Derivation of electron and photon energy spectra from electron beam central axis depth dose curves

A method for deriving the electron and photon energy spectra from electron beam central axis percentage depth dose (PDD) curves has been investigated. The PDD curves of 6, 12 and 20 MeV electron beams obtained from the Monte Carlo full phase space simulations of the Varian linear accelerator treatment head have been used to test the method. We have employed a 'random creep' algorithm to determine the energy spectra of electrons and photons in a clinical electron beam. The fitted electron and photon energy spectra have been compared with the corresponding spectra obtained from the Monte Carlo full phase space simulations. Our fitted energy spectra are in good agreement with the Monte Carlo simulated spectra in terms of peak location, peak width, amplitude and smoothness of the spectrum. In addition, the derived depth dose curves of head-generated photons agree well in both shape and amplitude with those calculated using the full phase space data. The central axis depth dose curves and dose profiles at various depths have been compared using an automated electron beam commissioning procedure. The comparison has demonstrated that our method is capable of deriving the energy spectra for the Varian accelerator electron beams investigated. We have implemented this method in the electron beam commissioning procedure for Monte Carlo electron beam dose calculations.     

Modelling of electron contamination in clinical photon beams for Monte Carlo dose calculation

The purpose of this work is to model electron contamination in clinical photon beams and to commission the source model using measured data for Monte Carlo treatment planning. In this work, a planar source is used to represent the contaminant electrons at a plane above the upper jaws. The source size depends on the dimensions of the field size at the isocentre. The energy spectra of the contaminant electrons are predetermined using Monte Carlo simulations for photon beams from different clinical accelerators. A 'random creep' method is employed to derive the weight of the electron contamination source by matching Monte Carlo calculated monoenergetic photon and electron percent depth-dose (PDD) curves with measured PDD curves. We have integrated this electron contamination source into a previously developed multiple source model and validated the model for photon beams from Siemens PRIMUS accelerators. The EGS4 based Monte Carlo user code BEAM and MCSIM were used for linac head sinulation and dose calculation. The Monte Carlo calculated dose distributions were compared with measured data. Our results showed good agreement (less than 2% or 2 mm) for 6, 10 and 18 MV photon beams.     

Basic dosimetry of radiosurgery narrow beams using Monte Carlo simulations: a detailed study of depth of maximum dose

In radiosurgery narrow photon beams, the depth of maximum dose d(max), in the beam central axis increases as the size of the additional collimator increases. This behavior is the opposite of what is observed in radiotherapy conventional beams. To understand this effect, experimental depth dose curves of the additional collimators were obtained for a Siemens KD2 linear accelerator in 6 MV photon mode and the shift of d(max) varied from 11.0 +/- 0.6 mm for the 5 mm collimator to 14.5 +/- 0.6 mm for the 23 mm collimator. Monte Carlo simulations showed that the photons that had no interactions in the additional collimators, contributing more than 90% to the total dose in water, were responsible for the shift in d(max). Monte Carlo simulations also showed that electrons originated from these photons and contributing to the dose deposit in water in the beam central axis could be divided in two groups: those that deposit energy far away from their point of origin (the point of the first photon collision in water) and those that deposit energy locally (originated at more than one photon collision in water). Applying a simplified model based on the fact that the photons originating Compton electrons (at the first and subsequent collisions) have similar characteristics in air for all the additional collimators, it was shown that these electrons were also responsible for the shift of d(max) in the beam central axis. Finally, it was shown that the changes in the initial gradients of the depth dose curves of the additional collimators were mainly due to electrons originated from the first photon collision in water.     

