Linear energy transfer distributions in the brainstem depending on tumour location in intensity-modulated proton therapy of paediatric cancer

An updated variable RBE model for proton therapy

Objective.While a constant relative biological effectiveness (RBE) of 1.1 forms the basis for clinical proton therapy, variable RBE models are increasingly being used in plan evaluation. However, there is substantial variation across RBE models, and several newin vitrodatasets have not yet been included in the existing models. In this study, an updatedin vitroproton RBE database was collected and used to examine current RBE model assumptions, and to propose an up-to-date RBE model as a tool for evaluating RBE effects in clinical settings.Approach.A proton database (471 data points) was collected from the literature, almost twice the size of the previously largest model database. Each data point included linear-quadratic model parameters and linear energy transfer (LET). Statistical analyses were performed to test the validity of commonly applied assumptions of phenomenological RBE models, and new model functions were proposed forRBEmaxandRBEmin(RBE at the lower and upper dose limits). Previously published models were refitted to the database and compared to the new model in terms of model performance and RBE estimates.Main results.The statistical analysis indicated that the intercept of theRBEmaxfunction should be a free fitting parameter and RBE estimates were clearly higher for models with free intercept.RBEminincreased with increasing LET, while a dependency ofRBEminon the reference radiation fractionation sensitivity (α/βx) did not significantly improve model performance. Evaluating the models, the new model gave overall lowest RMSE and highest R2 score. RBE estimates in the distal part of a spread-out-Bragg-peak in water (α/βx= 2.1 Gy) were 1.24-1.51 for original models, 1.25-1.49 for refits and 1.42 for the new model.Significance.An updated RBE model based on the currently largest database among published phenomenological models was proposed. Overall, the new model showed better performance compared to refitted published RBE models.

Linear energy transfer (LET) distribution outside small radiotherapy field edges produced by 6 MV X-rays

In modern radiotherapy with photons, the absorbed dose outside the radiation field is generally investigated. But it is well known that the biological damage depends not only on the absorbed dose but also on LET. This work investigated the dose-average LET (LΔ,D) outside several small radiotherapy fields to provide information that can help for better evaluating the biological effect in organs at risk close to the tumour volume. The electron fluences produced in liquid water by a 6 MV X-rays Varian iX linac were calculated using the EGSnrc Monte Carlo code. With the electron spectra, LΔ,D calculations were made for eight open small square fields and the reference field at water depths of 0.15 cm, 1.35 cm, 9.85 cm and 19.85 cm and several off-axis distances. The variation of LΔ,D from the centre of the beam to 2 cm outside the field's edge depends on the field size and water depth. Using radiobiological data reported in the literature for chromosomal aberrations as an endpoint for the induction of dicentrics determined in Human Lymphocytes, we estimated the maximum low-dose relative biological effectiveness, (RBEM) finding an increase of up to 100% from the centre of the beam to 2 cm from the field's edge.

A systematic approach for calibrating a Monte Carlo code to a treatment planning system for obtaining dose, LET, variable proton RBE and out-of-field dose

Objective. While integration of variable relative biological effectiveness (RBE) has not reached full clinical implementation, the importance of having the ability to recalculate proton treatment plans in a flexible, dedicated Monte Carlo (MC) code cannot be understated . Here we provide a step-wise method for calibrating dose from a MC code to a treatment planning system (TPS), to obtain required parameters for calculating linear energy transfer (LET), variable RBE and in general enabling clinical realistic research studies beyond the capabilities of a TPS.Approach. Initially, Pristine Bragg peaks (PBP) were calculated in both the Eclipse TPS and the FLUKA MC code. A rearranged Bortfeld energy-range relation was applied to the initial energy of the beam to fine-tune the range of the MC code at 80% dose level distal to the PBP. The energy spread was adapted by dividing the TPS range by the MC range for dose level 80%-20% distal to the PBP. Density and relative proton stopping power were adjusted by comparing the TPS and MC for different Hounsfield units. To find the relationship of dose per primary particle from the MC to dose per monitor unit in the TPS, integration was applied to the area of the Bragg curve. The calibration was validated for spread-out Bragg peaks (SOBP) in water and patient treatment plans. Following the validation, variable RBE were calculated using established models.Main results.The PBPs ranges were within ±0.3mm threshold, and a maximum of 5.5% difference for the SOBPs was observed. The patient validation showed excellent dose agreement between the TPS and MC, with the greatest differences for the lung tumor patient.Significance. Aprocedure for calibrating a MC code to a TPS was developed and validated. The procedure enables MC-based calculation of dose, LET, variable RBE, advanced (secondary) particle tracking and more from treatment plans.

Influence of beam pruning techniques on LET and RBE in proton arc therapy

Introduction

Proton arc therapy (PAT) is an emerging treatment modality that holds promise to improve target volume coverage and reduce linear energy transfer (LET) in organs at risk. We aimed to investigate if pruning the highest energy layers in each beam direction could increase the LET in the target and reduce LET in tissue and organs at risk (OAR) surrounding the target volume, thus reducing the relative biological effectiveness (RBE)-weighted dose and sparing healthy tissue.

Methods

PAT plans for a germinoma, an ependymoma and a rhabdomyosarcoma patient were created in the Eclipse treatment planning system with a prescribed dose of 54 Gy(RBE) using a constant RBE of 1.1 (RBE1.1). The PAT plans was pruned for high energy spots, creating several PAT plans with different amounts of pruning while maintaining tumor coverage, denoted PX-PAT plans, where X represents the amount of pruning. All plans were recalculated in the FLUKA Monte Carlo software, and the LET, physical dose, and variable RBE-weighted dose from the phenomenological Rørvik (ROR) model and an LET weighted dose (LWD) model were evaluated.

Results and discussion

For the germinoma case, all plans but the P6-PAT reduced the mean RBE-weighted dose to the surrounding healthy tissue compared to the PAT plan. The LET was increasingly higher within the PTV for each pruning iteration, where the mean LET from the P6-PAT plan was 1.5 keV / μm higher than for the PAT plan, while the P4- and P5-PAT plans provided an increase of 0.4 and 0.7 keV / μm , respectively. The other plans increased the LET by a smaller margin compared to the PAT plan. Likewise, the LET values to the healthy tissue were reduced for each degree of pruning. Similar results were found for the ependymoma and the rhabdomyosarcoma case. We demonstrated a PAT pruning technique that can increase both LET and RBE in the target volume and at the same time decreased values in healthy tissue, without affecting the target volume dose coverage.

