Mathematical Modelling of Blood Flow Through Unhealthy Arteries

Abstract:  Globally, most of the deaths occur because of heart attacks and strokes. These strokes are mainly caused by blockages in the arteries, which form due to the build-up of fatty deposits. The partial occlusion of the arteries due to stenosis obstruction, not only restricts the regular blood flow, but also characterizes the hardening and thickening of the arterial wall. This alters the blood flow dynamics, resulting in alterations of the functioning of various organs. Modelling of blood flow circulation in the human body is a challenging task.

The human body is an organism consisting of cells, the size scale of which ranges from several micrometers to several nanometers. Under such scale, the mobility behavior appears to be very significant. The mobility behaviors of the blood flow in an annulus with stenosis on flexible tapered blood vessel wall have been studied through a mathematical model. Blood is modelled as an incompressible polar fluid. The influence of various parameters which are arising out of the fluid and geometry considered, on the blood flow characteristics are analyzed. The mathematical understanding of the physiological fluid flow through unhealthy arteries with flexible walls is deemed to be a great help in the treatment of vascular diseases and also the biomedical engineers who are engaged in the design and development of artificial organs.