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Service de physique médicale et de radioprotection, Centre Intégré de Cancérologie, CHU de Québec – Université Laval et Centre de recherche du CHU de Québec, Québec, Québec, CanadaDépartement de Physique, de Génie Physique et d’Optique et Centre de Recherche sur le Cancer, Université Laval, Québec Québec G1V 0A6, Canada
Service de physique médicale et de radioprotection, Centre Intégré de Cancérologie, CHU de Québec – Université Laval et Centre de recherche du CHU de Québec, Québec, Québec, CanadaDépartement de Physique, de Génie Physique et d’Optique et Centre de Recherche sur le Cancer, Université Laval, Québec Québec G1V 0A6, Canada
Service de physique médicale et de radioprotection, Centre Intégré de Cancérologie, CHU de Québec – Université Laval et Centre de recherche du CHU de Québec, Québec, Québec, CanadaDépartement de Physique, de Génie Physique et d’Optique et Centre de Recherche sur le Cancer, Université Laval, Québec Québec G1V 0A6, Canada
Service de physique médicale et de radioprotection, Centre Intégré de Cancérologie, CHU de Québec – Université Laval et Centre de recherche du CHU de Québec, Québec, Québec, CanadaDépartement de Physique, de Génie Physique et d’Optique et Centre de Recherche sur le Cancer, Université Laval, Québec Québec G1V 0A6, Canada
TOPAS is user-friendly by using parameter files which do not require advanced coding knowledge.
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TOPAS is now a state-of-the-art Monte Carlo simulation toolkit for LDR brachytherapy.
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This work provides TOPAS users with a pre-made LDR brachytherapy geometries package.
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TOPAS provides a tutorial to help users create brachytherapy Monte Carlo simulations.
Abstract
Purpose:
This work has the purpose of validating the Monte Carlo toolkit TOol for PArticle Simulation (TOPAS) for low-dose-rate (LDR) brachytherapy uses.
Methods and Materials:
Simulations of 12 LDR sources and 2 COMS eye plaques (10 mm and 20 mm in diameter) and comparisons with published reference data from the Carleton Laboratory for Radiotherapy Physics (CLRP), the TG-43 consensus data and the TG-129 consensus data were performed. Sources from the IROC Houston Source Registry were modeled. The OncoSeed 6711 and the SelectSeed 130.002 were also modeled for historical reasons. For each source, the dose rate constant, the radial dose function and the anisotropy functions at 0.5, 1 and 5 cm were extracted. For the eye plaques (loaded with 125I sources), dose distribution maps, dose profiles along the central axis and transverse axis were calculated.
Results:
Dose rate constants for 11 of the 12 sources are within 4% of the consensus data and within 2% of the CLRP data. The radial dose functions and anisotropy functions are mostly within 2% of the CLRP data. In average, 92% of all voxels are within 1% of the CLRP data for the eye plaques dose distributions. The dose profiles are within 0.5% (central axis) and 1% (transverse axis) of the reference data.
Conclusion:
The TOPAS MC toolkit was validated for LDR brachytherapy applications. Single-seed and multi-seed results agree with the published reference data. TOPAS has several benefits such as a simplified approach to MC simulations and an accessible brachytherapy package including comprehensive learning resources.
Enhancements to commissioning techniques and quality assurance of brachytherapy treatment planning systems that use model-based dose calculation algorithms.
Report of the Task Group 186 on model-based dose calculation methods in brachytherapy beyond the TG-43 formalism: current status and recommendations for clinical implementation.
]. The MC method provides accurate calculations by simulating the fundamental physical interactions in the patient environment. As such, the geometry and composition of the patient, sources and applicators are considered. In the specific case of low-dose rate brachytherapy (LDR), the MC method further fully considers the interseed attenuation [
]. Compared with traditional MC codes, the TOPAS (TOol for PArticle Simulation) toolkit is gaining popularity by having a much-simplified set-up for particle simulation and geometry description [
]. Based on the general-purpose MC code Geant4, TOPAS is a user-friendly MC toolkit that creates complex geometries and simulations through simple text files [
Report of the Task Group 186 on model-based dose calculation methods in brachytherapy beyond the TG-43 formalism: Current status and recommendations for clinical implementation.
Med Phys.2012; 39 (URL http://onlinelibrary.wiley.com/doi/abs/10.1118/1.4747264)
]. Authors compared the photon emission energy spectrum, the air-kerma strength and the dose-rate constant of the MBDCA-WG generic Ir-192 source, the Joint AAPM/ESTRO/ABG MBDCA-WG test cases and three different clinical cases [
The present work serves as the complementary validation for low-energy photon emitting brachytherapy sources. Consequently, the purpose of this study is to validate TOPAS for LDR brachytherapy applications. To achieve the main goal, 10 LDR sources from the Joint AAPM/IROC Houston Registry of Brachytherapy Sources [
], the Oncoseed 6711 and the SelectSeed 130.002 were modeled. Their associated TG-43 parameters were extracted and compared with reference data. In addition, voxel-based dose calculations of clinical COMS eye plaque cases (producing major shielding effects) were performed.
Table 1Summary of Monte Carlo simulation items needed to follow the TG-268 recommendations for TOPAS brachytherapy applications.
