{"id":"14f7067b-2a32-4d83-8a29-fd40efc4889f","arxiv_id":"2411.17578","paper_version":1,"verdict":"CONDITIONAL","confidence":"MODERATE","novelty_score":5.0,"correctness_risk":"medium","formal_verification":"none","parameter_count":5,"one_line_summary":"Multi-IMPT, which alternates small subsets of beam angles across fractions and optimizes biologically effective dose, can match proton arc therapy plan quality in four treatment planning cases.","lead":"This paper proposes delivering a set of standard proton beam plans, each using a different small group of beam angles per treatment session, to mimic the dose quality of continuous proton arc therapy. The authors report that in four patient cases the new multi-IMPT approach achieves similar, sometimes better, dose distributions to arc therapy while avoiding the slow energy changes that make arc delivery inefficient.","discovery_kind":"new_method","skeptic_critique":{"model":"deepseek-v4-flash","headline":"Reported ARC and multi-IMPT plans violate the paper's own stated BED constraints (prostate ARC exceeds bladder/rectum BED50 and BED20 bounds; brain plans exceed brainstem and brain BEDmax bounds), so the equivalence comparison may be between infeasible, non-deliverable plans.","rationale":"The reader's conditional verdict correctly identifies the LQ/alpha-beta assumption and the ARC comparator as key simplifications, and the rationale also notes in passing that several reported BED constraints are violated by the ARC plans. I focus on constraint feasibility because it is the most immediately falsifiable and load-bearing issue: the entire evidence for equivalence is a table of BED metrics under stated upper bounds. If those bounds are not actually satisfied, the plans used in the comparison are not the constrained plans specified by Eq. (1), and the reported BED numbers cannot be interpreted as evidence that Multi-IMPT can deliver ARC-equivalent quality under the stated constraints. The pattern is not a minor reporting detail: feasibility is a precondition for any clinical transfer. The concrete check separates the two possible causes (post-hoc normalization versus failure of the ADMM/ICR solve) and forces the authors to either show feasible plans or weaken the claim. This concern does not change the overall verdict category: the paper still merits conditional acceptance only after the feasibility issue and the overclaims in the title and abstract are resolved.","tokens_in":11850,"tokens_out":12340,"duration_ms":119420,"concrete_test":"Re-run all four cases with the exact constraint values in Tables 1-4 and output, for every OAR metric, the achieved value and the slack (or violation) before and after the 95%-target normalization. Then repeat the ARC-vs-multi-IMPT comparison keeping only plans whose BED constraints are feasible; if the normalization is the cause, report both normalized and unnormalized plans and state whether the delivered plan satisfies the constraints. If the brain multi-IMPT plan still has brainstem BEDmax 87.91 Gy against an 83.7 Gy bound, or the prostate ARC plan still has bladder BED50 44.60 Gy against a 40 Gy bound, the central claim of BED-based equivalence is unsupported unless the constraint values or the objective are revised.","verdict_should_be":"CONDITIONAL","load_bearing_attack":"The central comparison is between BED-constrained plans, but Tables 1-4 contain repeated violations of the stated BED constraints. Prostate (Table 1): bladder BED50 upper bound 40 Gy, ARC reports 44.60 Gy; bladder BED20 upper bound 63 Gy, ARC 67.75 Gy; rectum BED50 upper bound 40 Gy, ARC 45.02 Gy; rectum BED20 upper bound 63 Gy, ARC 65.70 Gy. Brain (Table 3): brainstem BEDmax upper bound 83.7 Gy, ARC 85.25 Gy and multi-IMPT 87.91 Gy; brain BEDmax upper bound 96 Gy, ARC 104.31 Gy and multi-IMPT 109.37 Gy. The paper states that BEDp means at most p% of OAR voxels should receive BED greater than the upper bound, so these values are direct violations, not harmless reporting artifacts. The likely cause is the post-optimization normalization ensuring 95% of the target receives 100% of the prescription dose, which rescales OAR doses upward; alternatively, the ICR/ADMM solver did not enforce the constraints. In either case, the reported 'equivalent plan quality' is not demonstrated for clinically deliverable, constraint-satisfying plans. Since the brain case shows both comparators violating BEDmax constraints, the equivalence