Modeling Time-Dependent Recovery to Improve Esophagitis Prediction in Thoracic Reirradiation

Abstract

Background:

In re-irradiation, tumor control must be balanced against a high risk of adverse effects. We evaluated the feasibility of a time-dependent recovery model to improve toxicity prediction.

Methods:

Sixty-five high-risk thoracic re-irradiation patients, identified by BID treatment, were included for modeling grade ≥ 2 acute esophagitis. The median (range) re-RT dose was 45Gy (30-60) in 30 (20-40) fractions. Doses from each course were deformably registered to the most recent CT and converted to voxel-wise EQD2. We compared the discrimination of the last course dose, conventional direct accumulation without time consideration, and three time-dependent recovery models—mono-exponential, bi-exponential, and reciprocal time—each optimized via grid search with nested 5-fold cross-validation. Logistic regression with bootstrapping was used to assess the predictive value of mean and maximum dose. AUCs were compared using a bootstrap test. Covariates (age, chemotherapy, smoking status, history of esophagitis from a previous course of thoracic radiotherapy) were also evaluated.

Results:

After BID re-RT, 26.2% (17/65) of patients experienced grade ≥ 2 esophagitis. Incorporating time-dependent repair algorithms achieved a higher AUC than the last course dose and direct accumulation. The bi-exponential model incorporating history of prior esophagitis achieved the highest performance (mean dose AUC: 0.83 [95% CI: 0.70–0.94] vs. direct accumulation: 0.74 [0.61–0.87], p = 0.040; maximum dose AUC: 0.78 [0.65–0.89] vs. 0.67 [0.54–0.80], p = 0.015).

Conclusions:

Incorporating time-dependent recovery into dose accumulation is feasible, and our findings support its potential use over direct accumulation for more accurate toxicity prediction. These findings will pave the way for developing advanced outcome models for evidence-based re-irradiation, ultimately reducing toxicity and optimizing doses for personalized and effective re-irradiation.

Introduction:

As cancer survivorship improves, more patients return for re-irradiation (re-RT)¹. This treatment setting is marked by clinical uncertainty, requiring clinicians to balance tumor control with heightened toxicity risks^1-3. Lung cancer is the most diagnosed malignancy globally⁴. The lungs are also one of the most frequent metastasis sites⁴⁵. Thoracic re-RT is used to prolong local control and survival, relieve or prevent symptoms, delay systemic therapy, or enable surgery⁶.

Despite its growing use, re-RT planning lacks consensus, and there is significant practice variation⁶. In the thorax, cumulative dose assessment remains highly variable, with many practitioners still relying on point-based or non-3D methods despite the complexity of re-irradiation planning⁶. In addition to dose assessment challenges, there are uncertainties about re-RT constraints and how to integrate tissue recovery. While recommendations exist, they vary, and most constraints don’t account for the time between treatments, underscoring the need for additional data to support treatment decisions^7-10.

Most studies have focused on the central nervous system (CNS), where evidence suggests that tissues exhibit different radiosensitivity during re-RT and that at least partial recovery occurs, modulated by factors such as cumulative dose, time interval, initial dose, and patient age^6,11-14. The wide variability in inter-treatment intervals underscores the need for individualized recovery modeling. While models accounting for time-dependent recovery have recently been proposed for the CNS¹³, recovery dynamics are less understood in thoracic re-RT, and there is practice variability regarding whether and how to incorporate it⁶. When incorporated, recovery is typically accounted for as a fixed percentage dose reduction based on time thresholds^6,9. However, discounts are mostly based on expert consensus, and more data is urgently needed to guide those recommendations.

Inadequate modeling of cumulative dose and recovery may lead to inaccurate toxicity estimates for organs at risk (OARs). Overestimations of toxicity might lead to tumor undercoverage, while underestimation might lead to adverse events. These uncertainties highlight the need for models incorporating re-RT-related parameters to provide accurate toxicity predictions, allowing clinicians to make better-informed decisions. While strategies to optimize treatment plans, including integrating 3D Equivalent Dose in 2Gy fractions (EQD2) doses and tissue recovery, have been developed, accurately modeling recovery based on time and patient characteristics remains a significant challenge due to complexities in dose accumulation and a lack of understanding of recovery dynamics in humans^2,3,9,15,16.

