A mathematical model for hydrocephalus

Abstract

Hydrocephalus is a pathological condition of the brain, which is most commonly observed with infants, but can also be acquired at a later age. It is characterised by an abnormal accumulation of cerebrospinal fluid (CSF) inside the brain ventricules, accompanied by a considerable deformation of the surrounding brain tissue. Building on existing models, this work puts forward a mechanical model for the disease, based on quasi-steady, linearly poroelastic mechanisms. The model incorporates a strain dependence of the brain's permeability and also takes into account possible CSF absorption or production in the brain parenchyma, which leads to novel ideas about the development of different hydrocephalus types.

The mechanisms are examined in three different geometries: a spherical symmetric, one-dimensional geometry, a cylindrically symmetric, two-dimensional geometry, and a three-dimensional geometry without any symmetry. Analytic as well as numerical methods are used to solve the model equations, yielding qualitative and quantitative predictions for the development and treatment of hydrocephalus. The thesis concludes with some notes about the use of finite deformation elasticity in poroelastic hydrocephalus models.