Abstract
^{11}CABP688 is a new PET ligand to assess the subtype 5 metabotropic glutamate receptor (mGlu_{5}). The purpose of this study was to evaluate different methods for the analysis of human ^{11}CABP688 data acquired from 6 healthy, young volunteers. Methods: The methods were a 1tissuecompartment model (K_{1}, k_{2}″), a 2tissuecompartment model (K1–k4), and the noncompartmental method developed by Logan. Parameters related to receptor density were the total distribution volume (DV), DV″ (= K_{1}/k_{2}″, 1 tissue compartment); specific DV, DV_{C2} (= K_{1}/k_{2}′ × k_{3}′/k_{4}, 2 tissue compartments); and DV_{tot} for the noncompartmental method. Results: The 1tissuecompartment model was too simple to adequately fit the data. DV_{C2} calculated with the 2tissuecompartment model ranged from 5.45 ± 1.47 (anterior cingulate) to 1.91 ± 0.32 (cerebellum). The corresponding values for DV_{tot}, calculated with the 2tissuecompartment model and the Logan method (in parentheses), were 6.57 ± 1.45 (6.35 ± 1.32) and 2.93 ± 0.53 (2.48 ± 0.40). There was no clear evidence of a region devoid of mGlu_{5} receptors. The firstpass extraction fraction exceeded 95%. The minimal scan duration to obtain stable results was estimated to be 45 min. Conclusion: ^{11}CABP688 displays favorable kinetics for assessing mGlu_{5} receptors. For tracer kinetic modeling, 2tissuecompartment models are clearly superior to models with only 1 tissue compartment. In comparison to the compartmental models, the Logan method is equally useful if only DV_{tot} values are required and fast pixelwise parametric maps are desired. The lack of regions devoid of receptors limits the use of reference region methods that do not require arterial blood sampling. Another advantage of the tracer is the fast kinetics that allow for relatively short acquisitions.
As of today, 8 subtypes of the metabotropic glutamate receptor have been cloned (mGlu_{1}–mGlu_{8}). Based on their aminoacid sequence, pharmacology, and second messenger coupling, these receptors have been classified into 3 groups (I–III) (1). Group I includes mGlu_{1} and mGlu_{5} receptors; Group II includes mGlu_{2} and mGlu_{3} receptors; and Group III includes mGlu_{4}, mGlu_{6}, mGlu_{7}, and mGlu_{8} receptors. Recent discoveries of small molecules that selectively interact with receptors of Groups I and II have allowed significant advances in the understanding of the roles of these receptors in brain physiology and pathophysiology (2). Based on the wide and consistent effects of selective noncompetitive allosteric antagonists such as MPEP (2methyl6(phenylethynyl)pyridine) in animal models for anxiety (3,4), it has been hypothesized that the mGlu_{5} receptor could be a valuable target for the treatment of anxietyrelated disorders (5–7). Although several mGlu_{5} receptor antagonists have successfully been used in vitro to label mGlu_{5} receptors (8,9), the development of these ligands to useful PET tracers has proven difficult. Only recently has a series of PET ligands allowing in vivo imaging in rhesus monkeys been described (10). Lately, we identified another promising ligand: ^{11}CABP688 (3(6methylpyridin2ylethynyl)cyclohex2enoneO^{11}Cmethyloxime). This compound is a highly selective allosteric antagonist of the mGlu_{5} receptor in vitro, and initial studies have demonstrated a high selectivity for mGlu_{5} receptors in vivo (11,12). The major purpose of this study was to evaluate several methods of analyzing human ^{11}CABP688 data. The chosen methods were compartmental modeling using 1 and 2 tissue compartments and the method developed by Logan et al. (13).
