24.3 PET scanning
- Syllabus
- 9702–2028–2029
- Topic
- 24.3
- Level
- A2
Learning objectives
24.3.1A tracer is a substance containing radioactive nuclei that can be introduced• understand that a tracer is a substance containing radioactive nuclei that can be introduced into the body and is then absorbed by the tissue being studied24.3.2That a tracer that decays by β+ decay is used in positron emission• recall that a tracer that decays by β+ decay is used in positron emission tomography (PET scanning)24.3.3Annihilation occurs when a particle interacts with its antiparticle and that• understand that annihilation occurs when a particle interacts with its antiparticle and that mass–energy and momentum are conserved in the process24.3.4That, in PET scanning, positrons emitted by the decay of the tracer• 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 directions24.3.5The energy of the gamma-ray photons emitted during the annihilation of an• calculate the energy of the gamma-ray photons emitted during the annihilation of an electron-positron pair24.3.6The gamma-ray photons from an annihilation event travel outside the body and• understand that the gamma-ray photons from an annihilation event travel outside the body and can be detected, and an image of the tracer concentration in the tissue can be created by processing the arrival times of the gamma-ray photons
A radioactive tracer follows the tissue process being studied
A tracer is a substance containing radioactive nuclei that is introduced into the body and absorbed by the tissue or biological process being studied.
Its emitted radiation can be detected from outside the body, so the spatial distribution of tracer reveals where that labelled substance is taken up or metabolically active.
A useful tracer behaves chemically like the substance of interest, gives detectable radiation and has a half-life long enough for the scan but short enough to limit unnecessary dose.
The tracer is not merely the radiation: it is the administered radioactive substance whose uptake carries biological information.
PET uses a beta-plus-emitting tracer to create positrons inside the body
The PET tracer contains a radionuclide that undergoes β⁺ decay and emits a positron inside the tissue where the tracer has accumulated.
β+decay:ZAX→(AZ−1)Y++01e+νe
The positron is the antiparticle needed for the later electron-positron annihilation that produces detectable gamma photons.
PET does not inject a beam of free positrons and does not use β⁻ decay for this role: the administered tracer generates positrons by β⁺ decay in situ.
Particle-antiparticle annihilation conserves mass-energy and momentum
Annihilation occurs when a particle interacts with its antiparticle; their rest mass and any kinetic energy become energy of other particles, while total energy and total momentum are conserved.
electron+positron→gammaphoton+gammaphotone−+e+→γ+γ
If the electron-positron pair has negligible total momentum, one photon alone cannot leave zero final momentum. Two equal photons travelling in opposite directions give equal and opposite momenta.
Their combined rest energy 2mec² becomes photon energy (plus any initial kinetic energy). Matter has not vanished without accounting; its mass-energy has changed form.
Opposite directions follow from momentum conservation for an approximately stationary pair, not from energy conservation alone.
A PET positron annihilates with a tissue electron to produce two opposite gamma photons
- The β⁺ tracer decays in tissue and emits a positron. 2. The positron loses kinetic energy over a short distance. 3. It meets a tissue electron and the pair annihilates.
The electron and positron mass-energy becomes a pair of gamma-ray photons emitted in approximately opposite directions so that momentum is conserved.
Gamma photons are penetrating enough for many to leave the body and reach detectors around the patient; the scanner detects the paired event rather than the positron itself.
The two detected gamma photons are produced by later annihilation, not directly by β⁺ decay. The positron first travels and slows in tissue.
Each PET annihilation photon carries about 0.511 MeV
Etotal=2mec2foranapproximatelystationarye−e+pair
Momentum conservation gives two equal, opposite photons, so each photon receives half the total rest energy: Eγ=mec².
Eγ=(9.11×10⁻³¹)(3.00×10⁸)²=8.20×10⁻¹⁴ J.
Eγ=(8.20×10⁻¹⁴)/(1.60×10⁻¹⁹)=5.12×10⁵ eV=0.512 MeV (usually quoted as 0.511 MeV). Total photon energy is about 1.02 MeV.
Do not assign 2mec² to each photon. The two photons share the pair's total energy; initial kinetic energy is normally neglected in this syllabus calculation.
Coincident gamma arrival times locate PET events and map tracer concentration
A ring of detectors records pairs of gamma photons that leave the body and arrive nearly simultaneously at opposite detectors. Coincidence identifies them as one annihilation event.
The two hit detectors define a line of response on which the annihilation occurred. A difference in arrival times places the event closer to the detector reached first.
fordetectorseparationalongtheline:displacementfrommidpoints=cΔt/2
Processing many event lines and timing differences reconstructs event locations. Regions with more events contain a greater concentration/uptake of tracer and are displayed more strongly.
The PET image is primarily a functional map of tracer concentration or metabolic activity, not simply a direct map of tissue density.
One photon detection does not locate an event. Localization depends on paired coincidence geometry, and arrival-time difference refines position along that line.