Positron and Single Photon Emission Tomography

Robert T. Malison, Marc Laruelle, and Robert B. Innis

Modern brain imaging methods now afford unprecedented opportunities for the in vivo study of central nervous system (CNS) function. Within the field of psychopharmacology, interest in two radiotracer techniques, positron emission tomography (PET) and single-photon emission computed tomography (SPECT), has been particularly avid. Much of these methods' appeal derives from their conceptual relatedness to existing preclinical tools, including homogenate receptor binding, in vitro autoradiography, and radioimmunoassay. More compelling to clinical researchers, however, is the ability of PET and SPECT to provide noninvasive measurements of local neuronal activity, neurochemistry, and pharmacology in the living human brain. Despite their tremendous potential, these nascent technologies are as technically complex as they are promising. Thus, this chapter initially emphasizes the salient physical principles and intrinsic limitations of these methodologies before proceeding to a discussion of their specific applications in psychopharmacology (see Neurodevelopmental Perspectives on Schizophrenia, Maintenance Drug Treatment for Schizophrenia, and Amyloidogenesis in Alzheimer's Disease and Animal Models).

PET and SPECT are imaging techniques in which a radionuclide is synthetically introduced into a molecule of potential biological relevance and administered to a patient. Depending on the nature of the so-called radiopharmaceutical, it may be inhaled, ingested, or, most commonly, injected intravenously. The subsequent brain uptake of the radiotracer is measured over time and used to obtain information about the physiological process of interest. Because of the high-energy (g-ray) emissions of the specific isotopes employed and the sensitivity and sophistication of the instruments used to detect them, the two-dimensional distribution of radioactivity within a brain slice may be inferred from outside of the head. Thus, PET and SPECT are both emission and tomographic (from the Greek tomos for cut) techniques. Both features distinguish these modern imaging modalities from more conventional radiographic methods, like a chest X ray, where an external source of radiation is transmitted through the subject to create a planar silhouette of the body's organs and cavities. Whereas PET and SPECT rely on similar principles to produce their images, important differences in instrumentation, radiochemistry, and experimental applications are dictated by inherent differences in their respective physics of photon emission.

Unstable nuclides that possess an excess number of protons may take one of two approaches in an effort to reduce their net nuclear positivity. In one radioactive decay scheme, a proton is converted to a neutron and a particle called a positron (denoted e+ or b+) is emitted (33, 69). Of identical mass but opposite charge, positrons are the antimatter equivalent of electrons. When ejected from the nucleus, a positron collides with an electron, resulting in the annihilation of both particles and the release of energy. The principles of conservation of mass and momentum dictate that two g photons (rays) are produced, each of equivalent energy (511 keV) and exactly opposite trajectory (180° apart). For this reason, PET is sometimes referred to as dual photon emission tomography. Among the most commonly used positron-emitting nuclides in PET are included 11-carbon (11C), 13-nitrogen (13N), 15-oxygen (15O), and 18-fluorine (18F).

The unique spatial signature of back-to-back photon paths is cleverly exploited by PET scanners in locating the source of an annihilation event, a method known as coincidence detection (Fig. 1) (33, 50). A PET scanner may be conceptualized as a ringlike camera that surrounds the head. Instead of using photographic film, however, PET (and SPECT) scanners employ highly sensitive scintillation detectors made of dense crystalline materials (e.g., bismuth germanium oxide, sodium iodide, or cesium fluoride) which capture the invisible, high-energy g rays and convert them to visible light. This brief flash of light is converted into an electrical pulse by an immediately adjacent photomultiplier tube (PMT). The crystal and PMT together make up a radiation detector. Rather than using individual detectors in isolation, a PET camera is constructed such that opposing detectors are electronically connected. Thus, when separate scintillation events in paired detectors coincide (to within 3 to 10 nsec for practical purposes), an annihilation event is presumed to have occurred at some point along an imaginary line between the two. This information is registered by a computer and later used to reconstruct images using the principles of computed tomography (vide infra). Conversely, single events are ignored. Although it is conceivable that two unrelated photons from spatially separate annihilation events might reach opposing detectors in unison, these accidental coincidences are much less frequent than true ones. In fact, coincidence detection is a very efficient technique and contributes to PET's superior sampling rates and sensitivity. Nevertheless, random coincidences constitute one source of background noise in PET images (32, 33, 50).

One intrinsic limitation of PET derives from the nature of positron decay and the principle of coincidence detection. Specifically, PET recognizes the site of positron annihilation and not the site of radioactive decay. Since a positron must generally come to rest in tissues before being able to collide with an electron, annihilation often occurs some distance away from the positron's origin. The distance separating these two events, decay and annihilation, depends on the average kinetic energy of the positron as it leaves the nucleus, and varies according to the specific isotope involved (62) (Table 1). For 11C decay, this range is roughly 2 mm. In addition, if the positron is not entirely at rest at annihilation, photons will be emitted at an angle slightly different than 180°. Taken together, remote positron annihilation and photon noncolinearity place a theoretical limit on PET's achievable spatial resolution, which is estimated at 2–3 mm (50).

