(x)|^2 = |\nabla \hat{p}(x)|^2 + \hat{p}^2|\nabla n^+|^2 \leq |\nabla \rho(x)|^2 + r^2|\nabla n^+|^2 \leq |\nabla \rho(x)|^2 + \rho^2(x)|\nabla \eta|^2 = |\nabla u(x)|^2.$$
In $A$, the inequalities $|\hat{u}(x) - a| \leq r \leq \rho(x)$ hold. This and the monotonicity assumption on $W$ imply
$$\int_A W(\hat{u}(x)) \, dx \leq \int_A W(u(x)) \, dx$$
which is strict unless $|A^+| = 0$. The conclusion now follows from
$$\int_A \left\{ \frac{1}{2}|\nabla \hat{u}|^2 + W(\hat{u}) \right\} \, dx < \int_A \left\{ \frac{1}{2}|\nabla u|^2 + W(u) \right\} \, dx$$
and the fact that the transformation does not affect the unilateral constraint.
We now eliminate the hypothesis $\rho^+(x) > r$ on $A$. We set $B = \{x \in A|\rho^+(x) > r\}$. If $B = \emptyset$ we are done; if $B \neq \emptyset$, then $B$ is open in which case we can repeat the argument above by replacing $A$ with $B$. The proof of (5.12) is complete.
Now, define $w(x) = a^+ + \min\{\rho^+, r\}n(x) =: a^+ + \tilde{\rho}(x)n(x)$ and notice that $|\nabla \tilde{\rho}| \leq |\nabla \rho^+|$. By (5.12) and the monotonicity assumption on $W$, we have that
$$\int_A \left\{ \frac{1}{2} |\nabla w|^2 + W(w) \right\} \, dx < \int_A \left\{ \frac{1}{2} |\nabla u|^2 + W(u) \right\} \, dx$$
which is strict unless $\rho^+(x) \leq r$ a.e. This completes the proof of the lemma.
Now we are ready to establish the main result of this section.
**Theorem 5.1.** We assume that $W$ satisfies hypotheses $(h_1), (h_2)$. Then, we can determine $R_0 \geq 1$ and $\mu_0 \geq 1$, so that for $R > R_0$ and $\mu \geq \mu_0$, there exists a minimizer $u_{R,\mu}$ of the constrained problem which does not realize the constraint and thus satisfies, weakly in $W^{1,2}(\Omega_{R,\mu})$, the problem
\[
\begin{aligned}
\Delta u - W_{u}(u) &= 0, & \text{in } \Omega_{R,\mu}, \\
\frac{\partial u}{\partial n} &= 0, & \text{on } \partial \Omega_{R,\mu}.
\end{aligned}
\]
Moreover,
\[
(5.14) \quad u(x) \neq 0
\]
and
\[
(5.15) \quad u(x) \neq e_0(x_1), \ (e_0(0) = 0).
\]
Before we present the proof, we will make two remarks. First, the weak formulation of (5.13) is
$$\int_{\Omega_{R,\mu}} \left\{ \nabla u_{R,\mu} \nabla \phi + W(u_{R,\mu}) \phi \right\} \, dx = 0, \text{ for all } \phi \in C^1(\overline{\Omega_{R,\mu}}) \text{ and } u_{R,\mu} \in W^{1,2}(\Omega_{R,\mu}).$$
The solution provided by the theorem above is classical except at most at the corners.
Second, Corollary 4.1 implies that we can assume
\[
(5.16) \quad u_{R,\mu}(\Omega_{R,\mu}^+) \subseteq D,
\]
where $\Omega_{R,\mu}^+ = \Omega_{R,\mu} \cap \{x_1 \geq 0\}$, $D = \{u_1 \geq 0\}$. Because of this, we see that a lower bound on $W(u_{R,\mu}(x))$ in $\Omega_{R,\mu}^+$ is implied by a bound from below on $\rho_{R,\mu}^+(x)$. We notice now that such a lower bound on a sufficiently large subset of $\Omega_{R,\mu}^+$ would imply
$$\int_{\Omega_{R,\mu}} W(u_{R,\mu}(x)) \, dx \geq \text{const} \cdot R^2,$$
which in turn would run the risk of conflicting with the upper bound (3.5). We expect therefore, \( \rho_{R,\mu}^+(x) \) small in \( \Omega_{R,\mu}^+ \) except possibly near \( x_1 = 0 \). From the preceding reasoning we should be able to deduce, via estimate (5.10), that \( \rho_{R,\mu}^+(x) \) stays small and does not ‘touch’ \( r \) at \( x_1 = \eta R \) for large \( R \) and \( \mu \). This is our strategy.
**Proof.** In what follows we write \( u \) for \( u_{R,\mu} \), \( \rho \) for \( \rho_{R,\mu} \) etc. Consider the sets
\[
i_R := \{ x_1 \in (0, \eta R) \mid \text{there exists } x_2 \in (-R, R) \text{ with } \rho(x_1, x_2) \geq \frac{r}{2} \}
\]
and
\[
j_R := \{ x_1 \in i_R \mid \text{there exists } x_2 \in (-R, R) \text{ with } \rho(x_1, x_2) \leq \frac{r}{4} \}.
\]
The positivity property (5.16) implies the lower bound
\[
2 R w_0 |i_R \setminus j_R| \leq \int_{i_R \setminus j_R} W(u) \, dx_1 dx_2,
\]
where
\[
w_0 := \min_{|u-a| \geq r/4} W(u) > 0.
\]
From the definition of \( j_R \) we conclude that for \( x_1 \in j_R \) there is an interval \( L_{x_1} = (a_{x_1}, b_{x_2}) \) of \( x_2 \)-values such that
\[
\frac{r}{4} = \rho(x_1, a_{x_1}) \leq \rho(x_1, x_2) \leq \rho(x_1, b_{x_2}) = \frac{r}{2}, \quad \text{for all } x_2 \in L_{x_1}.
\]
It follows that
\[
\int_{L_{x_1}} W(u(x_1, \tau)) \, d\tau \geq w_0 |L_{x_1}|, \quad \text{for all } x_1 \in j_R.
\]
Moreover, we have
\[
\frac{r}{4} \leq \int_{L_{x_1}} \left| \frac{\partial \rho}{\partial x_2}(x_1, \tau) \right| \, d\tau \leq \left( |L_{x_1}| \int_{L_{x_1}} \left| \frac{\partial \rho}{\partial x_2}(x_1, \tau) \right|^2 \, d\tau \right)^{\frac{1}{2}}
\]
\[
\leq \left( |L_{x_1}| \int_{L_{x_1}} |\nabla u(x_1, \tau)|^2 \, d\tau \right)^{\frac{1}{2}}.
\]
From (5.18) and (5.19),
\[
\frac{1}{32} \frac{1}{|L_{x_1}|} r^2 + w_0 |L_{x_1}| \leq \int_{L_{x_1}} \frac{1}{2} |\nabla u(x_1, \tau)|^2 \, d\tau + \int_{L_{x_1}} W(u(x_1 \tau)) \, d\tau.
\]
Thus,
\[
\frac{r \sqrt{w_0}}{2 \sqrt{2}} \leq \int_{L_{x_1}} \frac{1}{2} |\nabla u(x_1, \tau)|^2 \, d\tau + \int_{L_{x_1}} W(u(x_1, \tau)) \, d\tau.
\]
22
To conclude,
\[ CR \geq 2 \int_{\Omega_{r,\mu}^R} \left\{ \frac{1}{2} |\nabla u|^2 + W(u) \right\} \, dx \geq \int_{-R}^{R} \int_{i_R}^{j_R} \left\{ \frac{1}{2} |\nabla u|^2 + W(u) \right\} \, dx \, dx_2 \]
(5.21)
\[ \geq \int_{-R}^{R} \int_{i_R \setminus j_R} \left\{ \frac{1}{2} |\nabla u|^2 + W(u) \right\} \, dx_1 \, dx_2 + \int_{-R}^{R} \int_{j_R} \left\{ \frac{1}{2} |\nabla u|^2 + W(u) \right\} \, dx_1 \, dx_2 \]
(5.17, 6.1)
\[ \geq 2 \left( 2 R w_0 |i_R \setminus j_R| + \frac{r_0 \sqrt{w_0}}{2\sqrt{2}} |j_R| \right). \]
(5.21) implies
\[ |j_R| \leq \frac{\sqrt{2}}{r/\sqrt{u_0}} CR; \quad |i_R| - |j_R| \leq \frac{C}{4w_0}. \]
Therefore, it follows that
\[ |i_R| \leq \frac{C}{\sqrt{w_0}} \left( \frac{1}{4\sqrt{w_0}} \frac{\sqrt{2}}{r} R \right) \leq \frac{C}{2w_0} R, \text{ for } R \geq \frac{\mu}{4\sqrt{2}w_0}. \]
Consequently, if we take \( R \) large in (5.21), we obtain \( |i_R| \leq (\sqrt{2} CR / r|w_0|) =: \eta_0 R \). If we take \( \eta > \eta_0 \) and fix it, then \( |i_R| < \eta R \) and therefore there is an \( \bar{x}_1 \in (0, \eta R) \) which does not belong to \( i_R \) and such that
\[ \rho(\bar{x}_1, x_2) < \frac{r}{2}, \text{ for all } x_2 \in (-R, R). \]
Applying now the chop-off lemma for the choice \( A = \{ (x_1, x_2) \mid \bar{x}_1 \leq x_1 \leq \bar{x}_1, \ |x_2| < R \} \) with \( \bar{x}_1 > \eta R \) such that \( \rho(\bar{x}_1, x_2) < r/2 \) (which always exists by Lemma 5.1 for \( \mu > \eta \) large enough and fixed), we conclude that \( \rho \leq r/2 \) in \( A \), and thus \( \rho < r \) on the line \( x_1 = \eta R \).
Thus, the minimizer of the constrained problem satisfies (5.13). To conclude, we now note that \( u(x) \neq 0 \) by the constraint. For excluding that
\[ u(x) \neq e_0(x_1), \quad (e_0(0) = 0), \]
we argue as in the proof of Theorem 10 below. Specifically, estimate (7.4) holds by the same argument. Thus, the proof of the theorem is complete.
6 The uniform exponential bound \([h_1, h_2, h_3]\)
The hypothesis \( h_3 \) allows the construction of a comparison function. Combining this with the exponential estimate in Corollary 5.1, we can derive, by a simple iteration argument, the sought estimate on \( |u_R - a^\pm| \).
**Proposition 6.1.** \([h_1, h_2, h_3]\) Suppose \( r < r_0 \), and \( \eta \) and \( \mu \) (finite or infinite) fixed as in the definition of the constrained problem in Section 3. We denote the minimizer \( u_{R,\mu} \) in (3.1) and the domain \( \Omega_{R,\mu} \) by \( u_R \) and \( \Omega_R \) respectively and assume that it possesses the property in Corollary 4.1.
Then, there exists $R_0 > 0$, such that for $x \in \Omega_R$, the estimate
$$
(6.1) \quad |u_R(x) - a^+| < M e^{-c|x_1|}, \quad \text{for } x_1 \geq 0, \quad R \geq R_0,
$$
holds, where $M$ is a constant depending on the set $C_0$ in ($h_2$).
**Corollary 6.1.** Under the hypotheses of Proposition 6.1, there exists $R_0$ such that
$$
(6.2) \quad |u_R(x) - a_\pm| < r, \quad \text{for } x \in \bar{C}_R^{\pm}\eta.
$$
Thus, $u_R(x)$ solves $\Delta u - W(u) = 0$ in $\Omega_R$, with homogeneous Neumann conditions on $\partial \Omega_R$.
We note that Corollary 6.1 establishes the result stated in Theorem 5.1 in a different and much simpler way under the additional global hypothesis ($h_3$).
**Proof.** Step 1. We begin by noting that by Lemma 4.1 we may assume that $u_R(x) \in C_0$.
Step 2. Suppose $Q(u)$ a $C^2$ convex function as in ($h_3$). We can check easily that the following holds true
$$
(6.3) \quad \Delta x Q(u(x)) = \text{tr}\{ (\partial^2 Q)(\nabla u)(\nabla u)^\top \} + Q_u(u(x)) \cdot \Delta x u(x) \geq Q_u(u(x)) \cdot \Delta x u(x).
$$
Step 3. Let $u_R$ be the minimizer. Then,
$$
(6.4) \quad Q(u_R(x)) \leq Ax_1 + B =: U(x_1, \eta R), \quad \text{for } x_1 \in [0, \eta R], \quad x = (x_1, x_2),
$$
where $A = \frac{r-B}{\eta R}$, $B$ a bound, and $Q(u_R(x)) \leq B$ for $x \in \Omega_R$, provided by Step 1.
To prove (6.4), from (6.3) in $\Omega_R \cap \{0 \leq x_1 \leq \eta R\}$, we have
$$
\Delta x Q(u_R(x)) \geq Q_u(u_R(x)) \cdot W_u(u_R(x)) \geq 0
$$
by (6.3), (4.6), ($h_3$); (6.4) now follows by the maximum principle.
We shall denote by $U(x_1; \theta)$ the function $\frac{r-B}{\eta}x_1 + B$. Then, $Q(u_R(x)) \leq U(x_1; \eta R)$ for $0 \leq x_1 \leq \eta R =: \bar{x}_0$. Next, we consider the equation
\[(6.5) \quad U(x_1; \eta R) = r_0,\]
which has the unique solution
$$\bar{x}_0 = \frac{B - r_0 \eta R}{B - r} = \delta \eta R, \text{ with } \delta = \frac{B - r_0}{B - r}, \quad 0 < \delta < 1.$$
By the definition of $Q$, $\rho_R^+ \leq r_0$, $\bar{x}_0 \leq x_1 \leq \mu R$ from which we obtain, via Lemma 5.1, for $\bar{x}_0$ in the place of $\eta R$,
\[(6.6) \quad \rho_R^+(x) \leq r_0 \cosh \left( c(\mu R - x_1) \right) \cosh \left( c(\mu R - \bar{x}_0) \right) =: r_0 \sigma(x_1; \bar{x}_0), \text{ for } \bar{x}_0 \leq x_1 \leq \mu R.\]
Evaluating (6.6) at $x_1 = \eta R$, we obtain for $\eta > \delta/(1 - \delta)$,
$$\rho_R^+(x) \leq 2r_0 e^{-\delta \eta R}.$$
The estimate forces, for $R$ and $\eta$ large enough, the strict inequality $\rho_R^+(x) < r$ and so by the remark following Corollary 5.1, $u_R$ solves the Neumann problem. Consequently, Corollary 6.1 holds. Note that (6.6) is independent of $\mu$ and thus it holds for $\mu = \infty$.
Now we continue the iteration. Let $\bar{x}_1^i$ be the solution to $r_0 \sigma(x_1; \bar{x}_0) = r$. As before, we have $Q(u_R(x)) \leq U(x_1; \bar{x}_1^i)$ for $x_1 \in \bar{\bar{x}_1}$, and therefore $\rho_R^+(x) \leq r_0$ for $x_1 \in [\bar{x}_1, \mu R]$, where $\bar{x}_1$ the solution to $U(x_1; \bar{x}_1) = r_0$. Consequently, we have the estimate
$$\rho_R^+(x) \leq r_0 \sigma(x_1; \bar{x}_1), \text{ for } \bar{x}_1 \leq x_1 \leq \mu R.$$
We denote the solution to $r_0 \sigma(x_1; \bar{x}_1) = r$ by $\bar{x}_2$ and keep going, thus generating two sequences $\{\bar{x}_i\}, \{\bar{x}_2^i\}$, for $i = 1, 2, \ldots$.
The iteration is terminated if for some $i$, the slope of the line $U(x_1; \bar{x}_1^i)$ which is $(r - B)/\bar{x}_1^i$, gets equal or less than $-c r_0$, the lower bound of the slope of $r_0 \sigma(x_1; \bar{x}_i)$ at the point $\bar{x}_i$. Consequently, since $\bar{x}_1^i$ is decreasing as $i \to \infty$ and
$$\left| \frac{d}{dx_1} \sigma(x_1; \bar{x}_i) \right| \leq c,$$
we may let $i \to \infty$. The iteration is terminated independently of $R$ and at a distance
$$\lim_{i \to \infty} \bar{x}_1^i = \frac{B - r}{c r_0} =: \delta^*$$
from the line $x_1 = 0$. Moreover, we have
$$\rho_R^+(x) \leq r_0 \sigma(x_1; \lim_{i \to \infty} \bar{x}_i), \quad \lim_{i \to \infty} \bar{x}_i \leq x_1 \leq \mu R,$$
from which it follows that $\rho_R^+(x) \leq r$ for $x_1 \geq \delta^*$ and $x_1 \leq \mu R$. Thus,
$$\rho_R^+(x) \leq r_0 \cosh \left( c(\mu R - x_1) \right) \cosh \left( c(\mu R - \delta^*) \right), \text{ for } \delta^* \leq x_1 \leq \mu R.$$
It follows that \( \rho_R^+(x) \leq 2r_0 e^{-c(x_1 - \delta^*)} \), for \( x_1 \geq \delta^* \).
Note that
\[
R_0 = -\frac{\ln \left( \frac{r}{2r_0} \right)}{c\delta}, \quad \delta = \frac{B - r_0}{B - r}, \quad \delta^* = \frac{B - r}{cr_0}.
\]
The proof is complete. \(\square\)
7 Taking the limit \([h_1, h_2, h_3, h_4]\)
In this section we will work with the infinite strip which we denote by \( \Omega_R \). The constrained problem in Section 3 provides a minimizer \( u_R \) which may be assumed to possess the positivity property of Corollary 4.1. Moreover, \( u_R \) satisfies the uniform exponential bound (6.1). By standard local estimates, the following limit exists
\[
(7.1) \quad u(x) = \lim_{R_n \to \infty} u_{R_n}(x),
\]
along a subsequence of \( R_n \to \infty \), and clearly \( u \) satisfies equation (1.1). The danger is that \( u \) may be a trivial solution. One a priori possibility is that \( u(x) \equiv 0 \) (zero-dimensional solution) which cannot be excluded on the basis of symmetry. The uniform exponential estimate however excludes this case since \( u \) satisfies the estimate
\[
|u(x) - a^+| < Me^{-c|x_1|}, \text{ for } x_1 \geq 0.
\]
A second danger is posed by the ‘scalar’ one-dimensional trajectory \( e_0 \). This will be excluded by an argument utilizing \((h_4)\).
**Theorem 7.1.** There exists a solution \( u \) to
\[
\Delta u - W_u(u) = 0, \text{ for } u : \mathbb{R}^2 \to \mathbb{R}^2,
\]
which is \( H_2^2 \)-equivariant and satisfies the estimate
\[
|u(x) - a^+| < Me^{-c|x_1|}, \text{ for } x_1 \geq 0.
\]
Moreover,
\[
(7.2) \quad u(x) \neq 0
\]
and
\[
(7.3) \quad u(x) \neq e_0(x_1), \quad (e_0(0) = 0),
\]
where \( e_0(x_1) \) is the scalar connection (see \((h_4)\)).
**Proof.** We only need to establish (7.3). We will proceed by contradiction. Thus, we assume that \( u(x) = e_0(x_1) \).
**Step 1. (Upper bound).** There exists \( C \) independent of \( R \) such that
\[
(7.4) \quad J_{\Omega_R}(u_R) \leq C + 2E(e_\pm)R,
\]
where
\[ J_{\Omega_R}(v) = \int_{\Omega_R} \left\{ \frac{1}{2} |\nabla v|^2 + W(v) \right\} \, dx. \]
To prove (7.4), we consider the function
\[ u(x_1, x_2) = \begin{cases} e_+(x_1), & \text{for } x_2 \geq 1, \\ \left( \frac{1+x_2}{2} \right) e_+(x_1) + \left( \frac{1-x_2}{2} \right) e_-(x_1), & \text{for } |x_2| \leq 1, \\ e_-(x_1), & \text{for } x_2 \leq -1, \end{cases} \]
where \( e_+(x_1) = (e^1_+(x_1), e^2_+(x_1)) \), \( e_-(x_1) = (e^1_-(x_1), e^2_-(x_1)) \).
First we show that \( \tilde{u} \) is equivariant. There holds that \( T_1 \tilde{u}(x) = \tilde{u}(T_1 x) \), by the equivariance of \( e_\pm(x_1) \), and
\[ T_2 \tilde{u}(x) = T_2 \left[ \left( \frac{1+x_2}{2} \right) e_+(x_1) + \left( \frac{1-x_2}{2} \right) e_-(x_1) \right] = \left( \frac{1+x_2}{2} \right) e_-(x_1) + \left( \frac{1-x_2}{2} \right) e_+(x_1) = \tilde{u}(T_2 x), \]
where we utilized \( T_2 e_+(x_1) = e_-(x_1) \). Thus equivariance has been checked.
Note that \( \tilde{u} \) satisfies the constraint \( |\tilde{u}(x_1, x_2) - a^+| \leq r \) for \( x_1 \geq \eta R \). Indeed, this follows from \( e_\pm(x_1) \to a^+, \, x_1 \to +\infty \). Consequently,
\[ J_{\Omega_R}(u_R) \leq J_{\Omega_R}(\tilde{u}). \]
Next we estimate
\[ J_{\Omega_R}(\tilde{u}) = \iint_{\Omega_R} \left\{ \frac{1}{2} |\nabla \tilde{u}|^2 + W(\tilde{u}) \right\} \, dx_1 \, dx_2 \]
\[ = \left( \iint_{\Omega_R \cap \{|x_2| \leq 1\}} + \iint_{\Omega_R \cap \{|x_2| \geq 1\}} \right) \left\{ \frac{1}{2} |\nabla \tilde{u}|^2 + W(\tilde{u}) \right\} \, dx_1 \, dx_2 \]
\[ \leq C' + 2(R-1)E(e_\pm) = C + 2RE(e_\pm). \]
**Step 2. (Lower bound).**
\[ \iint_{\Omega_R} \left\{ \frac{1}{2} \left| \frac{\partial u_R}{\partial x_1} \right|^2 + W(u_R) \right\} \, dx_1 \, dx_2 \geq 2E(e_\pm)R. \]
To prove (7.6), we set \( V_{x_2}(x_1) = u_R(x_1, x_2) \). From (6.1), \( |V_{x_2}(x_1) - a^+| < M e^{-c|x_1|} \), for \( x_1 \geq 0 \) (with an analogous estimate for \( x_1 \leq 0 \). By (h4), the minimizing property of the connection \[ \text{[5]}, \] and the exponential estimate, we conclude
\[ E(V_{x_2}) \geq E(e_\pm). \]
Integrating this inequality with respect to \( x_2 \), we obtain
\[ \int_{|x_2| < \xi} E(V_{x_2}) \, dx_2 \geq \int_{|x_2| < \xi} E(e_\pm) \, dx_2 \]
which is equivalent to (7.6).
Step 3.
(7.8) \[ \iint_{\Omega_R} |\frac{\partial u_R}{\partial x_2}|^2 \, dx_1 dx_2 < C, \]
where \( C \) is a constant independent of \( R \).
To prove (7.8), let
\[
C + 2E(e_\pm)R \geq J_{\Omega_R}(u_R)
\]
\[
= \iint_{\Omega_R} \left\{ \frac{1}{2} \left| \frac{\partial u_R}{\partial x_2} \right|^2 + \frac{1}{2} \left| \frac{\partial u_R}{\partial x_1} \right|^2 + W(u_R) \right\} \, dx_1 dx_2
\]
\[
\geq \iint_{\Omega_R} \left\{ \frac{1}{2} \left| \frac{\partial u_R}{\partial x_2} \right|^2 \right\} \, dx_1 dx_2 + 2E(e_\pm)R,
\]
where in the last inequality we utilized (7.6). The idea of the proof of (7.8) is taken from [1].
Step 4. For \( d > 0 \) arbitrary but fixed, we have
(7.9) \[ \lim_{n \to \infty} \iint_{|x_2|<d} \left\{ \frac{1}{2} |\nabla u_{R_n}|^2 + W(u_{R_n}) \right\} \, dx_1 dx_2 = \iint_{|x_2|<d} \left\{ \frac{1}{2} |\nabla u|^2 + W(u) \right\} \, dx_1 dx_2. \]
To prove (7.9), let
\[ W(u_{R_n}(x)) \to W(u(x)) \text{ pointwise} \]
and, by (6.1),
\[ W(u_{R_n}(x)) < Ce^{-c|x_1|} \]
Consequently, by the dominated convergence theorem
\[ \lim_{n \to \infty} \iint_{|x_2|<d} W(u_{R_n}) \, dx_1 dx_2 = \iint_{|x_2|<d} W(u) \, dx_1 dx_2. \]
The corresponding statement for the gradient term follows from the exponential estimate above and the equation
\[ \left\{ \begin{array}{ll} \Delta u_{R_n} - W_a(u_{R_n}) = 0, & \text{in the interior of } \Omega_{R_n}, \\ \frac{\partial u_{R_n}}{\partial n} = 0, & \text{on the boundary of } \partial \Omega_{R_n}, \end{array} \right. \]
which holds by Corollary 6.1. From (7.9) and the contradiction hypothesis it follows that
(7.10) \[ \lim_{n \to \infty} \iint_{|x_2|<d} \left\{ \frac{1}{2} |\nabla u_{R_n}|^2 + W(u_{R_n}) \right\} \, dx_1 dx_2 = 2dE(e_0). \quad (h_4) \]
Step 5 (Conclusion).
\[ C + 2E(e_\pm)R_n \geq J_{\Omega_{R_n}}(u_{R_n}) = \iint_{|x_2|<R_n} \left\{ \frac{1}{2} \left| \frac{\partial u_{R_n}}{\partial x_1} \right|^2 + \frac{1}{2} \left| \frac{\partial u_{R_n}}{\partial x_2} \right|^2 + W(u_{R_n}) \right\} \, dx_1 dx_2. \]
We fix $d > 0$, arbitrary, and we write the integral above as follows.
\[
\int\int_{|x_2| < d} \left\{ \frac{1}{2} \left| \frac{\partial u_{R_n}}{\partial x_1} \right|^2 + \frac{1}{2} \left| \frac{\partial u_{R_n}}{\partial x_2} \right|^2 + W(u_{R_n}) \right\} \, dx_1 dx_2 \\
+ \int\int_{R_n > |x_2| > d} \frac{1}{2} \left| \frac{\partial u_{R_n}}{\partial x_1} \right|^2 \, dx_1 dx_2 + \int\int_{R_n > |x_2| > d} \left\{ \frac{1}{2} \left| \frac{\partial u_{R_n}}{\partial x_1} \right|^2 + W(u_{R_n}) \right\} \, dx_1 dx_2
\]
\[
\geq 2dE(e_0) + o(1; d) + A(d) + \int\int_{R_n > |x_2| > d} \left\{ \frac{1}{2} \left| \frac{\partial u_{R_n}}{\partial x_1} \right|^2 + W(u_{R_n}) \right\} \, dx_1 dx_2,
\]
where $\lim_{n \to \infty} o(1; d) = 0$ for every $d$ fixed. Also, we have the estimate $|A(d)| < C$ by (7.8), $C$ independent of $d$. Thus, calling (*) the left-hand side of the inequality above, we have
\[
(*) \geq 2dE(e_0) + o(1; d) + A(d) + 2 \int_{-\infty}^{\infty} \left\{ \int_{-\infty}^{+\infty} \left\{ \frac{1}{2} \left| \frac{\partial u_{R_n}}{\partial x_1} \right|^2 + W(u_{R_n}) \right\} \, dx_1 \right\} \, dx_2
\]
\[
\geq 2dE(e_0) + o(1; d) + A(d) + 2(R_n - d)^2E(e_\pm).
\]
Therefore,
\[
C + 2E(e_\pm)R_n \geq 2dE(e_0) + o(1; d) + A(d) + 2(R_n - d)^2E(e_\pm),
\]
\[
C + 2dE(e_\pm) \geq 2dE(e_0) + A(d) + o(1; d),
\]
\[
\frac{C}{d} + 2E(e_\pm) \geq 2E(e_0) + \frac{A(d)}{d} + \frac{o(1; d)}{d}.
\]
We take now $n \to \infty$ ($d$ fixed) to conclude that
\[
(7.11) \quad \frac{C}{d} + 2E(e_\pm) \geq 2E(e_0) + \frac{A(d)}{d}.
\]
However, $A(d)$ is bounded by a constant independent of $d$ and $C$ is independent of $d$. Therefore, (7.11) leads to a contradiction by taking $d$ large in relation to the constants above and the difference $E(e_0) - E(e_\pm)$. The proof of Theorem \ref{thm:1} is complete. \hfill \Box
Theorem \ref{thm:1} suggests that the solution we have constructed is not trivial. Our next result is a direct statement on the two-dimensionality of this solution.
**Theorem 7.2.** Let $u$ be as in Theorem \ref{thm:1}. There exists a sequence $x_2^n \to \infty$ such that
\[
(7.12) \quad u(x_1, x_2^n) \to \tilde{e}_+(x_1), \quad u(x_1, -x_2^n) \to \tilde{e}_-(x_1),
\]
where $\tilde{e}_\pm$ connecting orbits of $a^+$, $a^-$ symmetric to each other, $\tilde{e}_\pm(0) = 0$ and distinct from the scalar $e_0$.
Recall that in contrast to \cite{1}, we do not assume uniqueness of the pair of connections minimizing the action. We generally expect multiple solutions and also that for a given solution, the limit as $x_2 \to \infty$ exists.
Proof. There exists a $C$ independent of $R$ such that
\begin{equation}
J_{\Omega_R}(u) \leq C + 2E(e_{\pm})R
\end{equation}
To prove (7.13), choose $R' > R$ but otherwise arbitrary. By the additivity of the integral,
\begin{equation}
J_{\Omega_{R'}}(u_{R'}) = J_{\Omega_R}(u_{R'}) + \int_{R \leq |x_2| \leq R'} \left\{ \frac{1}{2} |\nabla u_{R'}|^2 + W(u_{R'}) \right\} \, dx.
\end{equation}
We set $V_{x_2} := u_{R'}(x_1, x_2)$ and observe that
\begin{equation*}
\int_{R \leq |x_2| \leq R'} \left\{ \frac{1}{2} |\nabla u_{R'}|^2 + W(u_{R'}) \right\} \, dx \geq \int_{R \leq |x_2| \leq R'} E(V_{x_2}) \, dx_2 \geq 2E(e_{\pm})(R' - R).
\end{equation*}
Utilizing this inequality together with (7.4) for $R'$, we get from (7.14),
\begin{equation*}
C + 2E(e_{\pm})R' \geq J_{\Omega_R}(u_{R'}) + 2E(e_{\pm})(R' - R),
\end{equation*}
or,
\begin{equation*}
C' + 2E(e_{\pm})R \geq J_{\Omega_R}(u_{R'}).\end{equation*}
From this, (7.13) follows by taking the limit $R' \to \infty$, via the uniform exponential estimate.
The following bound follows immediately from (7.8).
\begin{equation}
\int_{\mathbb{R}^2} \left| \frac{\partial u}{\partial x_2} \right|^2 \, dx \leq C.
\end{equation}
To conclude, by elliptic theory, it follows easily from (7.15) (see [1], Lemma 5.2) that up to subsequences $x^n_2$, the limits $e(x_1) = \lim_{n \to \infty} u(x_1, x^n_2)$ exist and therefore solve the equation $\Delta u - W_u(u) = 0$. By the uniform exponential estimate (6.1), $e(x_1)$ is a connecting orbit of $a^+$ and $a^-$. Consequently, in order to complete the proof, it suffices to show that $e(x_1) \neq e_0(x_1)$, which is a genuine refinement of (7.3). We proceed by contradiction. Assume that $e(x_1) \equiv e_0(x_1)$.
We set
\begin{equation*}
V_{x_2}(x_1) := u(x_1, x_2).
\end{equation*}
By the uniform exponential estimate (6.1) which holds for $u$, the contradiction hypothesis gives
\begin{equation}
E(V_{x_2}) \to E(e_0), \text{ as } |x_2| \to \infty.
\end{equation}
For $\varepsilon > 0$, we select $R_0$ such that
\begin{equation}
E(V_{x_2}) \geq E(e_0) - \varepsilon, \text{ for } |x_2| \geq R_0.
\end{equation}
Let $R > R_0$ arbitrary and fixed. Integrating (7.17), we get
\begin{equation*}
\int_{|x_2| < R} E(V_{x_2}) \, dx_2 \geq \int_{|x_2| < R_0} E(V_{x_2}) \, dx_2 + \int_{R_0 \leq |x_2| < R} (E(e_0) - \varepsilon) \, dx_2,
\end{equation*}
or, equivalently,
\begin{equation*}
\int_{|x_2| < R} \left\{ \frac{1}{2} \frac{\partial u}{\partial x_1}^2 + W(u) \right\} \, dx_1 dx_2 \geq \int_{|x_2| < R_0} E(V_{x_2}) \, dx_2 + 2(E(e_0) - \varepsilon)(R - R_0),
\end{equation*}
which, via (7.13), is in contradiction, as $R \to \infty$, to (h4). The proof of Theorem 7.2 is complete. \qed
8 Higher-dimensional extensions
For Extension 1 in Section 2, under the hypotheses there, we establish the following
**Theorem 8.1.** There is a solution \( u \) of the system
\[
\Delta u - W_u(u) = 0, \text{ for } u : \mathbb{R}^3 \to \mathbb{R}^3,
\]
where \( u \) is \( \mathcal{H}_3^2 \)-equivariant and satisfies the estimate
\[
|u(x) - a^+| < Me^{-c|x_1|}, \text{ for } x_1 \geq 0.
\]
Moreover, if
\[
u(x_1, x_2, \pm x_3) \to p_\pm(x_1, x_2) = \left(p^1_\pm(x_1, x_2), p^2_\pm(x_1, x_2), p^3_\pm(x_1, x_2)\right), \text{ as } x_3 \to \infty,
\]
then \( p_\pm \) are solutions to (8.1) satisfying (8.2), with \( p^3_- = -p^3_+ \neq 0 \). An analogous statement holds for \( u(x_1, \pm x_2, x_3) \to q_\pm(x_1, x_3) \), as \( x_2 \to \infty \).
Note that the estimates in the proof provide compactness. Thus, either the limit as \( x_3 \to \infty \) exists, and so (8.3) and its analogs hold, or else there are distinct limits along distinct sequences. In either case, we have strong evidence of the three-dimensional nature of the solution.
**Proof.** The procedure we follow is analogous to the proof of Theorem 7.1. We work with a minimizer of the constrained problem. Here \( \Omega_R = \{(x_1, x_2, x_3) \in \mathbb{R}^3 \mid |x_2| < R, |x_3| < R\} \). As before, we can assume that \( u_R \) has the positivity property (4.16) from which the uniform exponential estimate (8.2) follows. By elliptic estimates, we have that along a sequence \( R_n \to \infty \) the limit
\[
u(x) = \lim_{R_n \to \infty} u_{R_n}(x)
\]
exists. Symmetry excludes that \( u(x) \equiv a^\pm \) and the exponential estimate excludes that \( u(x) \equiv 0 \).
The new element in the proof is the existence of the two-dimensional solutions that pose a threat to the existence of a genuine three-dimensional solution.
**Step 1. (Two-dimensional solutions).** Let
\[
\tilde{W}(u_1, u_2) := W(u_1, u_2, 0)
\]
and consider the problem
\[
\frac{\partial^2 \sigma_1}{\partial x_1^2} + \frac{\partial^2 \sigma_1}{\partial x_2^2} - \tilde{W}_u(\sigma_1) = 0,
\]
\[
\lim_{x_1 \to \pm \infty} \sigma_1(x_1, x_2) = (\pm a, 0)
\]
in the class of \( \mathcal{H}_2^2 \)-equivariant vector fields. For applying Theorems 7.1 and 7.2 we need to verify the hypotheses in Section 1. \( (h_4) \) is the only hypothesis that requires discussion. We
and the next, we construct two two-dimensional solutions, subscript \( u \), \( \sigma \) covariance of the gradient under linear transformations and the invariance of the Laplacian (8.10)
\[
(8.9) \quad \Delta
\]
and note that (8.1) transforms into (8.5), \( \sigma_1 : \mathbb{R}^2_x \to \mathbb{R}^2_u \), satisfying (by the uniqueness assumptions in (h_c)),
\[
(8.6) \quad \lim_{x_2 \to \pm \infty} \sigma_1(x_1, x_2) = e^1_\pm(x_1).
\]
Similarly, we define
\[
\tilde{W}(u_1, u_3) := W(u_1, 0, u_3)
\]
and obtain a solution \( \sigma_2 : \mathbb{R}^2_x \to \mathbb{R}^2_u \) to
\[
(8.7) \quad \begin{cases}
\frac{\partial^2 \sigma_2}{\partial x_1^2} + \frac{\partial^2 \sigma_2}{\partial x_3^2} - \tilde{W}_u(\sigma_2) = 0, \\
\lim_{x_1 \to \pm \infty} \sigma_2(x_1, x_3) = (\pm a, 0), \quad \lim_{x_3 \to \pm \infty} \sigma_2(x_1, x_3) = e^2_\pm(x_1).
\end{cases}
\]
By (7.13), the following estimates hold.
\[
(8.8) \quad \begin{cases}
\iint_{|x_2| < d} \left\{ \frac{1}{2} |\nabla \sigma_1|^2 + W(\sigma_1) \right\} \, dx_1 \, dx_2 \leq C + 2E_1d, \\
\iint_{|x_3| < d} \left\{ \frac{1}{2} |\nabla \sigma_2|^2 + W(\sigma_2) \right\} \, dx_1 \, dx_3 \leq C + 2E_1d.
\end{cases}
\]
Next, we construct two two-dimensional solutions, \( \sigma^*_3 \) and \( \sigma^*_4 \), with range in the \( u_2 = u_3 \) and the \( u_2 = -u_3 \) planes respectively and with corresponding asymptotic limits \( e^3, e^4 \), as \( |x_2| \to \infty \).
The discussion that follows could be compressed in a couple of sentences concerning the covariance of the gradient under linear transformations and the invariance of the Laplacian under orthogonal transformations. In more detail, set
\[
\{f_1, f_2, f_3\} := \{(1, 0, 0), (0, 1, 0), (0, 0, 1)\}
\]
\[
\{f'_1, f'_2, f'_3\} = \{(1, 0, 0), \left(0, \frac{1}{\sqrt{2}}, \frac{1}{\sqrt{2}}\right), (0, \frac{1}{\sqrt{2}}, \frac{1}{\sqrt{2}})\}
\]
and let \( u = Ru' \), \( R \in O(\mathbb{R}^3) \), that transforms \( f \)-coordinates to \( f' \)-coordinates. Set
\[
\tilde{W}(u') = W(R^\top u)
\]
and note that (8.1) transforms into
\[
(8.9) \quad \Delta u' - \tilde{W}_{u'}(u') = 0.
\]
We can moreover change to \( x' \) independent variables, \( x = Rx' \), by utilizing the invariance of the Laplacian under orthogonal transformations. Applying then Theorems 7.1 and 7.2 in the \( (x', u') \) setup, we obtain the existence of a two-dimensional \( H^2_2 \)-equivariant solution \( \sigma^*_3 = \sigma^*_3(x'_1, x'_2) \), as above, with asymptotic limits
\[
(8.10) \quad \begin{cases}
\lim_{x'_1 \to \pm \infty} \sigma^*_3(x'_1, x'_2) = (a^\pm, 0) \\
\lim_{x'_2 \to \pm \infty} \sigma^*_3(x'_1, x'_2) = e^3_\pm(x'_1)
\end{cases}
\]
32
Finally, we change back to the original independent and dependent variables
\[ \hat{\sigma}^*_3(x) = \sigma^*_3(x') \]
and note that \( \hat{\sigma}^*_3 \) is \( \mathcal{H}^2_2 \)-equivariant in \( x \). Overall, we obtain the existence of two solutions which, by abusing the notation and dropping the hat, we denote by
\[ (x_1, x_2) \rightarrow \sigma^*_3(x_1, x_2), \quad (x_1, x_2) \rightarrow \sigma^*_4(x_1, x_2), \]
which are \( \mathcal{H}^2_2 \)-equivariant and map the \((x_1, x_2)\)-plane into the \( u_2 = u_3 \) and \( u_2 = -u_3 \) planes respectively. Moreover, they satisfy the estimates
\[
\begin{align*}
\iint_{|x_2| < \delta} \left\{ \frac{1}{2} \nabla \sigma^*_3(x_1, x_2)^2 + W(\sigma^*_3(x_1, x_2)) \right\} dx_1 dx_2 & \leq C + 2E_{II}d, \\
\iint_{|x_1| < \delta} \left\{ \frac{1}{2} \nabla \sigma^*_4(x_1, x_2)^2 + W(\sigma^*_4(x_1, x_2)) \right\} dx_1 dx_3 & \leq C + 2E_{II}d,
\end{align*}
\] (8.11)
with asymptotic limits
\[
\begin{align*}
\lim_{x_1 \rightarrow \pm \infty} \sigma^*_3(x_1, x_2) & = (a^\pm, 0, 0), & \lim_{x_2 \rightarrow \pm \infty} \sigma^*_3(x_1, x_2) & = e^3_\pm(x_1), \\
\lim_{x_1 \rightarrow \pm \infty} \sigma^*_4(x_1, x_2) & = (a^\pm, 0, 0), & \lim_{x_2 \rightarrow \pm \infty} \sigma^*_4(x_1, x_2) & = e^4_\pm(x_1).
\end{align*}
\] (8.12)
Step 2. (The list of solutions). So far we have the following solutions.
- Zero-dimensional: \( u(x) \equiv (a, 0, 0) \), \( u(x) \equiv (-a, 0, 0) \), \( u(x) \equiv (0, 0, 0) \). Among these, only \( u(x) \equiv (0, 0, 0) \) is \( \mathcal{H}^2_2 \)-equivariant but it is excluded by the exponential estimate.
- One-dimensional: Among the nine connections, \( e_0 \) is the only equivariant one and will be excluded as a possible (trivial) three-dimensional candidate by \( E(e_0) > E_1 \).
- Two-dimensional: \( u(x) = \sigma_1(x_1, x_2) \), \( u(x) = \sigma_2(x_1, x_2) \), \( u(x) = \sigma_3^*(x_1, x_2) \), \( u(x) = \sigma_4^*(x_1, x_2) \). Among these, \( \sigma_1, \sigma_2 \) are the only \( \mathcal{H}^2_2 \)-equivariant ones when extended as maps from \((x_1, x_2, x_3)\) to \((u_1, u_2, u_3)\). They will be excluded by the hypothesis \( E_1 > E_{II} \).
Step 3. (Upper bound). There is a \( C \), independent of \( R \), such that
\[
J_{\Omega_R}(u_R) \leq C + E_{II}(2R)^2.
\] (8.13)
To prove (8.13), consider the function
\[
\tilde{u}(x_1, x_2, x_3) = \begin{cases}
\sigma^*_3(x_1, x_2), & \text{for } x_3 \geq 1, \\
\frac{1+x_3}{2}\sigma^*_3(x_1, x_2) + \left(\frac{1-x_3}{2}\right)\sigma^*_4(x_1, x_2), & \\
\sigma^*_4(x_1, x_2), & \text{for } x_3 \leq -1.
\end{cases}
\]
It can be easily checked that $\tilde{u}$ is equivariant and satisfies the constraint, hence
$$J_{\Omega_R}(u_R) \leq J_{\Omega_R}(\tilde{u}).$$
From this, $(8.13)$ follows via $(8.11)$.
**Step 4. (Lower bound).**
$(8.14)$
$$\int_{\Omega_R} \left\{ \frac{1}{2} \left| \frac{\partial u_R}{\partial x_1} \right|^2 + W(u_R) \right\} \, dx_1 dx_3 \geq (2R)^2 E_{II}.$$
To prove $(8.14)$, set $V_{x_2x_3}(x_1) := u_R(x_1, x_2, x_3)$. By the exponential estimate and the hypothesis $(h_c)$, especially $(2.5)$, we obtain $E(V_{x_2x_3}) \geq E_{II}$. $(8.14)$ now follows by integration.
**Step 5. (Gradient estimate).**
$(8.15)$
$$\int_{\Omega_R} \left\{ \left( \frac{\partial u_R}{\partial x_2} \right)^2 + \left( \frac{\partial u_R}{\partial x_3} \right)^2 \right\} \, dx \leq C.$$
The proof of $(8.15)$ is immediate from $(8.13)$, $(8.14)$.
**Step 6. ($u \neq \sigma_1, \sigma_2$)** We proceed by contradiction, hence assume that $u(x) = \sigma_1(x_1, x_2)$. For $d > 0$ arbitrary and fixed, we have, via the exponential estimate,
$(8.16)$
$$\lim_{n \to \infty} \int\int\int_{|x_2| < d} \int\int\int_{|x_3| < d} \left\{ \frac{1}{2} \left| \nabla u_{R_n} \right|^2 + W(u_{R_n}) \right\} \, dx_1 dx_2 dx_3 = 2d \int\int\int_{|x_2| < d} \left\{ \frac{1}{2} \left| \nabla \sigma_1 \right|^2 + W(\sigma_1) \right\} \, dx_1 dx_2.$$
Now,
$$C + E_{II} (2R)^2 \geq J_{\Omega_{R_n}}(u_{R_n}),$$
where $J_{\Omega_{R_n}}(u_{R_n})$ is expanded as
$$\int\int\int_{|x_2| < d} \left\{ \frac{1}{2} \left| \nabla u_{R_n} \right|^2 + W(u_{R_n}) \right\} \, dx + \int\int\int_{d < |x_2| < R_n} \int\int\int_{d < |x_3| < R_n} \left\{ \frac{1}{2} \left( \frac{\partial u_{R_n}}{\partial x_2} \right)^2 + \frac{1}{2} \left( \frac{\partial u_{R_n}}{\partial x_3} \right)^2 \right\} \, dx \quad \text{and thus bounded by}$$
$(8.17)$
$$\geq (2d)^2 E_I \quad \text{(by the contradiction hypothesis and $(h_c)$)} + A(d) \quad \text{($A(d) < C$ by $(7.16)$)} + 4((R_n - d)^2 + 2(R_n - d)d) E_{II} \quad \text{(by lower-bound estimates)} + o(1;d).$$
From $(8.17)$ we obtain a contradiction as in $(7.11)$.
So far we have established the analogue of Theorem $7.1$ for $(8.1)$. Next we proceed to establish the analog of Theorem $7.2$.
34
Step 7. There exists $C$ independent of $R$, such that
\begin{equation}
J_{\Omega_R}(u) \leq C + E_{\Omega}(2R)^2.
\end{equation}
This follows from (8.13). See the derivation of (8.2).
Step 8. For a constant $C$ independent of $R$, we have
\begin{equation}
\int \int \int_{\mathbb{R}^3} \left\{ \left( \frac{\partial u}{\partial x_2} \right)^2 + \left( \frac{\partial u}{\partial x_3} \right)^2 \right\} \, dx \leq C.
\end{equation}
which follows immediately from (8.15).
Step 9. (Conclusion). Assume that $u(x_1, x_2, \pm x_3) \to p_\pm(x_1, x_2)$, as $x_3 \to \infty$.
By equivariance, $p_3^3 = -p_3^4$. Suppose, for the sake of contradiction, that $p_3^3 = 0$. By the exponential estimate, we deduce that $E(u(\cdot, x_2, x_3)) \to E(p_+(\cdot, x_2))$, as $x_3 \to \infty$, uniformly in $x_2$. Since $p_+(x_1, x_2) \notin \{u_3 = 0\}$,
\begin{equation*}
E(p_+(\cdot, x_2)) \geq E_1, \text{ by (h_c)}.
\end{equation*}
Hence, given $\varepsilon > 0$, there is an $R_0$, such that for $R > R_0$ and arbitrary otherwise, we have
\begin{equation*}
\int_{|x_3| < R} E(u(\cdot, x_2, x_3)) \, dx_3 \geq \int_{|x_3| < R_0} E(u(\cdot, x_2, x_3)) \, dx_3 + 2(E_1 - \varepsilon)(R - R_0),
\end{equation*}
and therefore, by integrating in $x_2$, we obtain
\begin{equation*}
\int_{|x_2| < R} \int_{|x_3| < R} E(u(\cdot, x_2, x_3)) \, dx_2 \, dx_3 \geq \int_{|x_2| < R} \int_{|x_3| < R_0} E(u(\cdot, x_2, x_3)) \, dx_2 \, dx_3 + (2R)(E_1 - \varepsilon)(R - R_0).
\end{equation*}
This last estimate contradicts (2.5) for large $R$. Hence, we reached a contradiction, so $p_3^3$ cannot be identically zero.
The proof of Theorem 8.1 is complete. \hfill \Box
For Extension 2 in Section 2, under the hypotheses following there, we establish the following
**Theorem 8.2.** There is a bounded $G$-equivariant solution $u$ of the system
\begin{equation}
\Delta u - W_u(u) = 0,
\end{equation}
satisfying
\begin{equation}
\lim_{x_1 \to \pm \infty} u(x_1, x') = (\pm \alpha, 0'),
\end{equation}
which is nontrivial in the sense that there exists a connection $e$ minimizing the action $E$, such that, for any unit vector $\nu \in F' \cap \{x_1 = 0\}$, we have
\begin{equation}
\lim_{\lambda \to +\infty} u(x_1, \lambda r \nu) = re(x_1), \text{ for all } x_1 \in \mathbb{R}, \, r \in R'.
\end{equation}
(Without loss of generality we have assumed that $e(\mathbb{R}) \subset F'$.)
Sketch of proof. The argument is analogous to the proof of Theorem 7.1. In particular, one can derive the following upper and lower bounds for the energy $J(u, Q_L)$ of a minimizer of the constrained problem. We denote by $Q_L$ the cube
$$Q_L := \{x \in \mathbb{R}^n \mid -L < x_j < L, j = 1, \ldots, n\}$$
and by $u_L$ a minimizer of the constrained problem. Then,
$$J(u_L, Q_L) \leq (2L)^{n-1}(1 - e^{-k_0 \lambda})m + k_1 \lambda^{n-2}, \quad (8.23)$$
$$J(u, Q_L) \geq (2L)^{n-1}(1 - e^{-k_0 \lambda})m, \quad (8.24)$$
where $m$ is the minimum of the action among the connecting trajectories.
Condition (8.22) implies in particular that the entire solution $u$ in Theorem 8.3 cannot be represented with a function $v : \mathbb{R}^m \to \mathbb{R}^n$ with $m < n$. More precisely, for any given $v : \mathbb{R}^{n-1} \to \mathbb{R}^n$ and $2 \leq j \leq n$, there is an $x$ such that
$$u(x_1, \ldots, x_n) \neq v(x_1, x_2, \ldots, x_{j-1}, x_{j+1}, \ldots, x_n).$$
As a corollary to the theorem above we obtain the following
**Theorem 8.3.** Assume $W : \mathbb{R}^2 \to \mathbb{R}$ satisfies all the assumptions in Theorem 8.2 for $n = 2$ and define $V : \mathbb{R}^3 \to \mathbb{R}^3$ by setting
$$V(u_1, u_2, u_3) := W(u_1, \sqrt{u_2^2 + u_3^2}).$$
Then, there exists an entire solution $u$ of the system
$$\Delta u - V_u(u) = 0 \quad (8.27)$$
which satisfies the asymptotic condition
$$\lim_{\lambda \to +\infty} u(x_1, \lambda \rho \theta \nu) = \rho \theta e(x_1), \quad \text{for all } x_1 \in \mathbb{R}, \theta \in [0, 2\pi), \quad (8.28)$$
for some $e \in E$, where $\rho \theta : \mathbb{R}^2 \to \mathbb{R}^2$ is the rotation by $\theta$ around the $x_1$-axis.
**Sketch of proof.** Given $L > 1$, let $Q_L$ be the cube
$$Q_L := \{x \in \mathbb{R}^3 \mid -L < x_j < L, j = 1, 2, 3\}.$$
Let $u_L$ be a minimizer of $J(\cdot, Q_L)$. Define the comparison function $\hat{u}_L : Q_L \to \mathbb{R}^3$ by setting
$$\hat{u}_L(x_1, \lambda \rho \theta \nu) = \rho \theta e(x_1), \quad \text{for } \lambda > 1 \quad (8.29)$$
$$\hat{u}_L(x_1, \lambda \rho \theta \nu) = \lambda \rho \theta e(x_1), \quad \text{for } 0 \leq \lambda \leq 1. \quad (8.30)$$
The definition of $\hat{u}_L$ implies
$$J(\hat{u}_L, Q_L) \leq 4L^2(1 - e^{-k_0 \lambda})m + k_1 \ln \lambda, \quad (8.31)$$
for some constants $k_0, k_1 > 0$. Since $e$ is a minimizer of the connection problem, we also have
$$J(u, Q_L) \geq 4L^2(1 - e^{-k_0 \lambda})m \quad (8.32)$$
for all equivariant maps $u : Q_L \to \mathbb{R}^3$ that satisfy the constraints. \qed
Acknowledgements
NDA was partially supported by Kapodistrias Grant No. 70/14/5622 at the University of Athens. We would like to thank D. Sinikis for reading the manuscript and making suggestions and improvements at various places. We also want to thank G. Paschalides and O. Vantzos for their valuable help with the numerical calculations and N. Katzourakis for his valuable comments which contributed to an improved paper and also for the typing of the manuscript.
References
[1] S. Alama, L. Bronsard, and C. Gui. Stationary layered solutions in $\mathbb{R}^2$ for an Allen–Cahn system with multiple well potential. *Calc. Var.* 5 (1997), pp. 359–390.
[2] G. Alberti. Variational models for phase transitions, an approach via $\Gamma$-convergence. In *Calculus of variations and partial differential equations*, L. Ambrosio and N. Dancer eds. Springer-Verlag, Berlin, 2000.
[3] N. D. Alikakos, S. I. Betelú, and X. Chen. Explicit stationary solutions in multiple well dynamics and non-uniqueness of interfacial energy densities. *Eur. J. Appl. Math.* 17 (2006), pp. 525–556.
[4] N. D. Alikakos, S. I. Betelú and S. Dimitroula. In preparation.
[5] N. D. Alikakos and G. Fusco. On the connection problem for potentials with several global minima. *Ind. Univ. Math. J.* 57 No. 4 (2008), pp. 1871–1906.
[6] N. D. Alikakos and G. Fusco. Entire solutions to equivariant elliptic systems with variational structure. Preprint
[7] L. Bronsard, C. Gui, and M. Schatzman. A three-layered minimizer in $\mathbb{R}^3$ for a variational problem with a symmetric three-well potential. *Comm. Pure. Appl. Math.* 49 No. 7 (1996), pp. 677–715.
[8] L. Bronsard and F. Reitich. On three-phase boundary motion and the singular limit of a vector-valued Ginzburg–Landau equation. *Arch. Rat. Mech. Anal.* 124 No. 4 (1993), pp. 355–379.
[9] X. Chen. Private communication.
[10] L. C. Grove and C. T. Benson. *Finite reflection groups*. Graduate Texts in Mathematics 99, Springer-Verlag, Berlin, second edition, 1985.
[11] C. Gui and M. Schatzman. Symmetric quadruple phase transitions. *Ind. Univ. Math. J.* 57 No. 2 (2008), pp. 781–836.
[12] J. Jost and R. Schoen. On the existence of harmonic diffeomorphisms between surfaces. *Invent. Math.* 66 No. 2 (1982), pp. 353–359.
[13] A. Melas. An example of a harmonic map between Euclidean balls. *Proc. Amer. Math. Soc.* **117** No. 3 (1993), pp. 857–859.
[14] G. Paschalides. Private communication.
[15] P. H. Rabinowitz. Heteroclinics for a reversible Hamiltonian system. *Ergod. Th. & Dynam. Sys.* **14** No. 4 (1994), pp. 817–829.
[16] P. H. Rabinowitz. Solutions of heteroclinic type for some classes of semilinear elliptic partial differential equations. *J. Math. Sci. Univ. Tokyo* **1** No. 3 (1994), pp. 525–550.
[17] J. Rubinstein, P. Sternberg, and J. B. Keller. Fast reaction, slow diffusion, and curve shortening. *SIAM J. Appl. Math.* **49** No. 1 (1989), pp. 116–133.
[18] D. Sinikis. *Study of an elliptic system on the plane with a multi-well potential with several global minima*. Master’s thesis, University of Athens, 2007.
[19] P. Sternberg. Vector-valued local minimizers of nonconvex variational problems. *Rocky Mt. J. Math.* **21** No. 2 (1991), pp. 799–807.
[20] O. Vantzos. Private communication.
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Since January 2020 Elsevier has created a COVID-19 resource centre with free information in English and Mandarin on the novel coronavirus COVID-19. The COVID-19 resource centre is hosted on Elsevier Connect, the company's public news and information website.
Elsevier hereby grants permission to make all its COVID-19-related research that is available on the COVID-19 resource centre - including this research content - immediately available in PubMed Central and other publicly funded repositories, such as the WHO COVID database with rights for unrestricted research re-use and analyses in any form or by any means with acknowledgement of the original source. These permissions are granted for free by Elsevier for as long as the COVID-19 resource centre remains active.
Review
Responses of three urban U.S. Children’s Hospitals to COVID-19: Seattle, New York and New Orleans
Priya N. Jain a, Leron Finger b, John S. Schieffelin c, Danielle M. Zerr d, Patricia A. Hametz a,⇑
⇑Corresponding author at: Pediatric Quality and Safety Chief, Division of Pediatric Hospital Medicine, Department of Pediatrics, Children’s Hospital at Montefiore, Albert Einstein School of Medicine, 3415 Bainbridge Avenue, Bronx, NY 10467, United States.
E-mail address: [email protected] (P.A. Hametz).
Article info
Keywords:
COVID-19
United States
Children’s Hospitals
Abstract
Since January 2020, there has been a worldwide pandemic of COVID-19, caused by a novel coronavirus–severe acute respiratory syndrome coronavirus 2. The United States has been particularly affected, with the largest number of confirmed cases in a single country in the world. Healthcare systems for adults as well as children have dealt with challenges. This article will reflect on the experiences of selected children’s hospitals in Seattle, New York City, and New Orleans, three of the “hotspots” in the US and share common aspects and lessons learned from these experiences. This article discusses testing and cohorting of patients, personal protective equipment utilization, limiting workplace exposure, and information sharing.
© 2020 Elsevier Ltd. All rights reserved.
Introduction
In January 2020, a novel coronavirus–severe acute respiratory syndrome coronavirus 2 (SARS-CoV-2) [1]—was identified, and by March 11th the disease it causes, COVID-19, was declared a worldwide pandemic [2]. The United States has been particularly affected, with more than 1.7 million cases as of the end of May, the largest number of confirmed cases in a single country in the world [3]. The country has been in a state of emergency since the 13th of March [4], and by mid-March all fifty states, the District of Columbia, and four U.S. territories had reported cases of COVID-19 [5]. Although the majority of severe illness has been seen in adults, leading to immense challenges for hospitals and healthcare systems, COVID-19 also has profound impact on the healthcare systems for children as well. Seattle, New York City, and New Orleans were three “hotspots” of COVID-19 infections in the US [Table1], each with unique epidemiologic features contributing to their case rate [Fig. 1].
In this review, we reflect on the experiences of selected children’s hospitals (Seattle Children's, Children's Hospital at Montefiore in New York, and Children's Hospital New Orleans) in each of these cities, with the aim of identifying commonalities and lessons learned that might be applicable to future health crises.
https://doi.org/10.1016/j.prrv.2020.06.002
1526-0542/© 2020 Elsevier Ltd. All rights reserved.
Seattle
On January 21, 2020, a 35 year old man who had returned to Washington a few days prior after traveling to Wuhan, China became the first confirmed case of COVID-19 in the Seattle area [9,10]. In late February, the Seattle Flu Study identified COVID-19 in a 15 year old evaluated for influenza-like illness, and using sequence data, linked this case to the first adult case [11,12], demonstrating ongoing community transmission. Also in late February, a large ongoing outbreak was reported by an area nursing home, further reflecting and contributing to community spread. In response, regional hospitals braced for patient surges and planned for overwhelmed healthcare systems and alternate standards of care. By the end of March, approximately 200 new cases were being identified per day in King County (the Seattle region).
At Seattle Children’s Hospital, a multidisciplinary group began meeting regularly at the end of January to plan the response to COVID-19, and by the end of February an incident command structure was erected in order to provide for centralized decision-making and rapid escalation of questions and concerns. The experience in China suggested that children accounted for a very small proportion of COVID-19 cases and that their symptoms and signs were relatively mild compared to adults. Thus, while the hospital planned for a surge of pediatric patients out of caution, they also planned to care for the region's children who would otherwise be cared for at mixed adult-pediatric hospitals and prepared to admit sick young adults in the event the adult hospitals reached their capacity. In the end, perhaps in part due to suspension of all elective visits and surgeries, and the ‘shelter in place’ strategies employed as of March 23rd, the adult hospitals avoided exceeding their capacity and Seattle Children’s maintained available beds.
New York City
Nearly six weeks after the Seattle area saw its first case, the first case of COVID-19 in New York State was confirmed on March 1st: a woman who had returned home to New York City (NYC) after travel to Iran [14]. By March 15th, there were nearly 3000 identified cases in NYC and by the end of March, 3500–6000 new cases were being identified each day [7]. Multiple factors may have contributed to this huge increase, including high population density and reliance on crowded public transportation, in addition to the more than two-week period from when the first cases were reported until the official NYC shutdown began, and three week period until the definitive ‘stay at home’ order on March 22nd [15]. Given NYC’s accelerated rate of transmission, hospitals feared that a surge of pediatric patients in the emergency department, including the “worried well”, would lead to admissions. There was particular concern in the Bronx, the borough in which our hospital system is primarily located, given that it is one of the poorest areas of the state and the rates of obesity, asthma, and other comorbidities thought to exacerbate COVID-19 are very high [16,17]. Although ultimately the Bronx did experience a disproportionate number of cases and death in adults [7], pediatric ED visits and admissions remained low, and dropped even further after NYC public schools closed and non-urgent procedures were cancelled. Efforts were made in the Bronx to consolidate pediatric admissions at the Children’s Hospital at Montefiore in anticipation of the need to increase capacity for adult patients across NYC [18].
The Children’s Hospital at Montefiore (CHAM) is a part of a large health system and is situated within the main Montefiore Hospital campus. In order to help alleviate some of the burden on our adult colleagues and in preparation for an anticipated peak in the first two weeks of April, pediatric leadership met with institutional leadership regularly, and surge plans were put into place. Pediatric providers, nurses and staff employed a “surge in place” model, creating and staffing an adult COVID-19 unit [19]; increased the age limit on pediatric med-surg units to 30 years; and deployed multiple providers and staff to units run by adult providers.
New Orleans
The first case of presumptive COVID-19 in the greater metropolitan area of New Orleans was identified on March 9th, approximately one week after the first case in NYC. Over the next
week, several more cases were identified in individuals who had no significant travel history and were unrelated to each other, suggesting that there was previously unrecognized existence of disease and presence of community transmission in the area. New Orleans had recently celebrated Mardi Gras during the last two weeks of February, when nearly one million visitors from around the country and world visited the area. It has been suggested that the Mardi Gras celebration may have significantly accelerated transmission within the community and possibly led to the virus’s spread around the country [20]. Currently available sequencing data [21] indicate that a small number of closely related strains were introduced, likely in late February or early March, and those strains spread rapidly within the New Orleans community.
Within a week of the first case, state and local officials moved to decrease transmission. Schools were closed on March 20th, 2020 and restrictions on business activities followed shortly thereafter, leading to a predictable decline in visits to the pediatric Emergency Room at Children’s Hospital New Orleans (CHNOLA). As a part of a hospital system with four adult hospital partners, CHNOLA leaders were acutely aware of the stressors that colleagues across the system faced, and set up an Incident Command team on March 11th with broad representation. A subset of this group met twice a day with leaders from across the system so that decisions made at CHNOLA were based on the real-time activities at adult partner facilities. Pediatric acute and critical care units were consolidated in anticipation of the need to accommodate adult patients during the predicted surge. However, their adult partners expanded their own capacity to absorb the surge which peaked in the last week of March through the first week of April, and CHNOLA did not care for any adult patients. However, CHNOLA clinical and non-clinical team members were deployed to adult facilities to assist in a variety of ways. In addition, supplies including ventilators, medications, and personal protective equipment (PPE) were shared to meet the needs of each facility in the health system as dictated by clinical volumes.
**DISCUSSION**
As COVID-19 spread across the United States, there were factors unique to each city which influenced the individual experiences. Seattle was the first major US city to experience COVID-19, and therefore faced the need to implement COVID-19 policies immediately. New York City, with its high population density and delayed implementation of strict social distancing, had a rate of spread and acute surge that challenged hospitals and healthcare systems to an extent not seen in other US cities. New Orleans hosted a highly attended event in February before the threat of transmission in the US was fully appreciated, and thus likely had an increase in community spread that may have been initially under-recognized [5]. Despite these different starting points, the three children’s hospitals shared many similar experiences.
**Testing and cohorting patients**
All three institutions faced limited testing capabilities [22]. Each region initially relied on testing through local Public Health or Department of Health (DoH) centers, which pragmatically pre-
and face shields, were stored in a central location with controlled access.
Through the three hospitals’ experiences, several strategies for managing PPE shortages emerged as promising: controlling access immediately, monitoring supply closely including tracking utilization, and implementing conservation strategies that may need to change frequently to reflect degree and type of shortages. In addition, capitalizing on appropriate opportunities for PPE discontinuation was recognized as an important strategy [24]. In order to ensure effective use of available supplies, all three sites made PPE references, including donning and doffing protocols [24], easily accessible and interpretable by all frontline clinicians. Once adequate PPE supplies were ensured, each site was able to successfully implement universal masking.
Limiting exposure
Limiting workplace and nosocomial exposure to COVID-19 required a coordinated institutional response [25]. For example, in order to identify potentially infected people quickly and contain the risk of transmission, strategies for screening all staff prior to entering the hospital were implemented at each hospital. All three centers also implemented institutional policies to limit those at the bedside of admitted pediatric patients, in alignment with official recommendations [26] to one parent or primary caretaker. All three institutions suspended team rounds at the bedside, which had previously been a daily part of the workflow, in order to limit staff and patient exposure, and to maintain social distancing [25]. Technology was increasingly utilized, for example calling or face-timing patients and families to obtain histories and answer questions so that PPE could be conserved and movement in and out of patient rooms limited [27]. To minimize overall crowding in buildings and offices, institutions changed prior policies to allow a work-from-home option for non-clinical work. Ambulatory settings in each hospital have seen a marked increase in the use of telemedicine in an attempt to limit unnecessary visits to the hospital campus; this is a strategy that merits further exploration in the inpatient setting.
Information sharing and communication
Timely and accurate communication was crucial within each hospital to avoid any confusion or misinformation that might be potentially generated by the multiple streams of information existing within a complex hospital. All three institutions mitigated this risk by using a centralized system to collect and disseminate information such as treatment protocols, clinical trial information, and epidemiologic data. This allowed each hospital to maintain alignment throughout the organization, and ensure all staff was informed as protocols and policies changed. In addition, in-person communication was key to real-time response. At CHNOLA, members of the Incident Command team made regular rounds in all units to address any questions, concerns and misconceptions, and about PPE conservation in particular. At CHAM, leadership walk rounds and institution-wide virtual town halls occurred daily, allowing staff to interact with leadership and share concerns and successes directly. Pediatric leadership meetings were held twice weekly, to ensure information sharing and to address local issues. At Seattle Children’s, an incident command structure was used for escalation of problems and centralized decision-making. Organization-wide communications happened almost daily and leaders rounded to ensure uptake of the information and to answer questions. In addition, virtual town halls occurred on a regular cadence.
Communication between institutions and providers proved to be equally as important as communication within institutions. The internet and multiple means of electronic communications conferred an ability to disseminate information at a pace unprecedented in any previous health crisis. Federal, state and local agencies provided real-time updates via electronic posts and bulletins to wide audiences in order to ensure that both providers and the public had accurate information about all aspects of the emerging pandemic. Physician group “listservs” [an electronic mailing list] provided timely discussion of new findings as well as information to those in areas which had yet to experience a surge. Indeed, when Seattle Children’s circulated a summary of their experiences and protocols on numerous listservs in early March to members of the pediatric community across the country, CHAM and CHNOLA reaped the benefit of their experience, which enabled a more informed response and an incorporation of their lessons learned into their early planning. Webinars allow for rapid, widespread learning about a novel disease without needing to gather large groups of individuals together. In fact, institutions continue to use these channels to share information about the evolving clinical picture and treatment of the newly recognized covid-19 associated Multi-system Inflammatory Syndrome in Children (MIS-C). Lastly, social media platforms allow for sharing of reflections, provision of emotional support and communal mourning as well as celebration, which may be comforting to providers navigating the myriad challenges of the pandemic.
CONCLUSION
During the winter and spring of 2020, the three selected children’s hospitals in Seattle, New York City, and New Orleans initially experienced the COVID-19 pandemic differently because of unique contextual factors. However, all three institutions faced the challenges of addressing the needs of their communities with a strong spirit of cooperation, resilience, and adaptability among the pediatric staff, which allowed for the flexibility necessary to respond to the fluid nature of the situation. With emerging knowledge about the virus and by accumulating experience managing it, the three institutions independently developed solutions which, taken together, can inform our understanding and can drive responses to future recurrences or new pandemics should they arise.
DIRECTIONS FOR FUTURE RESEARCH
- Determine the impact of transmission mitigation strategies on the inpatient experience for patients and their families.
- Identify which of the PPE conservation strategies utilized are most effective in maintaining adequate supply.
- Characterize effective use of telemedicine and other electronic communication with patients in the inpatient setting.
FUNDING
None.
Acknowledgements
The authors would like to thank Dr. Margaret Aldrich for providing data regarding COVID-19 testing at CHAM.
References
[1] Centers for Disease Control and Prevention. Coronavirus Disease 2019, Cases in the U.S. [https://www.cdc.gov/coronavirus/2019-ncov/cases-updates/cases-in-us.html. Accessed May 20, 2020.]
[2] World Health Organization. Rolling updates on coronavirus disease (COVID-19). [2020; https://www.who.int/emergencies/diseases/novel-coronavirus-2019/events-as-they-happen. Accessed May 31, 2020.]
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Indigenous language technologies in Canada: Assessment, challenges, and successes
Patrick Littell
National Research Council of Canada
1200 Montreal Road
Ottawa, ON, K1A 0R6
[email protected]
Anna Kazantseva
National Research Council of Canada
5071 West Saanich Road
Victoria, BC, V9E 2E7
[email protected]
Roland Kuhn
National Research Council of Canada
1200 Montreal Road
Ottawa, ON, K1A 0R6
[email protected]
Aidan Pine
National Research Council of Canada
5071 West Saanich Road
Victoria, BC, V9E 2E7
[email protected]
Antti Arppe
University of Alberta
4-32 Assiniboia Hall
Edmonton, AB, T6G 2E7
[email protected]
Christopher Cox
Carleton University
1125 Colonel By Drive
Ottawa, ON, K1S 5B6
[email protected]
Marie-Odile Junker
Carleton University
1125 Colonel By Drive
Ottawa, ON, K1S 5B6
[email protected]
Abstract
In this article, we discuss which text, speech, and image technologies have been developed, and would be feasible to develop, for the approximately 60 Indigenous languages spoken in Canada. In particular, we concentrate on technologies that may be feasible to develop for most or all of these languages, not just those that may be feasible for the few most-resourced of these. We assess past achievements and consider future horizons for Indigenous language transliteration, text prediction, spell-checking, approximate search, machine translation, speech recognition, speaker diarization, speech synthesis, optical character recognition, and computer-aided language learning.
1 Introduction
There are approximately 60 Indigenous\textsuperscript{1} languages from 10 distinct language families (Rice, 2008) currently spoken in Canada. Several of these languages have tens of thousands of speakers and are still acquired by most children, whereas others have a few tens or hundreds of mostly-elderly speakers; in all, 260,550 report speaking an Indigenous language at at least a conversational level (Statistics Canada, 2016). All of these languages are under significant pressure from English and French, but also have many young people interested in learning. The resurgent strength of community-driven Indigenous linguistic and cultural reclamation in Canada is at the heart of the growing demand for Indigenous language courses, materials and technology.
Indigenous languages are of paramount importance to the nations that speak them and the benefits associated with their use are wide-ranging (Whalen et al., 2016; Reyhner, 2010; Oster et al., 2014; Marmion et al., 2014). As a specific example, research in psychology has shown a compelling correlation
\textsuperscript{1}In this document, “Indigenous languages” will specifically refer to Indigenous languages spoken in Canada.
between Indigenous language use and a decrease in youth suicide rates on reserves in British Columbia (Chandler, 1998; Hallett et al., 2007). With increased awareness of these benefits has come increased interest by both Indigenous communities and federal and provincial governments in language technology development, to promote the revitalization and documentation of these languages.
However, the development of Indigenous language technologies faces many challenges: most of these languages are highly morphologically complex, there is relatively little text and speech data available, and there can be significant differences in dialects and orthographies that make it difficult to develop applications that work for all users. Well-known “flagship” language technologies that require large amounts of training data, like machine translation and automatic speech recognition, are therefore probably only feasible to develop for a few of the better-resourced languages such as Inuktitut.
There are nonetheless many practical language technologies that would be feasible to develop for a large number of these languages, and in some cases already have been developed. In this document we assess the feasibility of text (§4), speech (§5), image (§6), and educational (§7) technologies for Indigenous languages, based on past efforts in developing them for these and other low-resource languages.
Disclaimer This document represents the personal opinions of the authors regarding the feasibility of certain technologies, and is not a statement of Government of Canada policy or priorities.
2 Scope and organization
This document will primarily assess user-level applications like search and spell-checking, rather than software that primarily exists to enable linguistic research. This delineation is very approximate, however, as many such applications will have benefits for both kinds of users.
This document also will not be a general inventory of digital resources such as online corpora and lexica. The collection and dissemination of these resources is, of course, highly important and is often the foundational work that makes these technologies possible; it is just that such an inventory would be outside the scope of a document of this size.
In terms of organization, technologies will be clustered from the point-of-view of the practical application of a technology (e.g., spell-checking or text prediction), rather than be organized by the computational model that makes the application possible (e.g., a finite-state transducer or statistical language model). A finite-state grammar of a language (e.g., Snoek et al. (2014), Dunham (2014), Arppe et al. (2017a), Bowers et al. (2017), Harrigan et al. (2017)) can power a number of practical applications from spell-checking, to morphologically-aware search and browsing of dictionaries and corpora, to computer-aided language learning (Arppe et al., 2016).
This document will categorize technologies into five groups, according to the feasibility of developing these for a wide range of Indigenous languages, ranging from “already available” to “infeasible for most languages” (§8). It should be emphasized that these are not ratings of desirability, impact, worthiness for funding, or the relative importance of these technologies to language communities. By contrast, Krauwer (2003) proposed BLARKs - Basic Languages Resource Kits that list basic language technologies and resources needed for successful support and further research of under-represented languages in the European context. Arppe et al. (2016) extend the model to define resource and application priorities for the endangered languages of Canada - EL-BLARK (BLARK for Endangered Languages). This survey finds many similarities with the applications proposed by Arppe et al. (2016).
3 General challenges
There are many challenges that are commonly encountered during the development of Indigenous language technologies, and are encountered in almost all Indigenous languages.
---
2The inventory of existing technologies presented here is likely incomplete, as many language technologies are not published academically or publicized outside of their communities.
3An extensive inventory of open-source resources, in both Indigenous and other languages, is available at github.com/RichardLitt/endangered-languages. There are also a number of Indigenous language education and reference apps on the iOS App Store and Google Play; Animikii (www.animikii.com) maintains a growing list of these at www.animikii.com/blog/apps-for-learning-an-indigenous-language.
3.1 Morphological complexity
Indigenous languages are typically very morphologically complex, with most being polysynthetic or agglutinative. It is commonly the case that a single word carries the meaning of what would be an entire clause in English and French.
(1) iah th-a-etsi-te-w-ate-wistohsera-’arih-a:t-ha-k-e’
no NOT-WOULD-AGAIN-WE-ALL-OWN-butter-HOT-CAUSE-HABIT-CONTIN-PERF.
‘We will no longer keep heating up our butter.’ Mohawk (Mithun, 1996, p. 170)
(2) Qanniqlaunngikkalauqtuqlu, aninngittunga
qanniq-lak-uq-ngit-galauq-tuq-lu, ani-ngit-junga
snow-a.little-frequently-NOT-although-3.IND.S-and go.out-NOT-1.IND.S
‘And even though it’s not snowing a great deal, I’m not going out.’
Inuktitut (Micher, 2017, p. 102)
This complexity presents a challenge for many applications and algorithms, especially those that encode assumptions about the atomic word being the basic unit of meaning/structure, or even the assumption that concatenative morphological analysis is sufficient for finding sub-word units (Arppe et al., 2017a).
3.2 Limited training data
For most languages, there is little to no digitized text or audio available for use as training data, at least not at the scale required for modern statistical or neural NLP. Existing technologies for Indigenous languages have therefore, with a few exceptions, been exclusively rule-based.
A further problem related to the lack of training data is that available training data often comes from only a single domain. For example, the bulk of Inuktitut parallel text comes from Nunavut Legislative Assembly transcripts, but this genre is highly self-similar, and the application of a machine translation system trained on this corpus will likely have difficulties translating other genres like conversation or literature.
A promising research frontier to address limited training data is multilingual modeling; many of the least-resourced Indigenous languages are reasonably closely related to a more-resourced language. For example, automatic speech recognition in Seneca could be trained in part on other Iroquoian languages like Mohawk and Oneida (Jimerson and Prud’hommeaux, 2018), since they have similar phonetic inventories but more available speech data.
3.3 Dialectal and orthographic variation
Most Indigenous languages have a variety of dialects, but often sources and research articles only represent one dialect, or the orthographic standards were developed for a particular dialect and it is unclear how they apply to related dialects. It is sometimes the case that the roadblock to providing technology more widely in a language community is that the dialectal situation is poorly understood, and more basic research on dialectal differences is needed.
Furthermore, even within a single dialect, published works can use a variety of orthographies, and even works using the same orthography often differ in the details such as the encoding of particular diacritics or which morphemes/enclitics are written as separate words or joined. This variety can even be seen in single works, such as those with multiple contributors or transcribers.
Dialectal and orthographic variation pose a particular problem to rule-based text processing systems, since these are usually based on one relatively-well-studied dialect and use particular writing conventions that user-contributed data do not always share. A promising frontier of research to address this, as seen in Micher (2017), is to begin with an existing rule-based system and use it to bootstrap a statistical or neural system (in this case a recurrent neural network) that is more robust when faced with noisy data and unknown morphemes.
4 Text technologies
4.1 Fonts and keyboard layouts
Given the widespread adoption of Unicode and a substantial expansion of character coverage in standard Windows and MacOS fonts like Times New Roman, font coverage of Indigenous languages is currently very good so far as desktop operating systems are concerned. Both Windows and MacOS ship with the Euphemia font for Canadian Aboriginal Syllabics (§6.2), although for some languages Euphemia can display incorrect character orientations.\(^4\)
Special Roman characters, diacritics, and Syllabics are not always supported by system-installed keyboard layouts, necessitating the development of custom keyboard layouts. Fortunately, keyboard layout coverage of Indigenous languages is extensive; LanguageGeek\(^5\) provides Windows and MacOS keyboards in almost every Indigenous language, while Tavultesoft Keyman\(^6\) and FirstVoices\(^7\) have developed keyboards for iOS and Android that offer complete coverage of Indigenous languages as well as support for other non-Indigenous languages.
4.2 Predictive text
One common request concerning keyboards (particularly mobile keyboards) is “predictive text” or “autocomplete”, in which the keyboard offers shortcut buttons that suggest probable next words to the user depending on what they have already typed. This technology is especially desirable because it appeals to young users as well as to advanced second language learners.
The Multiling O\(^8\) keyboard app for Android offers dictionary-based predictive text in the SENCO-FFEN language.
Maheshwari et al. (2018) examine word and character-based language models for text prediction of Mi’kmaq, based on a small web corpus.
Given the relative paucity of digital text corpora for many languages, it is likely that most predictive text systems will not be able to rely entirely on statistical models, and will instead be built on rule-based (e.g. finite state) or hybrid statistical/rule-based systems.
4.3 Orthography conversion
Almost all Indigenous languages have been written in several different orthographies. While there is a general trend towards orthographic unification in most communities, it is still common to find geographical or generational differences in how languages are written.
Conversion between modern orthographies is generally straightforward, and there exist many applications that manage these conversions\(^9,10,11,12,13,14\). Conversion between historical and modern orthographies can be more difficult, as historical orthographies often made different assumptions about the vowel and consonant inventories of these languages. There exists a rule-based transliterator between historical and modern Kwak'wala text\(^15\), but the correspondences are somewhat irregular and thus the results are not completely reliable.
4.4 Spell-checking
Although Indigenous languages of Canada have a relatively short tradition of writing, it is quickly gaining steam, especially among young users and learners. However, writing—especially writing “correctly”
\(^{4}\)www.eastcree.org/cree/en/resources/how-to/cree-fonts/syllabic-font-orientation/
\(^{5}\)www.languagegeek.com/keyboard_general/all_keyboards.html
\(^{6}\)keyman.com
\(^{7}\)firstvoices.com
\(^{8}\)play.google.com/store/apps/details?id=kl.ime.oh
\(^{9}\)syllabics.atlas-ling.ca/
\(^{10}\)nuktitutcomputing.ca/Transcoder/
\(^{11}\)nuuktitutcomputing.ca/Transcoder/
\(^{12}\)mothertongues.org/#convertextract (Pine and Turin, 2018)
\(^{13}\)www.eastcree.org/cree/en/resources/syllabic-convertor/
\(^{14}\)www.giellatekno.uit.no/index.eng.html
\(^{15}\)orth.nfshost.com/?lang=kwk&input=umista&output=boas
according to official community standards—can be particularly difficult for English- or French-dominant writers, since it requires making sound distinctions that English and French lack. Spell-checking is therefore a frequently-requested technology.
Since all Indigenous languages are morphologically complex, a purely word-list based spell-checking system is typically infeasible; a given stem can have hundreds or even millions of possible derivations/inflections. Corpus-based spell-checkers would have a similar problem; even when a digital corpus is available, only a small fraction of possible derivations/inflections will occur. Therefore, efforts to develop spell-checkers in Indigenous languages typically concentrate on finite-state technology, since this allows the specification of very large lexicons in an efficient and succinct manner.
A Plains Cree spell-checker based on FST technology is available for system-wide use in recent versions of MacOS, and versions for Microsoft Office and Libre Office are in development (Arppe et al., 2016). The Giella infrastructure (Moshagen et al., 2013) offers an easy way to create FST-based spell-checkers that can be integrated into LibreOffice and, to a limited extent, into Microsoft Office. The spell-checkers use finite-state transducers as a backend, but it is possible to specify spelling relaxations as well as to include modules for likely or common errors. Theoretically the framework allows other types of language models as well, but they have been relatively untested.
An unexpected problem with integrating spell-checkers into mainstream office software is tokenization, since some Indigenous languages use commas, colons, and apostrophes to indicate phonetic differences, whereas many text processing systems assume internally that these are token boundaries. This points to a need for more flexible tokenization within mainstream office software to accommodate these languages.
4.5 Paradigm generation
It has generally been acknowledged that effectively teaching polysynthetic languages requires teaching morphology (Kell, 2014). Since all Indigenous languages have complex verb morphology, one frequent educational need is verb conjugators (Junker and MacKenzie, 2010; Junker and MacKenzie, 2011; Baraby and Junker, 2011; Arppe et al., 2017b), either stand-alone or integrated into an online dictionary.
For most Indigenous languages, learning morphology automatically from corpora is not a viable option. However, symbolic systems, especially those based on finite-state transducers (FSTs) have been successfully implemented for a number of languages. For example, Arppe et al. (2017b) developed an FST for East Cree by leveraging a lexical database. Arppe et al. (2016) and Arppe et al. (2017a) do not release stand-alone verb conjugators, but make verb conjugations available as a part of morphologically-aware online dictionaries for Plains Cree and Tsuut’ina languages respectively.
4.6 Approximate search
Approximate (or “fuzzy”) search is a key language technology in situations where the language has not been widely written, or where a large proportion of technology users are learners. Moreover, whole-word search is problematic in highly polysynthetic/agglutinative languages, since the user’s query may not use the inflectional form that appears in the dictionary or corpus. Both of these situations are common for Indigenous languages, and therefore the incorporation of approximate search is appropriate in nearly any text technology for these languages.
In general, approximate search can be done in a language-independent way—i.e., by simply counting the number of deletions, insertions, changes, and transpositions (Damerau, 1964; Levenshtein, 1966), without consideration of any language-specific properties—and can be done efficiently even on a large lexicon (Schulz and Mihov, 2002). There are three ways the user experience can be further improved for a particular language: by adapting to actual user queries, by building phonetic knowledge into the system, by making the search aware of morpheme breakdowns.
The East Cree\textsuperscript{16} and Innu\textsuperscript{17} dictionaries utilize relaxed search rules based on users’ habits (Junker and Stewart, 2008).
\textsuperscript{16}dictionary.eastcree.org
\textsuperscript{17}dictionnaire.innu-aimun.ca
Mother Tongues Dictionaries\cite{mother_tongues} incorporates phonological background knowledge (e.g., that two sounds are similar and likely to be confused by users) in a finite-state approximate phonological search algorithm (Littell et al., 2017). It concentrates on Pacific Northwest languages where, due to the extensive consonant inventories and phonological complexity of these languages, approximate search is particularly important. This algorithm powers the search function in e-dictionaries for 17 Indigenous languages spoken in British Columbia, including FirstVoices'\cite{firstvoices} mobile dictionary applications for iOS and Android, with dictionaries for 11 more languages currently in development.
Morphologically-aware search allows the user to find instances of their search query that may differ in one or more morphemes\cite{morpho_search}. The Giella infrastructure offers morphology-aware search in dictionaries that are generated by linking a morphological model with lexical resources (and possibly with text corpora). A user can search with any inflected word form of a lemma (or root), possibly taking into account common spelling errors and spelling relaxations (Moshagen et al., 2013). Snoek et al. (2014) and Harrigan et al. (2017) use this technology to allow searching a dictionary of Plains Cree for specific lemmas. Similar capabilities exist for East Cree (Arppe et al., 2017b), Tsuut’ina (Arppe et al., 2017a), Northern Haida (Lachler et al., 2018) and Odawa (Bowers et al., 2017).
\section{4.7 Machine translation}
Machine translation is one of the best-known language technologies, and receives significant attention from academia, industry, and the general public, so one of the more common queries from Indigenous groups is whether machine translation would be feasible for their languages.
The current state-of-the-art of machine translation is relatively language neutral, but requires very large amounts of parallel text, which is currently unavailable in most Indigenous languages save Inuktitut. Even then, given the complexity of Inuktitut morphology and the limited corpus available, it is probable that such systems will be, at best, aides to human translators working within that domain, rather than a general-purpose consumer technology like Google Translate.
Several prerequisite steps for Inuktitut machine translation have been achieved, including morphological segmentation (the Uqailaut analyzer\cite{uqailaut} and its neural generalization (Micher, 2017), and sentence and word-level alignment (Martin et al., 2003; Langlais et al., 2005). There are several Inuktitut-English machine translation systems currently under development.
The prerequisite steps can themselves power practical technology. For example, the WeBInuk translation memory system, an adaptation of the WeBiText system (Désilets et al., 2008) mines Inuktitut-English text and uses word alignments to suggest translations to Inuktitut translators.
\section{5 Speech technologies}
There has been little development of Indigenous language speech technology so far, but consultation with language communities has suggested that speech technologies are greatly desired, as these languages and cultures are traditionally oral. Text technologies typically expect the user to be able to write their language using the same conventions that the developer expects, which is a problematic expectation in languages without widespread agreement about written conventions. Speech technologies therefore offer an attractive proposition for users more accustomed to speaking and hearing their language than writing and reading it.
\subsection{5.1 Automatic speech recognition}
Full-vocabulary automatic speech recognition (ASR) currently requires large amounts of transcribed audio, and is therefore unlikely to be feasible in most Indigenous languages for the foreseeable future, at least not at a high degree of accuracy. However, even a low degree of accuracy can significantly assist human transcription; this technology, sometimes called Transcription Acceleration (TA), would probably be feasible for at least some languages now.
\cite{mother_tongues}
\cite{firstvoices}
\cite{altlab}
\cite{uqailaut}
Jimerson and Prud’hommeaux (2018) has developed a preliminary ASR system for the Seneca language, and the Persephone ASR (Adams et al., 2018) system is being adapted to provide transcription acceleration within the Dative Online Linguistic Database interface (Dunham, 2014), which currently powers dozens of Indigenous language documentation efforts in Canada.
The frontier in speech recognition that is most promising for low-resource languages is multilingual recognition, in which a model trained on a large variety of languages can help compensate for a lack of transcribed speech data in the target language. A challenge for multilingual speech recognition is that some Indigenous languages, particularly in the Pacific Northwest, are global outliers in terms of phonological complexity, with large consonant inventories, rare consonants such as [t], and sometimes long sequences of consonants without the need for intervening vowels. At the very least, the development of practical multilingual recognition models would allow such languages to pool their resources, even if the difference between these and languages outside the region is too great to use a “universal” model.
5.2 Audio keyword search
The primary challenge of ASR in any language is the wide range of inputs the system might encounter— basically, anything that a person might talk about. On the other hand, ASR can also be used to find a particular word in an audio recording: the decision is not “what words are these?” but the simpler decision “is this part of the recording an instance of this word?”.
This problem, of audio keyword search, is more tractable, but still potentially very useful for making un-transcribed speech recordings more accessible to the public, allowing users to search more quickly through long audio recordings in search of particular words or topics. The National Research Council of Canada (NRC), is collaborating with the Computer Research Institute of Montréal (CRIM) and the Pirurvik Centre on an audio keyword search project for Canadian Broadcasting Company (CBC) radio broadcasts in the Inuktitut and Cree languages.
5.3 Speech/text alignment
Even when resources are too limited to allow full, “open-vocabulary” ASR, prerequisite steps to ASR can be valuable in their own right. One of the prerequisite steps to both ASR and speech synthesis is speech/text alignment (sometimes called “forced alignment”), which involves taking a speech recording and a transcription of it and determining which segments of audio correspond to words and/or phonemes in the transcription.
This intermediate step can itself be of value for education, in creating time-aligned closed-captions from transcribed recordings, and read-along activities such as those available on the East Cree language portal (Luchian and Junker, 2004; Junker et al., 2016) and in the Inuktitut-language Uqalimaarluk (“Read To Me”) app for iPad.
5.4 Audio segmentation and speaker diarization
Even if automatic speech recognition (“what was said?”) is beyond the means of current technology, speaker diarization (“who spoke when?”) can be of great value, helping users to more quickly comb through large amounts of audio data in search of examples by a particular speaker or in a particular language.
The NRC-CRIM collaboration mentioned above (§5.2) will also be developing tools for automatic segmentation and speaker diarization. These are relatively language-neutral technologies that could be used in other languages as well.
5.5 Speech synthesis
The converse of automatic speech recognition, text-to-speech (TTS) is somewhat more feasible in low-resource situations. A limited-domain text-to-speech system (such as a talking clock or public transit announcement system) can be trained with just minutes or hours of total recordings, so long as the samples are adequately representative of the target domain.
Interest in text-to-speech has come from communities where interested learners outnumber fluent speakers, such that the learner might want to know how a word is pronounced but does not currently have access to a speaker to model pronunciation for them. Interest has also come from communities working on projects such as talking online dictionaries, in which the inflectional complexity of the language (§3.1) has meant that it is not feasible to record every possible inflection of a word. In such projects, TTS could allow the user to hear the pronunciation of any inflected form of the word, rather than just uninflected stems.
To our knowledge there are not yet any complete speech-synthesis project in an Indigenous language spoken in Canada, but Synscenter Refsnæs and Oqaasileriffik (the Language Secretariat of Greenland) have developed a general-purpose text-to-speech system for Kalaallisut\textsuperscript{24} (West Greenlandic), which is closely related to Inuktitut.
6 Image technologies
6.1 Optical character recognition for Roman orthographies
Optical character recognition (OCR) has been successfully been applied to Indigenous language documents, including historical manuscripts printed using pre-digital presses (Fig. 1). Hubert et al. (2016) report a high degree of success on OCR with only a few pages of training data, suggesting that OCR would be feasible to implement for a wide range of Indigenous languages.
The challenge for OCR on many Roman orthographies for Indigenous languages is the proliferation of diacritics and superscript letters, particularly in languages with extensive consonant inventories. Diacritics and superscripts are difficult to differentiate from punctuation and from each other, and depending on the font resources, some letter-diacritic combinations may be very hard to distinguish. For example, British Columbian orthographies based on the Royal B.C. Museum recommendations often use underlined ⟨g⟩ for a uvular voiced plosive, and in some fonts (or in typewritten documents), this underline can overlap the descender on the ⟨g⟩.
6.2 Optical character recognition for Canadian Aboriginal Syllabics
While most Indigenous languages are written using a Roman orthography, several varieties of Inuktitut, Cree, and Ojibwe\textsuperscript{25} use a system called Canadian Aboriginal Syllabics (Fig. 1).
Canadian Aboriginal Syllabics (often simply called “Syllabics”) is a “rotational syllabary” in which the shape of the glyph indicates the syllable’s consonant and its rotational orientation to the vowel. There are also smaller, superscript characters that indicate consonants where no vowel follows (e.g. in a syllable
\textsuperscript{24}http://oqaasileriffik.gl/langtech/martha/
\textsuperscript{25}Syllabics have also historically been used for Blackfoot and some Athabascan languages such as Dakelh (Carrier), but have fallen out of use in favor of Roman orthographies.
coda). Like superscript characters in Roman orthographies, superscript characters in Syllabics can pose a problem for OCR, since due to their size and position they are easily confused for punctuation marks or with each other. Nonetheless, there have been several successful Syllabics OCR projects (e.g. Posgate and Leekam (2014)), and Inuktitut has since been included in the Tesseract OCR project\textsuperscript{26} (Smith, 2007).
7 Computer-aided language learning
7.1 Course modules
Computer-aided language learning (CALL) course modules are widely available for Indigenous languages, particularly through the FirstVoices Language Tutor (FVLT) portal\textsuperscript{27}, which offers approximately 50 online courses covering many Indigenous languages, with exercises on listening, speaking, reading, and vocabulary development, as well as online language-learning games.
There are also language-specific CALL portals, including but not limited to:
- Tusaalanga\textsuperscript{28} from the Pirurvik Centre, which offers exercises in five varieties of Inuktut.
- The Institut Tshakapesh learning portal\textsuperscript{29}, which offers educational games in the Innu language (Junker and Torkornoo, 2012; Junker et al., 2016). These were modeled after the eastcree.org lessons\textsuperscript{30} for teaching syllabics, vocabulary and literacy.
- The nêhiyawêtân CALL portal for Plains Cree\textsuperscript{31} fuses CALL and text technologies, in which students receive targeted feedback made possible by the integration of a finite-state morphology model (Arppe et al., 2016; Bontogon et al., 2018).
- The Yukon Native Language Centre\textsuperscript{32} offers online audiovisual adaptations of language courses in eight Indigenous languages.
Several international CALL products have been adapted for Indigenous languages. 7000 Languages\textsuperscript{33} adapts the Transparent Language software for low-resource and endangered languages, and offers courses on Denesuline, Dakota, and several varieties of Cree, Ojibwe, and Oji-Cree through partnerships with Grassroots Indigenous Multimedia\textsuperscript{34} and the Manitoba First Nations Education Resource Centre\textsuperscript{35}. Rosetta Stone\textsuperscript{36} has also developed courses for Labrador Inuittitut and Kahnawá:ke Mohawk.
A forthcoming project headed by Dr. Marianne Ignace at Simon Fraser University presents an innovative “chat-based” UI (what is sometimes called “No-interface UI”) for CALL apps, in which an AI tutor interacts with the student in a web-chat-like interface.
7.2 Phonetic tutorial
Some education applications focus more narrowly on the acquisition of speech sounds. Phonetic tutorials are particularly important in languages with rarer sounds, like lateral fricatives or ejective plosives.
The Yukon Native Language Centre\textsuperscript{37} has developed a phonetic learning game in which players must count the number of instances of a particular sound (e.g., [t]) in a recording to mush a dog sled.
The Tiga Talk\textsuperscript{38} app for iOS, originally a collection of speech-language pathology games for English, is currently being adapted to Cree to help support child acquisition.
