Positronium lifetime validation measurements using a long-axial field-of-view positron emission tomography scanner

Abstract

Background: Positron emission tomography (PET) traditionally uses coincident annihilation photons emitted from a positron interacting with an electron to localize cancer within the body. The formation of positronium (Ps), a bonded electron-positron pair, has not been utilized in clinical applications of PET due to the need to detect either the emission of a prompt gamma ray or the decay of higher-order coincident events. Assessment of the lifetime of the formed Ps, however, can potentially yield additional diagnostic information of the surrounding tissue because Ps properties vary due to void size and molecular composition. To assess the feasibility of measuring Ps lifetimes with a PET scanner, experiments were performed in a Biograph Vision Quadra (Siemens Healthineers). Quadra is a long-axial field-of-view (LA-FOV) PET scanner capable of producing list-mode data from single interaction events.

Results: Ortho-Ps (o-Ps) lifetimes were measured for quartz-glass and polycarbonate samples using a $_{}^{22}\text{Na}$ positron source. Results produced o-Ps lifetimes of 1.538 ± 0.036 ns for the quartz glass and 1.927 ± 0.042 ns for the polycarbonate. Both o-Ps lifetimes were determined using a double-exponential fit to the time-difference distribution between the emission of a prompt gamma ray and the annihilation of the correlated positron. The measured values match within a single standard deviation of previously published results. The quartz-glass samples were additional measured with $_{}^{82}\text{Rb}$ , $_{}^{68}$ Ga and $_{}^{124}\text{I}$ to validate the lifetime using clinically available sources. A double-exponential fit was initially chosen as a similar methodology to previously published works, however, an exponentially-modified Gaussian distribution fit to each lifetime more-accurately models the data. A Bayesian method was used to estimate the variables of the fit and o-Ps lifetime results are reported using this methodology for the three clinical isotopes: 1.59 ± 0.03 ns for $_{}^{82}\text{Rb}$ , 1.58 ± 0.07 ns for $_{}^{68}\text{Ga}$ and 1.62 ± 0.01 ns for $_{}^{124}\text{I}$ . The impact of scatter and attenuation on the o-Ps lifetime was also assessed by analyzing a water-filled uniform cylinder (20 $\varphi$ $\times$ 30 cm $_{}^3$ ) with an added $_{}^{82}\text{Rb}$ solution. Lifetimes were extracted for various regions of the cylinder and while there is a shape difference in the lifetime due to scatter, the extracted o-Ps lifetime of the water, 1.815 ± 0.013 ns, agrees with previously published results.

Conclusion: Overall, the methodology presented in this manuscript demonstrates the repeatability of Ps lifetime measurements with clinically available isotopes in a commercially-available LA-FOV PET scanner. This validation work lays the foundation for future in-vivo patient scans with Quadra.

Keywords: Molecular imaging; Positron emission tomography; Positronium imaging.

Fig. 1

Diagram depicting a series of single interactions with coincidence windows

Fig. 2

Time-sorted and energy qualified spectra of triple events for the quartz-glass measurement containing approximately 4.7 MBq of $_{}^{124}$I in the FOV with energy windows of 460–545 keV for the annihilation photons and 568–639 keV for the prompt gamma ray

Fig. 3

Diagram depicting a triple-interaction event composed of a prompt gamma ray and two annihilation photons

Fig. 4

Histo-images of the axial view summed over all Y planes (a) and transaxial view summed over all Z planes (b) of a uniform cylinder (20 $\varphi$ $\times$ 30 cm$_{}^3$) filled with 16.3 MBq of $_{}^{18}$F. The dashed red lines denote the region of interest for extracting Ps lifetime information

Fig. 5

Time-difference distribution produced from the ROI denoted in Fig. 4 with all events and with a 30-crystal distance threshold applied to the prompt gamma ray and annihilation photon interactions

Fig. 6

Decay scheme for $_{}^{176}$Lu

Fig. 7

The distance between the prompt gamma-ray interaction, $\overrightarrow{x_p}$, and either annihilation photon interaction, $\overrightarrow{x_0}$ or $\overrightarrow{x_1}$, in space assuming an 8 mm depth of interaction within a crystal for interactions with a time difference between $-$0.025 and 0.025 ns. Data is shown where the prompt gamma ray is the first photon detected (red) and where the prompt gamma ray is the second photon detected (blue) to visualize if there was a difference between the two types of series of interactions

Fig. 8

Photographs of an experiment used to measure the o-Ps lifetime of quartz-glass samples using the $_{}^{22}$Na sources from Spectrum Techniques. The $_{}^{22}$Na sources were suspended on a wire and measured by themselves (a). The quartz-glass samples were then placed around the $_{}^{22}$Na sources to measure the o-Ps lifetime of the quartz glass (b)

Fig. 9

Photographs of an experiment used to measure the quartz-glass o-Ps lifetime using $_{}^{68}$Ga. Drops of the $_{}^{68}$Ga solution were placed on each disk shown in (a). Another disk of the same material was then placed on top and the two disks were taped together as shown in (b)

Fig. 10

Histo-images of the axial view summed over all Y planes (a) and transaxial view summed over all Z planes (b) of the measurement shown in Fig. 9

Fig. 11

Measured lifetime spectrum of the quartz-glass samples with the $_{}^{22}$Na sources, the measured lifetime spectrum produced from the $_{}^{22}$Na sources themselves and the net quartz-glass spectrum

Fig. 12

Net time-difference spectra for the quartz glass and polycarbonate measurements with a $_{}^{22}$Na source. Fits are shown using Eq. (5)

Fig. 13

Time-difference spectra measured for a quartz-glass sample using four radioisotopes that emit a prompt gamma ray

Fig. 14

Bayes fit using Eq. (7) to quartz glass data with the contributions of the Ps lifetime components

Fig. 15

Pair plot of the posterior distributions for the parameters ${\tau }_3$, $B{R}_3$, $\sigma$ and $\mathrm{\Delta }$ for the $_{}^{124}$I quartz glass data

Fig. 16

Histo-images of the axial view summed over all Y planes (a) and transaxial view summed over all Z planes (b) of a uniform cylinder filled with an estimated initial activity of 73.3 MBq of $_{}^{82}$Rb. The dashed red lines denote the regions of interest for extracting Ps lifetime information

Fig. 17

Comparison of the time-difference spectra extracted from the uniform cylinder shown in Fig. 16 with the quartz-glass sample measured using $_{}^{82}$Rb. The various radii data are from the smallest to largest radii as shown in Fig. 16

Fig. 18

Bayesian fit result for the homogeneous $_{}^{82}$Rb cylinder with the three lifetime components