ELEC5622 Chap.7 Positron Emission Tomography
Positron Emission Tomography
This chapter explains PET, the unit's functional modality. A positron-emitting tracer such as FDG decays, each positron annihilates with an electron, and two 511 keV photons travel in opposite directions to a ring of scintillation detectors. Coincidences define lines of response that fill a sinogram, attenuation correction restores quantitation, and FBP or OSEM reconstructs the image.
Decay and sinogram geometry are worked with numbers. Because PET measures function rather than anatomy, the chapter also explains why it is so often paired with CT. It also explains the three detector properties, spatial, energy and time resolution, that decide how clean the raw data are.
What this chapter covers
- 01
Radiotracers, positron decay and half-life
- 02
Annihilation and back-to-back 511 keV photons
- 03
Scintillation crystals and photomultiplier tubes
- 04
True, scattered and random coincidences
- 05
Spatial, energy and time resolution of detectors
- 06
Sinograms and projection geometry
- 07
Attenuation correction and PET/CT
- 08
Filtered back projection and OSEM
Worked example · free
Tracer decay and a sinogram coordinate
- 155 minutes is half a half-life, so A = 370 × 0.5^0.5 = 370 × 0.707 ≈ 261.6 MBq.
- 1At φ = 0°, s = x cos 0° + y sin 0° = −20 mm.
- 1At φ = 90°, s = 15 mm; the sinusoid's amplitude is √(20² + 15²) = 25 mm.
Key terms
- Line of response
- A line of response is the line joining the two detectors that register a coincidence event.
- Sinogram
- A sinogram is the raw PET data histogram indexed by projection angle and distance from the gantry centre.
- OSEM
- OSEM is ordered subsets expectation maximisation, the most widely used iterative PET reconstruction method.
- Radiotracer
- A radiotracer is a radioactive substance used to follow a biological process, such as 18F-FDG for glucose uptake.
- Attenuation correction
- Attenuation correction compensates PET counts for photons absorbed or scattered inside the body before quantification.
Positron Emission Tomography FAQ
Why does PET need attenuation correction?
Photons crossing more tissue are attenuated more, so uncorrected images show artefacts such as lungs and skin with higher apparent uptake than muscle, and quantitation becomes wildly inaccurate. PET/CT uses the CT image to correct.
What makes a random coincidence different from a scattered one?
A random coincidence pairs photons from two unrelated annihilations that happen to arrive within the timing window. A scattered coincidence comes from one annihilation, but one photon changed direction, so its line of response is misplaced.
Why are PET images blurrier than CT images?
PET locates annihilations indirectly through detector pairs, and detector size, positron travel and scatter all limit precision. The lecture quotes 4 to 5 mm at best for PET against about 1 mm for CT.
Why are the two PET photons 511 keV each?
Annihilation converts the rest mass of the positron and the electron into two gamma photons of 511 keV that travel in opposite directions. Detecting both at once defines the line on which the annihilation happened.
What is the difference between 2D and 3D PET acquisition?
With septa of absorbing material between rings, data are collected as 2D slices, though the stacked images still give 3D information. Without septa, coincidences from all axial angles are accepted, making a fully 3D acquisition.
How does a scintillation detector turn a gamma photon into a signal?
The crystal converts the gamma photon into many optical photons in proportion to its energy. A photomultiplier tube turns that light into an amplified electrical pulse, and front-end electronics condition it so coincidences can be timed and energies checked.
Exam move
Draw a detector ring and sketch the three coincidence types until you can explain each in one line. Practise half-life arithmetic with whole and fractional numbers of half-lives. Then trace a single point through a sinogram at several angles to see the sinusoid, and summarise FBP against OSEM in two sentences. Then compare PET with CT on resolution, contrast mechanism and what each image answers, in three short lines.
Practise naming which detector property limits each kind of unwanted event: energy resolution for scatter and time resolution for randoms.
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