OPTIMAL DESIGN OF ARTERIAL BYPASS PROSTHESES DIAMETER

The objectives of this paper are: (1) to analyze how the bypass diameter and the degree of the stenosis affect the flow-induced wall shear stresses in the stenotic and bypass vessels and (2) to propose a clinically usable method for a proper selection of the bypass diameter. The problem is solved in the following stages: First, the steady pressure and flow within the vessels are obtained using general laws of mass and energy conservation. Then, on the basis of modified Womersley's theory to take into account the nonlinear mechanical properties of the vessels, the oscillating pressure and flow within the vessels are calculated. They are used to derive expressions for the reflection coefficients at the distal (converging) bifurcation and to calculate wall shear stresses. We hypothesize that the minimal differences in the wall shear stresses of the normal artery, stenotic artery and the bypass graft mitigate the development of anastomotic neointimal hyperplasia and graft pseudo intima. Using cost functions, based on steady and mean wall shear stresses, we calculated the optimal value of the undeformed bypass diameter for various degrees of stenosis. We found that the sum of cross-sectional areas of the optimal graft and the stenotic artery (normalized with respect to the cross-sectional area of the normal artery) varies between 1.14 and 1.28, an interval, which is consistent with the findings of McDonald (1974) for the area of the major branches in the body. Thus we conclude that the results obtained are consistent with the stated hypothesis.