\textsuperscript{26} github.com/tesseract-ocr
\textsuperscript{27} tutor.firstvoices.com
\textsuperscript{28} tusaalanga.ca
\textsuperscript{29} jeux.tsakapesh.ca
\textsuperscript{30} lessons.eastcree.org
\textsuperscript{31} oahpa.no/nehiyawetan/
\textsuperscript{32} www.ynlc.ca
\textsuperscript{33} 7000languages.org
\textsuperscript{34} gim-ojibwe.org
\textsuperscript{35} mfnerc.org
\textsuperscript{36} www.rosettastone.com/endangered/projects
\textsuperscript{37} ynlc.ca
\textsuperscript{38} tigatalk.com/app/
The UBC eNunciate\textsuperscript{39} tools use ultrasound to illustrate to students the articulatory gestures of the tongue and vocal tract that cannot ordinarily be seen, in the Upriver Halqemeylem, SEN\textsuperscript{40}CO\textsuperscript{41}EN, Secwepemc, and Blackfoot languages (Bliss et al., 2016).
7.3 Augmented reality and virtual reality
Augmented and virtual reality technologies are not specifically language or learning technologies, but there is a growing amount of interest in their application to Indigenous language education primarily due to their ability to be naturally integrated into popular “place-based eduction” (Sobel, 2004) practices.
The feasibility of implementing augmented and virtual reality projects is aided by the widespread interest in the technology and 3D game engines like Unity and Unreal. However, there are still very few implementations for Indigenous languages in Canada. Some examples include Tuwitames, an augmented reality story-telling app narrated in Secwepemctsin (Lacho, 2018), an augmented reality companion app to a Blackfoot card game (Goff et al., 2017), and Schoolù, a virtual reality application for teaching Cree syllabics. Yet another augmented reality app, Wikiup\textsuperscript{40}, is designed to take users on tours throughout Canadian cities, transforming landmarks by telling AR-enhanced Indigenous stories and histories, but not necessarily involving Indigenous languages.
8 Summary
Wide available Successful technologies that are already available for many Indigenous languages
Keyboard layouts (§4.1), Approximate search (§4.6), Computer-aided language learning (§7).
Ready for wider implementation Technologies that have been developed for some languages, and that could feasibly be developed for most or all Indigenous languages: Orthography conversion (§4.3), Optical character recognition (§6.1, §6.2).
Awaiting implementation Technologies for which there is already a technological basis in a few languages (e.g., a finite-state analyzer has been written), or for which there exists a language-neutral technological basis, but for which practical user interfaces or language-specific implementations are not yet developed or widely available: Spell-checking (§4.4), Paradigm generation (§4.5), Speech/text alignment (§5.3).
Experimental Technologies that have not yet proven to be successful on Indigenous languages, but show promise in other low-resource language situations: Predictive text (§4.2), Transcription acceleration (§5.1), Audio keyword search (§5.2), Audio segmentation and speaker diarization (§5.4), Text-to-speech (§5.5).
Restricted feasibility Technologies that will likely be feasible only in more-resourced languages (e.g. Inuktitut, Cree): Machine translation (§4.7), Automatic speech recognition (§5.1).
From the above, it is clear that there are a number of text, speech, image, and CALL technologies that are either already available, or could be made more widely available, in many cases with relatively reasonable further investment. The boundary between the first three categories at various stages of implementability and the two last experimental and restricted ones appears to determined by the existence of technological solutions that work with typically quite sparse data resources that can be reasonably expected for Indigenous languages. Meanwhile, new developments (particularly in multilingual and finite-state/neural hybrid modeling) may make technologies possible that until recently seemed infeasible for Indigenous languages.
\textsuperscript{39}eunuciate.arts.ubc.ca
\textsuperscript{40}wikiupedia.com
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Abstract: Fluorescence spectroscopy is an optical spectroscopic method that has been applied for the assessment of environmental quality extensively during the last 20 years. Most of the earlier works have used conventional light sources in spectrofluorometers to assess quality. Many recent works have used laser sources of light for the same purpose. The improvement of the energy sources and of the higher resolution spectrometers has led to a tremendous increase in applications. The motivation for the present review study is the increasing use of laser sources in environmental applications. The review is divided in two parts. The fundamental principles of fluorescence spectroscopy are described in the first part. The environmental applications are described in the second part.
Keywords: conventional lamps; fluorescence; laser sources; laser induced fluorescence; environmental quality
1. Introduction
Optical spectroscopy deals with the study of interactions between matter and light such as absorption, emission and scattering, among others. Fluorescence spectroscopy (or fluorometry) is based on the emission of photons from a substance after excitation from light absorption. The molecules, due to their vibrational energy levels, emit light of lower energy (longer wavelength) than the absorbed light. This is called Stokes’ shift and happens due to an energy loss in non-radiative decay. These processes are shown in the so-called Jablonski diagram in Figure 1a. When a molecule is in the ground level (S\textsubscript{0}) and absorbs a photon of sufficient energy, an electron is promoted to a higher energy singlet level (S\textsubscript{1} or S\textsubscript{2}) equal to the energy of the absorbed photon. If the electron, following a relaxation pathway, returns to its original state emitting a photon, it is called photoluminescence. The two types of photoluminescence are fluorescence and phosphorescence. Fluorescence refers to when the electron from a singlet excited level decays radiatively to the ground singlet state, within a characteristic decay time of the order of 10\textsuperscript{−10} s to 10\textsuperscript{−7} s. Phosphorescence occurs when the electron, after a transition from a singlet excited state to a triplet state, returns radiatively to the ground singlet state. Since the last process involves change of the electron spin, the phosphorescence time could be from 10\textsuperscript{−6} s up to seconds.
For a compound, its emission spectrum and absorption spectrum (excitation spectrum) are usually almost mirror images as shown in Figure 1b for the radiative transition from S\textsubscript{0} to S\textsubscript{1} and vice versa. This symmetry is attributed to the same vibrational levels structures that are involved in each of these processes.
Figure 1. (a) Perrin–Jablonski diagram with the possible radiative transitions (straight arrows) of absorption, fluorescence and phosphorescence, as well as the non-radiative transitions (wavy arrows) of vibrational relaxation, internal conversion (IC) and intersystem crossing (ISC). (b) Illustration of the spectra for the radiative transitions between electronic states that shown in (a). (c) Characteristic times for each transition. Reprinted from [1]. 2012, John Wiley and Sons.
1.1. Light Sources
Fluorescence excitation can be induced by a lamp, a light-emitting diode (LED) or a laser source. When a laser is used for the excitation, the fluorescence is called laser induced fluorescence (LIF). As lamps are conventional sources of light, the fluorescence is considered as conventional in that case. For multispectral light sources, a spectral filter or monochromator is used for selecting the excitation wavelength.
Typically, the commercial spectrofluorometers utilize arc-lamps as light sources for the excitation of compounds. The main sources used for ultraviolet (UV) and visible light are high-pressure and low-pressure lamps of Xenon (Xe) and mercury (Hg). The line spectrum emission of low-pressure Hg-Ar and Hg lamps are used mainly for calibration purposes. The high-pressure Xe and Hg lamps provide broadband light emissions from 250 nm and
from 350 nm, respectively, up to IR. The intensities of high-pressure Hg lamps are higher compared with Xe lamps. There are also high-pressure Xe-Hg lamps with higher intensities than Xe lamps. Deuterium lamps are also used, providing continuum emission in UV, from 160 nm to 400 nm. The tungsten-halogen lamps are less used in fluorescence spectroscopy than the previously mentioned ones due to their weak light emission below 400 nm [2].
In the last two decades, the light-emitting diodes (LEDs) began to appear as light sources in spectrofluorometers. The LED is an electroluminescence device that produces photon emission by the recombination of electrons with electron holes at semiconductor junction. They are inexpensive light sources with bright illumination and the development of LEDs emitted up to deep UV range make them very attractive for fluorescence excitation [3].
The laser sources are categorized in four types according to the active medium: solid state, gas, liquid and semiconductors/diode lasers. Among the solid state lasers, the Neodymium-doped Yttrium/Aluminium Garnet (Nd: YAG) is the most common type used in fluorescence spectroscopy [4]. The fundamental wavelength of the laser is in the infrared (IR) at 1064 nm but with the use of nonlinear crystal the second or higher harmonics could be produced, providing laser wavelength at 532 nm, 355 nm, 266 nm or even 213 nm.
The most common gas lasers include argon ion, HeNe, nitrogen and excimers [5]. Argon ion lasers emit radiation at 488 nm (blue) and 514 nm (green); hence, they are called also blue-green lasers. They are relatively large lasers and external cooling is required. Helium-neon (HeNe) lasers operate at a single wavelength of light, most often at 632 nm. They do not produce high-power light (from few to tens mW), but they are more stable and are often used for metrology applications. HeNe lasers are more compact than argon ion lasers and do not require external cooling. Another type of gas lasers used in spectroscopy are nitrogen lasers, which operate in the UV range, as they emit radiation at 337 nm. They have been used for air pollution monitoring. Excimer lasers are another type of gas lasers for UV emission. The laser medium are short-live dimeric molecules generated in excited state of inner noble gas atoms themselves (excimer) such as argon, krypton, xenon or by their combination with halogens (exciplex) such as fluorine or chlorine gas atoms.
The liquid lasers consist of a dye as lasing material. An organic dye dissolved in water or other solvent (at a typical concentration of the order of 1 part in 10000), is radiated by an intense light source [6]. After the absorption of light in one wavelength, the dye emits light over a broad range of visible wavelengths. Different dyes can produce a variety of wavelength emissions. Coumarin and Rhodamine are some of the most used dyes [7,8]. By changing the cavity length, or through other techniques, the output wavelength can be easily tuned in a wide range of tens of nm. Their drawbacks are that the dye undergoes photodecomposition and needs to be renewed by circulation, either in a container cell or as stream of jet in open air. In addition, the dyes are hazardous toxic materials and great attention when handling them is needed.
The last category of lasers is the diode (or semiconductor) lasers that work on a somewhat different principle. Light is emitted by flowing electrical current through the semiconductor due to the energy gap in the diode’s junction. They are compact lasers that emit wavelengths typically from visible to IR, but recently there are devices emitting in the UV region [9]. Their output has a wide range of power from low to moderate. They have small size, are lightweight and less expensive than other lasers [10].
Generally, the choice of laser type depends on the wavelength range that is needed in each research. The application of laser depends on the properties (monochromaticity, directionality, spatial and temporal characteristics) of the laser beam.
1.2. Detectors
The fluorescence light is detected and quantified either by a photomultiplier tube (PMT) or avalanche photodiodes (APD) or by a charge-coupled device (CCD). The majority of commercial fluorometers use photomultiplier tubes (PMT) to detect the low light intensity of fluorescence [2]. A PMT is a vacuum glass tube that consists of a photocathode where
incident photon induces electron emission, a series of dynodes for electron multiplication and an anode. The material that the photocathode is made from determines the spectral range of the photomultiplier. In order to cover the whole UV-visible range, two types of photocathodes are required.
The APD is another low-intensity light detector used in fluorescence spectroscopy. In a photodiode an electron-hole pair generated when a photon is captured in the diode junction area. In APD, a high reverse bias voltage creates a strong electric field where the electron generated from photon is accelerated to produce secondary electrons by impact ionization. The resulting electron avalanche produces measurable electrical signal even from few photons [11].
Another type of detector used in fluorometers is the CCD with which the whole fluorescence spectrum can be analyzed at once without the need for wavelength scanning with a monochromator. It is mainly used when the emitted light is of higher intensity, such as in LIF. The CCD consists of an array of semiconductive photosensitive elements (pixels) where photons induce an electrical charge which is accumulatively stored in each of them. Then, the read out of each element charge is made in series by shifting the charge of each element to their neighbor toward the charge measurement circuit where it is also digitized.
Typical schemes of a conventional and a laser induced fluorescence system are shown in Figure 2.
**Figure 2.** Schemes of a conventional (a) and a laser-induced (b) fluorescence spectroscopy system.
### 1.3. Fluorescent Compounds
The compounds that absorb visible and/or UV light are called chromophores. The compounds that emit light are called fluorophores. Compounds with fluorescent characteristics are those with several aromatic (fused) rings and/or with conjugated double bonds. There are two types of fluorophores depending on the groups: those with electron-donating groups, such as -OH, -NH₂ and -OCH₃ that increase fluorescence, and those with electron-withdrawing groups, such as COOH and -N=N- that reduce fluorescence. There are some exceptions, for example fluorophores such as tryptophan and tyrosine, that showed lower quantum yields than expected [12]. Compounds such as halogens, oxygen and acrylamide are also known to reduce fluorescence and will be described in the next section. Heterocyclic compounds do not fluoresce significantly unless they are attached to an aromatic ring.
The major characteristics of a fluorophore include the fluorescence lifetime ($\tau_F$) and the quantum yield ($\Phi$). Fluorescence lifetime is defined as the average time that the molecule remains in the excited state before it returns to its ground state, of the order of ns. The quantum yield is defined as the ratio of the number of the emitted photons to the number of the excited molecules. The higher the quantum yield, the higher is the fluorescence. It is
The intensity of fluorescence \((I_F)\) is proportional to the molecule’s concentration in diluted solutions \((\varepsilon \cdot b \cdot C < 0.05)\), as described from the following equation:
\[
I_F = k \cdot I_o \cdot \Phi \cdot (\varepsilon \cdot b \cdot C)
\]
(1)
where:
- \(k\): a constant dependent on the instrument;
- \(I_o\): the intensity of the incident light;
- \(\Phi\): the quantum yield;
- \(\varepsilon\): the molar absorptivity;
- \(b\): the path length and
- \(C\): the molecule’s concentration.
The optical properties of standard organic fluorophores are founded in many databases and include: the wavelengths of maximum absorption and emission and their bandwidths (full width at half maximum), extinction coefficient, photoluminescence quantum yield and fluorescence lifetime [13].
1.4. Factors That Affect Fluorescence
The factors that affect fluorescence include solvents, temperature, pH and ionic strength as well as the presence of other substances. The decrease in fluorescence intensity caused by any factor is called quenching, while the substances that may induce this are called quenchers. The decrease in the fluorescence intensity happens either by intramolecular or by intermolecular interactions.
One of the most frequently present quenchers is the molecular oxygen which quenches almost all known fluorophores. Other quenchers are acrylamide, amines and halogens. Table 1 summarizes examples for quenchers of some typical fluorophores. There are two mechanisms of quenching: static and dynamic. Static quenching happens when a non-fluorescent complex is formed between the fluorophore and the quencher. Dynamic quenching, otherwise called collisional quenching, happens when the quencher interferes with the fluorophore during the lifetime of the excited state. The excited molecule is then deactivated either by contacting other molecules or by intermolecular interactions (collisions). The Stern–Volmer equation describes the fluorescence quenching as follows [2]:
\[
\frac{I_o}{I} = 1 + K_q \cdot \tau_F \cdot [Q]
\]
(2)
where:
- \(I_o\): the intensity without quencher;
- \(I\): the intensity with quencher;
- \(K_q\): the quencher rate coefficient;
- \(\tau_F\): the fluorescence lifetime and
- \(Q\): the quencher’s concentration.
Table 1. Examples of typical fluorophores and their quenchers.
| Typical Fluorophores | Quenchers |
|-----------------------------------------------|-------------------------------------------------------------|
| Polycyclic aromatic hydrocarbons (PAHs) | Nitrocompounds, nitromethane [14,15] |
| Anthracene | Diethylaniline [16] |
| Tyrosine | Disulfides [17], phosphates [18] |
| Tryptophan, indole | Acrylamide [19,20], cations [21], anions [22] |
| Aromatic hydrocarbons | Aromatic and aliphatic amines, pyridinium salts [23] |
| Majority of known fluorophores | Oxygen [24,25] |
The fluorescence of a compound can be affected from the solvent used for the fluorophore solution. The solvent effect can be observed as a shift of the spectral maxima (solvatochromic shift), as a change of the intensity of the spectral line or band and as a change of the shape and width of the band [26]. By increasing the solvent polarity, shifts of the emission spectrum to longer wavelengths (red shifts) are usually observed.
The pH parameter affects fluorescence as the structure of a molecule can be altered by altering the pH. For example, a compound can become a spherical or linear shape in different pH values [27]. The ionization of a molecule after pH modification may alter the molecular orbital of the excitable electrons. Furthermore, H⁺ ions compete with metal ions in complexation with dissolved organic matter (DOM) and thus, there are metals that increase the fluorescence in water samples [28].
Additionally, the effect of temperature is very important. The electrons return to the ground state by radiationless processes. By decreasing the temperature from 45 °C to 10 °C, it was found that the intensity of DOM has been increased by 48%. [29]. Finally, the ionic strength affects fluorescence by changing the conformity and by charge transfer [30].
1.5. Types of Laser Induced Fluorescence
Laser induced fluorescence (LIF) is classified as steady-state (or continuous wave, CW) when only the spectral information of the emission is recorded, or as time-resolved LIF, where information of the fluorescence lifetime is derived [1]. For CW LIF, where the time integrated fluorescence is recorded, both CW and pulsed laser sources can be used. In time-resolved LIF, for the fluorescence analysis in time domain, a pulsed laser is necessary with pulse duration below ns, while in frequency-domain techniques, an optical modulation of CW laser can be used. Most types of lasers can operate in both CW and pulsed mode, while there are few types that in principle cannot be run in CW mode.
The LIF spectroscopy can also be categorized according to its spectral operation, as excitation LIF when selecting the excitation wavelength or as emission LIF when the emitted light is spectrally analyzed. In excitation LIF spectroscopy, the excitation wavelength is varied using a tunable laser and each time the total emitted light is detected using a filter in front of the detector to remove any scattered laser light. In emission LIF spectroscopy, a fixed wavelength laser is used to excite the sample and the emission spectrum is measured by using a monochromator before the detector to scan the wavelength or by using a spectrometer [31].
The high intensity light, achieved from focusing the pulsed laser beam, is able to induce fluorophore excitation by the simultaneous absorption of two or more photons of lower energy (longer wavelength) [32]. Multiphoton excitation has a rather small probability, as it depends non-linearly to the light intensity (photon fluence) and becomes efficient only in the region of the focal spot. For the two-photon absorption, there is quadratic dependence on laser intensity. The excitation photons originate from one laser beam or by different laser sources. The two-photon absorption spectrum may differ in shape from the one-photon spectrum, as there are different selection rules applied for them that allow or prohibit specific transitions [33]. The two-photon absorption laser induced fluorescence (TALIF) spectroscopy could be complementary to the conventional LIF capable of revealing energy states not accessible from one-photon transition, to excites in UV range using laser of double wavelengths that are more easily available to clearly separate the excitation laser wavelength from the detected emitted light.
LIF spectroscopy is often combined with the laser-induced breakdown spectroscopy (LIBS) as an emerging analytical technique for the elemental analysis of various samples [34]. In LIBS, the sample is irradiated by a high-power pulsed laser to generate localized plasma and breakdown the material into excited ionic and atomic species, whose emission is then spectroscopically analyzed. By utilizing a second laser beam tuned to selectively excite the plasma species, a great enhancement of their emission capability is achieved [35].
1.6. Fluorescence Recording
The fluorescence signals could be recorded in several ways. In emission LIF spectroscopy, the intensity for each wavelength of the emitted light is recorded for a fixed excitation wavelength to derive the fluorescence emission spectrum. In excitation LIF spectroscopy, the intensity of the total light emitted is recorded whilst scanning the excitation wavelength to derive the fluorescence excitation spectrum.
There are other sophisticated methods of conventional fluorescence spectroscopy that also apply in LIF, such as the synchronous fluorescence spectroscopy (SFS), the total synchronous fluorescence spectroscopy (TSFS) and the excitation-emission matrix (EEM). In SFS, the emission spectrum is recorded while both the excitation and emission wavelengths are scanned simultaneously but maintaining a constant difference (offset) between them $\Delta \lambda$ [36]. Synchronous spectra provide more information compared to a single scan. In TSFS, the output result is a contour map that contains numerous synchronous spectra at different offsets. Finally, the EEM method that was introduced in 1977 [37,38] results in a three-dimensional (3D) plot of fluorescence excitation wavelength versus emission wavelength and intensity. It provides full detailed information that can be used to identify several fluorophores present in complex mixtures. They are easily distinguished because the maximum fluorescence intensity for each of them is resulted only from one pair of $\lambda_{ex}/\lambda_{em}$ in the matrix.
Furthermore, for quantitative measurements, the data from recording spectra need to be quantified. For this purpose, many standard fluorescence indices have been developed and are defined as the ratios of emission intensity at two different points or areas [39]. The data obtained from EEM are often reduced with statistical methods, with parallel factor analysis (PARAFAC) being the most popular discriminant analysis.
1.7. Interferences in Fluorescence Measurement
Scattering is a major problem encountered in fluorescence measurements. There are two types of scattering: the Raman (inelastic) and the Rayleigh (elastic) scattering. Rayleigh scattering occurs when there are molecules of smaller size than the wavelength of the excitation light, while the scattered light has the same wavelength. It is easily filtered out from the longer wavelengths of emission. The Rayleigh scatter in EEM appears as a visible diagonal line at the emission wavelength equal to the excitation wavelength, while for the second order of Rayleigh scatter, the bright line appears at the emission wavelength equal to double the excitation wavelength. Raman scatter happens because the light is absorbed and re-emitted with a loss in photon energy. The loss is due to the vibrational states and the scattered light having a higher wavelength than the excitation light. Water has scattering properties from the vibration of O-H bonds, and in aqueous samples the Raman line appears in EEM as a diagonal line at excitation wavelengths from 260 to 350 nm and at emission wavelengths from 280 to 400 nm.
The inner filtering effect (IFE) is another phenomenon that affects the recorded fluorescence. The excitation IFE occurs because a part of the incident light is absorbed from the fluorophore before reaching the sample area from where the fluorescence emission is collected in. Therefore, when increasing the fluorophore concentration, the fluorescence intensity increases up to a certain point and then starts to decrease. Moreover, the emission of IFE is caused by the self-absorption of the emitted light by the fluorophore before it reaches the detector. This results in a reduction of the recorded spectrum, where the absorption overlaps with the emission which changes the shape of the recorded spectrum in the low wavelength portion. Additionally, IFE could be induced due to presence of other chromophores that absorb the excitation or the emission light. In most environmental samples, the main reason for the IFE is the naturally dissolved humic material [40]. The IFE problem is compensated by reducing the path length in the sample for the excitation or/and emission light and by diluting the water samples to have an absorbance of less than 0.1 at 254 nm [41].
2. Applications of Fluorescence in Environmental Samples
The detection of target pollutants in liquid and solid environmental samples has been extensively implemented by chromatographic methods coupled with fluorescence detectors. Fluorescence detectors are of high selectivity as there are few compounds that fluoresce. They are also of higher sensitivity (10–1000 times) compared to diode array UV detectors. A tremendous number of publications are dedicated to the determination of pollutants such as polycyclic aromatic hydrocarbons (PAHs) in water [42–44], in soils [45,46], in sediments [47,48], in pesticides in water [49,50], in pharmaceuticals in water [53,54], in soils [55,56], in sediments [57,58] and in metals in water [59,60] by chromatographic techniques coupled with fluorescence detectors. In all publications, a preconcentration of the samples is required, as the pollutants exist in very low concentrations. The preconcentration can be achieved by liquid–liquid extraction, solid phase extraction or solid phase microextraction for aqueous samples. For the solid samples such as soils and sediments, solid-liquid extraction and fractionation according to pH have usually been applied. Besides, fluorescence has been used for the direct characterization of quality of environmental samples without preconcentration. The applications of fluorescence in environmental samples without preconcentration are described as follows.
2.1. Applications of Conventional Fluorescence in Various Types of Water
Without any sample preconcentration and/or pretreatment (except filtration if necessary), conventional fluorescence has revealed useful information about the water and wastewater quality. The majority of studies have focused on the dissolved organic matter (DOM), which is the major water constituent, while less have focused on oil pollution.
The first significant studies were those of Coble [61,62] that have characterized marine and terrestrial DOM in seawater by EEM fluorescence spectroscopy. The peaks were classified into five categories and named as A, B, C, T and M. Both peaks A and C were of humic-like fluorescence, with peak A irradiated by UV excitation and peak C by visible excitation. Peaks B and T were of tyrosine-like and tryptophan-like fluorescence, respectively. Peak M was specific for marine humic-like fluorescence.
The distinguishing between surface water from eastern (Atlantic and modified polar water) and western (Canada-basin polar water) Arctic sectors was detected by using EEM fluorescence spectroscopy [63]. In this work, the Eurasian polar water showed higher visible DOM fluorescence signals than the water from the Canada basin.
The characterization and monitoring of wastewater in surface waters has been achieved by EEM fluorescence spectroscopy [64]. The peaks T (living and dead cellular material and their exudates) and C (microbially reprocessed organic matter) from wastewater samples presented much higher intensity compared with those from natural waters. Furthermore, peak T fluorescence was highly reduced after the biological treatment process, while peak C was almost completely removed after the chlorination and reverse osmosis processes.
Another application of EEM coupled with principal component analysis and second derivative analysis has characterized wastewater samples after each treatment process in a municipal wastewater plant [65]. Figure 3 shows an example of a wastewater sample after anaerobic treatment.
Another work [66] has used EEMs to distinguish the origin and the distribution of DOM in different water samples such as oligotrophic oceanic waters, reef waters, river waters and groundwater. The fluorophores that were identified within the samples were: humic-like A, humic-like C, marine humic-like M, tryptophan-like T1 and T2 and tyrosine-like B1 and B2. Some unknown peaks (U1 and U2) have also been identified.
Huang [67] identified six fluorophores by EEC-PARAFAC in the eutrophicated lake Taihu during autumn. They were named A, B, C, N, M and T. The results showed that red shift happened with increasing fluorescence intensity for peaks A (UV humic-like) and C (terrestrial humic-like) while peak M had the reverse red shift. From another survey in the same lake, only four fluorophores were detected during one month [68] by EEC-PARAFAC.
The majority of these studies have used solid state lasers. Generally, the main fluorophores and their positions as identified by most researchers [62,72] in various types of water are summarized in Table 2.
| Name | Letter | Ex (nm)/Em (nm) |
|-----------------------|--------|--------------------------|
| Humic-like | C | 340–360/420–480 |
| Fulvic-like | A | 240–260/380–460 |
| Tyrosine-like | B (B1, B2) | 265–285/290–310 |
| Tryptophan-like | T (T1, T2) | 265–285/290–340 |
| Microbial-like (Marine-like) | M | 310–330/390–410 |
| Humic-like | H | 370–390/480–500 |
2.2. Applications of LIF in Various Types of Water
Laser induced fluorescence has also been used for the characterization of water quality without any preconcentration. The majority of these studies have used solid state lasers.
Uebel [75] applied the LIF method in order to detect water pollutants and their possible interactions with phytoplankton and break-down products (yellow-substances) in situ. They used a frequency doubled dye laser as an excitation source with a pulse energy of 10 mJ and a pulse duration of 10 ns. The substances were excited in the range from 265 nm to 400 nm while the fluorescence signal was recorded in the range of 310 nm–750 nm. Different fluorescence spectra appeared during ageing and dying of the phytoplankton.
For the detection of PAHs and oils in groundwater, Baumann [76] chose a nitrogen laser and time-resolved LIF based on the different decay times of humic substances and PAHs. They calculated the concentrations of 16 PAHs and found a good correlation with the results obtained by HPLC coupled with a fluorescence detector.
In a work of Sivaprakasam and Killinger [77], two different LIF instruments were tested for the determination of DOC and quinine sulfate in natural water samples, bottled distilled and bottled drinking water samples, where it was found that plastic-related compounds were leached into the water from the containers. One instrument utilizes a UV tunable dye laser (200–285 nm, 0.2–5 µJ, 10 Hz) with a spectrometer and CCD detector, while the other one is a portable system utilizing a fixed wavelength microchip laser (at 266 nm, 1 µJ, 8 KHz) with a gated PMT detector and bandpass interference filters. Although both systems use laser pulses of the same energy, the higher repetition rate in the latter system provides a much greater signal-to-noise ratio (SNR) measurements due to the high pulse averaging and the higher total energy output. In conjunction with the detection system, it was found to have a 10 times higher sensitivity than the first system, but with much slower processing time to obtain a full emission spectrum. It was found to have up to 100 times higher sensitivity from the best commercial portable spectrofluorometer, while it was tested in situ for the determination of plastics and DOC in seawater samples [78]. Additionally, they upgraded it to have two interchangeable microchip lasers operating at 266 nm and 355 nm, achieving the tracking of DOC in the clean ocean water by continuously operating the portable LIF system for five days [79].
The same portable LIF unit was tested to measure the fluorescence from tap water and sea water after being treated by reverse osmosis [80] and in ground and drinking water samples [81]. It was found that the deeper UV laser showed more distinct spectra with quantitative features and gave better separation of the LIF from the Raman peak allowing the detection of unique spectral features. Most of the LIF systems utilize laser sources in deep UV.
Ghervase et al. [82] have chosen the fourth harmonic output of an Nd:YAG laser for the excitation of both microbial and humic-like substances due to the high energy of the excitation photons (266 nm). They detected the impact from human and chicken waste in rivers and found that chicken waste had a specific fluorescence signature.
LIF and excitation-emission matrix (EEM) fluorescence were applied in river samples from the lower basin of the Arges River. They detected urban sewage contamination by picking up fluorescence signals, such as that from tyrosine and the presence of folded and unfolded tryptophan residues [83].
Recently, Du et al. [84] have used a UV laser at 266 nm in order to detect the presence of three aromatic amino acids in seawater (tryptophan, tyrosine, and phenylalanine) in situ. The peaks of tryptophan, tyrosine and phenylalanine were detected at 350, 300 and 280 nm, respectively, as shown in Figure 4, and their concentrations were quantified.
In a recent work [85] a small-sized spectrofluorometer operated at 278 nm was used for the identification of oil products in seawater. They found that the spectral features were changed depending on the state of the oil product.
A combination of LIBS and LIF was used in order to detect trace amounts of heavy metals in water samples. Specifically, lead was detected by using a Q-switched Nd:YAG laser to produce plasma, at 1064 nm or 532 nm [86]. In another work, lead was detected by micro-LIBS with LIF by using a 170 µJ laser pulse for ablation and a 10 µJ laser pulse for re-excitation [87]. Other metals that were detected with LIBS were cadmium after
enrichment with a resin [88] and chromium [89,90]. In addition, LIBS portable compact systems were employed for in situ seawater analysis for deep sea [91–95].
A totally different application of LIF was used for the classification of viruses. In a recent study [94], a laser at 266 nm with a pulse repetition of 10 kHz and a power of 25 mW has been used for virological analysis of environmental samples. Although the high repetition rate of high energy pulses, the SNR was not always adequate to discriminate the virus in small concentrations. However the LIF method could significantly reduce the time and operational cost of virus analysis.
2.3. Applications of Conventional Fluorescence in Soils and Sediments
Conventional fluorescence has been applied in soils and sediments after isolation of the target components such as humic substances, oils, etc.
Surface marine sediments were extracted by proper solvent and examined for the presence of bulk PAH levels by a portable fluorescence apparatus [95]. The results showed good correlation with the lab results.
EEM and synchronous scans were obtained by [96] to examine the concentrations of PAHs in soils. By using a fluorescence fingerprints library with several EEM and SFS maps for various dilutions of Romanian crude oil in methanol, they confirmed the identity of the soil pollutant. They created a calibration to estimate the pollutant concentrations.
EEM–PARAFAC was used in a study [97] conducted in lake bottom sediments of selected lobelia lakes in order to assess their properties and their origin. The optical properties of HA extracted from the sediments were compared to the parameters that describe their structural and chemical properties. Four components were identified: two protein-like (C2 and C4), one humic-like (C1), and one fulvic-like (C2). The more dominant component was C2 and the less dominant one was C4. Each of the components revealed different information. The results showed that the organic matter (OM) present in the bottom sediments from sampled lakes had autochthonic origin and consisted of mostly labile organic compounds.
Five fluorescent components were identified by EEM-PARAFAC in soils and sediments from two different estuaries in Spain and were found in both FA and HA fractions with different abundance [98].
In surface and deep sediments from Toulon Bay in France, EEM-PARAFAC identified two components [99]: a “fresh” particulate OM in surface sediments, which produces protein like high molecular weight-DOM and low molecular weight-DOM and a “buried”
particulate OM in the deeper sediment layer. In porewaters, three components were identified: C1, C2—both humic-like—and C3 of protein-like fluorescence.
From another study [100] conducted in a forested watershed, three fluorescent compounds were identified from soil/sediment HS: a terrestrial humic-like (C1), a microbial humic-like or fulvic-like (C2) and a protein-like component (C3) as shown in Figure 5. Component C3 was probably related to an autochthonous organic input to the reservoir sediments and/or phenolic compounds. They used EEM-PARAFAC spectroscopy.
![Figure 5. The three fluorescent components identified by EEM-PARAFAC. Adapted with permission from Ref. [100]. 2017, Springer Nature.](image)
EEM-PARAFAC has also distinguished soils that were treated with mineral fertilizers and organic manure from those treated with only mineral fertilizer and those without fertilization [101].
Synchronous fluorescence at Δλ = 20 nm has been applied in different types of soil samples and revealed the presence of five main peaks at 360, 470, 488, 502 and 512 nm. They assessed the soil humification degree in different types of soils [102].
2.4. Applications of LIF in Soils and Sediments
LIF has been applied to soil samples without any chemical and or/physical pretreatment and extraction procedures.
The influence of a sewage-sludge addition on the OM of a Brazilian oxysol was studied by an argon laser emitted at 351 nm with an output power of 400 mW [103]. The application of LIF was performed on unfractonated soil samples, fractionated with chemical methods and fractionated by physical methods (particle size). The results indicate that every particle size fraction showed a different shape, revealing differences in organic compounds bounded to them. It was also used to obtain LIF spectra of pelletized whole soils from different origins and various depths [104]. A similar apparatus, utilizing a CW laser of 20 mW power at 405 nm for the excitation, was used for the characterization of OM in pelletized soil samples [105].
The LIBS spectra of soils were obtained using a Q-switched Nd:YAG laser at 1064 nm [106]. The humification degree (HD) of OM was evaluated for the first time by LIBS. The results show high correlation with those determined by LIF using a CW diode laser at 405 nm.
The results from the previous studies were compared in a review by Senesi [107] and it was found that there is a high correlation between (HD) LIBS and (H) LIF index values, and that LIBS can be used to evaluate the humification degree of soil organic matter (SOM).
LIF was also applied in dry and hydrated crusts by an Nd:YAG laser operating at 532 nm with 7 ns pulses [108]. The microphytobenthos (MPB) showed three peaks (two main at 570 and 650 nm, and a secondary at 720 nm) as is shown in Figure 6. Furthermore, the only slight difference between bare soil, either dry or hydrated, was the intensity of the peaks.
3. Remote Sensing
LIF has the great advantage of being expended to the outdoor environment. It is a technique that can also be applied as remote sensing and, hence, it is called laser remote sensing system LIDAR (light detection and ranging). It makes it possible to analyze compounds from long distances and it can operate under full sunlight.
There are many studies about LIDAR systems for the measurements of hydrographic parameters and substances in water. Nunes [109] has used a LIDAR using the 2nd harmonic of Nd: YAG laser system with a pulse energy of 200 mJ, a duration of 10 ns and a repetition rate of 10 Hz to measure chlorophyll a (685 nm) and DOM (from 540 to 620 nm) in deep sea water. Babichenko [110] has used a LIDAR Nd: YAG laser at 355 nm and a four-channel detector (355, 403, 450 and 680 nm) in order to measure chlorophyll a and DOM (from 540 to 620 nm) in deep sea water. Babichenko [110] has used a LIDAR Nd: YAG laser at 355 nm and a four-channel detector (355, 403, 450 and 680 nm) in order to measure chlorophyll a and other pigments in the Black Sea [111,112] and in the Danube Delta [113].
Other researchers have used the laser beam of an excimer (308 nm) and of a tunable dye laser (367 and 460 nm) to measure dissolved organic matter (DOM), chlorophyll a and other pigments in the Black Sea [111,112] and in the Danube Delta [113].
The disadvantages of excimer lasers are their high purchase and maintenance costs and the continuous need for gas supply compared with the solid state Nd:YAG lasers [114].
To the best of our knowledge, there are not any applications of LIDAR for monitoring soil quality. The only recent application had the aim to evaluate the soil surface and furrow cross-sectional area after a trailing shoe sweep [115].
4. Conclusions
The present study reveals the benefits of the application of fluorescence spectroscopy to environmental samples in order to assess their quality. Fluorescence can be achieved by the excitation of the compounds either by lamps or by lasers. In the first occasion, it is considered as conventional fluorescence, while in the second it is called laser induced fluorescence (LIF). Both of them have been applied mainly for the characterization of DOM in various types of water, soil and sediment samples. In a lesser extent, they have been applied for the detection of pollutants such as oil products in these samples.
In conventional fluorescence spectroscopy, the most common lamps are Xe and Hg. The most use recording technique in conventional fluorescence is EEM combined with PARAFAC analysis. It has been applied mainly for the characterization of DOM in various types of water. For the majority of the studies, the results from EEM showed the presence of peaks that have been categorized in five categories. The application of conventional spectroscopy in soil and sediment samples after pretreatment for isolation has led to the categorization of the same fluorophores.
In LIF spectroscopy, the common light source is the solid state laser Nd:YAG, as it was found to be more suitable for the detection of DOC and pollutants, followed by dye lasers that offer excitation tunability for the recording the fluorescence intensity versus emission wavelength. LIF has been applied less than conventional spectroscopy, especially in soil samples, although no sample pretreatment was necessary. Furthermore, LIF has been used for remote sensing measurements of various water systems by excimer and dye lasers. LIF has proven to be a powerful tool for assessing the environmental quality and its use is continuously extending. Lasers have the advantages of high sensitivity and selectivity, as well as being versatile sources. Furthermore, the problem of quenching is minimized because laser sources have very high intensities compared with the potential quenching. The disadvantage is the restriction in excitation tunability that makes it difficult to record the EEM in order to gain more information about the complexity of the environmental samples.
**Funding:** This research is financed by the Project “Strengthening and optimizing the operation of MODY services and academic and research units of the Hellenic Mediterranean University”, funded by the Public Investment Program of the Greek Ministry of Education and Religious Affairs.
**Conflicts of Interest:** The authors declare no conflict of interest.
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Article
Gender-Based Differences in the Consumption of Food Rich in Fibre and Its Relationship with Perceived Mood Status: A Cross-Sectional Study
Mudi H. Alharbi 1,* and Sehad N. Alarifi 2
1 Clinical Nutrition Department, College of Applied Medical Sciences, Taibah University, Madinah 42353, Saudi Arabia
2 Department of Food and Nutrition Science, Al-Quwayiyah College of Sciences and Humanities, Shaqra University, Shaqra 11971, Saudi Arabia; [email protected]
* Correspondence: [email protected]
Abstract: It is unclear whether gender-based differences in dietary fibre intake exist in the relationship between daily fibre consumption and the prevalence of mood disorders. This study aims to examine the effects of dietary fibre consumption on mood status between genders in Saudi Arabia. A total of 359 Saudi participants completed the survey. The data showed that women consumed 14 g fibre/day and had a mild depression score, while men consumed 12 g/day and had very severe stress. The consumption of low-to-moderate servings of fruit or very low servings of nuts and seeds was associated with stress in men. Moderate levels of depression among women were likely to occur with low-to-moderate servings of nuts and seeds. Moderate-to-high stress levels among women appeared to be associated with low-to-moderate servings of vegetables, while depressed men consumed vegetables in low-to-moderate servings. However, anxious women who experienced mild levels consumed low-to-moderate servings of vegetables, and those with a mild-to-moderate level of anxiety consumed low-to-moderate servings of bread, whole grains, and cereals. The preliminary results showed that the consumption of 12 g fibre/day is not enough to relieve stress among men, while 14 g/day reduces the level of depression to mild among women. Fibre-rich foods, e.g., vegetables, nuts and seeds, fruit, bread, cereals and legumes, lower the degree of negative moods, but this is not only attributed to fibre, as there are other influential nutrients.
Keywords: source of fibre; men and women; depression; anxiety; stress
1. Introduction
A considerable body of literature has developed around the relationship between fibre and mental health; however, the mechanism of its influence on mental health is still unknown [1]. The definition of fibre is clarified by Stephen et al. [2] as “Carbohydrate polymers with three or more monomeric units (MU) that are neither digested nor absorbed in the human intestine, and it includes: (1) non-starch polysaccharides (NSP) from fruit, vegetables, cereals and tubers, whether intrinsic or extracted, chemically, physically and/or enzymically modified or synthetic (MU \( \geq 10 \)); (2) resistant (non-digestible) oligosaccharides (RO) (MU 3–9); and (3) resistant starch (RS) (MU \( \geq 10 \))”. In general, wholegrain products and cereals, fruit, vegetables, legumes, seeds and nuts are considered as foods that are high in fibre. The recommended fibre intake for an adult is 25 g for women and 30–38 g/day for men (14 g per 1000 kcal per day) [3]. However, the diet of many of people in Middle Eastern countries is lacking in foods sufficient for the recommended consumption of fibre [4]. Additionally, evidence from previous studies indicates conflicting findings on gender-based differences in diet and nutritional intake [5,6]. Thus, this maybe highlights the gender differences in the consumption of fibre and the health consequences it may have. Accordingly, studies conducted in developing countries such as Bangladesh illustrate a reduced incidence of fibre intake in women, leading to a higher risk of nutrient
deficiency and health-related problems compared to men [6]. However, the consumption of adequate amounts of fibre has several health benefits, including a lower incidence of mood disorders such as depression, stress and anxiety [7]. Lately, the importance of the correlation between dietary fibre intake and mood disorders in managing mental well-being has attracted considerable interest [7]. Indeed, epidemiological studies have demonstrated that adherence to healthy dietary patterns, including those with a high consumption of fibre, is associated with a lower risk of depression [8]. However, the nature of these correlations is complex due to the two-way causal effects between dietary fibre intake and mood disorders. For instance, changes in food preferences due to short-term mood status, such as eating comfort foods during mood swings or experiencing changes in appetite due to stress, are general human experiences. A more recent explanation for how fibre intake may affect mood status is the effect of dietary patterns on the gut microbiota: the human microbiota is increasingly recognized as a main factor impacting well-being and health, with diverse possible benefits including enhanced cognition and mood [9]. Recognizing the need for a better understanding of gender-based differences in the consumption of fibre and acknowledging the relationships between diet and mood status, this study aims to examine potential gender differences in the consumption of dietary fibre intake and whether and to what extent such differences affect perceived mood status in adult men and women in Saudi Arabia. A greater understanding of gender-based differences in dietary fibre intake would be useful in optimizing existing nutritional interventions and facilitating the execution of new comprehensive interventions intended to enhance the nutritional status and health profile of populations [5].
2. Materials and Methods
2.1. Design and Study Participants
The present study, a quantitative cross-sectional exploratory study in Al-Madinah Al-Munawwarah and surrounding areas in Saudi Arabia, was started in November 2018 and terminated in June 2019. Eligible participants for this study were identified using a health and lifestyle questionnaire. Advertisements on social media and flyers on university campuses were also employed as recruitment strategies. The inclusion criteria for the target population for the present study were as follows: healthy adults aged ≥19 to ≤45 years with a body mass index (BMI) >18.5 and <25 kg/m². The exclusion criteria were pregnancy and breastfeeding; premenstrual syndrome (PMS); considerable incidents such as weight loss, weight gain or dietary change within the past six months; suffering from food intolerances such as lactose intolerance or gluten sensitivity; suffering from disorders such as adverse gastrointestinal symptoms, depression, or cardiovascular or metabolic diseases; continuous long-term consumption of corticosteroid drugs; using fibre or supplements, e.g., probiotics or prebiotics; and smoking cigarettes more than 14 times per week or shisha or hookah more than once per week. In total, 390 participants were invited to take part in the study, of whom 31 were removed. Finally, after excluding respondents who did not meet the criteria, 359 participants (179 men and 180 women) were included for data analysis, with a response rate of 92.05%. A sample size of 359 provides a power of at least 94%, with a margin of error of 5%. Participation in the study was voluntary and anonymous. Participants gave their informed consent before participating in the study, which was conducted in accordance with the Declaration of Helsinki. This study was ethically approved by Taibah University (no CLN201806)
2.1.1. Data Collection Measures
Demographic and Anthropometric Data
Gender, marital status, income, education level and age were recorded in the demographics, and BMIs were recorded as the anthropometrics, as well as smoking status. All this information was obtained from the health and lifestyle questionnaire, and the energy intake per day was also recorded from 24 h dietary recall.
Dietary Assessment Methods
This study adopted an FFQ [10] and a 24 h dietary recall to assess the consumption of dietary fibre in the target populations. The semi-quantitative FFQ questionnaire concentrated on usual consumption during the last six months (on average). It measured the consumption of some major fibre-containing food items such as cereals and bread, vegetables and fruit, nuts and seeds, and legumes. The participants were asked how often they consumed certain food products. Consumption was divided into three groups: (1) no consumption or very low consumption, (2) low-to-mild consumption, and (3) moderate-to-high consumption.
Each response on the frequency of food consumption was inserted under one of the three main categories as follows: (1) no consumption or very low consumption: responses of “never or less than once a month” and “one to three servings a month”; (2) low-to-moderate consumption: responses of “once a week” and “two to four servings a week”; (3) moderate-to-high consumption: responses of “five to six times a week”, “once a day”, “two to three servings a day”, “four to five servings a day” and “six plus times a day”.
A 24 h dietary recall was obtained from the participants, who were asked to recall all food items and beverages consumed from waking up until going to sleep the previous day. The information requested included estimates of the amount consumed of food items that contained fibre, such as cereals, wholegrain products, fruit and vegetables, nuts; pulses such as beans, lentils or chickpeas; and salads. The average amount of each food item was determined in relation to commonly used household utensils and with a handy guide to portion sizes, with photographs that indicated different portion sizes of certain food items. This enabled participants to make more accurate estimates of the quantities of food consumed, minimizing errors in estimation. These results were analysed using the software Dietplan7 (Forestfield Software Ltd, Horsham, UK).
Depression Anxiety Stress Scales (DASS) Questionnaire
The prevalence and severity of the negative mood statuses of the participants were assessed using the 21-item self-administered Depression Anxiety Stress Scales (DASS-21) questionnaire with seven categories per subscale [11], which has been validated for non-clinical use in populations and research [12], including in the Arabic language [13]. Each of the questions is scored from 0 (did not apply to me at all) to 3 (applied to me very much), resulting in a total score of 0 to 21. In relation to symptoms of depression, participants with total scores of 0–4 were classified as normal, 5–6 as mild, 7–10 as moderate, 11–13 as severe and >14 as very severe. The scores for anxiety were 0–3 (normal), 4–5 (mild), 6–7 (moderate), 8–9 (severe) and >10 (very severe), and for stress 0–7 (normal), 8–9 (mild), 10–12 (moderate), 13–16 (severe) and >17 (very severe), respectively [11].
Statistical Analysis
All statistical analyses were carried out using the Statistical Package for Social Sciences (SPSS version 24.0 (IBM, Armonk, NY, USA)). Values are exhibited as mean ± standard deviation (SD) for continuous variables with t-testing to find the differences between genders, and as percentages for qualitative variables with chi-squared testing to find differences between genders. Descriptive statistics were evaluated for all parameters. The significance of differences in dietary fibre intake between men and women was analysed using the Kruskal–Wallis H test. Logistic regression was used to find the relationship between dietary fibre intake and perceived mood status (depression, anxiety and stress). In
the analysis, all the potential confounding variables were analysed (Table S1) and with a significant association were included. Odds ratios (OR) calculated with 95% confidence intervals (CI) were calculated for both crude and adjusted data. One by one, variables with a \( p \geq 0.15 \) have been excluded from the model by Wald statistic (backward method). The goodness of fit test was used to verify the model. The results are presented as odds ratios that are adjusted for confounding variables and accepted as significant at the level of \( p < 0.05 \). Mood was categorized into five levels: normal (treated as the reference category), mild, moderate, severe and extremely severe. Food consumption was divided into three levels: (1) no consumption or very low consumption, (2) low-to-mild consumption, and (3) moderate-to-high consumption.
3. Results
3.1. General Characteristics of the Study Population and Food Consumption
The demographic and anthropometric characteristics of the study population by gender are presented in Table 1. Of the 359 participants, 180 (50.1%) were women and the remainder were men (49.8%). The mean ages for men and women were similar. Both men and women had normal BMI, whereby men had a slightly higher mean BMI than women. The mean energy intake for men was higher than that of women participants. The mood test showed non-significant differences between both genders. The comparison between men and women in the study population showed significant differences in BMI, energy intake and smoking \((p < 0.05)\), but not in age, income, education level and marital status \((p > 0.05)\). However, the mean dietary fibre intake (according to the 24 h dietary recall) was significantly higher among women \((14.0 \pm 1.19)\) than men \((12.0 \pm 1.16)\).
Table 1. Characteristics of demographic, anthropometric, mood test and food consumption by gender of the total study population.
| Particulars | Men | Women |
|---------------------------------|----------------------------|----------------------------|
| | Mean (SD) | Mean (SD) |
| Age (years) | 23.6 (5.54) | 23.2 (5.21) |
| BMI * | 23.47 (2.28) | 22.31 (2.17) |
| Marital Status (%) | n (%) | n (%) |
| Married | 89 (49.7) | 81 (45) |
| Unmarried | 90 (50.3) | 99 (55) |
| Income (SAR/month) (%) | n (%) | n (%) |
| Low (<5000) | 88 (49.16) | 90 (50) |
| Average (5000–10,000) | 41 (22.91) | 43 (23.89) |
| Moderate (10,001–15,000) | 30 (16.76) | 28 (15.56) |
| High (>15,000) | 20 (11.17) | 19 (10.55) |
| Education Level (%) | n (%) | n (%) |
| High school | 79 (44.13) | 80 (44.44) |
| Diploma | 14 (7.82) | 12 (6.67) |
| Graduate | 62 (34.64) | 66 (36.67) |
| Post-Graduate | 24 (13.41) | 22 (12.22) |
| Physical Activity (%) | n (%) | n (%) |
| Yes | 112 (62.6) | 108 (60) |
| No | 67 (37.4) | 72 (40) |
| Smoking or/and tobacco products (%) * | n (%) | n (%) |
| Yes | 120 (67) | 55 (31) |
| No | 59 (33) | 125 (69) |
| Supplements (%) $ ^ | n (%) | n (%) |
| Yes | 36 (20) | 42 (23) |
| No | 143 (80) | 138 (77) |
Table 1. Cont.
| Particulars | Men | Women |
|------------------------------------|--------------------------|---------------------------|
| Energy intake, mean (SD)\textsuperscript{*} | 1379.12 (242.34) | 1181.35 (227.09) |
| Total Daily fibre intake, mean (SD)\textsuperscript{*} | 12.44 (2.88) | 14.17 (3.09) |
| DASS-Stress score mean (SD) | 11.15 (9.61) | 12.86 (11.31) |
| DASS-Anxiety score mean (SD) | 11.25 (9.09) | 10.78 (9.78) |
| DASS-Depression score mean (SD) | 14.11 (10.31) | 12.32 (9.55) |
SAR: Saudi Arabia Riyal, * trend p-value indicates statistical significance < 0.05, \textsuperscript{1} from 24 dietary recall, \textsuperscript{2} supplements: minerals and vitamins, n; total number of participants.
3.2. Gender Differences in Consumption
Table 2 shows the frequency of consumption by men and women of each of the different food groups that contain fibre. There were significant differences in the intake of vegetables, bread and cereals, nuts and seeds, and legumes, but not fruit. In more detail, there were significant differences between men and women in terms of vegetable consumption (p < 0.05). A significantly greater percentage of men consumed low-to-moderate servings of vegetables (≤4 times/week) (72.6%), while 52.22% of women consumed a moderate-to-high servings of vegetables (≥once a day or 5 to 6 times per week), significantly more than the number of men who consumed moderate-to-high serving of vegetables (25.7%). In addition, a significantly greater percentage of women consumed low-to-moderate servings (≤4 servings/week) of bread, whole grains and cereals than men (women: 72.22%, men: 36.9%), albeit with men having a significantly moderate-to-higher consumption of bread, whole grains and cereals (≥once a day or 5 to 6 times per week) than women (men: 54.7%, women: 23.34%, p < 0.05). Additionally, men have a significantly greater moderate-to-high consumption of legumes than women (men: 44.13%, women: 35.56%, p < 0.05). However, a greater percentage of the study population, either men or women, consumed low-to-moderate servings of fruit (≤4 serving/week), with no significant differences between them (women: 69.4%, men: 67%, p > 0.05). Furthermore, a significantly higher percentage of women consumed moderate-to-high servings of nuts and seeds (≥once a day or 5 to 6 times per week) (54.44%), while a higher percentage of men consumed low-to-moderate servings of nuts and seeds (≤4 servings/week) (men: 49.2%, women: 25%, p < 0.05).
3.3. Relationship between Dietary Fibre Intake and Mood Status of the Study Population by Gender
Table 3 displays the logistic regression analysis of the significant relationship between mood status (stress, anxiety and depression) and a selection of various foods that are rich in fibre by gender, while controlling for potential confounding factors. See Table S2A&B (supplementary material) for the logistic regression analysis. In Table 3, women who experienced moderate (OR = 0.52, p = 0.025) to high (OR = 0.41, p = 0.006) stress levels were more likely to eat low-to-moderate servings of vegetables (≤4 servings) compared to unstressed women. The stressed men were likely to consume low-to-moderate servings of fruit (OR = 0.70, p = 0.017) or a very low serving of nuts and seeds (OR = 0.67, p = 0.049) (1–3 servings/month), or consumption total dietary fibre of ≤12 g per day (OR = 1.36, p = 0.033). Women who experienced mild levels of anxiety (OR = 0.60, p = 0.001) consumed low-to-moderate vegetable servings (≤4 serving/week), and more of those with mild-to-moderate anxiety consumed low-to-moderate servings of bread, whole grains and cereals (≤4 serving/week) than the non-anxious women (mild: OR = 0.65, p = 0.002, moderate: OR = 0.61, p = 0.011). Men who consumed low-to-moderate servings of vegetables (≤4 times per week) appeared to be more depressed (OR = 1.64, p = 0.038). Women who experienced moderate levels of depression were likely to consume low-to-moderate servings of nuts (≤4 serving/week) (OR = 0.81, p = 0.025), and a mild level of depression was associated with insufficient fibre intake per day (≤14 g; OR = 0.83, p = 0.043).
### Table 2. Frequency of fibre-rich food consumption according to gender.
| Fibre-Rich Food | Men | Women |
|-----------------------|------------------------------------|-------------------------------------|
| | n (%) | n (%) |
| *Vegetables* | | |
| No consumption or very low consumption | 3 (1.7%) | 2 (1.1%) |
| Low-to-moderate consumption | 130 (72.6%) | 84 (46.7%) |
| Moderate-to-high consumption | 46 (25.7%) | 94 (52.2%) |
| *Fruit* | | |
| No consumption or very low consumption | 10 (5.6%) | 5 (2.8%) |
| Low-to-moderate consumption | 120 (67%) | 125 (69.4%) |
| High consumption | 49 (27.4%) | 50 (27.8%) |
| *Bread, whole grains and cereals* | | |
| No consumption or very low consumption | 15 (8.4) | 8 (4.44) |
| Low-to-moderate consumption | 66 (36.9%) | 130 (72.22%) |
| Moderate-to-high consumption | 98 (54.7%) | 42 (23.34%) |
| *Nuts and seeds* | | |
| No consumption or very low consumption | 36 (20.1%) | 37 (20.56%) |
| Low-to-moderate consumption | 88 (49.2%) | 45 (25%) |
| Moderate-to-high consumption | 55 (30.7%) | 98 (54.44%) |
| *Legumes* | | |
| No consumption or very low consumption | 26 (14.53%) | 58 (32.22%) |
| Low-to-moderate consumption | 74 (41.34%) | 58 (32.22%) |
| Moderate-to-high consumption | 79 (44.13%) | 64 (35.56%) |
* trend p-value indicates statistical significance < 0.05.
### Table 3. Logistic regression analysis for significant relationship between fibre-rich food consumption and mood status among gender.
| Food Category | Stress Adj.OR (95%CI) | p-Value | Anxiety Adj.OR (95%CI) | p-Value | Depression Adj.OR (95%CI) | p-Value |
|--------------------------------|------------------------|---------|------------------------|---------|--------------------------|---------|
| Vegetables | 0.52 (0.04–0.69) | 0.025 | 0.60 (0.45–0.82) | 0.001 | 1.64 (1.03–2.62) | 0.038 |
| Fruit | 0.70 (0.01–1.41) | 0.017 | | | | |
| Cereals, bread, whole grains | 0.56 (0.39–0.81) | 0.002 | | | | |
| Nuts and seeds | 0.67 (0.45–1.99) | 0.049 | | | 0.81 (0.68–0.97) | 0.025 |
| Daily fibre intake * | 1.36 (1.02–1.79) | 0.03 | | | 0.83 (0.69–0.99) | 0.043 |
* female, † male, 1 mild effect, 2 moderate effect, 3 severe effect, 4 extremely severe effect, logistic regression with adjusted for BMI, smoking and energy intake, + obtained from 24 dietary recall, OR, odd ratio; CI, confidence interval.
### 4. Discussion
The present study investigated gender-based differences in dietary fibre intake and the prevalence and severity of negative mood statuses (stress, anxiety and depression) between men and women in Saudi Arabia. The study observed a significantly higher intake of dietary fibre in women compared to men $p < 0.05$, in particular, a higher intake of vegetables, nuts and seeds, and total fibre per day (14 g) in women, although neither gender’s fibre...
consumption met the recommended daily fibre intake in adults, which is 25 g per day for women and 30–38 g per day for men [14]. Another important finding was that men showed a higher intake of bread, whole grains, and cereals than women, whereas there was a higher consumption of legumes by both genders. There was a similar consumption of fruit by both genders. The outcomes showed that women who consumed vegetables in low-to-moderate servings (≤4 serving per week) experienced moderate-to-severe stress. A similar finding was reported by Stephen et al. [15], who found that vegetable consumption was lower among stressed female students than male students. Additionally, Fernstrand et al. [16] demonstrated that greater perceived stress was associated with decreased vegetable consumption. Moreover, women in the present study experienced mild-to-moderate anxiety levels with low-to-moderate intake of bread, whole grains and cereals of less than or equal to four times per week. Additionally, they experienced mild anxiety with low to moderate intake of vegetables of less than or equal to four servings per week. These results are similar to those of Abbassi-Ghanavati et al. [17], who found that a higher intake of vegetables and whole grains is associated with decreased levels of anxiety and depression.
The scores show that women experience moderate depression with a low-to-moderate intake of nuts and seeds (≤4 serving per week). This echoes a study conducted by Arab et al. [18], which concluded that depression scores significantly decrease among nut consumers compared to non-nut consumers.
Female participants experienced mild depression with the consumption of 14 g of fibre per day. Despite this being less than the recommended total fibre intake per day for women, 14 g of fibre daily still lowered the level of depression experienced, and this needs to be investigated further. In addition, Xu et al. [19] found that 21 g per day of dietary fibre intake lowered the risk and severity of depression. However, in the present study, men experienced extremely severe stress with a consumption of 12 g of fibre per day, and the level of stress could be lowered by increasing the amount of fibre per day to, for example, 14 g or 21 g, so this needs to be investigated further. Grunberg and Straub [20] found that stressed men ate less fibre than non-stressed men, which could illustrate a decreased intake of healthy food and fibre among stressed men. The present study observed no association between total dietary fibre intake and depression in men with 12 g of intake, in contrast to the association in women with 14 g, which was significant. Additionally, in terms of stress, an association was observed between dietary fibre intake (12 g) and extremely severe stress in men, which was not the case in women (14 g). This could lead to the following conclusion: daily consumption of at least 14 g of fibre could perhaps help to decrease the level of depression among women, but not stress. With men, the opposite is the case: daily consumption of at least 12 g of fibre is not enough to reduce the level of stress. Several studies have reported an inverse relationship between depression and high consumption of fibre-rich foods such as vegetables, legumes, fruit and nuts [21,22].
Dietary fibre intake in the present study ranged between 12 g and 14 g per day, highlighting a gap between the current intake levels of the study participants and the recommended levels (25–38 g/day) in all age groups and in both men and women [3]. Similar findings were reported in a previous study where dietary fibre intake was reported to be below the recommended levels in men and women [3]. The observed gender differences may be attributed to the consumption of fibre from different dietary sources. A common concern in dietary studies that administer self-report questionnaires is the issue of cautious or unconscious underestimation [23]. This, to some extent, might explain the observed extremely low fibre intake in both men and women. In contrast to the present findings, a recent study by Abassi et al. [24] did not report any significant differences in dietary fibre intake between men and women in Tunisia. However, the present findings agree with a previous study by Kiefer et al. [25], where females (children, adolescents and adults) were inclined to consume more dietary fibre than males. This could be attributed to the more health-conscious nature of women and their tendency to comply with dietary recommendations more than men [25]. However, again in contrast to the present findings, a study by
Bennett et al. [5] showed that men tend to have a higher fibre intake than women in the United Kingdom (UK).
A finding of the present study is that high consumption of vegetables, fruit, bread and cereals, nuts and seeds, and legumes was correlated with lower levels of stress, anxiety, and depression. These food groups are rich in fibre, omega-3 fatty acids, folate, tryptophan, magnesium, phytochemicals, and inositol. In fact, the full effects of fibre may not yet be recognized, and the overall effect is not attributable to it. Previous studies have documented a positive effect of these food groups on individuals’ mental well-being [26,27]. In addition, the present study observed that low consumption of vegetables, fruit, nuts, seeds and legumes was positively associated with stress, anxiety and depression. It is possible, therefore, that altered brain–gut interactions play a role in the mood status; for instance, changes in the psychological state of rodents after changes in their gut microbiota suggest the correlation of a depression-like state in humans with adverse changes in the gut microbiota [28,29]. The hypothesis that the consumption of fibre could affect the mood status seems to be a good fit given the relatively rapid effect of diet on mood disorders observed in humans [8], which follows a two-way interaction with the brain using neural, hormonal and inflammatory signalling [30].
Fibre-rich foods are considered to transform the gut microbiota and affect the brain function and mood status [8]. Remarkably, gender disparities in the impacts of dietary fibre intake on gut microbiota have been observed in humans, with a trend for larger dietary effects in men than in women. Additionally, susceptibility to mood disorders differs between the genders [31]. Hence, microbial differentiations could be the underlying reasons for gender differences in the relationship between dietary fibre intake and the mood status [3].
The present study has various strong points. First, this study was conducted with a representative sample of men and women covering a wide age range, allowing gender-based differences in dietary fibre intake to be examined. Second, the investigation of dietary fibre intake was based on the collection of an FFQ questionnaire and a 24 h dietary fibre assessment, which may ensure that the data collected are representative of fibre intake at the individual level. The dietary fibre intake information collected by the 24 h assessment approach is considered to improve the accuracy of fibre intake estimates in adults.
However, this study is not without limitations, and the present findings must be considered in light of the following. In this study, there were no laboratory assessments of dietary fibre intake. Assessment of the prevalence of depression, anxiety and stress was based on self-reporting, which might have led to recall bias and could necessitate a larger sample size. Given this, using another tool in addition to the DASS to assess the mood status might be more effective. Moreover, the cross-sectional nature of the present study does not indicate the causal effects and mechanisms underlying the potential effects of dietary fibre intake on depression and stress, and these need to be investigated in future studies. The limitations of the present study necessitate future research to further assess the potential effects of gender differences, especially in terms of fibre-rich food consumption and the real effect of fibre without an overlap with other nutrients. Although the present findings revealed that lower consumption of fibre-rich food items per day is associated with stress and depression, further studies are needed to determine the possible beneficial effect of specific amounts of fibre per day on the prevalence and severity of stress and depression. The integration of subjective assessment with objective assessment, including laboratory assessment of dietary fibre intake, is necessary to further explore its relationship with mood status.
Of interest in this study is the fact that gender-based differences in dietary fibre intake were noticeably associated with the prevalence of very severe stress in men and a mild level of depression in women during their adult years. These findings call for concerted dietary interventions aimed at improving nutrition and mood status for men and women, putting more emphasis on the quality of the fibre-rich foods consumed, in addition to their quantity, as this would lay the foundation for the empowerment of such interventions as
well as the soundness of people in the future. Furthermore, the present outcomes have also highlighted higher intakes of dietary fibre in women compared to men, thus highlighting the need for interventions within particular and clear contexts pointed toward advancing better dietary habits in the Saudi population.
5. Conclusions
Taken together, the findings from the present study show that women consumed more fibre than men, even though their consumption of fibre did not meet the recommended level. However, 14 g of fibre per day may help to lower the depression score to mild among women, while 12 g of fibre per day may not lower the degree of stress among men. Additionally, regular consumption of foods that are rich in fibre, moderate-to-high servings (more than four times per week) of vegetables, nuts and seeds, fruit, bread, cereals and legumes may contribute significantly to decreasing levels of depression, anxiety and stress in men and women. However, this study cannot base the effect of fibre-rich food only on fibre, but there may be a contribution of other nutrients to this effect. Despite the study limitations, this study has clarified and suggested the association between dietary fibre intake and the prevalence of depression, anxiety and stress in Saudi women and men, as well as the associated gender-based differences. These findings also highlight the importance of the sources of dietary fibre as a factor influencing mood disorders. Therefore, future studies should confirm the effects of different doses of fibre and also the effect of different types of dietary fibre from different sources on mood disorders.
Supplementary Materials: The following supporting information can be downloaded at: https://www.mdpi.com/article/10.3390/healthcare10040730/s1, Table S1: Logistic regression analysis for the relationship between fiber-rich food consumption and mood status among women-model1. Table S2 A & B: Logistic regression analysis for relationship between fibre-rich food consumption and mood status among gender.
Author Contributions: Conceptualization, M.H.A. and S.N.A.; methodology, M.H.A.; software, M.H.A.; formal analysis, M.H.A.; investigation, M.H.A. and S.N.A.; resources, M.H.A. and S.N.A.; data curation, M.H.A. and S.N.A.; writing—original draft preparation, M.H.A. and S.N.A.; writing—review and editing, M.H.A.; visualization, M.H.A. and S.N.A.; supervision, M.H.A.; project administration, M.H.A. All authors have read and agreed to the published version of the manuscript.
Funding: This research received no external funding.
Institutional Review Board Statement: The study was conducted in accordance with the Declaration of Helsinki and approved by the Taibah University no (CLN201806).
Informed Consent Statement: Written informed consent has been obtained from all participants to publish this paper.
Data Availability Statement: Not applicable.
Acknowledgments: The authors would like to thank all the participants and those who have helped in gathering the data.
Conflicts of Interest: The authors declare no conflict of interest.
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Experimental studies of a throughput of the distribution systems of planetary hydraulic motors
A Voloshina\textsuperscript{1,5}, A Panchenko\textsuperscript{1}, O Titova\textsuperscript{2}, V Pashchenko\textsuperscript{3} and A Zasiadko\textsuperscript{4}
\textsuperscript{1}Department of Mechatronic Systems and Transport Technologies, Dmytro Motorny Tavria State Agrotechnological University, B. Khmelnytsky ave. 18, Melitopol, Ukraine
\textsuperscript{2}Department of Foreign Languages, Dmytro Motorny Tavria State Agrotechnological University, B. Khmelnytsky ave. 18, Melitopol, Ukraine
\textsuperscript{3}Department of Tactics, National Academy of the National Guard of Ukraine Zakhysnykov, Ukrainy sq., 3, Kharkiv, Ukraine
\textsuperscript{4}Department Berdyansk college of the Tavria State Agrotechnological University, Eastern ave. 23, Berdyansk, Ukraine
\textsuperscript{5}Email: [email protected]
Abstract. As a result of the study, an experimental test bench was developed for testing high-torque hydraulic motors. A methodology for experimental studies of a unified series of planetary hydraulic motors has been developed. It has been established that an increase in the throughput of a hydraulic motor with a modernized distributed system makes it possible to increase the hydromechanical efficiency of the modernized hydraulic motor by 11 to 14\%, the volumetric efficiency by 2 to 4\%, and the overall efficiency by 7 to 9\%. The increase in the values of the hydromechanical, volumetric and overall efficiency of the modernized hydraulic motor explains the increase in the throughput of its distributed system. It has been established that the torque of the developed serial hydraulic motor is 300 to 325 min\(^{-1}\), which is a sign of the rigid characteristics of this hydraulic motor. The stability of the torque (within 1.5\%) developed by the modernized hydraulic motor 370 to 375 Н \cdot m in the frequency range of 75 to 450 min\(^{-1}\) is confirmed by its rigid characteristic.
1. Introduction
High-torque low-speed gerotor [1, 2], orbital [3] and planetary [4] hydraulic motors are most commonly used to drive active working bodies and running systems of road, construction, agricultural and other self-propelled equipment. One of the main units causing a decrease in the functional parameters of hydraulic motors is a working fluid distribution system that creates a rotating hydraulic field necessary for the movement of the inner rotor of these hydraulic machines [5, 6]. The main disadvantage of the distribution system is the fluctuations in the flow of the working fluid supplied to the hydraulic motor, caused by the unevenness of its throughput [6].
The throughput of the distribution system of the planetary hydraulic motor is understood as the total area of overlap of its working windows. Irrational design of the elements of the distribution system leads to fluctuations in the overlap area and a change in the output characteristics of the hydraulic motor as a whole, which is confirmed by parametric studies [5, 6]. Therefore, conducting experimental studies of planetary hydraulic motors in order to determine the effect of the throughput of their distribution systems on changing the functional parameters of planetary hydraulic motors is an
urgent task.
2. Analysis of recent studies and publications
A mechatronic system of active control of dynamic spatial positioning of the executive body is considered [7]. A method for designing hydraulic mechatronic systems with elements of multicriteria optimization has been developed, which makes it possible to design a mechatronic system with given output characteristics [8]. The dynamic model of the drive is proposed [9]. The dynamic processes occurring in mechatronic systems with planetary hydraulic motors are investigated in order to predict changes in their output characteristics [10]. The parameters of variation are substantiated, which determine the change in the output characteristics of the hydraulic motor, depending on the design features of its system of rotors and the distribution system. Regression equations are obtained that describe the change in the output characteristics of the hydraulic motor during operation, for a given range of changes in its operating parameters [11]. A methodology for experimental research and construction of control characteristics is proposed [12]. Experimental studies of mechatronic systems with volumetric hydraulic machines were not considered.
The conditions for static equilibrium of the mobile complex were established [13]. An engineering method for determining radial compliance is proposed, taking into account the radial clearance and contact deformations of parts [14]. Using nonlinear models and the method of analyzing the response surface, the parameters of thin-walled structures have been substantiated [15], studies have been carried out to develop adequate models for analyzing the response of thin-walled structures to a load [16]. The dependences of the contact pressure on the external forces that act on them [17] are considered, the distribution of contact pressures is determined [18], the regularities of the distribution of contact pressure are investigated [20]. Issues related to research in the design and operation of hydraulic machines with cycloidal rotors were not considered.
It is known [1, 3, 8, 11] that in mechatronic systems with a hydraulic drive, gerotor [1, 2], orbital [3, 5] and planetary [4, 6] hydraulic machines with cycloidal rotors are mainly used. The proposed theoretical method for predicting the characteristics of an engine with constant difference orbital piston engines [21]. Experiments have been carried out to confirm the theoretical model [22]. Numerical modeling, modeling and forecasting of the production depth were carried out, which as a result is compared with the results of experimental studies [23]. The implemented method for determining the reliability of a hydraulic motor by modeling changes in the technical state of internal and external rotors [24] analyzes the performance of the orbital engine and conduct experimental research [25]. A comprehensive study of a hydrostatic unit with a low speed of rotation of an orbital rotor in a hydrostatic transmission system is presented. Using the actual parametric values, the general dynamic model is confirmed experimentally [26]. Issues related to experimental study of planetary hydraulic machines were not considered.
Calculation formulas are proposed and a comparative assessment is carried out according to the criterion of the channel cross-section of a hydraulic machine with a planetary rotor with a central gear wheel in the shape of a wave and floating satellites [27]. The systematization and comparative analysis of the schemes of mechanisms of planetary rotary hydraulic machines [28]. Cavitation phenomena occurring in the working fluid distribution zone have been investigated [29]. Promising methods for the production and application of carbon nanoparticles in tribology [30] were reviewed, the results of tribosystems testing with the use of liquid crystal additives [31] are given, experimental studies are considered, taking into account the effect of an electrostatic field on the working fluid of a volumetric hydraulic drive [32]. The values of pressure loss, flow rate and velocity distribution over the cross-section of the pipeline in a straight section and in a turn have been determined [33]. A comparison of the use of the SST turbulence model taking into account the curvature of streamlines and flow rotation [34] is presented, the application of the RANS approach using the corrected SST turbulence model is considered, which allows one to determine all the main characteristics of the vortex flow [35]. A 3D model has been proposed that takes into account the dynamically changing volume of the working
fluid in the working chambers [36], mathematical expressions are given to assess the flow rate of the working fluid [37] in gerotor hydraulic machines. It should be noted that the operation of the rotors of a gerotor pump differs fundamentally from the operation of the rotors of a planetary (orbital) hydraulic motor. For functioning of the planetary hydraulic motor, a rotating hydraulic field of the working fluid created by the distribution system is required [6, 38]. The cyclic rotation of the hydraulic field depends on the number of working chambers formed by the external and internal rotors and is characterized by the kinematic diagram of the distribution system [6]. The kinematic diagrams of the distribution systems of planetary hydraulic motors have been substantiated [6], a technique has been developed for displacing the distribution windows of a movable distributor, which makes it possible to reduce fluctuations in the flow of the working fluid (throughput), and as a result, to improve the output characteristics of the planetary hydraulic motor [39]. The influence of the shape of distribution windows on the output characteristics of a planetary hydraulic motor, which can be made in the form of a segment [38], a circle [4] and a groove [40], has been investigated. Experimental studies of the throughput of the distribution system have not been carried out.
When carrying out parametric studies of the influence of the distribution system of the planetary hydraulic motor, a number of assumptions and limitations were made [4, 6, 38, 40]. Therefore, comparative experimental research of hydraulic motors with serial and modernized distribution systems is one of the most important and urgent tasks.
3. Statement of the objective and tasks of the study
To conduct experimental studies, in order to determine the influence of the throughput of the distribution system of the planetary hydraulic motor on the change in its functional parameters, it is necessary:
- to develop a test bench for testing high-torque low-speed planetary-type hydraulic motors;
- to develop a methodology for conducting study of the influence of the throughput of the distribution system of a planetary hydraulic motor on the change in its output characteristics experimental studies of the influence of the distribution system of a planetary hydraulic motor on the change in its output characteristics;
- to study the influence of the throughput of the distribution system of a planetary hydraulic motor on the change in its output characteristics.
4. The basic part of the study
Earlier parametric studies [4, 6, 39] determining the influence of the transmission capacity of the distribution system of a planetary hydraulic motor on the change in its functional parameters are associated with a number of assumptions and limitations. Therefore, in order to confirm and correct the previously obtained results of parametric studies, comparative bench tests of planetary hydraulic motors with serial and modernized distribution systems should be conducted.
The developed test bench for testing planetary hydraulic motors (Figure 1, a) consists of four main units: a pumping station (Figure 1, b), a loading device (Figure 1, c), a unit for measuring the flow rate and changing the direction of the working fluid flow (Figure 1, d) and the control panel (Figure 1, f). This test bench allows testing a family of unified series of planetary hydraulic motors with a power of 6.5; 11; 22 and 33 kW, respectively. The pumping station consists (Figure 1, b) of a frame with a tank for working fluid with a thermometer, an axial piston variable pump with a working volume of 89 cm$^3$ with a drive motor, a feed pump and three safety (overflow) valves. For the conditioning of the working fluid, the pumping station has two fine filters, two heat exchangers, two pressure gauges and shut-off valves.
The loading device (Figure 1, c) is designed to simulate the load on the hydraulic motor shaft by braking and is a powder brake placed on the frame together with the tested hydraulic motor. When measuring the output characteristics of the hydraulic motor under test, two pressure gauges are used to control the pressure and a tachometer with a pulse sensor to determine the angular velocity.
The unit for measuring the flow rate and changing the direction of the flow of the working fluid (Figure 1, d) is designed to measure the amount of working fluid passed through the hydraulic motor
and for reversing the activation of hydraulic motors during testing. It consists of a frame with two electrically controlled distributors, two calibrated axial piston hydraulic motors with tachometers and impulse sensors with discs, and two fine filters.
**Figure 1.** Experimental test bench for testing planetary hydraulic motors: a – general view; b – pumping station; c – load device; d – unit for measuring the flow rate and changing the direction of the flow of the working fluid; f – control panel.
The control panel (Figure 1, f) is designed to control the electrical elements of the test bench according to the corresponding algorithm: drive motors, flow distributors, tachometers, powder brakes, etc.
Test bench studies were carried out on a serial and modernized PRG-22 series hydraulic motors with a working volume of 160 cm³. The modernization of the hydraulic motor consisted in changing
the geometric and functional parameters of the movable and stationary distributors, other parts of the hydraulic motor remained serial. The studies were carried out for planetary hydraulic motors with a kinematic distribution system 7/6 [6]. The number of distribution windows of the movable distributor is 12 (6 working and 6 discharge windows), and the number of distribution ports of the fixed distributor is 14 (7 delivery ports and 7 drain windows). In the serial distribution system, 3 discharge windows are used as additional working ones, and the gap between the windows of the movable and fixed distributor is 0°51'. In the modernized distribution system of the hydraulic motor, 2 unloading windows are used as additional working ones, and the gap between the distribution windows is 0° [39].
The throughput of the distribution systems of the tested hydraulic motors was determined by the total flow area of the working windows of the system under consideration. For a serial hydraulic motor, the flow area of the working windows ranges from 222 to 226 mm², while the average area was 223 mm². For a modernized hydraulic motor, the flow area of the working windows is constant and equal to 226 mm².
The required value of the flow rate of the working fluid passing through the hydraulic motor is equal to 50, 70, 90 and 110 l/min, respectively, was set using a variable pump when the test hydraulic motor was idling (no load). The required load was set using the test bench brake in the range of 25...400 N·m with a step of 25 N·m.
The main factors that determine the change in the functional parameters of the planetary hydraulic motor in the study of the distribution system are: the rotational speed of the hydraulic motor shaft, the pressure difference and the gap between the distribution windows of the movable and fixed distributors [4, 6, 38, 40]. The study of changes in the functional parameters of the serial and modernized hydraulic motors was evaluated based on the results of comparative tests of these hydraulic motors.
The mechanical, volumetric and overall efficiency of the tested hydraulic motor was determined according to the standard method according to the results of measuring the pressure drop, torque, rotation frequency of the hydraulic motor shaft and the flow rate of the working fluid.
As a result of the research, the dependences of the efficiency of the tested hydraulic motor on the frequency of rotation of its shaft were determined (Figure 2). It has been established that the nature of the patterns of change in the efficiency of serial and modernized hydraulic motors in the entire range of change in rotational speeds is similar.
With an increase in the speed of the hydraulic motor shaft to 300 min⁻¹, the hydromechanical efficiency (Figure 2, a) of both hydraulic motors increases, taking the value 0.75 to 0.81 for the serial (curve 1) and 0.89 to 0.92 for the modernized (curve 2) hydraulic motors. The maximum value of the hydromechanical efficiency of both hydraulic motors is in the range of rotation frequencies of its shaft 150 to 450 min⁻¹. An increase in the rotation frequency of the hydraulic motor shaft to 670 min⁻¹ leads to a significant decrease in its hydromechanical efficiency to values of 0.65 for the serial and 0.75 for the modernized hydraulic motors. The hydromechanical efficiency of a hydraulic motor (Figure 2, a) with a modernized distribution system (curve 2) is 11 to 14% higher than that of a hydraulic motor with a serial distribution system (curve 1).
The volumetric efficiency of a hydraulic motor (Figure 2, b) with an upgraded distribution system (curve 2) is 2 to 4% higher than that of a hydraulic motor with a serial distribution system (curve 1) and remains practically unchanged over the entire range of speed variation.
The change in the overall efficiency from the rotational speed (Figure 2, s) has the same character as the dependence of the hydromechanical efficiency, which is explained by low volumetric losses. The overall efficiency of a hydraulic motor with a modernized distribution system (curve 2) is 7 to 9% higher than that of a hydraulic motor with a serial system distribution (curve 1).
The increase in the value of the hydromechanical, volumetric and overall efficiency of the modernized hydraulic motor is explained by the throughput of its distribution system.
Studies of changes in the output characteristics of a planetary hydraulic motor (Figure 3) have established that the nature of the change in torque depending on the rotation frequency (Figure 3, a) for serial and modernized hydraulic motors are similar. In the rotation frequency range from 75 to 550
min⁻¹, the torque developed by the serial hydraulic motor is 300 to 325 N·m (curve 1) and changes insignificantly (within 8%), which is a sign of the rigid characteristics of this hydraulic motor. The stability of the torque (within 1.5%) developed by the modernized hydraulic motor 370 to 375 N·m (curve 2) in the rotation frequency range of 75 to 450 min⁻¹ confirms its rigid characteristic. The stiffness of the characteristics of a hydraulic motor is understood as its ability to provide stable torque readings over a wide range of speed changes, especially at low rpm.
Figure 2. Dependence of efficiency on the frequency of rotation of the output shaft of the hydraulic motor at the nominal pressure: a – hydromechanical; b – volumetric; c – general; 1 – serial hydraulic motor; 2 – modernized hydraulic motor.
Figure 3. Change in the output characteristics of the planetary hydraulic motor: a – the dependence of the torque on the rotational speed of the output shaft of the hydraulic motor; b – dependence of the speed of rotation of the output shaft of the hydraulic motor on the flow rate of the working fluid; 1 – serial hydraulic motor; 2 – modernized hydraulic motor.
The increased stability of the torque developed by the modernized hydraulic motor and the 14% increase in the absolute value of the torque is explained by the rational design of the structure of the elements of the distribution system of this hydraulic motor.
Analysis of the dependence of the change in the speed of the hydraulic motor shaft on the flow rate of the working fluid (Figure 3, b) shows that these parameters, both for the serial (curve 1) and for the modernized (curve 2) hydraulic motors, are in a linear relationship and with an increase in the flow
rate of the working fluid increase. Modernization of the distribution system has practically no effect on the change in the considered dependencies.
Thus, studies of the influence of the distribution system of a planetary hydraulic motor on the change in its output characteristics have established that elimination of the pulsation of the working fluid flow and an increase in the throughput of a hydraulic motor with a modernized distribution system makes it possible to increase the hydromechanical efficiency of a modernized hydraulic motor by 11 to 14%, volumetric efficiency by 2 to 4%, and the total – by 7 to 9%.
5. Conclusions
As a result of the study, an experimental test bench was developed for testing high-torque hydraulic motors, which allows testing a family of unified series of planetary hydraulic motors with a power of 6.5; 11; 22 and 33 kW, respectively. A methodology for experimental studies of a unified series of planetary hydraulic motors has been developed.
The maximum value of the hydromechanical efficiency of both hydraulic motors is in the range of rotation frequencies of its shaft 150 to 450 min\(^{-1}\). The hydromechanical efficiency of a hydraulic motor with a modernized distribution system is 11 to 14% higher than that of a hydraulic motor with a serial distribution system.
The volumetric efficiency of a hydraulic motor with a modernized distribution system is 2 to 4% higher than that of a hydraulic motor with a serial distribution system and remains practically unchanged over the entire range of speed variation. The overall efficiency of a hydraulic motor with a modernized distribution system is 7 to 9% higher than that of a hydraulic motor with a serial distribution system. The increase in the values of the hydromechanical, volumetric and general efficiency of the modernized hydraulic motor is accounted for by the increase in the throughput of its distribution system.
Studies of changes in the output characteristics of a planetary hydraulic motor (Figure 3) have established that in the range of rotation frequencies of 75 to 550 min\(^{-1}\), the torque developed by a serial hydraulic motor is 300 to 325 Н⋅m and changes slightly (within 8%), which is a sign of a rigid characteristics of this hydraulic motor. The stability of the torque (within 1.5%) developed by the modernized hydraulic motor 370 to 375 Н⋅m in the range of rotation speeds of 75 ÷ 450 min\(^{-1}\) confirms its tough characteristic.
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Development of a Circular Oriented Bioprocess for Microbial Oil Production Using Diversified Mixed Confectionery Side-Streams
Sofia Tsakona 1, Aikaterini Papadaki 1,2,*©, Nikolaos Kopsahelis 2©, Vasiliki Kachrimanidou 3©, Seraphim Papanikolaou 1 and Apostolis Koutinas 1,*©
1 Department of Food Science and Human Nutrition, Agricultural University of Athens, Iera Odos 75, 11855 Athens, Greece
2 Department of Food Science and Technology, Ionian University, 28100 Argostoli, Greece
3 Department of Food and Nutritional Sciences, University of Reading, Reading RG6 6AD, UK
* Correspondence: [email protected] (A.P.); [email protected] (A.K.)
Received: 23 June 2019; Accepted: 29 July 2019; Published: 31 July 2019
Abstract: Diversified mixed confectionery waste streams were utilized in a two-stage bioprocess to formulate a nutrient-rich fermentation media for microbial oil production. Solid-state fermentation was conducted for the production of crude enzyme consortia to be subsequently applied in hydrolytic reactions to break down starch, disaccharides, and proteins into monosaccharides, amino acids, and peptides. Crude hydrolysates were evaluated in bioconversion processes using the red yeast Rhodosporidium toruloides DSM 4444 both in batch and fed-batch mode. Under nitrogen-limiting conditions, during fed-batch cultures, the concentration of microbial lipids reached 16.6–17 g·L⁻¹ with the intracellular content being more than 40% (w/w) in both hydrolysates applied. R. toruloides was able to metabolize mixed carbon sources without catabolite repression. The fatty acid profile of the produced lipids was altered based on the substrate employed in the bioconversion process. Microbial lipids were rich in polyunsaturated fatty acids, with oleic acid being the major fatty acid (61.7%, w/w). This study showed that mixed food side-streams could be valorized for the production of microbial oil with high unsaturation degree, pointing towards the potential to produce tailor-made lipids for specific food applications. Likewise, the proposed process conforms unequivocally to the principles of the circular economy, as the entire quantity of confectionery by-products are implemented to generate added-value compounds that will find applications in the same original industry, thus closing the loop.
Keywords: food-processing; circular economy; bioprocess development; Rhodosporidium toruloides; microbial oil; oleic acid
1. Introduction
The concept of the circular economy is emerging as a worldwide strategy to transit from the current linear economy model of production and consumption to efficient resource exploitation [1,2]. Within this framework, bio-economy encompasses the holistic valorization of renewable resources towards the development of biorefinery concepts and bioprocessing schemes to produce high value-added products. Evidently, microbial lipid production constitutes a research area of paramount significance. In particular, the production of highly unsaturated microbial lipids has gained the attention of many researchers, as they could be widely employed in functional food formulations, eliciting high nutritional composition [3].
Microbial lipids are secondary metabolites synthesized by oleaginous yeasts, fungi, and algae, exhibiting an intracellular accumulation of more than 20% [4]. Nonetheless, the industrial production...
of microbial oil impairs numerous impediments associated with the downstream separation of intracellular lipids, carbon source, and operating cost of the fermentative process. Actually, an economic assessment of large-scale fermentation of *R. toruloides* using glucose resulted in an estimated unitary production cost of $3.4·kg\(^{-1}\) at an annual production capacity of 10,000 t [5]. Hence, to establish an economically feasible and sustainable process, it is imperative to fulfill certain criteria, including high productivity, the development of biorefinery concepts that generate multiple high-value end-products, or a high-end market price of the formulated product. For instance, Kopsahelis et al. [6] presented a biorefinery process suggesting the simultaneous production of protein isolate, tartrates, ethanol, polyphenols, and microbial oil from wine lees and cheese whey. Ochsenreither et al. [3] speculated that commercialization could only be achieved via the manufacture of high-value products, such as the addition of polyunsaturated fatty acids in food applications. It is also unequivocal that the cost of the initial on-set material should be negligible; thus, waste and by-products streams exhibit ideal zero or low-cost substrates for the fermentative production of microbial oil.
Among the various oleaginous microorganisms, *Rhodosporidium* species have been widely investigated for microbial oil production via the valorization of an ample range of carbon sources, including glucose, glycerol, fructose, inulin, and xylose, among them [7]. Specifically, *R. toruloides* exhibits advantages over other oleaginous yeasts, including rapid proliferation and high lipid accumulation on low-cost resources [8]. Leiva-Candia et al. [9] reported a microbial oil production ranging 18.1–19.2 g·L\(^{-1}\) using different sunflower meal hydrolysates, deriving from the fractionation of sunflower meal, along with crude glycerol as fermentation supplements. Likewise, *R. toruloides* was recently employed for microbial oil production, using a nutrient supplement deriving from flour-rich waste streams (FRW) and wheat milling by-products [10]. Actually, authors proposed a process to contribute towards the valorization of the massive amounts of annual waste streams that occur from confectionery manufacturing industries and bakeries, or equally as discarded, damaged, or out of date products that return on site. Current waste treatments for these streams include animal feed, composting, or disposal in landfills. The process proposed as an alternative option by Tsakona et al. employed a two-stage bioprocess, where high final lipid concentrations and conversion yields were achieved [10,11]. However, only part of the confectionery waste streams (flour-rich streams) was evaluated in the fermentation process. Besides, it is a fact that the majority of studies, dealing with microbial lipids, have been mostly applied for biodiesel and biolubricants production [3,9,12]. Nevertheless, in the context of the circular economy, some recent studies focused on the valorization of food side-streams for the development of microbial oil-based food additives, such as wax esters [13] or directed specifically on the synthesis of high oleic acid microbial lipids [14,15]. Oleic acid resulted in more than the US $350 million in revenues for 2016, whereas a constant increase is projected based on the chemical industry applications [16]. On top of that, the possibility to modulate the fractions of oleic acid in the produced lipids would enable the production of tailor-made microbial lipids for specifically targeted applications [8]. It is thus imperative that in the frame of the circular economy, food waste streams should emerge as a potential feedstock for the synthesis of microbial lipids, targeting special food applications. For instance, oleogels deriving from high unsaturated vegetable oils are desirable for the substitution of trans fat content in foods [17], which has been recently banned by U.S. Food and Drug Administration (FDA) [18].
The aim of this study was the consolidated valorization of diversified confectionary waste streams, rich in mixed carbohydrates and other micronutrients for the fermentative production of microbial lipids using the oleaginous red yeast *R. toruloides*. The present study constitutes a more integrated extension of our previous work [10,11], that implemented only part of the confectionery waste streams (flour-rich waste streams) in the investigation during the hydrolysis and fermentation process. Nonetheless, it is crucial to configure a bioprocess that will exploit the full potential of the confectionery waste streams, to generate value-added products that can be reintroduced in the food supply chain under the context of zero waste and enhanced sustainability. More specifically, the present study targeted the valorization of all different confectionery waste streams (containing sucrose, starch, and lactose, among others), which
was not previously reported, towards the development of a holistic cascade bioprocess. The effect of the different confectionery side-streams was evaluated on the ability of *R. toruloides* to metabolize confectionary hydrolysates and shift the carbon flux towards lipid synthesis under nitrogen limitation conditions. The fatty acid profile was also evaluated, aiming to identify tailor-made food applications. Interestingly, valorization in a two-stage bioprocess of mixed confectionery waste streams, as described in the present study, entailed modifications in the composition of microbial oil. A higher degree of unsaturated lipids was obtained, advocating the potential to enhance the feasibility of the proposed scheme for further integration in existing facilities, targeting the development of high value-added products, which under the frame of the circular economy might be applied in food formulation within the initial industry.
2. Materials and Methods
2.1. Microorganisms
The fungal strain *Aspergillus awamori* 2B.361 U2/1 that was originally obtained from ABM Chemicals, Ltd. (Woodley, UK), and was kindly provided by Professor Colin Webb (University of Manchester, Manchester, UK), was employed for the production of crude enzyme consortia during solid-state fermentation (SSF). Storage, maintenance, sporulation, and inoculum preparation of the fungal strain *A. awamori* 2B.361 U2/1 have been previously reported by Tsakona et al. [11].
The oleaginous yeast strain *Rhodosporidium toruloides* DSM 4444 was used in the fermentative production of microbial oil. The strain was maintained at 4 °C, on slopes containing glucose (10 g·L⁻¹), yeast extract (10 g·L⁻¹), peptone (10 g·L⁻¹), and agar (2%, w/v). A liquid pre-culture with the same composition was prepared as fermentation inocula.
2.2. Raw Materials
Wheat-milling by-products containing (w/w) 12% starch, 20% protein, and 1.1% phosphorus were employed as the solid substrate in SSF with the fungal strain *A. awamori*. Mixed food for infants (MFI), mixed confectionery waste streams (MCWS), and mixed waste streams (MWS), obtained from different categories of confectionery waste streams, were all supplied by Jotis S.A. (Athens, Greece), a Greek confectionery industry. They were involved in enzymatic hydrolytic reactions, for the formulation of fermentative substrates and subsequent microbial oil production. MFI contained (w/w) 33% starch, 17% sucrose, and 27% lactose. MCWS demonstrated a similar composition (32.3% starch, 16% sucrose, 27% lactose) along with 7% (w/w) of lipids. Lipids were extracted with n-hexane (Sigma-Aldrich, St. Louis, MO, USA) for seven days before utilization. Likewise, the composition of FRW (84.8% starch, 7.3% protein) has been previously described [10]. MWS contained a ratio of 1:1:1 MFI:MCWS:FRW and presented a final composition of (w/w) 50% starch, 11% sucrose, and 18% lactose.
2.3. Solid-State Fermentation and Enzymatic Hydrolytic Experiments
SSFs were conducted in 250 mL Erlenmeyer flasks for the production of crude enzyme consortia, as described by Tsakona et al. [11]. Briefly, 5 g of wheat milling by-products were added in each flask and autoclaved at 121 °C for 20 min. Subsequently, the solids were inoculated with a fungal spore suspension (2 × 10⁶ spores·mL⁻¹) of *A. awamori* that was also used to adjust the moisture content of the substrate.
The fermented solids of five flasks (after 3 days of incubation at 30 °C) were suspended in 500 mL sterilized tap water and subsequently macerated using a kitchen blender. After centrifugation (9000×g for 10 min), individual hydrolysis of each waste stream (MFI, MCWS, or MWS) was performed by adding the supernatant in 1 L Duran bottles containing known quantities (50, 100, 150 g·L⁻¹) of MFI, MCWS, or MWS. The suspension was mixed employing magnetic stirrers, and enzymatic hydrolysis was carried out at 55 °C and uncontrolled pH conditions.
At the end of enzymatic hydrolysis, the produced hydrolysates were centrifuged (9000×g for 10 min), and the supernatant was filter-sterilized using a 0.2 μm filter unit (Polycap TM AS, Whatman Ltd., Maidstone, UK). The pH of the hydrolysate was adjusted to 6, which is optimum for yeast growth, using 5 M NaOH.
2.4. Microbial Oil Fermentations
Shake flask experiments were carried out in 250 mL Erlenmeyer flasks with a working volume of 50 mL, using commercial carbon sources. Carbon sources were selected based on the composition in the hydrolysates obtained after enzymatic reactions, as indicators of the yeast performance in these hydrolysates. More specifically, commercial glucose, sucrose, fructose, and galactose were individually evaluated for yeast proliferation and microbial oil accumulation by *R. toruloides*. Subsequently, shake flask cultivations were performed to study the potential of *R. toruloides* in the hydrolysates of the three waste streams, as described in Section 2.2. All flasks were inoculated with 10% (v/v) of a 24 h exponential pre-culture of *R. toruloides* and incubated at 27 °C in an orbital shaker (ZHWW – 211C Series Floor Model Incubator, Zhicheng, Shanghai, China) using an agitation rate of 180 rpm. The pH value was adjusted during fermentation using 5 M NaOH when needed. Fermentations were carried out in duplicates and the respective analyses in triplicates. Data presented are the mean values of those measurements.
Bioreactor fermentations were conducted in a 3 L bioreactor (New Brunswick Scientific Co., Edison, New Jersey, USA) with a working volume of 1.5 L. The temperature and aeration were set at 27 °C and 1.5 vvm, respectively, whereas pH value was automatically adjusted to 6 with 10 M NaOH. A 10% (v/v) inoculum was applied using a 24 h exponential pre-culture. The agitation rate was controlled in the range of 150–500 rpm to maintain the dissolved oxygen concentration at 20% of saturation.
