Heart failure is the main cause of death in developed countries. A heart transplantation is not available for most patients, due to the shortage of donor organs. Ventricular assist devices (VADs) that support the failing heart for several years, can be used as a bridge to transplant or even as a bridge to recovery. However, their development is complicated, costly and time-consuming, while the availability of blood samples for in-vitro tests is limited at the same time. The reliable computational prediction of blood flow and blood damage within a VAD is a very valuable tool in the design phase. While the flow prediction with computational fluid dynamics is well established in engineering, the prediction of blood damage using computational hemodynamics is a matter of ongoing research.This thesis provides a numerically stable approach to hemolysis prediction for complex domains, that tries to take the physiological behavior of red blood cells (RBCs) into account. Here, we follow a three-step-approach: the blood flow is computed first; then we predict the deformation of RBCs within that flow field, using the so-called morphology model; the release of hemoglobin to the blood plasma is finally predicted by a pore formation model, based on the RBCs deformation and the flow properties. Especially the morphology simulation is very challenging, due to the frequent occurrence of unphysical, negative eigenvalues in the shape tensor, which lead to diverging simulations. We apply a logarithmic transformation of the shape tensor — inspired by the work of Knechtges — that preserve the positive eigenvalues by design, and derive its variational multiscale (VMS) stabilized finite element formulation. The usage of the pore formation model — first proposed by Vitale et al. — in an Eulerian frame of reference, is a novelty of this thesis. Furthermore, we propose to consistently use the multiple reference frames (MRF) approach for all three simulation steps, for which we derive the constitutive equations. This allows faster, steady-state simulations, which result in time-averaged approximations to the, in principle, transient fields. It lets us compute the quantities-of-interest directly, like the pressure head provided by the pump or the averaged plasma-free hemoglobin content at the outflow, which are also obtained by experiments.Our model predictions show a good agreement with experimental results for the FDA’s benchmark blood pump. Furthermore, we use this modeling approach to predict the hemocompatibility of a state-of-the-art centrifugal VAD.
Stefan Thomas Haßler (Wed,) studied this question.