is between infeasible plans, and the conclusion that Multi-IMPT can replace ARC in clinical practice is not supported by the presented data.","agreement_with_reader":"partial"},"referee_report":{"model":"deepseek-v4-flash","summary":"The paper proposes multi-IMPT, a delivery scheme in which a different subset of four beam angles is used in each treatment fraction, and optimizes the biologically effective dose (BED) to organs at risk while maintaining physical dose to the target, with the goal of approximating proton arc therapy (ARC) plan quality. The authors formulate a non-convex BED-constrained optimization problem, solve it with iterative convex relaxation and ADMM, and present planning comparisons against an ARC model (equal dose per fraction, beams spaced at 15° over 360°) for prostate, lung, brain, and head-and-neck cases. They report similar or slightly better plan quality for multi-IMPT in most cases and conclude that multi-IMPT is biologically equivalent to ARC.","tokens_in":12181,"tokens_out":5275,"duration_ms":50565,"significance":"If substantiated, the approach would be clinically valuable: proton centers without arc delivery capabilities could approximate ARC dosimetric benefits using standard IMPT delivery. The paper has several strengths: it formulates a concrete, reproducible optimization model; the method is computationally tractable; and the planning comparisons cover four distinct anatomical sites. The central claim, however, rests on the reported plans satisfying the stated BED constraints and on the ARC comparator faithfully representing clinical proton arc therapy. The manuscript also makes a falsifiable prediction that multi-IMPT can match ARC's OAR BED, which is a useful contribution. The main weaknesses are that several reported plans violate the paper's own constraints, the ARC model is simplified, and the results are descriptive rather than statistically quantified.","major_comments":[{"comment":"The reported plans violate the BED constraints that the paper defines as hard constraints in Eq. (1). In Table 1, ARC bladder BED50 is 44.60 Gy against an upper bound of 40 Gy, bladder BED20 is 67.75 Gy against 63 Gy, rectum BED50 is 45.02 Gy against 40 Gy, and rectum BED20 is 65.70 Gy against 63 Gy. In Table 3, brainstem BEDmax is 85.25 Gy (ARC) and 87.91 Gy (multi-IMPT) against 83.7 Gy, and brain BEDmax is 104.31 Gy (ARC) and 109.37 Gy (multi-IMPT) against 96 Gy. Since the paper states that BEDp means at most p% of OAR voxels should receive BED greater than the upper bound, these values are direct violations, not reporting artifacts. The equivalence comparison is therefore between infeasible, non-clinically-deliverable plans, and the conclusion that multi-IMPT can replace ARC is not supported by the presented data. The authors should re-optimize with constraints enforced or provide a clear explanation of why these violations are acceptable.","section":"Tables 1 and 3"},{"comment":"There is an internal inconsistency between the stated target DVH-min constraint and the implemented constraint. Section 2.1, constraint 4, defines a physical-dose constraint: at least p fraction of target voxels receive physical dose d_jt^T >= d_min. However, Eq. (1) and Eq. (2) replace this with a BED constraint of the form sum_t z_jt^T + rho_T sum_t (z_jt^T)^2 >= BED_DVH^T, which is a different object and is not defined in the text. This means the optimization that produced the reported plans may not match the problem formulation in the paper. Please clarify which constraint was actually used, define BED_DVH^T and rho_T, and correct the equations accordingly.","section":"Section 2.1 and Eq. (1)"},{"comment":"The ARC comparator is modeled as u_t = u for all fractions, i.e., the same plan is delivered in every fraction with all fields active. This equal-dose-per-fraction assumption is a simplification of clinical proton arc therapy, where the gantry rotates continuously and the delivered dose per control point may vary. The equivalence claim is therefore only with respect to this simplified ARC model. The authors should justify that this is a representative ARC baseline or investigate how the comparison changes under a more general ARC delivery model.","section":"Section 2.2"},{"comment":"The results are based on four single-patient cases (one per site) and are compared descriptively, with no error bars, uncertainty quantification, or statistical tests. The statement in