Patient-dependent beam-modifier physics in Monte Carlo photon dose calculations

A phase space model of a Versa HD linear accelerator for application to Monte Carlo dose calculation in a real-time adaptive workflow

PURPOSE

This study aims to develop and validate a simple geometric model of the accelerator head, from which a particle phase space can be calculated for application to fast Monte Carlo dose calculation in real-time adaptive photon radiotherapy. With this objective in view, the study investigates whether the phase space model can facilitate dose calculations which are compatible with those of a commercial treatment planning system, for convenient interoperability.

MATERIALS AND METHODS

A dual-source model of the head of a Versa HD accelerator (Elekta AB, Stockholm, Sweden) was created. The model used parameters chosen to be compatible with those of 6-MV flattened and 6-MV flattening filter-free photon beams in the RayStation treatment planning system (RaySearch Laboratories, Stockholm, Sweden). The phase space model was used to calculate a photon phase space for several treatment plans, and the resulting phase space was applied to the Dose Planning Method (DPM) Monte Carlo dose calculation algorithm. Simple fields and intensity-modulated radiation therapy (IMRT) treatment plans for prostate and lung were calculated for benchmarking purposes and compared with the convolution-superposition dose calculation within RayStation.

RESULTS

For simple square fields in a water phantom, the calculated dose distribution agrees to within ±2% with that from the commercial treatment planning system, except in the buildup region, where the DPM code does not model the electron contamination. For IMRT plans of prostate and lung, agreements of ±2% and ±6%, respectively, are found, with slightly larger differences in the high dose gradients.

CONCLUSIONS

The phase space model presented allows convenient calculation of a phase space for application to Monte Carlo dose calculation, with straightforward translation of beam parameters from the RayStation beam model. This provides a basis on which to develop dose calculation in a real-time adaptive setting.

A contemporary review of stereotactic radiotherapy: inherent dosimetric complexities and the potential for detriment

OBJECTIVE

The advantages of highly localised, conformal treatments achievable with stereotactic radiotherapy (SRT) are increasingly being extended to extracranial sites as stereotactic body radiotherapy with advancements in imaging and beam collimation. One of the challenges in stereotactic treatment lies in the significant complexities associated with small field dosimetry and dose calculation. This review provides a comprehensive overview of the complexities associated with stereotactic radiotherapy and the potential for detriment.

METHODS

This study is based on a comprehensive review of literature accessible via PubMed and other sources, covering stereotactic radiotherapy, small-field dosimetry and dose calculation.

FINDINGS

Several key issues were identified in the literature. They pertain to dose prescription, dose measurement and dose calculation within and beyond the treatment field. Field-edge regions and penumbrae occupy a significant portion of the total field size. Spectral and dosimetric characteristics are difficult to determine and are compounded by effects of tissue inhomogeneity. Measurement of small-fields is made difficult by detector volume averaging and energy response. Available dosimeters are compared, and emphasis is given to gel dosimetry which offers the greatest potential for three-dimensional small-field dosimetry. The limitations of treatment planning system algorithms as applied to small-fields (particularly in the presence of heterogeneities) is explained, and a review of Monte Carlo dose calculation is provided, including simplified treatment planning implementations. Not incorporated into treatment planning, there is evidence that far from the primary field, doses to patients (and corresponding risks of radiocarcinogenesis) from leakage/scatter in SRT are similar to large fields.

CONCLUSIONS

Improved knowledge of dosimetric issues is essential to the accurate measurement and calculation of dose as well as the interpretation and assessment of planned and delivered treatments. This review highlights such issues and the potential benefit that may be gained from Monte Carlo dose calculation and verification via three-dimensional dosimetric methods (such as gel dosimetry) being introduced into routine clinical practice.

