Application of the electron pencil beam redefinition algorithm to electron arc therapy

This project investigated the potential of summing fixed-beam dose distributions calculated using the pencil-beam redefinition algorithm (PBRA) at small angular steps ( 1 ° ) to model an electron arc therapy beam. The PRBA, previously modified to model skincollimation, was modified further by incorporating two correction factors. One correction factor that is energy, SSD (source-to-surface distance), and field-width dependent constrained the calculated dose output to be the same as the measureddose output for fixed-beam geometries within the range of field widths and SSDs encountered in arc therapy. Another correction factor (single field-width correction factor for each energy) compensated for large-angle scattering not being modeled, allowing a more accurate calculation of dose output at mid arc. The PBRA was commissioned to accurately calculate dose in a water phantom for fixed-beam geometries typical of electron arc therapy. Calculated central-axis depth doses agreed with measureddoses to within 2% in the low-dose gradient regions and within 1- mm in the high-dose gradient regions. Off-axis doses agreed to within 2 mm in the high-dose gradient regions and within 3% in the low-dose gradient regions. Arced-beam calculations of dose output and depth dose at mid arc were evaluated by comparing to data measured using two cylindrical water phantoms with radii of 12 and 15 cm at 10 and 15 MeV . Dose output was measured for all combinations of phantom radii of curvature, collimator widths (4, 5, and 6 cm ), and arc angles ( 0 ° , 20 ° , 40 ° , 60 ° , 80 ° , and 90 ° ) for both beam energies. Results showed the calculated mid-arc dose output to agree within 2% of measurement for all combinations. For a 90 ° arc angle and 5 × 20 cm 2 field size, the calculated mid-arc depth dose in the low-dose gradient region agreed to within 2% of measurement for all depths at 10 MeV and for depths greater than depth of dose maximum R 100 at 15 MeV . For depths in the buildup region at 15 MeV the calculations overestimated the measureddose by as much as 3.4%. Mid-arc depth dose in the high-dose gradient region agreed to within 2.2 mm of measureddose. Calculated two-dimensional relative dose distributions in the plane of rotation were compared to dosemeasurements using film in a cylindrical polystyrene phantom for a 90 ° arc angle and field widths of 4, 5, and 6 cm at 10 and 15 MeV . Results showed that off-axis dose at the ends of arc (without skincollimation) agreed to within 2% in the low-dose gradient region and to within 1.2 mm in the high-dose gradient region. This work showed that the accuracy of the PBRA arced-beam dose model met the criteria specified by Van Dyk et al. [Int. J. Radiat. Oncol. Biol. Phys.26, 261–273 (1993)] with the exception of the buildup region of the 15 MeV beam. Based on the present results, results of a previous study showing acceptable accuracy in the presence of skincollimation, and results of a previous study showing acceptable accuracy in the presence of internal heterogeneities, it is concluded that the PBRA arced-beam dose model should be adequate for planning electron arc therapy.