Point kernels and superposition methods for scatter dose calculations in brachytherapy

Point kernels have been generated and applied for calculation of scatter dose distributions around monoenergetic point sources for photon energies ranging from 28 to 662 keV. Three different approaches for dose calculations have been compared: a single-kernel superposition method, a single-kernel superposition method where the point kernels are approximated as isotropic and a novel 'successive-scattering' superposition method for improved modelling of the dose from multiply scattered photons. An extended version of the EGS4 Monte Carlo code was used for generating the kernels and for benchmarking the absorbed dose distributions calculated with the superposition methods. It is shown that dose calculation by superposition at and below 100 keV can be simplified by using isotropic point kernels. Compared to the assumption of full in-scattering made by algorithms currently in clinical use, the single-kernel superposition method improves dose calculations in a half-phantom consisting of air and water. Further improvements are obtained using the successive-scattering superposition method, which reduces the overestimates of dose close to the phantom surface usually associated with kernel superposition methods at brachytherapy photon energies. It is also shown that scatter dose point kernels can be parametrized to biexponential functions, making them suitable for use with an effective implementation of the collapsed cone superposition algorithm.