Stability Analysis of a Reaction-Diffusion System Modeling Atherogenesis

Akif Ibraguimov, Lake Ritter, Jay Walton

Research output: Contribution to journalArticle

Abstract

This paper presents a linear, asymptotic stability analysis for a reaction-diffusion-convection 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 initiat
Original languageEnglish
Pages (from-to)2150–2185
JournalSIAM J. Appl. Math
DOIs
StatePublished - Apr 14 2010

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