MATERIALS AND METHODS
Synthesis of ^{11}CABP688
The synthesis of ^{11}CABP688 has been described in detail elsewhere (12). Briefly, desmethyl ABP688 was reacted with ^{11}Cmethyl iodide produced from the GE PET trace system at 90°C for 5 min. The product was purified by semipreparative highperformance liquid chromatography using a reversedphase column. ^{11}CABP688 for in vivo administration to humans was formulated using 0.15 M phosphate buffer and ethanol. Specific activity ranged from 70 to 95 GBq/μmol at the time of injection. This activity corresponds to 0.71–1.04 μg of cold ABP688.
Study Population
Six healthy male volunteers (mean age, 25 y; range, 21–33 y) were studied. None of the subjects had a history of neurologic disorders. The study was approved by the local ethical committee, and written consent was obtained from each volunteer.
PET
The PET studies were performed in 3dimensional mode on a wholebody scanner (Discovery LS, GE Healthcare). This scanner has an axial field of view of 14.6 cm and a reconstructed inplane resolution of 7 mm. Before positioning of the volunteers on the scanner, catheters were placed in an antecubital vein for tracer injection and the contralateral radial artery for blood sampling. A 10min ^{68}Ge transmission scan was acquired for correction of photon attenuation. Transaxial images of the brain were reconstructed using filtered backprojection (128 × 128 matrix, 35 slices, 2.34 × 2.34 × 4.25 mm voxel size).
H_{2}^{15}O PET.
Each ABP688 study was preceded by an evaluation of cerebral perfusion (cerebral blood flow [CBF]) using H_{2}^{15}O. For this purpose, 400–500 MBq of H_{2}^{15}O were injected intravenously using an automatic injection device, which delivers a predefined dose of H_{2}^{15}O over 20 s. After arrival of the bolus in the brain, a series of eighteen 10s scans was initiated. The time course of the arterial radioactivity was continuously assessed in a coincidence counter (GE Healthcare), through which blood from the radial artery was run.
^{11}CABP688 PET.
Ten minutes after the H_{2}^{15}O measurement, 300–350 MBq of ^{11}CABP688 was injected as a slow bolus over 2 min, and a series of 20 scans was initiated (10 × 60; 10 × 300 s; total study duration, 60 min). For determination of the arterial input curve, arterial blood samples were collected every 30 s for the first 6 min and then at increasing intervals until the end of the study. An aliquot of whole blood and plasma was measured in a γcounter. Authentic tracer and labeled metabolites in plasma were separated using Waters SepPak tC18 cartridges. A solution of 200 μL of plasma diluted with 2.5 mL of water was passed through the cartridges and eluted with 5 mL of water. Previous highperformance liquid chromatography studies had shown that the authentic compound was adsorbed in the cartridge and the metabolites were collected in the eluted fraction.
MRI
MRI was performed to exclude a cerebral pathologic condition. For each subject, T1weighted (3dimensional spoiled gradient echo, 0.86 × 0.86 × 1.5 mm pixel size) and T2weighted (fast spin echo, 0.43 × 0.43 × 5 mm pixel size) wholebrain images were acquired on a 1.5T Signa Excite system (GE Healthcare).
Data Analysis
CBF Measurement.
Quantitative parametric maps representing regional CBF were calculated from the H_{2}^{15}O images using the integration method described by Alpert (14). The method yielded maps of K_{1} and k_{2}, which represent regional CBF and regional CBF/p, respectively (p = partition coefficient). The underlying model is depicted in Figure 1.
Models and Parameters for Receptor Density.
