Geometry-Aware Neural Solver for Fast Bayesian Calibration of Brain Tumor Models

Ivan Ezhov, Tudor Mot, Suprosanna Shit, Jana Lipkova, Johannes C. Paetzold, Florian Kofler, Chantal Pellegrini, Marcel Kollovieh, Fernando Navarro, Hongwei Li, Marie Metz, Benedikt Wiestler, Bjoern Menze

Research output: Contribution to journalArticlepeer-review

5 Scopus citations


Modeling of brain tumor dynamics has the potential to advance therapeutic planning. Current modeling approaches resort to numerical solvers that simulate the tumor progression according to a given differential equation. Using highly-efficient numerical solvers, a single forward simulation takes up to a few minutes of compute. At the same time, clinical applications of tumor modeling often imply solving an inverse problem, requiring up to tens of thousands of forward model evaluations when used for a Bayesian model personalization via sampling. This results in a total inference time prohibitively expensive for clinical translation. While recent data-driven approaches become capable of emulating physics simulation, they tend to fail in generalizing over the variability of the boundary conditions imposed by the patient-specific anatomy. In this paper, we propose a learnable surrogate for simulating tumor growth which maps the biophysical model parameters directly to simulation outputs, i.e. the local tumor cell densities, whilst respecting patient geometry. We test the neural solver in a Bayesian model personalization task for a cohort of glioma patients. Bayesian inference using the proposed surrogate yields estimates analogous to those obtained by solving the forward model with a regular numerical solver. The near real-time computation cost renders the proposed method suitable for clinical settings. The code is available at

Original languageEnglish
Pages (from-to)1269-1278
Number of pages10
JournalIEEE Transactions on Medical Imaging
Issue number5
StatePublished - 1 May 2022


  • Bayesian inference
  • Glioma
  • MRI
  • Model personalization
  • Physics-based deep learning
  • Tumor modeling


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