Polytopal Methods for Multiphysics Flow Dynamics with Applications to the Human Brain
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The interstitial/cerebrospinal fluid (CSF) plays a pivotal role in brain physiology, by clearing misfolded proteins, transporting ions, and protecting the brain from impacts. Impaired flow or overproduction of CSF are strongly associated with neurodegenerative diseases and hydrocephalus, underscoring its clinical relevance. The CSF generation and dynamics are tightly linked with blood pulsation, respiration, and flow-tissue interaction, all taking place in the brain's highly convoluted geometry. To model these phenomena, we employ a coupled system combining Multiple-network Poro-Elasticity (MPE) equations for tissue perfusion and Stokes equations for CSF flow in the brain ventricles. We develop a Polytopal Discontinuous Galerkin (PolyDG) method to efficiently discretize the brain's complex geometry. Using the PolyDG library lymph (https://lymph.bitbucket.io/) and FEniCS/multiphenics (https://github.com/multiphenics/multiphenics), we analyze CSF flow in 2D and 3D geometries, investigating pulsatility, interface conditions, and fluid inertia. Numerical experiments also demonstrate the method's computational efficiency in dealing with detailed geometries. Furthermore, since the solution of this kind of multiphysics problems in patient-specific 3D geometries can entail a very high computational cost, we present the a posteriori analysis of a fluid-poroelastic structure interaction computational model, to lay the grounds for mesh adaptivity and thus further improve efficiency.