Positron Emission Tomography

Introduction

Positron emission tomography is an analytical scanning technique that allows the measurement of biochemical processes in vivo, using the injection of compounds labelled with positron emitting radioisotopes. [1]

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Unlike other nuclear medical scans where gamma radiation detectors directly detect the gamma radiation emitted by an injected radiotracer, such as in Single Photon Emission Computed Tomography (SPECT), in PET scanning the radiation detected by the detectors is instead the annihilation radiation emitted when a positron (emitted by a radiotracer) annihilates with an electron in the body. [2] It is worth nothing that SPECT is now rarely used due to widespread supply and production issues with the required radiopharmaceuticals. [3]

 

The Science Behind PET Scanning

Positron Emission and Annihilation Radiation

In order to become more stable, neutron deficient radionuclides can decay either by positron emission or electron capture. These are isobaric decay processes, meaning that the mass numbers of the parent and daughter nuclei are equal.  

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In lower mass nuclei like those used in radiopharmaceuticals, positron emission is favoured. Otherwise, in higher mass nuclei, the energy released by a decay is smaller than the positron decay threshold energy of 1.02 MeV, twice the mass energy of a positron, so only electron capture takes place. [4] 

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Positron emission is schematically represented by: 

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When a proton in the nucleus transitions into a neutron, a positron (the antimatter equivalent of the electron) and an electron neutrino are released. The neutrino escapes without interacting with the surrounding material, but the positron travels only a short distance before being slowed in scattering processes (Coulomb interactions) with the electron clouds of the surrounding material (patient tissues in the case of PET scanning). [1]

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As positrons travel through the surrounding material and lose energy until they reach thermal energies, they interact with electrons in the material by way of annihilation. This causes either the production of a pair of 511 keV (the rest energy of an electron/positron) photons which are anti-parallel in the positron's frame, or the formation of a hydrogen-like orbiting couple called positronium (which is very short-lived, with a mean lifetime of only 8ns [4]). The decay of this unstable positronium particle is dependent on its form. In the ground state, the spins of positron and electron can be parallel (ortho-positronium) or anti-parallel (para-positronium). Para-positronium decays by self-annihilation, generating two 511keV photons, where ortho-positronium decays by the emission of three photons (these will not be registered as decays by the gamma detectors). [5] Both positronium forms are susceptible to the pick-off process, where the positron in the positronium annihilates with a free electron, rather than the electron belonging to the positronium particle. [6] Self-annihilation and the pick-off process are responsible for around 80% of annihilation events, yielding  pairs of photons that can be detected by the gamma detectors in the scanner. [7] Conservation of momentum means that the two photons are emitted in opposite directions. Variations in the initial momentum of the interacting particles means that the two particles will not be emitted at a perfect 180 degrees to one another, but rather there is a probability distribution around a mean of 180 degrees in the observer's frame. [7]

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To find out more about the positron sources used, and their production, please click here. 

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Detection of Radiation

Gamma detectors on opposite sides of a patient recognise the arrival of two photons as an annihilation event if they are detected almost simultaneously (typically within 3-15ns). This is the timing window of the coincidence circuit. Requiring that both photons are detected within a time window is the fundamental basis of the coincidental detection method and is termed electronic collimation. The annihilation is assumed to have taken place somewhere on the straight line between the two detectors (named the line of response). By collating millions of events and considering the intersections of the lines of response, computers are able to map the quantity and location of positrons in the patient being scanned. [1]

 

The detectors consist of small bismuth germinate crystals which are coupled to photo-multiplier tubes (photoemissive devices in which the absorption of a photon results in the emission of an electron, before the signal is amplified) and their resulting voltages are digitised. Each detector generates a voltage peak upon the arrival of a photon. These pulses are then combined in coincidence circuitry, being deemed coincident if the fall within the window of coincidence (see figure 1). The data require corrections for accidental coincidences (and attenuation effects if combining with CT or MRI data). 

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Image Processing 

Originally, PET scanners used a simple back projection algorithm (much like in CT scans) to reconstruct 2D images. 3D images were formed by stacking 2D images. This was due to an inability to reconstruct events from photons that were off axis (i.e. they arrived at sensors on different rings of the detector). 

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Technological advances mean that iterative algorithms like maximum-likelihood (ML) and ordered subset expectation maximization (OSEM) methods are now used in image reconstruction. These methods give a less noisy image and slower convergence in regions of low counts compared to the areas with higher counts. They also can be used to directly construct 3D images. 

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The improved physical characteristics of new scanners (with fast signal decay time, high output, and improved energy resolution) have led to the ability to produce fully 3D images with minimal additional computing. [1]

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Limiting Factors to Spatial Resolution   

The depth within the body of radiotracer accumulation is not a large factor determining the spatial resolution. This is because of the double detection (where both photons have experienced similar conditions), so depth largely does not change the spatial resolution. 

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Factors which do affect spatial resolution include:

• The positron range – this is larger in less dense tissues and leads to a greater uncertainty in the emission position. 

• The small random deviation from linearity of the photons (owing to conservation of initial particle momentums). The full-width-half-maximum of the resultant angular distribution is around 0.5 degrees.  

• Detector crystal dimensions – multiple scattering events are required to stop the gamma ray, so there is an uncertainty (which increases with detector thickness) in where the photon first hit. 

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Overall spatial resolution is a combination of all of these components. ​[1]

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References:  

[1] Basu, S. et al. (2011). Fundamentals of PET and PET-CT scanning, New York: New York Academy of Sciences. pp. 1-7.

[2] Nuclear Medicine. Available at: https://www.nibib.nih.gov/science-education/science-topics/nuclear-medicine[Accessed 01/02/19]

[3] PET vs. SPECT. Available at:  https://www.dicardiology.com/article/pet-vs-spect-will-pet-dominate-over-next-decade  [Accessed 01/02/19]

[4] Pans, J. M. (no date). Positron Emission Tomography. University Medical Center Groningen, The Netherlands. pp. 362-379

[5] Evans, R D. (1955) The Atomic Nucleus. New York: McGraw-Hill

[6] Ivanov, I. A. and Mitroy, J. (2002). Pick-off annihilation in positronium scattering from alkali-metal ions.Phys. Rev. A 65(3). 

[7] Rickey, D. W. et al. (1992)On lifting the inherent limitations of positron emission tomography by using magnetic fields (MagPET) Automedica, 14 pp. 355-369 

[8] What is a neutrino? Available at: https://www.scientificamerican.com/article/what-is-a-neutrino/[Accessed 28/02/19]

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