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arxiv: 2605.12558 · v2 · submitted 2026-05-11 · ⚛️ physics.med-ph

Recognition: 2 theorem links

· Lean Theorem

Voxel-aware oxygen kinetics resolves radiation-induced DNA damage retention across LET-oxygen conditions

Renato III Fernan Bolo , Ramon Jose C. Bagunu
Authors on Pith no claims yet

Pith reviewed 2026-05-15 05:18 UTC · model grok-4.3

classification ⚛️ physics.med-ph
keywords OERLETDNA damage retentionparticle therapyhypoxiaoxygen kineticsZ-orderingvoxel-scale planning
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The pith

Voxel-aware oxygen kinetics enables particle-specific modeling of DNA damage retention across LET and oxygen conditions at clinical planning speeds.

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

The paper develops the Voxel-Aware Oxygen Model (VOxA) to predict how low-oxygen tumor regions resist radiation in a way that depends on the particle type used. It combines dual sigmoidal transitions for LET-OER dependence that increase with atomic number Z and Michaelis-Menten kinetics for oxygen, plus a voxel-aware term that tracks local energy heterogeneity at individual DNA breaks with one calibrated sensitivity parameter per particle. The model is fitted to 233 OER measurements spanning 10 particle types and reproduces the observed helium-carbon-neon ordering in survival data while running over a million times faster than full Monte Carlo chemistry. A sympathetic reader would care because this supplies the first particle-specific OER tool fast enough for routine voxel-scale treatment planning in heavy-ion therapy.

Core claim

VOxA encodes particle-specific LET-OER dependence through dual sigmoidal transitions constrained to increase monotonically with atomic number Z, combined with Michaelis-Menten oxygen kinetics. The voxel-aware extension resolves per-DSB local energy heterogeneity via a calibrated particle-specific sensitivity parameter. On the calibration set it yields R^2 = 0.719 and MAE = 0.300, reproduces the Furusawa heavy-ion Z-ordering with 28.4 percent lower survival OER error than the clinical standard, and evaluates in under 10^{-3} ms per voxel.

What carries the argument

The Voxel-Aware Oxygen Model (VOxA) that uses dual sigmoidal LET-OER transitions increasing with Z together with Michaelis-Menten kinetics and one particle-specific sensitivity parameter to resolve per-DSB heterogeneity.

If this is right

  • Reproduces helium less than carbon less than neon Z-ordering in survival OER that universal models cannot capture.
  • Achieves 28.4 percent lower survival OER mean absolute error than the clinical standard on heavy-ion data.
  • Supplies committed-break coordinates at whole-nuclear scale for inter-break topological analysis.
  • Enables hypoxic LET painting at voxel resolution in treatment planning.
  • Evaluates more than 10^6 times faster than Monte Carlo chemistry simulations.

Where Pith is reading between the lines

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

  • The monotonic Z-constraint permits extrapolation to untested particles such as oxygen ions without new full recalibration.
  • The per-DSB heterogeneity term could be combined with chromosome topology models to predict aberration rates.
  • Application to mixed-particle fields in space radiation or therapy would test whether the single sensitivity parameter remains adequate.
  • Routine clinical use would require direct comparison against patient local-control data in particle therapy cohorts.

Load-bearing premise

The dual sigmoidal LET-OER transitions that increase monotonically with Z, combined with Michaelis-Menten oxygen kinetics and a single calibrated sensitivity parameter per particle, are sufficient to capture the biology across the full range of LET and oxygen conditions.

What would settle it

New OER measurements for neon or argon ions that violate the monotonic Z-ordering or yield retention probabilities outside the range predicted by the calibrated sensitivity parameter.

Figures

Figures reproduced from arXiv: 2605.12558 by Ramon Jose C. Bagunu, Renato III Fernan Bolo.

