Positronium imaging in J-PET with an iterative activity reconstruction and a multistage fitting algorithm

Abstract

Positronium imaging is a new technique complementary to positron emission tomography (PET) based on the histogramming of time delay between the emission of a de-excitation photon, and a consequent electron-positron annihilation, to estimate the mean lifetime of orthopositronium (o-Ps), which depends on the local size of the voids, concentration of oxygen and bioactive molecules. We improve the resolution and reduce noise in positronium imaging by building time-delay spectra from the PET activity reconstructed by a 3-photon time-of-flight maximum likelihood expectation maximisation. The method was tested on the data measured for four human-tissue samples injected by ²²Na and put in the Jagiellonian PET “Big barrel” scanner. Due to an ill-posed problem of fitting time-delay histograms, a multistage optimisation procedure was explored along with inferential analysis of the solution space. Run in parallel for multiple sets of initial guesses, we compared the second-order Levenberg- Marquardt algorithm (LMA) and the direct search Nelder-Mead simplex (NMS) method. The LMA proved to be faster and more precise, but the NMS was more stable with a higher convergence rate. The estimated mean o-Ps lifetimes in the 1.9 ns – 2.6 ns range were consistent with the reference results, while other fitting parameters allowed differentiation between the two patients who provided the tissue samples.