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.     

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.     

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.     

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.     

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.     

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。     

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.     

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.     

Using a photon phase-space source for convolution/superposition dose calculations in radiation therapy

For a given linac design, the dosimetric characteristics of a photon beam are determined uniquely by the energy and radial distributions of the electron beam striking the x-ray target. However, in the usual commissioning of a beam from measured data, a large number of variables can be independently tuned, making it difficult to derive a unique and self-consistent beam model. For example, the measured dosimetric penumbra in water may be attributed in various proportions to the lateral secondary electron range, the focal spot size and the transmission through the tips of a non-divergent collimator; the head-scatter component in the tails of the transverse profiles may not be easy to resolve from phantom scatter and head leakage; and the head-scatter tails corresponding to a certain extra-focal source model may not agree self-consistently with in-air output factors measured on the central axis. To reduce the number of adjustable variables in beam modelling, we replace the focal and extra-focal sources with a single phase-space plane scored just above the highest adjustable collimator in a EGS/BEAM simulation of the linac. The phase-space plane is then used as photon source in a stochastic convolution/superposition dose engine. A photon sampled from the uncollimated phase-space plane is first propagated through an arbitrary collimator arrangement and then interacted in the simulation phantom. Energy deposition kernel rays are then randomly issued from the interaction points and dose is deposited along these rays. The electrons in the phase-space file are used to account for electron contamination. 6 MV and 18 MV photon beams from an Elekta SL linac are used as representative examples. Except for small corrections for monitor backscatter and collimator forward scatter for large field sizes (<0.5% with <20 x 20 cm2 field size), we found that the use of a single phase-space photon source provides accurate and self-consistent results for both relative and absolute dose calculations.     

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.     

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.     

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%.     

Derivation of the distribution of extrafocal radiation for head scatter factor calculation

Head scatter factors for high energy photon beams from linear accelerators can be modeled using a two-source model consisting of focal and extrafocal radiation. The focal radiation can be approximated as a point source, and the distribution of the extrafocal radiation is a two-dimensional (2D) radial symmetric function. Various methods, including analytical, Monte Carlo, and empirical trial functions, have been used to determine the radial symmetric function of extrafocal radiation distribution. This article describes a method for directly determining the extrafocal radiation distribution without assuming any empirical trial function. The extrafocal radiation distribution is determined with measured head scatter factors for rectangular fields defined by the lower jaw (X) fixed at 40 cm and the upper jaw (Y) varying from 3 to 40 cm. The derivatives of the measured head scatter factors, with respect to the Y jaw position projected in the plane of extrafocal radiation, are proportional to the one-dimensional (1D) projection (also called the line spread function) of the extrafocal radiation distribution. Two methods are used to solve the radial function of extrafocal radiation from the 1D projection. The first method uses a 2D filtered backprojection algorithm, originally developed for parallel beam computed tomography reconstruction, to directly derive the radial dependence of the extrafocal radiation distribution. The method has been applied to 6 and 18 MV photon beams from a Siemens linear accelerator and has been tested by comparing measured and calculated head scatter factors for square and rectangular fields. The second method uses a Fourier transform followed by a Fourier-Bessel transform to solve the problem. The distributions of extrafocal radiation derived from these two methods are virtually identical.     

Photonuclear dose calculations for high-energy photon beams from Siemens and Varian linacs