In an alternative scheme to positron emission, certain proton-rich radionuclides may instead capture an orbiting electron, once again transforming a proton to a neutron (69). The resulting daughter nucleus often remains residually excited. This metastable arrangement subsequently dissipates, thereby achieving a ground state and producing a single g photon in the process. Isotopes that decay by electron capture and/or g emission are used in SPECT, and include both 123-iodine (123I) and the long-lived metastable nuclide 99m-technetium (99mTc). Because g rays are emitted directly from the site of decay, no comparable theoretical limit on spatial resolution exists for SPECT. However, the emission of a single photon means that instrumentation in SPECT must be intrinsically different from that in PET. Instead of coincidence detection, SPECT utilizes a technique known as collimation (Fig. 2)(39). A collimator may be thought of as a lead block containing many tiny holes that is interposed between the subject and the radiation detector. The holes are sufficiently long and narrow so as to permit only photons of essentially parallel trajectory to pass through the collimator and reach the detector. Given knowledge of the orientation of a collimator's holes, the original path of a detected photon is linearly extrapolated. In contrast to parallel photons, g rays, which deviate slightly are absorbed by the lead and go undetected (Fig. 2). As might be imagined, collimation is less efficient than coincidence detection, because many potentially informative photons are filtered out (6). Although collimation is less sensitive than PET, advances in collimator design and radiation detection have made SPECT sufficiently sensitive for routine use in nearly all of the same applications (17, 39 ).

Although the physical principles relating to photon emission and detection are different, the means by which PET and SPECT translate information about photon paths into cross-sectional brain images are largely the same (5, 15, 59). Because only information about a photon's direction, not depth, is known, views of photon trajectories from multiple angles around the entire head are required. A set of measurements from a given angle or viewpoint is referred to as a projection. In PET, multiple projections are obtained by a ring of essentially contiguous radiation detectors (Fig. 1), whereas SPECT cameras typically use several detector heads that rotate around the subject in synchrony and collect data over an entire 360° (Fig. 2). After recording many thousands of trajectories from multiple projections, a picture of the distribution of radioactivity within a given brain slice is created by retracing or "backprojecting" the trajectories of g rays across the field of view for every imaging angle. The method of backprojection, although complex, is conceptually analogous to the simple childhood puzzle in which numbers in a square grid are inferred from their sums along each row. However, PET and SPECT images consist of much larger matrices (e.g., 128 x 128 or 256 x 256 elements) of radiation density values. Thus, fast computer coprocessors and efficient mathematical algorithms (fast Fourier transformations) are required to handle the enormous amounts of data and the intensive calculations involved. Once their radiation values are determined, individual matrix elements are assigned corresponding shades of color and displayed as picture elements or pixels on a video terminal. In this manner, a PET or SPECT image of the distribution of radioactivity within the brain is produced (Fig. 3).

In practice, the method of simple backprojection is rarely used for reconstructing images today. Rather a modified technique known as filtered backprojection is nearly universally applied (33, 39). The reason for filtering relates to quantitative imaging artifacts introduced by the method of backprojection itself, even in the absence of other sources of statistical noise (vide infra). In retracing a photon's path, the actual point of decay is indeterminate. Thus, the backprojection algorithm is forced to assume an equal probability of radioactive decay, and hence radiation value, for every point along the line of trajectory. Areas of the brain that have high concentrations of radioactivity will standout as many trajectories from multiple projections are superimposed and their probability values summed. However, areas that contain no radioactivity will bear the residual imprint of the algorithm's statistical guess, and small, but finite, values are ascribed to areas where none should exist. Although this problem decreases with increased spatial sampling and greater numbers of projections (8, 36), a filter is still required to restore quantitative accuracy by subtracting spurious values from the images. Multiple filtering techniques have been developed (e.g., Ramp, Butterworth, Hanning, etc.) (59), and the considerations involved in choosing one, although important, are beyond the scope of this chapter. However, suffice it to say that trade-offs between filters exist with respect to their relative impact on spatial resolution and noise amplification. Thus, filter selection depends on the imaging context.

Several physical factors affect the quantitative accuracy of PET and SPECT, including the statistics of radioactive decay, attenuation, scatter, limited spatial resolution, and partial volume effects (33, 50, 69).

The process of radioactive decay can be mathematically described by an exponential curve (69). The radioactive half-life, or T1/2 value, is the measure most commonly used to quantify the decay rate, and refers to the time required for half of the radioactive atoms to undergo transformation. Values of T1/2 vary between species, and can be determined for a given nuclide by taking multiple measurements of an isotopically pure sample over time. The characteristic T1/2 values of several commonly used PET and SPECT isotopes are listed in Table 1.

Although the half-life of an isotopic species is characteristically constant, the process of radioactive decay is fundamentally statistical. In other words, if one were to measure a radioisotope of essentially infinite half-life (i.e., infinitely constant radioactivity) over identical intervals of time, variations in individually recorded values would be observed. From the average of many values, the true radioactivity could be inferred. Importantly, this variation in sampling is independent of detection method and instead derives from the intrinsic probabilistic nature (as described by the Poisson distribution) of radioactive decay and the random fluctuation in individual decay events from moment to moment. The spatial equivalent of this temporal variation in sampling is a mottled appearance to images obtained from a container (or phantom) having a uniform concentration of radioactivity. Thus, the statistical nature of radioactive decay itself accounts for random inconsistencies in both PET and SPECT images. This statistical noise is inversely related to the square root of the counts acquired (7) and is easily reduced in images by collecting more counts. Longer sampling times and greater instrument sensitivity are the two principle ways in which PET and SPECT improve counting statistics. Depending on which approach is taken, however, improvements in statistical noise are generally traded for sacrifices in either temporal or spatial resolution, respectively. For example, larger collimator holes in SPECT allow greater numbers of events to be counted, albeit at the expense of including slightly less than parallel photons.

A significant number of high-energy g photons escape detection by PET and SPECT scanners as a result of their interactions with surrounding tissues. Two major types of interactions exist, Compton scattering and photoelectric absorption (69), and together they result in only a fraction of an internal radioactive signal reaching external radiation detectors. The physical basis for these attenuation effects derives from the interaction of g rays with atomic electrons. In Compton scattering, a g photon is deflected from its original trajectory after colliding with an electron and loses a fraction of its original energy in the process. Alternatively, collision may instead result in the complete absorption of a photon's energy. In the latter instance, the imparted kinetic energy is generally sufficient to eject the electron from the atom, and thus g radiation is said to be ionizing.

