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Dynamic Models of Biology and Medicine, Volume II

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A special issue of Applied Sciences (ISSN 2076-3417). This special issue belongs to the section "Applied Biosciences and Bioengineering".

Deadline for manuscript submissions: closed (15 July 2020) | Viewed by 45024

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Special Issue Editors

Prof. Dr. Yang Kuang

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Guest Editor

School of Mathematical and Statistical Sciences, Arizona State University, Tempe, AZ 85287, USA
Interests: mathematical and computational biology and medicine; delay differential equations; mathematical models; applied mathematics
Special Issues, Collections and Topics in MDPI journals

Dr. Kevin Flores

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Guest Editor

North Carolina State University, Raleigh, NC, USA
Interests: applied mathematics; inverse problems; mathematical biology; precision medicine; machine learning
Special Issues, Collections and Topics in MDPI journals

Dr. Erica Rutter

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Guest Editor

North Carolina State University/ University of California – Merced, Raleigh, NC, USA
Interests: mathematical biology; mathematical oncology; machine learning
Special Issues, Collections and Topics in MDPI journals

Special Issue Information

Dear Colleagues,

Mathematical and computational modeling approaches in biological and medical research are experiencing exponential growth globally. This Special Issue intends to catch a glimpse of this exciting phenomenon. Areas covered include general mathematical methods and their applications in biology and medicine, with an emphasis on work related to mathematical and computational modeling and to nonlinear and stochastic dynamics.

Topics appropriate for this Special Issue include, but are not limited to, all areas of mathematical biology and medicine that employ dynamic (differential equation) models to describe observed nonlinear dynamics that aim to understand life science problems. To be considered for this Special Issue, a paper should be in one (or a combination) of the following three categories. (a) papers developing and mathematically analyzing dynamic models that have concrete applications in biology or medicine; (b) papers devoted to mathematical theory and methods, with a clear life science motivation, whose results may lead to an improved understanding of the underlying problem; and (c) papers using numerical simulations, experiments, or both to reveal or explain some new life science phenomena, where mathematical analysis plays a useful role in the process.

All papers must contain a comprehensive introductory section and an in-depth discussion section that is closely tied to applications. The scientific importance and motivation of the paper and its conclusions should be made clear at the outset.

Prof. Dr. Yang Kuang
Dr. Kevin Flores
Dr. Erica Rutter
Guest Editors

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Submitted manuscripts should not have been published previously, nor be under consideration for publication elsewhere (except conference proceedings papers). All manuscripts are thoroughly refereed through a single-blind peer-review process. A guide for authors and other relevant information for submission of manuscripts is available on the Instructions for Authors page. Applied Sciences is an international peer-reviewed open access semimonthly journal published by MDPI.

Please visit the Instructions for Authors page before submitting a manuscript. The Article Processing Charge (APC) for publication in this open access journal is 2400 CHF (Swiss Francs). Submitted papers should be well formatted and use good English. Authors may use MDPI's English editing service prior to publication or during author revisions.

Keywords

Dynamic system
mathematical biology
mathematical medicine
simulation
stability
bifurcation

Published Papers (12 papers)

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Research

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32 pages, 1596 KiB

Open AccessArticle

Moth Mating: Modeling Female Pheromone Calling and Male Navigational Strategies to Optimize Reproductive Success

by Tracy L. Stepien, Cole Zmurchok, James B. Hengenius, Rocío Marilyn Caja Rivera, Maria R. D’Orsogna and Alan E. Lindsay

