Biomathematics of intracranial CSF and haemodynamics. Simulation and analysis with the aid of a mathematical model.

Abstract

A mathematical model of the isolated intracranial system including autoregulation of cerebral blood flow with the aid of a variable cerebrovascular resistance is described. The rate of formation of cerebrospinal fluid is assumed to depend on the regional blood flow through the choroid plexuses. This model is extended by cardiovascular components including the left ventricle of the heart, the aorta and the peripheral resistance. Additionally the model contains control circuits to simulate the short-time behaviour of the blood pressure regulation with the aid of the baroreceptor reflex. Disturbances of central regulation of blood pressure are simulated depending on changes of the regional blood flow through the brain stem. The application of the model is demonstrated by the analysis of the influence of arterial blood pressure upon the intracranial pulse pressure relationship (PPR) and upon the pressure response to a volume pressure test. Theoretical considerations and simulations reveal an opposite effect of arterial blood pressure (ABP) and its amplitude upon PPR. The ICP amplitude rises with decreasing ABP or increasing ABP amplitude. Breakpoints and other deviations from a linear PPR over the whole ICP range are studied by the analysis of the transfer function. The application of the model concerning parameter estimation methods is demonstrated and discussed. Simulations of rhythmic phenomena with the aid of the extended model point out possible approaches to quantitative descriptions of disturbances of central regulation.