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Background: Boron neutron capture therapy (BNCT) is a targeted radiotherapy that relies on the 10 B (n, α) 7 Li reaction, which produces secondary particles with high linear energy transfer (LET), leading to a high relative biological effectiveness (RBE) in tumors. The biological effectiveness of BNCT is influenced by factors such as boron distribution and concentration, necessitating improved methods for assessing its radiobiological effects and clarifying the sensitivity of the differences in different factors to the biological effects., Purpose: This paper introduces a method to evaluate the biological effects of BNCT using the cellular repair model. This method aims to overcome some of the limitations of current evaluation approaches. The primary goal is to provide guidance for clinical treatments and the development of boron drugs, as well as to investigate the impact of the synergistic effects of mixed radiation fields in BNCT on treatment outcomes., Methods: The approach involves three key steps: first, extending the radial energy deposition distribution of BNCT secondary particles using Geant4-DNA. This allows for the calculation of initial DNA double-strand breaks (DSBs) distributions for a given absorbed dose. Next, the obtained initial DSB distributions are used for DNA damage repair simulations to generate cell survival curves, then thereby quantifying RBE and compound biological effectiveness (CBE). The study also explores the synergistic effects of the mixed radiation fields in BNCT on assessing biological effects were also explored in depth., Results: The results showed that the RBE of boronophenylalanine (BPA) and sodium borocaptate (BSH) drugs at cell survival fraction 0.01 was 2.50 and 2.15, respectively. The CBE of the boron dose component was 3.60 and 0.73, respectively, and the RBE of the proton component was 3.21, demonstrating that BPA has a significantly higher biological impact than BSH due to superior cellular permeability. The proton dose significance in BNCT treatment is also underscored, necessitating consideration in both experimental and clinical contexts. The study demonstrates that synergistic effects between disparate radiation fields lead to increased misrepairs and enhanced biological impact. Additionally, the biological effect diminishes with rising boron concentration, emphasizing the need to account for intercellular DNA damage heterogeneity., Conclusions: This methodology offers valuable insights for the development of new boron compounds and precise assessment of bio-weighted doses in clinical settings and can be adapted to other therapeutic modalities., (© 2024 American Association of Physicists in Medicine.)

Background: Phenomenological relative biological effectiveness (RBE) models for proton therapy, based on the dose-averaged linear energy transfer (LET), have been developed to address the apparent RBE increase towards the end of the proton range. The results of these phenomenological models substantially differ due to varying empirical assumptions and fitting functions. In contrast, more theory-based approaches are used in carbon ion radiotherapy, such as the microdosimetric kinetic model (MKM). However, implementing microdosimetry-based models in LET-based proton therapy treatment planning systems poses challenges., Purpose: This work presents a LET-based version of the MKM that is practical for clinical use in proton radiotherapy., Methods: At first, we derived an approximation of the Mayo Clinic Florida (MCF) MKM for relatively-sparsely ionizing radiation such as protons. The mathematical formalism of the proposed model is equivalent to the original MKM, but it maintains some key features of the MCF MKM, such as the determination of model parameters from measurable cell characteristics. Subsequently, we carried out Monte Carlo calculations with PHITS in different simulated scenarios to establish a heuristic correlation between microdosimetric quantities and the dose averaged LET of protons., Results: A simple allometric function was found able to describe the relationship between the dose-averaged LET of protons and the dose-mean lineal energy, which includes the contributions of secondary particles. The LET-based MKM was used to model the in vitro clonogenic survival RBE of five human and rodent cell lines (A549, AG01522, CHO, T98G, and U87) exposed to pristine and spread-out Bragg peak (SOBP) proton beams. The results of the LET-based MKM agree well with the biological data in a comparable or better way with respect to the other models included in the study. A sensitivity analysis on the model results was also performed., Conclusions: The LET-based MKM integrates the predictive theoretical framework of the MCF MKM with a straightforward mathematical description of the RBE based on the dose-averaged LET, a physical quantity readily available in modern treatment planning systems for proton therapy., (© 2024 American Association of Physicists in Medicine.)

Background: Proton linear energy transfer (LET) is associated with the relative biological effectiveness of radiation on tissues. Monte Carlo (MC) simulations have been known to be the preferred method to calculate LET. Detectors have also been built to measure LET, but they need to be calibrated with MC simulations., Purpose: To propose and test a MC-free method for determining LET from the measured integral depth dose (LFI) of the protons of interest., Method and Materials: LFI consists of three steps: (1) IDD measurements, (2) extraction of energy spectrum (ES) from the IDD, and (3) LET determination from the extracted ES and the stopping power of each energy. To validate the accuracy of the extraction of ES, we use Gaussian ES to synthesize IDD, extract ES from the synthesized IDD, and then compare the original (ground truth) and extracted ES. LETs calculated from the original and extracted ES are also compared. To obtain the LET of protons of interest, we measure IDDs by a large-area plane-parallel ionization chamber in water. Finally, TOPAS MC is employed to simulate IDDs, ES, and LETs. From the simulated IDD, the extracted ES and LET are compared with the simulations from TOPAS MC., Results: From the synthesized IDDs, the LETs agreed excellently when the peak energies ≥10 and 1.25 MeV with depth resolutions 0.1 and 0.01 mm, respectively. For energy <1.25 MeV, even higher depth resolution than 0.01 mm is required. From the MC simulated IDDs, our track-averaged LET excellently agreed with MC simulation, but not the LET d . Our LET d was smaller than MC simulated LET d in the shallow region but larger in the distal Bragg peak region., Conclusion: LET can be accurately determined from the IDD. This method can be used in the clinic to commission or validate LETs from other measurement methods or a treatment planning system., (© 2023 American Association of Physicists in Medicine.)

Background: The Relative Biological Effectiveness (RBE) of kilovoltage photon beams has been previously investigated in vitro and in silico using analytical methods. The estimated values range from 1.03 to 1.82 depending on the methodology and beam energies examined., Purpose: The focus of this work was to independently estimate RBE values for a range of clinically used kilovoltage beams (70-200 kVp) while investigating the suitability of using TOPAS-nBio for this task., Methods: Previously validated spectra of clinical beams were used to generate secondary electron spectra at several depths in a water tank phantom via TOPAS Monte Carlo (MC) simulations. Cell geometry was irradiated with the secondary electrons in TOPAS-nBio MC simulations. The deposited dose and the calculated number of DNA strand breaks were used to estimate RBE values., Results: Monoenergetic secondary electron simulations revealed the highest direct and indirect double strand break yield at approximately 20 keV. The average RBE value for the kilovoltage beams was calculated to be 1.14., Conclusions: TOPAS-nBio was successfully used to estimate the RBE values for a range of clinical radiotherapy beams. The calculated value was in agreement with previous estimates, providing confidence in its clinical use in the future., (© 2024 The Authors. Medical Physics published by Wiley Periodicals LLC on behalf of American Association of Physicists in Medicine.)

Background: Brachytherapy for ocular melanoma is based on the application of eye plaques with different spatial dose nonuniformity, time-dependent dose rates and relative biological effectiveness (RBE)., Purpose: We propose a parameter called the equivalent uniform RBE-weighted dose (EUD RBE ) that can be used for quantitative characterization of integrated cell survival in radiotherapy modalities with the variable RBE, dose nonuniformity and dose rate. The EUD RBE is applied to brachytherapy with 125 I eye plaques designed by the Collaborative Ocular Melanoma Study (COMS)., Methods: The EUD RBE is defined as the uniform dose distribution with RBE = 1 that causes equal cell survival for a given nonuniform dose distribution with the variable RBE > 1. The EUD RBE can be used for comparison of cell survival for nonuniform dose distributions with different RBE, because they are compared to the reference dose with RBE = 1. The EUD RBE is applied to brachytherapy with 125 I COMS eye plaques that are characterized by a steep dose gradient in tumor base-apex direction, protracted irradiation during time intervals of 3-8 days, and variable dose-rate dependent RBE with a maximum of about 1.4. The simulations are based on dose of 85 Gy prescribed to the farthest intraocular extent of the tumor (tumor apex). To compute the EUD RBE in eye plaque brachytherapy and correct for protracted irradiation, the distributions of physical dose have been converted to non-uniform distributions of biologically effective dose (BED) to include the biological effects of sublethal cellular repair, Our radiobiological analysis considers the combined effects of different time-dependent dose rates, spatial dose non-uniformity, dose fractionation and different RBE and can be used to derive optimized dose regimens brachytherapy., Results: Our simulations show that the EUD RBE increases with the prescription depths and the maximum increase may achieve 6% for the tumor height of 12 mm. This effect stems from a steep dose gradient within the tumor that increases with the prescription depth. The simulations also show that the EUD RBE increase may achieve 12% with increasing the dose rate when implant duration decreases. The combined effect of dose nonuniformity and dose rate may change the EUD RBE up to 18% for the same dose prescription of 85 Gy to tumor apex. The absolute dose range of 48-61 Gy (RBE) for the EUD RBE computed using 4 or 5 fractions is comparable to the dose prescriptions used in stereotactic body radiation therapy (SBRT) with megavoltage X-rays (RBE = 1) for different cancers. The tumor control probabilities in SBRT and eye plaque brachytherapy are very similar at the level of 80% or higher that support the hypothesis that the selected approximations for the EUD RBE are valid., Conclusions: The computed range of the EUD RBE in 125 I COMS eye plaque brachytherapy suggests that the selected models and hypotheses are acceptable. The EUD RBE can be useful for analysis of treatment outcomes and comparison of different dose regimens in eye plaque brachytherapy., (© 2024 American Association of Physicists in Medicine.)

Background: The static magnetic field present in magnetic resonance (MR)-guided radiotherapy systems can influence dose deposition and charged particle collection in air-filled ionization chambers. Thus, accurately quantifying the effect of the magnetic field on ionization chamber response is critical for output calibration. Formalisms for reference dosimetry in a magnetic field have been proposed, whereby a magnetic field quality conversion factor k B,Q is defined to account for the combined effects of the magnetic field on the radiation detector. Determination of k B,Q in the literature has focused on Monte Carlo simulation studies, with experimental validation limited to only a few ionization chamber models., Purpose: The purpose of this study is to experimentally measure k B,Q for 11 ionization chamber models in two commercially available MR-guided radiotherapy systems: Elekta Unity and ViewRay MRIdian., Methods: Eleven ionization chamber models were characterized in this study: Exradin A12, A12S, A28, and A26, PTW T31010, T31021, and T31022, and IBA FC23-C, CC25, CC13, and CC08. The experimental method to measure k B,Q utilized cross-calibration against a reference Exradin A1SL chamber. Absorbed dose to water was measured for the reference A1SL chamber positioned parallel to the magnetic field with its centroid placed at the machine isocenter at a depth of 10 cm in water for a 10 × 10 cm 2 field size at that depth. Output was subsequently measured with the test chamber at the same point of measurement. k B,Q for the test chamber was computed as the ratio of reference dose to test chamber output, with this procedure repeated for each chamber in each MR-guided radiotherapy system. For the high-field 1.5 T Elekta Unity system, the dependence of k B,Q on the chamber orientation relative to the magnetic field was quantified by rotating the chamber about the machine isocenter., Results: Measured k B,Q values for our test dataset of ionization chamber models ranged from 0.991 to 1.002, and 0.995 to 1.004 for the Elekta Unity and ViewRay MRIdian, respectively, with k B,Q tending to increase as the chamber sensitive volume increased. Measured k B,Q values largely agreed within uncertainty to published Monte Carlo simulation data and available experimental data. k B,Q deviation from unity was minimized for ionization chamber orientation parallel or antiparallel to the magnetic field, with increased deviations observed at perpendicular orientations. Overall (k = 1) uncertainty in the experimental determination of the magnetic field quality conversion factor, k B,Q was 0.71% and 0.72% for the Elekta Unity and ViewRay MRIdian systems, respectively., Conclusions: For a high-field MR-linac, the characterization of ionization chamber performance as angular orientation varied relative to the magnetic field confirmed that the ideal orientation for output calibration is parallel. For most of these chamber models, this study represents the first experimental characterization of chamber performance in clinical MR-linac beams. This is a critical step toward accurate output calibration for MR-guided radiotherapy systems and the measured k B,Q values will be an important reference data source for forthcoming MR-linac reference dosimetry protocols., (© 2023 The Authors. Medical Physics published by Wiley Periodicals LLC on behalf of American Association of Physicists in Medicine.)

