Validation and Reproducibility of Measurement of 5-HT 1A Receptor Parameters with [ carbonyl - 11 C]WAY-100635 in Humans: Comparison of Arterial and Reference Tissue Input Functions

Abstract

Serotonin 5-HT_1A receptors are implicated in the pathophysiology of neuropsychiatric conditions. The goal of this study was to evaluate methods to derive 5-HT_1A receptor parameters in the human brain with positron emission tomography (PET) and [carbonyl-¹¹C]WAY 100635. Five healthy volunteer subjects were studied twice. Three methods of analysis were used to derive the binding potential (BP), and the specific to nonspecific equilibrium partition coefficient (k₃/k₄). Two methods, kinetic analysis based on a three compartment model and graphical analysis, used the arterial plasma time-activity curves as the input function to derive BP and k₃/k₄. A third method, the simplified reference tissue model (SRTM), derived the input function from uptake data of a region of reference, the cerebellum, and provided only k₃/k₄. All methods provided estimates of regional 5-HT_1A receptor parameters that were highly correlated. Results were consistent with the known distribution of 5-HT_1A receptors in the human brain. Compared with kinetic BP, graphical analysis slightly underestimated BP, and this phenomenon was mostly apparent in small size-high noise regions. Compared with kinetic k₃/k₄, the reference tissue method underestimated k₃/k₄ and the underestimation was apparent primarily in regions with high receptor density. Derivation of BP by both kinetic and graphical analysis was highly reliable, with an intraclass correlation coefficient (ICC) of 0.84 ± 0.14 (mean ± SD of 15 regions) and 0.84 ± 0.19, respectively. In contrast, the reliability of k₃/k₄ was lower, with ICC of 0.53 ± 0.28, 0.47 ± 0.28, and 0.55 ± 0.29 for kinetic, graphical, and reference tissue methods, respectively. In conclusion, derivation of BP by kinetic analysis using the arterial plasma input function appeared as the method of choice because of its higher test—retest reproducibility, lower vulnerability to experimental noise, and absence of bias.

Serotonin (5-HT) projections, arising from the dorsal and median raphe nuclei, innervate virtually all regions of the brain (Steinbusch, 1981). 5-HT_1A receptors are somatodendritic autoreceptors in the raphe nuclei and postsynaptic receptors in the neocortex, hippocampus, and other limbic structures (Wright et al., 1995; Blier et al., 1998). Abnormalities in the density of these receptors have been described in postmortem brain samples from subjects with schizophrenia, and less consistently, in depressed subjects and suicide victims (see reference lists in Arango et al., 1995; Gurevich and Joyce, 1997). Modulation of 5-HT_1A receptor function has also been implicated in the mechanism of action of antidepressant drugs (Blier et al., 1998). However, the exact function of these receptors and their involvement in neuropsychiatric conditions remains to be elucidated. Imaging 5-HT_1A receptors with positron emission tomography (PET) provides a unique opportunity to better characterize the function of 5-HT_1A receptors.

WAY-100635 [N-(2-(4-(2-methoxyphenyl)-1-piperazinyl)ethyl)-N-(2-pyridinyl) cyclohexane carboxamide] is a 5-HT_1A antagonist with high affinity and selectivity for 5-HT_1A receptors (K_D = 0.1–0.4 nmol/L)(Forster et al., 1995; Gozlan et al., 1995). Initial PET studies in monkeys and humans supported the potential of WAY-100635 labeled with ¹¹C in the O-methyl position as a PET radiotracer (Mathis et al., 1994; Pike et al., 1995a). However, [O-methyl-¹¹C]WAY-100635 is rapidly metabolized into a more polar metabolite, [O-methyl-¹¹C]WAY-100634, which crosses the blood-brain barrier and has high affinity for both 5-HT_1A and adrenergic α₁ receptors (Osman et al., 1996). An elegant solution to this problem was provided by Pike et al. (1995b), who suggested placement of the C-11 labeling atom in the cyclohexanecarbonyl moiety of the molecule (that is, [carbonyl-¹¹C]WAY-100635). In contrast with [O-methyl-¹¹C]WAY-100635, the radioactive metabolite generated by the hydrolysis of [carbonyl-¹¹C]WAY-100635 does not cross the blood-brain barrier. As a result, the brain time-activity curves were not contaminated with radioactively labeled metabolites, the signal-to-noise ratio of [carbonyl-¹¹C]WAY-100635 was dramatically enhanced compared with [O-methyl-¹¹C]WAY-100635, and quantitative derivation of 5-HT_1A receptors parameters became feasible (Pike et al., 1995b).

Quantification of human 5-HT_1A receptors with [¹¹C]WAY 100635 (from here on, [¹¹C]WAY 100635 designates [carbonyl-¹¹C]WAY-100635) was initially reported by Farde et al. (1998). Kinetic analyses based on a three compartment model, graphical analysis, and transient equilibrium analysis methods were used to compare the binding potential (BP) normalized to the cerebellum distribution volume (denoted here as k₃/k₄) in four regions of the human brain. Each method generated different estimates of k₃/k₄. Gunn et al. (1998) quantified 5-HT_1A receptor k₃/k₄ in four human brain regions. Two kinetic methods were evaluated: one method used the arterial plasma concentration as the input function, and the second method used an input function derived from a background region (reference tissue model). Again, discrepancies between estimates of k₃/k₄ by the two methods were reported. Recently, two groups, both using the reference tissue model, reported generalized decreases in [¹¹C]WAY 100635 k₃/k₄ in patients with major depression (Drevets et al., 1999; Sargent et al., 2000).

The general scope of the current investigation was to further evaluate quantification of 5-HT_1A receptor parameters in the human brain with [¹¹C]WAY 100635. The first aim of the current study was to compare the test—retest variability (TRV) of two receptor parameters, BP and k₃/k₄. In this paper, the term BP refers to the distribution volume of the specifically bound radiotracer relative to the plasma concentration, and k₃/k₄ refers to BP normalized to the distribution volume of a reference region devoid of receptors. The second aim of the study was to evaluate the discrepancies between the values of k₃/k₄ as returned by different analytical approaches (kinetic, graphical, and reference tissue models) in more detail. The third aim was to determine the reliability of 5-HT_1A parameter measurements in small and discrete limbic brain regions. Previously published studies restricted their analyses to relatively large brain regions, such as the medial temporal lobe (with the notable exception of the dorsal raphe). The medial temporal lobe encompasses several limbic structures of interest, such as the amygdala, the hippocampal formation, the parahippocampal gyrus, the uncus, and the entorhinal cortex. To evaluate the potential of [¹¹C]WAY 100635 imaging for studying the role of 5-HT_1A receptors in the limbic system, the authors investigated the reliability of 5-HT_1A receptor measurements in these subregions of the medial temporal lobe.

Five healthy male volunteer subjects were studied twice with [¹¹C]WAY 100635, and data were analyzed with three general methods: three compartment kinetic analysis using an arterial input function (Mintun et al., 1984), graphical analysis using an arterial input function (Logan et al., 1990), and kinetic analysis based on an input function derived from a region of reference, that is, the cerebellum (Lammertsma and Hume, 1996). Outcome measures derived with these three methods were compared using several criteria, including identifiability, stability, variability, and reliability.

MATERIALS AND METHODS

Human subjects

Five healthy male volunteer subjects age 29 ± 4 years (mean ± SD) were scanned twice on the same day to evaluate the reproducibility of the outcome measures. The study was approved by the Columbia Presbyterian Medical Center Institutional Review Board, and subjects provided written informed consent after receiving an explanation of the study. The absence of medical, neurologic, and psychiatric history (including alcohol and drug abuse) was assessed by history, review of systems, physical examination, routine blood tests, urine toxicology, and electrocardiogram. Subjects were not taking any medication for at least two weeks before the scans.

