Comparison of linear energy transfer scoring techniques in Monte Carlo simulations of proton beams

Technical note: Determination of proton linear energy transfer from the integral depth dose

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 LETd. Our LETd was smaller than MC simulated LETd 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.

Comparison of linear energy transfer measurement for therapeutic carbon beam using CR-39 and TLD

The measurement of linear energy transfer (LET) is crucial for the evaluation of the radiation effect in heavy ion therapy. As two detectors which are convenient to implant into the phantom, the performance of CR-39 and thermoluminescence detector (TLD) for LET measurement was compared by experiment and simulation in this study. The results confirmed the applicability of both detectors for LET measurements, but also revealed that the CR-39 detector would lead to potential overestimation of dose-averaged LET compared with the simulation by PHITS, while the TLD would have a large uncertainty measuring ions with LET larger than 20 keVμm-1. The results of this study were expected to improve the detection method of LET for therapeutic carbon beam and would finally be benefit to the quality assurance of heavy ion radiotherapy.

A linear energy transfer distributions computation method for inhomogeneous medium by using the water equivalent ratio approximation

Dose-averaged linear energy transfer (LET), LETd is widely used in proton therapy. Compared with analytical models, Monte Carlo (MC) simulations are more accurate in obtaining LETd distributions, but they are time-consuming. This study used the 3D LETd distributions of proton beam spots in water by MC simulations as a benchmark data set. Subsequently, by combining the water equivalent ratio of various human tissues, the 3D LETd distributions of clinical cases could be quickly obtained. Our method was applied to a single spot of 160 MeV proton beam in a water-bone phantom and a pelvic case. We also computed the 3D LETd distributions for multiple proton beam spots in the pelvic case and a lung case. The results of our method were compared with the results of MC simulations, demonstrating that our method can rapidly provide 3D LETd distributions of clinical cases with acceptable differences from MC simulations.

Linear Energy Transfer Measurements and Estimation of Relative Biological Effectiveness in Proton and Helium Ion Beams Using Fluorescent Nuclear Track Detectors

PURPOSE

Our objective was to develop a methodology for assessing the linear energy transfer (LET) and relative biological effectiveness (RBE) in clinical proton and helium ion beams using fluorescent nuclear track detectors (FNTDs).

METHODS AND MATERIALS

FNTDs were exposed behind solid water to proton and helium (4He) ion spread-out Bragg peaks. Detectors were imaged with a confocal microscope, and the LET spectra were derived from the fluorescence intensity. The track- and dose-averaged LET (LETF and LETD, respectively) were calculated from the LET spectra. LET measurements were used as input on RBE models to estimate the RBE. Human alveolar adenocarcinoma cells (A549) were exposed at the same positions as the FNTDs. The RBE was calculated from the resulting survival curves. All measurements were compared with Monte Carlo simulations.

RESULTS

For protons, average relative differences between measurements and simulations were 6% and 19% for LETF and LETD, respectively. For helium ions, the same differences were 11% for both quantities. The position of the experimental LET spectra primary peaks agreed with the simulations within 9% and 14% for protons and helium ions, respectively. For the RBE models using LETD as input, FNTD-based RBE values ranged from 1.02 ± 0.01 to 1.25 ± 0.04 and from 1.08 ± 0.09 to 2.68 ± 1.26 for protons and helium ions, respectively. The average relative differences between these values and simulations were 2% and 4%. For A549 cells, the RBE ranged from 1.05 ± 0.07 to 1.47 ± 0.09 and from 0.89 ± 0.06 to 3.28 ± 0.20 for protons and helium ions, respectively. Regarding the RBE-weighted dose (2.0 Gy at the spread-out Bragg peak), the differences between simulations and measurements were below 0.10 Gy.

CONCLUSIONS

This study demonstrates for the first time that FNTDs can be used to perform direct LET measurements and to estimate the RBE in clinical proton and helium ion beams.

Integrating microdosimetricin vitroRBE models for particle therapy into TOPAS MC using the MicrOdosimetry-based modeliNg for RBE ASsessment (MONAS) tool

Objective.In this paper, we present MONAS (MicrOdosimetry-based modelliNg for relative biological effectiveness (RBE) ASsessment) toolkit. MONAS is a TOPAS Monte Carlo extension, that combines simulations of microdosimetric distributions with radiobiological microdosimetry-based models for predicting cell survival curves and dose-dependent RBE.Approach.MONAS expands TOPAS microdosimetric extension, by including novel specific energy scorers to calculate the single- and multi-event specific energy microdosimetric distributions at different micrometer scales. These spectra are used as physical input to three different formulations of themicrodosimetric kinetic model, and to thegeneralized stochastic microdosimetric model(GSM2), to predict dose-dependent cell survival fraction and RBE. MONAS predictions are then validated against experimental microdosimetric spectra andin vitrosurvival fraction data. To show the MONAS features, we present two different applications of the code: (i) the depth-RBE curve calculation from a passively scattered proton SOBP and monoenergetic12C-ion beam by using experimentally validated spectra as physical input, and (ii) the calculation of the 3D RBE distribution on a real head and neck patient geometry treated with protons.Main results.MONAS can estimate dose-dependent RBE and cell survival curves from experimentally validated microdosimetric spectra with four clinically relevant radiobiological models. From the radiobiological characterization of a proton SOBP and12C fields, we observe the well-known trend of increasing RBE values at the distal edge of the radiation field. The 3D RBE map calculated confirmed the trend observed in the analysis of the SOBP, with the highest RBE values found in the distal edge of the target.Significance.MONAS extension offers a comprehensive microdosimetry-based framework for assessing the biological effects of particle radiation in both research and clinical environments, pushing closer the experimental physics-based description to the biological damage assessment, contributing to bridging the gap between a microdosimetric description of the radiation field and its application in proton therapy treatment with variable RBE.

Variable RBE in proton radiotherapy: a comparative study with the predictive Mayo Clinic Florida microdosimetric kinetic model and phenomenological models of cell survival

Objectives. (1) To examine to what extent the cell- and exposure- specific information neglected in the phenomenological proton relative biological effectiveness (RBE) models could influence the computed RBE in proton therapy. (2) To explore similarities and differences in the formalism and the results between the linear energy transfer (LET)-based phenomenological proton RBE models and the microdosimetry-based Mayo Clinic Florida microdosimetric kinetic model (MCF MKM). (3) To investigate how the relationship between the RBE and the dose-mean proton LET is affected by the proton energy spectrum and the secondary fragments.Approach. We systematically compared six selected phenomenological proton RBE models with the MCF MKM in track-segment simulations, monoenergetic proton beams in a water phantom, and two spread-out Bragg peaks. A representative comparison within vitrodata for human glioblastoma cells (U87 cell line) is also included.Main results. Marked differences were observed between the results of the phenomenological proton RBE models, as reported in previous studies. The dispersion of these models' results was found to be comparable to the spread in the MCF MKM results obtained by varying the cell-specific parameters neglected in the phenomenological models. Furthermore, while single cell-specific correlation between RBE and the dose-mean proton LET seems reasonable above 2 keVμm-1, caution is necessary at lower LET values due to the relevant contribution of secondary fragments. The comparison within vitrodata demonstrates comparable agreement between the MCF MKM predictions and the results of the phenomenological models.Significance. The study highlights the importance of considering cell-specific characteristics and detailed radiation quality information for accurate RBE calculations in proton therapy. Furthermore, these results provide confidence in the use of the MCF MKM for clonogenic survival RBE calculations in proton therapy, offering a more mechanistic approach compared to phenomenological models.

Proposing a Clinical Model for RBE Based on Proton Track-End Counts

PURPOSE

In proton therapy, the clinical application of linear energy transfer (LET) optimization remains contentious, in part because of challenges associated with the definition and calculation of LET and its exact relationship with relative biological effectiveness (RBE) because of large variation in experimental in vitro data. This has raised interest in other metrics with favorable properties for biological optimization, such as the number of proton track ends in a voxel. In this work, we propose a novel model for clinical calculations of RBE, based on proton track end counts.

