In the positron emission tomography (PET), the density distribution of points of positron-electron annihilations, reflecting an image of metabolism rate of the radiopharmaceutical administered to the patient, is used for the diagnosis. The current PET technique does not take advantage of the fact that positron and electron may form a positronium atom. Yet, in up to about 40% cases [1, 2], positron-electron annihilations inside the human body proceed via the creation of the metastable positronium atom which in turn in quarter of cases appears as para-positronium (pPs) decaying to two photons and in three quarter of cases as ortho-positronium (oPs) decaying in vacuum into three photons. When trapped in the body, the ortho-positronium creation probability and mean lifetime strongly depend on the tissue’s nanostructure and the concentration of bio-active molecules (e.g., free radicals, reactive oxygen species, and antioxidants) which can interact with the emitted positrons as well as with the formed positronium [1]. The mean ortho-positronium lifetimes in the tissues varies from about 1.8 ns (as in pure water) to about 4 ns as measured for the human skin [3]. Whereas, the mean ortho-positronium lifetime differences for healthy and cancerous tissues are in the range of about 50 ps to about 200 ps [4–6]. In particular, ortho-positronium lifetime depends significantly on the size of free volume between atoms whereas its formation probability depends on their concentration. While both lifetime and formation probability depend on the concentration and type of biofluids and bio-active molecules [7]. Therefore, these ortho-positronium properties may be considered as diagnostic indicators complementary to the presently available SUV index [1, 8]. Recently, the in vitro studies indicated that indeed positronium mean lifetime and its production probability as well as the average time of direct annihilation differ for healthy and cancerous uterine tissues operated from the patients [4, 9]. Another in vitro measurements, performed with blood taken from patients before and after the chemotherapy or radiotherapy, demonstrated dependence of positronium properties in blood on the time after anti-neoplastic therapy [5]. In Fig. 1, an example of the hemoglobin molecule and the main mechanisms for the positronium annihilations inside the cells is presented.
The positron annihilation lifetime spectroscopy (PALS) is a well-established method in the material science [10–12]. However, in order to make use of the positronium properties in the in vivo medical diagnostics, development of the system combining PET and PALS is required [1, 7].
Recently, a method of positronium mean lifetime imaging, in which the lifetime, production probability, and position of positronium are determined on an event-by-event basis using oPs→3γ decay, was described [1, 8]. The place and time of ortho-positronium decay are reconstructed by the application of the trilateration technique [13, 14] which uses times and positions of registrations of three photons from oPs→3γ decay. The method is applicable for radiopharmaceuticals labeled with β+ decaying isotope emitting prompt gamma (e.g., 44Sc) [15, 16], where prompt gamma is used to determine the time of the ortho-positronium formation. The 3γ events were chosen because in case of the registration of the 3 γ in principle one can reconstruct the annihilation point with better spatial precision with respect to the case when only two photons are available. It was shown [1] that for the total-body J-PET scanner, when administering to the patient a typical activity of 370 MBq, one can expect about 700 registered events per cubic centimeter of the examined patient after 20 min of data collection. This is a promising result; however, the expected statistics is rather low. Low rate of oPs→3γ decays inside the tissue is due to the interaction of positronium with electrons from the surrounding atoms (pick-off process [17]) and due to the conversion [18–20] of ortho-positronium into para-positronium via interactions with the bio-active molecules (Fig. 1). Because of these processes, the ortho-positronium lifetime decreases in the tissue to the range of few nanoseconds [4, 9] and the fraction of its decay rate into three photons foPs→3γ decreases from foPs→3γ=1 in vacuum to foPs→3γ= τtissue/τvacuum in the tissue [21], where τtissue and τvacuum denote the ortho-positronium mean lifetime in the tissue and in vacuum, respectively (τvacuum=142 ns). For example, in case of τtissue = 2 ns, the ortho-positronium decays 70 times more frequent to 2 γ than to 3 γ.
