Main research findings
Mathematical modelling of brain parenchyma mechanics and fluid dynamics is a powerful tool to better understand clearance mechanisms, and investigate mechanistic hypotheses that cannot be verified with in vivo experiments. Single and multiple network poroelasticity theory (MPET) can be used to model the behaviour of different types of porous media. In addition, MPET has been used in the past decade to understand better how the different fluid compartments exchange mass in the brain and, more generally, the brain’s clearance process. Nonetheless, the MPET equations applied to brain modelling present several numerical and modelling challenges. Therefore, in the articles collected in this thesis, an analysis of the system of equations from a numerical and computational viewpoint using both theoretical proofs and practical numerical experiments is presented.
In particular, we present parameter-robust formulations and preconditioners for the MPET equations in order to solve the system in an efficient and accurate manner. In addition, brain parenchyma pulsatility is modelled via linear elasticity and single network poroelasticity equations in a realistic human brain domain.
Prior to the defence, on Wednesday 8 February at 14:00, Eleonora presented her trial lecture "Physics informed machine learning for fluid mechanics," on Zoom.
- Associate Professor Carmen Rodrigo Cardiel, University of Zaragoza
- Professor Paola Antonietti, Politecnico di Milano
- Professor Kenneth H. Karlsen, University of Oslo
- Chief Research Scientist Marie Elisabeth Rognes, Simula Research Laboratory
- Professor Kent-Andre Mardal, University of Oslo
Read moreat the UiO Department of Mathematics web page.