Deep Probabilistic Modeling of Glioma Growth

Fabian Isensee; Jens Petersen; J\"urgen Debus; Klaus H. Maier-Hein; Martin Bendszus; Paul F. J\"ager; Philipp Kickingereder; Sabine Heiland; Simon A. A. Kohl; Ulf Neuberger

arxiv: 1907.04064 · v1 · pith:YN2I22CLnew · submitted 2019-07-09 · 📡 eess.IV · cs.CV· cs.LG

Deep Probabilistic Modeling of Glioma Growth

Jens Petersen , Paul F. J\"ager , Fabian Isensee , Simon A. A. Kohl , Ulf Neuberger , Wolfgang Wick , J\"urgen Debus , Sabine Heiland

show 3 more authors

Martin Bendszus Philipp Kickingereder Klaus H. Maier-Hein

This is my paper

Pith reviewed 2026-05-25 00:10 UTC · model grok-4.3

classification 📡 eess.IV cs.CVcs.LG

keywords gliomatumor growthprobabilistic modelingdeep learningsegmentationrepresentation learningbrain tumorlongitudinal imaging

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The pith

A probabilistic deep model learns distributions of future glioma appearances directly from sequences of past tumor images.

A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.

The paper replaces explicit biological models of cell diffusion with an implicit approach that uses probabilistic segmentation and representation learning to capture glioma growth dynamics from image data alone. It demonstrates that the model can generate a range of plausible future tumor states conditioned only on earlier scans of the same patient. A sympathetic reader would care because this sidesteps the need to specify biological parameters and instead lets the data reveal the growth patterns. The central object carrying the argument is the learned conditional distribution over future tumor images.

Core claim

Existing glioma growth models rely on biologically inspired cell diffusion equations whose parameters are fit to image data. This work instead trains a probabilistic segmentation and representation learning system that implicitly extracts growth dynamics directly from sequences of tumor images without any explicit biological model. Evidence is presented that the resulting model produces a distribution of plausible future tumor appearances conditioned on past observations of the same tumor.

What carries the argument

Probabilistic segmentation and representation learning system that implicitly extracts growth dynamics from image sequences to produce conditional distributions over future tumor appearances.

If this is right

Future tumor states can be sampled from a learned distribution rather than from a single deterministic simulation.
Growth modeling no longer requires hand-specified diffusion or proliferation parameters.
Predictions remain conditioned on the specific history of each individual tumor.
Uncertainty in future appearance is represented explicitly through the output distribution.

Where Pith is reading between the lines

These are editorial extensions of the paper, not claims the author makes directly.

The same implicit learning setup could be tested on longitudinal data from other slowly evolving lesions where explicit biological models are unavailable.
If the learned distributions prove stable across scanners and protocols, they could serve as priors for treatment-response forecasting.
Discrepancies between sampled futures and observed growth might flag cases where additional biological factors are needed.

Load-bearing premise

Image sequences of tumors contain enough information for the learning system to capture the true underlying growth dynamics without any explicit biological model.

What would settle it

Generate future tumor images from the model on held-out patient sequences and check whether the actual later scans fall outside the predicted distribution at rates inconsistent with the claimed coverage.

Figures

Figures reproduced from arXiv: 1907.04064 by Fabian Isensee, Jens Petersen, J\"urgen Debus, Klaus H. Maier-Hein, Martin Bendszus, Paul F. J\"ager, Philipp Kickingereder, Sabine Heiland, Simon A. A. Kohl, Ulf Neuberger, Wolfgang Wick.

**Figure 1.** Figure 1: The architecture employed in this work. Following the approach in [5], a UNet [12] is augmented with two additional encoders, one for the prior and one for the posterior. The prior encoder maps the inputs of present and past scans to an N-dimensional diagonal Gaussian while the posterior does the same with additional access to the ground truth segmentation from the future. During training, a sample from t… view at source ↗

**Figure 2.** Figure 2: Qualitative Examples: (a) Prior mean prediction (solid purple) and sample with best volume match (dashed purple) as well as future ground truth (red) overlaid on FLAIR. The approach is able to model growth or shrinkage, but is unable to represent tumors with both growth and shrinkage in different locations (for multiple foci, dotted and solid overlap). (b) Regular grid samples from prior, with mean highlig… view at source ↗

**Figure 3.** Figure 3: Quantitative results for Query Volume Dice and Surprise, for groups with moderate and large change and median indicated in red, p-values from Wilcoxon ranksum test. For large changes, our approach can represent the future much better than the lower bound. The low surprise in our model indicates that our model’s learned prior assigns higher likelihood than the lower bound to the real future tumor appearanc… view at source ↗

read the original abstract

Existing approaches to modeling the dynamics of brain tumor growth, specifically glioma, employ biologically inspired models of cell diffusion, using image data to estimate the associated parameters. In this work, we propose an alternative approach based on recent advances in probabilistic segmentation and representation learning that implicitly learns growth dynamics directly from data without an underlying explicit model. We present evidence that our approach is able to learn a distribution of plausible future tumor appearances conditioned on past observations of the same tumor.

Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, simulated authors' rebuttal, and a circularity audit. Tearing a paper down is the easy half of reading it; the pith above is the substance, this is the friction.

Desk Editor's Note private letter to a colleague

The paper replaces explicit diffusion models for glioma growth with a learned probabilistic model that generates distributions of future tumor appearances from image sequences.

read the letter

The central contribution is the shift to implicit learning of growth dynamics via probabilistic segmentation and representation learning, without any hand-crafted biological equations. This produces a conditional distribution over plausible future images given past observations of the same tumor, which is a clean framing distinct from the parameter-fitting approaches in the cited literature. The paper does a straightforward job of stating the modeling choice and its motivation from recent deep learning advances. That part reads as honest and scoped correctly to the subfield. No load-bearing circularity or invented entities appear in the description. The citation pattern aligns with standard references on tumor modeling and probabilistic DL methods. The main limitation is that the abstract supplies no datasets, metrics, baselines, or error bars, so it is impossible to judge whether the learned distributions actually match real growth trajectories or outperform simpler alternatives. The full paper may contain those details, but the current evidence level leaves the practical utility open. The core assumption—that longitudinal images contain enough signal to capture the dynamics implicitly—could be reasonable for short-term prediction but risks missing biologically grounded constraints that explicit models enforce. This work is aimed at researchers in medical imaging and neuro-oncology who are already exploring data-driven tumor models. A reader in that niche would find the alternative approach worth examining for its own sake. It is coherent enough on its own terms to merit peer review, even if the experiments ultimately need strengthening.

Referee Report

1 major / 1 minor

Summary. The manuscript proposes a data-driven alternative to biologically inspired diffusion models for glioma growth. It uses probabilistic segmentation and representation learning to implicitly capture growth dynamics from longitudinal image sequences, claiming to learn a conditional distribution over plausible future tumor appearances given past observations of the same tumor.

Significance. If the central claim holds with proper validation, the work provides a flexible complement to explicit parametric models by leveraging recent advances in deep probabilistic methods to handle uncertainty in tumor evolution predictions. No machine-checked proofs or parameter-free derivations are present, but the implicit modeling choice is a clear modeling strength if supported by experiments.

major comments (1)

[Abstract] Abstract: the assertion that 'evidence is presented' for learning the conditional distribution is load-bearing for the central claim, yet the abstract supplies no information on datasets, validation metrics, baselines, error bars, or experimental design, preventing assessment of whether the results actually support the claim.

minor comments (1)

The weakest assumption (image sequences contain sufficient information for implicit dynamics without explicit biology) is stated but not tested against an explicit-model baseline; adding such a comparison would strengthen the contribution.

Simulated Author's Rebuttal

1 responses · 0 unresolved

We thank the referee for their thoughtful review and constructive comment on the abstract. We address the point below and will incorporate revisions in the next version of the manuscript.

read point-by-point responses

Referee: [Abstract] Abstract: the assertion that 'evidence is presented' for learning the conditional distribution is load-bearing for the central claim, yet the abstract supplies no information on datasets, validation metrics, baselines, error bars, or experimental design, preventing assessment of whether the results actually support the claim.

Authors: We agree that the abstract would be strengthened by including concise experimental details to better support the central claim. In the revised version we will expand the abstract to briefly note the use of longitudinal MRI sequences from glioma patients, the evaluation protocol (prediction of held-out future time points), key quantitative metrics (e.g., segmentation overlap and distributional similarity measures), and reference to baseline comparisons. This addition will remain within standard abstract length limits while allowing readers to assess the presented evidence more readily. revision: yes

Circularity Check

0 steps flagged

No significant circularity

full rationale

The paper's approach relies on training probabilistic segmentation and representation learning models directly on external longitudinal image sequences of gliomas to implicitly capture growth dynamics, without any explicit biological model or derivation chain. No equations, fitted parameters renamed as predictions, or load-bearing self-citations are described in the provided text; the central claim of learning conditional distributions over future appearances is presented as an empirical outcome of data-driven learning rather than a self-referential reduction. This makes the method self-contained against external benchmarks.

