Quantifying the Dosimetric Impact of Proton Range Uncertainties on RBE-Weighted Dose Distributions in Intensity-Modulated Proton Therapy for Bilateral Head and Neck Cancer

Background: In current clinical practice, intensity-modulated proton therapy (IMPT) head and neck cancer (HNC) plans are generated using a constant relative biological effectiveness (cRBE) of 1.1. The primary goal of this study was to explore the dosimetric impact of proton range uncertainties on RBE-weighted dose (RWD) distributions using a variable RBE (vRBE) model in the context of bilateral HNC IMPT plans. Methods: The current study included the computed tomography (CT) datasets of ten bilateral HNC patients who had undergone photon therapy. Each patient’s plan was generated using three IMPT beams to deliver doses to the CTV_High and CTV_Low for doses of 70 Gy(RBE) and 54 Gy(RBE), respectively, in 35 fractions through a simultaneous integrated boost (SIB) technique. Each nominal plan calculated with a cRBE of 1.1 was subjected to the range uncertainties of ±3%. The McNamara vRBE model was used for RWD calculations. For each patient, the differences in dosimetric metrices between the RWD and nominal dose distributions were compared. Results: The constrictor muscles, oral cavity, parotids, larynx, thyroid, and esophagus showed average differences in mean dose (Dmean) values up to 6.91 Gy(RBE), indicating the impact of proton range uncertainties on RWD distributions. Similarly, the brachial plexus, brain, brainstem, spinal cord, and mandible showed varying degrees of the average differences in maximum dose (Dmax) values (2.78–10.75 Gy(RBE)). The Dmean and Dmax to the CTV from RWD distributions were within ±2% of the dosimetric results in nominal plans. Conclusion: The consistent trend of higher mean and maximum doses to the OARs with the McNamara vRBE model compared to cRBE model highlighted the need for consideration of proton range uncertainties while evaluating OAR doses in bilateral HNC IMPT plans.


Introduction
The recognition of intensity-modulated proton therapy (IMPT) as an advanced modality in radiation therapy for the management of head and neck (HN) cancer is growing [1][2][3].IMPT has the potential to lower the occurrence of radiation-treatment-related toxicities such as dysphagia and xerostomia [4].In the current clinical practice, IMPT HN plans are generated using a constant relative biological effectiveness (cRBE) of 1.1 [5].However, studies [5,6] indicate that the RBE can exhibit variability based on factors such as dose, treatment technique, cell type, radiosensitivity of the tissues, α/β ratio, oxygenation, clinical or biological endpoint, and linear energy transfer (LET).Numerous phenomenological models incorporating variable relative biological effectiveness (vRBE) have been developed [7,8].
Studies have shown that the RBE can be correlated to the dose-averaged LET (LET d ) for therapeutic proton energies [9,10].The highest LET d in the proton plan occurs at the very distal part of the spread-out Bragg peak (SOBP) [11].More recently, Underwood et al. [12] reviewed clinical studies on vRBE in proton therapy.Out of twenty-two studies reviewed by Underwood et al. [12], six studies concluded that they had found clinical evidence for vRBE, whereas twelve studies showed inconclusive results, and four studies did not find clinical evidence for vRBE.Several investigators [13][14][15][16][17][18][19] have delved into the dosimetric effects of vRBE models for various disease sites in IMPT.The vRBE along the path of protons presents an additional factor contributing to the uncertainty in IMPT planning.The increasing LET d can lead to higher RBE-weighted dose (RWD) distributions [11,20].Moreover, uncertainties in proton range could further influence the LET d distributions [21][22][23], thereby impacting the RWD to the OARs located in close proximity to the clinical target volume (CTV).
While previous investigations [13][14][15][16][17][18][19] have explored the dosimetric impact of vRBE models for various cancers, the impact of combining proton range uncertainties and vRBE models in bilateral HN IMPT planning remains largely unexplored.Investigating the combined effect of proton range uncertainties and vRBE models for bilateral HN cancer is critical for several reasons.Firstly, bilateral HN cancers involve tumors situated near OARs, making accurate dose delivery essential to minimize toxicity and maintain treatment efficacy.Secondly, the use of IMPT allows for highly conformal dose distributions, but uncertainties in proton range and vRBE introduce complexities that can affect treatment outcomes.Thirdly, HN cancer patients often experience radiotherapy-induced side effects, such as xerostomia and dysphagia [24][25][26], highlighting the importance of optimizing treatment plans to minimize the dose to the surrounding critical structures.Therefore, the primary goal of the current study was to explore the influence of proton range uncertainties on the RWD to the OARs in the context of bilateral HN cancer treatment plans generated by employing the IMPT technique.