Fermentations were conducted under fed-batch mode to evaluate the utilization of MFI and MCWS hydrolysates using an optimum carbon to Free Amino Nitrogen (FAN) ratio (C/FAN) based on the results presented by Tsakona et al. [10]. Carbon was calculated based on the carbon content of sugars, whereas the FAN corresponded to the nitrogen contained in the free amino groups of amino acids and peptides in the hydrolysate. The initial FAN concentration was 292–340 mg·L\(^{-1}\), whereas initial total sugar concentration was ~50 g·L\(^{-1}\). Fed-batch fermentation strategy was achieved by the periodic addition of a concentrated solution derived from each hydrolysate (70%, w/v). The feeding solution was added in the bioreactor under aseptic conditions to sustain microbial proliferation and microbial oil synthesis. Production of total dry weight (TDW) and lipid synthesis indicated the termination of the bioprocess, which lasted up to 120 h. Samples were withdrawn to assess sugar and nitrogen consumption along with biomass, lipid, and intracellular polysaccharides (IPS) concentration. Residual cell weight (RCW) was determined by subtracting the produced microbial oil (g·L\(^{-1}\)) from TDW (g·L\(^{-1}\)).
2.5. Analytical Methods
The analytical methods used in this study were previously described in detail by Tsakona et al. [11]. Briefly, FAN concentration was measured with the ninhydrin colorimetric method, whereas inorganic phosphorus (IP) concentration was analyzed by the ammonium molybdate spectrophotometric method. The concentration of sugars was quantified using a High-Performance Liquid Chromatography unit (Waters 600E, Waters, Milford, MA, USA) equipped with an Aminex HPX-87H column (300 mm × 7.8 mm, Bio-Rad, Hercules, CA, USA) and a differential refractometer (RI Waters 410). Operating conditions were as follows: sample volume 20 µL; mobile phase 0.005 M H\(_2\)SO\(_4\); flow rate 0.6 mL·min\(^{-1}\); column temperature 65 °C. TDW was measured by drying the yeast biomass at 105 °C for 24 h, and microbial oil (MO) was determined according to the method proposed by Folch et al. [19]. Following the disruption of dried yeast cell mass, the Folch solution, chloroform/methanol mixture at a ratio of 2:1 (v/v), was added to the cell debris. The suspension was centrifuged (9000 × g, 4 °C, 5 min), the solvent phase was collected, washed with 0.88% KCl (w/v), dried with anhydrous Na\(_2\)SO\(_4\), and evaporated under vacuum. The fatty acid profile of microbial oil was analyzed through the production of fatty acid methyl esters (FAME) following a two-step reaction with methanol using sodium methoxide (MeONa) and HCl as catalysts. FAME was analyzed by a Gas Chromatography Fisons 8060 (Fisons Instruments, Mainz, Germany) unit equipped with a chrompack column (60 m × 0.32 mm) and an FID detector. Helium was used as carrier gas (2 mL·min\(^{-1}\)). The analysis was carried out at 200 °C with the injector at 240 °C and the detector at 250 °C. The split ratio was 1:50, and the sample injection
volume was 1 μL. Peak identification was accomplished by comparison of retention times with those of a certified reference FAME mixture (Supelco 37 Component FAME mix, Sigma-Aldrich, St. Louis, MO, USA). Fatty acid data were expressed as the area percentage of FAME.
The concentration of IPS was calculated using a modified method, described by Liang et al. [20]. Briefly, 50 mg of TDW was treated with 20 mL HCl (2.5 M). Acidification of the suspension was performed at 100 °C for 30 min followed by neutralization to pH 7 with KOH. Samples were filtered (Whatman filter paper), analyzed via the 3,5-dinitrosalicylic acid assay, and IPS were expressed as glucose equivalents, as previously described [11].
3. Results and Discussion
3.1. Enzymatic Hydrolysis of Different Mixed Confectionery Waste Streams
In a previous study, Tsakona et al. presented the production of a nutrient-rich fermentation feedstock deriving from the hydrolysis of FRW using crude enzymatic extracts obtained via SSF with A. awamori on wheat milling by-products (WMB) [11]. In this study, a similar approach was employed to hydrolyze mixed and diversified confectionery waste streams, e.g., MFI, MCWS, MWS, therefore, exploiting all potential waste streams.
The aforementioned streams contain not only starch, compared to FRW, but also other sources of carbohydrates, e.g., sucrose and lactose. Thus, the study initially targeted the hydrolysis of all carbohydrate sources into their respective monomeric sugars, to be readily assimilated by microbial entities. Likewise, the hydrolysis of proteins into adequate quantities of amino acids and peptides that can be readily metabolized during a fermentation process was also of high importance. Table 1 presents the degree of hydrolysis of starch, sucrose, and lactose content of all applied waste streams (MFI, MCWS, and MWS). Conversion of starch to glucose reached more than 95% when an initial concentration of 50 g L⁻¹ of MFI was applied. The conversion yield of sucrose to glucose and fructose reached 79.4–91.9%, whereas a similar pattern of lactose conversion to glucose and galactose was observed (75.1–89.2%) for all initial MFI solid concentrations. Starch and sucrose hydrolysis yields of MCWS and MWS (91–96.9% and 78.4–92.1%, respectively) were similar to those of MFI, while lactose conversion yields ranged from 70.1–72.3% for MCWS, and from 73.8–88.9% for MWS. The final sugar composition of the MFI and MCWS hydrolysates presented similar composition. MFI was comprised of 73.4 ± 2.1% glucose, 10.5 ± 1% fructose, and 16.1 ± 2.4% galactose, whereas MCWS contained 74.0 ± 2.7% glucose, 11.1 ± 1.3% fructose, and 14.9 ± 1.6% galactose. MWS hydrolysate contained mainly glucose (83 ± 2.7%) and lower amounts of fructose (6.6 ± 0.7%) and galactose (10.4 ± 0.9%).
The fungal strain A. awamori is of high industrial importance for bioprocesses; hence, it has been widely evaluated, particularly, in solid-state fermentation for the production of hydrolytic enzymes [11,21–23]. Smaali et al. reported on the production of extracellular thermostable invertase during submerged cultures, triggered by the addition of sucrose (1%) [23]. Bertolin et al. studied the production of glucoamylase via SSF of A. awamori on wheat bran [24]. Grape pomace was employed as the sole substrate for the production of cellulase, xylanase, and pectinase with A. awamori 2B.361 U2/1 [25]. The authors reported cellulase activity up to 9.6 ± 0.76 IU/gds during the first 24 h of fermentation. Cellulases comprise three distinct categories, e.g., endo-1,4-β-glucanase, exo-1,4-β-D-glucanase, and β-glucosidase, cleaving the β-1.4 linkages in cellulose. McGhee et al. studied the cultivation of A. awamori on wheat bran to produce α-galactosidase and invertase [26]. The proliferation of two different Aspergillus strains, including A. awamori, on several agro-industrial by-products, were evaluated for the production of α-galactosidase [27]. Tsakona et al. [10,11] employed the same process to formulate fermentation supplements from FRW. In that case, the authors reported on the enzymatic hydrolysis of starch to glucose. Hence, the results obtained from our study are in accordance with previous studies, indicating that the crude enzymatic extracts produced after SSF contain the essential hydrolytic enzymes to break down polysaccharides and oлиgosaccharides present in MFI and MCWS to generate a rich supplement for bioconversion processes (Table 1).
Therefore, the novelty of the present work focuses on the enzymatic hydrolysis of mixed confectionery waste streams containing all sugars to generate the respective monomers. This will allow for the development of a more consolidated process to exploit all waste streams, under the frame of developing bioconversion processes that can integrate and fit into the circular economy concept.
| Waste Stream Concentration | Composition | MFI | MCWS | MWS |
|----------------------------|-------------|---------------|---------------|---------------|
| 50 g·L⁻¹ | Starch | 95.6 ± 0.42 | 96.9 ± 0.89 | 93.6 ± 0.89 |
| | Sucrose | 91.9 ± 1.48 | 90.9 ± 1.96 | 92.1 ± 0.67 |
| | Lactose | 89.2 ± 0.92 | 72.3 ± 2.75 | 88.9 ± 1.28 |
| 100 g·L⁻¹ | Starch | 93.4 ± 1.06 | 94.5 ± 0.85 | 91.3 ± 1.62 |
| | Sucrose | 83.9 ± 2.26 | 88.9 ± 1.02 | 83.6 ± 1.34 |
| | Lactose | 81.8 ± 3.54 | 71.3 ± 0.98 | 78.1 ± 0.71 |
| 150 g·L⁻¹ | Starch | 91 ± 1.63 | 93.6 ± 0.56 | 91 ± 0.99 |
| | Sucrose | 79.4 ± 2.19 | 84.2 ± 1.93 | 78.4 ± 1.59 |
| | Lactose | 75.1 ± 2.83 | 70.1 ± 1.63 | 73.8 ± 2.59 |
3.2. Shake Flask Fermentations for Microbial Oil Production
As demonstrated in Table 1, the high degree of hydrolysis in MFI entailed the formulation of hydrolysates rich in glucose, fructose, and galactose. The similar composition was obtained in the hydrolysates of MCWS and MWS (Table 1). Thus, the next step would target the consumption of these sugars sources for the proliferation and microbial oil synthesis by the strain *R. toruloides*. Experiments were initiated by the fermentation of pure commercial sources of each sugar using shake flasks, and the results are presented in Table 2. It can be easily seen that after 140 h, substrate consumption was terminated yielding 36–43% of intracellular microbial oil. These experiments were the preliminary step to ensure that *R. toruloides* could consume glucose, sucrose, fructose, and galactose, thus the potential to utilize the hydrolysates obtained from MFI, MCWS, and MSW.
| Substrate | Fermentation Time (h) | Consumed Substrate (g·L⁻¹) | TDW (g·L⁻¹) | MO (g·L⁻¹) | Oil Content (% w/w) |
|-----------|-----------------------|----------------------------|-------------|------------|---------------------|
| Glucose | 141 | 30 ± 0.3 | 9.4 ± 0.1 | 3.7 ± 0.3 | 39.3 ± 2.4 |
| Sucrose | 147 | 30 ± 0.2 | 10.5 ± 0.3 | 4.6 ± 0.3 | 43.8 ± 1.5 |
| Fructose | 147 | 29.4 ± 0.9 | 9.7 ± 0.4 | 3.5 ± 0.1 | 36.1 ± 0.9 |
| Galactose | 147 | 29.6 ± 0.6 | 9.1 ± 0.1 | 3.6 ± 0.1 | 39.6 ± 1.9 |
Hence, the next step employed the utilization of these hydrolysates as the sole fermentation supplements for lipid synthesis. Figure 1 illustrates the consumption of total sugars along with TDW and lipid production expressed in g·L⁻¹, using the three different hydrolysates (a: MFI, b: MCWS, c: MWS). In all cases, the initial total sugar concentration was in the range of 80–100 g·L⁻¹, whereas FAN concentration ranged from 197–243 mg·L⁻¹. Lipid synthesis started approximately after 44 h of fermentation, triggered by nitrogen depletion in the medium (Figure 1). One of the targets of these experiments was to also identify the better performing substrate as a fermentation feedstock. The hydrolysates from MFI and MCWS resulted in a maximum 42.6% and 52.9% intracellular content of lipids, respectively, whereas in the case of MWS hydrolysate, the microbial oil content did not exceed 37.5%. The highest oil productivity was achieved in the case of MCWS (0.077 g·L⁻¹·h⁻¹), followed by MFI (0.069 g·L⁻¹·h⁻¹) and MWS (0.054 g·L⁻¹·h⁻¹). Interestingly, *R. toruloides* presented higher specific
growth rate (0.28–0.29 h⁻¹) when MFI and MCWS were employed as substrates, as compared to MWS (0.12 h⁻¹). Notably, the consumption rate of total sugars was lower in the first hours of fermentation when MCWS hydrolysate was tested compared to MFI hydrolysate. More specifically, the consumption rate was 0.43 and 0.31 g·L⁻¹·h⁻¹ in the case of MFI and MCWS, respectively, at the early phase of the fermentation (44 h). Still, in all used substrates, the obtained conversion yield of lipids to TDW was more than 0.3 (g g⁻¹).
Figure 1. Concentration of sugars (●), free amino nitrogen (FAN) (■) and production of total dry weight (TDW) (□) and microbial lipids (○), during shake flask cultures of R. toruloides on (a) mixed food for infant (MFI) hydrolysates, (b) mixed confectionery waste streams (MCWS) hydrolysates, and (c) mixed waste streams (MWS) hydrolysates.
The strain *R. toruloides* constitutes an industrially important strain for the production of microbial lipids, carotenoids, and various enzymes [8]. Xu et al. reported the ample range of carbohydrates strains belonging to *Rhodotorula* species could consume, including glucose, fructose, xylose, arabinose, sucrose, starch, inulin, and glycerol [7]. In particular, for *R. toruloides*, the ability to synthesize lipids via cultivation on cassava starch, glucose, xylose, glycerol, and distillery wastewater has been well established [7].
So far, co-cultivation of *R. toruloides* was studied in the viewpoint of exploiting the hydrolysates obtained from lignocellulosic biomass, targeting either lipids or even carotenoids production [28,29]. Contradictive results have been reported based on the combination of substrates and the specificity of strains. For instance, Matsakas et al. demonstrated the parallel consumption of glucose and fructose using the strain *R. toruloides* CCT 0783 on dried sorghum stalks, achieving a final lipid concentration of 13.77 g·L⁻¹ [28]. On the other hand, the combination of glucose, xylose, and arabinose resulted in the utilization of xylose after glucose depletion, whereby arabinose was not metabolized [30]. The authors employed detoxified sugarcane bagasse hydrolysates, reaching a lipid production equal to 12.3 ± 0.5. Similarly, Martins et al. evaluated a carob pulp syrup for carotenoids production during fed-batch fermentation of *R. toruloides* NCYC 921, where they demonstrated that glucose was first metabolized, whereas sucrose was not consumed, thus indicating a growth-limiting factor [29]. Bommareddy et al. presented a reconstructed metabolic model, using genomic and proteomic approach, on cell growth and synthesis of triglycerides (TAG) on glycerol, glucose xylose, arabinose, and various combinations [31]. Fermentation of glycerol and glucose presented catabolite repression phenomena whereby causing the sequential consumption of glycerol after glucose.
Table 3 shows the fatty acid profile of *R. toruloides* lipids generated during shake flask cultures on commercial sugars (glucose, sucrose, fructose, and galactose). The major fatty acids were oleic (C18:1) and palmitic (C16:0), whereas lower quantities of stearic (C18:0) and linoleic (C18:2) acids were observed. Oleic and palmitic acids corresponded to more than 75% (w/w) of the total amount of fatty acids synthesized by *R. toruloides*. This is in accordance with the results reported by Tchakouteu et al. [32], whereby oleic and palmitic acid reached 76.7% of the total fraction of lipids produced. Slininger et al. reported that cultivation of *R. toruloides* NRRL Y-1091 using lignocellulosic hydrolysate resulted in 72.9% of oleic and palmitic [33], whereas in another study, *R. toruloides* Y4 reached 66.9%, after 134 h of fed-batch fermentation [34].
Table 3. Fatty acid composition of lipids produced during shake flask cultures of *R. toruloides* on commercial sugars (glucose, sucrose, fructose, galactose).
| Fermentation Time (h) | C14:0 | C16:0 | Δ9 C16:1 | C18:0 | Δ9 C18:1 | Δ9,12 C18:2 | Δ9,12,15 C18:3 |
|-----------------------|-------|-------|----------|-------|----------|-------------|----------------|
| | | | | | | | |
| Glucose | | | | | | | |
| 60 | 1.8 | 34 | 0.3 | 7.6 | 43.2 | 8.4 | 4.13 |
| 92 | 1.3 | 27.4 | 0.8 | 8 | 46.9 | 9.5 | 3.5 |
| 140 | 0.9 | 24.5 | 0.8 | 5.9 | 51.5 | 12.3 | 4 |
| Sucrose | | | | | | | |
| 23 | 1.9 | 34.7 | - | 7.9 | 42.8 | 8.6 | 4.1 |
| 103 | 1.2 | 27.1 | 0.8 | 8.5 | 48.9 | 9.7 | 3.7 |
| 147 | 0.9 | 24.9 | 0.8 | 6.1 | 50.7 | 12.4 | 4 |
| Fructose | | | | | | | |
| 45 | 1.6 | 28.1 | 1.1 | 7.5 | 46.8 | 10.9 | 2.7 |
| 103 | 1.4 | 27.9 | 0.7 | 7.9 | 48.7 | 9.5 | 3.6 |
| 147 | 0.9 | 24.5 | 0.9 | 5.7 | 51.5 | 12.3 | 3.7 |
| Galactose | | | | | | | |
| 24 | 1.2 | 26.2 | 0.9 | 6.8 | 45.3 | 11.1 | 2.7 |
| 105 | 1.6 | 27.5 | 0.7 | 7.5 | 49.7 | 8.9 | 3.8 |
| 140 | 0.9 | 24.9 | 0.9 | 6.8 | 50.3 | 11.3 | 4.6 |
Similarly, in our previous study using FRW hydrolysate during fed-batch bioreactor experiments, almost 80% of the total concentration of fatty acid corresponded to oleic and palmitic acid [10].
3.3. Fed-Batch Bioreactor Cultures Using MFI and MCWS Hydrolysates
One of the major targets of this study was to identify the potential of MFI, MCWS, and MWS hydrolysates as sole fermentation substrates for lipids production. Following the results from shake flask cultures, the next step employed the evaluation of the best performing substrates (MFI and MCSW) in bioreactor cultures.
Nitrogen limitation is known to induce de novo synthesis of lipids in oleaginous strains as it is a secondary activity, occurring while the carbon source is in excess [35,36]. Deficiency of nitrogen in the fermentation broth leads to the low activity of isocitrate dehydrogenase; thus, metabolic flux is directed to lipid overproduction [35,37]. This case is induced at high carbon to nitrogen (C/N) ratios, whereby biomass production is hindered, and the carbon source is channeled into lipogenesis [37].
In this study, the initial C/N ratio was selected following our previous work with *R. toruloides* and FRW hydrolysates [10], hence adjusted to ~70–80 g·g⁻¹. Figure 2a presents the time course consumption of total sugars (glucose, fructose, and galactose), along with FAN utilization, whereas in Figure 2b, the production of TDW, microbial lipids, and IPS are presented. Initial total sugar concentration was ~50 g·L⁻¹, with glucose being the main sugar, whereas fructose and galactose were present in low concentrations (5.4 and 6.4 g·L⁻¹, respectively). Intermittent additions of the feeding solution were performed, when sugars’ concentration was lower than 20 g·L⁻¹. Maximal concentration of microbial lipids was observed after 92 h of fermentation (16.6 g·L⁻¹) with an intracellular content of 43.3% (w/w) and a productivity of 0.18 L⁻¹·h⁻¹.
Similarly, Figure 3 depicts the results obtained when MCWS hydrolysate was evaluated by applying a fed-batch strategy. In this case, lipid production reached 17 g·L⁻¹ after 98 h, resulting in productivity of 0.17 g·L⁻¹·h⁻¹. The lipid content was 45.6% (w/w).
It is easily observed that when both MFI and MCWS hydrolysates were employed, FAN depletion from the media channeled carbon flux to lipid overproduction. This observation was also confirmed by the fact that RCW remained constant until the end of fermentation. It is also interesting to note that consumption of glucose, fructose, and galactose occurred at the same time in both cases, without indicating carbon catabolite repression phenomena in the presence of glucose. These results are in agreement with the results reported by Matsakas et al., where glucose and fructose were equally consumed [28].
Studies on the simultaneous consumption of carbon sources have been recently initiated, and significant work is undertaken on transcriptomic and proteomic levels to understand the metabolic network [31,38]. Bommareddy et al. presented a metabolic model of *R. toruloides* by using different carbon sources. When glucose was compared with glycerol during bioreactor fermentations, increased biomass was noted in the case of glucose, regardless of the final production of lipids, which was almost equal in both cases [31]. Following flux distribution analysis, the authors showed that when glucose comprised the sole carbon and energy source, 63% of NADPH derived from the pentose phosphate (PP) pathway, complimented by the cytosolic malic enzyme [31]. On the other hand, when glycerol alone was employed, NADPH was supplied by the cytosolic malic enzyme, indicating a reduction in PP pathway. Similarly, using the pentoses xylose and arabinose, high PP pathway was observed to meet the demand for NADPH uptake [31]. The same authors, further performed transcriptomics to investigate gene expression during the combined fermentation of glucose with glycerol [38]. Significant findings concerning the upregulation and downregulation of genes were presented, particularly during the phase of nitrogen starvation [38].
Similarly, in our previous study using FRW hydrolysate during fed-batch bioreactor experiments, almost 80% of the total concentration of fatty acid corresponded to oleic and palmitic acid [10].
3.3. Fed-Batch Bioreactor Cultures Using MFI and MCWS Hydrolysates
One of the major targets of this study was to identify the potential of MFI, MCWS, and MWS hydrolysates as sole fermentation substrates for lipids production. Following the results from shake flask cultures, the next step employed the evaluation of the best performing substrates (MFI and MCWS) in bioreactor cultures.
Nitrogen limitation is known to induce de novo synthesis of lipids in oleaginous strains as it is a secondary activity, occurring while the carbon source is in excess [35,36]. Deficiency of nitrogen in the fermentation broth leads to the low activity of isocitrate dehydrogenase; thus, metabolic flux is directed to lipid overproduction [35,37]. This case is induced at high carbon to nitrogen (C/N) ratios, whereby biomass production is hindered, and the carbon source is channeled into lipogenesis [37]. In this study, the initial C/N ratio was selected following our previous work with *R. toruloides* and FRW hydrolysates [10], hence adjusted to ~70–80 g·g$^{-1}$. Figure 2A presents the time course consumption of total sugars (glucose, fructose, and galactose), along with FAN utilization, whereas in Figure 2B, the production of TDW, microbial lipids, and IPS are presented. Initial total sugar concentration was ~50 g·L$^{-1}$, with glucose being the main sugar, whereas fructose and galactose were present in low concentrations (5.4 and 6.4 g·L$^{-1}$, respectively). Intermittent additions of the feeding solution were performed, when sugars’ concentration was lower than 20 g·L$^{-1}$. Maximal concentration of microbial lipids was observed after 92 h of fermentation (16.6 g·L$^{-1}$) with an intracellular content of 43.3% (w/w) and a productivity of 0.18 ·L$^{-1}$·h$^{-1}$.
Combination of glucose with glycerol entailed a diauxic growth; however, glycerol addition improved lipid synthesis. Wiebe et al. evaluated C5 and C6 sugars, particularly glucose, xylose, arabinose, and their combinations, during batch and fed-batch cultures. They stated that lipid production in the mixture was lower compared to individual application of glucose or xylose, regardless of the proportions of glucose and xylose in the mixture [39]. In another study, Easterling et al. used the oleaginous strain *R. glutinis* during fermentation of dextrose, xylose, and glycerol and their mixtures, demonstrating that mix substrate cultivations resulted in increased biomass production compared to individual carbon sources [40]. On top of that, the strain *R. toruloides* has been previously shown to produce IPS [11,32], which was also observed in this study (~1.2 g·L$^{-1}$). Analysis of IPS by HPLC at the end of the fermentation demonstrated that they were primarily (>60%) comprised of mannose and glucose and to a lesser extent of galactose and fructose.
**Figure 2.** (a) Concentration of glucose (●), fructose (□), galactose (◊), free amino nitrogen (FAN) (●) and (b) production of total dry weight (TDW) (□), microbial lipids (○), intracellular polysaccharides (IPS) (◊) during fed-batch bioreactor fermentations of *R. toruloides* on mixed food for infants (MFI) hydrolysates.
Similarly, Figure 3 depicts the results obtained when MCWS hydrolysate was evaluated by applying a fed-batch strategy. In this case, lipid production reached 17 g·L\(^{-1}\) after 98 h, resulting in a productivity of 0.17 g·L\(^{-1}\)·h\(^{-1}\). The lipid content was 45.6% (w/w).
Figure 3. (a) Concentration of glucose (○), fructose (□), galactose (◊), free amino nitrogen (FAN) (●) and (b) production of total dry weight (TDW) (□), microbial lipids (○), intracellular polysaccharides (IPS) (◊) during fed-batch bioreactor fermentations of *R. toruloides* on mixed confectionery waste streams (MCWS) hydrolysates.
Table 4 presents the fatty acid profile of the microbial lipids produced during fed-batch experiments using MFI and MCWS hydrolysates. As expected, oleic (C18:1), stearic (C18:0), palmitic (C16:0), and linoleic (C18:2) were the major fatty acids identified. Compared to FRW employed in our previous work [10], the proportions of the individual fatty acid were modified, an observation deriving probably by the different composition of the substrate. More specifically, oleic acid (C18:1) remained the major fatty acid produced; however, it was increased from approximately 52.5–61.4% when MFI and MCWS were used. When the latter substrates were employed, the fractions of palmitic acid (C16:0) and linoleic (C18:2) were significantly reduced, whereby the fractions of stearic acid (C18:0) increased almost 2-fold compared to FRW hydrolysates. Similarly, the fraction of palmitic acid was decreased when MFI and
MCWS were used in fed-batch experiments compared to shake flask cultures, where individual carbon sources were used. On the other hand, oleic acid was increased when MFI and MCWS were applied for lipid bioconversion. The differences found in fatty acid composition when different substrates (FRW, MFI, and MCWS) were employed may be attributed to their different sugar composition. In fact, FRW contains only glucose, whereas MFI and MCWS contain also fructose and galactose. The effect of substrate composition on the fatty acid profile of *R. toruloides* microbial oil has been highlighted also by previous studies [7,14]. Further research studies focused on proteomics and transcriptomics have demonstrated that gene expression and substrate specificity have a key role in lipid synthesis [41]. Specifically, Fillet et al. mentioned that the final chain length of the fatty acid relates to the substrate preference of the elongase 3-ketoacyl-CoA [42]. Furthermore, Zhu et al. pointed that the yield of polyunsaturated fatty acids depends on the number of an acyl carrier protein (ACP), which is part of the fatty acid synthase system, exhibiting a significant role in the chain-elongation process [36].
### Table 4. Fatty acid composition of plant-derived oils compared with the composition of the microbial lipids produced during fed-batch bioreactor cultures of *R. toruloides* using the hydrolysates from mixed food for infants (MFI) and mixed confectionery waste streams (MCWS).
| Oil Source | C14:0 | C16:0 | C16:1 | C18:0 | C18:1 | C18:2 | C18:3 | Reference |
|--------------|-------|-------|-------|-------|-------|-------|-------|-----------|
| Soybean | 6–10 | 0.1 | 2–5 | 20–24.9 | 50–60 | 4.3–11 | | [43–47] |
| Rapeseed | 2.8–14| 0.9–2 | 13.6–64.1 | 11.8–26 | 7.5–13.2 | | | [43–47] |
| Cottonseed | 27–28.7| – | 0.9–2 | 13–18 | 51–58 | 8 | | [43–47] |
| Sunflower | 4.6–6.4| 0.1 | 2.9–3.7 | 17–62.8 | 27.5–74 | 0.1–0.2 | | [43–47] |
| Palm oil | 36.7–44 | 0.1 | 5–6.6 | 3–46.1 | 8.6–11 | 0.3 | | [43–47] |
| Olive oil | <0.1 | 7.5–20 | 0.3–3.5 | 0.5–5 | 55–83 | 3.5–21.0 | ≤1.0 | [48] |
| FRW | 1.5 | 28.7 | 0.6 | 7.5 | 50.3 | 9.5 | 1.4 | [10] |
| MFI | 1.4 | 10.3 | 0.7 | 14.5 | 61.2 | 5.3 | 0.4 | This study|
| MCWS | 0.9 | 15.2 | 0.9 | 13.8 | 61.7 | 6.1 | 0.1 | | |
*FRW: flour-rich waste.*
The applied feeding strategy during fed-batch cultures, oxygen saturation, and primarily carbon source constitute key factors on the final profile analysis of TAGs produced. The effect of feeding strategy and dissolved oxygen was beyond the scope of the current study; thus, the emphasis was given on the carbon source. When FRW hydrolysates were used [10], unsaturated content was found to be 61.8%, a proportion that increased in both cases where MFI and MCWS were employed (72.1 and 69.7%, respectively). It is generally accepted that de novo synthesis of lipids in *R. toruloides* results mainly in unsaturated fatty acids (e.g., oleic and linoleic acid) [7]. Fei et al. used corn stover hydrolysates and reported that oleic acid (C18:1) was the major fatty acid produced in all applied strategies, followed by palmitic (C16:0) [49]. Wiebe et al. reported that stearic, linoleic, and palmitic fractions were affected in the presence of mixed carbon sources compared to pure glucose fermentation experiments, whereby xylose and arabinose addition induced an increase in C16:0 and C18:2 fatty acids [39]. Patel et al. noted that palmitic acid was not detected when glucose and fructose were used as fermentation sources with *R. kratochvilovae* HIMPA1 [50]. The presence of glucose and fructose led to increased monounsaturated fatty acids, whereas sucrose increased polyunsaturated fatty acids. Interestingly, Bommareddy et al. [31] showed a content of 57% in saturated fatty acids when glucose alone was employed, whereas, during shake flask cultures in our study, the corresponding amount reached approximately 37.6% (Table 3). This could be attributed to the conditions during fermentation (bioreactor compared to shaking flasks), thus indicating future research. Zeng et al. undertook the utilization of food waste hydrolysates containing glucose as the major carbon source during flask experiments, demonstrating that oleic (75.8%) was the predominant fatty acid, followed by palmitic, linoleic, and lower quantities of stearic [51]. As previously noted, oxygen in the fermentation medium is also crucial for the formulation of lipid fractions. Minkevich et al. also stated the variation between saturated and unsaturated fatty acid profile with oxygen limitation [52], whereby Bommareddy et al.
pointed the production of saturated fatty acids following un-controlled oxygen supply [31]. On the other hand, the provision of glycerol in the fermentation media resulted in increased saturated fractions. For instance, a combination of crude glycerol and sunflower meal hydrolysates [9] resulted in 43.1% of saturated fatty acids, whereas Signori et al. reported 42.2–42.4% of saturated content when pure and crude glycerol were used, respectively [53].
Previous studies on microbial oil production through bioconversion processes focus primarily to evaluate the lipids for biodiesel production through transesterification processes [54,55]. However, under the viewpoint of bio-economy transition, emphasis should be also given to novel applications of microbial lipids for the production of lipid-based products with improved quality and specific applications [13]. The production of food products with a limited amount of saturated fat has emerged to be of paramount importance for food industries during the last years. For instance, high unsaturated vegetable oils (i.e., soybean oil) are preferred for the production of oleogels, which are considered a healthier substitute for trans and saturated fats in food products [17]. Bharathiraja et al. reviewed the application of microbial lipids in food formulations, stating how they could replace plant-derived lipids (e.g., cocoa butter, palm oil) and further utilized as stabilizing and thickening agents, emulsifiers, and water-binding compounds [56]. Equally, given the high content of oleic acid in the produced lipids, it could be also used as a substitute for cocoa butter, based on the high content of unsaturated fatty acids.
Apart from texture, fatty acids can also regulate the aroma and flavor of specific types of food. Likewise, fatty acids can be implemented in pharmaceutical applications, and more specifically, to formulate fortified foods and/or beverages with polyunsaturated fatty acids, entailing possible health effects [56]. Concerning microbial lipids from R. toruloides, Papadaki et al. conducted a study on the valorization of yeast lipid derivatives to formulate bio-based wax esters through a two-stage biocatalysis reaction [57]. Implementation of molasses as fermentation supplement led to the production of 8.1 g·L\(^{-1}\) microbial oil, containing mainly oleic acid (51%), palmitic acid, and stearic acid. The generated oleogels, using olive oil as the base oil, successfully simulated commercial margarine, thus demonstrating their potential for future applications in spreadable fat-products [57]. It should be stressed that the results obtained in the present study highlight that the valorization of the whole confectionery waste streams through the proposed process enhance the feasibility for further integration in existing facilities. Likewise, the proposed scheme leads to the production of lipids with a higher degree of unsaturation, a result that could be exploited under the frame of the circular economy towards the development of high value-added products for targeted food formulations within the initial industry.
4. Conclusions
The potential of generating nutrient-rich fermentation supplements deriving from diversified confectionery waste streams has been well established. All the evaluated hydrolysates performed well both in shake flask cultures and fed-batch bioreactor cultivations using R. toruloides to produce microbial lipids. Implementation of mixed substrates containing glucose, fructose, and galactose did not affect the consumption rates, however, resulted in modifications in the fractions of fatty acids. The possibility to produce tailor-made microbial lipid fractions for the production of lipid-based products was also presented. A consolidated bioprocess previously developed to valorize mixed confectionery waste streams could be further expanded to also target future food applications of microbial lipids under the context of the bio-economy era.
Author Contributions: Conceptualization, N.K., S.P., and A.K.; Methodology, S.T., A.P., V.K., and N.K.; Investigation, S.T. and A.P.; Resources, S.T., A.P., and V.K.; Writing—Original Draft Preparation, S.T., A.P., and V.K.; Writing—Review and Editing, N.K., S.P., and A.K.; Supervision, N.K. and A.K.
Funding: This work is funded by the research project “NUTRI-FUEL” (09SYN-32-621), implemented within the National Strategic Reference Framework (NSRF) 2007–2013 and co-financed by National (Greek Ministry—General Secretariat of Research and Technology) and Community Funds (E.U.—European Social Fund).
Conflicts of Interest: The authors declare no conflict of interest.
Abbreviations: FRW—Flour-rich waste streams, SSF—Solid-state fermentation, MFI—Mixed food for infants, MCWS—Mixed confectionery waste streams, MWS—Mixed waste streams, FAN—Free amino nitrogen, TDW—Total dry weight, RCW—Residual cell weight, IP—Inorganic phosphorus, MO—Microbial oil, FAME—Fatty acid methyl esters, IPS—Intracellular polysaccharides, WMB—Wheat milling by-products, TAG—Triglycerides.
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Recent evolution of low reynolds number flyers: Paving way for Micro Air Vehicles (MAV)
Armaan Aditya¹, a) and Srinivas G. ², b)
¹U.G. Student, B.Tech (Aeronautical Engg), Manipal Institute of Technology, Manipal Academy of Higher Education, Manipal, Udupi, Karnataka - 576104, India.
²Assistant Professor (Sr Scale), Dept. of Aero & Auto Engg, Manipal Institute of Technology, Manipal Academy of Higher Education, Manipal, Udupi, Karnataka - 576104, India.
a) [email protected]
b)Corresponding author: [email protected]
Abstract. For a number of manmade and natural flyers the aerodynamics of low Reynolds number plays a crucial role. Active study of birds and insects is growing rapidly for development of Micro Air Vehicles (MAVs). MAVs are capable of performing tasks like surveillance, environmental monitoring and threat assessment in hostile environment. When compared to general civilian aircrafts MAVs fly at low Reynolds number regime of $10^5$ or lower. A considerable change of aerodynamic characteristics is seen between aircrafts that operate in low and high Reynolds number regimes. Low Reynolds number flyers are sensitive to wing gust and deformation because of being lightweight and operating at low speeds. The birds have nature’s finest locomotion system when it comes to maneuvering effectively through space. This review paper will assist further studies in the field of low Reynolds number flyers that can be used for future development on MAVs. A holistic review of past two decades of research work and studies done on low Reynolds number flyers has been presented in this paper. The Theoretical, Experimental and Numerical techniques followed by researchers have been highlighted so that the study on biological and manmade flyers can be systematically presented. It was found that researchers preferred Numerical and Experimental techniques while conducting aerodynamic analysis of low Reynolds number flyers. An attempt has been made in this paper to fill the research gap that is there in mimicking the flight of animals and thus developing man-made systems having higher efficiency.
1. Introduction
Biological flyers have been of interest to scientists and researchers for a long time because of the excellent flying capabilities possessed by them. Birds, bats and insects are capable of carrying out manoeuvring flight with extreme precision because of a number of design features that these have adapted to over millions of years of evolutionary process. Out of the 13000 species of birds and mammals nearly 10000 species can successfully fly. Out of those 10,000 flying species, 9000 are of birds and 1000 of bats. Man-made flyers like SR-71 have been able to attain speeds of about 32 body lengths per second. But a simple natural flyer like a pigeon travels at about 75 body lengths per second. It can be said that birds fly professionally but humans fly for commercial reasons.
This paper reviews various literature on studies that have been conducted to understand and evaluate the aerodynamics of biological flyers. An overview of different low Reynolds number flyers has been presented and their flight characteristics along with scaling laws have been discussed. The
developmental work on new technologies like Micro Air Vehicles (MAVs) and morphing structures has also been reviewed. The development of MAVs depends primarily on the study of aerodynamics of avian flight because MAVs cannot be developed by solely using classical aerodynamic theories. Initially the MAVs were defined as having a maximum size of 15 cm with a flight speed of around 10 m/s. Just like biological flyers MAVs operate at low Reynolds number regime of $10^5$ or lower. The development of MAVs depends on a number of factors like availability of materials, miniaturisation of power systems, communication system development etc. Different groups of MAVs have been developed that have fixed, rotary and flapping wings based on biological inspiration from flapping wing insect like dragonflies. The hovering technology has taken inspiration from hummingbirds which can hover effortlessly. The bat’s wing inspired researchers for development of actively morphing technologies because wings of bats have live tissue which allows them to change the wing properties like camber during flight itself. Development of flapping wing involves great challenges because of the structural movement and unsteady aerodynamics involved with it. The aerodynamics of fixed wing conventional airplanes is far simpler than that of flapping wings. The scaling laws show that with reduction in body size of flyers the flapping speed increases and a reduced wing loading is experienced. Birds, bats and insects employ different flapping styles in various flight modes like forward flight, hovering, reverse flight etc. As the flyer operates in low Reynolds number regime the wing of the flyer generates lower lift-to-drag ratio. Flapping wings help overcome several problems of low Reynolds number flight.
2. LITERATURE SURVEY
The ability of birds to fly has made them one of the most studied animals by biologists and researchers. Because of the capability to fly birds are able to find the most suitable climate and seasons for their reproduction and survival. In the search for appropriate climate for breeding birds migrate to distances more than 10,000 km by flying non-stop. The ability of birds to fly non-stop for such long distances surpasses the range and endurance of any man-made flying vehicle. Anders Hedenstrom [1] has aimed at reviewing the aerodynamic approach taken by researchers in order to study bird flight. With modifications in the aerodynamic theory of aircrafts, the study of bird flights has been possible so that obstacles related to animal flights can be addressed. With proper application of theory of flight to birds it has been possible for humans to calculate data related to bird flight like the range, moderate speed and the migration strategies adopted by birds. Without using aerodynamic theory it becomes impossible for ecologists to analyse the flapping flight of birds due to the physiological complications involved. For modelling bird flight aerodynamics there exists two major approaches as shown in figure 1. First method involves the calculation of local force that acts on a wing-strip and thus integrating the result obtained over the whole wingspan. The other approach is called ‘Vortex Wake’ method. Flapping wings tend to disturb the surrounding air thus Impulse of the wake and momentum change have an impact on the aerodynamic force, is made use of by the vortex wake method. Thus lift and drag can be calculated by using topology and kinetic energy stored in the wake of flying bird.
![Figure 1. To study aerodynamic force on birds two approaches were taken. (a) Here aerodynamic forces were calculated for thin wing sections. (b) Here aerodynamic force calculation was done using wake properties [1].](image-url)
For small birds having rounded and low aspect ratio wings, the most common form of flight is intermittent bounds flight. Intermittent flight involves phases of flapping mixed with flexed-wing bounds. In flexed-wing bounds the wings are kept motionless and flexed against the body. But small birds having pointed high aspect ratio wings carry out intermittent bounds along with glides whenever required. During glides the wings are extended. It has been observed that as the mass of birds increases the use of intermittent bounds decreases. In general for small birds, flap-bounding is a commonly used style. In flap-bounding flapping phases are in alternate with flexed-wing bounds. The reason for flap-bounding to be a common flight style is the body lift. For separately studying the importance of body and tail in lift and drag Bret W. Tobalske et al [2] made use of Particle Image Velocimetry (PIV). The bird taken into consideration was zebra finch and its wake properties were studied using PIV experiment when flying at 6-10 m/s. The air velocity was kept between 2-12 m/s when specimens were used. The body angle of specimens varied from -15 to 50 degrees. For conducting the experiment five live zebra finch and four specimens were used. The whole set of experiments was performed in a variable speed wind tunnel.
Balajee Ramakrishnananda et al [3] aims at applying the principles of aerodynamics for conducting physical animation of bird flight. For animating the forward flight of birds a physical model has been described and an initial condition was taken. Initially only that motion was considered in which the coordination between the two wings of a bird was symmetric. It was assumed that no sideward component of the wind is coming into play. Balajee Ramakrishnananda et al developed three approaches for doing the physical animation. After changing various geometric parameters of the wing and varying the airfoil cross section, the wing of a bird was generated. Various motions of the wing were taken as functions of time. Aerodynamic and gravitational force distribution acting on the wings were used in order to predict the bird’s trajectory during flight. The three motions that birds perform are flapping, twisting motion and lead-lag. Newton’s laws of motions were applicable for the basic equations of bird flight also. Now for decreasing the time taken for computation two assumptions were made. One is that the induced velocity was neglected and the other is that quasisteady assumption was taken while analysing the flow. In order to verify the capability and working of the system animation sequences were made for different phases of flight.
Bats are flying animals having unique capabilities that distinguish them greatly from the other flying animals like the birds and insects. Bat wings are compliant and they have an echolocation sensory system that gives them several advantages over the birds and insects. The aerodynamics of a flying bat is greatly influenced by the echolocation capability that allows the bat to fly in during night also. The oldest bat fossil found dates 55 million years back. Since that time the body structure of bats have diversified to adapt to different ecological conditions of the surroundings. The bat wings have various sizes and vary from short to broad sizes. Short wings allow bats to fly in small places while the species that live in open regions have broad wings. The bat airframe is different from other flying species of animals. The natural structure of the wing surface is unique in bats. In other flying animals like birds the wing is made up of dead skin thus limiting the ability of the birds to control the shape of the wing. On the other hand the bat wings are made up of live skin that stretches from the elongated arms. The skin in a bat’s wing is 4-10 times thinner compared to wings of other animals and also the wing bones are light weight. The overall weight of a bat wing is considerably less than expected. The skin on the wing of bats has several properties like being made up of elastic fibers, having sensors and better compliance. The camber of the bats wings is controlled by the intrinsic muscles which is not joined to any of the bones. Anders Hedenstrom et al[4] have reviewed that the intrinsic muscles are active during certain phases of flight which improves the aerodynamic performance of the bats. Interestingly the efforts of humans to create morphing aircraft structures have not yielded any fruitful results but bats have been using morphing technology for a long time. Bats have the morphing ability because of the fact that the wings are stretched by the fingers thus giving them the ability to vary the shape of wing. Because of the fingers the wing can be turned to various degrees and also the wing area
can be changes thus taking the shape whichever best suites the flight conditions. It has been found by researchers that for slow flights where the lift requirement is high the wings have larger surface area and higher camber. The mechanism that gives the wing stiff leading edges is called Norberg mechanism.
Today one of the major challenges in aviation sector is to reduce the fuel consumption done by aircrafts because the fossil fuel reserves are depleting very rapidly. The fuel consumption can be significantly reduced by reducing the drag during flight. For reducing the drag a number of approaches have been proposed by researchers for a long time as the reduction of surface and skin friction drag is essential to reduce fuel consumption. The importance of drag reduction is such that even natural creatures have evolved over the time to reduce the drag. In case of shark, the whole body is covered with micro-riblets which lead to significant reduction in drag. This is called “shark skin effect”. It was observed that these riblets over the body of shark lead to around 8% reduction in fluid drag. Similar to sharks birds have evolved over time to reduce the air drag during flight. The streamlined shape of birds and the presence of hollow shaft of feathers are evidence of the evolution of bird structure over thousands of years. In birds the presence of herringbone riblets of feathers has substantial role in drag reduction while flying. In feathers of birds due to the perfect linking of barbs the herringbone riblets are able to align along the shafts of each feather thus reducing the drag considerably. Huawei chen et al [5] have conducted Scanning Electron Microscope(SEM) analysis of microstructures of secondary feathers of pigeons and thus obtained structural parameters by statistical methods. Huawei chen et al [5] have proposed the biomimetic herringbone riblets having narrow smooth edges for getting surface drag reduction.
While in a gliding flight the bird wings show a dihedral configuration as shown in figure 2. The dihedral is in the shape of a V-attitude. It is possible for the birds to alter and vary the dihedral of their wing thus having an effect on their flight performance. By varying the dihedral an effect on lateral-directional stability is also seen. The amount of dihedral shown by different birds varies greatly. Some birds create small V-attitudes and only in certain portions, like outer, of the wing dihedral is present. When the V-attitude angle made by the bird is in downward direction it is referred to as anhedral. But there are birds like herons, pigeons which show very large values of V-attitude angles. The reason for exhibiting large values of dihedral may be related to efficient manoeuvres and improved stability during flight. Also it has been seen that while gliding at low speeds extremely large values of V-attitude angles are used by birds. Birds that exhibit large dihedral are also seen to have rotary oscillations in the roll axis. To study the aerodynamics of bird wings having large dihedral it is important to develop sophisticated aerodynamic methods. It becomes difficult to analyse the aerodynamics of large dihedral in wings because of the high V-attitude angles which produce a 3D flow field. The 3D flow field is a result of the mutual interference between both the wing halves in case of large dihedral. Gottfried sach et al [6] have given an aerodynamic method that can tackle with the problems in analysing high dihedral of wings. Using the proposed method it will be possible to study large dihedral bird wings and aerodynamic data can be generated for such wings. Large dihedrals were found to have substantial impact on the flight of a bird and significant change in the lift and drag characteristics of birds having large dihedral wings was seen.
Designs inspired from nature have been used for long time for constructing air vehicles. Most of the designs being used today have been inspired from nature because nature finds the most efficient designs that can be made. Inspite of putting in best efforts to mimic nature’s best flyers the man-made air vehicles have hardly attained the effectiveness and agility of natural flyers. It is well known fact that the body structures of all the species on earth have evolved over millions of years of evolution. By the way of evolution nature establishes the law of survival of the fittest. The process of evolution of any species gets affected by a number of factors including physical restraints like camouflage for protection from predators, mating etc. One feature that has remained same in all natural flyers over the years of evolution is the use flapping wings for flight. The reason for flapping wings to be used by most of natural flying animals can be accounted to the low Reynolds number effect. Natural flyers fly in low Reynolds number region thus the phenomena of unsteady aerodynamics and viscous forces need to be considered as they affect bird flight. Benefit of flapping wing is that they have the ability to generate additional aerodynamics force for flight via unsteady flow mechanism. Aspect Ratio (AR) plays a major role on the performance of flapping wings. More lift is produced with wings of high AR. Jua-Jiang Fu et al aims to study the effects on aerodynamics of natural flyers due to the structural traits of their body especially wings. For the experiment rectangular wings having AR 1, 2 and 4 were chosen that performed at their wingtips hovering sinusoidal kinematics. Results of the experiments conducted showed that the AR had no effect on the values of force coefficients.
The aerodynamics characteristics of a bat differ greatly from that of birds and insects. This difference is mainly because of the difference in the body structure of bats and other flying animals. In order to generate high aerodynamic forces, the wing of a bat undergoes complex deformations and this makes the flight features of bats different from that of birds and insects. Creating camber along the chordwise direction, twisting of the wing from root to tip, variation of wing area etc. are some of the actively morphing techniques that bats use. It was found that twisting of the wing and cambering in bat wings have effect on the high thrust and lift generation respectively. During flight of a bat the overall wing morphing leads to creation of maximum lift and thrust during the downstroke only. During an upstroke negligible amount of thrust and lift forces are generated. The ability of bat wings to change its area and bend results in amplification of positive force in a downstroke and reducing the negative forces for an upstroke. When considering flight of birds and insects wing deformations are neglected while studying mechanisms for aerodynamic force generation. Wing deformation is a major mechanism for aerodynamic force generation in bat flight and hence cannot be neglected as in case of other flying animals. Bat is one of the few species of flying animals which uses new mechanisms along with flapping wings and hence bat flight attracts a lot of attention from researchers and scientists. Yonglian Yu et al [8] used several morphing models and flapping models to compare the aerodynamic forces generated by them. It was found that a twisting wing increases the lift along with decrease in the fluctuations for an entire stroke. The cambering wing has the ability to significantly increase the lift generated.
The origin of avian flight has been debated for long because of lack of critical information like traditional fossils which are required for documenting the origins of avian flight. The study of fossil remains of extinct organisms has been the only way to study the origin of flight. Researchers started debating about the origin of birds in 1861 after a skeleton of *Archaeopteryx* was found in Germany. After obtaining data from hundreds of preserved fossils of small coelurosaurids and birds it was suggested that the beginning of avian flight was from trees (tree-down theory) and not ground (ground-up theory). The fossils discovered so far show that adaptations have taken place that are necessary in order to enable wing-assisted climbing on trees. By studying traditional fossils Sankar Chatterjee et al [9] have been able to identify six stages of evolution of avian flight. These include arboreal leaping, parachuting, monoplane gliding, undulating flight, and manoeuvring flapping flight. It has been proposed that during arboreal life brain enlargement took place along with an increase in visual activity leading to development of more sophisticated vision. Sankar Chatterjee et al have developed a computer model for simulating flight performance of protobirds that will help in supporting the arguments for evolutionary pathways. The emergence of powered flight in birds has been a key adaptation for birds. Flying requires relatively less energy as compared to walking and running. Flying helped birds in escaping predators and allowed them to explore new resources and seasons thus making them more versatile than other dinosaurs that walked on earth.
A number of species of flying birds exist and every species have their own flight style. Medium to large birds like pigeons, swans etc. fly with their wings continuously flapping and have nearly constant frequency, amplitude and flying speed. Other varieties of small birds follow intermittent flight strategies like ‘bounding’. Bounding refers to quick, high-amplitude periods of flapping interspersed with bounds. While carrying out bounding flight the wings remain firmly stuck to bird’s body. Small birds like woodpeckers and little owls generally carry out bounding flight. But it is not necessary for small birds to bound in order to fly and many small birds never bound. Birds of medium and large size fly using a different intermittent flight style known as ‘flap-glide’. In flap-glide, during periods between flapping the body of bird gets supported by outstretched gliding wings. Flap-glide has been used as a characteristic flight style by predator birds like eagles. During normal direct, level flight also eagles use flap-glide. Again it is not necessary for all large birds to use flap-glide as can be seen in the case of geese and swans which flap continuously while in air. In general it has been seen that aerodynamically economical flights are steady and levelled. But in many small birds it was observed that flapping and bounding styles of flight are far from being aerodynamically or mechanically optimum. Also flap-glide style when used for cruising flight doesn’t show aerodynamic efficiency. James Richard Usherwood[10] aims at considering cost of muscle activation in terms of physiological cost. Also a wide range of aerodynamic and geometric constraints have been considered by James Richard Usherwood[10] to account for energetic advantages. It was observed that in small birds that use bounding have to experience high costs due to activation of muscle for power while contracting. On the other hand the strategy adopted by flap-gliding birds reduces the physiological cost of work.
It has been proved by scientists that bumblebees do not produce sufficient lift from their wings needed to support their weight. As the lift generated is less than required, technically bumblebees should not fly. But on the contrary, bumblebees fly effortlessly in nature thus giving rise to a new set of controversies. There are many such insects like bumblebees which theoretically don’t produce enough lift to fly but they do fly. This makes researchers question the effectiveness of conventional aerodynamic theory in predicting the lift force of these insects. In the case of bird flight quasi-steady assumption is valid and works effectively. For insects the quasi-steady assumption fails and needs to be discarded because of constraints in its application. For example in an insect if the value of lift coefficient, that is needed to provide sufficient lift, is greater than lift coefficient value for normal airfoil then quasi-steady assumption is discarded. Further for applying quasi-steady assumption it is required that the wing travels in air a distance equal to a few wing chords. Hence, conventional
aerodynamic theory is rejected in case of flight analysis of most insects. For a flapping hawkmoth and a mechanical insect, Anders Hedenstrom[11] studied and compared flow visualisation around their wings. The results obtained explain the reason behind the ability of most of the insects to stay airborne. Novel unsteady mechanisms were found to satisfactorily explain the insect flight. In case of flapping wings the induced downward has fluctuating nature and this is referred to as unsteady mechanisms.
For a normal thin wing kept in an incompressible flow the lift slope coefficient is \(2\pi\). For this wing the position of Aerodynamic Center (AC) is calculated to be at the quarter-chord point. These results for a thin wing are calculated after making a suitable assumption that the thin wing in consideration is impermeable. But in nature not all wings are necessarily impermeable like the bird wing. In a bird wing the aft portion is made up of feathers and thus becomes permeable to air. Earlier aircrafts also used to have wings having unpainted paper over them thus making them permeable surfaces. Gil losilevskii[12] studies the effects of permeability of a wing surface like the position of AC in permeable wing surface etc. For experiments Gil losilevskii[12] considers a thin wing section, kept in steady incompressible fluid flow, made up of impermeable forward portion and having permeable aft region. Values of coefficient of lift and pitching-moment (\(C_L\) and \(C_M\)) of this wing are found using closed-form relations. The results obtained show that with increase in the permeability the value of lift slope coefficient decreases. The AC for the wing in consideration changes its conventional position from quarter-chord point of wing to quarter-chord point of forward part. If the forward part has width less than half the chord then AC first goes backward and then moves to the forward portion.
Hao Liu [13] aims to carry out rigorous and integrated modelling of flapping flight of insects for simulation. The natural flyers like insects perform flapping wing style because it helps them create both lift and thrust required for staying aloft and moving forward respectively. Flapping allows insects to carry out amazing manoeuvres along with periods of rapid acceleration and deceleration. Insect flight is generally carried out at moderate Reynolds Number having unsteady motions due to large vortex structures and flexible-wing structures. A general conclusion about the insect flight is that insects make use of high-lift, unsteady aerodynamic mechanisms resulting from formation of complex vortices. A versatile method was followed by Hao Liu[13] that integrates modelling of realistic flapping wing, realistic wing-body morphology and unsteady flight aerodynamics of insects. The insect flight simulator was validated by considering three insects that perform hovering flight. The insects were hawkmoth, honeybee and fruitfly and these were tested for Reynolds number ranging from order of \(10^2\) to \(10^4\).
Birds fly using different flight styles depending on the conditions of surrounding, need and the path they have to follow. Gliding, soaring and flapping are a few styles that the birds commonly use. In gliding the bird keeps its wing held out to the side of body and no flapping takes place. This flight is similar to a fixed-wing flight. In soaring height of the bird remains constant with respect to the ground. During soaring the bird uses rising air current in order to climb without even flapping the wings. Flapping is the most common style which we see in birds and it involves a downstroke and an upstroke. During downstroke most of the required lift is produces while in upstroke very little or negligible thrust is produced. Mehdi ghommem et al [14] investigates for two birds namely the Giant Petrel and Dove Prion the effect of wing morphing on the flight dynamics. The experiment is carried by flow simulation over rigid and morphing wings. The simulation results of rigid flapping wings show that for generating sufficient lift the wing root of the bird should be kept at a particular angle of attack. It has been observed that birds use active wing morphing techniques like twisting and bending in order to considerably increase the thrust produced. Hence wing morphing helps in increasing the amount of thrust generated. For calculating the aerodynamic power and forces 3D Unsteady Vortex Lattice Method was used for simulating flow over the flapping wings in consideration.
Among vertebrates the maximum amount of O₂ requirement has been shown by the flight muscles of hummingbird. The flight muscles of a humming bird are large when compared to flight muscles of other birds. In a humming bird the pectoral muscles (small and large) account for around 25% to 30% of body weight. In other birds the pectoral muscles account for a maximum of 17% of body weight. The down-stroke wing depressor M. pectoralis generates maximum amount of power for flight. The pectoral muscles of hummingbird possess high aerobic capacity. In case of hummingbird critical structural determinant for supplying O₂ are the capillary-to-fibre geometrical relations. The volume of capillary and the surface available for exchange depends on the capillary length per fibre volume. The O₂ flux rates are determined by the size of the capillary-to-fiber interface. O. Mathieu-Costello et al [15] conducted investigations on the structural characteristics for high O₂ flux in case of humming birds. The hummingbird’s pectoralis and supracoracoideus muscles were prepared for electron microscopy and then analysis was conducted for morphometry. It was found that the capillary-to-fiber interface was high in the muscles.
Vast number of computational and experimental research work has been conducted on the insect flight. The failure of conventional aerodynamic theory i.e. the Kutta-Joukowski theorem to explain the flight of insect has already been proved. The insect flight has been an intriguing subject of research because of the large amount of lift that the small wings of an insect produce. The motion while carrying out normal hovering flight consists of nearly constant mid-stroke translational velocity and wing rotation near wing reversal. Unsteady forces created during the hovering motion are the cause for Phenomena like dynamic stall, rotation, acceleration and wing-wake interaction. While studying hovering flight the wing is considered to be rigid. Lin Du et al [16] have numerically investigated the hovering flight by taking the wing as freely vibrating in the vertical direction. By using immersed boundary condition the 2D Navier-Stokes equation had been solved.
Similarities have been found between the evolving Nectarivorous bats and the humming birds in order to be small in size and feed on floral nectar. It has been seen that nectar bats (Glossophagasoricina) during feeding are capable of carrying out hovering flight of several seconds which is energetically expensive. Nectar bats directly fuel there metabolism by utilising the immediately ingested sugars and this has been possible due to their strong intestines which are capable of sugar assimilation. Hummingbirds also have similar strong intestinal capabilities for sugar assimilation. The recently ingested sugars supply around 80% of energy required for hovering flight of nectar bats. Given the several similarities that nectar bats and hummingbirds possess, R.K. Suarez et al [17] conducted study to find similarity between the flight muscle of nectar bats and hummingbirds. The biochemical capacities during hovering flight with flux rates were also compared. The results of the study further strengthen the theory of convergent evolution of nectar bats and hummingbirds in terms of physiological and biochemical traits.
Humming bird is one of the smallest bird species and unlike other birds humming bird skilfully performs hovering flight. The special abilities of hummingbird can be attributed to the low Reynolds number (10³-10⁴) flight and unsteady aerodynamics involved. The flight style of a hummingbird resembles more to insects than to birds. But significant dissimilarities exist between the body structure of hummingbirds and insects which shows that these two can never have the exactly same flight style. The unsteady effects in hummingbird flight can be best observed during hovering. Quite a less number of research work has been done on the 3D vortex structures and the unsteady aerodynamics involved. Songyuan Yang et al [18] have presented a study on the Computational Fluid Dynamics (CFD) of the hovering flight aerodynamics of rufous hummingbirds (Selasphorousrufus). On the wing surface of a hovering hummingbird conical and stable Leading Edge Vortices (LEVs) having spanwise flow inside their core were found. In a hummingbird majority of lift was produced due to the presence of attached bound vortex around the wing of hummingbird. Based on kinematic and morphological data a model of rufous hummingbird was made and the governing equations were solved. Songyuan Yang et al have
focused on the properties of wing kinematics, far-field wake and the aerodynamic force that is produced in hovering flight of hummingbirds.
In analysis of flapping wings quasi-steady method has been frequently used. In order to analyse the unique features of flapping wings, modifications have been made in the quasi-steady method to accommodate acceleration effect, rotational force and translational force. Unlike the Computational Fluid Dynamics (CFD) models the quasi-steady model cannot explain 3D flow pattern but the quasi-steady model conducts analysis in very less time. Jialei song et al [19] has presented a quasi-steady model that describes the hovering flight aerodynamics for a Ruby-throated hummingbird. The quasi-steady model was developed in order to study the limit of low-order model in representing flow physics of birds. For the model real-life wing kinematics were taken. CFD simulation of a revolving-wing model was used to calibrate the quasi-steady model. It was observed that the quasi-steady model was able to accurately calculate the lift production but failed to account for the forced oscillations.
Hummingbirds are different and distinctive when compared to the other bird species. The reason for this has been closely related to the evolution of the hummingbirds primary source of energy i.e. the floral nectar. The evolution of hummingbird has been greatly affected by the presence of floral nectar around the hummingbirds. A number of changes came in the form and function of hummingbirds like changes in anatomical and locomotors systems. Douglas warrick et al [20] describes how various pressure and constraints of nature shaped the evolutionary cycle of hummingbirds. While removing nectar from the flowers flying is preferred compared to landing but for this the locomotor system of the hummingbird must operate continuously and precise modulation is needed for safe approach and steady feeding. Hovering flight is unconditionally the most energetically expensive phase of flight compared to any intermediate forward flight. Birds reduce the energy expense by spending less time while hovering. Due to limited quantities of nectar produced by flowers the evolution of hummingbird led to adopting small body sizes to reduce energy consumption. Small size isn’t the only solution to reducing energy consumption. For providing weight support the recovery stroke of wings has negligible contribution. For small hovering birds like hummingbird double the weight support must be produced by the downstroke.
It has been observed and suggested by many researchers that a hoveringbird can more quickly move from one flower to another compared to the birds that perch. But this ability comes at the high cost of energy that hovering requires compared to perching. Graham H. Pyke[21] has aimed at estimating this trade-off between speed and cost for the perching honeyeaters and hovering hummingbirds in two filed situations. Australian hummingbirds (Trochilidae) and Australian honeyeaters (Meliphagidae) are ecologically similar but differences exist in their foraging behaviour. While foraging hummingbirds always hover at the flower and then collect the nectar. But the honeyeaters are found to perch at the nearby stems while collecting nectar. The character of hovering and perching is found to have relation with the body size of the respective birds. In general honeyeaters are found to have larger body size compared to the hummingbirds.
When considering natural low-altitude hovering flight the first species that come into mind are the honeybees. Honeybees have the marvellous capability to fly effortlessly through the harshest of climatic conditions. Earlier researches focused on study of insect flight in well and clean environment but the need to develop water repellent surface made scientists to observe the flight of honeybees in dew and mist conditions. Youjianliang et al [22] used high-speed cameras, to record the flight of honeybees through mists and drizzling rain, in order to study the mechanism behind the incredible flight of honeybees through these rugged environmental conditions. Atomic force microscopy and scanning electron microscopy was used by researchers to study the microstructure of the wings of honeybees. The wings of honeybees were found to remain dry even on exposure to steam. In case of honeybees it was found that the hydrophobicity not only depended on the wing topography but also on the chemical constituents of the wing. It was found that on the body of honeybees the amount of
hydrophobic proteins was more than that of hydrophilic proteins. The results showed that the wings of honeybees have rough surface with distribution of bristle on both dorsal and ventral sides. Presence of hydrophobic protein containing minimum of one hydrophobic tetra-peptide was discovered on the honeybee wings. The structure and chemical composition of wings of honeybees will help in discovering new and advanced hydrophobic structures.
High altitude flight offers several advantages along with challenges to the natural flyers. Ecological advantages offered by the high-elevated habitats include decrease in competition, reduced risk to predation etc. Along with these benefits the disadvantages of high-elevation flight include physiological challenges because of reduction in density of air and oxygen availability. The constraints that high-altitude flight offers severely affect various manoeuvring capabilities of the birds. These flight manoeuvres are necessary for birds in order to escape predators, compete with rivals and foraging. To study impact of high altitude on individual manoeuvres of the birds, Paolo S. Segre et al [23] calculated the free-flight styles/manoeuvres of male Anna’s hummingbirds. Initially performance was measured by placing hummingbirds in a large chamber kept at high altitude and later the chamber was translocated to a low-elevation. For studying the large number of manoeuvres performed by the hummingbird a multi-camera tracking system was used. The manoeuvres were studied on the basis of body position and orientation. It was found that when flying at high-altitudes the translational and rotational velocities of hummingbirds decreased and the birds refrained from carrying out demanding turn. For determining the effect of mechanical and metabolic constraints separately another experiment was performed by Paolo S. Segre et al in which the hummingbirds were placed in an airtight chamber. normoxicheliox or nitrogen was infused in the chamber. It was observed that hypodense treatment resulted in reduction in hummingbird’s performance but the hypoxic treatment has negligible effect on manoeuvring of birds.
By using adaptation capabilities butterflies have the ability to fly effortlessly by maintaining the required flapping-of-wing flight in extreme environmental conditions like gust etc. Butterflies possess unique adaptive function because of effective interaction between body, nervous system and environment. This adaptive system is called “Mobiligence”. In case of Mobiligence of butterflies the environment is the generated flow field. The objective of Kei Senda et al [24] is to study the stabilisation principle in case of flapping flight of butterflies. The flapping flight of butterflies has rhythmic and cyclic motion. For analysing the aerodynamics of a butterfly an experimental setup was done using a low-speed wind tunnel. For getting dynamic model of butterflies flight Lagrange’s method was used. The validation of the model was carried out upon comparison with experimental data. Senda et al studies the impact of wake-induced flow and torsional wings on the stability of a butterfly flight. The results suggest that the wake-induced flow and torsional wings lead to reduction in the flight stability.
During 1980s it was discovered that the insect wings possess deforming ability and this has significant effect on their flight. The studies done found that wing morphology, kinematics and the flight behaviour of an insect were closely related to each other. The storage of elastic power is essential element in case of insect flight and without storing elastic power insects cannot fly. For decreasing the complexities involved in calculation and modelling most of the studies done on insect flight have assumed the wings of an insect to be rigid and flat. T.T. Nguyen et al [25] modelled a wing and then studied the effect of wing flexibility on aerodynamic performance of the modelled wing. Initially the effect of distribution of stiffness property on the deflection under static and inertial loading was analysed. Wings having Leading Edge Reinforced (LER) was found whose deformation on trailing edge resembled to that of the insect wings during flight. In LER type wings the stiffness was found to reduce significantly towards the tip of the wing. The class of LER type wings was found to be superior to rigid wings in terms of aerodynamics.
Igor Kovale[26] has experimentally studied the effect of presence of hollow region in butterfly \textit{Pyrameisatalanta}. Presence of complex microstructure was found on the butterfly scale and it was seen that higher lift is generated on the butterfly wings having scales. Movable appendages having size 30μm to 120μm are present on the wing surface of butterfly. The scale of butterfly is resembles a sack of lower and upper laminae as shown in figure 3. Hollow region is present between both the laminae. Trabeculae emerge from the flat plate shaped lower laminae to connect to the upper laminae.
Butterflies possess some peculiar features like being the youngest insects when evolutionary history is considered. The scale microstructure and appendage mobility of a butterfly have evolved over years of natural selection. The scale microstructure of a butterfly has multiple role like reducing vibrations, regulating body temperature, absorbing the ultrasonic squeaks of predators like bats and reducing the noise. Also the colourful and optical effects on the wings are due to the presence of scales. The wing motion of a butterfly is multi-oscillatory because the wings flaps (about the base) and rotate (about the longitudinal axis) simultaneously. Igor Kovale used two oscillating models for measurement of aerodynamic forces. The experimentally obtained data showed that the presence of hollow region increased the lift by 1.5 times and reduced the damping coefficient by 1.38 times.
The shape and size of wing plays a crucial role in determining the flight performance. Flight performance depends on the number of factors like body morphology, behaviour, physical environment etc. For flying animals having small body size dissipation of viscous effects, due to small perturbation, takes place more quickly compared to flying animals of larger body sizes. For large body, small perturbations lead to significant unsteadiness of the flow fields surrounding the wings. David Outomuro et al [27] aims at exploring the correlation between wing shape and wing size for territorial males of damselfly family Calopterygidae. For the analysis, wing coloration was also included because it was also found to have an effect on wing shape. The analysis by David Outomuro et al was conducted using two techniques namely non-dimensional radius of the second moment of wing area (RSM) and geometric morphometrics. A complex relationship was found between RSM and wind size in damselflies. The complexity of relation can be accounted to wing coloration and specific behaviour (like courtship). The results suggest that taxa-specific relation exists between wing shape and size.
The flight skill of dragonflies is way more than impressive compared to other insects because of the structural and chemical composition of a dragonfly’s wings. In the wing of dragonflies the major structural component are the veins. The veins are joined by resilin having higher elasticity at particular joints. By flapping quickly the dragonflies are able to produce the required aerodynamic force for flight. In case of dragonflies the wings have capability to deform and this has a huge significance during flight. The wings change their shape from time to time in order to have better distribution of aerodynamic forces so that higher lift can be generated. Unlike birds and bats insect
wings (like of dragonflies) don’t possess muscles in main part of the wing. Hence, the deformation of wings in dragonflies is caused by the flight loads, aerodynamic and inertial forces generated due to flapping. Resilin, a hydrophilic protein, was discovered on some vein joints in the wings of dragonflies. One of the classifications of vein joints of dragonflies can be done on the basis of resilin present on the joints. Dan Hou et al [28] created a 3D finite element model of the dragonfly wing. While developing the model soft vein joints were also considered. Studies were conducted on the passive deformations due to aerodynamic loads and active flapping motion. The results showed that the soft vein joints improved chordwise flexibility during passive deformations. During active flapping the rigidity of the wing has to be maintained in spanwise direction in order to achieve required amplitude.
Humans have taken inspiration from nature to invent and develop new systems that are more efficient and have better capabilities than the existing systems. Nature always finds the best of the designs and systems to incorporate the most efficient structures. Even after a century of successful development in aircraft structures, the mechanism of flight by natural fliers is very impressive and more advanced than some of our best aeronautical structures. G.K. Suryanarayan et al [29] formed the aerodynamics of dragonfly as the basis for developing passive configurations in order to generate steady lift. While carrying out forward flight the fore-wings of a dragonfly flap alone while the aft wings remain stationary. This mechanism shows that there must be some aerodynamic coupling between the fore and aft wings while having a forward flight. In order to mimic the flapping of the fore-wings, the fore-wings were replaced by a cylinder because the cylinder is known to shed discrete vortices. The cylinder was used in combination with a flat plate kept downstream and below as shown in figure 4. During the initial transients once the shed vortices pass over the plate, it was observed the vortices shedding nearly stops and a trapped vortex is formed over the plate.
![Figure 4. Configuration of cylinder and flat-plate [29].](image)
Richard J. Bomphrey et al [30] has aimed at synthesising and enhancing the knowledge available on dragonflies and damsselflies relating to their mechanics and aerodynamics of flight. Significant amount of data like dragonfly wing morphology, gliding flight aerodynamics, aerodynamic efficiency etc. has been collected. New techniques like laser-line mapping of wing topographies, computational fluid dynamics simulation of wing morphologies, particle image velocimetry etc. have been used. The determination of homologous structure in dragonflies has been a challenging task primarily because of complex muscle arrangement. Most of the muscles in dragonflies and damsselflies inert on the radial veins thus giving the insects ability to actively control angle of attack, camber, twist etc. Vein curvature, vein cross sections (that promote torsion but resist bending) etc. passively control the regional positioning of the wing. The wings of dragonflies are not smooth surface and corrugations are present all over them. These complex geometries on the wing surface provide sophisticated mechanical advantages to resist longitudinal bending.
The independent four wings flapping of dragonflies allows them to manoeuvre effectively during flight. Carnivorous predators like dragonflies are capable of preying and mating during flight itself. The dragonflies have complex flapping mechanism because they can control both their forewing and hindwing separately. Depending on the mode of flight a dragonfly can vary the phase angle between
the forewing and hindwing. Unlike most insects the dragonflies can precisely manoeuvre and accelerate because they have direct musculature control of the wings. Hidetoshi Takahashi et al [31] using a flying ornithopter established that the phase angle control effects the aerodynamic performance. The phase angle of the designed ornithopter varied according to phase lag between slider-cranks of forewing and hindwing. Microelectromechanical differential pressure sensors were installed, on the centre of both forewing and hindwing, for calculating aerodynamic performance during flapping motion whenever change in phase angle takes place. The phase angle was varied both in tethered and free-flight condition and the results showed that performance of forewing remained nearly same while the hindwing showed variation in the performance. The conclusion of experiments was that a flying ornithopter can control flight force balance by simple changes in phase angle.
Dragonflies are well known for their agility, endurance and predating capabilities. Dragonflies can fly at low-speeds, hover and even fly backwards. In evolution insects generally reduced a pair of wings but dragonflies and damselflies have retained their distinctive four-winged form. Unlike other insects in dragonflies direct musculature acts at the wing base that allows the dragonflies to have direct and independent control of each wing. It has been found that four wings are not very helpful in lift generation. James R. Usherwood et al [32] has used a mechanical model of dragonfly to show that even after not being suitable for lift generation, four-wing configuration is aerodynamically efficient for flight. The two pairs of wings of dragonflies become aerodynamically efficient by extracting energy from the wake that gets swirled. It was found that by appropriately phasing fore-hind wing the power required can be reduced by 22% when compared to single pair of wing configuration.
Researchers have been able to study the unsteady aerodynamics involved in hovering flight of insects but the aerodynamic effects of wing deformation have still not been investigated because of lack of analysis methods. For analysing the lift generating mechanism while hovering considering wing deformation was not important as the generation of force takes place near the wing tip. But passive wing deformation is a crucial factor that needs to be considered while analysing flapping flight. Masaki Hamamoto et al [33] developed a free-flight simulator using Fluid Structure Interaction (FSI) and Finite Element Analysis (FEA) based on Lagrangian-Eulerian method. The simulator can quantitatively study the correlation between wing deformation and its surrounding flow. The numerical model of the dragonfly could do rapid turning at 1200 degree per second of yaw angular velocity which was inspired by flapping motion in nature.
Aerodynamic lift generation for insect flight has been studied in both quasi-steady and unsteady regimes. During hovering flight aerodynamic drag has no role in vertical force. Some of the finest hovering insects like dragonflies and hoverflies use inclined stroke planes where the downward and upward drags don’t cancel out each other. By computing an ideal dragonfly wing motion it was found that for supporting about three quarters of its weight the dragonfly uses drag. Hovering insects fly at large angle of attack in order to generate high transient force by taking advantage of dynamic stall. Z. Jane Wang [34] for investigating the generation of force and energy consumption during hovering flight studied wing motion where inclined angle of stroke plane was taken as the parameter. The results suggest that because of the flow being severely stalled the lift and the drag are nearly same. The aerodynamic efficiency was found to be same upto an inclined angle of 60 degrees.
Most of the biological flyers have flexible wings which allow them to perform acrobatic tasks in air. The 3D deformations and kinematics of the wings have significant impact on the structural, aerodynamics and control aspects of insect flight. Scientists believe that new mechanisms can be discovered for lift generation by properly studying the wing flexibility and deformation techniques from nature. Christopher Koehler et al [35] have suggested a subdivision surface reconstruction method which can reconstruct the wing deformations and kinematics of flying insects. The method
does not consider the wing as rigid. The muscles near the root of wing were used for inducing chordwise camber in the wing’s portion near the specimen’s body.
The wings of a dragonfly function as ultralight airfoils during gliding. For static reasons the wings of dragonflies are having cross-sectional corrugation which forms valley where rotating vertices develop. The configuration of this cross-section varies along the longitudinal axis of the dragonfly’s wing. Due to such variation there exist different aerodynamic characteristics locally on a wing. When the $C_L/C_D$ ($C_L$ and $C_D$ refer to coefficient of Lift and Drag respectively) characteristics were analysed by Antonia B. Kesel et al [36] Reynolds number 7880 and 10000 by using a force balanced system it was found that the cross-sectional geometries produce drag as low as that of a flat plate. The value of $C_{D,min}$ goes below 0.06. But unlike flat plate the wing profiles are able to generate much higher lift. The lift forces are comparable to technical wing profiles when placed in low Reynolds number. Because of rotating vertices along the chord it was found that the pressure relationship along the profile changes when pressure measurements were done at Reynolds number of 9300.
Many aspects of insect flight are affected by the 3D dynamic shape of flapping wing. The deformations of the wing are controlled by architecture of the wing. The study on flexural stiffness of the insect wings hasn’t been extensively done yet. S.A. Combes et al [37] have designed a method to measure the displacement along the wing when a point force was applied. This method was used to measure flexural stiffness variation for the hawkmoth Manduca sexta and the dragonfly Aeshna multicolour. Flexural stiffness was found to rapidly decrease from the wing base to the tip and from leading edge to the trailing edge. The rate of variation is approximately exponential. The finite element models of Manduca sexta forewings show that while transferring bending to the edges in proximal regions the rigidity is preserved by flexural stiffness.
Presence of Leading Edge Vortex (LEV) was found above the wings during the end of downstroke. Richard J. Bomphrey et al [38] have presented the first of its kind Digital Particle Image Velocimetry (DPIV) analysis of the flow field around wings of Manduca sexta. The smoke visualisation and DPIV result analysis matches with the experimental results of flow visualisation experiments done before. The experiment provides the flow field above the thorax. Upon study it was found from detailed DPIV results that by the end of downstroke the structure of LEV is same as that seen in free flying insects. According to DPIV results the magnitude of velocity for spanwise flow in the LEV is less than 1ms$^{-1}$.
Flapping flight aerodynamics has been the area of interest for researchers for a long time and the design of man-made aircrafts are somewhat primarily inspired from the nature. A major task in designing the Micro-Air Vehicles (MAVs) is to simulate the flapping flight of natural flyers. The flapping flight of insects (or MAVs) operates via non-conventional mechanisms for increasing the aerodynamic loads and this is done by creating unsteady and nonlinear flow fields. It is know that Leading Edge Vortex (LEV) is used as a high lift mechanism by insects. The same principle is also used for lift generation in the case of highly swept and delta wings of manmade aircrafts. During LEV the bound vortex is augmented on the wing leading to left generation. LEV is similar to dynamic stall phenomena where a rapid variation in Angle of Attack (AOA) of the wing is seen. But unlike dynamic stall the LEV has stable nature owing to the outward spanwise flow that convects the LEV towards the wing. The generation of spanwise flow in insects takes place via rotational motion that creates spanwise velocity gradient. During insect flight it has been found that LEV is the major mechanism for lift production but two other mechanisms are also there namely rotational lift and wake-capture effects. Haithem E. Taha et al [39] has presented for the aerodynamics of flapping wings a state-space representation. Duhamel’s principle has been used on non-conventional lift curves in order to find the contribution of LEV. The validation of the model proposed was conducted by comparing it with Navier-Stokes simulation for hovering insects.
The attempts to develop a Micro Air Vehicle (MAV) started back in 1997 because of the limitations of available class of surveillance flying vehicles like UAVs, satellites etc. These vehicles do not possess the capability to enter inside buildings and carry out espionage activities. For such purpose there has been the need to develop advance MAVs which are easily portable and can function in any type of dull and dusty surrounding. The idea for developing and designing of an efficient MAV comes from the flapping flight of insects. Wing designing for a MAV is a complex task and a number of aerodynamic effects need to be considered. This is because in an insect the wings perform the combined task of generating lift, propulsion and manoeuvres simultaneously. The flapping wings function both as lift generating device and also as propulsion system and due to this complex aerodynamics comes into effect. Hence there is need for an aerodynamic tool that can help in studying the parametric design space and coverage on more than one configuration. S.A. Ansari et al [40] aims at conducting a review of the aerodynamic modelling approaches that have been used till now. The approaches have been categorised into steady-state, quasi-steady, semi-empirical and fully unsteady methods.
Gunther Pass has reviewed the biological composition of the wings of an insect. Wings of an insect are mostly made up of lifeless cuticles. The veins in the insect wings have a number of tissues and sensory systems present in them. These tissues need regular supply of oxygen and other nutrients. Gunther Pass [41] has surveyed about the role of tracheal and circulatory system in transporting the required minerals to the wings. In case of most of the insects circulation via veinal network is done by hemolymph. Researchers are still studying the technique used by insects for providing hydration to the wing cuticle so that the cuticles don’t lose their flexibility. Wing has fascinated researchers the most because it a delicate body structure but still allows the insects to fly. For controlling wing movement and body stabilisation the sensory organs on insect wings are mechanoreceptors. There are also insects in whose wings sound pressure mechanoreceptors are present which helps them in intraspecific communication. The mechanosensation is a crucial multimodal sensory input because it helps the insects in quick collection of information and its further processing. The wing mechanoreceptors not only function during flight but also during periods of inactivity of insects. Maximum number of mechanoreceptors is present on the joint region between the thorax and wing base. Also there are mechanoreceptors present on the wing blades.
Jennifer L. Palmer et al [42] describes the methods for studying and developing aerodynamic tools that are necessary for design and development of a bio-inspired Micro-Air Vehicle (MAV) that is fully mission capable. There are various challenges that come in the way of designing a fully-functional MAV for surveillance that has flying qualities of natural flyers like insects. The researches done on MAV were categorised into analytical, experimental and numerical investigations that will help in making a flapping wing MAV. Numerous MAVs have been developed till date but not even single one of them can match the hovering and flight capabilities of naturally flying insects. Jennifer L. Palmer et al has focused on the aerodynamic characteristics of MAVs like the forces and moments that wings generate. The design and control of a bio-inspired MAV is affected by the set of wings having a particular shape and structure. The mission capabilities like stability, endurance etc. of a MAV are constrained by the aerodynamics of the system. Figure 5 shows the testbed developed for aerodynamic testing. The challenges involved in MAV designing include wing arrangement like the number and position of wings. Other challenges include flapping mechanism which should have particular wing kinematics, flapping rate etc. Conducting a scaling analysis of natural flying species that do hovering flight allows researchers to formulate basic rules for flapping-wing MAV designs. Observations suggest that a viable design for flapping wing MAV is a simple four-wing device having basic wing design. The MAV will have single active axis for flapping.
A new exceptionally small Nano Aerial Vehicle (NAV) was being designed based on nature. The NAVs have a vast range of new capabilities to offer compared to Micro Aerial Vehicles (MAVs). As the work in NAV started very rapidly proper study could not be done to explore the properties of MAV. Mohd. Firdaus Bin Abas et al [43] have reviewed the latest development of MAV like kinematics and membranes. Mohd. Firdaus Bin Abas et al had also studied the probability of using piezoelectric transmission for the flapping wings.
The information sensing and gathering techniques will be revolutionised by the use of Micro Air Vehicles (MAVs). W.Shyy et al [44] has aimed at reviewing the work done in aeroelasticity and flapping wing aerodynamics. A change in Reynolds number suggests a change in Leading Edge Vortex (LEV) and spanwise flow structures. Wing tip vortices lead to energy loss in stationary wing theory. But these tip vortices interact with LEV during flapping flight to increase lift produced. With decrease in the size of MAVs, fixed wing designs are not working and face serious problems like flight control and lift generation.
Hao Liu et al [45] have conducted a study relating to aerodynamics of flexible wings and stability of passive flight dynamics. The study has been done on a flapping Micro Air Vehicle (MAV) by combining force evaluation, kinematics of flapping wings and computational approach. The prototype of MAV has weight of 2.4g-3.0g and has X-type wing with wingspan of 12-15cm. For evaluating the flexible wing performance of MAV dynamic flight simulator has been used. The flight characteristics of MAVs are substantially affected by the surroundings due to MAVs being light weight and low speed aerial vehicles. The fluid and structural dynamics of a MAV are interrelated and thus making the analysis of whole MAVs difficult task. The dynamic simulator used provides the MAVs evaluation in terms of vortex and wake structures.
SriyuliantiWidhiarini et al [46] have proposed a Micro Air Vehicle (MAV) having up-down and twisting wing system like birds. The development of Flapping-wing Micro Air Vehicle (FMAVs) resembles the bird flight very closely. FMAV discussed has a wingspan of 50cm and double-crank drive system. The abilities of FMAV was significantly increased by adopting several features from birds like bird-mimetic wing shape and an up-down and twisting wing drive mechanism. By installing flight control computer autonomous flight system was implemented. A reduction in effective angle of attack and presence of 3D flow structure during flight was found due to the small size of FMAVs. This makes the vehicle sensitive to gust and other disturbances. Experiments in wind tunnel showed that FMAV having high-camber wing and double-crank system produces more lift.
Akira Obata et al [47] have presented a deep study of low-speed flow for the designing of ultra-light dragonfly. In designing the flying robots special attention was given to the gliding capability of dragonflies. One of the major obstacle in constructing ultra-light dragonflies is the increase in viscous flow at low Reynolds number. The reason for dragonflies being superior flyers is the corrugated wing structures and thus this can be used in developing the flying robots. The dragonfly configuration of the flying robots was found to have higher compatibility with high lift devices and propellers used. Development will allow scientists to expand the flight envelope of a flying robot.
Du CP et al [48] has investigated the modelling and control design of a dragonfly based Micro Air Vehicle (MAV) which has flapping wings. Initially for the flapping wings an aerodynamic force model has been developed. The model was developed using wing’s local air velocity and local angle of attack. At last for the flapping MAV an entire mathematical model was developed by relating kinematic model and aerodynamic force model. The MAV developed is taken to be a six degree-of-freedom body. In order to successfully mimic the dragonflies the tail of MAV can only swing instead of having proper control surfaces like other aircrafts. The controller iteratively solves for desired control signal by using Newton-Raphson method.
Insect species like dragonflies, damselflies etc. use wings that are pleated along the chord. The insect wings are very light and membranous thus allowing them to support different aerodynamic and inertial force. The benefit of having pleated framework is resistance to span-wise bending. Dragonflies fly in ultralow Reynolds number regime that ranges from $10^2$ to $10^4$. Shwetanshu Gaurav et al [49] have conducted extensive numerical simulation of fluid dynamics based on the pleated wing section of AeshnaCyanea. The experiments had been done in ultra-low Reynolds number region in order to find potential application of pleated airfoils in Micro Air Vehicle (MAV). Number of vibrations and forces are seen whenever the wings of a dragonfly interacts with the surrounding airflow. The results suggest that pleated airfoils generate higher lift and lesser drag leading to an increase in the aerodynamic performance. This suggests that pleated airfoils are a good choice for application as fixed wings in Micro Air Vehicle (MAV) [50].
3. Literature Summary
Researchers have adopted multiple techniques for analysis and evaluation of low Reynolds number flight of animals. These techniques can be broadly categorised into Theoretical, Experimental and Numerical methods. It was observed that scientists have preferred Experimental and Numerical techniques because these methods give more accurate result. Experimental methods give better visualisation of the unsteady aerodynamics involved with low Reynolds number flight.
Modelling of flight aerodynamics was done by researchers which involve estimating the aerodynamic forces acting on a bird in flight. Different methods of modelling were used according to the complexity of the problem. Newton’s laws of motion are applicable to bird flight and hence can be used for estimating bird’s velocity and position. After making certain assumptions basic equations can be used for modelling. First is that the induced velocity is neglected because it is very small compared to freestreamvelocity. Other assumption is that the flow is quasi-steady.
The experimental methods mostly made use of wind tunnel setups. The researchers used to develop a life size of the bird and insect in consideration and then this model was subjected to required conditions in the wind tunnel for approximation. Many times live birds were also analysed by using high-speed cameras. One method that widely used by scientists was Particle Image Velocimetry (PIV).
For generating numerical solution of the bird aerodynamics a series of steps need to be followed. First domain discretisation has to be done and then the flow properties need to be evaluated for each cell of the respective domain. The domain discretisation can be done using ICEM-CFD and for enhancing mesh quality, mesh smoothing process can be carried out. Smooth mesh will ensure that the
solutions converge quickly. Many papers used FLMNAV solver for carrying out computations. FLMNAV is based on finite volume approximation. Numerical methods also include carrying out simulations where unstructured triangular mesh was employed which is based on finite volume approximation. The software used was ANSYS-14.0. Navier-Stokes equation has been widely used for numerical solutions.
4. Conclusion and Future Scope
Low Reynolds number biological flyers use flapping wing mechanism for flying and this allows them to fly effortlessly with minimum resistance. For example birds experience G-forces of about 10-14G regularly whereas the best military aircrafts can experience a maximum upto 8-10G. Study of fluid dynamics using simulation has been fast growing to evaluate the aerodynamic effects of natural flyers. Researchers have been preferring to use Numerical and Experimental techniques to investigate the unsteady aerodynamics involved in flight of natural flyers. Various lift generating mechanisms like Leading Edge Vortices (LEV), wake capture etc. are used by birds and insects. Flexible wings reduce the stall and also enhance other aerodynamic characteristics like lift etc. Wind tunnel tests and Particle Image Velocimetry (PIV) have been widely used for flow visualisation and to study flow interaction of flyers with surrounding air. By flapping the wings flying animals are able to create both lift and thrust as per requirement. On keeping the wing simply stretched out without flapping birds are able to produce only lift without generating thrust. Such type of flight refers to gliding flight. The hovering motion of an animal depends on its size, degrees of freedom, moment of inertia etc. Hovering is a technique mostly used by small flyer like birds and insects. Different flight styles from animals can be adopted to design a Micro Air Vehicle (MAV). The study of MAVs becomes difficult because of unsteady aerodynamic involved. Studies are going on to efficiently develop MAV system which have efficiency and capabilities similar to those of natural flyers.
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Acknowledgments
First of all I would like to express my gratitude for my guide Srinivas G. sir without whom this paper wouldn’t have been completed. His constant motivation and hard work behind me helped me in achieving a lot of things. My family helped me throughout my journey in writing this paper. Amma and Nanu have always been the support system that I need while doing such brain storming tasks. Parth and Anish (my siblings) were a source of constant motivation for me.
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WIMPy Leptogenesis With Absorptive Final State Interactions
Jason Kumar and Patrick Stengel
Department of Physics and Astronomy,
University of Hawaii, Honolulu, HI 96822 USA
Abstract
We consider a class of leptogenesis models in which the lepton asymmetry arises from dark matter annihilation processes which violate $CP$ and lepton number. Importantly, a necessary one-loop contribution to the annihilation matrix element arises from absorptive final state interactions. We elucidate the relationship between this one-loop contribution and the $CP$-violating phase. As we show, the branching fraction for dark matter annihilation to leptons may be small in these models, while still generating the necessary asymmetry.
I. INTRODUCTION
The baryon asymmetry of the universe (BAU) is both evident in observation [1, 2] and well-motivated theoretically at a variety of scales and epochs. The existence of non-baryonic dark matter (DM) is also well established by observational signatures of its gravitational interactions at several different scales [1, 3–5]. Calculations of primordial light element abundances predicted by big bang nucleosynthesis (BBN) [6], recent observations of cosmic microwave background (CMB) anisotropy by the Wilkinson Microwave Anisotropy Probe (WMAP) [3] and Planck satellite [7], the galaxy power spectrum obtained by the Sloan Digital Sky Survey (SDSS) [4], and a variety of other data create a combined picture indicating that the densities of baryonic and dark matter in our universe are
\[
\Omega_b h^2 \sim 0.022,
\]
\[
\Omega_{DM} h^2 \sim 0.12.
\]
Both BAU and DM are strong motivations for physics beyond the Standard Model (SM), as neither significant baryon number (B) violation nor appropriate non-luminous gravitationally interacting fields exist within the SM. The most common models that explain DM provide a Weakly Interacting Massive Particle (WIMP) to account for the observed density [5]. A typical WIMP, with weak scale mass and couplings, will depart from equilibrium in the early universe when self-annihilation freezes out, yielding roughly the correct relic DM density. It is natural to wonder if the annihilation process which determines the dark matter density can also yield a baryon asymmetry.
Many models have been proposed to explain BAU [2], but generally, in order for a process to produce the observed baryon asymmetry, the Sakharov conditions [8] for baryogenesis must be satisfied. The Sakharov conditions require:
- a violation of baryon number (or lepton number (L), if the asymmetry is generated above the electroweak phase transition (EWPT)),
- a violation of \(C\) and \(CP\),
- a departure from thermal equilibrium.
Although decaying dark matter with a weak scale mass has been suggested as a model for baryogenesis [9], a WIMP framework which satisfies the first two conditions would automatically accommodate the third. This mechanism of “WIMPy baryogenesis” was recently proposed by Cui, Randall and Shuve [10]. In a typical WIMPy model, dark matter, denoted \(X\) with \(m_X \sim \text{TeV}\), annihilates to an additional new weak scale field, denoted \(H\),
and a quark (or lepton) via CP-violating interactions. The CP-violating phase arises from interference between tree-level and loop diagrams. $H$ then subsequently decays into light particles, including particles which are uncharged under Standard Model gauge symmetries, thus sequestering any negative baryon (or lepton) asymmetry. Between the time $X$ begins to depart from equilibrium, $T \sim m_X$, and when $X$ freezes out with the correct relic density, the correct baryon asymmetry can also be produced. If DM annihilates to leptons, then any lepton asymmetry is transferred to baryons through electroweak sphalerons at temperatures above the EWPT.
While in Ref. [10], UV-complete models mediated by weak scale pseudoscalars are presented, generalization to an effective field theory (EFT) was more recently shown by Bernal, Josse-Michaux and Ubaldi [11]. The EFT WIMPy model achieves results similar to a UV-complete model, with DM annihilating to $H$ and quarks through all possible dimension six operators. This allows one to focus on aspects of the generation of a baryon asymmetry which can arise from many different UV completions.
Subsequent work [12] provided a general analysis of how washout processes can erase an asymmetry. The key constraint on WIMPy baryogenesis models, either constructed in a UV-complete or EFT formalism, is that the couplings which must be added to generate needed one-loop contributions also introduce dangerous tree-level washout processes. These processes are “dangerous” because they are not Boltzmann-suppressed, even when some of the external particles are heavy. As a result, features of the model must be chosen to render these processes less dangerous. This work focused on the particular case where $m_H \sim m_X$, and found a class of models in which $H$ may decay entirely into Standard Model particles, while still generating the required baryon asymmetry. For these processes, the asymmetry is largely generated after the washout processes are frozen out.
In this work, we consider WIMPy leptogenesis [13], in which dark matter annihilation directly produces a lepton asymmetry which is converted into a baryon asymmetry by electroweak sphalerons. We focus on an effective field theory approach, in which dark matter annihilation can be parametrized in terms of a set of effective operators. In contrast to previous work, here we will obtain a CP-violating phase at tree-level from the interference between dimension six operators. We will find that one-loop corrections effects are necessary for generating an asymmetry, but they can be sequestered in absorptive terms in the final state interactions of $H$. Because these terms do not directly affect either the Standard Model or dark sector, we will be able to relax some of the parameter space constraints typically
---
1 If dark matter annihilation directly produces a baryon asymmetry, then $H$ would have to be charged under $SU(3)_{\text{qcd}}$. Models of this form are constrained by direct searches for color-charged particles at colliders [14], and Standard Model quarks produced by the decay of $H$ would affect the baryon asymmetry. Though such models are certainly possible, we will for simplicity focus on the case where dark matter annihilation directly produces a lepton asymmetry, along with a particle $H$ whose decay does not affect the baryon or lepton asymmetry.
found in WIMPy baryogenesis models.
We will find that some dangerous tree-level washout processes, which are often introduced by the interactions needed to obtain CP-violation, are not present in the models we consider. Moreover, the ratio of CP-violating to CP-conserving interactions is not controlled by the scale of new physics. As a result, one can generate the correct baryon asymmetry for \( \sim 1.5 \) TeV dark matter even if the scale of new physics is as large as 10 TeV.
The outline of the paper is as follows. In section II, we review the reason why a one-loop contribution is necessary, and describe our class of models. In section III we describe the solution of the Boltzmann equations which govern the dark matter and lepton densities. In section IV, we present our results and compare to those of other models of WIMPy baryogenesis. We conclude with a discussion of our results in section V.
II. OUR MODEL
We will consider models with a single dark matter candidate \( X \) (stabilized by a \( Z_2 \) symmetry) whose annihilation can be modeled with a set of effective four-point operators. Each effective operator can be written as a product of an initial state dark matter bilinear and a final state bilinear. This final state bilinear couples a Standard Model lepton (\( L \)) and an exotic fermion (\( H \)). In order for the annihilation process to contribute to a lepton asymmetry, the effective operators must violate \( C, CP \) and \( L \).
We can already constrain the set of effective operators which are relevant. For dark matter annihilation to contribute to a baryon asymmetry, there must be interference between two matrix element terms with different phases (otherwise, any \( CP \)-violating phase would cancel in the squared matrix element). At lowest dimension, there are only two sets of fermionic dark matter bilinears which can interfere in an annihilation process [16]:
- \( iX\gamma^5X \) and \( X\gamma^0\gamma^5X \) can both annihilate an \( S = 0, L = 0, J = 0 \) (\( CP \)-odd) initial state.
- \( \bar{X}\gamma^iX \) and \( \bar{X}\sigma^{0i}X \) can both annihilate an \( S = 1, L = 0, J = 1 \) (\( CP \)-even) initial state.
If the dark matter is spin-0, then there are no dimension 2 or dimension 3 bilinears which can interfere. Moreover, if dark matter is a Majorana fermion, the second set of bilinears above vanish.
