Photon beam characterization and modelling for Monte Carlo treatment planning

Photon beams of 4, 6 and 15 MV from Varian Clinac 2100C and 2300C/D accelerators were simulated using the EGS4/BEAM code system. The accelerators were modelled as a combination of component modules (CMs) consisting of a target, primary collimator, exit window, flattening filter, monitor chamber, secondary collimator, ring collimator, photon jaws and protection window. A full phase space file was scored directly above the upper photon jaws and analysed using beam data processing software, BEAMDP, to derive the beam characteristics, such as planar fluence, angular distribution, energy spectrum and the fractional contributions of each individual CM. A multiple-source model has been further developed to reconstruct the original phase space. Separate sources were created with accurate source intensity, energy, fluence and angular distributions for the target, primary collimator and flattening filter. Good agreement (within 2%) between the Monte Carlo calculations with the source model and those with the original phase space was achieved in the dose distributions for field sizes of 4 cm x 4 cm to 40 cm x 40 cm at source surface distances (SSDs) of 80-120 cm. The dose distributions in lung and bone heterogeneous phantoms have also been found to be in good agreement (within 2%) for 4, 6 and 15 MV photon beams for various field sizes between the Monte Carlo calculations with the source model and those with the original phase space.     

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.     

蒙特卡罗方法研究均整器对6MVX线能谱的影响

目的：用蒙特卡罗方法计算Varian Trilogy加速器无均整器条件下6MVX射线能谱。分析均整器对能谱的影响。方法：先用BEAMnrc分别模拟计算Varian Trilogy加速器6MV射线在具备均整器和无均整器条件下,方野边长分别为4cm、6cm、8cm、10cm、20cm和40cm时的相空间文件。以相空间文件为输入用BEAMDP分析光子能谱。结果：无均整器条件下光子注量增大,在光子能谱峰值附近最明显．射野边长为4cm时去掉均整器后光子注量增加的最多为6．284倍,随着射野增大增加倍数减小,射野边长为40cm时最小为2．398倍．无均整器条件下光子谱峰值能量降低,光子谱整体左移,平均能量明显减小。结论：去除均整器后,加速器的输出光子能谱发生较大变化。随之剂量特性发生改变,临床上可能产生一定的获益或未知情况,尚需要进一步的研究支持。     

A Monte Carlo study of a flattening filter-free linear accelerator verified with measurements

A Monte Carlo model of an Elekta Precise linear accelerator has been built and verified by measured data for a 6 and 10 MV photon beam running with and without a flattening filter in the beam line. In this study the flattening filter was replaced with a 6 mm thick copper plate, provided by the linac vendor, in order to stabilize the beam. Several studies have shown that removal of the filter improves some properties of the photon beam, which could be beneficial for radiotherapy treatments. The investigated characteristics of this new beam included output, spectra, mean energy, half value layer and the origin of scattered photons. The results showed an increased dose output per initial electron at the central axis of 1.76 and 2.66 for the 6 and 10 MV beams, respectively. The number of scattered photons from the accelerator head was reduced by (31.7 ± 0.03)% (1 SD) for the 6 MV beam and (47.6 ± 0.02)% for the 10 MV beam. The photon energy spectrum of the unflattened beam was softer compared to a conventional beam and did not vary significantly with the off-axis distance, even for the largest field size (0-20 cm off-axis).     

An empirical model for megavoltage x-ray output factors

An empirical model of the factors that determine the central axis dose at 10 cm depth in water for 4 MV, 6 MV and 18 MV photon beams is presented. Backscattering from the variable collimators into the dose monitoring ionization chamber can cause a variation of -0.5% to +1.8% in the dose per monitor unit in accelerators with an electron facility. Forward emission towards the isocentre from the beam flattening filter and upper collimators is more dependent on the position of the upper variable collimator blades than the lower blades, so that they are not interchangeable in determining output factors, which can differ by up to 2%. The model includes the product of the monitor backscatter factor, normalized phantom scatter factor, normalized head scatter factor and inverse square law, corrected for the displacement of the virtual x-ray focus from the target. It can predict the dose to -/+0.83% for 4 MV, -/+0.80% for 6 MV photons and -/+0.82% for 18 MV photons. The normalized head scatter factor is a second-order polynomial of the modified equivalent square collimator, whose coefficients do not vary significantly with x-ray energy. The model was tested by comparison with independent measurements of output factor and generally agreed to around 1%.     

