Generalized monitor unit calculation for the Varian enhanced dynamic wedge field

The generalized monitor unit (MU) calculation equation for the Varian enhanced dynamic wedge (EDW) is derived. The assumption of this MU calculation method is that the wedge factor of the EDW at the center of the field is a function of field size, the position of the center of the field in the wedge direction, and the final position of the moving jaw. The wedge factors at the center of the field in both symmetric and asymmetric fields are examined. The difference between calculated and measured wedge factors is within 1.0%. The method developed here is easy to implement. The only datum required in addition to the standard set of conventional physical wedge implementation data is the off-axis output factor for the open field in the reference condition. The off-center point calculation is also examined. For the off-center point calculation, the dose profile in the wedge direction for the largest EDW field is used to obtain the relative off-center ratio in any smaller wedge field. The accuracy of the off-center point calculation decreases when the point of calculation is too close to the field edge.     

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.     

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.     

6MV-15MV下物理楔形因子和动态楔形因子的比较

目的:探讨不同能量下,Varian21EX直线加速器中物理楔形因子和动态楔形因子受照射野大小和深度的影响。方法:在固体水膜体中利用0.6 cc电离室对6 MV和15 MV射线束下不同角度物理楔形板和动态楔形板分别测量加和不加楔形滤片时的剂量率来计算楔形因子。通过测量不同角度的物理楔形板和动态楔形板在固定照射野(10 cm×10 cm)的不同深度下的楔形因子来研究楔形因子随深度的变化规律。同时,对于楔形因子随射野大小的变化规律,还测量了不同角度的物理楔形板和动态楔形板在固定深度(d=10 cm)下的不同射野大小的楔形因子。为了更好地分析物理楔形因子与动态楔形因子的差异,引入了相对楔形因子NWF。结果:深度对于物理楔形板的楔形因子较为明显,深度增加时楔形因子增大,且随着楔形角的增大变化更明显。对于150、300、450、600的物理楔形板,当深度由最大深度增加到20 cm时对于6 MV能量楔形因子分别增加了1.86%、3.79%、4.99%、7.95%;对于15 MV能量1.29%、1.35%、1.49%、2.03%。而动态楔形因子随深度变化不明显,最大变化不到1%。射野大小对于物理楔形因子也有一定的影响,楔形因子随射野增加而增加,但是增加幅度不大;而对于动态楔形板,在6 MV和15 MV射线束下楔形因子受射野的增大都有明显的减小。对于100、150、200、250、300、450、600的动态楔形板,从参考射野(10 cm×10 cm)到最大射野,楔形因子分别减少了7.91%、11.04%、14.08%、16.96%、19.7%、28.03%、35.89%对于6 MV和5.72%、8.17%、10.41%、12.85%、15.08%、21.82%、30.59%对于15 MV能量。结论:对于物理楔形板,深度和射野大小都对物理楔形因子有影响,所以临床剂量计算时必须考虑深度和射野大小对物理楔形因子的影响并对它进行修正。对于动态楔形板,深度对动态楔形因子影响较小,在临床剂量计算时可以忽略;而射野大小对动态楔形因子影响比较明显,在临床剂量计算时只须考虑相对射野楔形因子。     

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.     

Monitor unit calculations for wedged asymmetric photon beams

Algorithms for calculating monitor units (MUs) in wedged asymmetric high-energy photon beams as implemented in treatment planning systems have their limitations. Therefore an independent method for MU calculation is necessary. The aim of this study was to develop an empirical method to determine MUs for points at the centre of wedged fields, asymmetric in two directions. The method is based on the determination of an off-axis factor (OAF) that corrects for the difference in dose between wedged asymmetric and wedged symmetric beams with the same field size. Measurements were performed in a water phantom irradiated with 6 and 18 MV photon beams produced by Elekta accelerators, which are fitted with an internal motorized wedge that has a complex shape. The OAF perpendicular to the wedge direction changed significantly with depth for the 18 MV beam. Dose values measured for a set of 18 test cases were compared with those calculated with our method. The maximum difference found was 6.5% and in 15 cases this figure was smaller than 2.0%. The analytical method of Khan and the empirical method of Georg were also tested and showed errors up to 12.8%. It can be concluded that our simple formalism is able to calculate MUs in wedged asymmetric fields with an acceptable accuracy in most clinical situations.     