Lifetime of the decaying object may be determined by the measurement of any of its decay channels, and hence, the ortho-positronium mean lifetime imaging can be performed based on the oPs→3γ decay [1], as well as based on the pick-off and conversion processes leading to the two back-to-back photons. In this article, we assess the feasibility of the 2γ ortho-positronium lifetime imaging for the total-body PET scanners assuming that the radiopharmaceutical is labeled with 44Sc isotope emitting positrons and prompt photon with energy of 1160 keV and using two back-to-back photons for the reconstruction of the ortho-positronium decay time and decay position. The prompt photon is used to determine the time of the creation of positronium. Reconstruction of the time difference between annihilation and emission of the positron enables to disentangle between processes when para-positronium decays to two photons (black arrows in Fig. 1) and ortho-positronium converts to two photons (magneta and violet arrows in Fig. 1). The lifetime of para-positronium (equal to 125 ps in vacuum) does not alter much as a function of properties of the tissues nanostructure (reaches about 230 ps) whereas the lifetime of ortho-positronium varies in the tissue in the range of few nanoseconds [4] and may occur to be useful as a diagnostic indicator [1, 7].
A statistical method of lifetime image reconstruction are yet to be conceived. Most recently, for the single detectors, 30 ps time resolution was achieved which is equivalent to position resolution of 4.5 mm along the line of response [22], and there is a continuous effort to improve it further even down to 10 ps [23, 24] which would enable to reconstruct the 2γ annihilation point along the LOR with precision of 1.5 mm. Such spatial precision of the reconstruction of annihilation point for each event would enable a direct reconstruction of the image as a density distribution of the reconstructed annihilation points. In such case, an iterative reconstruction procedures would not be needed and the spatial resolution of the image would be equivalent to the spatial resolution of the annihilation point reconstruction. Hence, the resolution of the ortho-positronium mean lifetime image will directly depend on the time resolution of the PET detector. At present, the newest TOF-PET scanners are characterized by the TOF resolution of about 210 ps [25] corresponding to the spatial resolution along the line of response (LOR) of about 3.8 cm. Recently, a detector design with SiPM has been reported, with CRT = 85 ps for 2×2×3 mm3 LSO:Ce doped with 0.4%Ca crystals and CRT of 140 ps for 2×2×20 mm3 crystals with the length as used in the current PET devices [26]. Thus, the TOF resolution, and consequently spatial resolution for a single event, is gradually improving by the development of new crystals, SiPMs [27], fast high frequency electronics [23], signal filtering [28] applications of the time ordered statistics [29, 30], signal waveform sampling [31, 32] including fast and cost-effective sampling in voltage domain [33], and advent of machine learning techniques [34].
In this context, it is worth mentioning that recently a new quenching circuit (QC) and single photon avalanche diode (SPAD) technology were introduced with 7.8 ps resolution [35] resulting in the resolution of 17.5 ps for the full chain of SiPM with QC and TDC [36].
In this article, based on the Monte Carlo simulations, we argue that with the time resolution in the order of tens of picoseconds and the advent of the high sensitivity total-body PET systems [37–39], the 2γ + γprompt mean lifetime positronium imaging based on time measurements may become possible in the future.
In the next section, the main assumptions applied in the simulations are presented. Further on, the sensitivity for the simultaneous registration of the back-to-back photons from positronium decay and prompt photon including selection of the image forming events is estimated for the total-body PET scanners built from LYSO crystal as well as for the cost-effective version of the total-body PET built from plastic scintillators. Next, the results of detailed Monte Carlo simulations of the response of the J-PET total-body scanner to the point-like sources arranged in the configuration as described in the NEMA norm are performed, and the regular PET 2 γ annihilation images as well as ortho-positronium mean lifetime images are reconstructed and compared for the four cases of assumed coincidence resolving time (CRT) of 500 ps, 140 ps, 50 ps, and 10 ps. Finally, it is shown that, owing to the large axial field-of-view of the total body scanners, the sensitivity for the positronium lifetime imaging is even larger than the present sensitivity for the 2γ metabolic imaging with the PET scanners having 20 cm axial length, even though the discussed positronium lifetime imaging requires registration of triple coincidence events including the prompt gamma and the two back-to-back photons.