SCANNER PHYSICS

Positron emission tomography (PET) takes advantage of the unique characteristics of positron decay. A proton-rich nucleus, such as ⁸²Rb or ¹⁸F, can eliminate its excess charge by emitting a positron, which is the antiparticle of the electron. The positron will scatter around in the body (within a millimeter or so of where the decay took place) until it meets an electron, and then they are annihilated. The annihilation converts the mass of the positron and electron into energy, in this case two 511-keV photons that travel in nearly opposite directions (Fig. 23-1). If both of these photons can be detected, then it is known that there is activity somewhere along the line between the two responding detectors. After enough of these events have been recorded, the information can be combined to form an image.

FIGURE 23-1 Depiction of coincidence detection and the basic physics involved in PET imaging. The nuclide decays, giving off a positron that eventually meets an electron and annihilates into two 511-keV photons. These two photons are detected, giving the information that a decay took place between the two detectors. Events that happen this way, as is desired, are called true events.

At the heart of a PET camera are scintillation detectors. A scintillation detector is a crystal that gives off many low-energy photons when a high-energy photon interacts with its molecules. The low-energy photons are collected by photomultiplier tubes, which convert them into an electronic signal. The precise time of arrival of the event and the energy of the event are recorded. This is diagrammed in Figure 23-2. The timing is critical because it is used to decide if two photons came from the same annihilation. If two photons are detected within a very short time (called the time window, typically 3 to 12 ns, depending on the type of detector used in the scanner), it is assumed that they were created from a single positron-electron annihilation that occurred somewhere on the line that connects the two recording detectors. This is called a coincident event, and the line is termed a line of response. If the time between detecting two photons is greater than the time window, the two detected events must have originated from two separate annihilations because light travels at approximately 0.3 m/ns and the scanner is only about 1 m in diameter. The primary data set from the scanner is the number of coincident events that are recorded for each line of response.

FIGURE 23-2 Schematic of a scintillation detector typical of those used in PET scanners. The high-energy (511 keV) photon interacts in the detector crystal, which then glows in a shower of low-energy (visible) photons. These visible photons are collected by the photomultiplier (PM), which converts the light into an electronic signal. The electronics identify the time of the event and the area of the pulse, which is proportional to energy.

Recording the energy of the event is important to determine first if the photon came from a positron annihilation and then if it scattered off tissue in the body on its way to the detector. If the photon arrives with 511 keV of energy, it is overwhelmingly likely that it originated in a positron-electron annihilation. This is useful for preventing background events of different energy from entering the data stream. The detectors are not perfect, and there are some physical effects that cause the energy to vary, so scanner electronics are generally set to accept events with a range of energies, typically 430 to 650 keV. One of the physical effects is scatter. When a photon scatters, it loses some energy to the scatterer. Hence, with better energy resolution, the number of contaminating background and scattered events accepted into the primary data set can be reduced.

A PET camera is made by arranging detectors in a cylindrical geometry as depicted in Figure 23-3. All detectors are continually monitoring for photons. The main advantage of PET imaging over SPECT is the vastly increased count rate capability. All detectors in the PET ring are continuously monitoring for events versus a gamma camera, which uses a lead collimator to detect only events along certain projections at any given time.

FIGURE 23-3 Depiction of the geometry in a typical PET scanner and the nature of a random event. The scanner is made of many small individual detectors arranged in a cylinder. The scanner electronics can record events between any pair of these detectors. Note that the photons need not be “in the plane” of a particular detector ring. A true event and a random event are depicted. In the random event, two separate decays have led to photons that are detected by the scanner. Unfortunately, neither of the decays takes place on the line connecting the two responding detectors. These types of events must be removed from the data set before an accurate image can be reconstructed.