Because a photon's chances of being scattered or absorbed become greater as the distance a photon must travel increases, attenuation is said to be depth dependent and results in a progressive underestimation of radioactivity, which is greatest at the brain's center. The diminishment in signal strength can be significant, or roughly 4 to 5 times greater for deep as compared to superficial structures (39, 50). Accurately compensating for undetected photons is therefore critical for comparing levels of radioactivity in different regions of the brain (35). The most rigorous attenuation correction approaches utilize a preceding transmission study. In a manner exactly analogous to a CT scan, an individualized attenuation map of the entire head is produced by directing radiation from an external ring source through the subject. Such an approach is generally optimal since the size and shape of patients' heads vary and because the attenuation properties of bone, tissue, fluid, and air differ. Although most PET scanners currently employ this technique, SPECT cameras have only recently implemented transmission scanning in research applications.

Photon attenuation is less problematic for PET than for SPECT. Since photons in PET have higher energies (i.e., 511 keV) than those in SPECT (typically 80–160 keV), they are less prone to attenuation (Table 1). Moreover, linear attenuation is largely depth independent in PET because of coincidence detection. More simply explicated, the probability that dual photons will be detected is equal for all such pairs along a given trajectory because the combined distance traveled by each pair is identical. As a result, a less rigorous, mathematical estimation is often reasonable in PET brain imaging. This first-order approximation involves fitting an ellipse to images of the brain and uniformly assigning a single attenuation value (typically equal to that of water) to all points within the ellipse (14). At present, most commercially available SPECT cameras utilize this second approach, despite uncertainties as to the precise levels of error incurred. Thus, estimating the error associated with algorithmic approximations, and correcting for these, whether by instrumentation or reconstruction techniques, is currently an area of active research, and should help to improve the quantitative potential of SPECT.

Accurate reconstruction in PET and SPECT depends on the detection of high-energy photons that travel in a straight path. However, Compton effects cause photons to deviate from their original trajectories. Since many scattered photons retain a sufficient degree of energy to escape from the brain, the detection of scattered events leads to the misinterpretation of photon trajectories (Fig. 2) and produces errors in image reconstruction. The net effect of such errors is similar to that of accidental coincidences, namely an increase in background noise that compromises image contrast.

Current methods of correcting for scatter most commonly rely on the loss of energy incurred by photons as a result of their interactions with electrons. PET and SPECT cameras are routinely equipped to measure the energy spectrum of photons, a range that not only includes the primary photopeak of unaffected g rays but also the lower energy components that constitute scattered events. Accurately discriminating between true and scattered photons is often difficult, however, since the energy resolution of current PET and SPECT scanners is limited and photopeak energies are normally distributed. Thus, scatter and photopeak windows inevitably overlap. Algorithms for subtracting the scatter fraction from the photopeak window can partially compensate for this problem. As noted above, however, Compton scattering is a depth-dependent phenomenon and occurs in proportion to the electron density of the medium traversed. Hence, the development of more sophisticated correction methods to address regional differences in scatter and incorporate a priori information about brain structure is among the most active areas of research in image reconstruction (39).

Immediately apparent to the first-time observer of PET and SPECT images is a fuzzy or blurred quality to the pictures. This impressionistic appearance, although permitting a general sense of gross anatomical features, hinders discrimination of finer structures. In fact, this subjective sense of imprecision in visual detail is the qualitative consequence of emission tomography's limited spatial resolution. Less readily recognized, yet more critically important, are the quantitative implications of finite resolution and their influence on the measured radioactivity in individual brain regions (33, 50). The opposite side of the same conceptual coin, partial volume effects specifically denote the latter repercussions and require a more objective understanding of spatial resolution and its definition.

Definitions of spatial resolution in PET and SPECT derive from the desire to specify that distance by which two objects must be separated to perceive them as discrete (Fig. 4). In an ideal detection device, an infinitely small isotopic source might be rendered graphically as a vertical line whose infinitely narrow width reflected perfect spatial resolution. When viewed in an actual PET or SPECT scanner, however, radioactivity from such a point source is spread-out and appears as a Gaussian curve. This so-called point (or line) spread function characterizes a camera's resolving capacity and reflects the degree of spatial diffusion of imaged radioactivity. The full-width-at-half-maximum (FWHM), or the width of the Gaussian at half of the curve's peak activity, is the parameter most commonly used to define resolution. When two points are separated by the distance equal to the FWHM, the peaks of both sources begin to be distinguishable.

Apart from theoretical limitations arising from positron range (62), image resolution is principally determined by instrumentation and physical factors, such as the precision of collimation, the number and size of detectors, and the accuracy in localizing scintillation events within the crystalline elements. Although rapid advances in instrumentation may make these published numbers obsolete, resolution currently averages 5 to 6 mm and 6 to 8 mm FWHM for PET and SPECT scanners, respectively. However, researchers have already developed a single-slice PET instrument that approaches theoretical limits of accuracy (3 mm FWHM; University of California at Berkeley), and improvements in collimation and detector technology are likely to lead to similar advances for future SPECT instruments.

One type of partial volume effect arises intuitively from the apparent spatial diffusion of activity created by limited scanner resolution. Much as the ambient light in that part of a room distant from two lamps depends on the relative brightness and closeness of each, so too the measured radioactivity in a given brain region reflects the relative activity and geometric relationship of neighboring structures. Thus, brain regions having relatively lower concentrations of radioactivity will appear "hotter" in PET and SPECT images as imaged activity spills over from adjacent (more active) areas. Conversely, as the physical dimensions of a relatively more active region become less than 2 to 3 times the FWHM resolution, the measured concentration of radioactivity is effectively diluted, as averaging with adjacent (less active) areas from within the overall field of resolution occurs (31, 43). Brain regions of identical radioactivity therefore appear to have differing concentrations based on their relative sizes (53). By visual analogy, the combined effects of partial voluming result in sharp peaks and steep canyons of brain radioactivity being rendered as short hills and shallow valleys in PET and SPECT images.