METHODS AND MATERIALS

We developed an effective dose concept to translate between the total proton track-end count per unit mass in a voxel and a proton RBE value. Dose, track end, and dose-averaged LET (LETd) distributions were simulated using Monte Carlo models for a series of water phantoms, in vitro radiobiological studies, and patient treatment plans. We evaluated the correlation between track ends and regions of elevated biological effectiveness in comparison to LETd-based models of RBE.

RESULTS

Track ends were found to correlate with biological effects in in vitro experiments with an accuracy comparable to LETd. In patient simulations, our track end model identified the same biological hotspots as predicted by LETd-based radiobiological models of proton RBE.

CONCLUSIONS

These results suggest that, for clinical optimization and evaluation, an RBE model based on proton track end counts may match LETd-based models in terms of information provided while also offering superior statistical properties.

Double scattering and pencil beam scanning Monte Carlo workflows for proton therapy retrospective studies on radiation-induced toxicities

PURPOSE

Monte Carlo (MC) simulations can be used to accurately simulate dose and linear energy transfers (LET) distributions, thereby allowing for the calculation of the relative biological effectiveness (RBE) of protons. We present hereby the validation and implementation of a workflow for the Monte Carlo modelling of the double scattered and pencil beam scanning proton beamlines at our institution.

METHODS

The TOPAS/Geant4 MC model of the clinical nozzle has been comprehensively validated against measurements. The validation also included a comparison between simulated clinical treatment plans for four representative patients and the clinical treatment planning system (TPS). Moreover, an in-house tool implemented in Python was tested to assess the variable RBE-weighted dose in proton plans, which was illustrated for a patient case with a developing radiation-induced toxicity.

RESULTS

The simulated range and modulation width closely matches the measurements. Gamma-indexes (3%/3mm 3D), which compare the TPS and MC computations, showed a passing rate superior to 98%. The calculated RBE-weighted dose presented a slight increase at the necrosis location, within the PTV margins. This indicates the need for reporting on the physical and biological effects of irradiation in high dose regions, especially at the healthy tissues and increased LET distributions location.

CONCLUSION

The results demonstrate that the Monte Carlo method can be used to independently validate a TPS calculation, and to estimate LET distributions. The features of the in-house tool can be used to correlate LET and RBE-weighted dose distributions with the incidence of radiation-induced toxicities following proton therapy treatments.

Biophysical characterization of collimated and uncollimated fields in pencil beam scanning proton therapy

Objective. The lateral dose fall-off in proton pencil beam scanning (PBS) technique remains the preferred choice for sparing adjacent organs at risk as opposed to the distal edge due to the proton range uncertainties and potentially high relative biological effectiveness. However, because of the substantial spot size along with the scattering in the air and in the patient, the lateral penumbra in PBS can be degraded. Combining PBS with an aperture can result in a sharper dose fall-off, particularly for shallow targets.Approach. The aim of this work was to characterize the radiation fields produced by collimated and uncollimated 100 and 140 MeV proton beams, using Monte Carlo simulations and measurements with a MiniPIX-Timepix detector. The dose and the linear energy transfer (LET) were then coupled with publishedin silicobiophysical models to elucidate the potential biological effects of collimated and uncollimated fields.Main results. Combining an aperture with PBS reduced the absorbed dose in the lateral fall-off and out-of-field by 60%. However, the results also showed that the absolute frequency-averaged LET (LET_F) values increased by a maximum of 3.5 keVμm^-1in collimated relative to uncollimated fields, while the dose-averaged LET (LET_D) increased by a maximum of 7 keVμm^-1. Despite the higher LET values produced by collimated fields, the predicted DNA damage yields remained lower, owing to the large dose reduction.Significance. This work demonstrated the dosimetric advantages of combining an aperture with PBS coupled with lower DNA damage induction. A methodology for calculating dose in water derived from measurements with a silicon-based detector was also presented. This work is the first to demonstrate experimentally the increase in LET caused by combining PBS with aperture, and to assess the potential DNA damage which is the initial step in the cascade of events leading to the majority of radiation-induced biological effects.

MOQUI: an open-source GPU-based Monte Carlo code for proton dose calculation with efficient data structure

Objective.Monte Carlo (MC) codes are increasingly used for accurate radiotherapy dose calculation. In proton therapy, the accuracy of the dose calculation algorithm is expected to have a more significant impact than in photon therapy due to the depth-dose characteristics of proton beams. However, MC simulations come at a considerable computational cost to achieve statistically sufficient accuracy. There have been efforts to improve computational efficiency while maintaining sufficient accuracy. Among those, parallelizing particle transportation using graphic processing units (GPU) achieved significant improvements. Contrary to the central processing unit, a GPU has limited memory capacity and is not expandable. It is therefore challenging to score quantities with large dimensions requiring extensive memory. The objective of this study is to develop an open-source GPU-based MC package capable of scoring those quantities.Approach.We employed a hash-table, one of the key-value pair data structures, to efficiently utilize the limited memory of the GPU and score the quantities requiring a large amount of memory. With the hash table, only voxels interacting with particles will occupy memory, and we can search the data efficiently to determine their address. The hash-table was integrated with a novel GPU-based MC code, moqui.Main results.The developed code was validated against an MC code widely used in proton therapy, TOPAS, with homogeneous and heterogeneous phantoms. We also compared the dose calculation results of clinical treatment plans. The developed code agreed with TOPAS within 2%, except for the fall-off and regions, and the gamma pass rates of the results were >99% for all cases with a 2 mm/2% criteria.Significance.We can score dose-influence matrix and dose-rate on a GPU for a 3-field H&N case with 10 GB of memory using moqui, which would require more than 100 GB of memory with the conventionally used array data structure.

Changes of the linear energy transfer (LET) and beam width of therapeutic carbon ion beam in density heterogeneous phantoms

This work aims to investigate the changes in the linear energy transfer (LET) spectra distribution and the beam spot width of a therapeutic carbon ion beam in density heterogeneous phantoms. Three different heterogeneous phantoms were fabricated using a combination of solid water, lung, and bone tissue slabs and irradiated by a single energy carbon beam (276.5 MeV u^-1). CR-39 detectors were used for experimental measurements and the Monte Carlo toolkit Geant4 was employed for theoretical simulations. The results demonstrated that the measured LET spectra agree well with the simulation results. The lung and bone tissues displayed no obvious effect on the spectral distribution of LET. The dose-average LET was invariant and showed no obvious difference in the different materials, while the track-average LET increased in the lung and decreased in the bone materials. Similarly, the beam spot size increased in the lung, and decreased in the bone materials. Additionally, the fluence of the secondary fragments varied in different tissues. These findings are expected to provide cross-validation data for the quality assurance of carbon ion therapy and to be beneficial for validating the base data in treatment planning systems.

Towards harmonizing clinical linear energy transfer (LET) reporting in proton radiotherapy: a European multi-centric study

BACKGROUND

Clinical data suggest that the relative biological effectiveness (RBE) in proton therapy (PT) varies with linear energy transfer (LET). However, LET calculations are neither standardized nor available in clinical routine. Here, the status of LET calculations among European PT institutions and their comparability are assessed.

MATERIALS AND METHODS

Eight European PT institutions used suitable treatment planning systems with their center-specific beam model to create treatment plans in a water phantom covering different field arrangements and fulfilling commonly agreed dose objectives. They employed their locally established LET simulation environments and procedures to determine the corresponding LET distributions. Dose distributions D1.1 and DRBE assuming constant and variable RBE, respectively, and LET were compared among the institutions. Inter-center variability was assessed based on dose- and LET-volume-histogram parameters.

RESULTS

Treatment plans from six institutions fulfilled all clinical goals and were eligible for common analysis. D1.1 distributions in the target volume were comparable among PT institutions. However, corresponding LET values varied substantially between institutions for all field arrangements, primarily due to differences in LET averaging technique and considered secondary particle spectra. Consequently, DRBE using non-harmonized LET calculations increased inter-center dose variations substantially compared to D1.1 and significantly in mean dose to the target volume of perpendicular and opposing field arrangements (p < 0.05). Harmonizing LET reporting (dose-averaging, all protons, LET to water or to unit density tissue) reduced the inter-center variability in LET to the order of 10-15% within and outside the target volume for all beam arrangements. Consequentially, inter-institutional variability in DRBE decreased to that observed for D1.1.

