Agosti, A. and Ciarletta, P. and Garcke, H. and Hinze, M. (2020) Learning patient-specific parameters for a diffuse interface glioblastoma model from neuroimaging data. MATHEMATICAL METHODS IN THE APPLIED SCIENCES, 43 (15). pp. 8945-8979. ISSN 0170-4214, 1099-1476
Full text not available from this repository. (Request a copy)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.
| Item Type: | Article |
|---|---|
| Uncontrolled Keywords: | TUMOR-GROWTH; BRAIN-TUMORS; MATHEMATICAL-MODEL; GLIOMA GROWTH; RADIOTHERAPY; SIMULATION; APPROXIMATION; PROLIFERATION; degenerate Cahn-Hilliard equation; diffuse interface model; finite elements; model order reduction; parameter estimation; personalised medicine |
| Subjects: | 500 Science > 510 Mathematics |
| Divisions: | Mathematics > Prof. Dr. Harald Garcke |
| Depositing User: | Dr. Gernot Deinzer |
| Date Deposited: | 22 Mar 2021 05:41 |
| Last Modified: | 22 Mar 2021 05:41 |
| URI: | https://pred.uni-regensburg.de/id/eprint/44341 |
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