Biomechanics of the brain; some remarks on Biot\'s equations of consolidation theory with deformation-dependent permeability

Abstract

We revisit models of hydrocephalus in the literature. In particular, we examine the class of models based on Biot\'s theory of consolidation with fixed boundary forcing. Instead of fixed boundaries we take free boundaries. We prove existence and uniqueness of solutions. As in the fixed boundary forcing, we show that in a free boundary, the pressure is higher when the permeability depends on deformation. On the other hand, the total filtration is lower. Unlike the fixed forcing, the effect of the deformation on permeability reduces over time:

Journal of the Nigerian Association of Mathematical Physics Vol. 10 2006: pp. 511-516