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arxiv: 2310.01281 · v1 · submitted 2023-10-02 · ⚛️ physics.med-ph

An in-silico study of conventional and FLASH radiotherapy iso-effectiveness: Radiolytic oxygen depletion and its potential impact on tumor control probability

Isabel Gonz\'alez-Crespo , Faustino G\'omez , \'Oscar L\'opez Pouso , Juan Pardo-Montero This is my paper

Pith reviewed 2026-05-24 06:17 UTC · model grok-4.3

classification ⚛️ physics.med-ph
keywords FLASH radiotherapyradiolytic oxygen depletiontumor control probabilitylinear-quadratic modeloxygen enhancement ratioin-silico modelingreaction-diffusion simulation
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The pith

Mathematical models show radiolytic oxygen depletion produces lower tumor control probability for FLASH radiotherapy than conventional radiotherapy, while preclinical tumor volumes remain similar.

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

The paper builds a reaction-diffusion model of tumor oxygenation that includes radiolytic oxygen depletion to compare FLASH and conventional radiotherapy. From the resulting oxygen maps it computes cell surviving fractions via the linear-quadratic model with oxygen enhancement ratios, then feeds those fractions into a tumor-growth model and a Poisson tumor-control-probability calculation. The calculations indicate that surviving-fraction differences appear most clearly in low alpha/beta and hypoxic cells, yet these differences do not produce measurable divergence in simulated tumor-volume curves. When the same surviving fractions are used to generate tumor-control-probability curves, FLASH radiotherapy yields noticeably lower control probabilities than conventional radiotherapy. The authors note that unmodeled biological processes could still preserve iso-effectiveness in real tumors.

Core claim

ROD causes differences in SF between FLASH-RT and CONV-RT, especially in low α/β and poorly oxygenated cells. These changes do not lead to significant differences in the evolution of preclinical tumors. However, when extrapolating this effect to TCP curves, we observed important differences between both techniques (TCP is lower in FLASH-RT).

What carries the argument

Spatiotemporal reaction-diffusion model of tumor oxygenation that incorporates radiolytic oxygen depletion, linked to linear-quadratic cell survival with oxygen enhancement ratios and to Poisson-LQ tumor control probability.

If this is right

  • Surviving fractions differ most between the two techniques in low α/β and hypoxic cells.
  • Preclinical tumor volume trajectories remain nearly identical under both irradiation methods.
  • Extrapolated tumor control probability curves are lower for FLASH radiotherapy.
  • Other unmodeled effects could still restore iso-effectiveness in actual tumors.

Where Pith is reading between the lines

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

  • If TCP differences persist in patients, FLASH radiotherapy might require higher doses than conventional radiotherapy to achieve equivalent control.
  • The model implies that endpoints based on volume curves versus control probability can give contradictory impressions of iso-effectiveness.
  • Vascular or repair mechanisms omitted from the simulation could counteract the oxygen-depletion effect inside tumors.

Load-bearing premise

The linear-quadratic model with oxygen enhancement ratios and the chosen reaction-diffusion parameters accurately capture the dominant biological response to radiolytic oxygen depletion without needing additional unmodeled repair or vascular effects.

What would settle it

A clinical trial that directly measures tumor control probability after matched FLASH and conventional doses would show whether the modeled TCP difference appears in patients.

Figures

Figures reproduced from arXiv: 2310.01281 by Faustino G\'omez, Isabel Gonz\'alez-Crespo, Juan Pardo-Montero, \'Oscar L\'opez Pouso.

