Critical Discretization Issues in 3-D S_N Simulations Relevant to Dosimetry and Medical Physics

Dosimetry problems inherently involve dose determinations among widely varying materials and densities, and may require complex, detailed investigations of the angular, spatial, and energy behavior of the applied radiation transporting throughout the simulation geometry. Traditionally, Monte Carlo codes have been implemented in solving these types of problems using voxelized geometries and phantoms. The motivation of this work is to investigate the discretization requirements for deterministic radiation transport simulations for these problems via direct solutions of the linear Boltzmann transport equation, focusing on the discrete ordinates (S_N) method. The S_N method can yield accurate global solutions, provided the inherent discretizations among the angular, spatial, and energy domains properly represent problem physics. In this paper, the S_N approach is implemented using a three-dimensional (3-D) ⁶⁰Co photon transport simulation to highlight the critical issues encountered in performing deterministic photon simulations in dosimetry problems. Calculations were performed using the PENTRAN parallel S_N code to obtain a 3-D distribution of flux and dose computed using a collisional kerma approximation. For an acceptable result, we determined that a minimum angular Legendre-Chebychev quadrature of S₃₂ with P₃ anisotropy is required, with block-adaptive meshes on the order of 1 cm, even in air regions, implemented with an adaptive differencing scheme (implemented in the PENTRAN code) to yield optimal solution convergence. Also, photon cross-section libraries should be carefully evaluated for the problem studied; for our test problem, the BUGLE-96 photon library yielded the closest results to Monte Carlo (MCNP5) among those tested. Overall, this work details the levels of discretization involved in performing deterministic computations in dosimetry problems and will be useful in enabling future efforts to perform rapid deterministic computations of phantom doses.