A Systematic Review of LET-Guided Treatment Plan Optimisation in Proton Therapy: Identifying the Current State and Future Needs

The well-known clinical benefits of proton therapy are achieved through higher target-conformality and normal tissue sparing than conventional radiotherapy. However, there is an increased sensitivity to uncertainties in patient motion/setup, proton range and radiobiological effect. Although recent efforts have mitigated some uncertainties, radiobiological effect remains unresolved due to a lack of clinical data for relevant endpoints. Therefore, RBE optimisations may be currently unsuitable for clinical treatment planning. LET optimisation is a novel method that substitutes RBE with LET, shifting LET hotspots outside critical structures. This review outlines the current status of LET optimisation in proton therapy, highlighting knowledge gaps and possible future research. Following the PRISMA 2020 guidelines, a search of the MEDLINE® and Scopus databases was performed in July 2023, identifying 70 relevant articles. Generally, LET optimisation methods achieved their treatment objectives; however, clinical benefit is patient-dependent. Inconsistencies in the reported data suggest further testing is required to identify therapeutically favourable methods. We discuss the methods which are suitable for near-future clinical deployment, with fast computation times and compatibility with existing treatment protocols. Although there is some clinical evidence of a correlation between high LET and adverse effects, further developments are needed to inform future patient selection protocols for widespread application of LET optimisation in proton therapy.

Linear Energy Transfer and Relative Biological Effectiveness Investigation of Various Structures for a Cohort of Proton Patients With Brain Tumors

Purpose

The current knowledge on biological effects associated with proton therapy is limited. Therefore, we investigated the distributions of dose, dose-averaged linear energy transfer (LET_d), and the product between dose and LET_d (DLET_d) for a patient cohort treated with proton therapy. Different treatment planning system features and visualization tools were explored.

Methods and Materials

For a cohort of 24 patients with brain tumors, the LET_d, DLET_d, and dose was calculated for a fixed relative biological effectiveness value and 2 variable models: plan-based and phenomenological. Dose threshold levels of 0, 5, and 20 Gy were imposed for LET_d visualization. The relationship between physical dose and LET_d and the frequency of LET_d hotspots were investigated.

Results

The phenomenological relative biological effectiveness model presented consistently higher dose values. For lower dose thresholds, the LET_d distribution was steered toward higher values related to low treatment doses. Differences up to 26.0% were found according to the threshold. Maximum LET_d values were identified in the brain, periventricular space, and ventricles. An inverse relationship between LET_d and dose was observed. Frequency information to the domain of dose and LET_d allowed for the identification of clusters, which steer the mean LET_d values, and the identification of higher, but sparse, LET_d values.

Conclusions

Identifying, quantifying, and recording LET distributions in a standardized fashion is necessary, because concern exists over a link between toxicity and LET hotspots. Visualizing DLET_d or dose × LET_d during treatment planning could allow for clinicians to make informed decisions.

Hypoxia adapted relative biological effectiveness models for proton therapy: a simulation study

In proton therapy, a constant relative biological effectiveness (RBE) factor of 1.1 is applied although the RBE has been shown to depend on factors including the Linear Energy Transfer (LET). The biological effectiveness of radiotherapy has also been shown to depend on the level of oxygenation, quantified by the oxygen enhancement ratio (OER). To estimate the biological effectiveness across different levels of oxygenation the RBE-OER-weighted dose (ROWD) can be used. To investigate the consistency between different approaches to estimate ROWD, we implemented and compared OER models in a Monte Carlo (MC) simulation tool. Five OER models were explored: Wenzl and Wilkens 2011 (WEN), Tinganelliet al2015 (TIN), Strigariet al2018 (STR), Dahleet al2020 (DAH) and Meinet al2021 (MEI). OER calculations were combined with a proton RBE model and the microdosimetric kinetic model for ROWD calculations. ROWD and OER were studied for a water phantom scenario and a head and neck cancer case using hypoxia PET data for the OER calculation. The OER and ROWD estimates from the WEN, MEI and DAH showed good agreement while STR and TIN gave higher OER values and lower ROWD. The WEN, STR and DAH showed some degree of OER-LET dependency while this was negligible for the MEI and TIN models. The ROWD for all implemented models is reduced in hypoxic regions with an OER of 1.0-2.1 in the target volume. While some variations between the models were observed, all models display a large difference in the estimated dose from hypoxic and normoxic regions. This shows the potential to increase the dose or LET in hypoxic regions or reduce the dose to normoxic regions which again could lead to normal tissue sparing. With reliable hypoxia imaging, RBE-OER weighting could become a useful tool for proton therapy plan optimization.

A case-control study of linear energy transfer and relative biological effectiveness related to symptomatic brainstem toxicity following pediatric proton therapy

BACKGROUND AND PURPOSE

A fixed relative biological effectiveness (RBE) of 1.1 (RBE_1.1) is used clinically in proton therapy even though the RBE varies with properties such as dose level and linear energy transfer (LET). We therefore investigated if symptomatic brainstem toxicity in pediatric brain tumor patients treated with proton therapy could be associated with a variable LET and RBE.

MATERIALS AND METHODS

36 patients treated with passive scattering proton therapy were selected for a case-control study from a cohort of 954 pediatric brain tumor patients. Nine children with symptomatic brainstem toxicity were each matched to three controls based on age, diagnosis, adjuvant therapy, and brainstem RBE_1.1 dose characteristics. Differences across cases and controls related to the dose-averaged LET (LET_d) and variable RBE-weighted dose from two RBE models were analyzed in the high-dose region.

RESULTS

LET_d metrics were marginally higher for cases vs. controls for the majority of dose levels and brainstem substructures. Considering areas with doses above 54 Gy(RBE_1.1), we found a moderate trend of 13% higher median LET_d in the brainstem for cases compared to controls (P = .08), while the difference in the median variable RBE-weighted dose for the same structure was only 2% (P = .6).

CONCLUSION

Trends towards higher LET_d for cases compared to controls were noticeable across structures and LET_d metrics for this patient cohort. While case-control differences were minor, an association with the observed symptomatic brainstem toxicity cannot be ruled out.

Quantifying Systematic RBE-Weighted Dose Uncertainty Arising from Multiple Variable RBE Models in Organ at Risk

PURPOSE

Relative biological effectiveness (RBE) uncertainties have been a concern for treatment planning in proton therapy, particularly for treatment sites that are near organs at risk (OARs). In such a clinical situation, the utilization of variable RBE models is preferred over constant RBE model of 1.1. The problem, however, lies in the exact choice of RBE model, especially when current RBE models are plagued with a host of uncertainties. This paper aims to determine the influence of RBE models on treatment planning, specifically to improve the understanding of the influence of the RBE models with regard to the passing and failing of treatment plans. This can be achieved by studying the RBE-weighted dose uncertainties across RBE models for OARs in cases where the target volume overlaps the OARs. Multi-field optimization (MFO) and single-field optimization (SFO) plans were compared in order to recommend which technique was more effective in eliminating the variations between RBE models.

