MATHEMATICAL PRESSURE-VOLUME MODELS OF THE CEREBROSPINAL-FLUID

Numerous mathematical models have emerged in the medical literature ov er the past two decades attempting to characterize the pressure and vo lume dynamics of the central nervous system compartment. These models have been used to study the behavior of this compartment under such pa thological clinical conditions as hydrocephalus, head injury and brain edema. The number of different approaches has led to considerable con fusion regarding the validity, accuracy or appropriateness of the vari ous models. In this paper we review the mathematical basis for these m odels in a simplified fashion, leaving the mathematical details to app endices. We show that most previous models are in fact particular case s of a single basic differential equation describing the evolution in time of the cerebrospinal fluid pressure (CFS). Central to this approa ch is the hypothesis that the rate of change of CSF volume with respec t 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 i nformation on the behavior of the brain itself. More recent models (so lved numerically using the Finite Element Method) have begun to addres s this issue but have difficulties due to the lack of information abou t the mechanical properties of the brain. Suggestions are made on how development of models which account for these mechanical properties mi ght be developed. (C) 1998 Elsevier Science Inc. All rights reserved.