Unsteady response of blood flow through a couple of irregular arterial constrictions to body acceleration

Abstract

A two-dimensional (2D) nonlinear mathematical model to study the response of the pulsatile flow of blood through a couple of irregular stenoses influenced by externally imposed periodic body acceleration is developed. The model is 2D and axisymmetric with an outline of the stenosis obtained from the three-dimensional (3D) casting of a mildly stenosed artery. The combined influence of an asymmetric shape and surface irregularities of the constrictions is explored in a computational study of blood flow through arterial stenoses with 48% areal occlusion. The arterial wall is treated as an elastic (moving wall) cylindrical tube having a couple of stenoses in its lumen, while the streaming blood is considered to be Newtonian. Solutions of the time-dependent nonlinear Navier-Stokes equations in the cylindrical coordinate system are obtained using a finite difference method based on the nonuniform and nonstaggered grids. The finite difference approximation helps to estimate the effects of body acceleration on the doubly constricted flow phenomena through several graphical representations quantitatively in order to validate the applicability of the present, improved mathematical model.