A non-linear haemodynamic model for the arterial pulsatile component of the intracranial pulse wave

An indication that pressure pulses in cerebral arteries may play a role in the configuration of intracranial pressure pulsations is given by the observation that vasospasm of cerebral arteries narrows the amplitude of the intracranial pressure wave. The present work develops a mathematical model for the transmission of arterial pressure pulses across the compliant arterial wall to the surrounding intracranial space. Compliance of both the arterial segment and the intracranial space are considered. So as to retain accuracy at higher values of the mean intracranial pressure, a physiological range in which pulse transmission is enhanced due to lower pressure gradients but intracranial compliance is not necessarily decreased, a logistic fit is used to model the intracranial pressure-volume relationship. A sequence of approximations (with error bounds) is obtained for the induced intracranial pressure pulse amplitude as a function of arterial pulse amplitude, mean transmural pressure, and mean intracranial pressure. It is found that at higher mean intracranial pressures, where the usual exponential assumption for the intracranial pressure-volume curve loses validity, the amplitude of the transmitted arterial pressure pulse depends non-linearly on the mean intracranial pressure.