A Nonlinear Analysis of Pulsatile Blood Flow Applied to Investigate Shear Stress in Arterial Prostheses

Abstract

Although the main function of an arterial graft is to restore distal blood flow, there is evidence that certain local parameters of blood flow, particularly wall shear stresses, are important in determining the graft's long-term patency. Wall shear stresses were associated with intimal hyperplasia, intimal proliferation, and endothelial cell development, morphology, and attachment. Here we present a detailed method which permits the investigation of the wall shear stress acting on arteries and prostheses in dogs. The theory takes into account the nonlinear terms of the Navier-Stokes equations as well as the nonlinear behaviour and large deformation of the arterial wall. It is based on the numerical resolution of the nonlinear equations by the Crank-Nicolson method which was selected for its unconditional stability. Through the locally measured values of the pressure, pressure gradient, radius and flow rate, the velocity distribution and wall shear stress at a given location along the artery or the prosthesis, can be determined. Complete results on the same dog are presented for the distal aorta and for the middle of a chemically processed prosthesis, implanted as substitute in the thoracic aorta.