Mathematical modelling of non-Newtonian blood flow through a tapered stenotic artery

Abstract

A mathematical model of non-Newtonian blood flow through a tapered stenotic artery is considered. It has been established that the regional blood rheology is altered once a stenosis develops. A stenosis is defined as the partial occlusion of the blood vessels due to the accumulation of cholesterols and fats and the abnormal growth of tissue. The non-Newtonian model chosen is characterized by the generalized Power-Law model and the effect of tapering on the arterial segment is incorporated in the analysis due to the pulsatile nature of blood flow. The flow is assumed to be unsteady, laminar, two-dimensional and axisymmetric. The equations of motion in terms of the viscous shear stress in the cylindrical coordinate system are first derived and then transformed using the radial coordinate transformation before they are solved numerically using a finite difference scheme. Numerical results obtained show that the blood flow characteristics such as the velocity profiles, flow rate, and wall shear stress have lower values while the resistive impedances have higher values compared to the values obtained from the Newtonian model.