Analysis of Blood Flow through Stenosed Curved Artery with Einstein Viscosity

Abstract

The presence of arterial stenosis considerably disrupts normal blood flow, posing heightened risks and exerting a more significant impact on the cardiovascular system compared to other geometric abnormalities. The investigation of flow parameters in a curved artery with mild stenosis requires analyzing the varying viscosity of blood from the central core line to the vessel wall. This study employs the Navier-Stokes equation in cylindrical polar coordinates to examine fluid dynamics in axisymmetric directions, considering the effective viscosity of blood at varying radial distances (Einstein coefficient of blood viscosity).By solving this equation with appropriate boundary conditions, analytical expressions for the velocity profile, volumetric flow rate, pressure drop, wall shear stress, and the ratios of pressure drop and shear stress are derived for the stenosed curved artery, using the Einstein coefficient of blood viscosity. Additionally, variations in plasma viscosity, curvature, and hematocrit are examined in relation to these flow parameters in the stenosed curved artery region. These findings underscore that as hematocrit, curvature, and viscosity uniformly increase, blood velocity decreases. The volumetric flow rate decreases approximately linearly with uniform increases in plasma viscosity, curvature, and hematocrit. The ratio of pressure drop to shear stress increases uniformly with the rise in hematocrit and curvature, indicating a linear relationship with stenosis height. The complexity of blood flow dynamics underscores the critical importance of incorporating significant factors, such as the Einstein coefficient of blood viscosity, to advance our understanding of vascular physiology in the presence of stenosis.