Cardiac hemodynamics simulations with fluid-structure interaction and reduced valve modeling
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The development of efficient physiological simulations of the complete fluid-structure interaction (FSI) phenomena involved in the heart is a challenging problem. In order to reduce the compu- tational complexity of this problem, kinematic uncoupling approaches (i.e., displacements are enforced on the boundaries of the fluid cavities) in combination with reduced models of valve dynamics are often considered as an alternative to cardiac FSI. These formulations enable the simulation of blood flow patterns within the cardiac cavities at a reduced computational cost, but at the price of ne- glecting parts of the cardiac cycle, such as the isovolumetric phases, or of introducing spurious pressure oscillations during opening/closing. In order to circumvent these issues, we propose an hybrid modeling approach which integrates FSI in the myocardium with reduced models of the valves dynamics. We also introduce for the latter a new reduced model based on unidirectional velocity constraints. An appropriate discrete treatment of the interface FSI coupling (based on a Robin-Robin loosely coupled scheme) is considered to handle the fully enclosed fluid during the isovolumetric phases. The benefits of the pro- posed approach are investigated and compared with kinematic uncoupling on a simplified model and in the left heart.
