Pith. sign in

REVIEW 3 major objections 5 minor 94 references

Direct probabilistic IMPT treatment planning with setup and range errors for neuro-oncological patients

T0 review · 3 major / 5 minor · reviewed 2026-08-02 · deepseek-v4-flash

Challenge this review Re-run · record.json Download PDF Read on arXiv ↗ Review JSON

Pith's one-line read Probability-based proton planning improves coverage and cuts organ dose

desk verdict Credible feasibility study of a previously published probabilistic IMPT method, but the headline trade-off gains are not yet quantitatively secure given the PCE error band and n=5. read the letter →

arxiv 2607.13869 v1 pith:7W44XB74 submitted 2026-07-15 physics.med-ph

Jelte R. de Jong , Sebastiaan Breedveld , Steven J. M. Habraken , Mischa S. Hoogeman , Jenneke I. de Jong , Danny Lathouwers , Zoltán Perkó This is my paper · ORCID
classification physics.med-ph
keywords probabilistictreatmentplanningIMPTintensity-modulatedprotontherapypercentile-basedoptimizationpolynomialchaosexpansionsetupuncertaintyrangerobust
verification ladder T0 review T1 audit T2 compute T3 formal

The pith

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

The reading

This paper argues that proton therapy plans for brain and skull-base tumors should be optimized for how likely each error scenario actually is, rather than for the single worst-case scenario. To do this, the authors use a percentile-based objective: instead of asking that every voxel be covered in every error scenario, they ask that the prescribed dose be delivered to the target in at least 90% of scenarios and that organs at risk stay below their limits in at least 95%. In five neuro-oncological patients, the resulting plans matched or improved target coverage while reducing cumulative organ-at-risk dose by up to 33 GyRBE compared with mini-max robust plans. The price is computation: full optimization took 44 to 141 hours, though a simple change (dropping the outer-loop warm-start) cut that below 10 hours for two patients. The approach matters because it turns robustness from an arbitrary scenario choice into a clinically meaningful probability of meeting each goal.

What carries the argument

The core object is the percentile-based objective function, in which the α-th percentile of voxel dose is estimated as the expected dose plus or minus a δ-factor times an approximate standard deviation. The δ-factor is not fixed in advance; an outer loop repeatedly recomputes accurate percentiles from a polynomial chaos expansion of the dose-influence matrix (sampled 100,000 times) and updates δ until convergence, while an inner loop optimizes beam weights for the current percentile estimate. A memory-efficient diagonal covariance representation keeps the optimization tractable.

What would settle it

Recalculate the final probabilistic and robust plans for these five patients using exact, scenario-by-scenario Monte Carlo dose calculation (or a validated independent dose engine) and compare the empirical 10th-percentile D99.8% and OAR DVH metrics; if the probabilistic plan's coverage improvement falls below roughly 0.2 GyRBE or reverses, the central claim is unsupported.

Watch

Extended reading notes

Core claim

The central claim is that a percentile-based, direct probabilistic optimizer can produce IMPT plans that are dosimetrically superior to mini-max robust plans when evaluated with the same probabilistic metrics. For the patient with adequate robust target coverage, the probabilistic plan had identical 10th-percentile D99.8% while lowering summed OAR DVH-measures by 19 GyRBE. For three of four patients whose robust plans could not cover the target enough, the probabilistic plan raised the 10th percentile of D99.8% by up to 0.93 GyRBE while also cutting summed OAR DVH-measures by 15 to 33 GyRBE; the fourth gained coverage at the cost of a within-constraint OAR increase of 8.1 GyRBE. The authors

Load-bearing premise

The comparison assumes the polynomial chaos expansion computes dose percentiles accurately enough—within the reported error of roughly ±0.7 to 1.2 GyRBE—so that the 0.19 to 0.93 GyRBE coverage improvements are real plan differences rather than approximation artifacts.

Editorial extensions

If this is right

  • Probabilistic planning can replace or complement mini-max robust planning for IMPT, giving planners control over the exact probability of meeting each clinical goal.
  • The reported trade-off gains (up to 33 GyRBE OAR reduction or 0.93 GyRBE coverage gain) would translate to clinically meaningful reductions in the risk of radiation toxicity for neuro-oncological patients.
  • Optimization times can be brought within a clinically acceptable range (below 10 hours) by updating percentile estimates inside the inner loop instead of via an outer-loop warm-start, suggesting the method is practically deployable.
  • The approach is directly applicable to other modalities with steep dose gradients, such as photon stereotactic body radiotherapy.

Reading between the lines

Editorial extensions of the paper, not claims the author makes directly.

  • If the reported gains hold under exact (non-PCE) dose calculation, the field's reliance on mini-max robustness and scenario-set selection could shift toward probability-based acceptance criteria, much as margin-based planning was replaced by robust optimization.
  • The PCE approximation error band (± roughly 1 GyRBE in voxel dose percentiles) overlaps some of the claimed coverage gains (0.19 to 0.93 GyRBE), so an independent Monte Carlo validation would strengthen confidence in the comparison.
  • The same percentile-optimization machinery could be extended to directly optimize pDVH metrics (e.g., D99.8% or D0.03cc) instead of voxel-wise percentiles, which the authors note is a current mismatch.
Share X Bluesky LinkedIn Reddit HN

Signed reviews

No signed human review yet.

Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, and a circularity audit.

Referee Report

3 major / 5 minor

Summary. The manuscript reports a feasibility study of a percentile-based probabilistic IMPT planning approach applied to five neuro-oncological patients. The method approximates voxel-dose percentiles by E[d] ± δ_i · σ̃_i, where the expected dose and an approximate standard deviation are obtained from a polynomial chaos expansion of the dose-influence matrix, and an outer loop updates δ_i until the percentile estimate converges. The probabilistic plans are compared with automated mini-max robust plans. Results: patient 1 achieved the same 10th percentile of D99.8% while reducing summed OAR-related DVH metrics by 19 GyRBE; patients 2–5 improved the 10th percentile of D99.8% by up to 0.93 GyRBE, with summed OAR DVH changes ranging from +8.1 to −33.0 GyRBE. Total optimization times were 44–226 h, reduced to below 10 h for two patients when the outer-loop warm-starting was omitted. The authors conclude that the probabilistic approach yields improved probabilistic trade-offs between target coverage and OAR sparing.

