Fluid-structure Interaction Simulations For Medical Applications

Abstract

Fluid-structure interaction (FSI) is a multiphysics coupling between a solid structure and the surrounding fluid. When a fluid flow hits the structure, stresses and strains are exerted on the solid body. Large forces can lead to large deformations, especially if the structure is made of a soft material. Then, the fluid domain around the solid is subjected to significant changes, and as a result the velocity and pressure fields of the fluid modify. In general, this can happen not only in the proximity of the structure, but also downstream for some distance. So, an FSI problem has to be treated as a two-way coupled interaction problem. This thesis focuses on FSI problems with biomedical applications, therefore the fluid considered is blood while the structure is the vessel that contains it. In our model, blood is considered as an incompressible Newtonian fluid and a hyperelastic solid is used to represent vessel wall tissue. We describe the solid motion in a Lagrangian way, while the fluid is observed in a Eulerian fashion. The deformation of the fluid domain is taken into account according to an Arbitrary Lagrangian Eulerian (ALE) approach. Three main medical applications are considered: stented intracranial aneurysms, magnetic drug targeting (MDT) procedures in human arteries and venous valves. In the first application, we study FSI simulations of stenting technology where flow diverters are modeled as porous media [8, 83, 108]. The goal of this study is verifying whether or not the porous medium approach is reliable in an FSI framework. In the second application, we perform an MDT computational study [53, 61] that takes into account the bidirectional coupling between blood flow and the vessel walls. The aim of the study is to investigate if there is a change in the capture efficiency predictions caused by a solid deformation. Finally, in the third application, we extend our ALE scheme to solve the solver instabilities that may arise in venous valves simulations due to large structural displacements. We implement each of these applications in the C++ in-house finite element library FEMuS (Finite Element Multiphysics Solver), and provide numerical results for each problem.