To address these challenges, we developed a standardized thoracic re-RT database and dose accumulation framework integrating time-dependent recovery models. This study evaluates the feasibility and predictive discrimination of such models using esophagitis as a clinically relevant endpoint in a high-risk patient cohort undergoing thoracic re-RT.

Materials and Methods

BID high-risk thoracic re-RT cohort

All patients who received BID schemes (twice daily 150 cGy per fraction) for high-risk thoracic re-RT at our institution from 2014 to 2024 were included based on ICD-10 codes (C15, C33, C34, C37, C38, C45, C77, C78, C79.5 and R91.1). High-risk was defined based on overlap or proximity of volumes. The median re-RT dose was 45Gy (range: 30-60) in 30 (range: 20-40) fractions. Total courses ranged from 2 to 5, and most patients had two courses of treatment (73.8%, 48/65). Patients < 18 years old or who did not have enough information on previous treatment were excluded. Patient’s characteristics are presented in Table 1. This study was approved by the institutional review board at Johns Hopkins University (IRB00461902).

Table 1.

Patients’ baseline characteristics (n = 65)

Age at re-RT (years), median (range)	68.8 (19.3 - 84.3)
Sex assigned at birth, n (%)
Female	30 (46.2)
Male	35 (53.8)
Race, n (%)
Asian	2 (3.1)
Black or African American	9 (13.8)
White	52 (80.0)
Other	2 (3.1)
Smoking history, n (%)
Current	9 (13.8)
Former	44 (67.7)
Never	12 (18.5)
Primary, n (%)
Lung	50 (76.9)
Thoracic (non-lung)	4 (6.2)
Other (metastatic)	11 (16.9)
Total thoracic RT courses, n (%)	2 (2 - 5)
2	48 (73.8)
3	9 (13.8)
4	4 (6.2)
5	4 (6.2)
Previous RT-related esophagitis, n(%)
Yes	13 (21.7)
No	47 (78.3)
Time from cancer diagnosis to BID re-RT (months), median (IQR)	32.9 (40.0)
Concurrent systemic therapy, n (%)
Yes	46 (70.8)
No	19 (29.2)
BID re-RT dose (Gy), median (range)	45 (30 - 60)
BID re-RT fractions (n), median (range)	30 (20 - 40)
Proton BID re-RT	7 (10.8)

Database development

The study data was collected and managed using REDCap¹⁷ electronic data capture tools integrated with the electronic medical record system (Epic Systems, Verona, WI), the radiation record and verify system (Mosaiq, Elekta, Stockholm, Sweden), and our institutional analytical database that systematically collects and stores treatment and clinical data, Oncospace¹⁸. A physician with radiation oncology training also retrospectively reviewed all records and classified the toxicities according to the Common Terminology Criteria for Adverse Events (CTCAE) v5.0¹⁹ and assessed the relationship between the adverse effect and the re-RT course²⁰. Toxicities graded possible, probable, or definite were included in the analysis as the maximum grade after BID re-RT. Only esophagitis had enough events for modeling and was thus used for this study. Details of database development and variables are in the supplemental material (page. 2).

Endpoint definition

First, exploratory analysis was conducted to describe toxicities (the maximum grade of toxicity experienced after BID re-RT, with a possibly, probable, or definite relationship to treatment). Acute post re-RT esophagitis (onset during re-irradiation or within 30 days of completion) was chosen for this study because it had the highest number of events. Other toxicities did not have enough events for proper modeling with this patient cohort.

After BID re-RT, 26.2% (17/65) of patients experienced grade ≥ 2 esophagitis. Of these 17 patients, 15 (15/65, 23%) developed grade 2 toxicity, and 2 (2/65, 3%) developed grade 3. No grade 4 or 5 events occurred. The historical rates of grade ≥ 2 esophagitis in our institution were 16.8% (631/3758) for all patients receiving thoracic RT between 2014 and 2024.