METHODS

Fifteen brain tumor patients were selected based on their profile where their target volume overlaps with both the brain stem and the optic chiasm. In this study, 6 RBE models were analyzed to determine the RBE-weighted dose uncertainties. Both MFO and SFO planning techniques were adopted for the treatment planning of each patient. RBE-weighted dose uncertainties in the OARs are calculated assuming( α β ) x of 3 Gy and 8 Gy. Statistical analysis was used to ascertain the differences in RBE-weighted dose uncertainties between MFO and SFO planning. Additionally, further investigation of the linear energy transfer (LET) distribution was conducted to determine the relationship between LET distribution and RBE-weighted dose uncertainties.

RESULTS

The results showed no strong indication on which planning technique would be the best for achieving treatment planning constraints. MFO and SFO showed significant differences (P <.05) in the RBE-weighted dose uncertainties in the OAR. In both clinical target volume (CTV)-brain stem and CTV-chiasm overlap region, 10 of 15 patients showed a lower median RBE-weighted dose uncertainty in MFO planning compared with SFO planning. In the LET analysis, 8 patients (optic chiasm) and 13 patients (brain stem) showed a lower mean LET in MFO planning compared with SFO planning. It was also observed that lesser RBE-weighted dose uncertainties were present with MFO planning compared with SFO planning technique.

CONCLUSIONS

Calculations of the RBE-weighted dose uncertainties based on 6 RBE models and 2 different( α β ) x revealed that MFO planning is a better option as opposed to SFO planning for cases of overlapping brain tumor with OARs in eliminating RBE-weighted dose uncertainties. Incorporation of RBE models failed to dictate the passing or failing of a treatment plan. To eliminate RBE-weighted dose uncertainties in OARs, the MFO planning technique is recommended for brain tumor when CTV and OARs overlap.

Quantitative analysis of dose-averaged linear energy transfer (LETd ) robustness in pencil beam scanning proton lung plans

PURPOSE

The primary objective of our study was to perform a quantitative robustness analysis of the dose-averaged linear energy transfer (LET_d ) and related RBE-weighted dose in robustly optimized (in terms of the range and set up uncertainties) pencil beam scanning (PBS) proton lung cancer plans.

METHODS

In this study, we utilized the 4DCT data set of six anonymized lung patients. PBS lung plans were generated using a robust optimization technique (range uncertainty: ±3.5% and setup errors: ±5 mm) on the CTV for a total dose of 5000 cGy(RBE) in 5 fractions using RBE of 1.1. For each patient, the LET_d distributions were calculated for the nominal plan and three groups. Group 1: two plan robustness scenarios for range uncertainties of ±3.5%; Group 2: twelve plan robustness scenarios (range uncertainty (±3.5%) in conjunction with setup errors (±5 mm)); and Group 3: ten different breathing phases of the 4DCT data set. RBE-weighted dose to the OARs was evaluated for all robustness scenarios and breathing phases. The variation (∆) in the mean LET_d and mean RBE-weighted dose from each group was recorded.

RESULTS

The mean LET_d in the CTV of nominal PBS lung plans among six patients ranged from 2.2 to 2.6 keV/μm. On average, for the combined range and setup uncertainties, the ∆ in the mean LET_d among 12 scenarios of all six patients was 0.6 keV/μm, which is slightly higher than when only the range uncertainties were considered (0.4 keV/μm). The ∆ in the mean LET_d in a patient was ≤1.7 keV/μm in the heart and ≤1.2 keV/μm in the esophagus and total lung. The ∆ in the mean RBE-weighted dose in a patient was up to 79 cGy for the total lung, 165 cGy for the heart, and 258 cGy for the esophagus. For ten breathing phases, the ∆ in the mean LET_d in a patient was ≤0.3 keV/μm in the CTV, ≤0.5 keV/μm in the heart, ≤0.4 keV/μm in the esophagus, and ≤0.7 keV/μm in the total lung.

CONCLUSION

The addition of setup errors to the range uncertainties resulted in slightly less homogeneous LET_d distributions. The variations in the mean LET_d among ten breathing phases were slightly larger in the total lung than in the heart and esophagus. The combination of setup and range uncertainties had a greater impact than the effect of breathing phases on the variations in the mean RBE-weighted dose to the OARs. Overall, the LET_d distributions in the CTV were less sensitive than those in the OARs to setup errors, range uncertainties, and breathing phases for robustly optimized PBS proton lung cancer plans. This article is protected by copyright. All rights reserved.

Towards harmonizing clinical linear energy transfer (LET) reporting in proton radiotherapy: a European multi-centric study

BACKGROUND

Clinical data suggest that the relative biological effectiveness (RBE) in proton therapy (PT) varies with linear energy transfer (LET). However, LET calculations are neither standardized nor available in clinical routine. Here, the status of LET calculations among European PT institutions and their comparability are assessed.

MATERIALS AND METHODS

Eight European PT institutions used suitable treatment planning systems with their center-specific beam model to create treatment plans in a water phantom covering different field arrangements and fulfilling commonly agreed dose objectives. They employed their locally established LET simulation environments and procedures to determine the corresponding LET distributions. Dose distributions D1.1 and DRBE assuming constant and variable RBE, respectively, and LET were compared among the institutions. Inter-center variability was assessed based on dose- and LET-volume-histogram parameters.

RESULTS

Treatment plans from six institutions fulfilled all clinical goals and were eligible for common analysis. D1.1 distributions in the target volume were comparable among PT institutions. However, corresponding LET values varied substantially between institutions for all field arrangements, primarily due to differences in LET averaging technique and considered secondary particle spectra. Consequently, DRBE using non-harmonized LET calculations increased inter-center dose variations substantially compared to D1.1 and significantly in mean dose to the target volume of perpendicular and opposing field arrangements (p < 0.05). Harmonizing LET reporting (dose-averaging, all protons, LET to water or to unit density tissue) reduced the inter-center variability in LET to the order of 10-15% within and outside the target volume for all beam arrangements. Consequentially, inter-institutional variability in DRBE decreased to that observed for D1.1.

CONCLUSION

Harmonizing the reported LET among PT centers is feasible and allows for consistent multi-centric analysis and reporting of tumor control and toxicity in view of a variable RBE. It may serve as basis for harmonized variable RBE dose prescription in PT.

