Mathematical model of pulsatile blood flow in a distensible aortic bifurcation subject to body acceleration

Abstract

The present analytical investigation has been dealt with pulsatile flow characteristics of blood in a distensible bifurcated artery having a stenosis when it is subjected to whole body acceleration. The geometry of the bifurcated artery developed by the present first two authors (S. Chakravarty, P.K. Mandal, Int. J. Eng. Sci. 35 (1997) 409–422) has been used to carry out the present analysis. It incorporates the arterial wall motion by treating it as an anisotropic, linear viscoelastic incompressible material. The unsteady flow mechanism in the bifurcated artery subject to a pulsatile pressure gradient arising from the normal functioning of the heart as also the body acceleration is presented mathematically. The effect of the surrounding connective tissues on the motion of the arterial wall is also paid due consideration. The effect of the wall distensibility on the bifurcated flow phenomena has been accounted for through suitably formulated continuity conditions. The equations governing the motion of the system are sought in the Laplace transform space and their relevant solutions are obtained in the transformed domain by using an appropriate finite difference scheme. Their inversions to the physical domain lead to calculate the velocity profile of the flowing blood in both the parent and the daughter arteries together with the arterial wall displacements. From the computational results based on the short-time-range approximations, one may disclose that the body acceleration and the wall distensibility do not change the flow patterns in the parent aorta, but there is a drastic change in the daughter artery, which in turn, causes an appreciable increase in the shear stresses developed on both the parent and its daughter arterial walls. The pulsatile flow helps inducing the wall shear stress to change the direction over a cycle which may be important in the mechanism of atherosclerosis.