LDR Brachytherapy sources (one 131Cs, seven 125I, four 103Pd) and COMS eye plaques (10 and 20 mm in diameter)
Materials
TOPAS allows the use of materials and compounds already defined in Geant4
Source description
Simulation of radioactive decay using photon decay spectra from NNDC. Emission of photons in TOPAS is taken care of by the volumetric source type. The sources details are described in the supplementary materials section.
Enhancements to commissioning techniques and quality assurance of brachytherapy treatment planning systems that use model-based dose calculation algorithms.
Tables and graphs of electron-interaction cross sections from 10 eV to 100 GeV derived from the LLNL Evaluated Electron Data Library (EEDL), Z=1–100 tech. rep UCRL-50400-Vol.31.
Lawrence Livermore National Lab., CA (United States),
1991
Tables and graphs of atomic subshell and relaxation data derived from the LLNL Evaluated Atomic Data Library (EADL), Z=1–100 tech. rep UCRL-50400-Vol.30.
Lawrence Livermore National Lab., CA (United States),
1991
Photon fluence and absorbed dose (collisional kerma) scored in water or medium. Voxel size depends of the simulation, see sections 2.2 and 2.3.
–
Number of histories/statistical uncertainty
10 photons per simulation. Between 8–30 simulations were required per TG-43 parameter extraction or eye plaque case. Type A uncertainties were 2% or lower and taken into account by reporting the standard deviation at k = 1.
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Statistical methods
History-by-history method.
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Postprocessing
Dose to voxels converted into dose at location of the voxel’s center point.
To accomplish this work, the TOPAS MC toolkit version 3.7 (Geant4 version 10.6) was used. The photon and electron interactions down to about 250 eV were modeled with the g4em-Livermore physics list constructor [
Tables and graphs of electron-interaction cross sections from 10 eV to 100 GeV derived from the LLNL Evaluated Electron Data Library (EEDL), Z=1–100 tech. rep UCRL-50400-Vol.31.
Lawrence Livermore National Lab., CA (United States),
1991
Tables and graphs of atomic subshell and relaxation data derived from the LLNL Evaluated Atomic Data Library (EADL), Z=1–100 tech. rep UCRL-50400-Vol.30.
Lawrence Livermore National Lab., CA (United States),
1991
]. The Geant4 collaboration has a benchmarking group (G4-Med) for medical physics applications. Interested readers are referred to the group report for a comprehensive discussion on the different Geant4 physics constructors and their benchmarking[
]. This method allows an end-user to define arbitrary geometries and designate them as radioactive sources. Table 1 summarizes the items that the TG-268 recommends to report.
2.2 LDR brachytherapy sources and TG43 parameters
A set of 12 LDR sources were modeled. The set included, one 131Cs source (Proxcelan CS-1 Rev2[
Safigholi H, Chamberland MJP, Taylor REP, Allen CH, Martinov MP, Rogers DWO, et al. Update of the CLRP TG-43 parameter database for low-energy brachytherapy sources. Med Phys 2473-4209n/a(n/a). URL.
], and the historically used OncoSeed 6711 and SelectSeed 130.002 models. Detailed source description and references are presented in the appendix.
To validate the seed geometries, TG-43 parameters extracted with TOPAS were compared with published reference data. The references comprise data from the Carleton Laboratory for Radiotherapy Physics (CLRP TG-43 Parameter Database for Brachytherapy)[
]. Relative differences of TOPAS results with respect to the reference data were calculated.
The average photon per disintegration used were 0.8139 photons/Bq, 1.5951 photons/Bq and 0.85758 photons/Bq, for the 131Cs, 125I and 103Pd, respectively[
]. A significant difference is present in the 125I spectra used by the CLRP and the one used in this study. Indeed, the CLRP completely omits the 3.77 keV peak in the probability distribution function of the 125I emission spectrum whereas it was included for this work[
]. According to the NNDC spectrum for 125I, the intensity for this energy is 0.149 on a total intensity of 1.5951 photons per Bq. To understand the impact of this energy in LDR brachytherapy cases, multiple air-kerma strengths were calculated using intensities of this energy ranging from 0 photons per Bq to 0.5 photons per Bq on a total of 1.9461 photons per Bq (25.69%) for the SelectSeed 130.002. Such values were then compared to the air-kerma strengths from the CLRP for this seed.
The air-kerma strengths of each seed were extracted from fluence simulations based on the Wide Angle Free Air Chamber (WAFAC) method[
]. The WAFAC method was chosen because it mimics the detector used in laboratories to calibrate brachytherapy sources by simulating an air cell having the same solid angle as the physical device[
]. With the source placed in vacuum, the fluence was scored with a 2.70.05 cm3 air cell with its center located 10.025 cm on the source transverse axis. For this simulation, an energy bin width of 0.1 keV was used. The maximal energy bin depended on the source used. In the case of a palladium source, the maximal energy bin was 40.1 keV and in the case of an iodine or cesium source, it was 35.6 keV. Note that another method commonly used to calculate the air-kerma strength is the point method which uses a 0.10.05 cm3 voxel with its center located 10.025 cm above the source[
] (as with the WAFAC method). An advantage of the WAFAC method over the point method is that it covers a greater surface angle relative to the source. The values of average photon per disintegration presented above were used for the calculation of the air-kerma strengths of each source. A geometrical correction factor[
The dose at the reference point was scored in water in a 0.1 mm side cubic voxel placed at 1 cm along the transverse axis (location of the reference point according to the TG-43 protocol). Throughout the simulations, dose scoring was done with a Track-Length Estimator (TLE)[
]. From the results of doses at the reference point and the air-kerma strengths, the dose-rate constants were calculated.
