Mathematical pressure volume models of the cerebrospinal fluid

摘要

Numerous mathematical models have emerged in the medical literature over the past two decades attempting to characterize the pressure and volume dynamics of the central nervous system compartment. These models have been used to study the behavior of this compartment under such pathological clinical conditions as hydrocephalus, head injury and brain edema. The number of different approaches has led to considerable confusion regarding the validity, accuracy or appropriateness of the various models. In this paper we review the mathematical basis for these models in a simplified fashion, leaving the mathematical details to appendices. We show that most previous models are in fact particular cases of a single basic differential equation describing the evolution in time of the cerebrospinal fluid pressure (CFS). Central to this approach is the hypothesis that the rate of change of CSF volume with respect to pressure is a measure of the compliance of the brain tissue which as a consequence leads to particular models depending on the form of the compliance function. All such models in fact give essentially no information on the behavior of the brain itself. More recent models (solved numerically using the Finite Element Method) have begun to address this issue but have difficulties due to the lack of information about the mechanical properties of the brain. Suggestions are made on how development of models which account for these mechanical properties might be developed.