In this section, the fundamentals of PET physics are described in the following order: starting from the physical basis of PET, data acquisition on the PET scanner, correcting the PET data and finally PET image reconstruction.
3.1.1 Physical Basis of PET
A positron (β+) is a positively-charged electron that is emitted from the nucleus of an unstable radioisotope due to the presence of excessive protons and a positive charge. After positron emission, the unstable radioisotope becomes stable by converting the proton to a neutron, hence removing the positive charge. The positron emitted from a radionuclide collides with a nearby electron to produce two photons or gamma rays of 511 keV (kilo-electro-voltage). This process is called annihilation (Figure 3.1). The gamma rays are emitted at approximately 180° to each other and the path that they travelled is called the coincidence line (Figure 3.1). It is the detection of the coincidence events that provide the unique scheme for forming tomographic images using the PET scanner.
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Figure 3.1: Image of a PET scan with details of positron-emission annihilation.
After the positron is emitted from the radionuclide, it travels some distance before colliding with an electron. The distance travelled is known as the positron range (Figure 3.1) and contributes to the uncertainty of the localisation of the decaying radionuclide. The higher the energy of the positron emitted, the larger the positron range. The list of commonly-applied radioisotopes in PET and their respective mean positron ranges and the half-lives of their isotopes are shown in table 3.1. After annihilation, the emitted gamma rays may not travel at exactly 180° to each other. These two factors thus lead to lower spatial resolution of the PET scanner.
Table 3.1: Commonly-applied positron emitting isotopes in PET studies [Valk et al., 2004]
Isotopes t1/2 Mean Positron Range (mm)
18F 109.8 min 0.6
11C 20.4 min 1.1
15O 2.04 min 2.5
13N 9.97 min 1.5
64Cu 12.7 hours 0.56
68Ga 68.1 min 2.9
124I 4.2 days 3.4
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3.1.2 Data Acquisition
In a PET scan, the radiolabeled compound is injected intravenously into the subject (radiolabeled syringe in Figure 3.1). The radiolabeled compound then travels throughout the human body into the various organs and undergoes various processes such as metabolism, absorption and excretion.
The position of the radioisotope in the body reflects the distribution of the radioisotopes. It can be determined by detecting the photons emitted during the annihilation of positron emitted from radionuclide with a nearby electron in a PET scanner (Figure 3.1).
Each 511 keV gamma-ray emitted is detected by the gamma detectors (Figure 3.1), which then converts the gamma rays into light photons. The light photon is converted into electrons, which then pass through a photon-multiplier tube (PMT) or semiconductor-based photodiodes, where the signal gets amplified and converted into electrical signals. The electrical signals from each detected event are recorded by the PET scanners, in terms of time of acquisition, the energy of each detected photons and the angular and linear positions of detecting an event. A time window is set on the PET scanner to identify coincidence events.
All the coincidence events detected by the PET scanner are stored in either list-mode data format or sinogram data format. The list-mode format stores all coincidence events, while the sinogram format stores the averaged counts within a predefined time window or PET frame. List-mode data are rebinned into sinogram data after the PET scan with the user-defined time window.
3.1.3 Data Correction
Before the sinogram data is reconstructed into PET image, the data needs to be corrected for radioactive decay and effects of attenuation, scatter and random on photons (Figure 3.2). As the correction of the PET data is not the focus of this project, only the sources of error are described.
Radioactive Decay
All radioisotopes will undergo decay and the rate of decay is dependent on the half-life of the radioisotope (Table 3.1). The shorter the half-life, the faster the rate of radioactive decay, where the activity of the radionuclide, with a half-life of t1/2, after a time period, t is:
𝐴𝑡 = 𝐴0𝑒−𝜆𝑡, (1)
where A0 is the initial radioactivity and λ = ln(2)/t1/2
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Figure 3.2: Effects of attenuation, scatter and random.