Several methods are currently available for dealing with errors due to limited spatial resolution and partial volume effects. In one approach, errors created by partial voluming are simulated in a plastic model or phantom. Models typically consist of cavities that are filled with radioactivity and approximate the actual distribution of tracer in the brain. For example, finely machined, polycarbonate brain phantoms are commercially available to recreate the geometry of gray and white matter. By imaging such phantoms, regionally specific correction factors, or recovery coefficients, are derived that may be applied when imaging human subjects. Although this method is convenient, it is unable to account for pathological and nonpathological variations in brain anatomy. As a result, investigators have increasingly utilized structural (e.g., CT, or MRI) scans from individual subjects. Once acquired, an MR or CT scan is aligned with a subject's own functional (i.e., PET or SPECT) study using one of a variety of computer-assisted, image coregistration techniques, thereby creating an individualized brain atlas of matching anatomical relationship (52, 61). Anatomical areas can be identified on the high-resolution structural image, and a redirected region of interest template can be applied to the high-sensitivity functional data. In addition, anatomical information may be combined with a priori functional (e.g., relative blood flow ratios in gray and white matter) and physical information (e.g., a PET or SPECT camera's three-dimensional point spread function) to mathematically correct for partial volume errors (55). Thus, in conditions where changes in brain anatomy are likely to accompany changes in brain physiology (e.g., cortical atrophy in Alzheimer's disease), the latter approach will be highly desirable and will help to tease apart the relative structural and functional contributions to imaging abnormalities.

With limited exceptions, an ideal radiopharmaceutical is one that can be synthesized in high chemical purity, in high radioactive yield, and in small mass quantities. These requirements, namely high purity and high specific activity (expressed in units of radioactivity per chemical quantity; e.g., Ci/mmol), help to insure that the specific biological system of interest is adequately measured, yet unperturbed, by the tracer. However, the physical nature of radioactive decay and the short half-lives of most suitable radionuclidic species (Table 1) work against these radiochemical goals. For example, although chemical yield generally improves with increasing reaction times, radioactivity diminishes with decay (16). As a result, optimal activities require a balanced synthetic scheme to maximize chemical yields, minimize unwanted reaction byproducts, and still enable prompt purification of the compound. For both PET and SPECT, specific activities of greater than 2000 Ci/mmol are generally desirable and achievable. Although a limited number of radiochemical syntheses are now automated and performed in robotically controlled hot cells (e.g., [18F]-2-fluoro-2-deoxyglucose; [18F]FDG), most radiopharmaceuticals are still manually prepared by radiochemists racing against the clock of a nuclide's decay.

The particularly narrow radiochemical window for positron-emitting radionuclides has special implications for the construction of PET-imaging facilities. Specifically, the most commonly used PET isotopes include 15O, 13N, 11C, and 18F, which have half-lives of 2, 10, 20, and 109 min, respectively. Because of their extremely rapid decay, essentially all PET isotopes must be produced on the premises. One exception is 18F, whose nearly 2-hr half-life could conceivably permit a regional facility to produce quantities for a large or nearby metropolitan center. Nevertheless, most PET centers have an on-site cyclotron, which generates radionuclides for real-time utilization. In contrast, SPECT isotopes, like 123I, have a sufficiently long half-life (13 hr) to enable centralized production at distant (>3000 miles) commercial reactors and to allow delivery via express mail. Alternatively, 99mTc (T1/2 = 6 hr) may be obtained from inexpensive molybdenum generators located in most hospital radiopharmacies. A cyclotron is expensive (typically $1 to $2.5 million) and requires a highly skilled staff for its operation and maintenance. Hence, the cost associated with PET is a significant disadvantage relative to SPECT.

The chemical nature of a radiotracer depends upon the physiological process to be studied. For example, the measurement of regional cerebral blood flow relies on relatively nonspecific diffusable tracers, which may be foreign to biological systems (e.g., the gaseous tracer 133Xe). Most neurochemical processes in the brain require greater biochemical selectivity. As a result, PET and SPECT radiotracers typically are naturally occurring substances, structural analogs, or pharmaceuticals that selectively label target sites in the brain. PET radiochemistry offers significant versatility here, because 11C can be relatively easily substituted for 12C in existing organic molecules without altering their chemical properties. Even though fluorine is not commonly found in human biochemistry, native hydrogen moieties may frequently be replaced by 18F without significant isotopic effects (e.g., [18F]FDG) (16). Thus, even though their half-lives are a liability, the chemical nature of PET radionuclides eases the radiochemist's task. In contrast, SPECT nuclides are not intrinsic to most neurotransmitters or biological substrates. The metallic nature and multiple valence states of 99mTc necessitate bulky complexing groups for its molecular stabilization. These barriers have thus far limited the use of 99mTc to nonselective processes (e.g., the blood flow agent [99mTc]-hexamethyl propyleneamine oxime; [99mTc]HMPAO). On the other hand, rapid advances in iododemetallation procedures and increasing knowledge of the structure–activity relationships of pharmacologically active compounds have fueled the development of 123I-containing tracers. For example, iodinated radioligands now permit SPECT imaging of several neurotransmitter receptors (38, 42, 45, 56) and uptake sites (57). In fact, the lipophilic nature of 123I may actually facilitate transfer across the blood–brain barrier and, in some instances, improve affinity of the parent compound at its site of action (46).