Mechanisms and Review of Clinical Evidence of Variations in Relative Biological Effectiveness in Proton Therapy

Proton therapy is increasingly being used as a radiation therapy modality. There is uncertainty about the biological effectiveness of protons relative to photon therapies as it depends on several physical and biological parameters. Radiation oncology currently applies a constant and generic value for the relative biological effectiveness (RBE) of 1.1, which was chosen conservatively to ensure tumor coverage. The use of a constant value has been challenged particularly when considering normal tissue constraints. Potential variations in RBE have been assessed in several published reviews but have mostly focused on data from clonogenic cell survival experiments with unclear relevance for clinical proton therapy. The goal of this review is to put in vitro findings in relation to clinical observations. Relevant in vivo pathways determining RBE for tumors and normal tissues are outlined, including not only damage to tumor cells and parenchyma but also vascular damage and immune response. Furthermore, the current clinical evidence of varying RBE is reviewed. The assessment can serve as guidance for treatment planning, personalized dose prescriptions, and outcome analysis.

A Monte Carlo study of different LET definitions and calculation parameters for proton beam therapy

The strongin vitroevidence that proton Relative Biological Effectiveness (RBE) varies with Linear Energy Transfer (LET) has led to an interest in applying LET within treatment planning. However, there is a lack of consensus on LET definition, Monte Carlo (MC) parameters or clinical methodology. This work aims to investigate how common variations of LET definition may affect potential clinical applications. MC simulations (GATE/GEANT4) were used to calculate absorbed dose and different types of LET for a simple Spread Out Bragg Peak (SOBP) and for four clinical PBT plans covering a range of tumour sites. Variations in the following LET calculation methods were considered: (i) averaging (dose-averaged LET (LET_d) & track-averaged LET); (ii) scoring (LET_dto water, to medium and to mass density); (iii) particle inclusion (LET_dto all protons, to primary protons and to particles); (iv) MC settings (hit type and Maximum Step Size (MSS)). LET distributions were compared using: qualitative comparison, LET Volume Histograms (LVHs), single value criteria (maximum and mean values) and optimised LET-weighted dose models. Substantial differences were found between LET values in averaging, scoring and particle type. These differences depended on the methodology, but for one patient a difference of ∼100% was observed between the maximum LET_dfor all particles and maximum LET_dfor all protons within the brainstem in the high isodose region (4 keVμm^-1and 8 keVμm^-1respectively). An RBE model using LET_dincluding heavier ions was found to predict substantially different LET-weighted dose compared to those using other LET definitions. In conclusion, the selection of LET definition may affect the results of clinical metrics considered in treatment planning and the results of an RBE model. The authors' advocate for the scoring of dose-averaged LET to water for primary and secondary protons using a random hit type and automated MSS.

The Organ Sparing Potential of Different Biological Optimization Strategies in Proton Therapy

Purpose

Variable relative biological effectiveness (RBE) models allow for differences in linear energy transfer (LET), physical dose, and tissue type to be accounted for when quantifying and optimizing the biological damage of protons. These models are complex and fraught with uncertainties, and therefore, simpler RBE optimization strategies have also been suggested. Our aim was to compare several biological optimization strategies for proton therapy by evaluating their performance in different clinical cases.

Methods and Materials

Two different optimization strategies were compared: full variable RBE optimization and differential RBE optimization, which involve applying fixed RBE for the planning target volume (PTV) and variable RBE in organs at risk (OARs). The optimization strategies were coupled to 2 variable RBE models and 1 LET-weighted dose model, with performance demonstrated on 3 different clinical cases: brain, head and neck, and prostate tumors.

Results

In cases with low (α/β)x in the tumor, the full RBE optimization strategies had a large effect, with up to 10% reduction in RBE-weighted dose to the PTV and OARs compared with the reference plan, whereas smaller variations (<5%) were obtained with differential optimization. For tumors with high (α/β)x, the differential RBE optimization strategy showed a greater reduction in RBE-weighted dose to the OARs compared with the reference plan and the full RBE optimization strategy.

Conclusions

Differences between the optimization strategies varied across the studied cases, influenced by both biological and physical parameters. Whereas full RBE optimization showed greater OAR sparing, awareness of underdosage to the target must be carefully considered.

Postsurgical geometrical variations of tumor bed and brainstem during photon and proton therapy for pediatric tumors of the posterior fossa: dosimetric impact and predictive factors

PURPOSE

Brainstem radionecrosis is an important issue during the irradiation of tumors of the posterior fossa. The aim of the present study is to analyze postsurgical geometrical variations of tumor bed (TB) and brainstem (BS) and their impact on dosimetry.

METHODS

Retrospective collection of data from pediatric patients treated at a single institution. Availability of presurgical magnetic resonance imaging (MRI) was verified; availability of at least two postsurgical MRIs was considered a further inclusion criterion. The following metrics were analyzed: total volume, Dice similarity coefficient (DSC), and Haudsdorff distances (HD).

RESULTS

Fourteen patients were available for the quantification of major postsurgical geometrical variations of TB. DSC, HD max, and HD average values were 0.47 (range: 0.08;0.76), 11.3 mm (7.7;24.5), and 2.6 mm (0.7;6.7) between the first and the second postoperative MRI, respectively. Postsurgical geometrical variations of the BS were also observed. Coverage to the TB was reduced in one patient (D95: -2.9 Gy), while D2 to the BS was increased for the majority of patients. Overall, predictive factors for significant geometrical changes were presurgical gross tumor volume (GTV) > 33 mL, hydrocephaly at diagnosis, Luschka foramen involvement, and younger age (≤ 8 years).

CONCLUSION

Major volume changes were observed in this cohort, with some dosimetric impact. The use of a recent co-registration MRI is advised. The 2-3 mm HD average observed should be considered in the planning target volume/planning organ at risk volume (PTV/PRV) margin and/or robust optimization planning. Results from wider efforts are needed to verify our findings.

A systematic review on the usage of averaged LET in radiation biology for particle therapy

Linear Energy Transfer (LET) is widely used to express the radiation quality of ion beams, when characterizing the biological effectiveness. However, averaged LET may be defined in multiple ways, and the chosen definition may impact the resulting reported value. We review averaged LET definitions found in the literature, and quantify which impact using these various definitions have for different reference setups. We recorded the averaged LET definitions used in 354 publications quantifying the relative biological effectiveness (RBE) of hadronic beams, and investigated how these various definitions impact the reported averaged LET using a Monte Carlo particle transport code. We find that the kind of averaged LET being applied is, generally, poorly defined. Some definitions of averaged LET may influence the reported averaged LET values up to an order of magnitude. For publications involving protons, most applied dose averaged LET when reporting RBE. The absence of what target medium is used and what secondary particles are included further contributes to an ill-defined averaged LET. We also found evidence of inconsistent usage of averaged LET definitions when deriving LET-based RBE models. To conclude, due to commonly ill-defined averaged LET and to the inherent problems of LET-based RBE models, averaged LET may only be used as a coarse indicator of radiation quality. We propose a more rigorous way of reporting LET values, and suggest that ideally the entire particle fluence spectra should be recorded and provided for future RBE studies, from which any type of averaged LET (or other quantities) may be inferred.