Cumulative dose evaluation method

To evaluate cumulative doses, all DICOM records for each thoracic RT course were imported into the RayStation treatment planning system (RaySearch Laboratories, Stockholm, Sweden) and deformed onto the most recent planning CT scan (reference image set) using RayStation’s ANACONDA deformable image registration algorithm with a cross-correlation similarity metric ²¹. This commercial algorithm has been evaluated for thoracic registrations and has shown good performance with an average 3-dimensional registration error (range) of 3.28 mm (1.26-3.91 mm)²². Evaluation of our dataset was also performed and is described in the supplemental material. After deformation, a customized Python script was used to convert voxel-level dose to EQD2. An α/β ratio of 3 was used for all courses based on prior esophageal toxicity studies and aligned with experimental radiobiology data ^23-25.

For each course, the final 3D-EQD2 distribution accounted for replans, adaptive plans, cone-down treatments, and adjustments for actual delivered dose (e.g., if 25 of 30 fractions were completed, only the delivered dose was considered). All proton plan doses were converted to biological dose using a fixed RBE of 1.1.

This common reference-frame workflow allowed us to (1) generate a direct accumulation composite by adding the 3D-EQD2 distributions across courses and (2) extract per-course dose metrics from the same reference CT. This enabled both traditional (direct accumulation) and time-dependent dose accumulation approaches to be tested within a consistent spatial framework. All doses are reported in EQD2.

Statistical Analysis

Associations between dose metrics and grade ≥ 2 esophagitis were evaluated using logistic regression models. The Mann–Whitney U test was used to compare non-normally distributed dose distributions between groups. Time-to-event data was described using the Kaplan–Meier method. A two-sided p-value < 0.05 was considered statistically significant. All p-values reported in this study are unadjusted for multiple comparisons and should be interpreted in an exploratory context. All analyses were done with Python version 3.11.7. ROC curve comparisons were done in R version 4.3.3.

Model definitions

Two esophageal dose metrics were evaluated: mean dose and maximum point dose (Dmax). The choice was made based on studies evaluating dosimetric prediction of esophagitis and thoracic re-irradiation guidelines^26,27. The mean dose was retrieved for each course and for the composite distribution generated by direct accumulation. For Dmax analysis, two approaches were used: (1) composite Dmax: the voxel receiving the maximum cumulative EQD₂ dose in the direct accumulation composite was identified, and the dose to that voxel was recorded for each individual course; (2) last-course Dmax: the maximum point dose within the last-course plan was identified independently, as it did not always correspond to the Dmax point in the composite. This allowed evaluation of peak-dose effects both across the entire treatment history and specific to the most recent course.

Traditional Methods Models (Direct accumulation and last dose)

Models were created to predict esophagitis using two approaches: (1) direct accumulation of the dose from all RT courses, and (2) dose from the last course alone. Grade ≥2 esophagitis was modeled with logistic regression, with bootstrapping applied to increase robustness. These models did not incorporate any time factor and are referred to here as traditional approaches

Time-discounted dose models

Models for time-dependent recovery were developed by creating discounted doses for previous courses. Time was calculated as the interval between the previous and the most recent course. For patients with more than two re-RT courses, time intervals were measured from each previous course relative to the last course. Three time-dependent recovery algorithms were created based on radiation repair models: mono-exponential (assumes a single constant repair rate) - Eq_1A, bi-exponential (assumes fast and slow repair components) - Eq_1B, and reciprocal time (assumes repair slows down gradually over time) - Eq_1C ²⁸, the equations are presented below. The assumption that recovery would follow the same function through time and across courses was considered.

$$\begin{gathered} {\text{Eq}}_{1\mathrm{A}}:\text{Mono-exponential}\text{-}\text{Eq}.(\mathrm{A}1):D_t=D_0\cdot e^{-\mu \cdot t} \\ {\text{Eq}}_{1\mathrm{B}}:\text{Bi-exponential}\text{-}\text{Eq}.(\mathrm{A}2):D_t=\left(f_1\cdot D_0\cdot e^{-{{\mu }_1}^t}\right)+\left(f_2\cdot D_0\cdot e^{-{{\mu }_2}^t}\right) \\ {\text{Eq}}_{1\mathrm{C}}:\text{Reciprocal time}\text{-}\text{Eq}.(\mathrm{A}3):D_t=\frac{D_0}{(1+z\cdot t)} \end{gathered}$$ Equations (Eq) 1:

Where $D_0$ is the initial dose, $D_t$ is the discounted dose at time $t$; $t$ is the time in days, $\mu$, ${\mu }_1$, ${\mu }_2$ are repair-rate constants (day⁻¹); $f$ is the fractional proportion with $f_1+f_2=1$ (here $f_1=0.6$ and $f_2=0.4$); and $z$ is the repair-rate constant (day⁻¹) reciprocal of the first half-time of repair²⁸. For the bi-exponential model $f_1$ and $f_2$ were taken from parameters based on experimental data^28,29.