Radiochemistry

[¹¹C]WAY 100635 was prepared as previously described (Hwang et al., 1999). Specific radioactivity at the time of injection was 1047 ± 288 Ci/mmol (n = 10, range 428 to 1355 Ci/mmol). Injected dose was 8.8 ± 3.0 mCi (n = 10, range 5.5 to 12.9 mCi). Injected mass was 3.7 ± 1.3 μg (n = 10, range 1.2 to 5.8 μg).

PET protocol

Subject preparation included placement of arterial and venous catheters, fiducial markers and a polyurethane head immobilizer. Four fiducial markers, filled with C-11 (about 2 μCi per marker at time of injection) were taped on the subject's heads. Head movement was minimized with a polyurethane head immobilizer system (Soule Medical, FL), molded around the head of the subject. This system provides better restraint than a thermoplastic mask (Mawlawi et al., 1999). PET imaging was performed with an ECAT EXACT 47 scanner (Siemens/CTI, Knoxville, TN). This camera generates 47 slices covering an axial field of view of 16.2 cm. The transverse and axial resolutions at the center of the field of view were 6.0 and 4.6 mm FWHM respectively in 3D mode. The axial sampling was 3.4 mm. A 10 minute transmission scan was obtained before radiotracer injection. [¹¹C]WAY 100635 was injected intravenously as a bolus over 45 seconds. Emission data were collected in the 3D mode for 120 minutes as 21 successive frames of increasing duration (3 × 20 seconds, 3 × 1 minute, 3 × 2 minutes, 2 × 5 minutes, 10 × 10 minutes). Images were reconstructed to a 128 × 128 matrix (pixel size of 2.5 × 2.5 mm²). Reconstruction was performed with attenuation correction using the transmission data and a Shepp reconstruction filter with a cutoff of 0.5 cycles/projection rays. Subjects were rested outside the camera for 15 to 30 minutes between injections.

Input function measurement

After radiotracer injection, arterial samples were collected every 5 seconds with an automated sampling system for the first 2 minutes, and manually thereafter at longer intervals. Thirty-one samples were obtained for each experiment. After centrifugation (10 minutes at 1,800 g), plasma was collected in 200 μL aliquots, and radioactivity was counted in a gamma counter (Wallac 1480 Wizard 3M Automatic Gamma Counter) calibrated at regular intervals with the PET camera using an ¹⁸F solution.

Samples collected at 2, 6, 12, 20, 40, and 60 minutes were processed by protein precipitation using acetonitrile followed by high pressure liquid chromatography (HPLC) to measure the fraction of unmetabolized [¹¹C]WAY 100635. Plasma samples (0.5 mL) were added to 0.7 mL acetonitrile, mixed, and centrifuged at 14,000 g for 3.5 minutes. The acetonitrile solution was separated and analyzed by HPLC. The HPLC system consisted of a Waters 510 isocratic pump (Waters, Milford, MA, U.S.A.), a Rheodyne injector with a 2-mL loop (Alltech Associates, Deerfield, IL, U.S.A.), a Phenomenex C18 ODS column (10 micron particle size, 250 × 4.6 mm; Torrance, CA, U.S.A.), and a Gamma detection system (Bioscan Flow Count Unit; Washington, DC, U.S.A.). The column was eluted with a solvent mixture of acetonitrile/0.1 mol/L aqueous ammonium formate (50/50) at a flow rate of 2 mL/min. Five fractions collected over 12 minutes were counted. A standard [¹¹C]WAY 100635 solution was processed with each experiment. Unmetabolized [¹¹C]WAY 100635 eluted with fractions 3 and 4. For each sample, the unmetabolized [¹¹C]WAY 100635 fraction was estimated by the decay-corrected ratio of activity in collections 3 and 4 to the total collection.

The six measured unmetabolized [¹¹C]WAY 100635 fractions were fit to the sum of one exponential and one constant, with the value at time zero constrained to one hundred percent. The input function was the product of total counts and interpolated unmetabolized [¹¹C]WAY 100635 fraction. The measured input function values (C_a(t), μCi/mL) were fit to a sum of three exponentials (this function was fit from the time of the peak to the last data point, whereas the rising part of the curve was fit as a straight line between the first point and the peak). The fitted values were used as input to the kinetic and graphical analyses. The clearance of the unmetabolized [¹¹C]WAY 100635 (C_L, L/h) was calculated as the ratio of the injected dose to the area under the curve of the input function (Abi-Dargham et al., 1994).

For the determination of the plasma free fraction (f₁), triplicate 200 μL aliquots of plasma collected before injection were mixed with radiotracer, pipetted into ultrafiltration units (Centrifree, Amicon, Danvers, MA), and centrifuged at room temperature (20 minutes at 4000 g). Plasma and ultrafiltrate activities were then counted, and f₁ was calculated as the ratio of ultrafiltrate to total activity concentrations. Triplicate aliquots of tracer in pH 7.4 Tris buffer were also processed to determine the filter retention of free [¹¹C]WAY 100635.

MRI acquisition and segmentation procedures

Magnetic resonance imagings (MRIs) were acquired on a GE 1.5 T Signa Advantage system (GE Medical Systems, Milwaukee, WI, U.S.A.). Following a sagittal scout (localizer), performed to identify the anterior commissure-posterior commissure plane (1 minute), a transaxial T1 weighted sequence with 1.5 mm slice thickness was acquired in a coronal plane orthogonal to the anterior commissure-posterior commissure plane over the whole brain with the following parameters: three-dimensional SPGR (Spoiled Gradient Recalled Acquisition in the Steady State); repetition time 34 milliseconds; echo time 5 milliseconds; flip angle of 45 degrees; slice thickness 1.5 mm and zero gap; 124 slices; field of view 22 × 16 cm; with 256 × 192 matrix, reformatted to 256 × 256, yielding a voxel size of 1.5 mm × 0.9mm × 0.9 mm; and time of acquisition 11 minutes. Magnetic resonance imaging segmentation between gray matter, white matter, and cerebrospinal fluid pixels was performed as previously described (Abi-Dargham et al., 2000).

Image analysis

Image analysis was performed with MEDx (Sensor Systems, Sterling, Virginia, U.S.A.) with PET-PET frame realignment, PET-MRI registration, and time-activity curve measurement.

Frame realignment. To correct for head movement, frames were coregistered to the first frame of the study using a least square algorithm for within modalities coregistration (automated image registration) (Woods et al., 1992). The x, y, and z coordinates of the pixel with highest intensity within each fiducial marker were used to monitor the quality of between frame coregistration. Only minimal head movement was observed in this study.

PET-MRI registration. After frame to frame registration, the 21 PET frames were summed, coregistered, and resampled to the MRI using automated image registration. The summed PET image was used because it contains counts from the initial flow-dependent activity distributions that enhance detection of boundaries of regions with low receptor density, such as the cerebellum. The parameters of the spatial transformation matrix of the summed PET data set were then applied to each individual frame. Thus, each PET frame was resampled in the coronal plane to a voxel volume of 1.5 × 0.9 × 0.9 mm³.

