Gray: a ray tracing-based Monte Carlo simulator for PET

Monte Carlo simulation software plays a critical role in PET system design. Performing complex, repeated Monte Carlo simulations can be computationally prohibitive, as even a single simulation can require a large amount of time and a computing cluster to complete. Here we introduce Gray, a Monte Carlo simulation software for PET systems. Gray exploits ray tracing methods used in the computer graphics community to greatly accelerate simulations of PET systems with complex geometries. We demonstrate the implementation of models for positron range, annihilation acolinearity, photoelectric absorption, Compton scatter, and Rayleigh scatter. For validation, we simulate the GATE PET benchmark, and compare energy, distribution of hits, coincidences, and run time. We show a 13.6 +/- 0.1 x speedup using Gray, compared to GATE for the same simulation, while demonstrating nearly identical results. We additionally simulate the Siemens Biograph mCT system with both the NEMA NU-2 scatter phantom and sensitivity phantom. We estimate the total sensitivity within 3 +/- 2% when accounting for differences in peak NECR. We also estimate the peak NECR to be 199.5 +/- 0.2 kcps, or within 0.5 +/- 0.1% of published experimental data. The activity concentration of the peak is also estimated within 1.3%.