The radial dose functions were calculated from doses scored within cubic voxels radially located along the transverse axis of the source. These voxels had sides of 0.1, 0.5 and 1 mm for 0.5 mm r 10 mm, 10 mm r 50 mm, and 50 mm r 100 mm, respectively. The 2D anisotropy function was extracted at 0.5, 1 and 5 cm with quarter cylinders as scorers containing 90 voxels each, thus giving a resolution of 1 degree. Throughout all simulations, the location of each voxel is defined by the position of its center point. Simulations for the radial dose and anisotropy functions immersed the source in a 30 cm side water cube. The statistical uncertainty of calculated parameters was less than 1%, which included the radial dose functions up to 2 cm and the anisotropy functions at 5 cm (except for the 103Pd sources, which was 2% at 5 cm), as it is in the CLRP data. Reported statistical uncertainties corresponded to k 1. For all simulations a 5 keV low-energy cutoff was used.
The TOPAS MC toolkit allows users to filter the scored quantities by given attributes such as charge, atomic number, kinetic energy, initial momentum, particle generation, among others. The 3.7 version adopted a filter based on the number of interactions (called InteractionCount). Based on this filter, the TotalInteractionCount filter was implemented, which considers the number of interactions from the particle’s ancestors. The TotalInteractionCount filter was used to decompose the radial dose function in Primary and Scatter Separated (PSS) dose data. That filter was validated against the CLRP MC database [
] using the SelectSeed 130.002 model. The seed was immersed in a 30 cm side water cube and the dose was scored in rings surrounding the source at 0.25, 0.5, 1, 2, 3, 4, 5, 7.5 and 10 cm. The dose data is reported as total dose, total scatter dose, primary dose, single scatter dose and multiple scatter dose. The statistical uncertainty was below 0.3% for the total dose.
2.3 Eye plaques
In addition to the single-seed calculations, two eye plaques for melanoma treatments were simulated. Such treatments employ the same LDR brachytherapy source models as the previously modeled geometries. Eye plaque cases allow to test TOPAS under a more complex scattering scenario such as a multiple-seed configuration alongside a highly attenuating component. The COMS eye plaque models of 10 and 20 mm were built in TOPAS as custom geometry components [
]. Incorporation of custom geometry components in TOPAS is made possible through its extension mechanism by coding in native C++/Geant4 language. Each eye plaque model contains 5 and 24 sources, respectively. For this part of the study, the OncoSeed 6711 source model was used. Two cases were studied per plaque model: the homogeneous (HOMO) case and the heterogeneous (HETERO) case [
]. The HOMO case simulated the seeds in water with no interseed effects while the HETERO case considered the plaque and seeds in water with interseed effects. A python script automated the generation of parameter files for multi-seed geometries. Such was done to give explicit definition of each seed to TOPAS. The dimensions of the plaques and the positions of the sources inside were taken from the TG-129 Report [
]. The geometry’s origin is 0.1 cm inwards from the surface of the eye, on the eye’s plaque side and inline with the center of the plaque. Relative to the origin, the dose scorer covered the volume −12.5 mm12.5 mm, −12.5 mm12.5 mm and −0.5 mm24.5 mm. Each voxel is 0.050.05 cm. Voxels covered by the plaque were omitted by applying a TOPAS scorer filter. From the simulations, the central axis depth dose profiles, the transverse dose profiles (at 0.5 cm and 1 cm) and dose distribution maps were produced. Results were then compared against reference data from the CLRP [
]. For efficient comparison, doses were normalized to the dose value at the origin. Such normalization allows to compare the differences relative to a clinically relevant reference point. In addition to the TG-129 and CLRP-like analysis, local dose differences were calculated for all cases. They are defined as where and are the dose volumes in absolute units (Gy/hist) and are not normalized at a given location. Calculations of the local dose differences for the 10 mm and 20 mm HETERO cases not using the 3.77 keV emission peak of 125I were also made. This was done in order to understand the impact of the 3.77 keV line on doses per photon. The latter analysis could reveal systematic differences which would otherwise remain unseen. From these local dose differences, distribution maps and histograms were produced to offer a general view of the systematic difference, if any. The statistical uncertainties (corresponding to ) are 0.5%, 0.5%, 0.2% and 0.7% for the HOMO 10 mm plaque, the HETERO 10 mm plaque, the HOMO 20 mm plaque and the HETERO 20 mm plaque, respectively. These values were taken at the opposite side of the sclera ( 0 mm, 0 mm, 22.6 mm).
