A convolution/superposition method is proposed for use with primary and scatter dose kernels formed for energy bins of X-ray spectra reconstructed as a function of off-axis distance. It should be noted that the number of energy bins is usually about ten, and that the reconstructed X-ray spectra can reasonably be applied to media with a wide range of effective Z numbers, ranging from water to lead. The study was carried out for 10-MV X-ray doses in water and thorax-like phantoms with the use of open-jaw-collimated fields. The dose calculations were made separately for primary, scatter, and electron contamination dose components, for which we used two extended radiation sources: one was on the X-ray target and the other on the flattening filter. To calculate the in-air beam intensities at points on the isocenter plane for a given jaw-collimated field, we introduced an in-air output factor (OPF(in-air)) expressed as the product of the off-center jaw-collimator scatter factor (off-center S (c)), the source off-center ratio factor (OCR(source)), and the jaw-collimator radiation reflection factor (RRF(c)). For more accurate dose calculations, we introduce an electron spread fluctuation factor (F (fwd)) to take into account the angular and spatial spread fluctuation for electrons traveling through different media.

We performed experimental studies on the convolution/superposition method reported in the former companion paper (Iwasaki in Radiol Phys Technol 4, 2011) using 10-MV X-ray beams from open-jaw-collimated fields. The method uses primary and scatter dose kernels formed for energy bins of X-ray spectra reconstructed as a function of off-axis distance. We made a comparison of calculations and measurements in water phantoms and thorax-like phantoms with respect to percentage depth dose curves, tissue-phantom ratio curves, and dose profiles. We made the dose calculation by taking into account the beam-hardening effect with depth and the off-axis radiation-softening effect. We found that the method could be used, in general, for performing accurate dose calculations.

We have reviewed applicable ranges for attenuating media and off-axis distances regarding the high-energy X-ray spectra reconstructed via the Iwasaki-Waggener iterative perturbation method for 4-20 MV X-ray beams. Sets of in-air relative transmission data used for reconstruction of spectra were calculated for low- and high-Z attenuators (acrylic and lead, respectively) by use of a functional spectral formula. More accurate sets of spectra could be reconstructed by dividing the off-axis distances of R = 0-20 cm into two series of R = 0-10 cm and R = 10-20 cm, and by taking into account the radiation attenuation and scatter in the buildup cap of the dosimeter. We also incorporated in the reconstructed spectra an adjustment factor (f (adjust) ≈ 1) that is determined by the attenuating medium, the acceleration voltage, and the set of off-axis distances. This resulted in calculated in-air relative transmission data to within ±2 % deviation for the low-Z attenuators water, acrylic, and aluminum (Al) with 0-50 cm thicknesses and R = 0-20 cm; data to within ±3 % deviation were obtained for high-Z attenuators such as iron (Fe), copper (Cu), silver (Ag), tungsten (W), platinum (Pt), gold (Au), lead (Pb), thorium (Th), and uranium (U) having thicknesses of 0-10 cm and R = 0-20 cm. By taking into account the radiation attenuation and scatter in the buildup cap, we could analyze the in-air chamber response along a line perpendicular to the isocenter axis.

Purposes: This paper highlights a 10-MV X-ray convolution dose calculation method in water using primary and scatter dose kernels formed for energy bins of X-ray spectra reconstructed as a function of the off-axis distance for a linear accelerator equipped with pairs of upper and lower jaws, a multileaf collimator (MLC) and a wedge filter. Methods: The reconstructed X-ray spectra set was composed of 11 energy bins. To estimate the in-air beam intensities at points on the isocenter plane for an MLC field, we employed an MLC leaf-field output subtraction method, using an extended radiation source on each of the X-ray target and the flattening filter as well as simplified twodimensional plates to simulate the three-dimensional jaws and MLC structures. A special correction factor was introduced for nonuniform incident beam intensities, particularly produced at MLC fields. The in-phantom dose calculation was performed by treating the phantom, the wedge filter, the wedge holder and the MLC as parts of a unified irradiated body, where we proposed to use a special factor for the density scaling theorem within the unified irradiated body. Conclusions: The phantom dose was generally separated into nine dosecomponents: the primary and scatter dose-components produced in the phantom; the primary and scatter dose-components emanating from the wedge, the wedge holder and the MLC; and the electron contamination dose-component. From the calculated and measured percentage depth dose (PDD) and off-center ratio (OCR) datasets, we may conclude that the convolution method can achieve accurate dose calculations even under MLC and/or wedge filtration.Keywords: convolution method; X-ray spectra; dose kernels; wedge; multileaf collimation; MLC leaf-field output subtraction Citation: Iwasaki A, Kimura S, Sutoh K, Kamimura K, Sasamori M, Seino M, Komai F, Takagi M, Terashima S, Hosokawa Y, Saitoh H, Miyazawa M. 10-MV X-ray dose calculation in water for MLC and wedge fields using a convolution method with X-ray spectra reconstructed as a function of off-axis distance. J