Introduction to PET Scans Revision Notes | A Level AQA Physics

1. Why PET Scans Are Different

Most medical imaging tells you what a structure looks like. PET scanning tells you what it is doing. That distinction is what makes PET one of the most powerful diagnostic tools in modern medicine.

An X-ray or CT scan reveals anatomy — the shape and density of tissues. A PET scan reveals metabolic activity: which regions of the body are consuming glucose rapidly, which cells are dividing unusually fast, and where blood flow is abnormal. This makes it invaluable for detecting cancer, assessing heart disease, and diagnosing neurological conditions such as Alzheimer's disease.

To understand how PET achieves this, you need to follow the physics from the nucleus outward — from a radioactive decay event all the way to a reconstructed image on a screen. That chain of events is what this lesson unpacks.

2. The Physics at the Heart of PET: Positron Emission and Annihilation

PET scanning begins with a specific type of radioactive decay called positron emission (also written as $\beta^+$ decay). In this process, a proton-rich nucleus converts a proton into a neutron, releasing a positron — the antimatter counterpart of an electron. The positron has the same mass as an electron but carries a positive charge of $+e$.

Once emitted, the positron travels only a very short distance through tissue — typically 1–2 mm — before it loses kinetic energy and encounters an ordinary electron. At that point, something remarkable happens: the two particles annihilate each other. Their combined mass-energy is converted entirely into electromagnetic radiation.

Conservation of energy and conservation of momentum both apply here. Because the positron and electron are essentially at rest at the moment of annihilation, their total momentum is approximately zero. To conserve momentum, the energy cannot be released as a single photon — it must be released as two photons travelling in exactly opposite directions (i.e. at 180° to each other).

These two 0.511 MeV gamma photons are called annihilation radiation. Their fixed energy and back-to-back geometry are the physical signatures that the PET scanner is designed to detect. Every annihilation event produces this same pair, regardless of where in the body it occurs — which is what makes the imaging geometry so precise.

3. Radiotracers: Getting the Radioactivity to the Right Place

The positron-emitting radionuclide cannot be injected on its own — it needs to be attached to a biologically active molecule that the body will naturally transport to the tissue of interest. This combination of molecule and radionuclide is called a radiotracer.

The most widely used radiotracer is fluorodeoxyglucose (FDG), which is a glucose analogue labelled with fluorine-18 ($^{18}$F). Because cancer cells and active brain tissue consume glucose at a higher rate than surrounding tissue, FDG accumulates preferentially in those regions. The $^{18}$F then undergoes $\beta^+$ decay, producing the annihilation photons that the scanner detects.

• Fluorine-18 ($^{18}$F): half-life approximately 110 minutes — used in FDG for oncology and neurology
• Carbon-11 ($^{11}$C): half-life approximately 20 minutes — used in neurotransmitter studies
• Oxygen-15 ($^{15}$O): half-life approximately 2 minutes — used in blood flow studies
• Nitrogen-13 ($^{13}$N): half-life approximately 10 minutes — used in cardiac perfusion imaging

The choice of radionuclide involves a careful balance. The half-life must be long enough for the tracer to be synthesised, transported to the patient, and administered — but short enough that the patient's radiation dose is minimised and the activity falls to a safe level quickly after the scan. This is why $^{18}$F with its 110-minute half-life is so practical: it gives a workable window for clinical use without exposing the patient to prolonged radiation.

A short half-life also means the radionuclide must be produced close to the scanner, typically in an on-site or nearby cyclotron. This is a significant logistical and financial consideration for hospitals using PET.

4. How the PET Scanner Works: Coincidence Detection

Picture a ring of gamma-ray detectors surrounding the patient. When an annihilation event occurs inside the body, two 0.511 MeV photons shoot outward in opposite directions. If both photons reach detectors on opposite sides of the ring at almost exactly the same time, the scanner records a coincidence event.

The line connecting the two detectors that fired simultaneously is called the line of response (LOR). The annihilation must have occurred somewhere along that line. By recording thousands of coincidence events from many different detector pairs and angles, the scanner can reconstruct a three-dimensional map of where annihilations are occurring — and therefore where the radiotracer has accumulated.

The time window for coincidence is typically a few nanoseconds. Any two detector signals arriving within this window are treated as originating from the same annihilation event. Signals outside this window are discarded as random or scattered events, which significantly reduces background noise in the image.

5. Image Reconstruction and What the Scan Shows

The raw data from a PET scan is a large set of lines of response. Mathematical reconstruction algorithms — similar in principle to those used in CT scanning — process these lines to produce a three-dimensional image showing the distribution of radiotracer concentration throughout the body.

