Efficient Monte Carlo simulation of multileaf collimators using geometry-related variance-reduction techniques

Assessment of Surface and Build-up Doses for a 6 MV Photon Beam using Parallel Plate Chamber, EBT3 Gafchromic Films, and PRIMO Monte Carlo Simulation Code

Background:

Accurate assessment of surface and build-up doses has a key role in radiotherapy, especially for the superficial lesions with uncertainties involved while performing measurements in the build-up region.

Objective:

This study aimed to assess surface and build-up doses for 6 MV photon beam from linear accelerator using parallel plate ionization chamber, EBT3 Gafchromic films, and PRIMO Monte Carlo (MC) simulation code.

Material and Methods:

In this experimental study, parallel plate chamber (PPC05) and EBT3 Gafchromic films were used to measure doses in a build-up region for 6 MV beam from the linear accelerator for different field sizes at various depths ranging from 0 to 2 cm from the surface with 100 cm source to surface distance (SSD) in a solid water phantom. Measured results were compared with Monte Carlo simulated results using PENELOPE-based PRIMO simulation code for the same setup conditions. Effect of gantry angle incidence and SSD were also analyzed for depth doses at the surface and build-up regions using PPC05 ion chamber and EBT3 Gafchromic films.

Results:

Doses measured at the surface were 14.78%, 19.87%, 25.83%, and 31.54% for field sizes of 5×5, 10×10, 15×15, and 20×20 cm², respectively for a 6 MV photon beam with a parallel plate chamber and 14.20%, 19.14%, 25.149%, and 30.90%, respectively for EBT3 Gafchromic films. Both measurement sets were in good agreement with corresponding simulated results from the PRIMO MC simulation code; doses increase with the increase in field sizes.

Conclusion:

Good agreement was observed between the measured depth doses using parallel plate ionization chamber, EBT3 Gafchromic films, and the simulated depth doses using PRIMO Monte Carlo simulation code.

Toolkit implementation to exchange phase-space files between IAEA and MCNP6 monte Carlo code format

PURPOSE

Some Monte Carlo simulation codes can read and write phase space files in IAEA format, which are used to characterize accelerators, brachytherapy seeds and other radiation sources. Moreover, as the format has been standardized, these files can be used with different simulation codes. However, MCNP6 has not still implemented this capability, which complicate the studies involving this kind of sources and the reproducibility of results among independent researchers. Therefore, the purpose of this work is to develop a tool to perform conversions between IAEA and MCNP6 phase space files formats, to be used for Monte Carlo simulations.

MATERIALS AND METHODS

This paper presents a toolkit written in C language that uses the IAEA libraries to convert phase space files between IAEA and MCNP6 format and vice versa. To test the functionality of the provided tool, a set of verification tests has been carried out. In addition, a linear accelerator treatment has been simulated with the PENELOPE library using the PenEasy framework, which is already capable to read and write IAEA phase space files, and MCNP6 using the developed tools.

RESULTS

Both codes show compatible depth dose curves and profiles in a water tank, demonstrating that the conversion tools work properly. Moreover, the phase space file formats have been converted from IAEA to MCNP6 format and back again to IAEA format, reproducing the very same results.

CONCLUSION

The toolkit developed in this work offers MCNP6 scientific community an external and validated program able to convert phase space files in IAEA format to MCNP6 internal format and use them for Monte Carlo applications. Furthermore, the developed tools provide also the reverse conversion, which allow sharing MCNP6 results with users of other Monte Carlo codes. This capability in the MCNP6 ecosystem provides to the scientific community the ability not only to share radiation sources, but also to facilitate the reproducibility among different groups using different codes via the standard format specified by the IAEA.

Experimental Validation of an Analytical Program and a Monte Carlo Simulation for the Computation of the Far Out-of-Field Dose in External Beam Photon Therapy Applied to Pediatric Patients

Background

The out-of-the-field absorbed dose affects the probability of primary second radiation-induced cancers. This is particularly relevant in the case of pediatric treatments. There are currently no methods employed in the clinical routine for the computation of dose distributions from stray radiation in radiotherapy. To overcome this limitation in the framework of conventional teletherapy with photon beams, two computational tools have been developed—one based on an analytical approach and another depending on a fast Monte Carlo algorithm. The purpose of this work is to evaluate the accuracy of these approaches by comparison with experimental data obtained from anthropomorphic phantom irradiations.

Materials and Methods

An anthropomorphic phantom representing a 5-year-old child (ATOM, CIRS) was irradiated considering a brain tumor using a Varian TrueBeam linac. Two treatments for the same planned target volume (PTV) were considered, namely, intensity-modulated radiotherapy (IMRT) and volumetric modulated arc therapy (VMAT). In all cases, the irradiation was conducted with a 6-MV energy beam using the flattening filter for a prescribed dose of 3.6 Gy to the PTV. The phantom had natLiF : Mg, Cu, P (MCP-N) thermoluminescent dosimeters (TLDs) in its 180 holes. The uncertainty of the experimental data was around 20%, which was mostly attributed to the MCP-N energy dependence. To calculate the out-of-field dose, an analytical algorithm was implemented to be run from a Varian Eclipse TPS. This algorithm considers that all anatomical structures are filled with water, with the exception of the lungs which are made of air. The fast Monte Carlo code dose planning method was also used for computing the out-of-field dose. It was executed from the dose verification system PRIMO using a phase-space file containing 3x109 histories, reaching an average standard statistical uncertainty of less than 0.2% (coverage factor k = 1 ) on all voxels scoring more than 50% of the maximum dose. The standard statistical uncertainty of out-of-field voxels in the Monte Carlo simulation did not exceed 5%. For the Monte Carlo simulation the actual chemical composition of the materials used in ATOM, as provided by the manufacturer, was employed.

