A critical study of different Monte Carlo scoring methods of dose average linear-energy-transfer maps calculated in voxelized geometries irradiated with clinical proton beams

A framework for in-field and out-of-field patient specific secondary cancer risk estimates from treatment plans using the TOPAS Monte Carlo system

Objective. To allow the estimation of secondary cancer risks from radiation therapy treatment plans in a comprehensive and user-friendly Monte Carlo (MC) framework.Method. Patient planning computed tomography scans were extended superior-inferior using the International Commission on Radiological Protection's Publication 145 computational mesh phantoms and skeletal matching. Dose distributions were calculated with the TOPAS MC system using novel mesh capabilities and the digital imaging and communications in medicine radiotherapy extension interface. Finally, in-field and out-of-field cancer risk was calculated using both sarcoma and carcinoma risk models with two alternative parameter sets.Result. The TOPAS MC framework was extended to facilitate epidemiological studies on radiation-induced cancer risk. The framework is efficient and allows automated analysis of large datasets. Out-of-field organ dose was small compared to in-field dose, but the risk estimates indicate a non-negligible contribution to the total radiation induced cancer risk.Significance. This work equips the TOPAS MC system with anatomical extension, mesh geometry, and cancer risk model capabilities that make state-of-the-art out-of-field dose calculation and risk estimation accessible to a large pool of users. Furthermore, these capabilities will facilitate further refinement of risk models and sensitivity analysis of patient specific treatment options.

Dosimetric study for breathing-induced motion effects in an abdominal pancreas phantom for carbon ion mini-beam radiotherapy

BACKGROUND

Particle mini-beam therapy exhibits promise in sparing healthy tissue through spatial fractionation, particularly notable for heavy ions, further enhancing the already favorable differential biological effectiveness at both target and entrance regions. However, breathing-induced organ motion affects particle mini-beam irradiation schemes since the organ displacements exceed the mini-beam structure dimensions, decreasing the advantages of spatial fractionation.

PURPOSE

In this study, the impact of breathing-induced organ motion on the dose distribution was examined at the target and organs at risk(OARs) during carbon ion mini-beam irradiation for pancreatic cancer.

METHODS

As a first step, the carbon ion mini-beam pattern was characterized with Monte Carlo simulations. To analyze the impact of breathing-induced organ motion on the dose distribution of a virtual pancreas tumor as target and related OARs, the anthropomorphic Pancreas Phantom for Ion beam Therapy (PPIeT) was irradiated with carbon ions. A mini-beam collimator was used to deliver a spatially fractionated dose distribution. During irradiation, varying breathing motion amplitudes were induced, ranging from 5 to 15 mm. Post-irradiation, the 2D dose pattern was analyzed, focusing on the full width at half maximum (FWHM), center-to-center distance (ctc), and the peak-to-valley dose ratio (PVDR).

RESULTS

The mini-beam pattern was visible within OARs, while in the virtual pancreas tumor a more homogeneous dose distribution was achieved. Applied motion affected the mini-beam pattern within the kidney, one of the OARs, reducing the PVDR from 3.78  ± $\pm$  0.12 to 1.478  ± $\pm$  0.070 for the 15 mm motion amplitude. In the immobile OARs including the spine and the skin at the back, the PVDR did not change within 3.4% comparing reference and motion conditions.

CONCLUSIONS

This study provides an initial understanding of how breathing-induced organ motion affects spatial fractionation during carbon ion irradiation, using an anthropomorphic phantom. A decrease in the PVDR was observed in the right kidney when breathing-induced motion was applied, potentially increasing the risk of damage to OARs. Therefore, further studies are needed to explore the clinical viability of mini-beam radiotherapy with carbon ions when irradiating abdominal regions.

NRG Oncology White Paper on the Relative Biological Effectiveness in Proton Therapy

This position paper, led by the NRG Oncology Particle Therapy Work Group, focuses on the concept of relative biologic effect (RBE) in clinical proton therapy (PT), with the goal of providing recommendations for the next-generation clinical trials with PT on the best practice of investigating and using RBE, which could deviate from the current standard proton RBE value of 1.1 relative to photons. In part 1, current clinical utilization and practice are reviewed, giving the context and history of RBE. Evidence for variation in RBE is presented along with the concept of linear energy transfer (LET). The intertwined nature of tumor radiobiology, normal tissue constraints, and treatment planning with LET and RBE considerations is then reviewed. Part 2 summarizes current and past clinical data and then suggests the next steps to explore and employ tools for improved dynamic models for RBE. In part 3, approaches and methods for the next generation of prospective clinical trials are explored, with the goal of optimizing RBE to be both more reflective of clinical reality and also deployable in trials to allow clinical validation and interpatient comparisons. These concepts provide the foundation for personalized biologic treatments reviewed in part 4. Finally, we conclude with a summary including short- and long-term scientific focus points for clinical PT. The practicalities and capacity to use RBE in treatment planning are reviewed and considered with more biological data in hand. The intermediate step of LET optimization is summarized and proposed as a potential bridge to the ultimate goal of case-specific RBE planning that can be achieved as a hypothesis-generating tool in near-term proton trials.

