A diffuse-interface model for GlioBlastoma growth informed by neuroimaging data

Speaker: Dr. Abramo Agosti

Seminario online.

Abstract: We present a nonlinear degenerate diffuse interface model, which describes the GlioBlastoma evolution integrating neuroimaging data, derived from a mixture model and consisting in a Cahn–Hilliard equation with a single-well potential and a degenerate mobility for the cell phase coupled with a reaction–diffusion equation for the nutrient concentration, including also therapy effects. We give some analytical results, regarding the existence of weak solutions to the model and their qualitative properties, and we introduce a family of well-posed numerical approximations which preserve the properties of the continuous solutions. We further present a constrained optimisation problem for parameter estimation formulated at the numerical level as a mathematical problem with equilibrium constraints (MPEC). Due to the high computational cost of solving the full-order model, the numerical solution of the MPEC is given through an iterative algorithm using model order reduction. These results have been recently obtained in a joint collaboration with Harald Garcke (University of Regensburg), Michael Hinze (University of Koblenz-Landau) and Pasquale Ciarletta (Politecnico di Milano). We conclude by introducing some recent developments and future perspectives.