A mathematical model of cerebral circulation and oxygen supply.

A compartment model of cerebral circulation and oxygen supply including an autoregulation mechanism is presented. The model is focused on the analysis of slow dynamical variations of long term neurophysiological parameters like the partial oxygen pressure of brain tissue or the cerebral blood flow. The circulatory part of the model is built up of seven compartments including arteries, capillaries, veins, brain tissue, cerebrospinal fluid, the sagittal sinus and an artificial compartment for the simulation of brain swelling. The description of oxygen supply is based on a Krogh model. Numerical calculations reproduce the experimentally well established connection between arterial blood pressure and the production of cerebrospinal fluid. Furthermore we found an approximately linear correlation of the partial oxygen pressure of brain tissue to the mean arterial blood pressure in the case of an impaired autoregulation mechanism. In a first test such a linear dependence could also be detected in clinical data from the neurosurgical intensive care monitoring.