Appl. Sci. 2020, 10(18), 6543; https://doi.org/10.3390/app10186543 - 18 Sep 2020

Cited by 12 | Viewed by 8064

Abstract

Male and female moths communicate in complex ways to search for and to select a mate. In a process termed calling, females emit small quantities of pheromones, generating plumes that spread in the environment. Males detect the plume through their antennae and navigate toward the female. The reproductive process is marked by female choice and male–male competition, since multiple males aim to reach the female but only the first can mate with her. This provides an opportunity for female selection on male traits such as chemosensitivity to pheromone molecules and mobility. We develop a mathematical framework to investigate the overall mating likelihood, the mean first arrival time, and the quality of the first male to reach the female for four experimentally observed female calling strategies unfolding over a typical one-week mating period. We present both analytical solutions of a simplified model as well as results from agent-based numerical simulations. Our findings suggest that, by adjusting call times and the amount of released pheromone, females can optimize the mating process. In particular, shorter calling times and lower pheromone titers at onset of the mating period that gradually increase over time allow females to aim for higher-quality males while still ensuring that mating occurs by the end of the mating period. Full article

(This article belongs to the Special Issue Dynamic Models of Biology and Medicine, Volume II)

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34 pages, 7430 KiB

Open AccessArticle

Quantifying the Biophysical Impact of Budding Cell Division on the Spatial Organization of Growing Yeast Colonies

by Mikahl Banwarth-Kuhn, Jordan Collignon and Suzanne Sindi

Appl. Sci. 2020, 10(17), 5780; https://doi.org/10.3390/app10175780 - 20 Aug 2020

Cited by 5 | Viewed by 3266

Abstract

Spatial patterns in microbial colonies are the consequence of cell-division dynamics coupled with cell-cell interactions on a physical media. Agent-based models (ABMs) are a powerful tool for understanding the emergence of large scale structure from these individual cell processes. However, most ABMs have focused on fission, a process by which cells split symmetrically into two daughters. The yeast, Saccharomyces cerevisiae, is a model eukaryote which commonly undergoes an asymmetric division process called budding. The resulting mother and daughter cells have unequal sizes and the daughter cell does not inherit the replicative age of the mother. In this work, we develop and analyze an ABM to study the impact of budding cell division and nutrient limitation on yeast colony structure. We find that while budding division does not impact large-scale properties of the colony (such as shape and size), local spatial organization of cells with respect to spatial layout of mother-daughter cell pairs and connectivity of subcolonies is greatly impacted. In addition, we find that nutrient limitation further promotes local spatial organization of cells and changes global colony organization by driving variation in subcolony sizes. Moreover, resulting differences in spatial organization, coupled with differential growth rates from nutrient limitation, create distinct sectoring patterns within growing yeast colonies. Our findings offer novel insights into mechanisms driving experimentally observed sectored yeast colony phenotypes. Furthermore, our work illustrates the need to include relevant biophysical mechanisms when using ABMs to compare to experimental studies. Full article

(This article belongs to the Special Issue Dynamic Models of Biology and Medicine, Volume II)

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20 pages, 19561 KiB

Open AccessArticle

The Hemodynamics of Aneurysms Treated with Flow-Diverting Stents Considering both Stent and Aneurysm/Artery Geometries

by Paulo R. Cillo-Velasco, Rafaello D. Luciano, Michael E. Kelly, Lissa Peeling, Donald J. Bergstrom, Xiongbiao Chen and Mauro Malvè

Appl. Sci. 2020, 10(15), 5239; https://doi.org/10.3390/app10155239 - 29 Jul 2020

Cited by 3 | Viewed by 2783

Abstract

Flow diverting stents are deployed to reduce the blood flow into the aneurysm, which would thereby induce thrombosis in the aneurysm sac; the stents prevent its rupture. The present study aimed to examine and quantify the impacts of different flow stents on idealized configurations of the cerebral artery. In our study, we considered a spherical sidewall aneurysm located on curved and tortuous idealized artery vessels and three stents with different porosities (70, 80 and 90%) for deployment. Using computational fluid dynamics, the local hemodynamics in the presence and absence of the stents were simulated, respectively, under the assumption that the blood flow was unsteady and non-Newtonian. The hemodynamic parameters, such as the intra-aneurysmal flow, velocity field and wall shear stress and its related indices, were examined and compared among the 12 cases simulated. The results illustrated that with the stent deployment, the intra-aneurysmal flow and the wall shear stress and its related indices were considerably modified depending on both stent and aneurysm/artery geometries, and that the intra-aneurysmal relative residence time increased rapidly with decreasing stent porosity in all the vessel configurations. These results also inform the rationale for selecting stents for treating aneurysms of different configurations. Full article

