Relative Biological Effectiveness of Carbon Ion Versus Photon Radiation Therapy for Acute Radiation-Induced Esophagitis in Locally Advanced Non-small Cell Lung Cancer Derived From Normal Tissue Complication Probability Modeling.

Introduction
Acute radiation-induced esophagitis (ARIE) is a common acute toxicity associated with thoracic radiation therapy, particularly in the treatment of non-small cell lung cancer (NSCLC).1 To assess the risk of ARIE, several normal tissue complication probability (NTCP) models have been developed and validated for both photon and proton radiation therapy.2, 3, 4 Among them, the Lyman-Kutcher-Burman (LKB), relative seriality, and Logit models are most widely used.5
Carbon-ion radiation therapy (CIRT) minimizes toxicity to surrounding organs at risk (OARs) through enhanced dose conformality while enabling the delivery of an adequate tumor dose owing to its distinct physical and biological advantages characterized by a sharp Bragg peak.6,7 The relative biological effectiveness (RBE) of carbon ions is generally higher than that of protons or photons, particularly within the Bragg peak region.8 However, RBE is affected by multiple factors, such as dose per fraction, linear energy transfer (LET), tissue type, and biological endpoint, and no universally accepted method for its clinical determination currently exists.6,9
Several models for RBE-weighted dose calculation are currently employed by different institutions, with the 2 most widely used being the local effect model (LEM) and the Microdosimetric Kinetic Model (MKM).10,11 Validated conversion methods between LEM and MKM, or between photon and CIRT plans, are still lacking,12 underscoring the need for clinical RBE estimation and standardized cross-model comparisons. In our previous study, we successfully explored the feasibility of estimating clinical RBE using the equivalent uniform dose corresponding to a 50% complication probability (TD50) derived from LKB NTCP modeling.13
In this study, we estimated the clinical RBE of CIRT by fitting an NTCP model for ARIE, using TD₅₀ as the reference parameter.

Methods and Materials

Patient selection and matching
Patients diagnosed with locally advanced NSCLC (LA-NSCLC) who underwent treatment at Fudan University Shanghai Cancer Center and Shanghai Proton and Heavy Ion Center between January 2016 and December 2023 were reviewed. Eligible patients met the following inclusion criteria: (1) stage III NSCLC according to the American Joint Committee on Cancer 8th edition; (2) definitive photon or CIRT; (3) age 18 to 80 years; (4) completion of the prescribed radiation therapy; and (5) availability of dose-volume histograms (DVH) data. Exclusion criteria were: (1) recurrent or metastatic NSCLC; (2) prior thoracic irradiation; (3) concurrent malignancies; and (4) incomplete follow-up.
To balance baseline differences between treatment groups, propensity score matching (PSM) was employed in a 1:1 ratio using the nearest-neighbor method with a caliper of 0.1 to pair patients who received CIRT with those treated with photon radiation therapy. Matching variables included sex, age, histological subtype (squamous cell carcinoma, adenocarcinoma, or other), TNM stage (IIIA, IIIB, or IIIC), tumor location (central vs peripheral), the minimum distance between the esophagus and gross tumor volume (GTV), and receipt of chemotherapy and/or immunotherapy. This study was approved by the institutional review board of the participating institution. Given the retrospective nature of the research, the requirement for informed consent was waived.

Radiation therapy and ARIE
All patients included in this study underwent definitive radiation therapy. Treatment planning for CIRT and conventional photon radiation therapy in locally advanced NSCLC has been previously described in detail.14,15 In the photon group, respiratory gating or active breathing control techniques were not routinely applied. Photon therapy was delivered using 6 MV x-ray beams generated by a Varian Clinac 21EX linear accelerator (Varian Medical Systems) with intensity-modulated radiation therapy. A conventional fractionation schedule was employed, consisting of 2 Gy per fraction, 5 fractions per week, to a total dose of 50 to 66 Gy. In the CIRT group, respiratory gating or active breathing control was implemented for tumors with motion exceeding 5 mm. Carbon-ion beams were produced by the IONTRIS system (Siemens) with beam energies ranging from 250 to 430 keV/μm. Intensity modulated CIRT was performed using the pencil beam scanning technique with fixed beam angles. Doses were prescribed in Gy (RBE), the gray equivalent to photons, based on the LEM embedded in the Syngo system. Patients received 3 to 4 Gy (RBE) per fraction, 5 times per week, for a total dose of 69 to 83.6 Gy (RBE).
Esophageal contouring was routinely performed during treatment planning for LA-NSCLC. Minimum esophagus-GTV distance was set to 0 cm when the shortest distance between the esophagus and GTV was <0.1 cm. For each patient, the esophageal DVH was generated from the treatment plan system.
Figure E1 shows the absolute physical and biological dose distributions for ARIE in 3 CIRT patients and 3 photon radiation therapy patients. The primary clinical endpoint was the occurrence of grade ≥2 ARIE, defined and graded according to the National Cancer Institute Common Terminology Criteria for Adverse Events version 5.0 as a disorder characterized by inflammation of the esophageal wall.16 Patients were monitored for ARIE from the start of radiation therapy until 3 months after radiation therapy completion.