Many useful in vitro radioligands may be entirely useless in vivo because of their handling by human physiology. For example, an ideal radiopharmaceutical must easily enter the brain. Hence, tracer binding to plasma proteins must be readily reversible, and its transport across the blood–brain barrier must be favorable. Except for tracers with facilitated carriers (e.g., [18F]-FDG), the latter necessitates that a ligand be sufficiently lipid-soluble to permit its passive diffusion into the brain. Equally important, and a counterbalancing factor in this regard, is the signal-to-noise properties of a tracer. Namely, measurable specific binding is often compromised for highly lipophilic tracers by high levels of nonspecific binding. Thus, lipophilicity as well as affinity are both important factors influencing an imaging agent's signal-to-noise ratio (42). Additionally, peripheral metabolism of the tracer must not be too rapid, or central availability will be secondarily reduced. Moreover, metabolites should either be hydrophilic, so that they do not cross the blood–brain barrier, or if lipophilic, be non–radioactive so as to prevent extraneous sources of central radioactivity from confounding central measurements.

Although PET and SPECT images provide measures of regional radioactivity, tracer concentrations in the brain are frequently influenced by processes other than the one of physiological interest, like the peripheral clearance of tracer from plasma and the regional cerebral blood flow. As a result, model-based methods are required to distill from imaging data that component of activity that reflects purely the process under study. Although such models are extremely important for analyzing PET and SPECT measurements, the complexity of such modeling techniques is beyond the scope of this chapter. A general introduction to basic concepts with a focus on neuroreceptor binding may nonetheless provide a basis for understanding more comprehensive discussions (10, 11, 30).

Approaches for quantitating physiological processes can be broadly divided into empirical ratio and model-based methods (12). Empirical ratio methods use the ratio of activity in a region of interest (ROI) compared to that in either the whole brain or a region of reference (e.g., a region devoid of receptors) as outcome measures. The principle advantage of this approach is simplicity, since multiple image acquisitions and multiple plasma measurements are not required. However, a major limitation of ratio methods is their inability to account for variations in regional radioactivity, which may arise from differences in blood flow, nonspecific binding, or peripheral clearance of the tracer. Hence, the impact of nonspecific factors on empirical methods must be first evaluated with model-based methods.

Model-based methods relate the observed concentration of activity in a brain ROI to that in the arterial circulation through a defined model. As opposed to empirical methods, model-based methods may require multiple measurements of both brain and arterial, metabolite-corrected, tracer concentration over time in order to derive quantitative physiological parameters (e.g., receptor density, Bmax; receptor affinity, 1/KD). Even though model-based methods are technically difficult to perform and less suited to routine clinical applications, they are needed to validate simpler empirical methods.

The type of physiological parameters that can be derived from a PET or SPECT study depends on whether equilibrium is reached during the experiment. For neuroreceptor binding, equilibrium is reached when the rate of association and dissociation to and from the receptors are equal. At equilibrium, the relationship between the specifically bound (Be) and the intracerebral level of free tracer (F) satisfies the Michaelis-Menten equation

During the initial phase following a bolus injection of tracer (uptake phase), the rate of association to receptors is higher than the rate of dissociation (Fig. 5), and specific binding (B) increases. This phase will last as long as B is lower than its calculated equilibrium value (Be). After variable periods of time (ranging from a few minutes to more than 24 hr), the specific binding reaches equilibrium (B = Be and the association is equal to the dissociation). Equilibrium is momentary, however, because F is continually falling due to peripheral clearance of the radioligand. As a result, B exceeds Be, dissociation increases relative to association, and B decreases as tracer leaves the brain (washout phase).

The time at which equilibrium occurs depends on several factors, including peripheral clearance, blood flow, tracer mass, association (kon) and dissociation (koff) rate constants, and receptor density (Bmax). For some ligands, several hours are required to reach equilibrium, and only the association phase is observed during the time frame of the experiment (typically 1 to 2 hr). From the standpoint of modeling, binding is sometimes referred to as irreversible under these circumstances. Conversely, when equilibrium occurs during the experiment, binding is said to be reversible. This distinction is important and determines the physiological parameters that can be derived from an experiment. For reversible ligands, the outcome measure of experiments performed at tracer doses (high specific activity) is the binding potential (BP) or equilibrium volume of distribution (V3; vide infra), which equals the product of receptor density and affinity (Bmax/KD) (54). For irreversible ligands, the outcome measure is the association rate (usually referred to as k3, vide infra). Experiments involving the administration of pharmacological (i.e., nontracer) doses are needed to obtain separate estimations of Bmax and KD. These parameters have been measured with paired tracer and pharmacological dose experiments for both reversible (19, 34) and irreversible ligands (70, 71).

Most model-based methods rely on the notion of a compartment. A compartment is a physiological or biochemical space in which the tracer concentration is assumed to be homogeneous at all times. A model consists of a given compartmental configuration and forms the basis for a mathematical description of a tracer's behavior in a biological system. One of the most general configurations for describing a neuroreceptor ligand's behavior is depicted in Fig. 6 (24, 25, 54). For brain regions with specific binding sites (i.e., receptors), a capillary compartment (C1), an intracerebral compartment (C2) in which the tracer is free, a nonspecifically bound compartment (C´2), and a specifically bound compartment (C3) are specified. The transfer of a tracer between compartments is governed by a corresponding set of fractional rate constants (i.e., k1 to k6). A fractional rate constant defines the direction and the rate of transfer between compartments, expressed as a fraction of the concentration in the originating compartment per unit of time. Thus, the change in tracer concentration in any given compartment can be expressed in mathematical terms as the amount of tracer entering and leaving per unit time.

