Validation of the final aperture superposition technique to calculate electron output factors and depth dose curves

The final aperture superposition technique (FAST) is a method to reproduce rapidly the electron-beam depth dose curves and output factors that would be calculated by a full Monte Carlo simulation. FAST uses precalculated Monte Carlo-based differential dose arrays and performs a superposition of open and shielded contributions to account for arbitrarily shaped insert openings. The objective of this work was to refine and validate the accuracy of the FAST method for a full range of treatment parameters. Compared to full simulations, raw FAST calculations tended to underestimate dose near the surface deposited by particles that crossed the shield-opening interface of the insert. In this study, a set of empirical correction curves was derived to reduce the errors from this "collimator effect." FAST and full simulation calculations were compared for every combination of six beam energies (6-21 MeV), four applicator sizes (10-25 cm), and two source-to-surface distances (SSDs) (100 and 110 cm). Validation tests were performed for a total of 192 fields using four sample insert openings: an open insert and 2, 3, and 5 cm diameter circular openings. Calculations were also performed for four patient inserts with irregularly shaped openings. Using the empirical correction curves, systematic errors were reduced, resulting in mean dose differences of less than 1% of the maximum full simulation dose. FAST relative output factors reproduced full simulation output factors to within 3% for all configurations except for the 2 and 3 cm diameter openings for the 6 and 9 MeV beams at 110 cm SSD. The maximum shift between the FAST and full simulation depth dose curves in the 90%-80% fall-off region was less than 3 mm for 97% of the fields. For the patient insert calculations, differences in output factors and mean differences in depth dose curves were within 1.5% with maximum shifts of 1.5 mm in the 90%-80% fall-off region. A small set measurements also demonstrated 3% accuracy in FAST output factors except for a 5% deviation for a 2 cm diameter insert for the 6 MeV beam at 110 cm SSD. These results demonstrate that FAST can be used to provide output factors and depth dose curves for most clinical cases.