Background: Variable relative biological effectiveness (RBE) models in treatment planning have been proposed to optimize the therapeutic ratio of proton therapy. It has been reported that proton RBE decreases with increasing tumor oxygen level, offering an opportunity to address hypoxia-related radioresistance with RBE-weighted optimization., Purpose: Here, we obtain a voxel-level estimation of partial oxygen pressure to weigh RBE values in a single biologically informed beam orientation optimization (BOO) algorithm., Methods: Three glioblastoma patients with [ 18 F]-fluoromisonidazole (FMISO)-PET/CT images were selected from the institutional database. Oxygen values were derived from tracer uptake using a nonlinear least squares curve fitting. McNamara RBE, calculated from proton dose, was then weighed using oxygen enhancement ratios (OER) for each voxel and incorporated into the dose fidelity term of the BOO algorithm. The nonlinear optimization problem was solved using a split-Bregman approach, with FISTA as the solver. The proposed hypoxia informed RBE-weighted method (HypRBE) was compared to dose fidelity terms using the constant RBE of 1.1 (cRBE) and the normoxic McNamara RBE model (RegRBE). Tumor homogeneity index (HI), maximum biological dose (Dmax), and D95%, as well as OAR therapeutic index (TI = gEUD CTV /gEUD OAR ) were evaluated along with worst-case statistics after normalization to normal tissue isotoxicity., Results: Compared to [cRBE, RegRBE], HypRBE increased tumor HI, Dmax, and D95% across all plans by on average [31.3%, 31.8%], [48.6%, 27.1%], and [50.4%, 23.8%], respectively. In the worst-case scenario, the parameters increase on average by [12.5%, 14.7%], [7.3%,-8.9%], and [22.3%, 2.1%]. Despite increased OAR Dmean and Dmax by [8.0%, 3.0%] and [13.1%, -0.1%], HypRBE increased average TI by [22.0%, 21.1%]. Worst-case OAR Dmean, Dmax, and TI worsened by [17.9%, 4.3%], [24.5%, -1.2%], and [9.6%, 10.5%], but in the best cases, HypRBE escalates tumor coverage significantly without compromising OAR dose, increasing the therapeutic ratio., Conclusions: We have developed an optimization algorithm whose dose fidelity term accounts for hypoxia-informed RBE values. We have shown that HypRBE selects bE:\Alok\aaeams better suited to deliver high physical dose to low RBE, hypoxic tumor regions while sparing the radiosensitive normal tissue., (© 2024 American Association of Physicists in Medicine.)

Background: Cancer is a highly heterogeneous disease, driven by frequent genetic alterations which have significant effects on radiosensitivity. However, radiotherapy for a given cancer type is typically given with a standard dose determined from population-level trials. As a result, a proportion of patients are under- or over-dosed, reducing the clinical benefit of radiotherapy. Biological optimization would not only allow individual dose prescription but also a more efficient allocation of limited resources, such as proton and carbon ion therapy. Proton and ion radiotherapy offer an advantage over photons due to their elevated Relative Biological Effectiveness (RBE) resulting from their elevated Linear Energy Transfer (LET). Despite significant interest in optimizing LET by tailoring radiotherapy plans, RBE's genetic dependence remains unclear., Purpose: The aim of this study is to better define the RBE/LET relationship in a panel of cell lines with different defects in DSB repair pathways, but otherwise identical biological features and genetic background to isolate these effects., Methods: Normal human cells (RPE1), genetically modified to introduce defects in DNA double-strand break (DSB) repair genes, ATM, BRCA1, DCLRE1C, LIG4, PRKDC and TP53, were used to map the RBE-LET relationship. Cell survival was measured with clonogenic assays after exposure to photons, protons (LET 1 and 12 keV/µm) and alpha particles (129 keV/µm). Gene knockout sensitizer enhancement ratio (SER) values were calculated as the ratio of the mean inactivation dose (MID) of wild-type cells to repair-deficient cells, and RBE values were calculated as the ratio of the MID of X-ray and particle irradiated cells. 53BP1 foci were used to quantify radiation-induced DSBs and their repair following irradiation., Results: Deletion of NHEJ genes had the greatest impact on photon sensitivity (ATM -/- SER = 2.0 and Lig4 -/- SER = 1.8), with genes associated with HR having smaller effects (BRCA1 -/- SER = 1.2). Wild-type cells showed RBEs of 1.1, 1.3, 5.0 for low- and high-LET protons and alpha particles respectively. SERs for different genes were independent of LET, apart from NHEJ knockouts which proved to be markedly hypersensitive across all tested LETs. Due to this hypersensitivity, the impact of high LET was reduced in cell models lacking the NHEJ repair pathway. HR-defective cells had moderately increased sensitivity across all tested LETs, but, notably, the contribution of HR pathway to survival appeared independent of LET. Analysis of 53BP1 foci shows that NHEJ-defective cells had the least DSB repair capacity after low LET exposure, and no visible repair after high LET exposure. HR-defective cells also had slower repair kinetics, but the impact of HR defects is not as severe as NHEJ defects., Conclusions: DSB repair defects, particularly in NHEJ, conferred significant radiosensitivity across all LETs. This sensitization appeared independent of LET, suggesting that the contribution of different DNA repair pathways to survival does not depend on radiation quality., (© 2023 The Authors. Medical Physics published by Wiley Periodicals LLC on behalf of American Association of Physicists in Medicine.)

Background: Predicting biological responses to mixed radiation types is of considerable importance when combining radiation therapies that use multiple radiation types and delivery regimens. These may include the use of both low- and high-linear energy transfer (LET) radiations. A number of theoretical models have been developed to address this issue. However, model predictions do not consistently match published experimental data for mixed radiation exposures. Furthermore, the models are often computationally intensive. Accordingly, there is a need for efficient analytical models that can predict responses to mixtures of low- and high-LET radiations. Additionally, a general formalism to calculate equieffective dose (EQDX) for mixed radiations is needed., Purpose: To develop a computationally efficient analytical model that can predict responses to complex mixtures of low- and high-LET radiations as a function of either absorbed dose or EQDX., Methods: The Zaider-Rossi model (ZRM) was modified by replacing the geometric mean of the quadratic coefficients in the interaction term with the arithmetic mean. This modified ZRM model (mZRM) was then further generalized to any number of radiation types and its validity was tested against published experimental observations. Comparisons between the predictions of the ZRM and mZRM, and other models, were made using two and three radiation types. In addition, a generalized formalism for calculating EQDX for mixed radiations was developed within the context of mZRM and validated with published experimental results., Results: The predictions of biological responses to mixed-LET radiations calculated with the mZRM are in better agreement with experimental observations than ZRM, especially when high- and low-LET radiations are mixed. In these situations, the ZRM overestimated the surviving fraction. Furthermore, the EQDX calculated with mZRM are in better agreement with experimental observations., Conclusion: The mZRM is a computationally efficient model that can be used to predict biological response to mixed radiations that have low- and high-LET characteristics. Importantly, interaction terms are retained in the calculation of EQDX for mixed radiation exposures within the mZRM framework. The mZRM has application in a wide range of radiation therapies, including radiopharmaceutical therapy., (© 2023 The Authors. Medical Physics published by Wiley Periodicals LLC on behalf of American Association of Physicists in Medicine.)

Background: Applying tolerance doses for organs at risk (OAR) from photon therapy introduces uncertainties in proton therapy when assuming a constant relative biological effectiveness (RBE) of 1.1., Purpose: This work introduces the novel dirty and clean dose concept, which allows for creating treatment plans with a more photon-like dose response for OAR and, thus, less uncertainties when applying photon-based tolerance doses., Methods: The concept divides the 1.1-weighted dose distribution into two parts: the clean and the dirty dose. The clean and dirty dose are deposited by protons with a linear energy transfer (LET) below and above a set LET threshold, respectively. For the former, a photon-like dose response is assumed, while for the latter, the RBE might exceed 1.1. To reduce the dirty dose in OAR, a MaxDirtyDose objective was added in treatment plan optimization. It requires setting two parameters: LET threshold and max dirty dose level. A simple geometry consisting of one target volume and one OAR in water was used to study the reduction in dirty dose in the OAR depending on the choice of the two MaxDirtyDose objective parameters during plan optimization. The best performing parameter combinations were used to create multiple dirty dose optimized (DDopt) treatment plans for two cranial patient cases. For each DDopt plan, 1.1-weighted dose, variable RBE-weighted dose using the Wedenberg RBE model and dose-average LET d distributions as well as resulting normal tissue complication probability (NTCP) values were calculated and compared to the reference plan (RefPlan) without MaxDirtyDose objectives., Results: In the water phantom studies, LET thresholds between 1.5 and 2.5 keV/µm yielded the best plans and were subsequently used. For the patient cases, nearly all DDopt plans led to a reduced Wedenberg dose in critical OAR. This reduction resulted from an LET reduction and translated into an NTCP reduction of up to 19 percentage points compared to the RefPlan. The 1.1-weighted dose in the OARs was slightly increased (patient 1: 0.45 Gy(RBE), patient 2: 0.08 Gy(RBE)), but never exceeded clinical tolerance doses. Additionally, slightly increased 1.1-weighted dose in healthy brain tissue was observed (patient 1: 0.81 Gy(RBE), patient 2: 0.53 Gy(RBE)). The variation of NTCP values due to variation of α/β from 2 to 3 Gy was much smaller for DDopt (2 percentage points (pp)) than for RefPlans (5 pp)., Conclusions: The novel dirty and clean dose concept allows for creating biologically more robust proton treatment plans with a more photon-like dose response. The reduced uncertainties in RBE can, therefore, mitigate uncertainties introduced by using photon-based tolerance doses for OAR., (© 2023 The Authors. Medical Physics published by Wiley Periodicals LLC on behalf of American Association of Physicists in Medicine.)

Background: In treatment planning for proton therapy a constant Relative Biological Effectiveness (RBE) of 1.1 is used, disregarding variations with linear energy transfer, clinical endpoint, or fractionation., Purpose: To present a methodology to analyze the variation of RBE with fractionation from clinical data of tumor control probability (TCP) and to apply it to study the response of prostate cancer to proton therapy., Methods and Materials: We analyzed the dependence of the RBE on the dose per fraction by using the LQ model and the Poisson TCP formalism. Clinical tumor control probabilities for prostate cancer (low and intermediate risk) treated with photon and proton therapy for conventional fractionation (2 Gy(RBE)×37 fractions), moderate hypofractionation (3 Gy(RBE)×20 fractions) and hypofractionation (7.25 Gy(RBE)×5 fractions) were obtained from the literature and analyzed aiming at obtaining the RBE and its dependence on the dose per fraction., Results: The theoretical analysis of the dependence of the RBE on the dose per fraction showed three distinct regions with RBE monotonically decreasing, increasing or staying constant with the dose per fraction, depending on the change of (α, β) values between photon and proton irradiation (the equilibrium point being at (α p /β p ) = (α X /β X )(α X /α p )). An analysis of the clinical data showed RBE values that decline with increasing dose per fraction: for low risk RBE≈1.124, 1.119, and 1.102 for 1.82 Gy, 2.73 Gy and 6.59 Gy per fraction (physical proton doses), respectively; for intermediate risk RBE≈1.119 and 1.102 for 1.82 Gy and 6.59 Gy per fraction (physical proton doses), respectively. These values are nonetheless very close to the nominal 1.1 value., Conclusions: In this study, we have presented a methodology to analyze the RBE for different fractionations, and we used it to study clinical data for prostate cancer and evaluate the RBE versus dose per fraction. The analysis shows a monotonically decreasing RBE with increasing dose per fraction, which is expected from the LQ formalism and the changes in (α, β) values between photon and proton irradiation. However, the calculations in this study have to be considered with care as they may be biased by limitations in the modeling assumptions and/or by the clinical data set used for the analysis., (© 2023 The Authors. Medical Physics published by Wiley Periodicals LLC on behalf of American Association of Physicists in Medicine.)

Background: In a recent study, we reported beam quality correction factors, f Q , in carbon ion beams using Monte Carlo (MC) methods for a cylindrical and a parallel-plate ionization chamber (IC). A non-negligible perturbation effect was observed; however, the magnitude of the perturbation correction due to the specific IC subcomponents was not included. Furthermore, the stopping power data presented in the International Commission on Radiation Units and Measurements (ICRU) report 73 were used, whereas the latest stopping power data have been reported in the ICRU report 90., Purpose: The aim of this study was to extend our previous work by computing f Q correction factors using the ICRU 90 stopping power data and by reporting IC-specific perturbation correction factors. Possible energy or linear energy transfer (LET) dependence of the f Q correction factor was investigated by simulating both pristine beams and spread-out Bragg peaks (SOBPs)., Methods: The TOol for PArticle Simulation (TOPAS)/GEANT4 MC code was used in this study. A 30 × 30 × 50 cm 3 water phantom was simulated with a uniform 10 × 10 cm 2 parallel beam incident on the surface. A Farmer-type cylindrical IC (Exradin A12) and two parallel-plate ICs (Exradin P11 and A11) were simulated in TOPAS using the manufacturer-provided geometrical drawings. The f Q correction factor was calculated in pristine carbon ion beams in the 150-450 MeV/u energy range at 2 cm depth and in the middle of the flat region of four SOBPs. The k Q correction factor was calculated by simulating the f Qo correction factor in a 60 Co beam at 5 cm depth. The perturbation correction factors due to the presence of the individual IC subcomponents, such as the displacement effect in the air cavity, collecting electrode, chamber wall, and chamber stem, were calculated at 2 cm depth for monoenergetic beams only. Additionally, the mean dose-averaged and track-averaged LET was calculated at the depths at which the f Q was calculated., Results: The ICRU 90 f Q correction factors were reported. The p dis correction factor was found to be significant for the cylindrical IC with magnitudes up to 1.70%. The individual perturbation corrections for the parallel-plate ICs were <1.0% except for the A11 p cel correction at the lowest energy. The f Q correction for the P11 IC exhibited an energy dependence of >1.00% and displayed differences up to 0.87% between pristine beams and SOBPs. Conversely, the f Q for A11 and A12 displayed a minimal energy dependence of <0.50%. The energy dependence was found to manifest in the LET dependence for the P11 IC. A statistically significant LET dependence was found only for the P11 IC in pristine beams only with a magnitude of <1.10%., Conclusions: The perturbation and k Q correction factor should be calculated for the specific IC to be used in carbon ion beam reference dosimetry as a function of beam quality., (© 2022 The Authors. Medical Physics published by Wiley Periodicals LLC on behalf of American Association of Physicists in Medicine.)

