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Mathematical pressure volume models of the cerebrospinal fluid

James M. Drake·Sivabal Sivaloganathan·Guiseppe Tenti
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Abstract

Numerous mathematical models have emerged in the medical literature over the past two decades attempting to characterize the pressure and volume dynamics the central nervous system compartment. These models have been used to study he behavior of this compartment under such pathological clinical conditions s hydrocephalus, head injury and brain edema. The number of different pproaches 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 mplified fashion, leaving the mathematical details to appendices. We show at 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 hypothsis that the rate 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 epending on the form of the compliance funtion. 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 chanical properties might be developed.

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James M. Drake, Sivabal Sivaloganathan, Guiseppe Tenti. 1996-04-01. Mathematical pressure volume models of the cerebrospinal fluid. https://arxiv.org/abs/math/9604245

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