The detector system used in all modern commercial PET systems is based on scintillation detectors coupled to some sort of photodetector readout. One of the most commonly used detector designs is the block detector [4]. In this design, an array of scintillation detector elements is coupled to a smaller number of PMTs, typically four, via a light guide. An example of a block detector is illustrated in Fig. 10.2. The light generated in scintillator following an interaction by a 511 keV photon is distributed between the PMTs in such a way that each detector element produces a unique combination of signal intensities in the four PMTs. To assign the event to a particular detector element, the signals from the PMTs are used to generate two position indices, X _pos and Y _pos:
where PMT_A, PMT_B, PMT_C, and PMT_D are the signals from the four PMTs.

This is similar to the positioning of events in a conventional scintillation camera; however, the X _pos and Y _pos values do not directly translate into a spatial position or a location of the individual detector elements in the block detector. Each module therefore has to be calibrated to allow an accurate detector element assignment following an interaction of a photon in the detector. The distribution of X _pos and Y _pos can be visualized if a block detector is exposed to a flood source of 511 keV photons. For each detected event, X _pos and Y _pos are calculated using an equation [1] and are then histogrammed into a 2-dimensional matrix which can be displayed as a gray-scale image. An example of this is shown in Fig. 10.3. As can be seen in this figure, the distribution of X _pos and Y _pos is not uniform, but instead the events are clustered around specific positions. These clusters are the X _pos and Y _pos values that correspond to a specific detector element in the array. As can be seen from the flood image, the location of the clusters does not align on an orthogonal or linear grid. Instead, there is a significant pincushion effect due to the nonlinear light collection versus the position of the detector elements. To identify each element in the detector block, a look-up table is generated based on a flood map like the one shown in Fig. 10.3. First, the centroid of each peak is localized (i.e., one peak for each detector element in the array). Then a region around each peak is generated that will assign the range of X _pos and Y _pos values to a particular element in the array. During a subsequent acquisition, the values of X _pos and Y _pos are calculated for each event; then the look-up table is used to assign the event to a specific detector element. Also associated with the positioning, look-up table is an element-specific energy calibration, which will accept or reject the event if it falls within or outside the predefined energy range.

To ensure that the incoming events are assigned to the correct detector element, the system has to remain very stable. A small drift in the gain in one or more of the PMTs would cause an imbalance and would affect the locations of the clusters in the flood map. This would in the end result in a misalignment between the calculated X _pos and Y _pos and the predetermined look-up table [5], which will result in a mispositioning of the events. As will be discussed below, to check gain balance between the tubes is one of the calibration procedures that need to be performed regularly.

The line connecting a pair of detector is referred to as a coincidence line or line of response (LOR). If the pair of detectors is in the same detector ring, this line can be described by a radial offset r from the origin with an angle θ. A set of LORs that all have the same angle (i.e., they are all parallel to each other), but they all have different radial offsets; these then form a projection of the object to be imaged at that angle. For instance, all lines with θ = 0° would produce a lateral projection, whereas all lines with a θ = 90° would produce an anterior-posterior view.

A complete set of projections necessary for image reconstruction would consist a large number of projections collected between 0° and 180°. If all the projections between these angles are organized in a 2-dimensional array, where the 1st dimension is the radial offset r and the 2nd dimension is the projection angle θ, then this arrangement or matrix forms a sinogram, as illustrated in Fig. 10.4. A sinogram is a common method of organizing the projection data prior to image reconstruction. The name sinogram comes from the fact that a single point source located at an off-center position in the field of view (FOV) would trace a sine wave in the sinogram. The visual inspection of a sinogram also turns out to be a very useful and efficient way to identify detector or electronic problems in a system.

Consider a one particular detector in the system and the coincidence lines it forms with the detectors on the opposite side in the detector ring (Fig. 10.4, right). In a sinogram, this fan of LORs would follow a diagonal line across the width of the FOV. By placing a symmetrical positron emitting source such as a uniform-filled cylinder with ⁶⁸Ge or ¹⁸F, at the center of the FOV of the scanner, all detectors in the system would be exposed to approximately the same photon flux. If all detectors in the system had the same detection efficiency, then each detector would record the same number of counts per second in this source geometry. In this source geometry, the summation of all the coincidences between a particular detector element and its opposing detector element is sometimes referred to as fan sum. The fan sums are used in some systems to derive the normalization correction that is used to correct for efficiency variations between the detector elements in the system. The fan sums can also be used to detect problems in the detector system

Figure 10.5 shows a normal sinogram of a uniform cylinder phantom in a PET system. In addition to the noise originating from the counting statistics, it contains a certain amount of a more structured noise or texture. The observed variation seen in the sinogram is normal and originates primarily from the fact that all detectors in the system do not have the same detection efficiency. There are several additional factors that contribute to this, such as variation in how energy thresholds are set, geometrical differences, differences in physical size of the each detector element, etc. These variations are removed using a procedure that is usually referred to as normalization, which is discussed later in this chapter.

