Implementation of apertures in a proton pencil-beam dose algorithm

The use of field-specific apertures, routine in scattered or uniform-scanned proton fields, are still a necessity in pencil-beam scanned (PBS) fields to sharpen the penumbral edge at low energies and in high fraction dose application beyond that achievable with small spot size. We describe a model implemented in our clinical pencil-beam algorithm that models the insertion of a shaped aperture, including shapes adapted per energy layer such as may be achieved with a multi-leaf collimator. The model decomposes the spot transport into discrete steps. The first step transport a uniform intensity field of high-resolution sub-pencil-beams at the layer energy through the medium. This transport only considers primary scattering in both the patient and an optional range-shifter. The second step models the aperture areas and edge penumbral transition as a modulation of the uniform intensity. The third step convolves individual steps over the uniform-transported field including the aperture-modified intensities. We also introduce an efficient model based on a Clarkson sector integration for nuclear scattered halo protons. This avoids the explicit modeling of long range halo protons to the detriment of computational efficiency in calculation and optimization. We demonstrate that the aperture effect is primarily due to in-patient and shifter scattering with a small contribution from the apparent beam source position. The model provides insight into the primary physics contributions to the penumbra and the nuclear halo. The model allowed us to fully deploy our PBS capacity at our two-gantry center without which PBS treatments would have been inferior compared to scattered fields with apertures. Finally, Monte Carlo calculations have (nearly) replaced phenomenological pencil-beam models for collimated fields. Phenomenological models do, however, allow exposition of underlying clinical phenomena and closer connection to representative clinical observables.