Investigation of an amorphous silicon EPID for measurement and quality assurance of enhanced dynamic wedge

This work assessed the dosimetric performance of an amorphous silicon electronic portal imaging device (EPID) for measurement and quality assurance of enhanced dynamic wedge (EDW) profile and wedge factor. EPID measurements of EDW profiles were corrected for pixel sensitivity variation and spectral over-response relative to ion chamber and compared to ion-chamber and diode-array measurements. The dependence of EPID measurements on wedge direction and source to EPID distance was assessed. The long-term stability was investigated by weekly measurement of EDW profiles and wedge factors over a seven month interval. An empirical correction method was developed to improve EPID profile agreement with diode-array measurements. The EPID profiles differed from conventional measurements by up to 5%. Backscatter from the EPID housing was also found to affect measurements by up to 4%, resulting in changes in EPID measured profile with the direction of the moving jaw and source to EPID distance. EPID profile measurements varied by a maximum of 0.3% (1 SD) within the umbra, and wedge factors varied by 0.3% (1 SD) over the seven month interval. The correction function improved agreement between EPID and diode array to within 2% for all wedge angles and energies. Due to the ease of use and reproducibility of the EPID-measured EDW profiles the device is highly suited to regular measurement of EDW.     

A pulse-rate dependence of dose per monitor unit and its significant effect on wedged-shaped fields delivered with variable dose rate and a moving jaw

Wedge-shaped dose distributions are delivered on some modern linear accelerators with a virtual wedge, combining variable dose rate and a moving jaw. Drift in the wedge factor and wedge angle of a 20 X 20 cm field for the 60 degree virtual wedge was found commonplace in several models of linear accelerator from one manufacturer. It was found that errors in dose delivery both on and off axis could exceed 5% if quality assurance checks are limited to 10 X 10 cm or smaller fields or wedge angles of 45 degrees or less. A procedure to easily identify and remedy the problem is presented. In each case the change was due to variation in dose per monitor unit (D/MU) with the electron beam pulse rate. The variation was traced to a pair of circuit boards in the dosimetry system, one for each output measurement channel. Wedge factors and dose profiles measured before and after board replacement on 4 accelerators, and for a set of defective boards placed on one of the accelerators, were compared. The effect was largest for the wedge with the steepest profile (60 degree wedge angle) and the largest field measured: 20 X 20 cm. In this case, a 1% variation in D/MU with a factor of 5 reduction in pulse rate corresponded to an average 0.8% change in wedge factor and 0.8% change in the off axis ratio at 8.5 cm off axis on the high dose side of the wedge field, 0.3% on the low dose side. After board replacement, wedge factors and profiles measured on the 4 machines generally agreed to 2% for the full range of wedge angles and field sizes. Quality assurance of virtual wedges is discussed in light of the new findings.     

On empirical methods to determine scatter factors for irregular MLC shaped beams

Multileaf collimators (MLCs) are in clinical use for more than a decade and are a well accepted tool in radiotherapy. For almost each MLC design different empirical or semianalytical methods have been presented for calculating output ratios in air for irregularly shaped beams. However, until now no clear recommendations have been given on how to handle irregular fields shaped by multileaf collimators for independent monitor unit (MU) verification. The present article compares different empirical methods, which have been proposed for independent MU verification, to determine (1) output ratios in air (Sc) and (2) phantom scatter factors (Sp) for irregular MLC shaped fields. Ten dedicated field shapes were applied to five different types of MLCs (Elekta, Siemens, Varian, Scanditronix, General Electric). All calculations based on empirical relations were compared with measurements and with calculations performed by a treatment planning system with a fluence based algorithm. For most irregular MLC shaped beams output ratios in air could be adequately modeled with an accuracy of about 1%-1.5% applying a method based on the open field aperture defined by the leaf and jaw setting combined with the equivalent square formula suggested by Vadash and Bj?rngard [P. Vadash and B. E. Bj?rngard, Med. Phys. 20, 733-734 (1993)]. The accuracy of this approach strongly depends on the inherent head scatter characteristics of the accelerator in use and on the irregular field under consideration. Deviations of up to 3% were obtained for fields where leaves obscure central parts of the flattening filter. Simple equivalent square methods for Sp calculations in irregular fields did not provide acceptable results (deviations mostly >3%). Sp values derived from Clarkson integration, based on published tables of phantom scatter correction factors, showed the same accuracy level as calculations performed using a pencil beam algorithm of a treatment planning system (in a homogeneous media). The separation of head scatter and phantom scatter contributions is strongly recommended for irregular MLC shaped beams as both contributions have different factors of influence. With rather simple methods Sc and Sp can be determined for independent MU calculation with an accuracy better than 1.5% for most clinical situations encountered in conformal radiotherapy.     