Results

In the out-of-the-field region, the absorbed dose was on average four orders of magnitude lower than the dose at the PTV. For the two modalities employed, the discrepancy between the central values of the TLDs located in the out-of-the-field region and the corresponding positions in the analytic model were in general less than 40%. The discrepancy in the lung doses was more pronounced for IMRT. The same comparison between the experimental and the Monte Carlo data yielded differences which are, in general, smaller than 20%. It was observed that the VMAT irradiation produces the smallest out-of-the-field dose when compared to IMRT.

Conclusions

The proposed computational methods for the routine calculation of the out-of-the-field dose produce results that are similar, in most cases, with the experimental data. It has been experimentally found that the VMAT irradiation produces the smallest out-of-the-field dose when compared to IMRT for a given PTV.

A comprehensive Monte Carlo study of CT dose metrics proposed by the AAPM Reports 111 and 200

PURPOSE

A Monte Carlo (MC) modeling of single axial and helical CT scan modes has been developed to compute single and accumulated dose distributions. The radiation emission characteristics of an MDCT scanner has been modeled and used to evaluate the dose deposition in infinitely long head and body PMMA phantoms. The simulated accumulated dose distributions determined the approach to equilibrium function, H(L). From these H ( L ) curves, dose-related information was calculated for different head and body clinical protocols.

METHODS

The PENELOPE/penEasy package has been used to model the single axial and helical procedures and the radiation transport of photons and electrons in the phantoms. The bowtie filters, heel effect, focal-spot angle, and fan-beam geometry were incorporated. Head and body protocols with different pitch values were modeled for x-ray spectra corresponding to 80, 100, 120, and 140 kV. The analytical formulation for the single dose distributions and experimental measurements of single and accumulated dose distributions were employed to validate the MC results. The experimental dose distributions were measured with OSLDs and a thimble ion chamber inserted into PMMA phantoms. Also, the experimental values of the C T D I 100 along the center and peripheral axes of the CTDI phantom served to calibrate the simulated single and accumulated dose distributions.

RESULTS

The match of the simulated dose distributions with the reference data supports the correct modeling of the heel effect and the radiation transport in the phantom material reflected in the tails of the dose distributions. The validation of the x-ray source model was done comparing the CTDI ratios between simulated, measured and CTDosimetry data. The average difference of these ratios for head and body protocols between the simulated and measured data was in the range of 13-17% and between simulated and CTDosimetry data varied 10-13%. The distributions of simulated doses and those measured with the thimble ion chamber are compatible within 3%. In this study, it was demonstrated that the efficiencies of the C T D I 100 measurements in head phantoms with nT = 20 mm and 120 kV are 80.6% and 87.8% at central and peripheral axes, respectively. In the body phantoms with n T = 40 mm and 120 kV, the efficiencies are 56.5% and 86.2% at central and peripheral axes, respectively. In general terms, the clinical parameters such as pitch, beam intensity, and voltage affect the D_eq values with the increase of the pitch decreasing the D_eq and the beam intensity and the voltage increasing its value. The H(L) function does not change with the pitch values, but depends on the phantom axis (central or peripheral).

CONCLUSIONS

The computation of the pitch-equilibrium dose product, D ̂ eq , evidenced the limitations of the C T D I 100 method to determine the dose delivered by a CT scanner. Therefore, quantities derived from the C T D I 100 propagate this limitation. The developed MC model shows excellent compatibility with both measurements and literature quantities defined by AAPM Reports 111 and 200. These results demonstrate the robustness and versatility of the proposed modeling method.

Monte Carlo simulation of conical collimators for stereotactic radiosurgery with a 6 MV flattening-filter-free photon beam

PURPOSE

Conical collimators, or cones, are tertiary collimators that attach to a radiotherapy linac and are suited for the stereotactic radiosurgery treatment of small brain lesions. The small diameter of the most used cones makes difficult the acquisition of the dosimetry data needed for the commissioning of treatment planning systems. Although many publications report dosimetric data of conical collimators for stereotactic radiosurgery, most of the works use different setups, which complicates comparisons. In other cases, the cone output factors reported do not take into account the effect of the small cone diameter on the detector response. Finally, few data exist on the dosimetry of cones with flattening-filter-free (FFF) beams from modern linac models. This work aims at obtaining a dosimetric characterization of the conical collimators manufactured by Brainlab AG (Munich, Germany) in a 6 MV FFF beam from a TrueBeam STx linac (Varian Medical Systems).

