Interplay-robust optimization for treating irregularly breathing lung patients with pencil beam scanning

Albin Fredriksson; Anders Forsgren; Ivar Bengtsson; Ye Zhang

REVIEW 4 major objections 6 minor 20 references

Interplay-robust optimization for treating irregularly breathing lung patients with pencil beam scanning

T0 review · 4 major / 6 minor · reviewed 2026-08-12 · deepseek-v4-flash

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Pith's one-line read This paper shows that explicitly modeling the time-dependent interference between pencil beam delivery and irregular breathing during plan optimization raises near-worst-case target coverage in lung proton therapy and, at equal coverage…

desk verdict A transparent simulation study extending IPRO to amplitude-irregular breathing; the advantage over 4DRO holds within the matched-distribution setup, but external motion variability remains untested. read the letter →

arxiv 2411.16230 v1 pith:4EAWL653 submitted 2024-11-25 physics.med-ph math.OC

Ivar Bengtsson , Anders Forsgren , Albin Fredriksson , Ye Zhang This is my paper · ORCID

classification physics.med-phmath.OC

keywords interplayeffectrobustoptimizationpencilbeamscanningprotontherapy4Ddosecomputationirregularbreathinglungcancersynthetic4DCT

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

Interplay-robust optimization (IPRO) treats the interference between the scanning beam's arrival times and the patient's breathing as an uncertainty to be optimized against, rather than averaged away. This paper asks whether IPRO still helps when breathing is irregular, varying in both period and amplitude, and when only one breathing cycle is available for planning. On synthetic 4DCTs built from 4DMRI motion patterns, IPRO and a single-cycle variant (IPRO-1C) improved the near-worst-case target coverage (5th percentile CTV D98) for every patient case compared with conventional 4D robust optimization. After scaling all plans to equal target coverage, IPRO with 49 scenarios lowered near-worst-case organ-at-risk dose by an average of 4.2%, and IPRO-1C with 9 scenarios, at the same computational cost as 4DRO, lowered it by 1.7%. If the result holds in the clinic, explicit modeling of interplay during planning could reduce the need for gating, breath-hold, and re-scanning.

What carries the argument

The central object is the 4D dose computation (4DDC) with phase sorting: each pencil beam spot's dose is computed on the motion state it hits during delivery, deformed to a reference state, and summed. Interplay-robust optimization minimizes a worst-case objective over a set of motion scenarios, each a random concatenation of breathing cycles; the delivery time structure is updated heuristically as spot weights change. IPRO-1C builds its scenario set from one breathing cycle, varied by period-scaling factors and start-phase shifts, to test how much robustness can be recovered when data are limited.

What would settle it

Simulate delivery of the IPRO and 4DRO plans using evaluation scenarios drawn from a breathing distribution with, say, 30% larger amplitudes and a uniformly random start phase per beam, and check whether the 5th-percentile CTV D98 of IPRO still exceeds 4DRO; if the margin vanishes or reverses, the claim fails for unrepresented motion states.

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Extended reading notes

Core claim

The authors claim that explicitly modeling the interplay effect, the time-dependent interference between pencil beam spot delivery and breathing motion, during robust optimization produces lung cancer proton plans that are more robust to irregular breathing than plans from phase-averaged 4D robust optimization. Using synthetic 4DCTs with multiple breathing cycles of varying period and amplitude, they show that IPRO, which optimizes against randomly concatenated breathing cycles, and IPRO-1C, which generates scenarios from a single breathing cycle with scaled periods and shifted start phases, both increase the 5th-percentile CTV D98 relative to 4DRO in all four patient cases. After normalizing each plan to match the 4DRO near-worst-case target coverage, the robustly optimized plans spare organs at risk more: IPRO with 49 scenarios reduces the 95th-percentile OAR dose by an average of 4.2%, and IPRO-1C with 9 scenarios by 1.7% while requiring no more dose computations than 4DRO.

Load-bearing premise

The evaluation scenarios are built from the same synthetic motion model and cycle statistics as the optimization scenarios, with every breathing cycle assumed to start at end-exhale; if a patient's real on-couch breathing differs in amplitude, period, or start phase, the reported robustness gain shrinks or disappears.

Editorial extensions

If this is right

IPRO and IPRO-1C raise the 5th-percentile CTV D98 relative to 4DRO in every patient case studied, with little change to dose homogeneity.
After normalizing to equal target coverage, IPRO with 49 scenarios reduces the near-worst-case (95th percentile) OAR dose by an average of 4.2%, and IPRO-1C with 9 scenarios by 1.7%.
Increasing the scenario count from 9 to 49 typically improves robustness, and using multiple breathing cycles outperforms a single cycle when that single cycle is unrepresentative of the evaluation motion.
IPRO-1C with 9 scenarios uses the same number of motion states and dose computations as 4DRO, so the robustness gain comes at no added computational cost.

