Direct optimization of the probability of lesion origin in proton treatment planning for low-grade glioma patients

Habiba Sallem; Julia Bauer; Martin Frank; Niklas Wahl; Oliver J\"akel; Semi Harrabi; Tim Ortkamp

arxiv: 2506.13539 · v2 · submitted 2025-06-16 · ⚛️ physics.med-ph

Direct optimization of the probability of lesion origin in proton treatment planning for low-grade glioma patients

Tim Ortkamp , Habiba Sallem , Semi Harrabi , Martin Frank , Oliver J\"akel , Julia Bauer , Niklas Wahl This is my paper

Pith reviewed 2026-05-19 09:15 UTC · model grok-4.3

classification ⚛️ physics.med-ph

keywords proton therapylow-grade gliomaPOLO modeltreatment planningoptimizationLET_dradiation-induced lesionsNTCP

0 comments

The pith

Direct integration of the POLO model into proton treatment planning minimizes predicted lesion risk for low-grade glioma patients while maintaining target coverage.

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

The paper establishes a method for automatically optimizing proton therapy plans for low-grade glioma by embedding the probability of lesion origin (POLO) model directly into the optimization process. Hand tuning of dose and dose-averaged linear energy transfer distributions is currently needed to lower the risk of contrast-enhancing brain lesions predicted by the POLO model, but this new approach automates the process through an extended model with volumetric correction and a linear reformulation. The reformulation supports custom objective and constraint functions based on the predicted probabilities. A sympathetic reader would care because the automation could produce more consistent plans that reduce late radiation effects without compromising tumor coverage, as shown in sample patient results with negligible shifts in key dose metrics.

Core claim

The paper claims that extending the original POLO model with a volumetric correction factor and applying a linear reformulation allows direct integration of POLO calculation into plan optimization. This produces clinically acceptable plans that minimize the model-based outcome predictions under small shifts in dose, LET_d, and POLO distributions while sustaining target coverage, with changes of approximately 0.00 Gy in PTV D95 and 0.03 Gy in GTV D95, even when normal tissue complication probability is strongly reduced.

What carries the argument

The linear reformulation of the extended POLO model, a multivariate logistic regression with volumetric correction, which enables its direct use as objective and constraint functions during treatment plan optimization.

If this is right

Clinically acceptable treatment plans can be generated that automatically incorporate outcome predictions from the POLO model.
Customized POLO model-based objective and constraint functions can be defined and applied during optimization.
POLO model-based outcome predictions can be minimized while sustaining target coverage under only expectable shifts in dose, LET_d, and POLO distributions.
Normal tissue complication probability can be strongly down-regulated alongside the minimization of POLO predictions.

Where Pith is reading between the lines

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

This direct optimization approach could reduce manual planning time and variability in how lesion risk is balanced against tumor control in proton therapy.
The method opens the possibility of testing alternative POLO-derived criteria to explore different risk-coverage trade-offs across patient groups.
If validated across larger cohorts, the technique might support routine use of predictive models for late effects in other radiation therapy sites.

Load-bearing premise

The original POLO model and its volumetric extension continue to accurately predict lesion origins when their outputs are used as the basis for direct plan optimization, and the linear reformulation preserves the essential predictive behavior without creating optimization artifacts.

What would settle it

Follow-up MRI data from patients treated with these optimized plans that show no reduction in contrast-enhancing brain lesion incidence compared to hand-tuned plans, despite the lower POLO values achieved.

Figures

Figures reproduced from arXiv: 2506.13539 by Habiba Sallem, Julia Bauer, Martin Frank, Niklas Wahl, Oliver J\"akel, Semi Harrabi, Tim Ortkamp.

**Figure 2.** Figure 2: Optimal 2D slice images of the RBE-weighted fractional dose [PITH_FULL_IMAGE:figures/full_fig_p014_2.png] view at source ↗

**Figure 3.** Figure 3: Optimal slice images of the RBE-weighted fractional dose [PITH_FULL_IMAGE:figures/full_fig_p016_3.png] view at source ↗

**Figure 4.** Figure 4: Optimal dose-volume histograms at different NTCP levels for all POLO model-based [PITH_FULL_IMAGE:figures/full_fig_p017_4.png] view at source ↗

