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arxiv: 2604.10227 · v3 · submitted 2026-04-11 · ⚛️ physics.med-ph

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Voxel-Based Conversion of Hypofractionated Radiotherapy Dose Distributions to 2 Gy-Equivalent OAR Constraints: Proof-of-Concept Demonstrating the Radiobiological Benefits of Hypofractionation in a Prostate Radiotherapy Case

Mazen Moussallem (1 , 2 , 3) , Dima Mahmoud (3) , Antoine Nassif (1) ((1) Healthy Innovations , Rachiine , Zgharta , Lebanon
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(2) Holy Family University Batroun (3) Tripoli Governmental Hospital Doctors Center Kobbe Tripoli Lebanon)
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Pith reviewed 2026-05-10 15:52 UTC · model grok-4.3

classification ⚛️ physics.med-ph
keywords hypofractionationradiotherapyorgan-at-risk constraintsvoxel-based conversionprostate cancerlinear-quadratic modelEQD2BED
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The pith

A voxel-based converter turns hypofractionated radiotherapy doses into 2 Gy-equivalent organ-at-risk constraints that match standard clinical limits.

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

The paper presents a voxel-based method to convert hypofractionated dose distributions into 2 Gy equivalent values for checking organ-at-risk constraints. Standard converters such as BED or EQD2 often produce unrealistic results in low-dose regions, which can distort safety assessments. The new approach uses the linear-quadratic model up to 7.5 Gy per fraction and switches to linear-quadratic-linear above that, with a special threshold rule for low doses that calculates an equivalent fraction number and applies a custom EQDx step. In a prostate cancer example the converted doses above the threshold align with EQD2 and existing constraint tables, while low-dose areas behave more like BED, yielding higher estimates under normofractionation. This matters because it lets planners apply familiar 2 Gy organ-at-risk rules to shorter, higher-dose-per-fraction courses without losing biological accuracy.

Core claim

The To2GyConstraints converter applies the LQ model for fraction doses at or below 7.5 Gy and the LQ-L model for higher doses. For voxels below a threshold set at the mean of the prescribed hypofractionated dose per fraction and 2 Gy, it first derives an equivalent number of fractions and then performs an EQDx conversion rather than a direct EQD2 conversion. Above the threshold the resulting values remain consistent with standard EQD2 calculations and fall within clinically used dosimetric limits, unlike BED which diverges. Below the threshold the converter behaves like BED by returning higher equivalent doses when viewed in a normofractionated frame. Applied to a prostate radiotherapy case,

What carries the argument

The To2GyConstraints converter, a voxel-wise tool that combines LQ and LQ-L models with a threshold-based equivalent-fraction calculation and EQDx conversion to reproduce normofractionated OAR response in low-dose regions.

Load-bearing premise

Defining the low-dose threshold as the mean between the hypofractionated fraction dose and 2 Gy, then calculating an equivalent fraction number and applying EQDx conversion, accurately reproduces how organs at risk respond in low-dose regions under standard fractionation.

What would settle it

A side-by-side comparison of the converted OAR dose values against observed clinical toxicity rates in patients treated with the same hypofractionated prostate plan.

read the original abstract

Objectives: Existing voxel-based dose converters transform hypofractionated dose distributions into biologically effective dose (BED) or equivalent dose in 2 Gy fractions (EQD2), but they are not reliably applicable to organ-at-risk (OAR) dose constraints, particularly in low-dose regions, which may lead to dose misinterpretation. This study develops and demonstrates a voxel-based method to convert hypofractionated dose distributions into 2 Gy-equivalent OAR constraints. Methods: To2GyConstraints converter (www.healthy-innovations.com) was applied to a prostate cancer case. The method uses the Linear Quadratic (LQ) model for doses per fraction less than or equal to 7.5 Gy and the Linear Quadratic Linear (LQ-L) model for higher doses. For voxel fraction doses below a threshold defined as the mean between the prescribed hypofractionated fraction dose and 2 Gy, an equivalent number of fractions is calculated. The method then applies an EQDx-type conversion, rather than EQD2, using this calculated fraction number to better reproduce normofractionated dose behavior. Results: For doses above the defined threshold, unlike BED, the To2GyConstraints model produced results consistent with EQD2 and provided clinically realistic dose values comparable to standard dosimetric constraints, thereby offering a clearer demonstration of the radiobiological benefits of hypofractionation in prostate cancer. For doses below the threshold, unlike EQD2, the To2GyConstraints model showed behavior consistent with BED, yielding higher dose estimates when converted to a normofractionation scheme. Conclusions: To2GyConstraints converter shows promising results for radiobiological interpretation of hypofractionation. Further multicenter validation is required. Advances in knowledge: A voxel-based method enabling application of normofractionation OAR constraints to hypofractionated dosimetry after conversion.

