Comprehensive Mathematical Modeling of Atherosclerotic Blood Flow: Impact of Porous Media on Hemodynamics

Dushyant Palia

Abstract: Atherosclerosis, characterized by the narrowing of arteries due to plaque buildup, disrupts normal blood flow and is a major contributor to cardiovascular diseases. This study develops a detailed mathematical model to investigate the hemodynamics of blood flow in arteries affected by atherosclerosis, specifically considering the porous nature of the arterial wall. By treating blood as a non - Newtonian fluid, modeled using Casson?s framework, and applying Navier - Stokes and continuity equations, study examines how these factors affect flow velocity, pressure distribution, and wall shear stress. The model addresses laminar, incompressible, and fully developed flow in an artery featuring axially non - symmetric but radially symmetric stenosis. Numerical solutions for volumetric flow rate, pressure drop, and wall shear stress are derived under relevant boundary conditions and presented graphically. The investigation shows that wall shear stress rises with the porous parameter, stenosis size, and stenosis length, but decreases as stenosis shape parameter increases. These findings are consistent with existing research, validating the model's relevance. The insights provided by this study are valuable for both biomedical researchers and medical practitioners, offering a deeper understanding of the impact of atherosclerosis on blood flow and potentially guiding better diagnostic and therapeutic approaches.

Keywords: Atherosclerosis, Cardiovascular diseases, Porous media, Non - Newtonian fluid, Casson?s fluid model, Stenosis, Blood flow dynamics