**Figure 5.** Figure 5: Optimal slice images of the dose-averaged linear energy transfer [PITH_FULL_IMAGE:figures/full_fig_p018_5.png] view at source ↗

**Figure 6.** Figure 6: Optimal LET-volume histograms at different NTCP levels for all POLO model-based [PITH_FULL_IMAGE:figures/full_fig_p020_6.png] view at source ↗

**Figure 7.** Figure 7: Optimal slice images of the probability of lesion origin [PITH_FULL_IMAGE:figures/full_fig_p021_7.png] view at source ↗

**Figure 8.** Figure 8: Optimal POLO histograms at different NTCP levels for all POLO model-based [PITH_FULL_IMAGE:figures/full_fig_p022_8.png] view at source ↗

**Figure 9.** Figure 9: NTCP curves for the baseline and optimal plans at different NTCP levels [PITH_FULL_IMAGE:figures/full_fig_p023_9.png] view at source ↗

read the original abstract

In proton therapy of low-grade glioma (LGG) patients, contrast-enhancing brain lesions (CEBLs) on magnetic resonance imaging are considered predictive of late radiation-induced lesions. From the observation that CEBLs tend to concentrate in regions of increased dose-averaged linear energy transfer (LET$_{\text{d}}$) and proximal to the ventricular system, the probability of lesion origin (POLO) model has been established as a multivariate logistic regression model for the voxel-wise probability prediction of the CEBL origin. To date, leveraging the predictive power of the POLO model for treatment planning relies on hand tuning the dose and LET$_{\text{d}}$ distribution to minimize the resulting probability predictions. In this paper, we therefore propose automated POLO model-based treatment planning by directly integrating POLO calculation and optimization into plan optimization for LGG patients. We introduce an extension of the original POLO model including a volumetric correction factor, and a model-based optimization scheme featuring a linear reformulation of the model together with feasible optimization functions based on the predicted POLO values. The developed framework is implemented in the open-source treatment planning toolkit matRad. Our framework can generate clinically acceptable treatment plans while automatically taking into account outcome predictions from the POLO model. It also supports the definition of customized POLO model-based objective and constraint functions. Optimization results from a sample LGG patient show that the POLO model-based outcome predictions can be minimized under expectable shifts in dose, LET$_{\text{d}}$, and POLO distributions, while sustaining target coverage ($\Delta_{\text{PTV}} \text{D95}_{RBE,fx}\approx{0.00}$, $\Delta_{\text{GTV}} \text{D95}_{RBE,fx}\approx{0.03}$), even when NTCP is strongly down-regulated.

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 folds the POLO model directly into proton plan optimization via a linear reformulation and volumetric correction, but the single-patient test leaves the practical reliability open.

read the letter

This paper shows how to optimize proton plans directly for lower POLO scores instead of adjusting by hand after the fact. They extend the original logistic regression with a volumetric correction factor, rewrite it in linear form so it fits inside the optimizer, and implement the whole thing in the open-source matRad toolkit. On their one low-grade glioma example the target coverage stays nearly identical while the POLO predictions drop, and the dose and LET_d maps shift in ways that look plausible at first glance. That is the concrete advance over the hand-tuning approach mentioned in the abstract. The soft spot is the evidence base. Everything rests on a single sample patient with only approximate deltas reported and no error analysis, no comparison against hand-tuned plans on the same case, and no check on whether the new dose-LET distributions stay inside the domain where the original model was fitted. If the optimizer drives the plan outside that domain the logistic output becomes an extrapolation whose gradient may not track real risk. This is aimed at medical physicists who already work with outcome models in proton planning and want to automate the risk term rather than tune it manually. A reader building similar model-driven objectives would get usable code and a working example. It deserves a serious referee because the integration is technically workable and the toolkit is public, even though reviewers will almost certainly ask for more patients and some test of model behavior on the optimized plans.

Referee Report

3 major / 1 minor

Summary. The paper proposes direct integration of an extended POLO (probability of lesion origin) model into proton treatment plan optimization for low-grade glioma patients. It adds a volumetric correction factor to the original multivariate logistic regression, introduces a linear reformulation to enable optimization of POLO-based objectives and constraints, and implements the framework in the open-source matRad toolkit. Results from a single sample patient show that POLO predictions can be minimized with only small shifts in dose, LET_d, and POLO distributions while maintaining target coverage (ΔPTV D95_RBE,fx ≈ 0.00, ΔGTV D95_RBE,fx ≈ 0.03) and allowing strong NTCP down-regulation.

