  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
$2\gamma$ 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
$2\gamma$ imaging by LYSO PET scanners with AFOV=20cm.