Region of interest tracing and activity sampling. Fifteen regions of interest (ROIs) and one region of reference (cerebellum) were reported. Region of interest boundaries were drawn on the MRI according to criteria (available upon request) based on brain atlases and published reports (see reference list in Abi-Dargham et al., 2000). Regions (mean ± SD size in mm³, n = 5, sum of right and left regions for bilateral regions) included dorsolateral prefrontal cortex (DLPFC, 32,575 ± 2,579 mm³), medial prefrontal cortex (MPFC, 9,104 ± 1,596 mm³), orbito-frontal cortex (OFC, 16,228 ± 3,191 mm³), anterior cingulate cortex (ACC, 8,005 ± 594 mm³), subgenual prefrontal cortex (SGPFC, 2,055 ± 302 mm³), temporal cortex (TC, 23,019 ± 3,271 mm³), parietal cortex (PC, 62,183 ± 5,979 mm³), occipital cortex (OC, 42,963 ± 6,776 mm³), amygdala (AMY, 3,422 ± 922 mm³), uncus (UNC, 905 ± 393 mm³), hippocampal formation (HIP, 5,824 ± 441 mm³), entorhinal cortex (ENT, 2,359 ± 536 mm³), parahippocampal gyrus (PHG, 7,825 ± 474 mm³), insula (INS, 8,245 ± 463 mm³), dorsal raphe nuclei (DRN, 880 ± 742 mm³), and cerebellum (CER, 113,701 ± 3,549 mm³). Except for the DRN, regions were drawn on the MRI to delineate the boundaries of the ROIs. Within these regions, only the voxels classified as grey matter were used to measure activity distribution (Abi-Dargham et al., 2000). The DRN ROI was traced directly on the PET scan (coregistered summed image) given the absence of MRI criteria to identify DRN boundaries. Because of the low level of specific binding detected in caudate, putamen, and thalamus, these values were not included in the analyses.

Quantitative analysis

Derivation of [¹¹C]WAY 100635 regional distribution volumes was performed with three general approaches: kinetic analysis using the arterial input function (Method 1); graphical analysis using the arterial input function (Method 2), and kinetic analysis using an input function derived from a reference region (Method 3, Table 1). A three compartment model (that is, two tissue compartment model) provided the general framework for each method. The model included the arterial plasma compartment (C_a), the intracerebral free and nonspecifically bound compartment (nondisplaceable compartment, C₂), and the specifically bound compartment (C₃). The equilibrium distribution volume of a compartment i (V_i, mL/g⁻¹) was defined as the ratio of the tracer concentration in this compartment to the free plasma concentration at equilibrium

$${\mathrm{V}}_{\mathrm{i}}=\frac{{\mathrm{C}}_{\mathrm{i}}}{{\mathrm{f}}_1{\mathrm{C}}_{\mathrm{a}}}$$

(1)

V₂ and V₃ were defined as the distribution volumes of the second (nondisplaceable) and third (specific) compartments, respectively. V₃ was equal to the ratio of the receptor density (B_max, nmol/L·g of tissue) and affinity (K_D, nmol/L·mL of brain water) (Mintun et al., 1984; Laruelle et al., 1994c). V_T was defined as the total regional equilibrium distribution volume, equal to the sum of V₂ and V₃.

TABLE 1.

Methods and outcome measures

Method #	Method	Model #	Model	Outcome measures
1	Kinetic analysis with arterial input function	1A	Unconstrained 3 compartment model with direct derivation of outcome measures by ratio of kinetic parameters	BP and k3/k4
		1B	Unconstrained 3 compartment model with indirect derivation of outcome measures by total distribution volumes	BP and k3/k4
		1C	Constrained 3 compartment model (where K1/k2 is constrained to VT in cerebellum), and with direct derivation of outcome measures by ratio of kinetic parameters	BP and k3/k4
2	Graphical analysis with arterial input function	2	No compartmental model assumed	BP and k3/k4
3	Kinetic analysis with input function derived from reference tissue	3A	Two tissue compartment model (“full reference tissue model,” FRTM)	k3/k4
		3B	One tissue compartment model(“simplified reference model,” SRTM)	k3/k4

All analyses (kinetic with arterial input function, graphical with arterial input function, and kinetic with reference tissue derived input function) shared two assumptions. First, given the negligible concentration of 5-HT_1A receptors in the cerebellum, cerebellar V_T was assumed to represent only free and nonspecific binding and to provide a reasonable estimate of V₂ in the ROIs. Second, the contribution of plasma total activity to the regional activity was calculated assuming a 5% blood volume in the ROI and subtracted from the regional activity before analysis (Mintun et al., 1984).

Kinetic analysis with arterial input function. Kinetic analysis was performed according to the following differential equations:

$$\frac{d{\mathrm{C}}_2(t)}{dt}={\mathrm{K}}_1{\mathrm{C}}_{\mathrm{a}}(t)-{\mathrm{k}}_2{\mathrm{C}}_2(t)-{\mathrm{k}}_3{\mathrm{C}}_2(t)+{\mathrm{k}}_4{\mathrm{C}}_3(t)$$

(2)

$$\frac{d{\mathrm{C}}_3(t)}{dt}={\mathrm{k}}_3{\mathrm{C}}_2(t)-{\mathrm{k}}_4{\mathrm{C}}_3(t)$$

(3)

with the kinetic parameters defined as

$${\mathrm{K}}_1=\mathrm{F}\mathrm{E}=\mathrm{F}(1-{\mathrm{e}}^{-\mathrm{P}\mathrm{S}/F})(\mathrm{m}\mathrm{L}{\mathrm{g}}^{-1}{min}^{-1})$$

(4)

$${\mathrm{k}}_2={\mathrm{K}}_1/{\mathrm{V}}_2{\mathrm{f}}_1({min}^{-1})$$

(5)

$${\mathrm{k}}_3={\mathrm{K}}_{\mathrm{o}\mathrm{n}}{{\mathrm{B}}_{max}}^{\mathrm{\prime }}/{\mathrm{V}}_2({min}^{-1})$$

(6)

$${\mathrm{k}}_4={\mathrm{k}}_{\mathrm{o}\mathrm{f}\mathrm{f}}({min}^{-1})$$

(7)

where F (mL g⁻¹ min⁻¹) is the regional blood flow, E (unitless) is the unidirectional extraction fraction, PS is (mL g⁻¹ min⁻¹) the permeability surface area product of the tracer, k_on is (nmol/L⁻¹·min⁻¹) the bimolecular ligand-receptor association rate constant, B_max (nmol/L) is the concentration of receptors available for binding (equal to B_max because experiments were performed at tracer dose), and k_off (min⁻¹) is the receptor dissociation rate constant.

In the ROIs, volumes of distribution can be directly derived from rate constants according to

$${\mathrm{V}}_2=\frac{{\mathrm{K}}_1}{{\mathrm{k}}_2{\mathrm{f}}_1}$$

(8)

$${\mathrm{V}}_3=\frac{{\mathrm{K}}_1{\mathrm{k}}_3}{{\mathrm{k}}_2{\mathrm{k}}_4{\mathrm{f}}_1}=\frac{{\mathrm{B}}_{max}}{{\mathrm{K}}_{\mathrm{D}}}$$

(9)

$${\mathrm{V}}_{\mathrm{T}}={\mathrm{V}}_2+{\mathrm{V}}_3=\frac{{\mathrm{K}}_1}{{\mathrm{k}}_2{\mathrm{f}}_1}(1+\frac{{\mathrm{k}}_3}{{\mathrm{k}}_4})$$

(10)

Substituting in Eq. 9 the terms K₁/k₂f₁, k₃, k₄ with Eq. 5, 6, and 7, respectively, and recalling that K_D equals k_off/k_on, establishes the equivalence between V₃ and B_max/K_D (Laruelle et al., 1994a).