Monte Carlo simulation of small electron fields collimated by the integrated photon MLC

In this study, a Monte Carlo (MC)-based beam model for an ELEKTA linear accelerator was established. The beam model is based on the EGSnrc Monte Carlo code, whereby electron beams with nominal energies of 10, 12 and 15?MeV were considered. For collimation of the electron beam, only the integrated photon multi-leaf-collimators (MLCs) were used. No additional secondary or tertiary add-ons like applicators, cutouts or dedicated electron MLCs were included. The source parameters of the initial electron beam were derived semi-automatically from measurements of depth-dose curves and lateral profiles in a water phantom. A routine to determine the initial electron energy spectra was developed which fits a Gaussian spectrum to the most prominent features of depth-dose curves. The comparisons of calculated and measured depth-dose curves demonstrated agreement within 1%/1?mm. The source divergence angle of initial electrons was fitted to lateral dose profiles beyond the range of electrons, where the imparted dose is mainly due to bremsstrahlung produced in the scattering foils. For accurate modelling of narrow beam segments, the influence of air density on dose calculation was studied. The air density for simulations was adjusted to local values (433?m above sea level) and compared with the standard air supplied by the ICRU data set. The results indicate that the air density is an influential parameter for dose calculations. Furthermore, the default value of the BEAMnrc parameter 'skin depth' for the boundary crossing algorithm was found to be inadequate for the modelling of small electron fields. A higher value for this parameter eliminated discrepancies in too broad dose profiles and an increased dose along the central axis. The beam model was validated with measurements, whereby an agreement mostly within 3%/3?mm was found.     

Electron beam modeling and commissioning for Monte Carlo treatment planning

A hybrid approach for commissioning electron beam Monte Carlo treatment planning systems has been studied. The approach is based on the assumption that accelerators of the same type have very similar electron beam characteristics and the major difference comes from the on-site tuning of the electron incident energy at the exit window. For one type of accelerator, a reference machine can be selected and simulated with the Monte Carlo method. A multiple source model can be built on the full Monte Carlo simulation of the reference beam. When commissioning electron beams from other accelerators of the same type, the energy spectra in the source model are tuned to match the measured dose distributions. A Varian Clinac 2100C accelerator was chosen as the reference machine and a four-source beam model was established based on the Monte Carlo simulations. This simplified beam model can be used to generate Monte Carlo dose distributions accurately (within 2%/2 mm compared to those calculated with full phase space data) for electron beams from the reference machine with various nominal energies, applicator sizes, and SSDs. Three electron beams were commissioned by adjusting the energy spectra in the source model. The dose distributions calculated with the adjusted source model were compared with the dose distributions calculated using the phase space data for these beams. The agreement is within 1% in most of cases and 2% in all situations. This preliminary study has shown the capability of the commissioning approach for handling large variation in the electron incident energy. The possibility of making the approach more versatile is also discussed.     

Mean energy in electron beams

The mean energy of the energy spectrum is an essential parameter for the dosimetry of therapeutic electron beams. Frequently it is assumed that the mean energy of such beams remains constant across the beam and only its degradation with depth is considered. The present work analyzes the variation of the mean energy of primary electrons with depth and lateral position in an electron beam using the Monte Carlo method. Results are compared with relations commonly employed for determination of mean energy at a depth. For the variation of the mean electron energy with depth in broad beams, good agreement was found between Monte Carlo results and an analytic continuous slowing down expression, which takes the variation of radiation stopping power with depth into account. Due to the calculated lateral variation of the mean energy, the relative absorbed dose profile determined with an air ionization chamber in a clinical beam should differ by less than 1% from the measured ionization profile.     

Dosimetry characteristics of degraded electron beams investigated by Monte Carlo calculations in a setup for intraoperative radiation therapy

Degraded electron beams, as used for intraoperative radiation therapy (IORT) or similar complicated dosimetric situations, have different characteristics compared to conventional electron therapy beams. If international dosimetry protocols are applied in a direct manner to such degraded beams, uncertainties will be introduced in the absorbed dose determination. The Monte Carlo method has been used to verify experimentally determined relative absorbed dose distributions and output factors in an IORT geometry. Monte Carlo generated dose distributions are mostly within +/-2% or +/-2 mm of measured data. The simulated output variation between the IORT cones (relative output factors) are mostly within 2% of measured values. By comparing IORT and conventional electron beam characteristics (e.g. energy spectra, angular distributions and the contributions of different system components to these quantities) limitations and uncertainties of commonly used dosimetric techniques in IORT electron fields are quantified. The intraoperative treatment field contains a larger amount of scattered electrons, which leads to a broader energy spectrum as well as a wider angular distribution of electrons at the phantom surface. The dose from the scattered electrons can contribute up to 40% of the total dose at a depth of dose maximum, compared to approximately 10% for standard beams. A study of the energy spectra at the reference depth reveals that an uncertainty of the order of 1% can be introduced if ionization chamber based dosimetry is used to determine output factors for the investigated IORT system. We recommend that relative absorbed dose distributions and output factors in IORT electron beams and for similar complicated dosimetric situations should be determined with detectors having a small energy and angular dependence (e.g. diamond detectors or p-Si diodes).     

