Monte Carlo modeling of small photon fields: Quantifying the impact of focal spot size on source occlusion and output factors, and exploring miniphantom design for small‐field measurements

Abstract

The accuracy with which Monte Carlo models of photon beams generated by linear accelerators (linacs) can describe small-field dose distributions depends on the modeled width of the electron beam profile incident on the linac target. It is known that the electron focal spot width affects penumbra and cross-field profiles; here, the authors explore the extent to which source occlusion reduces linac output for smaller fields and larger spot sizes. A BEAMnrc Monte Carlo linac model has been used to investigate the variation in penumbra widths and small-field output factors with electron spot size. A formalism is developed separating head scatter factors into source occlusion and flattening filter factors. Differences between head scatter factors defined in terms of in-air energy fluence, collision kerma, and terma are explored using Monte Carlo calculations. Estimates of changes in kerma-based source occlusion and flattening filter factors with field size and focal spot width are obtained by calculating doses deposited in a narrow 2 mm wide virtual "milliphantom" geometry. The impact of focal spot size on phantom scatter is also explored. Modeled electron spot sizes of 0.4-0.7 mm FWHM generate acceptable matches to measured penumbra widths. However the 0.5 cm field output factor is quite sensitive to electron spot width, the measured output only being matched by calculations for a 0.7 mm spot width. Because the spectra of the unscattered primary (psi(pi)) and head-scattered (psi(sigma)) photon energy fluences differ, miniphantom-based collision kerma measurements do not scale precisely with total in-air energy fluence psi = (psi(pi) + psi(sigma) but with (psi(pi)+ 1.2psi(sigma)). For most field sizes, on-axis collision kerma is independent of the focal spot size; but for a 0.5 cm field size and 1.0 mm spot width, it is reduced by around 7% mostly due to source occlusion. The phantom scatter factor of the 0.5 cm field also shows some spot size dependence, decreasing by 6% (relative) as spot size is increased from 0.1 to 1.0 mm. The dependence of small-field source occlusion and output factors on the focal spot size makes this a significant factor in Monte Carlo modeling of small (< 1 cm) fields. Changes in penumbra width with spot size are not sufficiently large to accurately pinpoint spot widths. Consequently, while Monte Carlo models based exclusively on large-field data can quite accurately predict small-field profiles and PDDs, in the absence of experimental methods of determining incident electron beam profiles it will remain necessary to measure small-field output factors, fine-tuning modeled spot sizes to ensure good matching between the Monte Carlo and the measured output factors.