Contouring and Treatment Planning
In this Institutional Review Board (IRB)-approved retrospective treatment planning study, we included anonymized computed tomography (CT) datasets of ten bilateral HN cancer patients who had undergone photon therapy.The CTV was categorized into CTV_High and CTV_Low.The OARs were contoured using Limbus AI (v1.7;Limbus AI Inc., Regina, SK, Canada) software and later reviewed by the treatment planners.
Treatment plans were created within RayStation (v11B; RaySearch Laboratories, Stockholm, Sweden).We utilized the beam model that is based on the IBA's ProteusOne PBS proton therapy system.Specifically, for each patient, a nominal IMPT treatment plan was generated using the Monte Carlo algorithm for both robust plan optimization (setup error: ±3 mm; range error: ±3%; 10,000 ions/spot) and final dose calculations (0.5% statistical uncertainty; 3 mm voxel size).Each plan included three beams with a range shifter of 4 cm water equivalent thickness (WET) to deliver doses to the CTV_High and CTV_Low for doses of 70 Gy(RBE) and 54 Gy(RBE), respectively, in 35 fractions through a simultaneous integrated boost (SIB) technique.All nominal plans used cRBE of 1.1.Plan normalization was performed to ensure that 99% of CTV_High received 69.3 Gy(RBE).Nominal plans were evaluated based on the institutional criteria for bilateral HN cancer.

Range Uncertainties
Each nominal plan calculated with a cRBE of 1.1 was subjected to the range uncertainties of ±3%.The range uncertainty in RayStation was modeled by scaling the mass density from the CT of the patient and was universal for all beams.The range uncertainties of −3% and +3% mean that the mass density was scaled by −3% and +3%, respectively.

LET d and RWD Calculations
The LET d distributions were calculated (3 mm voxel size) for the nominal and perturbed plans (±3% range uncertainty).In RayStation, LET d is defined as the voxelwise unrestricted, dose-averaged LET d [21].The RWD was then calculated for the CTVs and OARs (see Table 1).For RWD calculations, we used the phenomenological vRBE model developed by McNamara [9].
where p 0 , p  [7,9].The α/β ratios can vary for different tumors and critical structures; however, for this study, we utilized the α/β values consistent with those used in RWD-related publications [19,21,27,28].Specifically, an α/β ratio of 10 was applied to the CTVs, while an α/β ratio of 2 was used for all OARs.All RWD calculations were performed within the scripting environment of RayStation.

Dosimetric Analysis
For each patient, the differences (∆) between the RWD distributions (D vRBE ) and nominal dose distribution (i.e., D cRBE ) were compared.Specifically, the mean dose and the maximum dose to the OARs and CTVs were evaluated per institutional protocol.
where x = mean dose or maximum dose result.

Results
Table 1 shows the dosimetric differences between the RWD distributions and nominal dose distributions.Figure 1 illustrates the dose distributions (cRBE = 1.1) in a nominal plan (no range uncertainty) of an example HN patient as well as the LET d distributions in a nominal plan of the same patient.The differences are averaged over ten patients, as shown in Equation (4).

