Simulation study of the cerebral circulation

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1971

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Abstract

This study contains an extensive description of the development and interpretation of a first-generation model of the canine cerebral circulatory system, more specifically the circle of Willis of the arterial tree. The equations for the model were obtained from the equations of motion of fluid and membrane by making several reasonable assumptions. This derivation yielded a lumped-parameter approximation to the arterial system. The prototype circle of Willis was subdivided into eight short segments, and each of the efferent arteries to the brain tissues was represented by two segments in series. The values of the parameters were evaluated from anatomical and rheological data. The solutions to the equations for a single tube were applied to the system by maintaining the continuity of pressure and flow at each junction. The criteria necessary for the construction and description of the model were set forth. The data used represents an average sized dog. A computational scheme was devised and programmed on IBM 360 system. The pressure and flow pulses within the cerebral circulation can be computed from known pulses of pressure at the three afferent arterial ends of the system. The computed results were compared with the available measurements on animals and the records from previous model studies. The pulsatile wave forms and impedances in the system were examined. The changes in pressure and flow contour are related primarily to the presence of reflections and the presence of interaction among the three inflows. The circle of Willis functions efficiently both as a side-to-side anastomosis as well as an anterior-posterior one. It not only can distribute the blood flow uniformly in the main cerebral arteries but also increase the perfusion pressure considerably. This study also contained an attempt to integrate some of the previously developed models of the system. Various occlusion experiments were performed on the model, and indicated that extensive regulation mechanisms exist in the cerebral vascular bed. Further study on the control system is needed. The model was simulated on a digital computer. Some new computational procedures were developed for this model study.

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