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.

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.

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.

The experimental dose ranges influence the LETd dependency of the proton minimum RBE (RBEmin).

Cell experiments have shown the proton relative biological effectiveness (RBE) to vary with dose and linear energy transfer (LET), which has led to development of variable RBE models. The RBE is normally estimated from two independent functions, the RBEmax and RBEmin, describing the extreme RBE at low and high doses. While there is consensus that RBEmax increases with increasing LET, the RBEmin is not uniformly defined and its dependency on LET is deviating. In this work, we analysed this dependency and its sensitivity to variations of the experimental dose range. We performed a literature search to find data from existing monoenergetic proton cell survival experiments with (α/ß) x values below 5 Gy and dose averaged LET (LETd) values below 20 keV µm-1. From the experiments the doses and their corresponding survival data were extracted. Based on these data, multiple restricted databases were generated by sequential exclusion of low dose data in the experiments followed by a linear-quadratic (LQ) fit. The quadratic component from the LQ-fit was used to estimate RBEmin. The LETd dependency of RBEmin was determined by fitting a linear function to the RBEmin values estimated from the restricted databases. Our analysis showed the LETd dependency of RBEmin to be significantly influenced by the experimental dose range. By including experiments with doses below 1 Gy in the database, we found that RBEmin increased with increasing LETd. By excluding the low dose experiments in our database, the RBEmin became constant for all LETd values. For an LETd value of 5 keV µm-1, a restricted database including the data with the lowest doses gave an RBEmin of 1.4 ± 0.1, while databases with only high dose data (>2 Gy) gave an RBEmin of 1.0 ± 0.1. None of our restricted databases gave a decreasing RBEmin with increasing LETd. Our study showed that RBEmin has a small yet significant dependency on LETd for tissues with low (α/ß) x ratio. The LETd dependency of RBEmin varied substantially with the experimental dose range. Including experiments with high minimum dose in RBE models may lead to underestimation of the RBE.

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.

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.

Modelling of organ-specific radiation-induced secondary cancer risks following particle therapy.

BACKGROUND AND PURPOSE: Radiation-induced cancer is a serious late effect that may follow radiotherapy. A considerable uncertainty is associated with carcinogenesis from photon-based treatment, and even less established when including relative biological effectiveness (RBE) for particle therapy. The aim of this work was therefore to estimate and in particular explore relative risks (RR) of secondary cancer (SC) following particle therapy as applied in treatment of prostate cancer. MATERIAL AND METHODS: RRs of radiation-induced SC in the bladder and rectum were estimated using a bell-shaped dose-response model incorporating RBE and fractionation effects. The risks from volumetric modulated arc therapy (VMAT) were compared to intensity-modulated proton therapy (IMPT) and scanning carbon ions for ten patients. RESULTS: The mean estimated RR (95% CI) of SC for VMAT/C-ion was 1.31 (0.65-2.18) for the bladder and 0.58 (0.41-0.80) for the rectum. Corresponding values for VMAT/IMPT were 1.72 (1.06-2.37) and 1.10 (0.78-1.43). The radio-sensitivity parameter α had the strongest influence on the results with decreasing RR for increasing values of α. CONCLUSION: Based on the wide spread in RR between patients and variations across the included parameter values, the risk profiles of the rectum and bladder were not dramatically different for the investigated radiotherapy techniques.