Collimator effects in proton planning
  The present paper pertains to corrections which are due to the presence of beam-limiting and beam-shaping devices in proton planning. Two types of corrections are considered: those which are due to the nonzero thickness of such devices (geometrical effects) and those relating to the scattering of beam particles off their material. The application of these two types of corrections is greatly facilitated by decomposing the physical effects (i.e., the contribution to the fluence) of two-dimensional objects (i.e., of the apertures of the devices) into one-dimensional, easily-calculable contributions. To minimise the time requirements in the derivation of the scattering corrections, a two-step process is introduced. The first step occurs at beam-configuration phase and comprises the analysis of half-block fluence measurements and the extraction of the one parameter of the model which is used in the description of the beamline characteristics; subsequently, a number of Monte-Carlo runs lead to the determination of the parameters of a convenient parameterisation of the relevant fluence contributions. The second step involves (at planning time) the reconstruction of the parameters (which are used in the description of the scattering contributions) via simple interpolations, performed on the results obtained during the beam-configuration phase. It is shown that the inclusion of the scattering effects leads to substantial improvement in the reproduction of the experimental data. The contributions from the block-thickness and block-scattering effects have been presented separately in the case of a simple water phantom. In this example, the maximal contribution of the block-relating effects amounts to a few percent of the prescribed dose. 
Evangelos Matsinos