As defined above, V₃ is the optimal outcome measure because it is the only expression of the specific distribution volume which is exclusively dependent on receptor parameters (that is, K_D and B_max). However, this outcome measure requires the measurement of the plasma free fraction (f₁) which was found to be associated with poor reliability (see Results). Therefore, distribution volumes were expressed relative to the total (free and nonspecifically bound to plasma proteins) [¹¹C]WAY 100635 plasma concentration

$$\mathrm{B}\mathrm{P}=\frac{{\mathrm{K}}_1{\mathrm{k}}_3}{{\mathrm{k}}_2{\mathrm{k}}_4}=\frac{{\mathrm{f}}_1{\mathrm{B}}_{max}}{{\mathrm{K}}_{\mathrm{D}}}$$

(11)

Because BP, as defined in Eq. 11, requires the measurement of the arterial input function, BP was derived only for Methods 1 and 2. The specific to nonspecific equilibrium partition coefficient, k₃/k₄, is equivalent to V₃ normalized to the reference region distribution volume

$$\frac{{\mathrm{k}}_3}{{\mathrm{k}}_4}=\frac{{\mathrm{V}}_3}{{\mathrm{V}}_2}=\frac{{\mathrm{f}}_2{\mathrm{B}}_{max}}{{\mathrm{K}}_{\mathrm{D}}}$$

(12)

where f₂ is the free fraction in the nondisplaceable compartment (f₂ = 1/V₂). k₃/k₄ was derived with Methods 1, 2, and 3.

Kinetic analysis with arterial input function (Method 1)

Three approaches were used to derive BP and k₃/k₄ with Method 1 (Methods 1A, 1B and 1C). In Method 1A, ROI data were fit to an unconstrained three compartment model, and BP and k₃/k₄ were directly calculated by applying Eq. 8 and 9 with the rate constants provided by the analysis. The authors refer to Method 1A as the direct approach. In Method 1B, ROI data were fit to a unconstrained three compartment model, regional V_T were calculated using Eq. 10, and BP and k₃/k₄ were derived as

$$\mathrm{B}\mathrm{P}={\mathrm{V}}_{\mathrm{T}\mathrm{R}\mathrm{O}\mathrm{I}}-{\mathrm{V}}_{\mathrm{T}\mathrm{C}\mathrm{E}\mathrm{R}}$$

(13)

$$\frac{{\mathrm{k}}_3}{{\mathrm{k}}_4}=\frac{\mathrm{B}\mathrm{P}}{{\mathrm{V}}_{\mathrm{T}\mathrm{C}\mathrm{E}\mathrm{R}}}$$

(14)

where V_{T ROI} and V_{T CER} are the total distribution volumes in the ROI and the cerebellum, respectively. The authors refer to Method 1B as the indirect approach. In Method 1C, ROI data were fit to a three compartment model with the K₁/k₂ ratio constrained to the value of cerebellum V_T, and BP and k₃/k₄ were derived with Eq. 8 and 9, respectively. The authors refer to Method 1C as the constrained approach. Method 1A is the method used by Farde et al. (1998) in their kinetic analysis of human [¹¹C]WAY 100635 data. Gunn et al. (1998) used both Methods 1A and 1B. Method 1C has not been previously reported for [¹¹C]WAY 100635.

Graphical analysis with arterial input function (Method 2). Regional time-activity curves were graphically analyzed according to the equation

$$\frac{{\int }_0^{\mathrm{t}}{\mathrm{C}}_{\mathrm{R}\mathrm{O}\mathrm{I}}(\mathrm{t})\mathrm{d}\mathrm{t}}{{\mathrm{C}}_{\mathrm{R}\mathrm{O}\mathrm{I}}(\mathrm{t})}=\mathrm{a}\frac{{\int }_0^{\mathrm{t}}{\mathrm{C}}_{\mathrm{R}\mathrm{O}\mathrm{I}}(\mathrm{t})\mathrm{d}\mathrm{t}}{{\mathrm{C}}_{\mathrm{R}\mathrm{O}\mathrm{I}}(\mathrm{t})}+\mathrm{b}$$

(15)

where the value of the slope a and the intercept b were obtained by linear regression (Logan et al., 1990). This method allows for the determination of regional V_T of reversible ligands as the slope of the regression line without assuming a particular compartmental configuration. Assuming, as in the kinetic analysis, the equivalence between the cerebellum distribution volume (V_{T CER}) and the nondisplaceable distribution volume in the ROI, outcome measures BP and k₃/k₄ were calculated using Eq. 13 and 14. Methods 1 and 2 have been shown to allow derivation of distribution volumes that are independent of blood flow as long as the blood flow is constant during the time frame of the experiment (Logan et al., 1994).

Kinetic analysis with input function derived from a reference tissue region (Method 3). The authors evaluated the full (Method 3A) and simplified (Method 3B) reference tissue models. The full reference tissue method (FRTM) (Hume et al., 1992; Lammertsma et al., 1996) was derived from the Fourier transform of Eq. 2 and 3, and the substitution of the transform of C_a(t) in Eq. 3 by the equivalent term derived from Eq. 2. The inverse Fourier transform generates the operational equation given in Lammertsma et al. (1996). From this equation, the parameters R₁, k₂, and k₃/k₄ are derived, in which R₁ corresponds to the ratio of K₁ in the ROI to K₁ in the cerebellum. This method (FRTM) is referred to as Method 3A.

In the simplified reference tissue model (SRTM, Method 3B), (Lammertsma and Hume, 1996), the second and third compartments are collapsed, therefore the total distribution volume is expressed as

$${\mathrm{V}}_{\mathrm{T}}=\frac{{\mathrm{K}}_1}{{{\mathrm{k}}_2}^{\mathrm{\prime }}}$$

(16)

where k₂ = k₂/(1 + k₃/k₄). With this assumption, the operational equation simplifies to

$$\begin{array}{rl}{\mathrm{C}}_{\mathrm{R}\mathrm{O}\mathrm{I}}& ={\mathrm{R}}_1{\mathrm{C}}_{\mathrm{R}\mathrm{E}\mathrm{F}}+({\mathrm{k}}_2-\frac{{\mathrm{k}}_2{\mathrm{R}}_1}{1+{\mathrm{k}}_3/{\mathrm{k}}_4})\\ & {\mathrm{C}}_{\mathrm{R}\mathrm{E}\mathrm{F}}\otimes \exp \left(\frac{{\mathrm{k}}_2}{1+{\mathrm{k}}_3/{\mathrm{k}}_4}\right)\end{array}$$

(17)

Fitting the data to the operational equation of the simplified reference tissue method provides the parameters R₁, k₂, and k₃/k₄. Compared with the full reference tissue model, the simplified reference tissue model is more stable and parameter identification is improved (Gunn et al., 1998). For both reference tissue methods, the convolution sum was formed by interpolating the reference region data with cubic splines at intervals of 1 minute and integrating using trapezoidal sums.

For Methods 1 and 3, kinetic parameters were derived by nonlinear regression using a Levenberg—Marquart least squares minimization procedure implemented in MATLAB (Math Works, South Natick, MA, U.S.A.) as previously described (Laruelle et al., 1994b). Given the unequal sampling over time (increasing frame acquisition time from beginning to end of the study), the least squares minimization procedure was weighted by the square root of the frame acquisition time.

Between methods comparisons

Values of BP and k₃/k₄ derived by different methods were evaluated with five criteria: success rate, identifiability, stability, variability, and reliability.