Assessment of fluence- and dose-averaged linear energy transfer with passive luminescence detectors in clinical proton beams

Objective.This work investigates the use of passive luminescence detectors to determine different types of averaged linear energy transfer (LET-) for the energies relevant to proton therapy. The experimental results are compared to reference values obtained from Monte Carlo simulations.Approach.Optically stimulated luminescence detectors (OSLDs), fluorescent nuclear track detectors (FNTDs), and two different groups of thermoluminescence detectors (TLDs) were irradiated at four different radiation qualities. For each irradiation, the fluence- (LET-f) and dose-averaged LET (LET-d) were determined. For both quantities, two sub-types of averages were calculated, either considering the contributions from primary and secondary protons or from all protons and heavier, charged particles. Both simulated and experimental data were used in combination with a phenomenological model to estimate the relative biological effectiveness (RBE).Main results.All types ofLET-could be assessed with the luminescence detectors. The experimental determination ofLET-fis in agreement with reference data obtained from simulations across all measurement techniques and types of averaging. On the other hand,LET-dcan present challenges as a radiation quality metric to describe the detector response in mixed particle fields. However, excluding secondaries heavier than protons from theLET-dcalculation, as their contribution to the luminescence is suppressed by ionization quenching, leads to equal accuracy betweenLET-fandLET-d. Assessment of RBE through the experimentally determinedLET-dvalues agrees with independently acquired reference values, indicating that the investigated detectors can determineLET-with sufficient accuracy for proton therapy.Significance.OSLDs, TLDs, and FNTDs can be used to determineLET-and RBE in proton therapy. With the capability to determine dose through ionization quenching corrections derived fromLET-, OSLDs and TLDs can simultaneously ascertain dose,LET-, and RBE. This makes passive detectors appealing for measurements in phantoms to facilitate validation of clinical treatment plans or experiments related to proton therapy.

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.

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.

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.

A phenomenological model of proton FLASH oxygen depletion effects depending on tissue vasculature and oxygen supply

Introduction

Radiation-induced oxygen depletion in tissue is assumed as a contributor to the FLASH sparing effects. In this study, we simulated the heterogeneous oxygen depletion in the tissue surrounding the vessels and calculated the proton FLASH effective-dose-modifying factor (FEDMF), which could be used for biology-based treatment planning.

Methods

The dose and dose-weighted linear energy transfer (LET) of a small animal proton irradiator was simulated with Monte Carlo simulation. We deployed a parabolic partial differential equation to account for the generalized radiation oxygen depletion, tissue oxygen diffusion, and metabolic processes to investigate oxygen distribution in 1D, 2D, and 3D solution space. Dose and dose rates, particle LET, vasculature spacing, and blood oxygen supplies were considered. Using a similar framework for the hypoxic reduction factor (HRF) developed previously, the FEDMF was derived as the ratio of the cumulative normoxic-equivalent dose (CNED) between CONV and UHDR deliveries.

Results

Dynamic equilibrium between oxygen diffusion and tissue metabolism can result in tissue hypoxia. The hypoxic region displayed enhanced radio-resistance and resulted in lower CNED under UHDR deliveries. In 1D solution, comparing 15 Gy proton dose delivered at CONV 0.5 and UHDR 125 Gy/s, 61.5% of the tissue exhibited ≥20% FEDMF at 175 μm vasculature spacing and 18.9 μM boundary condition. This percentage reduced to 34.5% and 0% for 8 and 2 Gy deliveries, respectively. Similar trends were observed in the 3D solution space. The FLASH versus CONV differential effect remained at larger vasculature spacings. A higher FLASH dose rate showed an increased region with ≥20% FEDMF. A higher LET near the proton Bragg peak region did not appear to alter the FLASH effect.

Conclusion

We developed 1D, 2D, and 3D oxygen depletion simulation process to obtain the dynamic HRF and derive the proton FEDMF related to the dose delivery parameters and the local tissue vasculature information. The phenomenological model can be used to simulate or predict FLASH effects based on tissue vasculature and oxygen concentration data obtained from other experiments.

Comparing biological effectiveness guided plan optimization strategies for cranial proton therapy: potential and challenges

BACKGROUND

To introduce and compare multiple biological effectiveness guided (BG) proton plan optimization strategies minimizing variable relative biological effectiveness (RBE) induced dose burden in organs at risk (OAR) while maintaining plan quality with a constant RBE.

METHODS

Dose-optimized (DOSEopt) proton pencil beam scanning reference treatment plans were generated for ten cranial patients with prescription doses ≥ 54 Gy(RBE) and ≥ 1 OAR close to the clinical target volume (CTV). For each patient, four additional BG plans were created. BG objectives minimized either proton track-ends, dose-averaged linear energy transfer (LET_d), energy depositions from high-LET protons or variable RBE-weighted dose (D_RBE) in adjacent serially structured OARs. Plan quality (RBE = 1.1) was assessed by CTV dose coverage and robustness (2 mm setup, 3.5% density), dose homogeneity and conformity in the planning target volumes and adherence to OAR tolerance doses. LET_d, D_RBE (Wedenberg model, α/β_CTV = 10 Gy, α/β_OAR = 2 Gy) and resulting normal tissue complication probabilities (NTCPs) for blindness and brainstem necrosis were derived. Differences between DOSEopt and BG optimized plans were assessed and statistically tested (Wilcoxon signed rank, α = 0.05).

RESULTS

All plans were clinically acceptable. DOSEopt and BG optimized plans were comparable in target volume coverage, homogeneity and conformity. For recalculated D_RBE in all patients, all BG plans significantly reduced near-maximum D_RBE to critical OARs with differences up to 8.2 Gy(RBE) (p < 0.05). Direct D_RBE optimization primarily reduced absorbed dose in OARs (average ΔD_mean = 2.0 Gy; average ΔLET_d,mean = 0.1 keV/µm), while the other strategies reduced LET_d (average ΔD_mean < 0.3 Gy; average ΔLET_d,mean = 0.5 keV/µm). LET-optimizing strategies were more robust against range and setup uncertaintes for high-dose CTVs than D_RBE optimization. All BG strategies reduced NTCP for brainstem necrosis and blindness on average by 47% with average and maximum reductions of 5.4 and 18.4 percentage points, respectively.

CONCLUSIONS

All BG strategies reduced variable RBE-induced NTCPs to OARs. Reducing LET_d in high-dose voxels may be favourable due to its adherence to current dose reporting and maintenance of clinical plan quality and the availability of reported LET_d and dose levels from clinical toxicity reports after cranial proton therapy. These optimization strategies beyond dose may be a first step towards safely translating variable RBE optimization in the clinics.