Ultra-High Dose Rate Transmission Beam Proton Therapy for Conventionally Fractionated Head and Neck Cancer: Treatment Planning and Dose Rate Distributions

Simple Summary

Standard intensity-modulated proton therapy (IMPT) places the Bragg-peak in the target. However, it is also possible to use high energy proton transmission beams (TBs), where the Bragg-peak is placed outside the patient, irradiating with the beam section proximal to the Bragg-peak. TBs use only one energy, increase robustness, are insensitive to density changes and have sharper penumbras. TBs can also be delivered at ultra-high dose-rates (UHDRs, e.g., ≥40 Gy/s), which is one of the requirements for the FLASH-effect. The aim of this work was twofold: (1) comparison of TB-plan quality to IMPT and photon volumetric-modulated arc therapy (VMAT) for conventionally fractionated head-and-neck cancer; (2) analysis of TB-plan UHDR-metrics. We showed that TB-plan quality was comparable to IMPT for contoured organs at risk and better than VMAT. Any potential FLASH-effect would only further improve plan quality. TB plans can also be delivered quickly, which might facilitate higher patient through-put and enhance patient comfort.

Abstract

Transmission beam (TB) proton therapy (PT) uses single, high energy beams with Bragg-peak behind the target, sharp penumbras and simplified planning/delivery. TB facilitates ultra-high dose-rates (UHDRs, e.g., ≥40 Gy/s), which is a requirement for the FLASH-effect. We investigated (1) plan quality for conventionally-fractionated head-and-neck cancer treatment using spot-scanning proton TBs, intensity-modulated PT (IMPT) and photon volumetric-modulated arc therapy (VMAT); (2) UHDR-metrics. VMAT, 3-field IMPT and 10-field TB-plans, delivering 70/54.25 Gy in 35 fractions to boost/elective volumes, were compared (n = 10 patients). To increase spot peak dose-rates (SPDRs), TB-plans were split into three subplans, with varying spot monitor units and different gantry currents. Average TB-plan organs-at-risk (OAR) sparing was comparable to IMPT: mean oral cavity/body dose were 4.1/2.5 Gy higher (9.3/2.0 Gy lower than VMAT); most other OAR mean doses differed by <2 Gy. Average percentage of dose delivered at UHDRs was 46%/12% for split/non-split TB-plans and mean dose-averaged dose-rate 46/21 Gy/s. Average total beam-on irradiation time was 1.9/3.8 s for split/non-split plans and overall time including scanning 8.9/7.6 s. Conventionally-fractionated proton TB-plans achieved comparable OAR-sparing to IMPT and better than VMAT, with total beam-on irradiation times <10s. If a FLASH-effect can be demonstrated at conventional dose/fraction, this would further improve plan quality and TB-protons would be a suitable delivery system.

Variation in relative biological effectiveness for cognitive structures in proton therapy of pediatric brain tumors

BACKGROUND

Clinically, a constant value of 1.1 is used for the relative biological effectiveness (RBE) of protons, whereas in vitro the RBE has been shown to vary depending on physical dose, tissue type, and linear energy transfer (LET). As the LET increases at the distal end of the proton beam, concerns exist for an elevated RBE in normal tissues. The aim of this study was therefore to investigate the heterogeneity of RBE to brain structures associated with cognition (BSCs) in pediatric suprasellar tumors.

MATERIAL AND METHODS

Intensity-modulated proton therapy (IMPT) plans for 10 pediatric craniopharyngioma patients were re-calculated using 11 phenomenological and two plan-based variable RBE models. Based on LET, tissue dependence and number of data points used to fit the models, the three RBE models considered the most relevant for the studied endpoint were selected. Thirty BSCs were investigated in terms of RBE and dose/volume parameters.

RESULTS

For a representative patient, the median (range) dose-weighted mean RBE (RBE_d) across all BSCs from the plan-based models was among the lowest (1.09 (1.02-1.52) vs. the phenomenological models at 1.21 (0.78-2.24)). Omitting tissue dependency resulted in RBE_d at 1.21 (1.04-2.24). Across all patients, the narrower RBE model selection gave median RBE_d values from 1.22 to 1.30.

CONCLUSION

For all BSCs, there was a systematic model-dependent variation in RBE_d, mirroring the uncertainty in biological effects of protons. According to a refined selection of in vitro models, the RBE variation across BSCs was in effect underestimated when using a fixed RBE of 1.1.

Spatial Agreement of Brainstem Dose Distributions Depending on Biological Model in Proton Therapy for Pediatric Brain Tumors

Purpose

During radiation therapy for pediatric brain tumors, the brainstem is a critical organ at risk, possibly with different radio-sensitivity across its substructures. In proton therapy, treatment planning is currently performed using a constant relative biological effectiveness (RBE) of 1.1 (RBE_1.1), whereas preclinical studies point toward spatial variability of this factor. To shed light on this biological uncertainty, we investigated the spatial agreement between isodose maps produced by different RBE models, with emphasis on (smaller) substructures of the brainstem.

Methods and Materials

Proton plans were recalculated using Monte Carlo simulations in 3 anonymized pediatric patients with brain tumors (a craniopharyngioma, a low-grade glioma, and a posterior fossa ependymoma) to obtain dose and linear energy transfer distributions. Doses and volume metrics for the brainstem and its substructures were calculated using a constant RBE_1.1, 4 phenomenological RBE models with varying (α/β)_x parameters, and with a simpler linear energy transfer-dependent model. The spatial agreement between the dose distributions of constant RBE_1.1 versus the variable RBE models was compared using the Dice similarity coefficient.

Results

The spatial agreement between the variable RBE dose distributions and RBE_1.1 decreased with increasing isodose levels in all patient cases. The patient with ependymoma showed the greatest variation in dose and dose volumes, where V_50Gy(RBE) in the brainstem increased from 32% (RBE_1.1) to 35% to 49% depending on the applied model, corresponding to a spatial agreement (Dice similarity coefficient) between 0.79 and 0.95. The remaining patients showed similar trends, however, with lower absolute values due to lower brainstem doses.

