An MCNPX Monte Carlo model of a discrete spot scanning proton beam therapy nozzle

Treatment planning of scanned proton beams in RayStation

The use of scanned proton beams in external beam radiation therapy has seen a rapid development over the past decade. This technique places new demands on treatment planning, as compared to conventional photon-based radiation therapy. In this article, several proton specific functions as implemented in the treatment planning system RayStation are presented. We will cover algorithms for energy layer and spot selection, basic optimization including the handling of spot weight limits, optimization of the linear energy transfer (LET) distribution, robust optimization including the special case of 4D optimization, proton arc planning, and automatic planning using deep learning. We will further present the Monte Carlo (MC) proton dose engine in RayStation to some detail, from the material interpretation of the CT data, through the beam model parameterization, to the actual MC transport mechanism. Useful tools for plan evaluation, including robustness evaluation, and the versatile scripting interface are also described. The overall aim of the paper is to give an overview of some of the key proton planning functions in RayStation, with example usages, and at the same time provide the details about the underlying algorithms that previously have not been fully publicly available.

Monte Carlo simulation-based patient-specific QA using machine log files for line-scanning proton radiation therapy

BACKGROUND

Quality assurance (QA) is a prerequisite for safe and accurate pencil-beam proton therapy. Conventional measurement-based patient-specific QA (pQA) can only verify limited aspects of patient treatment and is labor-intensive. Thus, a better method is needed to ensure the integrity of the treatment plan.

PURPOSE

Line scanning, which involves continuous and rapid delivery of pencil beams, is a state-of-the-art proton therapy technique. Machine performance in delivering scanning protons is dependent on the complexity of the beam modulations. Moreover, it contributes to patient treatment accuracy. A Monte Carlo (MC) simulation-based QA method that reflects the uncertainty related to the machine during scanning beam delivery was developed and verified for clinical applications to pQA.

METHODS

Herein, a tool for particle simulation (TOPAS) for nozzle modeling was used, and the code was commissioned against the measurements. To acquire the beam delivery uncertainty for each plan, patient plans were delivered. Furthermore, log files recorded every 60 μs by the monitors downstream of the nozzle were exported from the treatment control system. The spot positions and monitor unit (MU) counts in the log files were converted to dipole magnet strengths and number of particles, respectively, and entered into the TOPAS. For the 68 clinical cases, MC simulations were performed in a solid water phantom, and two-dimensional (2D) absolute dose distributions at 20-mm depth were measured using an ionization chamber array (Octavius 1500, PTW, Freiburg, Germany). Consequently, the MC-simulated 2D dose distributions were compared with the measured data, and the dose distributions in the pre-treatment QA plan created with RayStation (RaySearch Laboratories, Stockholm, Sweden). Absolute dose comparisons were made using gamma analysis with 3%/3 mm and 2%/2 mm criteria for 47 clinical cases without considering daily machine output variation in the MC simulation and 21 cases with daily output variation, respectively. All cases were analyzed with 90% or 95% of passing rate thresholds.

RESULTS

For 47 clinical cases not considering daily output variations, the absolute gamma passing rates compared with the pre-treatment QA plan were 99.71% and 96.97%, and the standard deviations (SD) were 0.70% and 3.78% with the 3%/3 mm or 2%/2 mm criteria, respectively. Compared with the measurements, the passing rate of 2%/2 mm gamma criterion was 96.76% with 3.99% of SD. For the 21 clinical cases compared with pre-treatment QA plan data and measurements considering daily output variations, the 2%/2 mm absolute gamma analysis result was 98.52% with 1.43% of SD and 97.67% with 2.72% of SD, respectively. With a 95% passing rate threshold of 2%/2 mm criterion, the false-positive and false-negative were 21.8% and 8.3% for without and with considering output variation, respectively. With a 90% threshold, the false-positive and false-negative reduced to 11.4% and 0% for without and with considering output variation, respectively.

CONCLUSIONS

A log-file-based MC simulation method for patient QA of line-scanning proton therapy was successfully developed. The proposed method exhibited clinically acceptable accuracy, thereby exhibiting a potential to replace the measurement-based dosimetry QA method with a 90% gamma passing rate threshold when applying the 2%/2 mm criterion.

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.

A framework for voxel-based assessment of biological effect after proton radiotherapy in pediatric brain cancer patients using multi-modal imaging

INTRODUCTION

The exact dependence of biological effect on dose and linear energy transfer (LET) in human tissue when delivering proton therapy is unknown. In this study, we propose a framework for measuring this dependency using multi-modal image-based assays with deformable registrations within imaging sessions and across time.

MATERIALS AND METHODS

3T MRI scans were prospectively collected from 6 pediatric brain cancer patients before they underwent proton therapy treatment, and every 3 months for a year after treatment. Scans included T1-weighted with contrast enhancement (T1), T2-FLAIR (T2) and fractional anisotropy (FA) images. In addition, the planning CT, dose distributions and Monte Carlo-calculated LET distributions were collected. A multi-modal deformable image registration framework was used to create a dataset of dose, LET and imaging intensities at baseline and follow-up on a voxel-by-voxel basis. We modelled the biological effect of dose and LET from proton therapy using imaging changes over time as a surrogate for biological effect. We investigated various models to show the feasibility of the framework to model imaging changes. To account for interpatient and intrapatient variations, we used a nested generalized linear mixed regression model. The models were applied to predict imaging changes over time as a function of dose and LET for each modality.

RESULTS

Using the nested models to predict imaging changes, we saw a decrease in the FA signal as a function of dose; however, the signal increased with increasing LET. Similarly, we saw an increase in T2 signal as a function of dose, but a decrease in signal with LET. We saw no changes in T1 voxel values as a function of either dose or LET.

CONCLUSIONS

The imaging changes could successfully model biological effect as a function of dose and LET using our proposed framework. Due to the low number of patients, the imaging changes observed for FA and T2 scans were not marked enough to draw any firm conclusions.

