Positron Emission and Annihilation. Positron-emitting radionuclides as such do not emit γ-rays. Only when an emitted positron loses its energy by interacting with the surrounding medium within a short distance of the site of emission (average range is 0.22 mm in the case of ¹⁸F, see Table 5.2), it annihilates by combining with an electron, and two γ-rays with energies of 511 keV each are produced simultaneously (see Fig. 6.2). The pair of γ-rays produced by annihilation of a positron travel in opposite (almost 180 degrees apart) directions. In PET, these two γ-rays are used in a coincidence mode where both γ-rays are detected by a pair of detectors (e.g., BGO or LSO; Tables 8.1 and 8.2) that are linked to one another through a coincidence circuit. This powerful mechanism is referred to as coincidence detection, and is a significant feature of PET imaging, as we describe next.

Coincidence Detection. Consider two detectors in Figure 15.1 (shown in red) facing each other around a radioactive material containing patient. After annihilation, γ-rays shown by arrows interact with the crystals; the output of each detector is fed into a coincidence processor (also called coincidence circuit). A coincidence processor is used to determine whether the output of one detector originated simultaneously or within a very short time of the output of the second detector (of the order of nanoseconds [10^-9 seconds]). If this occurs, an event is assigned to the detector pair, and these events are called true coincidences. Each detector pair defines a field of view, often referred to as a line of response (LOR) in PET, as shown in green color in Fig. 15.1. It is a long, thin tube with a cross section of the same size as the two detectors. True coincidences occur only if the annihilation γ-rays originate from within the LOR. Annihilation produced outside this
area may hit only one detector and thus cannot produce a true coincidence. The important point is that LOR definition in PET is achieved without the use of a physical collimator. By contrast, we saw earlier that a collimator (Chapter 10) is an essential requirement to define a field of view if the detectors are used in single photon mode (without coincidence mode), as is the case in planar and SPECT imaging with the scintillation camera.

Two important attributes of coincidence detection are:

Data Acquisition. In principle, to perform PET, one can acquire data from a thin cross section using only a single pair of detectors shown in Figure 15.1, by linearly scanning a cross section from multiple directions as depicted in Figure 14.1. However, the sensitivity of such a device is poor. To increase the sensitivity, multiple pairs of detectors, arranged in a ring or a hexagonal array, are used, as shown in Figure 15.2. In this setup, each detector can communicate with multiple detectors in coincidence mode to form multiple LORs, resulting in a significant boost to sensitivity. The
PET instrument is quite complex as a large number of BGO or LSO crystals are used (commonly exceeding 10,000, about 5 mm × 5 mm × 30 mm in size) as radiation detectors. It is not practical to use 10,000 or more photomultiplier tubes (PMTs), one corresponding to each crystal. Instead, to reduce the electronic complexity related to such a large number of PM tubes, as well as the cost of the instrument, a large crystal block (shown in Figure. 15.3) is divided into smaller sections by making slits into the crystal block. Each smaller section then serves as one independent detector. The example block shown is divided into 8 × 8 smaller sections, thus producing 64 detector elements. The large crystal block is coupled to four PM tubes as shown in Figure 15.3.

Using the Anger logic similar to a scintillation camera, each crystal can be uniquely identified by the pulse height distribution generated in the four PM tubes. Thus, this particular type of arrangement reduces the number of PM tubes by a factor of 16 (4 instead of 64) compared with if one used one PM tube for each crystal element. Besides reducing the cost, this approach improves the electronic stability and performance of the PET instrument. When the crystal blocks are arranged in a circular or polygon array, they cover multiple axial cross sections at the same time, in this example eight. Moreover, placing multiple (e.g., 4) block rings or polygon arrays axially adjacent to one another, as is done quite often in PET instruments, yield many axial rings or cross sections simultaneously (32 in this example). Thus, an entire organ or a large body part of a patient can be imaged simultaneously.

2D versus 3D Mode. There are two modes to acquire PET data, 2D and 3D. In 2D mode of data acquisition (Fig. 15.4A), septa (lead or tungsten) are placed in between the axial crystals (e.g., 14 septa in between 15 axial crystal rings in the example shown in the figure) in order to only record coincidence pairs at detectors within the same (or very nearby) axial ring (center ring in the Fig. 15.4A). By contrast, in the 3D acquisition mode, septa are not used (Fig. 15.4B). This further increases the sensitivity of PET, but complications arise. Much more data are recorded and need to be processed. Also, the dead time, the amount of scatter, and random coincidences (discussed later), all increase. However, improvements in technology have tackled these issues. This includes the use of crystals with better energy discrimination resulting in more scatter removal, and electronics with reduced dead time and coincidence timing (the latter reducing random fractions). Furthermore, new computers and algorithms provide improved speed and correction for scatter and random coincidences. As a result, most scanners nowadays use 3D data acquisition only to benefit from the gains in sensitivity. As a result, there has been a transition from using retractable septa (allowing 2D or 3D option) to having no septa at all (only 3D option) in newer scanner designs.

Time-of-flight (TOF) PET. Another innovation that further improves the performance of a PET scanner is the use of the time difference in the detection of the two coincidence photons. For annihilation photons emitted along an LOR except at the very center, one photon reaches its detector faster than the other (because they travel different distances and the speed of light is the same for both). The ability to record this time difference between the two coincidence γ-rays can help better localize the point of origin of annihilation. This is the basis for the concept of TOF PET. In fact, TOF PET was studied in the 1980s, but was not clinically implemented given the success of BGO crystals (which are unable to measure these time
differences, but are very efficient at absorbing γ-rays; see Table 8.2). Since the 2000s, an increasing use of LSO crystals with their faster resolution time (better than 500 picoseconds [10^-12]) and thus a better ability to measure the time difference between the two coincidence events, has made TOF comeback possible. It is now available with many PET scanners.

This concept is shown in Figure 15.5. This is achieved by accurate measurement of the difference in arrival times of the two annihilation photons. With ideal timing resolution of the coincidence processor, the point of origin of the annihilation photons can be determined accurately, within a single pixel along the LOR. However, existing coincidence processors have a timing uncertainty of 300 to 500 picoseconds. This causes inaccuracy in the exact localization of the annihilation event along the LOR (Fig. 15.5; TOF). It is still better than when no TOF method is used (Fig. 15.5; conventional). The restricted area of detection along LOR with TOF is related to the timing resolution of the coincidence processor Δt, as follows:

where Δx is the position uncertainty and c is the speed of light. In current TOF PET scanners, positioning uncertainty is of the order of centimeters. In actual practice, this improvement in positional restriction along the LOR does not improve the overall spatial resolution. But it is still useful as it reduces noise significantly, as with each projection operation in image reconstruction, statistical noise is propagated within only a fraction of each LOR instead of the total LOR.