The investigated methods consisted of standard compartmental modeling and the method described by Logan et al. (13). Tracer kinetic modeling was performed using the models depicted in Figure 1. They contain 1 and 2 tissue compartments. The notation using primes is borrowed from Koeppe et al. (15). The meaning of the parameters is as follows. C_{1} denotes the concentration of specifically and nonspecifically bound ligand in the 1tissuecompartment model and denotes the concentration of nonspecifically bound ligand in the 2tissuecompartment model. C_{2} denotes the concentration of ligand bound to receptors. K_{1} describes uptake of tracer across the blood–brain barrier and is related to CBF and the firstpass extraction fraction EF (K_{1} = CBF EF). k_{2}″ and k_{2}′ represent backdiffusion from tissue to vascular space in the 1 and 2tissuecompartment models, respectively. k_{3}′ describes the transfer of ligand to the receptor, , where k_{5} and k_{6} denote the exchange of ligand between the free and nonspecific compartments in the full 3tissuecompartment model. The term is equivalent to the term f2 used by Mintun et al. (16) and others. k_{4} is equal to k_{off} and represents the dissociation constant. DV″ is the total DV of tissue activity calculated with the 1tissuecompartment model (K_{1}/k_{2}″). DV_{C1} is the DV of compartment C_{1} = K_{1}/k_{2}′. DV_{C2} is the DV of compartment C_{2} = K_{1}/k_{2}′k_{3}′/k_{4.} DV_{tot} is the total DV of tissue activity calculated with the 2tissuecompartment model (DV_{C1} + DV_{C2} = K_{1}/k_{2}′ (1 + k_{3}′/k_{4}).
Tracer exchange between the compartments is described by the following differential equations:Eq. 1Eq. 2Eq. 3
Equations 1 and 2 describe tracer exchange in the 2tissuecompartment model; Equation 3, in the 1tissuecompartment model. Because the total activity measured in a region is composed of counts from tissue and blood, all models contained a parameter (α) correcting for blood activity.Eq. 4where C_{VOI} is the PET counts in a volume of interest, α is the percentage of intravascular space in tissue, C_{tot} is the activity in the extravascular compartment (with the 2tissuecompartment model, C_{tot} is the sum of C_{1} and C_{2}, and C_{blood} is the total blood activity). C_{tot} was calculated by numeric integration of the differential equations, and α was fixed at 0.05.
Outcome measures related to the density of mGlu_{5} receptors are summarized in Table 1. Method A uses the 1tissuecompartment model, and the only useful outcome measure related to receptor density is the total DV, DV″. Methods B–D use the 2tissuecompartment model and several combinations of parameter coupling. The latter was described in detail previously (17). In short, if one assumes that certain parameters or combinations of parameters are equal among different brain regions, it may be useful to perform simultaneous fitting of all these regions with the constraint of common parameter values. In method C, it was assumed that DV_{C1} was equal in all regions; in method D, DV_{C1} and k_{4}. The coupling encompassed all gray matter regions. With the 2tissuecompartment model, measures related to receptor density were DV_{tot} and DV_{C2}.
The Logan plot (13) is a graphical method applicable for analyzing the uptake of reversible receptor tracers. Hereby, the transformed tissue activities are plotted as a function of the transformed plasma activities . After some equilibration time, the plotted values approach a linear function and can be described by a regression line. The start time of the linear section in the graphical plot was fitted using an error criterion of 10% as implemented in the dedicated PMOD software (www.pmod.com). It has been shown that the regression slope represents the total DV, DV_{tot}, plus the vascular fraction α. Because the Logan method is fast and robust, it is ideally suited for pixelwise analyses.
VolumeofInterest Analysis
For the determination of C_{voi} in Equation 4, volumes of interest were defined over various structures. For this purpose, the scans were summed and anatomic volumes of interest were defined for each subject individually. The volumes of interest encompassed 4 cortical regions (frontal, parietal, temporal, and occipital), 2 regions within the cingulate gyrus (anterior and posterior), 3 regions in the prosencephalon (caudate, putamen, and thalamus), 3 regions in the limbic systems (medial orbitofrontal cortex, amygdala, and mediotemporal lobe), 1 brain stem region, the cerebellar cortex, and a white matter region.
Tissue time–activity curves were then derived from these volumes of interest. The models were subsequently fitted to these time–activity curves using numeric integration of the operational Equation 4 and Marquart's leastsquares algorithm. In addition, parametric maps of K_{1} and DV_{C2} were calculated using model B, with DV_{C1} fixed to the value obtained from fitting the time–activity curves using model C. The parametric maps were calculated by voxelwise leastsquares fitting. All calculations were performed using PMOD.
