Katrin Stollenmaier (SRP NUPUS Scholarship Holder 2016)

Title of Master's thesis: Modelling of intra- and extracellular flow and transport processes

Supervisors: Rainer Helmig (Stuttgart),  Bernd Flemisch (Stuttgart), Tobias Köppl (Stuttgart), Timo Koch (Stuttgart), Kent-Andre Mardal (Oslo), Karl Erik Holter (Oslo)


Within this project, a model for intra- and extracellular flow and transport processes is set up. This model is inspired by the process of metabolite clearance in the brain's extracellular space that is currently subject of scientific research. To this end, a cell is modelled as a simple two-dimensional circular porous medium that is surrounded by an area where the flow is described by Stokes equations. The novelty of this model is that a concentration difference across the cell membrane that is actively maintained by ion channels is modelled. This concentration difference can influence the flow since osmotic effects are included in the model. Hence, it can be investigated whether the osmotic pressure gradient that is actively maintained by the cells aspects the ?ow that is driven by a hydraulic pressure gradient.

The resulting Darcy-Stokes problem is implemented using the open-source software collection FEniCS. Herein, the model equations are solved numerically using the finite element method. Since a combination of DG and BDM elements is used, Nitsche's method is used to weakly enforce Dirichlet boundary conditions and the interior penalty (IP) method is applied to stabilise the solution of Stokes equation in the free-flow domain.