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.     

Monte Carlo modelling of a virtual wedge

Compared with a set of physical photon wedges, a non physical wedge (virtual or dynamic wedge), realized by a moving collimator jaw, offers an alternative that allows creation of a wedged field with any arbitrary wedge angle instead of the traditional four physical wedges (15 degrees, 30 degrees, 45 degrees and 60 degrees). It is commonly assumed that non-physical wedges do not alter the photon spectrum compared with physical wedges that introduce beam hardening and loss of dose uniformity in the unwedged direction. In this study, we investigated the influence of a virtual wedge on the photon spectra of a 6-10 MV Siemens MD2 accelerator with the Monte Carlo code EGS4/BEAM. Good agreement was obtained between calculated and measured lateral dose profiles at the depth of maximum dose and at 10 cm depth for 20 x 20 cm2 fields for 6 and 10 MV photon beams. By comparing Monte Carlo models of a physical wedge and the virtual wedge that was studied in this work, it is confirmed that the latter has an insignificant effect on the beam quality, whereas the former can introduce significant beam hardening.     

Monte Carlo simulation of a dynamic MLC based on a multiple source model.

Detailed knowledge of the characteristics of the radiation field shaped by a multileaf collimator (MLC) is essential in intensity modulated radiotherapy (IMRT). A previously developed multiple source model (MSM) for a 6 MV beam was extended to a 15 MV beam and supplemented with an accurate model of an 80-leaf dynamic MLC. Using the supplemented MSM and the MC code GEANT, lateral dose distributions were calculated in a water phantom and a portal water phantom. A field which is normally used for the validation of the step and shoot technique and a field from a realistic IMRT treatment plan delivered with dynamic MLC are investigated. To assess possible spectral changes caused by the modulation of beam intensity by an MLC, the energy spectra in five portal planes were calculated for moving slits of different widths. The extension of the MSM to 15 MV was validated by analysing energy fluences, depth doses and dose profiles. In addition, the MC-calculated primary energy spectrum was verified with an energy spectrum which was reconstructed from transmission measurements. MC-calculated dose profiles using the MSM for the step and shoot case and for the dynamic MLC case are in very good agreement with the measured data from film dosimetry. The investigation of a 13 cm wide field shows an increase in mean photon energy of up to 16% for the 0.25 cm slit compared to the open beam for 6 MV and of up to 6% for 15 MV, respectively. In conclusion, the MSM supplemented with the dynamic MLC has proven to be a powerful tool for investigational and benchmarking purposes or even for dose calculations in IMRT.     

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.     

Validation of Monte Carlo calculated surface doses for megavoltage photon beams

Recent work has shown that there is significant uncertainty in measuring build-up doses in mega-voltage photon beams especially at high energies. In this present investigation we used a phantom-embedded extrapolation chamber (PEEC) made of Solid Water to validate Monte Carlo (MC)-calculated doses in the dose build-up region for 6 and 18 MV x-ray beams. The study showed that the percentage depth ionizations (PDIs) obtained from measurements are higher than the percentage depth doses (PDDs) obtained with Monte Carlo techniques. To validate the MC-calculated PDDs, the design of the PEEC was incorporated into the simulations. While the MC-calculated and measured PDIs in the dose build-up region agree with one another for the 6 MV beam, a non-negligible difference is observed for the 18 MV x-ray beam. A number of experiments and theoretical studies of various possible effects that could be the source of this discrepancy were performed. The contribution of contaminating neutrons and protons to the build-up dose region in the 18 MV x-ray beam is negligible. Moreover, the MC calculations using the XCOM photon cross-section database and the NIST bremsstrahlung differential cross section do not explain the discrepancy between the MC calculations and measurement in the dose build-up region for the 18 MV. A simple incorporation of triplet production events into the MC dose calculation increases the calculated doses in the build-up region but does not fully account for the discrepancy between measurement and calculations for the 18 MV x-ray beam.     