Success rate. A failure of kinetic analysis (Method 1 and 3) was declared if the nonlinear regression procedure failed to reach convergence criteria after n iterations (where n = 100 × p, and p is the number of estimated parameters), if the error in the outcome measure was more than 30%, or if any of the parameters assumed a negative value.

Identifiability. The term identifiability refers to the error in the parameter estimation caused by the inherent uncertainty of this estimation. The identifiability was assessed by the standard error of the parameters at convergence. The standard error of the parameters was given by the diagonal of the covariance matrix and expressed as a percentage of the parameters (coefficient of variation [%CV]). This standard error should not be confused with either the variance of the parameter in the investigated population (between subject SD or %CV), or with the lack of reproducibility (within subject SD or %CV). Identifiability was calculated for Methods 1 and 3.

Stability. Experimental data were collected for 120 minutes. The relationship between BP or k₃/k₄ derivation and the duration of the scan was evaluated by fitting increasingly shorter duration data sets and comparing the results to the reference value obtained with the 120-minute data set. For each region and each scan duration the average ± SD (n = 10) of the results expressed as a percentage of the reference value were calculated to provide an estimate of the bias (average) or dispersion (SD) induced in the outcome measure by analyzing shorter data sets. The parameter was considered stable relative to scan duration after time t if all results derived from time t to 120 minutes had a mean within 10% of the reference value and a SD that did not exceed 15% of the mean.

Variability. The TRV was calculated as the absolute value of the difference between test and retest values, divided by the mean of both measurements.

Reliability. To evaluate the within-subject (WS) variability relative to the between-subject (BS) variability, both WS SD and BS SD were calculated and expressed as a percentage of the mean value (WS %CV and BS %CV). The reliability of the measurements was assessed by the intraclass correlation coefficient (ICC), calculated as:

$$\frac{\mathrm{B}\mathrm{S}\mathrm{M}\mathrm{S}\mathrm{S}-\mathrm{W}\mathrm{S}\mathrm{M}\mathrm{S}\mathrm{S}}{\mathrm{B}\mathrm{S}\mathrm{M}\mathrm{S}\mathrm{S}+(\mathrm{n}-1)\mathrm{W}\mathrm{S}\mathrm{M}\mathrm{S}\mathrm{S}}$$

(18)

where BSMSS is the mean sum of squares between subjects, WSMSS is the mean sum of squares within subjects, and n is the number of repeated observations (n = 2 in the current study). This coefficient estimates the reliability of the measurement and ranges between −1 (no reliability, that is, BSMSS = 0) to 1 (maximum reliability, achieved in the case of identity between test and retest, that is, WSMSS = 0).

Statistical analysis

For each outcome measure and each subject (n = 5), the average of test and retest values were calculated, and results were given as mean ± SD of these five average measurements. Unless otherwise specified, SD refers to between-subject SD, that is, to the estimated variability in the investigated population (each subject counts only once, n = 5). When the SD refers to variability between the experiments rather than between subjects (such as for the injected dose), the SD is followed by n = 10. Statistical analysis was performed with factorial or repeated measures analysis of variance (ANOVA), as appropriate. Relations between continuous variables were analyzed with the Pearson product moment correlation coefficient. A two-tailed probability value of 0.05 was selected as the significance level.

RESULTS

Plasma analysis

Metabolism. [¹¹C]WAY 100635 underwent rapid metabolism in human plasma (Fig. 1). The TRV of the unmetabolized fraction increased with time (from 6 ± 5% at 2 minutes to 91 ± 75% at 60 minutes). However, the ICC went from negative (−0.26 at 2 minutes) to positive (0.61 at 60 minutes). In other terms, the initial values could be determined with greater accuracy, but only the late values provided significant information regarding true between-subject differences.

FIG. 1.

Fraction of plasma activity associated with unmetabolized [¹¹C]WAY 100635 (% total) after [¹¹C]WAY 100635 injection in humans. Each point is the average ± SD of 10 measurements (5 subjects studied twice). The solid line represents the sum of one exponential and a constant.

For reversible ligands, the terminal washout rate from a region of reference will tend toward the terminal rate of decrease of the unmetabolized [¹¹C]WAY 100635 in the plasma (Carson et al., 1993). Taking advantage of this property, cerebellum and total plasma terminal half-lives were compared to determine the most appropriate method to fit the unmetabolized [¹¹C]WAY 100635 fraction (Abi-Dargham et al., 2000). The cerebellum time-activity curves were fit to one exponential from 20 to 120 minutes, and the exponent (λ_cer) was −0.024 ± 0.009 min⁻¹ (n = 10), corresponding to a terminal half-life of 31 ± 10 minutes. Similarly, the total plasma (unmetabolized [¹¹C]WAY 100635 plus metabolites) time-activity curves were fit to one exponential over the same interval (20 to 120 minutes), and returned an exponent (λ_tot) of −0.024 ± 0.003 min⁻¹ (n = 10), corresponding to a terminal half-life of 28 ± 3 minutes. No significant differences were observed between λ_cer and λ_tot (repeated measures ANOVA, P = 0.90). Together, these data suggest that over the time of the study, the terminal exponent of the unmetabolized [11C]WAY 100635 fraction curve (λ_par) was very low, and that the unmetabolized [11C]WAY 100635 fraction curve could be interpolated over the time of the study by the sum of one exponential and a constant. This function was used to fit the unmetabolized [11C]WAY 100635 fraction value in each subject. The mean value of the constant term was 0.035 ± 0.021. This constant term was significantly different between subjects (ICC = 0.61).

Clearance. A typical input function and fit by three exponentials is represented in Fig. 2, left panel. Average clearance was 180 ± 24 L/h. Clearance measurements were highly reproducible (TRV, 7 ± 3%; ICC, 0.83). Thus, the input function was significantly different between subjects, and the measurement procedure was able to detect these differences with high reliability.

FIG. 2.

Plasma (left) and brain (right) [¹¹C]WAY 100635 time-activity curves measured after injection of 12.8 mCi in a human volunteer. Plasma: points are measured values of unmetabolized [¹¹C]WAY 100635; line represents the three exponential function fit to the data. Brain: regional activities in the cerebellum (triangles), dorsolateral prefrontal cortex (closed circles) and hippocampus (open circles). Points are measured values; lines are values fitted to a three compartment constrained model.

Free fraction. When dissolved in pH 7.4 Tris buffer, the [¹¹C]WAY 100635 free fraction was estimated as 76 ± 5% (n = 12), indicating 24 ± 5% binding of free [¹¹C]WAY 100635 to the filters used in the ultracentrifugation procedure. In plasma, the [¹¹C]WAY 100635 free fraction (f₁) was 5.8 ± 2.6%. Because f₁ determinations were not reproducible (ICC = 0.19, TRV 29 ± 37%) this correction factor was not used, and distribution volumes were expressed relative to the total unmetabolized [¹¹C]WAY 100635 rather than to the free unmetabolized [¹¹C]WAY 100635.