Background: For proton therapy, a relative biological effectiveness (RBE) of 1.1 has broadly been applied clinically. However, as unexpected toxicities have been observed by the end of the proton tracks, variable RBE models have been proposed. Typically, the dose-averaged linear energy transfer (LET d ) has been used as an input variable for these models but the way the LET d was defined, calculated, or determined was not always consistent, potentially impacting the corresponding RBE value., Purpose: This study compares consistently calculated LET d with other quantities as input variables for a phenomenological RBE model and attempts to determine which quantity that can best predicts proton RBE. The comparison was performed within the frame of introducing a new model for the proton RBE., Methods: High-throughput experimental setups of in vitro cell survival studies for proton RBE determination are simulated using the SHIELD-HIT12A Monte Carlo particle transport code. Together with LET, z ∗ 2 / β 2 $z^{*2}/\beta ^2$ , here called effective Q (Q eff ), and Q are scored. Each quantity is calculated using the dose and track averaging methods, because the scoring includes all hadronic particles, all protons or only primaries. A phenomenological linear-quadratic-based RBE model is subsequently applied to the in vitro data with the various beam quality descriptors used as input variables and the goodness of fit is determined and compared using a bootstrapping approach. Both linear and nonlinear fit functions were tested., Results: Versions of Q eff and Q outperform LET with a statistically significant margin, with the best nonlinear and linear fit having a relative root mean square error (RMSE) for RBE 2Gy ± one standard error of 1.55 ± 0.04 (Q eff, t, primary ) and 2.84 ± 0.07 (Q eff, d, primary ), respectively. For comparison, the corresponding best nonlinear and linear fits for LET d, all protons had a relative RMSE of 2.07 ± 0.06 and 3.39 ± 0.08, respectively. Applying Welch's t-test for comparing the calculated RMSE of RBE 2Gy resulted in two-tailed p-values of <0.002 for all Q and Q eff quantities compared to LET d, all protons ., Conclusions: The study shows that Q or Q eff could be better RBE descriptors that dose averaged LET., (© 2022 The Authors. Medical Physics published by Wiley Periodicals LLC on behalf of American Association of Physicists in Medicine.)

Background: Empirical data in proton therapy indicate that relative biological effectiveness (RBE) is not constant, and it is directly related to the linear energy transfer (LET). The experimental assessment of LET with high resolution would be a powerful tool for minimizing the LET hot spots in intensity-modulated proton therapy, RBE- or LET-guided evaluation and optimization to achieve biologically optimized proton plans, verifying the theoretical predictions of variable proton RBE models, and so on. This could impact clinical outcomes by reducing toxicities in organs at risk., Purpose: The present work shows the first 2D LET maps obtained at a proton therapy facility using the double scattering delivery mode in clinical conditions by means of new silicon 3D-cylindrical microdetectors., Methods: The device consists of a matrix of 121 independent silicon-based detectors that have 3D-cylindrical electrodes of 25-µm diameter and 20-µm depth, resulting each one of them in a well-defined micrometric radiation sensitive volume etched inside the silicon. They have been specifically designed for a hadron therapy, improving the performance of current silicon-based microdosimeters. Microdosimetry spectra were obtained at different positions of the Bragg curve by using a water-equivalent phantom along an 89-MeV pristine proton beam generated in the Y1 proton passive scattering beamline of the Orsay Proton Therapy Centre (Institut Curie, France)., Results: Microdosimetry 2D-maps showing the variation of the lineal energy with depth in the three dimensions were obtained in situ during irradiation at clinical fluence rates (∼10 8  s -1  cm -2 ) for the first time with a spatial resolution of 200 µm, the highest achieved in the transverse plane so far. The experimental results were cross-checked with Monte Carlo simulations and a good agreement between the spectra shapes was found. The experimental frequency-mean lineal energy values in silicon were 1.858 ± 0.019 keV µm -1 at the entrance, 2.61 ± 0.03 keV µm -1 at the proximal distance, 4.97 ± 0.05 keV µm -1 close to the Bragg peak, and 8.6 ± 0.1 keV µm -1 at the distal edge. They are in good agreement with the expected trends in the literature in clinical proton beams., Conclusions: We present the first 2D microdosimetry maps obtained in situ during irradiation at clinical fluence rates in proton therapy. Our results show that the arrays of 3D-cylindrical microdetectors are a reliable microdosimeter to evaluate LET maps not only in the longitudinal axis of the beam, but also in the transverse plane allowing for LET characterization in three dimensions. This work is a proof of principle showing the capacity of our system to deliver LET 2D maps. This kind of experimental data is needed to validate variable proton RBE models and to optimize LET-guided plans., (© 2022 The Authors. Medical Physics published by Wiley Periodicals LLC on behalf of American Association of Physicists in Medicine.)

Purpose: Challenges in proton therapy include identifying patients most likely to benefit; ensuring consistent, high-quality plans as its adoption becomes more widespread; and recognizing biological uncertainties that may be related to increased relative biologic effectiveness driven by linear energy transfer (LET). Knowledge-based planning (KBP) is a domain that may help to address all three., Methods: Artificial neural networks were trained using 117 unique treatment plans and associated dose and dose-weighted LET (LET D ) distributions. The data set was split into training (n = 82), validation (n = 17), and test (n = 18) sets. Model performance was evaluated on the test set using dose- and LET D -volume metrics in the clinical target volume (CTV) and nearby organs at risk and Dice similarity coefficients (DSC) comparing predicted and planned isodose lines at 50%, 75%, and 95% of the prescription dose., Results: Dose-volume metrics significantly differed (α = 0.05) between predicted and planned dose distributions in only one dose-volume metric, D 2% to the CTV. The maximum observed root mean square (RMS) difference between corresponding metrics was 4.3 Gy RBE (8% of prescription) for D 1cc to optic chiasm. DSC were 0.90, 0.93, and 0.88 for the 50%, 75%, and 95% isodose lines, respectively. LET D -volume metrics significantly differed in all but one metric, L 0.1cc of the brainstem. The maximum observed difference in RMS differences for LET D metrics was 1.0 keV/μm for L 0.1cc to brainstem., Conclusions: We have devised the first three-dimensional dose and LET D -prediction model for cranial proton radiation therapy has been developed. Dose accuracy compared favorably with that of previously published models in other treatment sites. The agreement in LET D supports future investigations with biological doses in mind to enable the full potential of KBP in proton therapy., (© 2022 American Association of Physicists in Medicine.)

Background: The relative biological effectiveness (RBE) of proton is considered to be dependent on biological parameters and fractional dose. While hyperfractionated photon therapy was effective in the treatment of patients with head and neck cancers, its effect in intensity-modulated proton therapy (IMPT) under the variable RBE has not been investigated in detail., Purpose: To study the effect of variable RBE on hyperfractionated IMPT for the treatment of pharyngeal cancer. We investigated the biologically effective dose (BED) to determine the theoretical effective hyperfractionated schedule., Methods: The treatment plans of three pharyngeal cancer patients were used to define the ΔBED for the clinical target volume (CTV) and soft tissue (acute and late reaction) as the difference between the BED for the altered schedule with variable RBE and conventional schedule with constant RBE. The ΔBED with several combinations of parameters (treatment days, number of fractions, and prescribed dose) was comprehensively calculated. Of the candidate schedules, the one that commonly gave a higher ΔBED for CTV was selected as the resultant schedule. The BED volume histogram was used to compare the influence of variable RBE and fractionation., Results: In the conventional schedule, compared with the constant RBE, the variable RBE resulted in a mean 2.6 and 2.7 Gy reduction of BED mean for the CTV and soft tissue (acute reaction) of the three plans, respectively. Moreover, the BED mean for soft tissue (late reaction) increased by 7.4 Gy, indicating a potential risk of increased RBE. Comprehensive calculation of the ΔBED resulted in the hyperfractionated schedule of 80.52 Gy (RBE = 1.1)/66 fractions in 6.5 weeks. When variable RBE was used, compared with the conventional schedule, the hyperfractionated schedule increased the BED mean for CTV by 7.6 Gy; however, this was associated with a 7.8 Gy increase for soft tissue (acute reaction). The BED mean for soft tissue (late reaction) decreased by 2.4 Gy., Conclusion: The results indicated a potential effect of the variable RBE on IMPT for pharyngeal cancer but with the possibility that hyperfractionation could outweigh this effect. Although biological uncertainties require conservative use of the resultant schedule, hyperfractionation is expected to be an effective strategy in IMPT for pharyngeal cancer., (© 2022 American Association of Physicists in Medicine.)

Background: In reference dosimetry, radiation quality correction factors are used in order to account for changes in the detector's response among different radiation qualities, improving dosimetric accuracy., Purpose: Reference dosimetry radiation quality corrections factors for the PTW microDiamond were calculated for preclinical X-ray and proton minibeams, and their impact in dosimetric accuracy was evaluated., Methods: A formalism for the calculation of radiation quality correction factors for absolute dosimetry in minibeam fields was developed. Following our formalism, radiation quality correction factors were calculated for the PTW microDiamond detector, using the Monte Carlo method. Models of the detector, and X-ray and proton irradiation platform, were imported into the TOPAS Monte Carlo simulation toolkit. The radiation quality correction factors were calculated in the following scenarios: (i) reference dosimetry open field to minibeam center of the central peak, (ii) different positions at the minibeam profile (along the peaks and valleys direction) to the center of the central minibeam, and (iii) some representative depth positions. In addition, the radiation quality correction factors needed for the calculation of the peak-to-valley dose ratio at different depths were calculated., Results: An important overestimation of the dose (about 10%) was found in the case of the open to minibeam field for both X-rays and proton beams, when the correction factors were used. Smaller differences were observed in the other cases., Conclusions: The usage of the PTW microDiamond detector requires radiation quality correction factors in order to be used in minibeam reference dosimetry., (© 2022 The Authors. Medical Physics published by Wiley Periodicals LLC on behalf of American Association of Physicists in Medicine.)

Purpose: To present particle arc therapy treatments using single and multi-ion therapy optimization strategies with helium ( 4 He), carbon ( 12 C), oxygen ( 16 O), and neon ( 20 Ne) ion beams., Methods and Materials: An optimization procedure and workflow were devised for spot-scanning hadron arc therapy (SHArc) treatment planning in the PRECISE (PaRticle thErapy using single and Combined Ion optimization StratEgies) treatment planning system (TPS). Physical and biological beam models were developed for helium, carbon, oxygen, and neon ions via FLUKA MC simulation. SHArc treatments were optimized using both single-ion ( 12 C, 16 O, or 20 Ne) and multi-ion therapy ( 16 O+ 4 He or 20 Ne+ 4 He) applying variable relative biological effectiveness (RBE) modeling using a modified microdosimetric kinetic model (mMKM) with (α/β) x values of 2, 5, and 3.1 Gy, respectively, for glioblastoma, pancreatic adenocarcinoma, and prostate adenocarcinoma patient cases. Dose, effective dose, linear energy transfer (LET), and RBE were computed with the GPU-accelerated dose engine FRoG and dosimetric/biophysical attributes were evaluated in the context of conventional particle and photon-based therapies (e.g., volumetric modulated arc therapy [VMAT])., Results: All SHArc plans met the target optimization goals (3GyRBE) and demonstrated increased target conformity and substantially lower low-dose bath to surrounding normal tissues than VMAT. SHArc plans using a singleion species ( 12 C, 16 O, or 20 Ne) exhibited favorable LET distributions with the highest-LET components centralized in the target volume, with values ranging from ∼80-170 keV/μm, ∼130-220 keV/μm, and ∼180-350 keV/μm for 12 C, 16 O, or 20 Ne, respectively, exceeding mean target LET of conventional particle therapy ( 12 C:∼55, 16 O:∼75 20 Ne:∼95 keV/μm). Multi-ion therapy with SHArc delivery (SHArc MIT ) provided a similar level of target LET enhancement as SHArc compared to conventional planning, however, with additional benefits of homogenous physical dose and RBE distributions., Conclusion: Here, we demonstrate that arc delivery of light and heavy ion beams, using either a single-ion species ( 12 C, 16 O, or 20 Ne) or combining two ions in a single fraction ( 16 O+ 4 He or 20 Ne+ 4 He) affords enhanced physical and biological distributions (e.g., LET) compared with conventional delivery with photons or particle beams. SHArc marks the first single- and multi-ion arc therapy treatment optimization approach using light and heavy ions., (© 2022 The Authors. Medical Physics published by Wiley Periodicals LLC on behalf of American Association of Physicists in Medicine.)