Reading between the lines

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

If the same margin persists under randomized start phases and day-to-day amplitude drift, IPRO could allow fewer re-scans or wider gating windows, shortening treatment times and improving comfort, an implication the authors state as motivation but do not demonstrate.
The 4.2% OAR improvement is likely an optimistic bound because evaluation scenarios are drawn from the same motion model used for optimization; a fairer clinical test would use independent motion data acquired on a different day.
The IPRO-1C result suggests that a single pre-treatment breathing cycle, augmented by period and phase perturbations, may be sufficient to capture the interplay uncertainty; a testable extension would compare IPRO-1C against gated delivery on the same patients.

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Editorial analysis

A structured set of objections, weighed in public.

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

Desk Editor's Note

read the letter

Quick take: this is a solid, transparent simulation study that extends IPRO from frequency-only uncertainty to amplitude-irregular breathing, and it adds a single-cycle variant (IPRO-1C) that looks clinically relevant. Within the stated simulation envelope, the claims hold up. The biggest caveat, which the authors themselves flag, is that the evaluation scenarios are generated from the same motion model and phase-start assumption as the optimization scenarios, so the magnitude of the benefit in real patients is still an open question.

What's new here is legitimate: prior IPRO work (Engwall et al.) varied breathing period only; this paper varies amplitude too, uses multi-cycle synthetic 4DCTs from 4DMRI data, and evaluates on held-out cycles. The IPRO-1C idea, generating scenarios by period-scaling and phase-shifting a single cycle, is a practical contribution because it can be done with the data you'd have in a typical clinic. The evaluation design, 500 scenarios per plan and disjoint optimization/evaluation cycle sets, is a clear step up from earlier studies.

The paper is also honest. The limitations section names the missing ribcage motion, the absence of range/setup errors, and the assumption that each beam starts at end-exhale. The post-hoc case 3b* is presented as an illustration, not hidden. The normalization to equal target coverage is described with its caveat (dose scaling without recomputing the time structure), which is minor since the scaling factors are small.

The soft spots are proportional. Four synthetic cases and no code or data mean the quantitative results shouldn't be treated as established. The matched-distribution evaluation is the main one: the held-out cycles are statistically similar to the optimization cycles (Table 1), and every cycle starts at end-exhale. If treatment-day breathing has different amplitudes or phase at beam start, the IPRO advantage could shrink. The authors acknowledge exactly this in Section 4. That doesn't undermine the study; it bounds it.

The spot-to-state assignment heuristic (updated every 10 iterations) is inherited from prior work and is a known limitation, not a new flaw.

Who is this for? Researchers in proton therapy motion management and robust optimization. It's a worthwhile contribution. I'd send it to peer review, asking the referees to focus on whether the evaluation distribution is wide enough and whether the OAR improvements survive a reasonable perturbation of the motion model.

Referee Report

4 major / 6 minor

Summary. The paper proposes and evaluates interplay-robust optimization (IPRO) for pencil beam scanning proton therapy of lung patients with irregular breathing, extending prior work on frequency uncertainty to include amplitude variability. Motion is modeled with synthetic 4DCTs derived from 4DMRI patterns; optimization and evaluation scenarios are generated by randomly concatenating held-out breathing cycles. IPRO and a single-cycle variant IPRO-1C are compared with 4DRO on four synthetic patient cases. The authors report improved near-worst-case target coverage for IPRO and IPRO-1C, and, after equal-coverage dose normalization, reduced OAR doses with average near-worst-case improvements of 4.2% (IPRO-49S) and 1.7% (IPRO-1C-9S).

Significance. If the result holds outside the simulated setting, it is clinically relevant: explicitly modeling the spot-to-phase interplay during optimization could reduce the need for gating or rescanning, and IPRO-1C-9S is claimed to have computational cost comparable to 4DRO. The study has notable strengths: it uses a published delivery-time model, evaluates each plan in 500 motion scenarios as recommended in the literature, and is transparent about its limitations. However, the evidence base is four synthetic cases with evaluation scenarios drawn from the same motion model used for optimization, so the quantitative improvements reported here should be read as conditional on that matched distribution until out-of-distribution robustness is demonstrated.

major comments (4)