METHODS

Percentage depth dose curves, lateral dose profiles and cone output factors were obtained using Monte Carlo simulations for the cones with diameters of 4, 5, 6, 7.5, 8, 10, 12.5, 15, 17.5, 20, 25, and 30 mm. The simulation of the linac head was carried out with the PRIMO Monte Carlo software, and the simulations of the cones and the water phantom were run with the general-purpose Monte Carlo code PENELOPE. The Monte Carlo model was validated by comparing the simulation results with measurements performed for the cones of 4, 5, and 7.5 mm of diameter using a stereotactic field diode, a microDiamond detector and EBT3 radiochromic film. In addition, for those cones, simulations and measurements were done for comparison purposes, by reproducing the experimental setups from the available publications.

RESULTS

The experimental data acquired for the cones of 4, 5, and 7.5 mm validated the developed Monte Carlo model. The simulations accurately reproduced the experimental depths of maximum dose and the dose ratio at 20- and 10-cm depth (PDD_20/10 ). A good agreement was obtained between simulated and experimental lateral dose profiles: The differences in the full-width at half-maximum were smaller than 0.2 mm, and the differences in the penumbra 80%-20% were smaller than 0.25 mm. The difference between the simulated and the average of the experimental output factors for the cones of 4, 5, and 7.5 mm of diameter was 0.0%, 0.0%, and 3.0%, respectively, well within the statistical uncertainty of the simulations (4.4% with coverage factor k = 2). It was also found that the simulated cone output factors agreed within 2% with the average of output factors reported in the literature for a variety of setup conditions, detectors, beam qualities, and cone manufacturers.

CONCLUSION

A Monte Carlo model of cones for stereotactic radiosurgery has been developed and validated. The cone dosimetry dataset obtained in this work, consisting of percentage depth doses, lateral dose profiles and output factors, is useful to benchmark data acquired for the commissioning of cone-based radiosurgery treatment planning systems.

First-stage validation of a portable imageable MR-compatible water calorimeter

PURPOSE

The purpose of this study is to design a water calorimeter with three goals in mind: (a) To be fully magnetic resonance (MR)-compatible; (b) To be imaged using kV cone beam computed tomography (CBCT), MV portal imaging or MRI for accurate positioning; (c) To accommodate both vertical and horizontal beam incidence, as well as volumetric deliveries or Gamma Knife®. Following this, the calorimeter performance will be measured using an accelerator-based high-energy photon beam.

METHODS

A portable 4°C cooled stagnant water calorimeter was built using MR-compatible materials. The walls consist of layers of acrylic plastic, aerogel-based material acting as thermal insulation, as well as tubing for coolant to flow to keep the calorimeter temperature stable at 4°C. The lid contains additional pathways for coolant to flow through as well as two hydraulically driven stirrers. The water calorimeter was positioned in an Elekta Versa using kV CBCT imaging as well as orthogonal MV image pairs. Absolute absorbed dose to water was then determined under a 6 MV flattening filter-free (FFF) beam. This was compared against reference dosimetry results that were measured under identical conditions with an Exradin A1SL ionization chamber with a calibration coefficient directly traceable to the National Research Council Canada.

RESULTS

The dose to water determined with the calorimeter (n = 30) agreed with the A1SL ionization chamber reference dose measurements (n = 15) to within 0.25%. The uncertainty associated with the water calorimeter absorbed dose measurement was estimated to be 0.54% (k = 1).

CONCLUSIONS

An MR-compatible water calorimeter was successfully built and absolute absorbed dose to water under a conventional 6 MV FFF beam was determined successfully as a first-stage validation of the system.

Validation of PRIMO Monte Carlo Model of Clinac®iX 6MV Photon Beam

Purpose

This study aims to model 6MV photon of Clinac^®iX linear accelerator using PRIMO Monte Carlo (MC) code and to assess PRIMO as an independent MC-based dose verification and quality assurance tool.

Materials and Methods

The modeling of Clinac^®iX linear accelerator has been carried out by using PRIMO simulation software (Version 0.3.1.1681). The simulated beam parameters were compared against the measured beam data of the Clinac^®iX machine. The PRIMO simulation model of Clinac^®iX was also validated against Eclipse^® Acuros XB dose calculations in the case of both homogenous and inhomogeneous mediums. The gamma analysis method with the acceptance criteria of 2%, 2 mm was used for the comparison of dose distributions.

Results

Gamma analysis shows a minimum pass percentage of 99% for depth dose curves and 95.4% for beam profiles. The beam quality index and output factors and absolute point dose show good agreement with measurements. The validation of PRIMO dose calculations, in both homogeneous and inhomogeneous medium, against Acuros^® XB shows a minimum gamma analysis pass rate of 99%.

Conclusions

This study shows that the research software PRIMO can be used as a treatment planning system-independent quality assurance and dose verification tool in daily clinical practice. Further validation will be performed with different energies, complex multileaf collimators fields, and with dynamic treatment fields.