(This article belongs to the Special Issue Dynamic Models of Biology and Medicine, Volume II)

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Graphical abstract

8 pages, 1599 KiB

Open AccessArticle

Wavelet Analysis of Microcirculatory Flowmotion Reveals Cardiovascular Regulatory Mechanisms–Data from a Beta-Blocker

by Henrique Silva, Étienne Roux, Alain-Pierre Gadeau and Luis Monteiro Rodrigues

Appl. Sci. 2020, 10(11), 4000; https://doi.org/10.3390/app10114000 - 09 Jun 2020

Cited by 1 | Viewed by 1971

Abstract

A variety of animal models exist for the study of cardiovascular function using many approaches from surgically induced ischemia to genetic manipulation. A murine physiological model was recently proposed for the non-invasive study of peripheral circulation and was strengthened by the wavelet transform analysis (WA) of laser Doppler flowmetry (LDF) signals. WA allows the extraction of cardiac, respiratory, sympathetic, endothelial, and myogenic components from the raw LDF signal. The present study was designed to evaluate the discernment capacity of the model through an analysis of the short-term effects of the well-known hypotensive cardiovascular drug, atenolol. Six male C57/BL6 mice (16 weeks old) were included in the study, with each animal serving as its own control. Following anesthesia with ketamine-xylazine, skin perfusions were continuously assessed in both hindlimbs by LDF during baseline and after two sequential atenolol administrations (2.5 and 5.0 mg/kg, as commonly prescribed). Expected atenolol-induced hypotension was present, associated with a significantly increased heart rate and peripheral perfusion with both dosages. Through the application of WA to the LDF signal, we could detail the mechanisms of the atenolol-induced peripheral perfusion modulation: an immediate amplitude decrease of the cardiac LDF spectrum with an amplitude increase of the sympathetic component (p < 0.05) and the endothelial and myogenic components (non-significant). These data suggested a regulatory crosstalk between the peripheral (baroreceptors) and the microcirculatory units, which ultimately resulted in hypotension, inotropic reduction, and tachycardia. In conclusion, WA offered insight that simply could not be seen with only the perfusion curve and, thus, was an effective tool to investigate this cardiovascular mechanism of regulation. Full article

(This article belongs to the Special Issue Dynamic Models of Biology and Medicine, Volume II)

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18 pages, 5376 KiB

Open AccessArticle

A Kinematic Model of the Shoulder Complex Obtained from a Wearable Detection System

by Jianfeng Li, Chunzhao Zhang, Mingjie Dong and Qiang Cao

Appl. Sci. 2020, 10(11), 3696; https://doi.org/10.3390/app10113696 - 27 May 2020

Cited by 6 | Viewed by 3867

Abstract

Due to the complex coupled motion of the shoulder mechanism, the design of the guiding movement rules of rehabilitation robots generally lacks specific motion coupling information between the glenohumeral (GH) joint center and humeral elevation angle. This study focuses on establishing a kinematic model of the shoulder complex obtained from a wearable detection system, which can describe the specific motion coupling relationship between the GH joint center displacement variable quantity relative to the thorax coordinate system and the humeral elevation angle. A kinematic model, which is a generalized GH joint with a floating center, was proposed to describe the coupling motion. Twelve healthy subjects wearing the designed detection system performed a right-arm elevation in the sagittal and coronal planes respectively, and the motion information of the GH joint during humeral elevation in the sagittal and coronal planes was detected and quantized, with the analytical formulas acquired based on the experimental data. The differences in GH joint motion during humeral elevation in the sagittal and coronal planes were also evaluated respectively, which also verified the effectiveness of the proposed kinematic model. Full article

(This article belongs to the Special Issue Dynamic Models of Biology and Medicine, Volume II)

