Stability Analysis of a Model of Atherogenesis: An Energy Estimate Approach II

Handle URI:
http://hdl.handle.net/10754/597015
Title:
Stability Analysis of a Model of Atherogenesis: An Energy Estimate Approach II
Authors:
Ibragimov, A. I.; McNeal, C. J.; Ritter, L. R.; Walton, J. R.
Abstract:
This paper considers modelling atherogenesis, the initiation of atherosclerosis, as an inflammatory instability. Motivated by the disease paradigm articulated by Russell Ross, atherogenesis is viewed as an inflammatory spiral with positive feedback loop involving key cellular and chemical species interacting and reacting within the intimal layer of muscular arteries. The inflammation is modelled through a system of non-linear reaction-diffusion-convection partial differential equations. The inflammatory spiral is initiated as an instability from a healthy state which is defined to be an equilibrium state devoid of certain key inflammatory markers. Disease initiation is studied through a linear, asymptotic stability analysis of a healthy equilibrium state. Various theorems are proved giving conditions on system parameters guaranteeing stability of the health state and conditions on system parameters leading to instability. Among the questions addressed in the analysis is the possible mitigating effect of anti-oxidants upon transition to the inflammatory spiral. © 2010 Taylor & Francis.
Citation:
Ibragimov AI, McNeal CJ, Ritter LR, Walton JR (2010) Stability Analysis of a Model of Atherogenesis: An Energy Estimate Approach II. Computational and Mathematical Methods in Medicine 11: 67–88. Available: http://dx.doi.org/10.1080/17486700802713430.
Publisher:
Hindawi Publishing Corporation
Journal:
Computational and Mathematical Methods in Medicine
KAUST Grant Number:
KUS-C1-016-04
Issue Date:
2010
DOI:
10.1080/17486700802713430
Type:
Article
ISSN:
1748-670X; 1748-6718
Sponsors:
This publication is based on work supported in part by Award No. KUS-C1-016-04, made by King Abdullah University of Science and Technology (KAUST).
Appears in Collections:
Publications Acknowledging KAUST Support

Full metadata record

DC FieldValue Language
dc.contributor.authorIbragimov, A. I.en
dc.contributor.authorMcNeal, C. J.en
dc.contributor.authorRitter, L. R.en
dc.contributor.authorWalton, J. R.en
dc.date.accessioned2016-02-23T13:52:31Zen
dc.date.available2016-02-23T13:52:31Zen
dc.date.issued2010en
dc.identifier.citationIbragimov AI, McNeal CJ, Ritter LR, Walton JR (2010) Stability Analysis of a Model of Atherogenesis: An Energy Estimate Approach II. Computational and Mathematical Methods in Medicine 11: 67–88. Available: http://dx.doi.org/10.1080/17486700802713430.en
dc.identifier.issn1748-670Xen
dc.identifier.issn1748-6718en
dc.identifier.doi10.1080/17486700802713430en
dc.identifier.urihttp://hdl.handle.net/10754/597015en
dc.description.abstractThis paper considers modelling atherogenesis, the initiation of atherosclerosis, as an inflammatory instability. Motivated by the disease paradigm articulated by Russell Ross, atherogenesis is viewed as an inflammatory spiral with positive feedback loop involving key cellular and chemical species interacting and reacting within the intimal layer of muscular arteries. The inflammation is modelled through a system of non-linear reaction-diffusion-convection partial differential equations. The inflammatory spiral is initiated as an instability from a healthy state which is defined to be an equilibrium state devoid of certain key inflammatory markers. Disease initiation is studied through a linear, asymptotic stability analysis of a healthy equilibrium state. Various theorems are proved giving conditions on system parameters guaranteeing stability of the health state and conditions on system parameters leading to instability. Among the questions addressed in the analysis is the possible mitigating effect of anti-oxidants upon transition to the inflammatory spiral. © 2010 Taylor & Francis.en
dc.description.sponsorshipThis publication is based on work supported in part by Award No. KUS-C1-016-04, made by King Abdullah University of Science and Technology (KAUST).en
dc.publisherHindawi Publishing Corporationen
dc.rightsThis 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.en
dc.rights.urihttp://creativecommons.org/licenses/by/3.0/en
dc.subjectAtherogenesisen
dc.subjectAtherosclerosisen
dc.subjectChemotaxisen
dc.subjectEnergy estimateen
dc.subjectStability analysisen
dc.titleStability Analysis of a Model of Atherogenesis: An Energy Estimate Approach IIen
dc.typeArticleen
dc.identifier.journalComputational and Mathematical Methods in Medicineen
dc.contributor.institutionTexas Tech University at Lubbock, Lubbock, United Statesen
dc.contributor.institutionDivision of Molecular Cardiology, Temple, United Statesen
dc.contributor.institutionScott and White, Temple, United Statesen
dc.contributor.institutionSouthern Polytechnic State University, Marietta, United Statesen
dc.contributor.institutionTexas A and M University, College Station, United Statesen
kaust.grant.numberKUS-C1-016-04en
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