A contact model based on the coefficient of restitution for simulations of bio-prosthetic heart valves

A new general contact model is proposed for preventing inter-leaflet penetration of bio-prosthetic heart valves (BHV) at the end of the systole, which has the advantage of applying kinematic constraints directly and creating smooth free edges. At the end of each time step, the impenetrability constraints and momentum exchange between the impacting bodies are applied separately based on the coefficient of restitution. The contact method is implemented in a rotation-free, large deformation, and thin shell finite-element (FE) framework based on loop's subdivision surfaces. A nonlinear, anisotropic material model for a BHV is employed which uses Fung-elastic constitutive laws for in-plane and bending responses, respectively. The contact model is verified and validated against several benchmark problems. For a BHV-specific validation, the computed strains on different regions of a BHV under constant pressure are compared with experimentally measured data. Finally, dynamic simulations of BHV under physiological pressure waveform are performed for symmetrical and asymmetrical fiber orientations incorporating the new contact model and compared with the penalty contact method. The proposed contact model provides the coaptation area of a functioning BHV during the closing phase for both of the fiber orientations. Our results show that fiber orientation affects the dynamic of leaflets during the opening and closing phases. A swirling motion for the BHV with asymmetrical fiber orientation is observed, similar to experimental data. To include the fluid effects, fluid-structure interaction (FSI) simulation of the BHV is performed and compared to the dynamic results.