Radiation therapy of large intact breasts using a beam spoiler or photons with mixed energies

Radiation treatment of large intact breasts with separations of more than 24 cm is typically performed using x-rays with energies of 10 MV and higher, to eliminate high-dose regions in tissue. The disadvantage of the higher energy beams is the reduced dose to superficial tissue in the buildup region. We evaluated 2 methods of avoiding this underdosage: (1) a beam spoiler: 1.7-cm-thick Lucite plate positioned in the blocking tray 35 cm from the isocenter, with 15-MV x-rays; and (2) combining 6- and 15-MV x-rays through the same portal. For the beam with the spoiler, we measured the dose distribution for normal and oblique incidence using a film and ion chamber in polystyrene, as well as a scanning diode in a water tank. In the mixed-energy approach, we calculated the dose distributions in the buildup region for different proportions of 6- and 15-MV beams. The dose enhancement due to the beam spoiler exhibited significant dependence upon the source-to-skin distance (SSD), field size, and the angle of incidence. In the center of a 20 x 20-cm(2) field at 90-cm SSD, the beam spoiler raises the dose at 5-mm depth from 77% to 87% of the prescription, while maintaining the skin dose below 57%. Comparison of calculated dose with measurements suggested a practical way of treatment planning with the spoiler--usage of 2-mm "beam" bolus--a special option offered by in-house treatment planning system. A second method of increasing buildup doses is to mix 6- and 15-MV beams. For example, in the case of a parallel-opposed irradiation of a 27-cm-thick phantom, dose to D(max) for each energy, with respect to midplane, is 114% for pure 6-, 107% for 15-MV beam with the spoiler, and 108% for a 3:1 mixture of 15- and 6-MV beams. Both methods are practical for radiation therapy of large intact breasts.

Monte Carlo source model for photon beam radiotherapy: photon source characteristics

A major barrier to widespread clinical implementation of Monte Carlo dose calculation is the difficulty in characterizing the radiation source within a generalized source model. This work aims to develop a generalized three-component source model (target, primary collimator, flattening filter) for 6- and 18-MV photon beams that match full phase-space data (PSD). Subsource by subsource comparison of dose distributions, using either source PSD or the source model as input, allows accurate source characterization and has the potential to ease the commissioning procedure, since it is possible to obtain information about which subsource needs to be tuned. This source model is unique in that, compared to previous source models, it retains additional correlations among PS variables, which improves accuracy at nonstandard source-to-surface distances (SSDs). In our study, three-dimensional (3D) dose calculations were performed for SSDs ranging from 50 to 200 cm and for field sizes from 1 x 1 to 30 x 30 cm2 as well as a 10 x 10 cm2 field 5 cm off axis in each direction. The 3D dose distributions, using either full PSD or the source model as input, were compared in terms of dose-difference and distance-to-agreement. With this model, over 99% of the voxels agreed within +/-1% or 1 mm for the target, within 2% or 2 mm for the primary collimator, and within +/-2.5% or 2 mm for the flattening filter in all cases studied. For the dose distributions, 99% of the dose voxels agreed within 1% or 1 mm when the combined source model-including a charged particle source and the full PSD as input-was used. The accurate and general characterization of each photon source and knowledge of the subsource dose distributions should facilitate source model commissioning procedures by allowing scaling the histogram distributions representing the subsources to be tuned.

Photon-beam subsource sensitivity to the initial electron-beam parameters

One limitation to the widespread implementation of Monte Carlo (MC) patient dose-calculation algorithms for radiotherapy is the lack of a general and accurate source model of the accelerator radiation source. Our aim in this work is to investigate the sensitivity of the photon-beam subsource distributions in a MC source model (with target, primary collimator, and flattening filter photon subsources and an electron subsource) for 6- and 18-MV photon beams when the energy and radial distributions of initial electrons striking a linac target change. For this purpose, phase-space data (PSD) was calculated for various mean electron energies striking the target, various normally distributed electron energy spread, and various normally distributed electron radial intensity distributions. All PSD was analyzed in terms of energy, fluence, and energy fluence distributions, which were compared between the different parameter sets. The energy spread was found to have a negligible influence on the subsource distributions. The mean energy and radial intensity significantly changed the target subsource distribution shapes and intensities. For the primary collimator and flattening filter subsources, the distribution shapes of the fluence and energy fluence changed little for different mean electron energies striking the target, however, their relative intensity compared with the target subsource change, which can be accounted for by a scaling factor. This study indicates that adjustments to MC source models can likely be limited to adjusting the target subsource in conjunction with scaling the relative intensity and energy spectrum of the primary collimator, flattening filter, and electron subsources when the energy and radial distributions of the initial electron-beam change.