Dosimetric Analysis
For each patient, the differences (Δ) between the RWD distributions (DvRBE) and nominal dose distribution (i.e., DcRBE) were compared.Specifically, the mean dose and the maximum dose to the OARs and CTVs were evaluated per institutional protocol.
where x = mean dose or maximum dose result.

Results
Table 1 shows the dosimetric differences between the RWD distributions and nominal dose distributions.Figure 1 illustrates the dose distributions (cRBE = 1.1) in a nominal plan (no range uncertainty) of an example HN patient as well as the LETd distributions in a nominal plan of the same patient.The differences are averaged over ten patients, as shown in Equation ( 4).

Mean Dose (Dmean) Evaluation for OARs
The vRBE model consistently yielded a higher mean dose to the OARs compared to the cRBE model.Within the vRBE model, the Dmean values exhibited variations among the three RWD distributions.Specifically, in a nominal scenario without the range uncertainty, the Dmean was higher than that in a +3% range uncertainty scenario but lower than that in a −3% range uncertainty scenario.The Δavg for the esophagus and oral cavity ranged from 2.76 to 3.40 Gy(RBE) and from 3.33 to 4.00 Gy(RBE), respectively.Analysis of the left and right parotids revealed Δavg values ranging from 3.72 to 5.02 Gy(RBE).Additionally, for the larynx and thyroid, the Δavg ranged from 5.18 to 6.91 Gy(RBE) and from 6.54 to 6.90 Gy(RBE), respectively.

Mean Dose (D mean ) Evaluation for OARs
The vRBE model consistently yielded a higher mean dose to the OARs compared to the cRBE model.Within the vRBE model, the D mean values exhibited variations among the three RWD distributions.Specifically, in a nominal scenario without the range uncertainty, the D mean was higher than that in a +3% range uncertainty scenario but lower than that in a −3% range uncertainty scenario.The ∆ avg for the esophagus and oral cavity ranged from 2.76 to 3.40 Gy(RBE) and from 3.33 to 4.00 Gy(RBE), respectively.Analysis of the left and right parotids revealed ∆ avg values ranging from 3.72 to 5.02 Gy(RBE).Additionally, for the larynx and thyroid, the ∆ avg ranged from 5.18 to 6.91 Gy(RBE) and from 6.54 to 6.90 Gy(RBE), respectively.

Maximum Dose (D max ) Evaluation for OARs
The evaluation of D max exhibited a similar trend to that of D mean , with the vRBE model predicting higher values compared to the cRBE model.Additionally, a consistent pattern was observed where the vRBE model's results for a nominal scenario were higher compared to a +3% range uncertainty scenario but lower compared to a −3% range uncertainty scenario.For the brachial plexus, the ∆ avg was up to 10.75 Gy(RBE).In the case of the brain and brainstem, the ∆ avg ranged from 4.93 to 6.59 Gy(RBE) and from 2.78 to 3.86 Gy(RBE), respectively.Regarding the spinal cord, the ∆ avg ranged from 2.13 to 5.19 Gy(RBE).However, for the mandible, the ∆ avg remained consistent at 7.10-7.20Gy(RBE) for both nominal and range uncertainty scenarios.

D mean and D max Evaluation for Target Volumes
Figure 2 illustrates the D mean and D max to CTV_70 in ten patients for cRBE and vRBE models.For D mean , the vRBE model always produced lower values compared to the cRBE model.On average, the D mean from RWD distributions (vRBE) was lower by 1.6 ± 0.3% for a nominal (i.e., unperturbed) scenario, 1.4 ± 0.4% for a range uncertainty of +3% scenario, and 1.8 ± 0.2% for a range uncertainty of −3% scenario.In evaluating D max results in all ten patients, there was no clear trend of the vRBE model producing either higher or lower than the cRBE model for different scenarios.On average, when compared to the cRBE model, the D max from the RWD distribution (vRBE) was lower by 0.7 ± 0.5% for a nominal (i.e., unperturbed) scenario, 0.1 0.9% for a range uncertainty of +3% scenario, and 1.1 ± 1.0% for a range uncertainty of −3% scenario.

