Monte Carlo simulation of large electron fields

Technical Note: Bremsstrahlung dose in the electron beam at extended distances in total skin electron therapy

PURPOSE

Electron beam from a linear accelerator is commonly used in total skin electron Therapy (TSET) at extended distances. Since Das et al (Med Phys 21, p.1733, 1994) reported 5% bremsstrahlung dose for a 6 MeV electron beam at extended distance of 500 cm it has been accepted as common knowledge. However, measurements by Chen et al (Int J. Rad Onc Biol Phys 59 p.872, 2004) and Monte Carlo simulations by Ding et al (Phys. Med. Biol. 66, 075010, 2021) were unable to reproduce such high bremsstrahlung dose. As bremsstrahlung dose contributes to whole-body dose which could produce bone marrow toxicity with serious complications for the outcome of the TSET, it is important to re-evaluate the magnitude of bremsstrahlung dose accurately.

METHODS

The EGSnrc Monte Carlo system is used to investigate bremsstrahlung doses from 6 MeV high dose rate total skin electron (HDTSe) beams from Varian TrueBeam and Clinac Accelerators. The measurements were carried out at depth of d_max and 5 cm in solid water and Acrylic phantoms at extended distances using a parallel-plate chamber and a cylindrical ion chamber.

RESULTS

We were able to reproduce previously reported high bremsstrahlung dose at extended distances by using a parallel plate ionization chamber. However, both the measurements by using a cylindrical chamber and Monte Carlo simulations showed an insignificant bremsstrahlung dose (∼1%) even at SSD = 500 cm.

CONCLUSION

The bremsstrahlung doses of a 6 MeV electron beam are 0.5% to 1% for SSD from 100 to 700 cm, although it increases with the increasing extended distance. The common belief of up to 5% bremsstrahlung dose at large extended distances is incorrect. Previously reported high bremsstrahlung doses might be due to poor signal-to-noise ratio of using parallel plate chamber for measuring very low dose or particular set-up. This article is protected by copyright. All rights reserved.

Stopping-power ratios for electron beams used in total skin electron therapy

PURPOSE

The electron beams for total skin electron therapy (TSET) are often degraded by a scatter plate in addition to extended distances. For electron dosimetry, both the AAPM TG-51 and IAEA TRS-398 recommend the use of two formulas developed by Burns et al [Med. Phys. 23, 489-501 (1996)] to estimate the water-to-air stopping-power ratios (SPRs). Both formulas are based on a fit to SPRs calculated for standard electron beams. This study aims to find: (1) if the formulas are applicable to beams used in TSET and (2) the impact of the ICRU report 90 recommendations on the SPRs for these beams.

METHODS

The EGSnrc Monte Carlo code system is used to generate 6 MeV high dose rate total skin electron (HDTSe) beams used in TSET. The simulated beams are used to calculate dose distributions and SPRs as a function of depth in a water phantom. The fitted SPRs using the empirical formulas are compared with MC-calculated SPRs.

RESULTS

The electron beam quality specifier, the depth in water at which the absorbed dose falls to 50% of its maximum value, R₅₀ , decreases approximately 1 mm for each additional 100-cm extended distance ranging from 2.24 cm at SSD = 100 to 1.72 cm at SSD = 700 cm. For beams passing through a scatter plate, R₅₀ is 1.76 cm (1.14) at SSD = 300 and 1.48 cm (0.85 cm) at SSD = 600 cm with an Acrylic plate thickness of 3 mm (9 mm), respectively. The discrepancy between fitted and MC-calculated SPRs at d_ref as a function of R₅₀ is <0.8%, and in many cases <0.4%. The difference between fitted and MC-calculated SPRs as a function of depth and R₅₀ is within 1% at depths <0.8R₅₀ for beams with R₅₀  ≥ 1.14 cm. The ICRU-90 recommendations decrease SPRs by 0.3%-0.4% compared to the use of data recommended in ICRU-37.