Assessment of Methods
Several criteria were used to assess the different models. Goodness of fit was evaluated using F test statistics, the Akaike information criterion (AIC) (18), and visual inspection of the residuals.
F test:Eq. 5
The AIC is defined as follows:Eq. 6
In Equations 5 and 6, Q_{A} and Q_{B} represent the sum of squares for the fit with models A and B, respectively; p_{A} and p_{B} are the number of parameters of models A and B; and n is the number of data points. With the F test, an F value greater than 3.63 corresponds to a significant improvement using model B (P < 0.05). With AIC, model B is considered to lead to significantly better fits than model A if AIC B is less than AIC A.
The percentage coefficient of variation (COV) across the 6 subjects was chosen as a measure of the stability of the estimated parameters: %COV = SD/mean × 100. Another measure was the COV derived from the covariance matrix calculated with the MarquardtLevenberg algorithm.
The effect of study duration on parameter stability was estimated by consecutively shortening the fitting interval in a simulation study from 90 to 5 min. For this purpose, time–activity curves representing a region with a high receptor density (anterior cingulate) were generated using a typical arterial input function and model B. For each study duration, 1,000 curves were generated, and each COV calculated from these parameter sets was taken as a measure of parameter stability.
An alternative to bolus injection is a protocol using a bolus plus a constant infusion. The advantage is that complete equilibrium may be achieved between the tracer concentrations in all relevant compartments. The ratio of tracer in tissue to tracer in plasma then directly reflects DV_{tot}. On the basis of the kinetic parameters determined in this study, a simulation was performed to estimate the time point at which equilibrium would be achieved with a “bolus plus constant infusion” protocol. The bolus fraction relative to the infusion rate was calculated as described by Carson et al. (19).
RESULTS
Time Course in Arterial Plasma
The time course of total ^{11}C activity in arterial plasma demonstrated the typical shape, with a peak at 30–60 s, which was followed by a rapid decline. The fraction of authentic ^{11}CABP688 dropped to 64%, 44%, 35%, 28%, 26%, and 25% at 5, 10, 15, 30, 45, and 60 min, respectively.
One Versus 2 Tissue Compartments
Examples of tissue time–activity curves of the mediotemporal lobe (high receptor density) and cerebellum (low receptor density) are displayed in Figure 2. Already, the residuals reveal a bias in the fit with the 1tissuecompartment model, indicating that this model is not sufficient to fit the data. This bias is confirmed by the data presented in Table 2. Adding a second tissue compartment significantly reduced the residual sum of squares in almost all subjects and all regions (F test). An exception was white matter, for which the 2tissuecompartment model was unstable. Introducing restrictions such as parameter coupling within the 2tissuecompartment model did not significantly worsen the fits. The superiority of the 2tissuecompartment model is furthermore demonstrated by the decline of the AIC and the underestimation of the total DV using the 1tissuecompartment model (Table 2).
Comparison of Variously Derived DVs
The results are summarized in Table 3. With all 2tissuecompartment models, the highest DV_{C2} was found in the anterior cingulate. The coupling of parameters yielded a markedly lower %COV of DV_{C2} in most regions, an effect that was most pronounced in the areas with high receptor density. The lowest %COV of DV_{C2} was achieved using model D, in which DV_{C1} and k_{4} were coupled. In contrast, the effect of parameter coupling on the %COV of DV_{tot} was less pronounced. The same result was obtained by comparing the %COV calculated from the covariance matrix. In the anterior cingulate, %COV for DV_{C2} was 9.5% for model B and dropped to 8.2% and 4.6% for models C and D, respectively (median value of all 6 subjects).
There was excellent agreement between DV_{tot} values calculated with the 2tissuecompartment model and the Logan method.