Significance. If validated across multiple cases, the work would enable automated, model-driven minimization of predicted late radiation-induced lesions in LGG proton plans without manual dose/LET tuning. The open-source matRad implementation and support for custom POLO-based functions are concrete strengths that support reproducibility and extension. The approach addresses a clinically relevant endpoint (CEBL origin probability) that is currently handled only heuristically.

major comments (3)

[Results] Results section: optimization outcomes are reported for a single sample patient only, with no multi-patient cohort, cross-validation, or quantitative error analysis (e.g., voxel-wise POLO prediction accuracy on held-out data or comparison to ground-truth lesion incidence). This is insufficient to substantiate the central claim of clinical acceptability and generalizability.
[Methods] Methods (linear reformulation subsection): the logistic regression is replaced by a linear approximation for tractable optimization; however, no quantitative assessment is provided of how closely the reformulated objective matches the original sigmoid-evaluated POLO on the final dose/LET_d maps, nor whether the fixed point of the optimizer coincides with the true model minimum.
[Discussion] Validation or Discussion: the extended POLO model (including volumetric correction) is applied to dose/LET_d distributions that are deliberately shifted by the optimizer; no check is performed to confirm that the new feature vectors remain inside the convex hull of the original training data, leaving the logistic predictions vulnerable to uncontrolled extrapolation.

minor comments (1)

[Abstract] Abstract and Results: the reported deltas are limited to PTV/GTV D95; additional metrics (e.g., mean dose to ventricles, LET_d histograms, or NTCP values before/after optimization) would clarify the magnitude of the observed shifts.

Simulated Author's Rebuttal

3 responses · 0 unresolved

We thank the referee for the thorough and constructive review of our manuscript. We address each of the major comments point by point below, indicating where revisions will be made to strengthen the paper.

read point-by-point responses

Referee: [Results] Results section: optimization outcomes are reported for a single sample patient only, with no multi-patient cohort, cross-validation, or quantitative error analysis (e.g., voxel-wise POLO prediction accuracy on held-out data or comparison to ground-truth lesion incidence). This is insufficient to substantiate the central claim of clinical acceptability and generalizability.

Authors: We concur that presenting results from only a single patient limits the ability to claim broad generalizability or clinical acceptability at this stage. Our manuscript frames the work as a proof-of-concept for the direct optimization framework rather than a full validation study. The key advance is the methodological integration and open-source implementation in matRad, which enables future multi-patient applications. In the revised version, we will expand the Discussion to highlight this limitation and propose directions for cohort-based validation. We note that the original POLO model was developed on a specific dataset, and adding cross-validation would require access to that data, which we will address by referencing the model's reported performance. revision: partial
Referee: [Methods] Methods (linear reformulation subsection): the logistic regression is replaced by a linear approximation for tractable optimization; however, no quantitative assessment is provided of how closely the reformulated objective matches the original sigmoid-evaluated POLO on the final dose/LET_d maps, nor whether the fixed point of the optimizer coincides with the true model minimum.

Authors: The linear reformulation was introduced to make the POLO-based objectives compatible with the convex optimization in matRad. We agree that a quantitative assessment of the approximation error would strengthen the Methods section. In the revision, we will include a comparison of the POLO values computed with the original logistic function versus the linear approximation on the optimized dose and LET_d maps for the presented case. This will quantify the fidelity of the approximation. We will also discuss that the optimizer finds the minimum of the approximated objective, which serves as a close proxy to the true minimum given the small shifts observed. revision: yes
Referee: [Discussion] Validation or Discussion: the extended POLO model (including volumetric correction) is applied to dose/LET_d distributions that are deliberately shifted by the optimizer; no check is performed to confirm that the new feature vectors remain inside the convex hull of the original training data, leaving the logistic predictions vulnerable to uncontrolled extrapolation.

