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.     

Portal dose image prediction for dosimetric treatment verification in radiotherapy. II. An algorithm for wedged beams

A method is presented for calculation of a two-dimensional function, T(wedge)(x,y), describing the transmission of a wedged photon beam through a patient. This in an extension of the method that we have published for open (nonwedged) fields [Med. Phys. 25, 830-840 (1998)]. Transmission functions for open fields are being used in our clinic for prediction of portal dose images (PDI, i.e., a dose distribution behind the patient in a plane normal to the beam axis), which are compared with PDIs measured with an electronic portal imaging device (EPID). The calculations are based on the planning CT scan of the patient and on the irradiation geometry as determined in the treatment planning process. Input data for the developed algorithm for wedged beams are derived from (the already available) measured input data set for transmission prediction in open beams, which is extended with only a limited set of measurements in the wedged beam. The method has been tested for a PDI plane at 160 cm from the focus, in agreement with the applied focus-to-detector distance of our fluoroscopic EPIDs. For low and high energy photon beams (6 and 23 MV) good agreement (approximately 1%) has been found between calculated and measured transmissions for a slab and a thorax phantom.     

Analytical representation of enhanced dynamic wedge factors for symmetric and asymmetric photon fields

The Enhanced Dynamic Wedge (EDW) presents many advantages over the physical wedge. However, in order to calculate monitor units (MUs) necessary to deliver a certain dose at a certain point, EDW factors (EDWFs) need to be determined. In this work, based on analysis of the golden segmented treatment table (GSTT) and the MU fraction model, an empirical analytic formula has been developed to calculate EDW factors for symmetric and asymmetric fields. This formalism is an extension of the MU fraction model. However in comparison with previous studies [J. P. Gibbons, Med. Phys. 25, 1411-1418 (1998) and M. Miften et al., Med. Dosim. 25, 81-86 (2000)], this formula is simpler, and easier to use. It is applicable to EDW fields of different sizes, wedge angles and different photon energies. For 6 and 18 MV beams from a Varian 21EX accelerator with 7 EDW angles (Varian Oncology Systems, Palo Alto, CA), more than 250 measured EDWFs for symmetric and asymmetric fields with different off-axis distances and field sizes were compared with model calculations. Results show that 80% and 98% of calculated EDWFs match corresponding measured values to within 0.5% and 1.0%, respectively, the maximum deviation being 1.3%.     

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.     

Monitor unit calculation on the beam axis of open and wedged asymmetric high-energy photon beams

An ESTRO booklet and a report of the Netherlands Commission on Radiation Dosimetry have been published recently describing empirical methods for monitor unit (MU) calculations in symmetrical high-energy photon beams. Both documents support the same basic ideas; firstly the separation of head scatter and volume scatter components and secondly the determination of head scatter quantities in a mini-phantom. Based on these ideas the methods previously described for MU calculations in symmetrical beams are extended to asymmetrical open and wedged beams in isocentric treatment conditions. All required dosimetric parameters (normalized head scatter factors, phantom scatter correction factors, wedge factors, off-axis ratios, quality index, and depth dose parameters) are determined as a function of beam axis position in order to study their off-axis dependence. Measurements are performed for 6 MV and 18 MV photon beams provided by two different dual-energy linear accelerators, a GE Saturne 42 and a Varian 2100 CD linac.     

Methods for beam data acquisition offered by a mini-phantom

Mini-phantoms are an important tool for measurement of basic head scatter parameters in high-energy photon beams, and recently they have also been used for beam quality specification. Therefore the feasibility and reliability of basic beam parameter acquisition using only a mini-phantom is checked in 6, 18 and 25 MV photon beams. These parameters include head scatter correction factors, phantom scatter correction factors, total scatter correction factors, wedge factors, off-axis ratios, as well as beam attenuation coefficients and beam hardening coefficients. In order to specify beam quality variations and beam quality modifications by a wedge, two different methods are compared: the first method uses a constant source to chamber distance of 1 m, the second method refers to narrow beam geometry. Mu values derived with two different beam quality specification methods show a systematic deviation. However, relative variations of the attenuation coefficient within the beam and the associated beam quality modifications observed with the two methods show good agreement in open and wedged beams. Phantom scatter correction factors are calculated from measured head scatter correction factors and total scatter correction factors as well as from attenuation coefficients. Measured and calculated phantom scatter correction factors agree within 1% with the values given in literature. For 18 and 25 MV photon beam, wedge factors measured in water or in the mini-phantom agree within 0.5%, but maximum deviations of approximately 1.5% are observed at 6 MV for the largest field sizes. It is demonstrated that the determination of several beam data related to full scatter conditions does not necessarily require the availability of a full scatter phantom. The mini-phantom is a reliable but very cheap and simple tool. It offers versatile possibilities to measure, check and verify basic beam parameters in high-energy photon beams.     

