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 g_L(r) and 2D anisotropy function F(r,θ) table entries for radial distance r and polar angle θ. The objectives of this study are as follows: 1) to evaluate interpolation methods in order to accurately derive g_L(r) and F(r,θ) from the reported data; 2) to determine the minimum number of entries in g_L(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 g_L(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 the four sources with the same grid.

Results: Linear interpolation of g_L(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 g_L(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 longitudinal-axis, polar angle step sizes of 1°-2° were sufficient to provide 2% accuracy for all sources.