Evaluation of a deterministic grid-based Boltzmann solver (GBBS) for voxel-level absorbed dose calculations in nuclear medicine

To evaluate the 3D Grid-based Boltzmann Solver (GBBS) code ATTILA (R) for coupled electron and photon transport in the nuclear medicine energy regime for electron (beta, Auger and internal conversion electrons) and photon (gamma, x-ray) sources. Codes rewritten based on ATTILA are used clinically for both high-energy photon teletherapy and Ir-192 sealed source brachytherapy; little information exists for using the GBBS to calculate voxel-level absorbed doses in nuclear medicine. We compared DOSXYZnrc Monte Carlo (MC) with published voxel-S-values to establish MC as truth. GBBS was investigated for mono-energetic 1.0, 0.1, and 0.01 MeV electron and photon sources as well as I-131 and Y-90 radionuclides. We investigated convergence of GBBS by analyzing different meshes (M-0, M-1, M-2), energy group structures (E-0, E-1, E-2) for each radionuclide component, angular quadrature orders (S-4, S-8, S-16), and scattering order expansions (P-0-P-6); higher indices imply finer discretization. We compared GBBS to MC in (1) voxel-Svalue geometry for soft tissue, lung, and bone, and (2) a source at the interface between combinations of lung, soft tissue, and bone. Excluding Auger and conversion electrons, MC agreed within approximate to 5% of published source voxel absorbed doses. For the finest discretization, most GBBS absorbed doses in the source voxel changed by less than 1% compared to the next finest discretization along each phase space variable indicating sufficient convergence. For the finest discretization, agreement with MC in the source voxel ranged from -3% to -20% with larger differences at lower energies (-3% for 1 MeV electron in lung to -20% for 0.01 MeV photon in bone); similar agreement was found for the interface geometries. Differences between GBBS and MC in the source voxel for Y-90 and I-131 were -6%. The GBBS ATTILA was benchmarked against MC in the nuclear medicine regime. GBBS can be a viable alternative to MC for voxel-level absorbed doses in nuclear medicine. However, reconciliation of the differences between GBBS and MC at lower energies requires further investigation of energy deposition cross-sections.