Dynamical System Analysis of a Mathematical Model of Mild Atherosclerosis

Abstract

Atherosclerosis, a long-term inflammatory affliction, occurs due to plaque accumulation in the intima, the innermost layer of artery. It is one of the prime causes of deaths from several cardio-vascular diseases. The primary interaction between oxidized low density lipoprotein (LDL) and macrophages in forming fatty steak is presented here in terms of a nonlinear reaction-diffusion system in one spatial dimension under Neumann boundary conditions. Both the spatio-temporal and the temporal models are analyzed qualitatively. Numerical simulations of both the model systems lead to three significant model parameters with respect to which bifurcations are found. Bifurcating parameters indicate possible developments of various therapeutic strategies in order to establish any preventative measures for an individual or group of patients. It has been found that ingestion rate of oxidized LDL by macrophages has a great impact on the plaque forming process.