Challenges in Computational Hemodynamics

Marek Behr

Chair for Computational Analysis of Technical Systems (CATS)

Center for Computational Engineering Science (CCES)

RWTH Aachen University

52056 Aachen, Germany

http://www.cats.rwth-aachen.de

Modeling and computational analysis play an increasingly-important role in bioengineering, particularly in the design of ventricular assist devices. Numerical simulation of flow in blood pumps has the potential to shorten the design cycle and give the designers important insights into causes of blood damage and suboptimal performance. A set of modeling techniques will be presented which are based on stabilized space-time finite element formulation of the Navier-Stokes equations, with a shear-slip mesh update used to accommodate the movement of the impeller with respect to a non-axisymmetric housing. The computed global flow characteristics (performance curves) are compared with experimentally measured data. This application presents a ripe target for shape optimization and optimal control. In order to assess the influence of the fluid constitutive model on the outcome of shape optimization tasks, a comparison of model problem computations based on the Navier-Stokes equations on one hand, and on a more accurate shear-thinning modified Cross model on the other, will be presented. More complex description of blood behavior takes into account viscoelastic phenomena, in particular via an Oldroyd-B constitutive model. Recent developments in stabilized methods of GLS-type for simulation of Oldroyd-B flows using low-order extra-stress interpolations will be outlined. Finally, in order to obtain quantitative hemolysis prediction, cumulative tensor-based measures of strain experienced by individual blood cells are being developed and correlated with available blood damage data. In the first approximation, red blood cells under shear are modeled as deforming droplets, and their deformation is tracked along pathlines of the computed flow field.