Coupled Numerical Scheme for Vascular Fluid-Tube Interaction using Large Deformation Theory

Abstract

A methodological approach is elaborated to study the vascular fluid-tube interaction under pulsatile blood flow within an asymmetrical nonlinear aneurysm and large deformation models. The aneurysm dynamics were modeled using a simplified Lagrangian nonlinear system describing the arterial wall motion with large deformation. The flow is governed by the Navier-Stokes equations in two-dimensional domain. A semi-implicit splitting scheme coupled with the finite difference method is developed to solve the flow equation in an irregular domain using a mesh transformation. On the other hand, the wall equations are solved using the Runge-Kutta method combined with the shooting technique by reducing the resulted boundary value problem to an initial value problem. Rigid and elastic aneurysms are considered and the effect of various geometrical and fluid parameters on the flow are investigated, mainly the Reynolds number, the aneurysm length and height. The study focused on the effect of the asymmetric curvatures of the tube walls and their deformations due to the pulsatile flow. The flow is examined under a steady inlet flow as well as under a pulsatile one for various aneurysm forms. The obtained numerical results validate the fluid and structure solvers and demonstrate significant differences between the rigid and elastic models of the structure as well as the effect of the asymmetric propriety of the arterial aneurysm.