Brain uptake

Activity concentrated in neocortical and limbic areas, with the highest uptake in temporal cortex and medial temporal structures (Fig. 3). Very low activity levels were measured in the striatum, thalamus, and cerebellum. An activity concentration was also visualized in midbrain and pons at the level of the floor of the fourth ventricle, corresponding to the location of the dorsal and median raphe nuclei. Uptake peaked within 10 to 15 minutes and was followed by an appreciable washout. Overall, the brain uptake was low; for example, the cerebellum uptake was 0.0022 ± 0.0001 %ID/g at peak uptake (2 minutes postinjection), and only 0.0004 ± 0.0001 %ID/g at 30 minutes (values not corrected for vascular contribution). In the anterior cingulate, a region with high density of 5-HT_1A receptors, the brain uptake was 0.0027 ± 0.0007 %ID/g at 2 minutes and 0.0016 ± 0.0005 %ID/g at 30 minutes. Assuming a 5% blood volume in the ROI, the contribution of the intravascular activity to the total cerebellar activity was about 20% throughout the scan.

FIG. 3.

Brain distribution of [¹¹C]WAY 100635 in a human volunteer. (upper row) PET: Transaxial, coronal, and sagittal views acquired over 60 minutes and starting 40 minutes after the injection of 12 mCi of [¹¹C]WAY 100635 in a 30-year-old male. (lower row) MRI: SPGR acquisitions in the corresponding planes. Activity concentrated in neocortical and limbic areas with very low activity in the striatum, thalamus, and cerebellum. This distribution corresponds to the anatomical distribution of the serotonin 5HT_1A receptor. The coronal section is at the level of the anterior hippocampus. The sagittal section was taken at midline to display activity corresponding to the 5HT_1A somatodendritic receptors in the dorsal raphe nuclei in the pons, at the level of the floor of the 4^th ventricle.

Activity ratios between receptor rich regions and the cerebellum were high (for example, 7.52 ± 1.9 in the anterior cingulate and 7.76 ± 3.26 in the hippocampus during the 30- to 60-minute interval).

Kinetic analysis with arterial input function

Cerebellum. Cerebellar time-activity curves (corrected for the vascular contribution) were fit to a 2 compartment model (2CM) and a 3 compartment model (3CM). Cerebellum V_T calculated with 2CM and 3CM were 0.64 ± 0.14 mL g⁻¹ and 0.89 ± 0.27 mL g⁻¹, respectively. Thus, cerebellar V_T was 39 ± 23% larger when calculated with a 3CM compared with a 2CM (repeated measures ANOVA, P = 0.002). Results of 2CM and 3CM were compared according to several criteria—goodness of fit, identifiability, stability over time, TRV, and ICC. The comparison results were as follows: (1) Goodness of fit. In all subjects, 2CM analyses resulted in a poor fit to the data. In contrast, 3CM analysis provided an excellent and significantly better fit (P < 0.01; Fig. 2, right panel), with smaller values of Akaike Information Criteria (data not shown); (2) V_T identifiability. The identifiability of cerebellar V_T derived with 2CM analysis (error of 8.41 ± 1.0%) was lower than that of 3CM analysis (error of 4.80 ± 1.59%; repeated measures ANOVA, P ≤ 0.001); (3) Time stability. Derivation of cerebellar V_T was stable over time with both 2CM and 3CM. All analyses performed on data sets longer than 25 minutes (2CM) or 45 minutes (3CM) generated V_T values with a mean within 10% of the reference value (V_T derived with 120 minutes of data) and with a SD less than 10%; (4) Reproducibility. The reliability of 3CM V_T (TRV = 21 ± 9%, ICC = 0.77) was better than that of 2CM V_T (TRV = 19 ± 19%, ICC = −0.47). Together, these data suggested that 3CM was the model of choice to derive cerebellum V_T. The relative contribution of the third compartement to the total cerebellum distribution volume was 58 ± 7%.

Success rates. Data from all of the other regions (number of regions = 15, number of subjects = 5, number of repeat measurements = 2, number of fits = 15 × 5 × 2 = 150) were fit to an unconstrained 3CM and to a 3CM with K₁k₂ constrained to the value of cerebellum V_T (derived with 3CM). The unconstrained 3CM converged in all cases, but the error associated with V_T was more than 30% in 4 out of the 150 fits (4 failures, 2.6% failure rate). The constrained 3CM failed to converge in 2 cases, and the error associated with V_T was higher than 30% in one case (3 failures, 2% failure rate). Because two individual regional fits failed with both methods, a total of 5 regional fits failed with either constrained or unconstrained 3CM (1 AMY, 1 HIP, 1 ENT and 2 DRN). These five values and their corresponding repeated measurement were excluded from the data set so that further between method comparisons were performed on similar data sets (140 regional fits). Both constrained and unconstrained models were associated with excellent goodness of fit. A typical 3CM constrained fit is represented in Fig. 2 (right panel).

Methods 1A and 1B. Regional V_T values derived by the unconstrained 3CM are presented in Table 2, as well as values of V₂, BP, and k₃/k₄ derived by Method 1A and Method 1B. V_T values ranged from 2.57 ± 0.78 mL g⁻¹ (DRN) to 7.83 ± 2.13 mL g⁻¹ (ENT). Values of V₂, as identified by the direct method, showed marked between region differences from 0.29 ± 0.05 mL g⁻¹ (DRN) to 0.81 ± 0.08 mL g⁻¹ (ENT). Such between region differences in nonspecific binding were not physiologically plausible. Furthermore, Method 1A V₂ values were highly correlated with V_T values (r² = 0.82; P < 0.001), a correlation not physiologically expected. Finally, Method 1A V₂ values were significantly lower than cerebellum V_T (0.89 ± 0.27 mL g⁻¹). Together, these results indicated that the direct approach results in a marked and variable underestimation of the nondisplaceable compartment distribution volume.

TABLE 2.

Distribution volumes of [¹¹C]WAY 100635 derived by the unconstrained 3 compartment model with arterial input function

Region	VT (mL g−1)	Direct analysis (Method 1A)			Indirect analysis (Method 1B)
		V2 (mL g−1)	BP (mL g−1)	k3/k4 (unitless)	V2 (mL g−1)	BP (mL g−1)	k3/k4 (unitless)
DLPFC	4.05 ± 1.16	0.45 ± 0.06	3.60 ± 1.10	7.98 ± 1.39	0.89 ± 0.27	3.15 ± 0.95	3.64 ± 0.79
MPFC	4.57 ± 1.30	0.47 ± 0.09	4.10 ± 1.22	8.71 ± 1.31	0.89 ± 0.27	3.68 ± 1.08	4.24 ± 0.87
OFC	3.83 ± 0.98	0.44 ± 0.08	3.39 ± 0.91	7.83 ± 0.90	0.89 ± 0.27	2.94 ± 0.76	3.43 ± 0.72
ACC	5.16 ± 1.49	0.49 ± 0.12	4.68 ± 1.37	9.61 ± 0.75	0.89 ± 0.27	4.27 ± 1.27	4.89 ± 0.96
SGPFC	5.28 ± 1.61	0.46 ± 0.10	4.83 ± 1.56	10.74 ± 3.52	0.89 ± 0.27	4.39 ± 1.45	5.05 ± 1.46
TC	6.08 ± 1.75	0.57 ± 0.12	5.50 ± 1.64	9.90 ± 1.15	0.89 ± 0.27	5.18 ± 1.50	5.94 ± 0.83
PC	3.98 ± 1.04	0.44 ± 0.08	3.54 ± 0.96	8.03 ± 0.76	0.89 ± 0.27	3.09 ± 0.82	3.59 ± 0.81
OC	3.44 ± 0.82	0.43 ± 0.09	3.01 ± 0.73	6.94 ± 0.30	0.89 ± 0.27	2.55 ± 0.56	2.96 ± 0.43
AMY	5.14 ± 1.75	0.50 ± 0.02	4.41 ± 1.41	9.05 ± 2.68	0.89 ± 0.27	4.02 ± 1.27	4.77 ± 1.67
UNC	6.60 ± 1.48	0.70 ± 0.15	5.90 ± 1.47	8.91 ± 2.33	0.89 ± 0.27	5.71 ± 1.23	6.59 ± 0.99
HIP	5.47 ± 2.52	0.46 ± 0.02	4.82 ± 2.44	10.48 ± 5.05	0.89 ± 0.27	4.38 ± 2.32	4.16 ± 2.64
ENT	7.83 ± 2.13	0.81 ± 0.08	7.02 ± 2.06	8.69 ± 1.84	0.89 ± 0.27	6.85 ± 1.94	7.09 ± 1.20
PHG	6.41 ± 2.04	0.61 ± 0.15	5.80 ± 1.94	9.90 ± 2.27	0.89 ± 0.27	5.52 ± 1.80	6.35 ± 1.18
INS	6.78 ± 1.93	0.55 ± 0.14	6.23 ± 1.81	11.59 ± 1.85	0.89 ± 0.27	5.88 ± 1.71	6.76 ± 1.36
DRN	2.57 ± 0.78	0.29 ± 0.05	2.29 ± 0.73	8.19 ± 1.37	0.89 ± 0.27	1.87 ± 0.53	2.40 ± 0.44
CER	0.89 ± 0.27	—	—	—	—	—	—