Out-of-Field Dose Calculation by a Commercial Treatment Planning System and Comparison by Monte Carlo Simulation for Varian TrueBeam®

PURPOSE

The calculation accuracy of treatment planning systems (TPSs) drops drastically when the points outside the field edges are considered. The real accuracy of a TPS and linear accelerator (linac) combination for regions outside the field edge is a subject which demands more study. In this study, the accuracy of out-of-field dose calculated by a TPS, used with a TrueBeam® (TB) linac, is quantified.

MATERIALS AND METHODS

For dose calculation, Eclipse™ version 13.7 commissioned for TB machine was used. For comparison, Monte Carlo (MC) methods, as well as the measurements, were used. The VirtuaLinac, a Geant 4-based MC program which is offered as a cloud solution, is used for the generation of input phase-space (PS) files. This PS file was imported into PRIMO (PENELOPE based MC program) for the simulation of out-of-field dose.

RESULTS

In this study, the accuracy of the out-of-field dose calculated by a TPS for a TB linac was estimated. As per the results in comparison with MC simulations, the TPS underestimated the dose by around 45% on an average for the off-axis-distance range considered in this study. As the off-axis distance increased, the underestimation of the dose also increased.

CONCLUSION

In this work, it was observed that the TPS underestimates doses beyond the edges of treatment fields for a clinical treatment executed on a TB machine. This indicates that the out-of-field dose from TPSs should only be used with a clear understanding of the inaccuracy of dose calculations beyond the edge of the field.

DPM as a radiation transport engine for PRIMO

Background

PRIMO is a dose verification system based on the general-purpose Monte Carlo radiation transport code penelope, which implements an accurate physics model of the interaction cross sections and the radiation transport process but with low computational efficiency as compared with fast Monte Carlo codes. One of these fast Monte Carlo codes is the Dose Planning Method (DPM). The purpose of this work is to describe the adaptation of DPM as an alternative PRIMO computation engine, to validate its performance against penelope and to validate it for some specific cases.

Methods

DPM was parallelized and modified to perform radiation transport in quadric geometries, which are used to describe linacs, thus allowing the simulation of dynamic treatments. To benchmark the new code versus penelope, both in terms of accuracy of results and simulation time, several tests were performed, namely, irradiation of a multi-layer phantom, irradiation of a water phantom using a collimating pattern defined by the multileaf collimator (MLC), and four clinical cases. The gamma index, with passing criteria of 1 mm/1%, was used to compare the absorbed dose distributions. Clinical cases were compared using a 3-D gamma analysis.

Results

The percentage of voxels passing the gamma criteria always exceeded 99% for the phantom cases, with the exception of the transport through air, for which dose differences between DPM and penelope were as large as 24%. The corresponding percentage for the clinical cases was larger than 99%. The speedup factor between DPM and penelope ranged from 2.5 ×, for the simulation of the radiation transport through a MLC and the subsequent dose estimation in a water phantom, up to 11.8 × for a lung treatment. A further increase of the computational speed, up to 25 ×, can be obtained in the clinical cases when a voxel size of (2.5 mm)³ is used.

Conclusions

DPM has been incorporated as an efficient and accurate Monte Carlo engine for dose estimation in PRIMO. It allows the concatenated simulation of the patient-dependent part of the linac and the patient geometry in static and dynamic treatments. The discrepancy observed between DPM and penelope, which is due to an artifact of the cross section interpolation algorithm for low energy electrons in air, does not affect the results in other materials.

PRIMO Monte Carlo software benchmarked against a reference dosimetry dataset for 6 MV photon beams from Varian linacs

BACKGROUND

The software PRIMO for the Monte Carlo simulation of radiotherapy linacs could potentially act as a independent calculation system to verify the calculations of treatment planning systems. We investigated the suitability of the PRIMO default beam parameters to produce accurate dosimetric results for 6 MV photon beams from Varian Clinac 2100 linacs and 6 MV flattening-filter-free photon beams from Varian TrueBeam linacs.

METHODS

Simulation results with the DPM algorithm were benchmarked against a published reference dosimetry dataset based on point measurements of 25 dosimetric parameters on a large series of linacs. Studied parameters (for several field sizes and depths) were: PDD, off-axis ratios, and output factors for open fields and IMRT/SBRT-style fields. For the latter, the output factors were also determined with radiochromic film and with a small-sized ionization chamber. Benchmark data, PRIMO simulation results and our experimental results were compared.

RESULTS

PDD, off-axis ratios, and open-field output factors obtained from the simulations with the PRIMO default beam parameters agreed with the benchmark data within 2.4% for Clinac 2100, and within 1.3% for TrueBeam. Higher differences were found for IMRT/SBRT-style output factors: up to 2.8% for Clinac 2100, and up to 3.3% for TrueBeam. Experimental output factors agreed with benchmark data within 1.0% (ionization chamber) and within 1.9% (radiochromic film).

CONCLUSIONS

PRIMO default initial beam parameters for 6 MV photon beams from Varian Clinac 2100 linacs and 6 MV FFF photon beams from Varian TrueBeam linacs allowed agreement within 3.3% with a dosimetry database based on measurements of a high number of linacs. This finding represents a first step in the validation of PRIMO for the independent verification of radiotherapy plans.

