Statistical Reconstruction of Positronium Lifetime Imaging Using Time-of-Flight Positron Emission Tomography

Abstract

The positronium lifetime imaging (PLI) reconstruction is a technique used in time-of-flight (TOF) positron emission tomography (PET) that involves measuring the lifespan of positronium, more preciselyortho-positronium (o-Ps), before annihilation, in addition to the traditional uptake image of PET tracer. PLI faces the challenge of limited time resolution in TOF PET systems, which introduces complexities in both statistics and physics. In this dissertation, we developed a maximum likelihood (ML) algorithm for PLI reconstruction and demonstrated that it can generate quantitatively accurate lifetime images for a 570 ps TOF PET system. Furthermore, we conducted investigations into the statistical properties of the algorithm, including the variability of the reconstruction results, the sensitivity of the algorithm to the number of acquired PLI events, and its robustness to hyperparameter choices. Our findings indicate that the proposed ML method produces stable images to enable reliable distinction of regions of interest in the images. Moreover, the number of PLI events required to produce quantitatively accurate images is computationally plausible. These results demonstrate the potential of the proposed method for advancing the capabilities of PLI. In real-world scenarios, in addition to o-Ps, other populations of positron that exhibit different lifetimes also exist. We subsequently introduced a novel two-component reconstruction model for PLI in TOF PET, incorporating both slow-decay and fast-decay components. This model enhances the accuracy of positronium imaging by providing a more detailed representation of positron lifetime distributions. We conducted simulation studies to evaluate the performance of our model and compared it with the existing single-component reconstruction model. The results demonstrate the superiority of the two-component model in capturing the intricacies of the positron populations, thus paving the way for more precise and informative PLI diagnostics.