PET scanning — practice questions

1. Identify the principle: The total rest mass of the positron and electron is converted into the energy of two gamma photons, governed by E = mc².
2. Calculate total mass: The total mass annihilated is the sum of the electron's mass and the positron's mass. m_total = m_electron + m_positron = 2 × (9.11 × 10⁻³¹ kg) = 1.822 × 10⁻³⁰ kg.
3. Calculate total energy in Joules: Substitute the total mass into the mass-energy equivalence formula. E_total = m_total × c² = (1.822 × 10⁻³⁰ kg) × (3.00 × 10⁸ m s⁻¹)² = 1.6398 × 10⁻¹³ J.
4. Calculate energy per photon in Joules: This total energy is shared equally between the two gamma photons. E_photon = E_total / 2 = (1.6398 × 10⁻¹³ J) / 2 = 8.199 × 10⁻¹⁴ J.
5. Convert energy to eV: To express the energy in electron-volts (eV), divide the energy in Joules by the elementary charge, e. E_photon (eV) = (8.199 × 10⁻¹⁴ J) / (1.60 × 10⁻¹⁹ J/eV) = 512,437.5 eV.
6. Convert to MeV: Convert from eV to Mega-electron-volts (MeV) by dividing by 10⁶. E_photon (MeV) = 512,437.5 eV / 10⁶ = 0.512 MeV.

Final Answer: The energy of each gamma photon is 0.512 MeV (to 3 significant figures).

1. Origin Localisation: When two gamma rays are detected simultaneously by detectors on opposite sides of the patient, the computer can deduce that the annihilation event must have occurred somewhere along a straight line connecting these two detectors. This line is known as the Line of Response (LOR).
2. Eliminating Ambiguity: If the gamma rays were emitted in random directions, it would be impossible for the scanner to determine the origin of the annihilation event from a single detection. The 180-degree relationship provides a direct geometric constraint.
3. Spatial Mapping: By collecting millions of these LORs from different angles as the detectors surround the patient, the computer can use reconstruction algorithms to precisely triangulate the points of highest tracer concentration. This allows for the creation of a clear, 3D map of metabolic activity.