A Mathematical Modeling of Blood Flow Through Artery with Bell-Shaped Stenosis

Abstract

This study investigates the effect of bell-shaped stenosis on blood flow within arteries, a critical factor in understanding cardiovascular health. Using the Navier-Stokes equation in cylindrical polar coordinates, we derive analytical solutions for key hemodynamic parameters, including velocity, pressure, pressure drop ratio, and wall shear stress. Numerical integration is applied to explore the dynamics of pressure drop, and shear stress ratios within the stenotic region and various flow parameters are investigated and analyzed in this work considering blood as a Newtonian fluid. Given the heightened risk posed by bell-shaped stenosis in conditions like ischemic heart disease and stroke, this research offers valuable insights into the behavior of blood flow in stenotic arteries. The findings contribute to the development of advanced analytical tools and therapeutic strategies in cardiology and bio-fluid mechanics, enhancing our ability to manage and treat cardiovascular diseases.