Detecting Gamma-Rays from PET Scanning (CIE A Level Physics)

• In the annihilation process, mass, energy and momentum are conserved
• The gamma-ray photons have an energy and frequency that is determined solely by the mass-energy of the positron-electron pair
• The energy of a photon is given by:

• The momentum of a photon is given by

• Where:
  • m_e = mass of the electron or positron (kg)
  • h = Planck's constant (J s)
  • f = frequency of the photon (Hz)
  • c = the speed of light in a vacuum (m s^–1)

• The patient lays stationary in a tube surrounded by a ring of detectors
• Images of slices of the body can be taken to show the position of the radioactive tracers
• The detector consists of two parts:
  • A crystal scintillator
  • A photomultiplier

Crystal scintillator

• When the gamma-ray (γ-ray) photon is incident on a crystal, an electron in the crystal is excited to a higher energy state
• As the excited electron travels through the crystal, it excites more electrons
• When the excited electrons move back down to their original state, the lost energy is transmitted as visible light photons

Photomultiplier

• The photons produced by the scintillator are very faint
• Therefore, they need to be amplified and converted to an electrical signal by a photomultiplier tube

PET scanner

Detecting gamma rays with a PET scanner

Creating an image from PET scanning

• The γ rays travel in straight lines in opposite directions when formed from a positron-electron annihilation
  • This is due to the conservation of momentum

• They hit the detectors in a line – known as the line of response
• The tracers will emit lots of γ rays simultaneously, and the computers will use this information to create an image
• The more photons formed at a particular point, the more tracer that is present in the tissue being studied, and this will appear as a bright point on the image
• An image of the tracer concentration in the tissue can be created by processing the arrival times of the gamma-ray photons