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.

Referee Report

3 major / 2 minor

Summary. The manuscript proposes a voxel-based converter, To2GyConstraints, for transforming hypofractionated dose distributions into 2 Gy-equivalent values suitable for applying organ-at-risk (OAR) constraints in radiotherapy planning. Using the linear-quadratic (LQ) model for fraction doses ≤7.5 Gy and linear-quadratic-linear (LQ-L) for higher doses, it introduces an ad-hoc low-dose threshold (mean of prescribed hypofractionated fraction dose and 2 Gy) below which an equivalent number of fractions is calculated to apply an EQDx conversion instead of standard EQD2. Demonstrated on a single prostate cancer case, the method claims to produce results consistent with EQD2 above the threshold (unlike BED) and with BED below the threshold (unlike EQD2), thereby better illustrating the radiobiological benefits of hypofractionation for OARs.

Significance. If rigorously validated with quantitative metrics, this converter could address a practical gap in applying established normofractionated OAR constraints to hypofractionated plans, potentially improving plan evaluation and highlighting hypo fractionation advantages in prostate cases. The single-case proof-of-concept limits immediate applicability, but the approach targets a known limitation of pure BED/EQD2 methods in low-dose regions.

major comments (3)
  1. [Methods] Methods (low-dose threshold): The threshold is defined as the mean between the prescribed hypofractionated fraction dose and 2 Gy, followed by calculation of an equivalent fraction number for EQDx conversion. This choice is ad-hoc, directly dependent on the input dose, and lacks derivation from the LQ/LQ-L equations or validation against clinical OAR tolerance data or direct LQ integration over the fractionation schedule, undermining the claim that the low-dose branch accurately reproduces normofractionated OAR behavior.
  2. [Results] Results: Claims of consistency with EQD2 above threshold (providing clinically realistic values) and with BED below threshold are asserted without any quantitative tables, numerical dose values, error analysis, or direct comparisons for the prostate case. The effect of the post-hoc threshold on these consistencies is not quantified, preventing assessment of whether the method improves fidelity or introduces bias.
  3. [Methods] Methods (model parameters): The LQ to LQ-L transition is fixed at 7.5 Gy per fraction and the low-dose threshold is tunable; no sensitivity analysis or justification is provided for how these free parameters affect outputs across different hypofractionation regimens, which is load-bearing for the general applicability claimed.
minor comments (2)
  1. [Results] The manuscript would benefit from at least one table or figure presenting example voxel conversions and constraint comparisons for the prostate case to ground the textual assertions.
  2. [Conclusions] Abstract and conclusions appropriately note the need for multicenter validation, but the discussion could specify concrete validation metrics such as comparison to direct LQ predictions or clinical OAR outcome data.

Simulated Author's Rebuttal

3 responses · 0 unresolved

We thank the referee for their constructive and detailed review of our proof-of-concept manuscript. We address each major comment below and will revise the manuscript to incorporate the suggested improvements where feasible.

read point-by-point responses

  1. Referee: [Methods] Methods (low-dose threshold): The threshold is defined as the mean between the prescribed hypofractionated fraction dose and 2 Gy, followed by calculation of an equivalent fraction number for EQDx conversion. This choice is ad-hoc, directly dependent on the input dose, and lacks derivation from the LQ/LQ-L equations or validation against clinical OAR tolerance data or direct LQ integration over the fractionation schedule, undermining the claim that the low-dose branch accurately reproduces normofractionated OAR behavior.