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22 pages, 896 KiB

Open AccessArticle

Optimising Hydrogel Release Profiles for Viro-Immunotherapy Using Oncolytic Adenovirus Expressing IL-12 and GM-CSF with Immature Dendritic Cells

by Adrianne L. Jenner, Federico Frascoli, Chae-Ok Yun and Peter S. Kim

Appl. Sci. 2020, 10(8), 2872; https://doi.org/10.3390/app10082872 - 21 Apr 2020

Cited by 17 | Viewed by 2969

Abstract

Sustained-release delivery systems, such as hydrogels, significantly improve cancer therapies by extending the treatment efficacy and avoiding excess wash-out. Combined virotherapy and immunotherapy (viro-immunotherapy) is naturally improved by these sustained-release systems, as it relies on the continual stimulation of the antitumour immune response. In this article, we consider a previously developed viro-immunotherapy treatment where oncolytic viruses that are genetically engineered to infect and lyse cancer cells are loaded onto hydrogels with immature dendritic cells (DCs). The time-dependent release of virus and immune cells results in a prolonged cancer cell killing from both the virus and activated immune cells. Although effective, a major challenge is optimising the release profile of the virus and immature DCs from the gel so as to obtain a minimum tumour size. Using a system of ordinary differential equations calibrated to experimental results, we undertake a novel numerical investigation of different gel-release profiles to determine the optimal release profile for this viro-immunotherapy. Using a data-calibrated mathematical model, we show that if the virus is released rapidly within the first few days and the DCs are released for two weeks, the tumour burden can be significantly decreased. We then find the true optimal gel-release kinetics using a genetic algorithm and suggest that complex profiles present unnecessary risk and that a simple linear-release model is optimal. In this work, insight is provided into a fundamental problem in the growing field of sustained-delivery systems using mathematical modelling and analysis. Full article

(This article belongs to the Special Issue Dynamic Models of Biology and Medicine, Volume II)

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16 pages, 2402 KiB

Open AccessArticle

Computational Simulation of Cardiac Function and Blood Flow in the Circulatory System under Continuous Flow Left Ventricular Assist Device Support during Atrial Fibrillation

by Selim Bozkurt

Appl. Sci. 2020, 10(3), 876; https://doi.org/10.3390/app10030876 - 27 Jan 2020

Cited by 5 | Viewed by 3364

Abstract

Prevalence of atrial fibrillation (AF) is high in heart failure patients supported by a continuous flow left ventricular assist device (CF-LVAD); however, the long term effects remain unclear. In this study, a computational model simulating effects of AF on cardiac function and blood flow for heart failure and CF-LVAD support is presented. The computational model describes left and right heart, systemic and pulmonary circulations and cerebral circulation, and utilises patient-derived RR interval series for normal sinus rhythm (SR). Moreover, AF was simulated using patient-derived unimodal and bimodal distributed RR interval series and patient specific left ventricular systolic functions. The cardiovascular system model simulated clinically-observed haemodynamic outcomes under CF-LVAD support during AF, such as reduced right ventricular ejection fraction and elevated systolic pulmonary arterial pressure. Moreover, relatively high aortic peak pressures and middle arterial peak flow rates during AF with bimodal RR interval distribution, reduced to similar levels as during normal SR and AF with unimodal RR interval distribution under CF-LVAD support. The simulation results suggest that factors such as distribution of RR intervals and systolic left ventricular function may influence haemodynamic outcome of CF-LVAD support during AF. Full article

(This article belongs to the Special Issue Dynamic Models of Biology and Medicine, Volume II)