Significance. If the findings are quantitatively secure, the work is a useful step toward direct probabilistic optimization for IMPT: it demonstrates a scalable implementation (diagonal covariance, PCE-based expected values and gradients), probabilistic hard constraints, and an independent automated robust-plan benchmark. The paper is commendably explicit about its limitations, including the mismatch between optimized voxel percentiles and evaluated pDVH metrics, heuristic acceptance probabilities, and the omission of random errors. The open-source PCE toolbox and the detailed convergence analyses are additional strengths. However, the current evidence supports feasibility rather than a proven dosimetric advantage over robust planning: the central plan-quality comparison is not yet anchored to dose-engine ground truth and rests on a small, heterogeneous patient sample.

major comments (3)
  1. [Appendix A, Table 6; §3.1–3.2, Table 2] The central comparison evaluates both plans with PCE-based percentiles, but the validation in Appendix A is only partial. It compares the Dij→di PCE used in optimization with the di PCE used in evaluation, for patient 4 only; the evaluation PCE itself is not checked against the actual dose engine for either arm. The reported voxel-percentile differences have ranges up to −0.74 to +1.16 GyRBE (Table 6), whereas the claimed 10thD99.8 gains are 0.19–0.93 GyRBE (Table 2). Because the same approximation is applied to both plans, systematic differences could bias the plan comparison, especially if probabilistic plans exploit steeper dose gradients and more nonlinear scenario dependence. Please validate the evaluation PCE on the final plans of both arms using direct scenario sampling from the dose engine (or an independent Monte Carlo engine) and report the resulting percentile differences and
  2. [§3.2, Tables 2–3; §2.5] The group-level claim rests on five patients with no confidence intervals or hypothesis testing, and the group B pattern is heterogeneous. Patient 4 is excluded from the mean coverage gain because it was scaled to identical target coverage; patient 2’s summed OAR DVH metric increases (+8.1 GyRBE) even though target coverage improves. The statement that the probabilistic approach achieves ‘improved trade-offs’ generalizes beyond what n=4/5 with scaled comparisons can support. Please either frame the results strictly as feasibility observations with per-patient reporting, or add uncertainty quantification (e.g., scenario bootstrap) and temper the generalization in the abstract and conclusions.
  3. [§2.4, §2.5, Discussion] The abstract and conclusions state that the method can ‘precisely optimize’ for clinical goals, but the optimized quantities are voxel-wise percentiles, while the reported evaluation metrics are pDVH quantities (10thD99.8%, 95thD0.03cc). Section 4 explicitly acknowledges this mismatch, the heuristic choice of 90%/95% acceptance probabilities, and patient-specific threshold adjustments. This does not invalidate the method, but it means the pDVH improvements are achieved indirectly. I recommend softening the ‘precisely’ wording and clearly distinguishing optimized voxel-percentile goals from the subsequently evaluated pDVH goals.
minor comments (5)
  1. [Abstract and §3.3, Table 4] The abstract says optimization times were 44–141 h, but Table 4 reports 226 h for patient 2. Please reconcile.
  2. [Appendix B.3, Table 14] The row ‘Total optimization time (original)’ lists 20.3 h for patient 4, inconsistent with Table 4 (79.8 h). Likely a typo; please correct.
  3. [Table 6 and Appendix B.2] Target structure labels such as ‘CTV (5940 cc)’ appear to use dose units (cGy, corresponding to 59.4 GyRBE) rather than volume units. Please fix the labels for clarity.
  4. [Appendix B.3, Table 12] Table 12 uses patient identifiers 10, 12, 32, 35 instead of patients 1–5 used elsewhere. Please unify the notation.
  5. [§2.4 and Appendix B.3.4] The phrase ‘eliminating warm-starting (i.e., the outer loop)’ is imprecise: in the no-outer-loop version, δ-factors are still updated within the inner optimization. Please rephrase to distinguish removal of the outer-loop warm-start from removal of δ-factor updating.

Circularity Check

0 steps flagged · score 1.0 of 10

No load-bearing circularity; comparison is against an external robust-plan benchmark, with only minor self-citation continuity.

full rationale

The central comparison is empirical: probabilistic plans are compared with independently optimized mini-max robust plans (Erasmus-iCycle), and both arms are evaluated with the same voxel-dose PCE percentiles. The robust arm was not constructed to match the probabilistic evaluation metric, so the reported gains (e.g., ΔD_OAR,DVH = −19 GyRBE for patient 1; 10th D99.8% increases up to 0.93 GyRBE) are not equivalent by construction to the optimization objective. The δ-factor update in Eq. 15 is a fixed-point consistency mechanism: δ_i is defined as the ratio of the accurate percentile deviation to the approximate SD, so inserting it into Eq. 3 recovers the accurate percentile at the current beam weights; this is an algorithmic self-consistency step, not a prediction derived from its own input. The main self-citations (de Jong et al. 2026 for the percentile pipeline; Perkó et al. 2016/Rojo-Santiago et al. 2021 for PCE settings) are continuity with prior validated work rather than a uniqueness argument, and the PCE settings are additionally checked in Appendix A against a separately constructed voxel-dose PCE. Appendix A explicitly states 'we consider the voxel dose PCE (and therefore its generated percentiles) to be true values' and does not compare the evaluation PCE to the dose engine; that is a real validation gap and a correctness risk, but it affects both plan arms symmetrically and does not make the trade-off claim definitional. No step of the claimed derivation reduces to its own input by construction.