A photon source model based on particle transport in a parameterized accelerator structure for Monte Carlo dose calculations

PURPOSE

An accurate source model of a medical linear accelerator is essential for Monte Carlo (MC) dose calculations. This study aims to propose an analytical photon source model based on particle transport in parameterized accelerator structures, focusing on a more realistic determination of linac photon spectra compared to existing approaches.

METHODS

We designed the primary and secondary photon sources based on the photons attenuated and scattered by a parameterized flattening filter. The primary photons were derived by attenuating bremsstrahlung photons based on the path length in the filter. Conversely, the secondary photons were derived from the decrement of the primary photons in the attenuation process. This design facilitates these sources to share the free parameters of the filter shape and be related to each other through the photon interaction in the filter. We introduced two other parameters of the primary photon source to describe the particle fluence in penumbral regions. All the parameters are optimized based on calculated dose curves in water using the pencil-beam-based algorithm. To verify the modeling accuracy, we compared the proposed model with the phase space data (PSD) of the Varian TrueBeam 6 and 15 MV accelerators in terms of the beam characteristics and the dose distributions. The EGS5 Monte Carlo code was used to calculate the dose distributions associated with the optimized model and reference PSD in a homogeneous water phantom and a heterogeneous lung phantom. We calculated the percentage of points passing 1D and 2D gamma analysis with 1%/1 mm criteria for the dose curves and lateral dose distributions, respectively.

RESULTS

The optimized model accurately reproduced the spectral curves of the reference PSD both on- and off-axis. The depth dose and lateral dose profiles of the optimized model also showed good agreement with those of the reference PSD. The passing rates of the 1D gamma analysis with 1%/1 mm criteria between the model and PSD were 100% for 4 × 4, 10 × 10, and 20 × 20 cm² fields at multiple depths. For the 2D dose distributions calculated in the heterogeneous lung phantom, the 2D gamma pass rate was 100% for 6 and 15 MV beams. The model optimization time was less than 4 min.

CONCLUSION

The proposed source model optimization process accurately produces photon fluence spectra from a linac using valid physical properties, without detailed knowledge of the geometry of the linac head, and with minimal optimization time.

Radiation dosimetry in magnetic fields with Farmer-type ionization chambers: determination of magnetic field correction factors for different magnetic field strengths and field orientations

The aim of this work was to determine magnetic field correction factors that are needed for dosimetry in hybrid devices for MR-guided radiotherapy for Farmer-type ionization chambers for different magnetic field strengths and field orientations. The response of six custom-built Farmer-type chambers irradiated at a 6 MV linac was measured in a water tank positioned in a magnet with magnetic field strengths between 0.0 T and 1.1 T. Chamber axis, beam and magnetic field were perpendicular to each other and both magnetic field directions were investigated. EGSnrc Monte Carlo simulations were compared to the measurements and simulations with different field orientations were performed. For all geometries, magnetic field correction factors, [Formula: see text], and perturbation factors were calculated. A maximum increase of 8.8% in chamber response was measured for the magnetic field perpendicular to chamber and beam axis. The measured chamber response could be reproduced by adjusting the dead volume layer near the chamber stem in the Monte Carlo simulations. For the magnetic field parallel to the chamber axis or parallel to the beam, the simulated response increased by 1.1% at maximum for field strengths up to 1.1 T. A complex dependence of the response was found on chamber radius, magnetic field strength and orientation of beam, chamber axis and magnetic field direction. Especially for magnetic fields perpendicular to beam and chamber axis, the exact sensitive volume has to be considered in the simulations. To minimize magnetic field correction factors and the influence of dead volumes on the response of Farmer chambers, a measurement set-up with the magnetic field parallel to the chamber axis or parallel to the beam is recommended for dosimetry.

Dosimetric impact assessment using a general algorithm in geant4 simulations for a complex-shaped multileaf collimator

PURPOSE

We have developed an inhouse algorithm for the multileaf collimator (MLC) geometry model construction with an appropriate accuracy for dosimetric tests. Our purpose is to build a complex type of MLC and analyze the influence of the modeling parameters on the dose calculation.

METHODS

Using radiochromic films as detector the following tests were done: (I) Density test field: to compare measured and calculated dose distributions in order to determine the tungsten alloy physical density value. (II) Leaf ends test field: to verify the penumbra shape sensitivity against the discretization level set to simulate the curved leaf ends. (III) MLC-closed field: to obtain the value of the air gap between opposite leaves for a closed configuration which completes the modeling of the MLC leakage radiation. (IV) Picket-fence field: to fit the leaf tilt angle with respect of the divergent ray emerging from the source.

RESULTS

For a 18.5g/cm³ density value we have obtained a maximum, minimum and mean leakage values of 0.43%, 0.36% and 0.38%, similar to the experimental ones. The best discretization level in the leaf ends field shows a 5.51mm FWHM, very close to the measured value (5.49mm). An air gap of 370μm has been used in the simulation for the separation between opposite leaves. Using a 0.44° tilt angle, we found the same pattern as the experimental values.