Monte Carlo framework for commissioning a synchrotron-based discrete spot scanning proton beam system and treatment plan verification

This study aimed to develop a Monte Carlo (MC) framework for commissioning the narrow proton beams (spot size sigma, 5.2 mm 2 mm at isocenter for 69.4 MeV-221.3 MeV for the main beam option and 4.1 mm 1.3 mm for the minibeam option respectively) of a synchrotron-based proton therapy system and design an independent absolute dose calculation engine for intensity-modulated proton treatments. A proton therapy system (Hitachi PROBEAT-V) was simulated using divergent and convergent beam models at the nozzle entrance. The innovative source weighting scheme for the MC simulation with TOPAS (TOol for PArticle Simulations) was implemented using dose output data for the absolute dose calculations. The results of the MC simulation were compared to the experimental data, analyzed and used to commission the treatment planning system. Two MC models, divergent and convergent beams were implemented. The convergent beam model produced a high level of agreement when MC and measurements were analyzed. The beam ellipticity did not result in significant differences between MC simulated and treatment planning system calculated doses. A model of a synchrotron-based spot scanning proton therapy system has been developed and implemented in the TOPAS MC transport code framework. The dose computation engine is useful for treatment plan verification with primary and minibeam beam option.

Experimental and Monte Carlo characterization of a dynamic collimation system prototype for pencil beam scanning proton therapy

PURPOSE

There has been a growing interest in the development of energy-specific collimators for low-energy pencil beam scanning (PBS) to reduce the lateral penumbra. One particular device that has been the focus of several recent published works is the dynamic collimation system (DCS), which provides energy-specific collimation by intercepting the scanned proton beam as it nears to target edge with a set of orthogonal trimmer blades. While several computational studies have shown that this dynamic collimator can provide additional healthy tissue sparing, there has not been any rigorous experimental work to benchmark the theoretical models used in these initial studies. Therefore, it was the purpose of this work to demonstrate an experimental method that could integrate an experimental prototype with a clinical PBS system and benchmark the Monte Carlo methods that have been used to model the DCS.

METHODS

An experimental DCS prototype was designed and built in house to actively collimate individual proton beamlets during PBS within a well-characterized experimental setup. Monte Carlo methods were initially used to assess construction tolerances and later benchmarked against measurements, including integral depth dose and lateral asymmetric beamlet profiles. The experimental apparatus and measurement geometry were modeled using MCNP6 benchmarked from measurements performed at the Northwestern Chicago Proton Center.

RESULTS

Gamma analysis tests were used to evaluate the agreement between the measured and simulated profiles with a strict 1 mm/1% criteria and 5% dose threshold. Excellent agreement was observed between the simulated and measured profiles, which included 1 mm/1% gamma analysis pass rates of at least 100% and 95% for the integral depth dose (IDD) profiles and lateral profiles, respectively. Differences in the relative profile shape were observed experimentally between beamlets collimated on- and off-axis, which was attributed to the partial transmission of the beam through an unfocused collimator. Exposure rates resulting from the activation of the device were monitored with survey meter measurements and were found to agree with Monte Carlo estimates of the exposure rate to within 20%.

CONCLUSION

A DCS prototype was constructed and integrated into a clinical dose delivery system. While the results of this work are not exhaustive, they demonstrate the effects of beam source divergence, device activation, and beamlet deflection during scanning, which were found to be successfully modeled using Monte Carlo methods and experimentally benchmarked. Excellent agreement was achieved between the simulated and measured lateral spot profiles of collimated beamlets delivered on- and off-axis in PBS. The Monte Carlo models adequately predicted the measured elevated plateau region in the integral depth-dose profiles from the low-energy scatter off the collimators.

Clinical commissioning of intensity-modulated proton therapy systems: Report of AAPM Task Group 185

Proton therapy is an expanding radiotherapy modality in the United States and worldwide. With the number of proton therapy centers treating patients increasing, so does the need for consistent, high-quality clinical commissioning practices. Clinical commissioning encompasses the entire proton therapy system's multiple components, including the treatment delivery system, the patient positioning system, and the image-guided radiotherapy components. Also included in the commissioning process are the x-ray computed tomography scanner calibration for proton stopping power, the radiotherapy treatment planning system, and corresponding portions of the treatment management system. This commissioning report focuses exclusively on intensity-modulated scanning systems, presenting details of how to perform the commissioning of the proton therapy and ancillary systems, including the required proton beam measurements, treatment planning system dose modeling, and the equipment needed.

Automated Monte-Carlo re-calculation of proton therapy plans using Geant4/Gate: implementation and comparison to plan-specific quality assurance measurements

OBJECTIVES

Software re-calculation of proton pencil beam scanning plans provides a method of verifying treatment planning system (TPS) dose calculations prior to patient treatment. This study describes the implementation of AutoMC, a Geant4 v10.3.3/Gate v8.1 (Gate-RTion v1.0)-based Monte-Carlo (MC) system for automated plan re-calculation, and presents verification results for 153 patients (730 fields) planned within year one of the proton service at The Christie NHS Foundation Trust.

METHODS

A MC beam model for a Varian ProBeam delivery system with four range-shifter options (none, 2 cm, 3 cm, 5 cm) was derived from beam commissioning data and implemented in AutoMC. MC and TPS (Varian Eclipse v13.7) calculations of 730 fields in solid-water were compared to physical plan-specific quality assurance (PSQA) measurements acquired using a PTW Octavius 1500XDR array and PTW 31021 Semiflex 3D ion chamber.

RESULTS

TPS and MC showed good agreement with array measurements, evaluated using γ analyses at 3%, 3 mm with a 10% lower dose threshold:>94% of fields calculated by the TPS and >99% of fields calculated by MC had γ ≤ 1 for>95% of measurement points within the plane. TPS and MC also showed good agreement with chamber measurements of absolute dose, with systematic differences of <1.5% for all range-shifter options.

CONCLUSIONS

Reliable independent verification of the TPS dose calculation is a valuable complement to physical PSQA and may facilitate reduction of the physical PSQA workload alongside a thorough delivery system quality assurance programme.

ADVANCES IN KNOWLEDGE

A Gate/Geant4-based MC system is thoroughly validated against an extensive physical PSQA dataset for 730 clinical fields, showing that clinical implementation of MC for PSQA is feasible.

Development of a Monte Carlo beam model for raster scanning proton beams and dosimetric comparison

PURPOSE

To develop a Monte Carlo (MC) beam model for raster scanning proton beams for dose verification purposes.

METHODS AND MATERIALS

MC program FLUKA was used in the model. The nominal energy, momentum spread and beam angular distribution in the model were determined by matching the simulation profiles with the measured integral depth dose (IDD) and in air spot size. Dosimetric comparison was done by comparing the measured and simulated dose distributions. The 1 D dose profile of cubic Spread Out Bragg Peak (SOBP) plans, and the 2 D dose distribution of previously treated breast cancer patients' clinical plans were measured by using Pinpoint chambers and 2 D array ionization chambers, respectively. Corresponding DICOM plan information was utilized for MC simulation.