Time-discounted dose models - Optimization and Cross-validation

The time-discounted models (mono-exponential, bi-exponential, and reciprocal time) were optimized using nested stratified 5-fold cross-validation to predict grade ≥ 2 esophagitis based on a time-discounted dose. Nested cross-validation involves two levels of data splitting. In the inner loop, the training portion was split into multiple training/validation sets, with models fit to each training set and hyperparameters selected based on validation performance³⁰. In the outer loop, the tuned model was evaluated on the held-out test fold, ensuring that the same patient was never used for both training and testing in the same iteration³⁰. Generalization error was estimated by averaging test-set scores across the five outer folds³⁰. This structure effectively separates parameter tuning from model evaluation, preventing information leakage and reducing overfitting risk, particularly important given the limited sample size (65 patients, 17 events) and sensitivity to hyperparameter³¹.

In the inner loop (approximately 52 patients, 13 events per fold), a grid search was conducted over a range of 0.0001 to 0.1 (500 evenly spaced candidate values) to identify the time-discounting constant(s) that maximized the AUC in a logistic regression model. These constants were applied to reduce prior course doses according to the time elapsed between the prior and last course, while the final course dose remained undiscounted (Eq2). The outer loop (approximately 13 patients, 4 events) evaluated model performance on independent test folds. The final decay constant was calculated as the average of the best-performing constants across outer folds and was used to generate the discounted dose applied in the final model.

$$\sum _{i=1}^{n-1}[D_i\times f(t_i)]+D_n$$ Equations (Eq) 2:

Where $D_i$ is the initial dose from course $i$; $f(t_i)$ is the time discount factor for course $i$, calculated from the interval between the end of the prior course and the start of the last course; and $D_n$ is the dose from the most recent course, for which no discount is applied $(f(t_n)=1)$

Model evaluation

ROC curves were generated for each model, and AUC was calculated to assess performance. As described above, decay constants were optimized in the inner loop of nested cross-validation and averaged across outer folds to obtain a single fixed constant per model. Bootstrap resampling was then performed to estimate 95% confidence intervals for the AUC, which are conditional on these fixed constants and therefore do not incorporate parameter-tuning uncertainty. Model discrimination was evaluated by comparing ROC curves using bootstrap-based tests. Comparisons were made between the last course dose or direct accumulation and time-dependent accumulation models.

Covariate analysis

Finally, the impact of covariates (age, concurrent chemotherapy, smoking, history of esophagitis from a previous course of thoracic radiotherapy) on grade ≥ 2 esophagitis was explored in univariate and multivariate models, employing log-likelihood ratio tests to compare null and extended models. A history of esophagitis from a previous course of thoracic radiotherapy refers to any documented episode of esophagitis that occurred during a prior course of RT and had resolved before the start of re-irradiation; no patients had ongoing esophagitis at the initiation of the re-irradiation course.

Results:

Sixty-five high-risk thoracic re-RT patients, identified by treatment with BID re-RT courses, were included in this analysis. Following BID re-RT, the median duration of follow-up was 13.4 months (interquartile range [IQR]: 8.8 – 21.5).

Toxicity modeling

Traditional methods – direct accumulation and last dose

Increasing esophageal dose was associated with significantly higher odds of esophagitis, ranging from 9 to 18% increase per EQD2 Gray (Gy). The direct accumulation of the esophagus mean dose had the highest AUC (0.74), and the direct accumulation of the D_max had the lowest AUC (0.67). Table 2 provides the odds ratios (ORs) and AUCs for the different models predicting grade ≥ 2 esophagitis.

Table 2.