CONCLUSIONS

Our code can reproduce complex MLC designs with a submilimetric dosimetric accuracy which implies the necessary background for dose calculation of high clinical interest small fields.

Monte Carlo systems used for treatment planning and dose verification

General-purpose radiation transport Monte Carlo codes have been used for estimation of the absorbed dose distribution in external photon and electron beam radiotherapy patients since several decades. Results obtained with these codes are usually more accurate than those provided by treatment planning systems based on non-stochastic methods. Traditionally, absorbed dose computations based on general-purpose Monte Carlo codes have been used only for research, owing to the difficulties associated with setting up a simulation and the long computation time required. To take advantage of radiation transport Monte Carlo codes applied to routine clinical practice, researchers and private companies have developed treatment planning and dose verification systems that are partly or fully based on fast Monte Carlo algorithms. This review presents a comprehensive list of the currently existing Monte Carlo systems that can be used to calculate or verify an external photon and electron beam radiotherapy treatment plan. Particular attention is given to those systems that are distributed, either freely or commercially, and that do not require programming tasks from the end user. These systems are compared in terms of features and the simulation time required to compute a set of benchmark calculations.

A geometrical model for the Monte Carlo simulation of the TrueBeam linac

Monte Carlo simulation of linear accelerators (linacs) depends on the accurate geometrical description of the linac head. The geometry of the Varian TrueBeam linac is not available to researchers. Instead, the company distributes phase-space files of the flattening-filter-free (FFF) beams tallied at a plane located just upstream of the jaws. Yet, Monte Carlo simulations based on third-party tallied phase spaces are subject to limitations. In this work, an experimentally based geometry developed for the simulation of the FFF beams of the Varian TrueBeam linac is presented. The Monte Carlo geometrical model of the TrueBeam linac uses information provided by Varian that reveals large similarities between the TrueBeam machine and the Clinac 2100 downstream of the jaws. Thus, the upper part of the TrueBeam linac was modeled by introducing modifications to the Varian Clinac 2100 linac geometry. The most important of these modifications is the replacement of the standard flattening filters by ad hoc thin filters. These filters were modeled by comparing dose measurements and simulations. The experimental dose profiles for the 6 MV and 10 MV FFF beams were obtained from the Varian Golden Data Set and from in-house measurements performed with a diode detector for radiation fields ranging from 3  ×  3 to 40  ×  40 cm(2) at depths of maximum dose of 5 and 10 cm. Indicators of agreement between the experimental data and the simulation results obtained with the proposed geometrical model were the dose differences, the root-mean-square error and the gamma index. The same comparisons were performed for dose profiles obtained from Monte Carlo simulations using the phase-space files distributed by Varian for the TrueBeam linac as the sources of particles. Results of comparisons show a good agreement of the dose for the ansatz geometry similar to that obtained for the simulations with the TrueBeam phase-space files for all fields and depths considered, except for the 40  ×  40 cm(2) field where the ansatz geometry was able to reproduce the measured dose more accurately. Our approach overcomes some of the limitations of using the Varian phase-space files. It makes it possible to: (i) adapt the initial beam parameters to match measured dose profiles; (ii) reduce the statistical uncertainty to arbitrarily low values; and (iii) assess systematic uncertainties (type B) by using different Monte Carlo codes. One limitation of using phase-space files that is retained in our model is the impossibility of performing accurate absolute dosimetry simulations because the geometrical description of the TrueBeam ionization chamber remains unknown.

Monte Carlo study for designing a dedicated "D"-shaped collimator used in the external beam radiotherapy of retinoblastoma patients

PURPOSE

Retinoblastoma is the most common intraocular malignancy in the early childhood. Patients treated with external beam radiotherapy respond very well to the treatment. However, owing to the genotype of children suffering hereditary retinoblastoma, the risk of secondary radio-induced malignancies is high. The University Hospital of Essen has successfully treated these patients on a daily basis during nearly 30 years using a dedicated "D"-shaped collimator. The use of this collimator that delivers a highly conformed small radiation field, gives very good results in the control of the primary tumor as well as in preserving visual function, while it avoids the devastating side effects of deformation of midface bones. The purpose of the present paper is to propose a modified version of the "D"-shaped collimator that reduces even further the irradiation field with the scope to reduce as well the risk of radio-induced secondary malignancies. Concurrently, the new dedicated "D"-shaped collimator must be easier to build and at the same time produces dose distributions that only differ on the field size with respect to the dose distributions obtained by the current collimator in use. The scope of the former requirement is to facilitate the employment of the authors' irradiation technique both at the authors' and at other hospitals. The fulfillment of the latter allows the authors to continue using the clinical experience gained in more than 30 years.

METHODS

The Monte Carlo code PENELOPE was used to study the effect that the different structural elements of the dedicated "D"-shaped collimator have on the absorbed dose distribution. To perform this study, the radiation transport through a Varian Clinac 2100 C/D operating at 6 MV was simulated in order to tally phase-space files which were then used as radiation sources to simulate the considered collimators and the subsequent dose distributions. With the knowledge gained in that study, a new, simpler, "D"-shaped collimator is proposed.