The flatness of Siemens linear accelerator x-ray fields

The primary definer for Siemens MXE and MDX linear accelerators projects a circular opening with a radius of 25 cm at 100 cm from the target. Our measurements of photon beam profiles, however, indicate that the photon fluence drops to 95% of the central axis value at a radius of 18 cm. The flattening filter for these machines projects a flattened field size that is much smaller than the primary definer would allow. The clinical implications of this mismatch for large rectangular fields and for fields defined by asymmetric jaws are discussed and solutions are considered. A large field flattener was designed for our Siemens MXE 6 MV beam using Monte Carlo simulation of the treatment head and water phantom. The accuracy required of source and geometry details for dose distributions calculation is presented. The key parameters are the mean energy and focal spot size of the electron beam incident on the exit window, the material composition, and thickness profile of the exit window, target, flattener, and primary collimator, and the position of the primary collimator relative to the target. Profiles were more sensitive than central axis depth doses to simulation details. The beam energy and primary collimator position were selected to achieve good agreement between measured and calculated dose distributions. The flattener we designed with Monte Carlo was machined from brass and mounted on our MXE treatment unit. Measurements demonstrate that the large field flattener extends the useful radius of the field out to 22 cm, right into the penumbra cast by the primary collimator.     

Monte Carlo study of photon fields from a flattening filter-free clinical accelerator

In conventional clinical linear accelerators, the flattening filter scatters and absorbs a large fraction of primary photons. Increasing the beam-on time, which also increases the out-of-field exposure to patients, compensates for the reduction in photon fluence. In recent years, intensity modulated radiation therapy has been introduced, yielding better dose distributions than conventional three-dimensional conformal therapy. The drawback of this method is the further increase in beam-on time. An accelerator with the flattening filter removed, which would increase photon fluence greatly, could deliver considerably higher dose rates. The objective of the present study is to investigate the dosimetric properties of 6 and 18 MV photon beams from an accelerator without a flattening filter. The dosimetric data were generated using the Monte Carlo programs BEAMnrc and DOSXYZnrc. The accelerator model was based on the Varian Clinac 2100 design. We compared depth doses, dose rates, lateral profiles, doses outside collimation, total and collimator scatter factors for an accelerator with and without a flatteneing filter. The study showed that removing the filter increased the dose rate on the central axis by a factor of 2.31 (6 MV) and 5.45 (18 MV) at a given target current. Because the flattening filter is a major source of head scatter photons, its removal from the beam line could reduce the out-of-field dose.     

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.     

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.     

Characteristics of an 18 MV photon beam from a Therac 20 Medical Linear Accelerator

The 18 MV photon beam characteristics of a Therac 20 Medical Linear Accelerator manufactured by Atomic Energy of Canada Ltd, are presented. Tissue phantom ratios (TRP's) and percent depth dose data are given; for a 10 x 10 cm field, the percent depth dose at a depth of 10 cm is 78.5 (SSD 100 cm). The relative dose factors (RDF'S) are given and are analyzed to elucidate the relative contributions from phantom scatter, collimator scatter, and backscatter from the top of the collimators into the monitor chambers. The effect of field size and depth on the penumbra is described. Crossplots of the beam at a depth of 5 cm indicate that the flattening filter could be improved; there are hot spots of 108% near the corners of 40 x 40 fields.     

