MATHEMATICAL ANALYSIS OF BLOCKAGE OCCURRED IN THE ARTYERY DUE TO BLOOD TRANSPORTATION

Abstract

In recent years, mathematical modelling, especially using the partial differential equations (PDEs), has proved to be a valuable tool for studying phenomena in science and engineering. In the present study, the flow behavior of blood in an artery with quadrilateral stenosis is examined, which is a typical case occurring in cardiovascular diseases. Some health-related issues, like high blood pressure, elevated cholesterol, diabetes, smoking, overweight, and various other factors have made arterial blockage a growing problem. For analyzing this problem, the governing equations for transport of the flow were applied along with the continuity equation describing the fluid flow behavior in a rectangular channel with an embedded quadrilateral obstruction in the channel. Various mesh configurations were used to improve the numerical accuracy such as coarse, normal, fine and extra-fine meshes. It analysed the flow behaviour, velocity distribution, pressure change, streamline patterns and vortex formation around the blockage in the case of inertia and power-law index. The results indicated that the changes in inertia and the power-law index markedly affect the flow characteristics. Vortices were observed near the corners of the blockage, and their size increased with variations in flow parameters. In addition, it is found that vortices gradually increased as the inertia increased as the power-law index increases; however, as the power-law index decreases with increasing inertia, vortices around the blockage were more pronounced and larger. These results may aid in the understanding of blood flow characteristics in blocked arteries and help make mathematical models of heart disease and other circulatory conditions.

Keywords: Arterial Blockage, Blood Flow, Mathematical Modeling, Partial Differential Equations, Computational Fluid Dynamics, Power-Law Fluid, Vortex Formation, Hemodynamics.