Journal Article

An axisymmetric and fully 3D poroelastic model for the evolution of hydrocephalus

Benedikt Wirth and Ian Sobey

in Mathematical Medicine and Biology: A Journal of the IMA

Published on behalf of Institute of Mathematics and its Applications

Volume 23, issue 4, pages 363-388
Published in print December 2006 | ISSN: 1477-8599
Published online December 2006 | e-ISSN: 1477-8602 | DOI:
An axisymmetric and fully 3D poroelastic model for the evolution of hydrocephalus

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  • Applied Mathematics
  • Biomathematics and Statistics


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We formulate in general terms the equations for axisymmetric and fully 3D models of a hydrocephalic brain. The model is developed using small strain poroelasticity that includes non-linear permeability. The axisymmetric model is solved for four ventricle shapes, an ellipsoid, a ‘peanut’ shape, a ‘cross’ shape and a ‘bone’ shape. The distribution of fluid pressure, velocity and content in the deformed parenchyma for a blocked aqueduct provides new qualitative insight into hydrocepahlus. Some observations are offered for two forms of cerebrospinal fluid flow abnormality, normal pressure hydrocephalus and idiopathic intracranial hypertension. The model is extended to include a gravitational term in the governing equations and the effect of hydrostatic pressure variation is considered. Results of a fully 3D simulations are described for two horn-like lateral ventricles and one case with two lateral ventricles and a third ventricle.

Keywords: hydrocephalus; poroelasticity; normal pressure hydrocephalus; benign intracranial hypertension; pseudotumor cerebri; idiopathic intracranial hypertension

Journal Article.  0 words. 

Subjects: Applied Mathematics ; Biomathematics and Statistics

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