CONCLUSION

The formulas used by the major protocols are accurate enough for clinical beams used in TSET and the error caused using the formulas is <1% to estimate SPRs as a function of depth and R₅₀ for depths <0.8R₅₀ for beams used in TSET with R₅₀  ≥ 1.14 cm. The impact of the ICRU-90 recommendations shows a decrease of SPRs by a fraction of a percent for beams used in TSET.

Validation of the dosimetry of total skin irradiation techniques by Monte Carlo simulation

Purpose

To validate the dose measurements for two total skin irradiation techniques with Monte Carlo simulation, providing more information on dose distributions, and guidance on further technique optimization.

Methods

Two total skin irradiation techniques (stand‐up and lay‐down) with different setup were simulated and validated. The Monte Carlo simulation was primarily performed within the EGSnrc environment. Parameters of jaws, MLCs, and a customized copper (Cu) filter were first tuned to match the profiles and output measured at source‐to‐skin distance (SSD) of 100 cm where the secondary source is defined. The secondary source was rotated to simulate gantry rotation. VirtuaLinac, a cloud‐based Monte Carlo package, was used for Linac head simulation as a secondary validation. The following quantities were compared with measurements: for each field/direction at the treatment SSDs, the percent depth dose (PDD), the profiles at the depth of maximum, and the absolute dosimetric output; the composite dose distribution on cylindrical phantoms of 20 to 40 cm diameters.

Results

Cu filter broadened the FWHM of the electron beam by 44% and degraded the mean energy by 0.7 MeV. At SSD = 100 cm, MC calculated PDDs agreed with measured data within 2%/2 mm (except for the surface voxel) and lateral profiles agreed within 3%. At the treatment SSD, profiles and output factors of individual field matched within 4%; d_max and R₈₀ of the simulated PDDs also matched with measurement within 2 mm. When all fields were combined on the cylindrical phantom, the d_max shifted toward the surface. For lay‐down technique, the maximum x‐ray contamination at the central axis was (MC: 2.2; Measurement: 2.1)% and reduced to 0.2% at 40 cm off the central axis.

Conclusions

The Monte Carlo results in general agree well with the measurement, which provides support in our commissioning procedure, as well as the full three‐dimensional dose distribution of the patient phantom.

Validation of a Monte Carlo model for multi leaf collimator based electron delivery

PURPOSE

To develop and validate a Monte Carlo model of the Varian TrueBeam to study electron collimation using the existing photon multi-leaf collimators (pMLC), instead of conventional electron applicators and apertures.

MATERIALS AND METHODS

A complete Monte Carlo model of the Varian TrueBeam was developed using Tool for particle simulation (TOPAS) (version 3.1.p3). Vendor-supplied information was used to model the treatment head components and the source parameters. A phase space plane was setup above the collimating jaws and captured particles were reused until a statistical uncertainty of 1% was achieved in the central axis. Electron energies 6, 9, 12, 16, and 20 MeV with a jaw-defined field of 20 × 20 cm² at iso-center, pMLC-defined fields of 6.8 × 6.8 cm² and 11.4 × 11.4 cm² at 80 cm source-to-surface distance (SSD) and an applicator-defined field of 10 × 10 cm² at iso-center were evaluated. All the measurements except the applicator-defined fields were measured using an ionization chamber in a water tank using 80 cm SSD. The dose difference, distance-to-agreement and gamma index were used to evaluate the agreement between the Monte Carlo calculations and measurements. Contributions of electron scattering off pMLC leaves and inter-leaf leakage on dose profiles were evaluated and compared with Monte Carlo calculations. Electron transport through a heterogeneous phantom was simulated and the resulting dose distributions were compared with film measurements. The validated Monte Carlo model was used to simulate several clinically motivated cases to demonstrate the benefit of pMLC-based electron delivery compared to applicator-based electron delivery.

