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Special algorithms for application to medical physical problems have been developed and implemented into the TITAN and PENTRAN 3-D parallel transport codes. TITAN is a 3-D parallel transport code with hybrid algorithms including 1) Sn and Characteristics, and 2) Sn with a fictitious quadrature set and ray-tracing. PENTRAN is a 3-D parallel transport code with adaptive differencing Sn formulation, full domain decomposition, and different angular quadrature types (including a characteristic option) with ordinate splitting. In this paper, we will discuss new algorithms developed in TITAN for image reconstruction in Single Photon Emission Computed Tomography (SPECT). It is demonstrated that TITAN projection images are in excellent agreement with the Monte Carlo MCNP5 predictions, while its computation time was up to 2787 times faster than the MCNP5 computation time for a 0.98° collimator acceptance angle. We will also discuss a novel algorithm developed in PENTRAN for dose calculations in heterogeneous, voxelized phantoms or other geometries. The new algorithm called EDK-Sn, or “Electron Dose Kernel-Discrete Ordinates (EDK-Sn)” yielded a speedup of ~8 over traditional highly parallel Monte Carlo calculation times, with <7% difference in dose among different organs (or smaller given stochastic uncertainties).

Unique formulations in TITAN and PENTRAN for medical physics applications