|Authors||V. Vinje, M. E. Rognes, K. Mardal and E. Piersanti|
|Title||The Brain as a Poroelastic Medium - Simulating pulsatile motion and flow|
|Project(s)||Waterscape: The Numerical Waterscape of the Brain|
|Publication Type||Talks, invited|
|Year of Publication||2017|
|Location of Talk||Hamburg, Germany|
|Keywords||Brain, Poroelasticity, Porous media, Total pressure, Waterscape|
This talk presents a general overview of the numerical work at the Waterscape group at Simula. First, I present the governing equations, together with standard solving schemes and how to handle discretization in FEniCS. The total pressure formulation is introduced, and an optimal preconditioner for the total pressure formulation is presented.
In the last five-ten years, fluid flow and solute transport in the human brain has gained rapid interest in the research community. The discoveries by Iliff and Nedergaard describing a glyphatic network washing solutes out of the brain through a bulk flow of fluid, followed by Xie et al.'s study claiming that sleep enhances this mechanism was discoveries that also gained significant media attention.
The brain has several more or less separated networks allowing for fluid flow; Blood vessels, paravascular spaces and interstitial fluid. The relation between fluid flow in these networks to each other and to the macroscoping displacement of brain tissue can be explained with the multiple network poroelastic theory (MPET). Because there are no consensus of the value of all material parameters the models we use need to be robust within a given parameter regime. In addition, as the number of networks grow, the system of equations becomes larger and the solvers we use must also be fast and efficient within the given range of the parameters.
The total pressure formulation, presented in this talk, restores convergence related to the problem of "locking", and allows for a parameter robust preconditioner. Proof that the scheme is stable has been given earlier, and the current work aims to extend this proof to a general number of networks.