3. Results
3.1 TG43 parameters
3.1.1 Air-kerma strengths of 125 i sources with modulated intensities for the 3.77 kev energy peak
Table 2 shows results for different air-kerma strengths of the SelectSeed 130.002 for different intensities of the 3.77 keV peak in the 125I probability distribution function. Such values are compared to the CLRP’s air kerma strengths for this seed. Intensities of 0%–25.59% for the 3.77 keV energy line were simulated to account for intensities lower and higher than the natural intensity (9.28%). These intensities correspond to 0 on 1.4461 photons per Bq, 0.05 on 1.4961 photons per Bq, 0.149 on 1.5951 photons per Bq (natural intensity) and 0.5 on 1.9461 photons per Bq. Equivalent differences to the were measured for the OncoSeed’s at different intensities for the 3.77 keV peak.
Table 2Results of different air kerma strengths () for the SelectSeed 130.002 LDR source obtained with modulated intensities for the 3.77 keV peak of the 125I emission spectrum and compared to the CLRP’s air kerma strength ( Gy cm hist−1)
Dose-rate constants (TOPAS and references) are presented in Table 3. Note that uncertainties (one standard deviation) are reported. Note that the TG-43 report suggested a value of 4.8% as a practical uncertainty on the consensus dose rate constants reported[
The radial dose functions, , of the AgX 100 (125I) model, the IAPd-103 A (103Pd) and the CS-1 Rev2 (131Cs) model are in Fig. 1. The top panel shows the radial dose function data from TOPAS (extracted results), CLRP, TG-43 consensus and from the study by Meigooni et al. [
]. The bottom panel presents the relative difference with respect to the CLRP data between and 5%. The complete set (all seed models) of radial dose functions results are given as supplementary material. The radial dose function of the SelectSeed model, decomposed in its PSS data, is presented in Fig. 2. The total dose for all radii was at 2.5% of the reference data. Agreement with reference data for the primary, the single scatter, and the multiple scatter components were all within 2.7%, 4.1%, and 4.0% (except the first point that was 7.0%) for radii 5 cm, respectively.
Fig. 1(Top panel) Radial dose functions for the AgX 100, IAPd-103 A and CS-1 Rev2 sources obtained with TOPAS and compared with the reference data. The reference data for AgX 100 source comes from the CLRP database V2 [50] and from the study by Mourtada et al. [51]. The reference data for the IAPd-103 A source comes from the CLRP database V2 [68], from the study by Meigooni et al. [53] and the study by Sowards et al. [54]. The reference data for the CS-1 Rev2 source comes from the CLRP database V2 [34] and the study by Rivard et al. [35]. (Bottom panel) Relative difference with respect to the CLRP database.
Fig. 2Radial dose function of the SelectSeed separated into total dose, total scatter dose, primary dose, single scatter, and multiple scatter dose. The separation was performed by using the TOPAS TotalInteractionCount filter. Dashed lines with symbols are CLRP data and the full lines represent TOPAS results.
Results of the 2D anisotropy functions at 1 cm for the AgX 100 (125I) model, the IAPd-103 A (103Pd) model and the CS-1 Rev2 (131Cs) models are presented in Fig. 3. The top panel depicts the anisotropy functions including the reference data of the CLRP database, the TG-43 consensus data and the data from the study by Meigooni et al. [
]. In the bottom panel, the relative differences with respect to the CLRP data are presented. The complete set of anisotropy functions, at 0.5 cm, 1 cm and 5 cm, are presented as supplementary material.
Fig. 3(Top panel) Anisotropy functions at 1 cm for the AgX 100 model, the IAPd-103 A model and the CS-1 Rev2 model obtained with TOPAS and compared with the reference data. The reference data for AgX 100 source comes from the CLRP database V2 [50] and from the study by Mourtada et al. [51]. The reference data for the IAPd-103 A source comes from the CLRP database V2 [68], from the study by Meigooni et al. [53] and the study by Sowards et al. [54]. The reference data for the CS-1 Rev2 source comes from the CLRP database V2 [34] and the study by Rivard et al. [35]. (Bottom panel) Relative difference with respect to the CLRP database.
Fig. 4 presents the results of the 20 mm eye plaque in the homogeneous media configuration and of the 10 mm eye plaque in the heterogeneous media. The top left panel and the top right panel show the relative dose difference map, at , with respect to the reference CLRP data for the HOMO 20 mm plaque model and the HETERO 10 mm plaque model. The white regions on the relative dose difference maps represent the location of the plaque. A filter was used to omit dose at the location of the plaque. Shown in the middle panels are histograms of the relative difference between TOPAS and egs_brachy (CLRP) for the normalized dose in each voxel. On the middle left is the histogram for the 20 mm HOMO case and the histogram for the 10 mm HETERO case is on the middle right. The normalized central axis dose profile and the normalized transverse dose profiles are presented in the bottom graphs of Fig. 4. The bottom left graph compares the central axis dose profile to the CLRP data, to data from Melhus [
]. The normalized transverse dose profiles at 0.5 cm and 1 cm are compared to CLRP results in the bottom right graph. The relative difference with respect to the CLRP is presented below each profile plot. Dose maps, dose profiles and relative difference histograms of the other cases are presented as supplementary material.
Fig. 5 depicts the results of local dose differences between TOPAS and egs_brachy (CLRP) for the 10 mm HETERO case and the 20 mm HOMO case. These results are represented by dose distribution maps at (top panels) and histograms (bottom panels). The results of the 10 mm HOMO case and 20 mm HETERO case are presented in the same way in the supplementary materials.