Purpose: We assessed whether adding sodium borocaptate (BSH) or 4-borono-l-phenylalanine (BPA) to cells irradiated with proton beams influenced the biological effectiveness of those beams against prostate cancer cells to investigate if the alpha particles generated through proton-boron nuclear reactions would be sufficient to enhance the biological effectiveness of the proton beams., Methods: We measured clonogenic survival in DU145 cells treated with 80.4-ppm BSH or 86.9-ppm BPA, or their respective vehicles, after irradiation with 6-MV X-rays, 1.2-keV/μm (low linear energy transfer [LET]) protons, or 9.9-keV/μm (high-LET) protons. We also measured γH2AX and 53BP1 foci in treated cells at 1 and 24 h after irradiation with the same conditions., Results: We found that BSH radiosensitized DU145 cells across all radiation types. However, no difference was found in relative radiosensitization, characterized by the sensitization enhancement ratio or the relative biological effectiveness, for vehicle- versus BSH-treated cells. No differences were found in numbers of γH2AX or 53BP1 foci or γH2AX/53BP1 colocalized foci for vehicle- versus BSH-treated cells across radiation types. BPA did not radiosensitize DU145 cells nor induced any significant differences when comparing vehicle- versus BPA-treated cells for clonogenic cell survival or γH2AX and 53BP1 foci or γH2AX/53BP1 colocalized foci., Conclusions: Treatment with 11 B, at concentrations of 80.4 ppm from BSH or 86.9 ppm from BPA, had no effect on the biological effectiveness of proton beams in DU145 prostate cancer cells. Our results agree with published theoretical calculations indicating that the contribution of alpha particles from such reactions to the total absorbed dose and biological effectiveness is negligible. We also found that BSH radiosensitized DU145 cells to X-rays, low-LET protons, and high-LET protons but that the radiosensitization was not related to DNA damage., (© 2022 American Association of Physicists in Medicine.)

Background: Proton relative biological effectiveness (RBE) is known to depend on physical factors of the proton beam, such as its linear energy transfer (LET), as well as on cell-line specific biological factors, such as their ability to repair DNA damage. However, in a clinical setting, proton RBE is still considered to have a fixed value of 1.1 despite the existence of several empirical models that can predict proton RBE based on how a cell's survival curve (linear-quadratic model [LQM]) parameters α and β vary with the LET of the proton beam. Part of the hesitation to incorporate variable RBE models in the clinic is due to the great noise in the biological datasets on which these models are trained, often making it unclear which model, if any, provides sufficiently accurate RBE predictions to warrant a departure from RBE = 1.1., Purpose: Here, we introduce a novel model of proton RBE based on how a cell's intrinsic radiosensitivity varies with LET, rather than its LQM parameters., Methods and Materials: We performed clonogenic cell survival assays for eight cell lines exposed to 6 MV x-rays and 1.2, 2.6, or 9.9 keV/µm protons, and combined our measurements with published survival data (n = 397 total cell line/LET combinations). We characterized how radiosensitivity metrics of the form D SF% , (the dose required to achieve survival fraction [SF], e.g., D 10% ) varied with proton LET, and calculated the Bayesian information criteria associated with different LET-dependent functions to determine which functions best described the underlying trends. This allowed us to construct a six-parameter model that predicts cells' proton survival curves based on the LET dependence of their radiosensitivity, rather than the LET dependence of the LQM parameters themselves. We compared the accuracy of our model to previously established empirical proton RBE models, and implemented our model within a clinical treatment plan evaluation workflow to demonstrate its feasibility in a clinical setting., Results: Our analyses of the trends in the data show that D SF% is linearly correlated between x-rays and protons, regardless of the choice of the survival level (e.g., D 10% , D 37% , or D 50% are similarly correlated), and that the slope and intercept of these correlations vary with proton LET. The model we constructed based on these trends predicts proton RBE within 15%-30% at the 68.3% confidence level and offers a more accurate general description of the experimental data than previously published empirical models. In the context of a clinical treatment plan, our model generally predicted higher RBE-weighted doses than the other empirical models, with RBE-weighted doses in the distal portion of the field being up to 50.7% higher than the planned RBE-weighted doses (RBE = 1.1) to the tumor., Conclusions: We established a new empirical proton RBE model that is more accurate than previous empirical models, and that predicts much higher RBE values in the distal edge of clinical proton beams., (© 2022 American Association of Physicists in Medicine.)

Background: The effectiveness of ionizing radiation regarding DNA damage induction depends on its spatial energy deposition pattern. For electrons an increased effectiveness is observed at low kinetic energies due to the enhanced density of energy deposition events at electron track ends., Purpose: A model is presented, which enables the calculation of the double-strand-break (DSB) yield and the relative biological effectiveness (RBE) for DSB induction of electrons., Methods: The model applies the mean free path between two ionizations and the assumption that two ionizations within a certain threshold distance are necessary to potentially lead to a DSB. Next to an expression for the electron RBE according to its common definition, a local RBE is determined, which describes the electrons' local effectiveness at a defined point on their track., Results: This local RBE allows a better understanding of microscopic processes resulting from radiation and can be used, for instance, to describe the mean effectiveness of the mixed electron radiation field as a function of the radial distance to the center of an ion track., Conclusions: The presented model reflects the experimentally observed increased effectiveness of low-energetic electrons. It will be used in a future work to improve RBE predictions for ions performed with the local effect model., (© 2022 The Authors. Medical Physics published by Wiley Periodicals LLC on behalf of American Association of Physicists in Medicine.)

Purpose: This work aims to simulate clustered DNA damage from ionizing radiation and estimate the relative biological effectiveness (RBE) for radionuclide (rBT)- and electronic (eBT)-based surface brachytherapy through a hybrid Monte Carlo (MC) approach, using realistic models of the sources and applicators., Methods: Damage from ionizing radiation has been studied using the Monte Carlo Damage Simulation algorithm using as input the primary electron fluence simulated using a state-of-the-art MC code, PENELOPE-2018. Two 192 Ir rBT applicators, Valencia and Leipzig, one 60 Co source with a Freiburg Flap applicator (reference source), and two eBT systems, Esteya and INTRABEAM, have been included in this study implementing full realizations of their geometries as disclosed by the manufacturer. The role played by filtration and tube kilovoltage has also been addressed., Results: For rBT, an RBE value of about 1.01 has been found for the applicators and phantoms considered. In the case of eBT, RBE values for the Esteya system show an almost constant RBE value of about 1.06 for all depths and materials. For INTRABEAM, variations in the range of 1.12-1.06 are reported depending on phantom composition and depth. Modifications in the Esteya system, filtration, and tube kilovoltage give rise to variations in the same range., Conclusions: Current clinical practice does not incorporate biological effects in surface brachytherapy. Therefore, the same absorbed dose is administered to the patients independently on the particularities of the rBT or eBT system considered. The almost constant RBE values reported for rBT support that assumption regardless of the details of the patient geometry, the presence of a flattening filter in the applicator design, or even significant modifications in the photon energy spectra above 300 keV. That is not the case for eBT, where a clear dependence on the eBT system and the characteristics of the patient geometry are reported. A complete study specific for each eBT system, including detailed applicator characteristics (size, shape, filtering, among others) and common anatomical locations, should be performed before adopting an existing RBE value., (© 2022 American Association of Physicists in Medicine.)

Background: Ion beam therapy allows for substantial sparing of normal tissues. Besides deterministic normal-tissue complications, stochastic long-term effects like secondary cancer (SC) induction are of importance when comparing different treatment modalities., Purpose: To develop a modeling approach for comparison of SC risk in proton and carbon ion therapy., Methods and Materials: The local effect model (LEM) is used to predict the relative biological effectiveness (RBE) of SC induction after particle therapy. A key feature of the new approach is the double use of the LEM, reflecting the competition between the two processes of mutation induction (leading to cancer development) and cell inactivation (leading to suppression of cancer development). Based on previous investigations, treatment plans were in this work analyzed for an idealized geometry in order to assess the underlying systematic dependencies of cancer induction. In a further step, relative SC risks were predicted for proton and carbon ion treatment plans prepared for 10 prostate cancer patients., Results: We investigated the impact of factors such as treatment plan geometry, fractionation scheme, and tissue radiosensitivity to photon irradiation on the ion beam SC risk. Our model studies do not result in a clear preference for either protons or carbon ions, but rather indicate a complex interplay of different aspects. Reduced lateral scattering leads to a lower SC risk for carbon ions compared to protons at the lateral field margins in the entrance channel, while an increased risk was found closely behind the tumor due to projectile fragmentation. The fractionation scheme had little impact on the expected risk ratio. With respect to sensitivity parameters, those characterizing RBE for cell killing of potentially cancerous cells as well as of the primary tumor had the most significant impact. The observed general systematic dependencies are in agreement with results from previous model studies. The prostate patient study reveals reduced SC risks predictions for skin and bones for carbon ions as compared to protons, but higher mean risks for bladder and rectum., Conclusion: The methods established in this work provide a basis for further investigating treatment optimizing strategies for ion beam therapy with regard to SC risk comparisons., (© 2022 The Authors. Medical Physics published by Wiley Periodicals LLC on behalf of American Association of Physicists in Medicine.)

Purpose: The Local Effect Model version one (LEM I) is applied clinically across Europe to quantify the relative biological effectiveness (RBE) of carbon ion beams. It requires the full particle fluence spectrum differential in energy in each voxel as input parameter. Treatment planning systems (TPSs) use beamline-specific look-up tables generated with Monte Carlo (MC) codes. In this study, the changes in RBE weighted dose were quantified using different levels of details in the simulation or different MC codes., Methods: The particle fluence differential in energy was simulated with FLUKA and Geant4 at 500 depths in water in 1-mm steps for 58 initial carbon ion energies (between 120.0 and 402.8 MeV/u). A dedicated beam model was applied, including the full description of the Nozzle using GATE-RTionV1.0 (Geant4.10.03p03). In addition, two tables generated with FLUKA were compared. The starting points of the FLUKA simulations were phase space (PhS) files from, firstly, the Geant4 nozzle simulations, and secondly, a clinical beam model where an analytic approach was used to mimic the beamline. Treatment plans (TPs) were generated with RayStation 8B (RaySearch Laboratories AB, Sweden) for cubic targets in water and 10 clinical patient cases using the clinical beam model. Subsequently, the RBE weighted dose was re-computed using the two other fluence tables (FLUKA PhS or Geant4)., Results: The fluence spectra of the primary and secondary particles simulated with Geant4 and FLUKA generally agreed well for the primary particles. Differences were mainly observed for the secondary particles. Interchanging the two energy spectra (FLUKA vs. GEANT4) to calculate the RBE weighted dose distributions resulted in average deviations of less than 1% in the entrance up to the end of the target region, with a maximum local deviation at the distal edge of the target. In the fragment tail, larger discrepancies of up to 5% on average were found for deep-seated targets. The patient and water phantom cases demonstrated similar results., Conclusion: RBE weighted doses agreed well within all tested setups, confirming the clinical beam model provided by the TPS vendor. Furthermore, the results showed that the open source and generally available MC code Geant4 (in particular using GATE or GATE-RTion) can also be used to generate basic beam data required for RBE calculation in carbon ion therapy., (© 2022 The Authors. Medical Physics published by Wiley Periodicals LLC on behalf of American Association of Physicists in Medicine.)