Maximum Dose (Dmax) Evaluation for OARs
The evaluation of Dmax exhibited a similar trend to that of Dmean, with the vRBE model predicting higher values compared to the cRBE model.Additionally, a consistent pattern was observed where the vRBE model's results for a nominal scenario were higher compared to a +3% range uncertainty scenario but lower compared to a −3% range uncertainty scenario.For the brachial plexus, the Δavg was up to 10.75 Gy(RBE).In the case of the brain and brainstem, the Δavg ranged from 4.93 to 6.59 Gy(RBE) and from 2.78 to 3.86 Gy(RBE), respectively.Regarding the spinal cord, the Δavg ranged from 2.13 to 5.19 Gy(RBE).However, for the mandible, the Δavg remained consistent at 7.10-7.20Gy(RBE) for both nominal and range uncertainty scenarios.

Dmean and Dmax Evaluation for Target Volumes
Figure 2 illustrates the Dmean and Dmax to CTV_70 in ten patients for cRBE and vRBE models.For Dmean, the vRBE model always produced lower values compared to the cRBE model.On average, the Dmean from RWD distributions (vRBE) was lower by 1.6 ± 0.3% for a nominal (i.e., unperturbed) scenario, 1.4 ± 0.4% for a range uncertainty of +3% scenario, and 1.8 ± 0.2% for a range uncertainty of −3% scenario.In evaluating Dmax results in all ten patients, there was no clear trend of the vRBE model producing either higher or lower than the cRBE model for different scenarios.On average, when compared to the cRBE model, the Dmax from the RWD distribution (vRBE) was lower by 0.7 ± 0.5% for a nominal (i.e., unperturbed) scenario, 0.1 ± 0.9% for a range uncertainty of +3% scenario, and 1.1 ± 1.0% for a range uncertainty of −3% scenario.

Discussion
The current clinical practice involves generating IMPT plans using a cRBE of 1.1.However, it is known that the RBE can vary based on several factors, leading to the development of models incorporating vRBE [7].Our study contributes to the evolving understanding of vRBE in IMPT for HN cancer.Specifically, we explored the influence of proton range uncertainties on the RWD to the OARs and target volumes in bilateral HN cancer treatment plans generated using the IMPT technique.
The results from our study revealed notable variations in Dmean values for the majority of OARs between the cRBE and vRBE models.The vRBE model consistently yielded higher Dmean values, with variations observed among different range uncertainty scenarios.The constrictor muscles, oral cavity, parotids, larynx, thyroid, and esophagus showed large differences in Dmean values, indicating the impact of proton range uncertainties on RWD distributions.Similarly, the evaluation of Dmax exhibited a consistent trend, with the vRBE model predicting higher values compared to the cRBE model.The brachial plexus,

