Learning patient‐specific parameters for a diffuse interface glioblastoma model from neuroimaging data. (29th June 2020)

• Record Type: Journal Article
• Authors: Agosti, A.; Ciarletta, P.; Garcke, H.; Hinze, M.
• Is Part Of: Mathematical methods in the applied sciences. Volume 43:Number 15(2020)
• Page Start: 8945
• Page End: 8979
• Publication Date: 2020-06-29
• Subjects: degenerate Cahn–Hilliard equation -- diffuse interface model -- finite elements -- model order reduction -- parameter estimation -- personalised medicine; Mathematics -- Periodicals; Technology -- Mathematics -- Periodicals; 519
• DOI: 10.1002/mma.6588
• Languages: English
• ISSNs: 0170-4214

Abstract

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 ROM heavily relies on the discrete empirical interpolation method, which has to be appropriately adapted in order to deal with the highly nonlinear and degenerate parabolic partial differential equations. A feature of the approach is that we iterate between full order solvers 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.