Accounting for high Z shields in brachytherapy using collapsed cone superposition for scatter dose calculation

Common clinical brachytherapy treatment planning algorithms perform at best one-dimensional corrections for high Z heterogeneities that will be inaccurate for intermediate energies (60-100 keV). The development of fast methods for a three-dimensional dose calculation to account for high Z materials in this energy range is important, e.g., to fully utilize the potential of patient individualized shields using isotopes such as 241Am and 169Yb. In this work we use the collapsed cone superposition algorithm to calculate the scatter dose contribution around partly lead-shielded point sources at 60, 100, and 350 keV. Methods to scale point kernels for water into kernels for high Z materials are derived. The scaling accounts for scattered photon spectral differences between materials and thus goes beyond the common density scaling approach. Compared to Monte Carlo simulations, the results of our algorithm yield agreements on the unshielded side to within 3% at 350 and 60 keV and to within 7% at 100 keV out to distances of 8 cm from the source. The effect of the shield in the center of the unshielded region is small at 350 keV but significant and occurs at short distances at 100 and 60 keV. At 60 keV, the shield causes a dose reduction of around 10%, 1 cm from the source on the unshielded side. At 100 keV, the reverse effect is seen, the insertion of shields leading to the total dose being increased by about 10% at 1 cm. That one-dimensional algorithms are incapable of predicting these changes shows the importance of accounting for the full three-dimensional geometry in correctly determining the scatter dose contribution.