PhD defence | Andrijana Burazin, Application of Mixture Theory to solid tumors and normal pressure hydrocephalus

In this thesis, the theory of poroelasticity - namely the Mixture Theory version: a homogenized, macroscopic scale approach used to describe fluid flow through a porous medium ­ is applied to three separate investigations pertaining to a biological phenomenon. The first study explores the behaviour of elevated interstitial fluid pressure (IFP) in solid tumors. The primary focus of the model is to capture the evolution of tumor IFP from a healthy state to a cancerous state, due the changes in the tumor environment. Next, a more mathematically inclined problem is tackled to test the validity of the assumption on the proportionality between pore pressure and volume dilatation - which is made in order to make the calculations more manageable. The results show a profound difference between the solutions with or without the proportionality relation.

Lastly, the pathogenesis of normal pressure hydrocephalus (a brain condition) is investigated. An existing explanation of the condition is that the cerebrospinal fluid is absorbed in the brain parenchyma through the bloodstream; however, the results in this Thesis, using mixture theory, do not agree with this hypothesis, which means that the mechanism responsible still remains unknown.