Colloquium: Positronium physics and biomedical applications

Positronium is the simplest bound state, built of an electron and a positron. Studies of positronium in vacuum and its decays in medium tell us about quantum electrodynamics (QED) and about the structure of matter and biological processes of living organisms at the nanoscale, respectively. Spectroscopic measurements constrain our understanding of QED bound state theory. Searches for rare decays and measurements of the effect of gravitation on positronium are used to look for new physics phenomena. In biological materials positronium decays are sensitive to the intermolecular and intramolecular structure and to the metabolism of living organisms ranging from single cells to human beings. This leads to new ideas of positronium imaging in medicine using the fact that during positron emission tomography (PET) as much as 40% of positron annihilation occurs through the production of positronium atoms inside the patient’s body. A new generation of the high sensitivity and multiphoton total-body PET systems opens perspectives for clinical applications of positronium as a biomarker of tissue pathology and the degree of tissue oxidation.

Figure 1

Diagram of the $e^{+}{e}^{-}$ annihilation processes in matter. The scheme indicates annihilations to $2\gamma$ and $3\gamma$ only; $f_{\mathrm{d}}$ and $f_{\mathrm{Ps}}$ indicate fractions of direct annihilations and annihilations via positronium formation, respectively. In biological materials, a $f_{\mathrm{d}}/f_{\mathrm{Ps}}$ ratio ranging between about $3/2$ ([96]; [136]) and about $1/4$ ([30]) has been reported. Note that $f_{\mathrm{d}}/f_{\mathrm{Ps}}$ ratios smaller than 1 are common in mesoporous materials; see [85]. The total decay rate is due to the positronium self-annihilation (${\lambda }_0$), pickoff processes (${\lambda }_{\mathrm{pick}\mathrm{off}}$), ortho-para conversion reactions (${\lambda }_{\mathrm{conv}}$), and other chemical processes such as oxidation (${\lambda }_{\text{other}}$): $\lambda ={\lambda }_0+{\lambda }_{\mathrm{pick}\mathrm{off}}+{\lambda }_{\mathrm{conv}}+{\lambda }_{\text{other}}$. In water ${\lambda }_0^p=7990.9{\mathrm{\mu }\mathrm{s}}^{-1}\gg {\lambda }_{\mathrm{pick}\mathrm{off}}=512.8{\mathrm{\mu }\mathrm{s}}^{-1}\gg {\lambda }_{\mathrm{conv}}+{\lambda }_{\text{other}}\approx 27{\mathrm{\mu }\mathrm{s}}^{-1}({\mathrm{O}}_2\text{saturated})>{\lambda }_0^0=7.0401{\mathrm{\mu }\mathrm{s}}^{-1}$. In mesoporous silica ${\lambda }_0^p=7990.9{\mathrm{\mu }\mathrm{s}}^{-1}\gg {\lambda }_{\mathrm{conv}}\approx 25{\mathrm{\mu }\mathrm{s}}^{-1}({\mathrm{O}}_2\mathrm{at}1\mathrm{atm})>{\lambda }_0^0=7.0401{\mathrm{\mu }\mathrm{s}}^{-1}>{\lambda }_{\mathrm{pick}\mathrm{off}}\approx 1{\mathrm{\mu }\mathrm{s}}^{-1}$. Explanation is given in the text.

Figure 2

Left panel: scanning electron microscope picture of the surface of a silicon positron-to-positronium converter with oxidized tunable nanochannels. From [153]. Right panel: illustration of positron thermalization in mesoporous material. Ionization places on a thermalization path are shown. They are composed of electrons ($-$), ions ($+$), and positrons (blue line). In the upper example a positron thermalizes, producing free electrons that quickly thermalize. Next positronium is formed by recombination with a thermalized electron and Ps is localized in the void. After bouncing between the walls in the void (black arrows), it leaves the material. In the lower example a thermalized positron scatters in the material and annihilates directly into two photons (red arrows).

Figure 3

(a) Decay of a ${}^{44}\mathrm{Sc}$ isotope; see Eq. (13). (b) Illustration of the basic processes leading to the annihilation of a positron in the intramolecular voids of a hemoglobin molecule. The most probable ways of annihilation are direct annihilation into two photons (yellow solid arrows), with the positron originating from the ${}^{44}\mathrm{Sc}$ decay, self-annihilation of $p$-Ps (green dotted arrows), self-annihilation of $o$-Ps (blue dashed arrows), $o$-Ps pickoff process (violet dotted arrows), and $o$-Ps conversion on an ${\mathrm{O}}_2$ molecule (red dashed arrows). The distances and the size of the atoms are shown to scale, with the diameter of positronium twice that of hydrogen.