CONCLUSION

Harmonizing the reported LET among PT centers is feasible and allows for consistent multi-centric analysis and reporting of tumor control and toxicity in view of a variable RBE. It may serve as basis for harmonized variable RBE dose prescription in PT.

A Monte Carlo study of different LET definitions and calculation parameters for proton beam therapy

The strongin vitroevidence that proton Relative Biological Effectiveness (RBE) varies with Linear Energy Transfer (LET) has led to an interest in applying LET within treatment planning. However, there is a lack of consensus on LET definition, Monte Carlo (MC) parameters or clinical methodology. This work aims to investigate how common variations of LET definition may affect potential clinical applications. MC simulations (GATE/GEANT4) were used to calculate absorbed dose and different types of LET for a simple Spread Out Bragg Peak (SOBP) and for four clinical PBT plans covering a range of tumour sites. Variations in the following LET calculation methods were considered: (i) averaging (dose-averaged LET (LET_d) & track-averaged LET); (ii) scoring (LET_dto water, to medium and to mass density); (iii) particle inclusion (LET_dto all protons, to primary protons and to particles); (iv) MC settings (hit type and Maximum Step Size (MSS)). LET distributions were compared using: qualitative comparison, LET Volume Histograms (LVHs), single value criteria (maximum and mean values) and optimised LET-weighted dose models. Substantial differences were found between LET values in averaging, scoring and particle type. These differences depended on the methodology, but for one patient a difference of ∼100% was observed between the maximum LET_dfor all particles and maximum LET_dfor all protons within the brainstem in the high isodose region (4 keVμm^-1and 8 keVμm^-1respectively). An RBE model using LET_dincluding heavier ions was found to predict substantially different LET-weighted dose compared to those using other LET definitions. In conclusion, the selection of LET definition may affect the results of clinical metrics considered in treatment planning and the results of an RBE model. The authors' advocate for the scoring of dose-averaged LET to water for primary and secondary protons using a random hit type and automated MSS.

Technical note: Providing proton fields down to the few-MeV level at clinical pencil beam scanning facilities for radiobiological experiments

PURPOSE

The adequate performance of radiobiological experiments using clinical proton beams typically requires substantial preparations to provide the appropriate setup for specific experiments. Providing radiobiologically interesting low-energy protons is a particular challenge, due to various physical effects that become more pronounced with larger absorber thickness and smaller proton energy. This work demonstrates the generation of decelerated low-energy protons from a clinical proton beam.

METHODS

Monte Carlo simulations of proton energy spectra were performed for energy absorbers with varying thicknesses to reduce the energy of the clinical proton beam down to the few-MeV level corresponding to μ m-ranges. In this way, a setup with an optimum thickness of the absorber with a maximum efficiency of the proton fluence for the provisioning of low-energy protons is supposed to be found. For the specific applications of 2.5-3.3 MeV protons and α -particle range equivalent protons, the relative depth dose was measured and simulated together with the dose-averaged linear energy transfer (LETd) distribution.

RESULTS

The resulting energy spectra from Monte Carlo simulations indicate an optimal absorber thickness for providing low-energy protons with maximum efficiency of proton fluence at an user-requested energy range for experiments. For instance, providing energies lower than 5 MeV, an energy spectrum with a relative total efficiency of 38.6 % to the initial spectrum was obtained with the optimal setup. The measurements of the depth dose, compared to the Monte Carlo simulations, showed that the dosimetry of low-energy protons works and protons with high LETd down to the range of α -particles can be produced.

CONCLUSIONS

This work provides a method for generating all clinically and radiobiologically relevant energies - especially down to the few-MeV level - at one clinical facility with pencil beam scanning. Thereby, it enables radiobiological experiments under environmentally uniform conditions.

A Critical Review of LET-Based Intensity-Modulated Proton Therapy Plan Evaluation and Optimization for Head and Neck Cancer Management

In this review article, we review the 3 important aspects of linear-energy-transfer (LET) in intensity-modulated proton therapy (IMPT) for head and neck (H&N) cancer management. Accurate LET calculation methods are essential for LET-guided plan evaluation and optimization, which can be calculated either by analytical methods or by Monte Carlo (MC) simulations. Recently, some new 3D analytical approaches to calculate LET accurately and efficiently have been proposed. On the other hand, several fast MC codes have also been developed to speed up the MC simulation by simplifying nonessential physics models and/or using the graphics processor unit (GPU)–acceleration approach. Some concepts related to LET are also briefly summarized including (1) dose-weighted versus fluence-weighted LET; (2) restricted versus unrestricted LET; and (3) microdosimetry versus macrodosimetry. LET-guided plan evaluation has been clinically done in some proton centers. Recently, more and more studies using patient outcomes as the biological endpoint have shown a positive correlation between high LET and adverse events sites, indicating the importance of LET-guided plan evaluation in proton clinics. Various LET-guided plan optimization methods have been proposed to generate proton plans to achieve biologically optimized IMPT plans. Different optimization frameworks were used, including 2-step optimization, 1-step optimization, and worst-case robust optimization. They either indirectly or directly optimize the LET distribution in patients while trying to maintain the same dose distribution and plan robustness. It is important to consider the impact of uncertainties in LET-guided optimization (ie, LET-guided robust optimization) in IMPT, since IMPT is sensitive to uncertainties including both the dose and LET distributions. We believe that the advancement of the LET-guided plan evaluation and optimization will help us exploit the unique biological characteristics of proton beams to improve the therapeutic ratio of IMPT to treat H&N and other cancers.

Measurement of therapeutic12C beam in a water phantom using CR-39

The motivation for this study was to explore a new method to test the particle spatial distribution for a therapeutic carbon beam. CR-39 plastic nuclear track detectors were irradiated to a 276.5 MeV u^-1mono-energy carbon beam at the heavy ion facility in the Shanghai Proton and Heavy Ion Center. The spatial distribution of the primary carbon beam and secondary fragments in a water phantom were systematically analyzed both in the transverse direction (perpendicular to the projection direction of the primary beam) and at different depths in the longitudinal direction (along the projection direction of the primary beam) with measured tracks on the CR-39 detectors. Meanwhile, the theoretically spatial distribution and linear energy transfer (LET) spectra of the primary beam and secondary fragments were calculated using the Monte Carlo (MC) toolkit Geant4. The results showed that the CR-39 detectors are capable of providing high lateral resolution of carbon ion at different depths. In the range of the primary carbon beam, the beam width simulated with MC is in good agreement with that of experimental measurement. The track size registered in the CR-39 has a good correlation with the particle LET. These findings indicate that the CR-39 can be used for measuring both the particle flux and its spatial distribution of carbon ions.

A systematic review on the usage of averaged LET in radiation biology for particle therapy

Linear Energy Transfer (LET) is widely used to express the radiation quality of ion beams, when characterizing the biological effectiveness. However, averaged LET may be defined in multiple ways, and the chosen definition may impact the resulting reported value. We review averaged LET definitions found in the literature, and quantify which impact using these various definitions have for different reference setups. We recorded the averaged LET definitions used in 354 publications quantifying the relative biological effectiveness (RBE) of hadronic beams, and investigated how these various definitions impact the reported averaged LET using a Monte Carlo particle transport code. We find that the kind of averaged LET being applied is, generally, poorly defined. Some definitions of averaged LET may influence the reported averaged LET values up to an order of magnitude. For publications involving protons, most applied dose averaged LET when reporting RBE. The absence of what target medium is used and what secondary particles are included further contributes to an ill-defined averaged LET. We also found evidence of inconsistent usage of averaged LET definitions when deriving LET-based RBE models. To conclude, due to commonly ill-defined averaged LET and to the inherent problems of LET-based RBE models, averaged LET may only be used as a coarse indicator of radiation quality. We propose a more rigorous way of reporting LET values, and suggest that ideally the entire particle fluence spectra should be recorded and provided for future RBE studies, from which any type of averaged LET (or other quantities) may be inferred.