Regional values are mean ± SD of five subjects, with each value measured twice, except for AMY, HIP and ENT (4 subjects), and DRN (3 subjects) because of convergence or identifiability failure. DLPFC, dorsolateral prefrontal cortex; MPFC, medial prefrontal cortex; OFC, orbito-frontal cortex; ACC, anterior cingulate cortex; SGPFC, subgenual prefrontal cortex; TC, temporal cortex; PC, parietal cortex; OC, occipital cortex; AMY, amygdala; UNC, uncus; HIP, hippocampus; ENT, entorhinal cortex; PHG, parahippocampal gyrus; INS, insula; DRN, dorsal raphe nuclei; CER, cerebellum.

This error had little impact on the estimation of BP. BP by Method 1A was 10 ± 7% higher than BP by Method 1B, and this difference was not significant (repeated measures ANOVA, P = 0.09). In contrast, this error induced a marked difference in the estimates of k₃/k₄ by Methods 1A and 1B, k₃/k₄ by Method 1A was 205 ± 48% higher than k₃/k₄ by Method 1B (repeated measures ANOVA, P < 0.001). The difference in impact of V₂ error on BP and k₃/k₄ derived from the large difference between [¹¹C]WAY 100635 specific and nondisplaceable compartments and because V₂ appears in the denominator calculation of k₃/k₄, whereas it appears as a subtraction term in the calculation of BP.

From these considerations, it was concluded that Method 1A is not an appropriate method for receptor parameters estimations, and that individual rate constants derived from the unconstrained fit had poor physiologic plausibility. Thus, derivation of BP and k₃/k₄ from the unconstrained fit required the indirect approach (Method 1B).

Method 1C. Results (rate constants and distribution volumes) from constrained 3CM are presented in Table 3. K₁ varied from 0.044 ± 0.004 mL g⁻¹ min⁻¹ in the DRN to 0.104 ± 0.016 mL g⁻¹ min⁻¹ in the insula, and significant between region differences were noted (ANOVA, region effect, P < 0.001). K₁ values were poorly (r² = 0.24), but significantly (P < 0.001), correlated with BP values. As blood flow varied between regions, a difference in K₁ between regions was expected. However, a relationship between BP and K₁ was not predicted and suggested some difficulties in the model in differentiating delivery from the forward binding constant. Values of k₃ varied from 0.056 ± 0.020 min⁻¹ (DRN) to 0.120 ± 0.040 min⁻¹ (UNC) and were significantly different between regions (ANOVA, P < 0.001). This between region difference was expected as k₃ includes the term B_max, and that receptor density varies between regions. In contrast, k₄ did not significantly differ between regions (ANOVA, regional factor, P = 0.20) as k_off was not expected to vary across regions. BP and k₃/k₄ derived by Method 1C were not significantly different from values derived by Method 1B and were perfectly correlated (BP, r² = 0.99; k₃/k₄, r² = 0.99).

TABLE 3.

Kinetic analysis of regional [¹¹C]WAY 100635 uptake in human brain (3CM constrained, Method 1C)

Regions	K1 (mL g−1 min−1)	k2 (min−1)	k3 (min−1)	k4 (min−1)	VT (mL g−1)	BP (mL g−1)	k3/k4 (unitless)
DLPFC	0.082 ± 0.018	0.098 ± 0.018	0.079 ± 0.007	0.022 ± 0.003	4.14 ± 1.19	3.25 ± 0.97	3.75 ± 0.84
MPFC	0.088 ± 0.019	0.104 ± 0.019	0.086 ± 0.008	0.020 ± 0.003	4.68 ± 1.33	3.79 ± 1.12	4.37 ± 0.91
OFC	0.068 ± 0.011	0.080 ± 0.011	0.082 ± 0.009	0.025 ± 0.008	3.89 ± 1.00	3.00 ± 0.78	3.50 ± 0.75
ACC	0.102 ± 0.023	0.120 ± 0.023	0.093 ± 0.016	0.019 ± 0.004	5.31 ± 1.54	4.41 ± 1.32	5.05 ± 1.01
SGPFC	0.083 ± 0.022	0.098 ± 0.022	0.105 ± 0.012	0.022 ± 0.007	5.38 ± 1.66	4.49 ± 1.51	5.16 ± 1.55
TC	0.087 ± 0.015	0.103 ± 0.015	0.117 ± 0.023	0.020 ± 0.004	6.16 ± 1.81	5.27 ± 1.56	6.02 ± 0.79
PC	0.095 ± 0.021	0.115 ± 0.021	0.071 ± 0.013	0.019 ± 0.004	4.13 ± 1.07	3.24 ± 0.85	3.76 ± 0.84
OC	0.093 ± 0.016	0.113 ± 0.016	0.058 ± 0.015	0.018 ± 0.004	3.63 ± 0.87	2.73 ± 0.62	3.16 ± 0.44
AMY	0.070 ± 0.011	0.090 ± 0.011	0.088 ± 0.024	0.020 ± 0.005	5.05 ± 1.56	4.53 ± 1.94	5.71 ± 2.42
UNC	0.076 ± 0.011	0.091 ± 0.011	0.120 ± 0.040	0.018 ± 0.006	6.72 ± 1.60	5.83 ± 1.36	6.70 ± 0.98
HIP	0.080 ± 0.019	0.104 ± 0.019	0.088 ± 0.041	0.018 ± 0.006	5.46 ± 2.53	4.87 ± 2.60	6.14 ± 3.29
ENT	0.082 ± 0.006	0.088 ± 0.006	0.134 ± 0.030	0.020 ± 0.007	7.89 ± 2.19	6.91 ± 1.99	7.14 ± 1.24
PHG	0.082 ± 0.013	0.097 ± 0.013	0.109 ± 0.021	0.018 ± 0.003	6.49 ± 2.15	5.60 ± 1.90	6.40 ± 1.07
INS	0.104 ± 0.016	0.125 ± 0.016	0.107 ± 0.025	0.016 ± 0.005	6.99 ± 2.07	6.10 ± 1.85	6.99 ± 1.47
DRN	0.044 ± 0.004	0.062 ± 0.004	0.056 ± 0.020	0.021 ± 0.006	2.75 ± 0.65	1.99 ± 0.49	2.65 ± 0.24

Regional values are mean ± SD of five subjects, with each value measured twice, except for AMY, HIP and ENT (4 subjects), and DRN (3 subjects), because of convergence or identifiability failure. DLPFC, dorsolateral prefrontal cortex; MPFC, medial prefrontal cortex; OFC, orbito-frontal cortex; ACC, anterior cingulate cortex; SGPFC, subgenual prefrontal cortex; TC, temporal cortex; PC, parietal cortex; OC, occipital cortex; AMY, amygdala; UNC, uncus; HIP, hippocampus; ENT, entorhinal cortex; PHG, parahippocampal gyrus; INS, insula; DRN, dorsal raphe nuclei; CER, cerebellum.

