Pub Date : 2024-07-24DOI: 10.55630/j.biomath.2024.06.286
C. Pokharel, P. N. Gautam, C. R. Bhatta, Jeevan Kafle
Arterial stenosis is the thickening of the arterial wall due to the growth of aberrant tissues that prevent adequate blood flow in the human circulatory system and induces cardiovascular diseases. Mild stenosis, may lead to serious or permanent damage if remains uncured. There are differences in the curvature response and material composition between the outer layers and the core. There are several locations in blood vessels where they are curved, which affects the blood flow and shear stress. The Navier-Stokes equation in the cylindrical polar coordinate system has been extended by incorporating curvature term in two-layered blood flow along the axial direction with appropriate boundary conditions. Mathematical expressions for hemodynamic parameters such as velocity profile, volumetric flow rate, pressure drop, and shear stress have been calculated analytically in the case of a curve artery with stenosis. Moreover, we have analyzed the effect of stenosis on different hemodynamic parameters with the variation of core and peripheral-layer viscosity and curvature. Flow quantities are affected by the habitancy of stenosis and stipulate different blood flow behavior in both layers in the case of curved artery. This modeling technique may help researchers in medicine, mathematical biology, and bio-engineering.
{"title":"Analysis of hemodynamic parameters on two-layered blood flow in a curved artery","authors":"C. Pokharel, P. N. Gautam, C. R. Bhatta, Jeevan Kafle","doi":"10.55630/j.biomath.2024.06.286","DOIUrl":"https://doi.org/10.55630/j.biomath.2024.06.286","url":null,"abstract":"Arterial stenosis is the thickening of the arterial wall due to the growth of aberrant tissues that prevent adequate blood flow in the human circulatory system and induces cardiovascular diseases. Mild stenosis, may lead to serious or permanent damage if remains uncured. There are differences in the curvature response and material composition between the outer layers and the core. There are several locations in blood vessels where they are curved, which affects the blood flow and shear stress. The Navier-Stokes equation in the cylindrical polar coordinate system has been extended by incorporating curvature term in two-layered blood flow along the axial direction with appropriate boundary conditions. Mathematical expressions for hemodynamic parameters such as velocity profile, volumetric flow rate, pressure drop, and shear stress have been calculated analytically in the case of a curve artery with stenosis. Moreover, we have analyzed the effect of stenosis on different hemodynamic parameters with the variation of core and peripheral-layer viscosity and curvature. Flow quantities are affected by the habitancy of stenosis and stipulate different blood flow behavior in both layers in the case of curved artery. This modeling technique may help researchers in medicine, mathematical biology, and bio-engineering.","PeriodicalId":52247,"journal":{"name":"Biomath","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2024-07-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141809338","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2024-07-12DOI: 10.55630/j.biomath.2024.06.196
Nabil Ben Ali, Nahla Abdellatif
We consider the acetogenesis and hydrogenotrophic methanogenesis phases of the anaerobic digestion model and we include the inhibition of methanogenics, first by volatile fatty acids (VFAs) then by acetogenics. We investigate mathematically the dynamics of two chemostat models described by systems of four nonlinear ordinary differential equations. We established the conditions of existence and stability of equilibrium points in each of the models with respect to the dilution rate. The operating diagrams allowed to reveal the similarities and the differences between regions of stability of the two models and to present the consequent transcritical bifurcations between boundary and positive equilibrium. Models are equivalent for low inlet substrate concentration and significantly different for high concentration. When inhibition is by acetogens and for high concentrations of inlet substrate, the upstream species tends to eliminate the downstream species from the vessel.