Figure 4

Schematic of Compton scattering of two photons originating from $p$-Ps annihilation. Owing to the momentum conservation ($\overrightarrow{k_1}=-\overrightarrow{k_2}$), the annihilated photons propagate back to back along the same axis in the $p$-Ps rest frame. ${\theta }_1$ and ${\theta }_2$ denote the scattering angles, ${\eta }_1$ and ${\eta }_2$ denote the angles between the scattering planes and the polarization directions ${\overrightarrow{\epsilon }}_1$ and ${\overrightarrow{\epsilon }}_2$, respectively, and $\phi$ indicates the relative angle between the scattering planes.

Figure 5

Positronium imaging of HER2-positive cancer cells. (a) The HER2 receptor (epidermal growth factor receptor) is scarcely expressed on the surface of healthy cells and significantly (100 times or more) overexpressed in cancer cells [such as breast cancer ([256]; [217])]. Different colors represent combinations of different units forming dimmers of the HER2 molecule. (b) Trastuzumab (herceptin), a humanized monoclonal antibody that binds to HER2, is labeled as a ${}^{44}\mathrm{Sc}$ isotope. (c) ${}^{44}\mathrm{Sc}$ isotope emits a prompt $\gamma$ and a positron ($e^{+}$) to form a positronium atom. (d) Positronium atoms annihilate in cells (with highest abundance in cancer), on their surface and within cell organelles (cell membranes and cytosol nuclei). Environmental factors like temperature, water content, and other specific tissue features like chemical and molecular composition determine ${\tau }_{o\text{−}\mathrm{Ps}}$ in the diagnosed tissue.

Figure 6

Left image: scheme of the example of total-body PET for the positronium and quantum entanglement imaging showing an axial cross section of the tomograph design composed of two detection layers. The single detection module consists of a scintillator and wavelength-shifting strips read out by silicon photomultiplier matrices. Here elements are not presented to scale. Dashed red arrows indicate example lines of response originating from $e^{+}{e}^{-}$ annihilation. $2\gamma$ originating from the brain scatter twice in the plastic scintillator and are shown as an example of an event usable for quantum entanglement tomography discussed in Sec. 6d. Violet dotted arrows indicate $3\gamma$ decay, and dashed red arrows together with solid black arrow indicate annihilation and the prompt photon useful for positronium imaging discussed in Sec. 6b. Superimposed charts indicate the sensitivity (in arbitrary units) along the axial field of view (AFOV). Right panel: sensitivity for the $2\gamma$ positronium imaging (2 times annihilation $\gamma$ plus a prompt photon) compared to the sensitivity for the standard $2\gamma$ PET imaging. Results for lutetium-yttrium oxyorthosilicate crystal (LYSO) PET and plastic PET are shown as a function of the scanner’s AFOV. The sensitivity gain is shown with respect to the 20 cm AFOV LYSO PET (indicated with a horizontal blue dotted line). From [178].

Figure 7

Comparison of partial pressure of oxygen molecules ($p{\mathrm{O}}_2$) in healthy and cancer tissues. The horizontal axis indicates a tissue type (1–12) explained beneath the graph. The right axes refer to water and indicate the concentration of oxygen ($C_{{\mathrm{O}}_2}$), the $o$-Ps annihilation rate ${\lambda }^o$ in water, and the change of the $o$-Ps mean lifetime $\mathrm{\Delta }t$ due to the concentration of oxygen molecules dissolved in water. Normal ${p\mathrm{O}}_2$ for healthy tissues (red circles) and hypoxia in cancer tissues (black squares) are shown based on experimental data summarized and reviewed in medians that do not show real patient variability ([255]; [161]; [241]; [254]). For head and neck tumors, sarcoma and normal subcutaneous tissue data were compiled from the studies by [195] and [26]. For a kidney and melanoma there were separate studies ([144]; [145]). The tissue type is numbered according to the increasing partial pressure difference between healthy and cancerous tissue, which is indicated by the blue dashed line.

Figure 8

Distribution of the angle $\phi$ between scattering planes of the photons emitted in $p\text{−}\mathrm{Ps}\to 2\gamma$ when the photons are each scattered at $\theta \sim 82°$. For definitions of these angles see Fig. 4. The black solid curve corresponds to the photon pair being entangled, the dashed blue curve relates to independent Compton interaction of the two photons, and the red dotted line indicates when the photon polarizations are uncorrelated, as when the photons originate from two different $p$-Ps decays.