Odds ratios (OR) and AUCs for the models predicting esophagitis grade ≥ 2 esophagitis

Model		OR (95% CI), p	AUC (95% CI)
Mean Dose	Direct Summation	1.09 (95% CI 1.03 – 1.16), p = 0.005	0.74 (0.61 – 0.87)
	Last Course	1.18 (95% CI 1.05 – 1.32), p = 0.005	0.71 (0.61, 0.87)
Dmax	Direct Summation	1.03 (95% CI 1.002 – 1.06), p = 0.037	0.67 (0.54 – 0.80)
	Last course	1.05 (95% CI 1.01 – 1.10), p = 0.013	0.70 (0.570, 0.839)

Time-dependent recovery models

The median time from the first course to BID re-RT was 23.8 months (IQR: 16.4 to 51.3). The median time between consecutive courses was 18.9 months (IQR: 10.9 – 31.6), and the median time from the first to last course was 25.0 months (IQR: 16.4 – 49.6). Figure 1 displays the median cumulative time and IQR across courses.

Figure 1. Cumulative time and interquartile range across radiotherapy courses.

The first course is set as the starting time. Median and interquartile intervals to subsequent courses are shown, highlighting substantial variability in timing between treatments.

The final decay constants used in the time-dependent models are summarized in Table 3. The resulting model curves, depicted in Supplementary Figure 1A-B, illustrate the recovery trajectories associated with each constant.

Table 3.

Decay constants for time-dependent recovery models

Mean dose
Model	Best decay constant
Mono-exponential	$\mu$	0.001080 day−1
Bi exponential	${\mu }_1$, ${\mu }_2$	0.000434 day−1, 0.005682 day−1
Reciprocal-time repair	$z$	0.001624 day−1
Dmax
Model	Best decay constant
Mono-exponential	$\mu$	0.002309 day−1
Bi exponential	${\mu }_1$, ${\mu }_2$	0.000891 day−1, 0.003974 day−1
Reciprocal-time repair	$z$	0.002743 day−1

Note: Decay constants were obtained via nested 5-fold cross-validation and fixed for subsequent analyses; reported values do not incorporate parameter-tuning uncertainty.

Time-dependent recovery models – mean dose

All three time-dependent recovery models yielded better AUCs than the ones obtained with direct accumulation or the last course dose (mono-exponential 0.80 [95% CI 0.65 - 0.92], bi-exponential 0.81 [95% CI 0.67 - 0.93], reciprocal-time repair 0.79 [95% CI 0.65 - 0.92]), but the difference was not significant (supplementary Table 1). The ROC curves for the different models are shown in Figure 2A. Although all models showed a significant difference in mean dose between patients with and without grade ≥ 2 esophagitis (p = 0.003 for direct accumulation, p = 0.010 for last course dose, and p < 0.001 for the bi-exponential model; Mann-Whitney U test), the box plot demonstrates better distributional separation and elimination of IQR overlap with the bi-exponential model (Figure 2B).

Figure 2. Performance of Traditional and Time-dependent Recovery Models using Esophageal Mean Dose.

(A) ROC curves show that time-dependent recovery models (mono-exponential, bi-exponential, reciprocal time) outperform traditional approaches (direct accumulation and last course dose). (B) Box plots of mean dose by esophagitis status. The time-dependent models show complete interquartile range separation between patients with and without grade ≥2 esophagitis, whereas traditional methods show overlap, limiting discrimination.

Time-dependent recovery models – max dose

All three time-dependent recovery models yielded better AUCs than the ones obtained with direct accumulation or the last course dose (mono-exponential 0.76 [95% CI 0.63–0.87], bi-exponential 0.76 [95% CI 0.61–0.88], reciprocal-time repair 0.75 [95% CI 0.59–0.87]), but the difference was not significant (supplementary Table 1). The ROC curves for the different models are shown in Figure 3A. All models also showed a significant difference in max dose between patients with and without grade ≥ 2 esophagitis (p = 0.036 for direct accumulation, p = 0.009 for last course dose, and p = 0.002 for the bi-exponential model; Mann-Whitney U test). Incorporating a time-dependent discount to the composite dose also seemed to improve the separation of distributions, but it did not eliminate IQR overlap (figure 3B).

Figure 3. Performance of Traditional and Time-dependent Recovery Models using Esophageal Max Dose.

