The Hemodynamic Importance of the Geometry of Bifurcations in the Circle of Willis (Glass Model Studies)

Abstract

The critical Reynolds number, Re_c, at which turbulence developed in glass model bifurcations was measured with an Evans blue indicator for bifurcations with a branch/trunk area ratio of unity, and bifurcation angles of 45°, 90°, 135°, and 180°. The Re_c dropped from 2,500 in a straight tube to 1,200 in the 180° bifurcation. Further drops occured with pulsatile flow (if the mean flow rate was used to calculate the velocity). Three sizes of aneurysms at the apex of the 90° bifurcation lowered the Re_c at small bifurcations, and less in the 180° ones. The curves for steady and pulsatile flow crossed at 135°. We did qualitative, but not quantitative, assessments of axial stream impingement on the apex of the bifurcation in the site of aneurysm formation, and of boundary layer separation and vortex shedding at the lateral angles. Both appeared to vary with the angle of the bifurcation and the Reynolds number. We also studied flow profiles in glass models of anterior cerebral-anterior communicating artery bifurcations and the posterior communicating artery origin from the internal carotid. The relevance of these studies to localization of intimal cushions, aneurysms, and atherosclerosis was discussed.