Model for calculating depth dose distributions for broad electron beams

Central axis electron beam depth dose distributions can be transformed by replacing dose by fluence and depth by a measure of angular dispersion. This transformation was applied to a set of broad beam central axis depth dose distributions calculated by Monte Carlo code for beams with initial energies ranging from 1 to 60 MeV in homogeneous media of water, aluminum, and copper. The resulting fluence distributions belong to a family of curves that can be parametrized by a single-valued function of initial beam energy and medium and can be used to calculate fluence distributions for accelerators. Fluence curves can be easily transformed to depth dose curves.     

Monte Carlo simulation of backscatter from lead for clinical electron beams using EGSnrc

In electron radiotherapy of superficial lesions in the eyelid, lip, buccal mucosa, ear, and nose, backscattered electrons are produced from the lead shield used to protect the critical tissue underneath the tumor. In this study, the backscattered electrons, produced by clinical electron beams using a Varian 21 EX linear accelerator, were studied using Monte Carlo simulations. The electron backscatter factor (EBF), defined as the ratio of dose at the tissue-lead interface to the dose at the same point without the presence of backscatter, was calculated using the Monte Carlo EGSnrc-based code. The calculated EBFs were verified with measurements using metal-oxide-semiconductor field effect transistor detectors. The effect of the (1) initial electron beam energy, (2) thickness of bolus over the lead shield, (3) beam's angle of incidence, and (4) presence of an aluminum sheet used to absorb backscattered electrons, on the EBF, were studied. It is found that for lead shielding positioned at any fixed depth, the EBF decreases with an increase in initial electron beam energy (4-16 MeV). In addition, for depths within the electron practical range, Rp, and at a particular beam energy, the EBF increases with depth (or thickness of the treatment volume). When the electron beam angle increases from 0 degrees to 5 degrees, the EBF only decreases slightly (<4%) for all energies. The influence of the beam obliquity on the EBF is important when the treatment surface is not flat and perpendicular to the central beam axis. The use of an aluminum sheet to reduce backscattered electrons was also investigated. For a relatively low electron beam energy (4 MeV), a 2 mm aluminum sheet can reduce backscattering by 31%. While the electron beam energy increased, less backscattered electrons were produced and therefore removed by the same thickness of aluminum (only about 6% for 16 MeV). The Monte Carlo calculated EBFs from this study, characterized by the electron beam energy, depth of bolus above the lead shield, beam obliquity, and presence of an aluminum sheet, may provide important clinical information for radiation oncology staff when considering the effect of electron backscatter on radiotherapy using internal shielding.     

Determination of effective bremsstrahlung spectra and electron contamination for photon dose calculations

A method is described for determining an effective, depth dose consistent bremsstrahlung spectra for high-energy photon beams using depth dose curves measured in water. A simple, analytical model with three parameters together with the nominal accelerating potential is used to characterise the bremsstrahlung spectra. The model is used to compute weights for depth dose curves from monoenergetic photons. These monoenergetic depth doses, calculated with the convolution method from Monte Carlo generated point spread functions (PSF), are added to yield the pure photon depth dose distribution. The parameters of the analytical spectrum model are determined using an iterative technique to minimise the difference between calculated and measured depth dose curves. The influence from contaminant electrons is determined from the difference between the calculated and the measured depth dose.     

