Mathematical Analysis and Simulation of a Coupled Nonlinear Fluid Structure Interaction Model With Applications to Aneurysms

Abstract

In this work, we will present a mathematical model that describes a coupled fluid-structure interaction between the arterial wall, the blood flow inside the wall and the cerebral spinal fluid outside the wall with applications to intracranial saccular aneurysms. The governing system of differential equations includes a nonlinear power-law fluid equation coupled with a nonlinear elasticity equation describing the wall in conjunction with blood pressure that is modeled via a Fourier series. The thrust of this work involves the analysis and simulation of the associated mathematical model using classical differential equation techniques. Besides proving existence and uniqueness of the solution to the related system, analytical expressions for the associated traveling wave solutions for the governing nonlinear differential equation is also derived for a special class of problems that is biologically tractable.