Numerical analysis of steady generalized Newtonian blood flow in a 2D model of the carotid artery bifurcation

Abstract

The stationary flow of blood in a two-dimensional model of the bifurcation of the human carotid artery is simulated numerically using a finite element method. The Reynolds number is taken as equal to 300, corresponding to the value during the end-diastolic phase of the heart cycle. As constitutive equations, the Newtonian model and the non-Newtonian power-law and Casson models are used. The chosen model parameters corresponded with blood. The flow in this geometry is determined by the branching of the artery and the existence of a reversed flow area in the internal carotid artery. From the results of this problem, we conclude that the general flow structure is not influenced by the generalized (non-)Newtonian models. However, there are differences that cannot be neglected. First, the generalized Newtonian models result in axial and secondary velocity profiles that have 5-10% lower maximum values compared to the Newtonian model. Second, the pressure has higher values in the case of the generalized Newtonian models, especially in the internal carotid artery where these models give maximal 25% higher pressure values. Third, along the divider wall, the wall shear stresses are lower for the generalized Newtonian models; near the apex, this difference is maximal 40% in case of the power-law model. The generalized Newtonian models give higher wall shear stresses along the non-divider wall than the Newtonian model, the maximum difference being 5%. And fourth, in the internal carotid artery the reversed flow area is 10% reduced by the generalized Newtonian models. In general, the differences are more pronounced in the case of the power-law model.