[Sec. 2.4 and Sec. 4] The central claim that IPRO and IPRO-1C improve target coverage for irregularly breathing lung patients is supported only under a matched-distribution simulation: evaluation scenarios are generated by randomly concatenating held-out breathing cycles from the same s4DCT motion model, and every cycle is assumed to start at end-exhale with no phase uncertainty at beam start (Sec. 2.4). The authors themselves state in Sec. 4 that the case that may compromise IPRO's robustness is when motion states occurring during delivery are not represented in the optimization scenarios. The abstract's phrasing that IPRO 'increased the target coverage for all patient cases' therefore overreaches beyond the simulation setting. Please add an explicit out-of-distribution test, for example evaluating with a random start-phase offset or with breathing amplitude/period distributions deliberately perturbed relative to the optimization set, and temper the conclusions accordingly.
[Sec. 3, Table 2] The normalized comparison used to support the OAR-sparing claims is affected by a modeling inconsistency: all evaluation doses are scaled by a constant factor to match the 4DRO 5th-percentile CTV D98, and 'the effect on the time structure was ignored.' Uniformly scaling spot weights changes the delivery time structure, which changes the spot-to-motion-state assignment in Eq. (2) and hence the actual interplay-affected dose that would be delivered. The reported OAR improvements, including the 4.2% average for IPRO-49S, are therefore computed from doses that would not be delivered by the scaled plans. Please re-optimize the normalized plans, include the time-structure effect of the scaling, or quantitatively assess the error introduced by ignoring it.
[Table 2 and Sec. 3] The key numerical results are point estimates without confidence intervals or hypothesis tests. The 5th and 95th percentiles over 500 simulated scenarios are random quantities, and differences of 1.7% or even 4.2% could be within scenario sampling noise. Please provide bootstrap confidence intervals or other uncertainty quantification for the reported changes, and state exactly which OAR metrics and patient cases are included in the 'averaging' that produced the 4.2% and 1.7% figures in the abstract.
[Sec. 3.4, Case 3b*] Case 3b* is introduced after observing that the initial IPRO-1C breathing cycle was unrepresentative of the evaluation motion (Sec. 3.4). This post-hoc selection means that the IPRO-1C results in Table 2 are a mixture of a pre-specified case and a repaired case, so they do not provide an unbiased estimate of the method's typical performance when a single cycle is chosen. Combined with the small number of geometries and motion patterns, this limits the strength of the claim that IPRO-1C reliably improves over 4DRO. Please present 3b* explicitly as a post-hoc sensitivity analysis and adjust the corresponding conclusions.

minor comments (6)

[Figure 3 caption] The caption states that the whiskers indicate the 5th and 95th percentiles but then repeats the same information; please clarify whether the box edges are quartiles and the whiskers are the stated percentiles, since this differs from standard Tukey boxplots.
[Sec. 2.7] The IPRO-1C scenario grids for period scaling and start-phase shift are described only in prose; a small table or equation would make the scenario construction easier to follow and reproduce.
[Abstract and Sec. 3] The abstract's '4.2 %' and '1.7 %' improvements should specify the exact set of OAR metrics and cases over which the average is taken, because Table 2 shows considerable variation by case and metric.
[Sec. 2.1, Eq. (1)] The set I^p(x; s) is introduced as 'I p(x; s)' in the text but printed with a superscript in Eq. (1); please unify the notation for readability.
[References] Reference [15] is cited as 's4DCT(MRI)' in the bibliography while the text uses 's4DCT'; please add a clear definition at first use and make the reference title consistent.
[Sec. 2.6] The text says the template plan was optimized with 40 iterations of 4DRO and that the 4DRO plan used 40 additional iterations; please clarify whether the total number of iterations for the final 4DRO plan is 80 and how this compares with the 40 iterations used for the other methods.

Circularity Check

0 steps flagged · score 0.0 of 10

No significant circularity; the IPRO evaluation uses disjoint held-out breathing cycles and the cited prior IPRO work is not load-bearing for the numerical claim.

