Analysis of pulsatile blood flow in constricted bifurcated arteries with vorticity-stream function approach

Abstract

This theoretical investigation deals with an analysis of pulsatile blood flow in a model bifurcated artery having a stenosis in the parent arterial lumen. The geometry of the bifurcated arterial segment with an implanted stenosis in the parent duct is given an appropriate mathematical shape with the introduction of suitable curvature at the lateral junction and the flow divider. The vascular wall deformability is duly accounted for although the development of atherosclerosis in the arteries reduces its elastic property to some extent. The streaming blood contained in the bifurcated artery is treated to be Newtonian. The flow dynamic analysis applies two-dimensional unsteady incompressible nonlinear Navier-Stokes equations rewritten in the vorticity-stream function formulation. Following a radial coordinate transformation, these equations are solved numerically by a finite difference scheme with the approximate choice of the inlet and boundary conditions in concert with the biophysical point of view. The final numerical results are highlighted at the end of the paper through the exhibition of the wall shear stress and several time-variant patterns of streamlines and vorticity contours of the flow phenomena, which are highly influenced by the severity of the stenosis and the angle of bifurcation. The applicability of the present model is thus established.

Keywords:

• Haemodynamics
• arteriosclerosis
• distensibility
• wall shear stress
• stream lines
• vorticity