Figure 1
Figure 1. Figure 1: Case fraction evolution with LET for four representative particle types (photon, proton, carbon, neon; four panels). Colored curves show the LET-dependent case fractions p1 (direct, red), p2 (hybrid, blue), and p3 (indirect, green) computed from Equations (3)–(5). Dotted horizontals: low-LET anchors p1 = 0.04, p2 = 0.32, p3 = 0.64. The progressive transfer of damage agency from indirect to direct mechanism… view at source ↗
Figure 2
Figure 2. Figure 2: OERretversus dose-averaged LET at near-anoxia (0.001% O2) for all seven calibrated particle types. Solid curves: VOxA Oxygen Model predictions; colored circles: 233 calibration observations. Particle-specific curves shift rightward with increasing atomic number Z, encoding Z-ordering by construction. LET axis is logarithmic; both axes are clipped to the calibrated range. The OM was calibrated on 233 OER ob… view at source ↗
Figure 3
Figure 3. Figure 3: Predicted versus observed OERretacross all 233 calibrated-particle observations. Solid diagonal: perfect agreement; dashed lines: ±0.15 OER unit absolute tolerance bands. 65.8% of observations fall within the tolerance bands. Kfix = 0.159% O2 and Krepair = 0.212% O2 are poorly constrained, with bootstrap CVs of 71% and 96% respectively and bivariate collinearity r = 0.935 ( [PITH_FULL_IMAGE:figures/full_f… view at source ↗
Figure 4
Figure 4. Figure 4: Oxygen fixation probability Pfix versus oxygen partial pressure (log scale), computed from Equation (6) with calibrated Kfix = 0.159% O2 and Krepair = 0.212% O2. Red dashed vertical: composite Kfix + Krepair = 0.371% O2 = 2.82 mmHg, the inflection point of the curve. Dotted horizontal: Pfix at normoxia (0.9901) [PITH_FULL_IMAGE:figures/full_fig_p017_4.png] view at source ↗
Figure 5
Figure 5. Figure 5: Bootstrap parameter ridge for the oxygen kinetics constants. Each point represents one of 500 bootstrap replicates. KDE density contours overlay the scatter. Red diamond: MLE operating point (Kfix = 0.159% O2, Krepair = 0.212% O2). The ridge orientation (slope ≈ −1) confirms that the composite sum Kfix + Krepair is the identifiable quantity; individual parameters are poorly constrained (Pearson r = 0.935).… view at source ↗
Figure 6
Figure 6. Figure 6: Q–Q plot of standardized calibration residuals (N = 233) against theoretical normal quantiles. Dashed line: normal reference. The bulk of the distribution follows the reference closely; departures are confined to the tails, consistent with a light-tailed heavy-ion OER dataset. Shapiro–Wilk W = 0.983, p = 7.25 × 10−3 . fits marginal OER magnitude. Because this dataset is in-sample for both VOxA and Scifoni … view at source ↗
Figure 7
Figure 7. Figure 7: Z-ordering validation on the Furusawa et al. (2000) heavy-ion dataset at near-anoxia (0.0013% O2). Four panels: proton, helium, carbon, neon. Solid gold: VOxA; dashed blue: Scifoni et al. (2013); dash-dot orange: Grimes (2020); filled circles: Furusawa data. The three particle￾specific VOxA curves shift rightward with Z at matching LET reproducing the experimental Z-ordering. Both Scifoni et al. and Grimes… view at source ↗
Figure 8
Figure 8. Figure 8: Oxygen response curve validation against the Ling et al. (1981) low-LET photon dataset (Ling convention: reference = anoxia, OER increases with pO2). Solid gold: VOxA; dashed blue: Grimes and Partridge (2015) analytical model; filled circles: Ling et al. CHO data. VOxA RMSE = 0.175; Grimes & Partridge (2015, Ling et al. b fit) RMSE = 0.160 [PITH_FULL_IMAGE:figures/full_fig_p021_8.png] view at source ↗
Figure 9
Figure 9. Figure 9: Neon hold-out Z-interpolation validation using all 54 calibration neon observations from eight sources (Furusawa 2000, Blakely 1979, Katz 1974, Raju 1978, Curtis 1982, and others); data points colored by cell line (V79, HSG, T1, other). Panel A: OERsurv versus LET. Solid gold: VOxA with calibrated neon parameters (fitted MAE = 0.246 OERsurv units); dashed green: VOxA with neon parameters recovered by Z-int… view at source ↗
Figure 10
Figure 10. Figure 10: Voxel-Aware calibration diagnostics. Left: Pareto frontier for each of the three calibrated particles: within-nucleus CV of p (i) DSB (horizontal axis) versus mean population error (vertical axis, log scale). Each curve sweeps over candidate δf values; the filled circle marks the chosen operating point (maximum CV while keeping mean error < 1%; dashed line). All operating points lie several orders of magn… view at source ↗
Figure 11
Figure 11. Figure 11: VA scaling battery: CV ratio (validation sample / calibration sample) for each of the three calibrated particle types. Diamond markers: observed CV ratios; error bars: 95% bootstrap confidence intervals; shaded band: ±20% equivalence tolerance. All three particles pass the primary TOST and Feltz–Miller equivalence tests, confirming that the within-nucleus CV of p (i) DSB is invariant to sample size. biolo… view at source ↗
Figure 12
Figure 12. Figure 12: Committed DSB counts per nucleus across five oxygen conditions, starting from 400 initial DSBs (≈ 10 Gy carbon pSOBP). Three particle types (electron 0.2 keV µm−1 ; proton 4.6 keV µm−1 ; carbon 40.9 keV µm−1 ) are shown with 95% Monte Carlo confidence interval error bars and a small horizontal offset for clarity. The carbon–electron gap widens substantially below mild hypoxia, reaching +67.5% at anoxia [… view at source ↗
read the original abstract

