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

1. Production of X-rays

X-rays are produced when high‑energy electrons are decelerated or when they strike a high‑Z target material. Two main mechanisms are:

• Bremsstrahlung (braking radiation): Electrons are deflected by the Coulomb field of nuclei, losing kinetic energy that is emitted as a continuous spectrum of X‑ray photons. The maximum photon energy equals the initial electron kinetic energy: \$E_{\text{max}} = eV\$, where \$V\$ is the accelerating voltage.
• Characteristic X-rays: When an inner‑shell electron is ejected, an outer‑shell electron transitions to fill the vacancy, emitting a photon with energy equal to the difference between the two energy levels: \$E = E{\text{inner}} - E{\text{outer}}\$. These lines are discrete and depend on the target element.

The X‑ray tube consists of a cathode that emits electrons via thermionic emission, an accelerating anode (usually tungsten), and a vacuum chamber. The accelerating voltage is typically 30–150 k \cdot for diagnostic imaging.

2. X-ray Energy and Applications

X-ray photons have energies ranging from a few ke \cdot to several hundred keV. Their penetration ability depends on energy and material density. Typical applications include:

3. Safety and Radiation Protection

Radiation safety follows the ALARA principle (As Low As Reasonably Achievable). Key measures include:

1. Shielding with lead or concrete to attenuate X-rays.
2. Collimation to restrict the beam to the area of interest.
3. Use of pulsed or gated exposure to reduce dose.
4. Monitoring of dose with dosimeters and maintaining cumulative exposure below regulatory limits.

Gamma-ray Photons from Annihilation Events and PET Imaging

1. Positron Emission and Annihilation

In positron emission tomography (PET), a radiotracer containing a positron‑emitting isotope (e.g. \$^{18}\$F) is injected into the body. The positron (\$e^+\$) travels a short distance before encountering an electron (\$e^-\$) and annihilating:

\$e^+ + e^- \;\rightarrow\; \gamma + \gamma\$

Each gamma photon carries an energy of \$511 \text{ keV}\$ (half the rest mass energy of the electron/positron pair). The two photons are emitted approximately 180° apart.

2. Detection of Gamma Photons

Detectors surrounding the patient convert gamma photons into electrical signals. Common detector technologies include:

• Scintillation crystals (e.g. LSO, BGO) coupled to photomultiplier tubes.
• Solid‑state detectors (e.g. silicon photomultipliers).

Coincidence detection requires that two detectors record photons within a narrow time window (typically \$10\,\text{ns}\$). This establishes a line of response (LOR) along which the annihilation event occurred.

3. Image Reconstruction from Arrival Times

Time‑of‑flight (TOF) PET adds the difference in arrival times of the two photons to localise the event along the LOR. The position \$x\$ along the LOR is given by:

\$x = \frac{c\,\Delta t}{2}\$

where \$c\$ is the speed of light and \$\Delta t\$ is the measured time difference. Processing the arrival times for many events allows reconstruction of the tracer concentration distribution using algorithms such as filtered back‑projection or iterative maximum‑likelihood expectation‑maximisation.

1. Collect coincidence events and record arrival times.
2. Calculate the position along each LOR using the TOF equation.
3. Bin events into a 3D histogram of tracer activity.
4. Apply reconstruction algorithm to generate an image.

4. Applications and Advantages

• Oncology: detection of malignant lesions via increased glucose uptake (FDG PET).
• Neurology: mapping brain metabolism and neurotransmitter systems.
• Cardiology: assessing myocardial perfusion and viability.
• Research: studying pharmacokinetics and drug distribution.

Key advantages of PET include high sensitivity, quantitative capability, and the ability to combine with CT or MRI for anatomical localisation.