Authors: This is an important point regarding the reliability of the model predictions under optimization-induced changes. We will revise the manuscript to include an analysis of the feature values (dose, LET_d, and volumetric factors) in the optimized plans compared to the training data range. Specifically, we will report the minimum and maximum values and check for outliers beyond the original data hull. If extrapolation is detected, we will discuss its potential impact and consider adding regularization or constraints in future extensions of the framework. revision: yes

Circularity Check

0 steps flagged

No significant circularity; integration of pre-existing model is independent

full rationale

The paper's derivation chain consists of taking the previously established POLO multivariate logistic regression (from historical CEBL observations), extending it with a volumetric correction factor, applying a linear reformulation to enable optimization, and embedding the resulting objective/constraint functions into matRad-based plan optimization. None of these steps reduce a claimed prediction or result to its own inputs by construction. The POLO model parameters originate from prior data outside this work, the optimization demonstrates concrete shifts in dose/LET_d/POLO distributions on a sample patient while preserving coverage metrics, and no uniqueness theorem or self-citation is invoked to force the framework. The central claim (clinically acceptable plans that automatically minimize POLO predictions) therefore retains independent computational content and is externally falsifiable via the reported patient-specific deltas.

Axiom & Free-Parameter Ledger

1 free parameters · 1 axioms · 0 invented entities

The approach depends on the validity of the pre-existing POLO logistic regression as a predictor and on the feasibility of its linear reformulation for optimization; the volumetric correction factor is introduced as an extension without independent validation details in the abstract.

free parameters (1)

volumetric correction factor
Added as an extension to the original POLO model to account for volume effects in the probability calculation.

axioms (1)

domain assumption The POLO model accurately predicts voxel-wise probability of contrast-enhancing brain lesion origin based on dose and LET_d.
Serves as the foundation for the optimization objectives and constraints.

pith-pipeline@v0.9.0 · 5886 in / 1298 out tokens · 33112 ms · 2026-05-19T09:15:05.490714+00:00 · methodology

discussion (0)

Lean theorems connected to this paper

Citations machine-checked in the Pith Canon. Every link opens the source theorem in the public Lean library.

IndisputableMonolith/Cost/FunctionalEquation.lean washburn_uniqueness_aczel unclear

?

unclear
Relation between the paper passage and the cited Recognition theorem.

p(η) = σ(η) = 1/(1+exp(−η)), η = −26.3 + β1·d + β2·(d∘ld) + 1.19·b; linear reformulation ˜p(η)=η; NTCP=1−∏(1−pi)
IndisputableMonolith/Foundation/RealityFromDistinction.lean reality_from_one_distinction unclear

?

unclear
Relation between the paper passage and the cited Recognition theorem.

fluence gradient ∇ϕfp = CT (∇ηp ∘ ∇pfp) with C=β1D+β2L

What do these tags mean?

matches: The paper's claim is directly supported by a theorem in the formal canon.
supports: The theorem supports part of the paper's argument, but the paper may add assumptions or extra steps.
extends: The paper goes beyond the formal theorem; the theorem is a base layer rather than the whole result.
uses: The paper appears to rely on the theorem as machinery.
contradicts: The paper's claim conflicts with a theorem or certificate in the canon.
unclear: Pith found a possible connection, but the passage is too broad, indirect, or ambiguous to say the theorem truly supports the claim.

Reference graph

Works this paper leans on

23 extracted references · 23 canonical work pages

[1]

Radiation induced contrast enhance- ment after proton beam therapy in patients with low grade glioma – How safe are protons? Radiotherapy and Oncology

Harrabi SB, Nettelbladt B von, Gudden C, et al. Radiation induced contrast enhance- ment after proton beam therapy in patients with low grade glioma – How safe are protons? Radiotherapy and Oncology. 2022;167:211–218. doi: https://doi.org/10. 1016/j.radonc.2021.12.035

work page 2022
[2]

Radiation-induced brain injury: A review

Greene-Schloesser D, Robbins M, Peiffer AM, Shaw E, Chan MD, and Wheeler KT. Radiation-induced brain injury: A review. Frontiers in Oncology. 2012;2. doi: 10.3389/ fonc.2012.00073. Last edited September 4, 2025 29 References

work page arXiv 2012
[3]

Late Contrast Enhancing Brain Lesions in Proton-Treated Patients With Low-Grade Glioma: Clini- cal Evidence for Increased Periventricular Sensitivity and Variable RBE

Bahn E, Bauer J, Harrabi SB, Herfarth K, Debus J, and Alber M. Late Contrast Enhancing Brain Lesions in Proton-Treated Patients With Low-Grade Glioma: Clini- cal Evidence for Increased Periventricular Sensitivity and Variable RBE. International journal of radiation oncology, biology, physics . 2020;107(3):571–578. doi: https : / / doi.org/10.1016/j.ijrobp...

