A calculation model for primary intensity distributions from cylindrically symmetric x-ray lenses

A calculation model for the quantitative prediction of primary intensity fluence distributions obtained by the Bragg diffraction focusing of kilovoltage radiation by cylindrical x-ray lenses is presented. The mathematical formalism describes primary intensity distributions from cylindrically-symmetric x-ray lenses, with a planar isotropic radiation source located in a plane perpendicular to the lens axis. The presence of attenuating medium inserted between the lens and the lens focus is accounted for by energy-dependent attenuation. The influence of radiation scattered within the media is ignored. Intensity patterns are modeled under the assumption that photons that are not interacting with the lens are blocked out at any point of interest. The main characteristics of the proposed calculation procedure are that (i) the application of vector formalism allows universal treatment of all cylindrical lenses without the need of explicit geometric constructs; (ii) intensity distributions resulting from x-ray diffraction are described by a 3D generalization of the mosaic spread concept; (iii) the calculation model can be immediately coupled to x-ray diffraction simulation packages such as XOP and Shadow. Numerical simulations based on this model are to facilitate the design of focused orthovoltage treatment (FOT) systems employing cylindrical x-ray lenses, by providing insight about the influence of the x-ray source and lens parameters on quantities of dosimetric interest to radiation therapy.