The importance of accurate linear accelerator head modelling for IMRT Monte Carlo calculations

Two Monte Carlo dose engines for radiotherapy treatment planning, namely a beta release of Peregrine and MCDE (Monte Carlo dose engine), were compared with Helax-TMS (collapsed cone superposition convolution) for a head and neck patient for the Elekta SLi plus linear accelerator. Deviations between the beta release of Peregrine and MCDE up to 10% were obtained in the dose volume histogram of the optical chiasm. It was illustrated that the differences are not caused by the particle transport in the patient, but by the modelling of the Elekta SLi plus accelerator head and more specifically the multileaf collimator (MLC). In MCDE two MLC modules (MLCQ and MLCE) were introduced to study the influence of the tongue-and-groove geometry, leaf bank tilt and leakage on the actual dose volume histograms. Differences in integral dose in the optical chiasm up to 3% between the two modules have been obtained. For single small offset beams though the FWHM of lateral profiles obtained with MLCE can differ by more than 1.5 mm from profiles obtained with MLCQ. Therefore, and because the recent version of MLCE is as fast as MLCQ, we advise to use MLCE for modelling the Elekta MLC. Nevertheless there still remains a large difference (up to 10%) between Peregrine and MCDE. By studying small offset beams we have shown that the profiles obtained with Peregrine are shifted, too wide and too flat compared with MCDE and phantom measurements. The overestimated integral doses for small beam segments explain the deviations observed in the dose volume histograms. The Helax-TMS results are in better agreement with MCDE, although deviations exceeding 5% have been observed in the optical chiasm. Monte Carlo dose deviations of more than 10% as found with Peregrine are unacceptable as an influence on the clinical outcome is possible and as the purpose of Monte Carlo treatment planning is to obtain an accuracy of 2%. We would like to emphasize that only the Elekta MLC has been tested in this work, so it is certainly possible that alpha releases of Peregrine provide more accurate results for other accelerators.

MCDE: a new Monte Carlo dose engine for IMRT

A new accurate Monte Carlo code for IMRT dose computations, MCDE (Monte Carlo dose engine), is introduced. MCDE is based on BEAMnrc/DOSXYZnrc and consequently the accurate EGSnrc electron transport. DOSXYZnrc is reprogrammed as a component module for BEAMnrc. In this way both codes are interconnected elegantly, while maintaining the BEAM structure and only minimal changes to BEAMnrc.mortran are necessary. The treatment head of the Elekta SLiplus linear accelerator is modelled in detail. CT grids consisting of up to 200 slices of 512 x 512 voxels can be introduced and up to 100 beams can be handled simultaneously. The beams and CT data are imported from the treatment planning system GRATIS via a DICOM interface. To enable the handling of up to 50 x 10(6) voxels the system was programmed in Fortran95 to enable dynamic memory management. All region-dependent arrays (dose, statistics, transport arrays) were redefined. A scoring grid was introduced and superimposed on the geometry grid, to be able to limit the number of scoring voxels. The whole system uses approximately 200 MB of RAM and runs on a PC cluster consisting of 38 1.0 GHz processors. A set of in-house made scripts handle the parallellization and the centralization of the Monte Carlo calculations on a server. As an illustration of MCDE, a clinical example is discussed and compared with collapsed cone convolution calculations. At present, the system is still rather slow and is intended to be a tool for reliable verification of IMRT treatment planning in the case of the presence of tissue inhomogeneities such as air cavities.

DOSSCORE: an accelerated DOSXYZnrc code with an efficient stepping algorithm and scoring grid

