Fluid-structure interaction methods in biological flows with special emphasis on heart valve dynamics

There are numerous examples of fluid-structure interactions (FSIs) within the human body. In all cases, a computer model capable of simulating the phenomenon can aid in the understanding of organ function, failure, and implant design or improvement. In the current paper, two approaches are examined for use in simulating the FSI problem of the dynamics of tissue heart valves. Valve leaflets have nonlinear anisotropic material properties, and undergo complex deformation. Their motion affects and is affected by the surrounding blood. This two-way coupling necessitates a robust algorithm in order to overcome numerical stiffness, convergence challenges, and stability issues. A locally refined Cartesian mesh, sharp interface method has been developed for the fluid flow solution. In the structural domain, the valve leaflet is represented in a Lagrangian fashion and moves based on its experimentally determined material properties. In computing leaflet motion, the anisotropic, nonlinear material properties of the valve leaflet are incorporated using a finite element solver, which calculates the leaflet deformation and stresses based on the stress imparted by the surrounding fluid. Two FSI algorithms have been studied in the context of a sharp-interface Cartesian grid setting, and each has been validated with benchmark results. The two approaches are compared, and ultimately one is selected as most appropriate for simulating tissue heart valves. In the selected approach, a strongly coupled, partitioned method is used in which subiterations of the fluid and structure solutions are performed at each time step. During the subiterations, the leaflet motion is used as a boundary condition on the fluid, and the fluid stresses act as a boundary condition on the leaflet. In this way, continuity is ensured and two-way coupling is achieved. The selected approach has overcome the challenges faced by previous simulations reported in the literature, and a robust FSI solution is achieved using physiologic Reynolds numbers, realistic material properties, highly resolved grids, and a dynamic simulation. This approach has the advantage of handling both thin and volumetric embedded objects in a unified fashion, and of treating rigid and deformable structures in the same way, thus allowing a spectrum of potential applications. Copyright (C) 2009 John Wiley & Sons, Ltd.