RESULTS

The MC results showed good agreement with measurements for the SOBP plans. The absolute comparison of the absorbed dose difference between the MC and the measurement was 0.93%±0.88%. For the patient plans, the overall passing rate of the gamma index analysis (γ-PR) between the MC simulation and measurement with the 2%-2 mm criteria was 97.78%, and only 1 case had a γ-PR less than 90%. With the 3%-3 mm criteria, γ-PR was never below 99% for all cases with and without the range shifter.

CONCLUSIONS

This work described a method for adapting a MC simulation model for a raster scanning proton beam. The good concordance between the simulations and measurements shows that the MC model is an accurate and reliable method. It has the potential to be used for patient specific quality assurance (PSQA) to reduce the beam time for the measurements in water.

Ionization quenching correction for a 3D scintillator detector exposed to scanning proton beams

The ionization quenching phenomenon in scintillators must be corrected to obtain accurate dosimetry in particle therapy. The purpose of this study was to develop a methodology for correcting camera projection measurements of a 3D scintillator detector exposed to proton pencil beams. Birks' ionization quenching model and the energy deposition by secondary electrons (EDSE) model were used to correct the light captured by a prototype 3D scintillator detector. The detector was made of a 20 cm × 20 cm × 20 cm tank filled with liquid scintillator, and three cameras. The detector was exposed to four proton-beam energies (84.6, 100.9, 144.9, and 161.6 MeV) at The University of Texas MD Anderson Cancer Center's Proton Therapy Center. The dose and track averaged linear energy transfer (LET) were obtained using validated Monte Carlo (MC) simulations. The corrected light output was compared to the dose calculated by the MC simulation. Optical artefact corrections were used to correct for refraction at the air-scintillator interface, and image perspective. These corrections did not account for the non-orthogonal integration of data off the central axis of the image. Therefore, we compared the light output to an integrated MC dose and LET along the non-orthogonal path. After accounting for the non-orthogonal integration of the data, the corrected light output reduced the dose error at the Bragg peak region from 15% to 3% for low proton-beam energies. Overall, the doses at the Bragg peak region using the Birks' model and EDSE model were less than ±3% and ±7% of the MC dose, respectively. We have improved the application of Birks' model quenching corrections in 3D scintillators by numerically projecting the dose and LET 3D grid to camera projections. This study shows that scintillator projections can be corrected using average LET values at the central axes.

A DNA damage multiscale model for NTCP in proton and hadron therapy

PURPOSE

To develop a first principle and multiscale model for normal tissue complication probability (NTCP) as a function of dose and LET for proton and in general for particle therapy with a goal of incorporating nanoscale radio-chemical to macroscale cell biological pathways, spanning from initial DNA damage to tissue late effects.

METHODS

The method is a combination of analytical and multiscale computational steps including (a) derivation of functional dependencies of NTCP on DNA-driven cell lethality in nanometer and mapping to dose and LET in millimeter, and (b) three-dimensional-surface fitting to Monte Carlo data set generated based on postradiation image change and gathered for a cohort of 14 pediatric patients treated by scanning beam of protons for ependymoma. We categorize voxel-based dose and LET associated with development of necrosis in NTCP.

RESULT

Our model fits well the clinical data, generated for postradiation tissue toxicity and necrosis. The fitting procedure results in extraction of in vivo radio-biological α-β indices and their numerical values.

DISCUSSION AND CONCLUSION

The NTCP model, explored in this work, allows to correlate the tissue toxicities to DNA initial damage, cell lethality and the properties and qualities of radiation, dose, and LET.

Validation and clinical implementation of an accurate Monte Carlo code for pencil beam scanning proton therapy

Monte Carlo (MC)‐based dose calculations are generally superior to analytical dose calculations (ADC) in modeling the dose distribution for proton pencil beam scanning (PBS) treatments. The purpose of this paper is to present a methodology for commissioning and validating an accurate MC code for PBS utilizing a parameterized source model, including an implementation of a range shifter, that can independently check the ADC in commercial treatment planning system (TPS) and fast Monte Carlo dose calculation in opensource platform (MCsquare). The source model parameters (including beam size, angular divergence and energy spread) and protons per MU were extracted and tuned at the nozzle exit by comparing Tool for Particle Simulation (TOPAS) simulations with a series of commissioning measurements using scintillation screen/CCD camera detector and ionization chambers. The range shifter was simulated as an independent object with geometric and material information. The MC calculation platform was validated through comprehensive measurements of single spots, field size factors (FSF) and three‐dimensional dose distributions of spread‐out Bragg peaks (SOBPs), both without and with the range shifter. Differences in field size factors and absolute output at various depths of SOBPs between measurement and simulation were within 2.2%, with and without a range shifter, indicating an accurate source model. TOPAS was also validated against anthropomorphic lung phantom measurements. Comparison of dose distributions and DVHs for representative liver and lung cases between independent MC and analytical dose calculations from a commercial TPS further highlights the limitations of the ADC in situations of highly heterogeneous geometries. The fast MC platform has been implemented within our clinical practice to provide additional independent dose validation/QA of the commercial ADC for patient plans. Using the independent MC, we can more efficiently commission ADC by reducing the amount of measured data required for low dose “halo” modeling, especially when a range shifter is employed.

Theoretical analysis of angular distribution of scattering in nozzle components using a response-function method for proton spot-scanning therapy

In spot-scanning proton therapy, highly precise beam control is required in the treatment nozzle such that the proton beam does not spread out during transportation by restraining the divergence of the beam angle and spot size, simultaneously. In order to evaluate the beam-broadening behaviour induced by passing through the various nozzle components, we have developed a new method to calculate the angular divergence profile of a proton beam in the nozzle. The angular divergence of the proton beam for each nozzle component is calculated by the Monte Carlo simulation code, Geant4, assuming that the initial beam has no divergence. The angular divergence profiles generated in the various nozzle components are then fitted by the analytic function formula with triple Gaussian distributions. The fitted profiles can be treated like analytic response functions and the angular divergence profile in the nozzle can be easily and systematically calculated by using a convolution theorem. The beam-broadening behaviour during transportation in the nozzle is carefully evaluated. The beam profiles are well-characterized by the proposed angular divergence analysis, i.e. triple Gaussian profile analysis. The primary Gaussian part of the beam profile is mainly generated by air and dose monitors with plate electrode components. The secondary and tertiary Gaussian parts are so-called wide-angle scattering and generated mainly by spot-position and profile monitors with metal window and wire components. The scattering of the nozzle component can be analysed using the proposed response function method for the angular distribution. Multiple convolved angular scattering can be determined from the response function of the individual nozzle components. The angular distribution from small to large angle regions can then be quantitatively evaluated by the proposed method. The method is quite simple and generalized, and is a straightforward way to understand the nozzle and component characteristics related to the beam-broadening behaviour.

