Development of a collimator representation in the TITAN transport code for SPECT simulation

A fast methodology for simulating single photon emission computed tomography (SPECT) is being developed using the hybrid deterministic transport code TITAN. The TITAN code is referred to as hybrid because it uses a discrete ordinates method in the phantom and a simplified ray-tracing algorithm in the air outside of the phantom. We are developing a method for the TITAN code to simulate the collimator in a SPECT system and using the MCNP5 Monte Carlo code for comparison. The phantom modeled is a simple cube of water with a smaller cube source of Tc-99m at its center. The model is symmetric so a row of collimators is simulated and the flux making it to the detector surface is computed. We consider collimator acceptance angles of 3.694E-02 radians (2.1°) and 0.135 radians (7.7°) and normalize our results to the peak flux. The MCNP5 benchmark model directly models each collimator hole, while the TITAN code uses a circular ordinate splitting (COS) technique. The TITAN code solves for the flux along directions within a user defined acceptance angle about each projection direction. The COS technique has been shown previously to be less accurate for small aspect ratios than for high aspect ratios. Here, we seek to test a weighted COS technique for accuracy over a wide range of collimator aspect ratios. Two modifications have been made to the original COS technique in TITAN to create the weighted COS technique: i) directions are weighted by the detector surface area projected along that direction to the front of the collimator and ii) split directions are chosen to better represent the acceptance angle space. Compared with the original COS technique, the weighted COS technique shows much better behavior as the number of splitting directions increases. Compared with the MCNP5 solution, the weighted COS technique has an average relative error of ≤8% using the 7.7° acceptance angle collimator for all examined parameters.