Accuracy assessment of the superposition principle for evaluating dose distributions of elongated and curved 103Pd and 192Ir brachytherapy sources

PURPOSE The current brachytherapy dose calculation formalism determines clinical dose distributions using the superposition principle. However, this approach cannot account for intersource attenuation for extended brachytherapy sources such as elongated and curved sources. The purpose of this study is to determine the line segment length required for optimal accuracy of dose calculations in the vicinity of elongated and curved 103Pd and 192Ir sources using the superposition technique intrinsic to the AAPM TG-43 formalism. METHODS Monte Carlo (MC) simulations were performed in water for 103Pd and 192Ir sources with linear, toroidal, and hairpin geometries. Dose distributions for 0.1-8.0 cm line segments from MC simulations were entered into treatment planning system (TPS) using the TG-43 approach with 0.05 cm spatial resolution. Line source dose distributions were benchmarked using MC-to-MC comparisons with the superposition principle, TPS-to-TPS fluence map comparisons, and MC-to-TPS gamma-index comparisons. Toroidal and hairpin geometries were constructed using line segments in the TPS, then TPS-calculated dose distributions were compared to the MC-simulation results. Gamma-index comparisons were performed in the iba(Dosimetry) Omni-Pro I'mRT software using 2 mm distance-to-agreement Ad and 2% dose error deltaD criteria, with a passing rate of > or = 98% of pixels meeting the gamma < or = 1.00 tolerance deemed acceptable. RESULTS For the MC-to-MC superposition check for line source, the average ratio of the superposition to the solid source length was 1.051 for 103Pd and 1.009 for 192Ir through the whole volume with maximum ratios of 1.34 and 1.32, respectively. TPS-to-TPS comparisons between a solid line source and multiple line segments also provided good agreement. The MC-to-TPS benchmarking indicated where the gamma-index comparison failed were inside the source and within 0.25 cm of the source long-axis. Excluding these regions, 99.6% and 99.9% of the 57 600 in-plane pixels satisfied the gamma-index criteria for 103Pd and 192Ir, respectively. The optimal line segment length for both 103Pd and 192Ir toroidal sources was about 0.5 cm or one-fifth of the torus diameter, whichever was smaller. For all toroidal geometries and all line segment lengths examined, at least 98.9% and 100.0% pixels met the gamma-index criteria for 103Pd and 192Ir, respectively. For both 103Pd and 192Ir hairpin source, all geometric variations had passing rates exceeding 99.2%. However, the best results were obtained from 0.4 cm line segments on the curved part for 103Pd while it was independent of line segment length for 192Ir. CONCLUSIONS A method for using a conventional TPS for brachytherapy treatment planning of elongated and curvilinear brachytherapy sources was developed and benchmarked. This method was evaluated using a gamma-index comparison technique, where appropriate pass-rate criteria were identified. Using a variety of subsegment lengths, the total length for a straight-line source was generally reproduced with accuracy improving as subsegment length increased, approaching the total straight-line length. Toroidal sources were similarly modeled with line segments, and an accuracy tradeoff was found between geometric errors and simulating dose anisotropy along the long-axes. The gamma-index comparison method to analyze the results was shown to be more powerful than point-wise comparison methods, and more versatile than dose ratios on the same plane.