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.

Linear energy transfer-inclusive models of brainstem necrosis following proton therapy of paediatric ependymoma.

Background and Purpose: Radiation-induced brainstem necrosis after proton therapy is a severe toxicity with potential association to uncertainties in the proton relative biological effectiveness (RBE). A constant RBE of 1.1 is assumed clinically, but the RBE is known to vary with linear energy transfer (LET). LET-inclusive predictive models of toxicity may therefore be beneficial during proton treatment planning. Hence, we aimed to construct models describing the association between brainstem necrosis and LET in the brainstem. Materials and methods: A matched case-control cohort (n = 28, 1:3 case-control ratio) of symptomatic brainstem necrosis was selected from 954 paediatric ependymoma brain tumour patients treated with passively scattered proton therapy. Dose-averaged LET (LETd) parameters in restricted volumes (L50%, L10% and L0.1cm3, the cumulative LETd) within high-dose thresholds were included in linear- and logistic regression normal tissue complication probability (NTCP) models. Results: A 1 keV/µm increase in L10% to the brainstem volume receiving dose over 54 Gy(RBE) led to an increased brainstem necrosis risk [95% confidence interval] of 2.5 [0.0, 7.8] percentage points. The corresponding logistic regression model had area under the receiver operating characteristic curve (AUC) of 0.76, increasing to 0.84 with the anterior pons substructure as a second parameter. 19 [7, 350] patients with toxicity were required to associate the L10% (D > 54 Gy(RBE)) and brainstem necrosis with 80% statistical power. Conclusion: The established models of brainstem necrosis illustrate a potential impact of high LET regions in patients receiving high doses to the brainstem, and thereby support LET mitigation during clinical treatment planning.

A hybrid multi-particle approach to range assessment-based treatment verification in particle therapy.

Particle therapy (PT) used for cancer treatment can spare healthy tissue and reduce treatment toxicity. However, full exploitation of the dosimetric advantages of PT is not yet possible due to range uncertainties, warranting development of range-monitoring techniques. This study proposes a novel range-monitoring technique introducing the yet unexplored concept of simultaneous detection and imaging of fast neutrons and prompt-gamma rays produced in beam-tissue interactions. A quasi-monolithic organic detector array is proposed, and its feasibility for detecting range shifts in the context of proton therapy is explored through Monte Carlo simulations of realistic patient models and detector resolution effects. The results indicate that range shifts of [Formula: see text] can be detected at relatively low proton intensities ([Formula: see text] protons/spot) when spatial information obtained through imaging of both particle species are used simultaneously. This study lays the foundation for multi-particle detection and imaging systems in the context of range verification in PT.

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.

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.

Plan Selection in Proton Therapy of Locally Advanced Prostate Cancer with Simultaneous Treatment of Multiple Targets.

PURPOSE: Intensity modulated proton therapy (IMPT) of locally advanced prostate cancer can spare the bowel considerably compared with modern photon therapy, but simultaneous treatment of the prostate (p), seminal vesicles (sv), and lymph nodes is challenging owing to day-to-day organ motion and range uncertainties. Our purpose was, therefore, to generate a plan library for use in adaptive IMPT to mitigate these uncertainties. METHODS AND MATERIALS: We retrospectively included 27 patients with a series of computed tomography scans throughout their treatment representing day-to-day variation. In 18 of the patients, target motion was analyzed using rigid shifts of prostate gold markers relative to bony anatomy. A plan library with different p and sv planning target volume (p/sv-PTV) positions was defined from the distribution and direction of these shifts. Delivery of IMPT using plan selection from the library was simulated for image guidance on bony anatomy, in the remaining patients and compared with nonadaptive IMPT. RESULTS: The plan library consisted of 3 small margin p/sv-PTVs: (1) p/sv-PTV shifted 1.5 systematic error (Σ) of the population mean in the anterior and cranial directions, (2) p/sv-PTV shifted 1.5Σ in the posterior and caudal directions, and (3) p/sv-PTV in the planning position. The conventional p/sv-PTV was also available for backup. Plan selection compared with nonadaptive IMPT resulted in a reduction of the rectum volume receiving 60 Gy relative biological effect (RBE) (V60GyRBE) from on average 12 mL to 9 mL. For the bladder the average V45GyRBE was reduced from 36% to 30%. Large and small bowel doses were also reduced, whereas target coverage was comparable or improved compared with nonadaptive IMPT. CONCLUSIONS: Plan selection based on a population model of rigid target motion was feasible for all patients. Compared with conventional IMPT, plan selection resulted in significant dosimetric sparing of rectum and bladder without compromising target coverage.

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.

Biological dose and complication probabilities for the rectum and bladder based on linear energy transfer distributions in spot scanning proton therapy of prostate cancer.