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.

4He dose- and track-averaged linear energy transfer: Monte Carlo algorithms and experimental verification

Objective. In the present hadrontherapy scenario, there is a growing interest in exploring the capabilities of different ion species other than protons and carbons. The possibility of using different ions paves the way for new radiotherapy approaches, such as the multi-ions treatment, where radiation could vary according to target volume, shape, depth and histologic characteristics of the tumor. For these reasons, in this paper, the study and understanding of biological-relevant quantities was extended for the case of 4He ion. Approach. Geant4 Monte Carlo based algorithms for dose- and track-averaged LET (Linear Energy Transfer) calculations, were validated for 4He ions and for the case of a mixed field characterised by the presence of secondary ions from both target and projectile fragmentation. The simulated dose and track averaged LETs were compared with the corresponding dose and frequency mean values of the lineal energy, y D ¯ and y ¯ F , derived from experimental microdosimetric spectra. Two microdosimetric experimental campaigns were carried out at the Italian eye proton therapy facility of the Laboratori Nazionali del Sud of Istituto Nazionale di Fisica Nucleare (INFN-LNS, Catania, I) using two different microdosimeters: the MicroPlus probe and the nano-TEPC (Tissue Equivalent Proportional Counter). Main results. A good agreement of L ¯ d Total and L ¯ t Total with y ¯ D and y ¯ T experimentally measured with both microdosimetric detectors MicroPlus and nano-TEPC in two configurations: full energy and modulated 4He ion beam, was found. Significance. The results of this study certify the use of a very effective tool for the precise calculation of LET, given by a Monte Carlo approach which has the advantage of allowing detailed simulation and tracking of nuclear interactions, even in complex clinical scenarios.

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.

Impact of RBE variations on risk estimates of temporal lobe necrosis in patients treated with intensity-modulated proton therapy for head and neck cancer

BACKGROUND

Temporal lobe necrosis (TLN) is a potential late effect after radiotherapy for skull base head and neck cancer (HNC). Several photon-derived dose constraints and normal tissue complication probability (NTCP) models have been proposed, however variation in relative biological effectiveness (RBE) may challenge the applicability of these dose constraints and models in proton therapy. The purpose of this study was therefore to investigate the influence of RBE variations on risk estimates of TLN after Intensity-Modulated Proton Therapy for HNC.

MATERIAL AND METHODS

Seventy-five temporal lobes from 45 previously treated patients were included in the analysis. Sixteen temporal lobes had radiation associated Magnetic Resonance image changes (TLIC) suspected to be early signs of TLN. Fixed (RWD_Fix) and variable RBE-weighed doses (RWD_Var) were calculated using RBE = 1.1 and two RBE models, respectively. RWD_Fix and RWD_Var for temporal lobes were compared using Friedman's test. Based on RWD_Fix, six NTCP models were fitted and internally validated through bootstrapping. Estimated probabilities from RWD_Fix and RWD_Var were compared using paired Wilcoxon test. Seven dose constraints were evaluated separately for RWD_Fix and RWD_Var by calculating the observed proportion of TLIC in temporal lobes meeting the specific dose constraints.

RESULTS

RWD_Var were significantly higher than RWD_Fix (p < 0.01). NTCP model performance was good (AUC:0.79-0.84). The median difference in estimated probability between RWD_Fix and RWD_Var ranged between 5.3% and 20.0% points (p < 0.01), with V_60GyRBE and D_Max at the smallest and largest differences, respectively. The proportion of TLIC was higher for RWD_Fix (4.0%-13.1%) versus RWD_Var (1.3%-5.3%). For V_65GyRBE ≤ 0.03 cc the proportion of TLIC was less than 5% for both RWD_Fix and RWD_Var.

CONCLUSION

NTCP estimates were significantly influenced by RBE variations. D_max as model predictor resulted in the largest deviations in risk estimates between RWD_Fix and RWD_Var. V_65GyRBE ≤ 0.03 cc was the most consistent dose constraint for RWD_Fix and RWD_Var.

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.

Handling of beam spectra in training and application of proton RBE models

Published data from cell survival experiments are frequently used as training data for models of proton relative biological effectiveness (RBE). The publications rarely provide full information about the primary particle spectrum of the used beam, or its content of heavy secondary particles. The purpose of this paper is to assess to what extent heavy secondary particles may have been present in published cell survival experiments, and to investigate the impact of non-primary protons for RBE calculations in treatment planning. We used the Monte Carlo code Geant4 to calculate the occurrence of non-primary protons and heavier secondary particles for clinical protons beams in water for four incident energies in the [100, 250] MeV interval. We used the resulting spectra together with a conservative RBE parameterization and an RBE model to map both the rise of RBE at the beam entry surface due to heavy secondary particle buildup, and the difference in estimated RBE if non-primary protons are included or not in the beam quality metric. If included, non-primary protons cause a difference of 2% of the RBE in the plateau region of an spread out Bragg peak and 1% in the Bragg peak. Including non-primary protons specifically for RBE calculations will consequently have a negligible impact and can be ignored. A buildup distance in water of one millimeter was sufficient to reach an equilibrium state of RBE for the four incident energies selected. For the investigated experimental data, 83 out of the 86 data points were found to have been determined with at least that amount of buildup material. Hence, RBE model training data should be interpreted to include the contribution of heavy secondaries.

Comparison of FLASH Proton Entrance and the Spread-Out Bragg Peak Dose Regions in the Sparing of Mouse Intestinal Crypts and in a Pancreatic Tumor Model

Simple Summary

FLASH radiotherapy is a treatment technique of interest that involves radiation delivered at ultra-high dose rates >100 times faster than traditional radiation therapy, which has been shown to spare radiation damage to normal tissue but maintain tumor control capabilities. Proton therapy uses spread-out proton Bragg peaks to reduce radiation dose to normal tissue by directing the highest dose of radiation to the tumor volume. In this study, irradiation of the whole abdomen of mice was performed with proton beams at FLASH dose rates in order to investigate the normal tissue sparing capabilities of the spread-out Bragg peak compared to the entrance region of the proton depth dose curve.