work page doi:10.1016/j.ijrobp.2020.03.013 2020
[4]

Voxel-based analysis in radiation oncology: A method- ological cookbook

Palma G, Monti S, and Cella L. Voxel-based analysis in radiation oncology: A method- ological cookbook. Physica Medica. 2020;69:192–204. doi: https://doi.org/10.1016/ j.ejmp.2019.12.013

work page 2020
[5]

Spatial descriptions of radiotherapy dose: normal tissue complication models and statistical associations

Ebert MA, Gulliford S, Acosta O, et al. Spatial descriptions of radiotherapy dose: normal tissue complication models and statistical associations. Physics in Medicine & Biology. 2021;66

work page 2021
[6]

Voxel-based analysis: Roadmap for clinical translation

McWilliam A, Palma G, Abravan A, et al. Voxel-based analysis: Roadmap for clinical translation. Radiotherapy and Oncology . 2023;188:109868. doi: 10.1016/j.radonc. 2023.109868

work page doi:10.1016/j.radonc 2023
[7]

Voxel-based population analysis for correlating local dose and rectal toxicity in prostate cancer radiotherapy

Acosta O, Drean G, Ospina JD, et al. Voxel-based population analysis for correlating local dose and rectal toxicity in prostate cancer radiotherapy. Physics in Medicine & Biology. 2013;58(8):2581. doi: 10.1088/0031-9155/58/8/2581

work page doi:10.1088/0031-9155/58/8/2581 2013
[8]

A Voxel-Based Approach to Explore Local Dose Differences Associated With Radiation-Induced Lung Damage

Palma G, Monti S, D’Avino V, et al. A Voxel-Based Approach to Explore Local Dose Differences Associated With Radiation-Induced Lung Damage. International Journal of Radiation Oncology*Biology*Physics. 2016;96(1):127–133. doi: https://doi.org/ 10.1016/j.ijrobp.2016.04.033

work page doi:10.1016/j.ijrobp.2016.04.033 2016
[9]

Voxel-based analysis unveils regional dose differ- ences associated with radiation-induced morbidity in head and neck cancer patients

Monti S, Palma G, D’Avino V, et al. Voxel-based analysis unveils regional dose differ- ences associated with radiation-induced morbidity in head and neck cancer patients. Scientific Reports. 2017;7. doi: 10.1038/s41598-017-07586-x

work page doi:10.1038/s41598-017-07586-x 2017
[10]

Optimized radiation therapy based on radiobiological objectives

Brahme A. Optimized radiation therapy based on radiobiological objectives. Seminars in Radiation Oncology . 1999;9(1). Radiation Therapy Treatment Optimization:35–47. doi: https://doi.org/10.1016/S1053-4296(99)80053-8. Last edited September 4, 2025 Ortkamp et al. (2025): Let’s play POLO 30

work page doi:10.1016/s1053-4296(99)80053-8 1999
[11]

Evaluation of a commer- cial biologically based IMRT treatment planning system.Medical Physics

Semenenko VA, Reitz B, Day E, Qi XS, Miften M, and Li XA. Evaluation of a commer- cial biologically based IMRT treatment planning system.Medical Physics. 2008;35(12):5851–

work page 2008
[12]

doi: https://doi.org/10.1118/1.3013556

work page doi:10.1118/1.3013556
[13]

Kierkels R, Korevaar E, Steenbakkers R, et al. Direct use of multivariable normal tissue complication probability models in treatment plan optimisation for individualised head and neck cancer radiotherapy produces clinically acceptable treatment plans. Radio- therapy and oncology : journal of the European Society for Therapeutic Radiology and Oncology. 20...

work page doi:10.1016/j.radonc.2014.08.020 2014
[14]

Personalized mid-course FDG- PET based adaptive treatment planning for non-small cell lung cancer using machine learning and optimization

Ajdari A, Liao Z, Mohan R, Wei X, and Bortfeld T. Personalized mid-course FDG- PET based adaptive treatment planning for non-small cell lung cancer using machine learning and optimization. Physics in Medicine & Biology . 2022;67(18):185015. doi: 10.1088/1361-6560/ac88b3

work page doi:10.1088/1361-6560/ac88b3 2022
[15]

