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

Shopa Roman Y., Dulski Kamil

Bio-Algorithms and Med-Systems

2023

Vol. 19, no. 1

54--63

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 LevenbergMarquardt 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.

Multi-photon time-of-flight MLEM application for the positronium imaging in J-PET

Shopa Roman Y., Dulski Kamil

Bio-Algorithms and Med-Systems

2022

Vol. 18, no. 1

135--143

We develop a positronium imaging method for the Jagiellonian PET (J-PET) scanners based on the timeof-flight maximum likelihood expectation maximisation (TOF MLEM). The system matrix elements are calculated on-the-fly for the coincidences comprising two annihilation and one de-excitation photons that originate from the ortho-positronium (o-Ps) decay. Using the Geant4 library, a Monte Carlo simulation was conducted for four cylindrical 22Na sources of β+ decay with diverse o-Ps mean lifetimes, placed symmetrically inside the two JPET prototypes. The estimated time differences between the annihilation and the positron emission were aggregated into histograms (one per voxel), updated by the weights of the activities reconstructed by TOF MLEM. The simulations were restricted to include only the o-Ps decays into back-to-back photons, allowing a linear fitting model to be employed for the estimation of the mean lifetime from each histogram built in the log scale. To suppress the noise, the exclusion of voxels with activity below 2% - 10% of the peak was studied. The estimated o-Ps mean lifetimes were consistent with the simulation and distributed quasi-uniformly at high MLEM iterations. The proposed positronium imaging technique can be further upgraded to include various correction factors, as well as be modified according to realistic o-Ps decay models.