Jay Walton (Texas A&M University)-Modeling Atherogenesis
Mathematics - Colloquium
Friday, August 31, 2012
11:00 AM-12:00 PM
ABSTRACT: Atherosclerosis is a disease of the cardiovascular system characterized by the development and growth of lipid rich lesions in arterial walls. In advanced stages of the disease, the lesions can nearly fill the luminal opening of an artery significantly obstructing the flow of blood. There are two somewhat distinct phases of the disease. The initial phase, called atherogenesis, involves a complex web of biochemical and immune systems interactions characteristic of inflammation that initiates the production and buildup of lipid rich lesions. The second phase involves growth of the incipient lesion that couples mechanical effects with the biochemical and immune system interactions.
In this talk I discuss modeling atherogenesis as an inflammatory instability. It is now widely accepted that atherosclerosis is a chronic disorder initiated by inflammatory processes taking place in the intimal layer of the arterial wall. In this talk, these inflammatory processes, which include foam cell formation, lipid oxidation by free radicals, free radical production and anti-oxidant mitigation, are modeled via a system of reaction-diffusion-chemotactic equations. The notion of a “healthy state” is then introduced as an equilibrium state in which inflammatory markers are absent. The mathematical question studied is the stability of this healthy state to small perturbations in the inflammatory markers. It is shown that the healthy state can be stabilized through diffusion processes and sufficiently strong anti-oxidant mitigation and destabilized through low anti-oxidant levels and strong chemotactic effects that promote localization of lesion formation and growth. An interesting feature of the model is that the principal source of two key component species in the inflammatory process is through the endothelial boundary between the lumen (where blood flows) and the intimal layer of the arterial wall. This results in coupled (third kind) boundary conditions on the inner intimal boundary that significantly affect the qualitative properties of the boundary value problem and complicate the stability analysis.
Suggested Audiences: Adult, College
Last Modified: July 31, 2012 at 2:56 PM