Finite element methods of studying mechanical factors in blood flow

This paper reviews some biomechanical analyses of blood flow in large arteries based on a general computer modeling using the finite element method. We study the following question: What is the role played by the interrelated factors of mechanical stress, flow irregularities, and diffusion through the endothelium on the etiology of atherosclerosis or the aggravation of vascular injury. It presents the computational features of the method and stresses the physiological significance of the results, such as the effect of geometric complexities, material nonlinearities, and non-Newtonian rheology of the blood. The specific mechanical and fluid dynamic factors analyzed are wall shear stress, flow profiles, and pressure variations. After simulating tubes of circular cross section, we apply the analysis to a number of physiological situations of significance, including blood flow in the entrance region, at bifurcations, in the annular region between an inserted catheter of varying diameter and the vessel. A model study of pulsatile flow in a 60 degree bifurcated channel of velocity profiles provided corroborative measurements of these processes with special emphasis on reversed or distributed flow conditions. The corresponding analysis was extended to the situation in which flow separates and reverses in the neighborhood of stagnation points. This required developing the nonlinear expression for the convective velocity change in the medium. A computer algorithm was developed to handle simultaneous effects of pressure and viscous forces on velocity change across the element and applied to the canine prebranch arterial segment. For mean physiological flow conditions, low shear stresses (0-10 dynes/cm2) are predicted near the wall in the diverging plane, higher values (50 dynes/cm2) along the converging sides of the wall. Backflow is predicted along the outer wall, pressure recovery prior to and into the branches, and a peak shear at the divider lip.