Embedding machine learning based toxicity mod- els within radiotherapy treatment plan optimization

Maragno D, Buti G, Birbil SI, et al. Embedding machine learning based toxicity mod- els within radiotherapy treatment plan optimization. Physics in Medicine & Biology . 2024;69(7):075003. doi: 10.1088/1361-6560/ad2d7e

work page doi:10.1088/1361-6560/ad2d7e 2024
[16]

Bauer J, Bahn E, Harrabi SB, Herfarth K, Debus J, and Alber M. How can scanned pro- ton beam treatment planning for low-grade glioma cope with increased distal RBE and locally increased radiosensitivity for late MR-detected brain lesions? Medical Physics. 2021;48(4):1497–1507. doi: https://doi.org/10.1002/mp.14739

work page doi:10.1002/mp.14739 2021
[17]

A model-based risk-minimizing proton treatment planning concept for brain injury prevention in low- grade glioma patients

Sallem H, Harrabi SB, Traneus E, Herfarth K, Debus J, and Bauer J. A model-based risk-minimizing proton treatment planning concept for brain injury prevention in low- grade glioma patients. Radiotherapy and Oncology. 2024;201(2). doi: https://doi. org/10.1016/j.radonc.2024.110579

work page doi:10.1016/j.radonc.2024.110579 2024
[18]

Development of the open-source dose calculation and optimization toolkit matRad

Wieser HP, Cisternas E, Wahl N, et al. Development of the open-source dose calculation and optimization toolkit matRad. Medical Physics. 2017;44(6):2556–2568. doi: 10 . 1002/mp.12251. Last edited September 4, 2025 31 References

work page 2017
[19]

On the implementation of an interior-point filter line- search algorithm for large-scale nonlinear programming

W¨ achter A and Biegler LT. On the implementation of an interior-point filter line- search algorithm for large-scale nonlinear programming. Mathematical Programming. 2006;106:25–57. doi: https://doi.org/10.1007/s10107-004-0559-y

work page doi:10.1007/s10107-004-0559-y 2006
[20]

e0404/matRad: Blaise v2.10.1

Ackermann B, Bangert M, Bennan ABA, et al. e0404/matRad: Blaise v2.10.1. Ver- sion 2.10.1. 2020. doi: 10.5281/zenodo.7107719. url: https://doi.org/10.5281/ zenodo.7107719

work page doi:10.5281/zenodo.7107719 2020
[21]

Fast calculation of the exact radiological path for a three-dimensional CT array

Siddon RL. Fast calculation of the exact radiological path for a three-dimensional CT array. Medical Physics. 1985;12(2):252–255. doi: https : / / doi . org / 10 . 1118 / 1 . 595715

work page 1985
[22]

A pencil beam algorithm for proton dose calculations

Hong L, Goitein M, Bucciolini M, et al. A pencil beam algorithm for proton dose calculations. Physics in Medicine & Biology . 1996;41(8):1305. doi: 10 . 1088 / 0031 - 9155/41/8/005

work page 1996
[23]

MA57—a code for the solution of sparse symmetric definite and indefinite systems

Duff IS. MA57—a code for the solution of sparse symmetric definite and indefinite systems. ACM Trans. Math. Softw. 2004;30(2):118–144. doi: 10.1145/992200.992202. Appendix Let ˜d = Drϕ ∈ Rnr + be the vectorized dose distribution in the volume of interest r, using the dose-influence matrix D ∈ Rn×m + and the fluence vector ϕ ∈ Rm +. Then, the dose optimiza...

work page doi:10.1145/992200.992202 2004

[1] [1]

Radiation induced contrast enhance- ment after proton beam therapy in patients with low grade glioma – How safe are protons? Radiotherapy and Oncology

Harrabi SB, Nettelbladt B von, Gudden C, et al. Radiation induced contrast enhance- ment after proton beam therapy in patients with low grade glioma – How safe are protons? Radiotherapy and Oncology. 2022;167:211–218. doi: https://doi.org/10. 1016/j.radonc.2021.12.035

work page 2022

[2] [2]

Radiation-induced brain injury: A review

Greene-Schloesser D, Robbins M, Peiffer AM, Shaw E, Chan MD, and Wheeler KT. Radiation-induced brain injury: A review. Frontiers in Oncology. 2012;2. doi: 10.3389/ fonc.2012.00073. Last edited September 4, 2025 29 References

work page arXiv 2012

[3] [3]