{"title":"Comparative analysis of two chemostat models including substrate and biomass inhibitions","authors":"Nabil Ben Ali, Nahla Abdellatif","doi":"10.55630/j.biomath.2024.06.196","DOIUrl":"https://doi.org/10.55630/j.biomath.2024.06.196","url":null,"abstract":"We consider the acetogenesis and hydrogenotrophic methanogenesis phases of the anaerobic digestion model and we include the inhibition of methanogenics, first by volatile fatty acids (VFAs) then by acetogenics. We investigate mathematically the dynamics of two chemostat models described by systems of four nonlinear ordinary differential equations. We established the conditions of existence and stability of equilibrium points in each of the models with respect to the dilution rate. The operating diagrams allowed to reveal the similarities and the differences between regions of stability of the two models and to present the consequent transcritical bifurcations between boundary and positive equilibrium. Models are equivalent for low inlet substrate concentration and significantly different for high concentration. When inhibition is by acetogens and for high concentrations of inlet substrate, the upstream species tends to eliminate the downstream species from the vessel.","PeriodicalId":52247,"journal":{"name":"Biomath","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2024-07-12","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141655261","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2024-05-15DOI: 10.55630/j.biomath.2024.03.126
Tereza Trencheva, Ivan Trenchev, Iglika Getova, Miglena Trencheva
With the advancement of Mixed Reality (MR) technologies and bioinformatics, researchers are exploring new ways to enhance the visualization and analysis of genomic data. The integration of MR technologies in bioinformatics research has the potential to revolutionize the way scientists interpret complex biological information. This article discusses the application of MR in genomic data visualization and analysis, highlighting its advantages in facilitating a more immersive and interactive experience. In particular, we will present case studies related to the implementation of the Unreal Engine in MR for bioinformatics research. As part of the research, the role of intellectual property in bioinformatics will be analyzed, providing insights into its significance and implications in the field. The integration of MR can improve collaboration among researchers and assist in the understanding of intricate patterns within genomic datasets. Furthermore, the article examines the challenges faced in implementing MR technologies in bioinformatics and addresses possible solutions to overcome these obstacles. Overall, the integration of MR in bioinformatics research has the potential to reshape the field and drive innovation in genomic data analysis.
{"title":"Integrating mixed reality technologies in genomic data visualization and analysis for bioinformatics research","authors":"Tereza Trencheva, Ivan Trenchev, Iglika Getova, Miglena Trencheva","doi":"10.55630/j.biomath.2024.03.126","DOIUrl":"https://doi.org/10.55630/j.biomath.2024.03.126","url":null,"abstract":"With the advancement of Mixed Reality (MR) technologies and bioinformatics, researchers are exploring new ways to enhance the visualization and analysis of genomic data. The integration of MR technologies in bioinformatics research has the potential to revolutionize the way scientists interpret complex biological information. This article discusses the application of MR in genomic data visualization and analysis, highlighting its advantages in facilitating a more immersive and interactive experience. In particular, we will present case studies related to the implementation of the Unreal Engine in MR for bioinformatics research.\u0000As part of the research, the role of intellectual property in bioinformatics will be analyzed, providing insights into its significance and implications in the field. The integration of MR can improve collaboration among researchers and assist in the understanding of intricate patterns within genomic datasets. Furthermore, the article examines the challenges faced in implementing MR technologies in bioinformatics and addresses possible solutions to overcome these obstacles.\u0000Overall, the integration of MR in bioinformatics research has the potential to reshape the field and drive innovation in genomic data analysis.","PeriodicalId":52247,"journal":{"name":"Biomath","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2024-05-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140973036","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2024-04-24DOI: 10.55630/j.biomath.2023.12.166
A. Atanasov, S. Georgiev, L. Vulkov
Several models on honeybee population dynamics have been considered in the past decades, which explain that the growth of beecolonies is highly dependent on the availability of food and social inhibition. The phenomenon of the Colony Collapse Disorder (CCD) and its exact causes remain unclear and here we are interested on the factor of social immunity. We work with the mathematical model in [1]. The core model, consisting of four nonlinear ordinary differential equations with unknown functions: brood and nurses B, iB, N and iN represent the number of healthy brood, infected brood, healthy nurses, and infected nurses, respectively. First, this model implements social segregation. High-risk individuals such as foragers are limited to contact only nectar-receivers, but not other vulnerable individuals (nurses and brood) inside the nest. Secondly, it includes the hygienic behavior, by which healthy nurses actively remove infected workers and brood from the colony. We aim to study the dynamics and the long-term behavior of the proposed model, as well as to discuss the effects of crucial parameters associated with the model. In the first stage, we study the model equilibria stability in dependence of the reproduction number. In the second stage, we investigate the inverse problem of parameters identification in the model based on finite number time measurements of the population size. The conjugate gradient method with explicit Frechet derivative of the cost functional is proposed for the numerical solution of the inverse problem. Computational results with synthetic and realistic data are performed and discussed.
