A Qualitative Analysis of the Inflammatory Response in Atherosclerosis with Emphasis on LDL Oxidation

Abstract

Atherosclerosis is an inflammatory disease that involves the accumulation of lipid deposits, cholesterol, and several other substances within the arterial wall. This buildup of what is known as the atherosclerotic plaque hardens and narrows the blood vessels, constricting the blood flow and causing heart attacks and strokes. In this work, we model the inflammatory stage of this disease through a system of reaction-diffusion partial differential equations. Low density lipoproteins (LDL), free radicals, oxidized low density lipoproteins (ox-LDL), macrophages, and pro-inflammatory cytokines are the main key role players that are taken into consideration. The stability analysis of the corresponding ODE system is performed and studied in detail. We then focus on proving the existence of traveling wave solutions of the system. In addition, we establish biological insights from the mathematical study, illustrated by numerical simulations. Finally, we emphasize the role of the rate of oxidation of LDL, which is an important factor in the set-up of this inflammatory disease.