Objective. Hypoxic tumor subvolumes resist radiation through elevated oxygen enhancement ratios (OER), yet no computational OER model is simultaneously particle-specific, mechanistically grounded, and fast enough for voxel-scale treatment planning. We present the VOxel-Aware Oxygen Model (VOxA) to address all three requirements. Approach. An Oxygen Model (OM) encodes particle-specific LET-OER dependence through dual sigmoidal transitions constrained to increase monotonically with atomic number Z, combined with Michaelis-Menten oxygen kinetics. A Voxel-Aware (VA) extension resolves per-DSB local energy heterogeneity via a calibrated particle-specific sensitivity parameter. Calibrated on 233 OER observations from 29 sources across 10 particle types (LET = 0.2-654 keV/um); DSB coordinates from TOPAS-nBio simulations. Main results. The OM achieves $R^2 = 0.719$ and MAE = 0.300 retention OER units; theoretical OER maximum 3.32 (2.4% from measurement), bootstrap median 3.37 [3.18, 4.09]. The composite $K_{\rm fix} + K_{\rm repair} = 2.82$ mmHg is tightly constrained despite high collinearity (r = 0.935). On the Furusawa heavy-ion subset, VOxA achieves 28.4% lower survival OER MAE than the clinical standard (63.1% on helium, 24.0% on carbon) and reproduces He < C < Ne Z-ordering that universal models cannot capture. The VA extension passes 18 tests confirming sample-size-invariant within-nucleus coefficient of variation of the per-DSB retention probability. VOxA evaluates in under $10^{-3}$ ms per voxel, more than $10^6$ times faster than Monte Carlo chemistry. Significance. VOxA is the first particle-specific OER model to reproduce Z-ordering analytically at clinical planning speed, validated on the largest OER calibration dataset for this model class. Committed-break coordinates at whole-nuclear scale provide the input for inter-break topological analysis and hypoxic LET painting.

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

2 major / 2 minor

Summary. The manuscript introduces the Voxel-Aware Oxygen Model (VOxA) consisting of an Oxygen Model (OM) that encodes particle-specific LET-OER dependence via dual sigmoidal transitions constrained to increase monotonically with atomic number Z, combined with Michaelis-Menten oxygen kinetics, plus a Voxel-Aware (VA) extension that resolves per-DSB local energy heterogeneity through a single calibrated particle-specific sensitivity parameter. Calibrated on 233 OER observations from 29 sources across 10 particle types (LET range 0.2-654 keV/μm) with DSB coordinates from TOPAS-nBio, the model reports R²=0.719, MAE=0.300, a theoretical OER maximum of 3.32, and 28.4% lower survival OER MAE than the clinical standard on the Furusawa heavy-ion subset while reproducing He < C < Ne Z-ordering and evaluating in <10^{-3} ms per voxel.