Proton therapy delivery method affects dose-averaged linear energy transfer in patients

The dosimetric advantages of proton therapy have led to its rapid proliferation in recent decades. This has been accompanied by a shift in technology from older units that deliver protons by passive scattering (PS) to newer units that increasingly use pencil-beam scanning (PBS). The biologic effectiveness of proton physical dose purportedly rises with increasing dose-weighted average linear energy transfer (LET_D). The objective of this study was to determine the extent to which proton delivery methods affect LET_D. We calculated LET_Dfrom simple, dosimetrically matched, and clinical treatment plans with TOPAS Monte-Carlo transport code. Simple treatment plans comprised single fields of PS and PBS protons in a water phantom. We performed simulations of matched and clinical treatment plans by using the treatment and anatomic data obtained from a cohort of children with craniopharyngioma who previously received PS or PBS proton therapy. We compared the distributions of LET_Dfrom PS and PBS delivery methods in clinically relevant ROIs. Wilcoxon signed-rank tests comparing single fields in water revealed that the LET_Dvalues from PBS were significantly greater than those from PS inside and outside the targeted volume (p < 0.01). Statistical tests comparing LET_D-volume histograms from matched and clinical treatment plans showed that LET_Dwas generally greater for PBS treatment plans than for PS treatment plans (p < 0.05). In conclusion, the proton delivery method affects LET_Dboth inside and outside of the target volume. These findings suggest that PBS is more biologically effective than PS. Given the rapid expansion of PBS proton therapy, future studies are needed to confirm the applicability of treatment evaluation methods developed for PS proton therapy to those for modern PBS treatments to ensure their safety and effectiveness for the growing population of patients receiving proton therapy. This study uses data from two clinical trials: NCT01419067 and NCT02792582.

Simultaneous Measurements of Dose and Microdosimetric Spectra in a Clinical Proton Beam Using a scCVD Diamond Membrane Microdosimeter

A single crystal chemical vapor deposition (scCVD) diamond membrane-based microdosimetric system was used to perform simultaneous measurements of dose profile and microdosimetric spectra with the Y1 proton passive scattering beamline of the Center of Proton Therapy, Institute Curie in Orsay, France. To qualify the performance of the set-up in clinical conditions of hadrontherapy, the dose, dose rate and energy loss pulse-height spectra in a diamond microdosimeter were recorded at multiple points along depth of a water-equivalent plastic phantom. The dose-mean lineal energy (y¯D) values were computed from experimental data and compared to silicon on insulator (SOI) microdosimeter literature results. In addition, the measured dose profile, pulse height spectra and y¯D values were benchmarked with a numerical simulation using TOPAS and Geant4 toolkits. These first clinical tests of a novel system confirm that diamond is a promising candidate for a tissue equivalent, radiation hard, high spatial resolution microdosimeter in beam quality assurance of proton therapy.

Microdosimetry of a therapeutic proton beam with a mini-TEPC and a MicroPlus-Bridge detector for RBE assessment

Proton beams are widely used worldwide to treat localized tumours, the lower entrance dose and no exit dose, thus sparing surrounding normal tissues, being the main advantage of this treatment modality compared to conventional photon techniques. Clinical proton beam therapy treatment planning is based on the use of a general relative biological effectiveness (RBE) of 1.1 along the whole beam penetration depth, without taking into account the documented increase in RBE at the end of the depth dose profile, in the Bragg peak and beyond. However, an inaccurate estimation of the RBE can cause both underdose or overdose, in particular it can cause the unfavourable situation of underdosing the tumour and overdosing the normal tissue just beyond the tumour, which limits the treatment success and increases the risk of complications. In view of a more precise dose delivery that takes into account the variation of RBE, experimental microdosimetry offers valuable tools for the quality assurance of LET or RBE-based treatment planning systems. The purpose of this work is to compare the response of two different microdosimetry systems: the mini-TEPC and the MicroPlus-Bridge detector. Microdosimetric spectra were measured across the 62 MeV spread out Bragg peak of CATANA with the mini-TEPC and with the Bridge microdosimeter. The frequency and dose distributions of lineal energy were compared and the different contributions to the spectra were analysed, discussing the effects of different site sizes and chord length distributions. The shape of the lineal energy distributions measured with the two detectors are markedly different, due to the different water-equivalent sizes of the sensitive volumes: 0.85 μm for the TEPC and 17.3 μm for the silicon detector. When the Loncol's biological weighting function is applied to calculate the microdosimetric assessment of the RBE, both detectors lead to results that are consistent with biological survival data for glioma U87 cells. Both the mini-TEPC and the MicroPlus-Bridge detector can be used to assess the RBE variation of a 62 MeV modulated proton beam along its penetration depth. The microdosimetric assessment of the RBE based on the Loncol's weighting function is in good agreement with radiobiological results when the 10% biological uncertainty is taken into account.

Microdosimetric measurements as a tool to assess potential in-field and out-of-field toxicity regions in proton therapy

Relative biological effectiveness (RBE) variations are thought to be one of the primary causes of unexpected normal-tissue toxicities during tumor treatments with charged particles. Unlike carbon therapy, where treatment planning is optimized on the basis of the RBE-weighted dose, a constant RBE value of 1.1 is currently used in proton therapy. Assuming a uniform value can lead to under- or over-dosage, not just to the tumor but also to surrounding normal tissue. RBE changes have been linked with dose/fraction, the biological endpoint and beam properties. Understanding radiation quality and the associated RBE can improve the prediction of normal-tissue toxicities. In this study, we exploited microdosimetry for characterizing radiation quality in proton therapy in-field, and off-beam at 20 (beam edge), 50 (close out-of-field) and 100 (far out-of-field) mm from the beam center. We measured the lineal energy y spectra in a water phantom irradiated with 152 MeV protons, from which beam quality as well as the physical dose could be obtained. Taking advantage of the linear quadratic model and a modified version of the microdosimetric kinetic model, the microdosimetric data were combined with radiobiological parameters (α and β) of human salivary gland tumor cells for assessing cell survival RBE and RBE-weighted dose. The results indicate that if a dose of 60 Gy is delivered to the peak, the beam edge receives up to 6 Gy while the close and far out-of-field regions receive doses on the order of 10^-3 Gy and 10^-4 Gy, respectively. The RBE estimate in-beam shows large variations, ranging from 1.0 ± 0.2 at the entrance channel to 2.51 ± 0.15 at the tail. The beam edge follows a similar trend but the RBE calculated at the Bragg peak depth is 2.27 ± 0.17, i.e. twice the RBE in-beam (1.05 ± 0.15). Out-of-field, the estimated RBE is always significantly higher than 1.1 and increases with increasing lateral distance, reaching the overall highest value of 3.4 ± 0.3 at a depth of 206 mm and a lateral distance of 10 mm. The combination of RBE and dose into the biological dose points to the beam edge and the end-of-range in-beam as the areas with the highest risk of potential toxicities.

Producing a Beam Model of the Varian ProBeam Proton Therapy System using TOPAS Monte Carlo Toolkit

PURPOSE

A Geant4-based TOPAS Monte Carlo toolkit was utilized to model a Varian ProBeam proton therapy system, with the aim of providing an independent computational platform for validating advanced dosimetric methods.

MATERIALS AND METHODS

The model was tested for accuracy of dose and linear energy transfer (LET) prediction relative to the commissioning data, which included integral depth dose (IDD) in water and spot profiles in air measured at varying depths (for energies of 70 to 240 MeV in increments of 10 MeV, and 242 MeV), and absolute dose calibration. Emittance was defined based on depth-dependent spot profiles and Courant-Snyder's particle transport theory, which provided spot size and angular divergence along the inline and crossline plane. Energy spectra were defined as Gaussian distributions that best matched the range and maximum dose of the IDD. The validity of the model was assessed based on measurements of range, dose to peak difference, mean point to point difference, spot sizes at different depths, and spread-out Bragg peak (SOBP) IDD and was compared to the current treatment planning software (TPS).