A simplified Monte Carlo algorithm considering large-angle scattering for fast and accurate calculation of proton dose

PURPOSE

The purpose of this study is to improve dose calculation accuracy of the simplified Monte Carlo (SMC) algorithm in the low-dose region. Because conventional SMC algorithms calculate particle scattering in consideration of multiple Coulomb scattering (MCS) only, they approximate lateral dose profiles by a single Gaussian function. However, it is well known that the low-dose region spreads away from the beam axis, and it has been pointed out that modeling of the low-dose region is important to calculated dose accurately.

METHODS

A SMC algorithm, which is named modified SMC and considers not only MCS but also large angle scattering resembling hadron elastic scattering, was developed. In the modified SMC algorithm, the particle fluence varies in the longitudinal direction because the large-angle scattering decreases residual range of particles in accordance with their scattering angle and tracking of the particles with large scattering angle is terminated at a short distance downstream from the scattering. Therefore, modified integrated depth dose (m-IDD) tables, which are converted from measured IDD in consideration of the fluence loss, are used to calculate dose.

RESULTS

In the case of a 1-liter cubic target, the calculation accuracy was improved in comparison with that of a conventional algorithm, and the modified algorithm results agreed well with Geant4-based simulation results; namely, 98.8% of the points satisfied the 2% dose/2 mm distance-to-agreement (DTA) criterion. The calculation time of the modified SMC algorithm was 1972 s in the case of 4.4 × 10⁸ particles and 16-threading operation of an Intel Xeon E5-2643 (3.3-GHz clock).

CONCLUSIONS

An SMC algorithm that can reproduce a laterally widespread low-dose region was developed. According to the comparison with a Geant4-based simulation, it was concluded that the modified SMC algorithm is useful for calculating dose of proton radiotherapy.

Use of a radial projection to reduce the statistical uncertainty of spot lateral profiles generated by Monte Carlo simulation

Monte Carlo (MC) simulation has been used to generate commissioning data for the beam modeling of treatment planning system (TPS). We have developed a method called radial projection (RP) for postprocessing of MC-simulation-generated data. We used the RP method to reduce the statistical uncertainty of the lateral profile of proton pencil beams with axial symmetry. The RP method takes advantage of the axial symmetry of dose distribution to use the mean value of multiple independent scores as the representative score. Using the mean as the representative value rather than any individual score results in substantial reduction in statistical uncertainty. Herein, we present the concept and step-by-step implementation of the RP method, as well as show the advantage of the RP method over conventional measurement methods for generating lateral profile. Lateral profiles generated by both methods were compared to demonstrate the uncertainty reduction qualitatively, and standard error comparison was performed to demonstrate the reduction quantitatively. The comparisons showed that statistical uncertainty was reduced substantially by the RP method. Using the RP method to postprocess MC data, the corresponding MC simulation time was reduced by a factor of 10 without quality reduction in the generated result from the MC data. We concluded that the RP method is an effective technique to increase MC simulation efficiency for generating lateral profiles for axially symmetric pencil beams.

A benchmarking method to evaluate the accuracy of a commercial proton monte carlo pencil beam scanning treatment planning system

AcurosPT is a Monte Carlo algorithm in the Eclipse 13.7 treatment planning system, which is designed to provide rapid and accurate dose calculations for proton therapy. Computational run-time in minimized by simplifying or eliminating less significant physics processes. In this article, the accuracy of AcurosPT was benchmarked against both measurement and an independent MC calculation, TOPAS. Such a method can be applied to any new MC calculation for the detection of potential inaccuracies. To validate multiple Coulomb scattering (MCS) which affects primary beam broadening, single spot profiles in a Solidwater^® phantom were compared for beams of five selected proton energies between AcurosPT, measurement and TOPAS. The spot Gaussian sigma in AcurosPT was found to increase faster with depth than both measurement and TOPAS, suggesting that the MCS algorithm in AcurosPT overestimates the scattering effect. To validate AcurosPT modeling of the halo component beyond primary beam broadening, field size factors (FSF) were compared for multi-spot profiles measured in a water phantom. The FSF for small field sizes were found to disagree with measurement, with the disagreement increasing with depth. Conversely, TOPAS simulations of the same FSF consistently agreed with measurement to within 1.5%. The disagreement in absolute dose between AcurosPT and measurement was smaller than 2% at the mid-range depth of multi-energy beams. While AcurosPT calculates acceptable dose distributions for typical clinical beams, users are cautioned of potentially larger errors at distal depths due to overestimated MCS and halo implementation.

Evaluation of the influence of double and triple Gaussian proton kernel models on accuracy of dose calculations for spot scanning technique

PURPOSE

The main purpose in this study was to present the results of beam modeling and how the authors systematically investigated the influence of double and triple Gaussian proton kernel models on the accuracy of dose calculations for spot scanning technique.

METHODS

The accuracy of calculations was important for treatment planning software (TPS) because the energy, spot position, and absolute dose had to be determined by TPS for the spot scanning technique. The dose distribution was calculated by convolving in-air fluence with the dose kernel. The dose kernel was the in-water 3D dose distribution of an infinitesimal pencil beam and consisted of an integral depth dose (IDD) and a lateral distribution. Accurate modeling of the low-dose region was important for spot scanning technique because the dose distribution was formed by cumulating hundreds or thousands of delivered beams. The authors employed a double Gaussian function as the in-air fluence model of an individual beam. Double and triple Gaussian kernel models were also prepared for comparison. The parameters of the kernel lateral model were derived by fitting a simulated in-water lateral dose profile induced by an infinitesimal proton beam, whose emittance was zero, at various depths using Monte Carlo (MC) simulation. The fitted parameters were interpolated as a function of depth in water and stored as a separate look-up table. These stored parameters for each energy and depth in water were acquired from the look-up table when incorporating them into the TPS. The modeling process for the in-air fluence and IDD was based on the method proposed in the literature. These were derived using MC simulation and measured data. The authors compared the measured and calculated absolute doses at the center of the spread-out Bragg peak (SOBP) under various volumetric irradiation conditions to systematically investigate the influence of the two types of kernel models on the dose calculations.

