Hemodynamic role of the circle of Willis in stenoses of internal carotid arteries. An analytical solution of a linear model

A mathematical model of blood flow through the circle of Willus was develop ed, within a linear framework. Comprehensive analytical solutions, includin g a remarkably small number of parameters, were derived in the cases of obs tructive lesions of extracranial carotid arteries. The influence of these l esions and the role of anterior and posterior communicating arteries on the blood pressure at the entry of the cerebral territories were quantified an d analyzed emphasizing that the responses of the system of Willis to obstru ctive carotid lesions are extremely varied, depending on the communicating artery anatomy. Comparison with numerical results obtained by using a non-l inear model showed no physiologically significant differences. Such a model might be an essential tool for an accurate assessment of the cerebral hemo dynamics in carotid diseases. (C) 2000 Elsevier Science Ltd. All rights res erved.