RESULTS

Simulated and commissioned spot sizes agreed within 2.5%. The single spot IDD range, maximum dose, and mean point to point difference of each commissioned energy agreed with the simulated profiles generally within 0.07 mm, 0.4%, and 0.6%, respectively. A simulated SOBP plan agreed with the measured dose within 2% for the plateau region. The protons/MU and absolute dose agreed with the current TPS to within 1.6% and exhibited the greatest discrepancy at higher energies.

CONCLUSIONS

The TOPAS model agreed well with the commissioning data and included inline and crossline asymmetry of the beam profiles. The discrepancy between the measured and TOPAS-simulated SOBP plan may be due to beam modeling simplifications of the current TPS and the nuclear halo effect. The model can compute LET, and motivates future studies in understanding equivalent dose prediction in treatment planning, and investigating scintillation quenching.

Standardizing Monte Carlo simulation parameters for a reproducible dose-averaged linear energy transfer

OBJECTIVE

Dose-averaged linear energy transfer (LETD) is one of the factors which determines relative biological effectiveness (RBE) for treatment planning in proton therapy. It is usually determined from Monte Carlo (MC) simulation. However, no standard simulation protocols were established for sampling of LETD. Simulation parameters like maximum step length and range cut will affect secondary electrons production and have an impact on the accuracy of dose distribution and LETD. We aim to show how different combinations of step length and range cut in GEANT4 will affect the result in sampling of LETD using different MC scoring methods.

METHODS

In this work, different step length and range cut value in a clinically relevant voxel geometry were used for comparison. Different LETD scoring methods were established and the concept of covariance between energy deposition per step and step length is used to explain the differences between them.

RESULTS

We recommend a maximum step length of 0.05 mm and a range cut of 0.01 mm in MC simulation as this yields the most consistent LETD value across different scoring methods. Different LETD scoring methods are also compared and variation up to 200% can be observed at the plateau of 80 MeV proton beam. Scoring Method one has one of the lowest percentage differences compared across all simulation parameters.

CONCLUSION

We have determined a set of maximum step length and range cut parameters to be used for LETD scoring in a 1 mm voxelized geometry. LETD scoring method should also be clearly defined and standardized to facilitate cross-institutional studies.

ADVANCES IN KNOWLEDGE

Establishing a standard simulation protocol for sampling LETD would reduce the discrepancy when comparing data across different centres, and this can improve the calculation for RBE.

First proton minibeam radiation therapy treatment plan evaluation

Proton minibeam radiation therapy (pMBRT) is a novel dose delivery method based on spatial dose fractionation. pMBRT has been shown to be promising in terms of reduced side effects and superior tumour control in high-grade glioma-bearing rats compared to standard irradiation. These findings, together with the recent optimized implementation of pMBRT in a clinical pencil beam scanning system, have triggered reflection on the possible application to patient treatments. In this context, the present study was designed to conduct a first theoretical investigation of the clinical potential of this technique. For this purpose, a dedicated dose engine was developed and used to evaluate two clinically relevant patient treatment plans (high-grade glioma and meningioma). Treatment plans were compared with standard proton therapy plans assessed by means of a commercial treatment planning system (ECLIPSE-Varian Medical systems) and Monte Carlo simulations. A multislit brass collimator consisting of 0.4 mm wide slits separated by a centre-to-centre distance of 4 or 6 mm was placed between the nozzle and the patient to shape the planar minibeams. For each plan, spread-out Bragg peaks and homogeneous dose distributions (±7% dose variations) can be obtained in target volumes. The Peak-to-Valley Dose Ratios (PVDR) were evaluated between 9.2 and 12.8 at a depth of 20 mm for meningioma and glioma, respectively. Dose volume histograms (DVHs) for target volumes and organs at risk were quantitatively compared, resulting in a slightly better target homogeneity with standard PT than with pMBRT plans, but similar DVHs for deep-seated organs-at-risk and lower average dose for shallow organs. The proposed delivery method evaluated in this work opens the way to an effective treatment for radioresistant tumours and will support the design of future clinical research.

The TOPAS tool for particle simulation, a Monte Carlo simulation tool for physics, biology and clinical research

PURPOSE

This paper covers recent developments and applications of the TOPAS TOol for PArticle Simulation and presents the approaches used to disseminate TOPAS.

MATERIALS AND METHODS

Fundamental understanding of radiotherapy and imaging is greatly facilitated through accurate and detailed simulation of the passage of ionizing radiation through apparatus and into a patient using Monte Carlo (MC). TOPAS brings Geant4, a reliable, experimentally validated MC tool mainly developed for high energy physics, within easy reach of medical physicists, radiobiologists and clinicians. Requiring no programming knowledge, TOPAS provides all of the flexibility of Geant4.

RESULTS

After 5 years of development followed by its initial release, TOPAS was subsequently expanded from its focus on proton therapy physics to incorporate radiobiology modeling. Next, in 2018, the developers expanded their user support and code maintenance as well as the scope of TOPAS towards supporting X-ray and electron therapy and medical imaging. Improvements have been achieved in user enhancement through software engineering and a graphical user interface, calculational efficiency, validation through experimental benchmarks and QA measurements, and either newly available or recently published applications. A large and rapidly increasing user base demonstrates success in our approach to dissemination of this uniquely accessible and flexible MC research tool.

CONCLUSIONS

The TOPAS developers continue to make strides in addressing the needs of the medical community in applications of ionizing radiation to medicine, creating the only fully integrated platform for four-dimensional simulation of all forms of radiotherapy and imaging with ionizing radiation, with a design that promotes inter-institutional collaboration.

In Silico Models of DNA Damage and Repair in Proton Treatment Planning: A Proof of Concept

There is strong in vitro cell survival evidence that the relative biological effectiveness (RBE) of protons is variable, with dependence on factors such as linear energy transfer (LET) and dose. This is coupled with the growing in vivo evidence, from post-treatment image change analysis, of a variable RBE. Despite this, a constant RBE of 1.1 is still applied as a standard in proton therapy. However, there is a building clinical interest in incorporating a variable RBE. Recently, correlations summarising Monte Carlo-based mechanistic models of DNA damage and repair with absorbed dose and LET have been published as the Manchester mechanistic (MM) model. These correlations offer an alternative path to variable RBE compared to the more standard phenomenological models. In this proof of concept work, these correlations have been extended to acquire RBE-weighted dose distributions and calculated, along with other RBE models, on a treatment plan. The phenomenological and mechanistic models for RBE have been shown to produce comparable results with some differences in magnitude and relative distribution. The mechanistic model found a large RBE for misrepair, which phenomenological models are unable to do. The potential of the MM model to predict multiple endpoints presents a clear advantage over phenomenological models.

Hybrid 3D analytical linear energy transfer calculation algorithm based on precalculated data from Monte Carlo simulations

PURPOSE

The dose-averaged linear energy transfer (LET_d ) for intensity-modulated proton therapy (IMPT) calculated by one-dimensional (1D) analytical models deviates from more accurate but time-consuming Monte Carlo (MC) simulations. We developed a fast hybrid three-dimensional (3D) analytical LET_d calculation that is more accurate than 1D analytical model.

METHODS

We used the Geant4 MC code to generate 3D LET_d distributions of monoenergetic proton beams in water for all energies and used a customized error function to fit the LET_d lateral profiles at various depths to the MC simulation. The 3D LET_d calculation kernel was a lookup table of these fitted coefficients, and LET_d was determined directly from spot energies and voxel coordinates during analytical dose calculations. We validated our new method by comparing the calculated LET_d distributions to MC results using 3D Gamma index analysis with 3%/2 mm criteria in 12 patient geometries. The significance of the improvement in Gamma index analysis passing rates over the 1D analytical model was determined using the Wilcoxon rank-sum test.

RESULTS

The passing rate of 3D Gamma analysis comparing LET_d distributions from the hybrid 3D method and the 1D method to MC simulations was significantly improved from 94.0% ± 2.5% to 98.0% ± 1.0% (P = 0.0003). The typical time to calculate dose and LET_d simultaneously using an Intel Xeon E5-2680 2.50 GHz workstation was approximately 2.5 min.