RESULTS

Calculated and measured percentage depth-dose (PDD) curves agree within 2% after normalization. The agreement between normalized percentage depth dose curves were evaluated using one-dimensional gamma analysis with a local tolerance of 2%/1 mm and the %points passing gamma criteria was 100% for all energies. For jaw-defined fields, calculated profiles agree with measurements with pass rates of >97% for 2%/2 mm gamma criteria. Calculated FWHM and penumbra width agree with measurements within 0.4 cm. For fields with tertiary collimation using an pMLC or applicator, the average gamma pass rate of compared profiles was 98% with 2%/2 mm gamma criteria. The profiles measured to evaluate the pMLC leaf scattering agreed with Monte Carlo calculations with an average gamma pass rate of 96.5% with 3%/2 mm gamma criteria. Measured dose profiles below the heterogenous phantom agreed well with calculated profiles and matched within 2.5% for most points. The calculated clinically applicable cases using TOPAS MC and Eclipse TPS for single enface electron beam, electron-photon mixed beam and a matched electron-electron beam exhibited a reasonable agreement in PDDs, profiles and dose volume histograms.

CONCLUSION

We present a validation of a Monte Carlo model of Varian TrueBeam for pMLC-based electron delivery. Monte Carlo calculations agreed with measurements satisfying gamma criterion of 1%/1 mm for depth dose curves and 2%/1 mm for dose profiles. The simulation of clinically applicable cases demonstrated the clinical utility of pMLC-based electrons and the use of MC simulations for development of advanced radiation therapy techniques.

Beam modeling and beam model commissioning for Monte Carlo dose calculation-based radiation therapy treatment planning: Report of AAPM Task Group 157

Dose calculation plays an important role in the accuracy of radiotherapy treatment planning and beam delivery. The Monte Carlo (MC) method is capable of achieving the highest accuracy in radiotherapy dose calculation and has been implemented in many commercial systems for radiotherapy treatment planning. The objective of this task group was to assist clinical physicists with the potentially complex task of acceptance testing and commissioning MC-based treatment planning systems (TPS) for photon and electron beam dose calculations. This report provides an overview on the general approach of clinical implementation and testing of MC-based TPS with a specific focus on models of clinical photon and electron beams. Different types of beam models are described including those that utilize MC simulation of the treatment head and those that rely on analytical methods and measurements. The trade-off between accuracy and efficiency in the various source-modeling approaches is discussed together with guidelines for acceptance testing of MC-based TPS from the clinical standpoint. Specific recommendations are given on methods and practical procedures to commission clinical beam models for MC-based TPS.

Feasibility of a GATE Monte Carlo platform in a clinical pretreatment QA system for VMAT treatment plans using TrueBeam with an HD120 multileaf collimator

Purpose

To evaluate the quality of patient‐specific complicated treatment plans, including commercialized treatment planning systems (TPS) and commissioned beam data, we developed a process of quality assurance (QA) using a Monte Carlo (MC) platform. Specifically, we constructed an interface system that automatically converts treatment plan and dose matrix data in digital imaging and communications in medicine to an MC dose‐calculation engine. The clinical feasibility of the system was evaluated.

Materials and Methods

A dose‐calculation engine based on GATE v8.1 was embedded in our QA system and in a parallel computing system to significantly reduce the computation time. The QA system automatically converts parameters in volumetric‐modulated arc therapy (VMAT) plans to files for dose calculation using GATE. The system then calculates dose maps. Energies of 6 MV, 10 MV, 6 MV flattening filter free (FFF), and 10 MV FFF from a TrueBeam with HD120 were modeled and commissioned. To evaluate the beam models, percentage depth dose (PDD) values, MC calculation profiles, and measured beam data were compared at various depths (D_max, 5 cm, 10 cm, and 20 cm), field sizes, and energies. To evaluate the feasibility of the QA system for clinical use, doses measured for clinical VMAT plans using films were compared to dose maps calculated using our MC‐based QA system.

