Determination of equivalent photon fields through integrated 1D convolution kernels

Abstract

The equivalent fields concept has been studied using a variation of the convolution dose calculation method. This allows a better understanding of this classic, widely-used concept and its relation to modern dose calculation techniques. Total scatter energy contribution as a function of field size was computed by radially integrating three-dimensional point interaction scatter kernels representing cobalt-60, 6 MV and 24 MV photon beam spectra and utilizing reciprocity. For arbitrarily shaped treatment fields, equivalent square or circular fields are chosen based on a conservation of energy approach. Associated depth dose curves are generated via convolution of primary fluence with pre-integrated scatter kernels. For the energy spectra used, the resulting equivalent circle to square relationships agree with the empirical equation recommended in the British Journal of Radiology Supplement 25 (BJR 25) (to within 2%). Tables converting rectangular fields to equivalent squares and circles have been generated and most (~63%) of the equivalent square (and circular) field sizes are within 0.5 cm of the BJR 25 tables. This agreement provides an explanation for the successful use of a single relationship for all therapeutic energies. Fields of different shape will be approximately equivalent only when the scatter kernels are similar in shape and total energy content. The equivalent field concept inevitably results in an optimal match of depth dose curves at a single depth only. These ideas are demonstrated for a highly elongated (2 × 30 cm2) field and its equivalent square field. The invalidity of the equivalent fields concept off-axis is demonstrated by examining predicted dose deposition for several points in and around a 15 × 15 cm2 cobalt-60 beam. Modern convolution techniques are shown to offer a unique approach to the classic equivalent fields method. The appropriate use of the BJR 25 equivalent fields tables is recommended for all photon energies.