Assumptions & free parameters 5 free parameters · 5 assumptions · 0 invented entities

The paper introduces no new physical entities. The δ-factor and diagonal-covariance surrogate are computational constructs, not independently evidenced entities. The main assumptions are that PCE approximation, Gaussian systematic errors, the robust benchmark, and the active-voxel surrogate are adequate for the feasibility claim.

free parameters (5)
  • Probabilistic acceptance probabilities (target 90%, OAR 95%) = 0.90 / 0.95
    Chosen heuristically because 'no consensus currently exists on probabilistic acceptance criteria'; these probabilities define every probabilistic constraint and therefore the reported trade-offs.
  • Per-voxel δ-factor δ_i = Not reported; updated iteratively via Eq. 15
    Compensates for the diagonal-covariance approximation of the standard deviation. By construction the percentile estimate is exact at convergence, but convergence of this surrogate determines the final plan.
  • PCE settings (GL=4, PO=5, thresholds) = GL=4, PO=5, Θ_di=0.01 GyRBE, Θ_Dij=10^-3 GyRBE
    Taken from prior PCE studies; directly controls percentile accuracy, which Appendix A shows is comparable to some reported plan differences.
  • Convergence tolerances and damping factors = τ_rel=0.01, τ_abs=1 GyRBE, d_low=5 GyRBE; κ=0.3/0.1 in no-warm-start runs
    Conservative choices substantially inflate optimization times (Table 5); loosened settings change plan metrics slightly and are central to the reported runtime reductions.
  • Probabilistic objective weights = Derived from Lagrange multipliers of the Erasmus-iCycle robust plan (Appendix B.2)
    These weights transplant the robust plan's trade-off priorities into the weighted-sum probabilistic optimization, influencing which OAR/target compromises are chosen.
assumptions (5)
  • domain assumption PCE of the dose-influence matrix accurately approximates the dose engine for all active voxels (Eqs. 1, 16-17).
    Used to compute expected dose, variance, and percentiles. Validated only for patient 4 in Appendix A, with residual percentile biases up to 1.16 GyRBE.
  • domain assumption Setup and range errors are Gaussian systematic errors with SDs 1.2 mm and 1% (range mean 1.2%); random errors are neglected.
    Based on the Van Herk margin recipe and clinical protocol; the paper notes the setup SD likely overestimates the measured 0.7 mm at HollandPTC.
  • domain assumption The automated mini-max robust plan is an appropriate clinical benchmark.
    Robust plans were generated by Erasmus-iCycle, not the actual clinical RayStation plans, and use MFO instead of the SFO used clinically; this may underestimate or alter the baseline plan quality.
  • ad hoc to paper The percentile estimate E ± δ·σ̃ with outer-loop δ updates converges to the true voxel-dose percentile.
    Eqs. 3 and 15 define δ so that the estimate is exact at convergence; however convergence is checked on active voxels only, and the paper acknowledges inactive voxels can violate goals.
  • domain assumption Probabilistic pDVH metrics (10th D99.8%, 95th D0.03cc) are clinically appropriate acceptance criteria.
    Used to scale plans and define success; based on EPTN/clinical practice, but the paper acknowledges no consensus exists and that optimization used voxel-wise percentiles while evaluation used pDVH metrics, creating a mismatch.

how reviews work

0 comments
Cite this review

Pith. "Pith review of Direct probabilistic IMPT treatment planning with setup and range errors for neuro-oncological patients." pith.science (2026). https://pith.science/paper/7W44XB74

@misc{pith2026260713869,
  author       = {Pith},
  title        = {Pith review of: Direct probabilistic IMPT treatment planning with setup and range errors for neuro-oncological patients},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/7W44XB74}},
  note         = {Machine review of arXiv:2607.13869}
}
abstract

To show clinical feasibility of a previously proposed probabilistic planning approach that can precisely optimize for clinical goals with patient-specific acceptance probabilities on a neuro-oncological patient group, we compared probabilistic plans with (automated) robust plans for one patient (group A) that could achieve sufficient clinical target coverage and for four patients (group B) where target coverage had to be compromised due to organ-at-risk (OAR) dose constraints. The probabilistic approach is percentile-based and uses the fact that a (dose) percentile can be approximated as a linear combination of its expected value and standard deviation. The optimization has a nested structure: the inner optimization optimizes the beam weights for a given percentile estimate, while an outer loop iteratively updates and improves the accuracy of the percentile estimate. For every outer iteration, the optimization is warm-started from the previous iteration. Percentiles are efficiently calculated by sampling a polynomial chaos expansion of the dose-influence matrix. The patient in group A achieved cumulative OAR dose reductions (of OAR-related DVH-metrics) of 19 GyRBE, for identical target coverage. Target coverage improved for all patients in group B (the 10th percentile of $D_{99.8\%}$ increased up to 0.93 GyRBE), at the same time reaching cumulative OAR dose reductions (of OAR-related DVH-metrics) up to 33 GyRBE. Probabilistic plans were optimized in 44h to 141h. For two representative patients, eliminating warm-starting (i.e., the outer loop) from the approach reduced total optimization times to below 10h (which took originally 80h and 141h). Compared to robust optimization methods, the probabilistic approach achieves improved trade-offs between probabilistic target coverage and OAR sparing, potentially leading to better treatments.

Figures

Figures reproduced from arXiv: 2607.13869 by the authors.

