A beam source model for scanned proton beams

Abstract

A beam source model, i.e. a model for the initial phase space of the beam, for scanned proton beams has been developed. The beam source model is based on parameterized particle sources with characteristics found by fitting towards measured data per individual beam line. A specific aim for this beam source model is to make it applicable to the majority of the various proton beam systems currently available or under development, with the overall purpose to drive dose calculations in proton beam treatment planning. The proton beam phase space is characterized by an energy spectrum, radial and angular distributions and deflections for the non-modulated elementary pencil beam. The beam propagation through the scanning magnets is modelled by applying experimentally determined focal points for each scanning dimension. The radial and angular distribution parameters are deduced from measured two-dimensional fluence distributions of the elementary beam in air. The energy spectrum is extracted from a depth dose distribution for a fixed broad beam scan pattern measured in water. The impact of a multi-slab range shifter for energy modulation is calculated with an own Monte Carlo code taking multiple scattering, energy loss and straggling, non-elastic and elastic nuclear interactions in the slab assembly into account. Measurements for characterization and verification have been performed with the scanning proton beam system at The Svedberg Laboratory in Uppsala. Both in-air fluence patterns and dose points located in a water phantom were used. For verification, dose-in-water was calculated with the Monte Carlo code GEANT 3.21 instead of using a clinical dose engine with approximations of its own. For a set of four individual pencil beams, both with the full energy and range shifted, 96.5% (99.8%) of the tested dose points satisfied the 1%/1 mm (2%/2 mm) gamma criterion.

Characterizing a proton beam scanning system for Monte Carlo dose calculation in patients

“…Kimstrand et al (Kimstrand et al 2007) and Clasie et al (Clasie et al 2012) have determined the energy spread in a different fashion. They obtained a set of mono-energetic peaks then weighted them with a Gaussian distribution.…”

Validation and clinical implementation of an accurate Monte Carlo code for pencil beam scanning proton therapy

“…The initial scanning angle and projected offset coordinate at the source plane (see Fig. 1) for each scanned spot is modeled by applying two effective focal points with a distance of $f_x$ = 1859.1 mm and $f_y$ = 2234.8 mm to the axis in X and Y direction respectively, which are extracted from measurements of the beam position at two planes for different beam deflections 11…”

“…Several papers9, 10, 11 have reported how to develop such beam source model by deriving source parameters through a set of simple measurements for individual beam lines. The major advantage is that this does not require knowledge of beam line or nozzle components and material compositions, and hence significantly reduces computing time without the need to model the nozzle.…”

Patient Dose Computation

“…For charged particles, the common assumption is that the angular distribution is Gaussian, and its propagation hence follows the Fermi-Eyges model. Some recent electron beam modeling work based on these principles has been published by Vatanen et al (2008) and Papaconstadopoulos and Seuntjens (2013) and for protons by, for example, Kimstrand et al (2007) and Schaffner (2008). The spectrum of a clinical beam can either be determined from Monte Carlo, for which the electron beam parameters have to be tuned such that measured depth dose curves match.…”

“…For charged particles, it is more convenient to express the spectral weights in terms of particle fluence by replacing the energy fluence differential in energy C E in eqn [11] with its particle fluence counterpart F E . The limited range of charged particles facilitates inversion of eqn [12] (see, e.g., Kimstrand et al (2007) or Bortfeld (1997) for proton beams and Li et al (2008) or Faddegon and Blevis (2000) for electron beams).…”