DOSSCORE is an accelerated version of DOSXYZnrc that allows photons to cross voxel boundaries of the same medium and utilizes a separate scoring grid superimposed on the geometrical grid. Two different stepping algorithms, the hownear method and the scaling method are implemented in DOSSCORE. The hownear method allows particles to travel larger distances in homogeneous regions where there is no interest in the dose deposition of these particles, whilst the scaling method utilizes a stepping algorithm in which particles are only slowed down by the boundaries of the geometrical voxels and not by the boundaries of the scoring voxels. For CT-based phantoms, only photon ray tracing is applied, which results in a rather modest speed gain of factor 1.2 compared to DOSXYZnrc. The hownear method and scaling method do not increase the speed for CT-based phantoms, but only for homogeneous phantoms and phantoms with a limited number of small heterogeneities. In cases where a small number of scoring voxels are needed, the hownear method performs better than the scaling method, whilst the opposite is true for cases when many scoring voxels are needed. The photon transport is accelerated by almost a factor of 2 for all phantoms (homogeneous, heterogeneous with much homogeneity and CT-based phantoms) compared to DOSXYZnrc. For a small number of scoring voxels, the hownear method is up to a factor of 2.6 and 1.9 faster than DOSXYZnrc for homogeneous and heterogeneous phantoms in the case of photon beams. For an electron beam, a speed gain of factor 2.4 is obtained. For a full scoring grid like the one used in DOSXYZnrc, the scaling method is up to a factor of 2.2 and 1.7 faster than DOSXYZnrc for homogeneous and heterogeneous phantoms in the case of photon beams. For an electron beam, a speed gain of factor 2 is obtained. A speed increase without biasing the results is very relevant. The use of two separate grids, the more efficient stepping algorithms and the accelerated photon transport can be applied to every EGS-based or other Monte Carlo code.

Summary and recommendations of a National Cancer Institute workshop on issues limiting the clinical use of Monte Carlo dose calculation algorithms for megavoltage external beam radiation therapy

Due to the significant interest in Monte Carlo dose calculations for external beam megavoltage radiation therapy from both the research and commercial communities, a workshop was held in October 2001 to assess the status of this computational method with regard to use for clinical treatment planning. The Radiation Research Program of the National Cancer Institute, in conjunction with the Nuclear Data and Analysis Group at the Oak Ridge National Laboratory, gathered a group of experts in clinical radiation therapy treatment planning and Monte Carlo dose calculations, and examined issues involved in clinical implementation of Monte Carlo dose calculation methods in clinical radiotherapy. The workshop examined the current status of Monte Carlo algorithms, the rationale for using Monte Carlo, algorithmic concerns, clinical issues, and verification methodologies. Based on these discussions, the workshop developed recommendations for future NCI-funded research and development efforts. This paper briefly summarizes the issues presented at the workshop and the recommendations developed by the group.

Using Monte Carlo simulations to commission photon beam output factors—a feasibility study

This study investigates the feasibility of using Monte Carlo methods to assist the commissioning of photon beam output factors from a medical accelerator. The Monte Carlo code, BEAMnrc, was used to model 6 MV and 18 MV photon beams from a Varian linear accelerator. When excellent agreements were obtained between the Monte Carlo simulated and measured dose distributions in a water phantom, the entire geometry including the accelerator head and the water phantom was simulated to calculate the relative output factors. Simulated output factors were compared with measured data, which consist of a typical commission dataset for the output factors. The measurements were done using an ionization chamber in a water phantom at a depth of 10 cm with a source-detector distance of 100 cm. Square fields and rectangular fields with widths and lengths ranging from 4 cm to 40 cm were studied. The result shows a very good agreement (< 1.5%) between the Monte Carlo calculated and the measured relative output factors for a typical commissioning dataset. The Monte Carlo calculated backscatter factors to the beam monitor chamber agree well with measured data in the literature. Monte Carlo simulations have also been shown to be able to accurately predict the collimator exchange effect and its component for rectangular fields. The information obtained is also useful to develop an algorithm for accurate beam modelling. This investigation indicates that Monte Carlo methods can be used to assist commissioning of output factors for photon beams.

Monte Carlo modelling of external radiotherapy photon beams

An essential requirement for successful radiation therapy is that the discrepancies between dose distributions calculated at the treatment planning stage and those delivered to the patient are minimized. An important component in the treatment planning process is the accurate calculation of dose distributions. The most accurate way to do this is by Monte Carlo calculation of particle transport, first in the geometry of the external or internal source followed by tracking the transport and energy deposition in the tissues of interest. Additionally, Monte Carlo simulations allow one to investigate the influence of source components on beams of a particular type and their contaminant particles. Since the mid 1990s, there has been an enormous increase in Monte Carlo studies dealing specifically with the subject of the present review, i.e., external photon beam Monte Carlo calculations, aided by the advent of new codes and fast computers. The foundations for this work were laid from the late 1970s until the early 1990s. In this paper we will review the progress made in this field over the last 25 years. The review will be focused mainly on Monte Carlo modelling of linear accelerator treatment heads but sections will also be devoted to kilovoltage x-ray units and 60Co teletherapy sources.