在过去的几十年中，人们已经研究了多个蜜蜂种群动态模型，这些模型解释了蜂群的增长在很大程度上取决于食物的供应和社会抑制。蜂群崩溃紊乱症（CCD）现象及其确切原因仍不清楚，在此，我们对社会免疫因素感兴趣。该核心模型由四个非线性常微分方程组成，其未知函数为：育雏器和哺乳器 B、iB、N 和 iN 分别代表健康育雏器、受感染育雏器、健康哺乳器和受感染哺乳器的数量。首先，该模型实现了社会隔离，高风险个体（如觅食者）只能接触花蜜接收者，而不能接触巢内其他易受感染的个体（哺育者和雏鸟）。其次，它还包括卫生行为，即健康的哺育者会主动将受感染的工蜂和雏蜂赶出蜂群。我们的目的是研究拟议模型的动态和长期行为，并讨论与模型相关的关键参数的影响。在第一阶段，我们研究了与繁殖数量相关的模型平衡稳定性。在第二阶段，我们研究了基于种群数量有限时间测量的模型参数识别逆问题。在逆问题的数值求解中，我们提出了带有成本函数显式弗雷谢特导数的共轭梯度法。
{"title":"Dynamical analysis combined with parameter identification for a model of infection in honeybee colonies with social immunity","authors":"A. Atanasov, S. Georgiev, L. Vulkov","doi":"10.55630/j.biomath.2023.12.166","DOIUrl":"https://doi.org/10.55630/j.biomath.2023.12.166","url":null,"abstract":"Several models on honeybee population dynamics have been considered in the past decades, which explain that the growth of beecolonies is highly dependent on the availability of food and social inhibition. The phenomenon of the Colony Collapse Disorder (CCD) and its exact causes remain unclear and here we are interested on the factor of social immunity.\u0000We work with the mathematical model in [1]. The core model, consisting of four nonlinear ordinary differential equations with unknown functions: brood and nurses B, iB, N and iN represent the number of healthy brood, infected brood, healthy nurses, and infected nurses, respectively.\u0000First, this model implements social segregation. High-risk individuals such as foragers are limited to contact only nectar-receivers, but not other vulnerable individuals (nurses and brood) inside the nest. Secondly, it includes the hygienic behavior, by which healthy nurses actively remove infected workers and brood from the colony.\u0000We aim to study the dynamics and the long-term behavior of the proposed model, as well as to discuss the effects of crucial parameters associated with the model. In the first stage, we study the model equilibria stability in dependence of the reproduction number.\u0000In the second stage, we investigate the inverse problem of parameters identification in the model based on finite number time measurements of the population size. The conjugate gradient method with explicit Frechet derivative of the cost functional is proposed for the numerical solution of the inverse problem.\u0000Computational results with synthetic and realistic data are performed and discussed.","PeriodicalId":52247,"journal":{"name":"Biomath","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2024-04-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140664477","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2024-03-14DOI: 10.55630/j.biomath.2023.12.036
Yao Messan
This study investigates the impact of melting/binding rates (referred to hereafter as the parameters) over the polymers and monomers on the dynamics of carbon-monoxide-mediated sickle cell hemoglobin (HbS) de-polymerization. Two approaches, namely the traditional sensitivity analysis (TSA) and the multi-parameter sensitivity analysis (MPSA), have been developed and applied to the mathematical model system to quantify the sensitivities of polymers and monomers to the parameters. The Runge-Kutta method and the Monte-Carlo simulation are employed for the implementation of the sensitivity analyses. The TSA utilizes the traditional sensitivity functions (TSFs). The MPSA enumerates the overall effect of the model input parameters on the output by perturbing the model input parameters simultaneously within large ranges. All four concentrations (namely, de-oxy HbS monomers, CO-bound HbS monomers, de-oxy Hbs polymer and CO-bound HbS polymer) as model outputs, and all four binding/melting rates (namely, the CO binding and melting rates for polymers and monomers) as input parameters are considered in this study. The sensitivity results suggest that TSA and MPSA are essentially consistent.
