OCR A Level Physics

Revision Notes

6.12.3 PET Scans

Test Yourself

Positron Emission Tomography (PET) Scanning

  • Positron Emission Tomography (PET) is defined as:

A type of nuclear medical procedure that images tissues and organs by measuring the metabolic activity of the cells of body tissues

  • In PET scanning, a beta-plus emitting radioactive tracer is used in order to stimulate positron-electron annihilation to produce gamma photons
    • These are then detected using a ring of gamma cameras

Principles of PET Scanning

Before the scan

  • The patient is injected with a beta-plus emitting isotope, usually fluorine-18 (F-18)

During the scan

  • The part of the body being studied is surrounded by a ring of gamma cameras
  • The positrons from the F-18 nuclei annihilate with electrons in the patient
  • The annihilation of a positron and an electron produces two identical gamma photons travelling in opposite directions
  • The delay time between these two gamma ray photons is used to determine the location of the annihilation due to the F-18 tracer
    • Photons that do not arrive within a nanosecond of each other are ignored, since they cannot have come from the same point

After the scan

  • Computer connected to the gamma cameras detect the signal and an image is formed by the computer

Detecting Gamma Rays, downloadable AS & A Level Physics revision notes

Detecting gamma rays with a PET scanner

Annihilation

  • When a positron is emitted from a tracer in the body, it travels less than a millimetre before it collides with an electron
  • The positron and the electron will annihilate, and their mass becomes pure energy in the form of two gamma rays which move apart in opposite directions
  • Annihilation doesn’t just happen with electrons and positrons, annihilation is defined as:

When a particle meets its equivalent antiparticle they are both destroyed and their mass is converted into energy

  • As with all collisions, the mass, energy and momentum are conserved

The Process of Annihilation, downloadable AS & A Level Physics revision notes

Annihilation of a positron and electron to form two gamma-ray photons

  • The gamma-ray photons produced have an energy and frequency that is determined solely by the mass-energy of the positron-electron pair
  • The energy E of the photon is given by

E = hf = mec2

  • The momentum p of the photon is given by

Calculating Energy of Gamma-Ray Photons equation 1

  • Where:
    • me = 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 s1)

Worked example

Fluorine-18 decays by β+ emission. The positron emitted collides with an electron and annihilates producing two γ-rays.

(a) Calculate the energy released when a positron and an electron annihilate.

(b) Calculate the frequency of the γ-rays emitted.

(c) Calculate the momentum of one of the γ-rays.

Part (a)

Step 1: Write down the known quantities

    • Mass of an electron = mass of a positron, me = 9.11 × 10–31 kg
    • Total mass is equal to the mass of the electron and positron = 2me

Step 2: Write out the equation for mass-energy equivalence

E = mec2

Step 3: Substitute in values and calculate energy E

E = 2 × (9.11 × 10-31) × (3.0 × 108)2 = 1.6 × 10–13 J

Part (b)

Step 1: Determine the energy of one photon

    • Planck's constant, h = 6.63 × 10−34 J s
    • Two photons are produced, so, the energy of one photon is equal to half of the total energy from part (a):

Calculating Energy of Gamma-Ray Photons Worked Example equation 1

Step 2: Write out the equation for the energy of a photon

E = hf

Step 3: Rearrange for frequency f, and calculate

Calculating Energy of Gamma-Ray Photons Worked Example equation 2

Part (c)

Step 1: Write out the equation for the momentum of a photon

Calculating Energy of Gamma-Ray Photons Worked Example equation 3

Step 2: Substitute in values and calculate momentum, p

Calculating Energy of Gamma-Ray Photons Worked Example equation 4

Diagnosis Using PET Scanning

  • Once the tracer is introduced to the body it has a short half-life, so, it begins emitting positrons (β+) immediately
    • This allows for a short exposure time to the radiation
    • A short half-life does mean the patient needs to be scanned quickly and not all hospitals have access to expensive PET scanners

  • In PET scanning:
    • Positrons are emitted by the decay of the tracer
    • They travel a small distance and annihilate when they interact with electrons in the tissue
    • This annihilation produces a pair of gamma-ray photons which travel in opposite directions

PET Scanning Machine (1), downloadable AS & A Level Physics revision notesPET Scanning Machine (2), downloadable AS & A Level Physics revision notes

Annihilation of a positron and an electron is the basis of PET Scanning

Image Formation on a Computer

  • The signals produced by the photomultiplier tubes are used to produce an image
  • The γ rays travel in straight lines in opposite directions when formed from a positron-electron annihilation
    • This happens in order to conserve 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 from 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

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