Stability Analysis of a Reaction-Diffusion System Modeling Atherogenesis

Ibragimov, Akif; Ritter, Laura; Walton, Jay R.

Stability Analysis of a Reaction-Diffusion System Modeling Atherogenesis

Type

Article

Authors

Ibragimov, Akif
Ritter, Laura
Walton, Jay R.

KAUST Grant Number

KUS-C1-016-04

Date

2010-01

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.

Citation

Ibragimov 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.

Acknowledgements

This 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).