A problem-oriented approach to the numerical modelling of haemodynamic problems

Abstract

A physiological problem-oriented approach to the numerical modelling of haemodynamic problems is presented. Numerical procedures based on two different approaches (1) the finite volume method (FVM) and (2) the finite element method (FEM) are described. Both methods employ the full threedimensional time-dependent Navier-Stokes and continuity equations, and can accommodate non-Newtonian fluid behaviour. In the FVM code, motion of the wall is allowed by using a transient gridding technique, which requires either a prescribed wall movement or a given pressure-radius relationship. In the FEM code, by contrast, the wall motion is predicted by solving the equations governing the motion of a linearly elastic, incompressible, isotropic solid undergoing small deformations. Basic testing cases are presented, with comparable theoretical solutions. The physiological validity of the predictions is assessed through comparisons with high precision in vivo ultrasound data for flow in (a) a porcine carotid artery, and (b) a canine peripheral artery bifurcation. Effects of various factors on the flow field and shear stress distributions are investigated. Physiological phenomena which should be taken into account in numerical modelling are also discussed.