Modeling, Computation and Simulation of Non-Linear Soft-Tissue Interaction with Flow Dynamics with Application to Aneurysms

Abstract

In this work, a computational model for the interaction of blood flow with the wall of an intracranial saccular aneurysm that is surrounded by cerebral spinal fluid is considered. The coupled fluid-structure interaction model presented includes growth and remodeling effects within the soft-tissue by incorporating elastin and collagen dynamics which are two of the main layers in the arterial wall. The resulting nonlinear system of coupled differential equations are solved numerically using implicit finite difference methods combined with the Newton's method. The linearized version of the nonlinear system was also considered and solved both analytically using Laplace transformation and numerically using implicit finite difference methods. We also validate our solutions using comparisons with a solution obtained employing a perturbation approach. The nonlinear effects on potential rupture of aneurysms was studied and compared for benchmark problems and the computational results indicate that the model proposed is robust and reliable. A potential model for extension to three-dimensions was also considered.