The sievert integral revisited: Evaluation and extension to ¹²⁵I, ¹⁶⁹YB, and ¹⁹²IR brachytherapy sources

Purpose: The goal of this study is to assess the accuracy of the Sievert integral dose calculation model for medium and low-energy brachytherapy sources (photon energy: 25-500 keV). A simple modification of the basic model, the isotropic scattering correction, is proposed that significantly improves its accuracy. Methods and Materials: Both the classical model and revised Sievert algorithms were tested against 2D dose distributions derived from Monte Carlo photon transport (MCPT) calculations for the following sources: a ¹⁶⁹Yb interstitial source, pulsed and high dose rate ¹⁹²Ir sources and the model 6702 ¹²⁵I source. The Sievert model was implemented as a 3D numerical integral over the radioactivity distribution and included photon attenuation and scattering by the surrounding medium. The Sievert filtration coefficients were approximated by linear energy absorption coefficients, parameters of best fit, and curve fits to simulated open-air transmission measurements. The revised model consists of using the Sievert integral only to calculate the primary dose distribution using contact absorber filtration coefficients. The dose component due to photon scattering in the medium is assumed to be isotropically distributed and is modeled by point-source scatter-to-primary dose ratios. Results: The classical Sievert integral produces maximum and RMS average dose-calculation errors ranging from -53 to -20% and 3 to 19%, respectively. In contrast, the revised model reproduces the MCPT dose distribution with maximum and RMS mean errors ranging from 5 to 13% and 1 to 6%, respectively. Conclusions: The classical Sievert model fails to accurately describe brachytherapy dose distributions around heavily filtered sources emitting photons with average energies of 28 to 400 keV. The revised Sievert model accurately models single-source dose distributions for a wide range of sources, using well-defined filtration coefficients and scatter ratios that can be measured or calculated without knowledge of the final dose distribution. The model is potentially useful as a single-source dose-array generator for clinical treatment planning in the low energy domain.