Mathematical challenges of modeling the fluid flow of the brain - brain clearance, sleep and dementia

Recent theories suggest that a fundamental reason for sleep is simply clearance of metabolic waste produced during the activities of the day. A crucial component of these theories are the fluid flow within and around the brain, in health and disease. In this talk we will present multi-physics problems and numerical schemes that target these applications. In particular, we will be lead from basic applications of neuroscience into multi-physics problems and interfaces coupled problems involving Stokes, Biot, and Darcy problems for describing the fluid-structure interaction between the brain and its fluids. Particular focus for us has been the exploitation of fractional solvers at the brain-fluid interface for creating efficient monolithic solvers. Contatto: paola.antonietti@polimi.it