Results

A LINAC QA system was analyzed by PDD and profile according to the secondary collimator and multileaf collimator (MLC). Values for MC calculations and TPS beam data obtained using CC13 ion chamber (IBA Dosimetry, Germany) were consistent within 1.0%. Clinical validation using a gamma index was performed for VMAT treatment plans using a solid water phantom and arbitrary patient data. The gamma evaluation results (with criteria of 3%/3 mm) were 98.1%, 99.1%, 99.2%, and 97.1% for energies of 6 MV, 10 MV, 6 MV FFF, and 10 MV FFF, respectively.

Conclusions

We constructed an MC‐based QA system for evaluating patient treatment plans and evaluated its feasibility in clinical practice. We observed robust agreement between dose calculations from our QA system and measurements for VMAT plans. Our QA system could be useful in other clinical settings, such as small‐field SRS procedures or analyses of secondary cancer risk, for which dose calculations using TPS are difficult to verify.

An experimental feasibility study on the use of scattering foil free beams for modulated electron radiotherapy

The potential benefit of using scattering foil free beams for delivery of modulated electron radiotherapy is investigated in this work. Removal of the scattering foil from the beamline showed a measured bremsstrahlung tail dose reduction just beyond R(p) by a factor of 12.2, 6.9, 7.4, 7.4 and 8.3 for 6, 9, 12, 16 and 20 MeV beams respectively for 2 × 2 cm(2) fields defined on-axis when compared to the clinical beamline. Monte Carlo simulations were matched to measured data through careful tuning of source parameters and the modification of certain accelerator components beyond the manufacturer's specifications. An accelerator model based on the clinical beamline and one with the scattering foil removed were imported into a Monte Carlo-based treatment planning system (McGill Monte Carlo Treatment Planning). A treatment planning study was conducted on a test phantom consisting of a PTV and two distal organs at risk (OAR) by comparing a plan using the clinical beamline to a plan using a scattering foil free beamline. A DVH comparison revealed that for quasi-identical target coverage, the volume of each OAR receiving a given dose was reduced, thus reducing the dose deposited in healthy tissue.

Linking computer-aided design (CAD) to Geant4-based Monte Carlo simulations for precise implementation of complex treatment head geometries

Most of the treatment head components of medical linear accelerators used in radiation therapy have complex geometrical shapes. They are typically designed using computer-aided design (CAD) applications. In Monte Carlo simulations of radiotherapy beam transport through the treatment head components, the relevant beam-generating and beam-modifying devices are inserted in the simulation toolkit using geometrical approximations of these components. Depending on their complexity, such approximations may introduce errors that can be propagated throughout the simulation. This drawback can be minimized by exporting a more precise geometry of the linac components from CAD and importing it into the Monte Carlo simulation environment. We present a technique that links three-dimensional CAD drawings of the treatment head components to Geant4 Monte Carlo simulations of dose deposition.

Treatment head disassembly to improve the accuracy of large electron field simulation

PURPOSE

The purposes of this study are to improve the accuracy of source and geometry parameters used in the simulation of large electron fields from a clinical linear accelerator and to evaluate improvement in the accuracy of the calculated dose distributions.

METHODS

The monitor chamber and scattering foils of a clinical machine not in clinical service were removed for direct measurement of component geometry. Dose distributions were measured at various stages of reassembly, reducing the number of geometry variables in the simulation. The measured spot position and beam angle were found to vary with the beam energy. A magnetic field from the bending magnet was found between the exit window and the secondary collimators of sufficient strength to deflect electrons 1 cm off the beam axis at 100 cm from the exit window. The exit window was 0.05 cm thicker than manufacturer's specification, with over half of the increased thickness due to water pressure in the channel used to cool the window. Dose distributions were calculated with Monte Carlo simulation of the treatment head and water phantom using EGSnrc, a code benchmarked at radiotherapy energies for electron scatter and bremsstrahlung production, both critical to the simulation. The secondary scattering foil and monitor chamber offset from the collimator rotation axis were allowed to vary with the beam energy in the simulation to accommodate the deflection of the beam by the magnetic field, which was not simulated.