CONCLUSIONS

Our new method significantly improved the LET_d calculation accuracy compared to the 1D method while maintaining significantly shorter calculation time even comparing with the GPU-based fast MC code.

Charged particle radiobiology beamline using tandem accelerator-based MeV protons and carbon ions: a pilot study on the track-end radiation quality, variable biological effectiveness and Bayesian beam dosimetry

For in vitro cell irradiation using tandem accelerator-based MeV protons and carbon ions, by TOPAS simulation, a pilot study of performance evaluation is presented on a collimation beamline for 3 MeV protons and 10 MeV carbon ions from a 2  ×  3 MV tandem accelerator. Based on the elements and source parameters, a collimated beam of 2.8 MeV protons or 2.5 MeV carbon ions, with 5.175 mm or 5.166 mm full width tenth maximum (FWTM), respectively, can be delivered to the target cell dish. TOPAS simulations and/or deterministic algorithms present a Bragg curve of linear energy transfer (LET) (10-70 keV μm^-1) along a 138 μm range of the proton beam, and a declining LET of the carbon beam (900-100 keV μm^-1) within 4 μm range. Based on the biophysical models for relative biological effectiveness (RBE) of protons, TOPAS RBE scorers presents a set of depth-variation curves of the proton RBE (for V79 and DU145 cells), linearly related to the Bragg curve of the proton LET. Based on the microdosimetric-kinetic (MK) theory, in the 4 μm range for a monolayer cell thickness, the mean RBEα (V79 cells) of the carbon ion beam is estimated as 3.612 (late S phase) and 1.737 (G ₁/S phase) for the mean LET of 492 keV μm^-1. For practical irradiations, a tunable proton RBE can be acquired by changing the thickness of the cell dish. For the low-energy high-fluence (rate) beams, indirect beam measurements are proposed to detect the proton-beam induced scattering/recoil protons from a beam-intercepting Mylar film, and the carbon-beam induced backscattered electrons from a gold-deposited Havar-foil beam window. Statistical dosimetry for the indirect measurement is established, using a Bayesian model based on the preset number of detection counts, by which the mean value of the whole-dish dose can be prescribed and the uncertainty introduced in the survival data can be corrected.

Physical and biological impacts of collimator-scattered protons in spot-scanning proton therapy

To improve the penumbra of low‐energy beams used in spot‐scanning proton therapy, various collimation systems have been proposed and used in clinics. In this paper, focused on patient‐specific brass collimators, the collimator‐scattered protons' physical and biological effects were investigated. The Geant4 Monte Carlo code was used to model the collimators mounted on the scanning nozzle of the Hokkaido University Hospital. A systematic survey was performed in water phantom with various‐sized rectangular targets; range (5–20 cm), spread‐out Bragg peak (SOBP) (5–10 cm), and field size (2 × 2–16 × 16 cm²). It revealed that both the range and SOBP dependences of the physical dose increase had similar trends to passive scattering methods, that is, it increased largely with the range and slightly with the SOBP. The physical impact was maximized at the surface (3%–22% for the tested geometries) and decreased with depth. In contrast, the field size (FS) dependence differed from that observed in passive scattering: the increase was high for both small and large FSs. This may be attributed to the different phase‐space shapes at the target boundary between the two dose delivery methods. Next, the biological impact was estimated based on the increase in dose‐averaged linear energy transfer (LET_d) and relative biological effectiveness (RBE). The LET_d of the collimator‐scattered protons were several keV/μm higher than that of unscattered ones; however, since this large increase was observed only at the positions receiving a small scattered dose, the overall LET_d increase was negligible. As a consequence, the RBE increase did not exceed 0.05. Finally, the effects on patient geometries were estimated by testing two patient plans, and a negligible RBE increase (0.9% at most in the critical organs at surface) was observed in both cases. Therefore, the impact of collimator‐scattered protons is almost entirely attributed to the physical dose increase, while the RBE increase is negligible.

A novel methodology to assess linear energy transfer and relative biological effectiveness in proton therapy using pairs of differently doped thermoluminescent detectors

A new methodology for assessing linear energy transfer (LET) and relative biological effectiveness (RBE) in proton therapy beams using thermoluminescent detectors is presented. The method is based on the different LET response of two different lithium fluoride thermoluminescent detectors (LiF:Mg,Ti and LiF:Mg,Cu,P) for measuring charged particles. The relative efficiency of the two detector types was predicted using the recently developed Microdosimetric d(z) Model in combination with the Monte Carlo code PHITS. Afterwards, the calculated ratio of the expected response of the two detector types was correlated with the fluence- and dose- mean values of the unrestricted proton LET. Using the obtained proton dose mean LET as input, the RBE was assessed using a phenomenological biophysical model of cell survival. The aforementioned methodology was benchmarked by exposing the detectors at different depths within the spread out Bragg peak (SOBP) of a clinical proton beam at iThemba LABS. The assessed LET values were found to be in good agreement with the results of radiation transport computer simulations performed using the Monte Carlo code GEANT4. Furthermore, the estimated RBE values were compared with the RBE values experimentally determined by performing colony survival measurements with Chinese Hamster Ovary (CHO) cells during the same experimental run. A very good agreement was found between the results of the proposed methodology and the results of the in vitro study.

Simultaneous optimization of RBE-weighted dose and nanometric ionization distributions in treatment planning with carbon ions

Inverse treatment planning in intensity modulated particle therapy (IMPT) with scanned carbon-ion beams is currently based on the optimization of RBE-weighted dose to satisfy requirements of target coverage and limited toxicity to organs-at-risk (OARs) and healthy tissues. There are many feasible IMPT plans that meet these requirements, which allows the introduction of further criteria to narrow the selection of a biologically optimal treatment plan. We propose a novel treatment planning strategy based on the simultaneous optimization of RBE-weighted dose and nanometric ionization details (ID) as a new physical characteristic of the delivered plan beyond LET. In particular, we focus on the distribution of large ionization clusters (more than 3 ionizations) to enhance the biological effect across the target volume while minimizing biological effect in normal tissues. Carbon-ion treatment plans for different patient geometries and beam configurations generated with the simultaneous optimization strategy were compared against reference plans obtained with RBE-weighted dose optimization alone. Quality indicators, inhomogeneity index and planning volume histograms of RBE-weighted dose and large ionization clusters were used to evaluate the treatment plans. We show that with simultaneous optimization, ID distributions can be optimized in carbon-ion radiotherapy without compromising the RBE-weighted dose distributions. This strategy can potentially be used to account for optimization of endpoints closely related to radiation quality to achieve better tumor control and reduce risks of complications.

Monte Carlo simulation of chemistry following radiolysis with TOPAS-nBio

Simulation of water radiolysis and the subsequent chemistry provides important information on the effect of ionizing radiation on biological material. The Geant4 Monte Carlo toolkit has added chemical processes via the Geant4-DNA project. The TOPAS tool simplifies the modeling of complex radiotherapy applications with Geant4 without requiring advanced computational skills, extending the pool of users. Thus, a new extension to TOPAS, TOPAS-nBio, is under development to facilitate the configuration of track-structure simulations as well as water radiolysis simulations with Geant4-DNA for radiobiological studies. In this work, radiolysis simulations were implemented in TOPAS-nBio. Users may now easily add chemical species and their reactions, and set parameters including branching ratios, dissociation schemes, diffusion coefficients, and reaction rates. In addition, parameters for the chemical stage were re-evaluated and updated from those used by default in Geant4-DNA to improve the accuracy of chemical yields. Simulation results of time-dependent and LET-dependent primary yields Gx (chemical species per 100 eV deposited) produced at neutral pH and 25 °C by short track-segments of charged particles were compared to published measurements. The LET range was 0.05-230 keV µm-1. The calculated Gx values for electrons satisfied the material balance equation within 0.3%, similar for protons albeit with long calculation time. A smaller geometry was used to speed up proton and alpha simulations, with an acceptable difference in the balance equation of 1.3%. Available experimental data of time-dependent G-values for [Formula: see text] agreed with simulated results within 7%  ±  8% over the entire time range; for [Formula: see text] over the full time range within 3%  ±  4%; for H2O2 from 49%  ±  7% at earliest stages and 3%  ±  12% at saturation. For the LET-dependent Gx, the mean ratios to the experimental data were 1.11  ±  0.98, 1.21  ±  1.11, 1.05  ±  0.52, 1.23  ±  0.59 and 1.49  ±  0.63 (1 standard deviation) for [Formula: see text], [Formula: see text], H2, H2O2 and [Formula: see text], respectively. In conclusion, radiolysis and subsequent chemistry with Geant4-DNA has been successfully incorporated in TOPAS-nBio. Results are in reasonable agreement with published measured and simulated data.