In practice, the four-compartment model described above is difficult to implement for reasons of mathematical and experimental complexity, and circumstances generally require simplification of the model. The model depicted in Fig. 7 represents a more workable model for PET and SPECT experiments. The parameters K1 and k2 describe the exchange of tracer across the blood–brain barrier and are dependent on blood flow and extraction (diffusion). Compartments C2 and C´2 are combined to form a single, nondisplaceable compartment. Pooling these compartments assumes that the rate of nonspecific binding in the brain is rapid relative to the rate of other processes measured in the experiment. The ratio of free-to-total tracer concentration in the arterial compartment (Ca) is designated f1; similarly, the ratio of free-to-total tracer in C2 is designated f2. Both f1 and f2 are assumed to be constant over time. Thus, k3 corresponds to the bimolecular process of receptor association [kon(Bmax - B)f2] and k4 represents the dissociation rate constant (koff).

In a PET or SPECT experiment, the arterial concentration of free tracer is experimentally measured over time [f1Ca(t)]. Simultaneously, the activity in a brain ROI [CROI(t)] is also measured. Thus, the activity measured in a brain ROI is the sum of activities in the second and third compartments [CROI(t) = C2(t) + C3(t)], after subtracting the amount of activity present in brain vasculature. The ratio of these two measures, namely the ratio of tissue to free arterial tracer, at time t is known as the tissue distribution volume [Va(t)]. A conceptual or virtual volume, Va(t) denotes the volume of tissue in which the tracer would be distributed were the tissue concentration equal to that of free tracer in plasma. The equilibrium distribution volume (V) of a compartment is the corresponding ratio at equilibrium, that is, when no net transfer occurs between the plasma and tissue compartments (Vi = Ci/f1Ca). For example, V2 and V3 are the equilibrium distribution volumes of the nondisplaceable and receptor compartments, respectively, and the total tissue equilibrium volume of distribution equals their sum (i.e., VT = V2 + V3). Thus, the binding potential may be expressed in several ways based on the following mathematical relationship.

Several model-based methods exist for quantitating receptors and can be divided into kinetic (54), graphical (51, 60), and equilibrium (19) approaches. Kinetic and graphical methods can be applied to both reversible and irreversible ligands, whereas equilibrium methods can be used only for reversible ligands.

The kinetic method yields quantitative information about receptors from the estimation of individual fractional rate constants (54). The rate constants are usually estimated by a least-squares procedure that minimizes the difference between the measured and modeled values of ROI activity. The modeled values of ROI activity are obtained from the arterial time-activity curve and the mathematical description of the system. In the corresponding mathematical language of signal processing, modeled values of ROI activity are said to derive from the convolution of the input and impulse response functions, respectively. The latter is generally defined by a sum of n exponential equations, where n is the number of observed compartments in the ROI.

In the graphical approach, the relationship between brain and blood activity data is linearized by various techniques, and the parameters of interest are obtained by linear regression (51, 60). Such techniques have the relative advantage of computational simplicity. For example, in the case of reversible ligands, the total tissue volume of distribution, VT, can be determined graphically by plotting ROI(t)/ROI(t) versus ROI(t)/Ca(t) (51). The slope of the linear portion of this graph is VT in a region with receptors. In a region of reference (i.e., devoid of receptors), the slope is equal to the nonspecific tissue distribution volume, V2. Assuming equal nonspecific binding in both regions, and given that VT = V2 + BP (vide supra), BP is easily obtained. Graphical methods for analyzing irreversibly bound tracers (e.g., [18F]FDG) have also been developed (29, 60). The ability of the latter methods to provide information about receptor density requires careful evaluation, however, because the relative ratio of k2 to k3 will determine whether linear regression provides information primarily about receptor density, blood flow, or a combination of both.

Equilibrium methods derive receptor parameters from the analysis of the activity distribution at equilibrium (19). The peak equilibrium method provides a measure of VT at peak uptake (Fig. 5). At this single point in time, a ratio of ROI activity (CROI) to free arterial tracer concentration [f1Ca(t)] yields VT. One difficulty associated with this method is the proper identification of the time of peak brain activity. Since plasma tracer concentration falls rapidly after bolus administration, errors in the estimation of the time of peak can lead to errors in the estimation of VT. To overcome these difficulties, a tracer may instead be administered as a bolus followed by a constant infusion (13, 48). Under these conditions, equilibrium will be sustained, and VT is measured directly from the ratio of ROI and plasma activities. As before, BP may be calculated if V2 is known, as determined either from a region of reference or as the ROI activity remaining after injection of a receptor-saturating dose of a nonradioactive competitor (48).

The uses of PET and SPECT brain imaging can be roughly divided into measurements of local neuronal activity, neurochemistry, or in vivo pharmacology.

Local neuronal activity is associated with energy consumption and can be measured with glucose metabolism which itself is usually positively coupled with blood flow. Thus, PET tracers for measurement of local neuronal activity include [18F]FDG (glucose metabolism) and [15O]H2O (blood flow). On the other hand, SPECT does not have a comparable tracer for glucose metabolism but does have 99mTc- and 123I-labeled agents, as well as 133Xe to provide measures of blood flow.

Neuronal metabolic demands are felt to primarily reflect terminal rather than cell body activity. That is, in any given volume of brain, the majority of [18F]FDG uptake is thought to be in terminals rather than cell bodies, a conclusion that is based upon a limited number of studies in which the cell bodies are anatomically distant from their terminals (41, 65). Whether this applies to cortical regions is unknown but may be a moot point if the majority of terminals in any region primarily derive from local circuit neurons. However, metabolic rate does not distinguish activity of excitatory and inhibitory neurons. Although increased [18F]FDG uptake is usually interpreted as increased functional activity of a region, it may, in fact, reflect an overall decreased activity based upon increased firing of inhibitory interneurons.