Purpose: Empirical relative biological effectiveness (RBE) models have been used to estimate the biological dose in proton therapy but do not adequately capture the factors influencing RBE values for treatment planning. We reformulate the McNamara RBE model such that it can be added as a linear biological dose fidelity term within our previously developed sensitivity-regularized and heterogeneity-weighted beam orientation optimization (SHBOO) framework., Methods: Based on our SHBOO framework, we formulated the biological optimization problem to minimize total McNamara RBE dose to OARs. We solve this problem using two optimization algorithms: FISTA (McNam-FISTA) and Chambolle-Pock (McNam-CP). We compare their performances with a physical dose optimizer assuming RBE = 1.1 in all structures (PHYS-FISTA) and an LET-weighted dose model (LET-FISTA). Three head and neck patients were planned with the four techniques and compared on dosimetry and robustness., Results: Compared to Phys-FISTA, McNam-CP was able to match CTV [HI, Dmax, D95%, D98%] by [0.00, 0.05%, 1.4%, 0.8%]. McNam-FISTA and McNam-CP were able to significantly improve overall OAR [Dmean, Dmax] by an average of [36.1%,26.4%] and [29.6%, 20.3%], respectively. Regarding CTV robustness, worst [Dmax, V95%, D95%, D98%] improvement of [-6.6%, 6.2%, 6.0%, 4.8%] was reported for McNam-FISTA and [2.7%, 2.7%, 5.3%, -4.3%] for McNam-CP under combinations of range and setup uncertainties. For OARs, worst [Dmax, Dmean] were improved by McNam-FISTA and McNam-CP by an average of [25.0%, 19.2%] and [29.5%, 36.5%], respectively. McNam-FISTA considerably improved dosimetry and CTV robustness compared to LET-FISTA, which achieved better worst-case OAR doses., Conclusion: The four optimization techniques deliver comparable biological doses for the head and neck cases. Besides modest CTV coverage and robustness improvement, OAR biological dose and robustness were substantially improved with both McNam-FISTA and McNam-CP, showing potential benefit for directly incorporating McNamara RBE in proton treatment planning., (© 2022 American Association of Physicists in Medicine.)

Purpose: To evaluate the biological effectiveness of magnetic resonance (MR)-guided proton beam therapy, comprehensively characterizing the dose and dose-averaged linear energy transfer (LET d ) distributions under a magnetic field is necessary. Although detailed analysis has characterized curved beam paths and distorted dose distributions, the impact of a magnetic field on LET d should also be explored to determine the proton relative biological effectiveness (RBE). Hence, this initial study aims to present a basic analysis of LET d distributions in the presence of a magnetic field using Monte Carlo simulation (MCS)., Methods: Geant4 MCS (version 10.1.p01) was performed to calculate the LET d distribution of proton beams. The incident beam energies were set to 70.2, 140.8, and 220 MeV, and both zero- and finite-emittance pencil beams as well as scanned field were simulated. A transverse magnetic field of 0-3 T was applied within a water phantom placed at the isocenter, and the three-dimensional dose and LET d distributions in the phantom were calculated. Then, the depth profiles of LET d along the curved trajectory and the lateral LET d profile at the Bragg peak (BP) depth were analyzed under changing energies and magnetic fields. In addition, for zero- and finite-emittance beams, the correlation of the lateral asymmetries between the dose and LET d distributions were analyzed. Finally, spread-out Bragg peak (SOBP) fields were simulated to assess the depth-dependent asymmetry of the LET d distributions., Results: A transverse magnetic field distorted the lateral LET d distribution of a pencil beam at close to the BP, and the magnitude of the distortion at the BP increased for higher energy beams and larger magnetic fields. For a zero-emittance beam, the differences in LET d between the left and right D 20 positions were relatively large; the difference in LET d was 1.5 and 2.3 keV/μm at 140.8 and 220 MeV, respectively, at a magnetic field of 1.5 T. These asymmetries were pronounced at positions where the dose asymmetries were large. The size of the asymmetry was less substantial for a finite-emittance beam and even less for a scanned field. However, a 1.5-keV/μm difference still remained between the left and right D 20 positions of a scanned field penumbra for a 220 MeV beam under the same magnetic field. For the SOBP field, it was found that the distal region of SOBP had the highest LET d distortions, followed by the central and proximal regions for the middle-sized SOBP (5 × 5 × 5 cm 3 ), whereas the degree of LET d distortion did not vary much with depth for the 10 × 10 × 10-cm 3 SOBP field., Conclusion: Our results indicate that not only the dose but also LET d distortions should be considered to accurately evaluate the biological effectiveness of MR-guided proton beam therapy., (© 2022 American Association of Physicists in Medicine.)

Background: The microdosimetric quantity lineal energy and its mean values have proven useful for quantifying radiation quality in many situations. The ratio of dose-mean lineal energies is perhaps the simplest quantity for quantifying differences between two radiation qualities. However, published dose-mean lineal energy values from different codes may differ significantly with potential influence on radiation quality estimates., Purpose: The purpose was to compare dose-mean lineal energy values from different track-structure data sets for condensed water vapor and liquid water, and to evaluate the influence on radiation quality estimations for some photon sources., Methods: Published dose-mean lineal energy values for 0.1 keV to 1 MeV electrons in spheres with diameters 2 nm to 1 μm, calculated with water vapor and liquid water track structure codes and proximity functions, were collected, analyzed, and compared. Data for cylinders were converted to spheres using a theoretical transformation published by Kellerer. A new set of dose-mean lineal energy values was calculated to cover the whole range of volumes of interest here using the GEANT4-DNA code. The influence from the differences between codes on radiation quality calculations was estimated using dose-mean lineal energy ratios for the photon sources 125 I, 169 Yb, and 192 Ir relative to 60 Co., Results: The theoretical relation for converting the dose-mean lineal energy between different geometrical volumes, results in differences up to 10% between cylinders and spheres depending on electron energy and target size, in agreement with published simulated results. For spheres with diameter above 100 nm, dose-mean lineal energy values for condensed water vapor and liquid water are with few exceptions within ±10%. Below 100 nm, the difference increases with decreasing diameter reaching a factor of two at 2 nm. The values from water vapor codes are in general larger than from liquid water codes. If the dose-mean lineal energy ratio is based on condensed water vapor instead of liquid water, the ratio differs less than 9% for the nuclides 125 I, 169 Yb, and 192 Ir relative to 60 Co independent of the volume simulated. However, a specific value of the dose-mean lineal energy ratio, is found at a larger target diameter in liquid water than in condensed water vapor., Conclusions: When ratios of the dose-mean lineal energy are used as a measure of the radiation quality it is important to compare values for geometrically equal target shapes. A practical method of converting values for cylinders of equal diameter and height to spheres was demonstrated. Although dose-mean lineal energy values calculated with water vapor and liquid water codes may differ significantly, the radiation quality, in terms of ratios of dose-mean lineal energy, for the three photon sources 192 Ir, 169 Yb, and 125 I relative to 60 Co, agree within 9%. The same ratio appears at a larger diameter when a liquid water code is used. It is therefore important to use the same code in radiation quality investigations. The present findings may be of special interest in studies related to the relative biological effectiveness (RBE)., (© 2021 American Association of Physicists in Medicine.)

Purpose: The increased relative biological effectiveness (RBE) of ions is one of the key benefits of ion radiotherapy compared to conventional radiotherapy with photons. To account for the increased RBE of ions during the process of ion radiotherapy treatment planning, a robust model for RBE predictions is indispensable. Currently, at several ion therapy centers the local effect model I (LEM I) is applied to predict the RBE, which varies with biological and physical impacting factors. After the introduction of LEM I, several model improvements were implemented, leading to the current version, LEM IV, which is systematically tested in this study., Methods: As a comprehensive RBE model should give consistent results for a large variety of ion species and energies, the particle irradiation data ensemble (PIDE) is used to systematically validate the LEM IV. The database covers over 1100 photon and ion survival experiments in form of their linear-quadratic parameters for a wide range of ion types and energies. This makes the database an optimal tool to challenge the systematic dependencies of the RBE model. After appropriate filtering of the database, 571 experiments were identified and used as test data., Results: The study confirms that the LEM IV reflects the RBE systematics observed in measurements well. It is able to reproduce the dependence of RBE on the linear energy transfer (LET) as well as on the α γ /β γ ratio for several ion species in a wide energy range. Additionally, the systematic quantitative analysis revealed precision capabilities and limits of the model. At lower LET values, the LEM IV tends to underestimate the RBE with an increasing underestimation with increasing atomic number of the ion. At higher LET values, the LEM IV overestimates the RBE for protons or helium ions, whereas the predictions for heavier ions match experimental data well., Conclusions: The LEM IV is able to predict general RBE characteristics for several ion species in a broad energy range. The accuracy of the predictions is reasonable considering the small number of input parameters needed by the model. The detailed quantification of possible systematic deviations, however, enables to identify not only strengths but also limitations of the model. The gained knowledge can be used to develop model adjustments to further improve the model accuracy, which is on the way., (© 2021 The Authors. Medical Physics published by Wiley Periodicals LLC on behalf of American Association of Physicists in Medicine.)

Purpose: In the scanning beam delivery of protons, different portions of the target are irradiated with different linear energy transfer protons with various time intervals and irradiation times. This research aimed to evaluate the spatially dependent biological effectiveness of protracted irradiation in scanning proton therapy., Methods: One and two parallel opposed fields plans were created in water phantom with the prescribed dose of 2 Gy. Three scenarios (instantaneous, continuous, and layered scans) were used with the corresponding beam delivery models. The biological dose (physical dose × relative biological effectiveness) was calculated using the linear quadratic model and the theory of dual radiation action to quantitatively evaluate the dose delivery time effect. In addition, simulations using clinical plans (postoperative seminoma and prostate tumor cases) were conducted to assess the impact of the effects on the dose volume histogram parameters and homogeneity coefficient (HC) in targets., Results: In a single-field plan of water phantom, when the treatment time was 19 min, the layered-scan scenario showed a decrease of <0.2% (almost 3.3%) in the biological dose from the plan on the distal (proximal) side because of the high (low) dose rate. This is in contrast to the continuous scenario, where the biological dose was almost uniformly decreased over the target by approximately 3.3%. The simulation with clinical geometry showed that the decrease rates in D 99% were 0.9% and 1.5% for every 10 min of treatment time prolongation for postoperative seminoma and prostate tumor cases, respectively, whereas the increase rates in HC were 0.7% and 0.2%., Conclusions: In protracted irradiation in scanning proton therapy, the spatially dependent dose delivery time structure in scanning beam delivery can be an important factor for accurate evaluation of biological effectiveness., (© 2021 American Association of Physicists in Medicine.)

Purpose: To predict and mitigate for the degradation in physical and biologically effective dose distributions of particle beams caused by microscopic heterogeneities in lung tissue., Materials and Methods: The TRiP98 treatment planning system was adapted to account for the beam-modulating effect of heterogeneous lung tissue in physical and biological inverse treatment planning. The implementation employs an analytical model that derives the degradation from the established "modulation power" parameter P mod and the total water-equivalent thickness of lung parenchyma traversed by the beam. Beam modulation was reproduced through an on-the-fly convolution of the reference Bragg curve with Gaussian kernels depending on the modulation power of lung tissue (upstream). For biological doses, the degradation was determined by modulating dose-averaged α , β , and LET distributions. Carbon SOBP measurements behind lung substitute material were performed to validate the code. The implementation was then applied to a phantom and patient case., Results: Experimental results show the passage through a 20-cm Gammex LN300 slab led to a decrease in target coverage and broadening of the SOBP distal fall-off. However, dose coverage was regained through optimization. A good agreement between calculated and measured SOBPs was also found. In addition, a patient case study revealed a 3.2% decrease in D 95 from degradation ( P mod = 450 μ m), which was reduced to a 0.4% difference after optimization. Furthermore, widening of the RBE distribution beyond the target distal edge was observed. This implies an increased degradation in the biological dose, which could be harmful to healthy tissues distal to the target., Conclusions: This is the first implementation capable of compensating for lung dose perturbations, which is more effective than margin extensions. A larger patient study is needed to examine the observed modulation in the RBE distribution and judge the clinical relevance also in IMPT, where margins might prove insufficient to recover target coverage., (© 2021 The Authors. Medical Physics published by Wiley Periodicals LLC on behalf of American Association of Physicists in Medicine.)

Purpose: A 5 and 10 μm thin silicon on insulator (SOI) 3D mushroom microdosimeter was used to characterize both the in-field and out-of-field of a 62 MeV proton beam., Methods: The SOI mushroom microdosimeter consisted of an array of cylindrical sensitive volumes (SVs), developed by the Centre for Medical Radiation Physics, University of Wollongong, was irradiated with 62 MeV protons at the CATANA (Centro di AdroTerapia Applicazioni Nucleari Avanzate) facility in Catania, Italy, a facility dedicated to the radiation treatment of ocular melanomas. Dose mean lineal energy, ( y D ¯ ), values were obtained at various depths in PMMA along a pristine and spread out Bragg peak (SOBP). The measured microdosimetric spectra at each position were then used as inputs into the modified Microdosimetric Kinetic Model (MKM) to derive the RBE for absorbed dose in a middle of the SOBP 2Gy (RBE D ). Microdosimetric spectra were obtained with both the 5 and 10 μm 3D SOI microdosimeters, with a focus on the distal part of the BP. The in-field and out-of-field measurement configurations along the Bragg curve were modeled in Geant4 for comparison with experimental results. Lateral out-of-field measurements were performed to study secondary particles' contribution to normal tissue's dose, up to 12 mm from the edge of the beam field, and quality factor and dose equivalent results were obtained., Results: Comparison between experimental and simulation results showed good agreement between one another for both the pristine and SOBP beams in terms of y D ¯ and RBED. Though a small discrepancy between experiment and simulation was seen at the entrance of the Bragg curve, where experimental results were slightly lower than Geant4. The dose equivalent value measured 12 mm from the edge of the target volume was 1.27 ± 0.15 mSv/Gy with a Q ¯ value of 2.52 ± 0.30, both of which agree within uncertainty with Geant4 simulation., Conclusions: These results demonstrate that SOI microdosimeters are an effective tool to predict RBED in-field as well as dose equivalent monitoring out-of-field to provide insight to probability of second cancer generation., (© 2021 American Association of Physicists in Medicine.)