There are several types of events that can be recorded in a PET scanner. The example shown in Figure 23-1 is called a true event. “True” comes from a positron-electron annihilation generating two photons that travel in opposite directions and are both recorded. This is the raw data that we desire to accurately reconstruct an image. Unfortunately, collecting data as described also results in recording of other types of events. It is possible for photons from two different positron annihilations that by random chance happen to decay within a few nanoseconds of each other to be detected in separate detectors within the time window. This situation is depicted in Figure 23-3. When this happens, there is the potential for incorrectly assuming that radioactivity is present between the two responding detectors. This type of event is called a random event because the two detectors that are involved and the time between detection of the two photons are both completely random. Random events add a uniform background to the primary data set.

The randomness in time between the two detections can be exploited to estimate the number of random events that are confounding the primary data set. The number of random events is estimated by one of two methods. The first method is the “delayed window” method. In this technique, a second data set is simultaneously acquired that includes only random events.¹ The second method probabilistically calculates the number of expected random events based on the count rates in each of the detectors. In either case, the estimate is subtracted from the primary data set to produce a random corrected data set.

A multiple event is a combination of a true event and a random event as shown in Figure 23-4. By random chance, a third photon falls within the time window of a true event. When this occurs, it is unknown which pair of detectors represents the true event and which pair represents the random event. In all cases, one of the potential lines of response can be eliminated because it does not go through the imaged field of view. This leaves two lines of response, one true and one random. Both of the events are recorded. On average, the random events are corrected in the process described earlier. Recording both events and later correcting for the random yields additional information that can be used to reconstruct the image. This is as opposed to the archaic practice of ignoring multiple events because it cannot be known which two detectors recorded the true event.

FIGURE 23-4 Two other types of events that can occur during a PET acquisition. The straight line represents a true event as depicted in Figure 23-1. The line with the x indicates an attenuation event. One of the photons heading toward the detectors is attenuated by the body, so a coincidence event could not be recorded. This leads to an underestimate of the amount of activity in the body. This is fixed by the attenuation correction derived from the collected CT scan. If these two events happen to occur at the same time, the event is termed a multiple. In this case, it is not clear from the collected data if there is activity along the dotted or solid line. The data set is corrected for multiple events during the correction for random events.

Photon attenuation by the patient’s body leads to potential underestimation of the amount of activity in the patient. This is also depicted in Figure 23-4. Keep in mind that unless both photons are detected, no event can be recorded. It is the total amount of tissue that both photons must traverse that determines the probability of attenuation. Note that the probability of an event’s being attenuated is greater if the line of response traverses the center of the patient. On the other hand, some of the events originating at the edge of the body can reach the detectors after traversing only a small amount of tissue. Because of this, more events that originate at the center of the body are attenuated compared with the edge of the body. If this is not taken into account when images are reconstructed, the center parts of the image will be depressed (Fig. 23-5).

FIGURE 23-5 A, Uncorrected emission image of ⁸²Rb uptake. Counts in the center of the image are underestimated because of photon attenuation by the patient’s body. This is most noticeable in the myocardial septum. B, A random event, scatter, and attenuation-corrected emission image of ⁸²Rb uptake. The depressed uptake in the myocardial septum and basal lateral wall has been recovered after attenuation correction is applied to the uncorrected image.

A scatter event is when one of the photons scatters in the patient so that the line of response between the two responding detectors does not include the location of the event (Fig. 23-6). Essentially all scattering of importance to PET is photons scattering off free electrons, called Compton scattering. When a photon scatters, it transfers some of its energy to the electron. The greater the scattering angle, the greater the energy transfer. A 511-keV photon that scatters by 30 degrees is reduced in energy to 450 keV, approximately the lower level threshold used in setting up PET detectors. Hence, if one or both of the annihilation photons scatter by less than 30 degrees, they can be recorded by the PET system. With this much scattering, a recorded event with a line of response that passes near the center of the scanner could be off by up to 10 cm. Scattering by small angles is more probable than by larger angles, so scatter affects PET images by reducing resolution and contrast.

FIGURE 23-6 Scatter event. One of the photons emanating from the positron-electron annihilation has scattered off of an electron in the body and so is detected by an inappropriate detector. If it is not removed from the data set, activity will be assumed to be present along the dotted line in error.

