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

Feby Abraham
Department of Mechanical Engineering and Materials Science

Marek Behr
Computational Analysis of Technical Systems (CATS)
RWTH Aachen, Germany

Matthias Heinkenschloss
Department of Computational and Applied Mathematics
Rice University


Computer Methods in Biomechanics and Biomedical Engineering,
Vol 8 (2005), pp. 201-212.


Abstract

This paper presents a numerical study of non-Newtonian effects on the solution of shape optimization problems involving unsteady pulsatile blood flow. We consider an idealized two-dimensional arterial graft geometry. Our computations are based on the Navier-Stokes equations generalized to non-Newtonian fluid, with the Carreau-Yasuda model employed to account for the shear-thinning behavior of blood. Using a gradient-based optimization algorithm, we compare the optimal shapes obtained using both the Newtonian and generalized Newtonian constitutive equations. Depending on the shear rate prevalent in the domain, substantial differences in the flow as well as in the computed optimal shape are observed when the Newtonian constitutive equation is replaced by the Carreau-Yasuda model. By varying a geometric parameter in our test case, we investigate the influence of the shear rate on the solution.

This paper complements Shape Optimization in Stationary Blood Flow: A Numerical Study of Non-Newtonian Effects.