NTCP model
Detailed NTCP model formulations and parameters are provided in the Supplementary Material. NTCP modeling was primarily performed using the LKB model, with the Logit model included for comparison.3, 4, 5 Parameters were fitted using maximum-likelihood estimation.

Estimation of RBE using TD₅₀
RBE is defined as the ratio of the absorbed doses from 2 radiation modalities that produce the same biological endpoint. The TD₅₀ derived from NTCP modeling based on generalized equivalent uniform dose (gEUD) serves as the reference for RBE calculations. Accordingly, the RBE of CIRT relative to photon radiation therapy was calculated as:
The dose units for both the carbon-ion and photon groups were expressed as physical dose (Gy). This approach is based on the assumption of equivalent clinical endpoints, specifically a 50% incidence of grade ≥2 ARIE, at their respective TD₅₀ dose levels.

Model performance and statistical analysis
The analysis was performed separately within the carbon-ion group and the photon group. Dose-volume metrics were compared with the Mann-Whitney U test. Associations between V5-V70, D1cc-D5cc, Dmean, and Dmax and the grade of ARIE were assessed with Spearman rank correlations. NTCP curves were fit by maximum-likelihood estimation and evaluated with 3-fold cross-validation, using the area under the receiver operating characteristic curve (ROC AUC) as the performance metric. Continuous variables were analyzed with the Wilcoxon signed-rank test, and categorical variables with the χ² test. Two-sided P < .05 was considered statistically significant. All statistical analyses were conducted using SPSS Statistics (version 29), while the NTCP model was developed and validated using custom code written in Python (version 3.12).

Results
A total of 330 patients with stage III NSCLC were included after PSM, with 165 patients in each treatment group. Baseline demographic and clinical characteristics were well balanced between groups and are summarized in Table 1. No grade 4 or 5 ARIE events were observed in either cohort, and no grade 3 events occurred in the CIRT group. The incidence of grade 2 or higher ARIE was significantly lower in the CIRT group compared to the photon group (11 [6.7%] vs 32 [19.4%], P ≤ .001). No significant differences were observed between groups in terms of age, sex, histology, TNM stage, tumor location, receipt of chemotherapy or immunotherapy, or the minimum distance between the esophagus and GTV.
Mean esophageal DVH curves were higher across a wide dose range in patients with grade ≥2 ARIE in both treatment groups (Fig. 1A, B). For CIRT (physical dose), the optimal parameters of the LKB NTCP model were TD₅₀ = 23.37 Gy, n = 0.15, and m = 0.18, with a corresponding AUC of 0.81 ± 0.14 (Table 2). For the photon group (physical dose), the optimal LKB parameters were TD₅₀ = 70.50 Gy, n = 0.14, and m = 0.33, with an AUC of 0.66 ± 0.17. Corresponding dose-response and ROC curves are shown in Figure 1C-F.
The Logit NTCP models based on Dmean and Dmax in the CIRT and photon groups are summarized in Table E3 and illustrated in Figures E2 and E3.
Based on TD₅₀ values derived from the LKB model, the estimated RBE of CIRT was 3.02 when compared with photon radiation therapy (Eq. 1).