Fig. 4(Top left panel) Relative difference map at 0 mm between TOPAS and egs_brachy results () for the 20 mm eye plaque HOMO. (Top right panel) Relative difference map at 0 mm between TOPAS and egs_brachy results () for 10 mm eye plaque HETERO. (Middle left panel) Histogram of the relative differences between TOPAS and egs_brachy results () for the 20 mm HOMO case for all voxels. (Middle right panel) Histogram of the relative differences between TOPAS and egs_brachy results () for the 10 mm HETERO case for all voxels. (Bottom left panel) Normalized dose along the central axis ( 0 cm) for the 10 mm HETERO case. (Bottom right panel) Transverse normalized dose ( 0 cm) at 0.5 cm and 1 cm for the 10 mm HETERO case.
Fig. 6 depicts the results of local dose differences between TOPAS and egs_brachy (CLRP) for the 10 mm and 20 mm HETERO cases where the 3.77 keV 125I emission peak is omitted from the TOPAS simulations. These results are represented by dose distribution maps at (top panels) and histograms (bottom panels).
Fig. 5(Top left panel) Local dose difference map at 0 mm between TOPAS and egs_brachy results (Gy/hist) for the 20 mm eye plaque HOMO. (Top right panel) Local dose difference map at 0 mm between TOPAS and egs_brachy results (Gy/hist) for 10 mm eye plaque HETERO. (Bottom left panel) Histograms of doses per history (Gy/hist) for the HOMO 20 mm case obtained with TOPAS and egs_brachy. (Bottom right panel) Histograms of doses per history (Gy/hist) for the HETERO 10 mm case obtained with TOPAS and egs_brachy.
Fig. 6(Top left panel) Local dose difference map at 0 mm between TOPAS and egs_brachy results (Gy/hist) for the 20 mm eye plaque HETERO without the 3.77 keV emission line. (Top right panel) Local dose difference map at 0 mm between TOPAS and egs_brachy results (Gy/hist) for 10 mm eye plaque HETERO without the 3.77 keV emission line. (Bottom left panel) Histograms of doses per history (Gy/hist) for the HETERO 20 mm case obtained with TOPAS without the 3.77 keV emission line and egs_brachy. (Bottom right panel) Histograms of doses per history (Gy/hist) for the HETERO 10 mm case obtained with TOPAS without the 3.77 keV emission line and egs_brachy.
4.1.1 Air-kerma strengths of 125 i seeds with modulated intensities for the 3.77 kev emission peak
It is observed that when using the intensity recommended by the NNDC for the 3.77 keV peak in the probability distribution function for 125I emission, the air-kerma strengths obtained for the SelectSeed 130.002 and the OncoSeed 6711 are respectively 9.53% and 9.64% lower than the CLRP’s values (4.0042 Gy cm2 hist−1 and 3.7666 Gy cm2 hist−1 respectively) these values are found through a link in the text on the webpage[
]. These results are in agreement with the ratio between the water-kerma per photon history obtained with the TG-43 recommended spectrum and the NNDC spectrum (ratio of 1.103 ± 0.002) presented in the study by Rivard et al.. when the 3.77 keV energy line is not included in the NNDC spectrum.[
]. This is due to photons of 3.77 keV attenuated by the titanium capsule and not contributing to the fluence measured by the air chamber in the WAFAC simulation. The fluence normalized by the number of histories (photons) produced initially in the 125I source is the parameter used to calculate the air-kerma strength. If the 3.77 keV peak is omitted, a larger portion of the produced particles will contribute to the measured fluence at the WAFAC. Inversely, if the 3.77 keV peak is considered for the same number of initial histories, this results in a higher air-kerma strength. As seen in Table 2, if the intensity of the 3.77 keV peak is approximately 25% higher, the air-kerma strength will be approximately 25% weaker. However, when relative values are calculated using doses and air-kerma strength, the dependency on the 3.77 keV energy line cancels out and is not as much relevant as with parameters in absolute units. This might explains why it has been left out from the recommended TG-43 and CLRP’s 125I spectrum.
4.1.2 Dose-rate constants
The relative differences between the TOPAS obtained dose rate constants and the CLRP reference dose rate constants are within 2%. When comparing with the AAPM consensus dataset, 7 out of the 12 dose rate constants are within a 3% difference. Best 2335 and STM1251 dose rate constants exhibit differences of −4% with the TG-43 consensus data but have relative differences to the CLRP data of 0.08% and -1% respectively. Comparing CLRP to TG-43 consensus, the differences for these two sources are -5% and -3%. This shows that there is agreement between TOPAS and CLRP results for the dose rate constants. The greatest relative difference with respect to the consensus data (-6.7%) is seen with the IAI-125 A and the IAPd-103 A. It is interesting to note that in these cases, the difference between the CLRP and the TG-43 consensus dose rate constants are also -6% and -5% respectively. Alternatively, the difference between TOPAS results and egs_brachy (CLRP) results are -0.9% and -1.94%, which shows excellent agreement between the two MC tools. Comparing CLRP data to TG-43 consensus data, the dose rate constant of 8 out of the 12 sources are shown to be within 3%, with the largest difference of −6% observed for the IAPd-103 A, as previously stated. Note that the CLRP reference data is fully based on MC simulations with the egs_brachy code [
Safigholi H, Chamberland MJP, Taylor REP, Allen CH, Martinov MP, Rogers DWO, et al. Update of the CLRP TG-43 parameter database for low-energy brachytherapy sources. Med Phys 2473-4209n/a(n/a). URL.
