Three-dimensional dose planning systems employing accurate proton transport algorithms are essential for calculating absorbed dose distributions in proton therapy. In this paper, a pencil beam algorithm for the transport of protons in materials of interest for radiation therapy is developed. The Fermi-Eyges multiple-scattering theory is used to derive transport equations for calculating proton fluence and absorbed dose distributions. The multiple-scattering theory of Molière is used to predict mean square scattering angles and to develop an expression for calculating the root mean square (RMS) radial spread of a proton pencil beam, as a function of depth, in an arbitrary scattering material. A correction factor is suggested to account for the decrease in the radial spread at the end of the range due to range straggling. The effects of neglecting large-angle scattering events and the possibility of incorporating such events into the pencil beam algorithm are discussed. An energy scaling technique for determining the water-equivalent surface energy at a given depth in a heterogeneous scattering medium is developed. The water-equivalent energy, giving the same Molière scattering parameter B in water, is determined and the 1/e angle in water is scaled to the appropriate width in the scattering material. By using stored analytically or Monte Carlo calculated pencil beam distributions in water, the large-angle single-scattering events may be incorporated by approximating the scattering in an arbitrary material by the scattering in water for protons of the appropriate water-equivalent surface energy.

This paper describes a dual-scattering-foil technique for flattening of radiotherapeutic charged particle beams. A theory for optimization of shapes and thicknesses of the scattering foils is presented. The result is a universal optimal secondary-scatterer profile, which can be adapted to any charged particle beam by a simple scaling procedure. The calculation of the mean square scattering angle of the beam after passing through the scattering foils is done using the generalized Fermi-Eyges model for charged particle transport. It is shown that the fluence profile in the plane of interest can be made flat to better than 1% inside a predefined beam radius provided the shaped secondary scatterer has the universal radial thickness profile. The thicknesses of the two foils are optimized to minimize the total energy loss. The theory has been tested experimentally in an 180 MeV clinical proton beam. The measured distributions agree well with the calculations.

The implementation of two algorithms for calculating dose distributions for radiation therapy treatment planning of intermediate energy proton beams is described. A pencil kernel algorithm and a depth penetration algorithm have been incorporated into a commercial three dimensional treatment planning system (Helax-TMS, Helax AB, Sweden) to allow conformal planning techniques using irregularly shaped fields, proton range modulation, range modification and dose calculation for non-coplanar beams. The pencil kernel algorithm is developed from the Fermi Eyges formalism and Molière multiple-scattering theory with range straggling corrections applied. The depth penetration algorithm is based on the energy loss in the continuous slowing down approximation with simple correction factors applied to the beam penumbra region and has been implemented for fast, interactive treatment planning. Modelling of the effects of air gaps and range modifying device thickness and position are implicit to both algorithms. Measured and calculated dose values are compared for a therapeutic proton beam in both homogeneous and heterogeneous phantoms of varying complexity. Both algorithms model the beam penumbra as a function of depth in a homogeneous phantom with acceptable accuracy. Results show that the pencil kernel algorithm is required for modelling the dose perturbation effects from scattering in heterogeneous media.

In brachytherapy, tissue heterogeneities, source shielding, and finite patient/phantom extensions affect both the primary and scatter dose distributions. The primary dose is, due to the short range of secondary electrons, dependent only on the distribution of material located on the ray line between the source and dose deposition site. The scatter dose depends on both the direct irradiation pattern and the distribution of material in a large volume surrounding the point of interest, i.e., a much larger volume must be included in calculations to integrate many small dose contributions. It is therefore of interest to consider different methods for the primary and the scatter dose calculation to improve calculation accuracy with limited computer resources. The algorithms in present clinical use ignore these effects causing systematic dose errors in brachytherapy treatment planning. In this work we review a primary and scatter dose separation formalism (PSS) for brachytherapy source characterization to support separate calculation of the primary and scatter dose contributions. We show how the resulting source characterization data can be used to drive more accurate dose calculations using collapsed cone superposition for scatter dose calculations. Two types of source characterization data paths are used: a direct Monte Carlo simulation in water phantoms with subsequent parameterization of the results, and an alternative data path built on processing of AAPM TG43 formatted data to provide similar parameter sets. The latter path is motivated of the large amounts of data already existing in the TG43 format. We demonstrate the PSS methods using both data paths for a clinical 192Ir source. Results are shown for two geometries: a finite but homogeneous water phantom, and a half-slab consisting of water and air. The dose distributions are compared to results from full Monte Carlo simulations and we show significant improvement in scatter dose calculations when the collapsed-cone kernel-superposition algorithm is used compared to traditional table based calculations. The PSS source characterization method uses exponential fit functions derived from one-dimensional transport theory to describe both the primary and scatter dose contributions. We present data for the PSS characterization method to different 192Ir, 137Cs, and 60Cs brachytherapy sources. We also show how TG43 formatted data can be derived from our data to serve traditional treatment planning systems, as to enable for a gradual transfer to algorithms that provides improved modeling of heterogeneities in brachytherapy treatment planning.