Abstract

Ultra-high dose rate FLASH proton radiotherapy (F-PRT) has been shown to reduce normal tissue toxicity compared to standard dose rate proton radiotherapy (S-PRT) in experiments using the entrance portion of the proton depth dose profile, while proton therapy uses a spread-out Bragg peak (SOBP) with unknown effects on FLASH toxicity sparing. To investigate, the biological effects of F-PRT using an SOBP and the entrance region were compared to S-PRT in mouse intestine. In this study, 8–10-week-old C57BL/6J mice underwent 15 Gy (absorbed dose) whole abdomen irradiation in four groups: (1) SOBP F-PRT, (2) SOBP S-PRT, (3) entrance F-PRT, and (4) entrance S-PRT. Mice were injected with EdU 3.5 days after irradiation, and jejunum segments were harvested and preserved. EdU-positive proliferating cells and regenerated intestinal crypts were quantified. The SOBP had a modulation (width) of 2.5 cm from the proximal to distal 90%. Dose rates with a SOBP for F-PRT or S-PRT were 108.2 ± 8.3 Gy/s or 0.82 ± 0.14 Gy/s, respectively. In the entrance region, dose rates were 107.1 ± 15.2 Gy/s and 0.83 ± 0.19 Gy/s, respectively. Both entrance and SOBP F-PRT preserved a significantly higher number of EdU + /crypt cells and percentage of regenerated crypts compared to S-PRT. Moreover, tumor growth studies showed no difference between SOBP and entrance for either of the treatment modalities.

Linear Energy Transfer Incorporated Spot-Scanning Proton Arc Therapy Optimization: A Feasibility Study

Purpose

To integrate dose-averaged linear energy transfer (LET_d) into spot-scanning proton arc therapy (SPArc) optimization and to explore its feasibility and potential clinical benefits.

Methods

An open-source proton planning platform (OpenREGGUI) has been modified to incorporate LET_d into optimization for both SPArc and multi-beam intensity-modulated proton therapy (IMPT) treatment planning. SPArc and multi-beam IMPT plans with different beam configurations for a prostate patient were generated to investigate the feasibility of LET_d-based optimization using SPArc in terms of spatial LET_d distribution and plan delivery efficiency. One liver and one brain case were studied to further evaluate the advantages of SPArc over multi-beam IMPT.

Results

With similar dose distributions, the efficacy of spatially optimizing LET_d distributions improves with increasing number of beams. Compared with multi-beam IMPT plans, SPArc plans show substantial improvement in LET_d distributions while maintaining similar delivery efficiency. Specifically, for the liver case, the average LET_d in the GTV was increased by 124% for the SPArc plan, and only 9.6% for the 2-beam IMPT plan compared with the 2-beam non-LET_d optimized IMPT plan. In case of LET optimization for the brain case, the SPArc plan could effectively increase the average LET_d in the CTV and decrease the values in the critical structures while smaller improvement was observed in 3-beam IMPT plans.

Conclusion

This work demonstrates the feasibility and significant advantages of using SPArc for LET_d-based optimization, which could maximize the LET_d distribution wherever is desired inside the target and averts the high LET_d away from the adjacent critical organs-at-risk.

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.

Mixed Effect Modeling of Dose and Linear Energy Transfer Correlations With Brain Image Changes After Intensity Modulated Proton Therapy for Skull Base Head and Neck Cancer

Purpose:

Intensity modulated proton therapy (IMPT) could yield high linear energy transfer (LET) in critical structures and increased biological effect. For head and neck cancers at the skull base this could potentially result in radiation-associated brain image change (RAIC). The purpose of the current study was to investigate voxel-wise dose and LET correlations with RAIC after IMPT.

Methods and Materials:

For 15 patients with RAIC after IMPT, contrast enhancement observed on T1-weighted magnetic resonance imaging was contoured and coregistered to the planning computed tomography. Monte Carlo calculated dose and dose-averaged LET (LET_d) distributions were extracted at voxel level and associations with RAIC were modelled using uni- and multivariate mixed effect logistic regression. Model performance was evaluated using the area under the receiver operating characteristic curve and precision-recall curve.

Results:

An overall statistically significant RAIC association with dose and LET_d was found in both the uni- and multivariate analysis. Patient heterogeneity was considerable, with standard deviation of the random effects of 1.81 (1.30–2.72) for dose and 2.68 (1.93–4.93) for LET_d, respectively. Area under the receiver operating characteristic curve was 0.93 and 0.95 for the univariate dose-response model and multivariate model, respectively. Analysis of the LET_d effect demonstrated increased risk of RAIC with increasing LET_d for the majority of patients. Estimated probability of RAIC with LET_d = 1 keV/μm was 4% (95% confidence interval, 0%, 0.44%) and 29% (95% confidence interval, 0.01%, 0.92%) for 60 and 70 Gy, respectively. The TD₁₅ were estimated to be 63.6 and 50.1 Gy with LET_d equal to 2 and 5 keV/μm, respectively.

Conclusions:

Our results suggest that the LET_d effect could be of clinical significance for some patients; LET_d assessment in clinical treatment plans should therefore be taken into consideration.

