Numerical Modeling of Brain Multiphysics Flow Dynamics and Waste Clearance by a Polytopal Discontinuous Galerkin Method
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Neurodegenerative diseases are typically associated with an impairment of waste clearance in the brain: this function is mainly carried out by the flow of the Cerebrospinal Fluid (CSF). This study addresses the modeling of CSF dynamics within the brain – exploring its filtration through the cerebral tissue and its flow in the ventricles – and the intrinsic connection between the generation of CSF and blood circulation. Specifically, we consider a multiphysics model coupling dynamic Multiple-network Poro-Elasticity (MPE) equations for the tissue poromechanics with Navier-Stokes equations for the CSF flow in hollow regions. To accurately capture the complex geometry of the brain, we develop a discontinuous Galerkin method based on polytopal grids for spatial discretization (PolyDG). We carry out an a-priori analysis of the method, highlighting the role of interface terms in its stability and convergence properties. Our method is verified in simplified and realistic geometries by its implementation in lymph, an open-source MATLAB library for the solution of multiphysics problems with the PolyDG method, developed at MOX. Its ability to simulate brain multiphysics flows in patient-specific geometries reconstructed from magnetic resonance images is assessed by relying on FEniCS.
