Trileaflet Aortic Valve (TAV). Vorticity Magnitude.

Simulating the hemodynamics of a trileaflet aortic heart valve at physiologic conditions requires capturing the complex interaction between blood flow and flexible valve leaflets. In FSI simulations of biological tissues, e.g. heart valve leaflet interaction with blood flow, it is critical to use a relevant and efficient structural model that is able to realistically represent the deformation of the tissue under loads imposed by the pulsatile blood flow. Such undertaking, however, is not a trivial task since the large deformations of the tissue and its underlying geometric non-linearity pose major modelingchallenges. To circumvent these challenges recent studies attempting to simulate FSI of tissue valves chose to either use simplified membrane-like materials or treat the valve leaflets as thick bodies. However, biological tissues of leaflets are normally thin and they exhibit significant bending. Therefore, a shell model for the solid body is a more appropriate choice. Most finite-element (FE) methodologies for handling shells, however, are computationally very demanding as they employ two or three nodal rotations alongside with three nodal translations, i.e. 5 or 6 degree of freedom per node. Note that the efficiency of the FE shell model becomes of paramount concern in FSI simulations of complex problems where the need to couple the fluid and structural solvers together can dramatically increase the computational cost per time step. For that, in this work we adapt and incorporate in the FSI methodology a previously developed nonlinear, rotation-free triangular shell element formulation, which has already been shown to provide accurate and robust solutions of various thin shell FE problems. Such an approach, however, has not been coupled before with a flow solver to simulate FSI problems and it is this coupling that constitutes one of the important contributions of our work.

The curvilinear immersed boundary method (CURVIB) is coupled with a rotation-free finite element (FE) model for thin shells enabling the efficient simulation of FSI problems with arbitrarily large deformation. Turbulent flow problems are handled using large-eddy simulation with the dynamic Smagorinsky model in conjunction with a wall model to reconstruct boundary conditions near immersed boundaries. The CURVIB and FE solvers are coupled together on the flexible solid–fluid interfaces where the structural nodal positions, displacements, velocities and loads are calculated and exchanged between the two solvers. Loose and strong coupling FSI schemes are employed enhanced by the Aitken acceleration technique to ensure robust coupling and fast convergence especially for low mass ratio problems. The nonlinear anisotropic May-Newman & Yin (MNY) model was used as a property of aortic valve tissue.

The calculated flowfields for one simulated systolic cardiac cycle are shown in presented video. Contours of instantaneous vorticity magnitude are plotted in this vodeo on a plane passing through the center of the aorta. As seen in this video, a well defined vortex ring forms as soon as the valve opens at early systole. Shear layers connecting the aortic valve vortex ring with the valve leaflets are also evident in vidro. As the valve leaflets continue to open, the vortex ring advances and impinges on the curved aorta wall and breaks up. The valve leaflet shear layers intensify as the flow rate through the valve increases and the flow in the wake of the valve leaflets is seen to break up into small-scale turbulence at approximately halfway within the accelerating phase of the cardiac cycle. By the time the peak systolic flow is reached and the valve has opened fully, the flow in the aorta is seen to have transitioned to a fully turbulent state downstream of the valve leaflets. This state persists even after the valve closes and the flow structures in the aorta gradually decay. The simulation shows the process of the opening trileaflet heart valve during the systolic phase at Re=6000.

A model of artificial heart valve with constant thickness and linear constitutive equations for leaflets has been used. We are currently extending the method to incorporate nonlinear constitutive equations with variation of thickness to enable simulations of native aortic valves. Moreover, in our model leakage flow is allowed at the end of cardiac cycle as there exist a small gap between the leaflet tips. This leakage flow exists in many types of tri-leaflet prosthetic valves as a design feature and it is well documented in the literature.