In living organisms the positron-electron annihilation (occurring during the PET imaging) proceeds in about 30% via creation of a metastable ortho-positronium atom. In the tissue, due to the pick-off and conversion processes, over 98% of ortho-positronia annihilate into two 511~keV photons. In this article we assess the feasibility for reconstruction of the mean ortho-positronium lifetime image based on annihilations into two photons. The main objectives of this work include: (i) estimation of the sensitivity of the total-body PET scanners for the ortho-positronium mean lifetime imaging using $2gamma$ annihilations, and (ii) estimation of the spatial and time resolution of the ortho-positronium image as a function of the coincidence resolving time (CRT) of the scanner. Simulations are conducted assuming that radiopharmaceutical is labelled with $^{44}Sc$ isotope emitting one positron and one prompt gamma. The image is reconstructed on the basis of triple coincidence events. The ortho-positronium lifetime spectrum is determined for each voxel of the image. Calculations were performed for cases of total-body detectors build of (i) LYSO scintillators as used in the EXPLORER PET, and (ii) plastic scintillators as anticipated for the cost-effective total-body J-PET scanner. To assess the spatial and time resolution the three cases were considered assuming that CRT is equal to 140ps, 50ps and 10ps. The estimated total-body PET sensitivity for the registration and selection of image forming triple coincidences is larger by a factor of 12.2 (for LYSO PET) and by factor of 4.7 (for plastic PET) with respect to the sensitivity for the standard $2gamma$ imaging by LYSO PET scanners with AFOV=20cm.
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