Positron emission tomography (PET) is another approach to nuclear medicine imaging that has several advantages over SPECT. PET uses positron-emitting radionuclides that result in the emission of collinear pairs of 511-keV annihilation photons. The coincidence detection of the annihilation photons obviates the need for collimation and makes PET far more efficient than SPECT for detecting radioactivity. Even more importantly, there are positron-emitting radionuclides for oxygen, carbon, nitrogen, and fluorine, which allows a wide range of molecules to be labeled as diagnostic agents. Many of these radionuclides have short half-lives and require an on-site cyclotron. However, 18F has a sufficient long half-life that it can be (and is) regionally provided, and there is no populated area of the United States where it is unavailable. Several others such as 82Rb and 68Ga are available from radionuclide generators that provide the radionuclides on demand despite their short half-lives.
Coincidence detection provides spatial resolution without the need for lead collimation by taking advantage of the fact that the annihilation photons resulting from positron emission are approximately colinear. Events are only counted if they are simultaneously detected by two opposed detectors. The sensitive volume defined by the coincidence detectors is called a line of response (LOR). Two single detection systems are used with an additional coincidence module. Each individual system will generate a logic pulse when they detect an event that falls in the selected energy window. If the two logic pulses overlap in time at the coincidence module, a coincidence event is recorded. PET systems use a large number (> 10,000) of detectors arranged as multiple rings to form a cylinder. Since any one detector can be in coincidence with other detectors in the cylinder, the resulting LORs provide sufficient sampling to collect the projection information required for tomography.
The intrinsic detection efficiency for a singles detector depends on the atomic number, density, and thickness of the detector. Ideally, the intrinsic detection efficiency should be 1, but at 511 keV that is difficult to achieve, although intrinsic efficiency for some of the detectors is greater than 0.8. Coincidence detection requires that both detectors register an event. Since the interactions at the two detectors are independent, the consistency intrinsic efficiency depends on the product of the intrinsic efficiency at each detector. As a result, coincidence detection efficiency is always less than that for a single detector, and that difference gets magnified for low-efficiency detectors. Because of the need for high intrinsic efficiency, scintillators are naturally the only materials currently used as detectors in PET imaging systems.
A coincidence event is recorded when there is an overlap of the singles logic outputs at the coincidence modules. The time width of the overlap depends on the scintillation characteristics of the detectors. For current PET scanners, that width ranges from 6 to 12 ns. Although that is a very short time compared to most human activities, it is fairly long compared to distances covered by photons traveling at the speed of light. Light travels approximately 30 cm / ns so that a 6 ns duration corresponds to a distance uncertainty of about 90 cm, which is the approximate detector ring diameter. As a result, the differential distance of the source between detectors has no observable effect on the timing of the coincidence events in conventional PET systems.
The arrival time of the annihilation photons is truly simultaneous only when the source is located fairly midway between the two opposed coincidence detectors. If the source is displaced from the midpoint, there will be a corresponding arrival time interval since one annihilation photon will have a short distance to travel than the other. As discussed above, this time differential is too small to be useful in conventionally designed PET systems. However, several of the scintillators used in PET tomographs (eg, LSO, LYSO) are capable of faster response than the 6 to 12 ns timing discussed above. With appropriate electronics, the coincidence timing window has been reduced to 600 ps for these detectors, yielding a source localization uncertainty of 9 cm. Even with reduction, time-of-flight localization can not be used to directly generate tomographic images, but it can be used to restrict the backprojection operation to areas where the sources are approximately located. In current implementation, the inclusion of time-of-flight information reduces noise in the reconstructed images by a factor of 2. Time-of-flight PET tomographs were actually commercially available for a short time in the 1980s. These systems used BaF2 detectors which are very fast, but unfortunately have very low detection efficiency. As a result, these devices did not compete well with the conventional PET tomographs based on BGO. In 2006, a time-of-flight machine based on LYSO detectors was reintroduced and is now commercially available.
The only criterion for recording a coincidence event is the overlap of output pulses at the coincidence module. True coincidences occur when a source lies on the LOR defined by two detectors. It is possible that events detected at the two coincidence detectors from sources not on the line of response could happen by chance. As the count rate at each of the singles detectors increases, the likelihood of false coincidences occurring from uncorrelated events increases. These events are called random or incidental coincidences . The random coincidence rate ( R ) is directly proportional to the width of the coincidence time window (t) and the product of the singles rate at the two detectors ( S 1 and S 2):
R = 2t S 1 S 2
It is easy to see that while the true coincidence event rate is linear with the source activity, the random coincidence rate increases proportional to the square of the activity. Thus, at high count rates, the random coincidence rate can exceed the true coincidence rate. The random coincidences provide false information and need to be removed from the acquired data prior to image reconstruction. It is also obvious that random coincidence rate can be reduced with a smaller coincidence time window. That requires detectors with a fast response time like LSO, LYOS, and GSO.
For sources in air, it is only possible to get a true coincidence event when the source lies in the refining volume between the two coincidence detectors. However, if the sources are distributed in some material, like human tissue, it is possible for one or both of the annihilation photons to be scattered into detectors that do not encompass the LOR of the source. Like the random coincidence event, this provides false information that requires correction. The number of scattered events can be reduced by energy discrimination, but this does not eliminate it all and additional scatter correction techniques are required for PET imaging.
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