Late Contrast Enhancing Brain Lesions in Proton-Treated Patients With Low-Grade Glioma: Clini- cal Evidence for Increased Periventricular Sensitivity and Variable RBE

Bahn E, Bauer J, Harrabi SB, Herfarth K, Debus J, and Alber M. Late Contrast Enhancing Brain Lesions in Proton-Treated Patients With Low-Grade Glioma: Clini- cal Evidence for Increased Periventricular Sensitivity and Variable RBE. International journal of radiation oncology, biology, physics . 2020;107(3):571–578. doi: https : / / doi.org/10.1016/j.ijrobp...

work page doi:10.1016/j.ijrobp.2020.03.013 2020

[4] [4]

Voxel-based analysis in radiation oncology: A method- ological cookbook

Palma G, Monti S, and Cella L. Voxel-based analysis in radiation oncology: A method- ological cookbook. Physica Medica. 2020;69:192–204. doi: https://doi.org/10.1016/ j.ejmp.2019.12.013

work page 2020

[5] [5]

Spatial descriptions of radiotherapy dose: normal tissue complication models and statistical associations

Ebert MA, Gulliford S, Acosta O, et al. Spatial descriptions of radiotherapy dose: normal tissue complication models and statistical associations. Physics in Medicine & Biology. 2021;66

work page 2021

[6] [6]

Voxel-based analysis: Roadmap for clinical translation

McWilliam A, Palma G, Abravan A, et al. Voxel-based analysis: Roadmap for clinical translation. Radiotherapy and Oncology . 2023;188:109868. doi: 10.1016/j.radonc. 2023.109868

work page doi:10.1016/j.radonc 2023

[7] [7]

Voxel-based population analysis for correlating local dose and rectal toxicity in prostate cancer radiotherapy

Acosta O, Drean G, Ospina JD, et al. Voxel-based population analysis for correlating local dose and rectal toxicity in prostate cancer radiotherapy. Physics in Medicine & Biology. 2013;58(8):2581. doi: 10.1088/0031-9155/58/8/2581

work page doi:10.1088/0031-9155/58/8/2581 2013

[8] [8]

A Voxel-Based Approach to Explore Local Dose Differences Associated With Radiation-Induced Lung Damage

Palma G, Monti S, D’Avino V, et al. A Voxel-Based Approach to Explore Local Dose Differences Associated With Radiation-Induced Lung Damage. International Journal of Radiation Oncology*Biology*Physics. 2016;96(1):127–133. doi: https://doi.org/ 10.1016/j.ijrobp.2016.04.033

work page doi:10.1016/j.ijrobp.2016.04.033 2016

[9] [9]

Voxel-based analysis unveils regional dose differ- ences associated with radiation-induced morbidity in head and neck cancer patients

Monti S, Palma G, D’Avino V, et al. Voxel-based analysis unveils regional dose differ- ences associated with radiation-induced morbidity in head and neck cancer patients. Scientific Reports. 2017;7. doi: 10.1038/s41598-017-07586-x

work page doi:10.1038/s41598-017-07586-x 2017

[10] [10]

Optimized radiation therapy based on radiobiological objectives

Brahme A. Optimized radiation therapy based on radiobiological objectives. Seminars in Radiation Oncology . 1999;9(1). Radiation Therapy Treatment Optimization:35–47. doi: https://doi.org/10.1016/S1053-4296(99)80053-8. Last edited September 4, 2025 Ortkamp et al. (2025): Let’s play POLO 30

work page doi:10.1016/s1053-4296(99)80053-8 1999

[11] [11]

Evaluation of a commer- cial biologically based IMRT treatment planning system.Medical Physics

Semenenko VA, Reitz B, Day E, Qi XS, Miften M, and Li XA. Evaluation of a commer- cial biologically based IMRT treatment planning system.Medical Physics. 2008;35(12):5851–

work page 2008

[12] [12]

doi: https://doi.org/10.1118/1.3013556

work page doi:10.1118/1.3013556

[13] [13]

Kierkels R, Korevaar E, Steenbakkers R, et al. Direct use of multivariable normal tissue complication probability models in treatment plan optimisation for individualised head and neck cancer radiotherapy produces clinically acceptable treatment plans. Radio- therapy and oncology : journal of the European Society for Therapeutic Radiology and Oncology. 20...

