Three dimensional fluid structural interaction of tissue valves

This thesis presents a stable fluid structural interaction technique to simulate the dynamics of tissue valves including bio-prosthetic heart valves and natural heart valves under physiological Reynolds numbers. A partitioned approach is implemented where the equations governing the flow and the displacement of the structure are solved using two distinct solvers. A FEAP based solid solver is strongly coupled to the p-ELAFINT flow solver using subiteration procedure. The flow solver has been massively parallelized so that the domain can be distributed among several processors. The fixed Cartesian method with adaptive mesh refinement in p-ELAFINT enables us to perform fast and efficient flow computations of problem involving moving boundaries such as heart valve leaflets. To capture the structure deformation, Enhanced Assumed Solid shell element has been implemented into the solid solver which is known for its locking free and superior bending characteristics. Aitken Relaxation method which dynamically computes the relaxation parameter is used for relaxing the solid displacement in the FSI coupling. This helps the subiteration procedure to achieve a faster convergence compared to traditional Subiterative procedures with fixed relaxation parameter. Fung type material model with experimentally derived parameters is used as the constitutive model to capture the realistic solid deformation.

Opening phase of a bicuspid aortic valve (BAV) model derived from a patient specific data and a pericardial bioprosthetic valve model were simulated using the FSI algorithm with realistic material parameters under physiological flow conditions. It was observed that the valves attained its fully open position under 35 milliseconds which is similar to the physiological opening. The bioprosthetic valve attained a fully circular orifice while the BAV attained an ellipsoidal shaped orifice at its fully open position. In the BAV, strong vortical patterns were observed at peak systole and recirculation zones were observed near the sino-tubular junction. The work presented in this thesis be seen as a platform from which complex patient specific data can be modeled under physiological conditions and as a base to include contact mechanics with which complete cardiac cycle can be simulated.