Analytical and Computational Methods for Fluid-Structure Interaction Applications to Aneurysms

Abstract

In this dissertation, we develop analytical and computational models for understanding soft tissue mechanics, fluid dynamics, and their interaction. Despite major advances in this area, there is still a need for more sophisticated models which provide better insight into understanding the biomechanics of aneurysms. Towards this end, this dissertation: Develops a hyperelastic membrane model which incorporates fluid-structure interaction for a cylindrical geometry undergoing radial inflation. Develops a fully three-dimensional elastic model which incorporates fluid-structure interaction for a cylindrical geometry undergoing radial inflation. Performs stability analysis on the governing equations derived for the membrane and elastic models. Develops computational algorithms using the finite element method to substantiate the results from analytical models. The models that will be derived in this research will be studied for a variety of biomechanical factors including viscoelasticity, radial anisotropy, and angular anisotropy.