Axiom & Free-Parameter Ledger

0 free parameters · 0 axioms · 0 invented entities

No free parameters, axioms, or invented entities are identifiable from the abstract alone. The method appears to rest on standard assumptions of deep learning such as sufficient training data and network expressivity, but these cannot be audited without the full text.

pith-pipeline@v0.9.0 · 5641 in / 1046 out tokens · 31439 ms · 2026-05-25T00:10:14.708071+00:00 · methodology

discussion (0)

Reference graph

Works this paper leans on

13 extracted references · 13 canonical work pages

[1]

Neurosurgery78(4), 572–580 (2016)

Akbari, H., Macyszyn, L., Da, X., Bilello, M., Wolf, R.L., Martinez-Lage, M., Biros, G., Alonso-Basanta, M., O’Rourke, D.M., Davatzikos, C.: Imaging surrogates of in- ﬁltration obtained via multiparametric imaging pattern analysis predict subsequent location of recurrence of glioblastoma. Neurosurgery78(4), 572–580 (2016)

work page 2016
[2]

Neuro-Oncology 16(9), 1159–1160 (2014)

Bi, W.L., Beroukhim, R.: Beating the odds: extreme long-term survival with glioblastoma. Neuro-Oncology 16(9), 1159–1160 (2014)

work page 2014
[3]

Journal of Mathematical Biology71(3), 551–582 (2015)

Engwer, C., Hillen, T., Knappitsch, M., Surulescu, C.: Glioma follow white matter tracts: a multiscale DTI-based model. Journal of Mathematical Biology71(3), 551–582 (2015)

work page 2015
[4]

NeuroImage 62(2), 782–790 (2012)

Jenkinson, M., Beckmann, C.F., Behrens, T.E.J., Woolrich, M.W., Smith, S.M.: FSL. NeuroImage 62(2), 782–790 (2012)

work page 2012
[5]

In: NeurIPS

Kohl, S.A.A., Romera-Paredes, B., Meyer, C., De Fauw, J., Ledsam, J.R., Maier- Hein, K.H., Eslami, S.M.A., Jimenez Rezende, D., Ronneberger, O.: A probabilistic u-net for segmentation of ambiguous images. In: NeurIPS. vol. 31 (2018)

work page 2018
[6]

IEEE Transactions on Medical Imaging preprint pp

Lipkova,J.,Angelikopoulos,P.,Wu,S.,Alberts,E.,Wiestler,B.,Diehl,C.,Preibisch, C., Pyka, T., Combs, S., Hadjidoukas, P., Van Leemput, K., Koumoutsakos, P., Lowengrub, J.S., Menze, B.: Personalized radiotherapy design for glioblastoma: Integrating mathematical tumor models, multimodal scans and bayesian inference. IEEE Transactions on Medical Imaging prepri...

work page 2019
[7]

IEEE Transactions on Medical Imaging36(3), 815–825 (2017)

Lê, M., Delingette, H., Kalpathy-Cramer, J., Gerstner, E.R., Batchelor, T., Unkel- bach, J., Ayache, N.: Personalized radiotherapy planning based on a computational tumor growth model. IEEE Transactions on Medical Imaging36(3), 815–825 (2017)

work page 2017
[8]

Frontiers in Neurology8 (2018)

Mann, J., Ramakrishna, R., Magge, R., Wernicke, A.G.: Advances in radiotherapy for glioblastoma. Frontiers in Neurology8 (2018)

work page 2018
[9]

In: Optimal Control in Image Processing, p

Menze, B.H., Stretton, E., Konukoglu, E., Ayache, N.: Image-based modeling of tumor growth in patients with glioma. In: Optimal Control in Image Processing, p. 12 (2011)

work page 2011
[10]

Information Processing in Medical Imaging22, 735–747 (2011)

Menze, B.H., Van Leemput, K., Honkela, A., Konukoglu, E., Weber, M.A., Ayache, N., Golland, P.: A generative approach for image-based modeling of tumor growth. Information Processing in Medical Imaging22, 735–747 (2011)

work page 2011
[11]

Medical Image Analysis16(2), 361–373 (2012)

Mosayebi, P., Cobzas, D., Murtha, A., Jagersand, M.: Tumor invasion margin on the riemannian space of brain ﬁbers. Medical Image Analysis16(2), 361–373 (2012)

work page 2012
[12]

In: Proc

Ronneberger, O., Fischer, P., Brox, T.: U-net: Convolutional networks for biomedical image segmentation. In: Proc. MICCAI. pp. 234–241 (2015) Deep Probabilistic Modeling of Glioma Growth 9

work page 2015
[13]

IEEE Transactions on Medical Imaging 37(2), 638–648 (2018)

