Atherosclerosis: A Mathematical Overview

Atherosclerosis is a chronic inflammatory disease occurs due to plaque accumulation in the intima, the innermost layer of artery. Atherosclerosis is one of the prime causes behind several cardiovascular diseases over the worldwide. Here the entire biochemical process of atherosclerotic plaque formation is presented in terms of an autonomous system of ten nonlinear ordinary differential equations. Concentrations of low density lipoproteins (LDLs), high density lipoproteins (HDLs), free radicals, oxidized LDLs, chemoattractant, monocytes, macrophages, T-cells, smooth muscle cells (SMCs) and the necrotic core (or plaque cells) are assumed as the dependent variables in this nonlinear system. The present model has been found to be globally stable. Quasi steady state approximation theory is used to reduce the ten dimensional nonlinear system into a three dimensional nonlinear system. Numerical analysis of this reduced system has revealed the impact of some significant model parameters, which can be taken forward to develop some clinical strategies in controlling this disease dynamics.