One thing that is clearly noticeable in the sinogram is the “crosshatch” pattern, which reflects the variation in detection efficiency as discussed above. As mentioned, it is expected to observe a certain amount of normal variation in detection efficiency. This can under most circumstances be calibrated or normalized out as long as the system is stable in there is no drift in the gain of the detector signals. Since a certain amount of electronic drift is inevitable, a normalization calibration needs to be performed at regular intervals. The frequency depends on the manufacturers specifications but can be as frequent as every single day as part of the daily QC or done monthly or quarterly.

If a detector drifts enough or fails, this is typically very apparent by a visual inspection of the sinogram. A detector failure of a PET detector block can either result in that the detector does not respond at all when exposed to a source or that the detector constantly produces event even when no source is present (i.e., noise). The cause of a detector failure could be many, ranging from simple problems such as a loose cable, which usually results in a nonresponding detector, to more complex problems as a faulty PMT, drift in PMT gains, and drift in set energy threshold. The latter issues may result in either a nonresponding detector or that a detector is producing an excessive count rate.

Examples of failing detectors or associated electronics are also illustrated in Fig. 10.5. A failing single detector element in the detector module would appear as a single dark diagonal line in the sinogram (Fig. 10.5b). This problem was fairly common in older PET systems where each detector element was coupled to its own PMT. A common cause of this type of failure was either a failing PMT or the associated electronics (e.g., amplifiers). In the case of a system that uses block detectors, a single dark line may also occur if the detector tuning software had difficulties identifying all detector elements in the detector array. This could be caused by poor coupling of the detector element to the light guide and/or the PMTs or poorly balanced PMTs.

Since the PMTs and associated electronics are shared by many detector elements in block detector, a failure in these components will affect a larger number of detector channels. This is then seen as a wider diagonal band across the sinogram, as illustrated in Fig. 10.5c. Another common detector problem is illustrated in Fig. 10.5d. In this case one of the detectors is generating a large number of random or noise pulses. This could be caused by an energy threshold that is set too low, which, for instance, could be caused by a failing or weak PMT.

As described above, the signals from a larger group of detector blocks are typically multiplexed into what is sometimes referred to as a detector controller. In the case of a failure of the detector controller, the signals from the entire detector group might be lost, which in the sinogram is visualized as an even broader band of missing data (Fig. 10.5e). A problem further downstream in the signal processing chain such as in the electronics determining coincidences may result in a problem illustrated in Fig. 10.5f. Here the signals from two entire detector groups are lost in the coincidence processor, which in this case is seen as a diamond-shaped area in the sinogram. A final example of a hardware failure is shown in Fig. 10.5g. In this case there is a problem with the histogramming system, where random counts are added to the sinogram in addition to the normal data.

There are naturally a large number of variations in other artifacts or patterns in the sinograms that are specific to the design or a particular system, but the sinogram patterns related to the front electronics as described in this section are common for most modern PET systems.

Thus, by a visual inspection of the sinograms from a phantom scan, it is possible to relatively quickly identify whether the system is operational or not. By looking at the patterns in the sinogram, it is also possible to figure out where in the signal chain a problem is occurring. A complete failure is very apparent in the sinogram and makes it easy to make the determination that the system is in need of repair. However, many times there are more subtle problems, such as a slow drift in the system that is not easily detected by visual inspection. Some systems therefore provide a numerical assessment that gives the user some guidance whether the system is operational or not. These tests usually require that the user acquires data of a phantom, such as a ⁶⁸Ge-filled cylinder every day at the same position in the FOV for a fixed number of counts. The daily QC scan is then compared to a reference scan (e.g., a scan acquired at the time of the most recent calibration or tuning). By comparing the number of counts acquired by each detector module in the QC scan to that in the reference scan, it is possible to determine if a drift has occurred in the system and the system needs to be retuned and recalibrated.

The purpose of the detector and system calibration is to make sure that the recorded events are assigned to the correct detector element in the detector module. An energy validation is performed such that only events within a certain energy range are passed on to the subsequent event processing. In addition to positioning and energy calibration of each detector module, each module has to be time calibrated to make sure that coincidence time windows between all detector modules are aligned.