Effect of electron beam obliquity on lateral buildup ratio: a Monte Carlo dosimetry evaluation

The impact of the oblique electron beam on the lateral buildup ratio (LBR), used in the electron pencil beam model to predict the per cent depth dose (PDD) and dose per monitor unit (MU) for an irregular electron field, was examined using Monte Carlo simulation. The EGSnrc-based Monte Carlo code was used to model electron beams produced by a Varian 21 EX linear accelerator for different beam energies, angles of obliquity and field sizes. The Monte Carlo phase space model was verified by measurements using electron diode and radiographic film. For PDDs of oblique electron beams, it is found that the depth of maximum dose (d(m)) shifts towards the surface as the beam obliquity increases. Moreover, for increasing the beam angle of obliquity, the depth doses just beyond d(m) decrease with depth. The depth doses then increase eventually in a deeper depth close to the practical range. The LBRs and pencil beam radial spread function, calculated using PDDs with different field sizes, are found varying with electron beam energies, angles of obliquity and cutout diameters. It is found that LBR increases along the normalized depth when the beam angle of obliquity increases. This results in a decrease of the radial spread function with an increase of beam obliquity. When the size of the electron field increases, the variation of LBR with beam angle of obliquity decreases. It should be noted that when calculating dose per MU for an oblique electron beam with an irregular field misunderstanding and neglecting the effect of beam obliquity would lead to a significant deviation. A database of LBRs for oblique electron beams can be created using Monte Carlo simulation conveniently and is recommended when an oblique beam is used in electron radiotherapy.     

基于GAMOS的蒙特卡罗方法模拟放疗电子线照射的剂量学研究

目的:探讨基于GAMOS的蒙特卡罗（MC）方法模拟电子线放疗的剂量精确性。方法:运用GAMOS MC程序,建立Varian Rapidarc加速器3档能量（6、9和12 MeV）及3种限光筒［（6×6）、（10×10）和（15×15） cm2］的束流模型,模拟束流在水模体中的剂量分布,并与测量得到的百分深度剂量和等平面剂量分布比较,评估GAMOS软件模拟电子线照射的精确性和运算效率。结果:模拟的粒子数越多,模拟与测量结果的误差越小;当模拟粒子的数量达到5×108时,各个能量的电子线射程（Rp）和50%剂量深度（R50）的模拟结果与测量结果一致;除建成区外,百分深度剂量模拟和测量的结果误差在2%以内;等平面剂量分布模拟和测量的结果误差也在2%以内,模拟的照射野大小与测量结果一致。运算效率中,能量越大,限光筒尺寸越大,并行同步模拟所用的时间越多,模拟时间的变化越大。结论:基于GAMOS的MC方法可准确地模拟放疗电子线照射剂量的分布,粒子数的增加可提高模拟的精确性,并行同步计算可提高模拟的效率。     

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.     

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.     

Monte Carlo calculation of output factors for circular, rectangular, and square fields of electron accelerators (6-20 MeV).

Monte Carlo (MC) techniques can be used to build a simulation model of an electron accelerator to calculate output factors for electron fields. This can be useful during commissioning of electron beams from a linac and in clinical practice where irregular fields are also encountered. The Monte Carlo code BEAM/EGS4 was used to model electron beams (6-20 MeV) from a Varian 2100C linear accelerator. After optimization of the Monte Carlo simulation model, agreement within 1% to 2% was obtained between calculated and measured (with a Si diode) lateral and depth dose distributions or within 1 mm in the penumbral regions. Output factors for square, rectangular, and circular fields were measured using two different plane-parallel ion chambers (Markus and NACP) and compared to MC simulations. The agreement was usually within 1% to 2%. This study was not primarily concerned with minimizing the simulation time required to obtain output factors but some considerations with respect to this are presented. It would be particularly useful if the MC model could also be used to calculate output factors for other, similar linacs. To see if this was possible, the primary electron energies in the MC model were retuned to model a recently commissioned similar linac. Good agreement between calculated and measured output factors was obtained for most field sizes for this second accelerator.     

A modified method of calculating the lateral build-up ratio for small electron fields

This note outlines an improved method of calculating dose per monitor unit values for small electron fields using Khan's lateral build-up ratio (LBR). This modified method obtains the LBR directly from the ratio of measured, surface normalized, electron beam percentage depth dose curves. The LBR calculated using this modified method more accurately accounts for the change in lateral scatter with decreasing field size. The LBR is used along with Khan's dose per monitor unit formula to calculate dose per monitor unit values for a set of small fields. These calculated dose per monitor unit values are compared to measured values to within 3.5% for all circular fields and electron energies examined. The modified method was further tested using a small triangular field. A maximum difference of 4.8% was found.     