Figure 1
Figure 1. The probabilistic approach is sequentially solving inner optimizations. The [PITH_FULL_IMAGE:figures/full_fig_p007_1.png] view at source ↗
Figure 2
Figure 2. A comparison of the dose population histogram between the probabilistic and [PITH_FULL_IMAGE:figures/full_fig_p010_2.png] view at source ↗
Figure 3
Figure 3. A comparison of the dose population histograms between robust and proba [PITH_FULL_IMAGE:figures/full_fig_p012_3.png] view at source ↗
Figures from the paper (6 more)
Figure 4
Figure 4. Figure 4: A comparison of the dose population histograms between the probabilistic and [PITH_FULL_IMAGE:figures/full_fig_p013_4.png]
Figure 5
Figure 5. Figure 5: A comparison between the Dij → di (dashed) and voxel dose PCE (solid) for some representative voxels of patient 4 for the CTV and optic system. 28 [PITH_FULL_IMAGE:figures/full_fig_p028_5.png]
Figure 6
Figure 6. Figure 6: A comparison between robust (dashed) and probabilistic (solid) plans for pa [PITH_FULL_IMAGE:figures/full_fig_p030_6.png]
Figure 7
Figure 7. Figure 7: A comparison between robust and probabilistic plans for a) patient 4 and b) [PITH_FULL_IMAGE:figures/full_fig_p031_7.png]
Figure 8
Figure 8. Figure 8: Percentile convergence of patient 2 for the (a) 10th percentile and (b) 90th [PITH_FULL_IMAGE:figures/full_fig_p039_8.png]
Figure 9
Figure 9. Figure 9: Convergence results for patient 4 (top) and 5 (bottom), showing the objective [PITH_FULL_IMAGE:figures/full_fig_p041_9.png]

Discussion (0). Continue with ORCID to comment.

Reference graph

Works this paper leans on

94 extracted references · 78 canonical work pages

  1. [1]

    Physics in Medicine &; Biology , publisher =

    de Jong, J R and Breedveld, S and Habraken, S J and Hoogeman, M S and Lathouwers, D and Perkó, Z , year =. Physics in Medicine &; Biology , publisher =. doi:10.1088/1361-6560/ae351c , number =

    work page doi:10.1088/1361-6560/ae351c

  2. [2]

    and Clasie, Benjamin M

    Kooy, Hanne M. and Clasie, Benjamin M. and Lu, Hsiao-Ming and Madden, Thomas M. and Bentefour, Hassan and Depauw, Nicolas and Adams, Judy A. and Trofimov, Alexei V. and Demaret, Denis and Delaney, Thomas F. and Flanz, Jacob B. , year =. International Journal of Radiation Oncology*Biology*Physics , publisher =. doi:10.1016/j.ijrobp.2009.06.065 , number =

    work page doi:10.1016/j.ijrobp.2009.06.065 2009

  3. [3]

    and Creutzberg, Carien L

    van de Sande, Mariska A.E. and Creutzberg, Carien L. and van de Water, Steven and Sharfo, Abdul Wahab and Hoogeman, Mischa S. , year =. Radiotherapy and Oncology , publisher =. doi:10.1016/j.radonc.2016.06.016 , number =

    work page doi:10.1016/j.radonc.2016.06.016 2016

  4. [4]

    Nathan and Ahmad, Salahuddin and Henson, Christina , year =

    Nguyen, My-Lien and Cantrell, J. Nathan and Ahmad, Salahuddin and Henson, Christina , year =. Medical Dosimetry , publisher =. doi:10.1016/j.meddos.2021.02.001 , number =

    work page doi:10.1016/j.meddos.2021.02.001 2021

  5. [5]

    Radiotherapy and Oncology , publisher =

    Stuschke, Martin and Kaiser, Andreas and P\". Radiotherapy and Oncology , publisher =. 2012 , month = jul, pages =. doi:10.1016/j.radonc.2012.03.017 , number =

    work page doi:10.1016/j.radonc.2012.03.017 2012

  6. [6]

    and Cuijpers, Johan P

    Verbakel, Wilko F.A.R. and Cuijpers, Johan P. and Hoffmans, Daan and Bieker, Michael and Slotman, Ben J. and Senan, Suresh , year =. International Journal of Radiation Oncology*Biology*Physics , publisher =. doi:10.1016/j.ijrobp.2008.12.033 , number =

    work page doi:10.1016/j.ijrobp.2008.12.033 2008

  7. [7]

    Physics in Medicine and Biology , publisher =

    Lomax, A J , year =. Physics in Medicine and Biology , publisher =. doi:10.1088/0031-9155/53/4/015 , number =

    work page doi:10.1088/0031-9155/53/4/015

  8. [8]

    Physics in Medicine and Biology , publisher =

    Lomax, A J , year =. Physics in Medicine and Biology , publisher =. doi:10.1088/0031-9155/53/4/014 , number =

    work page doi:10.1088/0031-9155/53/4/014

Show all 94 references
  1. [9]

    Seminars in Radiation Oncology , publisher =

    Bortfeld, T and Jiang, S and Rietzel, E , year =. Seminars in Radiation Oncology , publisher =. doi:10.1053/j.semradonc.2003.10.011 , number =

    2003 doi

  2. [10]

    Medical Physics , publisher =

    Liu, Wei and Li, Yupeng and Li, Xiaoqiang and Cao, Wenhua and Zhang, Xiaodong , year =. Medical Physics , publisher =. doi:10.1118/1.4711909 , number =

    doi

  3. [11]

    Medical Physics , publisher =

    Liu, Wei and Zhang, Xiaodong and Li, Yupeng and Mohan, Radhe , year =. Medical Physics , publisher =. doi:10.1118/1.3679340 , number =

    doi

  4. [12]

    and Li, Xiaoqiang and Li, Yupeng and Zhu, Ron

    Liu, Wei and Frank, Steven J. and Li, Xiaoqiang and Li, Yupeng and Zhu, Ron. X. and Mohan, Radhe , year =. Medical Physics , publisher =. doi:10.1118/1.4774363 , number =

    doi

  5. [13]

    and Chernyaev, Aleksander P

    Kiselev, Vasilii A. and Chernyaev, Aleksander P. and Belikhin, Mikhail A. and Zamaltdinov, Rail R. and Vladimirkin, Sergei A. and Gritsenko, Sergei E. and Nechesnyuk, Aleksey V. , year =. Journal of Applied Clinical Medical Physics , publisher =. doi:10.1002/acm2.70355 , number =

    doi

  6. [14]

    and Steenbakkers, Roel J

    van Dijk, Lisanne V. and Steenbakkers, Roel J. H. M. and ten Haken, Bennie and van der Laan, Hans Paul and van ‘t Veld, Aart A. and Langendijk, Johannes A. and Korevaar, Erik W. , editor =. PLOS ONE , publisher =. 2016 , month = mar, pages =. doi:10.1371/journal.pone.0152477 ,...