Determining the incident electron fluence for Monte Carlo-based photon treatment planning using a standard measured data set

An accurate dose calculation in phantom and patient geometries requires an accurate description of the radiation source. Errors in the radiation source description are propagated through the dose calculation. With the emergence of linear accelerators whose dosimetric characteristics are similar to within measurement uncertainty, the same radiation source description can be used as the input to dose calculation for treatment planning at many institutions with the same linear accelerator model. Our goal in the current research was to determine the initial electron fluence above the linear accelerator target for such an accelerator to allow a dose calculation in water to within 1% or 1 mm of the measured data supplied by the manufacturer. The method used for both the radiation source description and the patient transport was Monte Carlo. The linac geometry was input into the Monte Carlo code using the accelerator's manufacturer's specifications. Assumptions about the initial electron source above the target were made based on previous studies. The free parameters derived for the calculations were the mean energy and radial Gaussian width of the initial electron fluence and the target density. A combination of the free parameters yielded an initial electron fluence that, when transported through the linear accelerator and into the phantom, allowed a dose-calculation agreement to the experimental ion chamber data to within the specified criteria at both 6 and 18 MV nominal beam energies, except near the surface, particularly for the 18 MV beam. To save time during Monte Carlo treatment planning, the initial electron fluence was transported through part of the treatment head to a plane between the monitor chambers and the jaws and saved as phase-space files. These files are used for clinical Monte Carlo-based treatment planning and are freely available from the authors.

A virtual photon energy fluence model for Monte Carlo dose calculation

The presented virtual energy fluence (VEF) model of the patient-independent part of the medical linear accelerator heads, consists of two Gaussian-shaped photon sources and one uniform electron source. The planar photon sources are located close to the bremsstrahlung target (primary source) and to the flattening filter (secondary source), respectively. The electron contamination source is located in the plane defining the lower end of the filter. The standard deviations or widths and the relative weights of each source are free parameters. Five other parameters correct for fluence variations, i.e., the horn or central depression effect. If these parameters and the field widths in the X and Y directions are given, the corresponding energy fluence distribution can be calculated analytically and compared to measured dose distributions in air. This provides a method of fitting the free parameters using the measurements for various square and rectangular fields and a fixed number of monitor units. The next step in generating the whole set of base data is to calculate monoenergetic central axis depth dose distributions in water which are used to derive the energy spectrum by deconvolving the measured depth dose curves. This spectrum is also corrected to take the off-axis softening into account. The VEF model is implemented together with geometry modules for the patient specific part of the treatment head (jaws, multileaf collimator) into the XVMC dose calculation engine. The implementation into other Monte Carlo codes is possible based on the information in this paper. Experiments are performed to verify the model by comparing measured and calculated dose distributions and output factors in water. It is demonstrated that open photon beams of linear accelerators from two different vendors are accurately simulated using the VEF model. The commissioning procedure of the VEF model is clinically feasible because it is based on standard measurements in air and water. It is also useful for IMRT applications because a full Monte Carlo simulation of the treatment head would be too time-consuming for many small fields.