本研究探讨了聚合物和单体的熔化/结合率（以下简称参数）对一氧化碳介导的镰状细胞血红蛋白（HbS）脱聚合动力学的影响。为了量化聚合物和单体对参数的敏感性，我们开发了两种方法，即传统敏感性分析法（TSA）和多参数敏感性分析法（MPSA），并将其应用于数学模型系统。灵敏度分析采用 Runge-Kutta 方法和 Monte-Carlo 模拟。TSA 利用传统的灵敏度函数 (TSF)。MPSA 通过在较大范围内同时扰动模型输入参数，列举模型输入参数对输出的总体影响。本研究考虑了作为模型输出的所有四种浓度（即脱氧 HbS 单体、与 CO 结合的 HbS 单体、脱氧 Hbs 聚合物和与 CO 结合的 HbS 聚合物）和作为输入参数的所有四种结合率/熔化率（即聚合物和单体的 CO 结合率和熔化率）。灵敏度结果表明，TSA 和 MPSA 基本一致。
{"title":"Parameter sensitivity analysis for CO-mediated sickle cell de-polymerization","authors":"Yao Messan","doi":"10.55630/j.biomath.2023.12.036","DOIUrl":"https://doi.org/10.55630/j.biomath.2023.12.036","url":null,"abstract":"This study investigates the impact of melting/binding rates (referred to hereafter as the parameters) over the polymers and monomers on the dynamics of carbon-monoxide-mediated sickle cell hemoglobin (HbS) de-polymerization. Two approaches, namely the traditional sensitivity analysis (TSA) and the multi-parameter sensitivity analysis (MPSA), have been developed and applied to the mathematical model system to quantify the sensitivities of polymers and monomers to the parameters. The Runge-Kutta method and the Monte-Carlo simulation are employed for the implementation of the sensitivity analyses. The TSA utilizes the traditional sensitivity functions (TSFs). The MPSA enumerates the overall effect of the model input parameters on the output by perturbing the model input parameters simultaneously within large ranges. All four concentrations (namely, de-oxy HbS monomers, CO-bound HbS monomers, de-oxy Hbs polymer and CO-bound HbS polymer) as model outputs, and all four binding/melting rates (namely, the CO binding and melting rates for polymers and monomers) as input parameters are considered in this study. The sensitivity results suggest that TSA and MPSA are essentially consistent.","PeriodicalId":52247,"journal":{"name":"Biomath","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2024-03-14","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140243080","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2023-12-08DOI: 10.55630/j.biomath.2023.11.027
Neli Dimitrova
We consider a mathematical continuous-time model for biodegradation of 4-chlorophenol and sodium salicylate mixture by the microbial strain Pseudomonas putida in a chemostat. The model is described by a system of three nonlinear ordinary differential equations and is proposed for the first time in the paper [Y.-H. Lin, B.-H. Ho, Biodegradation kinetics of phenol and 4-chlorophenol in the presence of sodium salicylate in batch and chemostat systems, Processes, 10:694, 2022], where the model is only quantitatively verified. This paper provides a detailed analysis of the system dynamics. Some important basic properties of the model solutions like existence, uniqueness and uniform boundedness of positive solutions are established. Computation of equilibrium points and study of their local asymptotic stability and bifurcations in dependence of the dilution rate as a key model parameter are also presented. Thereby, particular intervals for the dilution rate are found, where one or three interior (with positive components) equilibrium points do exist and possess different types of local asymptotic stability/instability. Hopf bifurcations are detected leading to the occurrence of stable limit cycles around some interior equilibrium points. A transcritical bifurcation also exists and implies stability exchange between an interior and the boundary (washout) equilibrium. The results are illustrated by lots of numerical examples.
{"title":"Dynamical analysis of a chemostat model for 4-chlorophenol and sodium salicylate mixture biodegradation","authors":"Neli Dimitrova","doi":"10.55630/j.biomath.2023.11.027","DOIUrl":"https://doi.org/10.55630/j.biomath.2023.11.027","url":null,"abstract":"We consider a mathematical continuous-time model for biodegradation of 4-chlorophenol and sodium salicylate mixture by the microbial strain Pseudomonas putida in a chemostat. The model is described by a system of three nonlinear ordinary differential equations and is proposed for the first time in the paper [Y.-H. Lin, B.-H. Ho, Biodegradation kinetics of phenol and 4-chlorophenol in the presence of sodium salicylate in batch and chemostat systems, Processes, 10:694, 2022], where the model is only quantitatively verified. This paper provides a detailed analysis of the system dynamics. Some important basic properties of the model solutions like existence, uniqueness and uniform boundedness of positive solutions are established. Computation of equilibrium points and study of their local asymptotic stability and bifurcations in dependence of the dilution rate as a key model parameter are also presented. Thereby, particular intervals for the dilution rate are found, where one or three interior (with positive components) equilibrium points do exist and possess different types of local asymptotic stability/instability. Hopf bifurcations are detected leading to the occurrence of stable limit cycles around some interior equilibrium points. A transcritical bifurcation also exists and implies stability exchange between an interior and the boundary (washout) equilibrium. The results are illustrated by lots of numerical examples.","PeriodicalId":52247,"journal":{"name":"Biomath","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2023-12-08","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"138588113","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2023-12-01DOI: 10.55630/j.biomath.2023.11.177
J. Nava-Sedeño, Simon Syga, Andreas Deutsch
Several discrete models for diffusive motion are known to exhibit checkerboard artifacts, absent in their continuous analogues. We study the origins of the checkerboard artifact in the discrete heat equation and show that this artifact decays exponentially in time when following either of two strategies: considering the present state of each lattice site to determine its own future state (self-contributions), or using non-square lattice geometries. Afterwards, we examine the effects of these strategies on nonlinear models of biological cell migration with two kinds of cell-cell interactions: adhesive and polar velocity alignment. In the case of adhesive interaction, we show that growing modes related to pattern formation overshadow artifacts in the long run; nonetheless, artifacts can still be completely prevented following the same strategies as in the discrete heat equation. On the other hand, for polar velocity alignment we show that artifacts are not only strengthened, but also that new artifacts can arise in this model which were not observed in the previous models. We find that the lattice geometry strategy works well to alleviate artifacts. However, the self-contribution strategy must be applied more carefully: lattice sites should contribute to both their own density and velocity values, and their own velocity contribution should be high enough. With this work, we show that these two strategies are effective for preventing artifacts in spatial models based on the discrete continuity equation.