the conclusion that the dosimetric differences are 'not clinically significant' is consequently not substantiated. The authors should either add a quantitative analysis (e.g., multiple patients per site or at least explicit thresholds of clinical significance) or temper the claims to reflect the limited evidence.","section":"Section 3"}],"minor_comments":[{"comment":"The symbol 'px' is used for the prescription dose but is never defined; please define it explicitly.","section":"Eq. (1)"},{"comment":"The active index set uses the condition j >= p*n, which is ambiguous when p*n is not an integer; please clarify the rounding convention and whether the constraint should apply to the floor or ceiling of p*n.","section":"Section 2.1"},{"comment":"The projection formulas for z_jt contain expressions for q that are not fully legible due to typesetting; please rewrite them explicitly so the algorithm is reproducible.","section":"Appendix A"},{"comment":"Table 2 lists Heart BEDmean and Table 4 lists R Parotid BEDmax without upper bounds; please state explicitly whether these structures were unconstrained or whether the bounds were omitted from the table.","section":"Tables 2 and 4"},{"comment":"The definition of the active index set uses j >= p*n, but for a constraint that at most p% of voxels exceed the bound, the relevant index should be the first voxel above the allowed fraction; please reconcile the indexing with the stated clinical meaning.","section":"Section 2.1, BED-DVH constraint"},{"comment":"In the algorithm outline, Step 4b says 'update primal variables' and Step 4c says 'update dual variables', but in the Appendix the order of presentation is reversed; please make the algorithm listing and the detailed description consistent.","section":"Algorithm 1"}],"recommendation":"major_revision","confidential_remarks":"The constraint violations in Tables 1 and 3 are the most serious issue; they may stem from the post-optimization normalization or from the solver not fully enforcing the constraints, but either way the paper's central comparison is currently between infeasible plans. The internal inconsistency between the target DVH-min constraint in the text and the BED constraint in Eq. (1) also needs correction before the method can be reproduced. The novelty is moderate and the manuscript fits the journal's scope, but the load-bearing claims need additional work."},"author_rebuttal":null,"desk_editor":{"model":"deepseek-v4-flash","letter":"The new thing here is the multi-IMPT formulation: different subsets of four beam angles per fraction, with BED constraints on OARs and physical dose on target, solved by ICR/ADMM. That is a legitimate new application of the BED fractionation work from [20]-[24], and the paper is clearly written. Credit where due: the method is practical, the four clinical cases are a reasonable first test, and the comparison to ARC is a sensible way to frame the question.\n\nThe soft spots are real, and the stress-test note lands. Tables 1 and 3 show the ARC plans, and sometimes multi-IMPT, violating the stated BED bounds: prostate bladder BED50 is 44.6 Gy against a 40 Gy upper bound, bladder BED20 is 67.75 vs 63; rectum is 45.02 vs 40 and 65.7 vs 63. In the brain case, brainstem BEDmax is 85.25 Gy for ARC and 87.91 for multi-IMPT against an 83.7 Gy bound, and brain BEDmax is 104.31 and 109.37 against a 96 Gy bound. Since the paper defines BEDp as at most p% of voxels above the bound, these are direct violations, not reporting artifacts. The likely cause is the post-optimization normalization to 95% target coverage, but whatever the cause, the equivalence claim is between infeasible plans. That undermines the central conclusion.\n\nTwo other issues: the ARC comparator is a simplified equal-dose-per-fraction model, which may not represent clinical ARC delivery; and the BED model with alpha/beta = 2 for all OARs is used both as the constraint and as the comparison metric, making the 'biological equivalence' model-internal. Also, only four single-patient cases with no error bars, and no code or full parameters are released.\n\nThat said, the core idea is sound and the violations look fixable by re-optimizing after normalization or by relaxing constraints appropriately. The paper does not overclaim in its abstract as much as in the conclusion, but 'biologically equivalent' is too strong for a planning comparison.