First theoretical determination of relative biological effectiveness of very high energy electrons

Very high energy electrons (VHEEs, E > 70 MeV) present promising clinical advantages over conventional beams due to their increased range, improved penumbra and relative insensitivity to tissue heterogeneities. They have recently garnered additional interest in their application to spatially fractionated radiotherapy or ultra-high dose rate (FLASH) therapy. However, the lack of radiobiological data limits their rapid development. This study aims to provide numerical biologically-relevant information by characterizing VHEE beams (100 and 300 MeV) against better-known beams (clinical energy electrons, photons, protons, carbon and neon ions). Their macro- and microdosimetric properties were compared, using the dose-averaged linear energy transfer ([Formula: see text]) as the macroscopic metric, and the dose-mean lineal energy [Formula: see text] and the dose-weighted lineal energy distribution, yd(y), as microscopic metrics. Finally, the modified microdosimetric kinetic model was used to calculate the respective cell survival curves and the theoretical RBE. From the macrodosimetric point of view, VHEEs presented a potential improved biological efficacy over clinical photon/electron beams due to their increased [Formula: see text]. The microdosimetric data, however, suggests no increased biological efficacy of VHEEs over clinical electron beams, resulting in RBE values of approximately 1, giving confidence to their clinical implementation. This study represents a first step to complement further radiobiological experiments.

Radiochromic film dosimetry for protons up to 10 MeV with EBT2, EBT3 and unlaminated EBT3 films

Passive dosimetry with radiochromic films is widely used in proton radiotherapy, both in clinical and scientific environments, thanks to its simplicity, high spatial resolution and dose-rate independence. However, film under-response for low-energy protons, the so-called linear-energy transfer (LET) quenching, must be accounted and corrected for. We perform a meta-analysis on existing film under-response data with EBT, EBT2 and EBT3 GAFchromic™ films and provide a common framework to integrate it, based on the calculation of dose-averaged LET in the active layer of the films. We also report on direct measurements with the 10 MeV proton beam at the Center for Microanalysis of Materials (CMAM) for EBT2, EBT3 and unlaminated EBT3 films, focusing on the 20-80 keVμm^-1LET range, where previous data was scarce. Measured film relative efficiency (RE) values are in agreement with previously reported data from the literature. A model on film RE constructed with combined literature and own experimental values in the 5-80 keVμm^-1LET range is presented, supporting the hypothesis of a linear decrease of RE with LET, with no remarkable differences between the three types of films analyzed.

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.

Impact of Multiple Beams on Plan Quality, Linear Energy Transfer Distribution, and Plan Robustness of Intensity Modulated Proton Therapy for Lung Cancer

The increase of proton beam number might provide higher degrees of freedom in the optimization of intensity-modulated proton therapy planning. In this study, we aimed to quantitatively explore the potential benefits of the increased beam number, including dose volume histogram (DVH), linear energy transfer volume histogram, and DVH bandwidth metrics. Twelve patients with lung cancer are retrospectively selected. Four plans were created based on internal target volume (ITV) robust optimization for each patient using the RayStation treatment planning system. Four plans were generated using different numbers (three, five, seven, and nine) of evenly separated coplanar beams. The three-beam plan was considered as the reference plan. Biologically equivalent doses were calculated using both constant relative biological effectiveness (RBE) and variable RBE models, respectively. To evaluate plan quality, DVH metrics in the target [ITV: D_2%, CI, HI] and organs-at-risk [Lung: V_5Gy[RBE], V_20Gy[RBE], V_30Gy[RBE]; Heart D_2%; Spinal cord D_2%] were calculated using both RBE models. To evaluate LET distributions, LET volume histogram metrics [ITV LET_mean and LET_2%; Lung LET_mean and LET_2%; Heart LET_2%; Spinal cord LET_2%] were quantified. To evaluate plan robustness, the metrics using DVH bandwidth [ITV: D_2%, D_99%; Lung: V_5Gy[RBE], V_20Gy[RBE], V_30Gy[RBE]; Heart D_2%; Spinal cord D_2%] were also reported. For plan quality, the increase of proton beam number resulted in fewer target hot spots, improved target dose conformity, improved target dose homogeneity, lower median-dose lung volume, and fewer hot spots in spinal cord. As to LET distributions, target mean LET increased significantly as the beam number increased to seven or more. Lung LET hot spots were significantly reduced with the increase of proton beams. With respect to plan robustness, the robustness of target dose coverage, target hot spots, and low-dose lung volume were improved, while the robustness of heart hot spots became worse as the beam number increased to nine. The robustness of cord hot spots became worse using five and seven beams compared to that using three beams. As the proton beam number increased, plan quality and LET distributions were comparable or significantly improved. The robustness of target dose coverage, target dose hot spots, and low-dose lung volume were significantly improved.

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.

Report on G4-Med, a Geant4 benchmarking system for medical physics applications developed by the Geant4 Medical Simulation Benchmarking Group

BACKGROUND

Geant4 is a Monte Carlo code extensively used in medical physics for a wide range of applications, such as dosimetry, micro- and nanodosimetry, imaging, radiation protection, and nuclear medicine. Geant4 is continuously evolving, so it is crucial to have a system that benchmarks this Monte Carlo code for medical physics against reference data and to perform regression testing.

AIMS

To respond to these needs, we developed G4-Med, a benchmarking and regression testing system of Geant4 for medical physics.

MATERIALS AND METHODS

G4-Med currently includes 18 tests. They range from the benchmarking of fundamental physics quantities to the testing of Monte Carlo simulation setups typical of medical physics applications. Both electromagnetic and hadronic physics processes and models within the prebuilt Geant4 physics lists are tested. The tests included in G4-Med are executed on the CERN computing infrastructure via the use of the geant-val web application, developed at CERN for Geant4 testing. The physical observables can be compared to reference data for benchmarking and to results of previous Geant4 versions for regression testing purposes.

RESULTS

This paper describes the tests included in G4-Med and shows the results derived from the benchmarking of Geant4 10.5 against reference data.

DISCUSSION

Our results indicate that the Geant4 electromagnetic physics constructor G4EmStandardPhysics_option4 gives a good agreement with the reference data for all the tests. The QGSP_BIC_HP physics list provided an overall adequate description of the physics involved in hadron therapy, including proton and carbon ion therapy. New tests should be included in the next stage of the project to extend the benchmarking to other physical quantities and application scenarios of interest for medical physics.