The final type of event that needs to be considered for cardiac imaging is called a prompt gamma and is shown in Figure 23-7. This is a property of ⁸²Rb decay that is not present with ¹⁸F. When a rubidium nucleus decays, it converts to a krypton nucleus by giving off its charge in the form of a positron. A significant fraction of the time, the krypton is in an excited state and almost immediately gives off another gamma ray. This is a situation that looks very much like the multiple event depicted in Figure 23-4, but there is a significant difference. The prompt gamma event is not random. The annihilation photons and the prompt gamma all are generated from a single decay process. In this case, the true and random events are correlated in time, that is, they happen at the same time. (Actually, the prompt gamma can be delayed by a few picoseconds, but this extremely small time is insignificant compared with the duration of the time window.) Compared with a multiple event, the random is equally likely to occur at any time.

FIGURE 23-7 Prompt gamma event. This type of event can occur in scanning with rubidium (Rb). Rubidium decays to an excited state of krypton (Kr), which gives off its excess energy in the form of a photon. If all three of these photons are detected, the event has the appearance of a multiple event (see Fig. 23-4). The difference is that one event precipitated all three photons as opposed to the two decays that just happened to occur at the same time in Figure 23-4. Hence, there is no randomness in the timing between these photons, so a conventional correction for random events will not remove them from the data set. A separate prompt gamma contamination estimate must be performed to account for these events before an image is reconstructed.

PET Detectors

All of the different types of events need to be accounted for in image reconstruction. The first defense against the confounding types of events is the detector itself. There are several different types of detector materials (Table 23-1). The three main characteristics for the detector material in PET are the stopping power, energy resolution, and time resolution. The greater the stopping power, the less detector material is needed to stop one of the annihilation photons. This is important for economic and image quality reasons. The detector material is the dominating cost of a scanner, so it pays to have higher stopping power material. It can also lead to better images. If a photon is detected in a smaller detector, the line of response is better defined, which leads to better images. Finally, for detectors of equal size, the one with the higher stopping power is more likely to record the event, leading to a higher sensitivity scanner and, again, better images.

TABLE 23-1 PET Detector Material Properties

Energy resolution is important for determining whether an event is scattered or not as discussed earlier. Because no detector is perfect, some number of scattered photons will always be recorded. However, with better energy resolution, the lower level energy threshold can be increased, which reduces the maximal angle through which a photon can be scattered and still be recorded. There is a subtle point worth mentioning here. As more scattered photons are rejected, the number of recorded events decreases. Because almost all photons are scattered to some degree, a perfect scatter rejection would result in very few events being recorded, which would result in very poor images. The scattered events do carry information as to the location of the source of activity. Hence, it is beneficial always to accept some level of scatter. As computer power and the scatter estimation and image reconstruction routines improve, more scatter events should be included in the data set.

Finally, the time resolution of the detector is important because it affects the number of random events that are recorded. The better the time resolution, the smaller the time window, and the fewer random events will enter the data set. Random events truly are random and therefore are equally likely to occur at any time. Therefore, a detector that permits a time window half as large will result in a data set that has half the number of random events.

The choice of detector materials involves a tradeoff. Generally speaking, more detected events leads to better images. The number of detected events is greatly increased if the scanner is operated in three-dimensional mode. Unfortunately, the number of confounding events (randoms and scatter) is increased as well as the number of good events (true). At some point, the detriment of dealing with the bad events outweighs the benefit of collecting more good events. This tradeoff will be discussed later after a short discussion of three-dimensional imaging, which greatly increases the counts in PET imaging.

In many of the preceding diagrams, it appears as if the PET scanner is a ring of detectors within a single plane. Historically, this was the case. A volumetric PET scanner was built by stacking a set of independent detector rings to make a scanner. At some point, it was realized that if the detected events are limited to those occurring only within a plane, the number of detected events will be many times less than it could be. On the other hand, it takes much more computer memory and processing power to reconstruct images when nonplanar events are also included. The computing threshold was passed around 1999, and in modern scanners, the acceptance of events is opened up so that any pair of detectors can record an event. This is depicted in Figure 23-3.