Figure 1
Figure 1. Figure 1: Oxygen depletion curves in different solutions, obtained by fitting Equation (1) to the measure￾ments reported by Jansen et al. [18] (i, ii and iii), Van Slyke et al. [23] (iv) and El Khatib et al. [16] (v). It is represented the total amount of depleted oxygen during FLASH-RT, ∆p, divided by the delivered radiation dose against the initial oxygen partial pressure. Each oxygen distribution in the Ω sample … view at source ↗
Figure 2
Figure 2. Figure 2: Amount of depleted oxygen during FLASH-RT versus the initial oxygen partial pressure in preclinical tumors. The triangles represent in vivo data reported in [23], and the circles represent the sim￾ulated data for 100 tumors with different oxygenations distributed within the experimental range, obtained by solving Equation (2). The linear fitting of each data set is presented as a solid line and a dashed li… view at source ↗
Figure 3
Figure 3. Figure 3: Ratio of surviving fractions for FLASH-RT (SFF) and CONV-RT (SFC) for a dose of 20 Gy versus the oxygenation of the cells. 3.4 Analysis of CONV-RT and FLASH-RT iso-effectiveness from dose￾volume curves We used the results of the previous section to investigate the significance of the difference between tumor growth curves. This study was performed as follows: i) a random growth curve was generated by sampl… view at source ↗
Figure 4
Figure 4. Figure 4: Best-fits of tumor growth curves (mean values and standard deviations) presented by Diffend￾erfer et al. [9] (a, b) and Zhu et al. [32] (c, d). 3.5.2 Heterogeneously oxygenated tumors We also performed the same study in more realistic tumors with heterogeneous oxygen distributions. The populations of heterogeneous tumors were created as discussed in Section 2.4. Different αox/βox values were investigated: … view at source ↗
Figure 5
Figure 5. Figure 5: Simulated TCP-dose curves for homogeneously oxygenated tumors, with oxygenation p ranging from 1 to 30 mmHg. The results are presented for the whole range, as well as in 6 groups with oxygenations ranging from (0, 5], (5, 10], (10, 15], (15, 20], (20, 25], and (25, 30] mmHg. differences in D50 and D90 are summarized in [PITH_FULL_IMAGE:figures/full_fig_p011_5.png] view at source ↗
Figure 6
Figure 6. Figure 6: TCP values for CONV-RT (TCPC) and FLASH-RT (TCPF ) and differences between them (∆TCP) for a dose of 37.22 Gy (equivalent to D90 for the whole population with CONV-RT) according to tumor oxygenation, which was characterized by the median of their oxygen distribution, ˜p: poorly oxygenated (˜p ≤ 10 mmHg), moderately oxygenated (10 < p˜ ≤ 20 mmHg), and well oxygenated tumors (˜p > 20 mmHg) [PITH_FULL_IMAGE:… view at source ↗
Figure 7
Figure 7. Figure 7: TCP-dose curves for CONV-RT (solid lines) and FLASH-RT (dashed lines) in tumors with heterogeneous oxygen levels according to their median oxygen partial pressure, ˜p: poorly oxygenated (˜p ≤ 10 mmHg), moderately oxygenated (10 < p˜ ≤ 20 mmHg), and well oxygenated tumors (˜p > 20 mmHg). The αox/βox ratio was 10 Gy. 4 Conclusions In recent years, there has been significant interest in FLASH radiotherapy bec… view at source ↗
read the original abstract

FLASH radiotherapy (FLASH-RT) has shown the potential to spare normal tissue while seemingly maintaining the effectiveness of conventional radiotherapy (CONV-RT). It has been suggested that the protective effect arises from the radiolytic oxygen depletion (ROD) caused by FLASH-RT, but it is not entirely clear why this protective effect is not observed in tumors. Iso-effectiveness has been experimentally observed in time-volume curves of preclinical tumors irradiated with FLASH and conventional radiotherapy, but it may not translate to clinical trials, where tumor control probability (TCP) is typically the investigated endpoint. In this work, we used mathematical models to investigate the iso-effectiveness of FLASH-RT/CONV-RT on tumors, focusing on the role of ROD. We used a spatiotemporal reaction-diffusion model, including ROD, to simulate tumor oxygenation. From those oxygen distributions we obtained surviving fractions (SFs), using the linear-quadratic model with oxygen enhancement ratios (OER). We then used the calculated SFs to describe the evolution of preclinical tumor volumes through a mathematical model of tumor response. We also calculated TCPs using the Poisson-LQ approach. Our study suggests that ROD causes differences in SF between FLASH-RT and CONV-RT, especially in low $\alpha$/$\beta$ and poorly oxygenated cells. These changes do not lead to significant differences in the evolution of preclinical tumors. However, when extrapolating this effect to TCP curves, we observed important differences between both techniques (TCP is lower in FLASH-RT). Nonetheless, it cannot be discarded that other effects not modeled in this work could contribute to tumor control and maintain the iso-effectiveness of FLASH-RT.

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 uses a spatiotemporal reaction-diffusion model incorporating radiolytic oxygen depletion (ROD) to generate tumor oxygen distributions, from which surviving fractions (SFs) are derived via the linear-quadratic model with oxygen enhancement ratios (OER). These SFs feed a mathematical model of preclinical tumor volume evolution and a Poisson-LQ calculation of tumor control probability (TCP). The central claim is that ROD produces SF differences (especially for low α/β and hypoxic cells) that do not yield significant differences in tumor volume curves but do produce lower TCP for FLASH-RT than CONV-RT; other unmodeled effects may preserve iso-effectiveness.

Significance. If the extrapolation holds, the work shows that preclinical volume-based iso-effectiveness need not imply clinical TCP equivalence, which bears on the design and interpretation of FLASH-RT trials. The modeling chain is internally consistent and employs standard components (reaction-diffusion, LQ-OER, Poisson-LQ), but the TCP gap is a direct numerical consequence of literature-derived parameters without reported sensitivity analysis or validation against independent TCP data.

major comments (3)
  1. [TCP calculation (Poisson-LQ approach)] TCP calculation (Poisson-LQ approach): the reported TCP differences are obtained by direct application of the Poisson-LQ formula to the ROD-modified SFs; because α/β ratios, OER parameters, and cell-number assumptions are taken from prior literature without sensitivity analysis, the TCP gap is a constructed outcome of those inputs rather than an independent prediction.
  2. [LQ-OER and Poisson-LQ steps] Transition from oxygen fields to SFs and TCP: the claim that ROD-induced SF changes dominate the response (producing volume iso-effectiveness yet TCP differences) rests on the LQ-OER mapping and Poisson statistics; the manuscript does not test whether inclusion of repair kinetics, reoxygenation, or vascular response would erase or invert the TCP gap while leaving the volume result intact.
  3. [Tumor response and volume evolution model] Tumor volume evolution model: the absence of significant volume-curve differences despite SF variations is load-bearing for the preclinical-versus-clinical distinction; explicit demonstration is needed that this null result is robust to the chosen growth/response parameters and is not an artifact of the particular mapping from SF to volume.
minor comments (2)
  1. Parameter values (diffusion coefficient, depletion rate constant, α/β, OER factors) should be tabulated with their literature sources to improve reproducibility.
  2. The abstract and results should quantify what constitutes an 'important' TCP difference (e.g., shift in D50 or TCP at a fixed dose) rather than leaving the term qualitative.