Spectral reconstruction by scatter analysis for a linear accelerator photon beam

Pre-existing methods for photon beam spectral reconstruction are briefly reviewed. An alternative reconstruction method by scatter analysis for linear accelerators is introduced. The method consists in irradiating a small plastic phantom at standard 100 cm SSD and inferring primary beam energy spectral information based on the measurement with a standard Farmer chamber of scatter around the phantom at several specific scatter angles: a scatter curve is measured which is indicative of the primary spectrum at hand. A Monte Carlo code is used to simulate the scatter measurement set-up and predict the relative magnitude of scatter measurements for mono-energetic primary beams. Based on mono-energetic primary scatter data, measured scatter curves are analysed and the spectrum unfolded as the sum of mono-energetic individual energy bins using the Schiff bremsstrahlung model. The method is applied to an Elekta/SL18 6 MV photon beam. The reconstructed spectrum matches the Monte Carlo calculated spectrum for the same beam within 6.2% (average error when spectra are compared bin by bin). Depth dose values calculated for the reconstructed spectrum agree with physically measured depth dose data to within 1%. Scatter analysis is preliminarily shown to have potential as a practical spectral reconstruction method requiring few measurements under standard 100 cm SSD and feasible in any radiotherapy department using a phantom and a Farmer chamber.     

A model to determine the initial phase space of a clinical electron beam from measured beam data

Advanced electron beam dose calculation models for radiation oncology require as input an initial phase space (IPS) that describes a clinical electron beam. The IPS is a distribution in position, energy and direction of electrons and photons in a plane in front of the patient. A method is presented to derive the IPS of a clinical electron beam from a limited set of measured beam data. The electron beam is modelled by a sum of four beam components: a main diverging beam, applicator edge scatter, applicator transmission and a second diverging beam. The two diverging beam components are described by weighted sums of monoenergetic diverging electron and photon beams. The weight factors of these monoenergetic beams are determined by the method of simulated annealing such that a best fit is obtained with depth-dose curves measured for several field sizes at two source-surface distances. The resulting IPSs are applied by the phase-space evolution electron beam dose calculation model to calculate absolute 3D dose distributions. The accuracy of the calculated results is in general within 1.5% or 1.5 mm; worst cases show differences of up to 3% or 3 mm. The method presented here to describe clinical electron beams yields accurate results, requires only a limited set of measurements and might be considered as an alternative to the use of Monte Carlo methods to generate full initial phase spaces.     

Determining clinical photon beam spectra from measured depth dose with the Cimmino algorithm

A method to determine the spectrum of a clinical photon beam from measured depth-dose data is described. At shallow depths, where the range of Compton-generated electrons increases rapidly with photon energy, the depth dose provides the information to discriminate the spectral contributions. To minimize the influence of contaminating electrons, small (6 x 6 cm2) fields were used. The measured depth dose is represented as a linear combination of basis functions, namely the depth doses of monoenergetic photon beams derived by Monte Carlo simulations. The weights of the basis functions were obtained with the Cimmino feasibility algorithm, which examines in each iteration the discrepancy between predicted and measured depth dose. For 6 and 15 MV photon beams of a clinical accelerator, the depth dose obtained from the derived spectral weights was within about 1% of the measured depth dose at all depths. Because the problem is ill conditioned, solutions for the spectrum can fluctuate with energy. Physically realistic smooth spectra for these photon beams appeared when a small margin (about +/- 1%) was attributed to the measured depth dose. The maximum energy of both derived spectra agreed with the measured energy of the electrons striking the target to within 1 MeV. The use of a feasibility method on minimally relaxed constraints provides realistic spectra quickly and interactively.     

Monte Carlo simulation of large electron fields

Accurate simulation of large electron fields may lead to improved accuracy in Monte Carlo treatment planning while simplifying the commissioning procedure. We have used measurements made with wide-open jaws and no electron applicator to adjust simulation parameters. Central axis depth dose curves and profiles of 6-21 MeV electron beams measured in this geometry were used to estimate source and geometry parameters, including those that affect beam symmetry: incident beam direction and offset of the secondary scattering foil and monitor chamber from the beam axis. Parameter estimation relied on a comprehensive analysis of the sensitivity of the measured quantities, in the large field, to source and geometry parameters. Results demonstrate that the EGS4 Monte Carlo system is capable of matching dose distributions in the largest electron field to the least restrictive of 1 cGy or 1 mm, with D(max) of 100 cGy, over the full energy range. This match results in an underestimation of the bremsstrahlung dose of 10-20% at 15-21 MeV, exceeding the combined experimental and calculational uncertainty in this quantity of 3%. The simulation of electron scattering at energies of 15-21 MeV in EGS4 may be in error. The recently released EGSnrc/BEAMnrc system may provide a better match to measurement.     

