Functional fitting of interstitial brachytherapy dosimetry data recommended by the AAPM Radiation Therapy Committee Task Group 43

This work was undertaken to expedite implementation of the AAPM Task Group 43 recommendations, which call for significant modifications in the way dose is calculated for interstitial sources of192 Ir ,125 I , and103 Pd as well as significant changes in the dose rate constant for125 I sources. The TG43 recommendations include a new formalism for dose calculation at points defined by the radial distance, r , from the source center and the angle, θ, that such a radius makes with the source axis. For each source type, values are tabulated for the radial dose function, the anisotropy function, and the anisotropy factor. The TG43 report includes fitting functions for the radial dose function in the form of polynomials, which are poorly behaved outside the range of fitted data. No functions are offered for the anisotropy function data or the anisotropy factor data, both of which could profit from some smoothing by such functions. We have found a double exponential fit to the radial dose function that not only approximates the data adequately but also appropriately approaches zero for very large distances. The anisotropy function is conveniently fit with a form of type 1 − f ( r , θ ) cos ( θ ) e cr , which is exactly 1 at θ = 90 ° and approaches 1 for large r (for c < 0 ), where f ( r , θ ) is a selected polynomial in the two variables. The form chosen for the anisotropy factor was1 − ( a + br ) e cr , which appropriately approaches 1 for large r (and c < 0 ). Functional fits of these types are expected to facilitate implementation of TG43 recommendations, in that they may be either incorporated into dose algorithms or used to generate lookup tables of either the x , y or the r , θ format.