Significance. If the reported fits and Z-ordering hold, VOxA would constitute a meaningful advance as the first particle-specific OER model to deliver analytical Z-ordering at clinical planning speeds on the largest calibration dataset for this class. Credit is due for the bootstrap interval on the OER maximum, the 18 internal consistency tests on per-DSB CV, and the explicit quantification of MAE gains over the clinical standard on the cited subset; these elements support practical utility for hypoxic LET painting and inter-break topological analysis.

major comments (2)
  1. [Results, parameter estimation] Results, parameter estimation: the claim that the composite K_fix + K_repair = 2.82 mmHg is 'tightly constrained' is presented alongside r=0.935 collinearity between the individual rates; this collinearity directly affects identifiability of the Michaelis-Menten component and requires an explicit sensitivity analysis or reparameterization to substantiate the constraint claim.
  2. [Methods, model calibration] Methods, model calibration: the reported R²=0.719 and MAE=0.300 on 233 points, together with the 28.4% MAE improvement on the Furusawa subset, are derived from the same fitted parameters used for calibration; the manuscript should clarify whether an independent hold-out or k-fold cross-validation was performed and report the full list of fitted parameters with their uncertainties.
minor comments (2)
  1. [Abstract] Abstract: the bootstrap interval [3.18, 4.09] on the OER maximum is given without stating the number of resamples or confidence level; this detail should be added for reproducibility.
  2. [Results] Figure captions and text: the 18 internal consistency tests for sample-size-invariant within-nucleus CV are referenced but not enumerated; a brief table or supplementary list would improve clarity.

Simulated Author's Rebuttal

2 responses · 0 unresolved

We thank the referee for the constructive review and the recommendation for minor revision. We address each major comment below and will incorporate the requested clarifications and analyses in the revised manuscript.

read point-by-point responses

  1. Referee: Results, parameter estimation: the claim that the composite K_fix + K_repair = 2.82 mmHg is 'tightly constrained' is presented alongside r=0.935 collinearity between the individual rates; this collinearity directly affects identifiability of the Michaelis-Menten component and requires an explicit sensitivity analysis or reparameterization to substantiate the constraint claim.

    Authors: We acknowledge that the reported collinearity (r = 0.935) between K_fix and K_repair limits the identifiability of the individual Michaelis-Menten rates. The composite sum remains tightly constrained by the data, as indicated by the narrow bootstrap interval. To substantiate this, we will add an explicit sensitivity analysis in the revised Results section: we will fix the sum at 2.82 mmHg and vary the ratio of the two rates across the collinear range, showing that model predictions for OER and retention probabilities are robust. We will also discuss reparameterization using the sum and ratio as the fitted parameters. revision: yes

  2. Referee: Methods, model calibration: the reported R²=0.719 and MAE=0.300 on 233 points, together with the 28.4% MAE improvement on the Furusawa subset, are derived from the same fitted parameters used for calibration; the manuscript should clarify whether an independent hold-out or k-fold cross-validation was performed and report the full list of fitted parameters with their uncertainties.

    Authors: No independent hold-out or k-fold cross-validation was performed; the full set of 233 observations was used for calibration to preserve statistical power given the limited and heterogeneous nature of the OER literature data. We will add this explicit statement to the Methods section. In addition, we will include a new table in the revised manuscript that lists all fitted parameters together with their uncertainties obtained via bootstrap resampling. revision: yes

Circularity Check

3 steps flagged

Z-ordering forced by monotonic constraint; calibration metrics presented as validation

specific steps
  1. self definitional [Approach]
    "An Oxygen Model (OM) encodes particle-specific LET-OER dependence through dual sigmoidal transitions constrained to increase monotonically with atomic number Z, combined with Michaelis-Menten oxygen kinetics."

