Investigations of flow and pressure distributions in physical model of the circle of Willis.

The paper presents the results of experiments concerning flow in the model of cerebral supplying arteries and the circle of Willis (CW). Vascular phantom was prepared on the basis of anatomical specimens. The most typical artery shapes and dimensions were considered. Pressure distribution in six characteristic points is provided, and so are the average flow rates in the anterior, middle and posterior section of the brain. Tests were run in the conditions replicating the physiological state (i.e. when the supplying arteries were fully patent) and in pathological conditions, in which the internal carotid and vertebral arteries were occluded on one or both sides. Thus obtained results were compared with the results of computer simulations based on linear and non-linear flow models. To estimate the non-linear resistance of vascular segment two phenomenological formulae were proposed. High degree of correlation between the values obtained from experiments and those registered in non-linear computer model proves usefulness of proposed formulae. It verifies the hypothesis that non-linearity of flow characteristics of the vessel segments to a great extent is caused by their tortuousity and small length in relation to diameter. Non-linear effects are particularly pronounced in conditions of pathological occlusion of supplying vessels.