On the relationships between electron spot size, focal spot size, and virtual source position in Monte Carlo simulations

Purpose: Every year, new radiotherapy techniques including stereotactic radiosurgery using linear accelerators give rise to new applications of Monte Carlo (MC) modeling. Accurate modeling requires knowing the size of the electron spot, one of the few parameters to tune in MC models. The resolution of integrated megavoltage imaging systems, such as the tomotherapy system, strongly depends on the photon spot size which is closely related to the electron spot. The aim of this article is to clarify the relationship between the electron spot size and the photon spot size (i.e., the focal spot size) for typical incident electron beam energies and target thicknesses. Methods: Three electron energies (3, 5.5, and 18 MeV), four electron spot sizes (FWHM=0, 0.5, 1, and 1.5 mm), and two tungsten target thicknesses (0.15 and 1 cm) were considered. The formation of the photon beam within the target was analyzed through electron energy deposition with depth, as well as photon production at several phase-space planes placed perpendicular to the beam axis, where only photons recorded for the first time were accounted for. Photon production was considered for "newborn" photons intersecting a 45×45 cm² plane at the isocenter (85 cm from source). Finally, virtual source position and "effective" focal spot size were computed by backprojecting all the photons from the bottom of the target intersecting a 45×45 cm² plane. The virtual source position and focal spot size were estimated at the plane position where the latter is minimal. Results: In the relevant case of considering only photons intersecting the 45×45 cm² plane, the results unambiguously showed that the effective photon spot is created within the first 0.25 mm of the target and that electron and focal spots may be assumed to be equal within 3-4%. Conclusions: In a good approximation photon spot size equals electron spot size for high energy X-ray treatments delivered by linear accelerators.