The clinical uses of PET and SPECT imaging to measure local neuronal activity are largely restricted to neurological disorders and include localization of both cerebral ischemia and epileptic focus and distinguishing radiation necrosis from tumor growth. In at least the latter two conditions, imaging results can directly impact clinical care. For example, the neurosurgical treatment of patients with medication refractory epilepsy critically depends upon accurate localization of the seizure focus, which is often distant from the surface of the brain and poorly localized by scalp electrode electroencephalogram (EEG). In the interictal period, the seizure focus is hypometabolic and has decreased blood flow. PET and SPECT imaging has been used either as a primary means of localization or confirmation of other diagnostic tests to select the portion of the brain that is subsequently resected. In the ictal period, the seizure focus is associated with increased metabolism and increased blood flow and may have a greater likelihood of showing positive localization than interictal imaging.

Using [15O]H2O, PET imaging has been elegantly combined with neuropsychological activation studies to localize cognitive functions, including reading, speaking, and word associations. The short half-life of 15O (T1/2 of 2 min) allows multiple (often 8 to 10) bolus injections of the tracer in one experimental session. Thus, both baseline scans and those following neuropsychological tasks can be repeated and averaged.

Recently developed techniques in functional MRI offer great promise to provide measures of local neuronal activity similar to those from PET and SPECT imaging. The primary signal from functional MRI is believed to derive from the concentration of deoxyhemoglobin (58). Functional MRI is superior to PET and SPECT in that it involves no radiation exposure and has greater temporal (<1 sec) and spatial (<1 mm) resolutions. If these methods are fully developed with adequate quantitation, they may largely supplant PET and SPECT for measures of local neuronal activity.

Two major attributes of both PET and SPECT, high sensitivity and chemical selectivity, make these methods particularly well suited for in vivo neurochemical measurements. The sensitivity of PET and SPECT to detect radiotracers is less than 10-12 M, which is orders of magnitude greater than the sensitivity of MRI (10-3 to 10-5 M). In a manner exactly analogous to nonradioactive drugs, radiotracers can be developed to label specific target sites in the brain. These specific tracers can, thereby, provide measures of multiple neurochemical pathways in the brain, including synthesis and release of transmitters, receptors, reuptake sites, metabolic enzymes, and possibly even second messenger systems. Of these multiple neurochemical systems in the brain, the greatest effort has been devoted to imaging of dopaminergic transmission, and this system is now briefly summarized as an example of the types of measurements provided by these methods.

6-[18F]Fluoro-L-3,4-dihydroxyphenylalanine ([18F]- FDOPA) has been successfully used in animal and human studies to provide a measure of dopamine (DA) terminal innervation of the striatum (27). These studies have demonstrated decreased striatal uptake in Parkinsonian patients compared to healthy subjects (9). Furthermore, these studies have questioned the widely held notion that symptoms develop only after 85% to 90% depletion of endogenous DA levels. Imaging studies of patients with early signs of the disorder suggest symptoms may begin with only a 50% to 60% decrease in striatal DA terminal innervation (49).

Following injection of [18F]FDOPA in primates, the majority of striatal activity represents a combination of [18F]fluorodopamine and the metabolite [18F]fluoro-3-methoxydopamine (28). Thus, quantitation of the imaging results is not definitive, in part because of the presence of radiolabeled metabolites in striatum.

After conversion to [18F]fluorodopamine by aromatic L-amino acid decarboxylase, the striatal activity is believed to be largely trapped in the brain during the time of a typical PET experiment. Based upon studies in animals under normal physiological conditions, conversion of [18F]fluorodopamine to radiometabolites that leave the brain is considered negligible. However, DA turnover (measured as the ratio of metabolite to the transmitter) is typically increased in animals with nigrostriatal lesions and in postmortem Parkinsonian brain (40). A result of this enhanced turnover is that an increased proportion of radiometabolites may leave the brain of Parkinsonian patients compared to healthy subjects and thereby exaggerate the deficits in these patients measured with [18F]FDOPA.

A potential method for the measurement of transmitter release involves the displacement of receptor radiotracers by the endogenous transmitter. On first consideration, this displacement may seem impossible, since the endogenous transmitter tends to have a much lower affinity than the tracer for the receptor. For example, [11C]raclopride has an IC50 value (which is inversely related to affinity) for the dopamine D2 receptor of approximately 1 nM, whereas the IC50 value for dopamine itself may be as high as 1 mM (66). How then could dopamine effectively compete with [11C]raclopride for binding to the D2 receptor? This potentially confusing question can be more simply understood by considering equilibrium and dynamic conditions. In an equilibrium state, if the displacer (in this case, dopamine) is present at a concentration equal to its IC50 value, then 50% of the receptors will be occupied by the drug and 50% of the radioligand (which is associated with negligible receptor occupancy) will be displaced. Viewed in this more straightforward manner, the real questions of feasibility will be determined by physiological concentrations of DA in the synapse, the in vivo inhibition constant (Ki) of DA for the receptor, and whether adequate time has elapsed to establish equilibrium-binding conditions. Several investigators have provided evidence from in vivo labeling studies in rodents that both the resting levels of synaptic DA and stimulant-induced DA release are associated with significant D2 receptor occupancy, which is mirrored by comparable displacement of radiotracer from the receptor (63, 64, 73). Furthermore, recent PET and SPECT dopamine D2 receptor imaging studies in humans and monkeys support this notion and may in the future provide quantitative measures of DA release (18, 37).

