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

The critical Reynolds number, Re-e, 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 degrees, 90 degrees, 135 degrees, and 180 degrees. The Re-e dropped from 2,500 in a straight tube to 1,200 in the 180 degrees bifurcation. Further drops occurred with pulsatile flow (if the mean flow rate was used to calculate the velocity). Three sizes of aneurysms at the apex of the 90 degrees bifurcation lowered the Re-e to between 400 and 500 with a slight difference between steady and pulsatile flow, Reverse flow through the same bifurcation produced a more radical drop in the Re-e at small bifurcations, and less in the 180 degrees ones. The curves for steady and pulsatile flow crossed at 135 degrees. 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.