A viscoelastic approach to the modelling of hydrocephalus

In earlier work [Appl. Math. Comput. 94 (1998) 243, Can. Appl. Math. Quart. 7 (1999) 111], we modelled the brain as a porous elastic medium containing an incompressible fluid and solved the simplified problem analytically using consolidation theory. In this paper we apply linear viscoelasticity theory to the modelling of the brain in the same simplified geometry. The aim in both approaches is to be able to eventually accurately predict the ventricular wall configuration in shunted hydrocephalus which would be of practical use to the neurosurgeon in locating the optimal position for shunt implantation in the treatment and management of hydrocephalus. We use the elastic-viscoelastic analogy (EVA) to obtain analytic solutions for the case when the brain is considered to be composed of a viscoelastic solid (the so-called “standard solid”). We finally conclude with suggestions of how experimental data could be used to obtain realistic values for the mechanical parameters that appear in the constitutive relation for the viscoelastic solid.