Receptor studies have probably received the greatest effort among the various targets of neurochemical imaging. If a receptor is selectively altered in a specific disease, then imaging of this site may provide diagnostic information about the disorder. For the DA receptor system, the Johns Hopkins PET group has reported that drug-naive schizophrenic patients have a 2.5-fold elevation of dopamine D2 receptor density in the striatum using the virtually irreversible tracer [11C]N-methylspiperone and kinetic modeling (72). In contrast, the PET group at the Karolinska Institute, Sweden have reported normal levels of D2 receptor densities in drug-naive schizophrenic patients using the reversible radiotracer [11C]raclopride and an equilibrium approach (21). Reasons for these disparate results have received significant scrutiny but remain elusive (1, 66, 67). The use of different tracers and data-analyzing methods are presently being examined by each group using the probe developed at the other institution.

Several radiotracers for the DA transporter have been developed: [11C]cocaine, [11C]nomifensine, [11C]CFT (also designated WIN 35,428), [123I]b-CIT (also designated RTI-55), and [18F]GBR 13119 (2, 23, 44, 57, 68). [18F]GBR 13119 and [11C]nomifensine have relatively high nonspecific uptake. Radiolabeled cocaine may be particularly useful for studying the pharmacokinetics of the parent compound but has the limitations of relatively high nonspecific binding and rapid uptake and clearance from the brain. In comparison to cocaine, the analogs CFT and b-CIT have higher affinity (approximately 10- and 150-fold, respectively), lower nonspecific binding, and slower brain kinetics.

The transporter is located presynaptically on terminals of dopamine projections from substantia nigra to striatum. Thus, the transporter is a marker for DA terminal innervation, which is decreased in patients with idiopathic Parkinson's disease. The striatal uptake of both [11C]CFT (26) and [123I]b-CIT (38) have recently been shown to be markedly decreased in patients with Parkinson's disease in comparison to healthy subjects of similar mean age (Fig. 3). Imaging with these tracers may be a useful research tool for early diagnosis and for monitoring the progression of the disorder.

Metabolism of a neurotransmitter can be studied by injection of selective inhibitors of the catabolic enzymes. For example, deprenyl is an irreversible inhibitor of monoamine oxidase type B (MAO-B), and imaging with 11C-labeled deprenyl has been reported to provide a measure of regional enzyme activity in the brain (3, 22). With [11C]deprenyl, PET scanning may provide useful dose–response measurements in patients treated with MAO inhibitors (47). Furthermore, reversible MAO inhibitors like [11C]Ro19-6327 may have advantages relative to the irreversible agents in terms of data analysis and ease of performing in vivo occupancy studies (4).

Since receptors are frequently the targets of therapeutic medications, several investigators have argued that receptor imaging may be used to more accurately monitor drug treatment than is possible with measurement of plasma levels of the medications. For example, a nonresponding patient might have normal or even elevated levels of a medication that does not cross the blood–brain barrier and reach its target site in brain. In this case, neuroreceptor imaging would certainly demonstrate the lack of significant receptor occupancy. However, such a hypothetical clinical situation would appear to represent an essential abnormality in the patient's blood–brain barrier. Such a defect would presumably be associated with nonresponsiveness to a variety of centrally active medications and has not been clearly shown to exist.

Several pharmaceutical companies and academic researchers have begun to explore the role of receptor imaging in new drug development. The two basic methods are the radiolabeling of the target compound (e.g., with 11C) or the in vivo screening of the effects of the intravenously administered nonradioactive compound with previously developed radiotracers. The first method is probably better suited to PET radiochemistry, which can more easily provide a pharmacologically identical radiolabeled form of the target compound than SPECT, which would likely use an iodinated analog. However, the second method may be equally well performed with PET or SPECT provided that an appropriate radiotracer has been developed for each method.

Brain imaging studies of antipsychotic medications provide an example of advantages and limitations of both these methods. Several pharmaceutical companies are trying to develop atypical medications like clozapine, which would have superior efficacy and fewer side effects than typical antipsychotic medications. Studies with [11C]clozapine have been relatively disappointing because of the high nonspecific uptake of the radioactivity. In fact, these results may prove to be typical, since only a small percentage of potential compounds prove to be useful in vivo radiotracers with low nonspecific binding. On the other hand, studies of nonradioactive antipsychotic medications with established and selective receptor tracers have provided valuable information on both the receptor occupancy profiles and the pharmacokinetics of brain uptake. For example, Farde and coworkers (20) have shown that, in comparison to several typical neuroleptic medications, clozapine is associated with a disproportionately high occupancy of D1 relative to D2 receptors. Novel therapeutic compounds could be examined for both the pharmacokinetics of entry into the brain and their receptor occupancy profiles, which will provide the combined effect of the parent compound and any active metabolites. Although the authors are not aware of any therapeutic compound whose development has been significantly enhanced with neuroreceptor imaging, this potential application is receiving growing attention.

PET and SPECT imaging are methods of high sensitivity in which the injection of radioactively labeled drugs are used to provide measures of local neuronal activity, in vivo neurochemistry, or in vivo pharmacology. These methods are particularly attractive to clinical researchers, because they can be applied to the living human brain. The g-ray emissions pass directly through the skull, and the camera measurements truly provide a window on the brain. Perhaps the two greatest barriers to wider application of these research methods are their high cost and technical complexity. With regard to cost, further development and validation of SPECT is justified in the reasonable expectation that tracers and paradigms will be developed that are adequate for clinical research studies. With regard to technical complexity, both PET and SPECT will continue to require multidisciplinary collaboration from the fields of drug development, radiochemistry, instrumentation physics, pharmacology, compartmental modeling, radiation health physics, and the basic and clinical neurosciences. This field will require additional training and orientation by all members of the research group, and this chapter has reviewed several of the important methodological aspects of functional imaging that may be useful to those entering this exciting research field. R. T. Malison: Department of Psychiatry, Yale University School of Medicine, Connecticut Mental Health Center, New Haven, Connecticut 06508.

published 2000