Mathematical modeling of cardiac valve dynamics by a resistive method
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In the computational modeling of cardiac hemodynamics, the fluid domain is subject to complex deformations and topological changes, due to the contraction/relaxation of the heart and the opening/closing of the valves. Because of this, several unfitted methods for Computational Fluid Dynamics (CFD) have been proposed, to prevent mesh distortion and the possible need for remeshing. The Resistive Immersed Implicit Surface (RIIS) method belongs to this category. In this talk, we present recent developments in the use of the RIIS method for modeling cardiac valves, concerning two main aspects. First, we discuss the issue -- widely acknowledged, but little addressed -- of properly defining the ventricular pressure during the isovolumetric phases of the heartbeat, when all valves are closed. To solve this issue, we introduce an Augmented version of the RIIS method (ARIIS), extending a method proposed by This et al. to the case of a mesh not conforming to the valve. Second, we present an original multiscale Fluid-Structure Interaction model for valve dynamics, coupling a lumped-parameter model for the structural mechanics of the valve leaflets with the three-dimensional blood flow, via the RIIS method. Applications of this model to the cases of native and prosthetic valves will be presented.