\n\nBottom line: this deserves a serious referee. The formulation is new and potentially useful for proton centers that cannot deliver arc. A revision that resolves the constraint violations, validates or strengthens the ARC baseline, and adds uncertainty estimates would turn a promising planning study into a solid one.","headline":"Useful planning idea, but the reported plans violate the paper's own BED constraints, so the ARC-equivalence claim is not yet demonstrated.","tokens_in":12736,"tokens_out":1416,"would_cite":false,"duration_ms":14503,"reading_group":"maybe","serious_thinker":"yes","would_accept_peer_review":true},"rs_alignment":null,"lean_confirmation":null,"pith_extraction":{"msc":[],"pacs":[],"model":"deepseek-v4-flash","headline":"A scheme that rotates through six four-field IMPT plans can match proton arc therapy's plan quality using biologically effective dose as the comparison metric.","keywords":["biologically effective dose","proton arc therapy","intensity-modulated proton therapy","multi-IMPT","fractionation","inverse optimization","alternating direction method of multipliers","iterative convex relaxation"],"falsifier":"Recompute the four planning comparisons with OAR $\\alpha/\\beta$ set to, say, 3 Gy or 10 Gy, or measure normal-tissue damage in an animal model treated with both schedules, and check whether multi-IMPT's OAR BED stays within the paper's stated clinically insignificant margin of ARC; a reversal of the prostate bladder or rectum BED50 advantage or a widening lung difference would falsify the equivalence claim.","tokens_in":11629,"feed_emoji":"⚛️","tokens_out":9587,"duration_ms":80284,"temperature":0.7,"pith_summary":"The paper argues that proton arc therapy's dosimetric benefits do not require arc hardware: a multi-IMPT schedule that uses a different subset of four beam angles in each fraction can reproduce ARC's plan quality. The key is to optimize the biologically effective dose (BED) to organs at risk while keeping physical dose to the target, because BED punishes the per-fraction dose pattern, not just the total. In planning comparisons on prostate, lung, brain, and head-and-neck cases, multi-IMPT was equivalent to or slightly better than ARC in three cases and slightly worse in the brain case, and the authors judge the differences clinically insignificant. If the equivalence is correct, proton centers could deliver arc-like treatments with conventional stepped gantry deliveries, avoiding the slow energy changes of continuous rotation.","feed_headline":"Rotating four beam angles per fraction matches proton ARC","feed_subtitle":"BED-based planning lets standard gantry deliveries reproduce arc therapy's OAR sparing in four clinical cases.","key_machinery":"The load-bearing identity is the linear-quadratic biologically effective dose to an OAR voxel, $BED_j^m = \\sum_{t=1}^{T} d_{jt}^m + \\rho_m \\sum_{t=1}^{T} (d_{jt}^m)^2$ with $\\rho_m = 1/(\\alpha_m/\\beta_m)$, evaluated with $\\alpha/\\beta = 2$ Gy for every OAR. Because BED is nonlinear in per-fraction dose, changing which four beams are used in a fraction changes the OAR cost, letting the optimizer spread dose unevenly across fractions to reproduce an arc plan's cumulative BED. The optimization minimizes physical target dose deviation subject to BED-max, BED-mean, and BED-DVH constraints for OAR, DVH-min and max-dose constraints for the target, and a minimum-monitor-unit constraint, solved by iterative convex relaxation and the alternating direction method of multipliers.","core_discovery":"The central claim is that multi-IMPT—delivering a different subset of four beam angles in each fraction and optimizing BED for OAR while targeting physical dose to the target—produces plan quality equivalent to spot-scanning proton arc therapy. In the prostate case, multi-IMPT lowered bladder BED50 from 44.60 Gy to 24.49 Gy and rectum BED50 from 45.02 Gy to 24.69 Gy compared with ARC, while target conformity was similar. Lung and head-and-neck cases were dosimetrically similar; the brain case was slightly worse with conformity index 0.863 versus 0.904 for ARC. The paper concludes that the dosimetric differences are not clinically significant and that multi-IMPT is an ARC-equivalent delivery scheme.","pith_inferences":["The paper leaves implicit that its six fixed angle combinations are only one possible schedule; an optimizer that selects per-fraction angle subsets or plan order could push OAR BED even lower, and may be needed in anatomies