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.     

Modeling the extrafocal radiation and monitor chamber backscatter for photon beam dose calculation

A simple analytical approach has been developed to model extrafocal radiation and monitor chamber backscatter for clinical photon beams. Model parameters for both the extrafocal source and monitor chamber backscatter are determined simultaneously using conventional measured data, i.e., in-air output factors for square and rectangular fields defined by the photon jaws. The model has been applied to 6 MV and 15 MV photon beams produced by a Varian Clinac 2300C/D accelerator. Contributions to the in-air output factor from the extrafocal radiation and monitor chamber backscatter, as predicted by the model, are in good agreement with the measurements. The model can be used to calculate the in-air output factors analytically, with an accuracy of 0.2% for symmetric or asymmetric rectangular fields defined by jaws when the calculation point is at the isocenter and 0.5% when the calculation point is at an extended SSD. For MLC-defined fields, with the jaws at the recommended positions, calculated in-air output factors agree with the measured data to within 0.3% at the isocenter and 0.7% at off-axis positions. The model has been incorporated into a Monte Carlo dose algorithm to calculate the absolute dose distributions in patients or phantoms. For three MLC-defined irregular fields (triangle shape, C-shape, and L-shape), the calculations agree with the measurements to about 1% even for points at off-axis positions. The model will be particularly useful for IMRT dose calculations because it accurately predicts beam output and penumbra dose.     

Effective wedge angles with a universal wedge

Some recently designed x-ray-producing accelerators are equipped with a single built-in wedge, and different 'effective' wedge angles are obtained by combining an open (unwedged) and a wedged field in the appropriate proportions. This paper describes a technique for determining these proportions from measured isodose distributions of the two component fields. Our data for the Philips SL/75 6 MV accelerator are compared with two existing theoretical models. One model, in which the beams are weighted by the ratio of the tangents of the effective and nominal wedge angles, agrees with the data to within 3 degrees over the range of effective wedge angles and square field sizes examined. The second and simpler model, in which the beams are weighted by the ratio of the wedge angles directly, results in errors of as much as 11 degrees. It is shown that both of these models are approximations to an exact theoretical solution which may be formulated in terms of one free parameter. This parameter may be interpreted physically as the ratio of the slopes of the central-axis depth-dose curves for the open and wedged fields.     

Output ratio in air for MLC shaped irregular fields

For accurate monitor unit calculation, it is important to calculate the output ratio in air, Sc, for an irregular field shaped by MLC. We have developed an algorithm to calculate Sc based on an empirical model [Med. Phys. 28, 925-937 (2001)] by projecting each leaf position to the isocenter plane. Thus it does not require the exact knowledge of the head geometry. Comparisons were made for three different types of MLC: those with MLC replacing the inner collimator jaws; those with MLC replacing the outer collimator jaws; and those with MLC as a tertiary attachment. When the MLC leaf positions are substantially different from the secondary collimators (or the rectangular field encompassing the irregular field), one observes an up to 5% difference in the value of head-scatter correction factor, HCF, defined as the ratio of output ratio in air between the MLC shaped irregular field and that of the rectangular field encompassing the irregular field. No collimator exchange effect was observed for rectangular fields shaped by MLC (e.g., 5x30 and 30x5 cm2 diagonal) when the secondary collimators are fixed, unlike that for the rectangular fields shaped by the inner and outer collimator jaws, where it can be 1-2%. For the same MLC shaped irregular field, the value of Sc increases from the Elekta, to the Siemens, to the Varian accelerators, with an up to 4% difference. The calculation agrees with measurement to within 1.2% for points both on and off the central-axis. The fitting parameters used in the algorithm are derived from measurements for square field sizes on the central-axis.     

Compatibility of Varian 2100C gated operations with enhanced dynamic wedge and IMRT dose delivery

An enhanced dynamic wedge (EDW) is one of the latest technical innovations frequently used in the radiotherapy department. Its usage is enthusiastically supported by radiation therapists. Intensity modulated radiotherapy (IMRT) is the other, which has become popular within the past several years. Its usage is not as straightforward as the EDW. However, its ability to further increase dose conformity to the target and to spare the surrounding normal tissues has been evidenced. Both of these treatment modalities demand sophisticated software, which controls precision motion and speed of jaws or multileaf collimators as well as dose rate. This paper deals with the question of how accurately the EDW profiles and IMRT dose distributions be maintained when the additional constraint of linear accelerator gating is invoked. For this, square pulses mimicking breathing were used in gated and nongated modes for film dosimetry and ion chamber measurements using the Varian 2100C linear accelerator. The results show no observable difference between gated and nongated EDW profiles and IMRT dose distribution regardless of the machine repetition rate. Also studied in this paper are the "fuzzy" dose distributions caused by realistic finite gate window settings.     