有无均整器模式下臂架与准直器不同角度条件下的剂量学比较

目的:探讨臂架或准直器角度的改变对均整（FF）与非均整（FFF）两种模式的射线剂量的影响。方法:选用Versa HD直线加速器配备的6 MV/10 MV光子束FF/FFF模式4档能量在设定好九点位置的10 cm×10 cm标准射野内进行实验。首先,借助IMF等中心夹具将Mapcheck2固定于治疗机机头,并用Mapcheck2测量相同臂架与准直器角度条件下4种光子束输出的平面剂量值;其次,用Mapcheck2测量在相同臂架角度、不同准直器角度与相同准直器角度、不同臂架角度两种条件下4种光子束的中心轴剂量值;最后,固定准直器为0°,设立两组臂架对穿射野（0°与180°,90°与270°）。拆除Mapcheck2,采用固体水和FC65-G电离室建立一个测量模体来测量4种光子束在两组等中心对穿野的剂量。运用SPSS统计软件对该实验收集到的数据进行对比分析。结果:在相同臂架与准直器角度条件下,4种光子束辐照9个点的平面剂量之间均存在明显统计学差异（P6 MV FF =0.020, P6 MV FFF=0.017, P10 MV FF =0.030, P10 MV FFF=0.016）;而不同臂架角度或不同准直器角度条件下,4种能量光子束的中心轴点剂量值均无统计学差异。在0°与180°的对穿野,4种能量光子束的输出剂量存在统计学差异（P6 MV FF =0.001, P6 MV FFF=0.002, P10 MV FF =0.003, P10 MV FFF=0.001）,而在90°与270°的对穿野无统计学差异。结论:Versa HD直线加速器拥有优良的机械等中心性能。在实际工作时,臂架和准直器的旋转,均不影响光子束的中心轴剂量的准确输出。在FF模式下,射线能量越高,受治疗床影响越小;FFF模式射线由于射线质软,能量越高,更易受到治疗床的衰减作用,在实际中应引起重视。     

A monte carlo approach to electron contamination sources in the Saturne-25 and -41

The various components of the accelerator treatment head act as sources of contaminating electrons. The presence of contamination electrons increases the surface dose, which deteriorates the skin-sparing effect. The present study examines the sources of this 'contamination', the influence on the surface dose and the shape of the build-up curve. The Monte Carlo simulation of two linear accelerators, Saturne-25 and -41, allowed us to study the influence of electron contamination in various therapeutic energies and in different geometries. The Saturne-25 and -41 cover a wide range of therapeutic energies with nominal energies 12/23 MV and 6/15 MV, respectively. The analysis of the results shows that at a source-to-surface distance of 100 cm and a wide opening of the collimators, the main sources of contaminating electrons are the flattening filter and the air below it. The contribution of the secondary contamination electrons on the surface dose is 16% for 6 MV and 12 MV, 6% for 15 MV and 17% for 23 MV. The energy spectra of electrons coming from the flattening filter and the air below it are completely different. The air produces electrons of low energies. The mean energies of these spectra vary from 1 MeV to 2 MeV depending on the nominal energy of the photon beam. The secondary electrons generated by the flattening filter produce a wide energy spectrum with mean energies of the same order of the bremsstrahlung spectrum. The flattening filter absorbs the secondary electrons generated in the target, the primary collimator and the air inside the head.     

