This paper is only available as a PDF. To read, Please Download here.
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.
To read this article in full you will need to make a payment
Purchase one-time access:Academic & Personal: 24 hour online accessCorporate R&D Professionals: 24 hour online access
One-time access price info
- For academic or personal research use, select 'Academic and Personal'
- For corporate R&D use, select 'Corporate R&D Professionals'
Subscribe:Subscribe to Journal of the Neurological Sciences
Already a print subscriber? Claim online access
Already an online subscriber? Sign in
Register: Create an account
Institutional Access: Sign in to ScienceDirect
- Symptomatic occult hydrocephalus with “normal” cerebrospinal fluid pressure.New Engl. J. Med. 1965; 273: 117-126
- Tables of Integrals and Other Mathematical Data.in: The Macmillan Company, New York, N.Y1957: 128
- The distribution of intracranial forces in acute and chronic hydrocephalus.J. neurol. Sci. 1974; 21: 171-180
- Lectures on Physics. Vol. 2. Addison-Wesley, Reading, Mass1963: 1 ff (Chap. 38)
- The mechanism of normal pressure hydrocephalus.J. neurol. Sci. 1968; 7: 481-493
- The special clinical problem of symptomatic hydrocephalus with normal cerebrospinal fluid pressure — Observations on cerebrospinal fluid dynamics.J. neurol. Sci. 1965; 2: 307-327
- Traité de Mécanique Céleste.1807 (Supplement, Paris)
- The pressure-volume curve of the cerebrospinal fluid space in dogs.Acta neurol. scand. 1973; 49: 557-574
- Methods of Mathematical Physics. Vol. 1. McGraw-Hill, New York, N.Y1953: 114
- Pressure relaxation of the intracranial system in vivo.Amer. J. Physiol. 1973; 225-3: 513-517
- Relation of curvature of vessels and of hollow viscera to their internal pressure.Brit. med. J. 1922; 1: 260-262
- Cerebrospinal elasticity in cat and macaque.Amer. J. Physiol. 1932; 101: 668-677
Received: August 4, 1975
© 1976 Published by Elsevier Inc.