Comparison between the lateral penumbra of a collimated double-scattered beam and uncollimated scanning beam in proton radiotherapy

Intensity modulated proton radiotherapy ( IMPT) can reduce the dose to critical structures by optimizing the distribution and intensity of individual pencil beams. The IMPT can be delivered by dynamically scanning a pencil beam with variable intensity and energy across the tumor target volume. The lateral penumbra of an uncollimated pencil beam is compromised, however, by the scattering in air between the vacuum window and the patient, and by the initial beam size. In this study, we compare the transversal penumbra of a pencil beam to the one of a collimated Gaussian broad divergent beam, such as the one produced by the double scattering system, for different range compensator thicknesses, collimator-to-surface distances ( CSD), proton range and pencil beam sizes ( sigma(0)). The effect of vacuum and helium in the nozzle on the pencil beam lateral profile further downstream is also investigated. The lateral spatial intensity distribution for the collimated Gaussian broad divergent proton beam is modeled using the generalized Fermi-Eyges theory. The model is validated with measurements of the lateral profile in water at different depths for two different ranges ( 7.7 cm and 22.1 cm, respectively). Nearly 2500 treatment fields are analyzed to establish typical clinical beam configurations, such as the range compensator thicknesses, CSD and range, which we use to predict the 80%-20% lateral penumbra. The penumbra of the collimated broad divergent beam is calculated for fixed source-to-surface distance ( SSD) of 220 cm and source size of 2.5 cm ( sigma). The results show that the model predicts the penumbra at different water depths with accuracy better than 0.2 mm. At depths larger than 7.6 cm ( minimum range of the clinical fields analyzed), the accuracy is better than 3%. The treatment fields feature the following average configuration: the range compensator thickness of 6.5 +/- 2.8 cm( max 19.4 cm), CSD 11.9 +/- 3.8 cm ( max 29.4 cm) and range of 16.0 +/- 6.1 cm. The penumbra of a pencil beam at shallow depth is in general larger ( i.e., worse) than the penumbra of a collimated beam, but better at larger depths. The depth at which the two penumbras are identical exhibits only a small dependence on the proton range, but is strongly affected by the collimator-to-surface distance. For CSD 10 cm, range compensator thickness 6 cm, SSD 220 cm and source size 2.5 cm, this depth is 11.5 cm for a 5 mm pencil beam, and 9.1 cm for a 3 mm pencil beam. For most of the clinical sites considered, assuming the beam configurations of this study, the pencil beam penumbra is larger ( i.e., worse). By moving the vacuum window downstream or by replacing air with helium in the gantry nozzle, the dosimetrical benefit of scanning would be drastically improved, especially for small sigma(0) ( 5 mm or less).