Discussion
To our knowledge, this is the first study aiming to develop a clinically applicable method to estimate the RBE value based on NTCP modeling of grade ≥2 ARIE for both CIRT and photon radiation therapy. Baseline characteristics were balanced between groups using PSM to ensure comparability. Using the TD₅₀ from the LKB NTCP model for grade ≥2 ARIE as the reference parameter, we estimated the clinical RBE of CIRT to be 3.02 compared with photon radiation therapy in patients with LA-NSCLC. In addition, compared with photon radiation therapy, CIRT demonstrated improved dose conformity and greater consistency in meeting dose constraints, allowing for more precise dose delivery to the tumor volume (Fig. E1). Our findings suggest that CIRT significantly reduces esophageal dose exposure and lowers the risk of grade ≥2 ARIE.
DVH comparisons showed that patients with grade 2 or higher ARIE had significantly higher mean esophageal DVH curves across a wide dose range in both treatment groups (Fig. 1A, B). Within the CIRT group, patients who developed grade 2 or higher ARIE had significantly higher esophageal dose metrics, including mean dose, maximum dose, and D1cc-D5cc, V5Gy-V20Gy, V10Gy (RBE)-V70Gy (RBE) (Table E1). A similar pattern was observed in the photon group (Table E1). Spearman analysis further confirmed that the extent and severity of the high-dose hot region (Dmax, Dxcc, V≥20 to 40 Gy or Gy(RBE)) showed predictive performance for acute esophagitis that was not inferior to mean dose (Table E2), which is consistent with previous studies reporting that V50 or higher mean esophageal dose is the most accurate predictor of acute esophageal injury.17,18
The fitted values of m and n in the NTCP model for grade ≥2 ARIE aligned well with those reported by Burman et al,19 and all 3 LKB parameters showed narrow CIs. Model reliability was validated through 3-fold cross-validation, and predictive performance was evaluated using the area under the ROC curve (AUC). Both models demonstrated modest performance. The LKB model yielded an n value of 0.15 for CIRT, and 0.14 for photon radiation therapy supporting the esophagus as a serial organ and suggesting that ARIE is primarily driven by hot-spot high-dose regions. The TD₅₀, defined as the dose associated with a 50% probability of complication, was 23.37 Gy for CIRT and 70.50 Gy for photon radiation therapy. This highlights the higher biological effectiveness of CIRT, as a substantially lower dose was associated with a comparable 50% risk of grade ≥2 ARIE. The LKB model demonstrated strong predictive performance and provides a useful framework for refining dose constraints to normal tissues. Although gEUD-based modeling was also explored, the lack of direct DVH mapping required additional analyses. In the CIRT group, limiting Dmean to <23.00 Gy (RBE) and Dmax to <77.47 Gy (RBE) was associated with a predicted risk of grade ≥2 ARIE below 5% (Table E3, Figs. E2 and E3). In the photon group, Dmean <10.72 Gy and Dmax <49.40 Gy were similarly associated with a risk <5% (Table E3, Figs. E2 and E3).
The gEUD values used for estimating the RBE between carbon-ion and photon radiation therapy were based on physical dose distributions. Although the RBE of carbon ions is often assumed to be a constant value, its estimation is subject to considerable uncertainty, including variability arising from experimental conditions and biological context. The TD₅₀ of LKB NTCP model of grade ≥2 ARIE was 23.37 Gy for CIRT and 70.50 Gy for photons in our study. Accordingly, the clinical RBE of CIRT for grade ≥2 ARIE, estimated from the LKB-based TD₅₀ (physical dose), was 3.02 (Eq. 1). Because the gEUD formula accounts for both dose and volume information within the DVH, and the parameter n ranges from 0 to 1 (approximating Dmax at lower values, consistent with serial complications, and approaching Dmean at higher values, consistent with parallel complications), gEUD provides a more representative description of an organ’s spatial dose distribution.20 Under ideal conditions where irradiation techniques are standardized, toxicity grading is consistent, confounding factors are controlled, and a sufficiently large and representative patient cohort is available, the TD₅₀ parameter in the LKB model is expected to converge to a stable value for a given clinical endpoint. However, it should still be regarded as an empirical parameter derived from statistical modeling rather than a fixed biological constant.
Accurately determining the RBE of carbon ions for normal esophageal tissue remains challenging. Classical clonogenic assays are difficult to apply to primary esophageal epithelial cells because of limited tissue accessibility, poor in vitro viability, and low plating efficiency, especially when compared to tumor cell lines. In addition, there is currently no reliable animal model available to evaluate the RBE of radiation-induced esophageal injury. Therefore, using the TD₅₀ ratio derived from clinical NTCP modeling provides a more practical and clinically relevant approach for estimating RBE, as it directly reflects treatment-associated toxicity in real-world patient populations. In our cohort, the LKB-derived TD₅₀ yielded the most consistent clinical RBE estimate (3.02) for grade ≥2 ARIE. Notably, the use of TD₅₀ derived from robust models with balanced baseline characteristics strengthens the validity of RBE estimation in this context.
The RBE of CIRT is influenced by multiple factors, including dose per fraction, LET, tissue or cell type, hypoxic status, and the specific biological endpoint evaluated.21,22 For dose per fraction, RBE decreases when a larger dose is given per fraction or when fewer fractions are used.22 LET describes the energy deposited by charged particles per unit path length in tissue. Higher LET leads to denser ionizations and more complex DNA damage. The RBE reflects the biological effect per unit physical dose, and usually increases with rising LET, with a peak around ∼100 keV/μm, where carbon ions achieve their highest biological effectiveness.21 Beyond this LET, the RBE may plateau or even decline because of the “overkill” effect, where further energy deposition does not add to lethal damage.23 Current mainstream models for RBE calculation employ different parameters and methodologies. Heavy Ion Medical Accelerator in Chiba uses the MKM, based on in vitro data and clinical experience with neutron beams.11 Clinical centers such as Heidelberg Ion Therapy Center (HIT), Marburg Ion-Beam Therapy Center (MIT), Centro Nazionale di Adroterapia Oncologica (CNAO), MedAustron Ion Therapy Center (MedAustron), and Shanghai Proton and Heavy Ion Center (SPHIC) use the LEM, which takes photon-derived cell-survival data as the reference radiation.10 At our center, RBE-weighted doses for CIRT were calculated using the LEM I, which incorporates the above complex factors to provide a more biologically relevant estimation.10 However, the RBE derived from its default parameters may not fully reflect clinical outcomes.24 Therefore, from a clinical perspective, quantifying and comparing isoeffective biological responses in OARs between carbon ions and photons are essential. By identifying the physical dose levels that yield the same biological endpoint (eg, tumor response, adverse event), carbon-ion and photon isoeffective doses can be derived, which in turn enables a clinically relevant estimation of carbon-ion RBE under real-world treatment conditions.13,25 Previous studies have validated RBE estimation by comparing photon and carbon-ion doses at equivalent biological endpoints, such as a 50% probability of tumor control or radiation-induced lung fibrosis.26, 27, 28 Accordingly, estimating RBE using TD₅₀ or D₅₀ from NTCP models offers a novel approach.