    2016 doi

  7. [15]

    and Habraken, Steven J.M

    Korevaar, Erik W. and Habraken, Steven J.M. and Scandurra, Daniel and Kierkels, Roel G.J. and Unipan, Mirko and Eenink, Martijn G.C. and Steenbakkers, Roel J.H.M. and Peeters, Stephanie G. and Zindler, Jaap D. and Hoogeman, Mischa and Langendijk, Johannes A. , year =. doi:10.1...

    2019 doi

  8. [16]

    and Hoogeman, Mischa S

    Rojo-Santiago, Jesús and Korevaar, Erik and Perkó, Zoltán and Both, Stefan and Habraken, Steven J.M. and Hoogeman, Mischa S. , year =. doi:10.1016/j.radonc.2023.109729 , journal =

    2023

  9. [17]

    and Widesott, L

    Sterpin, E. and Widesott, L. and Poels, K. and Hoogeman, M. and Korevaar, E.W. and Lowe, M. and Molinelli, S. and Fracchiolla, F. , year =. doi:10.1016/j.radonc.2024.110365 , journal =

    2024

  10. [18]

    2022 , month = aug, pages =

    Kaplan, Laura Patricia and Placidi, Lorenzo and B\". 2022 , month = aug, pages =. doi:10.1016/j.radonc.2022.06.005 , journal =

    2022 doi

  11. [19]

    Physics in Medicine and Biology , publisher =

    Schaffner, B and Pedroni, E , year =. Physics in Medicine and Biology , publisher =. doi:10.1088/0031-9155/43/6/016 , number =

    doi

  12. [20]

    , year =

    van Herk, Marcel and Remeijer, Peter and Rasch, Coen and Lebesque, Joos V. , year =. International Journal of Radiation Oncology*Biology*Physics , publisher =. doi:10.1016/s0360-3016(00)00518-6 , number =

    doi

  13. [21]

    Physics in Medicine &; Biology , publisher =

    Unkelbach, Jan and Alber, Markus and Bangert, Mark and Bokrantz, Rasmus and Chan, Timothy C Y and Deasy, Joseph O and Fredriksson, Albin and Gorissen, Bram L and van Herk, Marcel and Liu, Wei and Mahmoudzadeh, Houra and Nohadani, Omid and Siebers, Jeffrey V and Witte, Marnix a...

    doi

  14. [22]

    Medical Physics , publisher =

    Fredriksson, Albin and Forsgren, Anders and Hårdemark, Bj\". Medical Physics , publisher =. 2011 , month = mar, pages =. doi:10.1118/1.3556559 , number =

    2011 doi

  15. [23]

    International Journal of Radiation Oncology*Biology*Physics , publisher =

    van der Voort, Sebastian and van de Water, Steven and Perkó, Zoltán and Heijmen, Ben and Lathouwers, Danny and Hoogeman, Mischa , year =. International Journal of Radiation Oncology*Biology*Physics , publisher =. doi:10.1016/j.ijrobp.2016.02.035 , number =

    2016 doi

  16. [24]

    Physics in Medicine and Biology , publisher =

    Unkelbach, Jan and Chan, Timothy C Y and Bortfeld, Thomas , year =. Physics in Medicine and Biology , publisher =. doi:10.1088/0031-9155/52/10/009 , number =

    doi

  17. [25]

    and Soukup, Martin , year =

    Unkelbach, Jan and Bortfeld, Thomas and Martin, Benjamin C. and Soukup, Martin , year =. Medical Physics , publisher =. doi:10.1118/1.3021139 , number =

    doi

  18. [26]

    Physics in Medicine and Biology , publisher =

    Fredriksson, Albin and Bokrantz, Rasmus , year =. Physics in Medicine and Biology , publisher =. doi:10.1088/0031-9155/61/5/2067 , number =

    doi

  19. [27]

    Physics in Medicine and Biology , publisher =

    Bokrantz, Rasmus and Fredriksson, Albin , year =. Physics in Medicine and Biology , publisher =. doi:10.1088/1361-6560/aa524d , number =

    doi

  20. [28]

    Physics in Medicine and Biology , publisher =

    Chen, Wei and Unkelbach, Jan and Trofimov, Alexei and Madden, Thomas and Kooy, Hanne and Bortfeld, Thomas and Craft, David , year =. Physics in Medicine and Biology , publisher =. doi:10.1088/0031-9155/57/3/591 , number =

    doi

  21. [29]

    Physics in Medicine and Biology , publisher =

    Pflugfelder, D and Wilkens, J J and Oelfke, U , year =. Physics in Medicine and Biology , publisher =. doi:10.1088/0031-9155/53/6/013 , number =

    doi

  22. [30]

    Medical Dosimetry , publisher =

    Janson, Martin and Glimelius, Lars and Fredriksson, Albin and Traneus, Erik and Engwall, Erik , year =. Medical Dosimetry , publisher =. doi:10.1016/j.meddos.2023.10.009 , number =

    2023 doi

  23. [31]

    The British Journal of Radiology , publisher =

    McGowan, S E and Burnet, N G and Lomax, A J , year =. The British Journal of Radiology , publisher =. doi:10.1259/bjr.20120288 , number =

    doi

  24. [32]

    and Cheung, Joey P

    Park, Peter C. and Cheung, Joey P. and Zhu, X. Ronald and Lee, Andrew K. and Sahoo, Narayan and Tucker, Susan L. and Liu, Wei and Li, Heng and Mohan, Radhe and Court, Laurence E. and Dong, Lei , year =. International Journal of Radiation Oncology*Biology*Physics , publisher =....

