On the initial angular variances of clinical electron beams

Electron beam radiotherapy treatment planning systems need to be fed with the characteristics of the high-energy electron beams (4-50 MeV) from the specifically 'applied accelerator. Beams can be characterized by their mean initial energy, effective initial angular variance, virtual source position and the resulting central axis depth dose distribution in water. This information is the only input to pencil beam dose calculation models. Newer calculation models like macro Monte Carlo, voxel Monte Carlo and phase space evolution require as input the full initial phase space or a parametrization of that initial phase space, generally consisting of a primary beam component and one or more scatter components. This primary beam component is often characterized by initial energy, primary beam initial angular variance and virtual source distance. The purpose of the present investigation was to investigate to what extent standard values can be used both for the effective initial angular variance as input to pencil beam models and for the primary beam initial angular variance. Comprehensive benchmark data were obtained on the initial angular variance of various types of accelerator, for various energies and field sizes. The initial angular variance as, has been derived from penumbra measurements in air by means of film dosimetry at various distances from the lower collimator. For the types of accelerator used in radiotherapy nowadays the measurements show values for sigma(theta)(x2)/T(E) of around 13 cm where T(E) is the ICRU-35 linear angular scattering power in air. This value can be chosen as standard value for the primary beam initial angular variance, only slightly compromising the dose calculation accuracy. As input to pencil beam models, an effective sigma(theta)(x2)/T(E) should be used incorporating the scatter from the lower collimator. For the case that the air gaps between lower collimator and patient are small (5-10 cm) an effective sigma(theta x)(2)/T(E) of 20 cm has been found and is recommended as the standard input for pencil beam models. Of the accelerators investigated, a different value was found only for the Elekta SL15, i.e. 50% higher for the effective sigma(theta x)(2)/T(E).