RESULTS

The authors investigated the difference between double and triple Gaussian kernel models. The authors found that the difference between the two studied kernel models appeared at mid-depths and the accuracy of predicting the double Gaussian model deteriorated at the low-dose bump that appeared at mid-depths. When the authors employed the double Gaussian kernel model, the accuracy of calculations for the absolute dose at the center of the SOBP varied with irradiation conditions and the maximum difference was 3.4%. In contrast, the results obtained from calculations with the triple Gaussian kernel model indicated good agreement with the measurements within ±1.1%, regardless of the irradiation conditions.

CONCLUSIONS

The difference between the results obtained with the two types of studied kernel models was distinct in the high energy region. The accuracy of calculations with the double Gaussian kernel model varied with the field size and SOBP width because the accuracy of prediction with the double Gaussian model was insufficient at the low-dose bump. The evaluation was only qualitative under limited volumetric irradiation conditions. Further accumulation of measured data would be needed to quantitatively comprehend what influence the double and triple Gaussian kernel models had on the accuracy of dose calculations.

Clinical evidence of variable proton biological effectiveness in pediatric patients treated for ependymoma

BACKGROUND AND PURPOSE

A constant relative biological effectiveness (RBE) is used for clinical proton therapy; however, experimental evidence indicates that RBE can vary. We analyzed pediatric ependymoma patients who received proton therapy to determine if areas of normal tissue damage indicated by post-treatment image changes were associated with increased biological dose effectiveness.

MATERIAL AND METHODS

Fourteen of 34 children showed T2-FLAIR hyperintensity on post-treatment magnetic resonance (MR) images. We delineated regions of treatment-related change and calculated dose and linear energy transfer (LET) distributions with Monte Carlo. Voxel-level image change data were fit to a generalized linear model incorporating dose and LET. Cross-validation was used to determine model parameters and for receiver operating characteristic curve analysis. Tolerance dose (TD50; dose at which 50% of patients would experience toxicity) was interpolated from the model.

RESULTS

Image changes showed dependence on increasing LET and dose. TD50 decreased with increasing LET, indicating an increase in biological dose effectiveness. The cross-validated area under the curve for the model was 0.91 (95% confidence interval 0.88-0.94).

CONCLUSIONS

Our correlation of changes on MR images after proton therapy with increased LET constitutes the first clinical evidence of variable proton biological effectiveness.

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.

Fast range measurement of spot scanning proton beams using a volumetric liquid scintillator detector

Accurate confirmation and verification of the range of spot scanning proton beams is crucial for correct dose delivery. Current methods to measure proton beam range using ionization chambers are either time-consuming or result in measurements with poor spatial resolution. The large-volume liquid scintillator detector allows real-time measurements of the entire dose profile of a spot scanning proton beam. Thus, liquid scintillator detectors are an ideal tool for measuring the proton beam range for commissioning and quality assurance. However, optical artefacts may decrease the accuracy of measuring the proton beam range within the scintillator tank. The purpose of the current study was to 1) develop a geometric calibration system to accurately calculate physical distances within the liquid scintillator detector, taking into account optical artefacts; and 2) assess the accuracy, consistency, and robustness of proton beam range measurement using the liquid scintillator detector with our geometric calibration system. The range of the proton beam was measured with the calibrated liquid scintillator system and was compared to the nominal range. Measurements were made on three different days to evaluate the setup robustness from day to day, and three sets of measurements were made for each day to evaluate the consistency from delivery to delivery. All proton beam ranges measured using the liquid scintillator system were within half a millimeter of the nominal range. The delivery-to-delivery standard deviation of the range measurement was 0.04 mm, and the day-to-day standard deviation was 0.10 mm. In addition to the accuracy and robustness demonstrated by these results when our geometric calibration system was used, the liquid scintillator system allowed the range of all 94 proton beams to be measured in just two deliveries, making the liquid scintillator detector a perfect tool for range measurement of spot scanning proton beams.

Evaluation of detectors for acquisition of pristine depth-dose curves in pencil beam scanning

Acquisition of quasi‐monoenergetic ("pristine") depth‐dose curves is an essential task in the frame of commissioning and quality assurance of a proton therapy treatment head. For pencil beam scanning delivery modes this is often accomplished by measuring the integral ionization in a plane perpendicular to the axis of an unscanned beam. We focus on the evaluation of three integral detectors: two of them are plane‐parallel ionization chambers with an effective radius of 4.1 cm and 6.0 cm, respectively, mounted in a scanning water phantom. The third integral detector is a 6.0 cm radius multilayer ionization chamber. The experimental results are compared with the corresponding measurements under broad field conditions, which are performed with a small radius plane‐parallel chamber and a small radius multilayer ionization chamber. We study how a measured depth‐dose curve of a pristine proton field depends on the detection device, by evaluating the shape of the depth‐dose curve, the relative charge collection efficiency, and intercomparing measured ranges. Our results show that increasing the radius of an integral chamber from 4.1 cm to 6.0 cm increases the collection efficiency by 0%–3.5% depending on beam energy and depth. Ranges can be determined by the large electrode multilayer ionization chamber with a typical uncertainty of 0.4 mm on a routine basis. The large electrode multilayer ionization chamber exhibits a small distortion in the Bragg Peak region. This prohibits its use for acquisition of base data, but is tolerable for quality assurance. The good range accuracy and the peak distortion are characteristics of the multilayer ionization chamber design, as shown by the direct comparison with the small electrode counterpart.

