Modelling red blood cell deformation in a rotary blood pump
Heart failure (HF) is a leading cause of death worldwide. Today, 1-2% of the adult population in western countries suffer from it. At the moment the preferred treatment for advanced HF is heart transplantation . But since donor hearts are rare, Ventricular Assist Devices (VAD) that support or take over the pumping function of the heart have become a viable alternative.
However, there are several severe health issues associated with the implantation of a VAD. One is the mechanical damage of the red blood cells (RBC) due to the high shear stresses inside the pump. This process – called hemolysis – reduces the ability of the blood to transport oxygen and causes pain and discomfort for the patients.
Up to now, a comprehensive understanding of hemolysis inside a VAD is still missing. With this study we lay the foundation for hemolysis assessment in a VAD based on the RBC’s membrane deformation.
In a first step, we conducted a macroscopic CFD simulation with particle tracking (turbulent, incompressible, Newtonian fluid with immersed Lagrangian particles) to identified characteristic tracks an RBC follows when being pumped through the device. In a second step, the velocity gradients along those tracks were used to model the deformation an RBC exhibits on its way through the pump. For this, we employed the OIF in ESPResSo framework, which models the fluid by the Lattice Boltzmann method and the cell by an elastic triangular spring network.
Although the one-way coupled model is not yet validated with experiments the results look promising, as some well known characteristics of an RBC in shear flow were reproduced: (1) The deformation is high if high stresses are present and low if stresses are low. (2) The cell retains its relaxed shape after deformation and (3) we observed the tank-treading motion of the membrane at high shear rates.
Detailed Figure Captions:
Figure 1: Here we see a characteristic particle track in the HVAD pump as calculated in the STAR-CCM+ simulation. The location of an RBC that moves along this track is marked with light grey dots for millisecond 0 to 19. Based on the velocity gradients along the track the deformation of the RBC could be calculated (see figure 2 or movie 1).
Figure 2: The blue curve shows the von Mises stress along the track shown in figure 1. The line in orange shows the maximum distance found between two nodes of the RBC model (maximum extent). In the background the cell deformation is graphically visualized.
 Edo Y. Birati and Mariell Jessup. Left ventricular assist devices in the management of heart failure. Cardiac Failure Review, 1(1):25–30, 2015.