General solutions to poroviscoelastic model of hydrocephalic human brain tissue

Hydrocephalus is a well-known disorder of brain fluidic system. It is commonly associated with complexities in cerebrospinal fluid (CSF) circulation in brain. In this paper, hydrocephalus and shunting surgery which is used in its treatment are modeled. Brain tissues are considered to follow a poroviscoelastic constitutive model in order to address the effects of time dependence of mechanical properties of soft tissues and fluid flow hydraulics. Our solution draws from Biot's theory of poroelasticity, generalized to account for viscoelastic effects through the correspondence principle. Geometrically, the brain is conceived to be spherically symmetric, where the ventricles are assumed to be a hollow concentric space filled with cerebrospinal fluid. A generalized Kelvin model is considered for the rheological properties of brain tissues. The solution presented is useful in the analysis of the disorder of hydrocephalus as well as the treatment associated with it, namely, ventriclostomy surgery. The sensitivity of the solution to various factors such as aqueduct blockage level and trabeculae stiffness is thoroughly analyzed using numerical examples. Results indicate that partial aqueduct stenosis may be a cause of hydrocephalus. However, only severe occlusion of the aqueduct can cause a significant increase in the ventricle and brain's extracellular fluid pressure. Ventriculostomy shunts are commonly used as a remedy to hydrocephalus. They serve to reduce the ventricular pressure to the normal level. However, sensitivity analysis on the shunt's fluid deliverability parameter has shown that inappropriate design or selection of design shunt may cause under-drainage or over-drainage of the ventricles. Excessive drainage of CSF may increase the normal tensile stress on trabeculae. It can cause rupture of superior cerebral veins or damage to trabeculae or even brain tissues which in turn may lead to subdural hematoma, a common side-effect of the surgery. These Post-Surgery Reaction (PSR) patterns might occur on much larger time scales than those of the surgery itself, depending on the flow conductivity parameters of the brain. The viscoelastic effects can be significant contingent on the long term tissue moduli and their contrast with the initial ones.