The dose from photon-induced nuclear particles (neutrons, protons, and alpha particles) generated by high-energy photon beams from medical linacs is investigated. Monte Carlo calculations using the MCNPX code are performed for three different photon beams from two different machines: Siemens 18 MV, Varian 15 MV, and Varian 18 MV. The linac head components are simulated in detail. The dose distributions from photons, neutrons, protons, and alpha particles are calculated in a tissue-equivalent phantom. Neutrons are generated in both the linac head and the phantom. This study includes (a) field size effects, (b) off-axis dose profiles, (c) neutron contribution from the linac head, (d) dose contribution from capture gamma rays, (e) phantom heterogeneity effects, and (f) effects of primary electron energy shift. Results are presented in terms of absolute dose distributions and also in terms of DER (dose equivalent ratio). The DER is the maximum dose from the particle (neutron, proton, or alpha) divided by the maximum photon dose, multiplied by the particle quality factor and the modulation scaling factor. The total DER including neutrons, protons, and alphas is about 0.66 cSv/Gy for the Siemens 18 MV beam (10 cm x 10 cm). The neutron DER decreases with decreasing field size while the proton (or alpha) DER does not vary significantly except for the 1 cm x 1 cm field. Both Varian beams (15 and 18 MV) produce more neutrons, protons, and alphas particles than the Siemens 18 MV beam. This is mainly due to their higher primary electron energies: 15 and 18.3 MeV, respectively, vs 14 MeV for the Siemens 18 MV beam. For all beams, neutrons contribute more than 75% of the total DER, except for the 1 cm x 1 cm field (approximately 50%). The total DER is 1.52 and 2.86 cSv/Gy for the 15 and 18 MV Varian beams (10 cm x 10 cm), respectively. Media with relatively high-Z elements like bone may increase the dose from heavy charged particles by a factor 4. The total DER is sensitive to primary electron energy shift. A Siemens 18 MV beam with 15 MeV (instead of 14 MeV) primary electrons would increase by 40% the neutron DER and by 210% the proton + alpha DER. Comparisons with measurements (neutron yields from different materials and neutron dose equivalent) are also presented. Using the NCRP risk assessment method, we found that the dose equivalent from leakage neutrons (at 50-cm off-axis distance) represent 1.1, 1.1, and 2.0% likelihood of fatal secondary cancer for a 70 Gy treatment delivered by the Siemens 18 MV, Varian 15 MV, and Varian 18 MV beams, respectively.     

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.     

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.     

Ionization chamber dosimetry of small photon fields: a Monte Carlo study on stopping-power ratios for radiosurgery and IMRT beams

Absolute dosimetry with ionization chambers of the narrow photon fields used in stereotactic techniques and IMRT beamlets is constrained by lack of electron equilibrium in the radiation field. It is questionable that stopping-power ratio in dosimetry protocols, obtained for broad photon beams and quasi-electron equilibrium conditions, can be used in the dosimetry of narrow fields while keeping the uncertainty at the same level as for the broad beams used in accelerator calibrations. Monte Carlo simulations have been performed for two 6 MV clinical accelerators (Elekta SL-18 and Siemens Mevatron Primus), equipped with radiosurgery applicators and MLC. Narrow circular and Z-shaped on-axis and off-axis fields, as well as broad IMRT configured beams, have been simulated together with reference 10 x 10 cm2 beams. Phase-space data have been used to generate 3D dose distributions which have been compared satisfactorily with experimental profiles (ion chamber, diodes and film). Photon and electron spectra at various depths in water have been calculated, followed by Spencer-Attix (delta = 10 keV) stopping-power ratio calculations which have been compared to those used in the IAEA TRS-398 code of practice. For water/air and PMMA/air stopping-power ratios, agreements within 0.1% have been obtained for the 10 x 10 cm2 fields. For radiosurgery applicators and narrow MLC beams, the calculated s(w,air) values agree with the reference within +/-0.3%, well within the estimated standard uncertainty of the reference stopping-power ratios (0.5%). Ionization chamber dosimetry of narrow beams at the photon qualities used in this work (6 MV) can therefore be based on stopping-power ratios data in dosimetry protocols. For a modulated 6 MV broad beam used in clinical IMRT, s(w,air) agrees within 0.1% with the value for 10 x 10 cm2, confirming that at low energies IMRT absolute dosimetry can also be based on data for open reference fields. At higher energies (24 MV) the difference in s(w,air) was up to 1.1%, indicating that the use of protocol data for narrow beams in such cases is less accurate than at low energies, and detailed calculations of the dosimetry parameters involved should be performed if similar accuracy to that of 6 MV is sought.     

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.     

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.