Opening up the scanner has advantages and disadvantages. The advantage is collecting many more counts. When you collect more counts, you have better statistics, and the images look much better. On the other hand, many more random, scatter, and prompt gamma events are also recorded. Consider a scatter event. It might stay within a plane of detectors or it might scatter outside the plane. Because the plane is very thin, the overwhelming probability is that it will scatter out of the plane. If you have only a two-dimensional scanner, these scatter events will not become part of the data. However, if the scanner is operating in three-dimensional mode, scatter into neighboring planes will be recorded. Because of this, the fraction of recorded events that are scattered in a three-dimensional scanner can approach 50%. Hence, a robust and accurate scatter correction must be performed. The same consideration can be applied to the detection of random events. If there is a possibility of detecting events between any pair of detectors anywhere within the scanner, it is much more likely that a random event will be recorded. In many imaging situations, when the time window can be reduced to approximately 6 ns or less, the advantage of collecting more events outweighs the disadvantages. For this reason, scanners that are made with the faster, better time resolution detectors are those that principally operate in three dimensions. The quantitative technique for calculating how these unwanted events affect image quality is called noise equivalent counting.

Conversion of CT Images to PET Attenuation Maps

Photon transmission through a dense body can be expressed in terms of the linear attenuation coefficient, µ [1/cm]; µ is a function of the photon energy and electron density of the material traversed. Photon attenuation at CT diagnostic energies is dominated by the photoelectric effect and Compton scattering. Measured linear attenuation coefficients in CT imaging are determined with a continuous photon spectrum composed of bremsstrahlung and characteristic x-rays ranging from approximately 10 keV to the peak x-ray tube potential. Reconstructed CT attenuation values are expressed relative to water and termed Hounsfield units [HU = 1000 (µ − µ_water)/µ_water]. PET imaging occurs at 511 keV, where photon attenuation is dominated by Compton scattering. Therefore, CT data cannot be used directly to correct for attenuation of PET emission data. Instead, CT data are converted to 511-keV linear attenuation coefficients by segmentation or direct scaling.

Segmentation takes advantage of there being only a few primary tissue types in the field of view, such as bone, tissue, and lung. CT numbers (Hounsfield units) that fall within one of these groups are replaced with the appropriate linear attenuation coefficient at 511 keV. The advantage of this technique is that it reduces variation and noise in the image. The disadvantage is that it does not permit interindividual or intraindividual variation in the coefficients. It also forces all tissues into one of the segmented types. This method is now rarely used.

Direct scaling assumes a linear relationship between CT and PET attenuation. This is a good assumption in low-density tissues such as lung and soft tissue. Bone is an exception because its CT attenuation is dominated primarily by photoelectric contributions. Therefore, the linear relationship depends on the effective energy of the CT scan. So, an appropriate calibration curve needs to be a combination of two or more linear curves that cover the range of attenuation commonly found in the body. A bilinear relationship is a common conversion technique used in PET/CT scanners (Fig. 23-8).

FIGURE 23-8 Bilinear conversion of CT numbers to 511-keV linear attenuation coefficients. The change in slope occurs at 0 HU (water) and is a function of the different attenuation properties of soft tissue and bone and the voltage on the x-ray tube.

CT data are collected at higher resolution (typically 1- × 1- × 1-mm voxels) than are PET data (typically 6- × 6- × 6-mm voxels), requiring the converted CT image to be down-sampled to the PET image matrix size and smoothed with an appropriate kernel to match the PET resolution (Fig. 23-9). The attenuation map data are then used to correct the emission data.

