Evaluation of interpolation methods for TG-43 dosimetric parameters based on comparison with Monte Carlo data for high-energy brachytherapy sources

Purpose: The aim of this work was to determine dose distributions for high-energy brachytherapy sources at spatial locations not included in the radial dose function gL(r) and 2D anisotropy function F(r,θ) table entries for radial distancer and polar angle θ. The objectives of this study are as follows: 1) to evaluate interpolation methods in order to accurately derive gL(r) and F(r,θ) from the reported data; 2) to determine the minimum number of entries in gL(r) and F(r,θ) that allow reproduction of dose distributions with sufficient accuracy.Material and methods: Four high-energy photon-emitting brachytherapy sources were studied: 60Co model Co0.A86, 137Cs model CSM-3, 192Ir model Ir2.A85-2, and 169Yb hypothetical model. The mesh used for r was: 0.25, 0.5, 0.75, 1, 1.5, 2–8 (integer steps) and 10 cm. Four different angular steps were evaluated for F(r,θ): 1°, 2°, 5° and 10°. Linear-linear and logarithmic-linear interpolation was evaluated for gL(r). Linear-linear interpolation was used to obtain F(r,θ) with resolution of 0.05 cm and 1°. Results were compared with values obtained from the Monte Carlo (MC) calculations for thefour sources with the same grid.Results: Linear interpolation of gL(r) provided differences ≤ 0.5% compared to MC for all four sources. Bilinear interpolation of F(r,θ) using 1° and 2° angular steps resulted in agreement ≤ 0.5% with MC for 60Co, 192Ir, and 169Yb, while 137Cs agreement was ≤ 1.5% for θ < 15°.Conclusions: The radial mesh studied was adequate for interpolating gL(r) for high-energy brachytherapy sources, and was similar to commonly found examples in the published literature. For F(r,θ) close to the source longitudinalaxis, polar angle step sizes of 1°-2° were sufficient to provide 2% accuracy for all sources.