    2013 doi

  25. [33]

    Physics in Medicine &; Biology , publisher =

    Sterpin, E and Rivas, Sara T and Van den Heuvel, F and George, B and Lee, J A and Souris, K , year =. Physics in Medicine &; Biology , publisher =. doi:10.1088/1361-6560/abd22f , number =

    doi

  26. [34]

    , year =

    Souris, Kevin and Barragan Montero, Ana and Janssens, Guillaume and Di Perri, Dario and Sterpin, Edmond and Lee, John A. , year =. Medical Physics , publisher =. doi:10.1002/mp.13749 , number =

    doi

  27. [35]

    doi:10.1016/j.ejmp.2025.104938 , journal =

    Fracchiolla, Francesco and Widesott, Lamberto and Righetto, Roberto and Algranati, Carlo and Amelio, Dante and Trianni, Annalisa and Sterpin, Edmond and Lorentini, Stefano , year =. doi:10.1016/j.ejmp.2025.104938 , journal =

    2025

  28. [36]

    Gordon, J. J. and Sayah, N. and Weiss, E. and Siebers, J. V. , year =. Medical Physics , publisher =. doi:10.1118/1.3273063 , number =

    doi

  29. [37]

    2019 , month = apr, pages =

    Tilly, David and Holm, sa and Grusell, Erik and Ahnesj\". 2019 , month = apr, pages =. doi:10.1016/j.phro.2019.03.005 , journal =

    2019 doi

  30. [38]

    Chan and Houra Mahmoudzadeh and Thomas G

    Timothy C.Y. Chan and Houra Mahmoudzadeh and Thomas G. Purdie , title =. doi:10.1016/j.ejor.2014.04.038 , year =

    2014 doi

  31. [39]

    Schild and Martin Bues and Wei Liu , title =

    Yu An and Jianming Liang and Steven E. Schild and Martin Bues and Wei Liu , title =. doi:10.1002/mp.12001 , year =

    doi

  32. [40]

    Sobotta and M

    B. Sobotta and M. S\". doi:10.1118/1.3457333 , year =

    doi

  33. [41]

    Physics in Medicine and Biology , publisher =

    Bohoslavsky, Román and Witte, Marnix G and Janssen, Tomas M and van Herk, Marcel , year =. Physics in Medicine and Biology , publisher =. doi:10.1088/0031-9155/58/11/3563 , number =

    doi

  34. [42]

    Physics in Medicine and Biology , publisher =

    Breedveld, Sebastiaan and Storchi, Pascal R M and Heijmen, Ben J M , year =. Physics in Medicine and Biology , publisher =. doi:10.1088/0031-9155/54/23/011 , number =

    doi

  35. [43]

    Physics in Medicine and Biology , publisher =

    Chu, Millie and Zinchenko, Yuriy and Henderson, Shane G and Sharpe, Michael B , year =. Physics in Medicine and Biology , publisher =. doi:10.1088/0031-9155/50/23/003 , number =

    doi

  36. [44]

    Physics in Medicine & Biology , publisher =

    Fabiano, Silvia and Torelli, Nathan and Papp, Dávid and Unkelbach, Jan , year =. Physics in Medicine & Biology , publisher =. doi:10.1088/1361-6560/ac858f , number =

    doi

  37. [45]

    doi:10.1016/j.jcp.2013.12.025 , journal =

    Perkó, Zoltán and Gilli, Luca and Lathouwers, Danny and Kloosterman, Jan Leen , year =. doi:10.1016/j.jcp.2013.12.025 , journal =

    2013 doi

  38. [46]

    Physics in Medicine and Biology , publisher =

    Perkó, Zoltán and van der Voort, Sebastian R and van de Water, Steven and Hartman, Charlotte M H and Hoogeman, Mischa and Lathouwers, Danny , year =. Physics in Medicine and Biology , publisher =. doi:10.1088/0031-9155/61/12/4646 , number =

    doi

  39. [47]

    Physics in Medicine &; Biology , publisher =

    Rojo-Santiago, Jesús and Habraken, Steven J M and Romero, Alejandra Méndez and Lathouwers, Danny and Wang, Yibing and Perkó, Zoltán and Hoogeman, Mischa S , year =. Physics in Medicine &; Biology , publisher =. doi:10.1088/1361-6560/acead1 , number =

    doi

  40. [48]

    2021 , issn =

    Radiotherapy and Oncology , volume =. 2021 , issn =. doi:https://doi.org/10.1016/j.radonc.2021.07.028 , author =

    2021 doi

  41. [49]

    and Unipan, Mirko and Both, Stefan and Bosmans, Geert and Perkó, Zoltán and Korevaar, Erik and Hoogeman, Mischa S

    Rojo-Santiago, Jesús and Habraken, Steven J.M. and Unipan, Mirko and Both, Stefan and Bosmans, Geert and Perkó, Zoltán and Korevaar, Erik and Hoogeman, Mischa S. , year =. doi:10.1016/j.radonc.2024.110441 , journal =

    2024

  42. [50]

    Physics in Medicine &; Biology , publisher =

    Oud, Michelle and Breedveld, Sebastiaan and Rojo-Santiago, Jesús and Giżyńska, Marta Krystyna and Kroesen, Michiel and Habraken, Steven and Perkó, Zoltán and Heijmen, Ben and Hoogeman, Mischa , year =. Physics in Medicine &; Biology , publisher =. doi:10.1088/1361-6560/ad2a98 ...

    doi

  43. [51]

    Medical Physics , publisher =

    Fredriksson, Albin , year =. Medical Physics , publisher =. doi:10.1118/1.4737113 , number =

    doi

  44. [52]

    Medical Physics , publisher =

    Wahl, Niklas and Hennig, Philipp and Wieser, Hans‐Peter and Bangert, Mark , year =. Medical Physics , publisher =. doi:10.1002/mp.12775 , number =

    doi

  45. [53]

    and Alapetite, Claire and Burnet, Neil G

    Lambrecht, Maarten and Eekers, Daniëlle B.P. and Alapetite, Claire and Burnet, Neil G. and Calugaru, Valentin and Coremans, Ida E.M. and Fossati, Piero and Høyer, Morten and Langendijk, Johannes A. and Méndez Romero, Alejandra and Paulsen, Frank and Perpar, Ana and Renard, Lau...