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20 pages, 4905 KiB

Open AccessArticle

Estimating Time-Varying Applied Current in the Hodgkin-Huxley Model

by Kayleigh Campbell, Laura Staugler and Andrea Arnold

Appl. Sci. 2020, 10(2), 550; https://doi.org/10.3390/app10020550 - 11 Jan 2020

Cited by 8 | Viewed by 3644

Abstract

The classic Hodgkin-Huxley model is widely used for understanding the electrophysiological dynamics of a single neuron. While applying a low-amplitude constant current to the system results in a single voltage spike, it is possible to produce multiple voltage spikes by applying time-varying currents, which may not be experimentally measurable. The aim of this work is to estimate time-varying applied currents of different deterministic forms given noisy voltage data. In particular, we utilize an augmented ensemble Kalman filter with parameter tracking to estimate four different time-varying applied current parameters and associated Hodgkin-Huxley model states, along with uncertainty bounds in each case. We test the efficiency of the parameter tracking algorithm in this setting by analyzing the effects of changing the standard deviation of the parameter drift and the frequency of data available on the resulting time-varying applied current estimates and related uncertainty. Full article

(This article belongs to the Special Issue Dynamic Models of Biology and Medicine, Volume II)

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12 pages, 2628 KiB

Open AccessArticle

Emotion, Respiration, and Heart Rate Variability: A Mathematical Model and Simulation Analyses

by Satoko Hirabayashi and Masami Iwamoto

Appl. Sci. 2019, 9(23), 5008; https://doi.org/10.3390/app9235008 - 20 Nov 2019

Cited by 3 | Viewed by 4045

Abstract

Although the generation mechanism of the low-frequency (LF) component of heart rate variability (HRV) is controversial, HRV is a potential candidate in designing objective measurement methodologies for emotions. These methodologies could be valuable for several biosignal applications. Here, we have conducted a simulation analysis using a novel mathematical model that integrates emotion, respiration, the nervous system, and the cardiovascular system. Our model has well reproduced experimental results, specifically concerning HRV with respiratory sinus arrhythmia and LF, the relation between HRV total power and the respiration frequency, and the homeostatic maintenance by the baroreflex. Our model indicates the following possibilities: (i) The delay in the heart rate control process of the parasympathetic activity works as a low-pass filter and the HRV total power decreases with a higher respiration frequency; (ii) the LF component of HRV and the Mayer wave are generated as transient responses of the baroreflex feedback control to perturbations induced by an emotional stimulus; and (iii) concentration on breathing to reduce the respiration frequency can reduce LF/HF and the reduction can be fed back to the emotional status. Full article

(This article belongs to the Special Issue Dynamic Models of Biology and Medicine, Volume II)

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11 pages, 2046 KiB

Open AccessArticle

Surface Topography-Based Positioning Accuracy of Maxillary Templates Fabricated by the CAD/CAM Technique for Orthognathic Surgery without an Intermediate Splint

by Jeong Joon Han and Soon Jung Hwang

Appl. Sci. 2019, 9(22), 4928; https://doi.org/10.3390/app9224928 - 16 Nov 2019

Viewed by 3141

Abstract

Computer-aided design/computer-aided manufacturing (CAD/CAM)-based maxillary templates can transfer a surgical plan accurately only when the template is positioned correctly. Our study aimed to evaluate the positioning accuracy of the CAD/CAM-based template for maxillary orthognathic surgery using dry skulls. After reconstruction of a three-dimensional (3D) virtual skull model, a surface-based surgical template for Le Fort I osteotomy was designed and fabricated using CAD/CAM and 3D printing technology. To determine accuracy, the deviation of the template between the planned and the actual position and the fitness of the template were evaluated. The mean deviation was 0.41 ± 0.30 mm in the medio-lateral direction, 0.55 ± 0.59 mm in the antero-posterior direction, and 0.69 ± 0.59 mm in the supero-inferior direction. The root mean square deviation between the planned and the actual position of the template was 1.21 ± 0.54 mm. With respect to the fitness of the template, the mean distance between the inner surface of the template and the underlying bone surface was 0.76 ± 0.24 mm. CAD/CAM-based templates showed precise positioning and good fitness. These results suggest that surface topography-based CAD-CAM templates can be considered as an alternative solution in replacing the traditional intermediate splints for the transfer of surgical plans. Full article