full rationale

The paper's central claim is that IPRO and IPRO-1C improve target coverage and OAR sparing relative to 4DRO under irregular-breathing scenarios. Evaluation (Sec. 2.5) uses 500 scenarios formed by randomly concatenating held-out breathing cycles (even indices), while IPRO optimization scenarios are formed by the same random-concatenation procedure from odd-index cycles (Sec. 2.4 and Sec. 2.7). This makes the evaluation in-distribution with the optimization scenario model, but it is not circular in the prohibited sense: no outcome quantity is used to define the method, no parameter is fitted to the evaluation data, and the evaluation scenarios are not the same scenarios used for optimization. The stated 4.2% and 1.7% OAR reductions arise from a fixed normalization to equal 5th-percentile CTV D98 and are computed on the evaluation set rather than being built into the objective. The paper explicitly acknowledges the generalizability boundary: 'the case that may compromise the robustness aimed at by IPRO is when the motion states that may occur during treatment delivery are not represented in the scenarios used during optimization' and 'Larger discrepancies between the data used for optimization and evaluation, respectively, are expected to decrease the robustness gain of IPRO.' These are honest limitations about distribution shift, not reductions by construction. The only self-citation with author overlap (Fredriksson is a coauthor of Engwall et al. [14]) is used to motivate the IPRO approach and a heuristic time-structure update; the present derivation and numerical comparisons are self-contained and do not rest on an unverified theorem from that citation. Therefore no circular step is exhibited and the score is 0.

Assumptions & free parameters 6 free parameters · 6 assumptions · 0 invented entities

The central result rests less on new physics than on a chain of modeling and algorithmic choices: the realism of the synthetic motion model, the accuracy of the phase-sorted 4D dose calculation, the validity of the fixed spot-to-state heuristic, and the hand-chosen scenario grids and objective weights. These choices are transparently described but not independently verified here.

free parameters (6)

Weighted-power-mean exponent (power=8) = 8
Hand-chosen smoothing of the max operator in Problem (4); it changes how much the worst scenarios influence the optimized plan.
IPRO-1C period scaling grid = e.g., {0.9,1,1.1} for 9S, up to {0.7,...,1.3} for 49S
Hand-chosen grid of breathing-period scaling factors used to generate scenarios from a single breathing cycle; not derived from data.
IPRO-1C start-phase shift grid = e.g., {-1,0,+1} for 9S, up to {-3,...,+3} for 49S
Hand-chosen grid of start-phase shifts; together with period scaling it defines the IPRO-1C scenario set.
Number of optimization scenarios = 9, 25, 49
Scenario counts are chosen for comparison; the reported OAR improvements increase with scenario count, so the quantitative result is contingent on this choice.
Patient-specific objective weights = Table 3 values, e.g., CTV min dose weights 400, 1200, 80
Objective weights are tuned per patient to meet RTOG 1308 dosimetric criteria; they determine the trade-off between target coverage and OAR dose, hence the normalized OAR comparisons.
Normalization dose-scaling factor = Per-plan factor to match 4DRO 5th percentile CTV D98
All evaluation doses are rescaled so that every plan has the same near-worst-case target coverage before reporting OAR improvements; the 4.2% and 1.7% numbers are conditional on this normalization.

assumptions (6)

domain assumption Synthetic 4DCTs from 4DMRI deformation accurately represent realistic irregular breathing motion, including amplitude variation.
Sec. 2.3.2 and 2.4; the entire scenario set is built from these s4DCTs, and no independent patient-verified motion model is used.
domain assumption Breathing can be decomposed into cycles, each starting at end-exhale, with no uncertainty in the breathing phase at beam start.
Sec. 2.4 states this assumption explicitly: 'there is no uncertainty about the breathing cycle phase at the start of the delivery of each beam.'
domain assumption Phase-sorted 4D dose computation with the fitted IBA delivery time model is accurate enough for comparing planning methods.
Sec. 2.1 and 2.3.1; the dose model, including the dose-rate fit, scanning-speed linear fit, and 1230 ms energy switch, is an input from Pfeiler et al. and is not validated here.
ad hoc to paper Fixing the spot-to-motion-state assignment during optimization and updating every 10 iterations is a valid heuristic for the non-convex interplay problem.
Sec. 2.2; this heuristic follows previous work and is necessary for tractability, but it is not proved to converge to a true minimax solution.
domain assumption The weighted-power-mean objective with parameter 8 adequately approximates the worst-case objective.
Sec. 2.7; the approximation smooths the max and may change which scenario drives the solution.
domain assumption 500 evaluation scenarios provide statistically accurate estimates of interplay dose variation.
Sec. 2.5, citing Pastor-Serrano et al.; the evaluation distributions rest on this recommendation.