]. Such differences in methodology explain part of the reported relative differences when comparing the data sets. Overall, there is a good agreement and the average relative difference between TOPAS and the reference data (CLRP and TG-43 consensus data combined) for the dose rate constants is -1.8%.
4.1.3 Radial dose functions
Compared to the CLRP data, all of the radial dose functions are within 2% between 0.5 and 4 cm. For the iodine sources, the average of the absolute relative differences with CLRP for these regions is 0.6%. These averages are 0.7% and 0.4% for the palladium and cesium sources. In comparison to the TG-43 consensus radial dose functions, such averages are respectively 0.8%, 1.6% and 0.5% for iodine, palladium and cesium sources. Good agreement with the reference data in this region (0.5 cm 4 cm) is implied by these averages. Similar to TOPAS versus TG-43 results, the average of the absolute relative differences between CLRP data and TG-43 consensus data for the radial dose functions are 0.8% (iodine), 1.8% (palladium) and 0.2% (cesium). Closer (0.06 to 0.5 cm) and further (beyond 4 cm) from the source, 10 of the 12 radial dose functions are within 5% of the CLRP data. The Best 2335 and the Theraseed200 Light are the two exceptions. For the Best 2335, the differences are greater than 5% only at distances very close and far away from the source (0.05 to 0.15 cm and beyond 8 cm). Within 0.06 to 6 cm, the differences for the Theraseed200 Light do not exceed 10%. Outside this radius range, the differences for this source increase as the radius increases. Considering the differences throughout all distances, iodine sources have an averaged absolute relative difference with respect to the CLRP data of 1 ± 2%, whereas for palladium sources this average was 3 ± 4%. A similar comparison is made between the consensus data (TG-43) and TOPAS data, where 8 of the 12 sources have a relative difference within 5% up to 6 cm. Greater relative differences (relative to TG-43 consensus) are again present in regions close ( 0.5 cm) to the surface of the source and far from it ( 4 cm). The region close to the source is susceptible to a significant dose gradient that enhances the discussed differences. The average of absolute relative differences in regard to all the reference data is 4% and within a more clinically relevant region (0.5 to 4 cm), this average drops down to 0.45%. This implies overall excellent agreement with the reference data for the radial dose functions.
The TOPAS TotalInteractionCount filter was able to correctly separate the SelectSeed radial dose function in its primary, single scatter and multiple scatter components, as seen in Fig. 2. The primary component had relative differences of up to 2.7% close to the source ( 1 cm). The single scatter component exhibited the greatest absolute difference at 3 cm, corresponding to a 3.2% relative difference. The multiple scatter component presented the biggest absolute difference at 1 cm. Note that for radii 1 cm, the multiple scatter component had relative differences of less than 2.4%. Despite such differences, the total dose was within 2.5% for all radii.
4.1.4 Anisotropy functions
The majority (83%) of the TOPAS anisotropy function data is within 2% with respect to the reference CLRP data for cm, 1 cm and 5 cm between 20° and 90°. Compared to all of the reference data sources (CLRP, TG-43 and others), 78% of TOPAS anisotropy function results are within 2% for the same interval (20°-90°). In this 20° to 90° region, the average of absolute relative differences to all the data is 1.8%, which implies very good agreement. There are similar results for the differences of CLRP versus TG-43 anisotropy functions. For instance, 71% of CLRP normalized doses are within 2% of the TG-43 consensus data between 20° and 90°. Differences with CLRP data over 5% are observed at angles equal or smaller than 20°. However, better agreement with TG-43 consensus data is seen where there is greater disagreement with CLRP data. Indeed, sources with a difference over 7% with respect to the CLRP data at angles smaller than 10°, are within 3% of the TG-43 consensus data. Differences with respect to the consensus data (combination of MC simulations and experimental data) also appear at greater angles for the Best 2335 at 1 cm. As discussed in the previous section, reference data sets are either fully MC-based or a combination of MC simulations and experimental results. When comparing MC-based results, differences commonly appear at small angles (less than 10°), as seen in Fig. 3. Note that at these smaller angles, the self-attenuation of the source is more pronounced due to its horizontal orientation. Hence, MC results are sensitive to the detailed modeling of the source. In general, the average of the absolute relative differences of all the reference data is 2%, which shows excellent agreement between TOPAS obtained results and the reference data.