FIGURE 23-9 CT image collected at 120 kVp (A), converted to 511 keV linear attenuation coefficients using the bilinear curve in Figure 23-8 (B), and down-sampled to the PET matrix size and smoothed with a 6-mm gaussian filter (C). The image in C is used to correct PET data for attenuation.

Attenuation Mismatch

Artifacts can arise from improper registration between the transmission and emission scans. The cause of such artifacts can be placed in three primary groups: (1) motion of the patient, such as large rigid body movements, which may occur during or between scans; (2) breathing motion, resulting from the mismatch in temporal resolution between the CT attenuation correction (acquired in <1 breath cycle) and the emission (acquired over many breath cycles) scans; and (3) drift of the contents of thoracic cavity drift, such as that induced by the administration of pharmacologic stressing agents and other factors leading to a shift in the heart’s position within the thoracic cavity. Each of these sources is discussed.

Motion of the Patient

Voluntary motion of the patient commonly occurs in response to discomfort experienced during long imaging scans. A motion event may occur between the CT and PET acquisition or, more commonly, during the PET study. Intra-scan motion is evident by mismatched boundaries and uptake in regions not normally associated with perfusion or increased metabolism (Fig. 23-10). Motion during a scan appears as blurred edges and loss of anatomic detail (Fig. 23-11).

FIGURE 23-10 A, Patient scanned with ⁸²Rb identified as having intra-scan motion evident from the apex of the myocardium positioned in the left chest wall. B, Lowering of the upper level display threshold of the PET scan makes the mismatch more apparent and reveals streak artifacts along the boundaries of the lungs, which is another sign of movement. C, A binary representation of myocardial uptake and attenuating tissue shows uptake overlying the left lung of the CT image. Overlying tissue is a strong indicator of misregistration. D, A binary myocardial uptake image overlaid on a segmented lung image again shows the myocardial uptake overlying the CT lung field.

FIGURE 23-11 Patient scanned with ⁸²Rb with no visual motion artifacts (A) and the same patient scanned earlier after moving during the emission study (B). Note the decreased blood pool to myocardium contrast and apparent loss of resolution.

Respiratory and Contractile Cardiac Motion

In dedicated PET systems, the long transmission time required for rotating radionuclide transmission sources around the body provides good respiratory and cardiac temporal averaging as is present in the emission scan. With the introduction of CT for attenuation correction, respiratory and contractile cardiac motion has considerably greater potential to unduly influence the attenuation correction because a fast helical CT scan fails to account for the time averaging observed in the emission acquisition (Fig. 23-12). As a result, the reported frequency of registration errors between the transmission and emission sequences has increased dramatically from dedicated PET systems² to PET/CT hybrid systems.³

FIGURE 23-12 An example of three different CT protocols for attenuation correction. A, Breath-hold CT at inspiration. This is unsuitable for attenuation correction. B, Free-breathing low-pitch CT. C, Free-breathing time-averaged cine CT. In B and C, note the superior alignment between the PET and CT images compared with the breath-hold CT.

Drift of Thoracic Contents

Drift of the thoracic contents, such as slow continuous movement of the heart, occurs in response to changes in the patient’s state, such as changes in lung volume as a result of the introduction of a pharmacologic stressing agent.² Misregistration caused by this mechanism is commonly observed as cardiac uptake overlying the CT lung field (Fig. 23-13). Furthermore, even in the presence of good respiratory averaged transmission data, drift of thoracic contents is still prevalent and is a main factor along with motion of the patient leading to registration errors in approximately one quarter of clinical perfusion studies. Given the nature of its mechanism, motion of the patient often cannot be accounted for by altering the transmission protocol and therefore requires that a post-reconstruction image registration method be available.

FIGURE 23-13 An example of misalignment between the emission and transmission examinations caused by drift of the heart. Notice that the myocardium in the PET image appears to have rotated relative to that in the CT image. A, Fused ⁸²Rb adenosine stress image. B, Segmented image of ⁸²Rb uptake overlaid on CT image. C, Segmented image of ⁸²Rb uptake overlaid on left lung of the CT volume.

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