---
2 In some models of [11] it is necessary to use a \( Z_4 \) symmetry, since one of the final state particles is also charged under this stabilizing symmetry. That is not the case here, unless the effective operator respects \( SU(2)_L \). In that case, we would also need a \( Z_4 \) symmetry under which \( X \) and \( H \) are charged, in order to protect \( H \) from Standard Model decays which could wash out the asymmetry.
We will thus consider two sets of effective operators:
\[ O_{S=0} = \frac{\lambda_1}{2M_*^2}(i\vec{X}\gamma^5 X)(\bar{H}P_L L) + \frac{\lambda_1^*}{2M_*^2}(i\vec{X}\gamma^5 X)(\bar{L}P_R H) \]
\[ + \frac{\lambda_2}{2M_*^2}(\vec{X}_\gamma\gamma^5 X)(\bar{H}\gamma^\mu P_L L) + \frac{\lambda_2^*}{2M_*^2}(\vec{X}_\gamma\gamma^5 X)(\bar{L}\gamma^\mu P_L H) \]
\[ O_{S=1} = \frac{\lambda_3}{M_*^2}(\vec{X}_\gamma\mu X)(\bar{H}\gamma_\mu P_L L) + \frac{\lambda_3^*}{M_*^2}(\vec{X}_\gamma\mu X)(\bar{L}\gamma_\mu P_L H) \]
\[ + \frac{\lambda_4}{M_*^2}(\vec{X}\sigma^{\mu\nu} X)(\bar{H}\sigma_{\mu\nu} P_L L) + \frac{\lambda_4^*}{M_*^2}(\vec{X}\sigma^{\mu\nu} X)(\bar{L}\sigma_{\mu\nu} P_R H) \] (2)
where \( L \) is a Standard Model lepton and \( H \) is an exotic field with no lepton number. Note that these operators cannot interfere with each other, as they annihilate initial states with different spin and/or orbital angular momentum. We may thus treat each operator separately. Both operators are maximally \( C \)-violating. Since both operators will yield similar results, we focus on the case of \( O_{S=0} \).
The quantum numbers of \( H \) depend on whether dark matter annihilates to a charged or neutral lepton (we have assumed for simplicity that dark matter annihilates to a left-handed lepton; similar results can be obtained if dark matter annihilates to a charged right-handed lepton). The quantum numbers of the new fields for all cases are summarized in Table I.
We assume our effective operators do not respect \( SU(2)_L \) and \( U(1)_Y \), in order to ensure that lepton number is not washed out by electroweak scale interactions between \( H \) and Standard Model particles. Thus, our effective operator couplings must scale with the vev of the Higgs field.
| Fields | \( SU(2)_L \) | \( Q_{U(1)_Y} \) | \( Q_{U(1)_L} \) | \( Z_2 \) |
|--------|--------------|----------------|----------------|---------|
| \( X \) | 1 | 0 | 0 | - |
| \( P_L L = l_L \) | \( \Box \) | -1/2 | +1 | + |
| \( H \) | 1 | 0 | 0 | + |
| \( P_L L = \nu_L \) | \( \Box \) | -1/2 | +1 | + |
| \( H \) | 1 | 0 | 0 | + |
TABLE I. Particle Content
The relative phase between the left-handed and right-handed components of \( X, L \) and \( H \) can be fixed by requiring that they all have real mass eigenvalues. The only phase rotations left are non-chiral rotations of these fields, which can be used to absorb any overall phase of the coefficients \( \lambda_1, \ldots, \lambda_4 \). Note that the top line of eq. 2 is \( CP \)-invariant if \( \lambda_1 \) is purely imaginary, while the last three lines are \( CP \)-invariant if \( \lambda_{2,3,4} \) are purely real. We thus see that a \( CP \)-violating term must be proportional to \( Re(\lambda_1\lambda_2^*) \) or \( Im(\lambda_3\lambda_4^*) \).
The authors are grateful to B. Garbrecht for pointing out these potentially large washout terms, discussed in [15]. Note, these washout terms can also be forbidden if the discrete symmetry group is enlarged to a \( Z_4 \) under which \( H \) is charged.
A. One-loop corrections and absorptive interactions
Consider the annihilation processes $XX \to Y$ and $XX \to \bar{Y}$, where $Y$ represents any multi-particle final state, and $\bar{Y}$ is the $CP$-conjugate final state. We may write the quantum matrix element for these processes as
$$\mathcal{M}_{XX \to Y} = \mathcal{M}_{XX \to Y}^{CP} + \mathcal{M}_{XX \to Y}^{CPV},$$
$$\mathcal{M}_{XX \to \bar{Y}} = \pm \left( \mathcal{M}_{XX \to Y}^{CP} - \mathcal{M}_{XX \to Y}^{CPV} \right),$$
(3)
where $\mathcal{M}_{X}^{CP}$ and $\mathcal{M}_{X}^{CPV}$ are the $CP$-invariant and $CP$-violating terms in the matrix element, respectively. The sign of $\mathcal{M}_{XX \to \bar{Y}}$ is determined by the $CP$ transformation properties of the initial state. The final state asymmetry is then governed by the relation
$$\sigma_{XX \to Y} - \sigma_{XX \to \bar{Y}} \propto \text{Re} \left[ \mathcal{M}_{XX \to Y}^{CP} \mathcal{M}_{XX \to Y}^{CPV} \right].$$
(4)
In order to generate a final state asymmetry, it is necessary that:
- there exist both $CP$-invariant and $CP$-violating contributions to the matrix element.
- the relative phase between the $CP$-invariant and $CP$-violating amplitudes differs from $\pm \pi/2$.
The first requirement above is satisfied by interference between two terms (parametrized by coefficients $\lambda_1$ and $\lambda_2$) in the operator $O_{S=0}$.
But for the $XX \to \bar{H}L$ matrix element generated by the operators in eq. 2, the $CP$-invariant part is purely real and the $CP$-violating part is purely imaginary. This is a result of the optical theorem, and as the second point above indicates, implies that there will be no observable consequence to $CP$-violation.
The above line of reasoning leads to the usual result indicating that the generation of an asymmetry from dark matter annihilation requires interference between tree-level and one-loop diagrams. The one-loop diagrams then generate a relative phase from regions of phase space where the intermediate particles go on-shell, again as a result of the optical theorem. The important point, however, is that the one-loop contribution is not needed to provide a $CP$-violating matrix element; it is needed to generate the correct phase between the $CP$-violating and $CP$-invariant terms in the matrix element.
But complex matrix element phases can also arise from final state absorptive interactions. Within the effective operator approach, this one-loop correction is already present in the $H$ external leg correction. Assuming $H$ is unstable, its fully-corrected propagator will have an imaginary contribution which is proportional to the total decay width, $\Gamma_H$. This imaginary
contribution will be sufficient to generate a relative phase between the $CP$-invariant and $CP$-violating amplitudes which differs from $\pm \pi/2$, yielding a lepton asymmetry.
To be concrete, we will consider the case where $H$ is unstable and decays through $H \to H'\phi$, where $H'$ is a fermion and $\phi$ is a scalar (for simplicity we will assume that $m_{H'}, m_\phi \ll m_H$, and that the Standard Model lepton $L$ is either stable, or has a much longer lifetime than $H$). It is easy to see why treating $H$ as an unstable particle allows us to generate an asymmetry between the total cross sections for the process $XX \to \phi^*\bar{H}'L$ and $XX \to \phi\bar{L}H'$. Consider the operator $O_{S=0}$ where we assume $\lambda_{1,2}$ are real. In this case, $\lambda_1$ is the coefficient of the $CP$-violating operator which couples to the right-handed Weyl spinor $H_R$, while $\lambda_2$ is the coefficient of the $CP$-invariant operator which couples to the left-handed Weyl spinor $H_L$. We will, for simplicity, assume that $H$ can only decay from the left-handed helicity (as with Standard Model fermions), through a $CP$-invariant operator
$$O_H = |g|(\phi^*\bar{H}'P_LH + \phi\bar{H}P_RH').$$
If $\Gamma_H/m_H$ is sufficiently small, the dark matter annihilation amplitude will have an intermediate $H$ which will be approximately on-shell. We then see that the $CP$-violating amplitude for $XX \to \bar{H}_R L_L \to \phi\bar{H}_R'L_L$ depends on the helicity-flip term in the propagator of $H$, while the $CP$-invariant amplitude for $XX \to \bar{H}_L L_L \to \phi\bar{H}_R'L_L$ depends on the helicity-preserving term in the $H$ propagator. We can write the corrected $H$ propagator as
$$S(p) = \frac{\hat{p}_H + (m_H - i\Gamma_H/2)}{p_H^2 - m_H^2 - im_H\Gamma_H},$$
where we see that the relative phase between the $CP$-violating and $CP$-invariant matrix elements arises from the $-i\Gamma_H/2$ contribution to the helicity-flip term of the propagator.
The necessity of a one-loop contribution is already familiar from previous work on WIMPy baryogenesis. The difference in this work is that, unlike previous cases, here the one-loop correction is not the source of $CP$-violation; $CP$-violation arises from the interference of two tree-level effective operators, and the one-loop propagator correction only changes the relative phase between those terms in the matrix element.
This difference has important phenomenological consequences. In models where the $CP$-violating phase is generated from loop diagrams, the required additional field content and vertices typically introduce new tree-level washout processes which can erase the asymmetry. This typically results in a more constrained parameter space. In our example, however, since the one-loop contributions are sequestered from the Standard Model and dark sectors, no new tree-level washout processes are introduced. Moreover, the absorptive terms can arise from strongly-coupled physics, even if the actual dark matter-Standard Model matter interactions are perturbatively calculable.
### III. Calculation of the Baryon Asymmetry
The tree-level cross section for dark matter annihilation is given by
\[
\sigma_{\text{tree}}^{XX \rightarrow H L \rightarrow \phi^* H'L} = \frac{s}{16\pi M_*^4} \left\{ |\lambda_1|^2 + \frac{4Im(\lambda_1^* \lambda_2) m_H m_X}{s} + |\lambda_2|^2 \left[ \frac{4}{3} \left( 1 - \frac{4m_X^2}{s} \right) + \frac{2m_H^2}{s} + \frac{4m_H^2 m_X^2}{3s^2} \right] \right\} \left[ 1 - \frac{m_H^2}{s} \right]^2, \tag{7}
\]
where \(\sqrt{s}\) is the energy in center-of-mass frame and for simplicity we assume \(m_{H'}, m_\phi, m_L \ll m_X\). At tree-level, the cross section for the conjugate process \(XX \rightarrow \bar{L}H \rightarrow \phi \bar{L}H'\) is the same. But when one includes loop-corrections to the \(H\) propagator, one finds an asymmetry in the annihilation cross sections:
\[
(\sigma^{XX \rightarrow \phi^* H'L} - \sigma^{XX \rightarrow \phi L H'}) \propto \Gamma_H \frac{Re(\lambda_1^* \lambda_2^*)}{M_*^4} \left[ 1 - \frac{m_H^2}{s} \right]^2 \tag{8}
\]
where \(\Gamma_H\) is the decay width of \(H\), and we have assumed the narrow-width approximation. If we define \(\epsilon\) as the ratio of the cross section asymmetry to symmetric part:
\[
\epsilon \equiv \frac{\sigma^{XX \rightarrow \phi^* H'L} - \sigma^{XX \rightarrow \phi L H'}}{\sigma^{XX \rightarrow \phi^* H'L} + \sigma^{XX \rightarrow \phi L H'}} \tag{9}
\]
then we find \(\epsilon \sim \Gamma_H/m_{H,X}\). Assuming \(m_X\) and \(m_H\) are comparable, the narrow-width approximation would be largely valid even for models with a cross section asymmetry as large as \(O(10\%)\).
The effective operator approximation will be largely valid if \(m_X \ll M_*\). To keep the heavy mediator effectively decoupled from low-energy physics, we set \(M_* = 10\ \text{TeV}\).
#### A. The Boltzmann equation
We can write the Boltzmann equations in terms of dimensionless variables \(x = m_X/T\) and \(Y = n/s\), where \(n\) is the number density and \(s\) is the entropy density. Assuming an adiabatic process, the entropy \(S\) should be constant, and \(Y\) is essentially a comoving number density.
We will assume that \(H'\) and \(\phi\) are light particles which remain in equilibrium throughout the relevant cosmological epoch, allowing us to make the approximation \(Y_\phi = Y_{\phi^*} = Y_{\phi_{\text{eq}}}\), \(Y_{H'} = Y_{H''} = Y_{H'_{\text{eq}}}\). \(L\) is a Standard Model lepton which is also light, but it will depart from equilibrium due to the generated lepton asymmetry. But this departure from equilibrium will be small when the lepton asymmetry is small compared to the total lepton density. We define \(Y_{\Delta L} \equiv Y_L - Y_{\bar{L}}\) as the asymmetry in \(L\), which is either a charged lepton or neutrino of a single generation, and we assume all generations have the same asymmetry. We can assume \(Y_L + Y_{\bar{L}} \approx 2Y_{L_{\text{eq}}}\). For dark matter annihilation to any Standard Model fermion/antifermion
pair, including the subdominant \(CP\)- and \(L\)-violating annihilations that are the source of leptogenesis, the coupled Boltzmann equations are [1]:
\[
\frac{x^2 H(m_X)}{s(m_X)} \frac{dY_X}{dx} = -\langle \sigma_A v \rangle (Y_X^2 - Y_{X_{eq}}^2),
\]
\[
\frac{x^2 H(m_X)}{s(m_X)} \frac{dY_{\text{eq}}^L}{dx} = \frac{1}{2} \left[ \langle \sigma_{XX \rightarrow \phi^* H' L^v} \rangle (Y_X^2 - Y_{X_{eq}}^2) - \langle \sigma_{XX \rightarrow \phi L^H v} \rangle \right] Y_L/Y_{L_{eq}}
\]
\[
-\langle \sigma_{XL \rightarrow \phi^* H' XH^v} \rangle Y_Y(Y_Y - Y_{L_{eq}}) + \langle \sigma_{XL \rightarrow \phi^* H^v} \rangle Y_Y(Y_Y - Y_{L_{eq}})
\]
\[+ ..., \]
(11)
where we have assumed the dark matter is a Majorana fermion and the “+...” terms involved suppressed \(2 \rightarrow 3\) processes in which there is no on-shell resonance. \(H(T)\) is the Hubble parameter at temperature \(T\) given a flat, radiation-dominated early universe. The equilibrium rates for the relevant \(3 \rightarrow 2\) processes are equal to the equilibrium rates for the reverse \(2 \rightarrow 3\) processes as a result of detailed balance. The actual rates for out-of-equilibrium \(3 \rightarrow 2\) processes are determined by rescaling the equilibrium rates by the ratio of the actual incoming particle densities to the equilibrium densities. \(dY_{\text{eq}}^L/dx\) is the rate at which a lepton asymmetry is injected by annihilation processes, not including the effects of electroweak sphalerons [4].
We can then rewrite the second equation Boltzmann equation as
\[
\frac{x^2 H(m_X)}{s(m_X)} \frac{dY_{\text{eq}}^L}{dx} \sim \langle \sigma^{CPV}_{XX} v \rangle (Y_Y^2 - Y_{X_{eq}}^2) - \langle \sigma^{CP}_{XX} v \rangle Y_{X_{eq}} Y_{L_{eq}} - \langle \sigma^{CP}_{XL} v \rangle Y_Y Y_{\Delta L},
\]
(12)
where
\[
\langle \sigma^{CP}_{XX} v \rangle \equiv \frac{1}{2} \left[ \langle \sigma_{XX \rightarrow \phi^* H' L^v} \rangle + \langle \sigma_{XX \rightarrow \phi L^H v} \rangle \right],
\]
\[
\langle \sigma^{CPV}_{XX} v \rangle \equiv \frac{1}{2} \left[ \langle \sigma_{XX \rightarrow \phi^* H' L^v} \rangle - \langle \sigma_{XX \rightarrow \phi L^H v} \rangle \right],
\]
\[
\langle \sigma^{CP}_{XL} v \rangle \equiv \frac{1}{2} \left[ \langle \sigma_{XL \rightarrow \phi^* XH^v} \rangle + \langle \sigma_{XL \rightarrow \phi^* H^v} \rangle \right].
\]
(13)
We can see that the first term on the right-hand side of eq. (12) drives the asymmetry, while the last two terms tend to wash it out. Note that these washout terms are both Boltzmann-suppressed.
\[4\] Note, if the coupling is proportional to the Higgs vev, then there can also be \(2 \leftrightarrow 4\) processes in which a Higgs boson is produced. We disregard these processes for simplicity, but they will not change the result significantly because they only rescale the inclusive cross-section by a factor proportional to the phase space integration. This rescaling can be absorbed into the couplings. Alternatively, the charges of \(H\) could be chosen such that the contacts operators respect \(SU(2)_L\) and \(U(1)_Y\), in which case there is no Higgs coupling. In this case, \(H\) and \(X\) could both be protected from contact with the Standard Model with charges under a \(Z_4\) discrete symmetry [11], but \(X\) would have to be Dirac due to its imaginary charges. Our numerical results do not change appreciably in this case.
In this scenario, the only washout processes are those generated from the original four-point effective operators via crossing symmetry. Since the necessary loop contribution arises only from the correction to the $H$ propagator, the introduction of the particles which appear in the loop does not yield new tree-level washout processes. As a result, there are no dangerous washout processes (in the sense of [12]) which are not Boltzmann suppressed.
Note that there is an asymmetry in the process $\phi \bar{L} H' \leftrightarrow \phi^* \bar{H}' L$ after one subtracts the real intermediate state (RIS) one-loop diagrams in which an intermediate $XX$ two-particle state goes on-shell (this RIS contribution is already accounted for in process $XX \leftrightarrow \phi \bar{L} H', \phi^* \bar{H}' L$).
The rates for the processes $\phi \bar{L} H' \leftrightarrow \phi^* \bar{H}' L$ can be related to the rates for the processes $XX \leftrightarrow \phi L H', \phi^* H' L$ using the CPT-theorem, which implies that the rates for the inclusive processes $\phi \bar{L} H' \rightarrow \text{anything}$ and $\phi^* \bar{H}' L \rightarrow \text{anything}$ are identical. We have implicitly included the rate asymmetries for these $3 \leftrightarrow 3$ processes in the Boltzmann equation, which thus satisfies detailed balance. We therefore generate no lepton asymmetry when the dark matter is in equilibrium, in contrast to previous models of leptogenesis [15]. Although we can safely ignore finite number density corrections to our calculation, we could equivalently use the CTP formalism [18] to manifestly demonstrate the generation of the asymmetry, but this is beyond the scope of our paper.
We have not specified the high-energy Lagrangian which generates the effective operators described. A particular UV model which generates these effective operators at low-energy may also generate other effective operators which contribute to washout processes, for example, operators of the form $(\bar{H} P_L L)^2$. However, this is a model-dependent question; there will exist UV-completions (for example, models where the mediating particle is exchanged in the $t$- or $u$-channel) in which such operators are not generated at tree-level. In keeping with our use of effective field theory, we will not assume the existence of any additional effective operators beyond the ones we have introduced.
Although it is necessary to assume that $H$ is unstable in order to generate a lepton asymmetry, we nevertheless were able to assume that the width of $H$ is relatively narrow. This implies that we should be able write equivalent Boltzmann equations in which we treat $H$ as a metastable particle which is initially in thermal equilibrium.
B. The effect of electroweak sphalerons
The expression for $d Y_{\Delta L}^{\text{inj}} / d x$ in the Boltzmann equation provides the source term in the differential equation for the lepton number density, which is coupled to the baryon number density through sphalerons. Given a number of generations $N_G$ and arbitrary lepton number sources $f_i$ for each generation $i$, we can write the evolution of the baryon and lepton number
The functions \( \eta(T) \) and \( \gamma(T) \) are defined in terms of the temperature \( T \), the temperature-dependent Higgs field expectation value \( v_{\text{min}} \), and the Chern-Simons diffusion rate \( \Gamma_{\text{diff}}(T) \):
\[
\eta(T) = \frac{\chi(T)}{1 - \chi(T)},
\]
\[
\gamma(T) = N_G^2 \rho(T) [1 - \chi(T)] \frac{\Gamma_{\text{diff}}(T)}{T^3},
\]
\[
\rho(T) = \frac{3 \left[ 65 + 136 N_G + 44 N_G^2 + (117 + 72 N_G) \left( \frac{v_{\text{min}}}{T} \right)^2 \right]}{2 N_G \left[ 30 + 62 N_G + 20 N_G^2 + (54 + 33 N_G) \left( \frac{v_{\text{min}}}{T} \right)^2 \right]},
\]
\[
\chi(T) = \frac{4 \left[ 5 + 12 N_G + 4 N_G^2 + (9 + 6 N_G) \left( \frac{v_{\text{min}}}{T} \right)^2 \right]}{65 + 136 N_G + 44 N_G^2 + (117 + 72 N_G) \left( \frac{v_{\text{min}}}{T} \right)^2}.
\]
The lattice and analytical calculations of \( v_{\text{min}} \) are consistent. The lattice and analytical calculation of \( \Gamma_{\text{diff}} \) differ by an order of magnitude in the range of overlap \( (T = 140 - 155 \text{ GeV}) \), but exhibit the same logarithmic slope. We will use the \( \Gamma_{\text{diff}}(T) \) determined from lattice calculations for \( T \geq 140 \text{ GeV} \) and use the analytical result for \( T \leq 140 \text{ GeV} \) after rescaling the analytical result by a constant factor to provide consistency with lattice calculations in the region of overlap. The \( v_{\text{min}}(T) \) and \( \Gamma_{\text{diff}}(T) \) which we use are plotted in figure [1].
Now we recast the coupled equations for the comoving baryon and lepton numbers in terms of our dimensionless source variables, noting \( N_G = 3 \) and assuming all lepton generations evolve equivalently.
\[
xH(T) \frac{dY_{\Delta B}}{dx} = -\gamma(T) [Y_{\Delta B} + 3 \eta(T) Y_{\Delta L}]
\]
\[
xH(T) \frac{dY_{\Delta L}}{dx} = -\frac{1}{3} \gamma(T) [Y_{\Delta B} + \eta(T) Y_{\Delta L}] + xH(T) \frac{dY_{\text{inj}}}{dx}
\]
(16)
FIG. 1. Lattice calculation of $v_{\text{min}}^2/(T^2 g_{\text{weak}}^2)$ (left) and $\log(\Gamma_{\text{diff}}/T^4)$ (right) through the transition region [20]. For $T < 140$ GeV, $\log(\Gamma_{\text{diff}}/T^4)$ is extrapolated from analytical calculations deep in the broken phase [19], with a constant rescaling to provide consistency with the lattice calculation for $T = 140 - 155$ GeV.
IV. RESULTS
We will assume that $m_H \leq 2m_X$, so that the process $\bar{X}X \rightarrow \bar{H}L$ is kinematically allowed. As in [10–12], we will assume $m_H \sim m_X$. We assume that the reheating temperature of the universe is large enough that the dark matter was in relativistic thermal equilibrium in the early universe ($x < 1$). We then numerically solve the coupled Boltzmann/sphaleron rate equations, using equilibrium at $x = 1$ as a boundary condition.
Sphaleron processes will start to decouple for temperatures $T \lesssim \mathcal{O}(100)$ GeV. We will thus find that, for $m_X \gg 100$ GeV, the lepton asymmetry is generated when sphalerons are active, and the magnitude of the baryon asymmetry is roughly the same as that of the lepton asymmetry at late times.
For all of the models we consider, we take $\langle \sigma A v \rangle = 1$ pb $\gg \langle \sigma_{\bar{X}X \rightarrow \bar{H}LV} \rangle$. As a result, $X$ will annihilate rapidly enough to ensure that its density does not exceed observational bounds, while the annihilation process $\bar{X}X \rightarrow \bar{H}L, \bar{L}H$ will not significantly affect the dark matter density (though it will impact the baryon asymmetry). For the case where only the operator $\mathcal{O}_{S=0}$ is present, the relevant parameters of the model are $m_X$, $m_H/m_X$, $\Gamma_H/m_H$ and $\text{Re}(\lambda_1 \lambda_2^*)$ (the last parameter is replaced by $\text{Im}(\lambda_3 \lambda_4^*)$ in the case where only $\mathcal{O}_{S=1}$ is present).
We can then illustrate our results with some benchmark points. In figure we plot the thermally-averaged cross sections for the processes $XX \rightarrow \phi^* \bar{H}'L$ (both $CP$-invariant and $CP$-violating terms) and $XL \rightarrow \phi H'X$ (the $CP$-invariant term) as a function of $x = m_X/T$. We also plot the contribution of these terms to the lepton source injection rate, as well as $Y_B$, $Y_X$ and $Y_{Xeq}$. We have chosen the “high-mass” benchmark parameters $m_X = 5$ TeV,
As we expected, the process $XL \rightarrow \phi H' X$ is kinematically-suppressed at low temperature. Note, however, that we have assumed the narrow-width approximation; this approximation will break down at sufficiently low temperatures, when the Boltzmann suppression required for the production of an on-shell $H$ is larger than the cross section suppression when $H$ is off-shell. But if we instead take $H'$ and/or $\phi$ to be massive, then even this off-shell process can be suppressed, while on-shell processes will be unaffected.
In figure 3 we plot the $Y_B$, $Y_X$, $Y_{X_{eq}}$ and the lepton injection rates (both source and washout terms) as a function of $x = m_X/T$ for a narrower-width benchmark model with $m_X = 5$ TeV, $m_H = 7$ TeV, $\lambda_1 = \lambda_2 = 0.5$, $\langle \sigma_A v \rangle = 1$ pb, $\Gamma_H/m_H = 0.05$ (left panel) and for a low-mass benchmark model with $m_X = 1.5$ TeV, $m_H = 2.2$ TeV, $\lambda_1 = \lambda_2 = 1$, $\langle \sigma_A v \rangle = 1$ pb, $\Gamma_H/m_H = 0.1$ (right panel). For all benchmark models, the couplings are chosen so that the final baryon asymmetry matches observation. Note that the narrower-width benchmark is nearly identical to the high mass benchmark, only washout processes freeze out slightly later. For the low-mass benchmark, sphalerons begin to decouple around when washout processes freeze out, thus forcing a sharper freeze out of baryon number. The parameters of these benchmark models are summarized in Table II.
It is interesting to note that the $CP$-violating part of the process $XX \leftrightarrow \bar{L}H, \bar{H}L$ begins to drive the asymmetry near $x \sim 1$, i.e. as soon as the dark matter becomes non-relativistic. This may seem counterintuitive, since the Sakharov conditions require a departure from thermal equilibrium and dark matter freeze out occurs much later, near $x \sim 20 - 30$. The
FIG. 3. Rate contributions and Boltzmann equation solutions for our narrower-width (left panel) and low-mass (right panel) benchmarks (colors same as in right panel of figure 2). Parameters are summarized in Table II.
| benchmark | $m_X$ | $m_H$ | $\Gamma_H/m_H$ | $\lambda_1 = \lambda_2$ | $\epsilon$ | $\langle \sigma_{XX \rightarrow \phi^* H^* L^v} \rangle / \langle \sigma_A v \rangle$ |
|-----------------|--------|--------|-----------------|--------------------------|------------|--------------------------------------------------|
| low-mass | 1.5 TeV | 2.2 TeV | 0.10 | 1.0 | 0.045 | 0.002 |
| high-mass | 5.0 TeV | 7.0 TeV | 0.10 | 0.5 | 0.045 | 0.008 |
| narrower-width | 5.0 TeV | 7.0 TeV | 0.05 | 1.0 | 0.022 | 0.033 |
TABLE II. Benchmarks
point is that the dark matter density departs slightly from the equilibrium density as soon as dark matter becomes non-relativistic. At freeze-out, dark matter stops tracking the equilibrium density and the departure from equilibrium becomes large. One can see this simply by considering the Boltzmann equation (eq. 10); if the dark matter density is equal to the equilibrium density, then $dY/dx = 0$. This relation is satisfied if dark matter is relativistic ($Y \sim \text{const}$), but is violated when dark matter is non-relativistic ($Y \sim x^{-3/2}e^{-x}$).
A slight departure from equilibrium is necessary to provide the excess annihilation which drives $Y$ to smaller values. Although the departure from equilibrium is very small before freeze out, the dark matter density at $x \sim 1$ is so much larger than at $x \sim 20$ that the driving contribution to the lepton asymmetry is largest at small $x$. However, at small $x$ the washout processes are also at their strongest and the net asymmetry is quite small. A large asymmetry begins to be generated as soon as the washout processes begin to freeze out, which for these models typically happens near $x \sim 10$, as in [12].
There are a few features which distinguish our results from those of other WIMPy baryogenesis models. First of all, in previous works, the interactions necessary to produce the needed one-loop diagrams also introduce tree-level washout diagrams in which $X$ does not appear as an initial or final state. These washout processes are essentially processes of the form $\bar{H}L \leftrightarrow LH$, and can be significant even when $T < m_X$. On the other hand, in the
class of models we consider, all washout diagrams have $X$ as a final state.
Note also that $\epsilon \sim \Gamma_H/2m_{H,X}$, and is independent of the mediator scale $M_*$. This is in contrast with other WIMPy baryogenesis models, where one typically finds $\epsilon \propto m_X^2/M_*^2$. This difference has some interesting effects. If we assume that $X$ constitutes all of the dark matter, then the total cross section for the annihilation process $XX \rightarrow \bar{H}L, \bar{L}H$ is bounded by $\sim 1$ pb. In order to generate a large enough asymmetry, $\epsilon$ cannot be too small; it appears that one would need $\epsilon \sim \mathcal{O}(0.01 - 0.1)$. If $\epsilon \sim (\lambda^2/4\pi)m_X^2/M_*^2$ and $\lambda \sim 1$, this would require that $M_* \lesssim 3m_X$. By contrast, in our low-mass benchmark model, the new physics scale $M_*$ can be much larger, since $\epsilon$ is independent of the scale of the new physics in the effective operator. As a result, the total $XX \rightarrow \bar{H}L, \bar{L}H$ cross section can be much smaller than the $\langle \sigma_A v \rangle \sim 1$ pb.
In all of the models we have considered, we have chosen $m_H \sim m_X$. It is difficult to find a successful model if one instead chooses $m_H \ll m_X$. The reason is because we have assumed the narrow-width approximation, in which $H$ acts as a resonance, and thus require $\Gamma_H \ll m_H$. In such a model, since we would also still require $\epsilon \propto \Gamma_H/m_X$, a light $H$ field would imply a small cross section asymmetry.
V. CONCLUSIONS
We have considered a model of WIMPy leptogenesis, in which a lepton asymmetry is generated by dark matter annihilation processes which violate $C$, $CP$ and lepton number. We have studied in detail the necessity for one-loop contributions to the annihilation process. In particular, we have found the $CP$-violating terms may all arise at tree-level, while one-loop diagrams may arise only in absorptive final state interactions in a sterile sector.
The advantage of this type of model is that it allows one to sequester the one-loop suppression from the generation of a $CP$-violating phase. In WIMPy baryogenesis models where this sequestration does not occur, the introduction of one-loop terms implies the presence of new tree-level process which are not Boltzmann suppressed and which can washout the baryon asymmetry. In the class of models we have considered, these dangerous washout processes do not occur. Moreover, because the ratio of $CP$-violating to $CP$-conserving terms in the cross section is independent of the scale of new physics, we find that WIMPy models with $m_X \sim 1.5$ TeV can work with a new physics scale $M_*$ as large as 10 TeV, and where the annihilation cross sections relevant for WIMPy leptogenesis are much smaller than 1 pb.
It is interesting to consider prospects for probing these dark matter interactions experimentally. Indirect detection may be feasible for WIMPy leptogenesis models in general, but
given our specific $CP$-violating processes, primary dark matter annihilation channels would likely dominate over any measurable imprint our subdominant channel would leave on the cosmic ray spectrum. Better prospects may lie with high energy/luminosity $e^+/e^-$ colliders, which may be able to probe lepton number- or lepton flavor-violating processes to which these operators could contribute.
For simplicity, we have focused on the approximation where, despite the presence of final state absorptive interactions, the sterile particle $H$ can be treated as a narrow resonance produced on-shell. But this assumption is not required, and if the narrow-width approximation does not hold, then all of the asymmetry-generating and washout processes would have to be fully treated as $2 \to 3$ processes. In this case, one would expect that one-loop suppression required for $CP$-violating annihilation rates would be significantly reduced. It would be interesting to study this scenario concretely.
Acknowledgements
We are grateful to S. Pakvasa, X. Tata, B. Thomas and L. Ubaldi for useful discussions. This work is supported in part by Department of Energy grants DE-FG02-04ER41291 and DE-FG02-13ER41913. We thank the organizers of TASI 2013 and the Center for Theoretical Underground Physics and Related Areas (CETUP) in South Dakota for their support and hospitality while this work was being completed.
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Research Article
Anatomical Evaluation of Mandibular Molars in a Saudi Population: An In Vivo Cone-Beam Computed Tomography Study
Mohammed Mashyakhy, Ahmad Jabali, Fatimah Saleem Alabsi, Abdulaziz AbuMelha, Mazen Alkahtany, and Shilpa Bhandi
1Department of Restorative Dental Science, College of Dentistry, Jazan University, Jazan, Saudi Arabia
2Department of Restorative Dental Sciences, College of Dentistry, King Khalid University, Abha, Saudi Arabia
3Department of Restorative Dental Sciences, College of Dentistry, King Saud University, Riyadh, Saudi Arabia
Correspondence should be addressed to Shilpa Bhandi; [email protected]
Received 19 January 2021; Revised 6 March 2021; Accepted 18 March 2021; Published 31 March 2021
Academic Editor: Cesar Rogério Pucci
Copyright © 2021 Mohammed Mashyakhy et al. 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.
Objective. This study assessed the canal configuration of mandibular molars according to Vertucci’s classification of a Saudi population using cone-beam computed tomography (CBCT). Methods. A total of 290 first and 367 second mandibular molars were analyzed. The CBCT images were evaluated in three sections to inspect the number of roots and canals and canal system. The data are presented as frequencies and percentages. The chi-squared test was used to assess differences between both sides. SPSS was used for analysis, with a significance level of \( \alpha \leq 0.05 \). Results. Among the first molars, 95.4% of the teeth had two roots, and 64.5% had three canals. Approximately 57.9% showed Vertucci type IV mesial roots. Between the second molars, 89.6% of teeth had two roots and 80.4% had three canals. The frequency of Vertucci type IV (39.4%) was the highest in mesial roots. The first molars showed a high prevalence of 3-rooted teeth (5.5%). Both the right and left sides showed teeth with similar external and internal anatomy (\( p < 0.05 \)). Conclusion. Most of the mandibular first and second molars had two roots and three canals. In the first mandibular molars, similar to the second mandibular molars, the majority of the mesial canals had Vertucci type IV, while the distal canals had Vertucci type I.
1. Background
The success of a root canal treatment (RCT) is highly dependent on adequate knowledge and understanding of the external and internal morphology of the root canal system (RCS), which permits proper chemomechanical cleaning and shaping of all the pulp spaces [1].
Clinicians should be aware of the possible variations in root and root canal morphology and employ the available diagnostic tools to avoid missing some RCS anatomy. Mandibular molars are characterized by the presence of two roots (mesial and distal); however, the prevalence of three-rooted mandibular molars is common [2, 3]. A complex morphology of the RCS may be encountered during the treatment of these teeth [4, 5]. Preoperative diagnosis is among the key aspects promoting a good prognosis of the endodontic treatment performed [6]. Preoperative endodontic imaging aids in assessing the root morphology, root size, internal structure, and periapical condition of the offending tooth. In the absence of radiographic images, pathology identification and treatment become perplexing [7]. Pretreatment evaluation reveals the challenges that the dentist may be faced with during treatment, such as calcified, tortuous, and intricate canal anatomy, in addition to the proximity of a pathology surrounding anatomic structures. For accurate analysis and treatment planning, the area of concern must be properly selected to determine supplementary investigations or further treatment plan [8].
Researchers have proposed numerous methods to study the anatomy of the tooth, such as various radiographs before treatment with varying angulations and analysis [9], staining techniques [10], tomography [11], and radiography using...
2 International Journal of Dentistry
3D software imaging program was used for the processing of exposure time and 0.25 mm voxel size and Morita’s i-Dixel with the following parameters: 5–8 mA, 90 kV, with 17.5 s was a three-dimensional Accuitomo 170 (MORITA, Japan) no. REC41/4/087). The CBCT device utilized for research for Scientific Research Ethics at Jazan University (Reference f_ he CBCT study was designed to evaluate the number of roots and root canals and internal morphology and compare the right and left permanent mandibular first and second molars.
2. Materials and Methods
The database archive of the College of Dentistry at Jazan University was searched for CBCT scans available from 2016 to 2017. A retrospective study consisting of 208 CBCT scans was performed. These radiographs included those of 100 males and 108 females in the age group ranging from 17 to 59 years. Scans were previously taken in different departments for diagnostic and treatment planning purposes. Ethical approval was obtained from the Standing Committee for Scientific Research Ethics at Jazan University (Reference no. REC41/4/087). The CBCT device utilized for research was a three-dimensional Accuitomo 170 (MORITA, Japan) with the following parameters: 5–8 mA, 90 kV, with 17.5 s exposure time and 0.25 mm voxel size and Morita’s i-Dixel 3D software imaging program was used for the processing of the CBCT radiographs.
A total of 657 mandibular first and second molars (290 first and 367 second molars) were analyzed in the current study. Teeth were included if they had fully developed roots and closed apices. The exclusion criteria were teeth with root canal treatment, calcified canals, and resorbed roots. Distorted or unclear teeth on CBCT scans were excluded. Three sections were acquired for each tooth (serial axial, coronal, and sagittal) to ensure the accuracy of the evaluation of the teeth. All the teeth were included in the evaluation of the external morphology. For internal morphology, however, teeth with a C-shaped configuration were excluded. The evaluated parameters were the number of roots, number of root canals, and root canal configurations according to Vertucci’s taxonomy [25]. A comparison between the right and left sides was also performed.
To reduce measurement errors, one observer evaluated 25% of the samples twice with an interval period of 3 weeks. The Kappa test results revealed an almost impeccable concordance between interpretations with a value of 88.4% and asymptotic standard error of ±9.5%.
2.1. Statistical Analysis. The Statistical Package for Social Sciences software program for Windows (SPSS V25; IBM, Chicago, IL, USA) was used for data analysis. In addition to the frequencies and percentages, the chi-squared test was used to determine the differences between the right and left sides. To compare variables with more than two categories, the contingency coefficient option was selected. The significance level was set at \( p < 0.05 \) for all analyses.
3. Results
In this study, 290 mandibular first molars were assessed (Table 1). The majority (94.5%) had two roots, and 16 (5.5%) teeth had three roots, in which the extra roots were all lingual (Figure 1). A total of 187 (64.5%) teeth had three canals, and 101 (34.8%) teeth had four canals (Figure 2). More than half of the sample (57.9%) had Vertucci type IV in the mesial canals. In contrast, 105 teeth (36.2%) had Vertucci type II canals. In contrast, 200 (69.0%) teeth had Vertucci type I and 50 (17.2%) teeth had Vertucci type III in the distal canals (Figure 3).
No significant difference was observed in the number of roots \( (p = 1.000) \), the number of canals \( (p = 0.361) \), and canal configurations in mesial roots \( (p = 0.312) \) and distal roots \( (P = 0.978) \) between the right and left sides. Additional details are provided in Table 2.
A total of 367 mandibular second molars were evaluated (Table 3). Of them, 329 (89.6%) teeth had two roots, 31 (8.5%) molars had one root (fused roots), and seven (1.9%) teeth had three roots. Regarding the internal morphology, 295 (80.4%) teeth had three canals, 23 (6.3%) teeth had two canals, and 20 (5.4%) teeth had four canals. Among the teeth with fused roots, 29 teeth (7.9%) displayed other canal configurations. The frequency of Vertucci type IV (39.4%) was the highest in mesial canals followed by Vertucci type II (25.4%). In contrast, Vertucci type I was the most frequent type in the distal canals (95.6%) and Vertucci type IV was not detected.
The distribution of the number of roots and the number of canals on both sides was nearly similar, with no significant difference \( (p = 0.935 \) and \( p = 0.857 \) ) and the same for both mesial \( (p = 0.780) \) and distal \( (p = 0.857) \) roots based on Vertucci’s classification. Additional details are provided in Table 4.
4. Discussion
In the current study, CBCT was used to study the root canal anatomy of mandibular first and second molars. The mandibular first molar is among the first permanent teeth to erupt in the oral cavity. It is most prone to caries owing to its immature enamel since its phase of mineralization concurs with early childhood caries and the window of infectivity.
erupts when the maintenance of oral hygiene is challenging, thus making it more susceptible to dental caries [26]. Owing to the complex root canal morphology of mandibular molars, especially in the mesial root, root canal therapy is a challenging task with an unexpected prognosis. The mesial root of the mandibular first molar is wide buccolingually and narrow mesiodistally. In comparison, the distal root is conical in shape [27]. The mandibular second molars mostly shared the same characteristics.
The root canal anatomy of the teeth has been discussed, researched, and categorized by many scholars based on the number of roots and root canals in the teeth. Weine et al. first classified the canal configuration of teeth with one root into four basic types [28]. However, this classification is not applicable to teeth with multiple roots. In 1984, Vertucci published a new classification by expanding Weine’s classification and using it to classify maxillary first premolars. He added four additional types of configurations to Weine’s classification [25]. Recently, Ahmed et al. [29, 30] introduced a new classification system based on 3D technology to describe quickly and precisely the RCS that could be applicable in research, clinical practice, and training. Despite certain drawbacks, Vertucci’s classification is the most commonly used classification system to date [31]. In the present study, Vertucci’s classification was used to study the root canal configuration in the Saudi population.
CBCT is the best imaging technique for the analysis of root canal morphology owing to its diagnostic accuracy and feasibility [16, 32, 33]. In the present study, CBCT was used to determine the number of roots, the number of root canals, and the internal canal configuration of the mandibular first and second molars. A comparison was also made between the contralateral mandibular molars.
The majority of mandibular first and second molar teeth presented with two roots (94.5% and 89.6%, resp.), similar to previous studies from different populations [3, 34–36]. In addition, 3-rooted molars were observed in higher incidence in the first molars (5.5%) than in the second molars (1.7%), consistent with a recent report on the Saudi population (3.05% and 1.48% for first and second molars, resp.) [2]. Other studies in different populations have shown a similar lower prevalence of extra rooted molars [34, 37]. However, in contrast, other studies in Asian populations showed a high number of extra rooted first molars: 21.6% in Malaysian [38] and 32.35% in Shanghai Chinese populations [39]. Therefore, the prevalence seems to be influenced by ethnicity; complex anatomy is expected in Asian origin.
In the current study, 34.8% of the molars had four canals. It was observed that 31.8% of the two-rooted first mandibular molars had four canals, and 87.5% of the three-rooted mandibular first molars had four canals. In contrast, 64.5% of teeth had three canals, of which 67.5% and 12.5%...
were in two- and in three-rooted molars, respectively (Table 1). This implies that most of the first molars in the Saudi population have three canals. This finding is in agreement with the research conducted by Mashyakhy et al. on the Saudi population [20], Abarca et al. on the Palestinian population [36], and Senan et al. on the Yemeni subpopulation [40]. In another study published by Silva et al. [41] on
CBCT images of mandibular first and second molars of a Brazilian population, the first molars had two separate roots (74%) with a greater occurrence of two canals in the mesial root and one canal in the distal root. In contrast, the mandibular second molars had two distinct roots with two canals; one canal in the mesial root and one in the distant root formed 54% of the sample size.
Additionally, in our study, it was observed that the canal configuration in the mesial root of the mandibular first molar was Vertucci’s type IV (57.9%) and that of the distal canal Vertucci’s type I (69%). This finding was in accordance with Zhang et al., in which 81% of the mesial canals were Vertucci’s type IV, and 84% of canals in distal canals were type I in the Chinese population [42]. However, our findings differed from the findings in the Yemeni population reported by Senan et al., where two roots and three canals were found in 89.4% of teeth, of which, in the mesial canal, 57% were type II and 35.6% were type IV. In a study published by Kantilieraki et al., the mesial canal in the mandibular first molar in the Greek population, 69.8% had a type II configuration, and the distal canal had a type I configuration in 81.7% [3]. In the study published by Torres et al., in Belgian and Chilean populations, 42.8% of the mesial canal in the mandibular first molar had a type V configuration, 33.5% had a type III configuration in the Belgian population, 28.9% had type III canals, and 18.9% had type II configuration in the Chilean population. In comparison, 72.8% of the distal canals had a type I configuration in the Belgian population and 78.8% had a type I population in the Chilean population [35].
In mandibular second molars, it was observed that, in most of the studies, two roots and three canals were more common, which was similar to our study wherein 89.4% of the 2nd molars had two roots and three canals with the structure of mesial canals being similar to Vertucci’s type IV.
| Table 2: Comparison amongst right and left edges among mandibular 1st molars N (%) |
|---------------------------------------------|-----------------|-----------------|-----------------|-----------------|-----------------|-----------------|
| All teeth (N = 290) | 2-rooted teeth (N = 274) | 3-rooted teeth (N = 16) |
| Number of canals | Right | Left | P | Right | Left | P | Right | Left | P |
| 2 canals | 2 (1.3) | 0 (0.0) | 0.361 | 2 (1.4) | 0 (0.0) | 0.352 | — | — | 1.000 |
| 3 canals | 95 (62.9) | 92 (66.2) | 94 (65.7) | 91 (69.5) | 1 (12.5) | 1 (12.5) |
| 4 canals | 54 (35.8) | 47 (33.8) | 47 (32.9) | 40 (30.5) | 7 (87.5) | 7 (87.5) |
| Total | 151 (52.1) | 139 (47.9) | 143 (52.2) | 131 (47.8) | 8 (50.0) | 8 (50.0) |
| M. root Vertucci types | Right | Left | P | Right | Left | P | Right | Left | P |
|---------------------------------------------|-------|------|------|-------|------|------|-------|------|------|
| Type I | 3 (2.0) | 0 (0.0) | 0.312 | 2 (1.4) | 0 (0.0) | 0.581 | 1 (12.5) | 0 (0.0) | 0.448 |
| Type II | 51 (33.8) | 54 (38.8) | 49 (34.3) | 51 (38.9) | 2 (25.0) | 3 (37.5) |
| Type III | 1 (0.7) | 3 (2.2) | 1 (0.7) | 2 (1.5) | 0 (0.0) | 1 (12.5) |
| Type IV | 91 (60.3) | 77 (55.4) | 86 (60.1) | 74 (56.5) | 5 (62.5) | 3 (37.5) |
| Type V | 5 (3.3) | 5 (3.6) | 5 (3.5) | 4 (3.1) | 0 (0.0) | 1 (12.5) |
| Total | 151 (52.1) | 139 (47.9) | 143 (52.2) | 131 (47.8) | 8 (50.0) | 8 (50.0) |
| D. root Vertucci types | Right | Left | P | Right | Left | P | Right | Left | P |
|---------------------------------------------|-------|------|------|-------|------|------|-------|------|------|
| Type I | 102 (67.5) | 98 (70.5) | 0.978 | 94 (65.7) | 90 (68.7) | 0.980 | 8 (100.0) | 8 (100.0) | NC |
| Type II | 5 (3.3) | 4 (2.9) | 5 (3.5) | 4 (3.1) | — | — | — | — | — |
| Type III | 28 (18.5) | 22 (15.8) | 28 (19.6) | 22 (16.8) | — | — | — | — | — |
| Type IV | 1 (0.7) | 1 (0.7) | 1 (0.8) | 1 (0.8) | — | — | — | — | — |
| Type V | 15 (9.9) | 14 (10.1) | 15 (10.5) | 14 (10.7) | — | — | — | — | — |
| Total | 151 (52.1) | 139 (47.9) | 143 (52.2) | 131 (47.8) | 8 (50.0) | 8 (50.0) |
| Table 3: Frequency of number of roots, number of canals, and Vertucci type among mandibular 2nd molars N (%) |
|---------------------------------------------------------------|-----------------|-----------------|-----------------|-----------------|
| All teeth (N = 367) | 1-rooted teeth† (fused; N = 31) | 2-rooted teeth (N = 329) | 3-rooted teeth* (N = 7) |
| Number of canals | Right | Left | P | Right | Left | P | Right | Left | P |
| 2 canals | 23 (6.3) | 1 (3.2) | — | 22 (6.6) | — | — |
| 3 canals | 295 (80.4) | 1 (3.2) | — | 294 (89.4) | — | — |
| 4 canals | 20 (5.4) | — | — | 13 (4.0) | 7 (100.0) | — | — |
| Other | 29 (7.9) | 29 (93.6) | — | — | — | — | — | — |
| M. Vertucci types | Right | Left | P | Right | Left | P | Right | Left | P |
|--------------------------------------------------------------|-------|------|------|-------|------|------|-------|------|------|
| Type I | 21 (6.2) | — | — | 21 (6.4) | — | — |
| Type II | 86 (25.4) | — | — | 84 (25.5) | 2 (28.6) | — |
| Type III | 54 (16) | — | — | 53 (16.1) | 1 (14.3) | — | — |
| Type IV | 133 (39.4) | 1 (50.0) | — | 130 (39.5) | 2 (28.6) | — | — |
| Type V | 44 (13) | 1 (50.0) | — | 41 (12.5) | 2 (28.6) | — | — | — |
| D. Vertucci types | Right | Left | P | Right | Left | P | Right | Left | P |
|--------------------------------------------------------------|-------|------|------|-------|------|------|-------|------|------|
| Type I | 323 (95.6) | 2 (100.0) | — | 315 (95.7) | 6 (85.7) | — | — |
| Type II | 3 (0.9) | — | — | 3 (0.9) | — | — | — |
| Type III | 3 (0.9) | — | — | 3 (0.9) | — | — | — |
| Type IV | — | — | — | — | — | — | — |
| Type V | 9 (2.6) | — | 8 (2.4) | 1 (14.3) | — | — | — | — |
†29 teeth had joined root canal system; they were excluded from internal morphology analysis. *All extra roots had one canal and Vertucci type I.
in 39.5% of teeth, and 25.5% of teeth had Vertucci’s type II configuration. In the distal root, the canals had Vertucci type II (28.6%), type IV (28.6%), and type V (28%) canals. A few teeth were also reported to have three roots with four canals (Table 3). In comparison to other studies, our outcomes were similar to those reported by Zhang et al. on mandibular first and second molars in the Chinese population. He reported similar to those reported by Zhang et al. on mandibular first and second molar anatomy were compared, and no significant differences were observed in the number of roots, number of root canals, and canal configurations of the mesial and distal roots (Tables 2 and 4). Our results are concurrent with a previous report on the Malaysian population using the same methodology [36]. Differences in side help the clinician predict the anatomy of the contralateral tooth when treating both sides.
5. Conclusion
Based on the findings of the present study, we conclude that the majority of the first and second mandibular molars have two roots and three canals and the presence of a third root is not uncommon. The configuration of the canals differs from population to population and depends on various factors such as race, genetics, and ethnicity. The configuration of the canals should be determined prior to treatment using CBCT for a better understanding of the root canal system.
Data Availability
The data are available from the corresponding author upon reasonable request.
Conflicts of Interest
The authors declare that they have no conflicts of interest.
References
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[15] I. B. Seltzer and S. Seltzer, “Roentgenographic and direct observation of experimental lesions in bone: I,” Journal of Endodontics, vol. 29, no. 11, pp. 707–712, 2003.
[16] S. B. Paurazas, J. R. Geist, F. E. Pink, M. M. Hoen, and H. R. Steiman, “Comparison of diagnostic accuracy of digital imaging by using CCD and CMOS-APS sensors with E-speed film in the detection of periapical bony lesions,” Oral Surgery, Oral Medicine, Oral Pathology, Oral Radiology, and Endodontology, vol. 89, no. 3, pp. 356–362, 2000.
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[38] J. Y. Y. Pan, A. Parolia, S. R. Chuah, S. Bhatia, S. Mutalik, and A. Pau, "Root canal morphology of permanent teeth in a Malaysian subpopulation using cone-beam computed tomography," *BMC Oral Health*, vol. 19, no. 1, p. 14, 2019.
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| 2025-03-05T00:00:00 |
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TASK 1A DCASE 2021: ACOUSTIC SCENE CLASSIFICATION WITH MISMATCH-DEVICES USING SQUEEZE-EXCITATION TECHNIQUE AND LOW-COMPLEXITY CONSTRAINT
Technical Report
Javier Naranjo-Alcazar\textsuperscript{1,2}, Sergi Perez-Castanos\textsuperscript{2}, Maximo Cobos\textsuperscript{2}, Francesc J. Ferri\textsuperscript{2}, Pedro Zuccarello\textsuperscript{1}
\textsuperscript{1} Instituto Tecnolórgico de Informática, València, Spain \{jnarnajo, pzuccarello\}@iti.es
\textsuperscript{2} Universitat de València, Burjassot, Spain, \{[email protected], \{maximo.cobos, francesc.ferri\}@uv.es\}
1. INTRODUCTION
Extracting information from audio signals can be a great improvement in existing applications or future products (home assistants, wildlife monitoring, autonomous cars, etc.). Machine listening is understood as the set of algorithms that are capable of extracting relevant information from audio. One of the most common tasks in this field is known as Acoustic Scene Classification (ASC) \cite{1,2,3,4,5}. The ultimate goal is to extract context information from the audio, more specifically, to predict the location where the audio is produced (park, metro station, airport, etc.). This problem has been addressed in all previous editions of DCASE, and has been modified with different restrictions. In this report an ASC system is designed to be limited by the size of the model and with the extra difficulty that the audios used in the training come from different audio sources (mismatch devices).
The motivation of DCASE 2021 Task 1a is to create an acoustic scene classifier that should work in real-time (low-complexity consideration) and capable of using different recording sources (microphones) \cite{5}. This subtask can be understood as a merge of both subtask in the 2020 edition in which the mismatch problem had no restriction on the model, and on the other hand, the low complexity subtask only used audios from the same recording source.
The approach proposed in this work consists in a CNN implemented with squeeze-excitation modules feed with a 2D audio representation using the Gammatone filter bank. The model is converted to TFLite format in order to accomplish the model size restriction. More information on the proposed framework is presented in Section 2 while the results obtained in the development stage are presented in Section 3. Some conclusions are drawn in Section 4.
2. METHODS
2.1. Audio Representation
Following the idea of last year submissions \cite{6,7} a Gammatone filter bank-based representation has been chosen for providing a slightly superior performance than other alternatives (e.g. Mel-scale filter banks) in preliminary tests.
All representations are calculated with a window size of 40 ms with 50\% overlapping, using a sampling rate of 44.1 kHz and 64 frequency bins. All frequency bins are normalize with 0 mean and standard deviation equal to 1 using all the provided data. Gammatone representations were computed by using the Auditory Toolbox presented in \cite{8} with Python implementation.
2.2. Convolutional Neural Network
The convolutional network trained with the audio information is composed of blocks defined as \textit{Conv-StandardPOST}. These blocks were proposed in \cite{9}. The aim of these blocks is to achieve improved accuracy by recalibrating the internal feature maps using residual \cite{10} and squeeze-excitation techniques \cite{11,12}. For more insight about this choice, please see \cite{9} where \textit{Conv-StandardPOST} is fully explained and compared to other competing blocks. The architecture of the network can be seen in Table 1.
2.3. Experimental details
2.3.1. Training
The optimizer used is Adam \cite{13}. The loss used is the one known as Focal Loss \cite{14}. This loss function assigns greater emphasis to those samples that are not classified correctly, forcing the system to correctly classify the more challenging samples (those related to devices with lower resolution). The hyperparameters are set as $\alpha = 0.25$ and $\gamma = 2$. During training, the learning rate (which starts at 0.001) is modified by a factor of 0.5 if the validation accuracy does not improve for 20 epochs. Training ends if this metric is not improved for 50 epochs. The maximum number of epochs is 500.
converted to TFLite format to reduce its size. Techniques is presented to improve its performance, which is then extended to be deployed in real-time solutions on edge devices for audios come from different sources) and complexity constraint (in-Table 2: Accuracy (%) results obtained compare with the proposed baseline.
| Model size (KB) |
|-----------------|
| Challenge Baseline | 47.70 |
| Proposed system | 64.18 |
Table 1: Network architecture. Conv-StandardPost is denoted with the number of filters (K), the kernel size and the ratio of the squeeze-excitation module (p). The Max Pooling layer is defined by the pool size and the Dropout by the rate. The classification layer corresponds to a Dense with 10 units.
2.3.2. Dataset
The dataset provided for the task is known as TAU Urban Acoustic Scenes 2020 Mobile [15]. In turn, this dataset is divided into two splits, the development split and the evaluation split. While the development split contains scenes recorded in 10 cities, the evaluation one contains scenes from 12 cities (there are two cities unseen in the development set). The development split contains audio recorded from 3 real devices and 6 simulated ones. The total amount of hours present in this specific split is 64 hours. The audio is provided in mono, 44.1 kHz of sampling rate and 24-bit format.
3. RESULTS
The results obtained by the system proposed can be seen in Table 2. The proposed approach surpass the baseline by 17 percentage points by only having 5 KB more than the baseline regarding model complexity.
| Accuracy (%) | Model size (KB) |
|--------------|-----------------|
| Challenge Baseline | 47.70 |
| Proposed system | 64.18 |
4. CONCLUSION
Understanding the sounds around us can be a great improvement in a multitude of applications. These solutions must deal with certain issues that may arise. In this task, scene classification problem is proposed with the extra issues of mismatch devices (available audios come from different sources) and complexity constraint (intended to be deployed in real-time solutions on edge devices for example).
In this an ASC system based on the Gammatone representation of the audio and a slim neural network using squeeze-excitation techniques is presented to improve its performance, which is then converted to TFLite format to reduce its size.
5. ACKNOWLEDGEMENTS
The participation of Dr. Cobos and Dr. Ferri is supported by ERDF and the Spanish Ministry of Science, Innovation and Universities under Grant RTI2018-097045-B-C21, as well as grants AICO/2020/154 and AEST/2020/012 from Generalitat Valenciana.
6. REFERENCES
[1] A. Mesaros, T. Heittola, and T. Virtanen, “Acoustic scene classification: an overview of dcase 2017 challenge entries,” in 2018 16th International Workshop on Acoustic Signal Enhancement (IWAENC). IEEE, 2018, pp. 411–415.
[2] ——, “Acoustic scene classification in dcase 2019 challenge: Closed and open set classification and data mismatch setups,” 2019.
[3] M. Valenti, A. Diment, G. Parascandolo, S. Squartini, and T. Virtanen, “Dcase 2016 acoustic scene classification using convolutional neural networks,” in Proc. Workshop Detection Classif. Acoust. Scenes Events, 2016, pp. 95–99.
[4] D. Barchiesi, D. Giannoulis, D. Stowell, and M. D. Plumbley, “Acoustic scene classification: Classifying environments from the sounds they produce,” IEEE Signal Processing Magazine, vol. 32, no. 3, pp. 16–34, 2015.
[5] I. Martín-Morató, T. Heittola, A. Mesaros, and T. Virtanen, “Low-complexity acoustic scene classification for multi-device audio: analysis of dcase 2021 challenge systems,” 2021.
[6] S. Perez-Castanos, J. Naranjo-Alcazar, P. Zuccarello, M. Cobos, and F. J. Ferri, “Cnn depth analysis with different channel inputs for acoustic scene classification,” arXiv preprint arXiv:1906.04591, 2019.
[7] J. Naranjo-Alcazar, S. Perez-Castanos, P. Zuccarello, and M. Cobos, “Task 1 dcase 2020: Asc with mismatch devices and reduced size model using residual squeeze-excitation cnns,” DCASE2020 Challenge, Tech. Rep. Tech. Rep., 2020.
[8] M. Slaney, “Auditory toolbox,” Interval Research Corporation, Tech. Rep, vol. 10, no. 1998, 1998.
[9] J. Naranjo-Alcazar, S. Perez-Castanos, P. Zuccarello, and M. Cobos, “Acoustic scene classification with squeeze-excitation residual networks,” IEEE Access, vol. 8, pp. 112 287–112 296, 2020.
[10] K. He, X. Zhang, S. Ren, and J. Sun, “Deep residual learning for image recognition,” in Proceedings of the IEEE conference on computer vision and pattern recognition, 2016, pp. 770–778.
[11] J. Hu, L. Shen, and G. Sun, “Squeeze-and-excitation networks,” 2018 IEEE/CVF Conference on Computer Vision and Pattern Recognition, Jun 2018. [Online]. Available: http://dx.doi.org/10.1109/CVPR.2018.00745
[12] A. G. Roy, N. Navab, and C. Wachinger, “Concurrent spatial and channel ‘squeeze & excitation’ in fully convolutional networks,” in International Conference on Medical Image Computing and Computer-Assisted Intervention. Springer, 2018, pp. 421–429.
[13] D. P. Kingma and J. Ba, “Adam: A method for stochastic optimization,” arXiv preprint arXiv:1412.6980, 2014.
[14] T.-Y. Lin, P. Goyal, R. Girshick, K. He, and P. Dollár, “Focal loss for dense object detection,” in Proceedings of the IEEE international conference on computer vision, 2017, pp. 2980–2988.
[15] A. Mesaros, T. Heittola, and T. Virtanen, “A multi-device dataset for urban acoustic scene classification,” in Proceedings of the Detection and Classification of Acoustic Scenes and Events 2018 Workshop (DCASE2018), November 2018, pp. 9–13. [Online]. Available: https://arxiv.org/abs/1807.09840
This figure "ASC.png" is available in "png" format from:
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$\sin(x)$
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http://arxiv.org/ps/2107.14658v1
This figure "models_1b.png" is available in "png" format from:
http://arxiv.org/ps/2107.14658v1
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Dissecting the Genotypic and Environmental Factors Underpinning the Quantitative Trait Variation in a Set of Wild Tomato (Solanum habrochaites LA1777) Introgression Lines
Pasquale Tripodi 1,*, Antonella Vitiello 2, Bruno D’Onofrio 1, Mario Parisi 1, and Maria Cammareri 2
Abstract: Exotic libraries have proven a powerful tool for the exploitation of wild relatives and quantitative trait loci (QTLs) detection in crop species. In early 2000, an introgression line (IL) population of the wild tomato Solanum habrochaites (SH) acc. LA1777 was developed and made publicly available. Despite the potentiality of the donor parent, so far, these lines have been poorly explored for their agronomic performance and for the identification of genomic regions underlying the variation of quantitative traits (QTLs). Here, we report the evaluation of 19 morpho-agronomic and chemical traits on a set of 39 ILs grown in three consecutive field seasons with the aim to: (a) Determine the overall phenotypic performances of the studied collection, (b) estimate the influence of the genotype (G) and the year of cultivation (Y) and their interaction on the traits analyzed, (c) investigate the plasticity of the traits, and (d) identify whole-genome QTLs in the wild SH background. The ILs showed lower productivity compared to the control genotype, while no major effects were found for the morphological fruit-related traits. Instead, a general increase in the soluble solids content was observed. The combined analysis of G × Y highlighted a major effect of the genotype on trait variation, although yield-related traits were more influenced by environmental factors. In total, 75 associations for 17 traits were detected. Major QTLs increasing soluble solids, pericarp thickness, and trichome density were respectively found on chromosomes 1, 5, and 11 with a percentage variation (PV) of 24.01%, 32.49%, and 200%. Furthermore, different QTLs increasing the color intensity and fruit shape were detected. These results suggest that SH could be a potential source of favorable alleles for qualitative traits despite its inferior phenotype compared to the cultivated parent. The evaluated set of SH LA1777 ILs is a potential for novel allele discovery in wild tomatoes and for breeding purposes towards the exploitation of the available introgressions and for the pyramiding of traits.
Keywords: introgression lines; Solanum habrochaites; QTL mapping; G × Y interaction; morpho-agronomic traits; soluble solids; tomato breeding
1. Introduction
Tomatoes (Solanum lycopersicum, Solanaceae; 2n = 2x = 24) are considered one of the world’s most important vegetable crops widely spread with a production estimation of ~180 million tons and particularly appreciated for their nutritional properties [1]. As a model in plant research, the tomato has been pioneering for exploiting exotic germplasms toward the dissection of the genetic factors underpinning the variations of complex traits. Since the early nineties, the interspecific hybridization of S. lycopersicum with wild relatives has led to the development of various recombinant mapping populations able to enhance the identification of loci involved in agronomic and quality traits, as well as in biotic and abiotic stresses resistance [2,3]. Among the different types of experimental populations,
introgression lines (ILs) were the most successful for allele transfer in precision breeding, providing, furthermore, an excellent material for quantitative trait loci (QTLs) mapping. ILs harbor a single marker-defined chromosome segment from the donor wild parent in the cultivated background [4]. The accuracy for mapping polygenes relies on the direct association of the phenotypic variation to the introgressed segment, minimizing the epistatic effects from other wild genome regions. Ideally, an IL population is supposed to cover the whole wild genome and is a permanent resource, being developed after subsequent backcross and self-fertilization cycles. This allows tests across multiple locations and seasons, providing a powerful tool to estimate the genotype (G) and the environmental (E) effects. In fact, dissection of the G and E factors and their interaction is essential for determining those traits highly inherited in the offspring and for the estimation of phenotypic plasticity as the capacity of a genotype to express different phenotypes according to different environmental conditions [5]. Therefore, ILs play a key role for successful genetic improvement programs, facilitating, furthermore, the pyramid breeding of favorable genes [6]. In this context, the genetic variability enclosed in wild relatives can be exploited to address the future challenges of agriculture, such as the growth of the global population, the adaptation to climate changes, and the demand for quality and sustainability for food supply [7]. In recent years, ILs and near-isogenic lines (NILs) sets were developed in tomatoes through hybridization with different wild species, including *S. pennellii* [8], *S. habrochaites* [9–12], *S. lycopersicoides* [13,14], *S. pimpinellifolium* [15], and, more recently, *S. sitiens* [16].
*Solanum habrochaites* S. Knapp and D.M. Spooner (previously, *Lycopersicum hirsutum* Dunal) is a potential source of beneficial alleles in tomato breeding, including quality traits [17], chilling tolerance [18,19], and disease resistances [3,20]. There are over 90 accessions distributed in the native origin area for the species [21]; among these, acc. LA1777 is a green-fruited accession widely studied for resistance to the main tomato and potato pathogens, including begomoviruses and fungi [22–24]. It is also reported as resistant to insect pests, thanks to the presence of trichomes and of secondary metabolites produced by their glandules [25–27]. Finally, this wild species is a valuable source of beneficial alleles involved in fruit ripening [28] and an increase of soluble solids [10,29,30]. Monforte and Tanksley [9] developed a set of 99 near-isogenic and backcross recombinant inbred lines from a cross between a processing tomato cultivar E6203 and *S. habrochaites* LA1777. The population provides coverage of more than 85% of the wild genome based on genotyping with ~93 RFLP (Restriction Fragment Length Polymorphism) markers. Despite that the population is publicly available, the enclosed potentialities for mapping plant and fruit traits have not yet been broadly investigated. Indeed, the identification of QTLs and genes affecting yield-related components have been, so far, mainly focused on the *S. pennellii* ILs, which have been extensively exploited for the identification of over 3000 QTLs [31,32] and for map-based cloning of the first two QTLs in tomatoes: *fw2.2* for fruit weight [33] and *brix9-2-5* for the soluble solids content [34]. Attempts toward the assessment of the agronomic performance of a subset of LA1777 ILs in hybrid combinations have been reported [35], although no QTL analysis has been performed. Instead, specific ILs were used for the fine mapping of QTLs for agronomic traits on the distal parts of chromosomes 1 and 4 [10,11]. Therefore, a lack of information at the whole-genome level still occurs for the LA1777 introgression library.
In the present study, we report the evaluation of 39 ILs for nineteen agronomic, morphological, and quality-related traits over three consecutive field seasons with the following objectives: (i) Determine the phenotypic performances of the selected set, (ii) estimate the genotypic and environmental effects and the plasticity of the traits, and (iii) identify wild introgressions responsible for the quantitative variations of the traits studied. The set of ILs was chosen based on the minimal number of introgressions able to cover, as much as possible, the whole genome, in agreement with previously reported data [9,36].
2. Materials and Methods
2.1. Plant Material
Plant material consisted of 39 *S. habrochaites* (acc. LA1777) (hereafter, SH) introgression lines and the recurrent parent *S. lycopersicum* cv E6203 (hereafter, SL). The population was developed through an advanced backcross scheme derived from the cross between SL and SH. From the generation of BC$_2$S$_3$ families and further marker-assisted selection, lines containing a single or few segments of the wild relative in the cultivated background were obtained [9].
The set of ILs was chosen in order to cover as much of the wild genome based on the published information [9]. Seeds were obtained by the C. M. Rick Tomato Genetics Resource Center (TGRC, University of California, Davis, CA, USA) [36] (Table 1).
**Table 1.** Chromosomal location, number, size, and percentage of the coverage of the wild fragments in the *Solanum habrochaites* LA1777 introgression lines phenotyped in the present study.
| LA Pedigree | TGRC a | TA IL Name b | Chromosomes Bearing Wild Segments c | N° of Donor Segments d | Introgession Size (cM) d | Total Percentage of Coverage e |
|-------------|--------|--------------|-----------------------------------|------------------------|-------------------------|-------------------------------|
| LA3921 | TA1105 | 2 | 1 | 118.50 | 8.11 | |
| LA3981 | TA1116 | 5 | 1 | 47.50 | 3.25 | |
| LA3969 | TA1121 | 12 | 1 | 87.25 | 5.97 | |
| LA3919 | TA1128 | 1 | 1 | 41.00 | 2.81 | |
| LA3916 | TA1223 | 1 | 1 | 59.50 | 4.07 | |
| LA3913 | TA1258 | 1 | 1 | 103.00 | 7.05 | |
| LA3922 | TA1266 | 2 | 1 | 61.45 | 4.21 | |
| LA3926 | TA1276 | 3 | 1 | 88.00 | 6.02 | |
| LA3931 | TA1280 | 4 | 1 | 67.30 | 4.61 | |
| LA3938 | TA1287 | 5 | 1 | 20.00 | 1.37 | |
| LA3939 | TA1293 | 5 | 1 | 47.50 | 3.25 | |
| LA3948 | TA1303 | 7 | 1 | 62.90 | 4.31 | |
| LA3949 | TA1304 | 7 | 1 | 113.00 | 7.73 | |
| LA3951 | TA1312 | 7 | 1 | 22.90 | 1.57 | |
| LA3953 | TA1316 | 8 | 1 | 46.25 | 3.17 | |
| LA3955 | TA1320 | 8 | 1 | 9.50 | 0.65 | |
| LA3956 | TA1324 | 9 | 1 | 61.10 | 4.18 | |
| LA3991 | TA1326 | 9 | 1 | 46.85 | 3.21 | |
| LA3958 | TA1330 | 9, 11 | 1 | 45.90, 57.50 | 7.08 | |
| LA3936 | TA1475 | 4 | 1 | 34.35 | 2.35 | |
| LA3937 | TA1473 | 4 | 1 | 33.50 | 2.29 | |
| LA3917 | TA1535 | 1, 2, 12 | 4 | 17.25, 21.00, 28.25 | 4.55 | |
| LA3920 | TA1536 | 3 | 1 | 10.00 | 0.68 | |
| LA3923 | TA1537 | 2 | 1 | 21.00 | 1.44 | |
| LA3944 | TA1539 | 3, 6 | 2 | 39.20, 21.30 | 4.14 | |
| LA3929 | TA1541 | 3, 8 | 2 | 42.00, 9.50 | 3.52 | |
| LA3933 | TA1542 | 4 | 1 | 13.75 | 0.94 | |
| LA3941 | TA1543 | 5 | 1 | 19.50 | 1.33 | |
| LA3945 | TA1545 | 6, 10 | 2 | 50.95, 7.50 | 4.00 | |
| LA3954 | TA1548 | 8 | 1 | 66.50 | 4.55 | |
| LA3961 | TA1551 | 10 | 1 | 78.50 | 5.37 | |
| LA3995 | TA1553 | 1, 11, 12 | 3 | 103.00, 24.50, 12.00 | 9.55 | |
| LA3966 | TA1554 | 10, 11, 12 | 3 | 29.00, 31.00, 41.50 | 6.95 | |
| LA3965 | TA1555 | 2, 10, 11 | 3 | 21.50, 29.00, 9.50 | 4.11 | |
| LA3947 | TA1559 | 6 | 1 | 21.75 | 1.49 | |
| LA4005 | TA1562 | 4 | 1 | 26.25 | 1.80 | |
| LA4002 | TA1645 | 1, 8, 12 | 3 | 11.50, 9.50, 30.75 | 3.54 | |
| LA4004 | TA1649 | 2, 3, 6 | 3 | 21.00, 56.55, 5.00 | 5.65 | |
| LA3914 | TA523 | 1 | 1 | 50.25 | 3.44 | |
a TGRC = Tomato Genetic Resource Center; LA is the accession prefix used by the TGRC germplasm bank. b TA is the name of each introgression line (IL) as reported by Monforte and Tanksley [9]. c Information reported in Monforte et al. (2000) and the Tomato Genetic Resource Center. d determined considering the chromosomal region covered by each introgression, plus the half-intervals between the flanking markers and nearest mapped loci. e Considering the tomato genome size equal to 1461 cM.
2.2. Field Trials and Phenotypic Characterization
Plants were grown in independent trials across three consecutive seasons at the experimental farm of the Research Centre for Vegetable Crops located at Battipaglia (Salerno, Italy). Geographical and pedological characteristics of the site and climatic conditions of each season are reported in Table 2.
Field tests were conducted using a completely randomized experimental design with 10 plants from each IL-SH and 40 plants from the control SL. Each year, the sowing was done in March, and the seedlings were transplanted in April in single rows, adopting distances of 100 cm between the rows and 30 cm along the rows. For plant fertilization, 200 kg ha\(^{-1}\) of N, 200 kg ha\(^{-1}\) of P\(_2\)O\(_5\), and 120 kg ha\(^{-1}\) of K\(_2\)O were applied according to what was established for the same site [37]. Irrigation scheduling was based on crop evapotranspiration. A total of 270, 260, and 290 mm of water were applied in 2014, 2015, and 2016, respectively, by drip irrigation, restoring 40% of the total available water depleted. The effective control of diseases and harmful insects was pursued, with the aim of having healthy plants until the end of the cycle. Other cultivation techniques included stakes as support and galvanized wires [38].
Agronomical and morphological traits were assessed when 95% of the plants of the control genotype (SL) had ripened fruits. Yield-related traits were performed on each plant and included: total yield (TY) (in kg), assessing the total weight of fruits (green and red), red yield (RY) (in kg) as the weight of whole, ripened fruits at commercial status, and green yield (GY) (in kg), including all unripe fruits at harvest time (in kg). Uniformity of fruit maturity (UM) was then measured as follows:
\[
GY = TY - RY, \quad (1)
\]
\[
UM = \left( \frac{RY}{TY} \right) \times 100, \quad (2)
\]
The weight of the vegetative part (PW) (in kg) was obtained weighing the epigeal portion of the plants after harvesting all fruits; biomass (BM) (in kg) was measured as:
\[
BM = TY + PW, \quad (3)
\]
The fruit traits assessment included the average weight (FW) (in gr) obtained by dividing the total yield by the number of fruits harvested, the length (FL) and the width (FD) (in cm) measured on 10 fruits/plant by using a ruler, and the fruit shape (FS) index as follows:
\[
FS = \frac{FL}{FD}, \quad (4)
\]
where values < 1 indicate fruits more flattened, and values > 1 indicate fruits more elongated. External (EC) and internal (IC) colors were measured by scale (1 = yellow fruits and 5 dark red fruits), as well as pericarp thickness (PER) and puffiness (PUF) (1 = thin pericarp, low puffiness and 3 = thick pericarp, high puffiness).
Chemical traits were measured on a bulk of 10 well-ripened fruits/plants. Fruits were washed and dried and then sliced and homogenized in a Waring blender (2-L capacity; Model HGB140, Waring Commercial, Stamford, CT, USA) for 1 min. Soluble solids content (SSC) was measured using a digital refractometer (Refracto 30PX, Mettler-Toledo, Novate Milanese, Italy), and the results were expressed as °Brix per 100 g of fresh weight (fw). The pH was determined using a pH-Matic 23 titroprocessor equipped with a pH electrode with a temperature sensor (model 5011T) (Crison Instruments, Barcelona, Spain).
The estimation of the yield of soluble solids produced per plant (BY) (in gr) was estimated as follows:
$$BY = RY \times SSC,$$
Trichome density (TRIC) for each plant was estimated at the base of the stem and on the pedicel of flowers using a visual scale (1 = no or low density of trichomes and 3 = high density of trichomes).
2.3. Data Analyses
All phenotypic traits were subjected to an analysis of variance (ANOVA) test. Trait means for the control and the set of ILs were compared by using Tukey’s HSD (honest significant difference) test. Results with p less than 0.05 were considered statistically significant. Broad-sense heritability ($H^2$) was estimated as:
$$H^2 = VG/VP,$$
where “VG” is the genotypic component of variance, and “VP” is the total phenotypic variance. The coefficient of variation (CV) in percentage was calculated as:
$$CV = (SD/m) \times 100,$$
in which “SD” is the standard deviation, and “m” is the mean for a trait.
A two-factorial linear model was used to determine the main effects of the genotype (G), season of cultivation (Y), and their interactions (G × Y) for each trait. Mean square values (MS) were used to estimate the magnitude of the observed effect, while the total sum of squares in percentage (TSS%) was calculated by dividing the TSS of the variable by the total TSS.
The coefficient of relative phenotypic plasticity (CRP) for each trait was calculated according to the formula of Dingemanse et al. [39] as follows:
$$CRP = Vi/VPP,$$
where “Vi” is the variance of the individual (i), and “VPP” is the overall phenotypic variance of the population. The CRP index close to 0 indicates no plasticity (high stability); on the contrary, higher values indicate an increase of plasticity (decrease of stability).
Correlations across the genotypes for phenotypic traits were calculated using the Pearson’s test at p < 0.01 after Bonferroni’s correction for multiple comparisons. The correlogram was constructed and visualized using the Corrplot package implemented in R version 3.0.2 (R Development Core Team). Principal component analysis (PCA) was carried out to determine what are most effective descriptors in discriminating among accessions using the computer package XLSTAT 2012.1 and visualizing the similarities among accessions. Experimental data were statistically elaborated using R. The relationships between pairs of phenotypic and molecular data matrices were computed by the Mantel test using Pearson’s r-value [40].
Chromosomal regions responsible for the quantitative variation for traits measured were detected comparing the mean phenotypic values of the tested ILs in each experiment to the recurrent parent SL using Dunnett’s test with Type I error $\alpha \leq 0.05$ [41]. When an IL showed significantly different effects compared to the control in one or more seasons, putative quantitative trait loci (QTLs) were assumed in the chromosomal region covered by the IL. If a QTL was detected in multiple ILs, the likely position was inferred on overlapping chromosome segments. For each IL, the percentage variation (PV) compared to the control, and underlying a QTL region was calculated as:
$$PV = \frac{m(\text{IL}) - m(\text{E6203})}{m(\text{E6203})} \times 100,$$
where, for each trait, “m” is the mean calculated across all replications.
3. Results
3.1. Phenotypic Variation and Trait Performances of SL and SH ILs
In Table 3, the ANOVA results and the parameters mean, minimum, maximum, coefficient of variation (CV), and broad sense of heritability ($H^2$) specify the performance of the recurrent parent SL “E6203” and the 39 SH ILs set for each trait. Considering the average of three years of cultivation, no significant differences between the sets of ILs and SL were found for GY, UM, PW, IC, EC, and TRIC, while PUF and SSC, as well as FS, differed at $p < 0.05$ and $p < 0.01$, respectively. In average, the wild SH alleles conferred less productivity when introgressed in the SL background, while no major effect was noticed for the morphological fruit-related traits. Instead, a general increase in the soluble solids content was detected in the tested ILs, although no effect was found for the production of the soluble solid. Across all years, the CV% was lower than 36% for fruit traits in both SH ILs and the recurrent parent. A higher variation was shown by yield-related traits, reaching peaks for GY. Overall, the lowest coefficient of variation was found for FS, highlighting very low or absent morphological segregation within the ILs. The broad-sense heritability ranged from 0.84 (GY and CI) to 0.96 (FS). The fruits and chemical traits showed, on average, a greater heritability (Table 3).
The mean, ranges, CV, and results of the post hoc Tukey’s considering each independent season in both SL and the set of SH ILs are reported in Table S1. Highly significant differences ($p < 0.001$) between the ILs and the recurrent parent were found for 17 out of the 19 traits analyzed. Only the fruit shape and trichomes differed at $p < 0.01$ and $p < 0.05$, respectively (Table S1).
The average phenotypic values and the percentage variation compared to the control revealed a large variability of the studied ILs set for the considered traits (Tables S2 and S3). In all trials, the introgression lines were less productive than the control. Overall, a decrease of the yield was observed in both E6203 and the ILs from the first to the third season. The same trend was observed for plant weight and biomass, with the lowest values exhibited during Y3. On the contrary, the weight of the fruits was higher during the second year of cultivation with respect to the other seasons, showing greater values in the control genotype across all trials (Table S2). The soluble solids content was found to be higher than the control in almost all lines during the three-year evaluation period (Figure 1). Only for Y2, variable levels were observed. Overall, the soluble solids values reached contents up to +55% with respect to E6203.
Table 3. Descriptive statistics of the traits analyzed in the 39 introgression lines (IL) and the control (SL) during three consecutive growing seasons.
| Traits | MS b | R b | F Value c | $H^2$ b | Mean SL Range SL | CV b | Mean IL Range IL | CV b | Prob > F |
|-----------------|------|-----|-----------|---------|------------------|------|------------------|------|----------|
| **Yield** | | | | | | | | | |
| Total yield | TY | 12.13 | 0.22 | 8.46 ** | 0.89 | 4.11 | 4.7–3.3 | 31.69 | 4.16–2.76 | *** |
| Red yield | RY | 13.53 | 0.22 | 8.49 ** | 0.89 | 3.77 | 4.67–2.96 | 36.53 | 4.06–2.32 | *** |
| Green yield | GY | 1.47 | 0.18 | 5.36 ** | 0.84 | 0.50 | 0.82–0.03 | 95.77 | 0.99–0.24 | 102.67 |
| Uniformity | UM | 974.95 | 0.21 | 8.33 ** | 0.89 | 91.01 | 99.26–80.45 | 11.55 | 90.98 | 96.54–83.43 | 13.38 |
| Maturity | | | | | | | | | |
| Plant weight | PW | 0.77 | 0.19 | 7.01 ** | 0.88 | 0.67 | 0.86–0.45 | 68.56 | 0.68 | 0.75–0.55 | ns |
| Biomass | BM | 13.68 | 0.19 | 7.37 ** | 0.88 | 4.79 | 5.45–3.75 | 33.43 | 4.08 | 4.89–3.31 | *** |
| Harvest index | HI | 0.06 | 0.27 | 11.50 ** | 0.92 | 0.86 | 0.88–0.84 | 6.93 | 0.83 | 0.85–0.81 | *** |
| **Fruit** | | | | | | | | | |
| Fruit weight | FW | 2029.75 | 0.25 | 10.28 ** | 0.91 | 74.27 | 83.52–67.85 | 20.16 | 62.96–57.08 | 25.76 |
| Fruit length | FL | 3.05 | 0.07 | 21.02 ** | 0.95 | 5.68 | 6.01–5.52 | 7.17 | 5.09 | 5.13–5.04 | *** |
| Fruit diameter | FD | 1.52 | 0.24 | 15.92 ** | 0.94 | 4.94 | 5.23–4.79 | 7.37 | 4.52 | 4.57–4.45 | *** |
| Fruit shape | FS | 0.07 | 0.41 | 21.51 ** | 0.96 | 1.15 | 1.15–1.15 | 4.29 | 1.13 | 1.13–1.12 | ** |
| External color | CE | 2.57 | 0.49 | 18.77 ** | 0.94 | 2.92 | 3.75–2.44 | 20.61 | 2.90 | 3.27–2.67 | ns |
| Internal color | CI | 1.69 | 0.60 | 13.73 ** | 0.84 | 3.11 | 3.81–2.73 | 17.04 | 3.09 | 3.36–2.93 | ns |
| Pericarp | PER | 1.51 | 0.22 | 8.41 ** | 0.89 | 2.07 | 2.22–1.67 | 22.76 | 1.90 | 1.93–1.87 | 24.56 |
| Puffiness | PUF | 2.52 | 0.27 | 11.20 ** | 0.92 | 1.68 | 2.16–1.24 | 35.18 | 1.57 | 1.76–1.33 | 34.48 |
| **Chemical** | | | | | | | | | |
| Soluble solids | SSC | 6.86 | 0.31 | 13.53 ** | 0.93 | 4.99 | 5.73–4.36 | 16.52 | 5.44 | 5.67–5.05 | *** |
| pH | pH | 1.44 | 0.36 | 36.05 ** | 0.94 | 4.52 | 4.6–4.41 | 4.21 | 4.40 | 4.47–4.34 | *** |
| SSC per plant | BY | 248.62 | 0.22 | 5.01 * | 0.89 | 18.23 | 19.9–15.09 | 36.54 | 16.73 | 19.96–12.87 | 41.99 |
| **Stem** | | | | | | | | | |
| Trichomes | TRIC | 2.99 | 0.17 | 6.37 ** | 0.86 | 1.00 | 1.00–1.00 | 0.00 | 1.30 | 3.00–1.00 | ns |
* Acronyms. * TY, RY, GY, PW, and BM are expressed in Kg; FW in g; FL and FD in cm; SSC is expressed in °Brix; CE, CI, PER, PUF, and TRIC are in scale; and FS, HI, and BY are derived indices. b MS: mean squares, R: R-square, CV: coefficient of variation, and $H^2$: heritability. c * Indicate significance at $p < 0.05$, ** indicate significance at $p < 0.01$, and *** indicate significance at $p < 0.001$; ns = not significant.
3.2. Genotypic and Environmental Components Underlying Trait Variation
The results of the combined analysis of variance for the traits evaluated across three years of cultivation are given in Table 4. A high level of significance ($p < 0.01$) was found for the genotypic component (G), while the variation due to the cultivation season ($Y$) was lower for trichomes and fruit characteristics showing $p < 0.05$ for FS and CE, and there was no significance for the CI. As for the $G \times Y$ interaction, highly significant differences ($p < 0.01$) were found in all traits, except for FW and pH, which showed a $p$ threshold $< 0.05$ and no significance, respectively.
For most traits, the main source of variability was due to $G$, which accounted, on average, for 61.90% of the total variation, expressed by TSS%, ranging from 12.35% for GY to 90.08% for TRIC. The traits under a strong genotypic effect were FL, CE, and CI, exhibiting TSS values above 80%. On average, G accounted for 43.01%, 75.28%, and 60.94% for yield-related traits, fruit characteristics, and chemical features, respectively. The partitioning of the TSS% in the other components affecting the variation indicated that $Y$ and $G \times Y$ accounted for, on average, 16.47% and 21.77%, respectively, resulting in, generally, less influence of $Y$ and $G \times Y$ than $G$ on the analyzed parameters.
Among the assessed traits, GY and RY were the traits most affected by seasonal fluctuations, showing a TSS of 65.21% and 37.72%, respectively, while for all fruit traits,
except puffiness, the effect was very little, with a variation of 1.96% on average. The G × Y interaction was, on average, higher for yield traits (TSS equal to 25.91%) with respect to fruit characteristics (TSS equal to 20.99%) and their main chemical features (TSS equal to 18.46%). Among these, HI and PER were those for which the variation was highly influenced by the G × Y interaction, with values of 33.30% and 36.02%, respectively.
Table 4. Analysis of variance and significant levels for the genotypic (G) and environmental effects due to growing season (Y) for Solanum habrochaites (SH) ILs and the SL control, and the combined effects for the traits evaluated.
| Trait | Genotype (G) | Year (Y) | G × Y | Total Error |
|-------|--------------|----------|-------|-------------|
| | MS | TSS% | F | MS | TSS% | F | MS | TSS% | F | df = 1108 |
| Yield | | | | | | | | | | |
| TY | 11.60 | 45.49 | 11.57 ** | 151.98 | 30.57 | 151.72 ** | 3.05 | 23.94 | 3.04 ** | 1109.89 |
| RY | 12.34 | 38.77 | 13.07 ** | 234.09 | 37.72 | 248.08 ** | 3.74 | 23.51 | 3.97 ** | 1045.53 |
| GY | 0.56 | 12.35 | 3.92 ** | 94.32 | 65.21 | 663.08 ** | 0.46 | 22.44 | 3.21 ** | 125.60 |
| UM | 946.65 | 39.85 | 13.1 ** | 13,639.01 | 29.45 | 188.68 ** | 364.62 | 30.70 | 5.04 ** | 80,094.20 |
| PW | 0.76 | 58.29 | 7.97 ** | 4.28 | 16.74 | 44.61 ** | 0.16 | 24.97 | 1.71 ** | 106.19 |
| BM | 12.69 | 43.66 | 9.43 ** | 191.67 | 33.82 | 142.5 ** | 3.27 | 22.53 | 2.43 ** | 1490.35 |
| HI | 0.08 | 62.64 | 17.76 ** | 0.10 | 4.07 | 22.48 ** | 0.02 | 33.30 | 4.72 ** | 4.85 |
| Fruit | | | | | | | | | | |
| FW | 2110.45 | 76.39 | 11.4 ** | 3122.66 | 5.80 | 16.87 ** | 245.99 | 17.81 | 1.33 * | 205,111.16 |
| FL | 3.11 | 81.24 | 23.99 ** | 0.95 | 1.27 | 7.33 ** | 0.33 | 17.49 | 2.58 ** | 22,962.97 |
| FD | 1.59 | 78.27 | 18.65 ** | 1.60 | 4.03 | 18.59 ** | 0.19 | 17.70 | 2.10 ** | 15,829.19 |
| FS | 0.07 | 73.70 | 25.90 ** | 0.01 | 0.62 | 4.23 * | 0.01 | 25.68 | 4.51 ** | 2.87 |
| CE | 2.08 | 85.50 | 19.98 ** | 0.65 | 0.68 | 6.29 * | 0.33 | 13.80 | 3.23 ** | 110.28 |
| CI | 2.92 | 89.75 | 23.70 ** | 0.05 | 0.04 | 0.38 NS | 0.33 | 12.96 | 2.69 ** | 90.69 |
| PER | 1.49 | 62.66 | 9.39 ** | 0.61 | 1.31 | 3.84 * | 0.43 | 36.02 | 2.70 ** | 176.04 |
| PUF | 2.48 | 54.72 | 15.84 ** | 16.58 | 18.79 | 106.03 ** | 0.60 | 26.50 | 3.83 ** | 173.06 |
| Chemical | | | | | | | | | | |
| SSC | 6.43 | 58.74 | 17.97 ** | 37.24 | 17.43 | 104.04 ** | 1.30 | 23.83 | 3.65 ** | 395.49 |
| pH | 0.44 | 77.47 | 18.29 ** | 3.09 | 14.33 | 128.6 ** | 0.02 | 8.20 | 0.96 NS | 25.51 |
| BY | 307.53 | 46.61 | 10.40 ** | 3863.56 | 30.03 | 130.6 ** | 77.08 | 23.36 | 2.61 ** | 32,776.91 |
| Stem | | | | | | | | | | |
| TRIC | 3.13 | 90.08 | 12.68 ** | 32.15 | 1.01 | 3.25 NS | 2.49 | 8.91 | 10.08 * | 27.32 |
df: degrees of freedom, * significant at p < 0.05, ** significant at p < 0.01, and NS: not significant. MS: mean squares, Err: error, TSS: total sum of squares, and F = F ratio.
The index of phenotypic plasticity (CRP) (Table S4) was highly variable for the traits tested in the 39 ILs and the control, ranging from 0.05 (UM) to 5.40 (FW). On average, the fruit shape and color traits were more stable, with average plasticity values below 0.62. The yield traits, instead, exhibited higher plasticity, with average indexes above 0.79. In the genotypes tested, most of the values were lower than 1.00. Several ILs had CRP less than 1.00 for all the assessed traits, such as TA1128, TA1536, TA1537, and TA1312. We instead found values above 2.00 for TA1105 on chromosome 2 and for several lines on chromosomes 2, 4, and 5. Only TA1316 (chromosome 8) had CRP values < 0.93 for all traits. The yield traits exhibited high plasticity for TA1276 (HI = 4.68), TA1542 (PW = 4.16), and TA1562 (UM = 4.88), while the maximum value (5.40) was found for FW in TA1548. Instead, the fruit shape and color traits had lower values of plasticity, with an average index below 0.61.
3.3. Multivariate Analysis and Correlations between Traits
The principal component analysis (PCA) in the first two dimensions explained 50.94% of the total variance (Figure 2).
Figure 2. Phenotypic variability in the studied introgression lines and the recurrent parent. Loading plot of the first (PC₁) and second (PC₂) principal components showed the variations for the 19 morphological and agronomic traits in the set of 39 introgressions lines and the control (cv E6203). Introgressions lines (ILs) carrying single introgressions are indicated in green font with a triangle symbol, whereas ILs carrying multiple fragments are indicated in blue font with a circular symbol. The control is indicated with a square in red font. The direction and distance from the center of the biplot indicate how each trait contributes to the first two components. The explanation for trait acronyms is reported in Table 3.
The genotypes were evenly distributed on the two axes of the biplot. The first component accounted for 27.95% of the total variance and was positively correlated with all the traits except SSC and BY. The second component accounted for 22.98% of the variance, being positively correlated with all yield-related traits and negatively correlated with the remaining ones. For the entire set analyzed, the total phenotypic variation was explained by the first 19 components (data not shown). The yield-related traits explained the largest part of the variation in the first two components, showing a contribution of the variables with values above 12% (Table S5). The projection of genotypes on the two-dimensional PCA graph showed the wide range of phenotypic variations enclosed in the SH IL set, highlighting how wild alleles can improve diverse traits. For each growing season, correlograms between pairs of variables were generated using Bonferroni correction (p < 0.01) (Figure 3). Correlations mainly occurred among the same trait categories. In all cultivation trials, strong negative correlations were found for UM and GY, PW and HI, and PW and UM, while strong positive correlations were found between FD and FL, FW and FD, CE and CI, and RY and HY, as well as among BY, BM, TY, and RY. Only in the first and second years of cultivation, TRIC was correlated negatively to UM and positively to GY (Figure 3a,b), while, during the third year, it was negatively correlated with BM (Figure 3c). Furthermore, a significant positive correlation between FW and PER was detected in the
third season. In all trials, the soluble solids were negatively correlated with the yield traits and harvest index, although a significance was only observed during the last year. The degree of relationship between the elements of the phenotypic matrices revealed significant correlations between the data of the independent growing seasons, highlighting the strongest correlations between the second and third seasons of the evaluation: Y1/Y2 ($r = 0.2$, $p < 0.0001$), Y1/Y3 ($r = 0.361$, $p < 0.0001$), and Y2/Y3 ($r = 0.607$, $p < 0.0001$).
**Figure 3.** Pearson’s rank correlation coefficients between the pairs of phenotypes. The correlation coefficients are indicated in each cell. Colored correlations are those with $p$-values $< 0.01$ after Bonferroni correction. The color intensity is directly proportional to the coefficients. On the right side of the correlogram, the color legend shows the correlation coefficients and the corresponding colors. (a) The correlogram for the traits scored in year 1, (b) year 2, and (c) year 3. The trait acronyms are in Table 3.
3.4. Genetic Regions Underlying the Phenotypic Variations
The overlaps between the introgressed fragments of the studied ILs determined the chromosomal regions (or BIN) carrying the wild alleles into the cultivated background. The size of each BIN was determined considering the overlapping regions, plus the half-intervals between the flanking markers and nearest mapped loci. The markers’ positions were updated based on the Tomato-EXPEN reference map [32]. In total, 61 BINs were detected, ranging from a minimum of three on chromosomes 2, 5, 7, 8, 9, and 10 to a maximum of seven on chromosome 1 (Figure 4). Based on the mean comparisons of each ILs with the recurrent parent (Table S2), we detected 75 associations for all traits except for puffiness and green yield. Forty-two associated regions were found across two independent seasons, whereas 33 were across all trials, covering 17 genomic regions on nine chromosomes and including sixteen out of the nineteen evaluated traits. Except for chromosome 8, wild alleles were responsible for the quantitative variations for the studied traits in two or three trials (Table 5).