4.2 Eye plaque cases
There is a general agreement between the TOPAS and egs_brachy reference data, as seen in the normalized dose maps (Fig. 4). Indeed, 90% of the voxels for the 10 mm HETERO case and 97% of the voxels for the 10 mm HOMO case are within 1% of the CLRP’s results. There is the same relative difference interval for 84% of the voxels for the 20 mm HETERO case and for 96% of the voxels for the 20 mm HOMO case. For all cases, this corresponds to an average of 92% of all voxels with a standard deviation of 5%. The most recurring relative differences (histogram maxima) for these voxel distributions are respectively at 0.3%, 0.2%, −0.08% and −0.3%, which shows good agreement. Greater variations up to 3% are reported near 20 mm and further. Noticeable differences to egs_brachy (down to −8% in the 20 mm HETERO case) are also present on the exterior surface of the plaque in the HETERO cases. Both farther regions () and exterior side plaque regions show low-dose deposition with doses ranging from 0.2% to 20% of that of the reference point dose. It must be pointed out that in lower dose regions, a small nominal difference can lead to a large relative difference. However, such differences have no significant clinical impact. To take that into account, doses below 10% of that of the reference point were excluded from the analysis. By doing so, 96% (10 mm HETERO), 94% (20 mm HETERO), 97% (10 mm HOMO) and 93% (20 mm HOMO) of the voxels in each case are within 1% of the CLRP’s results. This gives an average of 95% with 2% of standard deviation (versus the previous average of 92% with a standard deviation of 5%). Plaque contours (extending to 0.5 mm from the edge of the plaques geometry) in both HOMO and HETERO cases also show noticeable discrepancies with the reference data. Similar behavior is observed very close to seed geometries in their radial dose functions. Doses this close to the plaque surfaces are also not clinically relevant.
As a whole, the normalized central and transverse axis dose profiles are within 1% of the reference data. The normalized central axis dose profiles have average relative differences, with respect to the CLRP data, of 0.4%, 0.3%, 0.3% and 0.2% for the 10 mm plaque in the HETERO and HOMO case and for the 20 mm plaque in the HETERO and HOMO case, respectively. Note that the statistical uncertainties of simulations were 0.5%, 0.5%, 0.7% and 0.2% for each case. As such, the reported relative differences are within the TOPAS statistical uncertainties, which implies agreement between TOPAS and the CLRP reference data. The average differences, when compared to other reference data (TG-129, Melhus), are similar (ranging from 0.2% to 0.4%). As for the relative difference between CLRP and TG-129 results for the normalized central axis doses, they are in average 0.1% for the 10 mm HETERO case and 0.2% for all other cases. Comparably to differences seen with TOPAS data versus TG-129 data, they also range from 0% to 0.9%. The normalized transverse dose profiles (with 0.5 and 1 cm data combined) have differences to CLRP data that are in average 0.38%, 0.25%, 0.28% and 0.17% for the 10 mm HETERO and HOMO and for the 20 mm HETERO and HOMO cases, respectively. Such differences are similar to the ones found in the central axis dose profiles. Note that the transverse dose profiles are located closer to the eye plaques in high-dose regions (dose peeking at 0.4 for the 20 mm cases). Hence, there is a presence of smaller differences to CLRP compared to the doses in the low-dose regions.
For all cases, the local dose differences calculated in dose per history (absolute units) between egs_brachy and TOPAS are on average 11%. For the various calculation scenarios (HOMO 10 mm, HETERO 10 mm, HOMO 20 mm and HETERO 20 mm), the corresponding standard deviations are 3%, 0.5%, 1% and 10%, respectively. In line with the local dose difference maps, this illustrates the presence of a significant systematic difference, greater than the statistical uncertainty throughout each geometry. The reason for this systematic difference is the presence of the 3.77 keV energy in the probability distribution function of the 125I emission spectrum. It is the same reason as the differences present in air-kerma strength as explained previously. As it can be observed in Fig. 6, dose distributions per history between TOPAS and egs_brachy with the 3.77 keV removed from the TOPAS 125I emission spectrum are in agreement. Indeed, more than 90% of the voxels in both cases are within 0%–3% local dose difference to egs_brachy obtained data. Such differences (0%–3%) are expected as seen with previous parameter comparisons throughout this study.
The inclusion of the 3.77 keV energy line does not change most TG-43 parameters (, and ) since they are calculated relative to a dose at a reference point. However, since it has a significant impact on the , it is important to include it when studying cases with no normalization to a dose at a reference point, such as absolute dose distributions (measured in Gy) or doses per history (measured in Gy per history) in order to depicts the situation as realistically as possible. The same can be said for the 2.7 keV energy line of the 103Pd emission spectrum and the 4.11 keV energy line of the 131Cs emission spectrum.
This work compared simulations made with TOPAS of single and multiple-seed configurations to published reference data. In general, relative differences were more pronounced in the low-dose regions such as the end of the radial dose functions (single-seed) or at the exterior side plaque regions in the eye plaque cases (multiple-seed). Also, regions near the edges of geometry components, such as the seed end-tips or contours of the eye plaques, showed edge effects and differences were seen.
