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. 127-137.
Abstract
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 Carreau-Yasuda 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 right-angle 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.
See also
Shape Optimization in Unsteady Blood Flow:
A Numerical Study of Non-Newtonian Effects.