Purpose: To show that intrinsic radiosensitivity varies greatly for protons and carbon (C) ions in addition to photons, and that DNA repair capacity remains important in governing this variability., Methods: We measured or obtained from the literature clonogenic survival data for a number of human cancer cell lines exposed to photons, protons (9.9 keV/μm), and C-ions (13.3-77.1 keV/μm). We characterized their intrinsic radiosensitivity by the dose for 10% or 50% survival (D 10% or D 50% ), and quantified the variability at each radiation quality by the coefficient of variation (COV) in D 10% and D 50% . We also treated cells with DNA repair inhibitors prior to irradiation to assess how DNA repair capacity affects their variability., Results: We found no statistically significant differences in the COVs of D 10% or D 50% between any of the radiation qualities investigated. The same was true regardless of whether the cells were treated with DNA repair inhibitors, or whether they were stratified into histologic subsets. Even within histologic subsets, we found remarkable differences in radiosensitivity for high LET C-ions that were often greater than the variations in RBE, with brain cancer cells varying in D 10% (D 50% ) up to 100% (131%) for 77.1 keV/μm C-ions, and non-small cell lung cancer and pancreatic cancer cell lines varying up to 55% (76%) and 51% (78%), respectively, for 60.5 keV/μm C-ions. The cell lines with modulated DNA repair capacity had greater variability in intrinsic radiosensitivity across all radiation qualities., Conclusions: Even for cell lines of the same histologic type, there are remarkable variations in intrinsic radiosensitivity, and these variations do not differ significantly between photon, proton or C-ion radiation. The importance of DNA repair capacity in governing the variability in intrinsic radiosensitivity is not significantly diminished for higher LET radiation., (© 2021 American Association of Physicists in Medicine.)

A novel risk model has recently been proposed for the occurrence of late contrast-enhancing brain lesions (CEBLs) after proton irradiation of low-grade glioma (LGG) patients. It predicts a strong dependence on dose-weighted linear-energy transfer (LET d effect) and an increased radiosensitivity of the ventricular proximity, a 4-mm fringe surrounding the ventricular system (VP 4mm effect). On this basis, we investigated (A) how these two risk factors and patient-specific anatomical and treatment plan (TP) features contribute to normal tissue complication probability (NTCP) and (B) if conventional LET d -reduction techniques like multiple-field TP are able to reduce NTCP. (A) The LGG model cohort (N = 110) was stratified with respect to prescribed dose, tumor grade, and treatment field configuration. NTCP predictions and CEBL occurrence rates per strata were analyzed. (B) The effect of multiple-field TP was investigated in two patient groups: (i) nine high-risk subjects with extended lateral target volumes who had developed CEBLs after single-beam treatments were retrospectively replanned with a clinical standard two-field setting using almost orthogonal fields and strictly opposing fields, (ii) single-field treatments were simulated for seven low-risk patients with small central target volumes clinically treated with two strictly opposing fields. (A) In the model cohort, we identified the exposure of the radiosensitive VP 4mm fringe with proton field components of increased biological effectiveness as dominant NTCP driving factor. We observed that larger target volumes and location lateral to the main ventricles, both being characteristic for WHO°II tumors, presented with the highest complication risks. Among subjects of an equal dose prescription of 54 Gy(RBE), the highest median NTCP was obtained for the WHO°II group treated with two fields using sharp angles. (B) Regarding the effect of multiple-field plans, we found that an NTCP reduction was only achievable in the low-risk group where the LET d effect dominates and the VP 4mm effect is small. NTCP of the single-field plans was 23% higher compared to the clinical opposing field plan. In the high-risk group, where the VP 4mm effect dominates the risk, both two-field scenarios yielded 44% higher NTCP predictions compared to the clinical single-field plans. The interplay of an increased radiosensitivity in the VP 4mm fringe with proton field components of increased biological effectiveness creates a geometric complexity that can hardly be managed by current clinical TP. Our results underline that advanced biologically guided TP approaches become crucial for an effective risk minimization in proton therapy of LGG., (© 2021 The Authors. Medical Physics published by Wiley Periodicals LLC on behalf of American Association of Physicists in Medicine.)

Purpose: Application of linear-quadratic (LQ) model to large fractional dose treatments is inconsistent with observed cell survival curves having a straight portion at high doses. We have proposed a unified multi-activation (UMA) model to fit cell survival curves over the entire dose range that allows us to calculate EQD2 for hypofractionated SBRT, SRT, SRS, and HDRB., Methods: A unified formula of cell survival S = n / e D D o + n - 1 using only the extrapolation number of n and the dose slope of D o was derived. Coefficient of determination, R 2 , relative residuals, r, and relative experimental errors, e, normalized to survival fraction at each dose point, were calculated to quantify the goodness in modeling of a survival curve. Analytical solutions for α and β, the coefficients respectively describe the linear and quadratic parts of the survival curve, as well as the α/β ratio for the LQ model and EQD2 at any fractional doses were derived for tumor cells undertaking any fractionated radiation therapy., Results: Our proposed model fits survival curves of in-vivo and in-vitro tumor cells with R 2  > 0.97 and r < e. The predicted α, β, and α/β ratio are significantly different from their values in the LQ model. Average EQD2 of 20-Gy SRS of glioblastomas and melanomas metastatic to the brain, 10-Gy × 5 SBRT of the lung cancer, and 7-Gy × 5 HDRB of endometrial and cervical carcinomas are 36.7 (24.3-48.5), 114.1 (86.6-173.1),, and 45.5 (35-52.6) Gy, different from the LQ model estimates of 50.0, 90.0, and 49.6 Gy, respectively., Conclusion: Our UMA model validated through many tumor cell lines can fit cell survival curves over the entire dose range within their experimental errors. The unified formula theoretically indicates a common mechanism of cell inactivation and can estimate EQD2 at all dose levels., (© 2021 The Authors. Medical Physics published by Wiley Periodicals LLC on behalf of American Association of Physicists in Medicine.)

Purpose: Treatment plans in proton therapy are more sensitive to uncertainties than in conventional photon therapy. In addition to setup uncertainties, proton therapy is affected by uncertainties in proton range and relative biological effectiveness (RBE). While to date a constant RBE of 1.1 is commonly assumed, the actual RBE is known to increase toward the distal end of the spread-out Bragg peak. Several models for variable RBE predictions exist. We present a framework to evaluate the combined impact and interactions of setup, range, and RBE uncertainties in a comprehensive, variance-based sensitivity analysis (SA)., Material and Methods: The variance-based SA requires a large number (10 4 -10 5 ) of RBE-weighted dose (RWD) calculations. Based on a particle therapy extension of the research treatment planning system CERR we implemented a fast, graphics processing unit (GPU) accelerated pencil beam modeling of patient and range shifts. For RBE predictions, two biological models were included: The mechanistic repair-misrepair-fixation (RMF) model and the phenomenological Wedenberg model. All input parameters (patient position, proton range, RBE model parameters) are sampled simultaneously within their assumed probability distributions. Statistical formalisms rank the input parameters according to their influence on the overall uncertainty of RBE-weighted dose-volume histogram (RW-DVH) quantiles and the RWD in every voxel, resulting in relative, normalized sensitivity indices (S = 0: noninfluential input, S = 1: only influential input). Results are visualized as RW-DVHs with error bars and sensitivity maps., Results and Conclusions: The approach is demonstrated for two representative brain tumor cases and a prostate case. The full SA including ∼ 3 × 10 4 RWD calculations took 39, 11, and 55 min, respectively. Range uncertainty was an important contribution to overall uncertainty at the distal end of the target, while the relatively smaller uncertainty inside the target was governed by biological uncertainties. Consequently, the uncertainty of the RW-DVH quantile D 98 for the target was governed by range uncertainty while the uncertainty of the mean target dose was dominated by the biological parameters. The SA framework is a powerful and flexible tool to evaluate uncertainty in RWD distributions and DVH quantiles, taking into account physical and RBE uncertainties and their interactions. The additional information might help to prioritize research efforts to reduce physical and RBE uncertainties and could also have implications for future approaches to biologically robust planning and optimization., (© 2020 The Authors. Medical Physics published by Wiley Periodicals LLC on behalf of American Association of Physicists in Medicine.)

Purpose: The local depth dose gradient and the displacement correction factor for Farmer-type ionization chambers are quantified for reference dosimetry at shallow depth in single-layer scanned proton fields., Method: Integrated radial profiles as a function of depth (IRPDs) measured at three proton therapy centers were smoothed by polynomial fits. The local relative depth dose gradient at measurement depths from 1 to 5 cm were derived from the derivatives of those fits. To calculate displacement correction factors, the best estimate of the effective point of measurement was derived from reviewing experimental and theoretical determinations reported in the literature. Displacement correction factors for the use of Farmer-type ionization chambers with their reference point (at the center of the cavity volume) positioned at the measurement depth were derived as a ratio of IRPD values at the measurement depth and at the effective point of measurement., Results: Depth dose gradients are as low as 0.1-0.4% per mm at measurement depths from 1 to 5 cm in the highest clinical proton energies (with residual ranges higher than 15 cm) and increase to 1% per mm at a residual range of 4 cm and become larger than 3% per mm for residual ranges lower than 2 cm. The literature review shows that the effective point of measurement of Farmer-type ionization chambers is, similarly as for carbon ion beams, located 0.75 times the cavity radius closer to the beam origin as the center of the cavity. If a maximum displacement correction of 2% is deemed acceptable to be included in calculated beam quality correction factors, Farmer-type ICs can be used at measurements depths from 1 to 5 cm for which the residual range is 4 cm or larger. If one wants to use the same beam quality correction factors as applicable to the conventional measurement point for scattered beams, located at the center of the SOBP, the relative standard uncertainty on the assumption that the displacement correction factor is unity can be kept below 0.5% for measurement depths of at least 2 cm and for residual ranges of 15 cm or higher., Conclusion: The literature review confirmed that for proton beams the effective point of measurement of Farmer-type ionization chambers is located 0.75 times the cavity radius closer to the beam origin as the center of the cavity. Based on the findings in this work, three options can be recommended for reference dosimetry of scanned proton beams using Farmer-type ionization chambers: (a) positioning the effective point of measurement at the measurement depth, (b) positioning the reference point at the measurement depth and applying a displacement correction factor, and (c) positioning the reference point at the measurement depth without applying a displacement correction factor. Based on limiting the acceptable uncertainty on the gradient correction factor to 0.5% and the maximum deviation of the displacement perturbation correction factor from unity to 2%, the first two options can be allowed for residual ranges of at least 4 cm while the third option only for residual ranges of at least 15 cm., (© 2020 American Association of Physicists in Medicine.)

Purpose: Increased radiation response after proton irradiation, such as late radiation-induced toxicity, is determined by high dose and elevated linear energy transfer (LET). Steep dose-averaged LET (LET d ) gradients and elevated LET d occur at the end of proton range and might be particularly sensitive to uncertainties in range prediction. Therefore, this study quantified LET d distributions and the impact of range uncertainty in robust dose-optimized proton treatment plans and assessed the biological effect in normal tissues and tumors of patients., Methods: For each of six cancer patients (two brain, head-and-neck, and prostate), two nominal treatment plans were robustly dose optimized using single- and multi-field optimization, respectively. For each plan, two additional scenarios with ±3.5% range deviation relative to the nominal plan were derived by global rescaling of stopping-power ratios. Dose and LET d distributions were calculated for each scenario using the beam parameters of the corresponding nominal plan. The variability in relative biological effectiveness (RBE) and probability of late radiation-induced brain toxicity (P IC ) was assessed., Results: The optimization technique (single- vs multi-field) had a negligible impact on the LET d distributions in the clinical target volume (CTV) and in most organs at risk (OARs). LET d distributions in the CTV were rather homogeneous with arithmetic mean of LET d below 3.2 keV/µm and robust against range deviations. The RBE variability within the CTV induced by range uncertainty was small (≤0.05, 95% confidence interval). In OARs, LET d hotspots (>7 keV/µm) occurred and LET d distributions were inhomogeneous and sensitive to range deviations. LET d hotspots and the impact of range deviations were most prominent in OARs of brain tumor patients which translated in RBE values exceeding 1.1 in all brain OARs. The near-maximum predicted P IC in healthy brain tissue of brain tumor patients was smaller than 5% and occurred adjacent to the CTV. Range deviations induced absolute differences in P IC up to 1.2%., Conclusions: Robust dose optimization generates LET d distributions in the target volume robust against range deviations. The current findings support using a constant RBE within the CTV. The impact of range deviations on the considered probability of late radiation-induced toxicity in brain tissue was limited for robust dose-optimized treatment plans. Incorporation of LET d in robust optimization frameworks may further reduce uncertainty related to the RBE-weighted dose estimation in normal tissues., (© 2020 The Authors. Medical Physics published by Wiley Periodicals LLC on behalf of American Association of Physicists in Medicine.)