not tested here.","Because BED is nonlinear in per-fraction dose, the method suggests a general principle that spatiotemporal fractionation can buy normal-tissue sparing without arc hardware, a principle that could extend to photon therapy or to combining IMPT with ultra-high-dose-rate delivery.","A testable extension is a robustness study: if OAR $\\alpha/\\beta$ varies by patient or endpoint, one could optimize multi-IMPT across a range of $\\alpha/\\beta$ values and compare with equivalent ARC plans rather than the fixed 2 Gy used here."],"forward_implications":["Clinics with fixed-gantry or limited-angle proton systems could deliver plans with ARC-like OAR sparing by rotating through a handful of fixed-beam IMPT plans across fractions.","Standard IMPT delivery, quality assurance, and delivery workflows could be used, avoiding the energy-switching overhead and continuous gantry rotation of ARC delivery.","Because the optimization separates by fraction, the multi-IMPT inverse problem is computationally cheaper than a single full-arc optimization.","BED-based objectives give a principled way to evaluate nonuniform fractionation in which each fraction's dose distribution differs.","For prostate, multi-IMPT may improve on ARC for OAR BED while keeping target coverage; for brain, ARC retains a modest advantage."],"supporting_citations":[{"why":"Supplies the linear-quadratic BED model used to define the objective and constraints.","marker":"[18, 19, 20]"},{"why":"Supplies the BED-max, BED-mean, and BED-DVH constraint forms used for organs at risk.","marker":"[21, 22, 23, 24]"},{"why":"Defines spot-scanning proton arc therapy and its energy-switching delivery challenge that multi-IMPT is designed to avoid.","marker":"[5, 6]"},{"why":"Provides the iterative convex relaxation method used to handle the nonconvex BED constraints.","marker":"[33, 34]"},{"why":"Provides the alternating direction method of multipliers used to solve the augmented Lagrangian subproblems.","marker":"[35, 36]"},{"why":"Supplies the dose-calculation toolkit used to generate dose influence matrices for both plans.","marker":"[37]"},{"why":"Supplies the minimum-monitor-unit constraint that enforces deliverability of the optimized spot intensities.","marker":"[27, 28, 29, 30, 31, 32]"}],"fun_headline_variants":["Multi-IMPT delivers ARC-equivalent plans with 4 angles per fraction","Biologically optimized multi-IMPT matches proton ARC quality","Fraction-wise BED-optimized IMPT rivals proton ARC sparing","Rotating beam subsets per fraction replicate ARC dosimetry","Multi-IMPT: ARC-level OAR sparing without continuous gantry"],"cache_read_input_tokens":3200,"weakest_assumption_plain":"The equivalence holds only if the linear-quadratic BED model with $\\alpha/\\beta = 2$ Gy for all organs at risk describes real normal-tissue response, and only if modeling proton ARC as the same plan repeated identically in every fraction is faithful; if either fails, the biological equivalence result may not carry to patients.","fun_headline_variants_meta":{"raw":{"variants":["Multi-IMPT delivers ARC-equivalent plans with 4 angles per fraction","Biologically optimized multi-IMPT matches proton ARC quality","Fraction-wise BED-optimized IMPT rivals proton ARC sparing","Rotating beam subsets per fraction replicate ARC dosimetry","Multi-IMPT: ARC-level OAR sparing without continuous gantry"]},"model":"deepseek-v4-flash","effort":"low","cost_usd":0.000323,"raw_usage":{"total_tokens":1839,"prompt_tokens":992,"completion_tokens":847,"prompt_tokens_details":{"cached_tokens":384},"prompt_cache_hit_tokens":384,"prompt_cache_miss_tokens":608,"completion_tokens_details":{"reasoning_tokens":758}},"tokens_in":608,"tokens_out":847,"duration_ms":8370,"temperature":1.0,"reasoning_tokens":758,"cache_read_input_tokens":384,"cache_creation_input_tokens":0},"cache_creation_input_tokens":0},"created_at":"2026-08-12T11:57:41.114759+00:00","model_set":{"reader":"deepseek-v4-flash"},"falsifier":"Recompute the four planning comparisons with OAR $\\alpha/\\beta$ set to, say, 3 Gy or 10 Gy, or measure normal-tissue damage in an animal model treated with both schedules, and check whether multi-IMPT's OAR BED stays within the paper's stated clinically insignificant margin of ARC; a reversal of the prostate bladder or rectum BED50 advantage or a widening lung difference would falsify the equivalence claim.","supporting_citations":[],"review_version":1}