Functional forms for photon spectra of clinical linacs

Specifying photon spectra of clinical linacs using a functional form is useful for many applications, including virtual source modelling and spectral unfolding from dosimetric measurements such as transmission data or depth-dose curves. In this study, 11 functional forms from the literature are compiled and quantitatively compared. A new function is proposed which offers improvements over existing ones. The proposed function is simple, physics-based and has four free parameters, one of which is the mean incident electron kinetic energy. A comprehensive benchmark set of validated, high-precision Monte Carlo spectra is generated and used to evaluate the strengths and limitations of different functions. The benchmark set has 65 spectra (3.5-30 MV) from Varian, Elekta, Siemens, Tomotherapy, Cyberknife and research linacs. The set includes spectra on- and off-axis from linacs with and without a flattening filter, and in treatment and imaging modes. The proposed function gives the lowest spectral deviations among all functions. It reproduces the energy fluence values in each bin for the benchmark set with a normalized root-mean-square deviation of 1.7%. The mean incident electron kinetic energy, maximum photon energy, most-probable energy and average energy are reproduced, on average, within 1.4%, 4.3%, 3.9% and 0.6% of their true values, respectively. The proposed function is well behaved when used for spectral unfolding from dosimetric data. The contribution of the 511 keV annihilation peak and the energy spread of the incident electron beam can be added as additional free parameters.     

Large efficiency improvements in BEAMnrc using directional bremsstrahlung splitting

The introduction into the BEAMnrc code of a new variance reduction technique, called directional bremsstrahlung splitting (DBS), is described. DBS uses a combination of interaction splitting for bremsstrahlung, annihilation, Compton scattering, pair production and photoabsorption, and Russian Roulette to achieve a much better efficiency of photon beam treatment head simulations compared to the splitting techniques already available in BEAMnrc (selective bremsstrahlung splitting, SBS, and uniform bremsstrahlung splitting, UBS). In a simulated 6 MV photon beam (10 x 10 cm2 field) photon fluence efficiency in the beam using DBS is over 8 times higher than with optimized SBS and over 20 times higher than with UBS, with a similar improvement in electron fluence efficiency in the beam. Total dose efficiency in a central-axis depth-dose curve improves by a factor of 6.4 over SBS at all depths in the phantom. The performance of DBS depends on the details of the accelerator being simulated. At higher energies, the relative improvement in efficiency due to DBS decreases somewhat, but is still a factor of 3.5 improvement over SBS for total dose efficiency using DBS in a simulated 18 MV photon beam. Increasing the field size of the simulated 6 MV beam to 40 x 40 cm2 (broad beam) causes the relative efficiency improvement of DBS to decrease by a factor of approximately 1.7 but is still up to 7 times more efficient than with SBS.     

A flattening filter free photon treatment concept evaluation with Monte Carlo

In principle, the concept of flat initial radiation-dose distribution across the beam is unnecessary for intensity modulated radiation therapy. Dynamic leaf positioning during irradiation could appropriately adjust the fluence distribution of an unflattened beam that is peaked in the center and deliver the desired uniform or nonuniform dose distribution. Removing the flattening filter could lead to reduced treatment time through higher dose rates and reduced scatter, because there would be substantially less material in the beam; and possibly other dosimetric and clinical advantages. This work aims to evaluate the properties of a flattening filter free clinical accelerator and to investigate its possible advantages in clinical intensity modulated radiation therapy applications by simulating a Varian 2100-based treatment delivery system with Monte Carlo techniques. Several depth-dose curves and lateral dose distribution profiles have been created for various field sizes, with and without the flattening filter. Data computed with this model were used to evaluate the overall quality of such a system in terms of changes in dose rate, photon and electron fluence, and reduction in out-of-field stray dose from the scattered components and were compared to the corresponding data for a standard treatment head with a flattening filter. The results of the simulations of the flattening filter free system show that a substantial increase in dose rate can be achieved, which would reduce the beam on time and decrease the out-of-field dose for patients due to reduced head-leakage dose. Also close to the treatment field edge, a significant improvement in out-of-field dose could be observed for small fields, which can be attributed to the change in the photon spectra, when the flattening filter is removed from the beamline.     