Purpose: Beam quality correction factors provided in current codes of practice for proton beams are approximated using the water-to-air mass stopping power ratio and by assuming the proton beam quality related perturbation correction factors to be unity. The aim of this work is to use Monte Carlo simulations to calculate energy dependent beam quality and perturbation correction factors for a set of nine ionization chambers in proton beams., Methods: The Monte Carlo code EGSnrc was used to determine the ratio of the absorbed dose to water and the absorbed dose to the sensitive air volume of ionization chambers f Q 0 related to the reference photon beam quality ( 60 Co). For proton beams, the quantity f Q was simulated with GATE/Geant4 for five monoenergetic beam energies between 70 MeV and 250 MeV. The perturbation correction factors for the air cavity, chamber wall, chamber stem, central electrode, and displacement effect in proton radiation were investigated separately. Additionally, the correction factors of cylindrical chambers were investigated with and without consideration of the effective point of measurement., Results: The perturbation factors p Q were shown to deviate from unity for the investigated chambers, contradicting the assumptions made in dosimetry protocols. The beam quality correction factors for both plane-parallel and cylindrical chambers positioned with the effective point of measurement at the measurement depth were constant within 0.8%. An increase of the beam quality correction factors determined for cylindrical ionization chambers placed with their reference point at the measurement depth with decreasing energy is attributed to the displacement perturbation correction factors p dis , which were up to 1.045 ± 0.1% for the lowest energy and 1.005 ± 0.1% for the highest energy investigated. Besides p dis , the largest perturbation was found for the chamber wall where the smallest p wall determined was 0.981 ± 0.3%., Conclusions: Beam quality correction factors applied in dosimetry with cylindrical chambers in monoenergetic proton beams strongly depend on the positioning method used. We found perturbation correction factors different from unity. Consequently, the approximation of ionization chamber perturbations in proton beams by the respective water-to-air mass stopping power ratio shall be revised., (© 2020 The Authors. Medical Physics published by Wiley Periodicals LLC on behalf of American Association of Physicists in Medicine.)

Purpose: The purpose of this study was to investigate for the first time the performance of a synthetic single crystal diamond detector for the microdosimetric characterization of clinical 62 MeV ocular therapy proton beams., Methods: A novel diamond microdosimeter with a well-defined sensitive volume was fabricated and tested with a monoenergetic and spread-out Bragg peak (SOBP) of the CATANA therapeutic proton beam in Catania, Italy. The whole sensitive volume of the detector has an active planar-sectional area of 100 µm × 100 µm and a thickness of approximately 6.3 um. Microdosimetric measurements were performed at several water equivalent depths, corresponding to positions of clinical relevance. From the measured spectra, microdosimetric quantities such as the frequency mean lineal energy ( y ¯ F ), dose mean lineal energy ( y ¯ D ) as well as microdosimetric relative biological effectiveness (RBE µ ) values were derived for each depth along both a pristine Bragg curve and SOBP. Finally, Geant4 Monte Carlo simulations were performed modeling the detector geometry and CATANA beamline in order to calculate the average linear energy transfer (LET) values in the diamond active layer and water., Results: The microdosimetric spectra acquired by the diamond microdosimeter show different shapes as a function of the water equivalent depths. No spectral distortion, due to pile-up events and polarization effects, was observed. The experimental spectra have a very low detection threshold due to the electronic noise during the irradiation of about 1 keV/μm. The y ¯ F and y ¯ D values were in agreement with expected trends, showing a sharp increase in mean lineal energy at the distal edge of the Bragg peak. In addition, a good agreement between the mean lineal energy values and the calculated average LET ones was also observed. Finally, the RBE values evaluated with the diamond microdosimeter were in excellent agreement with those obtained with a mini tissue equivalent proportional counter as well as with radiobiological measurements in the same proton beam field., Conclusions: The microdosimetric performance of the tested synthetic single crystal diamond microdosimeter clearly indicates its suitability for quality assurance in clinical proton therapy beam., (© 2020 American Association of Physicists in Medicine.)

Purpose: Particle therapy is becoming increasingly available world-wide for precise tumor targeting, its favorable depth dose deposition, and increased biological damage to tumor tissue compared to conventional photon therapy. As demand increases for improved robustness and conformality, next-generation secondary dose calculation engines are needed to verify treatment plans independently and provide estimates for clinical decision-making factors, such as dose-averaged linear energy transfer (LET d ) and relative biological effectiveness (RBE)., Method: FRoG (Fast dose Recalculation on GPU) has been installed and commissioned at the Danish Centre for Particle Therapy (DCPT). FRoG was developed for synchrotron-based facilities and has previously demonstrated good agreement with gold-standard Monte Carlo simulations and measurements. In this work, additions and modifications to FRoG's pencil beam algorithm to support the ion beam delivery with cyclotron-based technology as used at the DCPT, range shifter (RS) implementation, and robustness analysis methods are presented. FRoG dose predictions are compared to measurements and predictions of the clinical treatment planning system (TPS) Eclipse (Varian Medical Systems, Palo Alto, United States of America, CA, v.13.7.16) in both homogenous and heterogeneous scenarios using a solid-water/water and a half-head anthropomorphic phantom, respectively. Additional capabilities of FRoG are explored by performing a plan robustness analysis, analyzing dose and LET d for ten patients., Results: Mid-target measurements in spread-out Bragg Peaks (SOBP) were on average within -0.19% ± 0.30% and ≤0.5% of FRoG predictions for irradiations without and with RS, respectively. Average 3%/2mm 3D γ-analysis passing rates were 99.1% for ~200 patient plan QA comparisons. Measurement with an anthropomorphic head-phantom yielded a γ-passing rate >98%. Overall, maximum target differences in D 02% of <2% between the TPS and FRoG were observed for patient plans. The robustness analysis study accounting for range, delivery, and positioning uncertainties revealed small differences in target dose and a maximum LET d VH 02% (LET d received by 2% of the volume having dose larger than 1% of maximum dose) values below 10.1 keV/µm to the brain stem., Conclusion: We demonstrate that auxiliary dose calculation systems like FRoG can yield excellent agreement to measurements comparable to clinical beam models. Through this work, application of FRoG as a secondary engine at third party cyclotron-based particle treatment facilities is now established for dose verification as well as providing further insight on LET d and variable RBE distributions for protons, currently absent from the standard clinical TPS., (© 2020 The Authors. Medical Physics published by Wiley Periodicals LLC on behalf of American Association of Physicists in Medicine.)

Purpose: The purpose of this study is to evaluate the sublethal damage (SLD) repair effect in prolonged proton irradiation using the biophysical model with various cell-specific parameters of (α/β) x and T 1/2 (repair half time). At present, most of the model-based studies on protons have focused on acute radiation, neglecting the reduction in biological effectiveness due to SLD repair during the delivery of radiation. Nevertheless, the dose-rate dependency of biological effectiveness may become more important as advanced treatment techniques, such as hypofractionation and respiratory gating, come into clinical practice, as these techniques sometimes require long treatment times. Also, while previous research using the biophysical model revealed a large repair effect with a high physical dose, the dependence of the repair effect on cell-specific parameters has not been evaluated systematically., Methods: Biological dose [relative biological effectiveness (RBE) × physical dose] calculation with repair included was carried out using the linear energy transfer (LET)-dependent linear-quadratic (LQ) model combined with the theory of dual radiation action (TDRA). First, we extended the dose protraction factor in the LQ model for the arbitrary number of different LET proton irradiations delivered sequentially with arbitrary time lags, referring to the TDRA. Using the LQ model, the decrease in biological dose due to SLD repair was systematically evaluated for spread-out Bragg peak (SOBP) irradiation in a water phantom with the possible ranges of both (α/β) x and repair parameters ((α/β) x  = 1-15 Gy, T 1/2  = 0-90 min). Then, to consider more realistic irradiation conditions, clinical cases of prostate, liver, and lung tumors were examined with the cell-specific parameters for each tumor obtained from the literature. Biological D 99% and biological dose homogeneity coefficient (HC) were calculated for the clinical target volumes (CTVs), assuming dose-rate structures with a total irradiation time of 0-60 min., Results: The differences in the cell-specific parameters resulted in considerable variation in the repair effect. The biological dose reduction found at the center of the SOBP with 30 min of continuous irradiation varied from 1.13% to 14.4% with a T 1/2 range of 1-90 min when (α/β) x is fixed as 10 Gy. It varied from 2.3% to 6.8% with an (α/β) x range of 1-15 Gy for a fixed value of T 1/2  = 30 min. The decrease in biological D 99% per 10 min was 2.6, 1.2, and 3.0% for the prostate, liver, and lung tumor cases, respectively. The value of the biological D 99% reduction was neither in the order of (α/β) x nor prescribed dose, but both comparably contributed to the repair effect. The variation of HC was within the range of 0.5% for all cases; therefore, the dose distribution was not distorted., Conclusion: The reduction in biological dose caused by the SLD repair largely depends on the cell-specific parameters in addition to the physical dose. The parameters should be considered carefully in the evaluation of the repair effect in prolonged proton irradiation., (© 2020 American Association of Physicists in Medicine.)

Purpose: A relative biological effectiveness (RBE) of 1.1 is commonly used in clinical proton therapy, irrespective of tissue type and depth. This in vitro study was conducted to quantify the RBE of scanned protons as a function of the dose-averaged linear energy transfer (LET d ) and the sensitivity factor (α/ß) X . Additionally, three phenomenological models (McNamara, Rørvik, and Jones) and one mechanistic model (repair-misrepair-fixation, RMF) were applied to the experimentally derived data., Methods: Four human cell lines (FaDu, HaCat, Du145, SKMel) with differential (α/ß) X ratios were irradiated in a custom-designed irradiation setup with doses between 0 and 6 Gy at proximal, central, and distal positions of a 80 mm spread-out Bragg peak (SOBP) centered at 80 mm (setup A: proton energies 66.5-135.6 MeV) and 155 mm (setup B: proton energies 127.2-185.9 MeV) depth, respectively. LET d values at the respective cell positions were derived from Monte Carlo simulations performed with the treatment planning system (TPS, RayStation). Dosimetric measurements were conducted to verify dose homogeneity and dose delivery accuracy. RBE values were derived for doses that resulted in 90 % (RBE 90 ) and 10 % (RBE 10 ) of cell survival, and survival after a 0.5 Gy dose (RBE 0.5Gy ), 2 Gy dose (RBE 2Gy ), and 6 Gy dose (RBE 6Gy )., Results: LET d values at sample positions were 1.9, 2.1, 2.5, 2.8, 4.1, and 4.5 keV/µm. For the cell lines with high (α/ß) X ratios (FaDu, HaCat), the LET d did not impact on the RBE. For low (α/ß) X cell lines (Du145, SKMel), LQ-derived survival curves indicated a clear correlation of LET d and RBE. RBE 90 values up to 2.9 and RBE 10 values between 1.4 and 1.8 were obtained. Model-derived RBE predictions slightly overestimated the RBE for the high (α/ß) X cell lines, although all models except the Jones model provided RBE values within the experimental uncertainty. For low (α/ß) X cell lines, no agreement was found between experiments and model predictions, that is, all models underestimated the measured RBE., Conclusions: The sensitivity parameter (α/ß) X was observed to be a major influencing factor for the RBE of protons and its sensitivity toward LET d changes. RBE prediction models are applicable for high (α/ß) X cell lines but do not estimate RBE values with sufficient accuracy in low (α/ß) X cell lines., (© 2020 The Authors. Medical Physics published by Wiley Periodicals LLC on behalf of American Association of Physicists in Medicine.)