{"title":"Artificial patterns in spatially discrete models of cell migration and how to mitigate them","authors":"J. Nava-Sedeño, Simon Syga, Andreas Deutsch","doi":"10.55630/j.biomath.2023.11.177","DOIUrl":"https://doi.org/10.55630/j.biomath.2023.11.177","url":null,"abstract":"Several discrete models for diffusive motion are known to exhibit checkerboard artifacts, absent in their continuous analogues. We study the origins of the checkerboard artifact in the discrete heat equation and show that this artifact decays exponentially in time when following either of two strategies: considering the present state of each lattice site to determine its own future state (self-contributions), or using non-square lattice geometries. Afterwards, we examine the effects of these strategies on nonlinear models of biological cell migration with two kinds of cell-cell interactions: adhesive and polar velocity alignment. In the case of adhesive interaction, we show that growing modes related to pattern formation overshadow artifacts in the long run; nonetheless, artifacts can still be completely prevented following the same strategies as in the discrete heat equation. On the other hand, for polar velocity alignment we show that artifacts are not only strengthened, but also that new artifacts can arise in this model which were not observed in the previous models. We find that the lattice geometry strategy works well to alleviate artifacts. However, the self-contribution strategy must be applied more carefully: lattice sites should contribute to both their own density and velocity values, and their own velocity contribution should be high enough. With this work, we show that these two strategies are effective for preventing artifacts in spatial models based on the discrete continuity equation.","PeriodicalId":52247,"journal":{"name":"Biomath","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2023-12-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"138615635","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2023-11-27DOI: 10.55630/j.biomath.2023.10.067
Pushpa Nidhi Gautam, C. Pokharel, G. R. Phaijoo, Parameshwari Kattel, J. Kafle
A hard layer, that develops in the inner wall of an artery, makes the blood flow difficult and it can harm the cardiovascular system because of the abnormality in blood supply. The problem becomes worse when the layer gets thicker due to increased deposition over time. The effect of increasing stenosis on flow characteristics in an artery is studied by taking blood as a non-Newtonian fluid. To address the effect of increasing stenosis over time, a non-dimensional temporal term is included in the geometry of stenosis and is applied to derive the flow parameters like velocity profile, volumetric flow rate and pressure drop. The maximum and minimum shear stress ratio and pressure drop ratio are also calculated using the term. The results obtained are analyzed to show the effect of increasing stenosis over time on these flow parameters. Volumetric flow rate, pressure drop and its ratio, and shear stress ratio are compared with the ratio of the thickness of the stenosis and normal artery radius while analyzing the results. It is found that the volumetric flow rate decreases with time, pressure drop and its ratio increases with time, and the shear stress ratio decreases as the time elapses. The result shows that it is appropriate to include the temporal term to understand the effect of increasing stenosis over time on blood flow parameters. The aim of this article is to correct the drawback that evolves while supposing the symmetric shape of the stenosis.
