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The growth and progression of brain tumors is governed by patient-specificdynamics. Even when the tumor appears well-delineated in medical imaging scans,tumor cells typically already have infiltrated the surrounding brain tissuebeyond the visible lesion boundaries. Quantifying and understanding thesegrowth dynamics promises to reveal this otherwise hidden spread and is key toindividualized therapies. Current treatment plans for brain tumors, such asradiotherapy, typically involve delineating a standard uniform margin aroundthe visible tumor on imaging scans to target this invisible tumor growth. This"one size fits all" approach is derived from population studies and often failsto account for the nuances of individual patient conditions. Here, we presentthe framework GliODIL which infers the full spatial distribution of tumor cellconcentration from available imaging data based on PDE-constrainedoptimization. The framework builds on the newly introduced method of Optimizingthe Discrete Loss (ODIL), data are assimilated in the solution of the PartialDifferential Equations (PDEs) by optimizing a cost function that combines thediscrete form of the equations and data as penalty terms. By utilizingconsistent and stable discrete approximations of the PDEs, employing amultigrid method, and leveraging automatic differentiation, we achievecomputation times suitable for clinical application such as radiotherapyplanning. Our method performs parameter estimation in a manner that isconsistent with the PDEs. Through a harmonious blend of physics-basedconstraints and data-driven approaches, GliODIL improves the accuracy ofestimating tumor cell distribution and, clinically highly relevant, alsopredicting tumor recurrences, outperforming all other studied benchmarks.

Individualizing Glioma Radiotherapy Planning by Optimization of a Data and Physics Informed Discrete Loss