Hemodynamic Analysis in an Idealized Artery Tree: Differences in Wall Shear Stress between Newtonian and Non-Newtonian Blood Models

Abstract

Development of many conditions and disorders, such as atherosclerosis and stroke, are dependent upon hemodynamic forces. To accurately predict and prevent these conditions and disorders hemodynamic forces must be properly mapped. Here we compare a shear-rate dependent fluid (SDF) constitutive model, based on the works by Yasuda et al in 1981, against a Newtonian model of blood. We verify our stabilized finite element numerical method with the benchmark lid-driven cavity flow problem. Numerical simulations show that the Newtonian model gives similar velocity profiles in the 2-dimensional cavity given different height and width dimensions, given the same Reynolds number. Conversely, the SDF model gave dissimilar velocity profiles, differing from the Newtonian velocity profiles by up to 25% in velocity magnitudes. This difference can affect estimation in platelet distribution within blood vessels or magnetic nanoparticle delivery. Wall shear stress (WSS) is an important quantity involved in vascular remodeling through integrin and adhesion molecule mechanotransduction. The SDF model gave a 7.3-fold greater WSS than the Newtonian model at the top of the 3-dimensional cavity. The SDF model gave a 37.7-fold greater WSS than the Newtonian model at artery walls located immediately after bifurcations in the idealized femoral artery tree. The pressure drop across arteries reveals arterial sections highly resistive to flow which correlates with stenosis formation. Numerical simulations give the pressure drop across the idealized femoral artery tree with the SDF model which is approximately 2.3-fold higher than with the Newtonian model. In atherosclerotic lesion models, the SDF model gives over 1 Pa higher WSS than the Newtonian model, a difference correlated with over twice as many adherent monocytes to endothelial cells from the Newtonian model compared to the SDF model.