A depth dependence determination of the wedge transmission factor for 4-10 MV photon beams

The depth dependence (up to 25 cm) of the in-phantom wedge transmission factor (WTF) has been determined for three medical linear accelerator x-ray beams with energies of 4, 6, and 10 MV containing 15 degrees-60 degrees (nominal) brass wedges. All measurements were made with a cylindrical ionization chamber in water, for a field size of 10 X 10 cm2 with a source-skin distance of 80 or 100 cm. We conclude that, for the accelerators studied, the WTF factor at depth is less than 2% different from that determined at dmax (for the nominal wedge angles and photon energies studied) unless the depth of interest is greater than 10 cm. Up to the maximum depth studied (25 cm) the relative wedge factor--that is, wedge factor at depth compared to that determined at dmax--was about equal to or less than 1.02 for the 15 degrees and 30 degrees wedges and any of the photon beam energies studied. For the seldom utilized combination of a nominal wedge angle in excess of 45 degrees with a depth greater than 10 cm, the WTF at depth can differ from the WTF determined at dmax, by up to 5%. Since the wedge transmission factor is reflective of relative percent dose data, our results also indicate that it is in error to use open field percent depth doses for certain combinations of wedge angle, photon energy, and depth.     

Influence of focal spot on characteristics of very small diameter radiosurgical beams

Percentage depth dose (PDD) distributions and beam profiles of very small diameter (1.5-5 mm) megavoltage radiosurgical beams calculated with Monte Carlo (MC) technique critically depend on the diameter of the circular focal spot used in the simulation: The smaller is the field diameter, the larger is the effect. Thus, in simulations of radiosurgical fields that have diameters of the order of the focal spot size, an accurate focal spot geometry should be used. We used a simplified moving slit technique in conjunction with a diode detector for evaluation of the focal spot size and shape of a megavoltage 6 MV linac as well as for determination of the equivalent focal spot diameter of the linac for use in MC simulations. The measured total diode signal contains three components: A direct focal spot signal, a background signal, and an extra-focal radiation signal. A single profile scan of the focal spot signal is Gaussian like in shape, and its full width at half maximum is used to define the focal spot dimension for this scan. The focal spot of our 6 MV linac is approximated with a Gaussian circle, and when the geometry of the effective focal spot circle is used in MC simulations, the agreement between MC-calculated and measured PDD distributions as well as beam profiles is good even for radiosurgical fields as small as 1.5 mm in diameter. Our results also confirm that matching the penumbral areas of accurately measured large-field beam profiles to the same areas of the MC-calculated beam profiles reliably leads to a realistic effective focal spot size for use in MC simulations of very small diameter 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.     

Two-effective-source method for the calculation of in-air output at various source-to-detector distances in wedged fields.

A simple algorithm was developed for calculation of the in-air output at various source-to-detector distances (SDDs) on the central axis for wedged fields. In the algorithm we dealt independently with two effective sources, one for head scatter and the other for wedge scatter. Varian 2100C with 18 and 8 MV photon beams was used to examine this algorithm. The effective source position for head scatter for wedged fields was assumed to be the same as that for open fields, and the effective source position for wedge scatter was assumed to be a certain distance upstream from the physical location of the wedge. The shift of the effective source for wedge scatter, w, was found to be independent of field size. Moreover, we observed no systematic dependency of w on wedge angle or beam energy. One value, w = 5.5 cm, provided less than 1% difference in in-air outputs through the whole experimental range, i.e., 6 x 6 to 20 x 20 cm2 field size (15 x 20 cm2 for 60 degrees wedge), 15 degrees-60 degrees wedge angle, 80-130 cm SDD, and both 18 and 8 MV photon beams. This algorithm can handle the case in which use of a tertiary collimator with an external wedge makes the field size for the determination of wedge scatter different from that for head scatter. In this case, without the two-effective-source method, the maximum of 4.7% and 2.6% difference can be given by the inverse square method and one-effective-source method in a 45 degrees wedged field with 18 MV. Differences can be larger for thicker wedges. Enhanced dynamic wedge (EDW) fields were also examined. It was found that no second effective source is required for EDW fields.     

Dosimetric characteristics of wedges mounted beyond the blocking tray.

In a beam accessory configuration for a linear accelerator using a prototype multileaf collimator, newly designed wedges were mounted beyond the blocking tray. The isodose curves, depth of maximum dose, surface dose, and wedge transmission factors were measured for the wedges designed for this unique configuration. The same set of wedges was used for both 6- and 18-MV x rays. The shape of the wedged isodose curves was essentially unchanged from those produced by the conventional wedges located above the blocking tray. The isodose curves exhibited the desired wedge angles over the range of field sizes from 5 x 5 to 15 x 40 cm. In the 10 x 10-cm field, the average difference between the observed wedge angle and the desired wedge angle was 3.8 degrees. The surface doses ranged from 18% to 35% for the wedged 10 x 10-cm fields as compared with about 15% for the same open field. Dosimetrically the wedges were acceptable for clinical use.     

