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 language | English (US) |
|---|---|
| Pages (from-to) | 2150-2185 |
| Number of pages | 36 |
| Journal | SIAM Journal on Applied Mathematics |
| Volume | 70 |
| Issue number | 7 |
| DOIs | |
| State | Published - Jan 2010 |
| Externally published | Yes |
Bibliographical note
KAUST Repository Item: Exported on 2020-10-01Acknowledged KAUST grant number(s): KUS-C1-016-04
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).
This publication acknowledges KAUST support, but has no KAUST affiliated authors.