Investigating Dependencies of Relative Biological Effectiveness for Proton Therapy in Cancer Cells

Purpose

Relative biological effectiveness (RBE) accounts for the differences in biological effect from different radiation types. The RBE for proton therapy remains uncertain, as it has been shown to vary from the clinically used value of 1.1. In this work we investigated the RBE of protons and correlated the biological differences with the underlying physical quantities.

Materials and Methods

Three cell lines were irradiated (CHO, Chinese hamster ovary; A549, human lung adenocarcinoma; and T98, human glioma) and assessed for cell survival by using clonogenic assay. Cells were irradiated with 71- and 160-MeV protons at depths along the Bragg curve and 6-MV photons to various doses. The dose-averaged lineal energy ( y‒D ) was measured under similar conditions as the cells by using a microdosimeter. Dose-averaged linear energy transfer (LET_d) was also calculated by using Monte Carlo (MC) simulations. Survival data were fit by using the linear quadratic model. The RBE values were calculated by comparing the physical dose (D_6MV/D_p) that results in 50% (RBE_0.5) and 10% (RBE_0.1) cell survival, and survival after 2 Gy (RBE_2Gy).

Results

Proton RBE values ranged from 0.89 to 2.40. The RBE for all 3 cell lines increased with decreasing proton energy and was higher at 50% survival than at 10% survival. Additionally, both A549 and T98 cells generally had higher RBE values relative to the CHO cells, indicating a greater biological response to protons. An increase in RBE corresponded with an increase in y‒D and LET_d.

Conclusion

Proton RBE was found to depend on mean proton energy, survival end point, and cell type. Changes in both y‒D and LET_d were also found to impact proton RBE values, but consideration of the energy spectrum may provide additional information. The RBE values in this study vary greatly, indicating the clinical value of 1.1 may not be suitable in all cases.

A real-time method to simultaneously measure linear energy transfer and dose for proton therapy using organic scintillators

PURPOSE

Currently, no detectors are capable of simultaneously measuring dose and linear energy transfer (LET) in real time. In this study, we evaluated the feasibility of exploiting the difference in the response of various organic plastic scintillation detectors to measure LET and dose in therapeutic proton beams. The hypothesis behind this work was that the ratio of the responses of different scintillators exposed to the same proton beam can be used to obtain a LET vs ratio calibration curve that can then be used to infer LET under any other measurement conditions.

METHODS

We first used similar scintillators with different ionization quenching factors. LET values for different irradiation conditions were calculated using a validated Monte Carlo model of the proton beam line. The quenching factors in the Birks equation for different scintillators as a function of LET were obtained from measurements in a 100-MeV pristine proton beam. We then used four different organic scintillation materials - polystyrene (BCF-12), poly (methyl methacrylate), polyvinyltoluene, and a liquid scintillator - for which the LET response varied with regard to not only quenching but also differences in material density and relative stopping power. We simultaneously exposed the four different organic scintillators and a plane-parallel ion chamber to passively scattered proton beams at fluence-averaged LET. Comparisons to the expected values obtained from the Monte Carlo simulations were made on the basis of both dose and LET.

RESULTS

The maximum difference in the quenching factor was 20%, resulting in a 5% change in LET with a response ratio over a range of 5 keV/μm. Among all the scintillators investigated, the ratio of PMMA to BCF-12 provided the best correlation with LET values and was therefore used to construct the LET calibration curve. The expected LET values in the validation set were within 2% ± 6%, which resulted in dose accuracy of 1.5% ± 5.8% for the range of LET values investigated in this work.

CONCLUSIONS

We demonstrated the feasibility of using the ratio of the light outputs of two organic scintillators to simultaneously measure LET and dose in therapeutic proton beams for fluence-averaged LET values from 0.47 to 1.26 keV/μm. Further studies are needed to verify the response for higher LET values and the reproducibility of this method.

Biological and dosimetric characterisation of spatially fractionated proton minibeams

The biological effectiveness of proton beams varies with depth, spot size and lateral distance from the beam central axis. The aim of this work is to incorporate proton relative biological effectiveness (RBE) and equivalent uniform dose (EUD) considerations into comparisons of broad beam and highly modulated proton minibeams. A Monte Carlo model of a small animal proton beamline is presented. Dose and variable RBE is calculated on a per-voxel basis for a range of energies (30-109 MeV). For an open beam, the RBE values at the beam entrance ranged from 1.02-1.04, at the Bragg peak (BP) from 1.3 to 1.6, and at the distal end of the BP from 1.4 to 2.0. For a 50 MeV proton beam, a minibeam collimator designed to produce uniform dose at the depth of the BP peak, had minimal impact on the open beam RBE values at depth. RBE changes were observed near the surface when the collimator was placed flush with the irradiated object, due to a higher neutron contribution derived from proton interactions with the collimator. For proton minibeams, the relative mean RBE weighted entrance dose (RWD) was ~25% lower than the physical mean dose. A strong dependency of the EUD with fraction size was observed. For 20 Gy fractions, the EUD varied widely depending on the radiosensitivity of the cells. For radiosensitive cells, the difference was up to ~50% in mean dose and ~40% in mean RWD and the EUD trended towards the valley dose rather than the mean dose. For comparative studies of uniform dose with spatially fractionated proton minibeams, EUD derived from a per-voxel RWD distribution is recommended for biological assessments of reproductive cell survival and related endpoints.

Optimization of Monte Carlo particle transport parameters and validation of a novel high throughput experimental setup to measure the biological effects of particle beams

PURPOSE

Accurate modeling of the relative biological effectiveness (RBE) of particle beams requires increased systematic in vitro studies with human cell lines with care towards minimizing uncertainties in biologic assays as well as physical parameters. In this study, we describe a novel high-throughput experimental setup and an optimized parameterization of the Monte Carlo (MC) simulation technique that is universally applicable for accurate determination of RBE of clinical ion beams. Clonogenic cell-survival measurements on a human lung cancer cell line (H460) are presented using proton irradiation.

METHODS

Experiments were performed at the Heidelberg Ion Therapy Center (HIT) with support from the Deutsches Krebsforschungszentrum (DKFZ) in Heidelberg, Germany using a mono-energetic horizontal proton beam. A custom-made variable range selector was designed for the horizontal beam line using the Geant4 MC toolkit. This unique setup enabled a high-throughput clonogenic assay investigation of multiple, well defined dose and linear energy transfer (LETs) per irradiation for human lung cancer cells (H460) cultured in a 96-well plate. Sensitivity studies based on application of different physics lists in conjunction with different electromagnetic constructors and production threshold values to the MC simulations were undertaken for accurate assessment of the calculated dose and the dose-averaged LET (LET_d ). These studies were extended to helium and carbon ion beams.

RESULTS

Sensitivity analysis of the MC parameterization revealed substantial dependence of the dose and LET_d values on both the choice of physics list and the production threshold values. While the dose and LET_d calculations using FTFP_BERT_LIV, FTFP_BERT_EMZ, FTFP_BERT_PEN and QGSP_BIC_EMY physics lists agree well with each other for all three ions, they show large differences when compared to the FTFP_BERT physics list with the default electromagnetic constructor. For carbon ions, the dose corresponding to the largest LET_d value is observed to differ by as much as 78% between FTFP_BERT and FTFP_BERT_LIV. Furthermore, between the production threshold of 700 μm and 5 μm, proton dose varies by as much as 19% corresponding to the largest LET_d value sampled in the current investigation. Based on the sensitivity studies, the FTFP_BERT physics list with the low energy Livermore electromagnetic constructor and a production threshold of 5 μm was employed for determining accurate dose and LET_d . The optimized MC parameterization results in a different LET_d dependence of the RBE curve for 10% SF of the H460 cell line irradiated with proton beam when compared with the results from a previous study using the same cell line. When the MC parameters are kept consistent between the studies, the proton RBE results agree well with each other within the experimental uncertainties.

