Fluid-structure Interaction Simulations of Deformable Soft Tissue

Soft tissue interacts with the surrounding fluid environment in many biological and biomedical applications. Simulating such an interaction is quite challenging due to the large non-linear deformations of tissue, flow pulsatility, transition to turbulence, and non-linear fluid-structure interaction. We have extended our previous three-dimensional fluid-structure interaction (FSI) framework for rigid bodies (Borazjani, Ge, and Sotiropoulos, Journal of Computational Physics, 2008) to deformable soft tissue by coupling our incompressible Navier-Stokes solver for fluids with a non-linear large deformation finite element method for soft tissue. We use Fung-type constitutive law for the soft tissue that can capture the stress-strain behavior of the tissue. The FSI solver adopts a strongly-coupled partitioned approach that is stabilized with under-relaxation and Aitken acceleration technique. We validate our solvers against the experimental data for tissue valves and elastic tubes. We show the capabilities of our solver by simulating the fluid-structure interaction of tissue valves implanted in the aortic positions and elastic collapsible tubes.