Conclusions

All phenomenological RBE models fully enclosed the isodose volumes of the constant RBE_1.1, and the volumes based on variable RBE spatially agreed. The spatial agreement was dependent on the isodose level, where higher isodose levels showed larger expansions and less agreement between the variable RBE models and RBE_1.1.

Implementation of a double scattering nozzle for Monte Carlo recalculation of proton plans with variable relative biological effectiveness

A constant relative biological effectiveness (RBE) of 1.1 is currently used in clinical proton therapy. However, theRBEvaries with factors such as dose level, linear energy transfer (LET) and tissue type. MultipleRBEmodels have been developed to account for this biological variation. To enable recalculation of patients treated with double scattering (DS) proton therapy, includingLETand variableRBE, we implemented and commissioned a Monte Carlo (MC) model of a DS treatment nozzle. The main components from the IBA nozzle were implemented in the FLUKA MC code. We calibrated and verified the following entities to experimental measurements: range of pristine Bragg peaks (PBPs) and spread-out Bragg peaks (SOBPs), energy spread, lateral profiles, compensator range degradation, and absolute dose. We recalculated two patients with different field setups, comparing FLUKA vs. treatment planning system (TPS) dose, also obtainingLETand variableRBEdoses. We achieved good agreement between FLUKA and measurements. The range differences between FLUKA and measurements were for the PBPs within ±0.9 mm (83% ⩽ 0.5 mm), and for SOBPs ±1.6 mm (82% ⩽ 0.5 mm). The differences in modulation widths were below 5 mm (79% ⩽ 2 mm). The differences in the distal dose fall off (D80%-D20%) were below 0.5 mm for all PBPs and the lateral penumbras diverged from measurements by less than 1 mm. The mean dose difference (RBE= 1.1) in the target between the TPS and FLUKA were below 0.4% in a three-field plan and below 1.4% in a four-field plan. A dose increase of 9.9% and 7.2% occurred when using variableRBEfor the two patients, respectively. We presented a method to recalculate DS proton plans in the FLUKA MC code. The implementation was used to obtainLETand variableRBEdose and can be used for investigating variableRBEfor previously treated patients.

Impact of range uncertainty on clinical distributions of linear energy transfer and biological effectiveness in proton therapy

PURPOSE

Increased radiation response after proton irradiation, such as late radiation-induced toxicity, is determined by high dose and elevated linear energy transfer (LET). Steep dose-averaged LET (LET_d ) gradients and elevated LET_d occur at the end of proton range and might be particularly sensitive to uncertainties in range prediction. Therefore, this study quantified LET_d distributions and the impact of range uncertainty in robust dose-optimized proton treatment plans and assessed the biological effect in normal tissues and tumors of patients.

METHODS

For each of six cancer patients (two brain, head-and-neck, and prostate), two nominal treatment plans were robustly dose optimized using single- and multi-field optimization, respectively. For each plan, two additional scenarios with ±3.5% range deviation relative to the nominal plan were derived by global rescaling of stopping-power ratios. Dose and LET_d distributions were calculated for each scenario using the beam parameters of the corresponding nominal plan. The variability in relative biological effectiveness (RBE) and probability of late radiation-induced brain toxicity (P_IC ) was assessed.

RESULTS

The optimization technique (single- vs multi-field) had a negligible impact on the LET_d distributions in the clinical target volume (CTV) and in most organs at risk (OARs). LET_d distributions in the CTV were rather homogeneous with arithmetic mean of LET_d below 3.2 keV/µm and robust against range deviations. The RBE variability within the CTV induced by range uncertainty was small (≤0.05, 95% confidence interval). In OARs, LET_d hotspots (>7 keV/µm) occurred and LET_d distributions were inhomogeneous and sensitive to range deviations. LET_d hotspots and the impact of range deviations were most prominent in OARs of brain tumor patients which translated in RBE values exceeding 1.1 in all brain OARs. The near-maximum predicted P_IC in healthy brain tissue of brain tumor patients was smaller than 5% and occurred adjacent to the CTV. Range deviations induced absolute differences in P_IC up to 1.2%.

CONCLUSIONS

Robust dose optimization generates LET_d distributions in the target volume robust against range deviations. The current findings support using a constant RBE within the CTV. The impact of range deviations on the considered probability of late radiation-induced toxicity in brain tissue was limited for robust dose-optimized treatment plans. Incorporation of LET_d in robust optimization frameworks may further reduce uncertainty related to the RBE-weighted dose estimation in normal tissues.

RBE for proton radiation therapy - a Nordic view in the international perspective

BACKGROUND

This paper presents an insight into the critical discussions and the current strategies of the Nordic countries for handling the variable proton relative biological effectiveness (RBE) as presented at The Nordic Collaborative Workshop for Particle Therapy that took place at the Skandion Clinic on 14th and 15th of November 2019.

MATERIAL AND METHODS

In the current clinical practice at the two proton centres in operation at the date, Skandion Clinic, and the Danish Centre for Particle Therapy, a constant proton RBE of 1.1 is applied. The potentially increased effectiveness at the end of the particle range is however considered at the stage of treatment planning at both places based on empirical observations and knowledge. More elaborated strategies to evaluate the plans and mitigate the problem are intensely investigated internationally as well at the two centres. They involve the calculation of the dose-averaged linear energy transfer (LET_d) values and the assessment of their distributions corroborated with the distribution of the dose and the location of the critical clinical structures.

RESULTS

Methods and tools for LET_d calculations are under different stages of development as well as models to account for the variation of the RBE with LET_d, dose per fraction, and type of tissue. The way they are currently used for evaluation and optimisation of the plans and their robustness are summarised. A critical but not exhaustive discussion of their potential future implementation in the clinical practice is also presented.

CONCLUSIONS

The need for collaboration between the clinical proton centres in establishing common platforms and perspectives for treatment planning evaluation and optimisation is highlighted as well as the need of close interaction with the research academic groups that could offer a complementary perspective and actively help developing methods and tools for clinical implementation of the more complex metrics for considering the variable effectiveness of the proton beams.

The FLUKA Monte Carlo code coupled with an OER model for biologically weighted dose calculations in proton therapy of hypoxic tumors

INTRODUCTION

The increased radioresistance of hypoxic cells compared to well-oxygenated cells is quantified by the oxygen enhancement ratio (OER). In this study we created a FLUKA Monte Carlo based tool for inclusion of both OER and relative biological effectiveness (RBE) in biologically weighted dose (ROWD) calculations in proton therapy and applied this to explore the impact of hypoxia.

