Finite element modelling of blood flow in artery stenosis

Recent work by our laboratories suggest that the endothelial cells that line blood vessels respond dramatically to shear stress gradients over millimeter and micrometer length scales, contributing to the progression of the atherosclerosis disease state. In this paper, we present a CFD model for the prediction and quantitative analyses of the hemodynamic behavior of blood flow in stenosed arteries of a guinea pig, comprised of a nearly axisymmetric vessel constriction. The blood is considered to be incompressible and the flow model is described by the Navier-Stokes and the continuity equations. A standard Galerkin finite element technique has been applied for the solution of the flow equations within a 2-D axisymmetric framework. Elemental discretization is based on the use of C⁰- continuous Taylor-Hood type isoparametric finite elements that are used for the approximation of the unknown field variables. An implicit-theta time-stepping scheme has been chosen for the temporal discretization of the flow equations. The rheological behaviour of blood is incorporated within the main flow model through the use of different non-Newtonian constitutive equations. Relationships of the stenosis severity and flow data such as flow rate and flow pressure are obtained from the numerical simulations. The results are presented in the form of velocity vectors and pressure surface plots and are examined for stability, convergence and theoretical consistency.