Influence of initial electron beam parameters on Monte Carlo calculated absorbed dose distributions for radiotherapy photon beams

Our aim in the present study was to investigate the effects of initial electron beam characteristics on Monte Carlo calculated absorbed dose distribution for a linac 6 MV photon beam. Moreover, the range of values of these parameters was derived, so that the resulted differences between measured and calculated doses were less than 1%. Mean energy, radial intensity distribution and energy spread of the initial electron beam, were studied. The method is based on absorbed dose comparisons of measured and calculated depth-dose and dose-profile curves. All comparisons were performed at 10.0 cm depth, in the umbral region for dose-profile and for depths past maximum for depth-dose curves. Depth-dose and dose-profile curves were considerably affected by the mean energy of electron beam, with dose profiles to be more sensitive on that parameter. The depth-dose curves were unaffected by the radial intensity of electron beam. In contrast, dose-profile curves were affected by the radial intensity of initial electron beam for a large field size. No influence was observed in dose-profile or depth-dose curves with respect to energy spread variations of electron beam. Conclusively, simulating the radiation source of a photon beam, two of the examined parameters (mean energy and radial intensity) of the electron beam should be tuned accurately, so that the resulting absorbed doses are within acceptable precision. The suggested method of evaluating these crucial but often poorly specified parameters may be of value in the Monte Carlo simulation of linear accelerator photon beams.     

Dosimetric characteristics of dynamic wedged fields: a Monte Carlo study.

We have developed a Monte Carlo (MC) technique using the EGS4/BEAM system to calculate dosimetric characteristics of dynamic wedges (DW) for photon beam radiotherapy. The simulation of DW was accomplished by weighting the history numbers of the electrons, which are incident on the target in accordance with the segmented treatment table. Calculations were performed for DW with wedge angles ranging from 15 degrees to 60 degrees as well as for open fields with different field sizes for both degrees 6 and 18 MV beams. The MC-calculated percentage depth dose (PDD) and beam profiles agreed with the measurements within +/- 2% (of the dose maximum along the beam axis) or +/- 2 mm in high dose gradient region. The DW slightly affects energy spectra of photons and contaminating electrons. These slight changes have no significant effects on PDD as compared to the open field. The MC-calculated dynamic wedge factors agree with the measurements within +/- 2%. The MC method enables us to provide more detailed beam characteristics for DW fields than a measurement method. This beam characteristic includes photon energy spectra, mean energy, spectra of contaminating electrons and effects of moving jaw on off-axis beam quality. These data are potentially important for treatment planning involving dynamic wedges.     

VarianClinaciX15MeV光子束能谱重建

目的：精确重建VarianClinaciX15MeV光子束能谱。方法：利用先验模型和遗传算法,以光子束中轴百分深度剂量（PDD）为基础数据实现医用直线加速器光子能谱重建。1．EGS模拟仿真VarianClinacix治疗头和标准水模体,获得15MeV光子束的模拟能谱以及单能光子中轴PDD数据;2．根据测量得到的中轴PDD数据以及模拟得到的单能光子中轴PDD数据,运用遗传算法优化求解先验模型的参数：3．将优化后的先验模型所计算的结果作为初始化种群．再用遗传算法二次优化重建光子能谱。结果：重建能谱与蒙特卡洛模拟得到的能谱具有良好的一致性,相关系数为0．9970;重建能谱的平均能量与由相空间文件分析所得平均能量的相对误差为1．16％;根据重建能谱计算得到的中轴PDD数据与实际测量的中轴PDD数据之间的相关系数为O．9999。结论：利用先验模型和遗传算法进行光子束能谱重建可靠有效．具有实用价值。     

