Stabilized Finite Element Simulation of the Left Ventricle Under LVAD Support
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Left ventricular assist devices (LVADs) play an important role in helping patients with heart disease, primarily as a bridge to transplantation [1]. We simulate the interaction between blood flow in the left ventricle, the LVAD flow rate, and the cannula inserted into the ventricle. To reduce complications such as thrombosis, it is important to study blood flow in the left ventricle under LVAD support. We identify areas of stagnation by solving transport equations for the Virtual Ink method in the ventricle under different LVAD operating conditions. Such areas of stagnation and low velocity are prone to thrombosis. From the point of view of computational mechanics, the definition of appropriate boundary conditions plays a crucial role in this project for the structural and fluid mechanics parts, respectively. The fluid boundary conditions at the valves and the LVAD cannula are obtained from a 0D lumped parameter network of the cardiovascular system. The interaction between the ventricular wall and the fluid is imposed by the wall motion. In our current work, we use a magnetic resonance imaging (MRI) based left ventricular geometry and interpolate the ventricular mesh motion with radial basis functions. The LVAD cannula is implanted at the apex and the pump flux is set as a time-dependent Dirichlet boundary condition. An in-house code [2] is used for the different stages of the simulation. It uses a stabilised finite element method to discretise time and space. The fluid is subject to the incompressible Navier-Stokes equations with a Newtonian material law. The key result is washout as a function of the LVAD operating conditions. REFERENCES [1] A.L. Marsden, Y. Bazilevs, C.C. Long, M. Behr, Recent Advances in Computational Methodology for Simulation of Mechanical Circulatory Assist Devices. Wiley Interdisciplinary Reviews: Systems Biology and Medicine, 6 (2014) 169-188. [2] L. Pauli, M. Behr, On Stabilized Space-Time FEM for Anisotropic Meshes: Incompressible Navier-Stokes Equations and Applications for Blood Flow in Medical Devices, International Journal for Numerical Methods in Fluids, 85 (2017) 189-209.