A contact model based on coefficient of restitution for simulations of tissue heart valves in an immersed boundary-thin shell finite element framework*

A simple and efficient contact model is introduced for inter-leaflet penetration prevention of tissue heart valves and added to a rotation-free, high-deformation thin shell finite element (FE) framework. The proposed method applies the impenetrability constraints and momentum exchange between the impacting bodies separately using coefficient of restitution. The contact method is verified and validated against several dynamic benchmark problems. Additionally, the strain distribution of a statically loaded bio-prosthetic heart valve (BHV) with an anisotropic and nonlinear material model is compared against experimental results. Then, the dynamic performance of the BHV for two fiber orientations is analyzed using a physiological pressure waveform for a complete cycle. Finally, the FE framework incorporating the new contact model is coupled with the sharp-interface curvilinear immersed boundary (CURVIB) incompressible Navier-Stokes flow solver. The validity of the CURVIB-FE framework for fluid-structure interaction simulations is established by comparing the results of an inverted elastic flag with experiments. Finally, the capabilities of the framework are demonstrated by simulating the complex cardiovascular flow of a BHV for both opening and closing phases of the cardiac cycle.