Numerical simulation of a 3D bileaflet mechanical heart valve: FSI coupling algorithm

Bileaflet Mechanical Heart Valves (BMHVs) are preferred for valve replacement. However, current BMHVs induce calcification and thromboembolism which is believed to be related to non-physiological flow. Therefore, numerical flow simulations can provide relevant information for design optimization. Such simulations can be achieved by implementing fluid-structure interaction (FSI). In this paper, we present a newly developed FSI coupling algorithm to simulate BMHV dynamics in a partitioned way. The coupling iterations between the flow solver and the leaflet motion solver are accelerated by using the Jacobian with the derivatives of the pressure and viscous moments acting on the leaflets with respect to the leaflet acceleration. This Jacobian is used in the leaflet motion solver when new positions of the leaflets are computed during the coupling iterations. The Jacobian is numerically derived from the flow solver by applying leaflet perturbations. Instead of calculating this Jacobian every time step, the Jacobian is extrapolated from previous time steps and a recalculation of the Jacobian is only done when needed. The convergence process is sped up by the use of extrapolations of angular accelerations and a variable time step size. This time step size depends on the maximum mesh motion, allowing a larger time step when leaflet motion is small and thus reducing the total number of time steps per time cycle. The algorithm is extended to accurately predict correct leaflet movement to and from the closed and opened position. The algorithm is used to simulate two 3D cases containing a BMHV. One geometry consists of a rigid straight tube. The second geometry is made asymmetrical by adding Valsalva sinuses downstream of the valve. The results show that the leaflets in this second geometry move asynchronously. An algorithm with two degrees of freedom is thus required in an asymmetrical geometry