Numerical Simulation of Fluid-Structure Interaction in the Left Heart with Reduced Valve Modeling
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The fluid-structure interaction (FSI) of the heart poses a challenging problem [1, 2]. In order to address its computational complexity, various authors have proposed less computationally demanding approaches. These approaches encompass complete electromechanical simulations of the heart using a 0D fluid [3, 4], kinematic uncoupling methods that impose displacements from electromechanical simulations onto the boundaries of the fluid cavities [5], and FSI approaches that consider either 0D [6] or 3D [7] models for the heart valves. However, many of these approaches encounter challenges, such as difficulties in properly capturing isovolumetric phases with less expensive numerical methods, and issues in handling enclosed domains for more costly numerical methods. In this work, we propose to study the fluid- structure interaction (FSI) of the left heart, utilizing a mathematically consistent and novel reduced valve model. Additionally, we take into account the effect of the right ventricle by incorporating a 0D fluid representation in that cavity. We introduce a novel fluid-structure interaction coupling based on a Robin- Robin loosely coupled scheme [8]. Our investigation aims to explore the advantages of employing this method in accurately capturing isovolumic phases and achieving a reduced computational cost.