    The model explicitly constrains the sigmoidal transitions to increase monotonically with Z; therefore the reproduction of He < C < Ne Z-ordering on the Furusawa subset follows by construction from the imposed ordering rather than emerging as a derived result.

  2. fitted input called prediction [Main results]
    "On the Furusawa heavy-ion subset, VOxA achieves 28.4% lower survival OER MAE than the clinical standard (63.1% on helium, 24.0% on carbon) and reproduces He < C < Ne Z-ordering"

    The Furusawa subset belongs to the 233 OER observations on which the model (including the particle-specific sensitivity parameter) was calibrated, so the reported MAE reduction and Z-ordering are in-sample fit statistics rather than independent predictions.

  3. fitted input called prediction [Main results]
    "The composite K_fix + K_repair = 2.82 mmHg is tightly constrained despite high collinearity (r = 0.935)."

    The sum is reported as tightly constrained, yet the high collinearity indicates that the tightness is an artifact of the fitting procedure on the calibration data rather than independent evidence for the parameter values.

full rationale

The OM imposes an explicit monotonicity constraint on dual sigmoidal LET-OER transitions with respect to atomic number Z. This structure directly enforces the reported He < C < Ne ordering, so the 'analytical reproduction' reduces to the modeling assumption rather than an independent derivation. Performance gains (28.4% MAE reduction on the Furusawa subset) and the composite K_fix + K_repair = 2.82 mmHg (tight despite r=0.935 collinearity) are computed on the same 233-point calibration set used to fit the parameters, including the single VA sensitivity parameter. These elements match the fitted-input-called-prediction and self-definitional patterns, producing partial circularity in the central claims while leaving the mechanistic Michaelis-Menten core and computational speed as independent content.

Axiom & Free-Parameter Ledger

3 free parameters · 2 axioms · 1 invented entities

Model rests on several fitted parameters calibrated to 233 observations and domain assumptions about monotonic Z-dependence and Michaelis-Menten oxygen kinetics; no independent evidence supplied for the new sensitivity parameter.

free parameters (3)
  • dual sigmoidal transition parameters
    Constrained to increase with Z and fitted to OER data across 10 particle types
  • K_fix + K_repair
    Composite constant reported as 2.82 mmHg; fitted despite noted collinearity r=0.935
  • particle-specific sensitivity parameter
    Calibrated for the VA extension to resolve per-DSB local energy heterogeneity
axioms (2)
  • domain assumption LET-OER dependence follows dual sigmoidal transitions that increase monotonically with atomic number Z
    Invoked to encode particle-specific behavior in the Oxygen Model component
  • domain assumption Oxygen-dependent DSB fixation and repair follow Michaelis-Menten kinetics
    Basis for the oxygen kinetics module
invented entities (1)
  • VOxA model no independent evidence
    purpose: Fast particle-specific OER calculation at voxel scale for treatment planning
    Newly introduced composite framework; no independent falsifiable evidence outside the calibration dataset

pith-pipeline@v0.9.0 · 5714 in / 1543 out tokens · 48400 ms · 2026-05-15T05:18:51.550815+00:00 · methodology

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Works this paper leans on

60 extracted references · 60 canonical work pages

  1. [1]

    and Howard-Flanders, P

    Alper, T. and Howard-Flanders, P. , title =. Nature , year =

    work page

  2. [2]

    and Rocher, V

    Arnould, C. and Rocher, V. and Finoux, A.-L. and others , title =. Nature , year =

    work page

  3. [3]

    and Paganetti, Harald and Schuemann, Jan , title =

    Bertolet, Alejandro and Ramos-Méndez, José and McNamara, Aimee and Yoo, Dohyeon and Ingram, Samuel and Henthorn, Nicholas and Warmenhoven, John-William and Faddegon, Bruce and Merchant, Michael and McMahon, Stephen J. and Paganetti, Harald and Schuemann, Jan , title =. Radiation Research , year =

    work page

  4. [4]

    Cancers , year =

    Chan, Chun-Chieh and Chen, Fang-Hsin and Hsueh, Kuang-Lung and Hsiao, Ya-Yun , title =. Cancers , year =

    work page

  5. [5]