CONCLUSIONS

A custom high-throughput, high-accuracy experimental design for accurate in vitro cell survival measurements was employed at a horizontal beam line. High sensitivity of the physics-based optimization establishes the importance of accurate MC parameterization and hence the conditioning of the MC system on a case-by-case basis. The proton RBE results from current investigations are observed to agree with a previous measurement made under different experimental conditions. This establishes the consistency of our experimental findings across different experiments and institutions.

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

BACKGROUND

For tumours near organs at risk, there is concern about unintended increase in biological dose from elevated linear energy transfer (LET) at the distal end of treatment fields. The objective of this study was therefore to investigate how different paediatric posterior fossa tumour locations impact LET and biological dose to the brainstem during intensity-modulated proton therapy (IMPT).

MATERIAL AND METHODS

Multiple IMPT plans were generated for four different simulated tumour locations relative to the brainstem for a five-year-old male patient. A prescribed dose of 59.4 Gy(RBE) was applied to the planning target volumes (PTVs). Plans with two lateral and one posterior non-coplanar fields were created, along with plans with modified field arrangements. The dose-averaged LET (LET_d) and the physical dose × RBE_LET (D × RBE_LET), where RBE_LET=1+c × LET_d, were calculated using the FLUKA Monte Carlo code. A scaling parameter c was applied to make the RBE_LET represent variations in the biological effect due to LET.

RESULTS

High LET_d values surrounded parts of the PTV and encompassed portions of the brainstem. Mean LET_d values in the brainstem were 3.2-6.6 keV/μm. The highest absolute brainstem LET_d values were seen with the tumour located most distant from the brainstem, whereas lower and more homogeneous LET_d values were seen when the tumour invaded the brainstem. In contrast, the highest mean D × RBE_LET values were found in the latter case (54.0 Gy(RBE)), while the case with largest distance between tumour and brainstem had a mean D × RBE_LET of 1.8 Gy(RBE).

CONCLUSIONS

Using IMPT to treat posterior fossa tumours may result in high LET_d values within the brainstem, particularly if the tumour volume is separated from the brainstem. However, the D × RBE_LET was greater for tumours that approached or invaded the brainstem. Changing field angles showed a reduction of LET_d and D × RBE_LET in the brainstem.

Nanoscale measurements of proton tracks using fluorescent nuclear track detectors

PURPOSE

The authors describe a method in which fluorescence nuclear track detectors (FNTDs), novel track detectors with nanoscale spatial resolution, are used to determine the linear energy transfer (LET) of individual proton tracks from proton therapy beams by allowing visualization and 3D reconstruction of such tracks.

METHODS

FNTDs were exposed to proton therapy beams with nominal energies ranging from 100 to 250 MeV. Proton track images were then recorded by confocal microscopy of the FNTDs. Proton tracks in the FNTD images were fit by using a Gaussian function to extract fluorescence amplitudes. Histograms of fluorescence amplitudes were then compared with LET spectra.

RESULTS

The authors successfully used FNTDs to register individual proton tracks from high-energy proton therapy beams, allowing reconstruction of 3D images of proton tracks along with delta rays. The track amplitudes from FNTDs could be used to parameterize LET spectra, allowing the LET of individual proton tracks from therapeutic proton beams to be determined.

CONCLUSIONS

FNTDs can be used to directly visualize proton tracks and their delta rays at the nanoscale level. Because the track intensities in the FNTDs correlate with LET, they could be used further to measure LET of individual proton tracks. This method may be useful for measuring nanoscale radiation quantities and for measuring the LET of individual proton tracks in radiation biology experiments.

Recent developments and comprehensive evaluations of a GPU-based Monte Carlo package for proton therapy

Monte Carlo (MC) simulation is commonly considered as the most accurate dose calculation method for proton therapy. Aiming at achieving fast MC dose calculations for clinical applications, we have previously developed a graphics-processing unit (GPU)-based MC tool, gPMC. In this paper, we report our recent updates on gPMC in terms of its accuracy, portability, and functionality, as well as comprehensive tests on this tool. The new version, gPMC v2.0, was developed under the OpenCL environment to enable portability across different computational platforms. Physics models of nuclear interactions were refined to improve calculation accuracy. Scoring functions of gPMC were expanded to enable tallying particle fluence, dose deposited by different particle types, and dose-averaged linear energy transfer (LETd). A multiple counter approach was employed to improve efficiency by reducing the frequency of memory writing conflict at scoring. For dose calculation, accuracy improvements over gPMC v1.0 were observed in both water phantom cases and a patient case. For a prostate cancer case planned using high-energy proton beams, dose discrepancies in beam entrance and target region seen in gPMC v1.0 with respect to the gold standard tool for proton Monte Carlo simulations (TOPAS) results were substantially reduced and gamma test passing rate (1%/1 mm) was improved from 82.7%-93.1%. The average relative difference in LETd between gPMC and TOPAS was 1.7%. The average relative differences in the dose deposited by primary, secondary, and other heavier particles were within 2.3%, 0.4%, and 0.2%. Depending on source proton energy and phantom complexity, it took 8-17 s on an AMD Radeon R9 290x GPU to simulate [Formula: see text] source protons, achieving less than [Formula: see text] average statistical uncertainty. As the beam size was reduced from 10  ×  10 cm² to 1  ×  1 cm², the time on scoring was only increased by 4.8% with eight counters, in contrast to a 40% increase using only one counter. With the OpenCL environment, the portability of gPMC v2.0 was enhanced. It was successfully executed on different CPUs and GPUs and its performance on different devices varied depending on processing power and hardware structure.

Analysis of the track- and dose-averaged LET and LET spectra in proton therapy using the geant4 Monte Carlo code

PURPOSE

The motivation of this study was to find and eliminate the cause of errors in dose-averaged linear energy transfer (LET) calculations from therapeutic protons in small targets, such as biological cell layers, calculated using the geant 4 Monte Carlo code. Furthermore, the purpose was also to provide a recommendation to select an appropriate LET quantity from geant 4 simulations to correlate with biological effectiveness of therapeutic protons.

METHODS

The authors developed a particle tracking step based strategy to calculate the average LET quantities (track-averaged LET, LETt and dose-averaged LET, LETd) using geant 4 for different tracking step size limits. A step size limit refers to the maximally allowable tracking step length. The authors investigated how the tracking step size limit influenced the calculated LETt and LETd of protons with six different step limits ranging from 1 to 500 μm in a water phantom irradiated by a 79.7-MeV clinical proton beam. In addition, the authors analyzed the detailed stochastic energy deposition information including fluence spectra and dose spectra of the energy-deposition-per-step of protons. As a reference, the authors also calculated the averaged LET and analyzed the LET spectra combining the Monte Carlo method and the deterministic method. Relative biological effectiveness (RBE) calculations were performed to illustrate the impact of different LET calculation methods on the RBE-weighted dose.

RESULTS

Simulation results showed that the step limit effect was small for LETt but significant for LETd. This resulted from differences in the energy-deposition-per-step between the fluence spectra and dose spectra at different depths in the phantom. Using the Monte Carlo particle tracking method in geant 4 can result in incorrect LETd calculation results in the dose plateau region for small step limits. The erroneous LETd results can be attributed to the algorithm to determine fluctuations in energy deposition along the tracking step in geant 4. The incorrect LETd values lead to substantial differences in the calculated RBE.

CONCLUSIONS

When the geant 4 particle tracking method is used to calculate the average LET values within targets with a small step limit, such as smaller than 500 μm, the authors recommend the use of LETt in the dose plateau region and LETd around the Bragg peak. For a large step limit, i.e., 500 μm, LETd is recommended along the whole Bragg curve. The transition point depends on beam parameters and can be found by determining the location where the gradient of the ratio of LETd and LETt becomes positive.