CONCLUSION

The results presented and discussed in this paper will aid users in tailoring physics lists to their particular application.

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.

Impact of range uncertainty on clinical distributions of linear energy transfer and biological effectiveness in proton therapy

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.

Proton monoenergetic arc therapy (PMAT) to enhance LETd within the target

We show the performance and feasibility of a proton arc technique so-called proton monoenergetic arc therapy (PMAT). Monoenergetic partial arcs are selected to place spots at the middle of a target and its potential to enhance the dose-averaged linear energy transfer (LETd) distribution within the target. Single-energy partial arcs in a single 360 degree gantry rotation are selected to deposit Bragg's peaks at the central part of the target to increase LETd values. An in-house inverse planning optimizer seeks for homogeneous doses at the target while keeping the dose to organs at risk (OARs) within constraints. The optimization consists of balancing the weights of spots coming out of selected partial arcs. A simple case of a cylindrical target in a phantom is shown to illustrate the method. Three different brain cancer cases are then considered to produce actual clinical plans, compared to those clinically used with pencil beam scanning (PBS). The relative biological effectiveness (RBE) is calculated according to the microdosimetric kinetic model (MKM). For the ideal case of a cylindrical target placed in a cylindrical phantom, the mean LETd in the target increases from 2.8 keV μm^-1 to 4.0 keV μm^-1 when comparing a three-field PBS plan with PMAT. This is replicated for clinical plans, increasing the mean RBE-weighted doses to the CTV by 3.1%, 1.7% and 2.5%, respectively, assuming an [Formula: see text] ratio equal to 10 Gy in the CTV. In parallel, LETd to OARs near the distal edge of the tumor decrease for all cases and metrics (mean LETd, L_D,2% and L_D,98%). The PMAT technique increases the LETd within the target, being feasible for the production of clinical plans meeting physical dosimetric requirements for both target and OARs. Thus, PMAT increases the RBE within the target, which may lead to a widening of the therapeutic index in proton radiotherapy that would be highlighted for low [Formula: see text] ratios and hyperfractionated schedules.

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.

Linear energy transfer weighted beam orientation optimization for intensity-modulated proton therapy

PURPOSE

In intensity-modulated proton therapy (IMPT), unaccounted-for variation in biological effectiveness contributes to the discrepancy between the constant relative biological effectiveness (RBE) model prediction and experimental observation. It is desirable to incorporate biological doses in treatment planning to improve modeling accuracy and consequently achieve a higher therapeutic ratio. This study addresses this demand by developing a method to incorporate linear energy transfer (LET) into beam orientation optimization (BOO).

METHODS

Instead of RBE-weighted dose, this LET weighted BOO (LETwBOO) framework uses the dose and LET product (LET  ×  D) as the biological surrogate. The problem is formulated with a physical dose fidelity term, a LET  ×  D constraint term, and a group sparsity term. The LET  ×  D of organs at risks is penalized for minimizing the biological effect while maintaining the physical dose objectives. Group sparsity is used to reduce the number of active beams from 600-800 non-coplanar candidate beams to between 2 and 4. This LETwBOO method was tested on three skull base tumor (SBT) patients and three bilateral head-and-neck (H&N) patients. The LETwBOO plans were compared with IMPT plans using manually selected beams with only physical dose constraint (MAN) and the initial MAN plan reoptimized with additional LET  ×  D constraint (LETwMAN).

RESULTS

The LETwBOO plans show superior physical dose and LET  ×  D sparing. On average, the [mean, maximal] doses of organs at risks (OARs) in LETwBOO are reduced by [2.85, 4.6] GyRBE from the MAN plans in the SBT cases and reduced by [0.9, 2.5] GyRBE in the H&N cases, while LETwMAN is comparable to MAN. cLET × Ds of PTVs are comparable in LETwBOO and LETwMAN, where c is a scaling factor of 0.04 μm/keV. On average, in the SBT cases, LETwBOO reduces the OAR [mean, maximal] cLET × D by [1.1, 2.9] Gy from the MAN plans, compared to the reduction by LETwMAN from MAN of [0.7, 1.7] Gy. In the H&N cases, LETwBOO reduces the OAR [mean, maximal] cLET × D by [0.8, 2.6] Gy from the MAN plans, compared to the reduction by LETwMAN from MAN of [0.3, 1.2] Gy.

CONCLUSION

We developed a novel LET weighted BOO method for IMPT to generate plans with improved physical and biological OAR sparing compared with the plans unaccounted for biological effects from BOO.

On the concepts of dose-mean lineal energy, unrestricted and restricted dose-averaged LET in proton therapy

To calculate 3D distributions of microdosimetric-based restricted dose-averaged LET (LETd) and dose-mean lineal energy ([Formula: see text]) in order to explore their similarities and differences between each other and with the traditional unrestricted LETd. Additionally, a new expression for optimum restricted LETd calculation is derived, allowing for disregarding straggling-associated functions in the classical microdosimetric theory. Restricted LETd and [Formula: see text] for polyenergetic beams can be obtained by integrating previously developed energy-dependent microdosimetric functions over the energetic spectrum of these beams. This calculation is extended to the entire calculation volume using an algorithm to determine spectral fluence. Equivalently, unrestricted LETd can be obtained integrating the stopping power curve on the spectrum. A new expression to calculate restricted LETd is also derived. Results for traditional and new formulas are compared for a clinical 100 MeV proton beam. Distributions of unrestricted LETd, restricted LETd and [Formula: see text] are analyzed for a prostate case, for microscopic spherical sites of 1 µm and 10 µm in diameter. Traditional and new expressions for restricted LETd remarkably agree, being the mean differences 0.05  ±  0.04 keV µm^-1 for the 1 µm site and 0.05  ±  0.02 keV µm^-1 for the 10 µm site. In the prostate case, the ratio between the maximum and the central value for central axis (CAX) profiles is around 2 for all the quantities, being the highest for restricted LETd for 1 µm (2.17) and the lowest for [Formula: see text] for 1 µm (1.78). Unrestricted LETd, restricted LETd and [Formula: see text] can be analytically computed and compared for clinical plans. Two important consequences of the calculation of [Formula: see text] are: (1) its distribution can be verified by directly measuring it in clinical beams; and (2), optimization of proton treatments based on these quantities is enabled as well as future developments of RBE models based on them.