    2018

  46. [54]

    Medical Physics , publisher =

    Cristoforetti, Remo and Hardt, Jennifer Josephine and Wahl, Niklas , year =. Medical Physics , publisher =. doi:10.1002/mp.17905 , number =

    doi

  47. [55]

    doi:10.48550/ARXIV.2601.08644 , author =

    2026 , copyright =. doi:10.48550/ARXIV.2601.08644 , author =

    2026 doi

  48. [56]

    doi:10.48550/ARXIV.2602.04375 , author =

    2026 , copyright =. doi:10.48550/ARXIV.2602.04375 , author =

    2026 doi

  49. [57]

    Smolyak, Sergey , booktitle=

  50. [58]

    Medical Physics , publisher =

    Bortfeld, Thomas , year =. Medical Physics , publisher =. doi:10.1118/1.598116 , number =

    doi

  51. [59]

    doi:10.2307/2371268 , year =

    Norbert Wiener , title =. doi:10.2307/2371268 , year =

    doi

  52. [60]

    doi:10.1137/s1064827501387826 , year =

    Dongbin Xiu and George Em Karniadakis , title =. doi:10.1137/s1064827501387826 , year =

    doi

  53. [61]

    2023 , month = mar, type =

    2023

  54. [62]

    doi:10.1016/j.semradonc.2017.11.005 , year =

    Jan Unkelbach and Harald Paganetti , title =. doi:10.1016/j.semradonc.2017.11.005 , year =

    2017 doi

  55. [63]

    Journal of Open Source Software , publisher =

    Biggs, Simon and Jennings, Matthew and Swerdloff, Stuart and Chlap, Phillip and Lane, Derek and Rembish, Jacob and McAloney, Jacob and King, Paul and Ayala, Rafael and Guan, Fada and Lambri, Nicola and Crewson, Cody and Sobolewski, Matthew , year =. Journal of Open Source Soft...

    doi

  56. [64]

    and Bortfeld, Thomas , year =

    Trofimov, Alexei and Unkelbach, Jan and DeLaney, Thomas F. and Bortfeld, Thomas , year =. Practical Radiation Oncology , publisher =. doi:10.1016/j.prro.2011.08.001 , number =

    2011 doi

  57. [65]

    2024 , howpublished =

    2024

  58. [66]

    Physics in Medicine &; Biology , publisher =

    Mescher, H and Ulrich, S and Bangert, M , year =. Physics in Medicine &; Biology , publisher =. doi:10.1088/1361-6560/aa8132 , number =

    doi

  59. [67]

    Physics in Medicine and Biology , publisher =

    Martin, Benjamin C and Bortfeld, Thomas R and Castañon, David A , year =. Physics in Medicine and Biology , publisher =. doi:10.1088/0031-9155/52/24/002 , number =

    doi

  60. [68]

    Physics in Medicine &; Biology , publisher =

    Quarz, A and Volz, L and Antink, C Hoog and Durante, M and Graeff, C , year =. Physics in Medicine &; Biology , publisher =. doi:10.1088/1361-6560/ad5bba , number =

    doi

  61. [69]

    Medical Physics , publisher =

    Wu, Qiuwen and Mohan, Radhe , year =. Medical Physics , publisher =. doi:10.1118/1.598932 , number =

    doi

  62. [70]

    Physics in Medicine &; Biology , publisher =

    van Haveren, R and Breedveld, S , year =. Physics in Medicine &; Biology , publisher =. doi:10.1088/1361-6560/ab1e17 , number =

    doi

  63. [71]

    Physics in Medicine and Biology , publisher =

    Unkelbach, J and Oelfke, U , year =. Physics in Medicine and Biology , publisher =. doi:10.1088/0031-9155/49/17/013 , number =

    doi

  64. [72]

    2010 , month = apr, pages =

    Journal of the ICRU , publisher =. 2010 , month = apr, pages =. doi:10.1093/jicru/ndq001 , number =

    2010 doi

  65. [73]

    and Habraken, Steven J.M

    de Jong, Jenneke I. and Habraken, Steven J.M. and Rojo-Santiago, Jesús and Lathouwers, Danny and Perkó, Zoltán and Breedveld, Sebastiaan and Hoogeman, Mischa S. , year =. doi:10.1016/j.radonc.2025.111171 , journal =

    2025

  66. [74]

    and Hong, Linda and Deasy, Joseph O

    Taasti, Vicki T. and Hong, Linda and Deasy, Joseph O. and Zarepisheh, Masoud , year =. Medical Physics , publisher =. doi:10.1002/mp.14148 , number =

    doi

  67. [75]

    International Journal of Particle Therapy , publisher =

    Zhang, Xiaodong , year =. International Journal of Particle Therapy , publisher =. doi:10.14338/ijpt-20-00078.1 , number =

    doi

  68. [76]

    doi:10.48550/ARXIV.2501.05818 , author =

    2025 , copyright =. doi:10.48550/ARXIV.2501.05818 , author =

    2025 doi

  69. [77]

