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

Production and Use of X‑rays

What are X‑rays?

X‑rays are a form of high‑energy electromagnetic radiation. Think of them as invisible “photons” that can pass through soft tissues but are absorbed by denser materials like bone. They are produced when fast electrons collide with a metal target and suddenly lose energy.

How are X‑rays produced?

In a typical X‑ray tube:

  1. Electrons are emitted from a heated filament.

  2. They are accelerated by a high voltage (kV) towards a metal target (usually tungsten).

  3. When the electrons hit the target, they decelerate rapidly, emitting X‑ray photons: \$E = h\nu\$.

  4. The X‑rays travel through the body and are recorded on a detector.

Positron Emission Tomography (PET) – A Special Kind of X‑ray Imaging

Unlike conventional X‑ray imaging, PET uses gamma photons produced when a positron (the antimatter counterpart of an electron) annihilates with an electron in the body. The annihilation event emits two gamma photons that travel in almost opposite directions.

Step 1: Radioactive Tracer

A small amount of a radioactive isotope (e.g., \$^{18}\$F) is attached to a biologically active molecule (like glucose). This tracer is injected into the patient and distributes according to the molecule’s natural behaviour.

Step 2: Positron Emission and Annihilation

The isotope decays: \$^{18}\text{F} \rightarrow ^{18}\text{O} + e^+ + \nu_e\$. The emitted positron travels a short distance (~1 mm) before it meets an electron. They annihilate: \$e^+ + e^- \rightarrow \gamma + \gamma\$. Each gamma photon carries an energy of 511 keV.

Step 3: Gamma Photon Detection

Surrounding the patient is a ring of detectors (scintillators + photomultipliers). When a gamma photon hits a detector, it creates a flash of light that is converted into an electrical pulse. Two detectors that record photons simultaneously are said to be in “coincidence.”

Step 4: Image Reconstruction

By recording many coincidence events, the system can determine the line along which the annihilation occurred. Using mathematical algorithms (filtered back‑projection or iterative reconstruction), the computer builds a 3‑D map of tracer concentration. The result is an image that shows where the tracer (and thus the biological process) is most active.

Exam Tips

  • Remember the key equation for annihilation: \$e^+ + e^- \rightarrow \gamma + \gamma\$.

  • Know the typical energy of PET gamma photons: 511 keV.

  • Understand the difference between coincidence detection and single photon detection.

  • Be able to explain why the tracer’s concentration can be visualised as an image.

  • Use the analogy of a “detective” chasing footprints (gamma photons) to remember the concept of coincidence.

  • When drawing a PET scanner, label the ring of detectors and the patient’s body.

Quick Quiz

  1. What is the energy of each gamma photon produced in a PET annihilation event? 🕵️‍♂️

  2. Why do PET detectors need to be placed in a ring around the patient? 🔄

  3. Explain in one sentence why the tracer’s concentration can be mapped to an image. 📈

Glossary

TermDefinition
X‑rayHigh‑energy photon used to image internal structures.
PositronAntimatter counterpart of the electron.
AnnihilationProcess where a particle and its antiparticle destroy each other, emitting photons.
Coincidence DetectionSimultaneous detection of two photons that originated from the same annihilation event.