Numerical Study of a Viscoelastic Model for Hydrocephalus

Abstract

Hydrocephalus is a clinical conditon where the brain tissue is deformed by the expanding ventricules. In this thesis, the mechanical deformation of a hydrocephalic brain is studied using a biomechanical model, where the material properties of the tissue are described by a viscoelastic model. A set of governing equations is derived when the motion is quasi-static motion and deformation is small. Then, finite element method is used for spatial discretization, and finite difference and trapezoidal rule are used for time-stepping. Moreover, the computational meshes are generated from medical images of patient's brain using level set method and a program called DistMesh. Numerical stability of the time-stepping scheme is also studied. <br /><br /> Several numerical studies are conducted to investigate several aspect of the brain with hydrocephalus. The state of stress of the tissue is found to be compressive everywhere in the brain. The viscoelastic properties of the brain are investigated and found to be dominated by elastic response. Lastly, the displacement made by the ventricular wall as it expands and shrinks is found to be non-uniform.