A kernel-based algorithm for the spectral fluence of clinical proton beams to calculate dose-averaged LET and other dosimetric quantities of interest

PURPOSE

To introduce a new analytical methodology to calculate quantities of interest in particle radiotherapy inside the treatment planning system. Models are proposed to calculate dose-averaged LET (LETd) in proton radiotherapy.

MATERIAL AND METHODS

A kernel-based approach for the spectral fluence of particles is developed by means of analytical functions depending on depth and lateral position. These functions are obtained by fitting them to data calculated with Monte Carlo (MC) simulations using Geant4 in liquid water for energies from 50 to 250 MeV. Contributions of primary, secondary protons and alpha particles are modeled separately. Lateral profiles and spectra are modeled as Gaussian functions to be convolved with the fluence coming from the nozzle. LETd is obtained by integrating the stopping power curves from the PSTAR and ASTAR databases weighted by the spectrum at each position. The fast MC code MCsquare is employed to benchmark the results.

RESULTS

Considering the nine energies simulated, fits for the functions modeling the fluence in-depth provide an average R 2 equal to 0.998, 0.995 and 0.986 for each one of the particles considered. Fits for the Gaussian lateral functions yield average R 2 of 0.997, 0.982 and 0.993, respectively. Similarly, the Gaussian functions fitted to the computed spectra lead to average R 2 of 0.995, 0.938 and 0.902. LETd calculation in water shows mean differences of -0.007 ± 0.008 keV/μm with respect to MCsquare if only protons are considered and 0.022 ± 0.007 keV/μm including alpha particles. In a prostate case, mean difference for all voxels with dose >5% of prescribed dose is 0.28 ± 0.23 keV/μm.

CONCLUSION

This new spectral fluence-based methodology allows for simultaneous calculations of quantities of interest in proton radiotherapy such as dose, LETd or microdosimetric quantities. The method also enables the inclusion of more particles by following an analogous process.

Dose- rather than fluence-averaged LET should be used as a single-parameter descriptor of proton beam quality for radiochromic film dosimetry

PURPOSE

The dose response of Gafchromic EBT3 films exposed to proton beams depends on the dose, and additionally on the beam quality, which is often quantified with the linear energy transfer (LET) and, hence, also referred to as LET quenching. Fundamentally different methods to determine correction factors for this LET quenching effect have been reported in literature and a new method using the local proton fluence distribution differential in LET is presented. This method was exploited to investigate whether a more practical correction based on the dose- or fluence-averaged LET is feasible in a variety of clinically possible beam arrangements.

METHODS

The relative effectiveness (RE) was characterized within a high LET spread-out Bragg peak (SOBP) in water made up by the six lowest available energies (62.4-67.5 MeV, configuration " b 1 ") resulting in one of the highest clinically feasible dose-averaged LET distributions. Additionally, two beams were measured where a low LET proton beam (252.7 MeV) was superimposed on " b 1 ", which contributed either 50% of the initial particle fluence or 50% of the dose in the SOBP, referred to as configuration " b 2 " and " b 3 ," respectively. The proton LET spectrum was simulated with GATE/Geant4 at all measurement positions. The net optical density change differential in LET was integrated over the local proton spectrum to calculate the net optical density and therefrom the beam quality correction factor. The LET dependence of the film response was accounted for by an LET dependence of one of the three parameters in the calibration function and was determined from inverse optimization using measurement " b 1 ." This method was then validated on the measurements of " b 2 " and " b 3 " and subsequently used to calculate the RE at 900 positions in nine clinically relevant beams. The extrapolated RE set was used to derive a simple linear correction function based on dose-averaged LET ( L d ) and verify the validity in all points of the comprehensive RE set.

RESULTS

The uncorrected film dose deviated up to 26% from the reference dose, whereas the corrected film dose agreed within 3% in all three beams in water (" b 1 ", " b 2 " and " b 3 "). The LET dependence of the calibration function started to strongly increase around 5 keV/μm and flatten out around 30 keV/μm. All REs calculated from the proton fluence in the nine simulated beams could be approximated with a linear function of dose-averaged LET (RE = 1.0258-0.0211 μm/keV L d ). However, no functional relationship of RE- and fluence-averaged LET could be found encompassing all beam energies and modulations.

CONCLUSIONS

The film quenching was found to be nonlinear as a function of proton LET as well as of the dose-averaged LET. However, the linear relation of RE on dose-averaged LET was a good approximation in all cases. In contrast to dose-averaged LET, fluence-averaged LET could not describe the RE when multiple beams were applied.

Exploring the advantages of intensity-modulated proton therapy: experimental validation of biological effects using two different beam intensity-modulation patterns

In current treatment plans of intensity-modulated proton therapy, high-energy beams are usually assigned larger weights than low-energy beams. Using this form of beam delivery strategy cannot effectively use the biological advantages of low-energy and high-linear energy transfer (LET) protons present within the Bragg peak. However, the planning optimizer can be adjusted to alter the intensity of each beamlet, thus maintaining an identical target dose while increasing the weights of low-energy beams to elevate the LET therein. The objective of this study was to experimentally validate the enhanced biological effects using a novel beam delivery strategy with elevated LET. We used Monte Carlo and optimization algorithms to generate two different intensity-modulation patterns, namely to form a downslope and a flat dose field in the target. We spatially mapped the biological effects using high-content automated assays by employing an upgraded biophysical system with improved accuracy and precision of collected data. In vitro results in cancer cells show that using two opposed downslope fields results in a more biologically effective dose, which may have the clinical potential to increase the therapeutic index of proton therapy.