(A) ROC curves show that time-dependent recovery models (mono-exponential, bi-exponential, reciprocal time) outperform traditional approaches (direct accumulation and last course dose). (B) Box plots of Dmax dose by esophagitis status. While both the last course dose and time-adjusted models improve separation compared to direct accumulation, interquartile overlap persists, limiting discrimination between patients with and without grade ≥2 esophagitis.

Covariates

On univariate analysis, there was no significant association between age (OR 0.97, 95% CI 0.92 - 1.01, p = 0.171), systemic therapy (OR 2.33, 95% CI 0.58 - 9.31, p = 0.230), smoking history (OR 1.62, 95% CI 0.31 - 8.41, p = 0.569), and previous esophagitis (OR 3.17, 95% CI 0.89 - 11.58, p = 0.081) with grade ≥ 2 esophagitis on the BID re -RT course.

Adding covariates did not improve the model fit. However, models including bi-exponential time-dependent accumulation and history of esophagitis from a previous course of thoracic radiotherapy achieved the highest AUC (0.83, 95% CI 0.70 - 0.94 for mean dose and 0.78, 95% CI 0.65 – 0.89 for D_max), and this difference was statistically significant when comparing with direct accumulation (p = 0.040 for mean dose; p = 0.015 for D_max), but it was not significant when comparing with the last course dose (p = 0.071 for mean dose; p = 0.183 for D_max).

Discussion

A re-RT database and dose accumulation framework addressing key challenges were successfully established. Models incorporating time-dependent recovery to discount the biological impact of previously received doses when creating the composite were feasible and suggested improved discrimination for toxicity prediction compared to direct accumulation or the last course dose alone. The best-performing models included time-dependent recovery and a history of esophagitis from a previous course of thoracic radiotherapy, underscoring the importance of risk assessment tools incorporating patient-specific factors.

A recent Swiss study evaluating the survivorship of 112 patients who underwent multiple repeat RT courses reported an interval of up to 8 years between the first and last course³². This variability aligns with our findings, where the interval from the first to the last course varied from 7 months to 13 years. This interval variability highlights the importance of accounting for time in tissue recovery when making treatment decisions, yet it remains a significant challenge for clinicians.

Recently, Sharma et al. evaluated time-dependent re-RT models for radionecrosis in the CNS¹³. The findings showed differences in the shape of dose-response curves and the normal tissue complication probability among non-recurrent and recurrent lesions with direct sum or incorporating time-dependent discount doses¹³. Despite differences in methodology and tissue, their findings also support the development of models that incorporate time to improve toxicity prediction.

The well-documented challenges associated with re-RT largely stem from uncertainties in optimal clinical practices. These uncertainties can be attributed to the absence of standardized and reliable clinical tools and procedures, particularly in the areas of image registration, adjustment of radiobiological doses, and the incorporation of tissue recovery factors³. This study provides a reproducible framework encompassing these aspects and employing commercially available registration/deformation software previously validated for clinical practice²¹. This approach generates 3D dose distributions and accumulations in EQD2 that can accommodate different α/β ratios and can be easily integrated into the planning software. Additionally, a proof-of-concept for a model incorporating time-dependent recovery is presented, showing promising results that could pave the way for developing new tissue recovery algorithms.

This study has limitations that should be acknowledged. First, it is a single-institution study, and the small sample size and the more homogeneous planning and dosimetric strategies limit the ability to generalize findings, though it is sufficient for our proof-of-concept aim. Secondly, our framework does not integrate uncertainties from processes like image registration, EQD2 calculations, contouring, and recovery estimations into final dose reporting³. These uncertainties are significant for patients who experience extreme anatomical variations between courses (e.g., surgery, tumor displacing organs, effusions) and represent an area of research and investigation².

In this study, deformable registration was performed using RayStation’s ANACONDA algorithm with a cross-correlation similarity metric, a clinically validated approach that combines intensity- and geometry-based information. Prior evaluations have shown good performance in thoracic applications, though some variability in accuracy can occur depending on anatomical site and image quality ^22,33. In our cohort, geometric metrics such as DSC and HD95 demonstrated modest agreement (Supplementary Materials), which is expected given the esophagus’s length and known positional variability across treatment courses, particularly in the superior and inferior regions. Importantly, dose-based validation showed strong preservation of dose mapping in the high-dose thoracic region, which is most relevant for toxicity modeling and ultimately for clinical decision-making. Given that such anatomic variability is inherent to real-world re-irradiation scenarios, assessing dose consistency, not only geometric similarity, is essential for developing and validating biologically informed accumulation models.

