Maximal wall shear stress (MWSS) in the convergent part of a stenosis is calculated by the interactive boundary-layer theory. A dimensional analysis of the problem shows that MWSS depends only on a few measurable parameters. A simple relationship between MWSS and these parameters is obtained, validated, and used to calculate the magnitude of MWSS in a carotid stenosis, as a function of the patency of the circle of Willis and the stenotic pattern. This demonstrates the huge effect of collateral pathways. Elevated MWSS are observed even in moderate stenoses, provided they are associated with a contralateral occlusion, a large anterior, and narrow posterior communicating arteries, suggesting a potential risk of embolus release in this configuration. [S0148-0731(00)01506-5]
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