Mathematical Considerations for Fluidstructure Interaction Simulation of Heart Valves

Abstract

We introduce a new approach to simulate fluid-structure interaction of the heart valves. Our approach is based on the Lagrange multiplier method, thus similar to the fictitious domain method. However, unlike the existing approaches, we avoid interpolations of the fluid velocity on the interface with the structure, and introduce equations of continuity around the interface as the constraint conditions instead. Through some mathematical considerations based on a weak formulation of the Navier-Stokes equation, we show the validity of the approach. We also introduce another constraint based on the same idea to achieve stability in the analysis of open-close behavior of the heart valves. A couple of simulations of aortic valves are successfully shown.