Impact of the differential fluence distribution of brachytherapy sources on the spectroscopic dose-rate constant.

Purpose: To investigate why dose-rate constants for 125I and 103Pd seeds computed using the spectroscopic technique, Λspec, differ from those computed with standard Monte Carlo (MC) techniques. A potential cause of these discrepancies is the spectroscopic technique’s use of approximations of the true fluence distribution leaving the source, φ full. In particular, the fluence distribution used in the spectroscopic technique, φ spec, approximates the spatial, angular, and energy distributions of φ full. This work quantified the extent to which each of these approximations affects the accuracy of Λspec. Additionally, this study investigated how the simplified water-only model used in the spectroscopic technique impacts the accuracy of Λspec. Methods: Dose-rate constants as described in the AAPM TG-43U1 report, Λfull, were computed with MC simulations using the full source geometry for each of 14 different 125I and 6 different 103Pd source models. In addition, the spectrum emitted along the perpendicular bisector of each source was simulated in vacuum using the full source model and used to compute Λspec. Λspec was compared to Λfull to verify the discrepancy reported by Rodriguez and Rogers. Using MC simulations, a phase space of the fluence leaving the encapsulation of each full source model was created. The spatial and angular distributions of φ full were extracted from the phase spaces and were qualitatively compared to those used by φ spec. Additionally, each phase space was modified to reflect one of the approximated distributions (spatial, angular, or energy) used by φ spec. The dose-rate constant resulting from using approximated distribution i, Λapprox,i , was computed using the modified phase space and compared to Λfull. For each source, this process was repeated for each approximation in order to determine which approximations used in the spectroscopic technique affect the accuracy of Λspec. Results: For all sources studied, the angular and spatial distributions of φ full were more complex than the distributions used in φ spec. Differences between Λspec and Λfull ranged from −0.6% to +6.4%, confirming the discrepancies found by Rodriguez and Rogers. The largest contribution to the discrepancy was the assumption of isotropic emission in φ spec, which caused differences in Λ of up to +5.3% relative to Λfull. Use of the approximated spatial and energy distributions caused smaller average discrepancies in Λ of −0.4% and +0.1%, respectively. The water-only model introduced an average discrepancy in Λ of −0.4%. Conclusions: The approximations used in φ spec caused discrepancies between Λapprox,i and Λfull of up to 7.8%. With the exception of the energy distribution, the approximations used in φ spec contributed to this discrepancy for all source models studied. To improve the accuracy of Λspec, the spatial and angular distributions of φ full could be measured, with the measurements replacing the approximated distributions. The methodology used in this work could be used to determine the resolution that such measurements would require by computing the dose-rate constants from phase spaces modified to reflect φ full binned at different spatial and angular resolutions.