Conference Agenda

Neurodegenerative diseases (NDs) are complex disorders that primarily affect the neurons in the brain and nervous system, leading to progressive deterioration and loss of function over time. A common pathological hallmark among different NDs is the accumulation of disease–specific misfolded aggregated prionic proteins in different brain areas (Aβ and tau in Alzheimer’s disease, α–synuclein in Parkinson’s disease). In this talk, we discuss the numerical modeling of the misfolding process of α–synuclein in Parkinson’s disease. To characterize the progression of misfolded proteins across the brain we consider a suitable mathematical model (based on Fisher– Kolmogorov equations). For its numerical discretization, we propose and analyze a high-order discontinuous Galerkin method on polyhedral grids (PolyDG) for space discretization coupled with a Crank-Nicolson scheme to advance in time. Numerical simulations in patient-specific brain geometries reconstructed from magnetic resonance images are presented. In the second part of the talk, we introduce and analyze a PolyDG method for the semi-discrete numerical approximation of the equations of Multiple-Network Poroelastic Theory (MPET) in the dynamic formulation. The MPET model can comprehensively describe functional changes in the brain considering multiple scales of fluids and can be regarded as a preliminary attempt to model the perfusion in the brain. In this context, cerebrospinal fluid transport plays an essential role as a mechanism for waste removal (clearance) from the central nervous system. We present and analyze the numerical approach and we present simulations in three-dimensional patient-specific geometries.