Stability Analysis of a Reaction-Diffusion System Modeling Atherogenesis

Akif Ibragimov, Laura Ritter, Jay R. Walton

Research output: Contribution to journalArticlepeer-review

8 Scopus citations

Abstract

This 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.
Original languageEnglish (US)
Pages (from-to)2150-2185
Number of pages36
JournalSIAM Journal on Applied Mathematics
Volume70
Issue number7
DOIs
StatePublished - Jan 2010
Externally publishedYes

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