Regions with high tracer uptake appear as bright areas (often shown in red or yellow on a colour scale). A tumour, for example, typically shows as a bright hotspot because its cells are metabolically hyperactive and consuming glucose rapidly. A region of the brain affected by Alzheimer's disease, by contrast, shows as a dark area of reduced activity.

In clinical practice, PET images are almost always fused with CT or MRI images. The PET scan provides functional information (metabolic activity), while the CT or MRI provides anatomical detail (precise location and structure). This combination allows clinicians to say not only that there is abnormal activity, but exactly where in the body it is located.

6. Comparing PET with Other Imaging Techniques

AQA examiners frequently ask you to compare imaging modalities. The key principle is that different techniques provide different types of information, and each has specific advantages and limitations.

The critical comparison point for exam answers is that PET detects functional changes, which often precede structural changes. A tumour may be metabolically active and detectable by PET before it is large enough to appear on a CT scan. This makes PET particularly valuable for early diagnosis and for monitoring treatment response.

7. Worked Example: Applying the Physics to an Exam Question

Exam questions on PET often ask you to apply conservation laws to the annihilation process, or to justify the choice of radionuclide. Here is a structured walkthrough of a typical multi-part question.

Worked example: Annihilation Radiation: Energy and Momentum Conservation

A positron emitted during $\beta^+$ decay comes to rest in tissue and annihilates with a stationary electron. (a) State the number and type of photons produced. (b) Calculate the energy of each photon in joules. (c) Explain why the photons must be emitted in opposite directions.

1. Two gamma photons are produced. — Positron-electron annihilation converts the rest-mass energy of both particles into electromagnetic radiation. A single photon cannot be produced because momentum would not be conserved (see step 3).
2. $E = m_e c^2$ $m_e = 9.11 \times 10^{-31}$ kg, $c = 3.0 \times 10^8$ m/s $c^2 = 3.0 \times 10^8 \times 3.0 \times 10^8 = 9.0 \times 10^{16}$ m$^2$ s$^{-2}$ $E = 9.11 \times 10^{-31} \times 9.0 \times 10^{16}$ $E = 8.20 \times 10^{-14}$ J — Each photon carries the rest-mass energy of one particle (electron or positron). Note: the total energy released is $2 \times 8.20 \times 10^{-14}$ J = $1.64 \times 10^{-13}$ J, split equally between the two photons. This corresponds to 0.511 MeV per photon.
3. Before annihilation: both particles at rest, so total momentum $p_{total} = 0$. After annihilation: momentum of photon 1 + momentum of photon 2 = 0. Therefore: $\vec{p}_1 = -\vec{p}_2$ — For the vector sum of the two photon momenta to equal zero, they must have equal magnitudes and opposite directions — i.e. they travel at 180° to each other. This is a direct consequence of conservation of momentum. [B1] for stating total initial momentum is zero; [B1] for concluding photons must travel in opposite directions.
4. $E = 8.20 \times 10^{-14}$ J $\div$ $1.6 \times 10^{-13}$ J/MeV $= 0.5125$ MeV $\approx 0.511$ MeV — This matches the known value of 0.511 MeV for annihilation photons, confirming the calculation is correct.

Answer: (a) Two gamma photons. (b) Each photon has energy $8.20 \times 10^{-14}$ J (0.511 MeV). (c) Because the positron and electron are at rest before annihilation, total momentum is zero. Conservation of momentum requires the two photons to have equal and opposite momenta, so they must travel in exactly opposite directions (180° apart).

8. Exam Technique: Scoring Full Marks on PET Questions

PET questions at A-level test three distinct skills: recall of the physical process, application of conservation laws, and evaluation of the technique's clinical value. Each requires a different approach.

For describe questions, work through the sequence in order: decay produces positron → positron annihilates with electron → two 0.511 MeV photons emitted at 180° → coincidence detection defines line of response → reconstruction produces image. Each arrow in that chain is a potential mark.

For explain questions about why photons travel in opposite directions, always anchor your answer to conservation of momentum. State that the particles are at rest (so total momentum is zero), then conclude that the two photons must have equal and opposite momenta. Saying only "they go in opposite directions" without the momentum argument will not earn the explanation mark.

Every spec requirement for PET scanning connects back to one central idea: the fixed, predictable geometry of annihilation radiation is what makes precise, non-invasive functional imaging possible. Keep that physical principle at the centre of every answer you write.