Analytical representation for varian EDW factors at off-center points

The purpose of this study is to describe and evaluate a new analytical model for Varian enhanced dynamic wedge factors at off-center points. The new model was verified by comparing measured and calculated wedge factors for the standard set of wedge angles (i.e., 15 degrees, 30 degrees, 45 degrees and 60 degrees), different symmetric and asymmetric fields, and two different photon energies. The maximum difference between calculated and measured wedge factors is less than 2%. The average absolute difference is within 1%. The obtained results indicate that the suggested model can be useful for independent dose calculation with enhanced dynamic wedges.     

Beam characteristics of upper and lower physical wedge systems of Varian accelerators

The beam characteristics of a dual physical wedge system, upper and lower, for Varian accelerators are studied over the energy range 6-18 MV. Wedge factors for both systems are measured in a water phantom as a function of field size, depth and source-to-wedge (SWD) distance. Our results indicate that apart from their physical differences, dosimetrically, the two wedge systems have <2% difference in central axis percentage depth dose beyond the build-up region. The lower wedge central axis percentage depth dose is consistently lower than that of the corresponding upper wedge, with the effect more pronounced for large field sizes. The wedge profiles are identical within 2% for all field sizes, depths and energies. The wedge factors for both wedge systems are also within 2% for all field sizes and depths for both 6 and 15 MV photons and slightly higher for the 18 MV beam and 45 degrees-60 degrees wedge angle. The wedge factor variation with SWD reveals an interesting fact that thinner wedges (15 degrees and 30 degrees) result in a higher surface dose in the central axis region than thicker wedges. As the SWD increases beyond 80 cm, the reverse is true, i.e. thicker wedges produce higher surface dose than thinner wedges. It is also verified that the wedge factor at any depth and for any field size can be calculated from the wedged and open field central axis percentage depth dose, and the wedge factor at dmax, resulting in nearly 44% reduction in water phantom scanning and 80% reduction in point measurements during commissioning.     

不同照射条件下6MV X线对皮肤剂量的影响

目的:通过比较研究不同临床照射条件下,6 MV X线对皮肤剂量的影响。方法:在常规治疗模式下,利用平行板电离室在固体水中测量不同射野大小、不同源皮距(SSD)、(有/无)有机玻璃挡铅托板、动态楔形板、固定楔形板、多叶准直器(MLC)及低熔点合金挡铅等不同照射参数条件下皮肤相对受量。结果:皮肤剂量随着照射野由3 cm×3 cm到30 cm×30 cm时,其剂量由8%上升到30%;皮肤剂量随源皮距(SSD)的增加而逐渐降低,并且这种变化在大野时比较明显;有机玻璃挡铅托板的使用明显增加了皮肤受量且在大野时增加更为显著;在使用固定楔形板时(各角度),皮肤剂量较开野小,然而在使用动态楔形板时,皮肤剂量因楔角不同而不同,在小角度时皮肤受量与开野相似,但在大角度时,皮肤受量有较明显的降低;低熔点合金挡铅增加了皮肤剂量,MLC对皮肤剂量的影响类似低熔点合金挡铅,但增加效果没有合金挡铅明显。结论:在不同的照射条件下,皮肤的受量有较大的变化,因此本研究的意义在于揭示这种影响,为以后治疗计划设计提供参考意见。     

A new analytical model for Varian enhanced dynamic wedge factors

Dynamic and physical (hard) wedges are used in 3D conformal radiotherapy in order to improve dose distribution in patients. Unlike wedge factors for physical wedges that depend on wedge material and thickness, wedge factors for Varian dynamic wedges depend on the relationship between the position of the moving jaw and the number of delivered monitor units. In this study, we describe a new analytical model for dynamic wedge factors. We also review the existing analytical models and compare calculated and measured wedge factors. The comparison is performed for different wedge angles, symmetric and asymmetric fields and two different photon energies. The obtained results indicate that the new dynamic wedge model provides the best overall agreement (within 1%) with the measured wedge factors.     