Purpose: To model four-dimensional (4D) relative biological effectiveness (RBE)-weighted dose variations in abdominal lesions treated with scanned carbon ion beam in case of irregular breathing motion., Methods: The proposed method, referred to as bioWED method, combines the simulation of tumor motion in a patient- and beam-specific water equivalent depth (WED)-space with RBE modeling, aiming at the estimation of RBE-weighted dose changes due to respiratory motion. The method was validated on a phantom, simulating gated and free breathing dose delivery, and on a patient case, for which free breathing irradiation was assumed and both amplitude and baseline breathing irregularities were simulated through a respiratory motion model. We quantified (a) the effect of motion on the equivalent uniform dose (EUD) and the RBE-weighted dose-volume histograms (DVH), by comparing the planned dose distribution with "ground truth" 4D RBE-weighted doses computed using 4D computed tomography data, and (ii) the estimation error, by comparing the doses estimated with the bioWED method to "ground truth" 4D RBE-weighted doses., Results: In the phantom validation, the estimation error on the EUD was limited with respect to the motion effect and the median estimation error on relevant RBE-weighted DVH metrics remained within 5%. In the patient study, the estimation error as computed on the EUD was smaller than the corresponding motion effect, exhibiting the largest values in the baseline irregularity simulation. However, the median estimation error over all simulations was below 3.2% considering relevant DVH metrics., Conclusions: In the evaluated cases, the bioWED method showed proper accuracy when compared to deformable image registration-based 4D dose calculation. Therefore, it can be seen as a tool to test treatment plan robustness against irregular breathing motion, although its accuracy decreases as a function of increasing soft tissue deformation and should be evaluated on a larger patient dataset., (© 2020 American Association of Physicists in Medicine.)

Purpose: This work has two related objectives. The first is to estimate the relative biological effectiveness of two radioactive heavy ion beams based on experimental measurements, and compare these to the relative biological effectiveness of corresponding stable isotopes to determine whether they are therapeutically equivalent. The second aim is to quantitatively compare the quality of images acquired postirradiation using an in-beam whole-body positron emission tomography scanner for range verification quality assurance., Methods: The energy deposited by monoenergetic beams of 11 C at 350 MeV/u, 15 O at 250 MeV/u, 12 C at 350 MeV/u, and 16 O at 430 MeV/u was measured using a cruciform transmission ionization chamber in a water phantom at the Heavy Ion Medical Accelerator in Chiba (HIMAC), Japan. Dose-mean lineal energy was measured at various depths along the path of each beam in a water phantom using a silicon-on-insulator mushroom microdosimeter. Using the modified microdosimetric kinetic model, the relative biological effectiveness at 10% survival fraction of the radioactive ion beams was evaluated and compared to that of the corresponding stable ions along the path of the beam. Finally, the postirradiation distributions of positron annihilations resulting from the decay of positron-emitting nuclei were measured for each beam in a gelatin phantom using the in-beam whole-body positron emission tomography scanner at HIMAC. The depth of maximum positron-annihilation density was compared with the depth of maximum dose deposition and the signal-to-background ratios were calculated and compared for images acquired over 5 and 20 min postirradiation of the phantom., Results: In the entrance region, the h b o x RBE 10 was 1.2 ± 0.1 for both 11 C and 12 C beams, while for 15 O and 16 O it was 1.4 ± 0.1 and 1.3 ± 0.1, respectively. At the Bragg peak, the RBE 10 was 2.7 ± 0.4 for 11 C and 2.9 ± 0.4 for 12 C, while for 15 O and 16 O it was 2.7 ± 0.4 and 2.8 ± 0.4, respectively. In the tail region, RBE 10 could only be evaluated for carbon; the RBE 10 was 1.6 ± 0.2 and 1.5 ± 0.1 for 11 C and 12 C, respectively. Positron emission tomography images obtained from gelatin targets irradiated by radioactive ion beams exhibit markedly improved signal-to-background ratios compared to those obtained from targets irradiated by nonradioactive ion beams, with 5-fold and 11-fold increases in the ratios calculated for the 15 O and 11 C images compared with the values obtained for 16 O and 12 C, respectively. The difference between the depth of maximum dose and the depth of maximum positron annihilation density is 2.4 ± 0.8 mm for 11 C, compared to -5.6 ± 0.8 mm for 12 C and 0.9 ± 0.8 mm for 15 O vs -6.6 ± 0.8 mm for 16 O., Conclusions: The RBE 10 values for 11 C and 15 O were found to be within the 95% confidence interval of the RBEs estimated for their corresponding stable isotopes across each of the regions in which it was evaluated. Furthermore, for a given dose, 11 C and 15 O beams produce much better quality images for range verification compared with 12 C and 16 O, in particular with regard to estimating the location of the Bragg peak., (© 2020 American Association of Physicists in Medicine.)

Introduction: To revisit the formulation of the mean chord length in microdosimetry and replace it by the particle mean free path appropriate for modelings in radiobiology., Methods: We perform a collision-by-collision followed by event-by-event Geant4 Monte Carlo simulation and calculate double-averaged stepping length, 〈〈l〉〉, for a range of target sizes from mm down to μm and depth in water. We consider 〈〈l〉〉 to represent the particle mean free path., Results: We show that 〈〈l〉〉 continuously drops as a function of depth and asymptotically saturates to a minimum value in low energies, where it exhibits a universal scaling behavior, independent of particle nominal beam energy. We correlate 〈〈l〉〉 to linear density of DNA damage, complexities of initial lethal lesions and illustrate a relative difference between predictive RBEs in model calculations using mean chord length vs the proposed mean free path. We demonstrate consistency between rapid increase in RBE within and beyond the Bragg peak and 〈〈l〉〉, a decreasing function of depth., Discussion and Conclusion: An interplay between localities in imparted energy at nanometer scale and subsequent physio-chemical processes, causalities and pathways in DNA damage requires substitution of geometrical chord length of cell nuclei by mean-free path of proton and charged particles to account for a mean distance among sequential collisions in DNA materials. To this end, the event averaging over cell volume in the current microdosimetry formalism must be superseded by the collision averaging scored within the volume. The former, is fundamentally a global attribute of the cell nuclei surfaces and boundaries and is characterized by their membrane diameters, hence such global indices are not appropriate to quantitatively represent the radiobiological strength of the particles and their RBE variabilities that is associated with the sensitivities to local structure of the collisions and their spatio-temporal collective patterns in DNA materials., (© 2020 American Association of Physicists in Medicine.)

Purpose: To estimate relative biological effectiveness (RBE) ascribed to secondary fragments in a lateral distribution of carbon ion irradiation. The RBE was estimated with the microdosimetric kinetic (MK) model and measured linear energy transfer (LET) obtained with CR-39 plastic detectors., Methods: A water phantom was irradiated by a 12 C pencil beam with energy of 380 MeV/u at the Gunma University Heavy Ion Medical Center (GHMC), and CR-39 detectors were exposed to secondary fragments. Because CR-39 was insensitive to low LET, we conducted Monte Carlo simulations with Geant4 to calculate low LET particles. The spectra of low LET particles were combined with experimental spectra to calculate RBE. To estimate accuracy of RBE, we calculated RBE by changing yield of low LET particles by ± 10% and ± 40%., Results: At a small angle, maximum RBE by secondary fragments was 1.3 for 10% survival fractions. RBE values of fragments gradually decreased as the angle became larger. The shape of the LET spectra in the simulation reproduced the experimental spectra, but there was a discrepancy between the simulation and experiment for the relative yield of fragments. When the yield of low LET particles was changed by ± 40%, the change in RBE was smaller than 10%., Conclusions: An RBE of 1.3 was expected for secondary fragments emitted at a small angle. Although, we observed a discrepancy in the relative yield of secondary fragments between simulation and experiment, precision of RBE was not so sensitive to the yield of low LET particles., (© 2019 American Association of Physicists in Medicine.)

Purpose: Although carbon-ion therapy is becoming increasingly attractive to the treatment of tumors, details about the ionization pattern formed by therapeutic carbon-ion beam in tissue have not been fully investigated. In this work, systematic calculations for the nanodosimetric quantities and relative biological effectiveness (RBE) of a clinically relevant carbon-ion beam were studied for the first time., Methods: The method combining both track structure and condensed history Monte Carlo (MC) simulations was adopted to calculate the nanodosimetric quantities. Fragments and energy spectra at different positions of the radiation field of a clinically relevant carbon-ion pencil beam were generated by means of MC simulations in water. Nanodosimetric quantities such as mean ionization cluster size ( M 1 ), the first moment of conditional cluster size ( M 1 C 2 ), cumulative probability ( F 2 ), and conditional cumulative probability ( F 3 C 2 ) at these positions were then acquired based on the spectra and the pre-calculated nanodosimetric database created by track structure MC simulations. What's more, a novel approach to calculate RBE based on the said nanodosimetric quantities was introduced. The RBE calculations were then conducted for the carbon-ion beam at different water-equivalent depths., Results: Lateral distributions at various water-equivalent depths of both the nanodosimetric quantities and RBE values were obtained. The values of M 1 , M 1 C 2 , F 2 , and F 3 C 2 were 1.49, 2.67, 0.30, and 0.38 at the plateau at the beam central axis and maximized at 2.79, 5.69, 0.47, and 0.68 at the depths around the Bragg peak, respectively. At a given depth, M 1 and F 2 decreased laterally with increasing the distance to the beam central axis while M 1 C 2 and F 3 C 2 remained nearly unchanged at first and then decreased except for M 1 C 2 at the rising edge of the Bragg peak. The calculated RBE values were 1.07 at the plateau and 3.13 around the Bragg peak. Good agreement between the calculated RBE values and experimental data was obtained., Conclusions: Different nanodosimetric quantities feature the track structure of therapeutic carbon-ion beam in different manners. Detailed ionization patterns generated by carbon-ion beam could be characterized by nanodosimetric quantities. Moreover the combined method adopted in this work to calculate nanodosimetric quantities is not only valid but also convenient. Nanodosimetric quantities are significantly helpful for the RBE calculations in carbon-ion therapy., (© 2019 American Association of Physicists in Medicine.)

Purpose: The purpose of this study was to study the field size effect on the estimated Relative Biological Effectiveness (RBE) for carbon scanning beam irradiation., Methods: A silicon-on-insulator (SOI) microdosimeter system developed by the Centre for Medical Radiation Physics, University of Wollongong, Australia, was used for lineal-energy measurements (microdosimetric quantity). The RBE values were derived based on the modified microdosimetric kinetic model (MKM) at different depths in a water phantom in the scanning carbon beam for various scanned areas., Results: Our study shows that the difference in RBE values derived from the SOI microdosimeter measurements with the MKM model and from the Treatment Planning System (TPS). The difference of the RBE values is within 6.5 % at the peak point of the spread-out Bragg Peak (SOBP) region. Compared to the spot-beam, RBE values obtained in the scanned-beam with a larger scanned area of 1.0 × 1.0 cm 2 have better agreement with which estimated by the TPS., Conclusions: This study shows the possibility of using the SOI microdosimeter system as a quality assurance (QA) tool for RBE evaluation in carbon-pencil beam scanning radiotherapy., (© 2019 American Association of Physicists in Medicine.)

Purpose: The enhanced relative biological effectiveness (RBE) at the end of the proton range might increase the risk of radiation-induced toxicities. This is of special concern for intracranial treatments where several critical organs at risk (OARs) surround the tumor. In the light of this, a retrospective analysis of dose-averaged linear energy transfer (LET d ) and RBE-weighted dose (D RBE ) distributions was conducted for three clinical cases with suspected treatment-related toxicities following intracranial proton therapy. Alternative treatment strategies aiming to reduce toxicity risks are also presented., Methods: The clinical single-field optimized (SFO) plans were recalculated for 81 error scenarios with a Monte Carlo dose engine. The fractionation D RBE was 1.8 Gy (RBE) in 28 or 30 fractions assuming a constant RBE of 1.1. Two LET d - and α/β-dependent variable RBE models were used for evaluation, including a sensitivity analysis of the α/β parameter. Resulting distributions of D RBE and LET d were analyzed together with normal tissue complication probabilities (NTCPs). Subsequently, four multi-field optimized (MFO) plans, with an additional beam and/or objectives penalizing protons stopping in OARs, were created to investigate the potential reduction of LET d , D RBE , and NTCP., Results: The two variable RBE models agreed well and predicted average RBE values around 1.3 in the toxicity volumes, resulting in an increased near-maximum D RBE of 7-11 Gy (RBE) compared to RBE = 1.1 in the nominal scenario. The corresponding NTCP estimates increased from 0.8%, 0.0%, and 3.7% (RBE = 1.1) to 15.5%, 1.8%, and 45.7% (Wedenberg RBE model) for the three patients, respectively. The MFO plans generally allowed for LET d , D RBE , and NTCP reductions in OARs, without compromising the target dose. Compared to the clinical SFO plans, the maximum reduction in the near-maximum LET d was 56%, 63%, and 72% in the OAR exhibiting the toxicity for the three patients, respectively., Conclusions: Although a direct causality between RBE and toxicity cannot be established here, high LET d and D RBE correlated spatially with the observed toxicities, whereas setup and range uncertainties had a minor impact. Individual factors, which might affect the patient-specific radiosensitivity, were however not included in these calculations. The MFO plans using both an additional beam and proton track-end objectives allowed the largest reductions in LET d , D RBE , and NTCP, and might be future tools for similar cases., (© 2019 American Association of Physicists in Medicine.)