RESULTS

The energy varied linearly with bending magnet current to within 1.4% from 6.7 to 19.6 MeV, the bending magnet beginning to saturate at the highest beam energy. The range in secondary foil offset used to account for the magnetic field was 0.09 cm crossplane and 0.15 cm inplane, the range in monitor chamber offset was 0.14 cm crossplane and 0.07 cm inplane. A 1.5%/0.09 cm match or better was obtained to measured depth dose curves. Profiles measured at the depth of maximum dose matched the simulated profiles to 2.6% or better at doses of 80% or more of the dose on the central axis. The profiles along the direction of MLC motion agreed to within 0.16 cm at the edge of the field. There remained a mismatch for the lower beam energies at the edge of the profile that ran parallel to the direction of jaw motion of up to 1.4 cm for the 6 MeV beam, attributed to the MLC support block at the periphery of the field left out of the simulation and to beam deflection by the magnetic field. The possibility of using these results to perform accurate simulation without disassembly is discussed. Phase-space files were made available for benchmarking beam models and other purposes.

CONCLUSIONS

The match to measured large field dose distributions from clinical electron beams with Monte Carlo simulation was improved with more accurate source details and geometry details closer to manufacturer's specification than previously achieved.

The accuracy of EGSnrc, Geant4 and PENELOPE Monte Carlo systems for the simulation of electron scatter in external beam radiotherapy

Three widely used Monte Carlo systems were benchmarked against recently published measurements of the angular distribution of 13 MeV and 20 MeV electrons scattered from foils of different atomic numbers and thicknesses. Source and geometry were simulated in detail to calculate electron fluence profiles 118.2 cm from the exit window. Results were compared to the measured fluence profiles and the characteristic angle where the fluence drops to 1/e of its maximum value. EGSnrc and PENELOPE results, on average, agreed with measurement within 1 standard deviation experimental uncertainty, with EGSnrc estimating slightly lower scatter than measurement and PENELOPE slightly higher scatter. Geant4.9.2 overestimated the characteristic angle for the lower atomic number foils by as much as 10%. Retuning of the scatter distributions in Geant4 led to a much better agreement with measurement, close to that achieved with the other codes. The 3% differences from measurement seen with all codes for at least some of the foils would result in clinically significant errors in the fluence profiles (2%/4 mm), given accurate knowledge of the electron source and treatment head geometry used in radiotherapy. Further improvement in simulation accuracy is needed to achieve 1%/1 mm agreement with measurement for the full range of beam energies, foil atomic number and thickness used in radiotherapy. EGSnrc would achieve this accuracy with an increase in thickness of the mylar sheets in the monitor chamber, PENELOPE with a decrease in thickness.

Determination of electron energy, spectral width, and beam divergence at the exit window for clinical megavoltage x-ray beams

Monte Carlo simulations of x-ray beams typically take parameters of the electron beam in the accelerating waveguide to be free parameters. In this paper, a methodology is proposed and implemented to determine the energy, spectral width, and beam divergence of the electron source. All treatment head components were removed from the beam path, leaving only the exit window. With the x-ray target and flattener out of the beam, uncertainties in physical characteristics and relative position of the target and flattening filter, and in spot size, did not contribute to uncertainty in the energy. Beam current was lowered to reduce recombination effects. The measured dose distributions were compared with Monte Carlo simulation of the electron beam through the treatment head to extract the electron source characteristics. For the nominal 6 and 18 MV x-ray beams, the energies were 6.51 +/- 0.15 and 13.9 +/- 0.2 MeV, respectively, with the uncertainties resulting from uncertainties in the detector position in the measurement and in the stopping power in the simulations. Gaussian spectral distributions were used, with full widths at half maximum ranging from 20 +/- 4% at 6 MV to 13 +/- 4% at 18 MV required to match the fall-off portion of the percent-depth ionization curve. Profiles at the depth of maximum dose from simulations that used the manufacturer-specified exit window geometry and no beam divergence were 2-3 cm narrower than measured profiles. Two simulation configurations yielding the measured profile width were the manufacturer-specified exit window thickness with electron source divergences of 3.3 degrees at 6 MV and 1.8 degrees at 18 MV and an exit window 40% thicker than the manufacturer's specification with no beam divergence. With the x-ray target in place (and no flattener), comparison of measured to simulated profiles sets upper limits on the electron source divergences of 0.2 degrees at 6 MV and 0.1 degrees at 18 MV. A method of determining source characteristics without mechanical modification of the treatment head, and therefore feasible in clinics, is presented. The energies and spectral widths determined using this method agree with those determined with only the exit window in the beam path.