Throughout this study, differences in results obtained with different Monte Carlo tools (TOPAS and egs_brachy) in the 1%–3% range were presented. In order to have a deep understanding of these differences, the following needs to be considered. The mean energy for the isotopes used in this study (I125, Pd103 and Cs131) are 27.3, 20.9 and 30.3 keV. Since low energies are involved, the photoelectric effect plays a major role. This implies that changes in material definition can have a significant impact on the results. For the same reason, brachytherapy simulations are sensitive to small geometry changes (even changes of the order of a few micrometers). This is demonstrated with the TheraSeed 200 source and its Light and Heavy versions of the seed. The only difference between these two sources is the thickness of the palladium coating ( difference), which is enough to produce different TG-43 parameters. For example, the difference between their dose-rate constants is 1.5% and their radial dose functions maxima have a difference of 4.4%. Note that the TG-43 report only presents results of a single TheraSeed 200 source but mentions that Monroe and Williamson[
Additionally, the relative comparisons in the low-dose regions are sensitive to small absolute differences. As a result, a more refined analysis is necessary, as seen in the eye plaque cases. Also, note the intrinsic uncertainty of the Monte Carlo simulations. Decreasing further the statistical uncertainty means high consumption of computing resources. However, results between two similar MC simulations are equivalent within uncertainties since the same physical events converge toward the same outcome. The statistical uncertainty in this study accounts for up to a 2% difference. These factors make simulating brachytherapy geometries (seeds and eye plaques) a challenge in the low-dose regime. The most challenging case was the 20 mm HETERO eye plaque because of the complexity of its geometry and the numerous sources present in it. Even for this challenging case, valid results according to the reference data were produced via TOPAS. The consistency in the valid results presented in this study, for all cases, demonstrates that TOPAS is a reliable MC tool for LDR brachytherapy applications.
4.3 Brachytherapy package for TOPAS
Simulations of low-energy photon-emitting brachytherapy sources performed with TOPAS showed good agreement with respect to published reference data. Single-seed simulations ensured the acceptable modeling of such sources based on available information and further tested TOPAS under different conditions of seeds internal structure, encapsulation and highly anisotropic dose distributions. In addition, the eye plaque cases benchmarked TOPAS for multi-seed voxel-based dose calculations in the presence of strong shielding. TOPAS users are given full access to the 12 presented source geometries as they have been included in TOPAS version 3.7. that already-released package also includes 3 HDR sources (Flexisource, TG 186, MicroSelectronV2), the TG 186 applicator and the TLE used for dose scoring [
]. A video tutorial was created to give insights on the source models and how such models are created. Additionally, some common simulation setups (e.g. extracting a couple of TG-43 parameters) are provided. The scaling of MC results to compare with the dosimetry calculated with a treatment planning system is described. Finally, a multi-source setup is also explained. A website gives general access to the tutorial [
]. The COMS eye plaque geometries, from 10 to 22 mm, are also provided as part of TOPAS version 3.8.
5. Conclusions
The purpose of this study was to validate the TOPAS MC toolkit for LDR brachytherapy applications. An advantage of using TOPAS is its capacity to create and simulate multiple radioactive sources and environments in a relatively simple manner. Overall, the results produced via TOPAS simulations were in good agreement with the reference data. The calculated dose rate constants, radial dose functions and anisotropy functions have averages of the absolute relative differences with respect to the reference data of 1.6%, 4% and 2%. TOPAS seed models are equivalent to CLRP models and to the models presented in the TG-43 reports. The normalized dose distributions, measured from the eye plaque simulations, have relative differences with respect to the CLRP data of 1% for almost all voxels. The dose profiles along the central and transverse axes are respectively within 0.5% and 1% of the reference data. Similar relative differences between TOPAS data versus consensus data and CLRP data versus consensus data were seen throughout this study. Therefore even if some differences between MC codes are seen, the extracted TG43 parameters (dose rate constants, radial dose functions and anisotropy functions) are in agreement with the reference data. The TOPAS extension mechanism allows advanced users to customize the toolkit and add geometries such as the COMS eye plaque models. This work validates TOPAS for LDR brachytherapy which complements the validation previously done for HDR brachytherapy [
]. Taking into account the easy setup of geometries and simulations and the TOPAS package of brachytherapy sources (included in TOPAS version 3.7), TOPAS is now a fully validated state-of-the-art MC toolkit for brachytherapy simulations. All validated geometries are provided to TOPAS users as a starting point for their LDR brachytherapy applications. The brachytherapy package and the tutorial provide a comprehensive solution for students, researchers and clinical medical physicists, to get the needed skills and tools to perform brachytherapy MC simulations.
Acknowledgments
This work is partially supported by the Natural Sciences and Engineering Research Council of Canada (NSERC) grant RGPIN-2019-05038 and the National Institutes of Health (NIH)/National Cancer Institute (NCI), United States grant U24 CA215123. Francisco Berumen acknowledges support by the Fonds de Recherche du Québec Nature et Technologies (FRQNT). This research was enabled in part by the support provided by Calcul Québec (www.calculquebec.ca) and Digital Research Alliance (ccdb.computecanada.ca).
Appendix A. Supplementary data
The following is the Supplementary material related to this article.
The supplementary materials include detailed descriptions of each source geometry and the TG-43 parameter curves associated to each of them. It also includes results for all eye plaque cases done.
Enhancements to commissioning techniques and quality assurance of brachytherapy treatment planning systems that use model-based dose calculation algorithms.
Report of the Task Group 186 on model-based dose calculation methods in brachytherapy beyond the TG-43 formalism: current status and recommendations for clinical implementation.
Report of the Task Group 186 on model-based dose calculation methods in brachytherapy beyond the TG-43 formalism: Current status and recommendations for clinical implementation.
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Safigholi H, Chamberland MJP, Taylor REP, Allen CH, Martinov MP, Rogers DWO, et al. Update of the CLRP TG-43 parameter database for low-energy brachytherapy sources. Med Phys 2473-4209n/a(n/a). URL.
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