Characteristics of photon beams from Philips SL25 linear accelerators

The Philips SL25 accelerator is a multimodality machine offering asymmetric collimator jaws and a new type of beam bending and transport system. It produces photon beams, nominally at 6 and 25 MV, and a scattered electron beam with nine selectable energies between 4 and 22 MeV. Dosimetric characteristics for the 6- and 25-MV photon beams are presented with respect to field flatness, surface and depth dose characteristics, isodose distribution, field size factors for both open and wedged fields, and narrow beam transmission data in different materials.     

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.     

A practical method to calculate head scatter factors in wedged rectangular and irregular MLC shaped beams for external and internal wedges

Factor based methods for absorbed dose or monitor unit calculations are often based on separate data sets for open and wedged beams. The determination of basic beam parameters can be rather time consuming, unless equivalent square methods are applied. When considering irregular wedged beams shaped with a multileaf collimator, parametrization methods for dosimetric quantities, e.g. output ratios or wedge factors as a function of field size and shape, become even more important. A practical method is presented to derive wedged output ratios in air (S(c,w)) for any rectangular field and for any irregular MLC shaped beam. This method was based on open field output ratios in air (S(c)) for a field with the same collimator setting, and a relation f(w) between S(c,w) and S(c). The relation f(w) can be determined from measured output ratios in air for a few open and wedged fields including the maximum wedged field size. The function f(w) and its parametrization were dependent on wedge angle and treatment head design, i.e. they were different for internal and external wedges. The proposed method was tested for rectangular wedged fields on three accelerators with internal wedges (GE, Elekta, BBC) and two accelerators with external wedges (Varian). For symmetric regular beams the average deviation between calculated and measured S(c,w) / S(c) ratios was 0.3% for external wedges and about 0.6% for internal wedges. Maximum deviations of 1.8% were obtained for elongated rectangular fields on the GE and ELEKTA linacs with an internal wedge. The same accuracy was achieved for irregular MLC shaped wedged beams on the accelerators with MLC and internal wedges (GE and Elekta), with an average deviation < 1% for the fields tested. The proposed method to determine output ratios in air for wedged beams from output ratios of open beams, combined with equivalent square approaches, can be easily integrated in empirical or semi-empirical methods for monitor unit calculations.     

Measurements of primary off-axis ratios in wedged asymmetric photon fields: a formalism for dose and monitor unit calculations

Asymmetric collimators or heavily blocked fields with physical wedges are still encountered in daily practice. In such cases, a reliable dosimetry system is necessary to perform manual dose and monitor unit calculations in order to independently verify the calculations of commercial treatment planning systems. In this work, primary wedged off-axis ratios (POAR(w)s) that account for changes in the beam intensity along both the wedge gradient and perpendicular directions of the photon field, when asymmetric collimators are applied, were measured experimentally at specific depths. The measurements were made in phantom with an ion chamber along the wedge gradient and the perpendicular directions under 'good geometry' conditions. A consistent formalism was presented that could easily be implemented in the clinical environment as an independent verification of the calculations by a treatment planning system. The accuracy of the method was found to be dependent on the specific wedge used, off-axis distance and depth in the phantom. In our study, the accuracy was within 2% in most cases for both energies. We concluded that the primary wedged off-axis ratios when used along with open symmetric field dosimetric parameters could provide adequate accuracy for manual monitor unit calculations.     

Head-scatter factors and effective x-ray source positions in a 25-MV linear accelerator.

The behavior of the effective source position and the correction factor associated with the collimator opening (head-scatter factor) were investigated for the 6- and 25-MV x-ray beams of a linear accelerator. The primary photon fluence was measured in air for square field sizes from 5 x 5 cm to 40 x 40 cm at distances from the nominal source of 80 to 140 cm, for open and wedged fields (wedge angle 60 deg). An inverse-square analysis shows that, for open fields, the effective source position of the accelerator is about the same (approximately 1 cm downstream) at 6 and 25 MV, for all field sizes. For the wedged fields, the effective source position depends on field size and ranges from about 2 to 4 cm. The head-scatter correction factors for given collimator settings were found to be essentially independent of distance at both energies.     

Partially wedged radiation beams

To increase dose homogeneity within certain radiotherapy targets, we defined a partially wedged radiation beam as a beam with wedge modification in one part of the field only. Partially wedged beams may be beneficial in cases with curved surfaces inside parts of the beam only, where they may compensate for missing tissue and/or for variations in depth to the target region. Possible sites suitable for partially wedged beams include urinary bladder and tangential breast irradiation. Customized partially wedged beams were delivered applying dynamic collimation techniques. Two different linear detector arrays, a semiconductor diode array and an ionization chamber array, were used independently in the same standard water tank to verify that the partially wedged beams were delivered according to the definition. Dose calculations of partial wedge fields were implemented in our treatment planning system and compared with the measured dose distributions. We re-planned a representative treatment plan for both advanced urinary bladder cancer and tangential breast irradiation using partially wedged beams. For both patients the target dose homogeneity was improved, and the doses to surrounding critical normal tissues were reduced.     

