PET for students and teachers: physics, biology and a glossary

Few medical machines connect as directly to a physics syllabus as PET. It uses radioactive decay, antimatter, mass-energy equivalence, particle detection and a bit of mathematics to make a picture of what tissue is doing. Here, PET stands for positron emission tomography, a medical imaging method, and has nothing to do with animals. This page is written for upper secondary and early undergraduate level, and is organised so students can read it alone and teachers can lift sections for a lesson.

The page explains concepts only. It is not medical advice, and it says nothing about any individual person's scan. For patient-facing material, see what to expect on scan day. For more depth on the physics, see the physics of positron emission and annihilation.

For students

What is a positron?

A positron is the antiparticle of the electron: a particle equivalent to the electron but with a positive charge. In 1928 Paul Dirac formulated a relativistic quantum theory whose equation gave solutions he interpreted as such a particle, which experiments later confirmed (NobelPrize.org: Paul A.M. Dirac, Facts). Antimatter sounds exotic, yet some radioactive nuclei emit positrons as they decay. Hospitals use those nuclei every day.

Antimatter in a clinic

The quantities are tiny, and a positron does not last. Once it is emitted, it rapidly annihilates with an electron, producing two 511 keV gamma rays travelling in opposite directions (Pratt and colleagues, Nature Biomedical Engineering, 2023). There is no stored antimatter in a scanner. Positrons are made inside the patient's body by the tracer's decay, each one existing only for a very short time.

Where E = mc squared comes in

Annihilation is a textbook case of mass turning into energy. NIST's CODATA value for the electron's mass-energy equivalent is 0.51099895 MeV, which is about 511 keV (NIST: electron mass energy equivalent in MeV). That is the energy in E = mc squared for a single electron mass. Imagine a positron and electron that are almost at rest. Their combined rest energy is about 1.022 MeV (two lots of 511 keV), and it appears as two photons of 511 keV each. The mass does not vanish into nothing: it becomes the energy of the photons, which is why the number 511 is the same for every PET isotope. In reality the pair is not perfectly at rest, so this is the simplified picture.

Why detectors form a ring

The two photons head in opposite directions, so if two detectors on opposite sides of the patient fire at nearly the same moment, the annihilation probably happened somewhere along the line between them. Pratt and colleagues describe detection in coincidence, about 3.5 nanoseconds in the system they discuss, and call the virtual line connecting the two detectors a line of response (Pratt et al., 2023). A ring surrounding the body catches pairs from all directions. It is the pairs arriving together that define the lines of response.

Why the isotopes have short half-lives

Half-life is the time for half of the radioactive nuclei in a sample to decay. The same paper lists fluorine-18 at 109.7 minutes, carbon-11 at 20.36 minutes, nitrogen-13 at 9.96 minutes, oxygen-15 at 2.04 minutes and gallium-68 at 68 minutes. Short half-lives mean the radioactivity fades within hours. For fluorine-18, five half-lives is about 9 hours, after which roughly 3 percent remains (that is simple arithmetic, not a clinical figure). Imaging centres plan around this, and RadiologyInfo.org notes the tracer decays quickly, so a late arrival may require rescheduling (RadiologyInfo.org). The trade-off is logistics, because timing of delivery and appointments matters.

From lines to a picture

A scan produces a huge number of lines of response. Tong, Alessio and Kinahan explain that all the line integrals at one angle form a projection, and that collecting projections for all angles gives a sinogram. Mathematical algorithms, either analytic such as filtered backprojection or iterative such as OSEM, then reconstruct the cross-sectional distribution of the tracer. Iterative methods work by a forward project, compare, backproject and adjust cycle until the estimate settles (Tong et al., Imaging in Medicine, 2010). Filtered backprojection is also widely used in CT; for how the two scanners are combined, see PET-CT and PET-MRI.

The biology: why FDG

FDG is a glucose analogue, so it tends to gather where cells use a lot of glucose. An FDG scan is therefore a map of activity. That map is useful in cancer, but inflammation can also look active, which is why doctors read scans with other information (PET in cancer care).

For teachers

The topic fits several curriculum strands at once: nuclear decay and half-life, mass-energy equivalence, particle-antiparticle pairs, conservation laws, detector coincidence and basic tomography. It also supports cross-curricular links to biology (glucose metabolism) and ethics (risk and benefit). Where your syllabus differs, adapt the sequence.

A suggested lesson structure

The following outline assumes a lesson of roughly 50 to 60 minutes. It is a suggestion from the editors, not a tested plan, so adjust the timings to your class.

1. Starter (5 minutes): ask what antimatter is and whether it could be useful. Collect ideas without correcting them.
2. Core idea (15 minutes): positron emission, annihilation, 511 keV and the E = mc squared accounting.
3. Activity (15 minutes): students act as detectors, marking lines of response on a printed ring, then see how crossing lines locate a source.
4. Reconstruction (10 minutes): sum the lines on a small grid to show how repeated projections build up an image.
5. Discussion (10 minutes): use the questions below, and close with a one-sentence summary from each student.

Be careful with two common misconceptions. First, a scanner does not contain antimatter. Second, the picture is not a photograph of the tracer, because it is computed from detection events. Both are good points for discussion.

Discussion questions

1. Why would a positron emitter produce two photons of equal energy, and what conservation laws help explain their directions?
2. If a tracer's half-life were two days instead of under two hours, what would change for patients, staff and hospitals?
3. Why is detecting two photons at once more informative than detecting one, and what does the scanner learn from the pair?
4. FDG gathers in tissues that use lots of glucose. Which healthy organs might also appear bright, and why does that matter for interpretation?
5. Medical imaging involves a small amount of radiation to gain information. How should a doctor and a patient weigh benefit against risk, and who should decide? (See radiation dose in context.)

Glossary

Key terms used in PET physics and imaging

Term	Meaning
Positron	The antiparticle of the electron: equivalent to the electron but with a positive charge.
Antimatter	Matter made of antiparticles, such as positrons.
Annihilation	The event in which a positron meets an electron and their mass is converted into photons.
Photon	A particle of electromagnetic radiation.
Gamma ray	A high-energy photon. PET detects the 511 keV pair produced by annihilation.
keV	Kiloelectronvolt, a unit of energy equal to 1000 electronvolts.
Radioisotope	A form of an element whose nucleus is unstable and decays.
Half-life	The time taken for half of the radioactive nuclei in a sample to decay.
Radiotracer	A molecule carrying a radioactive label, used to follow a process in the body.
FDG	Fluorodeoxyglucose, a glucose analogue labelled with fluorine-18.
Detector ring	The ring of detectors surrounding the patient that registers incoming photons.
Coincidence	Two detections within a very short time window, suggesting a common source.
Line of response	The line joining two detectors that registered a coincidence.
Sinogram	A data display that collects projections for all angles as a function of position and angle.
Tomography	Imaging in cross-sectional slices.
Image reconstruction	The calculation that turns detection data into an image of the tracer distribution.
Filtered backprojection	An analytic reconstruction method that filters each projection and then projects it back.
OSEM	Ordered subsets expectation maximisation, an iterative reconstruction method.
Time of flight	Using the arrival-time difference of the two photons to narrow the position along the line of response.
SUV	Standardised uptake value, a normalised measure of uptake used in reports.

The short version

PET links nuclear decay, antimatter and mass-energy equivalence to a practical medical image. A positron annihilates with an electron, two 511 keV photons are detected in coincidence, and reconstruction turns many lines of response into a map of tracer. Teachers can use it to join physics, biology and ethics in a single lesson.