A Monte Carlo study on internal wedges using BEAM

To do calculations for wedged photon beams with the NRC Monte Carlo simulation package BEAM, a new Component Module for wedges called WEDGE has been designed and built. After an initial series of benchmarks using monoenergetic photon beams as well as realistic 6 MV and 10 MV beams, it was found, that the new CM did work fine for the large wedge (maximum field size 30 x 40 cm2) of the Elekta SL-linac. The next step was to calculate dose distributions and output factors for a range of wedged fields with field size from 3 x 3 cm2 to 30 x 30 cm2. Results from these simulations have been compared to measurements. Calculated values for the reference wedge transmission factor and the relative wedge transmission factors were within 1.5% from the measured data. Dose distributions showed an identical behavior; both depth-dose curves as well as cross profiles were within 1.5% from measured data, usually even better. Despite the increased mean energy, there was no indication that, as a result, the phantom scatter output factors will change for a 10 MV photon beam. It was found that by adding a wedge the contributions for the different sources of head scatter changed considerably as compared to the open fields, apart from the additional scatter from the wedge. Another consequence of inserting a wedge was an increase in the mean energy of both primary and scattered radiation with 0.3 MV and 0.7 MV, respectively, for all wedged fields with respect to the corresponding open fields. Despite the statistical uncertainty in the calculated data, which is in the same order of magnitude as the effect to be determined, it was possible to derive reliable data for the beam hardening from the calculated dose distributions. Only for the smallest field (field size 3 x 3 cm2) a large difference between the measured and calculated beam hardening factor was found due to the relative large voxel size of 1 x 1 x 1 cm3 compared to the field size. For a description of the influence of a wedge on a photon beam, the results of this study strongly support the use of a reference wedge transmission factor (determined under reference conditions) in combination with a relative wedge transmission factor. The product of these variables should replace the collimator scatter output factor used in open fields. The influence on the dose distribution should be incorporated by using the (field size dependent) beam hardening. The ultimate solution will be to make this beam hardening depending on the actual position in the radiation field, as the photon energy varies over the field (holds also for open fields).

Energy spectra, angular spread, fluence profiles and dose distributions of 6 and 18 MV photon beams: results of monte carlo simulations for a varian 2100EX accelerator

The purpose of this study is to provide detailed characteristics of incident photon beams for different field sizes and beam energies. This information is critical to the future development of accurate treatment planning systems. It also enhances our knowledge of radiotherapy photon beams. The EGS4 Monte Carlo code, BEAM, has been used to simulate 6 and 18 MV photon beams from a Varian Clinac-2100EX accelerator. A simulated realistic beam is stored in a phase space data file, which contains details of each particle's complete history including where it has been and where it has interacted. The phase space files are analysed to obtain energy spectra, angular distribution, fluence profile and mean energy profiles at the phantom surface for particles separated according to their charge and history. The accuracy of a simulated beam is validated by the excellent agreement between the Monte Carlo calculated and measured dose distributions. Measured depth-dose curves are obtained from depth-ionization curves by accounting for newly introduced chamber fluence corrections and the stopping-power ratios for realistic beams. The study presents calculated depth-dose components from different particles as well as calculated surface dose and contribution from different particles to surface dose across the field. It is shown that the increase of surface dose with the increase of the field size is mainly due to the increase of incident contaminant charged particles. At 6 MV, the incident charged particles contribute 7% to 21% of maximum dose at the surface when the field size increases from 10 x 10 to 40 x 40 cm2. At 18 MV, their contributions are up to 11% and 29% of maximum dose at the surface for 10 x 10 cm2 and 40 x 40 cm2 fields respectively. However, the fluence of these incident charged particles is less than 1% of incident photon fluence in all cases.

Sensitivity of megavoltage photon beam Monte Carlo simulations to electron beam and other parameters

The BEAM code is used to simulate nine photon beams from three major manufacturers of medical linear accelerators (Varian, Elekta, and Siemens), to derive and evaluate estimates for the parameters of the electron beam incident on the target, and to study the effects of some mechanical parameters like target width, primary collimator opening, flattening filter material and density. The mean energy and the FWHM of the incident electron beam intensity distributions (assumed Gaussian and cylindrically symmetric) are derived by matching calculated percentage depth-dose curves past the depth of maximum dose (within 1% of maximum dose) and off-axis factors (within 2sigma at 1% statistics or less) with measured data from the AAPM RTC TG-46 compilation. The off-axis factors are found to be very sensitive to the mean energy of the electron beam, the FWHM of its intensity distribution, its angle of incidence, the dimensions of the upper opening of the primary collimator, the material of the flattening filter and its density. The off-axis factors are relatively insensitive to the FWHM of the electron beam energy distribution, its divergence and the lateral dimensions of the target. The depth-dose curves are sensitive to the electron beam energy, and to its energy distribution, but they show no sensitivity to the FWHM of the electron beam intensity distribution. The electron beam incident energy can be estimated within 0.2 MeV when matching either the measured off-axis factors or the central-axis depth-dose curves when the calculated uncertainties are about 0.7% at the 1 sigma level. The derived FWHM (+/-0.1 mm) of the electron beam intensity distributions all fall within 1 mm of the manufacturer specifications except in one case where the difference is 1.2 mm.

