Polytopal DG discretizations for the numerical modeling of neurodegenerative diseases

Francesca Bonizzoni (Politecnico di Milano)

Abstract: Many neurodegenerative diseases are connected to the spreading of misfolded prionic proteins. In this talk, we introduce and analyze numerical methods for the discretization of the Fisher- Kolmogorov equation, modelling accumulation and spreading of both α-synuclein and Amyloid- β, related to Parkinson’s and Alzheimer’s diseases, respectively. The proposed approximation method couples the Discontinuous Galerkin (DG) method on polygonal/polyhedral grids for space discretization, with the θ-method for time integration.

We show that the proposed approach is structure-preserving, in the sense that it guarantees that the discrete solution is non-negative, a feature that is of paramount importance in practical applications. Several numerical tests will be presented, including simulations of the α-synuclein spreading in a two-dimensional brain slice and the Amyloid-β spreading in a patient-specific setting by using a three-dimensional geometry.