    Medical Physics , publisher =

    Liu, Jiulong and Zhu, Ya‐Nan and Zhang, Xiaoqun and Gao, Hao , year =. Medical Physics , publisher =. doi:10.1002/mp.17929 , number =

    doi

  70. [78]

    Medical Physics , publisher =

    Fan, Qingkun and Zhao, Lewei and Li, Xiaoqiang and Hu, Jie and Lu, Xiliang and Yang, Zhijian and Zhang, Sheng and Yang, Kunyu and Ding, Xuanfeng and Liu, Gang and Dai, Shuyang , year =. Medical Physics , publisher =. doi:10.1002/mp.17285 , number =

    doi

  71. [79]

    doi:10.48550/ARXIV.2504.10814 , author =

    2025 , copyright =. doi:10.48550/ARXIV.2504.10814 , author =

    2025 doi arXiv

  72. [80]

    Physics in Medicine & Biology , publisher =

    Pastor-Serrano, Oscar and Perkó, Zoltán , year =. Physics in Medicine & Biology , publisher =. doi:10.1088/1361-6560/ac692e , number =

    doi

  73. [81]

    Physics in Medicine & Biology , publisher =

    Holmes, Jason and Feng, Hongying and Zhang, Lian and Fix, Michael K and Jiang, Steve B and Liu, Wei , year =. Physics in Medicine & Biology , publisher =. doi:10.1088/1361-6560/ad67a7 , number =

    doi

  74. [82]

    Breedveld, Sebastiaan and Storchi, Pascal R. M. and Voet, Peter W. J. and Heijmen, Ben J. M. , year =. Medical Physics , publisher =. doi:10.1118/1.3676689 , number =

    doi

  75. [83]

    Dual-energy computed tomography to assess intra- and inter-patient tissue variability for proton treatment planning of patients with brain tumor

    Wohlfahrt, Patrick and M \"o hler, Christian and Troost, Esther G C and Greilich, Steffen and Richter, Christian. Dual-energy computed tomography to assess intra- and inter-patient tissue variability for proton treatment planning of patients with brain tumor. Int. J. Radiat. O...

    2019

  76. [84]

    Physics in Medicine &; Biology , publisher =

    Vazquez, Ivan and Gronberg, Mary P and Zhang, Xiaodong and Court, Laurence E and Zhu, X Ronald and Frank, Steven J and Yang, Ming , year =. Physics in Medicine &; Biology , publisher =. doi:10.1088/1361-6560/accc08 , number =

    doi

  77. [85]

    Physics in Medicine &; Biology , publisher =

    de Jong, Jenneke I and Habraken, Steven J M and Fredriksson, Albin and Sundstr\". Physics in Medicine &; Biology , publisher =. 2026 , month = May, pages =. doi:10.1088/1361-6560/ae6223 , number =

    2026 doi

  78. [86]

    Physics in Medicine and Biology , publisher =

    Aleman, Dionne M and Glaser, Daniel and Romeijn, H Edwin and Dempsey, James F , year =. Physics in Medicine and Biology , publisher =. doi:10.1088/0031-9155/55/18/013 , number =

    doi

  79. [87]

    SIAM Journal on Optimization , publisher =

    Gondzio, Jacek and Grothey, Andreas , year =. SIAM Journal on Optimization , publisher =. doi:10.1137/060678129 , number =

    doi

  80. [88]

    doi:10.1016/j.ejmp.2021.07.012 , journal =

    Fracchiolla, Francesco and Engwall, Erik and Janson, Martin and Tamm, Fredrik and Lorentini, Stefano and Fellin, Francesco and Bertolini, Mattia and Algranati, Carlo and Righetto, Roberto and Farace, Paolo and Amichetti, Maurizio and Schwarz, Marco , year =. doi:10.1016/j.ejmp...

    2021 doi

  81. [89]

    doi:10.1016/j.radonc.2021.02.034 , journal =

    Kouwenberg, Jasper and Penninkhof, Joan and Habraken, Steven and Zindler, Jaap and Hoogeman, Mischa and Heijmen, Ben , year =. doi:10.1016/j.radonc.2021.02.034 , journal =

    2021 doi

  82. [90]

    International Journal of Networked and Distributed Computing , publisher =

    Kalantzis, Georgios and Leventouri, Theodora and Tachibana, Hidenobu and Shang, Charles , year =. International Journal of Networked and Distributed Computing , publisher =. doi:10.2991/ijndc.2015.3.4.5 , number =

    2015 doi

  83. [91]

    Physics in Medicine &; Biology , publisher =

    Feng, Hongying and Holmes, Jason M and Vora, Sujay A and Stoker, Joshua B and Bues, Martin and Wong, William W and Sio, Terence S and Foote, Robert L and Patel, Samir H and Shen, Jiajian and Liu, Wei , year =. Physics in Medicine &; Biology , publisher =. doi:10.1088/1361-6560...

    doi

  84. [92]

    , year =

    Ma, Jiasen and Beltran, Chris and Seum Wan Chan Tseung, Hok and Herman, Michael G. , year =. Medical Physics , publisher =. doi:10.1118/1.4901522 , number =

    doi

  85. [93]

    doi:10.1016/j.radonc.2019.01.020 , journal =

    Loi, Mauro and Magallon-Baro, Alba and Suker, Mustafa and van Eijck, Casper and Sharma, Aman and Hoogeman, Mischa and Nuyttens, Joost , year =. doi:10.1016/j.radonc.2019.01.020 , journal =

    2019 doi

  86. [94]

    Physics in Medicine &; Biology , publisher =

    Buti, Gregory and Souris, Kevin and Maria Barragán Montero, Ana and Aldo Lee, John and Sterpin, Edmond , year =. Physics in Medicine &; Biology , publisher =. doi:10.1088/1361-6560/ac1265 , number =

    doi

Pith tools

Reviewed August 2, 2026 · model on record in the stance chip above.