CBF, K1, k3′, k4, and FirstPass EF
The data on CBF, K1, k3′, k4, and firstpass EF are shown in Table 4. K_{1} values calculated with the 1tissuecompartment model A are markedly (up to 50%) lower than those derived from the 2tissuecompartment models. Parameter coupling generally led to lower %COVs of K_{1}, k_{3}′, and k_{4} in most regions; however, there were quite a few exceptions. The largest effect of parameter coupling was observed on the %COV of k_{3}′. The %COV calculated from the covariance matrix revealed a similar result. In the anterior cingulate, the %COV of k3′ dropped from 9.7% with model B to 8.2% and 4.0% with models C and D, respectively (median value of all subjects).
The data listed in Table 4 allow estimation of the firstpass EF. Use of the equation EF = K_{1}/CBF yields a value for EF of 0.96 ± 0.05 (model B, mean among all regions and subjects).
The close correlation of K_{1} and CBF is furthermore demonstrated in the left panel of Figure 3. This panel also demonstrates the severe underestimation of K_{1} using the 1tissuecompartment model. On the other hand, no correlation was found between DV_{tot} (or DV_{C2}, data not shown) and CBF (right panel of Fig. 3).
Parametric maps of CBF, K_{1}, and DV_{C2} together with the MRI scans are demonstrated in Figure 4. Image quality was high. The similarity in the patterns of K_{1} and CBF is obvious, as is the difference from the pattern of DV_{C2}.
Effect of Study Duration on Parameter Stability
The results of the simulation study are presented in Figure 5. The least effect of shortening the scan duration was found for K_{1}. With a scan duration of 5 min, stable K_{1} values could already be calculated. Longer scan durations were needed to obtain stable results for DV values. A steep increase in %COV is seen for DV_{tot} and DV_{C2} for scan durations of less than 45 min, at which time %COV was on the order of 12.4% and 10.5%. This value dropped to under 10% with 60 min of data. The actual values of DV_{C2} and DV_{tot} were markedly underestimated with scan durations of less than 20 min. With scan durations of longer than 20 min, the bias dropped to under 3%.
“Bolus Plus Constant Infusion” Protocol
In the “bolus plus constant infusion” protocol, the optimal bolus fraction was dependent on the region. A bolus fraction of 53 times the infusion rate per minute was considered a suitable compromise. This value was the mean of the optimal fraction determined for the anterior cingulate (high receptor region) and cerebellum (low receptor region). The simulated time course of the ratio C_{tissue}/C_{plasma} is demonstrated in Figure 6 for the anterior cingulate and cerebellum. At 30 min, the ratio in the anterior cingulate and cerebellum reached 98% and 108%, respectively, of the equilibrium value. The corresponding values were 99% and 103% at 40 min, finally reaching 100% and 99.9% at 60 min.
DISCUSSION
Tissue Compartment Models and the Logan Method
This study clearly demonstrated that a 2tissuecompartment model is superior to a 1tissuecompartment model for analyzing ^{11}CABP688 data. With the latter, the fits in basically all regions were biased and K_{1} and the total DV were underestimated. One advantage of the 2tissuecompartment model is that specific and nonspecific binding can potentially be separated. In the present study, DV_{C2} in the putamen was 74% of total DV. A disadvantage of the 2tissuecompartment model is that the calculation of parametric maps is not as straightforward as with the 1tissuecompartment model. Although it is possible to compute DV_{C2} on a voxel basis, as is demonstrated in Figure 4, one has to fix DV_{C1} to a common value. Without such a measure, voxelwise fits using leastsquare methods become unstable (20).
An elegant alternative for computing parametric maps is the Logan method as used in this study. Its disadvantage is that only DV_{tot}—and no measure for specific binding—can be calculated. However, there are applications in which the assessment of DV_{tot} is sufficient. For example, in blockade studies the change in DV_{tot} from a baseline to blockade may yield the needed information. The excellent agreement between DV_{tot} calculated with the 2tissuecompartment model and the Logan method suggests that both methods are equally valid. The slight underestimation of DV_{tot} as estimated with the Logan method is most likely due to the presence of statistical noise, as has been described elsewhere (21).