    D-Kondo, Naoki and Masilela, Thongchai A. M. and Shin, Wook-Geun and Faddegon, Bruce and LaVerne, Jay and Schuemann, Jan and Ramos-Mendez, Jose , title =. Physics in Medicine and Biology , year =. doi:10.1088/1361-6560/ad87a7 , eid =

    work page doi:10.1088/1361-6560/ad87a7

  6. [6]

    and Schmitt, E

    Friedland, W. and Schmitt, E. and Kundrát, P. and Dingfelder, M. and Baiocco, G. and Barbieri, S. and Ottolenghi, A. , title =. Scientific Reports , year =

    work page

  7. [7]

    and Fukutsu, K

    Furusawa, Y. and Fukutsu, K. and Aoki, M. and Itsukaichi, H. and Eguchi-Kasai, K. and Ohara, H. and Yatagai, F. and Kanai, T. and Ando, K. , title =. Radiation Research , year =

    work page

  8. [8]

    Biomedical Physics & Engineering Express , year =

    Grimes, David Robert and Partridge, Mike , title =. Biomedical Physics & Engineering Express , year =

    work page

  9. [9]

    , title =

    Grimes, David R. , title =. Physics in Medicine and Biology , year =

    work page

  10. [10]

    Journal of Radiation Research , year =

    Hirayama, Ryoichi and Furusawa, Yoshiya and Fukawa, Takeshi and Ando, Koichi , title =. Journal of Radiation Research , year =

    work page

  11. [11]

    Radiation Research , year =

    Hirayama, Ryoichi and Ito, Atsushi and Tomita, Masanori and Tsukada, Teruyo and Yatagai, Fumio and Noguchi, Miho and Matsumoto, Yoshitaka and Kase, Yuki and Ando, Koichi and Okayasu, Ryuichi and Furusawa, Yoshiya , title =. Radiation Research , year =

    work page

  12. [12]

    Radiation Research , year =

    Hu, Ankang and Zhou, Wanyi and Luo, Xiyu and Qiu, Rui and Li, Junli , title =. Radiation Research , year =

    work page

  13. [13]

    untzelmann, Kim Annabel and Pardo, Laura Rozo and Sch\

    K\"untzelmann, Kim Annabel and Pardo, Laura Rozo and Sch\"afer, Myriam and Weidner, Jonas and Falkova, Iva and Toufar, Jiri and Toufarova, Lucie and Bestvater, Felix and Hausmann, Michael and Falk, Martin , title =. Nanoscale , volume =. 2026 , doi =

    work page 2026

  14. [14]

    Physics in Medicine and Biology , year =

    Lai, Youfang and Chi, Yujie and Jia, Xun , title =. Physics in Medicine and Biology , year =. doi:10.1088/1361-6560/ac8853 , eid =

    work page doi:10.1088/1361-6560/ac8853

  15. [15]

    Ling, C. C. and Michaels, H. B. and Gerweck, L. E. and Epp, E. R. and Peterson, E. C. , title =. Radiation Research , year =

    work page

  16. [16]

    Physica Medica , year =

    Sakata, Dousatsu and Lampe, Nathanael and Karamitros, Mathieu and others , title =. Physica Medica , year =

    work page

  17. [17]

    International Journal of Molecular Sciences , year =

    Schäfer, Myriam and Hildenbrand, Georg and Hausmann, Michael , title =. International Journal of Molecular Sciences , year =

    work page

  18. [18]

    and McNamara, A

    Schuemann, J. and McNamara, A. L. and Ramos-Méndez, J. and Perl, J. and Held, K. D. and Paganetti, H. and others , title =. Radiation Research , year =

    work page

  19. [19]

    and McNamara, A

    Schuemann, J. and McNamara, A. L. and Warmenhoven, J. W. and Henthorn, N. T. and Kirkby, K. J. and Merchant, M. J. and Ingram, S. and Paganetti, H. and Held, K. D. and Ramos-Mendez, J. and Faddegon, B. and Perl, J. and Goodhead, D. T. and Plante, I. and Rabus, H. and Nettelbeck, H. and Friedland, W. and Kundr. A new standard. Radiation Research , year =

