Shape Optimization in Stationary Blood Flow: A Numerical Study of Non-Newtonian Effects

We investigate the influence of the fluid constitutive model on the outcome of shape optimization tasks, motivated by optimal design problems in biomedical engineering. Our computations are based on the Navier-Stokes equations generalized to non-Newtonian fluid, with the CarreauYasuda model employed to account for the shear-thinning behavior of blood. The generalized Newtonian treatment exhibits striking differences in the velocity field for smaller shear rates. We apply sensitivity-based optimization procedure to a benchmark problem of flow through a rightangle cannula, and to a flow through an idealized arterial graft. For each of these problems we study the influence of the inflow velocity, and thus the shear rate. Furthermore for the arterial graft problem, we introduce an additional factor in the form of a geometric parameter, and study its effect on the optimal shape obtained.