Figure 4. Genetic map showing the position of the markers delimiting the ILs and used for the quantitative trait loci (QTL) analysis. Markers are indicated on the right side of each chromosome, whereas map distances in centiMorgan (cM) are indicated on the left side and are based on the Tomato-EXPEN 2000 and Tomato-EXPEN 1992 (with asterisks) mapping populations [32]. At the bottom of each chromosome, the total genetic length is mentioned. Black bars indicated ILs carrying a single homozygous introgression. Dashed lines indicate ILs with multiple introgressions. The empty part of each chromosome indicates the regions not covered by wild introgressions. Centromeres are indicated with gray dots. Light blue bars on the left of each chromosome indicate the genomic positions of the markers based on tomato reference annotation SL4.0. The total length in megabases is reported at the bottom. Only robust QTLs detected across the three consecutive seasons are reported. The QTLs are in italics and defined by the trait abbreviation, followed by the chromosomal BIN (region delimiting single or overlapping introgressions). In uppercase and blue font are the QTLs increasing the trait performances. In red and in lowercase are the indicated QTLs decreasing the traits.
Table 5. List of putative chromosome regions underlying the variations of the traits (QTL) identified across two or three independent trials. PV = percent of the phenotypic variance estimated and - = not available. In bold are indicated the positive PV (%). In capital letters are indicated those QTLs that increased the performance of the traits compared to the control. BIN sizes are determined considering the overlapping regions plus the half-intervals between flanking markers and the nearest mapped loci (see Figure 4).
| Trait | ILs | Marker(s) | Chr | BIN n° | BIN Position (cM) | BIN Size (cM) | QTL Name | PV (%) 2 Years | PV (%) 3 Years |
|-------|-----|-------------------|-----|--------|-------------------|--------------|----------|----------------|----------------|
| TY | TA1128 | TG184 | 1 | 1.2 | 10–40.5 | 30.5 | ty1.2 | −39.15 | |
| | TA1535 | TG59 | 1 | 1.3 | 61–79.25 | 18.3 | ty1.3 | −50.62 | |
| | TA1276-TA1649 | TG42, TG359, CG243 | 3 | 3.5 | 68.0–156.0 | 88.0 | ty3.5 | −52.35 | |
| | TA1551 | TG313, CT234, TG408 | 10 | 10.1 | 0.00–57.0 | 57 | ty10.1 | −45.21 | |
| | TA1554 | TG651 | 11 | 11.1 | 11.0–36.0 | 25 | ty11.1 | −44.51 | |
| | TA1121 | CT211, TG283, CT287a | 12 | 12.3 | 32.25–78.5 | 43.25 | ty12.3 | −33.51 | |
| RY | TA1535 | TG59 | 1 | 1.3 | 61–79.25 | 18.3 | ry1.3 | −51.38 | |
| | TA1276-TA1649 | TG42, TG359, CT243 | 3 | 3.5 | 68.0–156.0 | 88.0 | ry3.5 | −52.30 | |
| | TA1551 | TG313, CT234, TG408 | 10 | 10.1 | 0.00–57.0 | 57 | ry10.1 | −41.28 | |
| UM | TA1535 | TG59 | 1 | 1.3 | 61–79.25 | 18.3 | um1.3 | −14.25 | |
| | TA1280 | TG15, TG370, TG287 | 4 | 4.1 | 3.25–70.5 | 67.25 | um4.1 | −9.95 | |
| PW | TA1649 | TG244 | 3 | 3.6 | 156.0–171 | 15.0 | PW3.6 | −40.24 | 73.92 |
| BM | TA1128 | TG184 | 1 | 1.2 | 10–40.5 | 30.5 | bm1.2 | −44.70 | −44.70 |
| | TA1535 | TG59 | 1 | 1.3 | 61–79.25 | 18.3 | bm1.3 | −50.03 | |
| | TA1276 | TG42, TG359 | 3 | 3.4 | 68.0–114.45 | 46.45 | bm3.4 | −40.79 | |
| | TA1551 | TG313, CT234, TG408 | 10 | 10.1 | 0.00–57.0 | 57 | bm10.1 | −47.15 | |
| | TA1554 | TG651 | 11 | 11.1 | 11.0–36.0 | 25 | bm11.1 | −12.14 | −25.52 |
| HI | TA1535 | TG59 | 1 | 1.3 | 61–79.25 | 18.3 | hi1.3 | −16.43 | −16.43 |
| | TA1276 | TG42, TG359 | 3 | 3.4 | 68.0–114.45 | 46.45 | hi3.4 | −17.14 | |
| | TA1542-TA1562 | TG264 | 4 | 4.3 | 70.5–84.25 | 13.75 | hi4.3 | −25.52 | |
| | TA1649 | TG244 | 3 | 3.6 | 156.0–171 | 15.0 | hi3.6 | −17.14 | |
Table 5. Cont.
| Trait | ILs | Marker(s) | Chr | BIN n° | BIN Position (cM) | BIN Size (cM) | QTL Name * | PV (%) 2 Years | PV (%) 3 Years |
|-------|-----|-----------|-----|--------|-------------------|--------------|------------|---------------|---------------|
| FW | TA1266-TA1537-TA1649-TA1535 | TG620 | 2 | 2.4 | 110.5–131.5 | 21.0 | fw2.4 a | −30.49 |
| | TA1276-TA1649 | TG42, TG359, CT243 | 3 | 3.5 | 68.0–156.0 | 88.0 | fw3.5 | −27.91 |
| | TA1303-TA1304 | TG216, CT195 | 7 | 7.3 | 50.4–113 | 62.6 | fw7.3 | −42.33 |
| | TA1330 | CT198, CT112 | 9 | 9.3 | 63.1–109.0 | 45.9 | fw9.3 | −32.29 |
| | TA1545-TA1554-TA1555 | TG233 | 10 | 10.3 | 78.5–86.0 | 7.5 | fw10.3 | −35.63 |
| | TA1554 | TG651 | 11 | 11.1 | 11.0–36.0 | 25 | fw11.1 | −43.14 |
| | TA1330-TA1553 | TG36 | 11 | 11.3 | 93.5–69.0 | 24.5 | fw11.3 | −32.01 |
| | TA1554-TA1221 | TG296 | 12 | 12.4 | 78.5–108.0 | 29.5 | fw12.4 | −36.44 |
| FL | TA1541 | TG479 | 3 | 3.1 | 0.0–16.0 | 16.0 | fl3.1 | −13.82 |
| | TA1276 | TG42, TG359 | 3 | 3.4 | 68.0–114.45 | 46.45 | fl3.4 | −16.85 |
| | TA1280 | TG15, TG370, TG287 | 4 | 4.1 | 3.25–70.5 | 67.25 | fl4.1 | −9.95 |
| | TA1543 | TG60 | 5 | 5.3 | 99.5–119.0 | 19.5 | fl5.3 | −9.86 |
| | TA1545 | TG352, TG164 | 6 | 6.3 | 21.75–50.95 | 29.2 | fl6.3 | −11.38 |
| | TA1303-TA1304 | TG216, CT195 | 7 | 7.3 | 50.4–113 | 62.6 | fl7.3 | −19.05 |
| | TA1545-TA1554-TA1555 | TG233 | 10 | 10.3 | 78.5–86.0 | 7.5 | fl10.3 | −18.7 |
| | TA1330-TA1553 | TG36 | 11 | 11.3 | 93.5–69.0 | 24.5 | fl11.3 | −15.92 |
| | TA1121 | CT211, TG283, CT287a | 12 | 12.3 | 32.25–78.5 | 43.25 | fl12.3 | −14.83 |
| FD | TA1105 | CT140, TG554, TG553 | 2 | 2.1 | 8.0–70.15 | 62.2 | fd2.1 | −17.32 |
| | TA1276-TA1649 | TG42, TG359, CT243 | 3 | 3.5 | 68.0–156.0 | 88.0 | fd3.5 | −14.71 |
| | TA1473 | TG464, TG163 | 4 | 4.7 | 119–135 | 16.0 | fd4.7 | −11.21 |
| | TA1303-TA1304 | TG216, CT195 | 7 | 7.3 | 50.4–113 | 62.6 | fd7.3 | −19.03 |
| | TA1554 | TG651 | 11 | 11.1 | 11.0–36.0 | 25 | fd11.1 | −16.82 |
| | TA1555 | TG393 | 11 | 11.4 | 93.5–104.0 | 10.5 | fd11.4 | −15.53 |
| | TA1554-TA1221 | TG296 | 12 | 12.4 | 78.5–108.0 | 29.5 | fd12.4 | −16.14 |
| FS | TA1258 | TG607 | 1 | 1.4 | 79.25–114–75 | 35.5 | fs1.4 | 7.28 |
| | TA1258-TA523-TA1223 | TG245, TG17 | 1 | 1.5 | 114.75–153.5 | 38.8 | fs1.5 | 7.42 |
| | TA1266-TA1537-TA1649-TA1535 * | TG620 | 2 | 2.4 | 110.5–131.5 | 21.0 | fs2.4 b | −11.89 |
| | TA1541 | TG479 | 3 | 3.1 | 0.0–16.0 | 16.0 | fs3.1 | −5.96 |
| | TA1554 | TG651 | 11 | 11.1 | 11.0–36.0 | 25 | fs11.1 | −12.73 |
Table 5. Cont.
| Trait | ILs | Marker(s) | Chr | BIN n° | BIN Position (cM) | BIN Size (cM) | QTL Name a | PV (%) 2 Years | PV (%) 3 Years |
|-------|-----|-----------|-----|--------|-------------------|---------------|-------------|---------------|---------------|
| CE | TA1258 | TG607 | 1 | 1.4 | 79.25–114–75 | 35.5 | $ec1.4$ | –15.11 | |
| | TA1266-TA1537-TA1649-| | | | | | | | |
| | TA1535 | | | | | | | | |
| | * | | | | | | | | |
| | TA1473-TA1475 | CD39 | 4 | 4.6 | 101.5–119 | 17.5 | $EC4.6$ | 24.27 | |
| | TA1330 | CT198, CT112 | 9 | 9.3 | 63.1–109.0 | 45.9 | $EC9.3$ | 21.6 | |
| | TA1330-TA1553 | TG36 | 11 | 11.3 | 69.0–93.5 | 24.5 | $EC11.3$ | 18.97 | |
| CI | TA1535 | TG59 | 1 | 1.3 | 61–79.25 | 18.3 | $ic1.3$ | –25.85 | |
| | TA1258 | TG607 | 1 | 1.4 | 79.25–114–75 | 35.5 | $ic1.4$ | –25.19 | |
| | TA1266-TA1537-TA1649-| | | | | | | | |
| | TA1535 | | | | | | | | |
| | * | | | | | | | | |
| | TA1475 | TG345 | 4 | 4.5 | 96.75–101.5 | 4.75 | $IC4.5$ | 25.08 | |
| PER | TA1287 | CT101 | 5 | 5.1 | 0.0–20.0 | 20.0 | $PER5.1$ | 32.49 | |
| | TA1554 | TG651 | 11 | 11.1 | 11.0–36.0 | 25 | $per11.1$ | –38.69 | |
| SSC | TA1258-TA523-TA1223 | TG245, TG17 | 1 | 1.5 | 114.75–153.5 | 38.8 | $SSC1.5$ | 24.01 | |
| | TA1649 | TG244 | 3 | 3.6 | 156.0–171 | 15.0 | $SSC3.6$ | 26.36 | |
| | TA1543 | TG60 | 5 | 5.3 | 99.5–119.0 | 19.5 | $SSC5.3$ | 25.37 | |
| | TA1551 | TG313, CT234, TG408 | 10 | 10.1 | 0.00–57.0 | 57 | $SSC10.1$ | 26.47 | |
| PH | TA1535 | TG59 | 1 | 1.3 | 61–79.25 | 18.3 | $ph1.3$ | –8.91 | |
| | TA1473 | TG464, TG163 | 4 | 4.7 | 119–135 | 16.0 | $ph4.7$ | –4.73 | |
| | TA1554 | TG651 | 11 | 11.1 | 11.0–36.0 | 25 | $ph11.1$ | –8.50 | |
| | TA1330 | CT198, CT112 | 9 | 9.3 | 63.1–109.0 | 45.9 | $ph9.3$ | –4.24 | |
| BY | TA1128 | TG184 | 1 | 1.2 | 10–40.5 | 30.5 | $by1.2$ | –39.33 | |
| | TA1535 | TG59 | 1 | 1.3 | 61–79.25 | 18.3 | $by1.3$ | –49.15 | |
| | TA1276 | TG42, TG359 | 3 | 3.4 | 68.0–114.45 | 46.45 | $by3.4$ | –57.73 | |
| TRIC | TA1280 | TG15, TG370, TG287 | 4 | 4.1 | 3.25–70.5 | 67.25 | $TRIC4.1$ | 100 | |
| | TA1304 | TG202 | 7 | 7.2 | 23.9–50.4 | 26.5 | $TRIC7.2$ | 125 | |
| | TA1551 | TG313, CT234, TG408 | 10 | 10.1 | 0.00–57.0 | 57 | $TRIC10.1$ | 200 | |
a QTL name = trait abbreviation + BIN n°.
*b Not considering the additional wild introgression from TA1535.
*c Not considering the additional wild introgression from TA1535–TA1649.
*d Not considering the additional wild introgression from TA1649.
3.4.1. Yield Traits
For the total yield and red yield, in all cases, the wild alleles were responsible for the reduction of productivity, with the PV ranging from $-52.35\%$ to $-33.51\%$ for TY and from $-52.30\%$ to $-41.28\%$ for RY. In total, six QTLs were found to be significant in two growing seasons, while three robust associations were found across the three years, being located in both the short and long arm of chromosome 1 ($ty1.2$ and $ry1.3$) and on chromosome 10 ($ry10.1$).
For the uniformity of maturity, two regions on chromosomes 1 and 4 were responsible for a decrease of the traits, with a PV $-15\%$ in both instances. The wild alleles exerted the highest effect on chromosome 1, reducing the trait across all the seasons.
As concerns the biomass and harvest index, a total of nine QTLs were detected, with the larger effect of the wild alleles on the former trait leading to a reduction ranging from $-52.03\%$ to $-40.24\%$, whereas, for the latter, the PV ranged from $-25.52\%$ to $-12.14\%$. Two QTLs had significant effects during the three consecutive seasons, being responsible for the reduction of the traits for $-40.24\%$ ($bm1.2$) and $-25.52\%$ ($hi3.4$). On the contrary, only for the plant weights, the wild alleles located in a 15-cM chromosomal region on chromosome 3 were responsible for an increase ($PW3.6$), with a PV of 73.92%.
3.4.2. Fruit Traits
Numerous alleles were found to be responsible for the variations of the fruit traits. The fruit weight was affected by eight significant QTLs; in all cases, the SH alleles reduced the fruit sizes. The genomic regions underlying the FW were identified on seven chromosomes. Five QTLs were robust across the three years, with the strongest effect found for $fw11.1$, which accounted for a percentage of the phenotypic variance lower than $-43.14\%$. The lowest effect was found for $fw3.5$, with a PV of $-27.91\%$. Three QTLs were identified in two seasons on chromosomes 9, 10, and 11, with PV% ranging from $-35.63\%$ ($fw10.3$) to $-32.01\%$ ($fw11.3$).
For fruit morphological traits, a total of nine and seven QTLs were found to be significantly associated with the fruit lengths and fruit widths, respectively. The SH alleles decreased the two dimensions in all cases, leading to fruits with small sizes. Robust QTLs were found across the three years. A robust cluster was found on chromosome 7 ($fl7.3$ and $fd7.3$), with a PV of $-19\%$ in both instances. Closely located QTLs were found on chromosome 3 for both traits ($fl3.4$ and $fd3.5$) and on the bottom part of chromosome 12 for the fruit widths ($fl12.3$ and $fd12.4$). Overall, the reduction of the lengths and the widths of the fruits were lower than 20% for all the detected genomic regions.
In total, five QTLs for the fruit shape were detected; for three identified across all the trials, the SH alleles caused the fruit to be more flattened (decreasing of the FS). Among these, $fs3.1$ and $fs11.1$ had the highest and the lowest effects, respectively, with PV% ranging from $-12.73\%$ to $-5.96\%$. On the bottom of chromosome 1, we found alleles leading to more elongated fruits, with increased shapes of 7.42% ($FS1.5$) and 7.28% ($FS1.4$) during seasons two and three, respectively.
The wild SH alleles were responsible for both decreasing and increasing the intensity of the fruit colors. Four QTLs for the internal and external colors of the fruits were found to colocalize at the bottom of chromosomes 1 and 2. In all instances, the wild alleles led to a reduction of color intensity, from red to orange/yellow. The strongest effects were observed on chromosome 2, with a PV of $-53.95\%$ for the internal color across the three years of evaluation. Minor effects were instead found on chromosome 1, with variations on growing seasons two and three for the internal ($ic1.4$) and external ($ec1.4$) colors, respectively. The QTLs involved in the increase of the fruit color intensity were detected across two seasons on the long arms of chromosomes 4, 9, and 11, with a PV ranging from 18.97 ($EC11.3$) to 25.05 ($IC4.5$). Although not colocalizing, neighboring QTLs were found at the base of chromosome 4 in a region spanning 96.75–119.0 cM.
Finally, the QTLs involved in pericarp thickness were identified on chromosomes 5 and 11, respectively. The former was detected across all seasons, increasing the pericarp
thickness up to 32.49%, while the latter was detected only in two trials, leading to a reduction of \(-38.69\%\).
### 3.4.3. Chemical Traits
For the chemical traits, we found 11 associated regions in two or three growing seasons. In all cases, the SH alleles increased the soluble solids with a PV in the range of 24–27%. Most of the significant QTLs were detected during two seasons. Only SSCI.5, on the long arm of chromosome 1, had the greatest overall effect, being detected across all seasons. Despite the increase of the soluble solids, the product brix × red yield decreased in percentage, ranging from \(-57.73\%\) to \(-39.33\%\). In tomatoes, this trait provides the estimation of the paste amount during processing. We also found four QTLs associated to a reduction of pH on the long arms of chromosomes 6 and 9 in two seasons (average PV \(~4.5\%) and on chromosomes 1 and 11 across three seasons, with an average PV of 8%.
### 3.4.4. Trichomes
The amount of trichomes is of interest, as it provides an estimate of the level of tolerance/resistance to virus-carrying insects such as aphids and thrips [42]. This protection mechanism is exercised both as a mechanical opposition and through the production of volatile repellent substances contained in the trichromatic glands [26]. Although there are very advanced methods of investigation based on microscopic techniques, the scale we used serves to give an estimate of the putative QTLs underlying the trait. Three highly significant QTLs were found on chromosomes 4, 7, and 10 and were related to TA1280, TA1304, and TA1551, respectively. In all cases, the wild alleles provided an increase of the trichomes number in comparison to the control in a percentage range of 100–200%.
### 4. Discussion
#### 4.1. Performance of S. habrochaites Introgression Lines
Changes of the agricultural scenario in the coming decades will require efforts from breeders in finding novel sources of variations for the improvement of crops [7]. Wild tomato species have evolved in a wide range of habitats and, as a result of natural selection, represent a useful reservoir of genes for various agro-morphological, physio-biochemical, and resistances traits [2]. This exotic genome, once introgressed in the cultivated background, can be successfully exploited, breaking up the association with undesirable traits (linkage drag) and overcoming any occurring breeding barriers [43]. In the present study, a comprehensive approach aimed at assessing agronomic qualitative performances was carried out in multi-season trials on a set of 39 S. habrochaites LA1777 ILs. We firstly examined the performance of the ILs by focusing on the genetic and environmental factors affecting trait variations. Subsequently, we investigated those genomic regions underlying the studied traits and identified putative QTLs. A wide range of diversity was found among ILs for the considered traits with a medium-high level of heritability, which was maximized for fruit shape features. Despite the presence of genetically diverse lines and of additional introgressions for 26% of the lines, the fruit traits were minimally affected by environmental factors. In the set analyzed, we found trait plasticity depending on the chromosomal regions and type of traits, due likely to the different types of gene regions interacting with the environment.
Overall, the whole set of introgression lines resulted in being very promising for soluble solid contents rather than yield traits. The level of soluble solids measured as brix degrees is a measure of the total content of sugars and, in a minor extent, of the organic acids, together with small amounts of dissolved vitamins, fructans, proteins, pigments, phenolics, and minerals [44]. All these compounds influence the flavor and sweetness, which are important precursors of sensory quality [45].
Four lines at the bottom of chromosomes 1 (TA523 and TA1223) and 4 (TA1473 and TA1475) were previously used as a basis to fine map the agronomic traits [10,11]. Our results agree with earlier observations reporting an increase of soluble solids and a
decrease of yield traits at the bottom of chromosome 1 in the overlapping region between TA523 and TA1223 [10]. Moreover, we confirmed a general decrease in fruit weight and an increase in the soluble solids content and color intensity at the bottom of chromosome 4 [11].
Regarding productivity, the differences in performances of the control genotype and the IL set in each cultivation year were almost stable. We observed a decrease of the yield and uniformity of maturity from the first to the last season. As expected, similar trends of correlations were found across the years, particularly within the same category of traits. Interestingly, significative negative correlations were found between the yield traits and soluble solids in the last growing season characterized by less rainfall, humidity, and average temperatures. It is likely that the combination of these effects led to a general decrease of TY and RY compared to the previous years in both E6203 and the ILs. Instead, the first season was characterized by the highest average temperatures and humidity, leading to the best yield values.
The soluble solids tended to be stable across the three seasons, although slightly higher in the less productive ones. Within the ILs, the contrasting values observed in the second year mainly concerned lines with multiple introgressions and/or low brix values in the other seasons, suggesting a major effect of the environment in these cases. Previous evidence in tomatoes reported how increasing the water stress led to the increase of the soluble solids content [46]. Moreover, the rainfall and temperature changes could significantly impact the overall performance of the tomatoes [47].
Although the used drip irrigation restored the entire water requirements at the root level, it is likely that the whole soil moisture was affected by the conditions that occurred in the last season, leading to the observed correlations. Furthermore, it is known that *S. habrochaites* is a cold-tolerant species; therefore, it is possible to suggest that lower temperatures may have a role in the increase of the soluble solids. Since no previous evidence was reported in *S. habrochaites* acc. LA1777, further investigation is required.
### 4.2. QTL Mapping
Despite *S. habrochaites* being recognized as an important source of alleles of agronomic interest, the potential of the existing exotic libraries has not yet been extensively exploited. We identified 75 regions likely with underlying trait variations, and the multi-evaluation trials allowed the identification of 33 robust QTLs, removing any possibility of false discoveries.
Our results agree with previous studies involving diverse types of exotic libraries and experimental mapping populations developed from wild relatives [8,29,30,48–50]. Many QTLs reducing the yield performances and fruit weights confirm the preponderant effect of the wild Solanum alleles on these traits. We found specific regions associated with an increase in plant weights, soluble solids contents, internal and external color intensities, pericarp thickness, and trichome density. The results of this study confirmed that *S. habrochaites* could be a potential source of favorable alleles for horticultural traits, despite the inferior phenotype compared to the cultivated parent. Some genomic regions seem to be conserved across wild tomato relatives; as an example, the increase of soluble solids at the bottom of chromosome 1 fall in a region previously reported carrying alleles improving the trait in other wild species, including *S. pennellii*, *S. neorickii*, and *S. peruvianum* [8,48–50]. Furthermore, the additional QTLs detected on chromosomes 3 (SSC3.6) and 10 (SSC10.1) were also reported in *S. pennellii* introgression lines [8] and, for the one on chromosome 10, in advanced backcross lines of *S. peruvianum* [48,50]. These results confirm the existence of shared regions in various tomato wild species carrying alleles for improving the quality of cultivated ones. Clusters of QTLs involved in fruit weight and morphology were found at the long arms of chromosomes 3, 7, 11, and 12, suggesting a gene linkage. For all, the underlying alleles led to a reduction of fruit weights and shapes in agreement with the wild phenotype, which has an average weight fifty-fold less than the recurrent parent and rounder fruits. Fruit color is one of the main attributes of quality and an indicator of the contents of health-related compounds. Diverse orange, yellow, pink, and black tomatoes are
becoming increasingly popular by consumers who appreciate a rich and varied diet. The decrease of internal and external fruit color at the bottom of chromosome 2 was associated with *fw2.2*, a major gene modulating fruit sizes [33]. The same gene was reported being associated with increased color in *S. pimpinellifolium* due to a pleiotropic effect between the decreasing fruit size and pigment concentration [51]. Pleiotropy between the fruit size and color occurs also in SH, although with the opposite effect. In *S. pennelli*, a decrease in color was shown by the mutation of yellow flesh (*r*) on chromosome 3, responsible for the loss of function of the phytoene synthase, a key enzyme of the carotenoid biosynthetic pathway [52]. The mutation was carried by IL3-2, which defines the same region of TA1539 and TA1541. However, these two lines had additional introgressions, which likely masked a possible effect of any occurring mutation.
Therefore, the additional alleles part of the SH genomic background could be involved in fruit pigmentation. A strong QTL responsible for the increase of trichome density was found on chromosome 10. Recently, Barrantes et al. [15] identified a major QTL in the same chromosomal region in *S. pimpinellifolium* ILs. In agreement with our study, the trait was scored by the same scale. Trichomes are associated with insect resistance, although no candidate gene has been reported on chromosome 10. These results suggest that further studies are needed for a better investigation of the underlying region, although it cannot be excluded that this increase in the density of trichomes does not correspond to a resistance.
### 4.3. Future Prospects for Using *S. habrochaites* ILs in Tomato Breeding
Beyond QTL identification, the advantage of using introgression lines relies on the possibility of their direct use in breeding programs as parent lines. This offers an invaluable opportunity for transferring new traits for the improvement of modern varieties. The set of SH ILs analyzed in this study resulted in being promising for the diverse phenotyped traits. Furthermore, the number of QTLs detected in specific lines facilitates gene pyramiding; as an example, the improvement of soluble solids and pericarp thickness could be obtained by crossing TA1287 either with TA1223 or TA523, which, in addition, showed a slight increase of pH. The synergy of these QTLs could improve the processing yields, with less acidic fruits with greater pulp consistency. For a successful introgression program, it is very important to choose phenotypes stable across a wide range of environmental conditions. To that end, QTLs with large genetic effects are preferred. However, it must be considered, the occurrence of constraints such as pleiotropy, linkage-drag, epistatic effects, and relationships with other beneficial traits. For example, introgressing soluble solids is often challenging due to inverse correlations with the yield [53]. Moreover, pleiotropic effects may occur between the fruit size and color [51].
Despite one of the advantages in holding only a fraction of the entire wild genome being the reduction of fertility problems [8], it must be recognized that several *S. habrochaites* ILs still carry multiple wild segments, as well as large introgressed fragments, covering, in some instances, more than half the chromosome. Therefore, the linkage between the beneficial genes introduced during the backcrossing with the deleterious ones (linkage drag) could reduce the potentiality of ILs for both breeding and QTL mapping purposes. In the current set, we demonstrated how the availability of lines with reduced introgressions led to a major accuracy in the identification and positioning of QTLs with positive effects (e.g., *SSC1.5* and *PER5.1*). While linkage drag occurs for large introgression lines such as TA1304, with both the increasing of the trichome density and reduction of the fruit weight and size.
Our results suggest, in some instances, the necessity of generating new sub-ILs able to break up the linkage occurring with undesired traits and facilitate the fine mapping of QTLs. To that end, genomic platforms such as SNP (single nucleotide polymorphism) arrays or reduced-representation sequencing (e.g., ddRAD-seq: Double digest restriction-site associated DNA and GBS: Genotyping by sequencing) could serve as a key step for the generation of high-density marker data, speeding up the deep exploitation of the current *S. habrochaites* exotic library. These tools have been successfully applied in tomatoes and
other related species, providing large-scale and cost-effective genome scans and generating novel knowledge for genomic-assisted breeding [54,55].
5. Conclusions
The present study aims to provide a broad overview of S. habrochaites introgression lines in relation to the morpho-agronomic performance and chemical properties. Through the investigation of phenotypic performances, the G × Y interaction, and the QTL analysis, we provided novel information for genetic and breeding purposes. This study represents a step toward the exploitation of the hidden properties of S. habrochaites, to be implemented through the development of near-isogenic lines assisted by genomics approaches.
Supplementary Materials: The following are available online at https://www.mdpi.com/2073-3953/11/1/38/s1: Table S1: Parameters describing the trait performances of the recurrent parent “E6203” and the 39 SH ILs for each growing season. For each trait, the significant differences between the ILs and the recurrent parent is reported. Means in the same column with different letters are significantly different, according to Tukey's honest significant difference test; Table S2: Mean values for the introgression lines and the control genotype in each growing season (Y1, Y2, and Y3). In bold and with asterisks are indicated those means that significantly differ compared with the control, according to Dunnett’s test; Table S3: Percent of phenotypic variation with respect to the control for the introgression lines in each growing season (Y1, Y2, and Y3). In bold are indicated those values corresponding to significant differences according to Dunnett’s test; Table S4: The phenotypic plasticity index (PPI) for the traits analyzed in 39 S. habrochaites ILs and the control S. lycopersicum E6203. PPI values > 1.0 are in bold and gray highlighted. For each IL is indicated the chromosomes holding introgressions; Table S5: Variable contribution (VarPC), correlation coefficient (CorrPC), and Eigenvectors (Egv) for fruit descriptors in the two first principal components. Highlighted traits explained a variation >12% in the first or second PC.
Author Contributions: Conceptualization, P.T.; methodology, P.T., M.P., and B.D.; validation, P.T.; formal analysis, P.T.; data curation, P.T., M.C., and M.P.; writing—original draft preparation, P.T.; writing—review and editing, P.T., M.P., A.V., and M.C.; and supervision, P.T. All authors have read and agreed to the published version of the manuscript.
Funding: This research was funded by the Italian Ministry of Agriculture, Food and Forestry, grant name “RGV-FAO”. Part of this research is carried out in the context of a PhD funded by CREA—Council for Agricultural Research and Economics.
Acknowledgments: The authors wish to acknowledge Silvana Grandillo of CNR-IBBR, Luigi Frusciante of the University of Naples, and Massimo Zaccardelli of CREA-OF. We furthermore thank Armida Del Galdo, Rosaria Macellaro, Luigi Aliberti, and Giovanni Ragosta for the valuable support.
Conflicts of Interest: The authors declare no conflict of interest. The funders had no role in the design of the study; in the collection, analyses, or interpretation of data; in the writing of the manuscript; or in the decision to publish the results.
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Rural influences on the social network dynamics of district nursing services: A qualitative meta-synthesis
Jack Gillham | Ivaylo Vassilev | Rebecca Band
School of Health Sciences, University of Southampton, Southampton, England
Correspondence
Jack Gillham, Acute Hospital at Home, Dorset County Hospital, Williams Avenue, Dorchester DT1 2JY, England.
Email: [email protected]
Abstract
Background and Aims: As demands on healthcare services grow, fiscal restrictions place increased emphasis on services outside of traditional healthcare settings. Previous research into long-term-conditions suggests that social network members (including weaker ties such as acquaintances, community groups, and healthcare professionals) play a key role in illness management. There is limited knowledge about the engagement of social networks in supporting people who are receiving medical interventions at home. This qualitative metasynthesis explores the work and the interactions between district nurses (DN) and informal network members supporting people who are receiving medical interventions at home and living in rural areas.
Methods: A search was undertaken on CINAHL, Medline, and PsychINFO for qualitative research articles from 2009 to 2019. Studies that examined DN in rural locations and/or social network support in rural locations were eligible. Fourteen articles were selected.
Results: Thematic analysis of results and discussion data from the studies resulted in four themes being developed: the development of both transactional and friend-like nurse-patient ties in rural localities, engagement of the wider network in the delivery of good care, blurring of professional boundaries in close community relationships, and issues accessing and navigating formal and informal support in the context of diminishing resources in rural areas.
These findings suggest that DNs in rural localities work beyond professional specialties and experience to provide emotional support, help with daily tasks, and build links to communities. There was also evidence that nurses embedded within rural localities developed friend-like relationships with patients, and negotiated with existing support networks and communities to find support for the patient.
Conclusions: Findings indicated that developing strong links with patients and members of their networks does not automatically translate into positive outcomes for patients, and can be unsustainable, burdensome, and disruptive. DNs developing weak ties with patients and building awareness of the structure of individual networks.
1 | INTRODUCTION
Aging populations, driven by falling infant death rates, longer life expectancies, and increased availability of medical and pharmaceutical interventions – coupled with uncertain financial climates, rising populations, and increased co-morbidities has led to escalating costs, a high demand on hospital beds, and profound changes in how healthcare is delivered. Rising healthcare need and a slowdown in funding have led to National Health Service (NHS) debt rising to £13.4 billion in 2020.
As a way of addressing this gap in funding, more patients are being treated in community settings for increasingly complex conditions to reduce the costs associated with inpatient admission. Understanding the consequences of this shift in healthcare delivery style is set to increase in pertinence as wider policy moves health and social care closer to home and community settings. For example, the implementation of the “Long Term Plan” in the NHS in the UK (2019) emphasizes community healthcare by stating an annual primary care budget increase of £4.5 bn. These policies aim to increase service capacity and establish new provisions (such as “hospital at home” (HAH) services, online consultation services, increased general practitioner (GP) training, and “same day emergency care” units) that overcome barriers currently preventing some health conditions being treated at home by, for example, guaranteeing online tele-health consultations, and direct referrals to community services that means unnecessary visits to hospital can be avoided.
1.1 | Social networks and self-management
The role of social networks in supporting self-management has most extensively been researched in the context of long-term condition management. This research has focused on how the structure of people’s networks and the types and range of relationships shape the way in which people access different types of support with their health, practical, and emotional needs. Such studies have found that people who have access to diverse types of relationships, including both “strong,” intimate ties (eg, family members, close friends) and “weak,” more distant ties (eg, healthcare professionals [HCPs], acquaintances, and community group members) are most successful in managing their long term conditions (LTC) and receiving acceptable health, emotional, and practical support. This might be in part due to such networks being able to share the burden of illness work, sustain valued relationships, and have better access to relevant knowledge, skills, and experience. Consequently, access to social network support that is acceptable to people may facilitate improved use of medications, healthier lifestyles (eg, smoking cessation or healthy eating practices), improved experiences of poor health (eg, by managing adjustment; sharing the burden of health, emotional and practical work; and advocating/liaising with HCPs), and improved physical and mental wellbeing.
The increased focus on the community provision of healthcare is likely to result in a widening of the types of conditions and issues that require patients to self-manage. Beyond LTCs, this is likely to include potentially complex and acute conditions, both of which will require further research into the specific roles of social networks in these different contexts.
1.2 | The healthcare professional’s role in self-management support
Previous research has suggested that in a community context, HCPs may facilitate self-management by offering not only health work, but emotional and practical work too. However, the quality and acceptability of such support are often studied in isolation without considering how HCPs interact with the wider network members and the support they provide. Although there is a range of HCPs that are involved in providing good care for patients at home, it is most frequently the district nurse caring and treating that person. Therefore, exploring the relationship dynamics between patients and district nurses may be beneficial when taking a social network approach to exploring healthcare at home. This may include how patients engage with network support when interacting with district nurses; the role of different ties and how network engagement might be in tension or complement district nursing support; how such processes and relationships co-shape the provision of community services; and how dynamics might differ from what is already known about LTC self-management support when self-managing increasingly complex health conditions at home.
Furthermore, primary services like district nursing and other community nursing services such as HAH are more likely to occur in rural contexts where adapting to financial challenges has resulted in the scaling back of smaller, more remote hospitals; and as such, these localities must also be considered when exploring the role of district nurses in patient social networks. The definition of “rural” varies globally with, for example, the UK describing it as areas that fall outside of settlements with more than 10,000 residents; and in Australia, as all areas outside of major cities. Similarly, there is no standard definition of “rural” within healthcare but there is a consensus that the pressures...
and complexities of district nursing are exacerbated by rurality. This is in part because HCPs need to become generalists, healthcare services appear underfunded, operating in a context of poor infrastructure and services provided over long distances.\textsuperscript{22,23} Furthermore, the lack of peer support paired with the diverse patient group that district nurses treat can cause stress and poor staff retention among the workforce.\textsuperscript{22,24} All of which could impact on district nurses’ ability to provide self-management support in rural areas. There is some evidence to suggest that district nurses often live within, or near, the communities they serve,\textsuperscript{4} which may offer an opportunity for drawing on evidence to suggest that district nurses often live within, or near, the communities they serve,\textsuperscript{4} which may offer an opportunity for drawing on existing relationships, shared values, and local embeddedness to provide a motivation to overcome rural challenges. Whether this affects the way social network support is provided or whether it is qualitatively different from other urban settings, requires further exploration.
These factors contribute to the growing demands and complexity of healthcare and self-management support in rural areas and the growing pressures on healthcare professionals, individuals, and other members of their personal communities. The pressure on community-based services, in particular, is likely to increase because of the overwhelming demands on inpatient care, and current strategies and policies outlined in the NHS Long Term Plan,\textsuperscript{2} which encourage community-based public health interventions for increasingly complex and acute needs. These require patients and their social network to take greater responsibility for the management of their health conditions, which previous research has shown is a challenging prospect for patients when confounded by reduced function caused by poor health.\textsuperscript{11} This qualitative metasynthesis will explore the role that district nurses can play within the wider networks of people who are currently receiving professional medical care at home, for a diverse range of conditions, while living in rural areas. It will aim to identify the formal and informal processes that shape the involvement of HCPs with the self-management support of patients and the engagement with members of their social networks.
2 | AIMS
The review will synthesize the available evidence on the use of district nursing services to explore:
1. The way in which district nurses develop relationships with service users to mobilize and/or become part of their personal network and what impact this has on the ability to deliver good care.
2. How rurality affects professional-patient interactions, social network dynamics, and the ability to fulfill social, emotional, and practical needs.
3 | METHODS
Metasynthesis offers a rigorous and systematic approach to reviewing and analyzing the literature that allows the development of novel interpretations while ensuring that the findings are reliable and transferable.\textsuperscript{25}
3.1 | Search strategy
The literature search was undertaken by JG in CINAHL, Medline, and PsychINFO using terms related to social networks, rurality, and community nursing, as guided by an abbreviated version of the PICO (Population, Intervention, Context/Comparison, Outcome) framework (see Table 1 for search terms). The search was completed on July 25, 2019, using the article title and abstracts only. Initial scoping searches identified limited articles that contained all three themes (ie, social networks, rurality, and community nursing), therefore, the decision was made to undertake two separate searches: the first combining “social networks” and “district nursing,” and the second searching for articles related to “rurality” and “district nursing.” A systematic hand search was conducted on the reference lists of existing literature reviews within the search results to find any other relevant articles that may have been missed by the search strategy or poorly indexed.\textsuperscript{26}
3.2 | Article selection
To be eligible for inclusion, studies had to originate from the United Kingdom (UK), Europe, United States of America (USA), Canada, Australia, and New Zealand and be published from 1st January 2009 to 1st May 2019. This was to ensure cultural consistency between the data and to ensure the synthesis was relevant to current practice. Only qualitative or mixed method studies that were written in English were included (see Table 2). Articles reporting mixed methods were included\textsuperscript{27} (n = 1) but only the qualitative data (quotations from district nurses’ reflective accounts through semi-structured interviews; and the interpretations made by the original authors) was extracted when reading the full texts. Social networks were defined as personal communities of individuals that provide emotional, practical, or health support, therefore, any articles relating to online networks (such as social media, often referred to as “social networks”) or telehealth
| TABLE 1 | Search strategy showing the synonyms and Boolean phrases used to find all relevant articles for screening |
|---|---|
| S1 | AB “Social Participation” OR AB “Social Inclusion” OR AB “social exclusion” OR AB “social isolation” OR AB “Social relationship” OR AB “Social support theory” OR AB “Social support network” OR AB “Social support” OR AB “Social network” | 129,777 |
| S2 | AB “District nurses” OR AB “community nurses” OR AB “Hospital at home” OR AB “hospital in the home” | 7,132 |
| S3 | S1 AND S2 | 125 |
| S4 | AB “Rural health” OR AB “rural healthcare” OR AB “Rural” OR AB “Rural nursing” | 241 |
| S5 | S4 AND S2 | 229 |
| S6 | S3 OR S5 | 354 |
approaches were excluded. Rurality was included regardless of the defining characteristic chosen by the authors of the original research (e.g., population, distance to urban centers) and acknowledged during analysis. Figure 1 outlines the number of studies included and excluded at each stage of the identification and screening process. JG screened the full 354 articles found from the search at abstract level and at full text level if uncertainty remained. To ensure quality control, IV and RB each reviewed a separate 25% of the search results and the included/excluded studies were discussed until consensus was reached. Studies were excluded \((n = 343)\) for not including relevant themes \((n = 179)\), from outside the aforementioned westernized countries \((n = 66)\), not including research data (e.g., scoping searches or opinion) \((n = 45)\), on pediatric care or midwifery \((n = 38)\) or if it was an existing literature review \((n = 16)\). Thirteen articles met the criteria for inclusion. A further article was included after hand-searching from existing literature reviews: a total of 14 studies were, therefore, included in the final review. The articles were assessed for quality using the recognized “Criteria for the evaluation of qualitative research” tool for sociological research\(^{29}\) (see Table 3 for acknowledged limitations related to quality criteria of each study). Five articles focused primarily on the community healthcare professional’s role, five on rurality’s impact on healthcare, and three articles addressed both themes (see Table 3 for an overview of included studies).
### 3.3 Data extraction and translation
Two data types were extracted from the articles and organized in a table that also enabled the key information of each study, such as authors, publication dates, methodology, and country of study to be
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**TABLE 2** The inclusion and exclusion criteria used during the screening process
| Inclusion criteria | Exclusion criteria |
|-----------------------------------------------------------------------------------|---------------------------------------------------------|
| • Relevant to themes (social networks and synonyms, district nursing and synonyms) | • Does not include relevant themes |
| • Published since 2009 | • Published before 2009 |
| • Written in English | • Not written in English |
| • Qualitative study (or qualitative data of a mixed methods study) | • Quantitative study |
| • Originate from the UK, Europe, USA, Canada, Australia, New Zealand | • Does not originate from the UK, Europe, USA, Canada, Australia, New Zealand |
| • Existing literature review | • Existing literature review |
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**FIGURE 1** An adapted PRISMA (Preferred Reporting Items for Systematic Reviews and Meta-Analyses) flow diagram of the article selection and screening process\(^{28}\)
| Number, author, year, country | Study aims and objectives | Sample and context | Methodological approach | Data collection and analysis | Content supporting social networks (SN) | Limitations |
|-------------------------------|--------------------------|--------------------|-------------------------|----------------------------|----------------------------------------|-------------|
| 1. Crotty et al., 30 South Australia | To explore the experiences of patients with MH conditions and LTCs on their social network support. | N = 29. Users of community mental health services. | Semi-structured interviews | Potential Participants screened by community nurse. Grounded theory | Spouses are an important member of social networks, interacting and increasing the role of formal support. However, those in this group (LTCs and MH problems) have smaller networks and often befriend DNs for their practical and emotional work. This group shows mostly transient relationships and a degree of isolation. | Convenience sampling limits rigor and single site limits transferability |
| 2. Devik et al., 31 Norway | To explore the views of patients on the effect of long distances and poor infrastructure on their EoL care. | Patients over 65 diagnosed with advanced cancer (n = 9) and receiving EoL care at home in rural Norway. | Narrative, semi-structured interviews with patients. Using open ended questions | Convenience sampling. Phenomenological hermeneutic approach to analysis. Iterative approach from naïve to comprehensive interpretations | Despite being aware of worsening health outcomes patient would rather stay at home in the rural community. They feel they are able to remain a part of the community and hold some social capital and as such can draw on their relationships for support. Conversely, nursing visits restrict freedom of the patient | Authors have preconceptions as practicing nurses. Small cohort |
| 3. Farmer and Kilpatrick, 32 Scotland and Tasmania | Can front line HCPs stimulate changes in healthcare through entrepreneurial skills and could policy makers encourage HCPs into this role? | 38 HCPs (Tasmania n = 15, Scotland = 23) from rural areas. Primary healthcare services (GPs and DNs) | Mostly face-to-face (n = 31) semi-structured. “exploratory” interviews. Otherwise telephone (n = 7) | Participants recruited by advertisement, word of mouth and self-selection at research sites. Exploratory interviews were transcribed and thematically analyzed | HCPs can built patient’s social capital by identifying needs and then bridging and bonding to others. They feel obliged to become part of the community and use their own social capital to create opportunities for others. Some extreme examples where HCPs set up banks, shops, clubs for the communities. Large | Hard to generalize outside of the two countries. Self-selection biases. |
| Number, author, year, country | Study aims and objectives | Sample and context | Methodological approach | Data collection and analysis | Content supporting social networks (SN) | Limitations |
|-------------------------------|---------------------------|--------------------|-------------------------|----------------------------|----------------------------------------|-------------|
| 4. Findlay et al, 2013, Scotland | To increase the knowledge of emotional effects of living with frailty | N = 11. Semi-structured interviews with patients at a medical day | Longitudinal qualitative study. Semi-structured interviews | Secondary analysis of data from PhD study (n = 13). Thematic analysis | Patients wish to stay in their own home but only find contentment in doing so if they are able to connect with family and friends. Their health needs often become a barrier to maintaining relationships due to reduced mobility and district nurse visits restricting their free time. | Secondary analysis (n.b. original author on research team) |
| 5. Gossett-Zakrajsek et al, 2014, USA | How do older adults and HCPs experience and perceive transitions from hospital or integration back into communities? | HCPs (n = 7) from a “home health service” and patients (n = 6) recent discharged from inpatient care | Participatory Action Research. In context observation and interviews (conducted in pairs or triads) | Purposeful sampling. Field notes and interview transcriptions. Thematic analysis | Three main themes emerged on transmission to home: social support, communication, and reintegration. Informal care was highly valued by patient and HCP. Informal support allows for greater personalization, flexibility and planning of care but relies on good communication/collaboration between patient, carer, and HCP. | Observations abandoned after 6. Care involvement unplanned for. Lack of sample diversity |
| 6. Griffiths et al, 2015, England | How and why do DNs construct early support visits in EoL care? | DNs (n = 58) and patients (n = 10) who give or receive EoL care at home | Multiperspective. Qualitative focus groups, semi-structured interviews, observation | Self-selected nurses and patient Recordings and written field notes (collected by nurse researchers) transcribed | During EoL care at home, district nurses intertwined their health tasks with “having a chat.” This created an egalitarian and Self-selected participants patients likely to be most skilled and confident practitioners | |
| Number, author, year, country | Study aims and objectives | Sample and context | Methodological approach | Data collection and analysis | Content supporting social networks (SN) | Limitations |
|-------------------------------|--------------------------|-------------------|------------------------|-----------------------------|--------------------------------------|-------------|
| 7. Grunberg et al,36 Sweden | To use the experiences of DNs on detection and delivering mental health care to increase knowledge of good care | N = 25 DNs from Swedish community setting | Qualitative focus groups and interviews | Recruited using “snowballing” chain sampling. Same interviewer throughout. Transcriptions thematically analyzed | Humanistic relationship. Nurses felt this empowered the patients and their carers to take a lead role in their treatment. Themes emerging from the data were enlightenment, explanation and education, advice and instruction. | “Snowballing” recruitment means participants encourage only those with the same values. |
| 8. Hunsberger et al,21 Canada | Considering staff and resources shortages paired with varied and complex nature of rural healthcare practices, there is need to evaluate the workforce and how to sustain/improve it. | Nurse administrators (n = 21) and Staff nurses (n = 44) from Local Health Integrated Network, Ontario. Approximately 100 miles to a large hospital | Qualitative, Semi-structured interviews using previous research to guide themes for discussion | Recruitment using flyers and “snowball” technique. Transcripts thematically analyzed | The rural district nurse is likely to find the challenges unique to rural healthcare a stressor. These often outweigh the positives aspects and result in changing posts. The expectation to perform tasks outside of health work disgruntles staff. Demands, aging workforce and poor resources suggest rural nursing difficulties will worsen. To improve recruitment should target those from a rural background and | Self-selection and Snowballing recruitment means nurses encourage those with shared values to participate. Increasing bias |
| Number, author, year, country | Study aims and objectives | Sample and context | Methodological approach | Data collection and analysis | Content supporting social networks (SN) | Limitations |
|-------------------------------|---------------------------|--------------------|-------------------------|-----------------------------|---------------------------------------|------------|
| 9. Kaasalainen et al.³⁷ Canada | To explore nurses’ experiences of providing palliative care in rural areas with a particular focus on the impact of the physical residential setting. | District nurses (n = 21) who provide EoL care in rural communities | Qualitative exploratory techniques. Semi-structured interviews | District nurses recruited from previous quantitative survey. Purposeful sampling. Telephone interviews thematically analyzed. Interpretations shared with participants to ensure credibility | Rural district nurses face unique physical and emotional challenges to deliver EoL care. They frequently go beyond their role for the patient. The geographical distances meant support, supplies, and patient contact time were restricted. Isolated patients made them more reliant on the district nurse and made poorer health choices of their own. | Single nursing site reduced transferability. |
| 10. Reed et al.³⁸ Australia | How do DNs successfully advocate for rural Australian EoL care goals? | DNs (n = 7) from a nursing agency in rural Victoria, Australia | Pragmatism. Written reflective accounts and follow up semi-structured interviews. | Care agency DNs approached to take part voluntarily. Iterative analysis of reflective accounts. Semi-structured interviews transcribed and thematically analyzed | District nurses need to become generalists in the rural community as there is little/no specialist support. The district nurse can find support and resources due to their knowledge of the community. This requires flexible relationship boundaries as they often know the patient socially. The district nurse integrates into the patient’s family network and build strong rapport. This creates a reciprocal and trusting relationship that can facilitate holistic care | One practice setting limits transferability. Small sample |
| Number, author, year, country | Study aims and objectives | Sample and context | Methodological approach | Data collection and analysis | Content supporting social networks (SN) | Limitations |
|-------------------------------|--------------------------|--------------------|------------------------|-----------------------------|----------------------------------------|-------------|
| 11. Reed et al, 27 Australia | To create an initial understanding of how nurses practice EoL care in rural areas to provide a platform for further research that could inform practice | District nurses \(n = 7\) who deliver EoL care in rural areas of Australia. Wide spread areas across all states. | Sequential mixed methods. Nurses wrote reflective accounts the follow up semi-structured interviews | Recruited district nurses purposefully selected from initial those who completed a wide spread Likert style questionnaire. Reflections used to guide semi-structured interviews. Thematic analysis. | District nurses reported knowing the rural area so knew what resources were available. They have a good social capital so can advocate successfully. There is an issue with boundary crossing and confidentiality as the nurse often knows the patient and their family socially. They justify this by demonstrating the likely improved health outcomes. DNs have the emotional intelligence to manage this. | Self-reporting and reflections rely on timely completion and memory. Small sample size |
| 12. Roden et al, 39 Australia | To explore the strategies and sustainability of the health promotion (HP) role of the rural and urban DN | 10 district nurses from varying settings (rural \(n = 5\), urban \(n = 5\)) of New South Wales, Australia | Semi-structured Interviews following up on Likert questionnaire on the self-efficacy and burden on HP | DNs approached to participate in quantitative study then purposeful selection for interviews. Transcriptions thematically analyzed. | There is a lack of multidisciplinary support for DNs in rural areas. Their commitment to the community means the district nurse feels responsible to undertake health promotion activities and find them to be successful because they are valued members of the community. Health promotion is usually sacrificed when rural healthcare pressures build. | Only in New South Wales. Small sample interviewed. |
| 13. Terry et al, 40 Australia | To identify, which health and safety issues impact on the provision and quality of rural DN care. What strategies do DNs adopt to overcome these? | Experienced district nurses \(n = 15\) from three rural care areas, Australia | Phenomenological approach. Semi-structured interviews | Sample spread across 3 recruitment sites. Conducted interviews face to face \(n = 4\) or telephone \(n = 11\). Transcripts thematically analyzed and consensus reached. | Health and safety issues for rural DNs are primarily environmental; mainly long distances, isolation, poor infrastructure, and patient families creating difficulties. Management | Telephone interviews limits ability to clarify, probe, and interpret body language. |
(Continues)
| Number, author, year, country | Study aims and objectives | Sample and context | Methodological approach | Data collection and analysis | Content supporting social networks (SN) | Limitations |
|-------------------------------|--------------------------|-------------------|------------------------|-----------------------------|----------------------------------------|-------------|
| 14. Wang et al, 2021, Norway | What was important to the service users of a new HaH service; to guide planning in the future | Six patients transferred to HaH service in Norway | Nine patients recruited from concurrent quantitative study comparing inpatient to HaH experience | Six patients were randomized to HaH treatment. Semi-structured interviews were transcribed and thematically analyzed by a team of researchers | Participants discussed how they felt being treated at home compared to inpatient settings. Their social network was cited as a source of support during this time. Patients also discussed the relationship they shared with the district nurse and what work they undertook; which included some practical and emotional work alongside their healthcare role. | Small cohort, recruited from one inpatient setting limits transferability. |
easily managed (Table 3). Of the two types of data, in the first order, data included direct quotes from participants and verbatim extracts from the results chapters of each paper. Second-order constructs (the theories developed by the researchers of the original studies) were extracted from the discussions and analyses chapters of the original articles. As is best practice when conducting a metasynthesis, in order to assess reliability, 30% of articles from each search were data extracted by members of the study team; IV and RB. The findings were discussed and consensus reached on the data that should be included, and any areas of contention throughout data extraction were discussed between the research team. From the 14 included papers, 220 first-order quotations relevant to personal relationships, support, and relationships provided by district nurses or rural factors were included to answer the aims of this literature review. A further 83 second-order constructs by the original authors were extracted.
Translation and reconfiguration of the data is arguably the most subjective stage of the synthesis process, and therefore, as with the other stages of this metasynthesis, findings and interpretations were discussed, revised, and elaborated within the study team. In this synthesis, in order to translate the findings into one another and develop new meaning and understanding from the included themes, a line of argument synthesis was applied. This approach allowed data from primary studies that had different contexts, and theoretical and methodological approaches to be combined. This was an iterative process of repeated reading that identified recurring and juxtaposing results that could be translated into one another and identify the novel themes. Through this process the novel themes developed by the review team were: Blurred boundaries between the types of work nurses in rural areas; Transactional and friend-like nurse-patient ties in rural localities; Negotiating professional responsibilities and network engagement; and Local embeddedness and shaping relations within local communities. Table 4 provides an overview of the synthesis process.
4 | FINDINGS
4.1 | The development of both transactional and friend-like nurse-patient ties in rural localities
Rural settings impact on the relationships between nurses and patients in several ways, and result in two key types of relationship styles with service users. The first are those that are transactional in nature, and develop as the result of relatively infrequent, discontinuous, and unreliable interactions between nurses and patients in community contexts. This is often due to nurses serving patients in isolated areas with poorly developed infrastructures and phone networks, long distances and travel times between patients, and high levels of staff turnover and rotation (especially where long distances need to be shared). Within such contexts, patients have to “take whoever, whether you like them or not” meaning the building of trusting and therapeutic relationships between patients and nurses might become difficult. Patients cite that they “never feel like discussing things with them [district nurses they see less frequently] in the same way,” which contributes to relations in rural areas, which feel transactional, fleeting, and impersonal, although not necessarily ineffective.
However, the 1-to-1 contact in community settings and the interactional confidence that patients have due to being in their own homes where they “know what is what”, also opens possibilities for development of close, highly personalized relationships between patients and nurses, which are valued by the patient.
We have a good connection. It means a lot to me. She is more than a nurse...she is a person.
Being open to the development of such “comfortable” relations with patients fits with the perceptions of nurses of their professional role and they see it as an achievable aim and an effective way of supporting patients. To accomplish this, nurses may adopt certain interactional styles. For example, a “relaxed conversation style” and make themselves personally accessible to the patient by, for example, giving out their personal number;
your number is in the book, or you give them your personal number.
4.2 | Engagement of the wider network in the delivery of good care
Where nurses develop close relationships with the patient, there is evidence to suggest that the nurse may be (or become) part of the social network, as well as interact with other individuals within the wider social network. In this way, they often utilize interactions with patients as an opportunity to identify emotional and practical needs being unmet by the rest of the patient’s social network, and commonly feeling obliged to offer support in these areas. This support may include practical tasks such as stoking the fire, “Training the dog,” organizing or providing transport, organizing financial support in the form of “getting benefits,” and providing emotional support by spending time talking and discussing personal concerns. The rationale for undertaking practical roles might be in order to reduce negative events such as falls when less able patients attempt to do practical work independently; or even prevent self-neglect if patients cannot cook and wash clothing. The emotional work undertaken by nurses during health visits may be used as a “lever” for further assessment, which not only reduces negative effects associated with loneliness, isolation, and poor mental health, but also acts as a technique for identifying health needs. For example, district nurses would “just, you know, chat about things in general...like a social visit...and sometimes by just doing that, little problems will come out”.
When district nurses live and work in the same rural locality, there are often pre-existing relationships with the patient and/or
| Number, author, year, country | Translatable concept | Summary of second order interpretations by original author | Summary of third order interpretations |
|-----------------------------|--------------------------------------------------------------------------------------|--------------------------------------------------------------------------------------------------------------------------------|-----------------------------------------------------------------------------------------------------|
| 1. Crotty et al, 30 South Australia | Spousal networks, the impact spouses/no spouse has on use of DN. | Spousal networks were denser and more likely to be maintained. Spouses interact with DNs and improve their significance within the SN. When there is no spouse, friends are more valuable; when there is no friendship support DNs fill friendship roles. LTCs alongside poor mental health makes maintaining networks difficult so transient SN members are frequently used. | The DN acts as a conduit to other services adding more “weak,” “transient” relationships into the SN. This usually results in a network dominated by HCPs that is unlikely to provide long-term support and will be biomedically framed. This will likely lead to a lack of support with practical and emotional work; especially considering the mental health with long term condition cohort of this study. |
| 2. Devik et al, 31 Norway | Values of patients on rural healthcare and how it affects the quality of care. | Patients have to adapt to the change in lifestyle when requiring DN input in rural areas due to the interventions being delayed, interrupting schedules and routines, and being not readily available. Despite this being exacerbated by rurality patients prefer to remain here due to being a “brick” in history and place giving them increased social capital and a sense of self, security and control. | The social capital retained by aging in place means patients can retain their existing ties to help meet health, emotional and practical work. DNs are less likely to become part of the patients SN due to their visits being infrequently, on a healthcare schedule, and therefore, difficult to mobilize by the patient. Patients prefer to navigate the community to find support but targeted those with knowledge of healthcare (e.g. retired nurses). |
| 3. Farmer and Kilpatrick, 32 Scotland and Tasmania | HCPs outside of their healthcare role creating opportunities for patients to increase their function and social capital. In rural areas. | The DN role in a rural community is both bonding and bridging with others. Nurses have been known to be embedded in the social fabric of the community and their remit extends to lift-giving, delivery and involvement in community facilities. They use their social capital in communities to implement change and establish entrepreneurial services (often outside of healthcare, such as establishing social clubs). | DNs use their position within the network to identify patient, SN and community needs. Especially true in rural areas where resources are limited, DNs go beyond their role and take it upon themselves to meet the needs. They also bridge and bond to other services (often out of reach to the rural patient) as a form of mobilizing others into the SN and improve the patient’s social capital. Although not explicit in the data the improvement in social support and capital is likely to improve health; the DNs overarching goal. |
| 4. Findlay et al, 33 Scotland | Importance of a connection with family and friends when being treated at home. | Frustration and sadness at the lack of support were frequently cited, with contentment noted when friends and family were accessible. The timing of DN visits seem to restrict the ability to maintain existing relationships. | Some participants enjoyed the social aspects of the DN visits but due to timing most found them to be restricting and display ambivalence toward the service and the loneliness it brings. Ideally, individualizing services should reduce loneliness and improve associated mental and physiological health (e.g. frailty). |
| 5. Gossett-Zakrajsek et al, 34 USA | The balance of formal and informal SN members during transitions from hospital to home. | Support, communication and reintegration are the three themes identified during transitions home. Successful transitions occur when there is | A need for acute care creates changes to the patient’s function and a break from their existing SN support. If there are weak ties these may disperse during |
| Number, author, year, country | Translatable concept | Summary of second order interpretations by original author | Summary of third order interpretations |
|-----------------------------|----------------------|----------------------------------------------------------|----------------------------------------|
| 6. Griffiths et al,35 England | Relationship between DN and patient during EoL care. | DNs give information, advice, education and instruction. DNs carry out this work in a relaxed manner that empowers the patients, becomes egalitarian, and therefore, therapeutic. The physical tasks and assessment are intertwined with the social aspects of their visits; often unnoticed by the patient. The frequency of the visits also correlated to an improved self-efficacy. | The DNs relaxed approach allows them to integrate into the patient's SN. The egalitarian relationship, not dissimilar to a friend, allows greater information sharing in both directions. The DN, once part of the SN adds new information and support, mobilize others into the SN and help with practical work that alleviates emotional stresses that impacts on their physical and mental health; thus benefiting the patient and their SN. |
| 7. Grunberg et al,36 Sweden | Emotional support/work of the DN and how this helps identify needs and improve care. | DNs use informal dialog to lift patients' mood and facilitate open discussion that helps identify further needs. This was deemed important to allow an integration into the SN meaning the DN had the role to mobilize others, advocate and meet their emotional needs. These skills are intrinsic with the DN often unaware they are detecting mental health needs. However, time and resources appear a barrier. | Despite the lack of resources DNs can utilize their relaxed approach, intertwined with planned visits, to provide emotional work: either by improving mood or identifying mental health concerns. Their role becomes similar to a friend by using general conversation and joking. They can then integrate into the SN to meet emotional needs and to identify the correct people already in the SN to mobilize where needed. |
| 8. Hunsberger et al,21 Canada | Values of DNs on rural healthcare and how it affects care and themselves. | Rural healthcare can be rewarding and stressful. Often the initial attraction of open countryside become the stressor due to isolated practice. Acuity in these areas is increasing and experienced nurses are approaching retirement increasing demands on the services. More recently, only those already embedded in rural life appear to choose to work there. Urban policy and decision making frustrates rural healthcare, and therefore, rural specific training is needed. | The attraction of rural nursing is to help a community one is already embedded into. The shared community values helps integration into an SN to mobilize others. Willing DNs should nurture the attachment to the community to create stronger SN ties. However, the challenges of rural healthcare seem to outweigh the positives making recruitment a challenge. The blurring of boundaries between community member and DN cause confidentiality concerns and a burden on the DN who may be contacted out of hours or in public spaces. |
| 9. Kaasalainen et al,37 Canada | Physical and emotional challenges of EoL care in rural areas. | Rural nurses experience a unique challenge when delivering care to Patient needs and their SN. DNs need good communication with informal and formal support that is planned with an appreciation for the changes occurred during time spent in hospital. There needs to be good communication between patient and informal and formal support. | Lack of resources force DNs to become generalists but this (Continues) |
| Number, author, year, country | Translatable concept | Summary of second order interpretations by original author | Summary of third order interpretations |
|-------------------------------|----------------------|---------------------------------------------------------|----------------------------------------|
| 10. Reed et al.38 Australia | Rural DNs working and living in the same area and how this influences their role. | Successful EoL care requires DNs to be committed to the emotional work involved. Resonating with other studies, the knowledge of the people and resources available in the rural community was noted as valuable in advocating to the appropriate people. The DN needs to have a flexible relationship boundary with the patient create a reciprocal relationship for confident advocacy and emotional support. | EoL care increases the importance for DNs to become part of the SN of the patient and their family and should be encouraged. Increased tie strength and involvement in emotional work creates a reciprocal relationship and shared values that are conducive to good care. There is a risk of confidentiality breaches when advocating to other members of the rural community (e.g. priests). There is also a risk of emotional burden for the DN as they are likely to be unsupported in the rural setting. |
| 11. Reed et al.27 Australia | How local knowledge influences the way DNs care in rural areas. | DNs consider the values of patient and family to personalize care. Knowing the available resources in the rural area helps gather support for the patient. DNs have strong community relationships that empower them to advocate successfully. DNs possess the emotional intelligence to manage a personal and professional relationship and can justify it because of the likelihood of improved outcomes. | DNs face a challenge to meet patient's needs by nurturing a strong SN tie that could overburden them emotionally at EoL. If this is achieved they can successfully mobilize other members of the community and healthcare services. The challenges of burden, confidentiality and emotional distress are overcome by the DNs emotional intelligence. |
| 12. Roden et al.29 Australia | DNs use their social capital for health promotion (HP). The pressures on rural DNs make this hard to sustain. | There is a lack of support and competing priorities for a rural DN. However, DNs had a more positive and committed outlook on HP, possibly because they knew and felt responsible for the community they served. Patients were more likely to follow the HP advice due to the respect they had for the DN. HP was often sacrificed when rural challenges (workforce, infrastructure, resources) limited their availability to patients causing stress and disengagement by the DN. | Effective HP requires committed DNs to be embedded into the community. This increases the tie strength between patient and DN and the patient is then more likely to follow advice. Relationships are mutual, open and conducive to honest reporting of health behaviors. Rurality acts as a facilitator to shared values, community engagement, and therefore, stronger tie but also restricts the time and resources available to deliver HP effectively. DNs may neglect HP as a result of rurality to treat the patient's primary health need. |
TABLE 4 (Continued)
| Number, author, year, country | Translatable concept | Summary of second order interpretations by original author | Summary of third order interpretations |
|-------------------------------|----------------------|----------------------------------------------------------|----------------------------------------|
| 13. Terry et al.40 Australia | The health and safety (HS) issues of rural healthcare and how it affects quality of care. | HS issues are complex and largely environmental. These include isolation, long distances, and poor infrastructure. DNs cite “making do” and developing skills to overcome the HS issues. This includes rotating staff and dividing workload. Lack of funding, support, supervision, and specific training exacerbate the problem and result in poor staff retention. | The needs of the DN and patient cannot be met in parallel. The HS issues in rural communities result in DNs create physical and emotion distress among DNs. The coping strategies used makes them less available to the patient, poor continuity of care, and therefore, a weaker tie is developed within the SN; encompassed by patients “making do with who turns up” and “not speaking to them in the same way.” |
other social network members.27,33 For example, one nurse said she was able to help a man to “die at home with his three teenage sons – one of which I employed locally”.27 This is beneficial as it helps to create an egalitarian relationship that is based on shared norms and values.21,27 Moreover, the nurse may be well placed not only to successfully identify potential social networks of support37 but also have the increased social capital within the community to enable its successful mobilization.27,32,38 The quote that “People don’t say no to a health care professional as readily”32 epitomizes this increased social capital and nurses are seen as the “quarterback” of the community27; mobilizing other professionals and healthcare services.30,32,35,36,41 Nurses “Bridge or bond [patients to others]”32 such as churches, clubs, or charities32,36 but also, in some cases, proactively create new social networks of support by establishing their own clubs, community projects, or shops that offer an opportunity for interaction with others in the community.32
4.3 | Blurring of professional boundaries in close community relationships
However, the development of complex nurse-patient relationships may result in some degree of crossing the boundary of one’s professional role in order to fulfill key nursing responsibilities, especially in rural areas27,33,35,36,38,40,41. Individuals that carry out a formal service begin to undertake informal support roles.30
Nurses reported experiencing the pressure of expectations from patients to act as a substitute for the absent support from family, friends, and peers33; stating they “get calls at home – A lot of calls!”.37 Similarly, researchers highlighted that the familiarity patients had with nurses meant they found their “privacy was invaded”37 when they were “consulted about health issues in grocery stores or at sports events”.21 Such patient expectations are likely to be unrealistic given that rural factors outlined above restrict the time available to nurses to offer substantial emotional and practical support.37,38,40 This may leave nurses with difficult choices to make between disappointing raised patient expectations, fulfilling responsibilities to other patients, and the need to prioritize illness over all other types of work, such as domestic tasks or food shopping.39 Thus, close relationships between nurses and patients may be difficult to negotiate and manage,21 adding substantial amount of relational work to the nurse workload, and raising issues of overburden or “burnout,” confidentiality, and meeting professional and legal responsibilities and standards.27,31
Moreover, in rural community settings where social isolation can be common,27,40 some patients may act proactively use nurse visits as an opportunity for social contact26 and in the absence of network support, patients may actively seek district nurses to provide emotional and other types of support.30,31
I see her if I come in here to say hello...I'm not actually allowed to consult with her because I'm not classed as homeless.20
However, when district nurses practice “generosity exceeding what can be expected”31 relationships with patients strengthen and district nurses become more forthcoming with offering additional support and may come to be “perceived by patients as a friend.”38 It may also lead to reshaping existing relations between patients and members of their wider network. Relying on professionals for emotional and practical support can cause any available, existing support to dissipate leaving the patient vulnerable if formal support is discontinued,23 while also putting additional pressure on nurses to further extending the depth and range of support they provide.
4.4 Issues accessing and navigating formal and informal support in the context of diminishing resources in rural areas
While building close nurse-patient relationships may sometimes be associated with higher personal job satisfaction,21,38 the need to deal with complexity that such relations introduces associated negative experiences27 maybe less acceptable to newly qualified nurses who “may not be comfortable with all the different things [emotional and practical support] they had to do,” according to their more experienced peers.21 As with the community as a whole, smaller rural district nursing teams experience an increased sense of shared values and team spirit among themselves38 and are able to create an “extended family environment”21 but there is a relative lack of specialist support available; which not only means nurses practice as generalists but also that it restricts the services available that can be mobilized to support the patient.21,27,37–39 Furthermore, the aging workforce in rural areas means that recruitment from outside the local area is increasingly common. This reduces the embeddedness and shared values of the nurse in “both a geographical and social sense,”31 limits the knowledge the nurse has of the community, and therefore, the influence they have to mobilize other forms of support.21 Consequently, despite aiming to increase the social network of support through advocacy and mobilization of others, in an attempt to improve efficiency or through an unawareness of the local community dynamics, district nurses unintentionally limit the patient’s social capital if they are unable to participate in their usual social network interactions because of time-conflicting health interventions; arranged at a time to suit the professional.31,33 For example, patients feel “your life’s not your own”33 and that “much time is spent waiting...there might be other things you would rather like to do”.31 Patients with LTC and poor mental health have a more frequent use of paid and formal care use, and are, therefore, particularly vulnerable to this.20
5 DISCUSSION
This qualitative metasynthesis found that HCPs who work in rural areas are involved in wide ranging support for patients. This work goes beyond their professional specialty and experience and may include providing social and emotional support, help with daily tasks, and building links to local communities. Our findings indicate that taking on such a complex role is needed in order to provide effective and safe care for people living in rural areas. This review has found two dominant models in terms of how this is currently done in terms of developing relationships with patients and engaging with their wider networks of support: one model where nurse-patient relations are kept at an arms-length and another where nurses develop close relations with patients, which resemble friendships, with links extending to their wider networks, including families, friends, and the localities where they live. These findings indicate that neither of these models is optimal for delivering patient-centered care in the community. In the case of the former, this is in part due to lack of understanding of the patient context, resources, and structure of support, with minimal or no knowledge and engagement of the wider social network members, and thus with likely negative implications for patient care and support tailored to individual needs. In the case of the latter, this is due to building expectations among patients and their network members that nurses might be able to address multiple gaps in the provision of health and social support arising from structural inequalities and the structure of people’s networks. However, such relations are unrealistic and unsustainable over the longer term due to the risk of nurses becoming overburdened and because changes to healthcare service staff and provisions might make the nurse unreliable to patients; especially considering the uncertain finance, probable increase of complex community care and policy changes affecting healthcare, all of which reduces how effectively the nurse can deliver additional support.
Furthermore, as with other studies, this qualitative metasynthesis suggests that nurses developing an understanding of, and involvement with, patient’s social networks does not automatically translate into positive outcomes for patients.13,44 For example, such close ties can have negative impact on the wider network of support by restricting engagement with existing network members and the building of new links. Therefore, our findings have suggested that nurse-patient relations in rural areas work best where nurses are seen as trusted acquaintances with a broad understanding of the social and emotional needs of patients and the financial and relational resources accessible to them. Such relationships are currently ad hoc, but they might develop, and become most effective in localities that nurses are familiar with and have greater social capital within the community because they live in the area or because they have been professionally involved with it over a long period. This may be because in such circumstances nurses are more likely to be familiar to patients, their family members and the wider local community either directly or indirectly through personal and professional reputation and support.
These weak ties with patients paired with an understanding of local and individual structures of support, can allow nurses to help patients find, access, and mobilize other network members in a way that is acceptable to them but also make them aware of new relationships and support that might be available, thus increasing the diversity of support and information. Such relations with patients are likely to be sustainable over the longer term as, they are contextually sensitive, but also compared to strong ties, require lower levels of relational work (eg, in negotiating acceptable engagement with other network members) and thus reduce the risk of burnout of nurses. Adapting the role of DN would allow them to improve collaborative work with people’s informal network members while also delivering care that is better tailored to patient needs and context.
5.1 Implications for practice
Engagement with patient’s social networks is likely to add value for patients living in rural areas and for community-based nursing teams. However, expectations for developing close relations with patients as a part of the nursing role should be seen as unrealistic considering the tensions between the growing complexity, demand, and availability of services; but also due to additional tensions that such relations, and relational work (the interpersonal efforts that district nurses will invest in order to develop relationships between themselves and the patient, are likely to create. Developing weak ties of trustworthiness and familiarity with patients is consistent with the nursing role and is likely to help with providing effective patient care. In developing such relations, district nurses could focus on using health interactions to engage in conversations about family, friends, and peers; and what they do or do not do to support the patient. Such knowledge, together with awareness of local resources and informal support, can allow nurses to help patients shape relations with their network members, access, and negotiate relations within the community and healthcare services, mobilizing other sources of support that can diversify the patient’s existing network. This will add sustainability to the support; improve patient outcomes associated with improved health, practical, and emotional support; and reduce the potential burden of responsibility on the healthcare service and professional. However, such relations between patient and nurses are currently only developed ad hoc. Making them sustainable in the context of increasing acuity and demand is likely to require putting in place support for professional development, and building resources and infrastructure enabling links between relevant professional and community resources and support (eg, health trainers, social prescribers, befriending services).
6 Conclusions
This review used the systematic approach of a qualitative metasynthesis in order to gain insights into the effect of rurality on district nurse-patient relationships, where existing data had previously focused on the two themes in isolation. The focus of this review was to combine and address how the two factors influence, compliment, or conflict with one another; and develop further understanding of what approaches patients and professionals should adopt in these contexts. Findings demonstrated that HCPs in rural areas cross boundaries, first, with the work they carry out, and second, from a professional relationships one similar to friendship. There was also evidence of local embeddedness and nurses negotiating with the community in order to find support on the patient’s behalf. The discussion demonstrated that nurse-patient-social network relationships can be unsustainable if they are burdensome or disruptive to existing social networks. Developing weak ties of familiarity with patients and building awareness of, and connection to, local structures of support is likely to offer a promising avenue for developing community-based nursing support that is sustainable and tailored to patient needs. In this regard, this review contributes to the understanding of the key role that weak ties play in people’s networks by exploring such ties in a different context and focused on healthcare professionals, but further research is needed, across varying community nursing services, in order to develop a clear understanding of the dynamics of such a role and relationships and the necessary conditions and resources that might be needed for their embeddedness into practice.
7 Limitations
This review included only qualitative studies. Although this method fills gaps in understanding and underlying mechanisms left by quantitative studies, qualitative synthesizes cannot include the number of studies of a quantitative synthesis. Furthermore, as a review of a previously unexplored areas of rural healthcare paper, the outcomes identified are theoretical and may require empirical investigation to confirm.
Acknowledgments
We would like to acknowledge the University of Southampton and the Dorset County Hospital Foundation Trust for the joint funding and resources for the PhD program of the author JG. Without this, the author would not be able to dedicate the time required to complete this work. The views expressed are those of the authors and not necessarily those of the university or the NHS trust who took no part in designing the study or collection, analysis, and interpretation of data, writing of the report, or the decision to submit the report for publication.
Funding Information
The university of Southampton and the Dorset County Hospital have jointly funded the PhD programme of JG and therefore this study. Open access funding provided by the University of Southampton.
Transparency Statement
Jack Gillham affirms that this manuscript is an honest, accurate, and transparent account of the study being reported; that no important aspects of the study have been omitted; and that any discrepancies
from the study as planned (and, if relevant, registered) have been explained.
CONFLICT OF INTEREST
The authors declare that they have no conflicting interests.
AUTHOR CONTRIBUTIONS
Conceptualisation: Jack Gillham, Ivaylo Vassilev, Rebecca Band
Data Curation: Jack Gillham, Ivaylo Vassilev, Rebecca Band
Methodology: Jack Gillham, Ivaylo Vassilev, Rebecca Band
Writing: First Draft Preparation: Jack Gillham
Writing: Review and Editing: Jack Gillham, Ivaylo Vassilev, Rebecca Band
Supervision: Ivaylo Vassilev, Rebecca Band.
All authors have read and approved the final version of the manuscript.
Jack Gillham had full access to all of the data in this study and takes complete responsibility for the integrity of the data and the accuracy of the data analysis.
DATA AVAILABILITY STATEMENT
The authors confirm that the data supporting the findings of this study are available within the article and its supplementary materials.
ETHICAL STATEMENT
This is a qualitative metasynthesis of existing papers, all of which had ethical approval.
ORCID
Jack Gillham https://orcid.org/0000-0001-8938-7720
Ivaylo Vassilev https://orcid.org/0000-0002-2206-8247
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Perinatal Depressive Symptoms, Human Immunodeficiency Virus (HIV) Suppression, and the Underlying Role of Antiretroviral Therapy Adherence: A Longitudinal Mediation Analysis in the IMPAACT P1025 Cohort
Florence Momplaisir,1,2,a Mustafa Hussein,3,a Deborah Kacanek,4 Kathleen Brady,5 Allison Agwu,6 Gwendolyn Scott,7 Ruth Tuomala,8 and David Bennett9; for the IMPAACT P1025 Study Team
1Division of Infectious Diseases, Perelman School of Medicine at the University of Pennsylvania, Philadelphia, Pennsylvania, USA, 2Leonard Davis Institute, University of Pennsylvania, Philadelphia, Pennsylvania, USA, 3Joseph J. Zilber School of Public Health, University of Wisconsin-Milwaukee, Milwaukee, Wisconsin, USA, 4Department of Biostatistics, Harvard T. H. Chan School of Public Health, Boston, Massachusetts, USA, 5AIDS Activities Coordinating Office, Philadelphia Department of Public Health, Philadelphia, Pennsylvania, USA, 6Divisions of Pediatric and Adult Infectious Diseases, Johns Hopkins University School of Medicine, Baltimore, Maryland, USA, 7Division of Pediatric Infectious Disease and Immunology, University of Miami Miller School of Medicine, Miami, Florida, USA, 8Department of Obstetrics and Gynecology, Brigham and Women’s Hospital, Boston, Massachusetts, USA, and 9Department of Psychiatry, Drexel University School of Medicine, Philadelphia, Pennsylvania, USA
Background. Women with HIV have higher risk of depressive symptoms in the perinatal period. Evidence on how perinatal depressive symptoms affect viral suppression (VS) and adherence to antiretroviral therapy (ART) remains limited.
Methods. Perinatal depressive symptoms were assessed using 6 items from the AIDS Clinical Trials Group (ACTG) Quality of Life questionnaire. VS (viral load <400 copies/mL) was the outcome. Adherence was defined as no missed dose in the past 1–4 weeks using the ACTG Adherence Questionnaire. Generalized mixed-effects structural equation models estimated the association of depressive symptoms on VS and the mediating role of ART adherence among women enrolled in the IMPAACT P1025 Perinatal Core Protocol (2002–2013).
Results. Among 1869 participants, 47.6% were 21–29 years, 57.6% non-Hispanic Black. In the third trimester, the mean depressive symptoms score was 14.0 (±5.2), 68.0% had consistent adherence, and 77.3% achieved VS. At 6 months postpartum, depressive symptoms declined while adherence and VS fell to 59.8% and 53.0%, respectively. In the fully adjusted model, a 1-SD increase in depressive symptoms was associated with a 3.8-percentage-point (95% CI: −5.7, −1.9) decline in VS. This effect is the sum of the indirect effect of depressive symptoms on VS via ART adherence (−0.4; 95% CI: −.7, −.2) and the direct effect through other pathways (−3.4; −5.2, −1.5). The decline in adherence driven by depressive symptoms accounted for ≥11% of the total negative effect of depressive symptoms on VS.
Conclusions. Perinatal depressive symptoms were associated with decreased adherence and VS, highlighting the need to screen for, diagnose, and treat perinatal depression to optimize maternal outcomes.
Clinical Trials Registration. NCT00028145.
Keywords. women with HIV; perinatal period; depressive symptoms; ART adherence; viral suppression.
Depressive symptoms increase during pregnancy and the postpartum period, particularly for women living with human immunodeficiency virus (HIV) [1]. Perinatal depression is associated with adverse birth outcomes, including preterm birth and low birth weight [2], and adverse maternal outcomes such as pre-eclampsia and emergency cesarean delivery [3, 4]. For women living with HIV, however, the association between perinatal depressive symptoms and viral suppression (VS) at delivery and postpartum is less clear. Maternal VS can preserve maternal immune function and minimize the risk of perinatal HIV transmission [5]. Yet, the majority of studies examining the association between perinatal depression and VS were conducted outside the United States [6–8] where antiretroviral therapy (ART) is not as readily available and contextual factors differ from those in the United States. Studies from the United States have been...
cross-sectional and have found inconsistent associations between perinatal depression, ART adherence, and VS [9, 10].
Using longitudinal data from the International Maternal Pediatric Adolescent AIDS Clinical Trial Network (IMPAACT) Perinatal Core Protocol, P1025 prospective cohort study, we evaluated the associations of depressive symptoms with VS during the perinatal period, as well as the extent to which ART adherence mediates these associations, controlling for relevant demographic, clinical, and behavioral confounders. We hypothesized that depressive symptoms would be associated with poorer ART adherence and a lower likelihood of perinatal VS.
METHODS
IMPAACT P1025 Cohort
IMPAACT P1025 is a multicenter observational US study created to evaluate the safety and effectiveness of ART and other interventions intended to prevent perinatal HIV transmission. Methods for P1025 have been previously described [11]. The P1025 study population includes women living with HIV, age 13 years and older, with a viable pregnancy of 8 weeks or greater gestation who enrolled during pregnancy or immediately postpartum between 2002 and 2013 (n = 2756 mother–infant pairs followed for up to 1 year postpartum, with follow-up closing in 2013).
Study Sample and Inclusion Criteria
We evaluated changes from the prenatal to postpartum period in the relationship of depressive symptoms to ART adherence and VS. Accordingly, we excluded women who enrolled at delivery (n = 844) and those with missing data on basic demographic and HIV variables (n = 43), producing a final sample of 1869 women. If mothers had multiple pregnancies during the study, we analyzed data from only their first P1025-enrolled pregnancy. All sites had institutional review board approval and women provided written informed consent prior to participation.
Longitudinal Design
We classified all available longitudinal data into 7 observation periods: first, second, and third trimester; delivery (±14 days around delivery); and 1–3 months, 3–6 months, and 6–12 months postpartum. We limited our primary longitudinal regression analyses to the 4 periods with greatest enrollment (Supplementary Tables 1 and 2), namely the following: third trimester, delivery, 1–3 months postpartum, and 3–6 months postpartum. In secondary analyses, we added available data from the second trimester and accounted for the timing of study entry whenever applicable. In this study, we use the term perinatal to refer to the third trimester up to 6 months postpartum.
Measures
Main study variables include VS (outcome), depressive symptoms (exposure), and ART adherence (mediator), all measured longitudinally. Within each observation period, most participants (81%) had their depressive symptoms and adherence measurements temporally preceding their viral load (VL) measurement date. Measurements of ART adherence and depressive symptoms were often collected on the same date, however.
Viral Suppression
Viral suppression, obtained via medical chart abstraction, was defined as having a VL less than 400 copies/mL to account for differences in laboratory cut points and maintain consistency over the study period.
Depressive Symptoms
Participants completed the AIDS Clinical Trials Group (ACTG) SF-21 Quality of Life interview [12, 13]. This 21-item questionnaire encompasses validated subscales for domains relevant to mood disorders, including mental health, cognitive functioning, and fatigue [14–16]. We selected 6 items assessing the past-month frequency of depressive symptoms (ranging from 1 = “none of the time” to 6 = “all of the time,” with a possible total score of 6 to 36, with higher scores indicating more symptoms). Selected items were consistent with Diagnostic and Statistical Manual of Mental Disorders, 5th edition (DSM-V), criteria for major depressive disorder [17] and included 2 mood items (“Have you felt down-hearted and blue?”; reverse-coded “Have you been a happy person?”); 2 items related to diminished ability to think or concentrate (“Did you have difficulty reasoning or problem solving?”; “Did you have trouble keeping your attention on any activity for long?”); and 2 items related to fatigue/loss of energy (reverse-coded “Did you have enough energy to do the things you wanted to do?”; “Did you feel tired?”). While fatigue/loss of energy are likely symptoms of pregnancy as well, prior research establishes that these symptoms remain substantial indicators of depression among pregnant women, both in the prenatal and postnatal periods [18, 19]. The 6 items formed a single-factor solution in a principal components analysis, explaining 47% of the variance with good internal consistency (Cronbach’s α = 0.78). We converted depressive symptoms scores to z scores with a mean of zero and a standard deviation (SD) of 1 to facilitate modeling and interpretation.
ART Adherence
The P1025 cohort study assessed self-reported adherence using the ACTG Adherence Questionnaire [20]. Throughout the study, however, participants most consistently completed the “last-missed-dose” component of the ACTG Adherence Questionnaire, asking when they last missed ART doses (1–2, 2–4, >4 week ago, or never). While it does not capture the multidimensional nature of adherence, the “last-missed-dose” measure uniquely and reliably captures longer-term adherence behavior [21]. We categorized those who reported not
missing a dose in the last 4 weeks or less (compared with those who skipped a dose in the last 1–4 weeks) as having consistent adherence.
**Potential Confounders**
We considered demographic, clinical, and substance-use factors as potential confounders of the associations among depressive symptoms, adherence, and VS. Demographic variables included age at enrollment, race/ethnicity (non-Hispanic Black/African American, non-Hispanic White/other races, and Hispanic/Latino), and education (high school diploma, high school diploma/GED, any college). Clinical variables included number of previous pregnancies, trimester of entry into prenatal care, whether HIV diagnosis was made before or during pregnancy, years living with HIV, and calendar year of delivery (to account for changes in relevant clinical practice guidelines, particularly with respect to ART prescription). Substance use included time-varying use since the start of pregnancy of each of the following: alcohol, tobacco, marijuana, or other controlled/illicit substances (ie, cocaine, heroin, amphetamines, methamphetamine, barbiturates, ecstasy, or prescription opioids).
**Statistical Analysis**
**Missing Data**
Supplementary Table 3 gives a complete picture of the extent of missing data in the current study sample (N = 1869). Excluded observations due to incomplete data were more likely from participants who were younger, non-Hispanic Black, started prenatal care later in pregnancy, and enrolled in the study in 2006–2009, relative to those included in the current study (Supplementary Table 4). Education and HIV/pregnancy histories were comparable across the 2 groups.
To address missing data, we performed 2 sets of analyses: (1) our primary analytical models included only complete cases [22] with fully observed data on the 3 main study variables, substance use, and confounders, and (2) in secondary analyses, we performed multiple imputation (MI) of missing data followed by similar analytical models that incorporate MI data and account for uncertainty due to imputation [23].
To impute missing data, we performed 2-fold MI using chained equations (MICE), which leverages available time-varying and non–time-varying data, providing effective imputation in longitudinal settings [24, 25], outperforming standard MICE [26, 27]. We used linear and logistic 2-fold MICE models to impute missing data, respectively, for the continuous depressive symptoms score and for binary VS, ART adherence, smoking, and alcohol consumption. Our imputation models included all study variables, including those predictive of missingness (age, race, prenatal care entry, and enrollment year dummies). We created 100 MI datasets [28, 29] to ensure stability and reproducibility of the estimates [23, 28].
**Mediation Analysis**
We performed mediation analysis to estimate the overall association (ie, total effect) of depressive symptoms on VS throughout the perinatal period and to estimate the extent to which this association is mediated by ART adherence—that is, the indirect effect of depressive symptoms on VS that is through changes in adherence. To accomplish this, we built a longitudinal mediation model composed of 2 linear mixed models: (1) an “outcome model” of VS, regressed on depressive symptoms, adherence, and confounders, and (2) a “mediator model” of adherence, regressed on depressive symptoms and confounders. Both models also included person-specific random intercepts, which account for unobserved, between-person heterogeneity, a key confounder in longitudinal data. We implemented our longitudinal mediation approach, illustrated in Figure 1, in Stata’s generalized structural equation modeling (GSEM) suite “gsem” [30, 31]. Our approach follows recent work deriving causal mediation formulas in longitudinal mixed-effects models [32–34] and produces similar results to standard causal mediation routines [35–37] (see Figure 1).
We addressed major confounding through a tiered strategy over 4 sets of adjusted mediation models. Model 1 includes the random intercepts, visit period fixed effects (indicators), and timing of study entry. Model 2 and model 3 adjust known confounders: first, demographics including age, race, and education; then, HIV and pregnancy variables such as prenatal care entry, duration of HIV infection, and year of delivery. Model 4, our preferred specification, further adjusts time-varying smoking and alcohol use, which not only may especially confound the adherence–VS association but their perinatal shifts (Supplementary Figure 1) may drive depressive symptoms as well. We did not further adjust for marijuana or illicit substance use; in preliminary analyses, this adjustment did not change the findings and caused convergence problems. Finally, we also performed these 4 mediation models in the MI data to assess how findings change upon accounting for uncertainty due to missing data.
RESULTS
Characteristics of the Study Sample
Among 1869 participants included in the current study (Table 1), 47.62% were 21–29 years old, 57.57% were non-Hispanic Black, and 38.10% had not graduated high school. Most women (67.10%) initiated prenatal care in the first trimester and had an average of 3 pregnancies prior to their index P1025 pregnancy; 76.94% were known to have HIV before pregnancy and for an average of 5.8 years. Approximately 42.75% delivered/enrolled between 2006 and 2009. Based on complete data, 15.71% reported smoking during pregnancy, 6.27% consumed alcohol, 7.19% smoked marijuana, and 3.05% used illicit substances. As seen in Supplementary Figure 1, levels of smoking and drinking declined towards delivery, but substantially spiked postpartum.
Depressive Symptoms, ART Adherence, and Viral Suppression Over Time
In the third trimester, the mean depressive symptoms score was 14.0 (±5.24); 68.12% of women adhered to their ART consistently and 77.31% of women in the sample achieved VS (Table 1). At delivery, average depressive symptoms scores slightly declined while levels of adherence and VS steadily increased. However, while depressive symptoms continued to decline postpartum, adherence and VS fell precipitously, from 69.5% and 74.4% at delivery to 59.8% and 53.0% at 6 months postpartum, respectively (Figure 2). This pattern holds throughout study years (2002–2013), notwithstanding changes in ART guidelines (Supplementary Figure 2).
| Characteristic | Statistic |
|---------------|-----------|
| Age, % | |
| 13–20 years | 11.40 |
| 21–29 years | 47.62 |
| 30–34 years | 23.22 |
| ≥35 years | 17.76 |
| Race/ethnicity, % | |
| White/other Non-Hispanic | 11.72 |
| Black non-Hispanic | 57.57 |
| Hispanic | 30.71 |
| Education, % | |
| Less than high school | 38.10 |
| High school graduate | 42.22 |
| Some college or more | 19.69 |
| Total no. of pregnancies, mean (SD) | 3.38 (2.20) |
| Duration of HIV infection | |
| Diagnosed before pregnancy, % | 76.94 |
| Diagnosed during pregnancy, % | 23.06 |
| Years since diagnosis, mean (SD) | 5.80 (5.52) |
| Trimester first received prenatal care, % | |
| First trimester | 67.10 |
| Second trimester | 29.13 |
| Third trimester | 3.77 |
| Delivery year, % | |
| 2002–2005 | 23.65 |
| 2006–2009 | 42.75 |
| 2010–2013 | 33.60 |
| Substance use since pregnancy started, % | |
| Drink alcohol at least once a month, % | 6.27 |
| Currently smoke cigarettes, % | 15.71 |
| Marijuana at least once a month, % | 7.19 |
| Any controlled/illicit substance use, % | 3.05 |
**Supplementary Table 5.** We calculated the standard errors for all estimates using nonparametric bootstrapping (500 replications). For analyses of MI data, we estimated the models with bootstrapped standard errors in each MI dataset and then combined the estimates using Rubin’s rules [29], a method shown to provide valid bootstrap inference with MI [38].
Mediation Models of Depressive Symptoms, ART Adherence, and Viral Suppression
Adjusted associations and mediation estimates from the complete-case sample are shown in Table 2. The first 2 panels show coefficients directly from the outcome and mediator.
regressions followed by mediation estimates. Overall, based on the fully adjusted specification in model 4, a 1-SD increase in the depressive symptoms score is associated with a total of 3.8-percentage-point (%pts; 95% confidence interval [CI]: −5.7, −1.9) reduction in VS (total effect). This effect is the sum of the indirect effect of depressive symptoms on suppression via ART adherence (−.4%pts; 95% CI: −.7, −.2) and the direct effect through other pathways (−3.4%pts; 95% CI: −5.2, −1.5) (Table 2, column 4). The indirect effect reflects 2 components: (1) a positive effect of ART adherence on suppression, where having consistent adherence is associated with an increase in suppression by 6.6%pts (95% CI: 2.6, 10.5), and (2) a negative effect of depressive symptoms on adherence: a 1-SD increase in depressive symptoms is associated with a reduction in the probability of consistent adherence by 6.6%pts (95% CI: −8.7, −4.4). Together, the indirect effect mediated through adherence accounts for 11.3% of the total effect of depressive symptoms on suppression (Table 2, column 4). Sequential control for confounding in models 1 through 4 results in progressive, albeit small, attenuation of the estimates, with control for HIV/pregnancy variables (model 2→model 3) and alcohol/smoking (model 3→model 4) driving most attenuation in outcome and mediator regressions, respectively (Table 2).
Secondary Analyses
In Table 3, we present the results of a secondary analysis comparing the main model 4 estimates from the complete-case sample with their counterparts estimated in the MI data. As in columns 1 and 2, the total effect of depressive symptoms was smaller (−2.7%pts vs −3.8%pts in the complete-case sample), the direct effect was smaller (−2.1%pts vs −3.4%pts), and the indirect effect was larger (−0.6%pts vs −0.4%pts), now accounting for a much larger proportion of its total effect (22.4% vs 11.3%). While the effect of depressive symptoms on adherence is identical across MI and complete-case samples (−6.6%pts), the effect of adherence on suppression is much larger (9.3%pts vs 6.6%pts). Attenuation of estimates upon confounding control in MI data followed similar patterns to those in the main analysis with complete-case data (Supplementary Table 6).
DISCUSSION
This study examines the overall impact of depressive symptoms on VS throughout the perinatal period and the extent to which this association is mediated by ART adherence among pregnant women with HIV. Prior studies examining these associations were often exploratory analyses of small cross-sectional samples, usually lacking the longitudinal perspective of how these important variables change over the perinatal period [9, 10, 39]. Gaining such understanding is important as effective interventions to improve ART adherence and VS for women with HIV in the perinatal period continue to be needed. Our longitudinal
analysis revealed 2 key findings. First, a relatively moderate increase in depressive symptoms was associated with a potentially clinically important decline in VS as well as ART adherence. Second, the decline in adherence driven by depressive symptoms accounted for at least a sizable 11% of the total negative effect of depressive symptoms on the probability of VS. These observations are consistent with existing literature. For example, Psaros et al [40] and Peltzer et al [6] found that elevated depressive symptoms were associated with significantly lower ART adherence in pregnant women with HIV living in South Africa. A review of the literature also shows a moderate effect of depressive symptoms on ART adherence and suppression among the larger population of people living with HIV [41].
Our results highlight the need for universal screening for perinatal depressive symptoms, as recommended by national guidelines [42]. However, diagnosis and treatment are often left unaddressed, with up to 85% of women being untreated for perinatal depression [43]. Pharmacological treatment is thought to be generally safe despite the lack of robust data, since pregnant women are usually excluded from clinical trials [44]. In addition, psychotherapies such as interpersonal psychotherapy and cognitive behavioral therapy have been shown to be effective in treating perinatal depression [45]. Structural barriers often limit access to these effective treatments, with lack of health insurance coverage and limited workforce capacity in mental health being significant contributors [46, 47]. Addressing barriers, in addition to creating multidisciplinary care models to deliver family-centered care for pregnant or postpartum women with HIV, shows promise in improving maternal outcomes [48].
