Physics Contributions
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,) table entries for radial distance r and polar angle . The objectives of this study are as follows: 1) to evaluate interpolation methods in order to accurately derive gL(r) and F(r,) from the reported data; 2) to determine the minimum number of entries in gL(r) and F(r,) 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,): 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,) with resolution of 0.05 cm and 1°. Results were compared with values obtained from the Monte Carlo (MC) calculations for the four 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,) 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  < 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,) close to the source longitudinal-axis, polar angle step sizes of 1°-2° were sufficient to provide 2% accuracy for all sources.