BACKGROUND: The increased linear energy transfer (LET) at the end of the Bragg peak causes concern for an elevated and spatially varying relative biological effectiveness (RBE) of proton therapy (PT), often in or close to dose-limiting normal tissues. In this study, we investigated dose-averaged LET (LETd) distributions for spot scanning PT of prostate cancer patients using different beam angle configurations. In addition, we derived RBE-weighted (RBEw) dose distributions and related normal tissue complication probabilities (NTCPs) for the rectum and bladder. MATERIAL AND METHODS: A total of 21 spot scanning proton plans were created for each of six patients using a prescription dose of 78 Gy(RBE1.1), with each plan using two 'mirrored' beams with gantry angles from 110°/250° to 70°/290°, in steps of 2°. Physical dose and LETd distributions were calculated as well as RBEw dose distributions using either RBE = 1.1 or three different variable RBE models. The resulting biological dose distributions were used as input to NTCP models for the rectum and bladder. RESULTS: For anterior oblique (AO) configurations, the rectum LETd volume and RBEw dose increased with increasing angles off the lateral opposing axis, with the RBEw rectum dose being higher than for all posterior oblique (PO) configurations. For PO configurations, the corresponding trend was seen for the bladder. Using variable RBE models, the rectum NTCPs were highest for the AO configurations with up to 3% for the 80°/280° configuration while the bladder NTCPs were highest for the PO configurations with up to 32% for the 100°/260°. The rectum D1cm3 constraint was fulfilled for most patients/configurations when using uniform RBE but not for any patient/configuration with variable RBE models. CONCLUSIONS: Compared to using constant RBE, the variable RBE models predicted increased biological doses to the rectum, bladder and prostate, which in turn lead to substantially higher estimated rectum and bladder NTCPs.

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.

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.

Risk of radiation-induced secondary rectal and bladder cancer following radiotherapy of prostate cancer.

BACKGROUND: An elevated risk of radiation-induced secondary cancer (SC) has been observed in prostate cancer patients after radiotherapy (RT), rising to as high as one in 70 patients with more than 10 years follow-up. In this study we have estimated SC risks following RT with both previous and contemporary techniques, including proton therapy, using risk models based on different dose-response relationships. MATERIAL AND METHODS: RT plans treating the prostate and seminal vesicles with either conformal radiotherapy (CRT), volumetric modulated arc therapy (VMAT) or intensity-modulated proton therapy (IMPT) were created for 10 patients. The risks of radiation-induced cancer were estimated for the bladder and rectum using dose-response models reflecting varying degrees of cell sterilisation: a linear model, a linear-plateau model and a bell-shaped model also accounting for fractionated RT. RESULTS: The choice of risk models was found to rank the plans quite differently, with the CRT plans having the lowest SC risk using the bell-shaped model, while resulting in the highest risk applying the linear model. Considering all dose-response scenarios, median relative risks of VMAT versus IMPT were 1.1-1.7 for the bladder and 0.9-1.8 for the rectum. Risks of radiation-induced bladder and rectal cancers were lower from VMAT if exposed at 80 years versus IMPT if exposed at 50 years. CONCLUSIONS: The SC risk estimations for the bladder and rectum revealed no clear relative relationship between the contemporary techniques and CRT, with divergent results depending on choice of model. However, the SC risks for these organs when using IMPT were lower or comparable to VMAT. SC risks could be assessed when considering referral of prostate cancer patients to proton therapy, taking also general patient characteristics, such as age, into account.

Estimated risk of radiation-induced cancer following paediatric cranio-spinal irradiation with electron, photon and proton therapy.

BACKGROUND: Improvement in radiotherapy during the past decades has made the risk of developing a radiation-induced secondary cancer as a result of dose to normal tissue a highly relevant survivorship issue. Important factors expected to influence secondary cancer risk include dose level and dose heterogeneity, as well as gender and type of tissue irradiated. The elevated radio-sensitivity in children calls for models particularly tailored to paediatric cancer patients. MATERIAL AND METHODS: Treatment plans of six paediatric medulloblastoma patients were analysed with respect to secondary cancer risk following cranio-spinal irradiation (CSI), using either: 1) electrons and photons combined; 2) conformal photons; 3) double-scattering (DS) protons; or 4) intensity-modulated proton therapy (IMPT). The relative organ equivalent dose (OED) concept was applied in three dose-risk scenarios: a linear response model, a plateau response and an organ specific linear-exponential response. Life attributable risk (LAR) was calculated based on the BEIR VII committee's preferred models for estimating age- and site-specific solid cancer incidence. Uncertainties in the model input parameters were evaluated by error propagation using a Monte Carlo sampling procedure. RESULTS: Both DS protons and IMPT achieved a significantly better dose conformity compared to the photon and electron irradiation techniques resulting in a six times lower overall risk of radiation-induced cancer. Secondary cancer risk in the thyroid and lungs contributed most to the overall risk in all compared modalities, while no significant difference was observed for the bones. Variations between DS protons and IMPT were small, as were differences between electrons and photons. CONCLUSION: Regardless of technique, using protons decreases the estimated risk of secondary cancer following paediatric CSI compared to conventional photon and electron techniques. Substantial uncertainties in the LAR estimates support relative risk comparisons by OED.