An important question is whether quantification of mGlu_{5} density might be possible without arterial blood sampling, which is associated with some discomfort for volunteers or patients. Such methods exist if there is a reference region that is devoid of receptors (22–24). Often, the cerebellum or the brain stem is such a region. For ^{11}CABP688, the situation is not entirely clear yet. However, the fact that DV_{tot} values are only slightly more than 50% lower in the cerebellum than in the anterior cingulate indicates that mGlu_{5} density in the cerebellum is not negligible. This hypothesis is further supported by the finding that DV_{C1}, reflecting nonspecific binding, is only one third of DV_{tot} in the cerebellum. If the cerebellum were devoid of mGlu_{5} receptors, one would expect DV_{tot} to equal DV_{C1}. However, this study does not prove to what extent DV_{C1} really reflects nonspecific binding, and values derived from tracer kinetic modeling alone have to be interpreted with caution.
In methods C and D, the distribution of nonspecific binding was assumed to be the same in all regions. This assumption was supported by previous animal studies on mice and rats, which demonstrated a homogeneous ^{11}CABP688 distribution after blocking of mGlu_{5} (12,25).
CBF, K_{1}, k_{3}′, k_{4,} and FirstPass EF
The firstpass EF of 96% is extremely high and is likely due to the high lipophilicity of the tracer. As a consequence, K_{1} maps quantitatively reflect CBF, which is illustrated in the left panel of Figure 3. This high EF also leads to high image quality. However, high lipophilicity is often not an advantage for a receptor tracer. If it is coupled with a high k_{on} and a low k_{off}, a high fraction of the delivered tracer would remain bound to the receptors in a blood flow–dependent manner. However, this situation is not the case for ^{11}CABP688. The dissociation constant k_{4} is large enough to drive the tissue uptake toward an equilibrium state. Nevertheless, full equilibrium between tissue and plasma cannot be achieved with a bolus injection alone. That is why some mathematic algorithm is used to calculate DV or similar receptor density–related parameters. Alternatives to bolus injection are the protocols that add a constant infusion to the bolus. Such “bolus plus constant infusion” protocols have several advantages. They can lead to a fully equilibrated state in which the ratio of tracer in tissue to tracer in plasma is by definition DV_{tot}. Another advantage is that no arterial input function is needed. Such protocols have been used with various tracers. Recently, Koeppe et al. applied such a protocol to measurement of the vesicular monoamine transporter type 2 with ^{11}Cdihydrotetrabenazine (26). If the bolus fraction is large enough, tracer uptake reflects K_{1} at early time points and tracer accumulation is related to DV at later time points, when the compartments are at equilibrium. The ratio of bolus to infusion rate can be optimized as published by Carson et al. (19). Our analysis yielded an optimal bolustoinfusion rate ratio of 53. As demonstrated in Figure 6, equilibrium would then be achieved after 40 min, which would keep the scanning time reasonably short.
CONCLUSION
^{11}CABP688 displays favorable kinetics for assessing mGlu_{5} receptors. For tracer kinetic modeling, 2tissuecompartment models are clearly superior to models with only 1 tissue compartment. In comparison to the compartmental models, the Logan method is equally useful if only DV_{tot} values are required and if fast pixelwise parametric maps are desired. The lack of regions devoid of receptors limits the use of reference region methods that do not require arterial blood sampling. Another advantage of the tracer is the fast kinetics, which allow for relatively short acquisitions.
Acknowledgments
This study was financially supported in part by the Swiss National Science Foundation. We thank Milen Blagoev and Cyrill Burger for their support in this study.
Footnotes

COPYRIGHT © 2007 by the Society of Nuclear Medicine, Inc.
References
 Received for publication January 4, 2007.
 Accepted for publication March 23, 2007.