PACS number: 87.55.Qr

Improved efficiency in Monte Carlo simulation for passive-scattering proton therapy

The aim of this work was to improve the computational efficiency of Monte Carlo simulations when tracking protons through a proton therapy treatment head. Two proton therapy facilities were considered, the Francis H Burr Proton Therapy Center (FHBPTC) at the Massachusetts General Hospital and the Crocker Lab eye treatment facility used by University of California at San Francisco (UCSFETF). The computational efficiency was evaluated for phase space files scored at the exit of the treatment head to determine optimal parameters to improve efficiency while maintaining accuracy in the dose calculation. For FHBPTC, particles were split by a factor of 8 upstream of the second scatterer and upstream of the aperture. The radius of the region for Russian roulette was set to 2.5 or 1.5 times the radius of the aperture and a secondary particle production cut (PC) of 50 mm was applied. For UCSFETF, particles were split a factor of 16 upstream of a water absorber column and upstream of the aperture. Here, the radius of the region for Russian roulette was set to 4 times the radius of the aperture and a PC of 0.05 mm was applied. In both setups, the cylindrical symmetry of the proton beam was exploited to position the split particles randomly spaced around the beam axis. When simulating a phase space for subsequent water phantom simulations, efficiency gains between a factor of 19.9  ±  0.1 and 52.21  ±  0.04 for the FHTPC setups and 57.3  ±  0.5 for the UCSFETF setups were obtained. For a phase space used as input for simulations in a patient geometry, the gain was a factor of 78.6  ±  7.5. Lateral-dose curves in water were within the accepted clinical tolerance of 2%, with statistical uncertainties of 0.5% for the two facilities. For the patient geometry and by considering the 2% and 2mm criteria, 98.4% of the voxels showed a gamma index lower than unity. An analysis of the dose distribution resulted in systematic deviations below of 0.88% for 20% of the voxels with dose of 20% of the maximum or more.

The physics of proton therapy

The physics of proton therapy has advanced considerably since it was proposed in 1946. Today analytical equations and numerical simulation methods are available to predict and characterize many aspects of proton therapy. This article reviews the basic aspects of the physics of proton therapy, including proton interaction mechanisms, proton transport calculations, the determination of dose from therapeutic and stray radiations, and shielding design. The article discusses underlying processes as well as selected practical experimental and theoretical methods. We conclude by briefly speculating on possible future areas of research of relevance to the physics of proton therapy.

Experimentally validated pencil beam scanning source model in TOPAS

The presence of a low-dose envelope, or 'halo', in the fluence profile of a proton spot can increase the output of a pencil beam scanning field by over 10%. This study evaluated whether the Monte Carlo simulation code, TOPAS 1.0-beta 8, based on Geant4.9.6 with its default physics list, can predict the spot halo at depth in phantom by incorporating a halo model within the proton source distribution. Proton sources were modelled using three 2D Gaussian functions, and optimized until simulated spot profiles matched measurements at the phantom surface out to a radius of 100 mm. Simulations were subsequently compared with profiles measured using EBT3 film in Solidwater® phantoms at various depths for 100, 115, 150, 180, 210 and 225 MeV proton beams. Simulations predict measured profiles within a 1 mm distance to agreement for 2D profiles extending to the 0.1% isodose, and within 1 mm/1% Gamma criteria over the integrated curve of spot profile as a function of radius. For isodose lines beyond 0.1% of the central spot dose, the simulated primary spot sigma is smaller than the measurement by up to 15%, and can differ by over 1 mm. The choice of particle interaction algorithm and phantom material were found to cause ~1 mm range uncertainty, a maximal 5% (0.3 mm) difference in spot sigma, and maximal 1 mm and ~2 mm distance to agreement in isodoses above and below the 0.1% level, respectively. Based on these observations, therefore, the selection of physics model and the application of Solidwater® as water replacement material in simulation and measurement should be used with caution.

3D reconstruction of scintillation light emission from proton pencil beams using limited viewing angles-a simulation study

An accurate and high-resolution quality assurance (QA) method for proton radiotherapy beams is necessary to ensure correct dose delivery to the target. Detectors based on a large volume of liquid scintillator have shown great promise in providing fast and high-resolution measurements of proton treatment fields. However, previous work with these detectors has been limited to two-dimensional measurements, and the quantitative measurement of dose distributions was lacking. The purpose of the current study is to assess the feasibility of reconstructing three-dimensional (3D) scintillation light distributions of spot scanning proton beams using a scintillation system. The proposed system consists of a tank of liquid scintillator imaged by charge-coupled device cameras at three orthogonal viewing angles. Because of the limited number of viewing angles, we developed a profile-based technique to obtain an initial estimate that can improve the quality of the 3D reconstruction. We found that our proposed scintillator system and profile-based technique can reconstruct a single energy proton beam in 3D with a gamma passing rate (3%/3 mm local) of 100.0%. For a single energy layer of an intensity modulated proton therapy prostate treatment plan, the proposed method can reconstruct the 3D light distribution with a gamma pass rate (3%/3 mm local) of 99.7%. In addition, we also found that the proposed method is effective in detecting errors in the treatment plan, indicating that it can be a very useful tool for 3D proton beam QA.

Optical artefact characterization and correction in volumetric scintillation dosimetry

The goals of this study were (1) to characterize the optical artefacts affecting measurement accuracy in a volumetric liquid scintillator detector, and (2) to develop methods to correct for these artefacts. The optical artefacts addressed were photon scattering, refraction, camera perspective, vignetting, lens distortion, the lens point spread function, stray radiation, and noise in the camera. These artefacts were evaluated by theoretical and experimental means, and specific correction strategies were developed for each artefact. The effectiveness of the correction methods was evaluated by comparing raw and corrected images of the scintillation light from proton pencil beams against validated Monte Carlo calculations. Blurring due to the lens and refraction at the scintillator tank-air interface were found to have the largest effect on the measured light distribution, and lens aberrations and vignetting were important primarily at the image edges. Photon scatter in the scintillator was not found to be a significant source of artefacts. The correction methods effectively mitigated the artefacts, increasing the average gamma analysis pass rate from 66% to 98% for gamma criteria of 2% dose difference and 2 mm distance to agreement. We conclude that optical artefacts cause clinically meaningful errors in the measured light distribution, and we have demonstrated effective strategies for correcting these optical artefacts.

Geometrical splitting technique to improve the computational efficiency in Monte Carlo calculations for proton therapy

PURPOSE

To present the implementation and validation of a geometrical based variance reduction technique for the calculation of phase space data for proton therapy dose calculation.

METHODS

The treatment heads at the Francis H Burr Proton Therapy Center were modeled with a new Monte Carlo tool (TOPAS based on Geant4). For variance reduction purposes, two particle-splitting planes were implemented. First, the particles were split upstream of the second scatterer or at the second ionization chamber. Then, particles reaching another plane immediately upstream of the field specific aperture were split again. In each case, particles were split by a factor of 8. At the second ionization chamber and at the latter plane, the cylindrical symmetry of the proton beam was exploited to position the split particles at randomly spaced locations rotated around the beam axis. Phase space data in IAEA format were recorded at the treatment head exit and the computational efficiency was calculated. Depth-dose curves and beam profiles were analyzed. Dose distributions were compared for a voxelized water phantom for different treatment fields for both the reference and optimized simulations. In addition, dose in two patients was simulated with and without particle splitting to compare the efficiency and accuracy of the technique.