METHODS

The RBE-weighted dose was adapted for hypoxia by making RBE model parameters dependent on the OER, in addition to the linear energy transfer (LET). The OER depends on the partial oxygen pressure (pO₂) and LET. To demonstrate model performance, calculations were done with spread-out Bragg peaks (SOBP) in water phantoms with pO₂ ranging from strongly hypoxic to normoxic (0.01-30 mmHg) and with a head and neck cancer proton plan optimized with an RBE of 1.1 and pO₂ estimated voxel-by-voxel using [¹⁸F]-EF5 PET. An RBE of 1.1 and the Rørvik RBE model were used for the ROWD calculations.

RESULTS

The SOBP in water had decreasing ROWD with decreasing pO₂. In the plans accounting for oxygenation, the median target doses were approximately a factor 1.1 lower than the corresponding plans which did not consider the OER. Hypoxia adapted target ROWDs were considerably more heterogeneous than the RBE_1.1-weighted doses.

CONCLUSION

We realized a Monte Carlo based tool for calculating the ROWD. Read-in of patient pO₂ and estimation of ROWD with flexibility in choice of RBE model was achieved, giving a tool that may be useful in future clinical applications of hypoxia-guided particle therapy.

Linear energy transfer weighted beam orientation optimization for intensity-modulated proton therapy

PURPOSE

In intensity-modulated proton therapy (IMPT), unaccounted-for variation in biological effectiveness contributes to the discrepancy between the constant relative biological effectiveness (RBE) model prediction and experimental observation. It is desirable to incorporate biological doses in treatment planning to improve modeling accuracy and consequently achieve a higher therapeutic ratio. This study addresses this demand by developing a method to incorporate linear energy transfer (LET) into beam orientation optimization (BOO).

METHODS

Instead of RBE-weighted dose, this LET weighted BOO (LETwBOO) framework uses the dose and LET product (LET  ×  D) as the biological surrogate. The problem is formulated with a physical dose fidelity term, a LET  ×  D constraint term, and a group sparsity term. The LET  ×  D of organs at risks is penalized for minimizing the biological effect while maintaining the physical dose objectives. Group sparsity is used to reduce the number of active beams from 600-800 non-coplanar candidate beams to between 2 and 4. This LETwBOO method was tested on three skull base tumor (SBT) patients and three bilateral head-and-neck (H&N) patients. The LETwBOO plans were compared with IMPT plans using manually selected beams with only physical dose constraint (MAN) and the initial MAN plan reoptimized with additional LET  ×  D constraint (LETwMAN).

RESULTS

The LETwBOO plans show superior physical dose and LET  ×  D sparing. On average, the [mean, maximal] doses of organs at risks (OARs) in LETwBOO are reduced by [2.85, 4.6] GyRBE from the MAN plans in the SBT cases and reduced by [0.9, 2.5] GyRBE in the H&N cases, while LETwMAN is comparable to MAN. cLET × Ds of PTVs are comparable in LETwBOO and LETwMAN, where c is a scaling factor of 0.04 μm/keV. On average, in the SBT cases, LETwBOO reduces the OAR [mean, maximal] cLET × D by [1.1, 2.9] Gy from the MAN plans, compared to the reduction by LETwMAN from MAN of [0.7, 1.7] Gy. In the H&N cases, LETwBOO reduces the OAR [mean, maximal] cLET × D by [0.8, 2.6] Gy from the MAN plans, compared to the reduction by LETwMAN from MAN of [0.3, 1.2] Gy.

CONCLUSION

We developed a novel LET weighted BOO method for IMPT to generate plans with improved physical and biological OAR sparing compared with the plans unaccounted for biological effects from BOO.

Inter-patient variations in relative biological effectiveness for cranio-spinal irradiation with protons

Cranio-spinal irradiation (CSI) using protons has dosimetric advantages compared to photons and is expected to reduce risk of adverse effects. The proton relative biological effectiveness (RBE) varies with linear energy transfer (LET), tissue type and dose, but a variable RBE has not replaced the constant RBE of 1.1 in clinical treatment planning. We examined inter-patient variations in RBE for ten proton CSI patients. Variable RBE models were used to obtain RBE and RBE-weighted doses. RBE was quantified in terms of dose weighted organ-mean RBE ([Formula: see text] = mean RBE-weighted dose/mean physical dose) and effective RBE of the near maximum dose (D2%), i.e. RBED2% = [Formula: see text], where subscripts RBE and phys indicate that the D2% is calculated based on an RBE model and the physical dose, respectively. Compared to the median [Formula: see text] of the patient population, differences up to 15% were observed for the individual [Formula: see text] values found for the thyroid, while more modest variations were seen for the heart (6%), lungs (2%) and brainstem (<1%). Large inter-patient variation in RBE could be correlated to large spread in LET and dose for these organs at risk (OARs). For OARs with small inter-patient variations, the results show that applying a population based RBE in treatment planning may be a step forward compared to using RBE of 1.1. OARs with large inter-patient RBE variations should ideally be selected for patient-specific biological or RBE robustness analysis if the physical doses are close to known dose thresholds.

Normal tissue complication probability models in plan evaluation of children with brain tumors referred to proton therapy

Background: Children with brain tumors undergoing radiotherapy are at particular risk of radiation-induced morbidity and are therefore routinely considered for proton therapy (PT) to reduce the dose to healthy tissues. The aim of this study was to apply pediatric constraints and normal tissue complication probability (NTCP) models when evaluating the differences between PT and contemporary photon-based radiotherapy, volumetric modulated arc therapy (VMAT). Methods: Forty patients (aged 1-17 years) referred from Norwegian institutions to cranial PT abroad during 2014-2016 were selected for VMAT re-planning using the original CT sets and target volumes. The VMAT and delivered PT plans were compared by dose/volume metrics and NTCP models related to growth hormone deficiency, auditory toxicity, visual impairment, xerostomia, neurocognitive outcome and secondary brain and parotid gland cancers. Results: The supratentorial brain, temporal lobes, hippocampi, hypothalamus, pituitary glands, cochleas, salivary glands, optic nerves and chiasm received lower mean doses from PT. Reductions in population median NTCP were significant for auditory toxicity (VMAT: 3.8%; PT: 0.3%), neurocognitive outcome (VMAT: 3.0 IQ points decline at 5 years post RT; PT: 2.5 IQ points), xerostomia (VMAT: 2.0%; PT: 0.6%), excess absolute risk of secondary cancer of the brain (VMAT: 9.2%; PT: 6.7%) and salivary glands (VMAT: 2.8%; PT:0.5%). Across all patients, 23/38 PT plans had better or comparable estimated risks for all endpoints (within ±10% of the risk relative to VMAT), whereas for 1/38 patients all estimates were better or comparable with VMAT. Conclusions: PT reduced the volumes of normal tissues exposed to radiation, particularly low-to-intermediate dose levels, and this was reflected in lower NTCP. Of the included endpoints, substantial reductions in population medians were seen from the delivered PT plans for auditory complications, xerostomia, and risk of secondary cancers of the brain and salivary glands.

