Speaker
André Massing, Norwegian University of Science and Technology
Abstract
Computational models in neurosciences provide a plethora of examples of coupled multiphysics problems involving complex interfaces
and domains. A major challenge is often the generation of simulation-ready high-quality 3D volume meshes from image data generated
from sophisticated imaging technologies such as electron microscopy (EM) or magnetic resonance imaging (MRI). In this presentation,
we discuss how the Cut Finite Element Method can ease the burden of mesh generation for two prototypical computational neuroscience problems.
First, we introduce new cut finite element methods for the numerical solution of Biot’s consolidation model for poroelasticity. The Biot model describes
the coupled deformation of an elastic porous medium and the flow of viscous fluid within it, making it crucial for applications in geoscience, medicine,
and biophysics. Our approach combines the so-called total pressure formulation with cut finite element stabilization techniques resulting in geometrically
and parameter robust solution schemes. Numerical examples include both convergence studies, robustness tests as well as applications to brain-type geometries.
In the second part, we pass from simulating on the organ-level to computational models on the cell scale. More specifically, we present cut finite element methods
for the numerical solution of the so-called EMI (Extracellular-Membrane-Intracellular) model. The EMI model is an example of a mixed-dimensional problem that
couples an elliptic partial differential equation (PDE) on the extra/intracellular domains with a system of nonlinear ordinary differential equations (ODEs) over the cell membranes. We provide theoretical and numerical evidence for the robustness and convergence properties of the proposed CutFEM formulations and
demonstrate its flexibility by considering realistic neurone geometries.