RESULTS

A normalized computational efficiency gain of a factor of 10-20.3 was reached for phase space calculations for the different treatment head options simulated. Depth-dose curves and beam profiles were in reasonable agreement with the simulation done without splitting: within 1% for depth-dose with an average difference of (0.2 ± 0.4)%, 1 standard deviation, and a 0.3% statistical uncertainty of the simulations in the high dose region; 1.6% for planar fluence with an average difference of (0.4 ± 0.5)% and a statistical uncertainty of 0.3% in the high fluence region. The percentage differences between dose distributions in water for simulations done with and without particle splitting were within the accepted clinical tolerance of 2%, with a 0.4% statistical uncertainty. For the two patient geometries considered, head and prostate, the efficiency gain was 20.9 and 14.7, respectively, with the percentages of voxels with gamma indices lower than unity 98.9% and 99.7%, respectively, using 2% and 2 mm criteria.

CONCLUSIONS

The authors have implemented an efficient variance reduction technique with significant speed improvements for proton Monte Carlo simulations. The method can be transferred to other codes and other treatment heads.

Commissioning dose computation models for spot scanning proton beams in water for a commercially available treatment planning system

PURPOSE

To present our method and experience in commissioning dose models in water for spot scanning proton therapy in a commercial treatment planning system (TPS).

METHODS

The input data required by the TPS included in-air transverse profiles and integral depth doses (IDDs). All input data were obtained from Monte Carlo (MC) simulations that had been validated by measurements. MC-generated IDDs were converted to units of Gy mm(2)/MU using the measured IDDs at a depth of 2 cm employing the largest commercially available parallel-plate ionization chamber. The sensitive area of the chamber was insufficient to fully encompass the entire lateral dose deposited at depth by a pencil beam (spot). To correct for the detector size, correction factors as a function of proton energy were defined and determined using MC. The fluence of individual spots was initially modeled as a single Gaussian (SG) function and later as a double Gaussian (DG) function. The DG fluence model was introduced to account for the spot fluence due to contributions of large angle scattering from the devices within the scanning nozzle, especially from the spot profile monitor. To validate the DG fluence model, we compared calculations and measurements, including doses at the center of spread out Bragg peaks (SOBPs) as a function of nominal field size, range, and SOBP width, lateral dose profiles, and depth doses for different widths of SOBP. Dose models were validated extensively with patient treatment field-specific measurements.

RESULTS

We demonstrated that the DG fluence model is necessary for predicting the field size dependence of dose distributions. With this model, the calculated doses at the center of SOBPs as a function of nominal field size, range, and SOBP width, lateral dose profiles and depth doses for rectangular target volumes agreed well with respective measured values. With the DG fluence model for our scanning proton beam line, we successfully treated more than 500 patients from March 2010 through June 2012 with acceptable agreement between TPS calculated and measured dose distributions. However, the current dose model still has limitations in predicting field size dependence of doses at some intermediate depths of proton beams with high energies.

CONCLUSIONS

We have commissioned a DG fluence model for clinical use. It is demonstrated that the DG fluence model is significantly more accurate than the SG fluence model. However, some deficiencies in modeling the low-dose envelope in the current dose algorithm still exist. Further improvements to the current dose algorithm are needed. The method presented here should be useful for commissioning pencil beam dose algorithms in new versions of TPS in the future.

Quenching correction for volumetric scintillation dosimetry of proton beams

Volumetric scintillation dosimetry has the potential to provide fast, high-resolution, three-dimensional radiation dosimetry. However, scintillators exhibit a nonlinear response at the high linear energy transfer (LET) values characteristic of proton Bragg peaks. The purpose of this study was to develop a quenching correction method for volumetric scintillation dosimetry of proton beams. Scintillation light from a miniature liquid scintillator detector was measured along the central axis of a 161.6 MeV proton pencil beam. Three-dimensional dose and LET distributions were calculated for 85.6, 100.9, 144.9 and 161.6 MeV beams using a validated Monte Carlo model. LET values were also calculated using an analytical formula. A least-squares fit to the data established the empirical parameters of a quenching correction model. The light distribution in a tank of liquid scintillator was measured with a CCD camera at all four beam energies. The quenching model and LET data were used to correct the measured light distribution. The calculated and measured Bragg peak heights agreed within ±3% for all energies except 85.6 MeV, where the agreement was within ±10%. The quality of the quenching correction was poorer for sharp low-energy Bragg peaks because of blurring and detector size effects. The corrections performed using analytical LET values resulted in doses within 1% of those obtained using Monte Carlo LET values. The proposed method can correct for quenching with sufficient accuracy for dosimetric purposes. The required LET values may be computed effectively using Monte Carlo or analytical methods. Future detectors should improve blurring correction methods and optimize the pixel size to improve accuracy for low-energy Bragg peaks.

Comparison of MCNPX and Geant4 proton energy deposition predictions for clinical use

Several different Monte Carlo codes are currently being used at proton therapy centers to improve upon dose predictions over standard methods using analytical or semi-empirical dose algorithms. There is a need to better ascertain the differences between proton dose predictions from different available Monte Carlo codes. In this investigation Geant4 and MCNPX, the two most-utilized Monte Carlo codes for proton therapy applications, were used to predict energy deposition distributions in a variety of geometries, comprising simple water phantoms, water phantoms with complex inserts and in a voxelized geometry based on clinical CT data. The Gamma analysis was used to evaluate the differences of the predictions between the codes. The results show that in all the cases the agreement was better than clinical acceptance criteria.

Monte Carlo study of radial energy deposition from primary and secondary particles for narrow and large proton beamlet source models

In spot-scanning intensity-modulated proton therapy, numerous unmodulated proton beam spots are delivered over a target volume to produce a prescribed dose distribution. To accurately model field size-dependent output factors for beam spots, the energy deposition at positions radial to the central axis of the beam must be characterized. In this study, we determined the difference in the central axis dose for spot-scanned fields that results from secondary particle doses by investigating energy deposition radial to the proton beam central axis resulting from primary protons and secondary particles for mathematical point source and distributed source models. The largest difference in the central axis dose from secondary particles resulting from the use of a mathematical point source and a distributed source model was approximately 0.43%. Thus, we conclude that the central axis dose for a spot-scanned field is effectively independent of the source model used to calculate the secondary particle dose.

