A mathematical model that describes the relation of low-density lipoprotein and oxygen concentrations in a stenosed artery

Abstract

The cellular activities of the endothelium layer between lumen and intima are significantly linked to the origin of the disease atherosclerosis. Three stages of atherosclerosis were investigated in this study (40%-mild, 50%-modest, and 60%-acute) concerning the coronary arterial segment. The essence of the hemodynamic factors like flow velocity, pressure, and wall shear stress has been investigated, as well as the interrelationships between them. At all degrees of stenosis, the biophysical relationship between convection-diffusion of low-density lipoproteins (LDL) and convection-diffusion of oxygen in the bloodstream is investigated. The Finite Element Methods (FEM) are used to solve the modeled partial differential equation systems. The method adopted is numerical in nature providing accurate graphical solutions to the framed systems. The physical effects of the deposition of LDL on the arterial wall, like a decrease in the diameter of the lumen, and toughening of the walls, are analyzed through the evaluation of the physical parameters. The study revealed that the deposition of LDL molecules in the post stenotic region leads to the depletion of oxygen in the region leading to the rapid dysfunctioning of the endothelial layer of the lumen-intima boundary.