work page doi:10.1016/j.radonc.2014.08.020 2014

[14] [14]

Personalized mid-course FDG- PET based adaptive treatment planning for non-small cell lung cancer using machine learning and optimization

Ajdari A, Liao Z, Mohan R, Wei X, and Bortfeld T. Personalized mid-course FDG- PET based adaptive treatment planning for non-small cell lung cancer using machine learning and optimization. Physics in Medicine & Biology . 2022;67(18):185015. doi: 10.1088/1361-6560/ac88b3

work page doi:10.1088/1361-6560/ac88b3 2022

[15] [15]

Embedding machine learning based toxicity mod- els within radiotherapy treatment plan optimization

Maragno D, Buti G, Birbil SI, et al. Embedding machine learning based toxicity mod- els within radiotherapy treatment plan optimization. Physics in Medicine & Biology . 2024;69(7):075003. doi: 10.1088/1361-6560/ad2d7e

work page doi:10.1088/1361-6560/ad2d7e 2024

[16] [16]

Bauer J, Bahn E, Harrabi SB, Herfarth K, Debus J, and Alber M. How can scanned pro- ton beam treatment planning for low-grade glioma cope with increased distal RBE and locally increased radiosensitivity for late MR-detected brain lesions? Medical Physics. 2021;48(4):1497–1507. doi: https://doi.org/10.1002/mp.14739

work page doi:10.1002/mp.14739 2021

[17] [17]

A model-based risk-minimizing proton treatment planning concept for brain injury prevention in low- grade glioma patients

Sallem H, Harrabi SB, Traneus E, Herfarth K, Debus J, and Bauer J. A model-based risk-minimizing proton treatment planning concept for brain injury prevention in low- grade glioma patients. Radiotherapy and Oncology. 2024;201(2). doi: https://doi. org/10.1016/j.radonc.2024.110579

work page doi:10.1016/j.radonc.2024.110579 2024

[18] [18]

Development of the open-source dose calculation and optimization toolkit matRad

Wieser HP, Cisternas E, Wahl N, et al. Development of the open-source dose calculation and optimization toolkit matRad. Medical Physics. 2017;44(6):2556–2568. doi: 10 . 1002/mp.12251. Last edited September 4, 2025 31 References

work page 2017

[19] [19]

On the implementation of an interior-point filter line- search algorithm for large-scale nonlinear programming

W¨ achter A and Biegler LT. On the implementation of an interior-point filter line- search algorithm for large-scale nonlinear programming. Mathematical Programming. 2006;106:25–57. doi: https://doi.org/10.1007/s10107-004-0559-y

work page doi:10.1007/s10107-004-0559-y 2006

[20] [20]

e0404/matRad: Blaise v2.10.1

Ackermann B, Bangert M, Bennan ABA, et al. e0404/matRad: Blaise v2.10.1. Ver- sion 2.10.1. 2020. doi: 10.5281/zenodo.7107719. url: https://doi.org/10.5281/ zenodo.7107719

work page doi:10.5281/zenodo.7107719 2020

[21] [21]

Fast calculation of the exact radiological path for a three-dimensional CT array

Siddon RL. Fast calculation of the exact radiological path for a three-dimensional CT array. Medical Physics. 1985;12(2):252–255. doi: https : / / doi . org / 10 . 1118 / 1 . 595715

work page 1985

[22] [22]

A pencil beam algorithm for proton dose calculations

Hong L, Goitein M, Bucciolini M, et al. A pencil beam algorithm for proton dose calculations. Physics in Medicine & Biology . 1996;41(8):1305. doi: 10 . 1088 / 0031 - 9155/41/8/005

work page 1996

[23] [23]

MA57—a code for the solution of sparse symmetric definite and indefinite systems

Duff IS. MA57—a code for the solution of sparse symmetric definite and indefinite systems. ACM Trans. Math. Softw. 2004;30(2):118–144. doi: 10.1145/992200.992202. Appendix Let ˜d = Drϕ ∈ Rnr + be the vectorized dose distribution in the volume of interest r, using the dose-influence matrix D ∈ Rn×m + and the fluence vector ϕ ∈ Rm +. Then, the dose optimiza...

work page doi:10.1145/992200.992202 2004