Simulated Author's Rebuttal

3 responses · 0 unresolved

We thank the referee for their constructive review and the opportunity to clarify aspects of our modeling study. We respond point-by-point to the major comments, proposing revisions where they strengthen the manuscript while maintaining our core findings.

read point-by-point responses

  1. Referee: TCP calculation (Poisson-LQ approach): the reported TCP differences are obtained by direct application of the Poisson-LQ formula to the ROD-modified SFs; because α/β ratios, OER parameters, and cell-number assumptions are taken from prior literature without sensitivity analysis, the TCP gap is a constructed outcome of those inputs rather than an independent prediction.

    Authors: The TCP results are indeed obtained by applying the standard Poisson-LQ model to SFs computed from literature-derived parameters, which is the conventional approach in such radiobiological extrapolations. Our aim is to demonstrate the logical consequence of ROD under these accepted inputs rather than to claim an empirical prediction. In the revised manuscript we will add a dedicated sensitivity analysis on α/β, OER, and initial clonogen number to quantify how the TCP gap varies with these parameters. revision: yes

  2. Referee: Transition from oxygen fields to SFs and TCP: the claim that ROD-induced SF changes dominate the response (producing volume iso-effectiveness yet TCP differences) rests on the LQ-OER mapping and Poisson statistics; the manuscript does not test whether inclusion of repair kinetics, reoxygenation, or vascular response would erase or invert the TCP gap while leaving the volume result intact.

    Authors: We agree that the model isolates the ROD effect within the LQ-OER and Poisson-LQ framework and does not incorporate repair kinetics, reoxygenation, or vascular dynamics. These omissions are deliberate to focus on the immediate radiochemical consequence of ROD. In the revision we will expand the discussion to state this scope limitation explicitly and note that the observed TCP-volume dissociation illustrates why TCP should be examined separately from volume endpoints, even if additional biology could modulate the gap. revision: partial

  3. Referee: Tumor volume evolution model: the absence of significant volume-curve differences despite SF variations is load-bearing for the preclinical-versus-clinical distinction; explicit demonstration is needed that this null result is robust to the chosen growth/response parameters and is not an artifact of the particular mapping from SF to volume.

    Authors: We will include supplementary simulations that systematically vary the tumor growth rate, the functional mapping from SF to volume reduction, and the post-irradiation regrowth parameters. These additional runs will confirm that the lack of statistically significant volume-curve separation between FLASH and CONV remains consistent across plausible parameter ranges. revision: yes

Circularity Check

0 steps flagged

No significant circularity; forward simulation from literature parameters

full rationale

The derivation consists of a reaction-diffusion oxygen model (with ROD), followed by LQ-OER survival fractions, a tumor-volume evolution model, and Poisson-LQ TCP calculation. All parameters (diffusion, consumption, α/β, OER) are taken from external literature or stated as typical values; the TCP difference is a numerical output of these independent inputs rather than a self-definitional reduction, fitted prediction, or self-citation chain. The paper explicitly notes unmodeled effects could alter results, confirming the chain is not closed by construction.

Axiom & Free-Parameter Ledger

4 free parameters · 3 axioms · 0 invented entities

The central claims rest on standard reaction-diffusion and LQ models whose parameters are drawn from prior literature or chosen to reproduce typical tumor behavior; no new entities are postulated.

free parameters (4)
  • oxygen diffusion coefficient
    Taken from literature values or tuned to produce realistic hypoxic fractions
  • radiolytic oxygen depletion rate constant
    Fitted or chosen to match observed ROD in FLASH experiments
  • α/β ratios for tumor subpopulations
    Selected from typical ranges for low and high α/β cells
  • OER parameters
    Standard values adjusted for different oxygenation levels
axioms (3)
  • domain assumption Linear-quadratic model with oxygen enhancement ratio accurately describes cell survival under varying oxygenation
    Invoked when converting oxygen maps to surviving fractions
  • domain assumption Poisson statistics with LQ survival gives clinically relevant TCP
    Used for the TCP endpoint calculation
  • domain assumption Reaction-diffusion equation with constant consumption and diffusion coefficients suffices for spatiotemporal oxygen dynamics
    Core of the oxygenation simulation step

pith-pipeline@v0.9.0 · 5859 in / 1653 out tokens · 20852 ms · 2026-05-24T06:17:35.256744+00:00 · methodology

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Reference graph

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