Proton therapy for brain tumours in the area of evidence-based medicine

ADVANCES IN KNOWLEDGE

This review details the indication of brain tumors for proton therapy and give a list of the open prospective trials for these challenging tumors.

Proton Relative Biological Effectiveness - Uncertainties and Opportunities

Proton therapy treatments are prescribed using a biological effectiveness relative to photon therapy of 1.1, that is, proton beams are considered to be 10% more biologically effective. Debate is ongoing as to whether this practice needs to be revised. This short review summarizes current knowledge on relative biological effectiveness variations and uncertainties in vitro and in vivo. Clinical relevance is discussed and strategies toward biologically guided treatment planning are presented.

Exploration and application of phenomenological RBE models for proton therapy

The relative biological effectiveness (RBE) of protons varies with multiple physical and biological factors. Phenomenological RBE models have been developed to include such factors in the estimation of a variable RBE, in contrast to the clinically applied constant RBE of 1.1. In this study, eleven published phenomenological RBE models and two plan-based models were explored and applied to simulated patient cases. All models were analysed with respect to the distribution and range of linear energy transfer (LET) and reference radiation fractionation sensitivity ((α/β) _x ) of their respective experimental databases. Proton therapy plans for a spread-out Bragg peak in water and three patient cases (prostate adenocarcinoma, pituitary adenoma and thoracic sarcoma) were optimised using an RBE of 1.1 in the Eclipse^™ treatment planning system prior to recalculation and modelling in the FLUKA Monte Carlo code. Model estimated dose-volume parameters for the planning target volumes (PTVs) and organs at risk (OAR) were compared. The experimental in vitro databases for the various models differed greatly in the range of (α/β) _x values and dose-averaged LET (LET_d). There were significant variations between the model estimations, which arose from fundamental differences in the database definitions and model assumptions. The greatest variations appeared in organs with low (α/β) _x and high LET_d, e.g. biological doses given to late responding OARs located distal to the target in the treatment field. In general, the variation in maximum dose (D_2%) was larger than the variation in mean dose and other dose metrics, with D_2% of the left optic nerve ((α/β) _x   =  2.1 Gy) in the pituitary adenoma case showing the greatest discrepancies between models: 28-52 Gy(RBE), while D_2% for RBE_1.1 was 30 Gy(RBE). For all patient cases, the estimated mean RBE to the PTV was in the range 1.09-1.29 ((α/β) _x   =  1.5/3.1/10.6 Gy). There were considerable variations between the estimations of RBE and RBE-weighted doses from the different models. These variations were a consequence of fundamental differences in experimental databases, model assumptions and regression techniques. The results from the implementation of RBE models in dose planning studies should be evaluated in light of these deviations.

Modeling in vivo relative biological effectiveness in particle therapy for clinically relevant endpoints

BACKGROUND

The relative biological effectiveness (RBE) of particle therapy compared to photon radiotherapy is known to be variable but the exact dependencies are still subject to debate. In vitro data suggested that RBE is to a large extend independent of ion type if parametrized by the beam quality Q. This study analyzed the RBE dependence of pre-clinical data on late toxicity with an emphasis on the beam quality.

MATERIAL AND METHODS

Published pre-clinical RBE dose-response data of the spinal cord following one and two fractions of photon and carbon ion irradiation were compiled. The beam quality for each treatment condition was obtained from Monte Carlo simulations. The α_p and β_p parameters of the linear-quadratic (LQ) model for particle irradiation were determined from the pre-clinical data and was provided as a function of Q. An introduced model proposed α_p to increase linearly with Q and β_p to remain constant. RBE values predicted by the model were compared to the published data.

RESULTS

The α_p parameter was highly correlated with Q (R² = 0.96) with a linear slope of 0.019 Gy^-1. No significant variation of β_p with Q was found. RBE and Q were also highly correlated (R² = 0.98) for one and two fractions. The (extrapolated) RBE at Q = 0 (theoretical photon limit) for one and two fractions was 1.22 and significantly larger than 1 (p = .004). The model reproduced the dependence of RBE on fractionation well.

CONCLUSIONS

Fraction dose and beam quality Q were sufficient to describe the RBE variability for a late toxicity model within a carbon ion treatment field. Assuming the independence of the identified RBE parameters on the ion type might suggest the translation of variable (pre-) clinical RBE data from carbon ion to proton therapy.

Impact of respiratory motion on variable relative biological effectiveness in 4D-dose distributions of proton therapy

BACKGROUND

Organ motion during radiation therapy with scanned protons leads to deviations between the planned and the delivered physical dose. Using a constant relative biological effectiveness (RBE) of 1.1 linearly maps these deviations into RBE-weighted dose. However, a constant value cannot account for potential nonlinear variations in RBE suggested by variable RBE models. Here, we study the impact of motion on recalculations of RBE-weighted dose distributions using a phenomenological variable RBE model.

MATERIAL AND METHODS

4D-dose calculation including variable RBE was implemented in the open source treatment planning toolkit matRad. Four scenarios were compared for one field and two field proton treatments for a liver cancer patient assuming (α∕β)_x = 2 Gy and (α∕β)_x = 10 Gy: (A) the optimized static dose distribution with constant RBE, (B) a static recalculation with variable RBE, (C) a 4D-dose recalculation with constant RBE and (D) a 4D-dose recalculation with variable RBE. For (B) and (D), the variable RBE was calculated by the model proposed by McNamara. For (C), the physical dose was accumulated with direct dose mapping; for (D), dose-weighted radio-sensitivity parameters of the linear quadratic model were accumulated to model synergistic irradiation effects on RBE.

RESULTS

Dose recalculation with variable RBE led to an elevated biological dose at the end of the proton field, while 4D-dose recalculation exhibited random deviations everywhere in the radiation field depending on the interplay of beam delivery and organ motion. For a single beam treatment assuming (α∕β)_x = 2 Gy, D_95% was 1.98 Gy (RBE) (A), 2.15 Gy (RBE) (B), 1.81 Gy (RBE) (C) and 1.98 Gy (RBE) (D). The homogeneity index was 1.04 (A), 1.08 (B), 1.23 (C) and 1.25 (D).

CONCLUSION

For the studied liver case, intrafractional motion did not reduce the modulation of the RBE-weighted dose postulated by variable RBE models for proton treatments.