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 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 (RBE1.1) 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 RBE1.1 dose characteristics. Differences across cases and controls related to the dose-averaged LET (LETd) and variable RBE-weighted dose from two RBE models were analyzed in the high-dose region. RESULTS: LETd metrics were marginally higher for cases vs. controls for the majority of dose levels and brainstem substructures. Considering areas with doses above 54 Gy(RBE1.1), we found a moderate trend of 13% higher median LETd 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 LETd for cases compared to controls were noticeable across structures and LETd metrics for this patient cohort. While case-control differences were minor, an association with the observed symptomatic brainstem toxicity cannot be ruled out.

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 / ß ) 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 / ß ) 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.

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 (RBE1.1), 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 RBE1.1, 4 phenomenological RBE models with varying (α/ß)x parameters, and with a simpler linear energy transfer-dependent model. The spatial agreement between the dose distributions of constant RBE1.1 versus the variable RBE models was compared using the Dice similarity coefficient. RESULTS: The spatial agreement between the variable RBE dose distributions and RBE1.1 decreased with increasing isodose levels in all patient cases. The patient with ependymoma showed the greatest variation in dose and dose volumes, where V50Gy(RBE) in the brainstem increased from 32% (RBE1.1) 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 RBE1.1, 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 RBE1.1.

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 (RBEd) 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 RBEd at 1.21 (1.04-2.24). Across all patients, the narrower RBE model selection gave median RBEd values from 1.22 to 1.30. CONCLUSION: For all BSCs, there was a systematic model-dependent variation in RBEd, 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.

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.

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.

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.

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/ß) 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/ß) x values and dose-averaged LET (LETd). 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/ß) x and high LETd, 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 (D2%) was larger than the variation in mean dose and other dose metrics, with D2% of the left optic nerve ((α/ß) x = 2.1 Gy) in the pituitary adenoma case showing the greatest discrepancies between models: 28-52 Gy(RBE), while D2% for RBE1.1 was 30 Gy(RBE). For all patient cases, the estimated mean RBE to the PTV was in the range 1.09-1.29 ((α/ß) 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.

Monte Carlo simulations of a low energy proton beamline for radiobiological experiments.

BACKGROUND: In order to determine the relative biological effectiveness (RBE) of protons with high accuracy, radiobiological experiments with detailed knowledge of the linear energy transfer (LET) are needed. Cell survival data from high LET protons are sparse and experiments with low energy protons to achieve high LET values are therefore required. The aim of this study was to quantify LET distributions from a low energy proton beam by using Monte Carlo (MC) simulations, and to further compare to a proton beam representing a typical minimum energy available at clinical facilities. MATERIALS AND METHODS: A Markus ionization chamber and Gafchromic films were employed in dose measurements in the proton beam at Oslo Cyclotron Laboratory. Dose profiles were also calculated using the FLUKA MC code, with the MC beam parameters optimized based on comparisons with the measurements. LET spectra and dose-averaged LET (LETd) were then estimated in FLUKA, and compared with LET calculated from an 80 MeV proton beam. RESULTS: The initial proton energy was determined to be 15.5 MeV, with a Gaussian energy distribution of 0.2% full width at half maximum (FWHM) and a Gaussian lateral spread of 2 mm FWHM. The LETd increased with depth, from approximately 5 keV/µm in the entrance to approximately 40 keV/µm in the distal dose fall-off. The LETd values were considerably higher and the LET spectra were much narrower than the corresponding spectra from the 80 MeV beam. CONCLUSIONS: MC simulations accurately modeled the dose distribution from the proton beam and could be used to estimate the LET at any position in the setup. The setup can be used to study the RBE for protons at high LETd, which is not achievable in clinical proton therapy facilities.

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

BACKGROUND: For tumours near organs at risk, there is concern about unintended increase in biological dose from elevated linear energy transfer (LET) at the distal end of treatment fields. The objective of this study was therefore to investigate how different paediatric posterior fossa tumour locations impact LET and biological dose to the brainstem during intensity-modulated proton therapy (IMPT). MATERIAL AND METHODS: Multiple IMPT plans were generated for four different simulated tumour locations relative to the brainstem for a five-year-old male patient. A prescribed dose of 59.4 Gy(RBE) was applied to the planning target volumes (PTVs). Plans with two lateral and one posterior non-coplanar fields were created, along with plans with modified field arrangements. The dose-averaged LET (LETd) and the physical dose × RBELET (D × RBELET), where RBELET=1+c × LETd, were calculated using the FLUKA Monte Carlo code. A scaling parameter c was applied to make the RBELET represent variations in the biological effect due to LET. RESULTS: High LETd values surrounded parts of the PTV and encompassed portions of the brainstem. Mean LETd values in the brainstem were 3.2-6.6 keV/µm. The highest absolute brainstem LETd values were seen with the tumour located most distant from the brainstem, whereas lower and more homogeneous LETd values were seen when the tumour invaded the brainstem. In contrast, the highest mean D × RBELET values were found in the latter case (54.0 Gy(RBE)), while the case with largest distance between tumour and brainstem had a mean D × RBELET of 1.8 Gy(RBE). CONCLUSIONS: Using IMPT to treat posterior fossa tumours may result in high LETd values within the brainstem, particularly if the tumour volume is separated from the brainstem. However, the D × RBELET was greater for tumours that approached or invaded the brainstem. Changing field angles showed a reduction of LETd and D × RBELET in the brainstem.

A phenomenological biological dose model for proton therapy based on linear energy transfer spectra.

PURPOSE: The relative biological effectiveness (RBE) of protons varies with the radiation quality, quantified by the linear energy transfer (LET). Most phenomenological models employ a linear dependency of the dose-averaged LET (LETd ) to calculate the biological dose. However, several experiments have indicated a possible non-linear trend. Our aim was to investigate if biological dose models including non-linear LET dependencies should be considered, by introducing a LET spectrum based dose model. METHOD: The RBE-LET relationship was investigated by fitting of polynomials from 1st to 5th degree to a database of 85 data points from aerobic in vitro experiments. We included both unweighted and weighted regression, the latter taking into account experimental uncertainties. Statistical testing was performed to decide whether higher degree polynomials provided better fits to the data as compared to lower degrees. The newly developed models were compared to three published LETd based models for a simulated spread out Bragg peak (SOBP) scenario. RESULTS: The statistical analysis of the weighted regression analysis favored a non-linear RBE-LET relationship, with the quartic polynomial found to best represent the experimental data (P = 0.010). The results of the unweighted regression analysis were on the borderline of statistical significance for non-linear functions (P = 0.053), and with the current database a linear dependency could not be rejected. For the SOBP scenario, the weighted non-linear model estimated a similar mean RBE value (1.14) compared to the three established models (1.13-1.17). The unweighted model calculated a considerably higher RBE value (1.22). CONCLUSION: The analysis indicated that non-linear models could give a better representation of the RBE-LET relationship. However, this is not decisive, as inclusion of the experimental uncertainties in the regression analysis had a significant impact on the determination and ranking of the models. As differences between the models were observed for the SOBP scenario, both non-linear LET spectrum- and linear LETd based models should be further evaluated in clinically realistic scenarios.