A statistical reconstruction algorithm for positronium lifetime imaging using time-of-flight positron emission tomography

Positron emission tomography (PET) has been widely used for the diagnosis of serious diseases including cancer and Alzheimer based on the uptake of radiotracers that target diseases pathological signatures. Recently, positronium lifetime imaging (PLI) with time-of-flight (TOF) PET can provide supplemental information reflecting conditions of the tissue microenvironment via mechanisms that are independent of tracer uptake. However, the present TOF PET systems have a finite coincidence resolving time (CRT), and the PLI reconstruction problem has yet to be fully formulated for the development of accurate reconstruction methods. This work addresses this challenge by developing a statistical model for the PLI data and deriving from it a maximum-likelihood image reconstruction method for the lifetime image. The proposed lifetime reconstruction method does not require prior knowledge of the radiotracer distribution, nor direct measurement of the time delay between prompt gamma and annihilation photons. Simulation studies have shown that quantitatively correct lifetime images can be reconstructed for phantoms larger than 20 centimeters in diameter at millimeter-scale spatial resolution, which exceeds the resolution limit imposed by the system CRT.