    Authors: We agree that the low-dose threshold is a heuristic choice introduced to enable a practical transition between EQD2-like and BED-like conversion behaviors for OAR constraint application. It is not derived directly from the LQ or LQ-L equations. In the revised manuscript, we will expand the Methods section to provide a clearer rationale for this definition, explicitly note its dependence on the prescribed fraction dose, and discuss its limitations as an approximation rather than a fully validated model. We will also clarify that comprehensive validation against clinical OAR tolerance data is planned for future work beyond this proof-of-concept. revision: yes

  2. Referee: [Results] Results: Claims of consistency with EQD2 above threshold (providing clinically realistic values) and with BED below threshold are asserted without any quantitative tables, numerical dose values, error analysis, or direct comparisons for the prostate case. The effect of the post-hoc threshold on these consistencies is not quantified, preventing assessment of whether the method improves fidelity or introduces bias.

    Authors: The current version presents qualitative observations from a single prostate case as a proof-of-concept. We acknowledge that quantitative support is required to substantiate the claims of consistency and to evaluate the threshold's impact. In the revision, we will add tables reporting numerical dose values at key OAR points, direct side-by-side comparisons with BED and EQD2, and an analysis quantifying the effect of the threshold, including any potential bias or changes in fidelity. revision: yes

  3. Referee: [Methods] Methods (model parameters): The LQ to LQ-L transition is fixed at 7.5 Gy per fraction and the low-dose threshold is tunable; no sensitivity analysis or justification is provided for how these free parameters affect outputs across different hypofractionation regimens, which is load-bearing for the general applicability claimed.

    Authors: The 7.5 Gy transition is adopted from established literature on the LQ-L model for high-dose per fraction effects. The low-dose threshold is intentionally tunable to accommodate varying fractionation schemes. We will add a dedicated sensitivity analysis subsection in the revised Methods and Results to examine how changes in these parameters influence the converted dose distributions for the presented prostate case and to discuss implications for applicability to other hypofractionation regimens. revision: yes

Circularity Check

0 steps flagged

No significant circularity; method is a defined heuristic converter using standard models

full rationale

The paper proposes a practical voxel-based conversion method that applies the standard LQ model below 7.5 Gy/fx and LQ-L above, with an explicit rule for low-dose voxels: a threshold set as the mean of the prescribed hypofractionated fraction dose and 2 Gy, followed by calculation of an equivalent fraction number and EQDx conversion. This rule is presented as part of the method definition to achieve consistency with BED-like behavior in low doses and EQD2-like in high doses, but the paper does not claim or perform a first-principles derivation in which the output is mathematically forced to equal the input by construction. No equations reduce the converted doses to the threshold definition itself. The demonstration is a single-case proof-of-concept, conclusions explicitly call for multicenter validation, and no load-bearing self-citations or uniqueness theorems are invoked. The central claim concerns clinical interpretability of the converter rather than a derived result that collapses to its own inputs.

Axiom & Free-Parameter Ledger

2 free parameters · 2 axioms · 0 invented entities

The converter depends on two standard radiobiological models plus two explicit parameter choices whose justification is not independently derived from first principles or external data in the abstract.

free parameters (2)
  • Low-dose threshold = mean(prescribed fx dose, 2 Gy)
    Defined as the arithmetic mean of the prescribed hypofractionated fraction dose and 2 Gy to decide between EQD2-like and BED-like conversion.
  • LQ to LQ-L transition dose = 7.5 Gy
    Fixed cutoff at 7.5 Gy per fraction for switching models.
axioms (2)
  • domain assumption Linear-Quadratic model is appropriate for fraction doses ≤ 7.5 Gy
    Invoked to justify model choice for typical hypofractionated prostate doses.
  • domain assumption Linear-Quadratic-Linear model is appropriate for fraction doses > 7.5 Gy
    Invoked to handle high-dose-per-fraction effects in the conversion.

pith-pipeline@v0.9.0 · 5731 in / 1579 out tokens · 48096 ms · 2026-05-10T15:52:37.188801+00:00 · methodology

discussion (0)

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Reference graph

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