Effects of finite angular steps and extent of profile data on the calculation of rotational x-ray dose distributions

Computer algorithms for rotational therapy beams, in most cases, perform dose calculations by summing stored fixed beam data at finite angular steps. Such an algorithm, based on the Bentley beam model, was evaluated by comparing calculations with measured data for an 18-MV x-ray beam. Measurements were made in a specially constructed cylindrical water phantom of 15-cm radius using a 0.1-cm3 ionization chamber for an arc of 180 degrees and for a field size of 7.2 X 7.2 cm2 at 100-cm source-axis distance. This study revealed that the Bentley beam model, with fixed beams summed every 10 degrees, predicts the dose in the treatment volume, centered about the isocenter, with an accuracy of approximately 2%. However, dose at depths between the phantom surface and the treatment volume could be underestimated by as much as 10% (3% of isocenter). This was shown to be partially due to the truncated tails of the off-axis profiles in the Bentley model, which extend only 8 mm outside the edge of the radiation field, and the large angular increment of integration (10 degrees). Using beam profiles extending to 4 cm outside the edge of the radiation field and angular steps of 5 degrees or less for summation of fixed beams reduced errors to less than 5%. Therefore, extended beam profiles and smaller angular steps for summing fixed beams are recommended for photon rotation calculation when increased accuracy is required.