Absolute dose calculations for Monte Carlo simulations of radiotherapy beams

Monte Carlo (MC) simulations have traditionally been used for single field relative comparisons with experimental data or commercial treatment planning systems (TPS). However, clinical treatment plans commonly involve more than one field. Since the contribution of each field must be accurately quantified, multiple field MC simulations are only possible by employing absolute dosimetry. Therefore, we have developed a rigorous calibration method that allows the incorporation of monitor units (MU) in MC simulations. This absolute dosimetry formalism can be easily implemented by any BEAMnrc/DOSXYZnrc user, and applies to any configuration of open and blocked fields, including intensity-modulated radiation therapy (IMRT) plans. Our approach involves the relationship between the dose scored in the monitor ionization chamber of a radiotherapy linear accelerator (linac), the number of initial particles incident on the target, and the field size. We found that for a 10 x 10 cm2 field of a 6 MV photon beam, 1 MU corresponds, in our model, to 8.129 x 10(13) +/- 1.0% electrons incident on the target and a total dose of 20.87 cGy +/- 1.0% in the monitor chambers of the virtual linac. We present an extensive experimental verification of our MC results for open and intensity-modulated fields, including a dynamic 7-field IMRT plan simulated on the CT data sets of a cylindrical phantom and of a Rando anthropomorphic phantom, which were validated by measurements using ionization chambers and thermoluminescent dosimeters (TLD). Our simulation results are in excellent agreement with experiment, with percentage differences of less than 2%, in general, demonstrating the accuracy of our Monte Carlo absolute dose calculations.     

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。     

Effective wedge angles for 6-MV wedges

Measurements were undertaken with 30 degrees and 45 degrees large wedges on a 6-MV linac to determine the effective wedge angle for various combinations of open and wedged fields. The validity of Tatcher's equation, relating effective wedge angle to maximum dose weightings, was examined over a range of field sizes from 5 X 5 to 20 X 20 cm. An alternative equation involving only central axis quantities was also investigated. The results obtained from an analysis of point dose measurements indicate that, for these wedges, either equation yields sufficient accuracy for clinical purposes.     

Wedge factor dependence on depth and field size for various beam energies using symmetric and half-collimated asymmetric jaw settings.

The depth- and field-size dependence of the in-phantom wedge factor have been determined for a Cobalt-60 (Co-60) teletherapy unit and four medical linear accelerators with 4-, 6-, 10-, and 18-MV x-ray beams containing 15 degrees-60 degrees (nominal) lead, brass, and steel wedge filters. Measurements were made with ionization chambers in solid water or water with a source-skin distance of 80 or 100 cm. Field sizes varied from 4 x 4 cm up to a maximum allowable size for each wedge filter. Measurements were performed for symmetric and half-collimated asymmetric fields at depth of maximum dose, 5- and 10-cm depths. For half-collimated fields, wedge factor reference points were located at a fixed off-axis distance from the collimator's rotational axis. These systematic measurements on wedges indicate that the wedge factor dependence on depth and field size is a function of beam energy as well as the design of the treatment head and wedge filters. Significance of the results reported herein are discussed for the most commonly used treatment depths and field sizes with various beam energies and wedge filters.     

Verification of treatment parameter transfer by means of electronic portal dosimetry

Electronic portal imaging devices (EPIDs) are mainly used for patient setup verification during treatment but other geometric properties like block shape and leaf positions are also determined. Electronic portal dosimetry allows dosimetric treatment verification. By combining geometric and dosimetric information, the data transfer between treatment planning system (TPS) and linear accelerator can be verified which in particular is important when this transfer is not carried out electronically. We have developed a pretreatment verification procedure of geometric and dosimetric treatment parameters of a 10 MV photon beam using an EPID. Measurements were performed with a CCD camera-based iView EPID, calibrated to convert a greyscale EPID image into a two-dimensional absolute dose distribution. Central field dose calculations, independent of the TPS, are made to predict dose values at a focus-EPID distance of 157.5 cm. In the same EPID image, the presence of a wedge, its direction, and the field size defined by the collimating jaws were determined. The accuracy of the procedure was determined for open and wedged fields for various field sizes. Ionization chamber measurements were performed to determine the accuracy of the dose values measured with the EPID and calculated by the central field dose calculation. The mean difference between ionization chamber and EPID dose at the center of the fields was 0.8 +/- 1.2% (1 s.d.). Deviations larger than 2.5% were found for half fields and fields with a jaw in overtravel. The mean difference between ionization chamber results and the independent dose calculation was -0.21 +/- 0.6% (1 s.d.). For all wedged fields, the presence of the wedge was detected and the mean difference in actual and measured wedge direction was 0 +/- 3 degrees (1 s.d.). The mean field size differences in X and Y directions were 0.1 +/- 0.1 cm and 0.0 +/- 0.1 cm (1 s.d.), respectively. Pretreatment monitor unit verification is possible with high accuracy and also geometric parameters can be verified using the same EPID image.