Electron radiotherapy: a study on dosimetric uncertainty using small cutouts

This note investigated the dosimetric uncertainties due to the positional error when centring a small cutout to the machine central beam axis (CAX) in electron radiotherapy. A group of six circular cutouts with 4 cm diameter were made with their centres shifting 0, 2, 4, 6, 8 and 10 mm from the machine CAX for the 6 x 6 cm(2) applicator. The per cent depth doses, beam profiles and output factors were measured using the 4, 9 and 16 MeV clinical electron beams produced by a Varian 21 EX linear accelerator. The 2D isodose distributions in the z-x (or cross-line) and z-y (or in-line) plane were calculated by Monte Carlo simulation using the EGSnrc system. When the cutout centre was shifted away from the machine CAX for the 4 MeV beam, the d(m), R(80) and R(90) at the machine CAX had no significant change (<0.1 mm). For higher energies of 9 and 16 MeV beams, the d(m) was reduced by 0.45 and 1.63 mm per mm, between the cutout centre and the machine CAX with off-axis shift <6 mm respectively. R(80) and R(90) were reduced by more than 0.3 mm per mm off-axis shift for both energies. The isodose coverage of the in-line axis beam profile was reduced when the cutout centre was shifted away from machine CAX. It is important for oncology staff to note such dosimetric changes in the clinical electron radiotherapy, particularly when a high energy electron beam is used for small cutout. Such positional uncertainty is unavoidable in fabricating an electron cutout in the mould room.     

Monte Carlo investigation of electron beam output factors versus size of square cutout.

A major task in commissioning an electron accelerator is to measure relative output factors versus cutout size (i.e., cutout factors) for various electron beam energies and applicator sizes. We use the BEAM Monte Carlo code [Med Phys. 22, 503-524 (1995)] to stimulate clinical electron beams and to calculate the relative output factors for square cutouts. Calculations are performed for a Siemens MD2 linear accelerator with beam energies, 6, 9, 11, and 13 MeV. The calculated cutout factors for square cutouts in 10 X 10 cm2, 15 X 15 cm2, and 20 X 20 cm2 applicators at SSDs of 100 and 115 cm agree with the measurements made using a silicon diode within about 1% except for the smallest cutouts at SSD= 115 cm where they agree within 0.015. The details of each component of the dose, such as the dose from particles scattered off the jaws and the applicator, the dose from contaminant photons, the dose from direct electrons, etc., are also analyzed. The calculations show that inphantom side-scatter equilibrium is a major factor for the contribution from the direct component which usually dominates the output of a beam. It takes about 6 h of CPU time on a Pentium Pro 200 MHz computer to simulate an accelerator and additional 2 h to calculate the relative output factor for each cutout with a statistical uncertainty of 1%.     

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.     

Clinical implementation of a Monte Carlo treatment planning system.

The purpose of this study was to implement the Monte Carlo method for clinical radiotherapy dose calculations. We used the EGS4/BEAM code to obtain the phase-space data for 6-20 MeV electron beams and 4, 6, and 15 MV photon beams for Varian Clinac 1800, 2100C, and 2300CD accelerators. A multiple-source model was used to reconstruct the phase-space data for both electron and photon beams, which retained the accuracy of the Monte Carlo beam data. The multiple-source model reduced the phase-space data storage requirement by a factor of 1000 and the accelerator simulation time by a factor of 10 or more. Agreement within 2% was achieved between the Monte Carlo calculations and measurements of the dose distributions in homogeneous and heterogeneous phantoms for various field sizes, source-surface distances, and beam modulations. The Monte Carlo calculated electron output factors were within 2% of the measured values for various treatment fields while the heterogeneity correction factors for various lung and bone phantoms were within 1% for photon beams and within 2% for electron beams. The EGS4/DOSXYZ Monte Carlo code was used for phantom and patient dose calculations. The results were compared to the dose distributions produced by a conventional treatment planning system and an intensity-modulated radiotherapy inverse-planning system. Significant differences (>5% in dose and >5 mm shift in isodose lines) were found between Monte Carlo calculations and the analytical calculations implemented in the commercial systems. Treatment sites showing the largest dose differences were for head and neck, lung, and breast cases.     