Validation of linear energy transfer computed in a Monte Carlo dose engine of a commercial treatment planning system

The relative biological effectiveness (RBE) of protons is highly variable and difficult to quantify. However, RBE is related to the local ionization density, which can be related to the physical measurable dose weighted linear energy transfer (LET_D). The aim of this study was to validate the LET_D calculations for proton therapy beams implemented in a commercially available treatment planning system (TPS) using microdosimetry measurements and independent LET_D calculations (Open-MCsquare (MCS)). The TPS (RayStation v6R) was used to generate treatment plans on the CIRS-731-HN anthropomorphic phantom for three anatomical sites (brain, nasopharynx, neck) for a spherical target (Ø  =  5 cm) with uniform target dose to calculate the LET_D distribution. Measurements were performed at the University Medical Center Groningen proton therapy center (Proteus Plus, IBA) using a µ ⁺-probe utilizing silicon on insulator microdosimeters capable of detecting lineal energies as low as 0.15 keV µm^-1 in tissue. Dose averaged mean lineal energy [Formula: see text] depth-profiles were measured for 70 and 130 MeV spots in water and for the three treatment plans in water and an anthropomorphic phantom. The [Formula: see text] measurements were compared to the LET_D calculated in the TPS and MCS independent dose calculation engine. D · [Formula: see text] was compared to D · LET_D in terms of a gamma-index with a distance-to-agreement criteria of 2 mm and increasing dose difference criteria to determine the criteria for which a 90% pass rate was accomplished. Measurements of D · [Formula: see text] were in good agreement with the D · LET_D calculated in the TPS and MCS. The 90% passing rate threshold was reached at different D · LET_D difference criteria for single spots (TPS: 1% MCS: 1%), treatment plans in water (TPS: 3% MCS: 6%) and treatment plans in an anthropomorphic phantom (TPS: 6% MCS: 1%). We conclude that D · LET_D calculations accuracy in the RayStation TPS and open MCSquare are within 6%, and sufficient for clinical D · LET_D evaluation and optimization. These findings remove an important obstacle in the road towards clinical implementation of D · LET_D evaluation and optimization of proton therapy treatment plans. Novelty and significance The dose weighed linear energy transfer (LET_D) distribution can be calculated for proton therapy treatment plans by Monte Carlo dose engines. The relative biological effectiveness (RBE) of protons is known to vary with the LET_D distribution. Therefore, there exists a need for accurate calculation of clinical LET_D distributions. Previous LET_D validations have focused on general purpose Monte Carlo dose engines which are typically not used clinically. We present the first validation of mean lineal energy [Formula: see text] measurements of the LET_D against calculations by the Monte Carlo dose engines of the Raystation treatment planning system and open MCSquare.

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.

Benchmarking a GATE/Geant4 Monte Carlo model for proton beams in magnetic fields

Purpose

Magnetic resonance guidance in proton therapy (MRPT) is expected to improve its current performance. The combination of magnetic fields with clinical proton beam lines poses several challenges for dosimetry, treatment planning and dose delivery. Proton beams are deflected by magnetic fields causing considerable changes in beam trajectories and also a retraction of the Bragg peak positions. A proper prediction and compensation of these effects is essential to ensure accurate dose calculations. This work aims to develop and benchmark a Monte Carlo (MC) beam model for dose calculation of MRPT for static magnetic fields up to 1 T.

Methods

Proton beam interactions with magnetic fields were simulated using the GATE/Geant4 toolkit. The transport of charged particle in custom 3D magnetic field maps was implemented for the first time in GATE. Validation experiments were done using a horizontal proton pencil beam scanning system with energies between 62.4 and 252.7 MeV and a large gap dipole magnet (B = 0–1 T), positioned at the isocenter and creating magnetic fields transverse to the beam direction. Dose was measured with Gafchromic EBT3 films within a homogeneous PMMA phantom without and with bone and tissue equivalent material slab inserts. Linear energy transfer (LET) quenching of EBT3 films was corrected using a linear model on dose‐averaged LET method to ensure a realistic dosimetric comparison between simulations and experiments. Planar dose distributions were measured with the films in two different configurations: parallel and transverse to the beam direction using single energy fields and spread‐out Bragg peaks. The MC model was benchmarked against lateral deflections and spot sizes in air of single beams measured with a Lynx PT detector, as well as dose distributions using EBT3 films. Experimental and calculated dose distributions were compared to test the accuracy of the model.

Results

Measured proton beam deflections in air at distances of 465, 665, and 1155 mm behind the isocenter after passing the magnetic field region agreed with MC‐predicted values within 4 mm. Differences between calculated and measured beam full width at half maximum (FWHM) were lower than 2 mm. For the homogeneous phantom, measured and simulated in‐depth dose profiles showed range and average dose differences below 0.2 mm and 1.2%, respectively. Simulated central beam positions and widths differed <1 mm to the measurements with films. For both heterogenous phantoms, differences within 1 mm between measured and simulated central beam positions and widths were obtained, confirming a good agreement of the MC model.

Conclusions

A GATE/Geant4 beam model for protons interacting with magnetic fields up to 1 T was developed and benchmarked to experimental data. For the first time, the GATE/Geant4 model was successfully validated not only for single energy beams, but for SOBP, in homogeneous and heterogeneous phantoms. EBT3 film dosimetry demonstrated to be a powerful dosimetric tool, once the film response function is LET corrected, for measurements in‐line and transverse to the beam direction in magnetic fields. The proposed MC beam model is foreseen to support treatment planning and quality assurance (QA) activities toward MRPT.