{"title":"Effect of increasing stenosis over time on hemodynamics","authors":"Pushpa Nidhi Gautam, C. Pokharel, G. R. Phaijoo, Parameshwari Kattel, J. Kafle","doi":"10.55630/j.biomath.2023.10.067","DOIUrl":"https://doi.org/10.55630/j.biomath.2023.10.067","url":null,"abstract":"A hard layer, that develops in the inner wall of an artery, makes the blood flow difficult and it can harm the cardiovascular system because of the abnormality in blood supply. The problem becomes worse when the layer gets thicker due to increased deposition over time. The effect of increasing stenosis on flow characteristics in an artery is studied by taking blood as a non-Newtonian fluid. To address the effect of increasing stenosis over time, a non-dimensional temporal term is included in the geometry of stenosis and is applied to derive the flow parameters like velocity profile, volumetric flow rate and pressure drop. The maximum and minimum shear stress ratio and pressure drop ratio are also calculated using the term. The results obtained are analyzed to show the effect of increasing stenosis over time on these flow parameters. Volumetric flow rate, pressure drop and its ratio, and shear stress ratio are compared with the ratio of the thickness of the stenosis and normal artery radius while analyzing the results. It is found that the volumetric flow rate decreases with time, pressure drop and its ratio increases with time, and the shear stress ratio decreases as the time elapses. The result shows that it is appropriate to include the temporal term to understand the effect of increasing stenosis over time on blood flow parameters. The aim of this article is to correct the drawback that evolves while supposing the symmetric shape of the stenosis.","PeriodicalId":52247,"journal":{"name":"Biomath","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2023-11-27","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139233549","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2023-10-31DOI: 10.55630/j.biomath.2023.09.267
Georgi Bazlyankov, Tihomir Ivanov
In the present work, we consider a mathematical model of multiple sclerosis, extending a model, known in the literature, so that it can account for the process of remyelination. Our model comprises of a reaction-diffusion-chemotaxis system of partial differential equations with a time delay. As a first approximation, we consider the model under the assumption of radial symmetry, which is consistent, e.g., with Baló's concentric disease. We conduct numerical experiments in order to study the effect of the remyelination strength on the disease progression. Furthermore, we show that the modified model has greatly enriched dynamics, which is capable of describing qualitatively different types of multiple sclerosis (according to classical classifications of the disease progression) as well as giving a better agreement with experimental data.
{"title":"On the effect of remyelination in a mathematical model of multiple sclerosis","authors":"Georgi Bazlyankov, Tihomir Ivanov","doi":"10.55630/j.biomath.2023.09.267","DOIUrl":"https://doi.org/10.55630/j.biomath.2023.09.267","url":null,"abstract":"In the present work, we consider a mathematical model of multiple sclerosis, extending a model, known in the literature, so that it can account for the process of remyelination. Our model comprises of a reaction-diffusion-chemotaxis system of partial differential equations with a time delay. As a first approximation, we consider the model under the assumption of radial symmetry, which is consistent, e.g., with Baló's concentric disease. We conduct numerical experiments in order to study the effect of the remyelination strength on the disease progression. Furthermore, we show that the modified model has greatly enriched dynamics, which is capable of describing qualitatively different types of multiple sclerosis (according to classical classifications of the disease progression) as well as giving a better agreement with experimental data.","PeriodicalId":52247,"journal":{"name":"Biomath","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2023-10-31","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135813446","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2023-10-21DOI: 10.55630/j.biomath.2023.11.237
Grzegorz A. Rempala
This brief note highlights a largely overlooked similarity between the SIR ordinary differential equations used for epidemics on the configuration model of a Poisson network and the classical mass-action SIR equations introduced nearly a century ago by Kermack and McKendrick. We demonstrate that the decline pattern in susceptibles is identical for both models. This equivalence carries practical implications: the susceptibles decay curve, often referred to as the epidemic or incidence curve, is frequently used in empirical studies to forecast epidemic dynamics. Although the curves for susceptibles align perfectly, those for infections do differ. Yet, the infection curves tend to converge and become almost indistinguishable in high-degree networks. In summary, our analysis suggests that under many practical scenarios, it's acceptable to use the classical SIR model as a close approximation to the Poisson SIR network model.
这篇简短的文章强调了在泊松网络配置模型上用于流行病的 SIR 常微分方程与近一个世纪前由 Kermack 和 McKendrick 引入的经典质量作用 SIR 方程之间一个被忽视的相似性。我们证明，两种模型的易感人群下降模式是相同的。这种等效性具有实际意义：易感者衰减曲线通常被称为流行病或发病率曲线，在实证研究中经常被用来预测流行病的动态。虽然易感者的曲线完全一致，但感染者的曲线确实不同。然而，感染曲线趋于收敛，在高阶网络中几乎无法区分。总之，我们的分析表明，在许多实际情况下，使用经典 SIR 模型作为泊松 SIR 网络模型的近似值是可以接受的。
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