Monte Carlo simulation of large electron fields

Two Monte Carlo systems, EGSnrc and Geant4, the latter with two different 'physics lists,' were used to calculate dose distributions in large electron fields used in radiotherapy. Source and geometry parameters were adjusted to match calculated results to measurement. Both codes were capable of accurately reproducing the measured dose distributions of the six electron beams available on the accelerator. Depth penetration matched the average measured with a diode and parallel-plate chamber to 0.04 cm or better. Calculated depth dose curves agreed to 2% with diode measurements in the build-up region, although for the lower beam energies there was a discrepancy of up to 5% in this region when calculated results are compared to parallel-plate measurements. Dose profiles at the depth of maximum dose matched to 2-3% in the central 25 cm of the field, corresponding to the field size of the largest applicator. A 4% match was obtained outside the central region. The discrepancy observed in the bremsstrahlung tail in published results that used EGS4 is no longer evident. Simulations with the different codes and physics lists used different source energies, incident beam angles, thicknesses of the primary foils, and distance between the primary and secondary foil. The true source and geometry parameters were not known with sufficient accuracy to determine which parameter set, including the energy of the source, was closest to the truth. These results underscore the requirement for experimental benchmarks of depth penetration and electron scatter for beam energies and foils relevant to radiotherapy.     

DPM蒙卡方法在放疗剂量计算中的应用研究

目的:探讨最新推出基于蒙特卡罗方法的DPM(dose planning method)程序在放疗剂量计算中的应用,研究DPM程序计算放疗剂量的准确性及其临床应用的可行性。方法:对DPM源文件编译形成四个可执行文件,使其能在Windows系统下运行。(1)通过借助蒙卡BEAMnrc程序模拟我院Varian Clinac 21EX直线加速器治疗头,得到其相空间文件,并计算出SSD=100cm处的相空间(Phase Space)数据。(2)使用BEAMDP程序对该相空间文件进行能谱分析,获取到6MV-X线能谱分布。(3)修改DPM源程序,使之能调用该能谱。(4)DPM计算出水模体内百分深度剂量并用MATLAB软件显示PDD曲线分布,与实际测量进行拟合。(5)DPM计算非均匀组织内方野剂量,相同条件下与实测量、TPS计算值进行了比较。结果:蒙卡DPM程序调用直线加速器能谱计算水模体内的PDD曲线与实测曲线的拟合完全吻合,证明了DPM程序调用能谱方法可行而且计算准确。DPM蒙卡程序在非均匀组织中的计算也是准确的。结论:DPM蒙卡方法可应用实现组织中放疗剂量计算的研究。     

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.     

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.     

体元大小对基于MonteCarlo的剂量计算的影响

目的：在放射治疗计划系统中,剂量计算之前需要对人体密度数据体元化。对于蒙特卡罗方法的模拟过程,当一个自由程跨过体元界面时,会应用自由程近似。选取的体元越小,将导致越多的自由程近似。本文采用蒙特卡罗方法模拟一个虚拟射线源入射到水箱中的反应,计算水箱中的剂量分布,通过比较水箱分层和不分层两种情况下中心轴百分深度剂量分布和离轴比分布,来探讨选用不同大小的体元对剂量分布的影响。方法：本文以6MeV的方形电子射线源为外照射源、以三维水箱为介质模型。使用PENELOPE程序包模拟电子束垂直入射到水箱中引起的电子与物质的相互作用。比较水箱在分层和不分层情况下中心轴百分深度剂量和离轴比分布。结果：通过比较水箱在分层和不分层情况下中心轴百分深度剂量和离轴比分布,发现差异很小。结论：选用不同大小的体元,蒙特卡罗近似处理自由程对剂量计算精度的影响很小。研究结果对蒙特卡罗方法在放射治疗中的临床应用具有指导意义。     

Quantifying effects of lead shielding in electron beams: a Monte Carlo study

Lead shielding in contact with the patient's skin is often encountered in radiotherapy with electron beams. The influence of the lead shielding on dose distributions in the patient cannot fully be assessed using modern treatment planning systems. In this work the problem of quantifying the effect of lead shielding on dose distributions is addressed. Monte Carlo dose calculations were performed in a half-blocked water phantom shielded by lead, using a realistic model for the fluence of an electron linear accelerator. Electron beam energies of 6-20 MeV and lead thicknesses of 1-7 mm are used for 10 x 10 cm2 and 5 x 5 cm2 fields. The perturbation of the particle fluence and dose distributions in water introduced by the lead shielding is quantified. The effect of oblique electron beams on the dose perturbation is shown. A fictitious clinical example, the shielding of an eye in electron beam treatment, is used to demonstrate the usefulness of Monte Carlo based treatment planning algorithms that can incorporate the effects of lead shielding.     