In addition to depressive symptoms, factors at multiple levels contribute to the low rates of ART adherence and VS observed, particularly in the postpartum period when the stresses and demands of caring for a new baby are acute [49]. It is also important to note that, early in the study period, some women stopped taking their ART postpartum in accordance with treatment guidelines at the time; however, this alone does not explain the drop in VS postpartum as VS continued to decline regardless of study period. Unmeasured psychosocial and structural factors
| Table 2. Adjusted Associations and Mediation Estimates Over the Perinatal Period (Third Trimester–6 Months Postpartum) in the IMPAACT P1025 Cohort |
|---------------------------------|-----------------|-----------------|-----------------|-----------------|
| Model 1 | Model 2 | Model 3 | Model 4 (Main Model) |
| --- | --- | --- | --- |
| **Outcome model (viral suppression)** | | | |
| M: Adherence (a) | .086 (0.047, 0.125) | .079 (0.039, 0.119) | .065 (0.028, 0.103) | .066 (0.026, 0.105) |
| X: Depressive symptoms z score (b) | -0.041 (−0.059, −0.023) | -0.041 (−0.059, −0.022) | -0.035 (−0.051, −0.018) | -0.034 (−0.052, −0.015) |
| **Mediator model (adherence)** | | | |
| X: Depressive symptoms z score (c) | -0.082 (−0.104, −0.06) | -0.079 (−0.099, −0.058) | -0.074 (−0.095, −0.053) | -0.066 (−0.087, −0.044) |
| **Mediation estimates** | | | |
| Natural indirect effect (NIE = a × c) | -0.007 (−0.01, −0.004) | -0.006 (−0.009, −0.003) | -0.005 (−0.007, −0.002) | -0.004 (−0.007, −0.002) |
| Controlled direct effect (CDE = b) | -0.041 (−0.059, −0.023) | -0.041 (−0.059, −0.022) | -0.035 (−0.051, −0.018) | -0.034 (−0.052, −0.015) |
| Total effect (TE = CDE + NIE) | -0.048 (−0.056, −0.031) | -0.047 (−0.056, −0.028) | -0.039 (−0.056, −0.023) | -0.038 (−0.057, −0.019) |
| Percent mediated (NIE/TE) | 14.6% (13.3%) | 13.3% (12.3%) | 11.3% (11.3%) |
**Controls**
| Sample | CC | CC | CC | CC |
|--------------------------------|------|------|------|------|
| Person-specific random intercept| Yes | Yes | Yes | Yes |
| Visit period fixed effects | Yes | Yes | Yes | Yes |
| On/off-study status | Yes | Yes | Yes | Yes |
| Demographics | Yes | Yes | Yes | Yes |
| HIV and pregnancy variables | Yes | Yes | Yes | Yes |
| Alcohol and smoking | Yes | Yes | Yes | Yes |
**Sample**
| No. of observations | 2702 | 2702 | 2702 | 2702 |
|---------------------|------|------|------|------|
| No. of persons | 1375 | 1375 | 1375 | 1375 |
| ICC, outcome model | 46% | 44% | 39% | 39% |
| ICC, mediator model | 30% | 28% | 26% | 26% |
All estimates are in percentage-point units. Bootstrapped 95% confidence intervals (500 replications) in brackets. All P values < .01.
Abbreviations: CC, complete case; HIV, human immunodeficiency virus; ICC, intraclass correlation coefficient (residual); IMPAACT, International Maternal Pediatric Adolescent AIDS Clinical Trial Network.
associated with depression (such as stigma, intimate partner violence, housing, or food insecurity) likely play a role. Some studies have found that depressive symptoms can be higher prenatally than in the postpartum period for women with HIV [6, 50]. This can be explained by the elevated prevalence of unplanned pregnancy in that population [51] and stress of obtaining an HIV diagnosis during pregnancy (this occurred for about one-quarter of our sample).
Our study has several notable strengths, including its prospective design, use of a large multiethnic sample from a high-resource setting (addressing a key gap in the available literature), and the corroboration of our findings across modeling approaches. Although breastfeeding is not recommended for women living with HIV in the United States, our findings highlight the need for continued assessment of ART adherence and VS in the postpartum period for women who desire to breastfeed.
A few limitations deserve mention. First, P1025 lacked a validated depressive symptoms scale. While the items in our scale are consistent with DSM-V criteria and with clinically validated depressive symptom measures, its comparability is not formally established. Additionally, the dataset did not capture information on depression treatment, psychosocial and structural factors, or social support measures inside or outside of the clinic that might influence adherence and suppression prospects. Second, the cohort had large portions of missing data for key study variables. We addressed this using MI [23] and our models accounted for uncertainty due to imputation. Further, although our analyses adjusted for major confounding, residual confounding might be present. Our quantitative estimates should thus be cautiously interpreted. Third, study participants were limited to women in care in the United States; therefore, findings may not necessarily generalize to all pregnant women with HIV.
In conclusion, perinatal depressive symptoms were associated with significantly lower adherence to ART, and with lower VS. These results highlight the need to screen, diagnose, and treat perinatal depression to prevent mental and HIV-related complications that may adversely affect both mother and child.
### Supplementary Data
Supplementary materials are available at Clinical Infectious Diseases online. Consisting of data provided by the authors to benefit the reader, the posted materials are not copyedited and are the sole responsibility of the authors, so questions or comments should be addressed to the corresponding author.
### Notes
**Acknowledgments.** The authors thank the women and infants who participated in IMPAACT Protocol 1025 as well as all IMPAACT Protocol 1025 team members. Our findings were presented as an oral presentation at the International Workshop on Women and HIV, March 2017, Boston, Massachusetts.
**Disclaimer.** The content is solely the responsibility of the authors and does not necessarily represent the official views of the National Institutes of Health.
**Financial support.** This work was supported by the IMPAACT Network’s Scholar’s Program. Overall support for the International Maternal Pediatric Adolescent AIDS Clinical Trials Network (IMPAACT) was provided by the
### Table 3. Secondary Analyses of the Main Adjusted Associations and Mediation Estimates (Model 4) Over the Perinatal Period in the IMPAACT P1025 Cohort
| | Third Trimester–6 Months PP | Second Trimester–6 Months PP |
|---------------------------|-----------------------------|-----------------------------|
| | Complete Case (Main Model) | Multiple Imputation |
| M: Adherence (a) | .066 | .093 |
| | [.026, .105] | [.056, .13] |
| X: Depressive symptoms z score (b) | −.034 | −.021 |
| | [−.052, −.015] | [−.037, −.006] |
| Mediator model (adherence) | | |
| X: Depressive symptoms z score (c) | −.066 | −.066 |
| | [−.087, −.044] | [−.082, −.05] |
| Natural indirect effect (NIE = a × c) | −.004 | −.006 |
| | [−.007, −.002] | [−.009, −.003] |
| Controlled direct effect (CDE = b) | −.034 | −.021 |
| | [−.052, −.015] | [−.037, −.006] |
| Total effect (TE = CDE + NIE) | −.038 | −.027 |
| | [−.057, −.019] | [−.042, −.012] |
| Percent mediated (NIE/TE) | 11.3% | 22.4% |
| | 12.5% | 27.8% |
| Sample | | |
| No. of observations | 2702 | 7476 |
| No. of persons | 1375 | 1869 |
All estimates are in percentage-point units. Bootstrapped 95% confidence intervals (500 replications) in brackets. All P values < .01.
Abbreviations: IMPAACT, International Maternal Pediatric Adolescent AIDS Clinical Trial Network; PP, postpartum.
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Data Article
Dataset regarding the mechanical properties of roads unbound treated with synthetic fluid based on isoalkane and tall oil
Diego Maria Barbieri a,*, Baowen Lou a,b, Robert Jason Dyke c, Hao Chen a, Fusong Wang d, Billy Connor e, Inge Hoff a
a Norwegian University of Science and Technology, Department of Civil and Environmental Engineering, Høgskoleringen 7A, Trondheim, Trøndelag 7491, Norway
b Chang’an University, School of Highway, Nan Er Huan Road (Mid-section), Xi’an, Shaanxi 710064, China
*c Oslo Metropolitan University, Department of Civil Engineering and Energy Technology, Pilestredet 35, Oslo 0166 Norway
*State Key Laboratory of Silicate Materials for Architectures, Wuhan University of Technology, Luoshi road 122, Wuhan, Hubei 430070, China
d State Key Laboratory of Silicate Materials for Architectures, Wuhan University of Technology, Luoshi road 122, Wuhan, Hubei 430070, China
e College of Engineering and Mines, University of Alaska Fairbanks, Tanan Loop 1760, Fairbanks, Alaska 99709, United States
A R T I C L E I N F O
Article history:
Received 9 December 2021
Revised 20 December 2021
Accepted 21 December 2021
Available online 24 December 2021
Keywords:
Stabilized roads unbound
Isoalkane
Tall oil pitch
Repeated load triaxial test
Freeze-thaw cycles
Rolling bottle test
A B S T R A C T
The dataset revolves around the laboratory testing of an innovative additive technology for possible stabilization of unbound courses in road pavements. The product is a synthetic fluid based on isoalkane and tall oil pitch. Two test types are performed. Repeated load triaxial tests evaluate the elastic stiffness and the deformation properties of both untreated and treated aggregates. Moreover, some specimens are also tested before and after being subjected to freezing-thawing actions. A modified version of the rolling bottle test appraises the integrity with stripping loss on loose aggregates covered by the additive. Considering the necessity for road performance in cold regions, the tests were performed at different temperatures, and the results are presented in the dataset.
* Co-submitted with: Mechanical Properties of Roads Unbound Treated with Synthetic Fluid Based on Isoalkane and Tall Oil, Transportation Geotechnics
DOI of original article: 10.1016/j.trgeo.2021.100701
* Corresponding author.
E-mail addresses: [email protected] (D.M. Barbieri), [email protected], [email protected] (B. Lou), [email protected] (R.J. Dyke), [email protected] (H. Chen), [email protected] (F. Wang), [email protected] (B. Connor), [email protected] (I. Hoff).
https://doi.org/10.1016/j.dib.2021.107758
2352-3409/© 2021 The Author(s). Published by Elsevier Inc. This is an open access article under the CC BY license (http://creativecommons.org/licenses/by/4.0/)
Specifications Table
| Subject | Civil and Structural Engineering |
|---------|----------------------------------|
| Specific subject area | Stabilized roads unbound, Isoalkane, Tall oil pitch, Repeated load triaxial test, Freeze-thaw cycles, Rolling bottle test |
| Type of data | Table |
| How data were acquired | The data were collected by performing the following laboratory tests: Repeated Load Triaxial Test (RLTT) and modified version of Rolling Bottle Test (RBT). |
| Data format | Raw |
| Parameters for data collection | The two following laboratory tests were performed: Repeated Load Triaxial Tests (RLTTs) and modified version of Rolling Bottle Tests (RBTs). The stabilization effect related to a synthetic fluid based on isoalkane and tall oil pitch was evaluated. Six Linear Variable Differential Transducers (LVDTs) measured the vertical and horizontal deformations during RLTTs. The integrity with stripping loss was assessed by weighing each dried sample before and after RBTs. |
| Description of data collection | Repeated Load Triaxial Tests (RLTTs) and Rolling Bottle Tests (RBTs) were accomplished as for EN 13286-7 and EN 12697-11, respectively. 8 RLTTs samples were created and tested: 2 samples were untreated, while 6 samples were treated with different percentages of synthetic fluid and water; furthermore, 2 of these samples were also tested dried before and after being subjected to 10 Freeze-Thaw (FT) cycles. Linear Variable Differential Transducers (LVDTs) assessed the deformation of the samples inside the cyclic triaxial chamber. 84 RBT samples of loose aggregates were investigated in terms of integrity with stripping loss for fourteen rotation time intervals ranging from 1 hour to 24 hours. |
| Data source location | The research activities took place at the Department of Civil and Environmental Engineering, Norwegian University of Science and Technology (NTNU), Høgskoleringen 7A, Trondheim 7491, Norway. Aggregates came from a local quarry in Vassfjell, Heimdal, Norway. The synthetic fluid was provided by industrial producer (see Acknowledgments section). |
| Data accessibility | Dataset is uploaded on Mendeley Data |
| Repository name | Mechanical properties of roads unbound treated with synthetic fluid based on isoalkane and tall oil |
| Data identification number | DOI: 10.17632/x2s5mcwzdy.1 |
| Direct URL to data | https://data.mendeley.com/datasets/x2s5mcwzdy/1 |
| Related research article | D. M. Barbieri, B. Lou, R. J. Dyke, H. Chen, F. Wang, B. Connor, I. Hoff. Mechanical Properties of Roads Unbound Treated with Synthetic Fluid Based on Isoalkane and Tall Oil, Transportation Geotechnics. https://doi.org/10.1016/j.trgeo.2021.100701. |
Value of the Data
- Considering the high global amount of unbound layers belonging to road infrastructures that need maintenance and rehabilitation, the dataset characterizes an innovative synthetic fluid technology based on isoalkane and tall oil pitch for road stabilization.
- The dataset can be beneficial to all the road stakeholders (engineers, researchers, entrepreneurs, agencies, ...) that are interested in exploring the potential of new innovative technologies for road stabilization.
- The behaviour of aggregates for road construction stabilized with an innovative synthetic fluid technology according to different application percentages can be appraised. Moreover, it is possible to analyse the data according to several regression models.
1. Data Description
The dataset is created during a laboratory testing campaign focusing on a Synthetic Fluid (SF) technology based on isoalkane and tall oil pitch for road stabilization [1]. The application of SF product on road aggregates represents an innovative approach to road maintenance and rehabilitation [2–4]. The investigation encompasses two kinds of test, namely Repeated Load Triaxial Test (RLTT) and a modified version of the Rolling Bottle Test (RBT), and the dataset comprises raw data and photos of the samples (https://data.mendeley.com/datasets/x2s5mcwzdy/1). The experimental campaign encompasses both untreated (Unbound Granular Material, UGM) and treated aggregates.
1.1. Repeated Load Triaxial Test
The folder “Data of Repeated Load Triaxial Test” contains the data derived from Repeated Load Triaxial Tests (RLTTs) and is organized in 6 subfolders corresponding to as many testing conditions as detailed in Table 1, which reports on the SF amount and water content. For each specified condition two parallel samples (indicated as “01” and “02”) were tested and the following information are reported for each specimen: one spreadsheet with raw data (.xlsx) and two pictures (.jpg).
The structure according to which all the spreadsheets are arranged has the same logic [5]. As a RLTT comprises five loading sequences, five sheets contain the corresponding experimental data and are named as “Sequence 1”, “Sequence 2”, “Sequence 3”, “Sequence 4”, “Sequence 5”; in turn, every loading sequence comprises six loading steps, which are indicated in column A. Columns B, C, D and E collect information regarding time t, temperature T, deviatoric pulse number and frequency f, respectively. Columns F and G specify the values of the dynamic part (σ_{d,dyn}) and the static part (σ_{d,stat}) of the deviatoric stress σ_d they are subject to. Similarly, columns H and I contain information regarding of the dynamic part (σ_{t,dyn}) and the static part (σ_{t,stat}) of the triaxial stress σ_t. The deformations of each sample are appraised by means of
| Numbering | Subfolder name | SF (% mass) | water (% mass) |
|-----------|-----------------------|-------------|----------------|
| 01 | UGM | 0 | 0 |
| 02 | SF-1 low percentage | 1.5 | 1 |
| 02 | SF-2 medium percentage| 2.5 | 1 |
| 02 | SF-3 high percentage | 4.5 | 1 |
| 03 | after FT | 1.5 | 0 |
| 03 | before FT | 1.5 | 0 |
Table 1 Subfolders names and corresponding testing conditions for RLTT.
six Linear Variable Displacement Transformers (LVDTs), which measure the axial elastic components ($\varepsilon_{a,el,01}$, $\varepsilon_{a,el,02}$, $\varepsilon_{a,el,03}$ in columns J, L, N), axial plastic components ($\varepsilon_{a,pl,01}$, $\varepsilon_{a,pl,02}$, $\varepsilon_{a,pl,03}$ in columns K, M, O), radial elastic components ($\varepsilon_{r,el,01}$, $\varepsilon_{r,el,02}$, $\varepsilon_{r,el,03}$ in columns P, R, T) and radial plastic components ($\varepsilon_{r,pl,01}$, $\varepsilon_{r,pl,02}$, $\varepsilon_{r,pl,03}$ in columns Q, S, U).
Resilient modulus $M_R$ (defined in the next section) and the resistance against permanent deformation are the two main mechanical parameters that can be assessed by means of RLTTs. By way of example, the trend values of $M_R$ and axial plastic deformation for sample 01 treated according to SF-1 percentage (“Spec. SF-1 01”) are reported in Figs. 1a and 1b, respectively, as a function of load cycles number $N$. The five RLTT loading sequences correspond to as many colours in Fig. 1. Similar representations can be made for all the other RLTTs samples; furthermore, the data trend can be further analysed according to the several regression models available in literature [6,7].
1.2. Modified Version of Rolling Bottle Test
The folder “Data of modified version of Rolling Bottle Test” contains the file “Weight of RBT specimens.xlsx” and the folder “RBT sample pictures”. The former item specifies the weight of all the 84 RBT samples for three important conditions: dried with no SF, dried after SF application and dried after RBTs performed according to fourteen rotation time intervals (1 h, 2 h, 3 h, 4 h, 5 h, 6 h, 8 h, 10 h, 12 h, 14h, 16 h, 20 h and 24 h, reported in columns B, M). 42 samples are coated by the synthetic fluid (3% in mass) and 42 samples are not. Based on the measured weights, it is possible to quantify the parameter mass loss $ML_{RBT}$ as defined in the next section. Each rotation time comprises the test of three parallel samples, the pictures of which are sequentially named from “m1” to “m42”. These photos represent a supplemental visual information to observe the integrity with stripping loss and are available in .jpg format inside the folder “RBT sample pictures”, which is arranged in four subfolders “01 UGM after”, “01 UGM before”, “02 SF after”, “02 SF before”.
2. Experimental Design, Materials and Methods
The rock aggregates come from a local quarry located in Vassfjell, Heimdal, Norway, while the SF road stabilization technology is obtained from an industrial producer [2–4]. The research campaign took place at the Department of Civil and Environmental Engineering (Norwegian University of Science and Technology, Trondheim, Norway). The motivation of the investigation is connected with the global need to improve the maintenance and rehabilitation of road pavements [8,9]; this is particularly relevant when it comes to ensuring efficient construction and stabilization of road unbound layers [10,11].
Following the specifications of CEN standard “13286-7 Cyclic load triaxial test for unbound mixtures”, each RLTT was accomplished according to the Multi-Stage Low Stress Level (MS LSL) and comprised thirty loading sequences [12], where each of them corresponded to a combination of triaxial stress $\sigma_t$ and deviatoric stress $\sigma_d$ as reported in Fig. 2. The latter one is applied according to a sinusoidal path with 10 000 pulses. For a constant value of $\sigma_t$ and a dynamic
deviatoric stress $\Delta \sigma_{d,\text{dyn}}$, the resilient modulus $M_R$ is
$$M_R = \frac{\Delta \sigma_{d,\text{dyn}}}{\varepsilon_{a,\text{el}}}.$$ \hspace{1cm} (1)
with $\varepsilon_{a,\text{el}}$ the average axial resilient strain evaluated by the three axial LVDTs.
The RBT aims at estimating the adhesion between the bitumen covering loose aggregates and the aggregates themselves after exposure to mechanical stirring actions at room temperature [13]. According to the CEN standard “12697-11 Determination of the affinity between aggregate and bitumen”, the evaluation is performed visually, thus leading to possible unprecise outcomes. In light of this, a modified version of RBT was performed pivoting on the dry weight of the aggregates measured before ($M_1$) and after ($M_2$) testing. Furthermore, the standard RBT was generalized in this research as SF instead of bitumen was selected in the testing campaign and fourteen time intervals of rotations were considered (1 h, 2 h, 3 h, 4 h, 5 h, 6 h, 8 h, 10 h, 12 h, 14 h, 16 h, 20 h and 24 h) instead of the two ones (6 h and 24 h) defined by the code. The mass loss $ML_{\text{RBT}}$ is
$$ML_{\text{RBT}} = \frac{M_1 - M_2}{M_1},$$ \hspace{1cm} (2)
and can be expressed as a percentage.
**CRediT Author Statement**
**Diego Maria Barbieri**: Conceptualization, Methodology, Software, Validation, Formal analysis, Investigation, Resources, Data curation, Writing – original draft, Visualization, Project administration; **Baowen Lou**: Conceptualization, Methodology, Software, Validation, Formal analysis, Investigation, Resources, Data curation, Writing – Original Draft; **Robert Jason Dyke**: Conceptualization, Methodology, Formal analysis, Investigation, Resources, Data curation, Writing – Review & Editing; **Hao Chen**: Investigation, Resources, Writing, Review & Editing, Visualization; **Fusong Wang**: Writing – Review & Editing, Visualization; **Billy Connor**: Methodology, Writing – Review & Editing, Visualization, Supervision; **Inge Hoff**: Conceptualization, Methodology, Writing – Review & Editing, Visualization, Supervision, Project administration, Funding acquisition
**Declaration of Competing Interest**
This work was supported by Norwegian Public Roads Administration (VegDim project, grant number 605377) and by Research Council of Norway (HERMES project, grant number 299538).
**Acknowledgments**
This work was supported by Norwegian Public Roads Administration (VegDim project, Grant number 605377) and by Research Council of Norway (HERMES project, Grant number 299538). The support kindly provided by the laboratory assistants Bent Lervik, Jan Erik Molde, Lisbeth Johansen, Frank Stæhli and Tage Westrum is greatly acknowledged. Aggregates kindly provided by Franzefoss Pukkverk avd. Vassjell, Heimdal, Norway. Synthetic fluid (SECUR 35) kindly supplied by Midwest, Canton, USA. The above information regarding the additive trade name and its supplier are reported for informational purposes. The findings and opinions reported are those of the authors and not necessarily those of the supplier.
References
[1] D.M. Barbieri, B. Lou, R.J. Dyke, H. Chen, F. Wang, B. Connor, I. Hoff, Mechanical properties of roads unbound treated with synthetic fluid based on isoalkane and tall oil, Transp. Geotech. 32 (2022) https://doi.org/https://doi.org/, doi:10.1016/j.trgeo.2021.100701.
[2] G.B. Lunsford, J.P. Mahoney, Dust control on low volume roads. A review of techniques and chemicals used. Seattle, 2001. transs.
[3] D. White, P. Vennapusa, Low-cost rural surface alternatives literature review and recommendations, Ames, 2013.
[4] D. Jones, A. Kociolek, R. Surdahl, P. Bolander, B. Drewes, M. Duran, L. Fay, G. Huntington, D. James, C. Milne, M. Nahra, A. Scott, B. Vitale, B. Williams, Unpaved dust road management. A successful practitioner ’s handbook, Denver, 2013.
[5] D.M. Barbieri, J.-G. Dorval, B. Lou, H. Chen, B. Shu, F. Wang, I. Hoff, Dataset regarding the mechanical characterization of sedimentary rocks derived from Svalbard for possible use in local road constructions, Data Br. 34 (2021) 106735, doi:10.1016/j.dib.2021.106735.
[6] F. Lekarp, U. Isacsson, A. Dawson, State of the art. II: permanent strain response of unbound aggregates, J. Transp. Eng. 126 (2000) 76–83, doi:10.1061/ASCE0733-947X(2000)126:1(76).
[7] F. Lekarp, U. Isacsson, A. Dawson, State of the art. I: resilient response of unbound aggregates, J. Transp. Eng. 126 (2000) 66–75 https://doi.org/https://doi.org/, doi:10.1061/ASCE0733-947X(2000)126:1(66).
[8] A. Faiz, The promise of rural roads: Review of the role of low-volume roads in rural connectivity, poverty reduction, crisis management, and livability, 2012. https://doi.org/10.17226/22711.
[9] J.R. Meijer, M.A.J. Huijbregts, K.C.G.J. Schotten, A.M. Schipper, Global patterns of current and future road infrastructure, Environ. Res. Lett. 13 (2018), doi:10.1088/1748-9326/aabd42.
[10] D.M. Barbieri, I. Hoff, H. Mork, Laboratory investigation on unbound materials used in a highway with premature damage, 10th International Conference of the Bearing Capacity of Roads, Railways and Airfields, 2017.
[11] D.M. Barbieri, I. Hoff, M.B.E. Mørk, Mechanical assessment of crushed rocks derived from tunnelling operations, in: W.-C. Cheng, J. Yang, J. Wang (Eds.), 5th GeoChina International Conference 2018, Springer, 2019, pp. 225–241, doi:10.1007/978-3-319-95783-8_19. https://doi.org/https://doi.org/.
[12] CEN, ISO 13286-7 cyclic load triaxial test for unbound mixtures, Belgium, 2004.
[13] CEN, ISO 12697-11 determination of the affinity between aggregate and bitumen, 2020.
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Radiofrequency catheter ablation of premature ventricular contractions from the mitral annulus in patients without structural heart disease
Yoshibumi Antoku MD\textsuperscript{1,2} | Masao Takemoto MD, PhD\textsuperscript{1,2} \(\oplus\) | Atsushi Tanaka MD, PhD\textsuperscript{3,2} | Takahiro Mito MD, PhD\textsuperscript{5,2} | Akihiro Masumoto MD, PhD\textsuperscript{4} | Takafumi Ueno MD, PhD\textsuperscript{4} | Takuya Tsuchihashi MD, PhD\textsuperscript{1}
\textsuperscript{1} Cardiovascular Center, Steel Memorial Yawata Hospital, Kitakyusyu, Japan
\textsuperscript{2} Cardiology, Munakata Suikokai General Hospital, Fukuotsu, Japan
\textsuperscript{3} Saiseikai Fukuoka General Hospital, Fukuoka, Japan
\textsuperscript{4} Cardiology, Fukuoka Kinen Hospital, Fukuoka, Japan
\textsuperscript{5} Cardiology, Hakujyuji Hospital, Fukuoka, Japan
Correspondence
Masao Takemoto, MD, PhD, Cardiovascular Center, Steel Memorial Yawata Hospital, 1-1-1 Haruno-machi, Yahatahigashi-ku, Kitakyushu 805-8508, Japan.
Email: [email protected]
Authors Antoku, Tanaka, and Mito contributed equally to this paper.
Abstract
Introduction: We previously reported the clinical benefits of radiofrequency catheter ablation (RFCA) of premature ventricular contractions (PVCs) from the right ventricular outflow tract or near the His-bundle, which can often deteriorate the clinical status. PVCs from the mitral valve (MA-PVCs) also often deteriorate the patients’ clinical status. This study aimed to evaluate the effect of ablating MA-PVCs with RFCA from a trans-interatrial septal approach on the clinical status in symptomatic patients with frequent MA-PVCs without structural heart disease.
Methods: The frequency of PVCs per the total heart beats by 24-hours Holter monitoring and New York Heart Association (NYHA) functional class in 22 patients with MA-PVCs were evaluated before and 6 months after RFCA.
Results: Procedural success was achieved in 20 (91%) of 22 patients. Of the 22 patients, in 15 (68%) and 1 (5%) patient, a successful RFCA on the left ventricular side of the MA using the trans-interatrial septal approach and trans-coronary sinus approach was achieved. Interestingly, in four (18%) patients, a successful RFCA on the left atrial (LA) side of the MA using a trans-interatrial septal approach was achieved. Ablating MA-PVCs readily improved the NYHA functional class compared to that before. A \(\geq 0.62\) peak deflection index and \(\leq 30\) years old may be one of the important predictors of successfully ablated MA-PVCs from the LA side of the MA.
Conclusions: RFCA produces clinical benefits in patients with MA-PVCs. Further, it may be necessary to initially consider a trans-interatrial septal approach to ablate these PVCs.
Keywords
catheter ablation, clinical characteristics, clinical status, mitral annulus, premature ventricular contraction, trans-interatrial septal approach
1 INTRODUCTION
Isolated premature ventricular contractions (PVCs) are the most common arrhythmias observed in daily clinical practice even in patients without structural heart disease. Many patients with frequent PVCs not only often experience disabling symptoms, and sometimes, need long-term antiarrhythmic medication, but also they can cause left ventricular (LV) dysfunction and increase the incidence of heart failure and mortality. In recent years, radiofrequency catheter ablation (RFCA) has proven to be a safe and successful therapy for arrhythmias including PVCs. Moreover, we previously and recently reported the clinical benefit of RFCA of PVCs from the right ventricular outflow tract (RVOT-PVCs), which are one of the most common types of PVCs, and from near the His-bundle, which are a comparably uncommon type of PVC. In particular, eliminating frequent RVOT-PVCs by RFCA could steadily improve the clinical status. Although PVCs from near the mitral annulus (MA) (MA-PVCs) are also comparably uncommon, they also often cause a deterioration of the patients’ clinical status. Thus, the purpose of this study was to evaluate the effect of abating MA-PVCs with RFCA from a trans-interatrial septal approach on the clinical status of symptomatic patients with frequent MA-PVCs without structural heart disease.
2 MATERIAL AND METHODS
2.1 Study population and laboratory analysis
This study was approved by the institutional review committee and ethics review board of our hospitals. From 2014 to 2019, 22 consecutive intolerably symptomatic patients with drug (including beta-blockers, calcium-channel blockers, and class I agents of the Vaughan Williams classification) refractory MA-PVCs visited our hospitals to undergo RFCA. All patients had their history recorded, and underwent a physical examination, laboratory analysis, 12-lead electrocardiography (12-ECG), 24-hours Holter monitoring, and echocardiography, on admission or within at least 1 month before admission. All the echocardiography values were recorded during sinus rhythm, but not during PVC beats, nor post-PVC beats. The New York Heart Association (NYHA) functional class using a specific activity scale was evaluated on admission and 6-months after the RFCA. All patients also underwent exercise stress testing, cardiac catheterization with coronary angiography, and / or ²⁰¹thallium scintigraphy. Those examinations yielded no evidence of clinically overt structural heart disease, including coronary artery disease, valvular heart disease, congenital heart disease, LV hypertrophy, or right ventricular abnormalities in all patients.
2.2 Definition of MA-PVC
MA-PVCs were defined as having a characteristic electrocardiographic appearance of a right bundle branch block morphology in V1 and positive concordant R waves in the precordial leads including V1-6 (Figure 1A). Ventricular tachycardia (VT) was defined with standard electrocardiographic criteria including at least three consecutive PVCs at a rate of >120 beats per minute. Patients with VT and atrial tachyarrhythmias including atrial fibrillation, atrial flutter, atrial tachycardia, and paroxysmal supra-VT were excluded from this study because they may deteriorate the NYHA functional status. The patients who received hemodialysis during this study were also excluded from this study.
2.3 Mapping and catheter ablation procedure
All procedures were performed after written informed consent was obtained. Anti-arrhythmic drugs were withdrawn in all patients at least five half-lives before the procedure. The antihypertensive and antihypercholesterolemic agents and/or others were continued in patients with hypertension and dyslipidemia before and after the RFCA. The antidiabetic agents in patients with diabetes mellitus were continued before and after the RFCA but not on the procedural day. The QRS duration and peak deflection index (PDI) were measured before the RFCA. RFCA was performed under local anesthesia. After a 50 unit per kilogram administration of heparin was administered, 4- or 5-mm-tip electrode catheters (St. Jude Medical, St. Paul, MN, USA) were introduced percutaneously into the right ventricle and coronary sinus, respectively. A 100 unit per kilogram administration of heparin was administered following the trans-interatrial septal puncture guided by the intracardiac echocardiography (ViewFlex Xtra ICE catheter, Abbott, Plymouth, MN, USA) that was the most helpful tool to visualize the exact location of the tip of the ablation catheter with regard to the MA. Then, the heparinized saline was additionally infused to maintain the activated clotting time at 300 to 350 seconds. After left atrio- and ventriculography (Figure 2A), electroanatomical mapping during the PVCs was performed in the coronary sinus and around the MA, left atrium (LA), and LV near the MA in detail utilizing a 3D mapping system (EnSite NavX ™ Cardiac Mapping System, St. Jude Medical, St. Paul, MN) by a circular mapping catheter (Inquiry™ AFocuss™ Double Loop Catheter, St. Jude Medical) or high-density mapping catheter (Advisor™ HD Grid catheter, Abbott) during culprit PVCs. If the culprit PVC was not found during the procedure, an isoproterenol administration and/or programmed electrical stimulation with a digital stimulator (Cardiac Stimulator, Nihon Kohden Co., Tokyo, Japan) was performed to induce the culprit PVC. Then, an open irrigated 3.5-mm-tip ablation catheter (FlexAbility™, St. Jude Medical) through a steerable introducer (Agilis™ NxT, Abbott) was positioned at the MA. An optimal pace map was defined as a match of all 12 surface leads by comparing the R/S ratio and subtle notching in the QRS complex during pacing. An identical match was necessary in at least 11 of 12 leads. Further, based on the findings of the electroanatomical mapping and an optimal pace map, radiofrequency energy was delivered at the site of the unipolar potentials from the ablation catheter demonstrating a QS pattern and bipolar potentials from the tip of the ablation catheter preceding the QRS in the 12-ECG by at least 20-30 milliseconds during the PVC with a preset temperature of 43 to 50°C and power limit of 30-35 W. Further, when the radiofrequency energy was delivered from the coronary sinus, in order to avoid any complications, (a) heparinized saline was additionally infused to maintain the
activated clotting time at more than 300 seconds; (b) before the RFCA, left coronary angiography was performed to confirm that the ablation site was far enough away from the coronary arteries, (c) a maximum power setting of 20 W for the radiofrequency energy was chosen, and (d) careful attention to and observation of the patient was paid during the radiofrequency energy delivery as we previously reported. The radiofrequency energy application was terminated when an abnormal impedance rise (>30 Ω) was observed. A successful ablation was defined as no recurrence and non-inducibility of the culprit PVC with and without an isoproterenol administration and/or programmed electrical stimulation for at least 30 minutes after the ablation. Procedural success was defined as no recurrence of the culprit PVC within 24 hours after the procedure under electrocardiographic monitoring. If the recurrence of the culprit PVC was observed, a repeat RFCA was considered.
2.4 Statistical analysis
The numerical results are expressed in the text as the mean ± standard deviation. Paired data were compared by a Fisher’s exact test and Student’s t-test or Wilcoxon signed-rank test. The sensitivity and specificity of the PDI and age at the time the successful ablation was performed at a site on the LA side of the MA were evaluated by a receiver-operating characteristic (ROC) curve analysis. All analyses were performed with SAS version 9.2 software (SAS Institute, Cary, NC). A P of <.05 was considered to indicate statistical significance.
3 RESULTS
3.1 Clinical characteristics of the patients with MA-PVCs on admission
The baseline characteristics of all 22 patients (14 males and 8 females with a mean age of 61 ± 19 years, body mass index [BMI] of 25.3 ± 4.9 kg/m², and serum creatinine of 0.95 ± 0.78 mg/dl) are shown in Tables 1 and 2. The prevalence of an inferior axis of the PVC, coexistence of hypertension, dyslipidemia, diabetes mellitus, and ex- or current smoking was 95%, 50%, 27%, 18%, and 45%, respectively. All patients had MA-PVCs-associated symptoms including palpitations (95%), general fatigue (45%), chest discomfort/pain (32%), and fainting (14%). Although the LV ejection fraction (EF) (LVEF) by echocardiogram was preserved at 66 ± 11%, the NYHA functional class using a specific activity scale mildly deteriorated to 2.00 ± 0.62. Sixteen out of 22
FIGURE 1 Continued
FIGURE 2 The left atrio- and ventriculography (A) and the approach sites of the radiofrequency catheter ablation on the ventricular side of the mitral annulus (MA) from the supramitral valve (B), inframitral valve (C), and left atrial side of the MA (D) from the trans-interatrial septal approach, from the trans-coronary sinus approach (E), and from the trans-aortic approach (F). The LA, LV, MV, ABL, CS, and His-RV indicate the left atrium, left ventricle, mitral valve, ablation catheter, coronary sinus, and His-bundle and right ventricle, respectively. The upper and middle and lower panels were the right (RAO) and left anterior oblique (LAO) view of the LA and LV, respectively. The red, blue, and water blue bar indicate the ablation catheter and the electrodes placed on the CS and His-RV, respectively.
### TABLE 1 Clinical characteristics in patients with PVCs from the mitral annulus on admission
| | All (n = 22) | Successful (n = 20) | LA-G (n = 4) | P value; LV versus LA | CS-G (n = 1) | Unsuccessful (n = 2) |
|--------------------------|-------------|--------------------|-------------|----------------------|-------------|---------------------|
| **Male** | | | | | | |
| Age (years) | 61 ± 19 | 68 ± 12 | 36 ± 21 | .001 | 43 | 68 |
| **Body mass index (kg/m²)** | 25.3 ± 4.9 | 25.1 ± 4.6 | 24.3 ± 1.5 | .737 | 38.4 | 22.7 |
| **Serum creatinine (mg/dL)** | 0.95 ± 0.78 | 1.06 ± 0.94 | 0.68 ± 0.12 | .441 | 0.79 | 0.80 |
| **Electrocardiography:** Axis of PVC | | | | | | |
| Inferior axis | 21 (95%) | 14 (93%) | 4 (100%) | .948 | 1 (100%) | 2 (100%) |
| Superior axis | 1 (5%) | 1 (7%) | 0 (0%) | .948 | 0 (0%) | 0 (0%) |
| **Co-existence** | | | | | | |
| Hypertension | 11 (50%) | 8 (53%) | 1 (25%) | .341 | 1 (100%) | 1 (50%) |
| Dyslipidemia | 6 (27%) | 4 (27%) | 1 (25%) | .950 | 0 (0%) | 1 (50%) |
| Diabetes mellitus | 4 (18%) | 3 (20%) | 0 (0%) | .357 | 1 (100%) | 0 (0%) |
| Ex or current smoking | 10 (45%) | 7 (47%) | 1 (25%) | .464 | 1 (100%) | 1 (50%) |
| **Symptoms** | | | | | | |
| Palpitations | 21 (95%) | 14 (93%) | 4 (100%) | .620 | 1 (100%) | 2 (100%) |
| General fatigue | 10 (45%) | 7 (47%) | 1 (25%) | .464 | 1 (100%) | 1 (50%) |
| Chest discomfort/pain | 7 (32%) | 6 (40%) | 0 (0%) | .141 | 0 (0%) | 1 (50%) |
| Fainting | 3 (14%) | 2 (13%) | 0 (0%) | .468 | 0 (0%) | 1 (50%) |
| **Medications** | | | | | | |
| Beta blockers | 12 (55%) | 8 (53%) | 2 (50%) | .912 | 1 (100%) | 1 (50%) |
| Calcium channel blockers | 4 (18%) | 1 (7%) | 2 (50%) | .036 | 0 (0%) | 1 (50%) |
| class I agents | 5 (23%) | 3 (20%) | 1 (25%) | .839 | 0 (0%) | 1 (50%) |
| No medication | 6 (27%) | 4 (27%) | 1 (25%) | .950 | 0 (0%) | 1 (50%) |
**Abbreviations:** CS-G, group with an approach from the coronary sinus; LA-G, group with an approach from left atrial side of the mitral annulus; LV-G, group with an approach from the left ventricular side of the mitral annulus; PVC, premature ventricular contraction.
patients took medications including beta-blockers (55%), calcium channel blockers (18%), and/or class I agents of the Vaughan Williams classification (23%). No patients were on amiodarone, sotalol, or bepridil. Although those agents were not sufficiently effective in eliminating the PVC-associated symptoms before the RFCA, all of the patients with a successful procedure reported the absence of any PVC-associated symptoms and could discontinue the antiarrhythmic agents after the RFCA.
#### 3.2 Analysis of the 24-hours Holter monitoring, NYHA functional status, and echocardiogram
Table 2 summarizes the analysis of the 24-hour Holter monitoring, NYHA functional status, and echocardiogram. The frequency of the PVCs (%PVC) was calculated as: [number of PVC / number of total heart beats per 24 hours] × 100. The mean %PVC of the 22 patients in this study was 20.1 ± 8.6%. In both 20 and 2 patients who achieved successful and unsuccessful procedures, respectively, the number of total heart beats did not statistically differ before and after the RFCA. In 20 patients in whom procedural success was achieved, the RFCA significantly reduced the number of total PVCs and %PVCs with no evidence of a recurrence of the culprit PVC. There was no statistical difference in the frequency of premature atrial contractions before and after the RFCA between the three groups (data not shown). The NYHA functional status significantly improved in 20 patients who achieved procedural success, but not in two patients who did not achieve procedural success. There were no statistical differences in the LVEF and LV thickness of the interventricular septum and posterior wall on echocardiogram between that before and after RFCA.
#### 3.3 Electrophysiological findings and approach sites with a successful RFCA
Table 3 summarizes the results of the electrophysiological findings and successful ablation sites. An RFCA procedure for MA-PVCs was performed in 22 patients. Procedural success was achieved in 20 (91%) of 22 patients. No patients suffered from any procedure-related complications. During the follow-up, recurrence of the culprit MA-PVCs was observed in one patient (5%) whose successful ablation site was the ventricular side of the MA from the inframitral valve. This patient underwent a repeat RFCA with a successful result. The mean QRS...
duration and PDI of the PVCs in all 22 patients were 144 ± 28 ms and 0.60 ± 0.07, respectively. The frequency of the use of a circular mapping catheter (Inquiry™ AFocusII™ Double Loop Catheter, St. Jude Medical) and high-density mapping catheter (Advisor™ HD Grid catheter, Abbott) was 23% and 77%, respectively. The approach sites of the MA-PVCs for the RFCA are demonstrated in Figures 2B-F. Of the 22 patients, in 13 (59%), 2 (9%), and 1 (5%) patient, a successful RFCA on the ventricular side of the MA from the suprami-
tral valve (Figure 2B) and inframitral valve (Figure 2C) using the trans-interaltrial septal approach and trans-coronary sinus approach (Figure 2E) was achieved. Interestingly, in 4 (18%) patients, a successful RFCA on the LA side of the MA using a trans-interaltrial septal approach was achieved (Figure 2D). A successful RFCA of the MA-PVCs could be achieved in 20 patients with these steps. The notable point was that, of the 20 patients with a successful RFCA, in 19 (95%) patients, a successful RFCA using a trans-interaltrial septal approach could be achieved. However, in the remaining two patients, successful results could not be achieved even though additional RFCA using the trans-aortic approach was performed (Figure 2F).
Figures 1B-G demonstrate the EnSite™ 3D-mapping images of the earliest activation sites during the culprit PVCs (Figures 1B and 1E), intra-cardiac electrocardiograms (Figures 1C and 1F), and 12-ECGs of the pace map (Figures 1D and 1G) at the successful ablation sites. The EnSite™ 3D-mapping images demonstrated that the earliest activation sites during the culprit PVCs were confirmed in the white area on the LV (Figure 1B) and LA (Figure 1E) side of the MA. The yellow tags were the successful ablation sites. The findings from the unipolar potentials recorded by the ablation catheter demonstrated a QS pattern, bipolar potentials were recorded by the tip of the ablation catheter that preceded the QRS on the 12-ECG by 32 ms (Figure 1C) during the culprit PVC, and a suboptimal pace map during pace mapping at 9.9 V (Figure 1D) was obtained by the ablation catheter placed at the successful ablation site on the ventricular side of the MA using a suprami-
tral valve approach (Figure 3B). In 14 out of 15 patients (93%) who were successfully ablated from the LV side of the MA, the atrial potential were not confirmed by the tip of the ablation catheter. On the other hand, the findings from the unipolar potentials recorded by the ablation catheter demonstrated a QS pattern and bipolar potentials
### TABLE 2 Twenty four hours Holter monitoring, NYHA functional class, and serum BNP concentration, in patients with PVCs from the mitral annulus before and after RFCA
| | All (n = 22) | Successful (n = 20) | Unsuccessful (n = 2) |
|----------------------|-------------|--------------------|---------------------|
| **Before RFCA** | | | |
| 24-hours Holter monitoring | | | |
| Total heart beats (beats per day) | 107,654 ± 12,600 | 110,958 ± 12,650 | 97,888 ± 45,46 | .062 | 113,317 | 99,572 |
| Total PVC (beats per day) | 22,002 ± 10,806 | 23,628 ± 11,172 | 15,472 ± 33,28 | .175 | 39,661 | 14,040 |
| %PVC (%) | 20.1 ± 8.6 | 21.0 ± 8.9 | 15.9 ± 3.7 | .282 | 35.0 | 13.9 |
| **Functional status**| | | |
| NYHA functional class | 2.00 ± 0.62 | 1.93 ± 0.59 | 2.00 ± 0.82 | .855 | 3.00 | 2.00 |
| **Echocardiogram** | | | |
| LVEF (%) | 66 ± 11 | 67 ± 12 | 72 ± 2 | .384 | 65 | 50 |
| Inter-ventricular septum (mm) | 9.2 ± 1.0 | 9.4 ± 1.0 | 8.8 ± 0.5 | .259 | 10 | 8.5 |
| Posterior wall (mm) | 9.1 ± 0.9 | 9.2 ± 0.7 | 8.5 ± 1.0 | .115 | 10 | 8.5 |
| **After RFCA** | | | |
| 24-hours Holter monitoring | | | |
| Total heart beats (beats per day) | 105,628 ± 10,608 | 108,382 ± 10,891 | 99,020 ± 8,828 | .133 | 109,096 | 96,459 |
| Total PVC (beats per day) | 1300 ± 40,53 | 99 ± 126 | 63 ± 55 | .592 | 93 | 13,394 |
| %PVC (%) | 1.3 ± 4.2 | 0.09 ± 0.11 | 0.06 ± 0.06 | .676 | 0.09 | 13.9 |
| **Functional status**| | | |
| NYHA functional class | 1.09 ± 0.29 | 1.00 ± 0.00 | 1.00 ± 0.00 | .855 | 1.00 | 2.00 |
| **Echocardiogram** | | | |
| LVEF (%) | 68 ± 8 | 69 ± 7 | 73 ± 3 | .384 | 63 | 50 |
| Interventricular septum (mm) | 9.2 ± 1.0 | 9.2 ± 0.7 | 9.0 ± 0.0 | .539 | 10 | 8.5 |
| Posterior wall (mm) | 9.1 ± 0.9 | 9.4 ± 0.5 | 8.8 ± 0.5 | .259 | 10 | 8.5 |
Abbreviations: CS-G, group with an approach from the coronary sinus; LA-G, group with an approach from the left atrial side of the mitral annulus; LVEF, left ventricular ejection fraction; LV-G, group with an approach from the left ventricular side of the mitral annulus; NYHA, New York Heart Association; PVC, premature ventricular contraction; RFCA, radiofrequency catheter ablation.
*P < .05 versus before RFCA.
TABLE 3 Comparison of the electrophysiological findings, successful ablation site, successful rate, complications, and recurrence rate in patients with PVCs from the mitral annulus
| Electroantigraphy findings of PVCs | All (n = 22) | Successful (n = 20) | LV-G (n = 15) | LA-G (n = 4) | P value; LV versus LA | CS-G (n = 1) | Unsuccessful (n = 2) |
|---------------------------------|-------------|---------------------|--------------|-------------|-----------------------|-------------|---------------------|
| QRS duration (ms) | 144 ± 28 | 140 ± 29 | 150 ± 20 | .564 | 155 | 166 | 0.53 |
| Peak deflection index | 0.60 ± 0.07 | 0.58 ± 0.06 | 0.67 ± 0.05 | .016 | 0.53 | 0.63 | |
| Mapping catheter for the PVCs | | | | | | | |
| Circular mapping catheter | 5 (23%) | 4 (27%) | 0 (0%) | .270 | 1 (100%) | 0 (0%) | |
| High-density mapping catheter | 17 (77%) | 11 (73%) | 4 (100%) | .270 | 0 (0%) | 2 (100%) | |
Successful ablation site
Trans-interatrial septal approach
| Ventricular side of MA from supramitral valve | 13 (59%) | 13 (87%) | - | - | - | - |
| Ventricular side of MA from inframitral valve | 2 (9%) | 2 (13%) | - | - | - | - |
| Left atrial side of MA | 4 (18%) | - | 4 (100%) | - | - | - |
| Trans-coronary sinus approach | 1 (5%) | - | - | - | 1 (100%) | - |
| Trans-aortic approach | 0 (0%) | - | - | - | - | - |
| Successful rate | 20 (91%) | - | - | - | - | - |
| Recurrence rate for the first session | 1 (5%) | 1 (7%) | 0 (0%) | .620 | 0 (0%) | - |
| Recurrence rate for the second session | 0 (0%) | 0 (0%) | - | - | - | - |
| Complications | 0 (0%) | 0 (0%) | 0 (0%) | 1.00 | 0 (0%) | - |
Abbreviations: CS-G, group with an approach from the coronary sinus; LA-G, group with an approach from the left atrial side of the mitral annulus; LV-G, group with an approach from the left ventricular side of the mitral annulus; MA, mitral annulus; PVC, premature ventricular contraction.
recorded by the tip of the ablation catheter that proceeded the QRS on the 12-ECG by 48 ms (Figure 1F) during the culprit PVC obtained by the ablation catheter placed at the successful ablation site on the LA side of the MA (Figure 1E). Of course, in all four patients, the atrial potentials were confirmed by the tip of the ablation catheter, and pace mapping at varying outputs from 1.0 to 9.9 V on the LA side of the MA (Figure 1E) captured the LA but not the LV (Figure 1G). After radiofrequency energy was delivered at those points, the PVCs were steadily terminated. Figure 3 summarizes the earliest activation sites of the MA-PVCs that were successful (red, blue, green, and purple circles; n = 20) or unsuccessful (black circle; n = 2) RFCA sites in the left anterior oblique view of the MA. They were crowded in the direction from 0:00 to 3:00 in the left anterior oblique view of the MA. The red, blue, green, and purple circles indicate successful ablation sites on the ventricular side of the MA from the supramitral valve (Figure 2B), inframitral valve (Figure 2C), and LA side of the MA (Figure 2D) from the trans-interatrial septal approach and trans-coronary sinus approach (Figure 2E), respectively.
3.4 Comparison of successful ablation sites between the LV side and LA side of the MA
There were 15 and 4 patients whose successful ablation sites were on the LV side (LV group) and LA side (LA group) of the MA, respectively. Tables 1–3 summarize the clinical characteristics (Table 1), results of the analysis of the 24-hours Holter monitoring, clinical status, echocardiograms (Table 2), and electrophysiological findings (Table 3) of the two groups. The BMI and serum creatinine levels, prevalence of a male gender, inferior axis of the PVCs, coexistence of hypertension, dyslipidemia, and diabetes mellitus; ex- or current smoking; symptoms including palpitations, general fatigue, chest discomfort/pain, and fainting; and the results of the analysis of the 24-hours Holter monitoring, clinical status, echocardiogram results, and QRS duration of the PVCs did not statistically differ between the two groups. However, the mean age (36 ± 21 versus 68 ± 12 years; P = .001) and PDI (0.67 ± 0.05 versus 0.58 ± 0.06; P = .016) in the LA group were significantly younger and larger than that in the LV group. The ROC curve analysis of the PDI and age at the time of the successful ablation at a site on the LA side of the MA in patients with MA-PVCs is shown in Figure 4. Their specificity and sensitivity were 0.800 and 1.000 at a PDI of 0.62 and 1.000 and 0.750 for an age of 30 years old, respectively. The areas under the curve (AUC) were 0.908 and 0.925, respectively. Thus, a PDI ≥ 0.62 and age ≤ 30 years old may be one of the important predictors of a successful ablation of MA-PVCs from the LA side of the MA.
3.5 Outcome of patients with an unsuccessful RFCA
In 2 of the 22 patients, unfortunately, the procedure was unsuccessful during this study. One patient received a repeat RFCA with an unsuccessful result. The other did not want to receive a repeat RFCA. Thus, medical therapies were continued in those two patients. The
Thus, RFCA 12 years; DISCUSSION (Figure = 2E Clinical benefits of RFCA of MA-PVCs 21 versus 68 2D = The PDI 2D B and P .001) Clinical and electrophysiological factors including the %PVC, NYHA functional class, and LVEF obtained by echocardiography, in the two patients with an unsuccessful RFCA, still deteriorated further during the follow-up (Table 2).
4 | DISCUSSION
4.1 | Clinical and electrophysiological characteristics in patients with MA-PVCs
It has been reported that a PDI > 0.6 indicates that the origin of the PVC exists deep within the ventricle or at an epicardial site.5 The PDI in the LA group was significantly larger than that in the LV group (0.67 ± 0.05 versus 0.58 ± 0.06; P = .016) (Table 3). The ROC curve analysis of the PDI of a successful ablation site on the LA side of the MA in patients with MA-PVCs demonstrated that the specificity and sensitivity were 0.800 and 1.000 at a PDI of 0.62 (Figure 4A). Thus, the origins of MA-PVCs in the LA group may possibly be located deep within the MA, and it was hard to ablate it from the LV side of the MA. As shown in Figures 1E and 2D, if the origins of the MA-PVCs exist near the LA side of the MA, those MA-PVCs were able to be ablated from the LA side of the MA even though they existed deep within the MA or on the epicardial side of the LV. The mean age in the LA group was significantly younger than that in the LV group (36 ± 21 versus 68 ± 12 years; P = .001) (Table 1). There were no statistical differences in the LV wall thickness (Table 2). Unfortunately, the reason(s) why the younger patients (≤30 years old) were successfully ablated on the LA side of the MA was not completely elucidated in this study. Thus, when ablating MA-PVCs in those patients with a younger age (≤30 years old) (Figure 4B) and larger PDI (≥0.62) (Figure 4A), it may be necessary to consider ablating from the LA side of the MA.
4.2 | Clinical benefits of RFCA of MA-PVCs
The NYHA functional status significantly improved in 20 patients in whom procedural success without any adverse effects was achieved (Table 2), and RFCA is known to be safe and effective for the treatment of arrhythmias as compared to medical therapy.1,2 Thus, RFCA may be considered as the first choice of therapy in intolerable symptomatic patients with frequent MA-PVCs.
4.3 | RFCA of MA-PVCs
A recent report demonstrated that in 18 of 21 patients (86%), a successful ablation could be achieved in those with MA-PVCs/VT.7 Procedural success in this study was achieved in 20 (91%) of the 22 patients, which was slightly higher than that of the previous report.7 To achieve a high procedural successful rate, we tried and paid attention to the three points described below. (a) First, to gain strong support and contact force of the ablation catheter, the trans-interatrial septal approach was initially performed and a steerable introducer (Agilis™ NxT, Abbott) was routinely used. Actually, of those 20 patients with a successful procedure, in 19 (95%), a successful RFCA of the MA-PVCs could be achieved with a trans-interatrial septal approach on the ventricular side of the MA from the supramitral valve (59%) (Figure 2B) and inframitral valve (9%) (Figure 2C) and on the LA side of the MA (18%) (Figure 2D) (Table 3). Interestingly, in four patients (18%), a successful RFCA was achieved on the LA side of the MA using the trans-interatrial septal approach (Figure 2D). Thus, operators should try to ablate MA-PVCs on the LA side of the MA (Figure 2D), when those PVCs cannot be ablated on the ventricular side of the MA (Figures 2B and 2C). It may be hard for the ablation catheter to reach the LA using the trans-aortic approach (Figure 2E). Moreover, in the remaining two patients (9%) with an unsuccessful procedure, successful results could not be achieved even though a trans-aortic approach was additionally performed8 (Figure 2F). The trans-aortic approach was not considered to be able to gain stronger support and contact force than the trans-interatrial septal approach. Further, the remaining one patient (5%) underwent a successful procedure that could be achieved from a coronary sinus approach5,8 (Figure 2E). It may be a gentle treatment for patients to ablate MA-PVCs with only a right-sided (venous) approach without an aortic puncture. Thus, a right-sided approach including a trans-interatrial septal and coronary sinus approach may be considered as the first choice of therapy in intolerable symptomatic patients with frequent MA-PVCs. However, in the remaining two patients, a trans-aortic approach was additionally performed8 (Figure 2F).
the direction of the wave front propagation. On the other hand, the operators should take extreme care to avoid ensnaring the catheter in the mitral apparatus when using a circular mapping catheter near the mitral valve. Thus, the high-density mapping catheters may be much more useful and safer than the circular mapping catheters. In this study, we used high-density mapping catheters instead of circular mapping catheters since the high-density mapping catheters were commercially available in Japan. (c) Third, to obtain a stable lesion creation, an open irrigated 3.5-mm-tip ablation catheter (FlexAbility™, St. Jude Medical) was routinely used. However, unfortunately, in two patients (5%), successful results could not be achieved even though RFCA using an open irrigated ablation catheter from the various approach sites described in Figures 2B-F was performed. The recent advancements in the new technologies, including contact force catheters, which can facilitated a more stable lesion creation, were not used in this study, and they might have improved and helped during the RFCA procedure in those unsuccessful patients.
4.4 Distribution of the earliest activation sites of the MA-PVCs
The earliest activation sites of the MA-PVCs were crowded in the direction from 0:00 to 3:00 in the left anterior oblique view of the MA (Figure 3) where the left atrial appendage was attached. Although there has been a case report supporting a possible association between ventricular arrhythmias and the LA appendage, the detailed mechanism(s) of MA-PVCs still remains unidentified.
4.5 Treatment of patients with an unsuccessful RFCA
In 2 out of the 22 patients, the procedure was unsuccessful during this study. All of the parameters including the %PVC, NYHA functional class, and LVEF obtained by echocardiography, in the two patients with an unsuccessful RFCA, still deteriorated further during the follow-up (Table 2). Thus, intensive treatment of heart failure including the administration of renin-angiotensin system inhibitors and diuretics was started after the unsuccessful RFCA, resulting in a comparative improvement in the patient symptoms. The class I agents were discontinued because of the adverse effects of the long-term antiarrhythmic medications associated with those agents such as an increased mortality, probably due to their proarrhythmic effects, even though the occurrence of the PVCs was markedly suppressed.
4.6 Limitations of the study
Although our study was a multicenter trial, it was limited by a retrospective design and relatively small number of patients because MA-PVCs are comparatively rare arrhythmias. The patients in this study were also limited by having a high frequency of %PVCs (mean %PVC = 20.1 ± 8.6%) and disabling symptoms. Thus, the effect of the RFCA of the MA-PVCs in patients with a low frequency of %PVCs and/or asymptomatic patients was unfortunately unknown in this study. Moreover, our study could not clarify the long-term clinical benefit of RFCA of MA-PVCs. Thus, whether our results can safely be
extrapolated to the inclusion of a larger number of patients, whether the use of contact force catheters, and whether a longer follow-up period in these patients is needed should be determined in further studies.
5 | CONCLUSIONS
RFCA could steadily improve the clinical status in patients with MA-PVCs. Initially performing a trans-interatrial septal approach and using a steerable introducer to gain a stronger support and contact force of the ablation catheter, performing detailed electroanatomical mapping using by a circular mapping catheter or high-density mapping catheter to detect more precise earliest activation sites of the target MA-PVCs, and using open irrigated ablation catheters to obtain a stable lesion creation, may be important procedures to achieve a high success rate of the RFCA of MA-PVCs. Interestingly, a successful RFCA was achieved for the MA-PVCs from not only the LV side of the MA (Figures 2B and 2C) or coronary sinus (Figure 2E) but also from the LA side of the MA (Figure 2D) whose characteristics were a younger age (≤30 years old) and larger PDI (≥0.62). Thus, it may be necessary to understand the cardiac anatomy and try to ablate those PVCs from various approach sites, especially using a trans-interatrial septal approach initially may be helpful. Because these PVCs are often drug refractory, RFCA may be considered as the first choice of therapy in those patients.
ACKNOWLEDGMENTS
We thank Mrs. Kensuke Kawasaki, Tomomi Hatae, Ryo Okada, Tsutomu Yoshinaga, Shu Takata, Kazutaka Yamaguchi, and Takejiro Masumoto for their technical assistance with the electrophysiological study in the cardiac catheterization laboratory, and Mr. John Martin for his linguistic assistance with this paper.
AUTHOR CONTRIBUTIONS
All doctors were in charge of the patients in this study. Drs. Y. Antoku and M. Takemoto wrote this manuscript. Drs. Y. Antoku, M. Takemoto, A. Tanaka, A. Masumoto, and T. Mito performed the radiofrequency catheter ablation of the patients in this study. Dr. T. Moto performed the data analysis.
FUNDING SOURCES
None.
CONFLICT OF INTEREST
The authors report no relationships that could be construed as a conflict of interest.
ORCID
Masao Takemoto MD, PhD https://orcid.org/0000-0002-6047-9653
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How to cite this article: Antoku Y, Takemoto M, Tanaka A, et al. Radiofrequency catheter ablation of premature ventricular contractions from the mitral annulus in patients without structural heart disease. Pacing Clin Electrophysiol. 2020;43:1258-1267. https://doi.org/10.1111/pace.14063
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Performance Improvement of Dimmable OFDM-Visible Light Communication using Subcarrier Index Modulation and Reed Solomon Encoding
Nima Taherkhani\textsuperscript{a}, Kamran Kiasaleh\textsuperscript{*}
\textit{Abstract}—In this paper, we propose a new subcarrier index modulation scheme for orthogonal frequency division multiplexing (OFDM), which incorporates the Reed-Solomon (RS) encoding in a visible light communication (VLC) system. In this scheme, the incoming bits are first encoded using the RS encoder, then a set of symbols in the resulting RS codeword are punctured, and the remaining symbols are modulated and mapped onto the OFDM subcarriers. This system is referred to as RS-OFDM-IM. Unlike the traditional subcarrier index modulation (SIM) schemes, the proposed scheme operates based on conveying extra information by inactivating the selected subcarriers, which facilitates simultaneous clipping noise reduction and spectral efficiency enhancement in OFDM-VLC. The bit error rate (BER) and throughput of the proposed technique is theoretically and numerically analyzed. The simulation results show the superiority of the proposed technique as compared to the coded DCO-OFDM without SIM and the classical SIM in OFDM-VLC in a system with practical clipping conditions.
\textit{Index Terms}—Clipping noise, OFDM-VLC, Reed Solomon code, subcarrier index modulation.
I. INTRODUCTION
Demand for high data rates is increasing and the next-generation wireless networks, such as 5G, are predicted to offer high data transmission capacity for new applications. Millions of
Internets of Things (IoT) devices and seamless streaming of high-quality videos are predicted to demand a capacity per unit area of 100Mbps for the future indoor spaces [1]. VLC systems can be developed using the available illumination infrastructure inside buildings and can provide a robust data link for short-range applications. VLC can be operated for simultaneous medium illumination and data communication. Further, unlike RF systems, VLC systems do not require a circuitry chain for up/down RF conversion since they work based on direct intensity modulation/detection for data transmission. Orthogonal frequency division multiplexing (OFDM) technique, which is adopted in many recent telecommunication standards, including Long Term Evolution (LTE) and IEEE 802.11x [2], can also be integrated with VLC to overcome the limitation of light-emitting diode (LED) modulation bandwidth and to mitigate the channel dispersion effect in order to increase VLC sum-rate. VLC systems integrated with OFDM and using III-nitride laser diodes have been shown to achieve multi-Gigabit data rates [3, 4]. In OFDM-VLC, the output of the multiplexer needs to be real and positive since the intensity of LED is modulated. Different solutions have been considered to deal with the challenges that are facing OFDM-based VLC, which can be generally categorized into two classes; (1) a DC biased Optical-OFDM (DCO-OFDM) [5], and (2) asymmetrically clipped optical-OFDM (ACO-OFDM) [6]. In ACO-OFDM, information bits are only mapped onto the odd subcarriers and the time-domain signal is clipped at zero to generate a unipolar signal, while in DCO-OFDM, all subcarriers are employed to carry data and then time-domain signal is clipped and biased to generate a non-negative signal. As an alternative to these two dominating schemes, the Unipolar OFDM (U-OFDM) scheme has been proposed in [7], in which the negative and positive samples from the real bipolar OFDM symbol are extracted and transmitted separately by two successive OFDM symbols.
Recently, the concept of subcarrier index modulation (SIM) in OFDM has been proposed,
where indices of subcarriers in OFDM are employed to carry extra information bits. In [8-13], it is shown that SIM changes the spectral efficiency, peak-to-average power ratio (PAPR), bit error rate (BER), power efficiency, and throughput of OFDM system. In this technique, instead of modulating the entire OFDM frame, only a set of subcarriers are chosen to be modulated by M-ary symbols. In addition to these symbols, the combination of the subcarrier indices of the activated subcarriers also carries implicit information. In [8], one index bit is allocated to each subcarrier, and then those subcarriers associated with the subset of the majority bit-value are activated to be mapped by M-ary symbols. In [9], the frequency diversity order and the performance of OFDM with Index Modulation (OFDM-IM) in frequency selective fading channels are investigated. In [10]-[11], the throughput of OFDM-IM is improved by sending symbols of a different constellation on the selected remaining subcarriers, while in dual-mode (DM) OFDM-IM [10], selected and remaining subcarriers are modulated using two different M-ary constellations. In multiple-mode (MM) OFDM-IM multiple distinguishable modes and their permutations are used for symbol modulation [11]. A full review of the different SIM techniques in OFDM can be found in [14].
SIM has been recently extended to VLC to convey extra information bits in a more energy-efficient way. In [15], the system structure of an OFDM-based VLC integrated with SIM is proposed and its BER performance is presented. A hybrid-dimming scheme for both adjusting the illumination level and optimizing the indoor optical channel capacity in SIM-aided VLC is proposed in [16].
Although the energy per active subcarriers is improved by existing SIM in an OFDM with fixed transmission power, the clipping distortion caused by increasing the number of active subcarriers can raise the clipping events and subsequently limit the maximum throughput achievable by these
techniques in OFDM-VLC. Hence, the original SIM developed for RF OFDM are not suitable for OFDM-VLC with clipping constraint. Also, majority of the original SIM were originally developed for the uncoded systems and do not fully benefit from the flexibility that can be provided by a channel code. The application of RS codes for improving the reliability of both fiber and VLC is shown and analyzed via numerical and experimental analyses in [17]-[19]. Considering the new dimension introduced by the block code, a new SIM technique that can benefit from this feature must be considered.
Unlike the traditional SIM, which operates based on the activation of selected subcarriers, in RS-OFDM-IM, the SIM attempts to convey implicit information on the indices of a sets of available subcarriers. The process is equivalent to modulating a punctured codeword onto the OFDM frame where the puncturing is conducted by the index modulation in the proposed technique. Since the information is embedded on the nulled subcarriers, the proposed SIM allows a simultaneous data rate increase and clipping noise mitigation in OFDM-VLC.
In [21], the preliminary BER performance of a novel scheme was compared to the uncoded DCO-OFDM with the same bit rate. It was shown that this approach can substantially improve the error floor in OFDM-based VLC systems with clipping constraint. In this work, we extend our preliminary idea and theoretically analyze and explore the potential of the proposed technique in a VLC system with illumination requirements. The contribution of this paper is two-fold.
- A new subcarrier index modulation scheme based on RS encoding is proposed and compared with the traditional subcarrier index modulation employed in a coded OFDM-based VLC and with the DCO-OFDM with RS channel coding. An analytical expression for the lower bound of BER at the output of RS decoder as a function of the effective electrical signal-to-noise and distortion ratio (SNDR) in optical OFDM is derived, and the achievable throughput of the new
scheme in OFDM-based VLC under practical clipping conditions and in the presence of Gaussian noise is presented.
- A strategy based on the new scheme is proposed to adjust the dimming level of the OFDM-based VLC. Using the flexibility of RS-OFDM-IM, one can achieve the desire illumination level in the intensity domain while the target SE is maintained. This strategy determines the optimal parameters of RS block code in the transmitter such that the dimming level can be adjusted according to the varying illumination requirement without reducing the bit rate of the system.
The main rationale behind pursuing the proposed approach is to benefit from the new dimension created by the linear block code. Namely, redundancy in the linear block code is used simultaneously for both nonlinear noise mitigation and spectral efficiency. Integration of SIM and RS error-correcting code allows for an effective way of noise mitigation and provides a means to compensate for the bit rate loss caused by the block code.
II. RS EnCoded OFDM-VLC System Model
The technique introduced in this work can be integrated into DCO-OFDM as well as ACO-OFDM VLC systems. However, without the loss of generality, we adopt DCO-OFDM to model the RS-OFDM-IM in this section. The block diagram of RS-OFDM-IM is depicted in Fig. 1. In a DCO-OFDM transmitter with \( N_T \) (even) subcarriers, \( N_f = \frac{N_T}{2} \) subcarriers are available for individual symbol mapping due to the Hermitian symmetry (HS) requirement. To reduce the computation complexity that can be caused by SIM, \( N_f \) subcarriers are divided into \( G \) sub-blocks, where each sub-block is allocated \( N = \frac{N_f}{G} \) subcarriers (\( G \) is selected such that \( N \) remains an integer). The information bits are first distributed between sub-blocks and
then converted into a non-binary codeword using the Reed Solomon code block, where the length of codewords is determined by the maximum number of subcarriers allocated in each sub-block. The incoming $p_t$ bits in each sub-block are split into two sets; $p_1$ bits are sent to the index selector to be conveyed by SIM while $p_2$ bits are transmitted via $M$-ary constellation points.
Considering an RS code over the Galois field $GF(2^m)$ with code length $N = 2^m - 1$, the non-binary message vector of size $K$ which carries $p_2 = Km$ information bits is encoded to generate a codeword with $N$ RS symbols. The RS encoder can be represented by $RS (N, K, d = N - K + 1)$, with the code rate $r_c = \frac{K}{N}$. The encoder uses the message vector in its generator polynomial to generate codewords with a minimum distance of $d = N - K + 1$. As an erasure code, the RS decoder can detect and correct combinations of $\xi$ errors and $S$ erasures, if $2\xi + S \leq d - 1$. Given the linear block code $\mathcal{B} \in \mathcal{M}^N$, a set with $|\mathcal{B}|$ number of $N$-tuples over the alphabet $\mathcal{M} = \{0,1, ..., M - 1\}$ with hamming distance $d$ can generate $M^K$ distinct codewords which will be used in the scheme shown in Fig. 1 for the modulation of OFDM sub-blocks. Let $\phi = \{\omega_g\}_{g = \ldots}$.
1, ...G; \omega_g \in \mathcal{B}\} be the set of codewords used for the OFDM frame mapping, where \omega_g is the codeword allocated to the sub-block g. The index selector uses \(p_1 = \lfloor \log_2 \left( \frac{N}{S} \right) \rfloor\) bits to select the puncturing vector \(\theta_g = a_i\) from a predefined set \(\mathcal{A} = \{a_1, a_1, ..., a_{2p_1}\}\), where the elements of \(a_i\) determine the symbol indices in the codeword that will be punctured, and their corresponding subcarriers will be set to inactive. Considering the puncturing vector of the \(g^{th}\) sub-block given by
\[ \theta_g = \{\theta_{g,1}, ..., \theta_{g,S}\} \]
where \(\theta_{g,s} \in \{1, ..., N\}\), and after nulling subcarriers in \(\Theta_g\), the remaining subcarriers in the sub-block will be modulated using the intact part of the codeword. Now, the symbol vector \(\Omega_g \in \mathbb{C}^{N \times 1}\) can be expressed as
\[ X_g = [X_1^g, ..., X_N^g] \]
where \(X_i^g = 0\) when \(i \in \Theta_g\), and for \(i \notin \Theta_g\), \(X_i^g = U_m \in \{M - QAM\}\). After the formation of symbol vectors for every sub-block and applying HS, the frequency-domain OFDM block is created by concatenating the symbol vectors of all \(G\) sub-blocks. Upon applying the HS, the OFDM frame with total \(N_T\) subcarriers in the frequency-domain is represented by
\[ X = \left[ 0, X_1^1, ..., X_N^1, X_1^G, ..., X_N^G, 0, X_1^{G^*}, ..., X_N^{G^*}, X_1^{1^*}, ..., X_N^{1^*} \right] \]
where \(X_i^{l^*}\) indicates the complex conjugate of symbol \(X_i^l\). The extended frequency-domain block is then converted to the time-domain OFDM symbols by \(N_T\)-points Inverse Fast Fourier Transform (IFFT) operator given by (for ease of notation, \(X_k\) is used to denote the \(k^{th}\) symbol in the frequency-domain block)
\[ x_n = \frac{1}{\sqrt{N_T}} \sum_{k=1}^{N_T} X_k e^{\frac{2\pi j n k}{N_T}} \]
For large IFFT points, i.e., \(N_T > 64\), the output is known to be Gaussian distributed with zero
mean and standard deviation $\sigma_x$, i.e., $x_n \sim N(0, \sigma_x^2)$.
To make $x_n$, $1 \leq n \leq N_T$ transmittable in an LED with by $\Lambda = [I_L, I_H]$ dynamic range, bipolar time-domain signal is converted to a unipolar signal. This can be represented by
$$x_{n,t} = x_{n,c} + l_{bias};$$
$$x_{n,c} = \text{clip}(x_n) = \begin{cases} u_{lower} & x_n \leq u_{lower} \\ x_n & u_{lower} < x_n < u_{upper} \\ u_{upper} & x_n \geq u_{upper} \end{cases}$$
with $u_{lower} = (I_L - l_{bias})$ and $u_{upper} = (I_H - l_{bias})$, denoting the lower bound and upper bound, respectively, which are set relative to the standard deviation of $x_n$ by constant coefficients $\lambda_1$ and $\lambda_2$ [22], i.e. $u_{upper} = \lambda_1 \sigma_x$, $u_{lower} = \lambda_2 \sigma_x$. The probability of clipping at both ends of LED’s are calculated by $P_l = 1 - Q(\lambda_2)$ and $P_u = Q(\lambda_1)$, respectively, where $Q(a) = \frac{1}{\sqrt{2\pi}} \int_a^{\infty} \exp \left(-\frac{b^2}{2}\right) db$. The clipped signal is usually modeled using Bussgang theorem as [22]
$$x_{n,c} = \beta x_n + z_n$$
where $\beta$ is the attenuation factor given by $\beta = \frac{E[x_{n,c}x_n]}{E[x_n^2]}$ and $z_n$ is the clipping noise, which is assumed to be uncorrelated with the signal $x_n$. Using (5)-(7), the statistics of truncated Gaussian signal and clipping noise can be calculated by
$$\sigma_{x_c}^2 = \sigma_x^2 \left[ Q(\lambda_2) - Q(\lambda_1) + \phi(\lambda_2) \lambda_2 - \phi(\lambda_1) \lambda_1 + (1 - Q(\lambda_2)) \lambda_2^2 + Q(\lambda_1) \lambda_1^2 \right] - E[x_{n,c}]^2,$$
$$E[x_{n,c}] = \sigma_x \left[ \phi(\lambda_2) - \phi(\lambda_1) + (1 - Q(\lambda_2)) \lambda_2 + \lambda_1 Q(\lambda_1) \right],$$
$$\sigma_z^2 = \sigma_{x_c}^2 - \beta^2 \sigma_x^2$$
where $\phi(a) = \frac{1}{\sqrt{2\pi}} \exp \left(-\frac{a^2}{2}\right)$, and $\sigma_{x_c}^2$ is the variance of the truncated Gaussian signal. After adding the cyclic prefix to the OFDM symbols, the signal is transmitted over the linear time-invariant baseband VLC channel. The received signal using direct-detection is give
$$y_n = (\beta x_n + z_n + l_{bias}) \ast h_n + w_n$$
where $h_n$ denotes channel impulse response, $w_n \sim \mathcal{N}(0, \sigma_w^2)$ is a Gaussian noise, and $\ast$ denotes the convolution operation. The received frequency-domain symbols are given by
$$Y_k = \beta H_k X_k + H_k Z_k + W_k, \quad 1 \leq k \leq \frac{N_T}{2}$$ \hspace{1cm} (10)$$
where $Z_k$ and $H_k$ are clipping noise and the channel overall gain at $k$-th subcarrier, respectively. The receiver splits the frequency-domain symbols into $G$ sub-blocks, and detect the indices of nulled subcarriers and estimate the puncturing vectors to decode $p_1$ information bits. Also, by demodulating the symbols of the active subcarrier in each sub-block, its codeword is recovered and sent to the RS decoder for decoding of $p_2$ information bits that are transmitted by active subcarriers. Two detection algorithms, i.e., Maximum Likelihood (ML) and Log-Likelihood Ratio (LLR), can be used for null indices detection. However, due to the fairly large number of subcarriers and the $M$-ary modulation, the LLR detection with lower complexity is a more suitable candidate. Therefore, the LLR is employed in Fig. 1. The LLR detector calculates the ratio of a posteriori probabilities of the complex symbols in the frequency-domain based on the fact that the inactive subcarrier is null, while active subcarriers are modulated by M-QAM constellation points.
For subcarrier $k$ in the $g^{th}$ sub-block, this ratio is given by
$$\alpha_g(k) = \ln \frac{\sum_{m=1}^{M} P(X_k^g = U_m | Y_k^g)}{P(X_k^g = 0 | Y_k^g)}$$ \hspace{1cm} (11)$$
where $Y_k^g = Y_{N(g-1)+k}$ is the received signal on the $k^{th}$ subcarrier of the $g^{th}$ sub-block. Using Bayesian rule, (13) can be simplified to
$$\alpha_g(k) = \ln S - \ln (N - S) + \frac{|Y_k^g|^2}{\sigma_w^2} + \ln \left( \sum_{m=1}^{M} \exp \left( -\frac{1}{\sigma_w^2} |Y_k^g - H_k^g U_m|^2 \right) \right)$$ \hspace{1cm} (12)$$
The simplification in (12) is based on the following relations: $P(X_k^g = 0) = \frac{S}{N}$ and $\sum_{m=1}^{M} P(X_k^g = U_m) = \frac{N-S}{N}$. The LLR detector searches through all subcarriers and for each sub-
block it finds indices of \( S \) subcarriers with the lowest LLR values. Given the sorted LLR values as \( \alpha_g(q_1) > \alpha_g(q_2) > \ldots > \alpha_g(q_N) \), the puncturing vector is then estimate as
\[
\hat{\theta}_g = \{q_{N-S+1}, q_{N-S+2}, \ldots, q_N\} \quad \theta_G
\]
(13)
The index de-mapper uses the transmitter-receiver common look-up table to decode \( b_1 \) bits used in the transmitter for index selection and informs the decoder about the indices of the codeword erasure. The decoder performs the error-correction decoding using the remaining code redundancy. Finally, the recovered bits from index de-mapper and RS decoder collected from all \( G \) sub-blocks are concatenated to form the output information vector in the receiver.
III. SIM IN RS ENCODED OFDM-VLC
In this section, first, a strategy based on RS-OFDM-IM is proposed to improve BER when the dimming level of LED changes for illumination purposes.
A. Dimming level control strategy
Considering the RS encoded modulation, the size of symbols can be reduced such that the resulted signal in the time-domain experiences fewer clipping events. However, the coding rate and the number of punctured symbols in codewords should be determined such that the system’s target SE can be achieved.
A strategy based on the flexibility of coding parameters can be developed to reduce the clipping noise when the VLC dimming level alters. This strategy aims at controlling the probability of clipping by choosing the right values for the message length and number of punctured symbol that can achieve a target SE and also lead to a smaller magnitude in the envelope of the time-domain signal. Considering an LED with dynamic range \( \Lambda = [I_L, I_H] \), the dimming level is calculated as
\[
\eta = \frac{l_m - l_L}{I_H - I_L} \quad (0 \leq \eta \leq 1),
\]
where \( l_m \) is the average intensity of the LED. Rewriting the upper and
lower clipping bounds as $I_H - I_{bias} = \lambda_1 \sigma_x$ and $I_L - I_{bias} = \lambda_2 \sigma_x$, respectively, $I_m$ is given by
$$I_m = E\{x_{k,t}\} = \sigma_x [\lambda_1 Q(\lambda_1) + \lambda_2 Q(-\lambda_2) + \phi(\lambda_2) - \phi(\lambda_1)] + I_{bias} \quad (14)$$
where $E\{ \}$ is the ensemble average of the enclosed, and $\phi(u) = \frac{1}{\sqrt{2\pi}} e^{-u^2/2}$. Assuming the power normalized symbols on active OFDM subcarriers, the standard deviation of the time-domain signal, after inactivating $S$ subcarriers in each sub-blocks according to (4) is now given by
$$\sigma_x^* = \sqrt{\frac{N_T - 2GS - 2}{N_T}} \sigma_x \quad (15)$$
It can be seen that by nulling a set of subcarriers using SIM, the time-domain envelope of IFFT multiplexer is controlled. In a VLC system with fixed modulation bandwidth and $N_T$ total subcarriers and $G$ independent sub-blocks, the SE of RS-OFDM-IM with message length $K$ and assuming $M$-QAM employment is
$$SE_{RSO}(M, K, S) = \frac{G}{N_T} (K \log_2 M + \lfloor \log_2 C(N, S) \rfloor) \quad \text{(bit/s/Hz)} \quad (16)$$
where $C(a, b) = \frac{a!}{b!(a-b)!}$ denotes the binomial coefficient. It should be noted that the size of the RS code alphabet should not be greater than the number of points in the $M$-ary constellation used for symbol modulation, i.e., $N \leq M$.
In a VLC system with fixed bandwidth and subcarriers, RS-OFDM-IM can achieve a SE similar to DCO-OFDM with shorter message length and smaller code rate. Assume a DCO-OFDM modulation, with $RS (N, K', d = N - K' + 1)$ encoder, the SE of DCO-OFDM is given by
$$SE_{DCO}(M, K') = \frac{G}{N_T} K' \log_2 M \quad .$$
The set of parameters that can achieve the equal or greater SE in RS-OFDM-IM is represented by
$$\{(K_p, S_p)\} = \{(K, S) \mid SE_{RSO}(M, K, S) \geq SE_{DCO}(M, K')\} \quad (17)$$
Given that any 2-tuple in the set $\{(K_p, S_p)\}$ will satisfy the required data rate, the larger value
of $S_p$ will lead to greater $\lambda_1$ and $\lambda_2$ values. Stretching of clipping boundaries by increasing the number of punctured symbols in each sub-block’s codeword will reduce the probability of clipping and will keep the large signal in the intensity domain intact. This impact will become more pronounced in a VLC system with a highly varying illumination level. For quantitative analysis, we consider an OFDM-based VLC with $N_t=1024$ subcarriers and a LED with the dynamic range given by $\Lambda = [0,5]$. Information in this system is encoded over $GF(2^5)$ to generate codewords of length 31, and then are modulated by 32-QAM and then mapped over subcarriers in $G = 16$ sub-blocks. Table 1 shows the code parameters for two schemes and their corresponding clipping bounds at different dimming levels.
Table 1: Clipping bounds in RS-OFDM-IM and DCO-OFDM in VLC with $\Lambda = [0,5]$ physical constraint.
| RS-OFDM-IM | $(k,s)$ | upper-lower bounds | $\eta$: 0.1 | $\eta$: 0.3 | $\eta$: 0.5 | $\eta$: 0.7 | $\eta$: 0.9 |
|-------------|---------|--------------------|-------------|-------------|-------------|-------------|-------------|
| (20,3) | $\lambda_2$ | -0.95 | -1.75 | -2.67 | -3.58 | -4.39 | |
| | $\lambda_1$ | 4.39 | 3.58 | 2.67 | 1.75 | 0.95 | |
| (19,5) | $\lambda_2$ | -0.96 | -1.80 | -2.77 | -3.74 | -4.6 | |
| | $\lambda_1$ | 4.6 | 3.74 | 2.77 | 1.80 | 0.96 | |
| (18,7) | $\lambda_2$ | -0.99 | -1.86 | -2.88 | -3.91 | -4.79 | |
| | $\lambda_1$ | 4.79 | 3.91 | 2.88 | 1.86 | 0.99 | |
| DCO-OFDM | (22) | $\lambda_2$ | -0.93 | -1.6 | -2.54 | -3.3 | -4.15 |
| | $\lambda_1$ | 4.15 | 3.3 | 2.54 | 1.6 | 0.93 | |
Fig. 2. Clipping noise power in RS-OFDM-IM vs. RS Encoded DCO-OFDM.
Fig. 3. average SNDR comparison in dimmable OFDM-VLC at SNR = 30 dB.
A SE close to the target SE can be achieved by all different block code parameters that are shown in the table. However, as the number of null subcarriers increases in sub-blocks, the time-domain OFDM signal will experience a less severe clipping noise. Fig. 2 shows the reduction in clipping noise power for different puncturing numbers. Fig. 3 shows the level of change in the average Signal to Noise and Distortion Ratio (SNDR) of time-domain signal, calculated by
$$\text{SNDR} = \frac{\beta^2 \sigma_x^2}{\sigma_z^2 + \sigma_{AWGN}^2}$$
when the received signal has a SNR of 30 dB. Fig.2 and Fig.3 prove the improvement in the conditioning of the transmitted signal in RS-OFDM-IM compared to DCO-OFDM with a similar SE.
Considering an indoor medium with both line-of-sight and non-line-of-sight transmission path, the impact of channel in (10) can be compensated by the receiver equalization, e.g. Zero Forcing (ZF) before making decisions on the subcarrier’s status and their symbols. Hence, $H_k$ in (9) will become a factor in the equalization process and will result in equal SNR penalty in optical OFDM. Here we assume gain on different subcarriers to be 1 for simplicity. Note that no fading is assumed here as fading is not an issue in medium related to VLC for which the RS-OFDM-IM is primarily considered and developed. The SNDR of frequency-domain on $k$th active subcarrier when ZF equalization is used can be calculated by
$$\text{SNDR}_k = \frac{\frac{\beta^2 \sigma_x^2}{\sigma_z^2 + \left(\frac{A_{DC} \sigma_{AWGN}^2}{H_k^2}\right)}}{\left(\frac{\sigma_x^2}{\sigma_x^2} + \left(\frac{A_{DC}}{\text{SNR}_l H_k^2}\right)\right)}$$
(18)
where $\text{SNR}_l = E\{x_n^2\}/\sigma_{AWGN}^2$ is the electrical SNR of the original unclipped signal $x_n$. When the clipping is mild, the average power of the clipped signal is approximately the same as the original signal, $\text{SNR}_l$, and it can be rewritten as $\text{SNR}_l \approx \text{SNR}_l - I_{bias}/\sigma_{AWGN}^2$, where $\text{SNR}_l$ denotes the electrical SNR of LED’s transmitting signal. And $A_{DC} = (\sigma_x^2 + I_{bias})/\sigma_x^2$ is the attenuation of electrical power due to the DC biasing [22]. An erroneous decision on indices in (12) will lead to
error in the SIM embedded bits and also erasures of wrong symbols in the received codeword, which will further reduce the RS block code error-correction capability. The number of erroneous erasures in a codeword of the \( g^{th} \) sub-block is given by
\[
\pi_g = \frac{\|X_g - \hat{X}_g\|_0}{2}
\]
(19)
where \( \|A\|_0 \) is the \( l_0 \) norm of \( A \) and \( \hat{X}_g \) is an estimate of \( X_g \). The average number of symbol errors and erroneous erasures in the codeword is \( \Delta_g = \pi_g + N P_{SER} \). The symbol error probability, \( P_{SER} \), of data transmitted using a square M-QAM modulation in OFDM with an average subcarrier SNDR given by (18) is given by
\[
P_S = 2 \left( 1 - \frac{1}{\sqrt{M}} \right) \text{erfc} \left( \frac{3}{2(M-1)} \text{SNDR}_k \right) - \left( 1 - \frac{2}{\sqrt{M}} + \frac{1}{M} \right) \text{erfc}^2 \left( \frac{3}{2(M-1)} \text{SNDR}_k \right)
\]
(20)
Note that part of the redundancy that was punctured according to SIM cannot be used for codeword recovery. The remaining redundancy which is to be used by the decoder has to be sufficient for correcting both false erasure and erroneous symbol recovery. Considering that the active subcarriers in each sub-block in RS-OFDM-IM scheme belong to a common codeword, calculating the probability of correction when the LLR detector is used can be rather difficult due to the dependence between separate subcarriers. Considering a system with a large block code size, the frequency-domain symbols can be considered approximately uncorrelated, the probability of correct detection of active subcarriers in each sub-block can be approximated. Let the set of indices of active subcarriers be \( \Psi_g = \{ \psi_{g,1}, ..., \psi_{g,N-s} \} \). Also, let \( \Psi_g \) be a set that is a complement to \( \Theta_g \), i.e., \( \Psi_g \cup \Theta_g = \{ 1, 2, ..., N \} \). Now, a correct estimation of the puncture vector requires the receiver to distinguish between every active subcarrier in the set \( \Psi_g \) and every inactive subcarrier in \( \Theta_g \). Without the loss of generality, we first consider the probability of correctly distinguishing between the first active subcarrier \( \psi_{g,1} \) and the first inactive subcarrier \( \theta_{g,1} \) in the \( g^{th} \) sub-block.
whose symbols are given by $Y_g^\psi,1 = \beta X_g^\psi,1 + Z_g^\psi,1 + W_g^\psi,1$ and $Y_g^\theta,1 = Z_g^\theta,1 + W_g^\theta,1$, respectively. Using the results from [23] and [24], the probability of correctly distinguishing between $\psi_{g,1}$ and $\theta_{g,1}$ is given by
$$P_c = 1 - \frac{1}{2M} \sum_{m=1}^{M} e^{-\frac{u_m^2}{2(\sigma_w^2 + \sigma_z^2)}}$$ \hspace{1cm} (21)
with $U_m$ denoting the constellation points in the M-QAM constellation. Now, the probability of correctly distinguishing all active subcarriers from all inactive subcarriers can be calculated by
$$P_{cd} = \left(1 - \frac{1}{2M} \sum_{t=1}^{M} e^{-\frac{u_m^2}{2(\sigma_w^2 + \sigma_z^2)}} \right)^{s(N-s)}$$ \hspace{1cm} (22)
When the active subcarrier in a sub-block are detected correctly we will have $r = \|\theta_g - \hat{\theta}_g\|_0 = 0$. In this case, subcarrier index demolation will have zero error, and all the erroneous bits are only attributed to demodulation of symbols on active subcarriers. The symbol error probability at the decoder input is equal to that of M-QAM demodulation, i.e., $P_{S}^{\text{in}}(r = 0) = P_{\text{SER}}$. Now, the symbol error probability at the decoder’s output is calculated by
$$P_{S,\text{c}} = \sum_{v=t+1}^{N} \frac{v}{N} \binom{N}{v} P_{S}^{v} (1 - P_{S})^{N-v}$$ \hspace{1cm} (23)
Where $t = \left\lfloor \frac{N-K-s}{2} \right\rfloor$ denotes the number of correctable errors. In the case of incorrect index detection, the puncturing vector $\tilde{i}$ may be decoded incorrectly as one of the remaining $2^{p_1} - 1$ vectors in $\mathcal{A}$ with equal probability of $\frac{1-P_{cd}}{2^{p_1}-1}$. But the number of wrong errasures in a codeword will depends on how many different element the actual and estimated puncturing vectors have. Therefore, all possible number of differences in $\theta_g = a_i$ and $\hat{\theta}_g = a_{\tilde{i}}$ should be considered since decoder’s particular performance depends on the exact number of difference between these two vectors. Considering $r = \|\theta_g - \hat{\theta}_g\|_0 \neq 0$, symbol error probability at the decoder input is given by
\[ P_{S}^{\text{in}}(r) = \frac{r+(N-S-r)\times P_{S}^{\text{in}}(0)}{N-S} \]
(24)
By calculating the different realizations that will lead to \( r \) number of wrong erasures in the codeword, the symbols error probability at decoder’s output can be approximated by
\[ P_{S,\text{out}}^{\text{inc}} \approx \frac{1}{2p_{1}-1}\sum_{r=1}^{S} \sum_{v=0}^{N-r} \binom{N-S}{r} \binom{N-r}{v} \frac{v+r}{N} \left( P_{S}^{\text{in}} \right)^{v} \left( 1 - P_{S}^{\text{in}} \right)^{N-r-v} \]
(25)
Where \( \theta = \max(t - r + 1,0) \). Using (23)-(27), the RS decoder’s symbol error probability is calculated as
\[ P_{S,\text{out}} = P_{c,d}P_{S,\text{c}}^{\text{out}} + (1 - P_{c,d})P_{S,\text{inc}}^{\text{out}} \]
(26)
Now, The upper and lower bounds of decoder’s bit error probability, \( P_{b} \) in both cases can be calculated from its symbol error probability i.e. \( \frac{P_{S,\text{out}}}{m} \leq P_{b} \leq P_{S,\text{out}} \).
To calculate the total error rate, the probability of error for the information carried by the SIM should also be considered. The information conveyed SIM is in error only if the subcarriers’ status are detected incorrectly. Hence, subcarrier index demodulation contributes to the total BER when \( \| \theta_{g} - \hat{\theta}_{g} \|_{0} \neq 0 \). Note that different wrong puncturing vectors could lead to different number of erroneous bits in the subcarrier index demodulation. However, since all the wrong puncturing vectors are equally probable to be selected (\( \frac{1}{2p_{1}-1} \)), and because there is a total of \( \binom{p_{1}}{t} \) realizations that will have \( t \) erroneous bits, the average BER in subcarrier index demodulation can be approximated by
\[ P_{b}^{\text{SIM}} \approx \frac{1}{p_{1}(2p_{1}-1)} \sum_{t=1}^{p_{1}} t \binom{p_{1}}{t} \]
(27)
Recalling that each message contains \( p_{2} = Km \) information bits, the lower bound of total bit error probability in RS-OFDM-IM is calculated by
\[ P_{b} \geq P_{c,d} \frac{P_{S,\text{c}}^{\text{out}} \times K}{p_{1}+p_{2}} + \left( 1 - P_{c,d} \right) \frac{\left( p_{S,\text{inc}}^{\text{out}} \times K + P_{b}^{\text{SIM}} \right)}{p_{1}+p_{2}} \]
(28)
The bound can be calculated by substituting (23), (25), and (27) in (28). It should be noted that the probability of successful detection of non-signal subcarriers and RS decoding of signal subcarriers are not independent of the specific sequence of QAM symbols, and the expression in (28) is essentially computed by using the product of the average of two error rates, and it gives an approximation of the actual BER in the underlying systems. However, the results in the next section show its closeness for various encoding and modulation configurations. Using the overall BER and SE of VLC, we can also calculate:
\[ R_b = (1 - P_b)SE_{RSO}(M, K, S) \]
(29)
where \( R_b \) represent the throughput (bps/Hz), which accounts for the successful transmission rate per bandwidth that is achievable by RS-OFDM-IM in a VLC with the clipping constraint.
B. Complexity
The computational complexity in the receiver of RS-OFDM-IM is compared to the original OFDM system. The computational complexity of LLR detection in (14) for each subcarrier will be in the order of \( O(M) \), which is the same as the detection complexity in the original OFDM. Considering the \( 2^{P_1} \) possible realization for puncturing vector \( \theta_g \), and \( N - s \) active subcarriers in each sub-block and M-QAM employment, the ML detection in RS-OFDM-IM will entail \( O(2^{P_1}M^{N-s}) \) complex multiplication per sub-block. In a system with encoder and decoder that operates over a fairly large finite field and also use a high order of QAM modulation, LLR is a better option as it can achieve a trade-off between detection accuracy and complexity [9]. While the classical RS decoding algorithm in \( RS(N,K,N-K+1) \) code yields \( O(N^2) \) computational complexity, the recent works on reformulating the basis of syndrome polynomial and using FFT algorithm for decoding procedure have shown that the error-correction decoding algorithm over binary extension field \( GF(2^m) \) can be reduced to \( O(N\log(N - K) + (N - K)(\log_2(N-K))^2) \) [25],
while the fastest algorithm for the case of erasure decoding can achieve $O(N \log N)$ complexity [26].
IV. SIMULATION RESULTS
Given the discussion in the previous section, the coding based SIM can be used for obtaining a better SE by sending extra on non-signal subcarriers, and improving the system BER by mitigating the clipping noise. We compare the BER performance of RS-OFDM-IM with RS encoded DCO-OFDM and RS-encoded OFDM with classical index modulation in a Gaussian channel. First, the accuracy of the analytical expression for BER in RS-OFDM-IM with clipping and channel noise is examined. Then, we compare the BER performance of the three techniques mentioned above in both single-sided and double-sided clipping conditions. Furthermore, the performance of the proposed strategy in improving the throughput of OFDM-VLC subject to dimming level variation is presented and analyzed.
