Simulating The Left Ventricle with Implanted Left Ventricular Assist Device Using a Finite Element Method And MRI-Based Interpolation with Radial Basis Functions

  • Schuster, Maximilian (CATS, RWTH Aachen University)
  • Behr, Marek (CATS, RWTH Aachen University)
  • Hosters, Norbert (CATS, RWTH Aachen University)

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Left ventricular assist devices (LVADs) play an important role helping patients suffering from heart diseases, as they are primarily used as a bridge to transplant technology [1]. We examine the interaction between blood flow in the left ventricle (LV), LVAD, and the cannula inserted into the ventricle. We have determined stagnation and low velocity areas by solving transport equations for residence time and Virtual Ink in the ventricle under different operational conditions of the LVAD. Such areas of stagnation and low velocity are prone to thrombosis. From a computational mechanics perspective, defining appropriate boundary conditions plays a vital role in this project for the structural and fluid mechanics part, respectively. The fluid boundary conditions at the valves, which are modelled as circular planes, progress from simple constant boundary conditions to resistance boundary conditions. They replace the circulation in the blood vessels and the flow through the LVAD whose cannula is inserted at the apex of the ventricle. The interaction between ventricle wall and fluid is imposed by the wall movement. In our current work, we make use of a magnetic resonance imaging (MRI) based LV geometry and interpolate the motion of the ventricle wall with radial basis functions. The LVAD’s pump flux is set as a time-dependent Dirichlet boundary condition. The washout of blood in the LV is examined as a function of LVAD working conditions. For the different stages of the simulations, an in-house code [2] is used. It uses a stabilized finite element method to discretize time and space. The fluid is subject to the incompressible Navier-Stokes equations with a Newtonian material law. The stagnation time as a key result of the simulations is obtained by coupling a transport equation for the residence time to the fluid equations.