explain that, in PET scanning, positrons emitted by the decay of the tracer annihilate when they interact with electrons in the tissue, producing a pair of gamma-ray photons travelling in opposite directions
Positron Emission Tomography (PET) is a medical imaging technique that exploits the
annihilation of positrons (\$e^{+}\$) emitted by a radioactive tracer. The tracer is
introduced into the patient’s body, where it accumulates in tissues of interest.
The key physical process is:
\$e^{+} + e^{-} \;\rightarrow\; \gamma + \gamma\$
When a positron encounters an electron (\$e^{-}\$) in the tissue, they annihilate,
producing a pair of gamma‑ray photons each with an energy of \$511\ \text{keV}\$.
Conservation of momentum requires the two photons to travel in (approximately)
opposite directions, i.e. at \$180^{\circ}\$ to each other.
Sequence of Events in a PET Scan
Administration of a biologically active tracer (e.g., \$^{18}\$F‑fluorodeoxyglucose).
Radioactive decay of the tracer nuclei by \$\beta^{+}\$ emission, releasing a positron.
Thermalisation of the positron in the surrounding tissue (loss of kinetic energy).
Annihilation with a nearby electron, producing two \$511\ \text{keV}\$ gamma photons.
Detection of the coincident photons by a ring of scintillation detectors surrounding the patient.
Reconstruction of the emission locations to form a three‑dimensional image of tracer distribution.
Key Quantities
Quantity
Symbol
Typical \cdot alue
Notes
Positron rest mass
\$m_{e}\$
\$9.11 \times 10^{-31}\ \text{kg}\$
Same as electron
Photon energy after annihilation
\$E_{\gamma}\$
\$511\ \text{keV}\$
Corresponds to \$m_{e}c^{2}\$
Angle between photons
\$\theta\$
\$180^{\circ}\$ (ideal)
Small deviations due to residual positron momentum
Typical tracer half‑life
\$t_{1/2}\$
\$\sim 110\ \text{min}\$ for \$^{18}\$F
Determines timing of scan
Why PET Uses Gamma Photons Instead of X‑rays
Gamma photons from annihilation have a well‑defined energy (\$511\ \text{keV}\$), allowing precise energy discrimination.
The simultaneous detection of two photons in opposite directions provides a built‑in localisation method (coincidence detection).
Unlike conventional X‑ray imaging, PET directly maps metabolic activity rather than just anatomical structure.
Suggested diagram: Schematic of positron annihilation showing a positron (\$e^{+}\$) meeting an electron (\$e^{-}\$) and the emission of two \$511\ \text{keV}\$ gamma photons travelling in opposite directions, with a surrounding detector ring.