RESULTS

The proposed collimator delivers a dose distribution which is 2.4 cm wide along the inferior-superior direction of the eyeball. This width is 0.3 cm narrower than that of the dose distribution obtained with the collimator currently in clinical use. The other relevant characteristics of the dose distribution obtained with the new collimator, namely, depth doses at clinically relevant positions, penumbrae width, and shape of the lateral profiles, are statistically compatible with the results obtained for the collimator currently in use.

CONCLUSIONS

The smaller field size delivered by the proposed collimator still fully covers the planning target volume with at least 95% of the maximum dose at a depth of 2 cm and provides a safety margin of 0.2 cm, so ensuring an adequate treatment while reducing the irradiated volume.

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.

PRIMO: a graphical environment for the Monte Carlo simulation of Varian and Elekta linacs

BACKGROUND

The accurate Monte Carlo simulation of a linac requires a detailed description of its geometry and the application of elaborate variance-reduction techniques for radiation transport. Both tasks entail a substantial coding effort and demand advanced knowledge of the intricacies of the Monte Carlo system being used.

METHODS

PRIMO, a new Monte Carlo system that allows the effortless simulation of most Varian and Elekta linacs, including their multileaf collimators and electron applicators, is introduced. PRIMO combines (1) accurate physics from the PENELOPE code, (2) dedicated variance-reduction techniques that significantly reduce the computation time, and (3) a user-friendly graphical interface with tools for the analysis of the generated data. PRIMO can tally dose distributions in phantoms and computerized tomographies, handle phase-space files in IAEA format, and import structures (planning target volumes, organs at risk) in the DICOM RT-STRUCT standard.

RESULTS

A prostate treatment, conformed with a high definition Millenium multileaf collimator (MLC 120HD) from a Varian Clinac 2100 C/D, is presented as an example. The computation of the dose distribution in 1.86×3.00×1.86 mm3 voxels with an average 2% standard statistical uncertainty, performed on an eight-core Intel Xeon at 2.67 GHz, took 1.8 h-excluding the patient-independent part of the linac, which required 3.8 h but it is simulated only once.

CONCLUSION

PRIMO is a self-contained user-friendly system that facilitates the Monte Carlo simulation of dose distributions produced by most currently available linacs. This opens the door for routine use of Monte Carlo in clinical research and quality assurance purposes. It is free software that can be downloaded from http://www.primoproject.net.

A PENELOPE-based system for the automated Monte Carlo simulation of clinacs and voxelized geometries-application to far-from-axis fields

PURPOSE

Two new codes, PENEASY and PENEASYLINAC, which automate the Monte Carlo simulation of Varian Clinacs of the 600, 1800, 2100, and 2300 series, together with their electron applicators and multileaf collimators, are introduced. The challenging case of a relatively small and far-from-axis field has been studied with these tools.

METHODS

PENEASY is a modular, general-purpose main program for the PENELOPE Monte Carlo system that includes various source models, tallies and variance-reduction techniques (VRT). The code includes a new geometry model that allows the superposition of voxels and objects limited by quadric surfaces. A variant of the VRT known as particle splitting, called fan splitting, is also introduced. PENEASYLINAC, in turn, automatically generates detailed geometry and configuration files to simulate linacs with PENEASY. These tools are applied to the generation of phase-space files, and of the corresponding absorbed dose distributions in water, for two 6 MV photon beams from a Varian Clinac 2100 C∕D: a 40 × 40 cm(2) centered field; and a 3 × 5 cm(2) field centered at (4.5, -11.5) cm from the beam central axis. This latter configuration implies the largest possible over-traveling values of two of the jaws. Simulation results for the depth dose and lateral profiles at various depths are compared, by using the gamma index, with experimental values obtained with a PTW 31002 ionization chamber. The contribution of several VRTs to the computing speed of the more demanding off-axis case is analyzed.

RESULTS

For the 40 × 40 cm(2) field, the percentages γ(1) and γ(1.2) of voxels with gamma indices (using 0.2 cm and 2% criteria) larger than unity and larger than 1.2 are 0.2% and 0%, respectively. For the 3 × 5 cm(2) field, γ(1) = 0%. These figures indicate an excellent agreement between simulation and experiment. The dose distribution for the off-axis case with voxels of 2.5 × 2.5 × 2.5 mm(3) and an average standard statistical uncertainty of 2% (1σ) is computed in 3.1 h on a single core of a 2.8 GHz Intel Core 2 Duo processor. This result is obtained with the optimal combination of the tested VRTs. In particular, fan splitting for the off-axis case accelerates execution by a factor of 240 with respect to standard particle splitting.

CONCLUSIONS

PENEASY and PENEASYLINAC can simulate the considered Varian Clinacs both in an accurate and efficient manner. Fan splitting is crucial to achieve simulation results for the off-axis field in an affordable amount of CPU time. Work to include Elekta linacs and to develop a graphical interface that will facilitate user input is underway.

Ant colony algorithm implementation in electron and photon Monte Carlo transport: application to the commissioning of radiosurgery photon beams

PURPOSE

In this work, the authors describe an approach which has been developed to drive the application of different variance-reduction techniques to the Monte Carlo simulation of photon and electron transport in clinical accelerators.