An investigation of accelerator head scatter and output factor in air

Our purpose in this study was to investigate whether the Monte Carlo simulation can accurately predict output factors in air. Secondary goals were to study the head scatter components and investigate the collimator exchange effect. The Monte Carlo code, BEAMnrc, was used in the study. Photon beams of 6 and 18 MV were from a Varian Clinac 2100EX accelerator and the measurements were performed using an ionization chamber in a mini-phantom. The Monte Carlo calculated in air output factors was within 1% of measured values. The simulation provided information of the origin and the magnitude of the collimator exchange effect. It was shown that the collimator backscatter to the beam monitor chamber played a significant role in the beam output factors. However the magnitude of the scattered dose contributions from the collimator at the isocenter is negligible. The maximum scattered dose contribution from the collimators was about 0.15% and 0.4% of the total dose at the isocenter for a 6 and 18 MV beam, respectively. The scattered dose contributions from the flattening filter at the isocenter were about 0.9-3% and 0.2-6% of the total dose for field sizes of 4x4 cm2-40x40 cm2 for the 6 and 18 MV beam, respectively. The study suggests that measurements of head scatter factors be done at large depth well beyond the depth of electron contamination. The insight information may have some implications for developing generalized empirical models to calculate the head scatter.     

A virtual photon source model of an Elekta linear accelerator with integrated mini MLC for Monte Carlo based IMRT dose calculation

A dedicated, efficient Monte Carlo (MC) accelerator head model for intensity modulated stereotactic radiosurgery treatment planning is needed to afford a highly accurate simulation of tiny IMRT fields. A virtual source model (VSM) of a mini multi-leaf collimator (MLC) (the Elekta Beam Modulator (EBM)) is presented, allowing efficient generation of particles even for small fields. The VSM of the EBM is based on a previously published virtual photon energy fluence model (VEF) (Fippel et al 2003 Med. Phys. 30 301) commissioned with large field measurements in air and in water. The original commissioning procedure of the VEF, based on large field measurements only, leads to inaccuracies for small fields. In order to improve the VSM, it was necessary to change the VEF model by developing (1) a method to determine the primary photon source diameter, relevant for output factor calculations, (2) a model of the influence of the flattening filter on the secondary photon spectrum and (3) a more realistic primary photon spectrum. The VSM model is used to generate the source phase space data above the mini-MLC. Later the particles are transmitted through the mini-MLC by a passive filter function which significantly speeds up the time of generation of the phase space data after the mini-MLC, used for calculation of the dose distribution in the patient. The improved VSM model was commissioned for 6 and 15 MV beams. The results of MC simulation are in very good agreement with measurements. Less than 2% of local difference between the MC simulation and the diamond detector measurement of the output factors in water was achieved. The X, Y and Z profiles measured in water with an ion chamber (V = 0.125 cm(3)) and a diamond detector were used to validate the models. An overall agreement of 2%/2 mm for high dose regions and 3%/2 mm in low dose regions between measurement and MC simulation for field sizes from 0.8 x 0.8 cm(2) to 16 x 21 cm(2) was achieved. An IMRT plan film verification was performed for two cases: 6 MV head&neck and 15 MV prostate. The simulation is in agreement with film measurements within 2%/2 mm in the high dose regions (> or = 0.1 Gy = 5% D(max)) and 5%/2 mm in low dose regions (<0.1 Gy).     

Dosimetric properties of photon beams from a flattening filter free clinical accelerator

Basic dosimetric properties of 6 MV and 18 MV photon beams from a Varian Clinac 21EX accelerator operating without the flattening filter have been measured. These include dose rate data, depth dose dependencies and lateral profiles in a water phantom, total scatter factors and transmission factors of a multileaf collimator. The data are reviewed and compared with measurements for the flattened beams. The unflattened beams have the following: a higher dose rate by factors of 2.3 (6 MV) and 5.5 (18 MV) on the central axis; lower out-of-field dose due to reduced head scatter and softer spectra; less variation of the total scatter factor with field size; and less variation of the shape of lateral dose profiles with depth. The findings suggest that with a flattening filter free accelerator better radiation treatments can be developed, with shorter delivery times and lower doses to normal tissues and organs.