Mathematical modelling of blood flow in a catheterized artery with time variant multiple stenoses

Abstract

Mathematical modelling of Newtonian blood flow in a catheterized stenosed artery is considered. A catheter which is a long, and hollow thin tube is a clinical device to diagnose and treat certain diseases. However, the insertion of a catheter into the blood vessel will alter and disturb the hemodynamic characteristics of blood flow. In this research, the effect of physical parameters of the catheter in an eccentric position is investigated in a tapered artery with multiple stenoses taking the cosine shape varying with time. The governing equations which consist of a system of non-linear partial differential equations are analytically solved using the perturbation technique under the assumption of axisymmetric, unsteady, fully developed laminar flow. A Mathematica software package is developed to assist in the solution procedure which is complicated and tedious. The results for axial velocity have been compared and validated in the case of a single stenosis. In a multiple stenosed artery, it is found that with the increase of eccentricity parameter and radius of catheter, the axial velocities across the three stenoses decrease drastically. If the velocity of catheter is increased, the wall shear stress has the highest value in the case of diverging tapered multiple stenosed artery. The increase of catheter radius has significant effect on the impedance at the location of the first and third stenosis. In both single and multiple stenosed artery, the streamline patterns show that the trapping bolus is formed near the wall of stenosis and in between stenosis when the physical parameters of eccentric catheter increases. It is found that the ratio of the catheter’s size to the artery should be less than 0 . 2 and must be placed at an eccentric position of 0 . 1 to avoid artery’s rupture.