(This article belongs to the Special Issue Dynamic Models of Biology and Medicine, Volume II)

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16 pages, 3301 KiB

Open AccessArticle

In-Vitro Simulation of the Blood Flow in an Axisymmetric Abdominal Aortic Aneurysm

by Stefania Espa, Monica Moroni and Maria Antonietta Boniforti

Appl. Sci. 2019, 9(21), 4560; https://doi.org/10.3390/app9214560 - 27 Oct 2019

Cited by 1 | Viewed by 2113

Abstract

We investigated the blood flow patterns and the hemodynamics associated with an abdominal aortic aneurysm detected in an in vitro measurement campaign performed in a laboratory model of an aneurysm with rigid walls and an axisymmetric shape. Experiments were run in steady flow conditions and by varying the Reynolds number in the range 410 < Re < 2650. High spatial and temporal resolution 2D optical measurements of the velocity field were obtained through a particle tracking technique known as Hybrid Lagrangian Particle Tracking. Conversely to classical Particle Image Velocimetry, both the fluid particle trajectories and the instantaneous and time-averaged velocity fields are provided without constraints on the grid size and very close to the vessel boundary. All the most relevant quantities needed to investigate the flow features were evaluated, and in particular, we focused on the wall shear stress distribution both in the healthy aortic portion and within the aneurysm. Results show that the recirculation zone in correspondence of the cavity moves downstream, and this displacement is found to increase with Re. Very low wall shear stress values are recovered in correspondence of the aneurysmal cavity, while a sharp peak occurs in correspondence of the reattachment point. In agreement with the literature data, the peak value is found to decrease with Re and to be about equal to twice the upstream value. Full article

(This article belongs to the Special Issue Dynamic Models of Biology and Medicine, Volume II)

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Review

Jump to: Research

29 pages, 785 KiB

Open AccessFeature PaperReview

Review: Mathematical Modeling of Prostate Cancer and Clinical Application

by Tin Phan, Sharon M. Crook, Alan H. Bryce, Carlo C. Maley, Eric J. Kostelich and Yang Kuang

Appl. Sci. 2020, 10(8), 2721; https://doi.org/10.3390/app10082721 - 15 Apr 2020

Cited by 23 | Viewed by 5059

Abstract

We review and synthesize key findings and limitations of mathematical models for prostate cancer, both from theoretical work and data-validated approaches, especially concerning clinical applications. Our focus is on models of prostate cancer dynamics under treatment, particularly with a view toward optimizing hormone-based treatment schedules and estimating the onset of treatment resistance under various assumptions. Population models suggest that intermittent or adaptive therapy is more beneficial to delay cancer relapse as compared to the standard continuous therapy if treatment resistance comes at a competitive cost for cancer cells. Another consensus among existing work is that the standard biomarker for cancer growth, prostate-specific antigen, may not always correlate well with cancer progression. Instead, its doubling rate appears to be a better indicator of tumor growth. Much of the existing work utilizes simple ordinary differential equations due to difficulty in collecting spatial data and due to the early success of using prostate-specific antigen in mathematical modeling. However, a shift toward more complex and realistic models is taking place, which leaves many of the theoretical and mathematical questions unexplored. Furthermore, as adaptive therapy displays better potential than existing treatment protocols, an increasing number of studies incorporate this treatment into modeling efforts. Although existing modeling work has explored and yielded useful insights on the treatment of prostate cancer, the road to clinical application is still elusive. Among the pertinent issues needed to be addressed to bridge the gap from modeling work to clinical application are (1) real-time data validation and model identification, (2) sensitivity analysis and uncertainty quantification for model prediction, and (3) optimal treatment/schedule while considering drug properties, interactions, and toxicity. To address these issues, we suggest in-depth studies on various aspects of the parameters in dynamical models such as the evolution of parameters over time. We hope this review will assist future attempts at studying prostate cancer. Full article

(This article belongs to the Special Issue Dynamic Models of Biology and Medicine, Volume II)

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