It was discussed that inactivating an increased number of subcarriers in a sub-block can further reduce the clipping noise. However, this increase can compromise RS code’s error-correction capability. The overall effect of this increase on the BER is shown as a function of received SNR in Fig. 4. A system with $N_t=1024$ is considered, where from 512 available subcarriers before HS, 498 subcarriers are divided into $G = 16$ sub-blocks, with $N = 31$ subcarriers each and 16 overall subcarriers are left for guard band, and RS $(31, K, d = 31 - K + 1)$ encoder and 32-QAM modulation are employed for symbol modulation. The BER performance at two different message lengths $K = 19$ and 25 with corresponding coding rates $r_c \approx 65\%$ and 80\%, respectively, are presented. The SE of this OFDM system can be calculated as $\frac{16 \left( \left\lfloor \log_2 \left( \frac{31}{S} \right) \right\rfloor + K \log_2 32 \right)}{1024}$, and by increasing $S$, the size of information that are embedded on non-signal subcarriers are adjusted. Considering three different values of puncturing $S = 2, 4$ and 6 when $K = 19$, the SE of OFDM system yields 1.60, 1.70, and 1.78 (bit/s/Hz), respectively, while for $K =$
it gives 2.07, 2.17, and 2.25 (bit/s/Hz), respectively. Figs. 4 (a) and (b) show the effect of increasing $S$ in double-sided and single-sided clipping conditions. In double-sided clipping, bounds are assumed to be $u_{\text{lower}} = -2\sigma_x$, $u_{\text{upper}} = 2\sigma_x$ where for single-sided clipping, it’s $u_{\text{lower}} = -1.8\sigma_x$, $u_{\text{upper}} \to \infty$; and $E\{x_n^2\} = \sigma_x^2$ is the power of unclipped signal when no puncturing is applied and all subcarriers are active. It can be seen that in both clipping conditions, at a particular coding rate a system with greater puncturing number yields a better BER. Note than the error floors in Fig. 5 are due to the clipping noise which becomes dominant over channel noise at high SNR levels. Therefore as the number of punctured symbols increases, the reduction in clipping distortion on OFDM subcarriers outweights the loss in the RS code’s error-correction capability and yields a lower error floor. Also, reducing the coding rate in single-sided clipping condition has more notable effect in improving the overall BER, while in double-sided clipping with more severe clipping noise, the overall BER of the smaller coding rate is only slightly better for a particular puncturing number. This is because the erroneous bits are mainly related to the LLR detection of $p_1$ bits that are carried out by SIM. The correct recovery of these bits is mostly determined by the number of non-signal subcarriers. Hence, the BER to a large extend is independent of the coding rate under severe clipping. It should be noted that the improvements in SE and BER come at the expense of
more computations in the system since the size of the lookup table and the number of searches during LLR detection are proportional to $S$. It can be seen that the theoretical bound given in (28) shows a good match to the numerical values especially at higher SNR.
To see the advantage of the proposed SIM in RS-OFDM-IM, its performance is also compared to the RS coded OFDM with the traditional index modulation (OFDM-IM), where only active subcarriers are used to transmit both index embedded information and QAM symbols.
For the sake of a fair comparison, we assume that the codeword size and coding rate are the same in both RS-OFDM-IM and RS coded OFDM-IM. The number of employed subcarriers is determined such that a common SE can be achieved by both schemes. Considering a system with 1090 available subcarriers, and 545 independent subcarriers before applying HS, a total of $G = 16$ sub-blocks can be formed with 34 subcarriers in each. The codewords are generated over Galois field $GF(2^5)$ with a length of 31, modulated by 32-QAM, and then mapped on the OFDM frame and transmitted over a Gaussian channel. Suppose an $RS(31, K, 31-K+1)$ encoder in commonly employed in both schemes. In traditional OFDM-IM, the 31 symbols of each codeword are mapped on their associated subcarriers according to SIM in each sub-block. After modulating all 16 sub-blocks, the time-domain is generated and then clipped according to the optical front-end clipping bounds. At the receiver, given that the symbols of the codeword order during index modulation is preserved, the LLR detector can reconstruct the valid codewords without introducing a displacement error. The number of information bits that can be transmitted in one sub-block in traditional OFDM-IM is $p'_i = \left\lfloor log_2\left(\frac{34}{31}\right)\right\rfloor + K log_2^3$. In RS-OFDM-IM with the same coding rate, VLC can transmit $p_t = \left\lfloor log_2\left(\frac{31}{S}\right)\right\rfloor + K log_2^3$ bits per sub-block. Assuming $S = 3$, the same number of information bits and SE can be achieved by both schemes. The BER performances of the two schemes as a function of $SNR_l$ in a VLC with double-sided ($u_{lower} = -2\sigma_x$, $u_{upper} = 2\sigma_x$) and single-sided
(\(u_{\text{lower}} = -1.8\sigma_x, u_{\text{upper}} \to \infty\)) clipping are shown in Fig. 5(a) and Fig. 5(b), respectively. At two coding rates, \(r_c = 54\%\) (\(K=17\)) and \(r_c = 74\%\) (\(K=23\)), the total BER of the systems are presented.
Although the BER of both schemes plateau in both clipping conditions, the error floor in RS-OFDM-IM is significantly smaller. Note that the amount of information transmitted using SIM and the total bitrate are the same in both schemes. But the index demodulation error, which accounts for errors in bits transmitted by the SIM is smaller in RS-OFDM-IM. Since information is embedded in indices of a smaller number of subcarriers in RS-OFDM-IM as compared to the traditional OFDM-IM (31 < 34), the likelihood of an erroneous index detection due to clipping or channel noise is less in this scheme. Also, due to the increased number of non-signal subcarriers and reduced clipping noise, the LLR detector has better accuracy in indices estimation which improves the total BER performance in RS-OFDM-IM. The superiority of RS-OFDM-IM in achieving the same bitrate while substantially improving BER shows its advantage in comparison to the traditional SIM scheme in a coded OFDM system.
We also compare RS-OFDM-IM against the basic OFDM-based VLC in the absence of SIM. DCO-OFDM, which is well known for its superior SE when compared to ACO-OFDM, is used for the
comparison. In RS encoded DCO-OFDM, all available subcarrier are modulated and data are conveyed by QAM symbols. The BER performances of the two systems are compared and presented in Fig. 6. In a system with \( N_e = 1024 \) total subcarriers, and 512 available subcarriers before applying HS, 496 subcarriers are considered for data transmission. Information bits in DCO-OFDM are encoded in the frequency-domain by a non-binary encoder \( RS(31, K', 31-K'+1) \) over \( GF(2^5) \). Symbols of 16 codewords are then modulated by 32-QAM constellation and then mapped onto the data subcarriers. The SE of DCO-OFDM is given by \( SE_{DCO}(K') = (16 \times K' \log_2 32)/1024 \). In RS-OFDM-IM, the same 496 available subcarriers are divided and used for forming 16 sub-blocks with 31 subcarriers, where each sub-block is modulated by codewords generated using an \( RS(31, K, 31-K+1) \) encoder. Considering \( S \) puncturing in each codeword, SE is given by \( SE_{RSO}(M, K, S) = 16(K \log_2 32 + \lfloor \log_2 C(31, S) \rfloor)/1024 \). The modulation parameters are adjusted such that a similar SE can be achieved by RS-OFDM-IM and DCO-OFDM. Since in RS-OFDM-IM information is conveyed by both active and inactive subcarriers in, the length of the message at the input of the encoder could be smaller \( (K' > K) \) and it would still achieve a similar bitrate with a lower coding rate. Using (19), the \( \{K_p, S_p\} \) sets that generate an SE equal or greater than that of coded DCO-OFDM at two message length of \( K' = 26 \) and \( K' = 22 \) are calculated. For the first case, we have \( SE_{DCO}(32,26) = 2.03 \) (bit/s/Hz) in coded DCO-OFDM, while for RS-OFDM-IM (19) yields two alternative parameters sets \( \{(23,5), (23,6)\} \) with \( SE_{RSO}(32,23,5)=2.06 \) (bit/s/Hz) and \( SE_{RSO}(32,23,6)=2.09 \) (bit/s/Hz), respectively that generate an SE equal or greater than that of coded DCO-OFDM at two message length of \( K' = 26 \) and \( K' = 22 \) are calculated. For \( K' = 26 \), we have \( SE_{DCO}(32,26) = 2.03 \) (bit/s/Hz) in coded DCO-OFDM, while for RS-OFDM-IM (19) yields two alternative parameters sets \( \{(23,5), (23,6)\} \) with \( SE_{RSO}(32,23,5)=2.06 \) (bit/s/Hz) and \( SE_{RSO}(32,23,6)=2.09 \) (bit/s/Hz), respectively. For \( K' = 22 \) with \( SE_{DCO}(32,22) = 1.72 \) (bit/s/Hz), RS-OFDM-IM can achieve a similar result using \( \{(19,5), (19,6)\} \) with corresponding SE given by \( SE_{RSO}(32,19,5)=1.75 \) (bit/s/Hz) and \( SE_{RSO}(32,19,6)=1.78 \)
The BER performance of the two schemes with the given parameters under double-sided ($u_{lower} = -2\sigma_x$, $u_{upper} = 2\sigma_x$) and single-sided ($u_{lower} = -1.8\sigma_x$, $u_{upper} \to \infty$) clipping are shown in Fig. 6(a) and Fig. 6(b), respectively. It can be seen that RS-OFDM-IM has a weaker performance at low SNR due to the erroneous LLR detection and index demodulation caused by Gaussian noise, however at higher SNR when clipping noise is dominant it gives a significantly improved BER performance compared to coded DCO-OFDM at both SE levels. Note that for coded systems, focus is on the BER values below $10^{-5}$. Fig. 6 shows the superiority of proposed scheme in achieving $BER < 10^{-5}$ in both of clipping conditions. For instance, at $SNR_1 = 35$ dB in Fig. 6(a), the error floor reduces from $\sim 10^{-4}$ in coded DCO-OFDM with SE=2.03 (bit/s/Hz) to $10^{-7}$ in RS-OFDM-IM with SE= 2.09 (bit/s/Hz) due to the mitigated clipping noise. Fig. 6 also shows that, although increasing the puncturing number causes error-correction loss in codewords, it leads to a better overall BER and higher SE in the RS-OFDM-IM. As discussed before, the time-domain signal of RS-OFDM-IM undergoes a less significant distortion due to its reduced envelope when the clipping bounds of LED are adjusted for its illumination purposes. In Section III, we showed that as the dimming level changes, the clipping bounds need to be fixed...
such that the average optical power of VLC in (16) meets the required LED’s dimming level. Given that the optical power in DCO-OFDM scheme is mostly determined by the added biasing signal, when approaches either side of its margin, the clipping bound during bipolar to unipolar conversion on that side will become drastically smaller according to (6) to keep the converted signal within the LED’s dynamic range. This will increase clipping noise power and deteriorate the system’s BER performance. It was shown in section III that the RS-OFDM-IM will experience less clipping noise due to its reduced time-domain envelope, and therefore a higher SNDR can be obtained when the dimming level varies. To see the impact of this improvement on the overall transmission performance when the parameters of the physical layer are modified for illuminations requirement, the throughput of RS-OFDM-IM and coded DCO-OFDM are evaluated and compared as a function of $\eta$ at two $SNR_t$ levels. Fig. 7 presents the throughput of RS-OFDM-IM given by (30) in an OFDM-based VLC system with optical power limit given by $\Lambda = [0, 5]$, similar to the specification used in Table 1. We consider an LED transmitter in an OFDM system with $N_c=1024$ total subcarriers and 512 independent subcarriers available for data transmission before HS been applied. In the coded DCO-OFDM information are encoded by $RS(31, K, 31-K+1)$ encoder over $GF(2^5)$, and then codewords are modulated using 32-QAM and transmitted over a Gaussian channel. In RS-OFDM-IM data are encoded using $RS(31, K, 31-K+1)$ encoder where $S$ symbols are punctured according to SIM, and the remaining symbols are modulated by 32-QAM and mapped onto subcarriers. Considering SE of coded DCO-OFDM at two coding rates as the reference, the encoding parameter sets $(K,S)$ in RS-OFDM-IM are again calculated by (19) to achieve a similar SE. At coding rate $r_c = 83\%$ ($K'=26$) coded DCO-OFDM yields an SE of 2.03 [bit/s/Hz]. In RS-OFDM-IM two calculated sets $(K_p,S_p) = \{(24,3), (24,4)\}$ can similarly achieve 2.06 (bit/s/Hz) and 2.09 (bit/s/Hz), respectively. At $r_c = 70\%$ ($K'=22$), coded DCO-OFDM yields $SE_{DCO}(22,32) = 1.72$ (bit/s/Hz), while according to (19) the corresponding sets in RS-OFDM-IM will be $(19,5), (20,3)$, where each can achieve an SE of 1.75 (bit/s/Hz). The
throughput of the two schemes are measured at two particular $SNR_t$ level since it also accounts for the effect of change in the biasing signal due to the variation in the dimming level. Fig. 7 shows that RS-OFDM-IM supports a higher throughput than coded DCO-OFDM in a broad range of dimming levels. At $SNR_t=30$ dB, RS-OFDM-IM can provide a more consistent throughput during the variation of dimming level. This advantage is due to the fact that RS-OFDM-IM yields a higher SNDR when the dimming level approaches its limits as presented in Fig. 3. It also should be noted that since the $SNR_t$ takes the biasing signal into account, an increase in $I_b$ due to a rise in the illumination level will attenuate the useful electrical signal power and will deteriorate the system BER performance. This effect leads to an asymmetrical form in the throughput curves at $SNR_t = 25$ dB. This attenuation and the residual clipping noise which is more severe at $\eta = 0.9$ and $\eta = 0.1$ lead to erroneous subcarrier index demodulation and subsequently to erroneous RS decoding. This impact will become more pronounced when the puncturing number gets larger due to more loss in the RS code error-correction capability. However, it can be seen that for $0.2 < \eta < 0.9$, RS-OFDM-IM can provide higher throughput at both SNR levels even though the error-correction capability of its block code is compromised by puncturing.
Fig.7 Throughput comparison of RS-OFDM-IM and DCO-OFDM at varying dimming levels; (a) $SNR_t = 25$ dB, (b) $SNR_t = 30$ dB.
V. CONCLUSIONS
We proposed a novel modulation scheme based on Reed Solomon encoding and subcarrier index modulation for OFDM-based VLC with a physically constrained optical transmitter. In this scheme, the frequency-domain symbols are chosen from the RS encoded block. To overcome the burst error and distortion caused by the nonlinear clipping, a group of codeword symbols are punctured and their corresponding subcarriers are nulled to reduce the clipping probability. The subcarrier index modulation integrated with OFDM is used to compensate for the spectral efficiency loss caused by systematic encoding. The theoretical bound and simulation results show the BER performance superiority of the new scheme in comparison to the traditional OFDM-IM with channel coding and RS coded DCO-OFDM under both single-sided and double-sided clipping conditions.
The parameters involved in the encoding step of the new scheme provides the flexibility for both improving the spectral efficiency toward the desired range and removing the BER floor caused by clipping noise. This feature enables RS-OFDM-IM in achieving and maintaining a better BER and throughput in a physically constrained VLC while the required dimming level is subject to change.
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RESEARCH ARTICLE
Open Access
Differential regulation of osteoclastogenesis by Notch2/Delta-like 1 and Notch1/Jagged1 axes
Chiyoko Sekine1*, Akemi Koyanagi2, Noriko Koyama1,3, Katsuto Hozumi4, Shigeru Chiba5 and Hideo Yagita1,2
Abstract
Introduction: Osteoclastogenesis plays an important role in the bone erosion of rheumatoid arthritis (RA). Recently, Notch receptors have been implicated in the development of osteoclasts. However, the responsible Notch ligands have not been identified yet. This study was undertaken to determine the role of individual Notch receptors and ligands in osteoclastogenesis.
Methods: Mouse bone marrow-derived macrophages or human peripheral blood monocytes were used as osteoclast precursors and cultured with receptor activator of nuclear factor-kappaB ligand (RANKL) and macrophage-colony stimulating factor (M-CSF) to induce osteoclasts. Osteoclasts were detected by tartrate-resistant acid phosphatase (TRAP) staining. K/BxN serum-induced arthritic mice and ovariectomized mice were treated with anti-mouse Delta-like 1 (Dll1) blocking monoclonal antibody (mAb).
Results: Blockade of a Notch ligand Dll1 with mAb inhibited osteoclastogenesis and, conversely, immobilized Dll1-Fc fusion protein enhanced it in both mice and humans. In contrast, blockade of a Notch ligand Jagged1 enhanced osteoclastogenesis and immobilized Jagged1-Fc suppressed it. Enhancement of osteoclastogenesis by agonistic anti-Notch2 mAb suggested that Dll1 promoted osteoclastogenesis via Notch2, while suppression by agonistic anti-Notch1 mAb suggested that Jagged1 suppressed osteoclastogenesis via Notch1. Inhibition of Notch signaling by a gamma-secretase inhibitor suppressed osteoclastogenesis, implying that Notch2/Dll1-mediated enhancement was dominant. Actually, blockade of Dll1 ameliorated arthritis induced by K/BxN serum transfer, reduced the number of osteoclasts in the affected joints and suppressed ovariectomy-induced bone loss.
Conclusions: The differential regulation of osteoclastogenesis by Notch2/Dll1 and Notch1/Jagged1 axes may be a novel target for amelioration of bone erosion in RA patients.
Introduction
Notch signaling pathways play key roles in cell-fate decision and differentiation in many tissues during embryonic and postnatal development [1]. Four mammalian Notch receptors have been identified, designated as Notch1 to Notch4. Interaction of Notch receptors with membrane-bound ligands of the Delta and Jagged families (Delta-like1 (Dll1), Dll4, Jagged1, and Jagged2) induces gamma-secretase-mediated cleavage and translocation of Notch intracellular domain (ICD) into the nucleus, where it interacts with the transcription factor CSL. Once bound to CSL, Notch intracellular domain recruits other coactivators, including mastermind proteins, and this transcriptional activation complex induces the expression of downstream target genes, such as Hairy Enhancer of Split -1 (Hes-1) [2].
The importance of Notch signaling in osteoclastogenesis has recently been reported [3,4]. Osteoclasts are derived from the monocyte/macrophage lineage and are responsible for bone resorption [5]. Osteoclast differentiation is a multistep process that leads to expression of tartrate-resistant acid phosphatase (TRAP), multinucleation and bone-resorbing activity. It has been demonstrated that receptor activator of nuclear factor-kappaB ligand (RANKL) and macrophage-colony stimulating factor (M-CSF) are critical for osteoclast development [6]. CD51/CD61, TRAP and matrix metalloproteinase-9 are widely used as specific markers for osteoclasts [7]. Controlling osteoclastogenesis is important for bone homeostasis and an abnormal osteoclastogenesis leads to imbalance of bone remodeling that is related to various...
diseases such as osteoporosis, rheumatoid arthritis (RA), and multiple myeloma [5].
RA is a chronic autoimmune disease characterized by inflammation of synovial joints leading to erosion of bone and ultimately functional loss of joints. This bone destruction is caused by enhanced activity of osteoclasts [8]. In chronic inflammation, pro-osteoclastogenic factors often predominate, leading to increased osteoclast formation and pathological bone resorption. Current therapies to treat RA have focused on inhibition of inflammation in the joints. To prevent structural destruction of the joints, it is important to explore the regulation of osteoclasts as a new therapeutic approach for the treatment of RA.
A recent report demonstrated that deletion of Notch1 and/or Notch3 in mouse osteoclast precursor cells promoted osteoclast differentiation and overexpression of a Notch ligand Jagged1 suppressed osteoclastogenesis, suggesting a suppressive role for Notch/Jagged1 in osteoclastogenesis [3]. On the other hand, Notch2 has been shown to accelerate osteoclastogenesis in association with nuclear factor-kappaB, and induction of Notch signaling by Jagged1 promoted osteoclast differentiation [4]. Thus, possibly differential contributions of individual Notch receptors and ligands to the regulation of osteoclastogenesis remain elusive. In addition, the contribution of Notch receptors and ligands to human osteoclastogenesis has not been determined yet.
We have recently established a panel of monoclonal antibodies (mAbs) specific for mouse Notch receptors and ligands [9]. In this study, we investigated the effect of these mAbs on the differentiation of bone marrow (BM) cells into osteoclasts. We have also newly established mAbs against human Notch receptors and ligands, and determined their effects on the osteoclastogenesis from human peripheral blood monocytes (PB Mono). Our results suggest that Dll1/Notch2 interaction promotes osteoclastogenesis, whereas Jagged1/Notch1 interaction suppresses it in both mice and humans. Actually, treatment with anti-mouse Dll1 blocking mAb ameliorated K/BxN serum-induced arthritis, a mouse model of RA, and reduced osteoclasts number in the affected joints. The differential regulation of osteoclastogenesis by the Dll1/Notch2 and Jagged1/Notch1 axes may have pathological and therapeutic relevancies to RA.
Materials and methods
Mice
C57BL/6 mice were purchased from Charles River (Oriental Yeast, Tokyo, Japan). Dll1 conditional knockout mice were generated as described previously [10]. For inducible deletion of Dll1, four-week-old Dll1lox/lox Mx-Cre+ or littermate control Dll1lox/lox Mx-Cre- mice were injected with 0.3 mg of poly(I);(C) twice a week for two weeks, and used three weeks later. All animal experiments were approved by Juntendo University Animal Experimental Ethics Committee.
Reagents
The gamma-secretase inhibitor DAPT (N-[N-(3,5-difluorophenacyl-L- alanyl)-S-phenylglysin t-butylerster), was purchased from Calbiochem (San Diego, CA, USA). The mouse Jagged1-Fc and mouse Dll1-Fc fusion proteins were generated as previously described [11]. The mouse Jagged2-Fc and human Jagged1-Fc fusion proteins were purchased from R&D Systems (Minneapolis, MN, USA). The human Dll1-Fc fusion protein was purchased fromAlexis Biochemicals (Lausen, Switzerland). The human IgG Fc fragment was purchased from Acris Antibodies (Herford, Germany). Mouse Fc Block (2.4G2; BD Bioscience, San Jose, CA, USA) and Functional Grade Purified Human Fc(gamma)R-Binding Inhibitor (eBioscience, San Diego, CA, USA) were used to block non-specific binding of mAbs to Fc(gamma) receptors.
Generation of mAbs
To generate the mAbs specific for human Dll1, Dll4, Jagged1 and Jagged2, Balb/c mice (Charles River) were immunized by intraperitoneal injection of human Dll1- Fc or Jagged1-Fc fusion protein, recombinant human Dll4 (R&D Systems), or Jagged2-transfected CHO cells three times at seven-day intervals. Three days after the final immunization, the splenocytes were fused with P3U1 myeloma cells. After hypoxanthine aminopterin thymidine (HAT) selection, antibodies that react with human Dll1-, Dll4-, Jagged1- or Jagged2-transfected CHO cells, but not with untransfected CHO cells, were screened by flow cytometry. Each mAb was cloned by limiting dilution.
Balb/c mice were immunized by intraperitoneal injection of human Notch1-Fc, Notch2-Fc or Notch3-Fc fusion protein (R&D Systems), or Notch4-transfected CHO cells three times at seven-day intervals. The hybridoma cells were prepared as described above, and antibodies that react with human Notch1-, Notch2-, Notch3- or Notch4-transfected CHO cells, but not with untransfected CHO cells, were screened and cloned. All these mAbs were purified from ascites produced in pristan-primed ICR nude mice by the caprylic acid and ammonium sulfate precipitation method [12] and labeled with biotin for flow cytometric analysis.
Other antibodies
Generation and characterization of hamster IgG mAbs specific for mouse Notch1 (HMN1-12), Notch2 (HMN2-29), Notch3 (HMN3-133), Notch4 (HMN4-14), Dll1 (HMD1-5), Dll4 (HMD4-2), Jagged1 (HMJ1-29) and Jagged2 (HMJ2-1) have been described in our
recent papers [9,13]. Stimulating activity of the anti-receptor mAbs and blocking activity of the anti-ligand mAbs have been verified in vitro or in vivo [9,13-20]. Fluorescein isothiocyanate (FITC) -labeled mAbs against mouse CD11c (HL3), mouse CD61 (2C9.G3), human CD11c (3.9) and human CD51/CD62 (23C6), PE-labeled mAb against mouse CD11b (M1/70), and human CD14 (61D3), APC- or PE-conjugated streptavidin were obtained from eBioscience. FITC-labeled mAb against mouse F4/80 (CI:A3-1) was purchased from Cell Signaling (Beverly, MA, USA). Abs specific for cleaved-Notch1 (Val1744) and Notch2 intracellular domain (411801) were purchased from Cell Signaling (Beverly, MA, USA) at 37°C for five minutes. It was difficult to detach intact osteoclasts but a part of the osteoclasts could be analyzed by flow cytometry on Day 5. Cells were first incubated with Fc Block for mice or Fc(gamma)R-Binding Inhibitor for human, and then with an optimal dilution of biotinylated mAbs. After washing with 2% FBS in PBS, the cells were incubated with FITC- or PE-labeled mAbs or streptavidin, and also stained with 7-amino-actinomycin D (BD Pharmingen, San Jose, CA, USA) to exclude dead cells. After washing, the cells were analyzed on FACScan or FACScaliber (BD Bioscience) and analyzed with CellQuest (BD Bioscience).
Reverse transcription-polymerase chain reaction (RT-PCR)
Total RNA was isolated using STAT60 (Tel-Test, Friendswood, TX, USA) and was reverse transcribed to complementary DNA with oligo-dT and SuperScript RT (Invitrogen, Carlsbad, CA, USA). PCR consisted of 35 cycles of 45 seconds at 94°C, 1 minute at 58°C and 1 minute at 72°C. The primers were as follows: mouse Dll1 sense, 5'-ACCTCTTTTCCCGTATGCTTCAAG-3' and mouse Dll1 anti-sense, 5'-AGAGCTGTGATGGAGG GCTT-3'; mouse Dil4 sense, 5'-CGAGGGCGGA GGACCATGA-3' and mouse Dil4 anti-sense 5'-CCT GCCTTACCTCTGG-3'; mouse Jagged1 sense, 5'- ATTCGATCTACATAGCCCTTGAAG-3' and mouse Jagged1 anti-sense 5'-CTTACAGATGTATCCCAT CCGT-3'; mouse Jagged2 sense, 5'-TGTCAGCCAG CGAGCTCATT-3' and mouse Jagged2 anti-sense 5'- TCTACGTGGTCTTCTGGCTT-3'; mouse beta-actin sense, 5'-GTGGGCCGCTCTAGGCACCAA-3' and mouse beta-actin anti-sense 5'-CTTCTTTGTAGTGTCCAC GAGGCACATTTC-3'; human Dll1 sense, 5'-ACAGC GGAGCACATGAAACACT-3' and human Dll1 anti-sense, 5'-CGTGGAAATCCGCCCTTCT-3'; human Dil4 sense, 5'-TCAGCAAGATCGCCACATCA-3' and human Dil4 anti-sense 5'-AGGGTGTGCTTGTGATC-3'; human Hes-1 sense, 5'-GAGGCCCGCTCTCTG AACTCT-3' and human Hes-1 anti-sense 5'-CA TCTTTTGTAGTAAACGTGATGGGA-3'; human Jagged2 sense, 5'-AATGGAGTATTCTCGGATAGTT GACG-3' and mouse Jagged2 anti-sense 5'-GCG CACACCACACT-3'.
GGATAAA-3’ and human Hes-1 anti-sense 5’-TCAGCTGGCTCAGACTTTCA-3’. PCR products were separated by electrophoresis on 2.0% agarose gel with 0.5 μg/ml ethidium bromide and detected by UV.
**Immunoblotting**
Cells were lysed in SDS sample buffer (62.5 mM Tris-HCl, pH 6.8, 2% SDS, 20% sucrose, 0.02% pyronin G) and boiled. Samples were subjected to SDS polyacrylamide gel electrophoresis and transferred to a PVDF membrane. These membranes were incubated with diluted primary Abs in 5% Tris buffered saline/Tween 20 (BSA TBS/T) overnight at 4°C. After washing with TBS/T, membranes were incubated with a horseradish peroxidase-conjugated secondary Ab. The immunoreactive proteins were visualized using ECL Plus (GE Healthcare, Chalfont St Giles, Buckinghamshire, UK).
**Animal model of arthritis**
Experimental arthritis was induced by passive transfer of serum from arthritic K/BxN mice, which spontaneously develop arthritis resembling RA [21]. These mice were kindly provided by Drs. C. Benoist and D. Mathis (Harvard Medical School, Boston, MA, USA). Preliminary experiments showed that injection of 10 μl of pooled serum into the peritoneal cavity on Day 0 and Day 2 induced arthritis consistently in C57BL/6 mice. Mice with arthritis were treated by intraperitoneal injection of 0.25 mg of anti-mouse Dll1 mAb (HMD1-5) or control hamster IgG (eBioscience) twice a week for two weeks. Treatment was begun on Day 3. Arthritis in each limb of arthritic mice was assessed clinically by visual scoring from 1 to 4: 0, no swelling; 1, detectable swelling in one joint; 2, non-severe swelling in two or more joints; 3, severe swelling in two or more joints; and 4, severe swelling in two or more joints including digital swelling. The maximal score for an individual animal was 16. Arthritis scores were analyzed statistically by Student’s t test.
In histological examination, hindpaws were obtained and fixed in 10% buffered formalin, decalcified in 10% EDTA, and embedded in paraffin. Sections (4 μm) were stained with hematoxylin and eosin for histologic examination. All procedures met institutional regulations for animal experiments.
**Immunohistochemistry**
Paraffin-fixed tissue sections of hindpaw were deparaffinized, pretreated in Liberate Antibody Binding Solution (Polysciences, Inc., Warrington, PA, USA) for five minutes, and incubated with 4 μg/ml of anti-TRAP Ab (K-17; Santa Cruz Biotechnology, Inc., Santa Cruz, CA, USA). They were then incubated with biotinylated Ab against goat immunoglobulins (DAKO Cytomation, Glostrup, Denmark), and ABC reagent (VectorStain Elite ABC kit; Vector Laboratories, Burlingame, CA, USA) was used for detection. Color was developed with diaminobenzidine, whereas the sections were counterstained with hematoxylin. Diaminobenzidine-positive MNCs in the metatarsal joints were enumerated by observers in a blind manner to calculate the TRAP-positive osteoclasts per bone surface. The numbers of TRAP-positive osteoclasts were analyzed statistically by Student’s t test.
**Ovariectomy-induced bone loss**
Eight-week-old female C57BL/6 mice were either sham-operated or ovariectomized (OVX) under anesthesia. 0.25 mg of anti-mouse Dll1 mAb (HMD1-5), anti-mouse Jagged1 mAb (HMJ1-29) or control hamster IgG was administered intraperitoneally twice a week for four weeks. At the end of the experiments, right and left femora were removed and fixed in 70% ethanol. The femoral bone was examined radiographically using quantitative computed tomography (CT) (LCT-200; LaTheta, Aloka, Tokyo, Japan) according to the manufacturer’s instruction. CT scanning was performed at 96 μm intervals and 10 slices of trabecular bone were analyzed. Histomorphometric parameters for osteoclastogenesis were analyzed by staining of femoral bone sections with anti-TRAP Ab as mentioned above. Parameters obtained from microCT and histomorphometrical analysis were statistically analyzed by Student’s t test. All procedures met institutional guidelines for animal experiments.
**Results**
**Expression of Notch receptors and ligands during osteoclastogenesis from mouse BM**
Mouse BM cells cultured with rmM-CSF for 72 hours were used as osteoclast precursors (Day 0). Flow cytometric analysis showed CD11b was expressed on more than 90% of cells during osteoclastogenesis induced with rmM-CSF and rhRANKL. Among these CD11b+ osteoclast precursors, F4/80+ cells differentiate into osteoclasts although the terminally differentiated osteoclasts do not express F4/80 [5,22]. As shown in Figure 1a, a substantial part of the CD11b+ cells expressed F4/80 during osteoclastogenesis. Then, the expression of Notch receptors and ligands on CD11b+ cells were examined. CD11b+ F4/80+ osteoclast precursors expressed Notch2, Notch3 and Jagged1 expression on Day 3 (Figure 1b). A part of these cells differentiated into CD11b+CD61+ osteoclasts on Day 5 (Figure 1a). On Day 5, expression of Notch1, Dll1 and Jagged1 declined on CD11b+F4/80+ cells, and on CD11b+CD61+ osteoclasts (Figure 1b). CD11b+F4/80+ cells do not differentiate into osteoclasts but could potentially stimulate Notch receptors on CD11b+F4/80+ cells. However, Notch ligands were not expressed on CD11b+F4/80+ cells while Notch2 and Notch3 were expressed on Day 3.
Sekine et al. Arthritis Research & Therapy 2012, 14:R45
http://arthritis-research.com/content/14/2/R45
Figure 1 Expression of Notch receptors and ligands during osteoclastogenesis from mouse BM. BM cells cultured with rmM-CSF for 72 hours were used as osteoclast precursors (Day 0). These cells were further cultured with rmM-CSF and rhRANKL to induce osteoclasts. (a) CD11b⁺F4/80⁺ osteoclast precursors and CD11b⁺CD61⁺ osteoclasts were analyzed on days 0, 3 and 5. Percentages from three independent experiments are indicated. (b) Expression of Notch receptors and ligands on CD11b⁺F4/80⁺ osteoclast precursors was analyzed by flow cytometry on days 0, 3 and 5. Expression on CD11b⁺F4/80⁺ cells on Day 3 is also represented. CD11b⁺CD61⁺ osteoclasts were analyzed on Day 5. For comparison, BM cells were cultured with rmM-CSF alone for eight days and CD11b⁺F4/80⁺ cells were analyzed as BM-derived macrophages (BMMø), or with rmGM-CSF for eight days with LPS stimulation for the last 17 hours and CD11c⁺ cells were analyzed as BM-derived dendritic cells (BMDC). Filled histograms indicate the control hamster IgG. Open histograms indicate the Notch receptors or ligands. (c) Messenger RNA levels of Notch ligands were measured by RT-PCR on days 0, 3 and 5.
(Dll1), as well as on Day 0 and Day 5 (data not shown). RT-PCR analysis during osteoclastogenesis also showed an increase of Dll1 and Jagged1 messenger RNA levels in total cells on Day 3, although they were still detected on Day 5 (Figure 1c). BM derived-macrophages, which were derived from BM cells by culturing with rmM-CSF alone, showed Notch receptor and ligand expression similar to osteoclast precursors at Day 0 (Figure 1b). In contrast, BM derived-dendritic cells expressed only Notch2 (Figure 1b).
Dll1 enhances but Jagged1 suppresses osteoclastogenesis from mouse BM
Since both Notch receptors and ligands were expressed on CD11b⁺F4/80⁺ osteoclast precursors during osteoclastogenesis, we examined the role of Notch ligands. As shown in Figure 2a, blocking of Notch signaling by a gamma-secretase inhibitor, DAPT, significantly inhibited RANKL-induced osteoclastogenesis. Anti-mouse Dll1 blocking mAb also markedly inhibited the osteoclastogenesis. Anti-mouse Dll4 blocking mAb had no effect on osteoclast differentiation, consistent with no expression of Dll4 during osteoclastogenesis. Anti-mouse Jagged1 blocking mAb significantly enhanced osteoclastogenesis. Anti-mouse Jagged2 blocking mAb slightly enhanced osteoclastogenesis but not significantly. Blocking of Notch signaling with anti-mouse Dll1 or anti-mouse Jagged1 mAb, as well as DAPT, was shown by the inhibition of Hes-1 expression (Figure 2b). Combinational blockade of Dll1 with either Dll4, Jagged1 or Jagged2 also markedly decreased the osteoclastogenesis (Figure 2a). These results indicate that Dll1 plays a predominant role among Notch ligands in supporting osteoclast differentiation from mouse BM.
To confirm the effect of each Notch ligand on osteoclastogenesis, Notch receptors on osteoclast precursors were activated by Fc fusion protein of each Notch ligand. Accordingly, mouse Dll1-Fc significantly enhanced the osteoclastogenesis, whereas mouse Jagged1-Fc suppressed it (Figure 2c). Moreover, Dll1-deficient BM cells showed a greatly reduced osteoclastogenesis as compared with control cells (Figure 2d). Collectively, these results indicate that Dll1 enhances but Jagged1 suppresses osteoclastogenesis.
Notch2 promotes but Notch1 suppresses osteoclastogenesis from mouse BM
To investigate if the activation of each Notch receptor enhances or suppresses osteoclast differentiation,
Figure 2 Effects of Notch ligand blockade and Notch receptor stimulation on osteoclastogenesis from mouse BM. (a) Osteoclasts were induced from mouse BM as described in Figure 1. DAPT (10 μM), DMSO as a control, 20 μg/ml of the indicated mAb (D1, HMD1-5; D4, HMD4-2; J1, HMJ1-29; J2, HMJ2-1), or control hamster IgG (Ham) was added on Day 0 and Day 3. (b) Osteoclasts were induced as described in (a) and mRNA levels of Hes-1 and beta-actin were determined by RT-PCR on Day 3. (c and e) Osteoclast precursors were pre-incubated with Fc Block and then differentiated on the plate immobilized with 10 μg/ml of the indicated Fc chimera or control human IgG-Fc fragment (hIgG-Fc) (c), or with 5 μg/ml of the indicated mAb (N1, HMN1-12; N2, HMN2-29; N3, HMN3-133; N4, HMN4-14) or Ham (e). (d) BM cells from Dll1-conditional knockout or littermate control mice were differentiated into osteoclasts. ***, P < 0.001. (a, c-e) Osteoclasts were stained for TRAP. Representative stainings are shown. Original magnification: × 100. Data are indicated as the mean TRAP-positive MNCs per culture well ± SD of triplicated wells. #, P < 0.001 versus DMSO control. *, P < 0.05; **, P < 0.01; ***, P < 0.001 versus Ham or hIgG-Fc control. Similar results were obtained in three independent experiments.
Expression of Notch receptors and ligands during osteoclastogenesis from human PBmono
To study the role of Notch receptors and ligands in human osteoclastogenesis, we established mAbs specific for human Notch1, Notch2, Notch3, Notch4, Dll1, Dll4, Jagged1 and Jagged2 (Figure 3a, b). Then, the expression of Notch receptors and ligands during osteoclast differentiation from human PBmono were determined by flow cytometry. More than 92% of cells expressed CD14 during osteoclastogenesis induced with rhM-CSF and rhRANKL, which were analyzed as osteoclast precursors. 5 to 10% of CD14+ cells expressed CD51/CD61 on
Day 5, which were analyzed as osteoclasts. While Notch1 and Notch2 were expressed on PBmono, Notch3 expression was induced by rhM-CSF stimulation for 72 hours (Figure 3c, Day 0). The expression of Notch1, Notch2 and Notch3 was maintained during osteoclastogenesis, including CD14+CD51/CD61+ osteoclasts on Day 5 although the expression levels were higher on Day 0 (Figure 3c). Similarly to the mouse BM, induction of Dll1 expression on CD14+ osteoclast precursors was observed on Day 3 of RANKL stimulation, albeit at a low level. Meanwhile, Jagged1 was constitutively expressed (Figure 3c). RT-PCR analysis during osteoclastogenesis also showed the increase of Dll1 at messenger RNA level on Day 3 in total cells (Figure 3d). Monocyte-derived macrophages, which were induced with rhM-CSF alone, expressed only Notch2 and Jagged1 (Figure 3c). Monocyte-derived dendritic cells expressed Notch1, Notch2 and Jagged1 as did PBmono (Figure 3c).
**Dll1 enhances but Jagged1 suppresses osteoclastogenesis from human PBmono**
To determine the role of Notch ligands in osteoclast differentiation from human PBmono, Notch ligands were blocked by mAbs specific for human Dll1, Dll4, Jagged1 or Jagged2. Similar to the effect on osteoclastogenesis from mouse BM, DAPT significantly inhibited the differentiation of osteoclasts from human PBmono (Figure 4a). Blockade of Dll1 also significantly inhibited the differentiation of osteoclasts (Figure 4a). In contrast, blockade of Jagged1 significantly enhanced the osteoclast differentiation, while blockade of Dll4 or Jagged2 had no significant effect (Figure 4a). Suppression of Hes-1 expression with anti-human Dll1 or anti-human Jagged1 mAb, as well as DAPT, showed the inhibition of Notch signaling (Figure 4b). Conversely, stimulation with immobilized human Dll1-Fc enhanced the osteoclastogenesis, while human Jagged1-Fc suppressed it (Figure 4c). Decreasing the dose of RANKL clearly showed the enhancement of osteoclastogenesis by blockade of Jagged1, as well as by stimulation with human Dll1-Fc (Figure 4d). These results indicate that Dll1 positively regulates the osteoclastogenesis from PBmono but Jagged1 regulates it negatively.
**Notch2 promotes but Notch1 suppresses osteoclastogenesis from human PBmono**
Then, we determined the effect of each Notch receptor activation on the differentiation of osteoclasts from human PBmono. Similarly to the mouse BM (Figure 2e), osteoclastogenesis was significantly enhanced by stimulation with anti-Notch2 mAb but suppressed by anti-Notch1 mAb, while anti-Notch3 or anti-Notch4 mAb had no effect (Figure 4e). These results suggest that Notch2/Dll1 interaction promotes the differentiation of osteoclasts while Notch1/Jagged1 interaction suppresses it in both mice and humans.
**Preferential activation of Notch2 or Notch1 signaling by Dll1 or Jagged1 stimulation**
To address whether Notch1 preferentially interacts with Jagged1 and Notch2 preferentially interacts with Dll1, activation of Notch1 and Notch2 by Dll1-Fc or Jagged1-Fc stimulation during osteoclastogenesis was examined by immunoblotting of Notch1 and Notch2 intracellular domains (ICDs). As shown in Figure 5, Notch1 ICD was preferentially induced by the stimulation with Jagged1-Fc. On the other hand, Notch2 ICD was preferentially induced by the stimulation with Dll1-Fc. These results indicate the preferential interactions of Notch1/Jagged1 and Notch2/Dll1 during osteoclastogenesis.
**Blockade of Dll1 ameliorates arthritis and reduces osteoclasts in the affected joints**
Osteoclasts are known to play a pivotal role in the pathogenesis of bone erosion in RA, and our data indicated that osteoclastogenesis was dominantly supported by Dll1 among Notch ligands. In order to explore the role of Dll1 at the effector phase of arthritis, K/Bxn serum-induced arthritic mice, a mouse model for RA, were therapeutically treated with anti-mouse Dll1 mAb. K/Bxn T cell receptor-transgenic mice produce high-titer arthritogenic autoantibody and spontaneously develop erosive polyarthritis resembling RA [21]. Passive transfer of serum containing arthritogenic autoantibody from K/Bxn mice into normal mice also induces arthritis [23,24]. This serum-induced arthritis model makes it possible to focus on addressing the effector phase of arthritis so that it is induced without the induction phase, including complicated immune responses. Actually, arthritis score and hematoxylin and eosin staining demonstrated that anti-mouse Dll1 mAb treatment ameliorated K/Bxn serum-induced arthritis as compared to control hamster IgG treatment (Figure 6a). These arthritic mice developed joint deformity resembling RA, which can be determined visually. The incidence of joint deformity was decreased by the Dll1 blockade to 7.14% as compared to 57.1% of control (data not shown). TRAP immunohistochemistry showed that TRAP+ multinucleated osteoclasts in the affected joints were significantly reduced by the Dll1 blockade (Figure 6b).
**Blockade of Dll1 suppresses O VX-induced bone loss**
The reduction of osteoclasts in the affected joints of arthritic mice by the Dll1 blockade might be a result from the reduced inflammation. To investigate the direct effect of Dll1 blockade on osteoclastogenesis in vivo, the effect of anti-mouse Dll1 mAb on OVX-induced bone loss, a mouse model of osteoporosis, was evaluated. Trabecular and cortical bone mineral density (BMD) were markedly
reduced in OVX mice. The anti-mouse Dll1 mAb treatment significantly increased trabecular BMD of OVX mice as compared to the control hamster IgG treatment although it had no effect on sham-operated mice (Figure 7). Meanwhile, the Dll1 blockade was not affected on cortical BMD of OVX and sham-operated mice as compared to the control hamster IgG treatment (Figure 7). OVX-induced reduction of trabecular bone area, as well as trabecular bone volume/tissue volume (BV/TV), was also significantly prevented by the Dll1 blockade while OVX had no effect on cortical bone area (Figure 7). Histomorphometric parameters (osteoclast number/bone perimeter and osteoclast surface/bone surface)
revealed suppression of osteoclastogenesis by theDll1 blockade in OVX mice (Figure 7). These data indicate that blockade ofDll1 improves OVX-induced bone loss. Notably, the Jagged1 blockade did not show significant effect on these parameters of OVX and sham-operated mice (Figure 7).
Discussion
In this study, we demonstrated that mouse osteoclast precursors expressed multiple Notch receptors and ligands during osteoclastogenesis, but Notch2/Dll1 axis enhanced and Notch1/Jagged1 axis suppressed osteoclastogenesis selectively. A similar regulation of osteoclastogenesis by Notch2/Dll1 and Notch1/Jagged1 axes was also demonstrated in humans. Finally, we showed that blockade ofDll1 could suppress osteoclastogenesis in the affected joints in a murine arthritis model.
The inhibition of osteoclastogenesis by Dll1 blockade and the enhancement by stimulation with Dll1-Fc and anti-Notch2 mAb suggest that Dll1 promotes osteoclastogenesis via Notch2. On the other hand, the enhancement of osteoclastogenesis by Jagged1 blockade and the inhibition by stimulation with Jagged1-Fc and anti-Notch1 mAb suggest that Jagged1 suppresses osteoclastogenesis via Notch1. The preferential induction of Notch1 ICD by Jagged1-Fc stimulation and that of Notch2 ICD by Dll1-Fc stimulation supported this notion. Although we could not directly indicate the preferential Dll1/Notch2 and Jagged1/Notch1 interactions due to a lack of appropriate blocking mAbs against Notch1 and Notch2, such a preferential Notch2/Dll1 interaction also plays a key role in the development of marginal zone B cells in the spleen [25] and a preferential Notch1/Jagged1 interaction has been implicated in the maintenance of hematopoietic stem cells in the BM [26,27].
It has been known that interaction of Notch receptors with Dll versus Jagged ligands is affected by glycosylation of Notch extracellular domain by Fringe [28,29]. Therefore, a differential modification of Notch1 and Notch2 on osteoclast precursors by Fringe or a differential modification of Notch1 and Notch2 interactions with Jagged1 and Dll1 by Fringe might be responsible for the preferential Notch2/Dll1 and Notch1/Jagged1 interactions. Further studies are needed to address these possibilities.
The enhancement of osteoclastogenesis by stimulation with anti-Notch2 mAb and the suppression by anti-Notch1 mAb suggest a differential signaling via Notch1 versus Notch2. The inhibition of osteoclastogenesis by blockade of net Notch signaling by DAPT implies that the promotion via Notch2 is dominant over the suppression via Notch1 during osteoclastogenesis. The pro-osteoclastogenic function of Notch2 is consistent with a previous report demonstrating that silencing Notch2 with small hairpin RNA suppressed osteoclastogenesis and overexpression of Notch2 intracellular domain enhanced it [4]. The anti-osteoclastogenic function of Notch1 is also consistent with a previous report demonstrating that deletion of Notch1 in murine myeloid cells enhanced osteoclastogenesis and bone resorption [3]. Notch2 has been shown to act in conjunction with nuclear factor-kappaB, possibly by regulating the nuclear factor of activated T cells (NFAT)-c1 promoter during the terminal differentiation of osteoclasts [4]. In contrast, Jagged1-mediated Notch1 signaling could not cooperate with nuclear factor-kappaB but was likely to inhibit proliferation of osteoclast precursors [3].
Blockade of Dll1 suppressed the osteoclastogenesis not only in vitro but also in a murine arthritis model. Prevention of OVX-induced trabecular bone loss by the Dll1 blockade supported the effect in vivo. Notably, blockade of Dll1, as well as Jagged1, did not affect the parameters of bone strength and structure in the absence of any stimulation as shown in sham-operated mice. A high expression of Dll1 and Jagged1 as well as Notch1, Notch2 and Notch3 has been demonstrated in the synovium of RA patients [30,31]. We previously demonstrated that Dll1 was expressed on a part of the macrophage population and that inflammatory cytokines, such as tumor nuclear factor-alpha or interferon-gamma, induced the expression of Dll1 on macrophages [9]. Thus, Dll1 blockade may be a novel strategy to prevent bone erosion in RA patients by suppressing the inflammation-associated osteoclastogenesis. In addition, Dll1 has also been implicated in the development of pathogenic Th1 effector cells [32,33], while Jagged1 has been implicated in the development of Th2 or regulatory T cells [32,34,35]. Accordingly, we
Figure 6 Amelioration of arthritis and reduction of osteoclast numbers in the affected joints by blockade of Dll1. Mice with K/BxN serum-induced arthritis were treated with control hamster IgG (Ham) or HMD1-5 (D1). (a) Severity of arthritis was assessed by an arthritis score. Mean score ± SEM is shown (n = 7 mice per group). *, P < 0.05; **, P < 0.01 versus control hamster IgG. Representative hematoxylin and eosin staining of joints on Day 13 is shown. Original magnification ×100. Similar results were obtained in two independent experiments. (b) TRAP immunohistochemistry of joints. Number of TRAP+ MNCs in joints on Day 13 was measured. Shown are the mean number of TRAP+ MNCs relative to bone surface ± SEM of 10 joints from 5 mice per group. ***, P < 0.001 versus control hamster IgG. Representative staining is shown. Original magnification; ×100, ×400.
previously demonstrated that Dll1 blockade ameliorated experimental autoimmune encephalomyelitis while Jagged1 blockade exacerbated it [14]. Moreover, we recently demonstrated that Jagged1 blockade exacerbated collagen-induced arthritis [36]. Therefore, the blockade of Dll1/Notch2 axis and the enhancement of Jagged1/Notch1 axis may be beneficial for the treatment of RA through multiple mechanisms.
Conclusions
We demonstrate that Dll1 promotes osteoclastogenesis via Notch2, while Jagged1 suppresses osteoclastogenesis
via Notch1 in both mice and humans. Osteoclastogenesis is suppressed by inhibition of Notch signaling with a gamma-secretase inhibitor, implying that Notch2/Dll1-mediated enhancement is dominant. Notably, blockade of Dll1 with anti-Dll1 mAb in RA model mice ameliorates arthritis and reduces the number of osteoclasts in the affected joints. Prevention of OVX-induced trabecular bone loss by the Dll1 blockade supported the effect in osteoclastogenesis. We, therefore, propose that the differential regulation of osteoclastogenesis by Notch2/Dll1 and Notch1/Jagged1 axes could be a novel target for the treatment of RA to prevent bone erosion.
Abbreviations
BM: bone marrow; BMD: bone mineral density; BV/TV: bone volume/tissue volume; CT: computed tomography; Dll, Delta-like; FITC: Fluorescein isothiocyanate; HAT: hypoxanthine aminopterin thymidine; ICD: intracellular domain; M-CSF: macrophage-colony stimulating factor; MNCs: multinucleated cells; mAb: monoclonal antibody; NFAT: nuclear factor of activated T cells; OVX: ovariectomized; PBmono, peripheral blood monocytes; PBS: phosphate-buffered saline; RA: rheumatoid arthritis; RANKL: receptor activator of nuclear factor-kappaligand; rh: recombinant human; rm: recombinant mouse; RT-PCR: reverse transcription-polymerase chain reaction; TRAP: tartrate-resistant acid phosphatase.
Acknowledgements
Institut de Genetique et de Biologie Moleculaire et Cellulaire (IGBMC) in France kindly provided KRN transgenic mice as our source of K/BxN mouse serum. We thank Dr. Ushio (Juntendo University) for providing K/Bn mouse serum. This work was supported by Grants-In-Aid from the Ministry of Education, Culture, Sports, Science, and Technology, Japan.
Authors details
1Department of Immunology, Juntendo University School of Medicine, 2-1-1 Hongo, Bunkyo-ku, Tokyo, 113-8421, Japan. 2Division of Cell Biology, Biomedical Research Center, Juntendo University School of Medicine, 2-1-1 Hongo, Bunkyo-ku, Tokyo, 113-8421, Japan. 3Probiotics Research Laboratory, Juntendo University School of Medicine, 2-1-1 Hongo, Bunkyo-ku, Tokyo, 113-8421, Japan. 4Department of Immunology, Tokai University School of Medicine, 143 Shimokasuya, Isehara, Kanagawa, 259-1193, Japan. 5Department of Clinical and Experimental Hematology, Graduate School of Comprehensive Human Sciences, University of Tsukuba, 1-1-1 Tennnodai, Tsukuba, Ibaragi, 305-8573, Japan.
Authors’ contributions
CS carried out the experiments and the analysis of data, participated in the design of the study and drafted the manuscript. AK participated in the generation of monoclonal antibodies. NK participated in the generation of monoclonal antibodies. NY participated in the generation of monoab. HY conceived of the study, participated in its design and coordination, and edited the manuscript. All authors read and approved the final manuscript.
Competing interests
The authors declare that they have no competing interests.
Received: 5 April 2011 Revised: 27 January 2012 Accepted: 5 March 2012 Published: 5 March 2012
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doi:10.1186/ar3758
Cite this article as: Sekine et al.: Differential regulation of osteoclastogenesis by Notch2/Delta-like 1 and Notch1/Jagged1 axes. Arthritis Research & Therapy 2012, 14:R45.
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Polymerase chain reaction–based assays for the diagnosis of human brucellosis
Ying Wang¹, Zhanli Wang¹, Yaxian Zhang¹, Liyun Bai¹, Yue Zhao¹, Chunfang Liu¹, An Ma²* and Hui Yu¹*
Abstract
Polymerase chain reaction (PCR) is an in vitro technique for the nucleic acid amplification, which is commonly used to diagnose infectious diseases. The use of PCR for pathogens detection, genotyping and quantification has some advantages, such as high sensitivity, high specificity, reproducibility and technical ease. Brucellosis is a common zoonosis caused by Brucella spp., which still remains as a major health problem in many developing countries around the world. The direct culture and immunohistochemistry can be used for detecting infection with Brucella spp. However, PCR has the potential to address limitations of these methods. PCR are now one of the most useful assays for the diagnosis in human brucellosis. The aim of this review was to summarize the main PCR techniques and their applications for diagnosis and follow-up of patients with brucellosis. Moreover, advantages or limitation of the different PCR methods as well as the evaluation of PCR results for treatment and follow-up of human brucellosis were also discussed.
Keywords: Polymerase chain reaction techniques, Human brucellosis, Brucella spp, Molecular diagnosis
Introduction
Brucellosis is a widespread zoonotic disease caused by members of genus Brucella. Its prevalence is more than 10 per 100 000 population in some endemic countries [1]. Transmission of brucellosis from animals to humans occurs mainly through direct contact with infected animals, ingestion of raw dairy products of animal origin, or consumption of infected meat from domestic livestock [2]. Human brucellosis may lead to a variety of clinical presentations, such as fever, sweating, chills, headache, malaise, myalgia and even arthralgia of the large joints [3]. The presentations and phases of the disease may be acute, sub-acute, chronic, relapsed, active or inactive. Antibiotic treatment of human brucellosis often results in high treatment failure and relapse rates. Because the clinical presentation is non-specific, laboratory testing is required for confirmation.
Brucella species are gram-negative, facultative intracellular bacteria, which lack capsules, flagellae, endospores or native plasmids [4]. Currently, the genus Brucella consists of ten species: B. abortus, B. suis, B. ovis, B. melitensis, B. canis, B. neotomae, B. pinnipediais, B. cetti, B. microti and B. inopinata [5]. Four species of the genus Brucella are pathogenic for humans, namely B. melitensis, B. abortus, B. suis, and B. canis. B. melitensis is considered as the most pathogenic species, followed by B. suis, whereas B. abortus is the mildest type of brucellosis. Additionally, Brucella isolates from marine mammals can cause human infections. DNA-DNA hybridization studies demonstrated that there are high degrees of genetic similarity of Brucella spp. [6].
At present, there are various assays for diagnosis of human brucellosis such as standard microbiological tests for the isolation of Brucella spp. from blood, tissue specimens, body fluids and bone marrow, serological tests for the detection of anti-Brucella spp. antibodies and molecular methods for the detection of Brucella spp. DNA [7]. The most commonly used methods for detection and segregation of Brucella spp. were culture techniques and serological tests (standard agglutination tube test, anti-human globulin test, Rose-Bengal test, mercapta-based tests, enzyme-linked immunosorbent assay and brucellacapt) [8,9]. However, isolation of Brucella spp. is associated with a risk of laboratory-acquired infections and time consuming, and culture sampling sensitivity is often low, depending on the culture medium, Brucella species, disease stage and quantity of circulating bacteria. Serological tests seem to be more effective but can be unspecific due to cross reaction or subsensitive
reactions in samples from areas with a low or subclinical prevalence of brucellosis [10]. The principles and the main applications of these methods have been well reviewed elsewhere [11].
To ensure effective brucellosis disease prevention and control, a fast and accurate identification method is necessary. Polymerase chain reaction (PCR) technique offers a sensitive and specific way of detecting Brucella spp. from peripheral blood and other tissues [12]. The first brucellosis PCR-based test was introduced by Fekete et al. in 1990 [13]. They successfully amplified a 635 bp fragment of a 43 kDa outer membrane protein gene from B. abortus strain 19. Several studies have reported that PCR is a very useful tool for the rapid diagnosis of acute brucellosis and a good marker for the posttreatment follow-up and the early detection of relapses [14,15]. Moreover, many studies have developed PCR-based assays to differentiate 10 Brucella species [16-18]. Up to data, PCR assays have been used in diagnosis of both animal brucellosis and human brucellosis [19]. To our current knowledge, at least 200 reports have been published dealing with various methods based on PCR for laboratory diagnosis of human brucellosis. This review article highlights various PCR-based methods for the clinical diagnosis of human brucellosis. The principles, advantages or limitation of the different methods are also being discussed together with examples of applications taken from the literatures.
**Standard PCR**
For the diagnosis of human brucellosis, a PCR assay with one pair of primers was developed, which amplifies the target genomic sequence of Brucella species. Primer pairs include the primers for sequences encoding 16S rRNA [20,21], outer membrane protein (omp2a, omp2b) [22-24], 31-kDa immunogenic Brucella abortus protein (BCSP 31) [25,26], 16S-23S ribosomal DNA interspace region [27] and insertion sequence (IS711) [28,29]. Studies showed that standard PCR appeared to be a more sensitive technique than microbiological methods, not only for the diagnosis of a first episode of infection, but also for the early detection of relapses [30-32]. Some research groups also assessed the performances of standard PCR as diagnostic tools for human brucellosis with respect to conventional methods. Their results showed that standard PCR is a promising diagnostic tool for patients with clinical signs and symptoms, and negative serological results, allowing an accurate and early diagnosis of human brucellosis [33,34].
The standard PCR is simple and efficient. However, efficiency of this method is dependent on the specificity of the primers. Different primer pairs have previously been published for Brucella spp. detection, and only a few of them have been used in human samples. Baddour MM et al. compared sensitivity of 3 pairs of primers amplify 3 different fragments including a gene encoding BCSP 31 (B4/B5), a sequence 16S rRNA of B. abortus (F4/R2), and a gene encoding omp2 (JPF/JPR). The results showed that the sensitivity of the B4/B5 primer pair, JPF/JPR primer pair and F4/R2 primer pair was 98%, 88.4% and 53.1%, respectively [35]. Navarro et al. also compared PCR methods using these 3 pairs of primers as described above. Their results further indicated that the three primers assayed showed a difference in sensitivity by the presence of human genomic DNA [36]. Table 1 showed the efficiency of blood PCR assays using different primers.
In fact, blood samples are often used for the diagnosis of human brucellosis by the standard PCR [37]. Several factors were reported to affect PCR results in a blood specimen such as the high concentrations of leukocytes DNA and heme compounds [38]. Additionally, human genomic DNA affect the sensitivity of peripheral-blood PCR assay for the detection of Brucella DNA [36]. Zerva L et al. reported that serum samples should be used preferentially over whole blood for diagnosis of human brucellosis by PCR [39], but Mitka S et al. revealed that buffy coat and whole blood were the optimal specimens [14]. Moreover, sample volume used and efficient DNA extraction protocol are also the points of concern for the standard PCR to be used in routine laboratory testing for human brucellosis [34].
**Real time PCR**
Compared with the standard PCR, real-time PCR is a valuable technique in determining the quantification of nucleic acids in individual blood samples, as well as in automating the data. With the decreasing prices of real-time PCR thermocyclers and the reagents, many more people now have access to this technology to measure DNA copy number, mRNA expression levels and viral titers [40]. Recently, real-time PCR for the rapid detection and differentiation of Brucella species in clinical samples has recently been developed, targeting 16S-23S internal transcribed spacer region (ITS) and the genes coding omp25 and omp31 [41], BCSP 31 [42-44], and IS711 [45,46].
Real-time PCR seems to be highly reproducible, rapid, sensitive and specific. Additionally, this assay is easily standardized and minimises the risk of infection in laboratory workers. It is therefore a useful method for both the initial diagnosis of human brucellosis and the differentiation among inactive, seropositive, and active states. Queipo-Ortuño et al. reported that the sensitivities of a SYBR Green I LightCycler-based real-time PCR assay with serum samples was 93.3%, which is higher than 90% and 65% obtained by PCR-ELISA with whole blood samples and blood cultures, respectively [47]. This group further developed a LightCycler-based real-time PCR assay to
Table 1 Efficiency of blood PCR assays
| Primer | Sequence | Target gene | Sensitivity | Specificity | Positive predictive value | Negative predictive value | Reference |
|--------|----------|-------------|-------------|-------------|--------------------------|--------------------------|-----------|
| B4 | TGGCTCGGTGCGCAATATCAA | bcsP31 | 100 | 100 | 100 | 98 | 14 |
| B5 | CGGCTTCGCTTTCAGGCTG | omp2 | 98 | 100 | 100 | 96.1 | 14 |
| JPF | GCGTACAGGCTGCGACGCAA | omp2 | 99 | 100 | 100 | 98 | 14 |
| JPR | ACCAGCCATTGCCTCGGTA | bp26 | 98.5 | 100 | 100 | 97.1 | 14 |
| P1 | TGGAGTTCAGAAATGAAC | omp2 | 99 | 100 | 100 | 98 | 14 |
| P2 | GAGTCCGAAACGGACGC | omp2 | 99 | 100 | 100 | 98 | 14 |
| 26A | GCTGCTACATAACCCCGCTT | omp2 | 99 | 100 | 100 | 98 | 14 |
| 26B | GACGGTGACATTTCGCCGATA | omp2 | 99 | 100 | 100 | 98 | 14 |
| F4 | TCGAGCGCGCGCGAAAGGGG |omp2 | 99 | 100 | 100 | 98 | 14 |
| R2 | AACCATAGTGTCTCCACTAA |rRNA | 99 | 100 | 100 | 98 | 14 |
detect Brucella DNA in serum samples. This assay was found to be 91.9% sensitive and 95.4% specific when tested with 65 negative control samples and 62 serum samples from patients with active brucellosis [48].
Furthermore, Surucuoglu S et al. compared the TaqMan real time PCR technique to conventional methods using serum samples from patients with different clinical forms of brucellosis. The sensitivity, specificity, positive and negative predictive values of this PCR method were calculated as 88%, 100%, 100%, and 83%, respectively [49]. Alsayed Y et al. further investigated the potential of a combination of several tests (culture, ELISA and real-time PCR) to support the diagnosis in different clinical manifestations of brucellosis with peripheral blood samples. They found that if the agglutination test is negative, real-time PCR, and/or ELISA, and/or culture are recommended [50]. Moreover, using a panel of seven primer sets, Winchell JM et al. developed a real-time PCR method to differentiate members of the Brucella genus isolates, and has the potential to detect novel species [51]. Other studies also reported that real-time PCR allowed the rapid diagnosis of human brucellosis [52,53]. These results suggest that the high species specificity and selectivity of real-time PCR assay make it a useful tool for diagnosis of human brucellosis.
Just as standard PCR, efficiency of real-time PCR is also dependent on the specificity of the primers. Kattar MM et al. developed three real-time PCRs for diagnosis of human brucellosis at genus level with hybridization probes and primers from 16S-23S ITS, omp25 and omp31. Their results showed that real-time PCR with 16S-23S ITS primers and its probes was the most sensitive, indicating its potential for the diagnosis of human brucellosis in the clinical laboratory [41]. Additionally, a study analyzed the sensitivity and specificity of the 3 established real-time PCR methods using primers and TaqMan probes targeting the IS711, bcsP31 and per genes, and it also compared their efficiencies for the detection of the Brucella genus. The results showed that the IS711-based real-time PCR was the most sensitive, specific and efficient to detect Brucella spp. [54]. Table 2 showed that the sensitivity of the IS711 target was identical or 10 times higher that the sensitivity of the two other targets [54]. Moreover, the influences of other factors involved in the efficiency of the amplification process of real-time PCR for the diagnosis of human brucellosis were also reported, such as immunoglobulin G, which were extracted with the template DNA from serum samples [55].
Multiplex PCR
To overcome the inherent disadvantage of cost of the test, multiplex PCR has been developed to detect viral, bacterial, and/or other infectious agents. The advantages of using multiplex PCR technique are that it minimizes expense and recognizes many pathogens at once [56]. These advances have resulted in the appearance of numerous publications regarding the application of multiplex PCR in the diagnosis of human brucellosis.
Lübeck PS et al. developed and applied a multiplex PCR assay for Brucella diagnostics based on the peroxidase synthetase gene in 2003 [57]. El Kholy AA et al. also established a multiplex PCR technique using 2 sets of primers (B4/B5 and JPF/JPR) for the diagnosis of active human brucellosis in Egypt [58]. They found that this technique showed high sensitivity, specificity and accuracy, and could serve as important alternatives to culture methods for diagnosis of human brucellosis. Additionally, a multiplex PCR assay can be used to simultaneously detect and type Brucella species present in clinical samples. In 2007, Imaoka K et al. developed a multiplex PCR procedure to identify four major species of the genus Brucella in one reaction tube. Four pairs of primers targeting bcsP31, omp2b, omp2a and omp31 genes were used. The specific amplification for each Brucella spp. examined in this study was achieved with these primers [59]. Other groups also reported robust and rapid multiplex PCR assays, which
were able to identify and differentiate currently recognised *Brucella* species in a single test of less than an hour and a half [60-65]. The timely and accurate information provided by this assay would be valuable to trace sources of infection and may help in rapid diagnosis of human brucellosis. Furthermore, several multiplex PCRs have been described for identification of *Brucella* partly at the biovar level using different primer combinations. A 19-primer multiplex PCR specifically identified *B. neotomae*, *B. pinnipedialis*, *B. ceti*, and *B. microti* simultaneously. Also, this method was able to differentiate *B. abortus* biovars 1, 2, 4 from biovars 3, 5, 6, 9 [66]. A novel multiplex PCR assay for the rapid detection of *Brucella* genus at the species and at the biovar level has been described. The assay was shown to be ideal method for detection of *B. suis* at the biovar level and the differentiation of *B. suis*, *B. canis* and *B. microti* [67]. It is well knows that only a few biovars of *Brucella* species are pathogenic for humans, hence rapid identification of *Brucella* genus at the biovar level is necessary. Moreover, several multiplex PCRs have been described for the simultaneous detection of *Mycobacterium tuberculosis* (*M. tuberculosis*) complex and *Brucella* spp., targeting the IS711, bscp31 and omp2a genes for the identification of *Brucella* spp. and the IS6110, senX3-regX3 and cfp31 genes for the detection of the *M. tuberculosis* complex [68-70]. The results showed that this technique was a practical approach for the differential diagnosis between extrapulmonary tuberculosis and complicated brucellosis.
The primer pairs have substantial effect on the multiplex PCR efficiency. The presence of more than one primer pair in the multiplex PCR increases risk for primer-dimers. Thus, nonspecific products may be obtained [71]. Ideally, all the primer pairs in a multiplex PCR should not only eliminate non-specific PCR products, but also enable similar amplification efficiencies for their respective target. Therefore, the multiplex PCR requires laborious optimization [72].
**Nested and semi-nested PCR**
The nested PCR means that two different pairs of PCR primers are used for a single locus. The first pair is an amplified sequence. The second pair of primers (nested primers) is complementary to the sequence amplified by the first pair primers and produces a second PCR product that will be shorter than the first one [73]. Same as nested, semi-nested PCR has two different pairs of PCR primers, but the second pair of primers has one primer identical to the first pair [74]. The nested PCR and semi-nested PCR amplify only the specific sequences sought and are more specific than the standard PCR. Recently, nested PCR and semi-nested PCR assays were developed for identifying *Brucella* in samples of human blood and then to explore their clinical practice for the diagnosis of human brucellosis.
Two nested PCR assays have been applied for the diagnosis of human brucellosis in Kuwait. Two pairs of primers derived from IS711 were used. The results showed that the use of nested primers gave increased sensitivity and higher specificity providing a better molecular diagnostic approach for human brucellosis [75,76]. Lin GZ *et al.* also reported a nested PCR for the laboratory diagnosis of human brucellosis [77]. Moreover, a semi-nested PCR for diagnosis of human brucellosis were developed and evaluated with whole blood. The primers were from IS6501 and bscp31 genes [78]. We are now performing nested PCR combined with real-time PCR approach for the diagnosis of human brucellosis with the primers from bscp31 and VirB11 genes. *B. abortus* and *B. melitensis* can be rapidly identified. The results have not been reported. According to the results, this assay was sensitive and could be used for the diagnosis of human brucellosis in the clinical laboratory.
However, the nested PCR and semi-nested PCR have some disadvantages. For example, the assays increased risk of primer dimerization and cross-react of PCR products. In addition, the nested PCR or semi-nested PCR will only identify a set of *Brucella* bacteria, not a single specific species.
**Other PCR-based assays**
In addition to standard PCR and its derivatives (nested and semi-nested, multiplex and real-time PCR), there are other significant PCR-based assays have been developed in the last years. Fekete *et al.* developed the arbitrarily primed polymerase chain reaction (AP-PCR) to distinguish 25 different *Brucella* strains according to the banding patterns of their amplified DNA on agarose gels. The degrees of relatedness among these strains of the genus *Brucella*
### Table 2 Comparison of conventional and real-time PCR assays lower limit of detection (fg)
| *Brucella* | IS711 copy number | Conventional PCR | Real-time PCR |
|-----------|------------------|------------------|--------------|
| | | IS711 | bscp31 | per | IS711 | bscp31 | per |
| B. canis RM/66 | 6 | 100 | 1000 | 1000 | 2 | 20 | 20 |
| B. abortus 544 | 7 | 100 | 1000 | 1000 | 2 | 2 | 2 |
| B. melitensis 16 M | 7 | 1000 | 1000 | 1000 | 2 | 20 | 20 |
| B. ovis 63/290 | 38 | 100 | 1000 | 1000 | 0.2 | 2 | 2 |
(This table was taken from ref. [54]).
were revealed through the calculated similarity coefficients [79]. In 1994, AMOS PCR assays were used to identify vaccine strains from strains that cause infections based on the number and sizes of products amplified by PCR [80,81]. In 1996, Tcherneva et al. reported the REP-PCR as a promising fingerprinting method for the evaluation of Brucella outbreak [82]. Also, various PCR-RFLPs display sufficient polymorphism to distinguish Brucella species and biovars, and can serve as tools for diagnostic, epidemiological, taxonomic, and evolutionary studies [83]. In addition, Multiple-locus variable-number tandem-repeat assays (MLVA) were used to study the molecular epidemiological characterization of Brucella isolates from humans [84]. PCR methods have been used successfully to identify all Brucella species and most of the biovars, offering an improvement over conventional molecular genotyping methods [85,86]. Furthermore, Bruce-ladder multiplex PCR assay was evaluated using 625 Brucella strains. This method can differentiate in a single step all of the classical Brucella species, including strains from marine mammals and the S19, RB51, and Rev.1 vaccine strains [67]. Recently, the microfluidic Lab-on-Chip was also proposed as a rapid and specific detection method for the characterization of Brucella isolates [87,88].
PCR-based assays were shown to be valuable tools for detecting Brucella strains. PCR approaches have several advantages for the diagnosis of human brucellosis, such as speed, safety, high sensitivity and specificity [89]. This technique might be considered complementary to the traditional methods and followed up by serology and/or culture [90]. However, its disadvantages such as the higher cost, issues of quality control and quality assurance must be further evaluated on clinical samples before PCR can be used in routine laboratory testing for human brucellosis [9,91].
Evaluation of PCR results for treatment and follow-up of patients
Most patients with brucellosis suffer a relapse after receiving the duration and combination of antibiotic therapy. Therefore, it is necessary to evaluate the progress towards therapeutic failure or relapse [50]. The conventional methods are difficult for the diagnosis of these relapses. Several previous studies reported the applications of PCR for the diagnosis of post treatment follow-up and relapses. Queipo-Ortuño MI et al. examined the usefulness of PCR assay in post treatment follow-up and relapse of patients with brucellosis. They showed positive PCR tests for the relapse as well as negative once the relapse treatment was completed [26,30]. Nimri LF obtained the positive PCR results in the relapse cases, indicating that the assay could be a useful tool to confirm a relapse in cases of a treated brucellosis [21]. Navarro E et al. also developed a real-time PCR assay to monitor the evolution of Brucella melitensis DNA load in blood during therapy and post-therapy follow-up in patients with brucellosis. This assay showed 100% analytical sensitivity for both initial infections and relapses [92]. Moreover, Mitka S et al. showed that PCR assays were negative in all follow-up samples from patients who had completed a successful treatment and were positive in all follow-up samples from patients who had relapses in the first year after therapy, including the times of the relapses [14]. However, dead phagocytosed bacteria may present in the circulating mononuclear cells in certain patients who have concluded successful treatment. Because PCR cannot differentiate between DNA from live and dead organisms, therefore, the ability to amplify the DNA of Brucella DNA from dead or phagocytized cells should be considered when interpreting the results.
Conclusions
At present, PCR-based assays could allow rapid and more-sensitive identification of Brucella genus at the species and at the biovar level, compared with traditional techniques. The implementation of PCR-based assays into the clinical setting will likely improve therapeutic outcomes. However, PCR protocols lack standardization. As new methods for Brucella spp. identification and typing, PCR tests are still being developed and still await validation for use with clinical samples. For instance, the sensitivity and specificity of most PCR-based methods is associated with inhibitors in DNA samples such as EDTA, RNase or DNase, heme, heparin, phenol, and probably a host of other reagents. There is still a great deal of work required for standardization before any of these methods may be used in routine laboratory testing for brucellosis. Future studies should focus on the integration of these techniques into clinical decision making.
Competing interests
The authors declare no conflicts of interest.
Authors’ contributions
HY have made substantial contributions to conception, design and interpretation of data; YW, ZW, YZ, LB, YZ, CL and AM have been involved in drafting the manuscript or revising it critically for important intellectual content. All authors read and approved the final manuscript.
Acknowledgments
This work was in part by grants from the National Natural Science Foundation of China (No.81360242), Natural Science Foundation of Inner Mongolia Autonomous Region of China (No. 2014Q04, No. 2014MS0808) and Scientific Research Fund in Universities of Inner Mongolia Autonomous Region (No. NJZY14528).
Received: 24 March 2014 Accepted: 9 July 2014
Published: 1 August 2014
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doi:10.1186/s12941-014-0031-7
Cite this article as: Wang et al.: Polymerase chain reaction-based assays for the diagnosis of human brucellosis. Annals of Clinical Microbiology and Antimicrobials 2014 13:31.
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Hospitalization of Deliveries: the Change of Place of Birth in Denmark and Sweden from the Late Nineteenth Century to 1970
SIGNILD VALLGÅRDA*
Introduction
Sweden was one of the first countries in western Europe where deliveries in hospitals and clinics replaced home deliveries. Denmark, her close neighbour, was one of the last. This paper attempts to identify various factors involved in this change and especially to find out why it occurred so much earlier in Sweden.
At the end of the nineteenth century practically all Swedish and Danish women gave birth at home. By 1945, however, this was no longer the case. In Sweden only 27 per cent of women still gave birth at home compared with 63 per cent of Danish women. In Sweden the great change from home to hospital births took place in the 1920s and 1930s, in Denmark in the 1950s and 1960s (see Figure 1). In most other European countries the change occurred between these years: in England and Wales 25 per cent of births took place in hospital in 1938 1 and 66 per cent in 1954, 2 in Norway 74 per cent of children were born in hospital in 1951, 3 and in Finland 58 per cent in 1950; 4 only in the Netherlands were home births still common at 35 per cent in 1978. 5 In the eighteenth century in both Denmark and Sweden one maternity hospital was established as a political means to promote population growth. These hospitals were founded to provide unmarried mothers with a place of delivery, to prevent infanticide, and also to facilitate the education of midwives and doctors in midwifery, with the aim of reducing infant mortality. 6 During the nineteenth century six more maternity hospitals or departments in existing hospitals were
*Dr Signild Vallgård, Department of Social Medicine, University of Copenhagen, Blegdamsvej 3, 2200 Copenhagen N, Denmark.
Det Kommunale Momsfond has supported my study financially. Several people have made helpful criticisms of, and comments on, this paper, not least the referees of Medical History.
1 Irvine Loudon, Death in childbirth: an international study of maternal care and maternal mortality 1800–1950, Oxford, Clarendon Press, 1992, p. 231.
2 Alisoh MacFarlane, Miranda Mugford, Birth Counts. Statistics of pregnancy and childbirth, London, HMSO, 1984, p. 237.
3 Ida Blom, "Den huaade Dyst" Fødsler og fødsels hjælp gjennom 150 år, Oslo, Cappelen, 1998, p. 224.
4 Elina Hemminki, 'Obstetric practices in Finland 1950–1980', Medical Care, 1983, 21: 1131–43, on p. 1132.
5 P E Treffers, R Laan, 'Regional perinatal mortality rates and regional hospitalization at delivery in the Netherlands', Br. J. Obstet. Gynaec., 1986, 93: 690–3.
6 Confirmation paa Dronning Juliane Maries Gavebrev af 29. Jan. 1785, hvorved en Gaard og 25 vestindiske Aktier skienes til Fødselsstiftelsen; Gordon Norrie, 'Jordemodervesnetus Udvikling i Danmark', Tidsskrift for danske Jordemødre, 1895, 5: 143; Birger Lundqvist, 'Det svenska barnmorskeväsendets historia', in B Lundqvist (ed.), Svenska barnmorskor, Stockholm, Svenska yrkesförlaget, 1940, p. 50ff.
Signild Vallgårda
Figure 1: Home confinements as a proportion of all births in Denmark and Sweden.
Sources: Medicinalberetning I, Copenhagen, Sudhedsstyrelsen, annual publication; Förlossningsvårdens organisation, Socialstyrelsen redovisar no. 35, Stockholm, Socialstyrelsen, 1973.
created in Sweden, with a total of 216 beds and 4 to 5 per cent of the deliveries in 1900. In Denmark a second maternity hospital was established only as late as 1910. From the beginning of the twentieth century maternity hospitals and clinics were founded in both countries, but in greater numbers in Sweden. During this century, women have given birth in a variety of places: their own homes, hospitals, or maternity homes. The latter were either private, mainly for the better off, or were owned by municipalities, or charity organizations such as the Red Cross, for women of the poorer classes. The reasons for creating and using these establishments varied, depending on their type and the social class of the women utilizing them. Both types paved the way for hospital deliveries throughout the population. The use of these reached a peak in 1934 when 20 per cent of Swedish deliveries occurred in such smaller maternity institutions. By 1943 the figure had declined to 11 per cent. For Denmark there are no statistics available until 1950, when 14
---
7 Betänkande angående moderkapsskydd, Statens Offentliga Utredningar (hereafter SOU) 1929:28, Stockholm, Socialdepartementet, 1929.
8 Betänkande angående förlossningsvården och barnmorskeväsendet samt förebyggande mödra- och barnavård avgivet av befolkningskommissionen, SOU 1936:12, Stockholm, Socialdepartementet, 1936, p. 105; Betänkande om förlossningsvården avgivet af 1941 års befolkningskommission, SOU 1945:50, Stockholm, Socialdepartementet, p. 167; Betænkning II afgivet af det af Indenrigsministeriet nedsatte udvalg vedrørende fødselshjælp mv, Betænkning 160, Copenhagen, Indenrigsministeriet, 1956.
per cent of children were born in maternity homes; in 1970 the number was 16 per cent.
It is curious that the two countries differ so much as regards place of birth since, in general, they have very similar patterns of political and social development. They both have long traditions of democracy and public responsibility for social welfare, health and education. From the end of the nineteenth century onwards the labour unions and the Social Democratic parties have had an increasing influence, although larger in Sweden than in Denmark. The state and municipalities provided schools, relief for the poor, and health care to a varying extent, at least from the eighteenth century. Charity played a minor role in both countries. There are, however, differences. The degree of urbanization was higher in Denmark at the turn of the century (see Figure 2), but in Sweden urbanization and industrialization progressed very rapidly during the first decades of the nineteenth century. The change in Sweden was more radical in another sense as well. In Denmark the dominant form of industrialization mainly involved the establishment of small-scale industries. There was much similarity between farms and small industries in the way work was organized and in relations between workers and employers, but in Sweden heavy industry and large plants were more common. These created new communities and new types of social relations. Thus the social change in Sweden from agriculture to industry, and from rural to urban life, was faster and more fundamental than in Denmark. In spite
Figure 2: Proportion of the population living from farming.
Sources: Historisk statistik för Sverige, vol. 1, Stockholm, Statistiska Centralbyrån, 1969; Hans Chr. Johansen, Danmarks historie, vol. 9, Danish historical statistics 1814–1980, Copenhagen, Gyldendal, 1985.
of these differences, hospitals were built and expanded almost simultaneously, see below, but not maternity hospitals, as shown above.
Methods and Materials
When a specific change in health care is studied, many factors must be considered. These include changes in population and in society at large such as urbanization and industrialization, which are the results of individuals’ actions, and at the same time set the conditions for social behaviour. The ideas and actions of different groups involved in the health care process also need to be taken into account. In this study the relevant groups are: pregnant women, since their beliefs and wishes are decisive for the places where they give birth, at least when they have a choice; the midwives, who play a role, albeit not a very influential one, in advising pregnant women whether hospital deliveries should be favoured or not, and also through writing in their own journal and sometimes in the newspapers; and the doctors, who as “experts” tend to influence politicians, also write in journals and newspapers and, not least, are used as advisors and as members of different committees set up to deal with maternity care. The political administrative tradition in Sweden involves much more committee work, and many more reports and white papers are written and published than in Denmark. That type of source material is thus much more abundant in Sweden. Through their services, doctors also influence women. In addition, the ideas of politicians and bureaucrats must be studied. These last two groups, in particular, influence the societal framework, including the health care system, through finance and legal restrictions. They may well have different ideas and motives for trying to achieve a common goal, such as hospitalization of deliveries, or the opposite. Before analysing these ideas, I will look at the organization of health care in the two countries.
Organization and Resources of the Health Care Sector
To what extent can organizational differences in the health care sectors in the two countries explain the differences in the choice of place of delivery? Hospitals have been the responsibility of the counties in Denmark since the eighteenth century and in Sweden since 1860. Very few private hospitals existed in either country. The degree of centralization has been said to have influenced the degree of hospitalization of deliveries, since obstetricians exerted more influence over the state than over decentralized organizations.9 In this respect the two countries do not differ. The degree of centralization of health care decisions has not been a factor influencing the rate of hospitalization in the two countries.
Health insurance schemes existed in both countries, although coverage was more extensive in Denmark until the 1950s.10 In 1900 12.4 per cent of Danes were covered by health insurance schemes, as compared with 5.1 per cent of the Swedish population. Thirty years later the coverage was 46.5 per cent in Denmark and only 16.6 per cent in
9 A Torres, M R Reich, ‘The shift from home to institutional childbirth: a comparative study of the United Kingdom and the Netherlands’, Int. J. Health Stud., 1989, 19: 405–15.
10 Hirobumi Ito, Health insurance policy development in Denmark and Sweden 1860–1950, Copenhagen, Joint Center for Studies of Health Care Programs, 1978.
The Change of Place of Birth in Denmark and Sweden
Sweden. Until the mid-1930s state subsidies constituted a much larger part of the Danish health insurance schemes' total income than the Swedish ones, and a high proportion of the Danish health insurance schemes' expenditure was used on medical treatment, while in Sweden, until the 1940s, almost all expenditure went on cash benefits. Thus the Danish health insurance scheme was more developed and had a greater impact on the expansion of the health care system than the Swedish during the first half of the twentieth century. The health insurance scheme could provide some help in connection with births, but in neither country was it compulsory. The extent of this support has not yet been investigated.
Number and Availability of Midwives
For most women, a prerequisite for delivery at home was that assistance would be available. The number of trained midwives increased in both countries during the nineteenth century, although faster in Denmark than in Sweden. In Denmark, a system of district midwives financed by the municipalities was introduced in 1810, and it was well established by the turn of the century. The district midwife received a salary, heating and free housing for assisting the parturient women in her district, treating the poor free of charge and others according to their income. In 1791 the fees were fixed by the state: a farmer should pay 3 Marks, a peasant 2 Marks and a crofter 1 Mark. The first instructions for midwives were given in the church ordinance of 1539, which laid down that they should assist poor and rich alike. A later ordinance of 1685 declared that they should receive what was fair for their services and help the poor for the sake of God. In 1714 it was stated that midwives were not allowed to leave a poor woman “for the sake of filthy profit”. Solidarity with the poor thus had a long tradition in Denmark; until 1810, however, midwives were the only ones to pay a price for this solidarity. The district midwife system was abolished in 1973. In Sweden municipalities were requested by the state to engage midwives and by the end of the nineteenth century most of them had done so. Midwives were paid by the women they delivered according to regulated tariffs. In 1908 the municipalities were obliged to pay a minimum salary to midwives. During the 1920s the financial situation of midwives improved, and in 1937 an act was passed making all birth attendance free of charge, and all midwives were paid a fixed salary. In 1900 almost all Danish women giving birth were assisted by a trained midwife, while only 78 per cent of Swedish women were. Consequently, about 20 per cent of Swedish women had no trained assistance from either a midwife or a doctor, who hardly ever assisted at births without a midwife being present.
11 Hirobumi Ito, ‘Health insurance policy development in Denmark and Sweden 1860–1950’, Social Sci. Med., 1979, 13C: 143–60.
12 Besætnande, op. cit., note 7 above; H C Hansen, Historien om sygekasserne, Ålborg, De samvirkende centralforeninger af sygekasser i Danmark, 1974, p. 86.
13 Reglemente for Giordemodersvæsenets Indretning og Bestyrelse i begge Riger, Kiøbenhavns undtagen, 21 Nov. 1810; Rescript ang. at naar nogen herefter skulde wilde paatage sig Giordemødres forretnings i Kiøbenhavns og Christianshavns, 30 March 1714.
14 Ulf Högberg, Svagårens barn, Stockholm, Liber förlag, 1983, p. 133; Anders Brändström, De kärlekslösa modrorna, Umeå, Almqvist & Wiksell, 1984, p. 59; Medicinalberetning for Kongeriget Danmark, Copenhagen, Sundhedsstyrelsen, annual publication, p. 170; Christina Romlid, ‘The Swedish midwife system and the instrumental authorization of midwives’, in Hilary Marland and Anne Marie Rafferty (eds), What is to be done with the midwife? Midwives and society 1850–1990s, London, Routledge, forthcoming.
Signild Vallgårda
Since the end of the nineteenth century the number of midwives in Denmark has remained around 1,000 (see Figure 3), but the number of deliveries per midwife has differed widely (see Figure 4). In 1900 the annual number of deliveries per midwife in Denmark was 69, in 1925: 60 and in 1950: 100. In Sweden the numbers were in 1900: 49, in 1925: 36 and in 1950: 74. There are several reasons for these differences. The lower number of deliveries per midwife in Sweden could probably be partly explained by the fact that the country was so sparsely populated, and the very low number in 1925 was due to the sharp decline in fertility. The number of midwives started to fall towards the end of the 1920s. The higher number of deliveries per midwife in Denmark in 1950 could be ascribed to different tasks being undertaken by midwives in the two countries. In spite of the fact that a midwife at a hospital could manage more deliveries than a midwife assisting at home deliveries, Swedish hospital midwives were also supposed to care for lying-in women, while in Danish hospitals these women were cared for by nurses. At home births it was the task of the midwife to care for the lying-in woman and the child. However in Denmark from the Second World War, home nurses provided care for lying-in women, and they were paid for by either the women or the health insurance scheme. In 1972 (when statistics became available) lying-in women received an average of nine visits from a nurse. A system with maternity home care assistants like the one in the Netherlands never
Figure 3: Number of trained midwives in Denmark and Sweden.
Sources: Medicinalberetning for Kongeriget Danmark, Copenhagen, Sundhedsstyrelsen, annual publication; Allmän hälso–och sjukvård. Medicinalstyrelsen, Stockholm, Socialstyrelsen, annual publication.
15 Medicinalberetning, op. cit., note 14 above.
The Change of Place of Birth in Denmark and Sweden
Figure 4: Number of deliveries per midwife in Denmark and Sweden.
Sources: Medicinalberetning for Kongeriget Danmark, Copenhagen, Sundhedsstyrelsen, annual publication; Allmän hälso-och sjukvård. Medicinalstyrelsen, Stockholm, Socialstyrelsen, annual publication.
developed in either Denmark or Sweden. When it was a question of actual birth attendance midwives were present in both countries and they were responsible for all normal deliveries and gave assistance in the case of complicated ones, irrespective of whether the births took place in hospitals or in private homes. Doctors were summoned when complications arose, or threatened to arise, and when pain relief was required. Midwives in both countries participated in prenatal care.
In Sweden the number of midwives fell from about 3,000 in 1910 to about 1,500 in 1950, but rose again in the 1960s (see Figure 3). There are no reliable data on the problems of receiving midwife assistance at home, but the fear of not being able to receive it may have been an important factor which caused women to go to hospital instead. In Sweden the number of midwife districts was reduced from 2,000 in 1924 to 1,100 in
16 E R van Teilingen, ‘The profession of maternity home care assistant and its significance for the Dutch midwifery profession’, Int. J. nurs. Stud., 1990, 27: 355–66.
17 Allmän hälso och sjukvård, Stockholm, Socialstyrelsen, annual publication. The ratio between the midwives and the total population in Sweden was approximately the same as in the Netherlands. In 1895 the ratio was 1:5338 in Sweden, 1:5189 in Denmark, and 1:5793 in the Netherlands, see Hilary Marland, ‘The guardians of normal birth: the debate on the standard and status of the midwife in the Netherlands around 1900’, in Eva Abraham-van der Mark (ed.), Successful home birth and midwifery, Westport, Connecticut, Borgni & Garvey, 1993, p. 30.
179
1939, thus the area each midwife covered was increased. This is the question of the chicken and the egg. Did the number of district midwives decline because women went to hospital to give birth, or did women go to hospital because of a shortage of midwives? The reasons probably differed from place to place. In any case the total number of deliveries fell before the number of midwives fell, which indicates that it was rather a lack of work for midwives than a scarcity of the midwives themselves which was the first step in the change. The sharp decline in the number of midwives in Sweden during the first decades of this century may have contributed in part to the increase in hospital deliveries. The fact that the provision of midwives was more stable in Denmark and that they were well established throughout the country at an earlier time may be one reason why Danish women continued to give birth at home.
The geographical differences between Denmark and Sweden are huge, Sweden having large sparsely populated areas. If this factor has influenced the place of birth, one might imagine that women in these areas went to hospital to be sure of receiving help. If so, one would expect home deliveries to be abandoned first in the very sparsely populated areas in the north of Sweden. The opposite, however, is the case. Home deliveries persisted longest in the northern parts of Sweden, while the cities saw an early move towards hospital deliveries (see Figure 5). Geographical differences between the two countries are thus not valid as an explanation of the differences in the health care system, at least not in this case. The availability of hospitals is of course a crucial factor, and distances to hospitals were greatest in the north. In Denmark, however, most women lived comparatively close to hospitals without using them in the case of childbirth, and the most urbanized area, Copenhagen and its suburbs, had a high percentage of hospital deliveries at an early point in time (see Figure 6) parallel to the Swedish development. Figures are not available from Denmark before 1949.
Midwives’ Training and Competence
It has been suggested that the existence of well educated and independent professional midwives might favour the continuation of home deliveries. In the following section, I will examine the development of the training, competence and number of midwives in the two countries.
The teaching of midwifery, organized and financed by the central state, began in the late eighteenth century, and the legal status of trained midwives was the same in both
---
18 Betänkande med utredning och förslag angående barmmorskeutredning, 1944 års barmmorskeutredning, SOU 1942:17, Stockholm, Socialstyrelsen, 1942, p. 13.
19 Förlössningsvården organisation, Socialstyrelsen redovisar, no. 35, Stockholm, Socialstyrelsen, 1973.
20 The Swedish development in hospital deliveries is almost parallel to the development in the USA. See Loudon, op. cit., note 1 above, pp. 274–5, and Judith Waltzer Leavitt, Brought to bed: childbearing in America, 1750–1950, New York, Oxford University Press, 1986. There are some similarities between the USA and Sweden - both are sparsely populated countries, and both had a high proportion of the population living in the countryside during the first decades of the twentieth century. But I believe that the parallel change occurred because both countries strove to modernize society, believing in the possibilities of science to guide them, and because the changes in social life during this century were rapid and radical (see below, p. 189 ff).
21 Marland, op. cit., note 17 above, p. 23.
The Change of Place of Birth in Denmark and Sweden
Figure 5: Home deliveries as a percentage of all deliveries in Sweden in 1934.
Source: Betänkande angående förlossningsvården och barnmorskeväsendet samt förebyggande mödra-och barnvård, SOU 1936:12, Stockholm, Socialdepartementet, 1936.
Figure 6: Home deliveries as a percentage of all deliveries in Denmark in 1949.
Source: Medicinalberetning for Kongeriget Danmark 1949, Copenhagen, Sudhedsstyrelsen, 1951.
The Change of Place of Birth in Denmark and Sweden
countries. The first maternity hospitals were established at that time with the education of midwives as one of their central tasks. Some of the pupils attended the schools free of charge, others were paid for by the municipalities. Much of the training was practical. The theoretical education was given mainly by obstetricians. It was the duty of a trained midwife to be available to attend all deliveries; she would attend complicated deliveries with a doctor. Swedish midwives had a broader range of skills than their Danish colleagues. From 1829 they were entitled to use instruments, for example, forceps and instruments for embryotomy, provided they had passed a special examination. The right to use sharp instruments was abolished in 1919, but Swedish midwives sometimes still use the vacuum extractor. In the year 1900 almost 80 per cent of midwives had received such training. The training period for midwives was gradually extended. In Denmark it rose from six months in the late eighteenth century, to one year in 1895, two in 1927 and three in 1941. In Sweden a midwifery course lasted only three months at the beginning, this was extended in 1819 to six months, and in 1840 to nine months plus three months of instrument training. From 1921 the training lasted two years and in the 1940s the Swedish system changed so that midwifery training became a superstructure of nursing education. Neither in Sweden nor in Denmark did midwives experience real competition from general practitioners when assisting normal deliveries, as was the case in Great Britain and in the Netherlands. When in 1884, Leopold Meyer, a leading Danish obstetrician, suggested that doctors should attend all deliveries, the proposal was met with fierce resistance from both his colleagues and from midwives. Many doctors in both
22 Lundqvist, op. cit., note 6 above; Birger Lundqvist, 'Barmorskeväsendet', in W Kock (ed.), Medicinalväsendet i Sverige 1813–1962, Stockholm, Nordiska bokhandels förlag, 1963, p. 645ff; Karin Johannisson, Medicins öga. Sjukdom, medicin och samhälle, Stockholm, Norstedts förlag, 1990; Roger Qvarsehl, Vårdens idehistoria, Stockholm, Carlssons, 1991; Signild Vangarda, Sjukhus och fattigpolitik. Ett bidrag till de danska sjukhusens historia 1730–1880, Copenhagen, Fadis förlag, 1985. In the Netherlands clinical schools were set up in the 1820s, but they had few pupils. It was not until 1861 that a state school was started in Amsterdam. In England the statutory recognition of midwives was established in 1902. Marland, op. cit., note 17 above, p. 27ff; Loudon, op. cit., note 1 above, p. 207; O Moscucci, The science of women. Gynaecology and gender in England 1800–1929, Cambridge University Press, 1993, p. 73.
