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dc.contributor.authorIbragimov, Akif
dc.contributor.authorRitter, Laura
dc.contributor.authorWalton, Jay R.
dc.date.accessioned2016-02-28T06:07:57Z
dc.date.available2016-02-28T06:07:57Z
dc.date.issued2010-01
dc.identifier.citationIbragimov A, Ritter L, Walton JR (2010) Stability Analysis of a Reaction-Diffusion System Modeling Atherogenesis. SIAM Journal on Applied Mathematics 70: 2150–2185. Available: http://dx.doi.org/10.1137/08073490X.
dc.identifier.issn0036-1399
dc.identifier.issn1095-712X
dc.identifier.doi10.1137/08073490X
dc.identifier.urihttp://hdl.handle.net/10754/599705
dc.description.abstractThis paper presents a linear, asymptotic stability analysis for a reaction-diffusionconvection system modeling atherogenesis, the initiation of atherosclerosis, as an inflammatory instability. Motivated by the disease paradigm articulated by Ross, atherogenesis is viewed as an inflammatory spiral with a positive feedback loop involving key cellular and chemical species interacting and reacting within the intimal layer of muscular arteries. 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 a general framework is developed for constructing perturbations from a healthy state that exhibit blow-up, which are interpreted as corresponding to disease initiation. The analysis reveals key features that arterial geometry, antioxidant levels, and the source of inflammatory components (through coupled third-kind boundary conditions or through body sources) play in disease initiation. © 2010 Society for Industrial and Applied Mathematics.
dc.description.sponsorshipThis author's work was supported in part by NSF grant DMS-0908177.This author's work was supported in part by award KUS-C1-016-04 made by King Abdullah University of Science and Technology (KAUST).
dc.publisherSociety for Industrial & Applied Mathematics (SIAM)
dc.subjectAtherosclerosis
dc.subjectChemotaxis
dc.subjectInflammation
dc.subjectPartial differential equations
dc.subjectStability
dc.subjectTuring instability
dc.titleStability Analysis of a Reaction-Diffusion System Modeling Atherogenesis
dc.typeArticle
dc.identifier.journalSIAM Journal on Applied Mathematics
dc.contributor.institutionTexas Tech University at Lubbock, Lubbock, United States
dc.contributor.institutionSouthern Polytechnic State University, Marietta, United States
dc.contributor.institutionTexas A and M University, College Station, United States
kaust.grant.numberKUS-C1-016-04


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