Study limitations
However, several limitations should be acknowledged. The NTCP model for the photon cohort demonstrated only modest discriminative performance, potentially because of variations in treatment technique, dose distribution, or reporting bias inherent to retrospective data sets. In addition, late esophageal toxicity, which may have distinct dose-volume correlations compared to acute toxicity, was not evaluated and warrants further investigation.29 Another key limitation of this study is that the spatial heterogeneity of LET within the esophagus, and its implications for clinically relevant RBE, was not systematically characterized. Future studies should incorporate LET distribution metrics, such as LET volume histograms, to better capture the voxel-level LET structure within the OAR. Such approaches would enable more robust model-based RBE estimation directly informed by LET distributions, rather than relying solely on dose-based surrogates. Moreover, RBE estimation is inherently influenced by biological variability across patient populations, including differences in tissue sensitivity, comorbidities, and systemic therapies.8 The relatively small sample size, particularly after PSM, may limit the statistical power and generalizability of our findings. Heterogeneity in contouring practices, dose calculation algorithms, and model parameterization may further affect reproducibility. Finally, as RBE is a complex quantity, the use of TD₅₀ based on NTCP modeling provides a simplified representation and should be interpreted with caution. Prospective validation in larger, multi-institutional cohorts with standardized toxicity scoring and consistent dosimetry metrics is needed to confirm these results and refine the proposed approach for broader clinical application.

Conclusions
We developed a novel NTCP-based approach that allows clinical estimation of the RBE of CIRT in patients with LA-NSCLC based on grade ≥2 ARIE. Our findings provide a clinically motivated strategy to quantify the clinical biological effectiveness of carbon ions relative to photons. Further refinement and prospective external validation are warranted to ensure the robustness and broader applicability of this RBE estimation approach.

Disclosures
None.