A Differentiable Brain Tumor Mass Effect Solver
Abstract
A growing brain tumor mechanically deforms the surrounding healthy brain through mass effect. This compression and displacement of tissue affects both patient prognosis and treatment planning, so biophysical models of tumor growth must account for this deformation. Established mass-effect models are partial differential equation (PDE) solvers that couple growth to elasticity and calibrate parameters per patient, at substantial implementation, runtime, and calibration cost. We ask how much of this deformation a fully differentiable energy-based model can recover, and introduce a potential-spring model: a regular grid over the brain is driven outward by a tumor-concentration potential and held by an elastic spring lattice with tissue-specific stiffness. It shares the tumor-gradient driving force of continuum elasticity but uses a single global parameter and no per-patient inversion, minimized end-to-end by gradient descent. We benchmark it against established solvers by applying each displacement field to a healthy atlas and measuring tissue overlap with the patient's own segmentation on 134 BraTS patients. Our model yields the largest overall local overlap improvement at up to 100× shorter computation time, establishing a lightweight, differentiable solver for tumor mass effect. Because our model obeys mechanical laws and reflects the tumor-induced tissue loading, it remains physically plausible, a prerequisite for clinical use.
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BibTeX
@misc{wittrich2026differentiable,
title = {{A Differentiable Brain Tumor Mass Effect Solver}},
author = {Marco L. Wittrich and Michal Balcerak and Lucas Zimmer and Ivan Ezhov and Björn Menze and Marie-Christin Metz and Nicole Tueni and Benedikt Wiestler and Jonas Weidner},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.06097},
eprint = {2610.06097},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.06097},
}
RIS
TY - UNPB
TI - A Differentiable Brain Tumor Mass Effect Solver
AU - Marco L. Wittrich
AU - Michal Balcerak
AU - Lucas Zimmer
AU - Ivan Ezhov
AU - Björn Menze
AU - Marie-Christin Metz
AU - Nicole Tueni
AU - Benedikt Wiestler
AU - Jonas Weidner
PY - 2026
DA - 2026/10/05
PB - arXiv
DO - 10.48550/arxiv.2610.06097
UR - https://arxiv.org/abs/2610.06097
AB - A growing brain tumor mechanically deforms the surrounding healthy brain through mass effect. This compression and displacement of tissue affects both patient prognosis and treatment planning, so biophysical models of tumor growth must account for this deformation. Established mass-effect models are partial differential equation (PDE) solvers that couple growth to elasticity and calibrate parameters per patient, at substantial implementation, runtime, and calibration cost. We ask how much of this deformation a fully differentiable energy-based model can recover, and introduce a potential-spring model: a regular grid over the brain is driven outward by a tumor-concentration potential and held by an elastic spring lattice with tissue-specific stiffness. It shares the tumor-gradient driving force of continuum elasticity but uses a single global parameter and no per-patient inversion, minimized end-to-end by gradient descent. We benchmark it against established solvers by applying each displacement field to a healthy atlas and measuring tissue overlap with the patient's own segmentation on 134 BraTS patients. Our model yields the largest overall local overlap improvement at up to 100× shorter computation time, establishing a lightweight, differentiable solver for tumor mass effect. Because our model obeys mechanical laws and reflects the tumor-induced tissue loading, it remains physically plausible, a prerequisite for clinical use.
ER -