Vorschau

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Abstract

We consider a mathematical model of the formation of an atherosclerotic lesion that is based on a simplification of Russell Ross' paradigm of atherosclerosis as a chronic inflammatory response. Atherosclerosis is characterized by the accumulation of lipid-laden cells in the arterial wall that can result in lesions within the artery. Such lesions can cause an occlusion of the artery resulting in heart attack. The presented mathematical model describes, among others, a response of immune and smooth muscle cells to biochemical signals of chemoattractants and a build up of debris. It results in a coupled system of four nonlinear reaction-convection-diffusion equations including a free inner boundary that is permitted to move due to an additional evolution equation. We perform a numerical study of the problem using fully implicit finite volume discretization methods. The moving boundary is described implicitly using an evolution of a level set function. In such a way, a grid used in numerical simulation can remain fixed during the whole computations. In this report, we present preliminary results that demonstrates that our numerical model captures certain observed features such as the localization of immune cells, the build-up of debris, the isolation of a lesion by smooth muscle cells, and an occlusion of the artery.