Reconsideration of the power-law (Batho) equation for inhomogeneity corrections

The power-law (Batho) equation for inhomogeneity corrections to the dose calculated in a layered medium has been examined to elucidate the implicit approximations made in its derivation and hence to discover its limitations. Relationships based on primary and first scatter dose calculations are established between the Batho correction and the true correction from which several conclusions can be drawn. For dose corrections within water in a two-layer medium, the Batho method underestimates the correction when the electron density (rho) of the overlaying inhomogeneity relative to water is less than 1, and overestimates it when this density is greater than 1. Batho method is excellent for small fields and rho less than 1, but is poor for large fields and rho less than 1. When the power-law equation is extended to multilayer media, by assuming that the correction factor for each layer multiplies independently, the method gives less accurate results. The largest errors occur inside an inhomogeneity directly underneath a top layer of unit density, since the contribution from such a layer is inherently ignored. All of these conclusions are demonstrated in the paper by experimental measurements. Finally, relationships are shown between the Batho correction and both the correction factor proposed by MacDonald et al. and the differential scatter air ratio correction.