Characterization of an extendable multi-leaf collimator for clinical electron beams

An extendable x-ray multi-leaf collimator (eMLC) is investigated for collimation of electron beams on a linear accelerator. The conventional method of collimation using an electron applicator is impractical for conformal, modulated and mixed beam therapy techniques. An eMLC would allow faster, more complex treatments with potential for reduction in dose to organs-at-risk and critical structures. The add-on eMLC was modelled using the EGSnrc Monte Carlo code and validated against dose measurements at 6-21 MeV with the eMLC mounted on a Siemens Oncor linear accelerator at 71.6 and 81.6 cm source-to-collimator distances. Measurements and simulations at 8.4-18.4 cm airgaps showed agreement of 2%/2 mm. The eMLC dose profiles and percentage depth dose curves were compared with standard electron applicator parameters. The primary differences were a wider penumbra and up to 4.2% reduction in the build-up dose at 0.5 cm depth, with dose normalized on the central axis. At 90 cm source-to-surface distance (SSD)--relevant to isocentric delivery--the applicator and eMLC penumbrae agreed to 0.3 cm. The eMLC leaves, which were 7 cm thick, contributed up to 6.3% scattered electron dose at the depth of maximum dose for a 10 × 10 cm2 field, with the thick leaves effectively eliminating bremsstrahlung leakage. A Monte Carlo calculated wedge shaped dose distribution generated with all six beam energies matched across the maximum available eMLC field width demonstrated a therapeutic (80% of maximum dose) depth range of 2.1-6.8 cm. Field matching was particularly challenging at lower beam energies (6-12 MeV) due to the wider penumbrae and angular distribution of electron scattering. An eMLC isocentric electron breast boost was planned and compared with the conventional applicator fixed SSD plan, showing similar target coverage and dose to critical structures. The mean dose to the target differed by less than 2%. The low bremsstrahlung dose from the 7 cm thick MLC leaves had the added advantage of reducing the mean dose to the whole heart. Isocentric delivery using an extendable eMLC means that treatment room re-entry and repositioning the patient for SSD set-up is unnecessary. Monte Carlo simulation can accurately calculate the fluence below the eMLC and subsequent patient dose distributions. The eMLC generates similar dose distributions to the standard electron applicator but provides a practical method for more complex electron beam delivery.     

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。     

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.     

Validation of calculations for electrons modulated with conventional photon multileaf collimators

Treating shallow tumors with a homogeneous dose while simultaneously minimizing the dose to distal critical organs remains a challenge in radiotherapy. One promising approach is modulated electron radiotherapy (MERT). Due to the scattering properties of electron beams, the commercially provided secondary and tertiary photon collimation systems are not conducive for electron beam delivery when standard source-to-surface distances are used. Also, commercial treatment planning systems may not accurately model electron-beam dose distributions when collimated without the standard applicators. However, by using the photon multileaf collimators (MLCs) to create segments to modulate electron beams, the quality of superficial tumor dose distributions may improve substantially. The purpose of this study is to develop and evaluate calculations for the narrow segments needed to modulate megavoltage electron beams using photon beam multileaf collimators. Modulated electron radiotherapy (MERT) will be performed with a conventional linear accelerator equipped with a 120 leaf MLC for 6-20 MeV electron beam energies. To provide a sharp penumbra, segments were delivered with short SSDs (70-85 cm). Segment widths (SW) ranging from 1 to 10 cm were configured for delivery and planning, using BEAMnrc Monte Carlo (MC) code, and the DOSXYZnrc MC dose calculations. Calculations were performed with voxel size of 0.2 x 0.2 x 0.1 cm3. Dosimetry validation was performed using radiographic film and micro- or parallel-plate chambers. Calculated and measured data were compared using technical computing software. Beam sharpness (penumbra) degraded with decreasing incident beam energy and field size (FS), and increasing SSD. A 70 cm SSD was found to be optimal. The PDD decreased significantly with decreasing FS. The comparisons demonstrated excellent agreement for calculations and measurements within 3%, 1 mm. This study shows that accurate calculations for MERT as delivered with existing photon MLC are feasible and allows the opportunity to take advantage of the dynamic leaf motion capabilities and control systems, to provide conformal dose distributions.