Benchmarking of Monte Carlo simulation of bremsstrahlung from thick targets at radiotherapy energies

Several Monte Carlo systems were benchmarked against published measurements of bremsstrahlung yield from thick targets for 10-30 MV beams. The quantity measured was photon fluence at 1 m per unit energy per incident electron (spectra), and total photon fluence, integrated over energy, per incident electron (photon yield). Results were reported at 10-30 MV on the beam axis for Al and Pb targets and at 15 MV at angles out to 90 degrees for Be, Al, and Pb targets. Beam energy was revised with improved accuracy of 0.5% using an improved energy calibration of the accelerator. Recently released versions of the Monte Carlo systems EGSNRC, GEANT4, and PENELOPE were benchmarked against the published measurements using the revised beam energies. Monte Carlo simulation was capable of calculation of photon yield in the experimental geometry to 5% out to 30 degrees, 10% at wider angles, and photon spectra to 10% at intermediate photon energies, 15% at lower energies. Accuracy of measured photon yield from 0 to 30 degrees was 5%, 1 s.d., increasing to 7% for the larger angles. EGSNRC and PENELOPE results were within 2 s.d. of the measured photon yield at all beam energies and angles, GEANT4 within 3 s.d. Photon yield at nonzero angles for angles covering conventional field sizes used in radiotherapy (out to 10 degrees), measured with an accuracy of 3%, was calculated within 1 s.d. of measurement for EGSNRC, 2 s.d. for PENELOPE and GEANT4. Calculated spectra closely matched measurement at photon energies over 5 MeV. Photon spectra near 5 MeV were underestimated by as much as 10% by all three codes. The photon spectra below 2-3 MeV for the Be and Al targets and small angles were overestimated by up to 15% when using EGSNRC and PENELOPE, 20% with GEANT4. EGSNRC results with the NIST option for the bremsstrahlung cross section were preferred over the alternative cross section available in EGSNRC and over EGS4. GEANT4 results calculated with the "low energy" physics list were more accurate than those calculated with the "standard" physics list.

Measurement of multiple scattering of 13 and 20 MeV electrons by thin foils

To model the transport of electrons through material requires knowledge of how the electrons lose energy and scatter. Theoretical models are used to describe electron energy loss and scatter and these models are supported by a limited amount of measured data. The purpose of this work was to obtain additional data that can be used to test models of electron scattering. Measurements were carried out using 13 and 20 MeV pencil beams of electrons produced by the National Research Council of Canada research accelerator. The electron fluence was measured at several angular positions from 0 degree to 90 degrees for scattering foils of different thicknesses and with atomic numbers ranging from 4 to 79. The angle, theta 1/e at which the fluence has decreased to 1/e of its value on the central axis was used to characterize the distributions. Measured values of theta 1/e ranged from 1.5 degrees to 8 degrees with a typical uncertainty of about 1%. Distributions calculated using the EGSnrc Monte Carlo code were compared to the measured distributions. In general, the calculated distributions are narrower than the measured ones. Typically, the difference between the measured and calculated values of theta 1/e is about 1.5%, with the maximum difference being 4%. The measured and calculated distributions are related through a simple scaling of the angle, indicating that they have the same shape. No significant trends with atomic number were observed.