Zhang, L., Lu, L., Summers, R.M., Kebebew, E., Yao, J.: Convolutional invasion and expansion networks for tumor growth prediction. IEEE Transactions on Medical Imaging 37(2), 638–648 (2018)

work page 2018

[1] [1]

Neurosurgery78(4), 572–580 (2016)

Akbari, H., Macyszyn, L., Da, X., Bilello, M., Wolf, R.L., Martinez-Lage, M., Biros, G., Alonso-Basanta, M., O’Rourke, D.M., Davatzikos, C.: Imaging surrogates of in- ﬁltration obtained via multiparametric imaging pattern analysis predict subsequent location of recurrence of glioblastoma. Neurosurgery78(4), 572–580 (2016)

work page 2016

[2] [2]

Neuro-Oncology 16(9), 1159–1160 (2014)

Bi, W.L., Beroukhim, R.: Beating the odds: extreme long-term survival with glioblastoma. Neuro-Oncology 16(9), 1159–1160 (2014)

work page 2014

[3] [3]

Journal of Mathematical Biology71(3), 551–582 (2015)

Engwer, C., Hillen, T., Knappitsch, M., Surulescu, C.: Glioma follow white matter tracts: a multiscale DTI-based model. Journal of Mathematical Biology71(3), 551–582 (2015)

work page 2015

[4] [4]

NeuroImage 62(2), 782–790 (2012)

Jenkinson, M., Beckmann, C.F., Behrens, T.E.J., Woolrich, M.W., Smith, S.M.: FSL. NeuroImage 62(2), 782–790 (2012)

work page 2012

[5] [5]

In: NeurIPS

Kohl, S.A.A., Romera-Paredes, B., Meyer, C., De Fauw, J., Ledsam, J.R., Maier- Hein, K.H., Eslami, S.M.A., Jimenez Rezende, D., Ronneberger, O.: A probabilistic u-net for segmentation of ambiguous images. In: NeurIPS. vol. 31 (2018)

work page 2018

[6] [6]

IEEE Transactions on Medical Imaging preprint pp

Lipkova,J.,Angelikopoulos,P.,Wu,S.,Alberts,E.,Wiestler,B.,Diehl,C.,Preibisch, C., Pyka, T., Combs, S., Hadjidoukas, P., Van Leemput, K., Koumoutsakos, P., Lowengrub, J.S., Menze, B.: Personalized radiotherapy design for glioblastoma: Integrating mathematical tumor models, multimodal scans and bayesian inference. IEEE Transactions on Medical Imaging prepri...

work page 2019

[7] [7]

IEEE Transactions on Medical Imaging36(3), 815–825 (2017)

Lê, M., Delingette, H., Kalpathy-Cramer, J., Gerstner, E.R., Batchelor, T., Unkel- bach, J., Ayache, N.: Personalized radiotherapy planning based on a computational tumor growth model. IEEE Transactions on Medical Imaging36(3), 815–825 (2017)

work page 2017

[8] [8]

Frontiers in Neurology8 (2018)

Mann, J., Ramakrishna, R., Magge, R., Wernicke, A.G.: Advances in radiotherapy for glioblastoma. Frontiers in Neurology8 (2018)

work page 2018

[9] [9]

In: Optimal Control in Image Processing, p

Menze, B.H., Stretton, E., Konukoglu, E., Ayache, N.: Image-based modeling of tumor growth in patients with glioma. In: Optimal Control in Image Processing, p. 12 (2011)

work page 2011

[10] [10]

Information Processing in Medical Imaging22, 735–747 (2011)

Menze, B.H., Van Leemput, K., Honkela, A., Konukoglu, E., Weber, M.A., Ayache, N., Golland, P.: A generative approach for image-based modeling of tumor growth. Information Processing in Medical Imaging22, 735–747 (2011)

work page 2011

[11] [11]

Medical Image Analysis16(2), 361–373 (2012)

Mosayebi, P., Cobzas, D., Murtha, A., Jagersand, M.: Tumor invasion margin on the riemannian space of brain ﬁbers. Medical Image Analysis16(2), 361–373 (2012)

work page 2012

[12] [12]

In: Proc

Ronneberger, O., Fischer, P., Brox, T.: U-net: Convolutional networks for biomedical image segmentation. In: Proc. MICCAI. pp. 234–241 (2015) Deep Probabilistic Modeling of Glioma Growth 9

work page 2015

[13] [13]

IEEE Transactions on Medical Imaging 37(2), 638–648 (2018)

Zhang, L., Lu, L., Summers, R.M., Kebebew, E., Yao, J.: Convolutional invasion and expansion networks for tumor growth prediction. IEEE Transactions on Medical Imaging 37(2), 638–648 (2018)

work page 2018