A MATHEMATICAL MODEL OF BLOOD FLOW IN A CATHETERIZED ARTERY WITH A STENOSIS

Abstract

The present theoretical investigation is based on the flow characteristics of blood in a catheterized bifurcated artery under stenotic conditions through the use of a mathematical model. The geometry of the bifurcated arterial segment having stenosis in the daughter arterial lumen frequently appearing in the diseased arteries causing malfunction of the cardiovascular system, is constructed mathematically with the introduction of suitable curvatures at the lateral junction and the flow divider. The changed flow pattern in the catheterized artery is studied by considering the pressure gradient as pulsatile in nature. The flowing blood contained in the arterial segment under consideration is treated to be Newtonian and the flow is considered to be two dimensional. The motion of the arterial wall and its effect on local fluid mechanics is not ruled out from the present study. The flow analysis applies the two-dimensional unsteady incompressible nonlinear Navier–Stokes equations for Newtonian fluids. The resulting nonlinear differential equations together with the boundary conditions following the radial coordinate transformation are solved numerically by adopting a finite difference scheme. An extensive quantitative analysis is performed at the end of the paper in order to estimate the effects of the catheter, the wall distensibility, the stenosis and the viscous dissipation of blood in the flow characteristics of the blood stream and the wall shear stress so as to validate the applicability of the present mathematical model. Some of the several important findings of the present investigation discussed at length include the changing pattern of the flow-field in the parent aorta, the occurrence of back flow at and beyond the apex with the formation of several flow separation zones, and the generation of higher wall shear stresses on the inner wall than on the outer wall surface owing to the arterial catheterization. The arterial catheterization does influence the viscous dissipation more remarkably in the parent duct till its apex than in the branch arteries.