Mathematical Models and Numerical Simulations for the Blood Flow in Large Vessels

We are proposing a non-Newtonian, Cross type rheological model for the blood flow, under the conditions of an unsteady flow regime connected with the rhythmic pumping of the blood by the heart. We admit the incompressibility and homogeneity of the blood while its flow is laminar and the exterior body forces are neglected. We take also into account the viscoelastic behavior of the vessel walls. The mathematical equations and the appropriate boundary conditions are considered in cylindrical (axisymmetric) coordinates. Numerical experiments in case of stenosed artery and in artery with aneurysm (using COMSOL Multiphysics 3.3) are made. The variation of the wall shear stress, which is believed to have a special importance in the rupture of aneurysms, is calculated using both a Newtonian and a non-Newtonian model.