We recognize that registration uncertainty can be more influential in regions with steep dose gradients and could, in principle, affect the precision of accumulated dose estimates and model performance. Deformable image registration is a necessary common step for both direct dose accumulation and time-dependent accumulation approaches, and our objective was to ensure that the clinically available method, which reflects real-world practice, performed adequately for the proof-of-concept purpose. Given the retrospective design and demonstrated dose preservation, the expected impact on our conclusions is low. In retrospective settings where voxel-wise analysis/image-based data mining is used for response assessment/outcome modeling, such as our study, dose mapping uncertainties are considered to have a low impact on patient safety ². Uncertainties in deformable registration remain an inherent challenge in thoracic re-irradiation, and current clinical software represents the best available approach for dose accumulation in this setting.

Third, studies have suggested that there is complete recovery for acutely responding tissues³⁴, and this assumption might be a limitation for our esophagitis modeling. However, this is mainly derived from animal experiments³⁴, and questions still exist on whether there is a threshold above which tissues will experience less tolerance to re-RT, how recovery progresses with time, and what patient factors might influence recovery. In addition, esophagitis was chosen as a proof-of-concept due to the highest number of events. In future studies, we intend to utilize this framework in larger cohorts to investigate late and other adverse effects.

Fourth, although all time-dependent models improved discrimination, statistical significance was limited, likely because of a lack of power due to the sample size. This might also explain why covariates were not associated with toxicity, although a history of esophagitis suggests a higher risk of repeat toxicity, especially when also considering the time-dependent accumulation. Nonetheless, the consistent direction of effect across models, the observed associations, and the absolute improvement in discrimination collectively support the technical feasibility and potential clinical relevance of these approaches. Importantly, p-values should not be interpreted in isolation, as they do not convey the magnitude or clinical relevance of an observed effect³⁵. Given the exploratory nature of this analysis and our primary objective to assess the feasibility of time-dependent recovery models, rather than select a single “best” model or create a final clinical model, the results sufficiently justify further investigation with a larger cohort to increase power. Insufficient power is a constant problem in re-RT studies, and our study provides a novel framework with promising results. Furthermore, future studies should investigate recovery dynamics in more detail, including identifying the most appropriate model and refining parameters such as the repair constants and the fast/slow component fractions.

Additionally, the determination of dose metrics for time-dependent models can be complicated. While metrics such as mean dose are straightforward, volumetric measures such as V60Gy pose greater challenges. As the dose clouds can differ between courses, the volumetric measures from each course cannot be taken independently and then summed. However, as there can be repair, simply utilizing the volumetric measure from the composite may not be accurate. For this study, we utilized direct measures that could avoid these issues. In the future, these complexities will need to be explored to determine the best procedures for re-RT studies in order to study all types of DVH metrics.

While previously delivered doses cannot be removed, our model integrates its biological effect through time-based discounting. Based on the assumption that there is recovery, the effects of the previously received dose are expected to be lower. Therefore, providing a discounted dose is a useful way to integrate this previous dose with the biological framework we are accustomed to considering.

A fixed RBE of 1.1 was used for all proton dose calculations, consistent with current clinical proton treatment planning systems and most published outcome studies. We recognize that the RBE can vary with LET, dose per fraction, tissue type, and endpoint, and that this variability may be relevant for esophageal toxicity. This is an active area of investigation, and future work incorporating LET- and endpoint-specific RBE models may improve the biological accuracy of dose estimates³⁶.

Overall, the framework presented in this study provides an innovative approach to studying re-RT-related toxicity, allowing for the incorporation of more complex recovery dynamics. Future directions include identifying optimal recovery models, characterizing recovery kinetics, and determining which clinical or treatment-related factors influence toxicity. These findings also represent a call to action for multi-institutional collaboration to investigate the toxicity and allow for models evaluating rarer events where single institutional data is not likely to have enough data to model, such as grade 5 toxicities, but are crucially important. Re-RT is an increasingly pressing issue with limited current guidance, and our framework for standardized database and time-dependent models could help lead to reduced toxicity with improved patient-specific guidance for clinical care of re-RT patients.