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Cite this review

Pith. "Pith review of Interplay-robust optimization for treating irregularly breathing lung patients with pencil beam scanning." pith.science (2026). https://pith.science/paper/4EAWL653

@misc{pith2026241116230,
  author       = {Pith},
  title        = {Pith review of: Interplay-robust optimization for treating irregularly breathing lung patients with pencil beam scanning},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/4EAWL653}},
  note         = {Machine review of arXiv:2411.16230}
}

read the original abstract

The steep dose gradients obtained with pencil beam scanning allow for precise tumor targeting at the cost of high sensitivity to uncertainties. Robust optimization is commonly applied to mitigate uncertainties in density and patient setup, while its application to motion management, called 4D-robust optimization (4DRO), is typically accompanied by other motion mitigation techniques. In particular, current commercial implementations of 4DRO do not model the interplay effect between the delivery time structure and the patient's motion. Previously, it has been shown that Interplay-robust optimization (IPRO) can mitigate the interplay effect given uncertainty in the patient's breathing frequency. In this study, we investigate and evaluate IPRO in the context where the motion uncertainty is extended to also include variations in breathing amplitude. We model the patients' motion using synthetic 4DCTs, each created by deforming a reference CT based on a motion pattern obtained with 4DMRI. Each synthetic 4DCT contains multiple breathing cycles, partitioned into two sets for scenario generation: one for optimization and one for evaluation. Motion scenarios are then created by randomly concatenating breathing cycles varying in period and amplitude. In addition, a method considering a single breathing cycle for generating optimization scenarios (IPRO-1C) is developed to investigate to which extent robustness can be achieved with limited information. IPRO and IPRO-1C increased the target coverage for all patient cases in terms of the near-worst-case (5th percentile) CTV D98, compared to 4DRO. After normalization of plan doses to equal target coverage, IPRO with 49 scenarios resulted in the greatest decreases in OAR dose, with near-worst-case (95th percentile) improvements averaging 4.2 %. IPRO-1C with 9 scenarios, with comparable computational demands as 4DRO, decreased OAR dose by 1.7 %.

Figures

Figures reproduced from arXiv: 2411.16230 by the authors.

**Figure 2.** Amplitudes corresponding to the first 30 seconds of three scenarios [PITH_FULL_IMAGE:figures/full_fig_p008_2.png] view at source ↗

**Figure 3.** Distributions of CTV and medulla dose statistics for each of the [PITH_FULL_IMAGE:figures/full_fig_p013_3.png] view at source ↗

Figures from the paper (2 more)

**Figure 3.** Figure 3: (continued) Distributions of CTV and OAR dose statistics for each of 14 [PITH_FULL_IMAGE:figures/full_fig_p014_3.png]

**Figure 4.** Figure 4: The distribution of objective function values over the evaluation mo [PITH_FULL_IMAGE:figures/full_fig_p018_4.png]

Discussion (0). Continue with ORCID to comment.

Reference graph

Works this paper leans on

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Pith tools

Reviewed August 12, 2026 · model on record in the stance chip above.

[1] [1]

Treatment planning and verification of proton therapy using spot scanning: Initial experiences

A. J. Lomax et al. “Treatment planning and verification of proton therapy using spot scanning: Initial experiences”. Medical Physics 31.11 (2004)

2004

[2] [2]

Minimax optimization for handling range and setup uncertainties in proton therapy

A. Fredriksson, A. Forsgren, and B. H ˚ ardemark. “Minimax optimization for handling range and setup uncertainties in proton therapy”. Medical Physics 38.3 (2011)

work page 2011

[3] [3]

Treatment planning of scanned proton beams in RaySta- tion

M. Janson et al. “Treatment planning of scanned proton beams in RaySta- tion”. Medical Dosimetry. Treatment Planning in Proton Therapy 49.1 (1, 2024)

work page 2024

[4] [4]

A review of proton therapy – Current status and future di- rections

R. Mohan. “A review of proton therapy – Current status and future di- rections”. Precision Radiation Oncology6.2 (2022)

work page 2022

[5] [5]

A survey of practice patterns for real-time intrafrac- tional motion-management in particle therapy

Y. Zhang et al. “A survey of practice patterns for real-time intrafrac- tional motion-management in particle therapy”. Physics and Imaging in Radiation Oncology26 (1, 2023)

work page 2023

[6] [6]

Surveying the clinical practice of treatment adaptation and motion management in particle therapy

B. Kn¨ ausl et al. “Surveying the clinical practice of treatment adaptation and motion management in particle therapy”. Physics and Imaging in Radiation Oncology27 (1, 2023)

work page 2023

[7] [7]

A review of the clinical introduction of 4D particle therapy research concepts

B. Kn¨ ausl et al. “A review of the clinical introduction of 4D particle therapy research concepts”. Physics and Imaging in Radiation Oncology 29 (1, 2024)

work page 2024

[8] [8]

Intrafractional motion during proton beam scanning

J. Lambert et al. “Intrafractional motion during proton beam scanning”. Physics in Medicine & Biology50.20 (2005)

work page 2005