Photon Attenuation
As the emitted gamma rays or photons travel through a medium to reach the detectors, the photons are either absorbed or scattered (Figure 3.2). This leads to a reduction in the number of coincidence photons detected by the PET detectors. The magnitude of photon attenuation is expressed as:
∅= ∅0𝑒− ∫ 𝜇(𝑥,𝑦)𝑑𝑠𝑠 , (2)
where Ø0 and Ø are the numbers of incident and transmitted photons per unit area and ds is the differential thickness of the medium through which the annihilated photons travel along the path S. μ is the linear attenuation coefficient (cm-1), which is the probability that a photon will undergo an interaction when it passes through a unit thickness of tissue. The probability of photon attenuation is dependent on the photon energy, and the density and size of the object or medium through which the photons transverse. Therefore, a medium with a higher density or a greater size will result in a greater amount of photon attenuation.
The attenuation correction (AC) of the PET data involves determining a μ-map, which consists of the spatial information of the μ-values of the object within the field of view (FOV) of the PET scanner [Zaidi et al., 2003]. AC methods can be classified into transmissionless and transmission methods. Transmissionless methods involve the application of a μ-map (1) containing a uniform distribution of specified μ-values within a known volume or (2) determined by the segmentation of the PET emission data [Zaidi et al., 2003]. Transmission methods require transmission imaging with (1) a single-photon source (e.g., 137Cs, 57Co), (2) a coincidence-photon source (e.g., 68
Ge-68Ga) or (3) X-ray CT, to determine the μ-map. The attenuation correction of a PET image is normally carried out using a CT image in clinical studies in a hybrid PET-CT scanner. MRI images
33 have also been used to correct for attenuation of PET images in a hybrid PET-MRI scanner.
Photon Scattering
Apart from attenuation, photons also undergo scattering as they travel through a medium (Figure 3.2). The photons are scattered by Compton scattering, which is the interaction between an incoming photon with a loosely-bound outer shell electron, which resulted in a change in direction of the incoming photon and the ejection of the collided electron from the atom. The photon lost some of its energy to the electron, resulting in energy lower than 511 keV. This effect occurs in the energy range of 100 keV and 2 MeV.
Random Coincidence
The random effect occurs when two events from two different annihilation events are detected by the PET scanner as a coincidence event (Figure 3.2). This effect arises when the coincidence defined timing window is too large such that two temporally close events are detected as coincidence events. This leads to a false coincidence events and normally adds to background counts, hence reducing the signal-to-noise ratio (SNR) of the PET data. The random coincidence is commonly corrected using delayed time window or single count rate methods.
3.1.4 Image Reconstruction
The raw data from the list-mode data or, more commonly from the sinogram data, is reconstructed to form 3D/4D PET images. There are many reconstruction methods, of which filtered-back-projection (FBP) is most commonly applied and is often used as a standard reconstruction method for PET scanner evaluation. Essentially, all the measured activities along each line-of-response (LOR) are back-projected through the image to obtain an approximation of the “true” image. LOR is the straight line connecting the centers of two gamma detectors. The use of back-projection results in star artefacts, which can be reduced by means of a high-pass filter, such as ramp, Hamming, Hanning etc. However, the use of a filter may also introduce additional degradation of the spatial resolution of the scanner (e.g. a filter with a too high cutoff value introduces noise).
Although FBP is commonly applied and results in reliable quantitative PET image, the image is noisy and has poor SNR and hence poor image contrast for quantification of small regions of interest (ROIs). Other reconstruction methods exist, which relies on iterative algorithms such as Order-Subset Expectation Maximization (OSEM) and Maximum Likelihood Expectation Maximisation (MLEM). These reconstruction methods result in images of higher SNR due to
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lower noise in the background but can be computationally intensive and time-consuming due to a large number of iterations required until an optimised solution can be obtained.
There are no optimal reconstruction methods and some methods may be preferred over others depending on the SNR, consistency of the evaluated data across subjects, the processing time required, available reconstruction methods on the PET scanner etc. However, it is important to ensure all PET images analysed within a study are reconstructed using the same image reconstruction algorithm for accurate comparison.