Proton pencil beams in water, in a format suitable for treatment planning algorithms and covering the radiotherapy energy range (50-250 MeV), have been calculated using a modified version of the Monte Carlo code PTRAN. A simple analytical model has also been developed for calculating proton broad-beam dose distributions which is in excellent agreement with the Monte Carlo calculations. Radial dose distributions are also calculated analytically and narrow proton pencil-beam dose distributions derived. The physical approximations in the Monte Carlo code and in the analytical model together with their limitations are discussed. Examples showing the use of the calculated set of proton pencil beams as input to an existing photon treatment planning algorithm based on biological optimization are given for fully 3D scanned proton pencil beams; these include intensity modulated beams with range shift and scanning in the transversal plane.

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.

Methods for scatter dose calculations in brachytherapy have been developed based on the collapsed cone superposition algorithm. The methods account for effects on the scatter dose caused by the three-dimensional distribution of heterogeneities in the irradiated volume and are considerably faster than methods based on straightforward superposition of kernels or direct Monte Carlo simulations. Use of a successive-scattering approach, in which the dose contribution from once- and multiply scattered photons are calculated separately, was found superior to conventional superposition using a single point kernel for all scatter generations. Use of the successive-scattering approach significantly reduces artifacts stemming from steep fluence gradients, typical of the brachytherapy geometry and critical for the collapsed cone approximation. The algorithm is tested versus Monte Carlo simulations for point sources of energies 28.4, 100, 350, and 662 keV. Results agree well for both a homogeneous water phantom and an air-water half-phantom.