Elimination of field size dependence of enhanced dynamic wedge factors

Enhanced dynamic wedge factors (EDWF) are characterized by a strong field size dependence. In contrast to physical wedge factors, the EDWF decrease as the field size is increased: for 6 MV 60 degrees wedge, the EDWF decreases by 50% when the field size is increased from 4 x 4 cm2 to 20 x 20 cm2. A method that eliminates the field size dependence of EDWF was developed and investigated in this work. In this method, the wedged field shape is determined by a multileaf collimator. The initial position of the moving Y jaw is determined by the field size and the stationary Y jaw is kept fixed at 10 cm for field sizes < or = 20 cm in the wedged direction. For all other fields, the stationary Y jaw setting is determined by the field size. The modified method results in EDWF that are independent of field size, with no change in the wedge dose distribution when compared with the conventional use of EDW.     

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.     

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.     

Dose calculation for asymmetric photon fields with independent jaws and multileaf collimators

We have developed a simple method for dose calculation in dual asymmetric open and irregular fields with four independent jaws and multileaf collimators. Our calculation method extends the scatter correction method of Kwa et al. [Med. Phys. 21, 1599-1604 (1994)] based on the principle of Day's equivalent-field calculation. The scatter correction factor was determined by the ratio of the derived doses of a smaller asymmetric open field or irregular field to a larger symmetric field. The algorithm with the scatter correction method can be calculated from output factors, tissue maximum ratios, and off-axis ratios for conventional symmetric fields. The doses calculated by this method were compared with the measured doses for various asymmetric open and irregular fields. The agreement between the calculated and measured doses for 4 and 10 MV photon beams was within 0.5% at the geometric center of the asymmetric open fields. For the asymmetric irregular fields with the same geometrical center, agreement within 1% was found in most cases.     

Testing of the analytical anisotropic algorithm for photon dose calculation

The analytical anisotropic algorithm (AAA) was implemented in the Eclipse (Varian Medical Systems) treatment planning system to replace the single pencil beam (SPB) algorithm for the calculation of dose distributions for photon beams. AAA was developed to improve the dose calculation accuracy, especially in heterogeneous media. The total dose deposition is calculated as the superposition of the dose deposited by two photon sources (primary and secondary) and by an electron contamination source. The photon dose is calculated as a three-dimensional convolution of Monte-Carlo precalculated scatter kernels, scaled according to the electron density matrix. For the configuration of AAA, an optimization algorithm determines the parameters characterizing the multiple source model by optimizing the agreement between the calculated and measured depth dose curves and profiles for the basic beam data. We have combined the acceptance tests obtained in three different departments for 6, 15, and 18 MV photon beams. The accuracy of AAA was tested for different field sizes (symmetric and asymmetric) for open fields, wedged fields, and static and dynamic multileaf collimation fields. Depth dose behavior at different source-to-phantom distances was investigated. Measurements were performed on homogeneous, water equivalent phantoms, on simple phantoms containing cork inhomogeneities, and on the thorax of an anthropomorphic phantom. Comparisons were made among measurements, AAA, and SPB calculations. The optimization procedure for the configuration of the algorithm was successful in reproducing the basic beam data with an overall accuracy of 3%, 1 mm in the build-up region, and 1%, 1 mm elsewhere. Testing of the algorithm in more clinical setups showed comparable results for depth dose curves, profiles, and monitor units of symmetric open and wedged beams below dmax. The electron contamination model was found to be suboptimal to model the dose around dmax, especially for physical wedges at smaller source to phantom distances. For the asymmetric field verification, absolute dose difference of up to 4% were observed for the most extreme asymmetries. Compared to the SPB, the penumbra modeling is considerably improved (1%, 1 mm). At the interface between solid water and cork, profiles show a better agreement with AAA. Depth dose curves in the cork are substantially better with AAA than with SPB. Improvements are more pronounced for 18 MV than for 6 MV. Point dose measurements in the thoracic phantom are mostly within 5%. In general, we can conclude that, compared to SPB, AAA improves the accuracy of dose calculations. Particular progress was made with respect to the penumbra and low dose regions. In heterogeneous materials, improvements are substantial and more pronounced for high (18 MV) than for low (6 MV) energies.