Scatter dose for wedged fields

The behaviour of scatter dose in 4 and 8 MV wedged x-ray beams has been studied by calculating scatter-to-primary dose ratios (SPR) and comparing these with SPR for non-wedged beams. On the central axis the SPR for wedged and non-wedged beams differ only by a few per cent, a difference which increases slightly with wedge angle and field size. In other points within the field the differences are larger but generally less than 3% of the total dose on the central axis at the same depth. The product rule for points that do not lie in a principal plane is valid within the same limits as for non-wedged beams.     

Wedge factor dependence with depth, field size, and nominal distance--a general computational rule

We have investigated the dependence of the wedge factors with field size, depth, nominal, and extended distances for 4, 6, 18, and 24 MV photon beams. Analysis of the experimental data suggests a general linear dependence of the wedge factors with field size and depth. The study shows that changes in wedge factors are insignificant (< or = +/-1.0%) with respect to measurements at nominal SSD, SAD, or extended SSD. This independence of the wedge factors on source-to-surface distance was studied for different photon energies (4-24 MV) and for different attenuating wedges (external and internal wedges). For clinical applications, an algorithm is presented to calculate the wedge factor dependence with field size and depth. The new algorithm has been successfully implemented to replace wedge look-up tables for dose and MU calculations in PRISM 1.2 treatment planning system used in our department.     

Extension of CadPlan algorithm to model the dose distribution under a motorized wedge.

The CadPlan treatment planning system models the dose distribution in the non-wedge direction under a wedged field by converting the wedge thickness to an equivalent water thickness. The algorithm estimates the off-axis ratio (OAR) in the non-wedged direction using the open field OAR at a depth deeper by this equivalent water thickness. This model has been shown to work well for a Siemens Mevatron KD-2 Linac. However, the motorized wedge of the Elekta (formerly Philips) accelerators is tapered off-axis to give a flat dose profile in the non-wedged direction. The CadPlan model assumes that the wedge has a uniform thickness in the non-wedged direction and so cannot model the off-axis dose for the motorized wedge. For a 4 MV beam of a SL75/5 accelerator this leads to a 7% overestimate and a 9% underestimate of the OAR under the thin and thick edge of the wedge respectively. For 6 and 18 MV beams of a SL20 accelerator and a 6 MV beam of a SL75/5 accelerator, the model underestimates the OAR in the order of 10% under the thick end of the wedge. We have shown that by appropriate modification of the effective water thickness values at off-axis distances, the algorithm models the OAR in the non-wedged direction to within 2.5% of the measured values for the 4, 6 and 18 MV beams, for the Elekta motorized wedge.     

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.     

Optimization of combined electron and photon beams for breast cancer

Recently, intensity-modulated radiation therapy and modulated electron radiotherapy have gathered a growing interest for the treatment of breast and head and neck tumours. In this work, we carried out a study to combine electron and photon beams to achieve differential dose distributions for multiple target volumes simultaneously. A Monte Carlo based treatment planning system was investigated, which consists of a set of software tools to perform accurate dose calculation, treatment optimization, leaf sequencing and plan analysis. We compared breast treatment plans generated using this home-grown optimization and dose calculation software for different treatment techniques. Five different planning techniques have been developed for this study based on a standard photon beam whole breast treatment and an electron beam tumour bed cone down. Technique 1 includes two 6 MV tangential wedged photon beams followed by an anterior boost electron field. Technique 2 includes two 6 MV tangential intensity-modulated photon beams and the same boost electron field. Technique 3 optimizes two intensity-modulated photon beams based on a boost electron field. Technique 4 optimizes two intensity-modulated photon beams and the weight of the boost electron field. Technique 5 combines two intensity-modulated photon beams with an intensity-modulated electron field. Our results show that technique 2 can reduce hot spots both in the breast and the tumour bed compared to technique 1 (dose inhomogeneity is reduced from 34% to 28% for the target). Techniques 3, 4 and 5 can deliver a more homogeneous dose distribution to the target (with dose inhomogeneities for the target of 22%, 20% and 9%, respectively). In many cases techniques 3, 4 and 5 can reduce the dose to the lung and heart. It is concluded that combined photon and electron beam therapy may be advantageous for treating breast cancer compared to conventional treatment techniques using tangential wedged photon beams followed by a boost electron field.     

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.