Monte Carlo simulation and dosimetric verification of radiotherapy beam modifiers

Monte Carlo simulation of beam modifiers such as physical wedges and compensating filters has been performed with a rectilinear voxel geometry module. A modified version of the EGS4/DOSXYZ code has been developed for this purpose. The new implementations have been validated against the BEAM Monte Carlo code using its standard component modules (CMs) in several geometrical conditions. No significant disagreements were found within the statistical errors of 0.5% for photons and 2% for electrons. The clinical applicability and flexibility of the new version of the code has been assessed through an extensive verification versus dosimetric data. Both Varian multi-leaf collimator (MLC) wedges and standard wedges have been simulated and compared against experiments for 6MV photon beams and different field sizes. Good agreement was found between calculated and measured depth doses and lateral dose profiles along both wedged and unwedged directions for different depths and focus-to-surface distances. Furthermore, Monte Carlo-generated output factors for both open and wedged fields agreed with linac commissioning beam data within statistical uncertainties of the calculations (<3% at largest depths). Compensating filters of both low-density and high-density materials have also been successfully simulated. As a demonstration, a wax compensating filter with a complex three-dimensional concave and convex geometry has been modelled through a CT scan import. Calculated depth doses and lateral dose profiles for different field sizes agreed well with experiments. The code was used to investigate the performance of a commercial treatment planning system in designing compensators. Dose distributions in a heterogeneous water phantom emulating the head and neck region were calculated with the convolution-superposition method (pencil beam and collapsed cone implementations) and compared against those from the MC code developed herein. The new technique presented in this work is versatile, DICOM-RT compliant and accurate in the simulation of beam modulators. This paper addresses the need to reduce the sources of error in the modelling of beam modifiers since they remain a viable alternative to the MLC technique in the delivery of IMRT beams.

[Foundations of the Monte Carlo method for dose calculation in radiotherapy]

Monte Carlo (MC) methods applied in dose calculation are based on fundamental principles of radiation interaction with matter. In contrast to other methods, the accuracy of dose calculation achievable with MC depends only on the determination of the beam quality and the interaction coefficients. Using MC techniques it is possible to predict the dose for clinical photon and electron beams with an accuracy of > +/- 2%. Especially for inhomogeneous regions like head, neck, and lung, the MC technique can significantly improve the accuracy compared to conventional algorithms. Therefore, in the present paper the basic features of the MC method are reviewed in the context of treatment planning in radiation therapy. The main shortcoming in the past, i.e., that MC algorithms are too slow to be acceptable for clinical purposes, could be solved by using faster computers and by introducing new variance reduction (VR) techniques. These techniques decrease the statistical fluctuations without increasing the number of particle histories. Therefore, MC calculation times in the order of a few minutes are possible. A brief overview of VR methods is provided.

Description and dosimetric verification of the PEREGRINE Monte Carlo dose calculation system for photon beams incident on a water phantom

PEREGRINE is a three-dimensional Monte Carlo dose calculation system written specifically for radiotherapy. This paper describes the implementation and overall dosimetric accuracy of PEREGRINE physics algorithms, beam model, and beam commissioning procedure. Particle-interaction data, tracking geometries, scoring, variance reduction, and statistical analysis are described. The BEAM code system is used to model the treatment-independent accelerator head, resulting in the identification of primary and scattered photon sources and an electron contaminant source. The magnitude of the electron source is increased to improve agreement with measurements in the buildup region in the largest fields. Published measurements provide an estimate of backscatter on monitor chamber response. Commissioning consists of selecting the electron beam energy, determining the scale factor that defines dose per monitor unit, and describing treatment-dependent beam modifiers. We compare calculations with measurements in a water phantom for open fields, wedges, blocks, and a multileaf collimator for 6 and 18 MV Varian Clinac 2100C photon beams. All calculations are reported as dose per monitor unit. Aside from backscatter estimates, no additional, field-specific normalization is included in comparisons with measurements. Maximum discrepancies were less than either 2% of the maximum dose or 1.2 mm in isodose position for all field sizes and beam modifiers.

