Learning patient-specific parameters for a diffuse interface glioblastoma model from neuroimaging data

TL;DR

This paper develops a patient-specific glioblastoma growth model using model order reduction and neuroimaging data, significantly reducing computational effort in parameter estimation.

Contribution

It introduces a novel combination of POD and DEIM for efficient, patient-specific parameter estimation in a complex diffuse interface glioblastoma model.

Findings

Reduced computational time demonstrated in clinical cases

Effective incorporation of neuroimaging data for model personalization

Successful adaptation of DEIM for nonlinear PDEs in tumor modeling

Abstract

Parameters in mathematical models for glioblastoma multiforme (GBM) tumour growth are highly patient specific. Here we aim to estimate parameters in a Cahn-Hilliard type diffuse interface model in an optimised way using model order reduction (MOR) based on proper orthogonal decomposition (POD). Based on snapshots derived from finite element simulations for the full order model (FOM) we use POD for dimension reduction and solve the parameter estimation for the reduced order model (ROM). Neuroimaging data are used to define the highly inhomogeneous diffusion tensors as well as to define a target functional in a patient specific manner. The reduced order model heavily relies on the discrete empirical interpolation method (DEIM) which has to be appropriately adapted in order to deal with the highly nonlinear and degenerate parabolic PDEs. A feature of the approach is that we iterate between full order solves with new parameters to compute a POD basis function and sensitivity based parameter estimation for the ROM problems. The algorithm is applied using neuroimaging data for two clinical test cases and we can demonstrate that the reduced order approach drastically decreases the computational effort.