Dynamic wedge versus physical wedge: a Monte Carlo study

The purpose of this study is to analyze the characteristics of dynamic wedges (DW) and to compare DW to physical wedges (PW) in terms of their differences in affecting beam spectra, energy fluence, angular distribution, contaminated electrons, and dose distributions. The EGS4/BEAM Monte Carlo codes were used to simulate the exact geometry of a 6 MV beam and to calculate 3-D dose distributions in phantom. The DW was simulated in accordance with the segmented treatment tables (STT). The percentage depth dose curves and beam profiles for PW, DW, and open fields were measured and used to verify the Monte Carlo simulations. The Monte Carlo results were found to agree within 2% with the measurements performed using film and ionizing chambers in a water phantom. The present EGS4 calculation reveals that the effects of a DW on beam spectral and angular distributions, as well as electron contamination, are much less significant than those for a PW. For the 6 MV photon beam, a 45 degrees PW can result in a 30% increase in mean photon energy due to the effect of beam hardening. It can also introduce a 5% dose reduction in the build-up region due to the reduction of contaminated electrons by the PW. Neither this mean-energy increase nor such dose reduction is found for a DW. Compared to a DW, a PW alters the photon-beam spectrum significantly. The dosimetric differences between a DW and a PW are significant and clearly affect the clinical use of these beams. The data presented may be useful for DW commissioning.     

Commissioning stereotactic radiosurgery beams using both experimental and theoretical methods

The purpose of this investigation is to study the feasibility of using an alternative method to commission stereotactic radiosurgery beams shaped by micro multi-leaf collimators by using Monte Carlo simulations to obtain beam characteristics of small photon beams, such as incident beam particle fluence and energy distributions, scatter ratios, depth-dose curves and dose profiles where measurements are impossible or difficult. Ionization chambers and diode detectors with different sensitive volumes were used in the measurements in a water phantom and the Monte Carlo codes BEAMnrc/DOSXYZnrc were used in the simulation. The Monte Carlo calculated data were benchmarked against measured data for photon beams with energies of 6 MV and 10 MV produced from a Varian Trilogy accelerator. The measured scatter ratios and cross-beam dose profiles for very small fields are shown to be not only dependent on the size of the sensitive volume of the detector used but also on the type of detectors. It is known that the response of some detectors changes at small field sizes. Excellent agreement was seen between scatter ratios measured with a small ion chamber and those calculated from Monte Carlo simulations. The values of scatter ratios, for field sizes from 6 x 6 mm2 to 98 x 98 mm2, range from 0.67 to 1.0 and from 0.59 to 1.0 for 6 and 10 MV, respectively. The Monte Carlo calculations predicted that the incident beam particle fluence is strongly affected by the X-Y-jaw openings, especially for small fields due to the finite size of the radiation source. Our measurement confirmed this prediction. This study demonstrates that Monte Carlo calculations not only provide accurate dose distributions for small fields where measurements are difficult but also provide additional beam characteristics that cannot be obtained from experimental methods. Detailed beam characteristics such as incident photon fluence distribution, energy spectra, including composition of primary and scattered photons, can be independently used in dose calculation models and to improve the accuracy of measurements with detectors with an energy-dependent response. Furthermore, when there are discrepancies between results measured with different detectors, the Monte Carlo calculated values can indicate the most correct result. The data set presented in this study can be used as a reference in commissioning stereotactic radiosurgery beams shaped by a BrainLAB m3 on a Varian 2100EX or 600C accelerator.     

Monte Carlo Commissioning of Low Energy Electron Radiotherapy Beams using NXEGS Software

This work is a report on the commissioning of low energy electron beams of a medical linear accelerator for Monte Carlo dose calculation using NXEGS software (NXEGS version 1.0.10.0, NX Medical Software, LLC). A unique feature of NXEGS is automated commissioning, a process whereby a combination of analytic and Monte Carlo methods generates beam models from dosimetric data collected in a water phantom. This study uses NXEGS to commission 6, 9, and 12 MeV electron beams of a Varian Clinac 2100C using three applicators with standard inserts. Central axis depth-dose, primary axis and diagonal beam profiles, and output factors are the measurements necessary for commissioning of the code. We present a comparison of measured dose distributions with the distributions generated by NXEGS, using confidence limits on seven measures of error. We find that confidence limits are typically less than 3% or 3 mm, but increase with increasing source to surface distance (SSD) and depth at or beyond R(50). We also investigate the dependence of NXEGS' performance on the size and composition of data used to commission the program, finding a weak dependence on number of dose profiles in the data set, but finding also that commissioning data need be measured at only two SSDs.