    work page

  20. [20]

    and Tinganelli, W

    Scifoni, E. and Tinganelli, W. and Weyrather, W. K. and Durante, M. and Maier, A. and Krämer, M. , title =. Physics in Medicine and Biology , year =

    work page

  21. [21]

    and Durante, M

    Tinganelli, W. and Durante, M. and Hirayama, R. and others , title =. Scientific Reports , year =

    work page

  22. [22]

    and Li, J

    Zhu, H. and Li, J. and Deng, X. and Qiu, R. and Wu, Z. and Zhang, H. , title =. Medical Physics , year =

    work page

  23. [23]

    Acta Oncologica , year =

    Bassler, Niels and Toftegaard, Jakob and L. Acta Oncologica , year =. doi:10.3109/0284186X.2013.832835 , issn =

    work page doi:10.3109/0284186x.2013.832835 2013

  24. [24]

    International Journal of Molecular Medicine , year =

    Lei, Tiantian and Du, Suya and Peng, Zhe and Chen, Lin , title =. International Journal of Molecular Medicine , year =. doi:10.3892/ijmm.2022.5145 , note =

    work page doi:10.3892/ijmm.2022.5145 2022

  25. [25]

    and Torriani, F

    Strigari, L. and Torriani, F. and Manganaro, L. and Inaniwa, T. and Dalmasso, F. and Cirio, R. and Attili, A. , title =. Physics in Medicine and Biology , year =

    work page

  26. [26]

    and Nikitaki, Zacharenia and Kalospyros, Spyridon A

    Mavragani, Ifigeneia V. and Nikitaki, Zacharenia and Kalospyros, Spyridon A. and Georgakilas, Alexandros G. , title =. Cancers , year =

    work page

  27. [27]

    Physica Medica , year =

    Dahle, Tordis Johnsen and Rusten, Espen and Stokkevåg, Camilla Hanquist and Silvoniemi, Antti and Mairani, Andrea and Fjæra, Lars Fredrik and Rørvik, Eivind and Henjum, Helge and Wright, Pauliina and Boer, Camilla Grindeland and Forsback, Sarita and Minn, Heikki and Malinen, Eirik and Ytre-Hauge, Kristian Smeland , title =. Physica Medica , year =

    work page

  28. [28]

    and Okada, S

    Roots, R. and Okada, S. , title =. International Journal of Radiation Biology , year =

    work page

  29. [29]

    Physics in Medicine and Biology , volume =

    Wenzl, Tatiana and Wilkens, Jan J , title =. Physics in Medicine and Biology , volume =. 2011 , doi =

    work page 2011

  30. [30]

    International Journal of Radiation Biology , year =

    Ando, Koichi , title =. International Journal of Radiation Biology , year =

    work page

  31. [31]

    Barendsen, G. W. and Koot, C. J. and van Kersen, G. R. and Bewley, D. K. and Field, S. B. and Parnell, C. J. , title =. International Journal of Radiation Biology , year =

    work page

  32. [32]

    Blakely, E. A. and Tobias, C. A. and Yang, Tracy C. H. and Smith, K. C. and Lyman, J. T. , title =. Radiation Research , year =

    work page

  33. [33]

    Chapman, J. D. and Blakely, E. A. and Smith, K. C. and Urtasun, R. C. , title =. International Journal of Radiation Oncology, Biology, Physics , year =

    work page

  34. [34]

    Curtis, S. B. , title =. Radiation Research , year =

    work page

  35. [35]

    Curtis, S. B. and Schilling, W. A. and Tenforde, T. S. and Crabtree, K. E. and Tenforde, S. D. and Howard, J. and Lyman, J. T. , title =. Radiation Research , year =

    work page

  36. [36]

    Feola, J. M. and Lawrence, J. H. and Welch, G. P. , title =. Radiation Research , year =

    work page

  37. [37]

    Freyer, J. P. and Jarrett, K. and Carpenter, S. and Raju, M. R. , title =. Radiation Research , year =

    work page

  38. [38]

