Incorporation of the aperture thickness in proton pencil-beam dose calculations.

Field-specific apertures, of sufficient range-absorbing thickness, are used in the majority of proton-therapy treatments today. In current practice, these apertures are modelled as objects of infinitesimal thickness. Such an approximation, however, is not accurate if the aperture edge is close to, or extends over, the beam axis. Practical situations in which this occurs include off-axis patch fields, small apertures, and fields shaped with a multileaf collimator. We develop an extension of the pencil-beam dose model to incorporate the aperture thickness. We derive an exact solution as well as a computationally simpler approximate implementation. The model is validated using measurements of the lateral penumbra. For a set-up with a source size of 2.76 cm, a source-to-axis distance of 227 cm, and a aperture-to-axis distance of 35 cm, the maximum increase in penumbra for a 6 cm thick aperture compared to the thin-aperture model is about 2 mm. The maximum shift in the 95% isodose contour line is larger. The overall effect depends on the aperture thickness, the position of the aperture edge and the intrinsic source size and SAD, but is fairly insensitive to aperture-to-skin distance and depth in patient.