A procedure to determine the planar integral spot dose values of proton pencil beam spots

PURPOSE

Planar integral spot dose (PISD) of proton pencil beam spots (PPBSs) is a required input parameter for beam modeling in some treatment planning systems used in proton therapy clinics. The measurement of PISD by using commercially available large area ionization chambers, like the PTW Bragg peak chamber (BPC), can have large uncertainties due to the size limitation of these chambers. This paper reports the results of our study of a novel method to determine PISD values from the measured lateral dose profiles and peak dose of the PPBS.

METHODS

The PISDs of 72.5, 89.6, 146.9, 181.1, and 221.8 MeV energy PPBSs were determined by area integration of their planar dose distributions at different depths in water. The lateral relative dose profiles of the PPBSs at selected depths were measured by using small volume ion chambers and were investigated for their angular anisotropies using Kodak XV films. The peak spot dose along the beam's central axis (D(0)) was determined by placing a small volume ion chamber at the center of a broad field created by the superposition of spots at different locations. This method allows eliminating positioning uncertainties and the detector size effect that could occur when measuring it in single PPBS. The PISD was then calculated by integrating the measured lateral relative dose profiles for two different upper limits of integration and then multiplying it with corresponding D(0). The first limit of integration was set to radius of the BPC, namely 4.08 cm, giving PISD(RBPC). The second limit was set to a value of the radial distance where the profile dose falls below 0.1% of the peak giving the PISD(full). The calculated values of PISD(RBPC) obtained from area integration method were compared with the BPC measured values. Long tail dose correction factors (LTDCFs) were determined from the ratio of PISD(full)∕PISD(RBPC) at different depths for PPBSs of different energies.

RESULTS

The spot profiles were found to have angular anisotropy. This anisotropy in PPBS dose distribution could be accounted in a reasonable approximate manner by taking the average of PISD values obtained using the in-line and cross-line profiles. The PISD(RBPC) values fall within 3.5% of those measured by BPC. Due to inherent dosimetry challenges associated with PPBS dosimetry, which can lead to large experimental uncertainties, such an agreement is considered to be satisfactory for validation purposes. The PISD(full) values show differences ranging from 1 to 11% from BPC measured values, which are mainly due to the size limitation of the BPC to account for the dose in the long tail regions of the spots extending beyond its 4.08 cm radius. The dose in long tail regions occur both for high energy beams such as 221.8 MeV PPBS due to the contributions of nuclear interactions products in the medium, and for low energy PPBS because of their larger spot sizes. The calculated LTDCF values agree within 1% with those determined by the Monte Carlo (MC) simulations.

CONCLUSIONS

The area integration method to compute the PISD from PPBS lateral dose profiles is found to be useful both to determine the correction factors for the values measured by the BPC and to validate the results from MC simulations.

Parameterization of multiple Bragg curves for scanning proton beams using simultaneous fitting of multiple curves

Although Bortfeld's analytical formula is useful for describing Bragg curves, measured data can deviate from the values predicted by the model. Thus, we sought to determine the parameters of a closed analytical expression of multiple Bragg curves for scanning proton pencil beams using a simultaneous optimization algorithm and to determine the minimum number of energies that need to be measured in treatment planning so that complete Bragg curves required by the treatment planning system (TPS) can be accurately predicted. We modified Bortfeld's original analytical expression of Bragg curves to accurately describe the dose deposition resulting from secondary particles. The parameters of the modified analytical expression were expressed as the parabolic cylinder function of the ranges of the proton pencil beams in water. Thirty-nine discrete Bragg curves were measured in our center using a PTW Bragg Peak chamber during acceptance and commission of the scanning beam proton delivery system. The coefficients of parabolic function were fitted by applying a simultaneous optimization algorithm to seven measured curves. The required Bragg curves for 45 energies in the TPS were calculated using our parameterized analytical expression. Finally, the 10 cm width of spread-out Bragg peaks (SOBPs) of beams with maximum energies of 221.8 and 121.2 MeV were then calculated in the TPS and compared with measured data. Compared with Bortfeld's original formula, our modified formula improved fitting of the measured depth dose curves at depths around three-quarters of the maximum range and in the beam entrance region. The parabolic function described the relationship between the parameters of the analytic expression of different energies. The predicted Bragg curves based on the parameters fitted using the seven measured curves accurately described the Bragg curves of proton pencil beams of 45 energies configured in our TPS. When we used the calculated Bragg curves as the input to TPS, the standard deviations of the measured and calculated data points along the 10 cm SOBPs created with proton pencil beams with maximum energies of 221.8 and 121.2 MeV were 1.19% and 1.18%, respectively, using curves predicted by the algorithm generated from the seven measured curves. Our method would be a valuable tool to analyze measured Bragg curves without the need for time-consuming measurements and correctly describe multiple Bragg curves using a closed analytical expression.

A Monte Carlo pencil beam scanning model for proton treatment plan simulation using GATE/GEANT4

This work proposes a generic method for modeling scanned ion beam delivery systems, without simulation of the treatment nozzle and based exclusively on beam data library (BDL) measurements required for treatment planning systems (TPS). To this aim, new tools dedicated to treatment plan simulation were implemented in the Gate Monte Carlo platform. The method was applied to a dedicated nozzle from IBA for proton pencil beam scanning delivery. Optical and energy parameters of the system were modeled using a set of proton depth-dose profiles and spot sizes measured at 27 therapeutic energies. For further validation of the beam model, specific 2D and 3D plans were produced and then measured with appropriate dosimetric tools. Dose contributions from secondary particles produced by nuclear interactions were also investigated using field size factor experiments. Pristine Bragg peaks were reproduced with 0.7 mm range and 0.2 mm spot size accuracy. A 32 cm range spread-out Bragg peak with 10 cm modulation was reproduced with 0.8 mm range accuracy and a maximum point-to-point dose difference of less than 2%. A 2D test pattern consisting of a combination of homogeneous and high-gradient dose regions passed a 2%/2 mm gamma index comparison for 97% of the points. In conclusion, the generic modeling method proposed for scanned ion beam delivery systems was applicable to an IBA proton therapy system. The key advantage of the method is that it only requires BDL measurements of the system. The validation tests performed so far demonstrated that the beam model achieves clinical performance, paving the way for further studies toward TPS benchmarking. The method involves new sources that are available in the new Gate release V6.1 and could be further applied to other particle therapy systems delivering protons or other types of ions like carbon.