23 Cancelli Placat, Copenhagen, 29 Apr. 1791; Reglemente for Jorde-Gummine, Stockholm, 14 Oct. 1777. The Swedish decision was overturned the year after with reference to the freedom of citizens. In 1819 it was put forward again. Betänkande om förlösningssvärden, op. cit., note 8 above, pp. 7–8. In Norway, on the other hand, midwives and doctors should be called in only if the delivery became complicated, provided the distance or another reason did not make it impossible. 'Norsk lag om jordemødre. 10/12 1898', in Betankning om Jordemodvæsenet, Copenhagen, Medicinsk kommissionen, 1913; Rescript ang. naar nogen herefter skalde vilde paatte sig, Giordemødres forretning i København og Christianshavn, Copenhagen, 30 March 1714; Instruks for samtlige til Praxis berettigede Jordemødre, Copenhagen, 28 Sept. 1877 and 25 Nov. 1896; Reglemente for Jorde-Gummine, Stockholm, 14 Oct. 1777; Utdrag af Reglemente for Barmmorskor, Stockholm, 25 Aug. 1819.
24 Lundqvist, op. cit., note 22 above, pp. 697. 25 Helen Cliff, Jordemodertliv, Copenhagen, Borgen, 1992, p. 27; Lundqvist, op. cit., note 22 above, pp. 651.
26 Marland, op. cit., note 17 above, pp. 30; Loudon, op. cit., note 1 above, pp. 206–23; Moscucci, op. cit., note 22 above, pp. 65–74.
27 Leopold Meyer, 'Om en Udvildelse af Lægens Virksomhed som Fødselsshjælper', Hospitalstidende, 1884, 3Rk, Bd II, p. 146; S Meyer, '1 Anledning af Dr. med. Leopold Meyer's Artikkel: Om en Udvildelse af Lægens Virksomhed som Fødselsshjælper', Hospitalstidende, 1884, 3Rk, Bd II, p. 206; I Wegener, 'Nogle Betragtninger i Anledning af Dr. L. Meyers Artikkel', Hospitalstidende, 1884, 3Rk, Bd II, p. 317. See also, Anne Løkke, 'The antiseptic transformation of Danish midwives 1860–1920', in Marland and Rafferty (eds), op. cit., note 14 above.
countries supported the midwives and helped them to organize professionally and to edit journals, as in the Netherlands.\textsuperscript{28} Thus there is no indication that lower professional skills or less independence amongst Swedish midwives caused the early decline in home deliveries in Sweden. The respected and independent role of the Dutch midwife has been put forward as an explanation for the continued use of home deliveries in the Netherlands.\textsuperscript{29} But in Sweden, where the midwives had, and preserved, an independent position and competence, hospital deliveries became common early on. Hospital deliveries, however, do not necessarily imply, nor are they necessarily caused by, the same changes in professional relationships in all countries.
\textit{Availability of Doctors}
The possibility of summoning a doctor for assistance could be another factor influencing the choice of place of delivery. In the 1930s there were twice as many doctors per 1,000 inhabitants in Denmark as in Sweden, and a high percentage of Danish doctors were general practitioners (see Figure 7). Thus it was easier to receive help from a doctor for a home delivery in Denmark. Furthermore, general practitioners were evenly distributed over the whole country, mainly due to the contracts with the health insurance schemes, which reimbursed medical treatment by doctors to a much larger extent than in Sweden, see above. Danish doctors were very active in promoting the establishment of health insurance schemes, while Swedish doctors were indifferent towards them.\textsuperscript{30} In Sweden the distribution of doctors was uneven, with a concentration in the cities, and it is only recently that the country has reached the Danish level of physicians per 1,000 inhabitants. The availability of doctors and midwives in Denmark may have influenced some women living in the countryside to continue to give birth at home. Women in urban areas in Sweden, where doctors and midwives were more easily available, were, however, the first to go to hospital to give birth. A further investigation into rural/urban differences may be a useful way to pursue this question. Doctors could provide pain relief. Admittedly from 1944 Swedish midwives assisting at home births were provided with a transportable gas and air machine,\textsuperscript{31} but since at this time very few births took place at home in Sweden, it is unlikely this had an effect on the change of place of birth. Even in the 1950s Danish midwives were not allowed to handle these machines, probably because Danish doctors wanted to keep this task for themselves, and thereby the income from home birth attendance. Obstetricians worked mainly at the big hospitals, very few would assist at home deliveries in either country. Many smaller hospitals had only surgeons to assist at deliveries. The fact that there were doctors available to attend home deliveries may have facilitated continued home births in Denmark, while, before 1944, Swedish women had to go to hospital in order to get pain relief. In Denmark, the Netherlands and Britain the situation was similar, with fairly easy access to general practitioners. In Denmark, analysis of the background for the position of the Danish midwife see Løkke, op. cit., note 28 above.
\textsuperscript{28} Marland, op. cit., note 17 above, p. 35; M J van Lieburg and Hilary Marland, ‘Midwife regulation, education, and practice in the Netherlands during the nineteenth century’. \textit{Med. Hist.}, 1989, 33: 296–317. See also, Løkke, op. cit., note 27 above.
\textsuperscript{29} Torre and Reich, op. cit., note 9 above; Marland, op. cit, note 17 above, pp. 23. For an interesting
\textsuperscript{30} Ito, op. cit., note 10 above, p. 14.
\textsuperscript{29} Lundquist, ‘Barmmorskevåsendsret’, op. cit., see note 22 above, p. 651.
The Change of Place of Birth in Denmark and Sweden
Figure 7: Number of doctors per 1,000 inhabitants 1880–1970.
Sources: S Vallgårda, Sygehuse og sygehuspolitik i Danmark. Et bidrag til det specialiserede sygehusvæsens historie 1930–1987, Copenhagen, DJØFs forlag, 1992; Allmän hälso–och sjukvård. Medicinalstyrelsen, Stockholm, Socialstyrelsen, annual publication.
However, the general practitioners hardly ever attended normal deliveries alone without a midwife.
Hospitals and the Specialty of Obstetrics
A large number of hospital beds in Sweden would explain the earlier trend towards hospital deliveries, but Sweden did not have more hospital beds per 1,000 inhabitants than Denmark (see Figure 8). The rise in the number of hospital beds was parallel. This means that in Sweden beds were used for maternity purposes, whereas in Denmark they were used for other groups of patients. There is no reason to believe that there was a corresponding variation in health status, creating a greater “need” for hospitalization for parturient women or a reduced need for other patient groups in Sweden. Parturient women were given priority in Sweden at the expense of others.
It is often maintained that the development of medicine in itself is a determining factor for the specific organization and activities of health care. If in Sweden the specialty of
32 For examples see Signild Vallgårda, Sygehuse og sygehuspolitik i Danmark. Et bidrag til det specialiserede sygehusvæsens historie 1930–1987, Copenhagen, DJØFs forlag, 1992, pp. 106, 111, 158, 189.
Signild Vallgårda
Figure 8: Hospital beds per 1,000 inhabitants in Denmark and Sweden.
Sources: S Vallgårda, Sygehus og sygehospolitik i Danmark. Et bidrag til det specialiserede sygehusvæsens historie 1930–1987, Copenhagen, DJØFS forlag, 1992; Allmän hälsos–och sjukvård. Medicinalstyrelsen, Stockholm, Socialstyrelsen, annual publication.
Obstetrics could be said to be more developed with respect to scientific status, this could be a factor contributing to hospitalization. Obstetrics was mentioned at an early stage as a speciality in Swedish hospitals, while this was not the case in Denmark. This could indicate both the stronger position of Swedish obstetricians and the higher priority given to child-bearing women. The history of obstetrics in the two countries has not yet been investigated, but some indications of it can be given. In both countries, obstetrics was taught at the medical faculties from the eighteenth century, and students were given the opportunity for clinical practice at the established maternity hospitals. The first professors in obstetrics in Copenhagen and Stockholm were appointed in the same year, 1761. Outpatient clinics for pregnant women were established at the university hospitals in Copenhagen and Stockholm in the 1920s. The extent of scientific activity is difficult to judge. Acta Scandinavica Gynaecologica-Obstetrica was published from 1922, and a Scandinavian scientific society began in 1933. The focus of interest in obstetric research has, however, differed somewhat, with more research into eclampsia in Sweden and into pregnant diabetics in Denmark. Generally, there is no reason to believe that knowledge established in one of the countries was not swiftly transferred to the other, and that the development of obstetrics as such can explain the hospitalization of deliveries.
Among the characteristics of the health care sector it has only been possible to identify the early supply and availability of midwives, and the higher number of doctors and
The Change of Place of Birth in Denmark and Sweden
thereby the access to pain relief, as a partial explanation of why home deliveries persisted so much longer in Denmark.
Ideas and Motives
The organization of health care results from the activities of different groups and constitutes some of the conditions for their actions. To understand why the groups involved acted as they did, their ideas, motives, and arguments for and against home deliveries are analysed.
Midwives
In Denmark as well as in Sweden midwives opposed hospital confinements for all women.33 Fewer midwives were needed for hospital births than for the same number of home deliveries, and the change of place of birth was therefore seen as a threat to their employment. It is likely that this was the most important motive for their resistance. In hospitals, their autonomy would be reduced and, although doctors were not necessarily present at every delivery, the norms and standards were set by the consultant. Some Swedish midwives also opposed what they called the factory-like character of hospital confinements.34 According to two Swedish obstetricians, the opposition among Swedish midwives was more widespread than one understands from reading their journal.35 It is not possible to detect a difference in ideas between midwives from the two countries.
Doctors
Danish general practitioners, who received part of their income from home deliveries, therefore opposed hospital deliveries.36 As mentioned, the number of general practitioners was much higher in Denmark than in Sweden and they were better established as a group. This meant that they had greater influence than Swedish general practitioners. Although they were not the most influential group within the medical association, which organized practically all Danish doctors, they constituted half of the medical profession in the early 1930s.
Obstetricians in both countries preferred hospital deliveries to home deliveries for two reasons: hospital deliveries gave women a greater feeling of security, and they reduced morbidity and mortality among women and neonates. The hospitals also gave the doctors a feeling of security. “I always felt it unpleasant leaving my well-equipped ward and experienced midwives” to attend a home birth with an unknown midwife, a Swedish
33 Betänkande angående, op. cit, note 8 above, pp. 12ff; F Fiehn, ‘Födselsforhold’, Tidsskrift for Jordemødre, 1923, 33: 127–37; ‘Stockholms barnmorskor och allmänna barnbördshuset’, Jordemodern, 1913, 26: 200.
34 G Aurell, ‘Några ord om den tilltagande benägenheten att förlösa utanför hemmet’, Jordemodern, 1927, 40: 172.
35 Otto Gröné, ‘Något om barnmorskorna och barnbördshusen’, Läkartidningen, 1949, 4: 2564; L Simon, ‘Hemförsäkring kontra anstaltsförlossning’, Läkartidningen 1963, 60: 3528.
36 A Gullestrup, ‘Konfelter, udefødsler og sund fornuft’, Ugeskrift for læger, 1956, 118: 1476–8; A J Buntzen, ‘Om konfelter, udefødsler og sund fornuft’, Ugeskrift for læger, 1956, 118: 1534–5.
Signild Vallgärda
doctor wrote in retrospect in 1963. A common view expressed by both Danish and Swedish obstetricians was that all women ought to give birth in hospitals, preferably in obstetric departments. Before the Second World War, the issue was, however, hardly discussed among doctors in Denmark; why this was the case is difficult to tell. Unexpected risks were often used as arguments favouring hospital deliveries in both countries. In 1956 a Danish government report read: “Many, especially many serious and life-threatening birth complications . . . appear suddenly . . . At the hospital, doctors and technical equipment are immediately available . . .” And earlier, in 1936 in Sweden: “Unexpected complications, which can appear even in minor obstetrical interventions, are of course much easier handled in a hospital than at home.” Thus the opinions of doctors were contradictory, at least in Denmark, depending on whether they were those of obstetricians or general practitioners. Opposition came from doctors attending home deliveries, the number of which was much higher in Denmark.
Women
It is obvious that Swedish women changed their habits regarding the place of birth at an early period. In Sweden during the 1920s and 1930s hospital maternity wards were filled to overcapacity. Women changed their habits not only because maternity clinics were provided, i.e., it was not only a supplier-induced demand for hospital care. One can therefore assume that one of the reasons why local politicians provided maternity care in hospitals was in answer to demands from many women.
We have very little evidence of the ideas and motives of women in this regard. The study of several decades of women’s journals, both political and popular, has resulted in almost no findings. Giving birth has for some peculiar reason not been a subject that preoccupied women’s organizations or journalists. The reason for going to hospital most likely varied according to social class. In Sweden in the early 1940s midwives were asked by a government commission about women’s reasons for going to hospitals or maternity homes. According to the midwives, the cost of paying the travel expenses of the midwife to and from home was important. These increased as the districts grew larger. Scarcity of midwives and insufficient postnatal care were also mentioned as factors, as were the possibility of obtaining pain relief at the hospitals, the difficulty of receiving help when at home, and the fact that husbands wanted their wives to go to hospital. Overcrowding at home was seldom mentioned by the women themselves, but was brought up by the midwives. These reasons listed by midwives may of course have been coloured by their
37 Simon, op. cit., note 35 above, p. 3527.
38 Betänkning II, op. cit., note 8 above, p. 38; Mogens Ingerslev, ‘Hospitaliseringsbehovet’, Nordisk Medicin, 1962, 68: 1049.
39 Betänkning II, op. cit., note 8 above.
40 Betänkande angående, op. cit., note 8 above, p. 13. See also, E Essen-Möller, ‘II. Några ord om den tilltagande benägenheten att förlösa å barnbördshus’, Jordemodern, 1927, 40: 193–6; Otto Grönlind, ‘Barnbördsvården enligt statens sjukvårdskommittés förslag’, Jordemodern, 1935, 48: 4–16.
41 Betänkande om förlossningsvården, op. cit., note 8 above, p. 82; A Wallenthin, ‘Förhållanden ofta olidiga på BB-avdelningarna’, Morgonbris, 1944, no. 4, pp. 21–2.
42 Betänkande om förlossningsvården, op. cit., note 8 above, p. 12.
43 G Aurell, ‘III. Några ord om den tilltagande benägenheten att förlösa å barnbördshus’, Jordemodern, 1927, 40: 196–8, confirms this point about the husbands’ wishes.
188
The Change of Place of Birth in Denmark and Sweden
professional views and interests. Pain relief, the feeling of security, and overcrowding were the reasons most often given in Swedish government reports and by doctors as to why women wanted hospital deliveries.\(^{44}\) In Denmark as well, overcrowding, the need for peace and rest, and the demand for security in the case of complications were mentioned in a government report of 1938 as being the reasons why women went to hospital to give birth.\(^{45}\) No arguments for giving birth at home were given in the sources, but since that was what was considered “normal” and hospital deliveries were a new phenomenon, it was the latter which should be encouraged. Although most of these statements were made by politicians and public officials, I believe they contain a key to the understanding of women’s change in behaviour. The recurring issue of the higher feeling of security in hospitals can provide a clue to these changes.
According to anthropologists, transitional events, such as births, initiations, and deaths, involve rituals in most societies.\(^{46}\) Rituals, the setting, the persons involved, and the acts performed have meaning in accordance with the ways people interpret the world and their experiences. This interpretation can be religious, technological, medical, etc. A possible explanation for women’s changing habits could be that their social lives created a need for new rituals surrounding decisive events in their lives such as birth. This new attitude could be due to different living conditions caused by urbanization, industrialization, and the emergence of new social classes\(^ {47}\) and to new ideas about the role of science, technology, and hygiene, etc. The rituals surrounding deliveries at hospitals got their meaning from a scientific view of the world which assumed that man through technology could control nature.\(^ {48}\) It was women in urban areas who started the movement towards hospital confinements, and it was their way of life which differed most from previous life styles. In 1936 as many as 75 per cent of deliveries in Copenhagen took place outside women’s homes. The fact that the home continued to be the most common place of birth in rural areas and that hospital deliveries became common in the big cities at an early point in time thus
\(^{44}\) Betänkande angående, op. cit, note 8 above, p. 8; Betänkande med utredning, op. cit, note 18 above, p. 10; Grönè, op. cit., note 35 above, p. 2560; Simon, op. cit., note 35 above, p. 3529; Betänkande om förläggningvården, op. cit, note 8 above, p. 83ff.
\(^{45}\) Betenking afgivet af befolkningskommissionen af 1935 angaaende Moderens Rettigheder i Anledning af fødsel samt angaaende Seksualoplysning, Copenhagen, Befolkningskommissionen, 1938, p. 95–101.
\(^{46}\) Rituals surrounding births in early modern Europe have been described by Jacques Gelis, History of childbirth. Fertility, pregnancy and birth in early modern Europe, London, Polity Press, 1991. He does not, however, seem to consider modern birth attendance as a set of rituals: age-old values have disappeared with the industrial revolution “without offering anything in their place”, p. 96.
\(^{47}\) Jonas Frykman, Orvar Löfgren, ’På väg - bilder av kultur och klass’, in Jonas Frykman, Orvar Löfgren (eds), Modårna tider. Vision och vardag i folkhemmet, Lund, Liber förlag, 1985; Åke Elmér, Från Fattigsvverige till välfärdsstaten, Stockholm, Aldus/Bonniers, 1963.
\(^{48}\) This accords with B Jordan’s view: “It is not ‘scientific’ evidence which provides the major impetus for change, but rather perturbations and adjustments in the social, intellectual, and political structure with which the birthing system articulates.” See B Jordan, Birth in four cultures, Montreal, Eden Press, 1981, p. 66. I would, however, not reduce the influence of scientific changes to zero. On the ritual characteristics of hospital deliveries see R Davis-Floyd, ‘The role of obstetrical rituals in the resolution of cultural anomaly’, Social Sci. Med., 1990, 31: 175–89. Some points are also made by P Lomas, ‘An interpretation of modern obstetric practices’, in S Kitzinger, J A Davis (eds), The place of birth, Oxford University Press, 1978. See also, Eli Heiberg Endresen, ‘For sikkerheds skyld. Rutiner og ritualer i svangerskabskontrollen’, thesis, University of Oslo, 1986. The suggestion is supported by a Danish obstetrician, M Osler, who wrote: “Furthermore the increasing urbanization played a role both for the population and the midwives. The general change in living conditions may also in different ways be assumed to have had an influence.” ‘Jordemodervæsenet og svangreprofylaksen’, Bibliotek for læger, 1973, 165: 83–90.
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runs parallel to the spread of trained midwives in the nineteenth century, at least in Sweden. unlike women in rural areas, women in towns and cities lived in new conditions. It is therefore likely that they needed new social patterns and rituals when giving birth. Access and distance to midwives and hospitals also influenced women's choices.
The hypothesis that emerges from this is that the rapid change in living conditions experienced by women created a need for new rituals in connection with the decisive event of confinement. The fact that change in Sweden was both more rapid and radical could be a reason why the move towards hospital deliveries was faster there. It may not be possible to substantiate this hypothesis, considering the fallibility of oral sources, the fact that the majority of women who gave birth during the interwar years are now dead, and that they were most likely not conscious of the choice they were making. The example of countries like England and the Netherlands which experienced urbanization and industrialization much earlier without a simultaneous change in birth rituals might undermine this idea, but the changes there were neither as rapid nor as radical as in Sweden. Another factor could have contributed to the change in Sweden. This was the development of a strong trust in the ability of science to find solutions to a variety of problems, which coincided with the social changes in Sweden and the endeavours of large popular movements to alter the old ways of life.
Politicians
Politicians can favour a specific place of delivery through finance and regulation. Their ideas and motives for these decisions are thus important for understanding the changed conditions.
In Denmark home deliveries had been free of charge earlier than in Sweden and for a higher proportion of the population. In Sweden all birth attendance was made free in 1938, irrespective of the place of birth. At the same time, state subsidies were provided to establish maternity homes and maternity departments in hospitals. At this time, however, more than half the women gave birth in hospitals. The changed financing may have strengthened the trend towards hospital confinements, but the change had begun long before as a consequence of decisions made by women, doctors, and local politicians. Before 1938, hospital deliveries were more expensive than home deliveries, at least for members of health insurance schemes. In Denmark, state subsidies for bed days in connection with normal deliveries were given as late as in 1961. State subsidies were given to Danish hospitals in accordance with the number of bed days provided. In 1952, a central board, Sygehusrådet, stated that state subsidies should not be given for bed days in connection with normal deliveries. Many counties, however, had previously let women give birth at hospitals free of charge, provided they were members of a health insurance scheme. Why did Swedish politicians support maternity institutions so early? There were of course several reasons.
The first was the issue of social policy. There was an interest in providing a good birth environment for those women whose home conditions were bad. In 1914 an investigation
49 Brændström, op. cit., note 14 above, pp. 56–67.
50 P Lange, K A Møller, 'Udviklingen af det gynækologisk-obstetriske speciale inden for sygehusvæsenet i relation til lovgivningen', Bibliotek for læger, 1973, 165: 105–11.
51 Betænkning II, op. cit, note 8 above, p. 9; Betænkning afgivet, op. cit., note 45 above, p. 97.
52 G Steenhoff, 'Förlössningshem', Läkartidningen, 1923, 20: 97–102.
initiated by the Riksdag (Parliament) among 14,000 poor childbearing women showed they lived in very unhealthy surroundings. The Red Cross and some municipalities established small maternity homes to give these women an opportunity of having a calm and clean place to give birth. These institutions were not initially established to give them access to medical help. The social aspect also continued to play a role. In 1936 a government report stated that the question of maternity clinics was a “most important social issue” and that they should also be available to women not having complicated births. In 1933 the Danish social policy reform contained a request to counties and municipalities to establish maternity homes especially for poor women. The request was not fulfilled.
A second issue was population policy. During the first decades of the century, Swedish politicians were very concerned about the low level of population growth. This had two causes: huge emigration, mainly to the United States, and a declining birth rate. Both phenomena were seen in Denmark as well as in other European countries, but not to the same extent (see Figure 9 for the total fertility rate). Population increase was thus much
**Figure 9:** Total period fertility rate in Denmark and Sweden.
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Sources: *Befolkningens bevægelser*, Copenhagen, Danmarks statistik, annual publication; *Befolkningsrörelsen*, Stockholm, Statistiska Centralbyrån, annual publication; *Befolkningsutveckling och sundhedsförhold 1901–1960*, Copenhagen, Det statistiske departement, 1961; *Historisk statistik för Sverige*, vol. 1, Stockholm, Statistiska Centralbyrån, 1969.
---
53 *Betänkande angående*, op. cit., note 8 above, p. 10.
54 Ibid., p. 7; *Slutbetänkande avgivet av befolkningskommissionen*, SOU 1938:57, Stockholm, Socialdepartementet, 1938.
slower in Sweden. Between 1900 and 1930 it rose only 20 per cent, as compared with 45 per cent in Denmark.
The provision of maternity clinics was presented in government reports from the 1930s and 1940s in Sweden as a measure intended to counteract this demographic development in two ways. If women preferred to give birth in hospitals, they should have the opportunity to do so, because that could encourage them to have more children. The committee set up to look at the population issue suggested offering free maternity care and subsidies for maternity clinics. As mentioned earlier, women went to hospital to give birth to an extent which was beyond the capacity of the maternity wards, indicating a high demand for these services.
Another reason mentioned in the reports was that hospital confinements could result in reduced morbidity and mortality among mothers and children. Swedish infant mortality was low compared with other countries, but the regional and social differences were substantial, indicating that a further reduction was possible. Two conflicting arguments emerged. One assumed that improved medical technology could contribute to a decline in mortality. This was the line taken mainly by doctors and the Swedish National Board of Health. It was said that if a hospital had technical equipment, trained doctors and midwives to help in the case of complications, an increased number of hospital deliveries should lead to a reduction in infant mortality. In 1936 the National Board of Health wrote:
Obviously deliveries at hospitals, where doctors are always available and the technical possibilities of the medical institutions can be used without delay, result in certain advantages for both mother, fetus and the newborn child.
The second line of argument maintained that if in fact hospital confinements did lead to reduced mortality, the mortality rates would show this. Since there had been no reduction in the perinatal mortality rate during the years when hospital confinements became common, there was no reason to believe that further hospitalization would lead to a reduction in the mortality rates. A government report stated:
The fact that, in spite of an increase in hospital capacity, no manifest reduction in mortality in connection with confinements has been seen during the last decades, does not support the idea that hospitalization for all child-bearing women would contribute to the reduction of that risk.
This idea got further support at a medical meeting in 1942, where a doctor presented figures showing a slightly increasing perinatal mortality rate (see Figure 10). He explained that the rise
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55 Kungliga medicinalstyrelsens utlåtande och förslag angående förebyggande mödra- och barnavård, SOU 1935:19, Stockholm, Socialdepartementet, 1935; G Forsell, ‘Nativitet, humanitet och förlossningsvård’, Socialmedicinsk tidsskrift, 1944, 21: 143–7; Alva and Gunnar Myrdal, Kris i befolkningsfrågan, Stockholm, Albert Bonniers förlag, 1934, p. 103.
56 Betänkande angående, op. cit., note 8 above, p. 7. The same type of argument appeared later in Denmark. Betänkning II, op. cit., note 8 above.
57 Simon, op. cit., note 35 above, p. 3528. The translation of quotations from this report are mine.
58 Ibid., p. 10.
60 C Gyllenswärd, ‘Orsakerna till dödföddhetens och tidigdödhetens stigande i Sverige under de senaste åren’, in J P Edwardson (ed.), Förrhandlingar vid tjugoårsredje allmänna läkarmötet, Karlshamn, 1942, p. 84. See also, Signild Vallgårda, ‘Trends in perinatal death rates in Denmark and Sweden, 1915–1990’, Paediatr. perinatal Epidemiol., 1995, 9: 201–18.
resulted from the increased hospitalization of normal births, above all caused by the long distances women in labour had to travel. There was thus no empirical evidence that hospitals contributed to a lower perinatal mortality rate, nevertheless, this did not prevent many doctors and others from believing that they did. A government report in 1936 argued against hospitalization of all deliveries: "A delivery is, under normal circumstances, not equivalent to a disease . . . experience shows that, without any risk for the woman, it can take place in her own home."61
The same arguments were presented by the Danish population committee, set up in 1935 in order to find measures to improve the quantity and quality of the population. On the very same page they stated: "mortality for mothers and children . . . could [not] be reduced very much further" and "complications, which can appear during any delivery, can more easily and more safely be treated at a hospital, preferably in an obstetric ward."62 The concern about infant mortality was strongest in Denmark, whose mortality rate was the highest in Scandinavia.
The population policy, however, was concerned not only with the size of the population, but also with improving the quality; this could be achieved by preventing the birth of potentially undesirable members of society (such as criminals and alcoholics, as well as the mentally or physically handicapped).63 During the first decades of the twentieth
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61 Betänkande angående, op. cit., note 8, p. 10.
62 Betänkning, op. cit., note 45, p. 95.
63 G Broberg, M Tydén, Oönskade i folkhemmet, Stockholm, Gidlunds, 1991; Yvonne Hirdman, Att lägga livet till rätta - studier i svensk folkhemspolitik, Stockholm, Carlssons, 1989, p. 145; Alva and Gunnar Myrdal, op. cit., note 55; Lene Koch, 'The biological aspect', in Lisbeth Andersen Skov (ed.),
century, eugenics had a strong position among doctors and politicians in both countries, not least among the Social Democrats. More education in child care and better nutrition would also contribute to an improvement.64 In Sweden especially, several organizations (most founded in the late nineteenth century) worked to change the habits of the population. One of them was the temperance movement, which was almost non-existent in Denmark,65 others were the hygienic movement,66 and the sports movement. Old habits should be eradicated and replaced by more hygienic, educated, and disciplined behaviour. The labour movement also participated in these efforts, encouraging its members to gain respect and to achieve the other goals put forward.67 Thus in many areas of Swedish society there was an endeavour to create something new and modern and to repudiate the old in order to make Swedes richer, more hygienic, and more guided by scientific knowledge. These movements should consequently not only be seen as an attempt by the upper classes to change working-class life style, but also as a means for the working class to improve their position and to gain respect. It is, however, not the purpose of this article to investigate,68 why many of these movements for change were stronger in Sweden than in Denmark where the working class was much more traditional.69
In Sweden, more so than in Denmark, there was a strong belief that the state was entitled to change, and was actually capable of changing, the way the working class lived.70 Such intervention had a long tradition in Sweden.71 There was a belief that through scientific research one could find the right way to live and to teach others how to live.72 Trust in science, progress, rationality and general education had been strong among Radical Swedish intellectuals since the 1880s,73 and was especially so in the 1930s among intellectual Social Democrats. The best known exponents of these views were Alva and Gunnar Myrdal, whose widely read book on the population issue, Kris i befolkningsfrågan ('Crisis in the population problem'), stated: “Bad habits must be corrected. The ignorant enlightened. The irresponsible awakened. There is room for people to be extensively informed and for propaganda organized by society.” “Pure rationality may frighten some as being chilly. It can, however, only be a question of time before family problems can be
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63 Rescue-43. Xenofobia and exile, Copenhagen, Munksgaard, 1993; Karin Johannisson, ‘Folkhälsa. Det svenska projektet från 1900 till 2:a världskriget’, Lychnos, 1991, pp. 139–95.
64 Slutfattande avgivet av befolkningskommissionen, SOU 1938:57, Stockholm, Socialdepartementet, 1938, p. 42.
65 Sidsel Eriksen, ‘Väckelse och afholdsbevägelse. Et bidrag til studiet af den svenske og den danske folkekultur’, Scandia, 1988, 54: 251–95.
66 Eva Palmblad, Medicinen som samhällslära, Göteborg, Daidalos, 1990; K Jonsson, ‘En nybadad renrasi svensk på ett ’...’ i I framtidens tjänst. Ur folkhemmets idéhistoria, Malmö, Gidlunds, 1986.
67 Ronny Ambjörnsson, Den sköttsamme arbetaren. Idéer och ideal i ett norrländskt sågverks samhälle 1880–1930, Stockholm, Carlssons, 1988; Elmér, op. cit., note 47 above.
68 In an interesting article, Sidsel Eriksen (op. cit., note 65 above) explains the strength of the temperance movement in Sweden as being due to the influence of Anglo-American religious movements, where the improvement of one’s own and others’ life styles was an important task. Lutheranism in Denmark held that faith was a gift of grace and thus not obtainable through actions, and this attitude dominated the religious movements of the nineteenth century.69
69 Niels Finn Christiansen, Hartvig Frisch - mennesket og politikeren. En biografi, Copenhagen, Christian Ejlers Forlag, 1993.
70 Arbetarrörelsens efterkrigstid. Sammanfattning i 27 punkter, 1944, p. 17.
71 Tim Knudsen, ‘State-building in Scandinavia: Denmark in a Nordic context’, in Tim Knudsen (ed.), Welfare administration in Denmark, Copenhagen, Institute of Political Science, 1991, pp. 14–20.
72 Ron Eyerman, ‘Rationalizing intellectuals’, Theory and society, 1985, 14: 777–807.
73 Gunnar Aspelin, ’Tidsideer och tidsideal’, in Johan Cornell (ed.), De 50 åren - Sverige 1900–1950, vol. 3, Stockholm, 1950.
treated technically and rationally.\textsuperscript{74} Intellectual Social Democrats expressed these ideas very emphatically, with the aim of changing society from being backward, rural, filthy, superstitious and irrational to being clean, rational, scientifically organized, industrial and urban.\textsuperscript{75} In one of their manifestos, they called the first type of society B-Europe, and the second A-Europe. "With the help of horse-power, A-Europe has become the Europe of machines, banks, education and science, without them B-Europe has remained the Europe of agrarians, religious orthodoxy and illiterates."\textsuperscript{76} This modernization project involved all areas of society including the way people lived in their homes, carried out housework, and reared their children. In Denmark, on the other hand, at least among the leading Social Democrats, modernity was not seen as a positive value to strive for.\textsuperscript{77}
Housing played a central role in this change.\textsuperscript{78} Standards of housing were low in Sweden and efforts to improve them date back to the late nineteenth century.\textsuperscript{79} The tradition of having a big kitchen, in which most of the family’s activities took place, had been transferred from the countryside to towns and cities. The multifunctionality of these big kitchens was a thorn in the flesh of reformers, both from the Right and Left. They wanted separate areas for different functions; i.e., the kitchen ought to be small and used only for cooking.\textsuperscript{80} In government reports on the maternity question, overcrowding was often mentioned as a reason for women wanting to go to hospital to give birth, although, according to midwives, the women themselves seldom mentioned it. Overcrowding was no worse in the 1930s than at the beginning of the century, in fact the situation had improved due to falling birth rates. What can be seen here is a projection of the ideas of the middle and upper classes, especially the intellectuals. They certainly felt disgusted by the thought of confinements in small dwellings. In the modernization project, home births were seen as a remnant of the old way of living which should be abandoned. Hospital confinements, on the other hand, represented the new era: they were hygienic, scientific, and specialized. Hospital deliveries also provided the opportunity to teach women how to care for their babies, an argument especially favoured by doctors.\textsuperscript{81}
For Swedish politicians hospital confinements were part of social and population policy (including both its quantitative and qualitative aspects). The fertility issue attracted
\textsuperscript{74} Alva and Gunnar Myrdal, op. cit., note 55 above, quoted in Hirdman, op. cit., note 63 above, pp. 123, 22.
\textsuperscript{75} Alva and Gunnar Myrdal, op. cit., note 55 above; \textit{I framtidens tjänst}, op. cit., note 66 above; Eyerman, op. cit., note 72 above; Arne Ruth, ‘The second new nation: The mythology of modern Sweden’, \textit{Daedalus}, 1984, 113: 77.
\textsuperscript{76} Gunnar Asplund, \textit{et al.}, \textit{acceptera}, Stockholm, 1931, p. 17.
\textsuperscript{77} Anders Linde-Laursen, ‘Er Sverige interessant . . . ? Om modernitet och hundrede års danskhed’, in A Linde-Laursen, J O Nilsson (eds), \textit{Nationella identiteter i Norden - ett fullbordat projekt?}, Copenhagen, Nordiska Rådet, 1991.
\textsuperscript{78} Hirdman, op. cit., note 63 above; Roger Qvarsell, ‘Brott och sjukdom. Psykiatri och visioner om ett rationellt samhälle’, in \textit{I framtidens tjänst}, op. cit., note 66 above, pp. 126–47; Sverker Sörlin, ‘Utopin och verkligheten. Ludvig Nordström och det moderna Sverige’, in ibid., pp. 166–95; Asplund, \textit{et al.}, op. cit., note 76 above; Alva and Gunnar Myrdal, op. cit., note 55; Palmblad, op. cit., note 66 above.
\textsuperscript{79} Kerstin Thörn, ‘En god bostad för det riktiga livet. Den moderna bostadens ideologiska förutsättningar’, in \textit{I framtidens tjänst}, op. cit., note 66 above, pp. 196–213.
\textsuperscript{80} Hirdman, op. cit., note 63 above. See also, Mary Douglas, \textit{Purity and danger. An analysis of the concepts of pollution and taboo}, London, Routledge, 1992, on the importance of separation and order.
\textsuperscript{81} Otto Gröne, ‘Barnbördsvården enligt Statens sjukvårdsstammit’, \textit{Jordemodern}, 1935, 48: 4–16; H Wickbom, ‘Behovet av anstaltsvård, särskilt för ödemarksområdena’, \textit{Jordemodern}, 1937, 50: 363–8.
Signild Vallgårda
political interest in Denmark as well,\textsuperscript{82} but it was not as intensely debated as in Sweden, probably because the decline in fertility was lower. Population policy (both the quantitative and qualitative aspects) played a role in Denmark, and in 1929 it was the first country to pass an Act on eugenic sterilization.\textsuperscript{83} There were also some efforts to educate the population on how to do housework,\textsuperscript{84} and how to rear children.\textsuperscript{85} But these efforts did not have the importance of the corresponding Swedish ones and were not conducted with the same strong ideology of modernization. The difference between the two countries lay in the emphasis placed on the population issue rather than in its content.
Conclusion
The different pace at which hospital confinements spread throughout the two countries can only to a minor extent be ascribed to differences in which health care was organized as a whole. The resources dedicated to health care were fewer in Sweden and the country was poorer. The midwives were well educated, respected and relatively independent in both countries. Neither the development of obstetrics, i.e., the level of the science of obstetrics, nor the skill of the obstetricians can give a clue to the differences. The most prominent difference between the countries was that the provision of midwives and doctors to assist at home confinements was better in Denmark. The tentative conclusion of this paper is that the later but more rapid and radical social and economic changes in Sweden created a stronger need among pregnant women for new social patterns and rituals for the deliveries. The hospitals provided these rituals in a form which was in accordance with the new ideals held by politicians, popular movements, and probably by large segments of the population in general: modernity, hygiene, science, and technology. Women and politicians in Sweden wanted to extend the possibility of hospital deliveries, but for different reasons. Both groups, however, were influenced by the rapid change in Swedish society, and new ideas emerged from each, probably as a consequence of the modernization of society. The faster and more radical changes in Sweden could explain why the change occurred earlier than in Denmark. Among these ideas were new ways to establish causal relations where science and technology came to play a major role in the explanations of changes and improvements. The idea that hospitals reduced perinatal morbidity and mortality appeared earlier in Sweden than in Denmark. Finally, the stronger tradition of state intervention in Sweden may have made more acceptable the political means used to improve the population’s size and quality.
\textsuperscript{82} Adolph Jensen, \textit{Befolkningssspørgsmålet i Danmark}, Copenhagen, Studentersamfundets Oplysningsforening, 1937; \textit{Betænkning II}, op. cit., note 8 above; Hanne Caspersen, \textit{Moderskabspolitik i 1930’erne. Det modsætningsfylde moderskab}, Copenhagen, Danske historiske forening, 1985.
\textsuperscript{83} Koch, op. cit., note 63 above.
\textsuperscript{84} Vallgårda, op. cit., note 32 above, p. 129.
\textsuperscript{85} Act on health visitors for newborn children from 1937.
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Ghrelin peptide improves glial conditioned medium effects on neuronal differentiation of human adipose mesenchymal stem cells
Cristina Russo1 · Giuliana Mannino1 · Martina Patanè3 · Nunziatina Laura Parrinello2 · Rosalia Pellitteri3 · Stefania Stanzani3 · Rosario Giuffrida1 · Debora Lo Furno1 · Antonella Russo1
Accepted: 1 March 2021 / Published online: 16 March 2021
© The Author(s) 2021
Abstract
The influences of ghrelin on neural differentiation of adipose-derived mesenchymal stem cells (ASCs) were investigated in this study. The expression of typical neuronal markers, such as protein gene product 9.5 (PGP9.5) and Microtubule Associated Protein 2 (MAP2), as well as glial Fibrillary Acid Protein (GFAP) as a glial marker was evaluated in ASCs in different conditions. In particular, 2 µM ghrelin was added to control ASCs and to ASCs undergoing neural differentiation. For this purpose, ASCs were cultured in Conditioned Media obtained from Olfactory Ensheathing cells (OEC-CM) or from Schwann cells (SC-CM). Data on marker expression were gathered after 1 and 7 days of culture by fluorescence immunocytochemistry and flow cytometry. Results show that only weak effects were induced by the addition of only ghrelin. Instead, dynamic ghrelin-induced modifications were detected on the increased marker expression elicited by glial conditioned media. In fact, the combination of ghrelin and conditioned media consistently induced a further increase of PGP9.5 and MAP2 expression, especially after 7 days of treatment. The combination of ghrelin with SC-CM produced the most evident effects. Weak or no modifications were found on conditioned medium-induced GFAP increases. Observations on the ghrelin receptor indicate that its expression in control ASCs, virtually unchanged by the addition of only ghrelin, was considerably increased by CM treatment. These increases were enhanced by combining ghrelin and CM treatment, especially at 7 days. Overall, it can be assumed that ghrelin favors a neuronal rather than a glial ASC differentiation.
Keywords Human adipose mesenchymal stem cells · Ghrelin · Neural-like differentiation · Glial conditioned media · Olfactory ensheathing cells · Schwann cells
Abbreviations
ASC Adipose derived mesenchymal stem cells
ASC/OEC-CM ASC cultures in OEC-CM
Cristina Russo and Giuliana Mannino equally contributed to this work.
Debora Lo Furno
[email protected]
Cristina Russo
[email protected]
Giuliana Mannino
[email protected]
Martina Patanè
[email protected]
Nunziatina Laura Parrinello
[email protected]
Rosalia Pellitteri
[email protected]
Stefania Stanzani
[email protected]
Rosario Giuffrida
[email protected]
Antonella Russo
[email protected]
1 Physiology Section, Department of Biomedical and Biotechnological Sciences, University of Catania, via S. Sofia, 97, 95123 Catania, Italy
2 Division of Hematology, AOU “Policlinico-San Marco”, via S. Sofia, 78, 95123 Catania, Italy
3 Institute for Biomedical Research and Innovation, Italian National Research Council, Via P. Gaifami, 18, 95126 Catania, Italy
### Introduction
Experimental data indicate that Ghrelin peptide may play a role in multiple functions of the central nervous system. (Ferrini et al. 2009; Russo et al. 2018). It influences several neurological processes, such as learning and memory, stress response, sleep-awake cycle and behavior (Meyer et al. 2014; Jiao et al. 2017). Ghrelin also promotes neurogenesis (Sato et al. 2006). For example, its contribution has been reported in recovery and synaptic formation at the hippocampal level (Berrout and Isokawa 2012; Stoyanova et al. 2013; Kent et al. 2015). Moreover, emerging evidence indicates that ghrelin can also stimulate the proliferation, differentiation and migration of neural stem/progenitor cells (Xu et al. 2008).
The aim of this work was to test whether ghrelin affects Mesenchymal stem cell (MSC) neural differentiation. In fact, it has been demonstrated that MSCs can differentiate not only into mesenchymal cells, such as adipocytes, myocytes, osteocytes and chondrocytes (Maccarinelli et al. 2005; Kern et al. 2006; Lo Furno et al. 2013a; Naji et al. 2019), but also transdifferentiate into neural elements (Zhang et al. 2012; Goudarzi et al. 2018).
In previous studies, a neural differentiation of adipose-derived MSCs (ASCs) was achieved by their growth in a conditioned medium (CM) obtained from cultures of Olfactory Ensheathing cells (OECs) or Schwann cells (SCs) (Lo Furno et al. 2018a). OECs are specialized glial cells of the mammalian olfactory system characterized by continuous neurogenesis; they also support the growth of new olfactory receptor neurons (Pellitteri et al. 2010). OECs are found both outside and inside the central nervous system (Gómez et al. 2018) and, in physiological conditions, they drive the non-myelinated axons of receptor neurons towards the olfactory bulb by ensheathing nerve fibers and promoting their growth (Nazareth et al. 2015). SCs are located in the peripheral nervous system, where they myelinate large-diameter axons and provide trophic support for motor and sensory fibers. They contribute to the composition of the extracellular matrix, crucial for neuronal survival and axonal growth. SCs also contribute to axon restoration after injury (Golden et al. 2007). Both OECs and SCs originate from the neural crest (Barton et al. 2017) and produce numerous adhesion molecules, cytokines and neurotrophic factors, such as Brain-Derived Neurotrophic Factor (BDNF), Glial cell-Derived Neurotrophic Factor (GDNF), Nerve Growth Factor (NGF) and Neurotrophins.
In this investigation, ASC neural differentiation induced by OEC-CM or SC-CM was tested in combination with ghrelin added to the culture medium, to evaluate possible synergic or antagonist interactions. These combined effects were then compared to reference cultures consisting of ASCs cultured in OEC-CM or SC-CM, control ASCs grown in their basal medium, and control ASCs where ghrelin alone was added. ASC neural differentiation was assessed by evaluating the expression of typical neuronal markers such as Protein Gene Product 9.5 (PGP9.5) and Microtubule Associated Protein 2 (MAP2), as well as Glial Fibrillary Acid Protein (GFAP), indicative of a glial phenotype. Since interactions between ghrelin and its receptor have been recognized to be responsible for cell proliferation, differentiation and migration (Jiao et al. 2017), another set of experiments was devoted to explore the presence and possible modifications of the ghrelin receptor (GHSR-1a). In these experiments, both native and differently treated ASCs were investigated. Immunocytochemistry and flow cytometry were used to evaluate the presence and modifications of neural markers and GHSR-1a.
### Materials and methods
#### Conditioned medium preparation
Conditioned media were obtained from glial cells of 2-day old rat pups following experimental procedures carried out according to the Italian Guidelines for Animal Care (D. Lgs 26/2014), and the European Communities Council Directives (2010/63/EU). Protocols were approved by the ethics committee of the University of Catania (Organismo Preposto al Benessere Animale, OPBA; Authorization n. 174/2017-PR). All efforts were made to minimize animal suffering and to reduce the number of animals used.
#### OEC cultures and preparation of OEC-CM
Following procedures previously described (Pellitteri et al. 2009), olfactory bulbs were removed and OECs were isolated. Briefly, after removal, the bulbs were dissected (+ 4 °C) in Leibowitz L-15 cold medium (Sigma–Aldrich, Milan, Italy). They were digested in Minimum Essential Medium-H (MEM-H, Sigma–Aldrich)
containing collagenase (Invitrogen, Milan, Italy) and trypsin (Sigma–Aldrich) before adding Dulbecco's Modified Eagle's Medium (DMEM, Sigma–Aldrich) supplemented with 10% Fetal Bovine Serum (FBS, Sigma–Aldrich) to stop enzymatic activity. OECs were finally plated in flasks and kept in DMEM/FBS supplemented with cytosine arabinoside (10^-5 M) as the antimitotic agent to reduce fibroblast proliferation. Subsequently, OECs were cultured at 37 °C in DMEM/FBS with the addition of 1% penicillin/streptomycin. 24–48 h after reaching confluence, OEC-CM was collected, filtered to remove debris and detached cells and stored at −20 °C before further use. OECs were identified by immunostaining for S-100.
Schwann cell cultures and preparation of SC-CM
Schwann cells were harvested from sciatic nerves, which were exposed, removed, and kept in DMEM with the addition of 1% penicillin/streptomycin (Pellitteri et al. 2006). They were then digested in DMEM containing 0.1% collagenase and 2.5% trypsin, mechanically dissociated by trituration and filtered through a 150 μm nylon mesh. The day after seeding, the antimitotic agent cytosine arabinoside (10^-5 M) was added to reduce fibroblast proliferation. Finally, SCs were resuspended in fresh medium and plated on 25 cm² flasks. 24–48 h after reaching confluence, SC-CM was collected, filtered to remove debris and detached cells, aliquoted and stored at −20 °C before further use. SCs were identified by immunostaining for S-100.
ASC cultures
ASCs were isolated from adipose tissue, which was harvested from four healthy (32–38 years old) female donors undergoing liposuction procedures at the Cannizzaro Hospital, Catania (Italy). The donors were non-smokers and occasionally took non-steroidal anti-inflammatory drugs. Lipoaspirate was obtained after donors signed a written informed consent to use the lipoaspirate for experimental procedures, which were carried out in accordance with the Declaration of Helsinki. The protocol was approved by the local ethics committee (Comitato etico Catania1; Authorization n. 155/2018/PO).
The raw lipoaspirate (50–100 ml) was washed with sterile phosphate-buffered saline (PBS; Invitrogen) to remove red blood cells and debris, and incubated for 3 h at 37 °C with DMEM containing 0.075% of type I collagenase (Invitrogen). After inactivation of collagenase by adding an equal volume of DMEM/FBS, the lipoaspirate was centrifuged at 1200 rpm for 10 min. Pellets were then resuspended in PBS, and cells were filtered through a 100-μm nylon cell strainer (Falcon BD Biosciences, Milan, Italy). Following a final centrifugation/resuspension cycle, cells were plated in T75 culture flasks (Falcon BD Biosciences) with DMEM/FBS, 1% penicillin/streptomycin, 1% MSC growth supplement (MSCGS; ScienCell Research Laboratories, Milan, Italy). After 24 h of incubation at 37 °C with 5% CO₂, non-adherent cells were removed by replacing the culture medium. After reaching confluence (about 80% of total flask surface), all cultures were trypsinized and cells were cultured for 2–3 passages before the subsequent procedures.
Some ASC samples were tested for their MSC nature, according to a protocol previously described (Lo Furno et al. 2018b). After 3 days from seeding, immunostaining for typical MSC markers (CD44, CD73, CD90, and CD105) was verified, as well as their immunonegativity for typical hematopoietic stem cell markers (CD14, CD34, and CD45). For the present investigation, six groups of ASC cultures were prepared. One group served as control, consisting of ASCs kept in basal growth medium (ASC); ASCs of the second group were cultured in basal growth medium with the addition of 2 μM ghrelin (ASC + Ghre); ASCs of the third group were cultured in ASC-CM (ASC/OEC-CM); ASCs of the fourth group were cultured in OEC-CM, in which ghrelin was added (ASC/OEC-CM + Ghre); ASCs of the fifth group were cultured in SC-CM (ASC/SC-CM); and ASCs of the sixth group were cultured in SC-CM in which ghrelin was added (ASC/SC-CM + Ghre). From each group, some samples were stopped at 1 day; other samples were processed after 7 days of culture. At each time point, fluorescence immunocytochemistry and flow cytometry procedures were carried out for signal detection.
Flow cytometry
After trypsinization, cells of each sample were analyzed by flow cytometry. They were fixed with 2% paraformaldehyde in PBS for 20 min at 4 °C and permeabilized with 1% Triton for 5 min at 4 °C. After blocking nonspecific sites by BSA treatment (1% in PBS for 30 min), cells were incubated (60 min at room temperature) with primary antibodies: rabbit anti-PGP9.5 (1:100; Novus Biologicals, Milan, Italy; NB1-96612), mouse anti-MAP2 (1:100; Covance; SMI-52), and mouse anti-GFAP (1:100; Novus; NB120-10062). Finally, cells were incubated (60 min at room temperature in the dark) with goat anti-mouse or goat anti-rabbit secondary antibodies conjugated with fluorescein (FITC; 1:200; Abcam). Quantitative data were gathered using a Navios flow cytometer (Beckman Coulter, Milano; Italy). Samples were excited at 488 nm and fluorescence was monitored at 525 nm. Mean Fluorescence Intensity (MFI) values were calculated and recorded automatically. Kaluza Analysis Flow Cytometry Software was used for data processing.
Immunocytochemical staining was carried out following a protocol previously described (Lo Furno et al. 2013b). Briefly, cells were washed with PBS, fixed with 4% paraformaldehyde and incubated for 30 min with a 5% solution of normal goat serum (Sigma–Aldrich) in PBS containing 0.1% Triton (Sigma–Aldrich). They were then exposed overnight at 4 °C to primary antibodies: rabbit anti-PGP9.5 (1:100; Novus Biologicals, Milan, Italy), mouse anti-MAP2 (1:100; Covance), mouse anti-GFAP (1:100; Novus), and rabbit anti-GHSR-1a (1:100; Santa Cruz Biotechnology; sc-374515). The following day, cells were washed with PBS and incubated for 60 min at room temperature with secondary antibodies conjugated to different fluorochromes: FITC-conjugated goat anti-rabbit (Abcam) and/or Cy3-conjugated goat anti-mouse (Abcam). Finally, DAPI was applied for 10 min to identify cell nuclei. Some further samples were used to verify the specificity of immunostaining by omitting the primary antibody. Immunofluorescence was detected using a Leica DMRB Fluorescence Microscope equipped with the following Filter Cubes: Leica Filter Cube A (UV Excitation, P/N 513804); Leica Filter Cube I3 (Blue Excitation, P/N 513808); Leica Filter Cube N2.1 (Green Excitation, P/N 513812). A 40× oil objective was normally used (Leica PL FLUOTAR, 40X/1.00–0.50 OIL, ∞/-/C). Digital images were acquired by a computer-assisted digital camera (Leica DFC 320, 3.3 Megapixel; Software: Leica Application Suite 2.8.1).
Immunostaining quantification was carried out through the FIJI-ImageJ measure tool (NIH, Bethesda, MD, USA). From each group, at least three samples were examined at each time point. From each sample, three digital photomicrographs were randomly selected. From each photomicrograph, up to seven immunofluorescent cells were analyzed. Values were derived from the average grayscale intensity.
The integrated density, the cell area and the mean fluorescence of the selected cells were estimated. Three replicate measurements were performed for each capture region. The same procedure was applied to three different background areas, around the selected cell. Then, the Corrected Total Cell Fluorescence (CTCF) was calculated using the following equation: CTCF = integrated density—(cell area × background mean fluorescence).
Statistical analysis
Statistical analysis was performed using GraphPad Prism 7.0 (GraphPad Software, La Jolla, CA, USA). For each experimental condition, CTCF values are reported as mean ± SD. Differences between samples were assessed using one-way analysis of variance (one-way ANOVA) followed by post hoc Holm–Sidak test. p values of 0.01 or less were considered statistically significant.
Results
The stem cell profile of ASCs was verified by immunocytochemistry and flow cytometry. In accordance with previous studies (Lo Furno et al. 2018b), virtually all cells (98% or above) were immunopositive for typical MSC markers (CD44, CD73, CD90, and CD105), whereas less than 1% were positive for typical hematopoietic stem cell markers (CD14, CD34, and CD45). As expected, cell density at 7 days increased considerably when compared with day 1, especially in controls. In the same period, also cell morphology was noticeably changed. At 7 days, much larger cell bodies were more frequently found.
Neural marker expression in ASCs
Neural marker expression modifications were evaluated by analyzing data obtained by flow cytometry and immunostaining quantification. Results consistently show that only weak effects were induced on neural marker expression when ghrelin alone was added to ASC cultured in their basal medium; significant increases were observed when ASCs were cultured in glial CM; dynamic effects could be observed when ghrelin was added to ASCs cultured in glial CM.
In agreement with previous data (Lo Furno et al. 2018a), the expression of PGP9.5 was higher in the ASCs cultured with OEC- or SC-CM when compared to controls (Figs. 1, 5a, Table 1), especially after 7 days of culture. A stronger effect seems to be exerted by SC-CM rather than OEC-CM treatment. The addition of ghrelin to SC-CM further increased PGP9.5 expression, whereas no appreciable modifications were observed when the peptide was added to ASCs cultured in glial CM. When ghrelin alone was added to ASCs cultured in basal medium, significant increases were observed only after 7 days of treatment. Immunofluorescence quantification data (Fig. 5a) and MFI values (Table 1) obtained from the different samples illustrate these modifications. Namely, the lowest MFI values were measured in control ASCs (34.79 and 69.36 at 1 and 7 days, respectively); the highest values referred to the population of ASCs undergoing combined ghrelin and SC-CM treatment (79.66 and 131.66 at 1 and 7 days, respectively). Altogether, data indicate that positive effects may be exerted by the presence of ghrelin on neuronal differentiation of ASCs. These influences are more evident after 7 days of treatment and significantly reinforce SC-CM-induced effects.
Regarding MAP2 expression, considerable increases were induced for glial CM treatment when compared with control
Fig. 1 Modifications of PGP9.5 expression at 1 and 7 days of culture in ASCs undergoing different treatments. In panel a (1 day) and b (7 days), PGP9.5 immunoreactivity is shown in different groups of ASCs: ASC cultures in the basal medium (ASC); ASC cultures in OEC-CM (ASC/OEC-CM) or SC-CM (ASC/SC-CM); ASC cultures where ghrelin was added to the basal medium (ASC + Ghre), to OEC-CM (ASC/OEC-CM + Ghre) or to SC-CM (ASC/SC-CM + Ghre). In each flow cytometry plot, data obtained from each culture condition, with or without ghrelin, are merged. Histograms show cell frequency distribution of each population, according to FITC fluorescence intensity expressed in logarithmic scale. Histogram overlays are displayed as %Max, scaling each curve to the respective modal values = 100%. Scale bar: 50 μm
ASCs, at both day 1 and 7 of culture (Figs. 2, 5b, Table 1). Immunofluorescence quantification data (Fig. 5b) show that ghrelin addition to OEC-CM further enhances MAP2 expression, although weakly, at both time points. Instead, the addition of ghrelin to SC-CM considerably increased MAP2 expression, but only after 7 days. No evident changes were
detected by the addition of only ghrelin to ASCs cultured in basal medium. A similar trend can be recognized for MFI values showed in Table 1. Comparable low values were calculated for ASCs or ASC + Ghre (about 55), whereas the highest value referred to the population of ASCs undergoing combined ghrelin and SC-CM treatment at 7 days (122.95). It can be assumed that, although no effects seem to be exerted by ghrelin alone, a synergic influence occurs in combination with glial CM, especially for SC-CM at a longer time.
As expected, a robust increase of GFAP expression is easily appreciable at both 1 and 7 days (Figs. 3, 5c, Table 1) when ASCs are cultured in OEC-CM or, especially, SC-CM (Lo Furno et al. 2018a). However, as shown in Fig. 5c, these CM-induced increases were not greatly influenced by the addition of ghrelin; rather, unlike what was described for the other neural markers, slightly reduced glial-induced increases were observed. Again, only weak modifications were seen after the addition of ghrelin to ASCs cultured in basal medium. Table 1 shows that comparable low MFI values were measured for ASCs or ASC + Ghre (about 50), whereas the highest value referred to the population of ASCs cultured in SC-CM for 7 days (205.14). Also MFI values would suggest that ghrelin addition attenuates CM-induced increases; in particular, at day 7, MFI values decrease from 163.12 to 98.95 and from 205.14 to 167.89 for OEC-CM and SC-CM, respectively. From these results, it can be concluded that the presence of ghrelin would not support ASC differentiation toward a glial phenotype.
**Ghrelin receptor expression**
Experiments aimed at evaluating GHSR-1a expression on ASCs were carried out to explain ghrelin-induced influences. Immunocytochemistry (Fig. 4) and fluorescence quantification analysis (Fig. 5d) show that a basal GHSR-1a expression can be observed in control ASCs at both 1 and 7 days of detection. Instead, marked increases were induced by both CM treatments, especially on day 7. Such increases were weakly enhanced by the addition of ghrelin, once again after 7 days. Modest increases were detected by the addition of ghrelin alone.
**Discussion**
Data obtained in the present study confirm previous results in which a successful neural differentiation was induced in ASCs by using conditioned media from OECs or SCs (Lo Furno et al. 2018a). By this strategy, also in the present work the expression of PGP9.5, MAP2 and GFAP was considerably more expressed. Overall, these findings fit quite well with data in the literature, in which effects on neurogenesis and neural differentiation processes are described for OECs and SCs. Glial effects are likely induced by the release of several growth factors such as NGF, BDNF, CNTF, and GDNF (Barton et al. 2017). Indeed, it is difficult to assess that a marker by itself is surely indicative of a given phenotype. For example, although at lower levels, PGP9.5 is also expressed in neuroendocrine cells as well as in gonads and in transdifferentiating epithelia (Rooman et al. 2002). However, according to the literature, PGP9.5 was originally detected as a “brain-specific protein”, accounting for about 5% of total neuronal proteins (Day and Thompson 2010; Bishop et al. 2016).
MAP2 may also be found in reactive astrocytes and oligodendrocyte precursors (Vouyioukis and Brophy 1995; Charrigue-Bertrand et al. 1991), as well as in early neuronal and glial precursors (Rosser et al. 1997). However, it is generally considered as a neuronal, neurogenesis-associated, differentiation marker (Soltani et al. 2005; Korzhevskii et al. 2012; Kim et al. 2020). In fact, MAP2 is a neuron-specific cytoskeletal protein that stabilizes microtubules, especially in their dendritic arborization. Finally, although GFAP has been found in subpopulations of diseased neurons (Hol et al. 2003), or in multipotent neural stem cells of the adult mammalian brain (Mitteldorp et al. 2010), its expression is commonly considered specific of astrocytes (Zhang et al. 2019).
In the present investigation, both flow cytometry and fluorescence quantification data indicate that ghrelin addition induced dynamic effects on ASC neural differentiation. Indeed, very modest influences could be observed when the peptide alone was added to ASCs cultured in the basal medium. The only appreciable effects consisted of an increased PGP9.5 expression after 7 days of treatment. For this reason, similarly to what was described by Liu et al.
(2020), we tested whether ghrelin could induce synergistic effects in combination with other neural-differentiation promoting protocols. Based on our previous findings (Lo Furno et al. 2018a), the combination with glial conditioned media was tested. By this combined strategy, more evident ghrelin-induced modifications were observed. Results
Fig. 2 Modifications of MAP2 expression at 1 and 7 days of culture in ASCs undergoing different treatments. In panel a (1 day) and b (7 days), MAP2 immunoreactivity is shown in different groups of ASCs: ASC cultures in the basal medium (ASC); ASC cultures in OEC-CM (ASC/OEC-CM) or SC-CM (ASC/SC-CM); ASC cultures where ghrelin was added to the basal medium (ASC + Ghre), to OEC-CM (ASC/OEC-CM + Ghre) or to SC-CM (ASC/SC-CM + Ghre). In each flow cytometry plot, data obtained from each culture condition, with or without ghrelin, are merged. Histograms show cell frequency distribution of each population, according to FITC fluorescence intensity expressed in logarithmic scale. Histogram overlays are displayed as %Max, scaling each curve to the respective modal values = 100%. Scale bar: 50 μm
show that modest influences were noticeable when ghrelin was added to OEC-CM. In this case, a weak increased expression of PGP9.5 and MAP2 was recognizable at both 1 and 7 days of treatment. Instead, more marked effects were detected when ghrelin was added to ASCs cultured in SC-CM, particularly after 7 days of treatment. On the other
hand, an opposite tendency was revealed for GFAP expres-
sion modifications. In fact, by adding ghrelin to glial CM,
reduced glial-induced increases were detected, especially
after 7 days of treatment. In general, more marked increases
of neuronal marker expression were observed when ghrelin
was combined with SC-CM rather than with OEC-CM. Such
differences might be due to different interactions between
the peptide and glial-produced bioactive molecules. In this
respect, it should be considered that many factors, even if
produced by both OECs and SCs, can be released in dif-
ferent amounts, and might differently interact with ghrelin.
Although the molecular interplay of these influences was
beyond the purpose of this work, these interactions certainly
deserve to be investigated.
In a recent work by Liu et al. (2020), ghrelin effects on
ASC neural differentiation were investigated. Although rat
ASCs and different neural induction strategies were used,
results obtained largely match those here described. In fact,
these authors report that the addition of ghrelin, in combi-
nation with a neurogenic culture medium, induced a dose-
dependent increase of neural markers. Ghrelin effects were
explained by an upregulation of the phosphorylation levels
of AKT and mTOR, as well as the activation of the β-catenin
signaling pathway. Different findings were however reported
for GFAP, whose expression was found increased, although
to a lesser extent than other neural markers. This discrep-
ancy might be explained by taking into account the different
experimental approaches, i.e. the different sources of ASCs
and/or the different neural induction protocol. In our study,
the use of glial conditioned media was preferred for ASC
neural differentiation since this strategy would more closely
mimic the physiological composition of a neural microen-
vivo.
Overall, also taking into account the limited observation
period, ASCs would likely be at the early stages of neural
differentiation, in which both neuronal and glial markers
still coexist (Lo Furno et al. 2018b). However, based on these results, it is possible to conclude that, at least using the protocol adopted here, a neuronal rather than a glial commitment would be promoted. Otherwise, if a glial phenotype was favored, a further increase of GFAP expression should have been observed. This conclusion is in keeping with data reported by Gong et al. (2020), describing ghrelin effects on neural stem cells. In fact, whereas their differentiation towards dopaminergic neurons was enhanced through the activation of the Wnt/β-catenin pathway, a significant decrease of GFAP-positive cells was reported.
In later experimental steps, the expression of GHSR-1a was also investigated to explain ghrelin-induced effects. GHSR-1a is widely expressed in the hippocampus and in various other brain regions (Akalu et al. 2020). Notably, the expression of ghrelin and its receptor has been also demonstrated in OECs (Russo et al. 2020a, b). It is worth noting that also undifferentiated ASCs express appreciable levels of GHSR-1a. This basal expression was improved after the different ASC treatments. Analogously to what was found for neural marker modifications, only modest increases were observed by the addition of ghrelin alone. Instead, effects were considerably more pronounced when using glial conditioned media. For each group, increases were consistently more evident after 7 days of treatment. The increased expression of GHSR-1a after glial CM treatment might explain why ghrelin-induced effects were more evident in combination with CM, particularly after 7 days.
In conclusion, the present work confirms that ghrelin may play a role in neural differentiation processes. Although these effects might per se be of a modest entity, they would be reinforced by mutual interactions with growth factors or cytokines. As already suggested (Jiao et al. 2017), ghrelin neuroprotective and neurogenic roles may be usefully exploited in the development of therapeutic strategies for the treatment of neurodegenerative diseases. An in vivo administration would reveal whether ASCs predifferentiated following these combined strategies better work in the host tissue.
Acknowledgements The authors wish to thank Dr. Antony Bridgewood of the Scientific Bureau of the University of Catania for language support. This research was supported by University of Catania. UPB: 20130141061 – Budget 2020.
Author contributions CR and GM carried out most of the experimental investigation and performed the statistical analysis; MP and NLP...
contributed to data collection and interpretation: RP, SS and RG contributed to research activity, planning and execution; contributed to manuscript preparation; DLF and AR were responsible for conceptualization, data curation, writing—review & editing. All authors reviewed the manuscript and approved the version to be published.
**Funding** Open access funding provided by Università degli Studi di Catania within the CRUI-CARE Agreement. University of Catania. UPB: 20130141061—Budget 2020.
**Declarations**
**Conflict of interest** The authors declare no conflict of interest.
**Ethical approval** Ethics committee of the University of Catania (Organismo Preposto al Benessere Animale, OPBA; Authorization n. 174/2017-PR); Comitato etico CataniaI (Authorization n. 155/2018/PO).
**Informed consent to participate** All authors gave their consent to participate.
**Informed consent for publication** All authors gave their consent for publication.
**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/.
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Russo C, Russo A, Pellitteri R, Stanzani S (2018) Ghrelin-containing neurons in the olfactory bulb send collateralized projections into medial amygdaloid and arcuate hypothalamic nuclei: neuroanatomical study. Exp Brain Res 236:2223–2229. https://doi.org/10.1007/s00221-018-5298-z (Epub 2018 May 29 PMID: 29845448)
Russo C, Patanè M, Russo A, Stanzani S, Pellitteri R (2020a) Effects of ghrelin on olfactory ensheathing cell viability and neural marker expression. J Mol Neurosci. https://doi.org/10.1007/s12031-020-01716-3 (PMID: 32976692)
Russo C, Patanè M, Vicario N, Di Bella V, Cosentini I, Barresi V et al (2020b) Olfactory ensheathing cells express both ghrelin and ghrelin receptor in vitro: a new hypothesis in favor of a neurotrophic effect. Neuropeptides 79:101997. https://doi.org/10.1016/j.npep.2019.101997 (PMID: 31784044)
Sato M, Nakahara K, Goto S, Kaiya H, Miyazato M, Date Y et al (2006) Effects of ghrelin and des-acyl ghrelin on neurons of the rat fetal spinal cord. Biochim Biophys Res Commun 350:598–603. https://doi.org/10.1016/j.jbc.2006.09.088 (PMID: 17026962)
Soltani MH, Pichardo R, Song Z, Sangha N, Camacho F, Satyamoorthy K et al (2005) Microtubule-associated protein 2, a marker of neuronal differentiation, induces mitotic defects, inhibits growth of melanoma cells, and predicts metastatic potential of cutaneous melanoma. Am J Pathol 166(6):1841–1850. https://doi.org/10.0141/S0002-9440(10)62493-5 (PMID: 15920168)
Stoyanova II, le Feber J, Rutten WL (2013) Ghrelin stimulates synaptic formation in cultured cortical networks in a dose-dependent manner. Regul Pept 186:43–48. https://doi.org/10.1016/j.regpep.2013.07.004 (PMID: 23892033)
Vouyioukllis DA, Brophy PJ (1995) Microtubule-associated proteins in developing oligodendrocytes: transient expression of a MAP2c isoform in oligodendrocyte precursors. J Neurosci Res 42(6):803–817. https://doi.org/10.1002/jnr.490420609 (PMID: 8847742)
Xu G, Li Y, An W, Zhang W (2008) Ghrelin and cell differentiation. Acta Biochim Biophys Sin (Shanghai) 40:841–847. https://doi.org/10.1111/j.1745-7270.2008.00465.x (PMID: 18850048)
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Publisher’s Note Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.
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Case Report
May-Thurner Syndrome—a Rare Cause of Extensive Pelvic DVT, but Is there More to Know?
Vikash Kumar,1 Michelle Koifman,1 Bhavyakumar Vachhani,1 Dhir Gala,2 and Sumeet Bahl1
1The Brooklyn Hospital Center, 121 DeKalb Ave, Brooklyn, NY 11201, USA
2American University of the Caribbean School of Medicine, 1 University Drive at Jordan Dr, Cupecoy, Saint Martin
Correspondence should be addressed to Vikash Kumar; [email protected]
Received 13 July 2022; Accepted 6 October 2022; Published 25 October 2022
Copyright © 2022 Vikash Kumar et al. 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.
May-Thurner Syndrome (MTS) is a rare anatomical variant characterized by the compression of the left common iliac artery by the right common iliac artery against the vertebral body (Figure 1) [1]. It is a rare cause of extensive DVT, compared to the usual presentation of DVTs that are more commonly seen as a result of various underlying illnesses.
1. Introduction
May-Thurner syndrome (MTS), coined after Dr. May R. and Dr. Thurner J., is a condition describing the phenomenon of sinistral occurrence of thrombosis of the pelvic veins due to extrinsic venous outflow obstruction. It has been defined as the compression of the left iliofemoral vein by the right common iliac artery against the vertebral body (Figure 1) [1]. It is a rare cause of extensive DVT, compared to the usual presentation of DVTs that are more commonly seen as a result of various underlying illnesses.
2. Case Presentation
A 28-year-old African American male with a past medical history of tobacco use disorder presented to the hospital with a 3-day history of lumbar back and posterior left lower extremity pain. He denied any recent trauma, prolonged immobilization, history of thromboembolic disease, or family history of thromboembolic disorders. Vitals were significant for a heart rate of 104 bpm. Physical examination revealed warmth and tenderness to palpation of the left thigh, with associated moderate nonpitting edema of the left lower extremity. Labs were significant for WBC of 10.9, platelet count of 743,000, CRP of 286.13, lactic acid of 2.6, and D-dimer that was >4.40. EKG showed LV hypertrophy and sinus tachycardia. Initial assessment with a point of care ultrasound to the left lower extremity showed noncompressible left common femoral vein, left saphenofemoral junction, left superficial and deep femoral veins confluence, and left popliteal vein. CTA chest was unremarkable for pulmonary embolism or any other pulmonary pathology. CTA abdomen/pelvis showed occlusive thrombus in visualized portions of left superficial and deep femoral veins, extending into the left common femoral vein, and into the left external, internal, and common iliac veins, with compression of the left common iliac vein by the crossing right common iliac artery, findings were suggestive of MTS (Figure 2). There was also left para-aortic and left external iliac lymphadenopathy, possibly reactive, however metastatic disease could not be excluded. CTA abdomen/pelvis also showed an unusually narrow inferior vena cava (IVC) indicative of intrahepatic IVC stenosis (Figure 3(a)), with multiple intra-abdominal collaterals (Figure 3(b)). The Hematology-Oncology team
was consulted in concern of extensive lymphadenopathy and thrombocytosis, who further recommended workup, including PET-CT, to rule out malignancy. JAK2 mutation, CALR, and MPL testing ruled out a myeloproliferative neoplasm. Workup for thrombophilia (antiphospholipid antibodies, anticardiolipin antibodies, anti-beta-2-glycoproteins, Protein C and S, and homocysteine) was negative. The patient was started on therapeutic enoxaparin and switched to a heparin drip as per the Interventional Radiology (IR) team’s recommendations. The patient underwent a left lower extremity venogram by the IR team which showed an occluded left popliteal vein extending up to the left external iliac vein with a tram-track pattern (Figure 4). The patient was then transferred to a specialty facility where he underwent a repeat venogram with venoplasty and pharmacomechanical thrombectomy. He was further moved to the Medical ICU for close monitoring postoperatively. He was discharged on postoperative day 3 on apixaban for at least 6 months with close outpatient follow-up to determine the duration of anticoagulation.
3. Discussion
DVT is a common and potentially life-threatening problem, with the incidence of it varying with age. Annual incidence rates by age group is approximately 2–3 per 10,000 (30–49 years), 5 per 10,000 (50–59 years), 10 per 10,000 (60–69 years), and 20 per 10,000 (70–79 years) [2]. DVT usually occurs in the setting of predisposing factors such as recent surgery or trauma, immobilization of limbs, active cancer, acute medical illnesses, obesity, use of oral contraceptive medications, and thrombophilic disorders [3].
Venous stasis has been long known to be a predisposing factor for thrombosis and is part of the famous Virchow triad along with hypercoagulability and endothelial injury. One cause of venous stasis was first described in 1957 by May and Thurner during their study of 430 cadavers, where they found spur-like projections within the venous wall of 15–22% of the investigated cases. These spurs, which were believed to be a result of irritation...
Figure 2: (a, b, c) CT abdomen/pelvis with contrast significant for occlusive thrombus in visualized portions of deep femoral veins, extending into the left common femoral vein, and into the left external, internal, and common iliac veins.
Figure 3: (a) CT abdomen/pelvis with contrast showing intrahepatic IVC stenosis (blue arrow). (b) Seen is a large diaphragmatic venous collateral to the IVC (orange arrow), indicating that the thrombosis in this patient was acute on chronic pathology.
induced by the pulsation of the overlying artery, cause luminal narrowing and promote clot formation leading to thrombosis.
Based on a systematic review, the mean age of presentation for MTS is 25–50 years, more common in females with a female to male ratio of 2–4.7:1 [4], and most commonly involving the left side as the left common iliac vein crosses between the right common iliac artery and the L5 spine [5]. MTS presentation can vary from mild swelling or severe extensive DVT and PE. MTS is often overlooked in young patients without risk factors due to several reasons. Firstly, by review of the literature, there are very few cases of male patients presenting with DVT due to May-Thurner syndrome. Furthermore, MTS may be missed as a potential alternative diagnosis when common risk factors of DVT, such as prolonged bed rest, postsurgery, malignancy, or oral contraceptive pill use [6] are already confirmed and further workup is not performed. Finally, the low incidence of diagnosis is also related to the fact that a usual DVT is commonly diagnosed with an ultrasound, whereas diagnosing the defect that develops with MTS, which usually occurs higher in the pelvis, requires more specific studies such as a CT scan or an MRI [7].
Early diagnosis and prompt treatment of DVT due to MTS is essential. Diagnosis modalities include plain CT, CTA, however, IVUS with conventional venography is the gold-standard modality to diagnose MTS [8]. This can provide accurate sizing of the luminal diameter and even provide insights into the chronicity of the thrombus with the presence or absence of collateral venous and fibrotic changes. In our case, CTA abdomen/pelvis and venogram findings were consistent with the diagnosis of MTS. In addition, intrahepatic IVC stenosis with multiple collaterals was also seen. While the exact cause of the oddly narrow IVC is not obvious, a possible differential could include a congenital anomaly or consequences of chronic thrombosed lower extremity veins in our patient. What was initially thought to be MTS alone, was actually understood to be a stenotic IVC that in addition to the MTS itself led to thrombosis.
Treatment of MTS is guided by clinical presentation. It is generally accepted that a more invasive therapeutic approach is needed to prevent long-term-sequelae, as systemic anticoagulation may be insufficient [9]. Even though open surgery was used in the past, more recently, endovascular procedures such as catheter-directed thrombolysis and stent placement have been the preferred choice for treatment. Following stent placement, therapeutic anticoagulation is indicated, but there is no consensus regarding the optimal duration, type, and intensity of anticoagulation needed. For most patients, 6–12 months of anticoagulation following stent placement is usually sufficient.
Temporary IVC filters are yet another endovascular approach that may be considered in MTS. Similar to our young male patient, Hng et al. discussed the case of a 23-year-old male who presented with MTS. He underwent IVC filter placement, mechanical thrombectomy, thrombolysis, and further subcutaneous anticoagulation with the eventual removal of the IVC filter [10]. It is necessary to remove IVC filters as soon as possible to prevent filter-related DVT. As per a quantitative decision analysis, the benefit/risk profile is favorable for filter removal between 29 and 54 days after implantation [11].
4. Conclusion
While uncommon itself, MTS is even more rare in males. We believe the intrahepatic IVC stenosis in our young patient, together with the MTS lesion, led to a thrombophilic state triggering the thrombosis. The extensive collaterals identified on the CTA were indicative that the thrombosis was an acute event on a chronic pathology.
Considering the extensive nature of associated thrombosis, MTS if left untreated could lead to devastating consequences such as postthrombotic syndrome and chronic venous insufficiency. It is necessary to identify patients with high risk for MTS, especially younger individuals including males presenting with left-sided lower extremity swelling. Early recognition using US or CT venography techniques is necessary to prevent PE. Treatment involves anticoagulation, as well as endovenous management, including thrombolysis/thrombectomy, venous angioplasty, and stenting.
Data Availability
No data were used to support this study.
Ethical Approval
All procedures were performed in accordance with the ethical standards laid down in the 1964 Declaration of Helsinki and its later amendments.
Consent
Informed consent for this case report was obtained from the patient. This study does not contain identifying information of the patient.
Conflicts of Interest
We declare that we have no known competing financial interests, personal relationships, or competing interests that could have influenced the work reported in this study.
References
[1] R. May and J. Thurner, "The cause of the predominantly sinistral occurrence of thrombosis of the pelvic veins," *Angiology*, vol. 8, no. 5, pp. 419–427, 1957.
[2] F. J. Fowkes, J. F. Price, and F. G. Fowkes, "Incidence of diagnosed deep vein thrombosis in the general population: systematic review," *European Journal of Vascular and Endovascular Surgery*, vol. 25, no. 1, pp. 1–5, 2003.
[3] N. Moudgil, E. Hager, C. Gonsalves, R. Larson, J. Lombardi, and P. DiMuzio, "May-Thurner syndrome: case report and review of the literature involving modern endovascular therapy," *Vascular*, vol. 17, no. 6, pp. 330–335, 2009.
[4] M. R. Kibbe, M. Ujiki, A. L. Goodwin, M. Eskandari, J. Yao, and J. Matsumura, "Iliac vein compression in an asymptomatic patient population," *Journal of Vascular Surgery*, vol. 39, no. 5, pp. 937–943, 2004.
[5] C. T. Kaltenmeier, Y. Erben, J. Indes et al., "Systematic review of May-Thurner syndrome with emphasis on gender differences," *Journal of Vascular Surgery. Venous and Lymphatic Disorders*, vol. 6, no. 3, pp. 399–407.e4, 2018.
[6] A. Baburao, A. Singh, A. Babu, and A. Pandey, "May-Thurner syndrome: a forgotten cause of venous thromboembolism," *Indian Journal of Critical Care Medicine*, vol. 24, no. 1, pp. 66–68, 2020.
[7] K. S. McNally, L. Ganti, V. I. Diaz, A. L. Webb, and G. Alvarez, "Symptomatic May-Thurner syndrome without deep venous thrombosis," *Cureus*, vol. 11, no. 11, article e6178, 2019.
[8] M. G. Knuttinen, S. Naidu, R. Oklu et al., "May-Thurner: diagnosis and endovascular management," *Cardiovascular Diagnosis and Therapy*, vol. 7, Suppl 3, pp. S159–S164, 2017.
[9] M. Peters, R. K. Syed, M. Katz et al., "May-Thurner syndrome: a not so uncommon cause of a common condition," *Proceedings (Baylor University Medical Center)*, vol. 25, no. 3, pp. 231–233, 2012.
[10] J. Hng, S. Su, and N. Atkinson, "May-Thurner syndrome, a diagnosis to consider in young males with no risk factors: a case report and review of the literature," *Journal of Medical Case Reports*, vol. 15, no. 1, 2021.
[11] J. P. Morales, X. Li, T. Z. Irony, N. G. Ibrahim, M. Moynahan, and K. J. Cavanaugh Jr., "Decision analysis of retrievable inferior vena cava filters in patients without pulmonary embolism," *Journal of Vascular Surgery. Venous and Lymphatic Disorders*, vol. 1, no. 4, pp. 376–384, 2013.
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A Study on the Impact of Social Media on Consumer Buying Behaviour of Mobile Phones in Chennai
S. Gajashree
Department of Management Studies
SRM Valliammai Engineering College, Chennai, Tamil Nadu, India
J. Anand
Assistant Professor, Department of Management Studies
SRM Valliammai Engineering College, Chennai, Tamil Nadu, India
Abstract
This paper aims to investigate the impact of social media on consumer buying behavior. The primary purpose of this research is to identify the effect of social media on consumer buying decisions. Social Media have given many opportunities to consumers to adapt to different aspects of life. Facebook, Twitter and Instagram have played significant roles in expanding consumer's online purchases. This paper aims to know which consumers are mostly influenced by the online purchase of mobile through social media and the kinds of social media that are employed mainly by consumers in Chennai. The research carried out primary research methods and questionnaire to investigate the impact of social media sites on the user's changing behavior who aim to purchase online. The target of the research is to elucidate why, when, and the way social media has impacted on the consumer decision process. The theoretical framework rests on the literature of the consumer decision-making process, social media, and previous studies relating to social media marketing. The quantitative research method is tailored to the aim of this research. The empirical data was gathered by sending out an opinion poll to individuals. The study explains how individuals are attending processing and selecting the knowledge on social media before a sale. The findings indicate that individuals pursue an active role in information search on social media comparing to mass media. Yet, information exposure is selective and subjective during knowledge search. Results show that social media usage influences consumer satisfaction within the stages of data search and alternative evaluation, with happiness getting amplified. The consumer moves along the method towards the ultimate purchase decision and post-purchase evaluation.
Keywords: Social media, Consumer, Buying behaviour, Marketing, Online opportunities, Mobile phone, Decision, Perception
Introduction
This paper covers the impact of social media on consumer behavior of mobile phone purchases. Social media is that the online communications medium dedicated to community-based input, interaction, and content-sharing. Social media marketing features a brought a dramatic change in marketing tools because the social media user isn’t only an observer but also act as a lively participant because he gives input, reviews and opinion on the open platform. Social media helps to find unique discounts and promotions for mobile phones. The mobile phone has become an integral part of human daily and personal communication across the globe. Social media to find out about new mobile phones and specific stores of mobiles. According to a current report, the number of social media client worldwide in 2019 is 3.484 billion. As more and more people joining social media. The most crucial role of social media has changed the way of how consumers and marketers communicate.
Also, Social media can play a huge role in influencing consumers in their purchases of mobile phones. Social media usage affects consumer satisfaction within the stages of data search. Moreover, by using social media, consumers can influence other buyers through reviews of mobile phones used. The goal of this paper is to find the impact of social media on consumer purchase behavior of mobile phones. Among the many parameters in a social media impact of consumer buying behavior of mobile purchasing decision three main parameters have been considered in this research, namely reviews of different buyers, company or brand presentation on social networks and the difficulties of information search for mobile phone through social media. A quantitative survey was wont to retroactively plan to explore aspects of the phases within the decision process. A total of 50 participants completed the study, and their responses were used to analyze the decision-making process of their impact of social media on mobile purchase instances.
Review of Literature
According to McKinsey Company (2010) In his study, Social Media features a notable influence on customers, mainly who are first-time purchasers of a product. It’s a more significant influence on high priced products because the consumers want to conduct additional analysis and to urge opinions for purchasing the merchandise. This means that Social Media has an impression on customers in their data search stage of shopping for a product. As a result, customers will use Social Media to urge data concerning the product and services. Xia wang, Case Study of Lagos State University Students (2018) The examination researches peer correspondence through internet based life sites; singular level tie quality. Study information 292 members who occupied with peer correspondence about through online networking. Ionas Elisabeta; Ivona Stioca (2014) The paper manages the effect of online networking on buyer purchasing choice. Ethel Lee (2014) The goal of the investigation is to explain why, when, and the way internet based life has affected on shopper choice process.
Problem Statement
The purpose of the study was to identify the Social media usage influences consumer satisfaction. Moreover, this study aims to answers the subsequent questions precisely:
- What is the purpose of using social media?
- How social media impact on purchasing decision of consumers on mobile phones?
- Make a comparison between males and females on how social media impact on their buying?
Objectives
Primary Objectives: A Study on the impact of social media on consumer buying behavior of mobile phones in Chennai.
Secondary Objectives: To identify the factors, influence the consumers to purchase mobile phones through social media. To find out which is the best social media preferred by the consumer. To evaluate the various channels prepared by a consumer for buying decisions over traditional channels.
Research Methodology
The most important thing that has to understand that Research methodology is a system to solve the related problem. It is not only science but also art the way to do research scientifically. It’s the logic to be utilized in the context of research. The researcher has got to understand the matter, which provides him the direction the way to solve the issue. The research methodology consists of a series of actions or steps necessary to carry out research work effectively.
Research Design
“A research design is that the arrangement of conditions for collection and analysis of data during a fashion that aims to combine relevance to the research purpose with economy in procedure” Research design is that the framework of research methods and techniques chosen by a researcher. The
planning allows researchers to hone in on research methods suitable for the topic matter and found out their studies up for fulfillment. Here the descriptive research design is employed.
**Descriptive Research**
Descriptive research aims to correctly and systematically explain a population, situation, or phenomenon. It can answer what, when, where, when and how questions, but not why questions. Descriptive research is designed to describe something, such as demographical characteristics of consumers who use the products. It deals with determining the frequency with which something occurs or how two variables vary together. A descriptive research design can use a wide variety of research methods to investigate one or more variables. Unlike in experimental research, the researcher doesn’t control or manipulate any of the variables but only observes and measures them.
**Sampling Design**
Sampling is done to collect samples - the sampling techniques used for large numbers. The sampling techniques used in this study are convenience sampling under non-probability. In non-probability selection, the present chance of any particular unit in the population being into the sample is unknown. In convenience sampling, the samples from the population are chosen primarily based on the convenience of the researcher.
**Sampling Size**
The survey is going to be conducted on the idea of the sampling method. The study was conducted on Mobile Phone users. The researcher will develop sample design; the researcher will be collecting the information from 55 customers who were selected for the present study in Chennai city.
**Survey Questionnaire Method**
A survey questionnaire is a type of data gathering method utilized to collect, analyze, and interpret the different views of a group of people from a particular population. The survey questionnaire has been used in different fields like research, marketing, political opinions, psychology, etc.
**Questionnaire**
The questionnaire is an instrument for research, which consists of an inventory of questions, alongside the selection of answers, printed or typed during a sequence on a form used for acquiring specific information from the respondents. Generally, questionnaires are delivered to the persons concerned either by post or mail, requesting them to answer the questions and return them.
**Methods of Data Collection**
**Primary Data:** Primary data is known as firsthand information to determine a specific problem. Primary data is collected from its primary sources, i.e., the source of its origin, where the info is generated. It’s the first time organized by its investigator for statistical analysis.
**Secondary Data:** Secondary data are the data are in actual existence, in records, having been already collected and also treated statistically. In short, it is the data that has been already assembled, presented, tabulated, and located with analytical that have been collected by some agencies, government department and research workers are often obtained from records, books, government publications and journals. Utmost care has taken by the researcher while collecting the info from the varied sources.
**Statistical Design**
The statistical design of a web controlled experiment (a.k.a A/B test) is that the results of the interpretation of a substantive business question of interest into an investigation with a well-defined statistical model that permits the utilization of knowledge during a decision-making process within the presence of uncertainty. The planning should fully describe the experiment in terms of the choices relevant to its statistical model.
**Statistical Tools Used**
For the analysis of the info and its interpretation, various tools of research were used.
**Mann Whitney U-Test**
The Mann-Whitney U test compares the number of times a score from one sample is ranked above a score from another piece. Once the info is organized, calculations are going to be administered on the
ranks. Given the nonparametric nature of this statistical analysis, there are fewer assumptions to assess. In statistics, the Mann–Whitney U test may be a nonparametric test of the null hypothesis that, for randomly selected values X and Y from two populations, the probability of X being more significant than Y is adequate the possibility of Y being more significant than X.
| Ranks | Social media purchase | N | Mean Rank | Sum of Ranks |
|-------|-----------------------|----|-----------|--------------|
| Values| Triggers to Purchase Mobile | 55 | 58.00 | 3190.00 |
| | Change Attitude for Mobile Purchase | 55 | 53.00 | 2915.00 |
| Total | | 110 | | |
**Test Statistics**
| Values | |
|-----------------|----------------|
| Mann-Whitney U | 1375.000 |
| Wilcoxon W | 2915.000 |
| Z | -.992 |
| Asymp. Sig. (2-tailed) | .321 |
*a. Grouping Variable: Social media purchase*
**Interpretation:** From the above table, P-value (0.321) is more significant than LOS (0.05), H0 is accepted. Therefore, Social media change people’s attitude for mobile purchase but does not trigger the people for mobile investment.
**Chart 1: Profile of Respondents**
From chart one, we analyze. According to Gender, the majority of respondents are female (60%). According to Age, the majority of respondents are 20-25(94.5). According to Educational qualifications the majority of respondents are graduates (63.6%).
**Table 1: Classification of Social Media Site is Likely to buy Mobile Phones**
| S. No. | Particulars | No. of Respondents | Percentage |
|--------|-------------|--------------------|------------|
| 1 | Facebook | 6 | 10.9% |
| 2 | Instagram | 20 | 36.4% |
| 3 | WhatsApp | 10 | 18.2% |
| 4 | Others | 19 | 34.5% |
| Total | | 55 | 100% |
**Inference:** From the above table, it is inferred that 36.4% of respondents liked to buy the mobile on Instagram.
**Table 2: Classification of Social Media Trigger to Purchase a Mobile Phone**
| S. No. | Particulars | No. of Respondents | Percentage |
|--------|-------------|--------------------|------------|
| 1 | Yes | 33 | 60% |
| 2 | No | 22 | 40% |
| Total | | 55 | 100% |
**Inference:** From the above table, it is inferred that 60% of Respondents said social media triggers a mobile phone.
**Table 3: Classification of Social Media Influence Mobile buying Decision**
| S. No. | Particulars | No. of Respondents | Percentage |
|--------|-------------|--------------------|------------|
| 1 | Yes | 33 | 60% |
| 2 | No | 22 | 40% |
| Total | | 55 | 100% |
**Inference:** From the above table, it is inferred that 60% of respondents said that social media influence the mobile buying decision.
Table 4: Classification of Social Media Advertisements Influence to Try a new Mobile Brand
| S. No | Particulars | No of Respondents | Percentage |
|-------|------------------|-------------------|------------|
| 1 | Strongly Agree | 6 | 10.9% |
| 2 | Agree | 15 | 27.3% |
| 3 | Neutral | 24 | 43.6% |
| 4 | Disagree | 6 | 10.9% |
| 5 | Strongly Disagree| 4 | 7.3% |
| Total | | 55 | 100% |
Inference: From the above table, it is inferred that 43.6% of Respondents’ decision is neutral for social media advertisements influence to try new mobile phone brand.
Table 5: Classification of the Attitude Towards a Positive Comment about New Brands of Mobile
| S. No | Particulars | No of Respondents | Percentage |
|-------|-------------|-------------------|------------|
| 1 | Yes | 38 | 69.1% |
| 2 | No | 17 | 30.9% |
| Total | | 55 | 100% |
Inference: From the above table, it is inferred that 69.1% of respondents said that the positive comments on social media create an attitude towards a particular brand of mobile phones.
Table 6: Classification of the Social Network Channels is More Values Marketing Channels than the Traditional Media
| S. No | Particulars | No of Respondents | Percentage |
|-------|-----------------|-------------------|------------|
| 1 | Strongly Agree | 11 | 20% |
| 2 | Agree | 30 | 54.5% |
| 3 | Neutral | 8 | 14.5% |
| 4 | Disagree | 4 | 7.3% |
| 5 | Strongly Disagree| 2 | 3.6% |
| Total | | 55 | 100% |
Inference: From the above table, it is inferred that 54.5% of respondents agreed that the social network channels are more values marketing channels than the traditional ones.
Table 7: Classification of Social Media Sites that Influence Mobile Purchase on the Day to Day life
| S. No | Particulars | No of Respondents | Percentage |
|-------|-----------------|-------------------|------------|
| 1 | Daily | 7 | 12.7% |
| 2 | 1-2 times a week| 10 | 18.2% |
| 3 | 3-4 times a week| 6 | 10.9% |
| 4 | Once a month | 10 | 18.2% |
| 5 | Only when needed| 22 | 40% |
| Total | | 55 | 100% |
Inference: From the above table, it is inferred that 40% of respondents said that social media sites influenced only when they needed time for mobile purchase.
Findings
- 60% of respondents are Female.
- 94.5% of respondents are of the age of 20-25.
- 63.6% of respondents have completed their graduation.
- 36.4% of respondents are liked to buy mobile phones on Instagram.
- 45.5% of the respondents have to search always the information on social media before the mobile purchase.
- 60% of respondents said that social media trigger to purchase a mobile phone.
- 41.8% of respondents agreed that social media helps in acquiring information about mobile phones.
- 60% of respondents said that social media influence mobile buying decisions.
- 43.6% of Respondents’ decision is neutral for social media advertisements influence to try new mobile phone brand.
- 60% of respondents agreed that social media advertisements influence try new mobile phone brand.
- 69.1% of respondents said that positive comments on social media create an attitude towards a particular brand of mobile phones.
- 40% of respondents said that social media sites only influence when they needed time for mobile purchase.
- 54.5% of respondents agreed that the social
network channels are a more valuable marketing channel than the traditional ones.
- 52.7% of respondents agreed that social media is more influential than traditional media in your final purchase.
- 52.7% of respondents have Likely to buy the mobile online in the future.
**Suggestions**
- The marketers should Share valuable and informative content and Engage with the audience.
- The mobile companies which used social media strategies should build their brand authority.
- Social media marketers should overcome the bad reviews and comments with their high-quality, unique content and post videos to drive their reach.
- Having a social media profile and posting random content will not take social media marketers’ brand anywhere. Produce engaging content that grabs their audience’s eyeballs and further pushes them to like it and share it.
**Conclusion**
The research has considered various Social Websites that do the work of Networking that’s Facebook, WhatsApp, Twitter, and lots more. The study explains how individuals are attending processing and selecting the knowledge on social media before buying. The findings indicate that individuals pursue an active role in information search on social media comparing to mass media. Yet, information exposure is selective and subjective during knowledge search. Results show that social media usage influences consumer satisfaction within the stages of data search and alternative evaluation, with happiness getting amplified. The consumer moves along the method towards the ultimate purchase decision and post-purchase evaluation.
Results conducted through this study suggest that companies should specialize in being present on social networks, visible on search engines and supply continuous online feedback. Finally, results show companies should specialize in improving their online perception through customer engagement since it’s one of the most ways in which customers nowadays decide whether to shop for product or not.
**References**
Wanga, Xia, et al. “Social Media Peer Communication and Impacts on Purchase Intentions: A Consumer Socialization Framework.” *Journal of Interactive Marketing*, vol. 26, no. 4, 2012, pp. 198-208.
Ioanăs, Elisabeta, and Ivona Stoica. “Social Media and its Impact on Consumers Behavior.” *International Journal of Economic Practices and Theories*, vol. 4, no. 2, 2014, pp. 295-303.
Hutter, Katja, et al. “The Impact of User Interactions in Social Media on Brand Awareness and Purchase Intention: The Case of MINI on Facebook.” *Journal of Product & Brand Management*, vol. 22, 2013, pp. 342-351.
Lee, Ethel. *Impacts of Social Media on Consumer Behavior – Decision Making Process*, Turku University of Applied Sciences, 2013.
Bughlin, Jacques, et al. “A New Way to Measure word-of-mouth Marketing.” *Mckinsey Quarterly*, 2010.
Mamoria, C.B. *Personnel Management: (Management of Human Resources)*, Himalaya Publishing House, 1994.
Malhotra, R.K., et al. *Personnel Management*, Anmol Publications, 2003.
Tripathi, P.C. *Personnel Management and Industrial Relations*, Sultan Chand & Sons, 2013.
Kothari, C.R. *Research Methodology: Methods and Techniques*, Wishwa Prakashan, 1997.
**Author Details**
S. Gajashree, *Department of Management Studies, SRM Valliammai Engineering College, Chennai, Tamil Nadu, India*
Dr. J. Anand, *Assistant Professor, Department of Management Studies, SRM Valliammai Engineering College, Chennai, Tamil Nadu, India, Email ID: [email protected].*
| 2025-03-05T00:00:00 |
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