  A comprehensive mathematical model of the multiphysics flow of blood and
Cerebrospinal Fluid (CSF) in the brain can be expressed as the coupling of a
poromechanics system and Stokes' equations: the first describes fluids
filtration through the cerebral tissue and the tissue's elastic response, while
the latter models the flow of the CSF in the brain ventricles. This model
describes the functioning of the brain's waste clearance mechanism, which has
been recently discovered to play an essential role in the progress of
neurodegenerative diseases. To model the interactions between different scales
in the porous medium, we propose a physically consistent coupling between
Multi-compartment Poroelasticity (MPE) equations and Stokes' equations. In this
work, we introduce a numerical scheme for the discretization of such coupled
MPE-Stokes system, employing a high-order discontinuous Galerkin method on
polytopal grids to efficiently account for the geometric complexity of the
domain. We analyze the stability and convergence of the space semidiscretized
formulation, we prove a-priori error estimates, and we present a temporal
discretization based on a combination of Newmark's $\beta$-method for the
elastic wave equation and the $\theta$-method for the other equations of the
model. Numerical simulations carried out on test cases with manufactured
solutions validate the theoretical error estimates. We also present numerical
results on a two-dimensional slice of a patient-specific brain geometry
reconstructed from diagnostic images, to test in practice the advantages of the
proposed approach.