METHODS

The new approach considers the following techniques: Russian roulette, splitting, a modified version of the directional bremsstrahlung splitting, and the azimuthal particle redistribution. Their application is controlled by an ant colony algorithm based on an importance map.

RESULTS

The procedure has been applied to radiosurgery beams. Specifically, the authors have calculated depth-dose profiles, off-axis ratios, and output factors, quantities usually considered in the commissioning of these beams. The agreement between Monte Carlo results and the corresponding measurements is within approximately 3%/0.3 mm for the central axis percentage depth dose and the dose profiles. The importance map generated in the calculation can be used to discuss simulation details in the different parts of the geometry in a simple way. The simulation CPU times are comparable to those needed within other approaches common in this field.

CONCLUSIONS

The new approach is competitive with those previously used in this kind of problems (PSF generation or source models) and has some practical advantages that make it to be a good tool to simulate the radiation transport in problems where the quantities of interest are difficult to obtain because of low statistics.

Fast Monte Carlo simulation on a voxelized human phantom deformed to a patient

PURPOSE

A method for performing fast simulations of absorbed dose using a patient's computerized tomography (CT) scan without explicitly relying on a calibration curve is presented.

METHODS

The method is based on geometrical deformations performed on a standard voxelized human phantom. This involves spatially transforming the human phantom to align it with the patient CT image. Since the chemical composition and density of each voxel are given in the phantom data, a calibration curve is not used in the proposed method. For this study, the Monte Carlo (MC) code PENELOPE has been used as the simulation of reference. The results obtained with PENELOPE simulations are compared to those obtained with PENFAST and with the collapsed cone convolution algorithm implemented in a commercial treatment planning system.

RESULTS

The comparisons of the absorbed doses calculated with the different algorithms on two patient CTs and the corresponding deformed phantoms show a maximum distance to agreement of 2 mm, and in general, the obtained absorbed dose distributions are compatible within the reached statistical uncertainty. The validity of the deformation method for a broad range of patients is shown using MC simulations in random density phantoms. A PENFAST simulation of a 6 MV photon beam impinging on a patient CT reaches 2% statistical uncertainty in the absorbed dose, in a 0.1 cm3 voxel along the central axis, in 10 min running on a single core of a 2.8 GHz CPU.

CONCLUSIONS

The proposed method of the absorbed dose calculation in a deformed voxelized phantom allows for dosimetric studies in the geometry of a patient CT scan. This is due to the fact that the chemical composition and material density of the phantom are known. Furthermore, simulation using the phantom geometry can provide dosimetric information for each organ. The method can be used for quality assurance procedures. In relation to PENFAST, it is shown that a purely condensed-history algorithm (class I) can be used for absorbed dose estimation in patient CTs.

Determination of the optimal statistical uncertainty to perform electron-beam Monte Carlo absorbed dose estimation in the target volume

PURPOSE OF STUDY

Monte Carlo based treatment planning system are known to be more accurate than analytical methods for performing absorbed dose estimation, particularly in and near heterogeneities. However, the required computation time can still be an issue. The present study focused on the determination of the optimum statistical uncertainty in order to minimise computation time while keeping the reliability of the absorbed dose estimation in treatments planned with electron-beams.

MATERIALS AND METHODS

Three radiotherapy plans (medulloblastoma, breast and gynaecological) were used to investigate the influence of the statistical uncertainty of the absorbed dose on the target volume dose-volume histograms (spinal cord, intramammary nodes and pelvic lymph nodes, respectively).

RESULTS

The study of the dose-volume histograms showed that for statistical uncertainty levels (1 S.D.) above 2 to 3%, the standard deviation of the mean dose in the target volume calculated from the dose-volume histograms increases by at least 6%, reflecting the gradual flattening of the dose-volume histograms.

CONCLUSIONS

This work suggests that, in clinical context, Monte Carlo based absorbed dose estimations should be performed with a maximum statistical uncertainty of 2 to 3%.

Comparison between PENELOPE and electron Monte Carlo simulations of electron fields used in the treatment of conjunctival lymphoma

For the treatment of conjunctival lymphoma in the early stages, external beam radiotherapy offers a curative approach. Such treatment requires the use of highly conformed small radiation beams. The beam size is so small that even advanced treatment planning systems have difficulties in calculating dose distributions. One possible approach for optimizing the treatment technique and later performing treatment planning is by means of full Monte Carlo (MC) simulations. In this paper, we compare experimental absorbed dose profiles obtained with a collimator used at the University Hospital Essen, with MC simulations done with the general-purpose radiation transport code PENELOPE. The collimator is also simulated with the hybrid MC code electron Monte Carlo (eMC) implemented in the commercial treatment planning system Eclipse (Varian). The results obtained with PENELOPE have a maximum difference with experimental data of 2.3%, whereas the eMC code differs systematically from the experimental data about 7% in the penumbra tails. We also show that PENELOPE simulations are able to obtain absorbed dose maps with an equivalent statistical uncertainty to the one found with eMC in similar CPU times.