A mathematical model of cerebrospinal fluid dynamics

Abstract

The ability to solve systems of simultaneous non-linear differential equations by a combination of analytical and computational techniques has encouraged the development of valid mathematical models of biological phenomena. The dynamics of the cerebrospinal fluid (CSF) system has been the subject of closer scrutiny in recent years since the recognition of symptomatic low-pressure hydrocephalic states in man. A mathematical model has been derived from 7 assumptions: 1. (1) That the brain is a spherical shell. 2. (2) That CSF is secreted at a constant rate. 3. (3) That CSF absorption is linearly dependent on pressure. 4. (4) That flow between the CSF compartments is proportional to the pressure difference. 5. (5) That Laplace's Law holds for the visco-elastic properties of the brain. 6. (6) That there is compliance in the spinal compartment of the CSF system. 7. (7) That vascular pulsations in the cranial and spinal compartments are capacitatively coupled. Using known data (and estimates of as yet unknown values) for the several parameters, the validity of the model has been successfully tested against 3 clinical conditions. This model extends our understanding of derangements of CSF dynamics and suggests where further research may yield data at present lacking.