    Fu, K. K. and Phillips, T. L. , title =. Radiology , year =

    work page

  39. [39]

    and Lachet, B

    Guichard, M. and Lachet, B. and Malaise, E. P. , title =. Radiation Research , year =

    work page

  40. [40]

    and Bedford, Joel S

    Hall, Eric J. and Bedford, Joel S. and Oliver, Raymond , title =. The British Journal of Radiology , year =

    work page

  41. [41]

    Hall, E. J. and Bird, R. P. and Rossi, H. H. and Coffey, R. and Varga, J. and Lam, Y.-M. , title =. Radiation Research , year =

    work page

  42. [42]

    Hill, M. A. and Stevens, D. L. and Marsden, S. J. and Allott, R. and Turcu, I. C. E. and Goodhead, D. T. , title =. Physics in Medicine and Biology , year =

    work page

  43. [43]

    and Sharma, S

    Katz, R. and Sharma, S. C. , title =. Physics in Medicine and Biology , year =

    work page

  44. [44]

    Nias, A. H. W. and Greene, D. and Fox, M. and Thomas, R. L. , title =. International Journal of Radiation Biology , year =

    work page

  45. [45]

    Prise, K. M. and Folkard, M. and Davies, S. and Michael, B. D. , title =. International Journal of Radiation Biology , year =

    work page

  46. [46]

    Raju, M. R. and Gnanapurani, M. and Martins, B. and Howard, J. and Lyman, J. T. , title =. Radiology , year =

    work page

  47. [47]

    Raju, M. R. and Amols, H. I. and Bain, E. and Carpenter, S. G. and Cox, R. A. and Robertson, J. B. , title =. The British Journal of Radiology , year =

    work page

  48. [48]

    Raju, M. R. and Carpenter, S. G. and Chmielewski, J. J. and Schillaci, M. E. and Wilder, M. E. and Freyer, J. P. and Johnson, N. F. and Schor, P. L. and Sebring, R. J. and Goodhead, D. T. , title =. Radiation Research , year =

    work page

  49. [49]

    Skarsgard, L. D. and Harrison, I. , title =. Radiation Research , year =

    work page

  50. [50]

    and Janssen, H

    Sprong, D. and Janssen, H. L. and Vens, C. and Begg, A. C. , title =. International Journal of Radiation Oncology, Biology, Physics , year =

    work page

  51. [51]

    and Zukowski, D

    Staab, A. and Zukowski, D. and Walenta, S. and Scholz, M. and Mueller-Klieser, W. , title =. Radiation Research , year =

    work page

  52. [52]

    Tenforde, T. S. and Curtis, S. B. and Crabtree, K. E. and Tenforde, S. D. and Schilling, W. A. and Howard, J. and Lyman, J. T. , title =. Radiation Research , year =

    work page

  53. [53]

    and Martins, B

    Todd, P. and Martins, B. I. and Lyman, J. T. and Kim, J.-H. and Schroy, C. B. , title =. Cancer , year =

    work page

  54. [54]

    Wheeler, K. T. and Deen, D. F. and Leith, J. T. and Norton, K. L. , title =. Radiology , year =

    work page

  55. [55]

    , title =

    Howard-Flanders, P. , title =. Nature , year =

    work page

  56. [56]

    LaVerne, J. A. , title =. Radiation Research , year =

    work page

  57. [57]

    and O'Neill, P

    Nikjoo, H. and O'Neill, P. and Wilson, W. E. and Goodhead, D. T. , title =. Radiation Research , year =

    work page

  58. [58]

    and Neitzel, C

    Hausmann, M. and Neitzel, C. and Bobkova, E. and Nagel, D. and Hofmann, A. and Chramko, T. and Falk, M. , title =. Frontiers in Physics , year =

    work page

  59. [59]

    Physics in Medicine and Biology , year =

    Incorporating oxygenation levels in analytical. Physics in Medicine and Biology , year =

    work page

  60. [60]

    PLoS ONE , year =

    A closed parameterization of. PLoS ONE , year =

    work page