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/ßx) 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/ßx= 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.

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.

Impact of RBE variations on risk estimates of temporal lobe necrosis in patients treated with intensity-modulated proton therapy for head and neck cancer.

BACKGROUND: Temporal lobe necrosis (TLN) is a potential late effect after radiotherapy for skull base head and neck cancer (HNC). Several photon-derived dose constraints and normal tissue complication probability (NTCP) models have been proposed, however variation in relative biological effectiveness (RBE) may challenge the applicability of these dose constraints and models in proton therapy. The purpose of this study was therefore to investigate the influence of RBE variations on risk estimates of TLN after Intensity-Modulated Proton Therapy for HNC. MATERIAL AND METHODS: Seventy-five temporal lobes from 45 previously treated patients were included in the analysis. Sixteen temporal lobes had radiation associated Magnetic Resonance image changes (TLIC) suspected to be early signs of TLN. Fixed (RWDFix) and variable RBE-weighed doses (RWDVar) were calculated using RBE = 1.1 and two RBE models, respectively. RWDFix and RWDVar for temporal lobes were compared using Friedman's test. Based on RWDFix, six NTCP models were fitted and internally validated through bootstrapping. Estimated probabilities from RWDFix and RWDVar were compared using paired Wilcoxon test. Seven dose constraints were evaluated separately for RWDFix and RWDVar by calculating the observed proportion of TLIC in temporal lobes meeting the specific dose constraints. RESULTS: RWDVar were significantly higher than RWDFix (p < 0.01). NTCP model performance was good (AUC:0.79-0.84). The median difference in estimated probability between RWDFix and RWDVar ranged between 5.3% and 20.0% points (p < 0.01), with V60GyRBE and DMax at the smallest and largest differences, respectively. The proportion of TLIC was higher for RWDFix (4.0%-13.1%) versus RWDVar (1.3%-5.3%). For V65GyRBE ≤ 0.03 cc the proportion of TLIC was less than 5% for both RWDFix and RWDVar. CONCLUSION: NTCP estimates were significantly influenced by RBE variations. Dmax as model predictor resulted in the largest deviations in risk estimates between RWDFix and RWDVar. V65GyRBE ≤ 0.03 cc was the most consistent dose constraint for RWDFix and RWDVar.

Mixed Effect Modeling of Dose and Linear Energy Transfer Correlations With Brain Image Changes After Intensity Modulated Proton Therapy for Skull Base Head and Neck Cancer.

PURPOSE: Intensity modulated proton therapy (IMPT) could yield high linear energy transfer (LET) in critical structures and increased biological effect. For head and neck cancers at the skull base this could potentially result in radiation-associated brain image change (RAIC). The purpose of the current study was to investigate voxel-wise dose and LET correlations with RAIC after IMPT. METHODS AND MATERIALS: For 15 patients with RAIC after IMPT, contrast enhancement observed on T1-weighted magnetic resonance imaging was contoured and coregistered to the planning computed tomography. Monte Carlo calculated dose and dose-averaged LET (LETd) distributions were extracted at voxel level and associations with RAIC were modelled using uni- and multivariate mixed effect logistic regression. Model performance was evaluated using the area under the receiver operating characteristic curve and precision-recall curve. RESULTS: An overall statistically significant RAIC association with dose and LETd was found in both the uni- and multivariate analysis. Patient heterogeneity was considerable, with standard deviation of the random effects of 1.81 (1.30-2.72) for dose and 2.68 (1.93-4.93) for LETd, respectively. Area under the receiver operating characteristic curve was 0.93 and 0.95 for the univariate dose-response model and multivariate model, respectively. Analysis of the LETd effect demonstrated increased risk of RAIC with increasing LETd for the majority of patients. Estimated probability of RAIC with LETd = 1 keV/µm was 4% (95% confidence interval, 0%, 0.44%) and 29% (95% confidence interval, 0.01%, 0.92%) for 60 and 70 Gy, respectively. The TD15 were estimated to be 63.6 and 50.1 Gy with LETd equal to 2 and 5 keV/µm, respectively. CONCLUSIONS: Our results suggest that the LETd effect could be of clinical significance for some patients; LETd assessment in clinical treatment plans should therefore be taken into consideration.

Outcomes and patterns of radiation associated brain image changes after proton therapy for head and neck skull base cancers.

BACKGROUND AND PURPOSE: To characterize patterns and outcomes of brain MR image changes after proton therapy (PT) for skull base head and neck cancer (HNC). MATERIAL AND METHODS: Post-treatment MRIs ≥6 months were reviewed for radiation-associated image changes (RAIC) in 127 patients. All patients had received at least a point dose of 40 Gy(RBE) to the brain. The MRIs were rigidly registered to planning CTs and RAIC lesions were contoured both on T1 weighted (post-contrast) and T2 weighted sequences, and dose-volume parameters extracted. Probability of RAIC was calculated using multistate survival analysis. Univariate/multivariate analyses were performed using Cox Regression. Recursive partitioning analysis was used to investigate dose-volume correlates of RAIC development. RESULTS: 17.3% developed RAIC. All RAIC events were asymptomatic and occurred in the temporal lobe (14), frontal lobe (6) and cerebellum (2). The median volume of the contrast enhanced RAIC lesion was 0.5 cc at their maximum size. The RAIC resolved or improved in 45.5% of the patients and were stable or progressed in 36.4%. The 3-year actuarial rate of developing RAIC was 14.3%. RAIC was observed in 63% of patients when V67 Gy(RBE) of the brain ≥0.17 cc. CONCLUSION: Small RAIC lesions after PT occurred in 17.3% of the patients; the majority in nasopharyngeal or sinonasal cancer. The estimated dose-volume correlations confirm the importance of minimizing focal high doses to brain when achievable.

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 RBE1.1-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.

The influence of inter-fractional anatomy variation on secondary cancer risk estimates following radiotherapy.

PURPOSE: In silico studies comparing estimated risks of radiation-induced secondary cancer (SC) are frequently performed in assessment of radiotherapy techniques. Since inter-patient anatomy variations can result in considerable differences in estimated risk we aimed to explore the influence of inter-fractional organ motion patterns on SC risk. METHODS: Volumetric modulated arc therapy (VMAT) and intensity-modulated proton therapy (IMPT) plans were generated on the planning CT (pCT) scans of eight prostate cancer patients. In addition, the treatment plans were re-calculated on 8-9 repeat CTs (rCTs) of each patient acquired throughout the treatment course. Relative risk (RR) of SC (VMAT/IMPT) was calculated for the planned and the re-calculated dose distributions using the organ equivalent dose concept adapted to a linear and a bell-shaped competition dose-response model. RESULTS: Day-to-day variations in anatomy lead to fluctuations in SC risk estimates of the same order of magnitude as those caused by inter-patient variations. Using the competition model, the RR range for bladder cancer based on the pCTs was 0.4-3.4, while a considerably wider range was found when including all rCTs (0.2-6.7). There was nevertheless a correlation in RR based on repeat CTs for individual patients, indicating that patient-specific SC risks could be estimated. CONCLUSIONS: The estimated relative risks varied considerably across rCTs and could change the risk in favour of VMAT/IMPT depending on the anatomy of the day. The results demonstrate the importance of performing in silico studies of SC risk on a cohort of patients or multiple CTs when structures subject to organ motion are involved.