Womersley analysis for arbitrarily unsteady flow in elastic vessels

In the 1950's, Womersley developed a theoretical analysis of flow in elastic-walled vessels that is continuous and periodically unsteady. In this talk, we describe a similar analysis of flows that can have arbitrary non-periodic unsteadiness and are at some instant stationary, as are found in some of the smaller arteries. The resulting analytical flow relationships are compared with MRI measurements of flow-rate and of local-velocity time histories in the popliteal arteries of patients. They are found to be in good agreement over conditions that both precede and follow acute patient exercise.