Discussion
The current clinical practice involves generating IMPT plans using a cRBE of 1.1.However, it is known that the RBE can vary based on several factors, leading to the development of models incorporating vRBE [7].Our study contributes to the evolving understanding of vRBE in IMPT for HN cancer.Specifically, we explored the influence of proton range uncertainties on the RWD to the OARs and target volumes in bilateral HN cancer treatment plans generated using the IMPT technique.
The results from our study revealed notable variations in D mean values for the majority of OARs between the cRBE and vRBE models.The vRBE model consistently yielded higher D mean values, with variations observed among different range uncertainty scenarios.The constrictor muscles, oral cavity, parotids, larynx, thyroid, and esophagus showed large differences in D mean values, indicating the impact of proton range uncertainties on RWD distributions.Similarly, the evaluation of D max exhibited a consistent trend, with the vRBE model predicting higher values compared to the cRBE model.The brachial plexus, brain, brainstem, spinal cord, and mandible showed varying degrees of differences in D max values under different scenarios, highlighting the sensitivity of these structures to proton range uncertainties.Incorporating insights from other studies, such as the work by Garbacz et al. [27] and Hahn et al. [21], reinforces our findings.Hahn et al.'s study [21] observed the LET d hotspots in OARs, particularly in brain tumor patients.Garbacz et al. [27] highlighted that the challenges in treating tumors that are close to critical structures necessitate careful consideration of vRBE to avoid increased doses and extended beam ranges.
In assessing the CTVs, Rana et al. [22] and Hahn et al. [21] emphasized the importance of considering range uncertainties and highlighted the robustness of LET d distributions in the target volumes.Our study demonstrated that the vRBE model consistently produced lower D mean values to the CTVs compared to the cRBE model.However, the trend in D max values for the CTV was less clear, with no consistent pattern observed across range uncertainty scenarios.
A comprehensive review by Underwood et al. [12] explored the existing literature on vRBE in proton therapy, shedding light on the current state of knowledge in this field.The review considered twenty-two studies, revealing a variety of conclusions.Only six studies provided clinical evidence supporting the presence of vRBE, while twelve studies presented inconclusive results, and four studies did not find supporting evidence.Our study was performed based on the McNamara vRBE model for RWD calculations.Rorvik et al.'s study [12] highlighted considerable variations in estimations of RBE and RWD from different models.This emphasizes the importance of acknowledging these variations in the treatment planning study.In our study, the use of the SIB technique for treating HNC results in varying fractional doses-both high and low-was considered.Previous reports [30] indicate that a lower fractional dose can potentially increase the RBE.Future studies should explore how the combination of range uncertainty and different fractionation schemes can impact the RWD dose to the OARs.Additionally, we used the alpha/beta ratio of 2 for all the OARs.Resch et al. [31] provided insight into the uncertainty of alpha/beta ratios in nasopharyngeal and prostate cancer cases and their OAR overdosage.The findings from the above-mentioned studies [7,12,31] align with our emphasis on the need for standardized approaches in interpreting results from different RBE models.Moreover, the current ambiguity on clinical evidence of vRBE underscores the challenges in establishing a consistent understanding of the impact of variable RBE in proton therapy.

Conclusions
The consistent trend of higher mean and maximum doses to the OARs with the McNamara vRBE model compared to cRBE model highlighted the need for consideration of proton range uncertainties while evaluating OAR doses for bilateral HN cancer treatment plans generated by employing the IMPT technique.

Figure 1 .
Figure 1.(a) Dose distributions (cRBE = 1.1) in a nominal plan (no range uncertainty) of an example HNC patient.(b) LETd distributions in a nominal plan of the same patient shown in (a).

Figure 1 .
Figure 1.(a) Dose distributions (cRBE = 1.1) in a nominal plan (no range uncertainty) of an example HNC patient.(b) LET d distributions in a nominal plan of the same patient shown in (a).

Figure 2 .
Figure 2. (a) Mean dose to the CTV_70 and (b) maximum dose to the CTV_70 in nominal (cRBE), RWD of nominal, RWD of +3% range uncertainty, and RWD of −3% range uncertainty plans in ten patients.

Figure 2 .
Figure 2. (a) Mean dose to the CTV_70 and (b) maximum dose to the CTV_70 in nominal (cRBE), RWD of nominal, RWD of +3% range uncertainty, and RWD of −3% range uncertainty plans in ten patients.
1 , and p 2 are the fit parameters (p 0 = 0.99064, p 1 = 1.1012, and p 2 = −0.0039) in the McNamara model.The McNamara model is based on the linear quadratic model and incorporates the LET d distributions within the specified volume.The McNamara model was chosen for this study due to its extensive application in exploring proton RBE effects in the recent literature [19,21,27-29].Comprehensive details on the McNamara model are available in the referenced publications

Table 1 .
Dosimetric differences in D mean and D max between the RWD and nominal dose distributions.