Equivalent fields and scatter integration for photon fields

Equivalent fields are often used in radiation oncology for calculation of dose. This avoids the need to make a scatter integration but has limited applicability and some inaccuracy. We have evaluated the alternative of explicit integration of phantom-scatter dose using a functional representation, sigma, of the ratio between the scatter dose and the primary dose. The independent parameters are depth and the side of the square field. The function chosen has the advantage that the integral for a right triangle is available in closed form, which simplifies the determination of the dose from phantom-scattered photons for irregular fields by summation over such triangles. This approach accounts for the influence of depth and beam quality, which the commonly used equivalent-field tables and the area-over-perimeter relation ignore. The accuracy of this procedure is determined by the accuracy of the function sigma. This has about a 1% error of total dose for high-energy x-rays. We conclude that the tables and rules can be replaced by a computer-implemented integration of the phantom-scatter dose represented by this function sigma and using sectors or right triangles. Summing the closed-form contributions from component right triangles reduces the calculation time, which is particularly desirable when many fields are employed, as for intensity-modulated techniques and inverse planning. Measurements performed on irregular MLC-shaped fields compared well with the result from calculations.