Event detection in PET relies on electronic collimation. An event is regarded as valid if:
(i) two photons are detected within a predefined electronic time window known as the coincidence window,
(ii) the subsequent line-of-response formed between them is within a valid acceptance angle of the tomograph, and,
(iii) the energy deposited in the crystal by both photons is within the selected energy window.
Such coincident events are often referred to as prompt events (or "prompts").
However, a number of prompt events registered as having met the above criteria are, in fact, unwanted events as one or both of the photons has been scattered or the coincidence is the result of the "accidental" detection of two photons from unrelated positron annihilations (Fig. 3.1). The terminology commonly used to describe the various events in PET detection are:
(i) A single event is, as the name suggests, a single photon counted by a detector. A PET scanner typically converts between 1% and 10% of single events into paired coincidence events;
(ii) A true coincidence is an event that derives from a single positron-electron annihilation. The two annihilation photons both reach detectors on opposing sides of the tomograph without interacting significantly with the surrounding atoms and are recorded within the coincidence timing window;
(iii) A random (or accidental) coincidence occurs when two nuclei decay at approximately the same time. After annihilation of both positrons, four photons are emitted. Two of these photons from different annihilations are counted within the timing window and are considered to have come from the same positron, while the other two are lost. These events are initially regarded as valid, prompt events, but are spatially uncorrelated with the distribution of tracer. This is clearly a function of the number of disintegrations per second,
* Chapter reproduced from Valk PE, Bailey DL, Townsend DW, Maisey MN. Positron Emission Tomography: Basic Science and Clinical Practice. Springer-Verlag London Ltd 2003, 69-90.
Figure 3.1. The various coincidence events that can be recorded in PET are shown dia-grammatically for a full-ring PET system. The black circle indicates the site of positron annihilation. From top left clockwise the events shown are: a true coincidence, a scattered event where one or both of the photons undergo a Compton interaction (indicated by the open arrow), a multiple coincidence arising from two positron annihilations in which three events are counted, and a random or accidental coincidence arising from two positrons in which one of the photons from each positron annihilation is counted. In the case of the scattered event and the random event, the mis-assigned line of response is indicated by the dashed line.
and the random event count rate (Rab) between two detectors a and b is given by:
where N is the single event rate incident upon the detectors a and b, and 2t is the coincidence window width. Usually Na ~ Nb so that the random event rate increases approximately proportionally to N2. There are two common methods for removing random events: (i) estimating the random event rate from measurements of the single event rates using the above equation, or (ii) employing a delayed coincidence timing window. These methods are discussed in detail in Ch. 6.
(iv) Multiple (or triple) events are similar to random events, except that three events from two annihilations are detected within the coincidence timing window. Due to the ambiguity in deciding which pair of events arises from the same annihilation, the event is disregarded. Again, multiple event detection rate is a function of count rate;
(v) Scattered events arise when one or both of the photons from a single positron annihilation detected within the coincidence timing window have undergone a Compton interaction. Compton scattering causes a loss in energy of the photon and change in direction of the photon. Due to the relatively poor energy resolution of most PET detectors, many photons scattered within the emitting volume cannot be discriminated against on the basis of their loss in energy. The consequence of counting a scattered event is that the line-of-re-sponse assigned to the event is uncorrelated with the origin of the annihilation event. This causes inconsistencies in the projection data, and leads to decreased contrast and inaccurate quantification in the final image. This discussion refers primarily to photons scattered within the object containing the radiotracer, however, scattering also arises from radiotracer in the subject but outside the coincidence field of view of the detector, as well as scattering off other objects such as the gantry of the tomograph, the lead shields in place at either end of the camera to shield the detectors from the rest of the body, the floor and walls in the room, the septa, and also within the detector. The fraction of scattered events is not a function of count rate, but is constant for a particular object and radioactivity distribution.
The prompt count rate is given by the sum of the true plus random plus scattered event rates, as all of these events have satisfied the pulse height energy criteria for further processing. The corrections employed for random and scattered events are discussed in Ch. 6.
The sensitivity of a tomograph is determined by a combination of the radius of the detector ring, the axial length of the active volume for acquisition, the total axial length of the tomograph, the stopping power of the scintillation detector elements, packing fraction of detectors, and other operator-dependent settings (e.g., energy window). However, in general terms the overall sensitivity for true (T), scattered (S), and random (R) events are given by [1-3]:
where Z is the axial length of the acquisition volume, D is the radius of the ring, and L is the length of the septa. For a multi-ring tomograph in 2D each plane needs to be considered individually and the overall sensitivity is given by the sum of the individual planes.
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