A multiple source model for 6 MV photon beam dose calculations using Monte Carlo

A multiple source model (MSM) for the 6 MV beam of a Varian Clinac 2300 C/D was developed by simulating radiation transport through the accelerator head for a set of square fields using the GEANT Monte Carlo (MC) code. The corresponding phase space (PS) data enabled the characterization of 12 sources representing the main components of the beam defining system. By parametrizing the source characteristics and by evaluating the dependence of the parameters on field size, it was possible to extend the validity of the model to arbitrary rectangular fields which include the central 3 x 3 cm2 field without additional precalculated PS data. Finally, a sampling procedure was developed in order to reproduce the PS data. To validate the MSM, the fluence, energy fluence and mean energy distributions determined from the original and the reproduced PS data were compared and showed very good agreement. In addition, the MC calculated primary energy spectrum was verified by an energy spectrum derived from transmission measurements. Comparisons of MC calculated depth dose curves and profiles, using original and PS data reproduced by the MSM, agree within 1% and 1 mm. Deviations from measured dose distributions are within 1.5% and 1 mm. However, the real beam leads to some larger deviations outside the geometrical beam area for large fields. Calculated output factors in 10 cm water depth agree within 1.5% with experimentally determined data. In conclusion, the MSM produces accurate PS data for MC photon dose calculations for the rectangular fields specified.

Validation of a Monte Carlo dose calculation tool for radiotherapy treatment planning

A new EGS4/PRESTA Monte Carlo user code, MCDOSE, has been developed as a routine dose calculation tool for radiotherapy treatment planning. It is suitable for both conventional and intensity modulated radiation therapy. Two important features of MCDOSE are the inclusion of beam modifiers in the patient simulation and the implementation of several variance reduction techniques. Before this tool can be used reliably for clinical dose calculation, it must be properly validated. The validation for beam modifiers has been performed by comparing the dose distributions calculated by MCDOSE and the well-benchmarked EGS4 user codes BEAM and DOSXYZ. Various beam modifiers were simulated. Good agreement in the dose distributions was observed. The differences in electron cutout factors between the results of MCDOSE and measurements were within 2%. The accuracy of MCDOSE with various variance reduction techniques was tested by comparing the dose distributions in different inhomogeneous phantoms with those calculated by DOSXYZ without variance reduction. The agreement was within 1.0%. Our results demonstrate that MCDOSE is accurate and efficient for routine dose calculation in radiotherapy treatment planning, with or without beam modifiers.

Comparison of measured and Monte Carlo calculated dose distributions from the NRC linac

We have benchmarked photon beam simulations with the EGS4 user code BEAM [Rogers et al., Med. Phys. 22, 503-524 (1995)] by comparing calculated and measured relative ionization distributions in water from the 10 and 20 MV photon beams of the NRC linac. Unlike previous calculations, the incident electron energy is known independently to 1%, the entire extra-focal radiation is simulated, and electron contamination is accounted for. The full Monte Carlo simulation of the linac includes the electron exit window, target, flattening filter, monitor chambers, collimators, as well as the PMMA walls of the water phantom. Dose distributions are calculated using a modified version of the EGS4 user code DOSXYZ which additionally allows scoring of average energy and energy fluence in the phantom. Dose is converted to ionization by accounting for the (L/rho)water(air) variation in the phantom, calculated in an identical geometry for the realistic beams using a new EGS4 user code, SPRXYZ. The variation of (L/rho)water(air) with depth is a 1.25% correction at 10 MV and a 2% correction at 20 MV. At both energies, the calculated and the measured values of ionization on the central axis in the buildup region agree within 1% of maximum ionization relative to the ionization at 10 cm depth. The agreement is well within statistics elsewhere. The electron contamination contributes 0.35(+/- 0.02) to 1.37(+/- 0.03)% of the maximum dose in the buildup region at 10 MV and 0.26(+/- 0.03) to 3.14(+/- 0.07)% of the maximum dose at 20 MV. The penumbrae at 3 depths in each beam (in g/cm2), 1.99 (dmax, 10 MV only), 3.29 (dmax, 20 MV only), 9.79 and 19.79, agree with ionization chamber measurements to better than 1 mm. Possible causes for the discrepancy between calculations and measurements are analyzed and discussed in detail.