Quantification of the Multiplexing Effects in Multi-Pinhole Small Animal SPECT: A Simulation Study

Our goal is to study the trade-off between image degradation and improved detection efficiency and resolution from allowing multiplexing in multi-pinhole (MPH) SPECT, and to determine the optimal pinhole number for MPH design. We used an analytical 3D MPH projector and two digitized phantoms: the mouse whole body (MOBY) phantom and a hot sphere phantom to generate noise-free and noisy projections, simulating pinhole collimators fitted with pre-studied pinhole patterns. We performed three schemes to achieve different degrees of multiplexing: 1. Fixed magnification and detection efficiency; 2. Fixed detection efficiency and changed magnification; 3. Fixed magnification and changed detection efficiency. We generated various noisy data sets by simulating Poisson noise using differently scaled noise-free projections and obtained 20 noise realizations for each setting. All datasets were reconstructed using 3D MPH ML-EM reconstruction method. We analyzed the quantitative accuracy by the normalized-mean-square-error. We evaluated the image contrast for the hot sphere phantom simulation, and also the image noise by the average normalized-standard-deviation of certain pixels for different degrees of multiplexing. Generally, no apparent artifacts were observed in the reconstructed images, illustrating the effectiveness of reconstructions. Bias increased for increased degree of multiplexing. Contrast was not significantly affected by multiplexing in the specific simulation scheme (1). Scheme (2) showed that excessive multiplexing to improve image resolution would not improve the overall trade-off of bias and noise compared to no multiplexing. However, scheme (3) showed that when comparing to no multiplexing, the trade-off improved initially with increased multiplexing by allowing more number of pinholes to improve detection efficiency. The trade-off reached a maximum and decreased with further multiplexing due to image degradation from increased bias. The optimal pinhole number was 7 for a compact camera with size of 12 cm times 12 cm and 9 for a standard gamma camera with size of 40 cm times 40 cm in this scheme. We conclude that the gains in improved detection efficiency and resolution by increased multiplexing are offset by increased image degradations. All the aforementioned factors must be considered in the optimum MPH collimator design for small animal SPECT imaging.