Dose calculations using convolution and superposition principles: the orientation of dose spread kernels in divergent x-ray beams.

The convolution/superposition method of dose calculation has the potential to become the preferred technique for radiotherapy treatment planning. When this approach is used for therapeutic x-ray beams, the dose spread kernels are usually aligned parallel to the central axis of the incident beam. While this reduces the computational burden, it is more rigorous to tilt the kernel axis to align it with the diverging beam rays that define the incident direction of primary photons. We have assessed the validity of the parallel kernel approximation by computing dose distributions using parallel and tilted kernels for monoenergetic photons of 2, 6, and 10 MeV; source-to-surface distances (SSDs) of 50, 80, and 100 cm; and for field sizes of 5 x 5, 15 x 15, and 30 x 30 cm2. Over most of the irradiated volume, the parallel kernel approximation yields results that differ from tilted kernel calculations by 3% or less for SSDs greater than 80 cm. Under extreme conditions of a short SSD, a large field size and high incident photon energy, the parallel kernel approximation results in discrepancies that may be clinically unacceptable. For 10-MeV photons, we have observed that the parallel kernel approximation can overestimate the dose by up to 4.4% of the maximum on the central axis for a field size of 30 x 30 cm2 applied with a SSD of 50 cm. Very localized dose underestimations of up to 27% of the maximum dose occurred in the penumbral region of a 30 x 30-cm2 field of 10-MeV photons applied with a SSD of 50 cm.