Identifiability. Identifiability of V_T by Method 1B was excellent, with a mean error of 4.1 ± 3.2% (n = 140; range from 1.84 ± 0.77% in DLPFC to 12.2 ± 3.3% in the DRN). Identifiability of V_T by Method 1C was slightly lower, with a mean error of 5.9 ± 3.7% (n = 140; range from 3.45 ± 1.28% in TC to 18.9 ± 2.8% in the DRN). Regional BP mean error by Method 1C was 7.37 ± 5.16% (n = 140; range from 4.03 ± 1.48% in TC to 26.4 ± 4.8% in DRN). BP error by Method 1C was equal or less than 10% in all regions, except for the DRN. Identifiability of k₃/k₄ was similar to BP, with a mean error of 7.91 ± 5.42%, an error lower than 10% in all regions except DRN, and marginal DRN k₃/k₄ identifiability (26.4 ± 4%).

Stability over time. The minimal scanning time required to yield stable outcome measures derived with Methods 1B and 1C are presented for each region in Table 4. The average scanning time needed to yield stable BP was 76 ± 24 minutes for Method 1B and 94 ± 15 minutes for Method 1C and this difference was significant (repeated measures ANOVA, P < 0.001). Results were similar for k₃/k₄, with an average minimal scanning time of 79 ± 21 minutes and 93 ± 12 minutes for Methods 1B and 1C, respectively (repeated measures ANOVA, P < 0.001). The higher vulnerability of Method 1C to shorter scanning time is also illustrated for k₃/k₄ in Fig. 4, in which the aggregate regional mean ± SD of k₃/k₄ as a function of scanning time is presented. Although k₃/k₄ values derived with 1B were not significantly affected by shorter scanning times (panel A), k₃/k₄ values derived with Method 1C (panel B) showed a pronounced bias towards overestimation of k₃/k₄ with scanning times shorter than 90 minutes and large errors. Thus, outcome measures could be derived with shorter total scanning time with Method 1B compared with Method 1C.

FIG. 4.

Relationship between duration of data collection and derivation of k₃/k₄ (aggregate of all regions) by the unconstrained indirect kinetic method (Method 1B, panel A), the constrained kinetic method (Method 1C, panel B), the graphical method (Method 2, panel C), and the simplified reference tissue method (Method 3B, panel D). For each region (n = 15) and each experiment (n = 10), k₃/k₄ values derived with shorter data sets were expressed as a percentage of the reference value defined as the value measured with the whole data set (120 minutes of data collection). Each time point represents the mean ± SD of all regions in all subjects. Deviations from 100% indicate the bias associated with shorter data sets, whereas the SD indicates the error associated with shorter data sets. Solid lines identify the desired mean (100%) and the ± 10% boundaries. The graphs show no significant bias for Methods 1B and 2, but shorter data sets were associated with a bias towards over- and under-estimation of k₃/k₄ with Methods 1C and 3B, respectively. Methods also differed in the error terms, with Method 1C being associated with the larger errors followed by 1B, 2, and 3B.

Reproducibility. The reproducibility of regional BP and k₃/k₄ by Method 1B is presented in Table 5. Two factors had a significant effect on reproducibility—the nature of the outcome measure (BP vs. k₃/k₄) and the region. The TRV of BP and k₃/k₄ were 14 ± 6% and 20 ± 6%, respectively, and this difference was significant (repeated measures ANOVA, P = 0.03). The ICC of BP (0.84 ± 0.14) was significantly better than the ICC of k₃/k₄ (0.53 ± 0.33; repeated measures ANOVA, P < 0.001). Generally, outcome measures in large cortical regions (such as TC, with BP TRV = 6 ± 10%, ICC = 0.94) were more reproducible than in smaller regions (such as AMY, with BP TRV = 25 ± 17%, ICC = 0.66). The DRN was the region with the poorest reproducibility (BP TRV = 21 ± 22%, ICC = 0.44). DRN k₃/k₄ had a negative ICC (−0.24), indicating that more differences were observed within than between subjects. The reproducibility of BP and k₃/k₄ derived with Method 1C was similar to Method 1B (repeated measures ANOVA, P > 0.05 for four comparisons). Thus, Methods 1B and 1C provided similar outcome measures and were affected with similar TRV.

TABLE 4.

Minimal scanning time (minutes) needed to derive stable estimates of BP and k₃/k₄

Region	BP			k3/k4Kinetic analysis
	Kinetic analysis(Method 1B)	Kinetic analysis(Method 1C)	Graphical analysis(Method 2)	Kinetic analysis(Method 1B)	Kinetic analysis(Method 1C)	Graphical analysis(Method 2)	SRTM analysis(Method 3B)
DLPFC	50	80	60	70	80	70	80
MPFC	70	80	70	70	80	70	80
OFC	80	90	80	80	90	80	60
ACC	60	80	60	70	80	70	80
SGPFC	100	100	70	100	100	80	70
TC	50	80	70	60	80	80	90
PC	50	100	50	60	100	70	70
OC	50	100	60	60	100	50	70
AMY	100	90	80	100	90	80	90
UNC	120*	120*	80	120*	100	80	90
HIP	90	110	120*	100	110	90	90
ENT	80	80	90	70	80	90	90
PHG	80	100	100	70	90	100	90
INS	50	80	70	50	100	70	90
DRN	110	120*	120*	110	120*	120*	110
Mean±SD	76±24	94±15	79±21	79±21	93±12	80±16	83±12

Values are scan durations (in minutes) after [¹¹C]WAY 100635 injection needed to achieve stable B P estimates (see Methods for stability criteria).

*

Because the total duration of the scan was 120 minutes, values of 120 minutes signify that time-stability of BP could not be demonstrated.

DLPFC, dorsolateral prefrontal cortex; MPFC, medial prefrontal cortex; OFC, orbito-frontal cortex; ACC, anterior cingulate cortex; SGPFC, subgenual prefrontal cortex; TC, temporal cortex; PC, parietal cortex; OC, occipital cortex; AMY, amygdala; UNC, uncus; HIP, hippocampus; ENT, entorhinal cortex; PHG, parahippocampal gyrus; INS, insula; DRN, dorsal raphe nuclei; CER, cerebellum.

TABLE 5.

Reproducibility of [¹¹C]WAY 100635 BP and k₃/k₄ in human brain: kinetic analysis with arterial input function (Method 1B)

Reagion	Kinetic BP					Kinetic k3/k4BS STD
	Mean	BS STD(%CV)	WS STD(%CV)	VAR ± SD%	ICC	Mean	BS STD(%CV)	WS STD(%CV)	VAR ± SD%	ICC
DLPFC	3.15	0.95 (30)	0.14 (4)	9 ± 5	0.96	3.64	0.79 (22)	0.41 (11)	19 ± 14	0.58
MPFC	3.68	1.08 (29)	0.15 (4)	8 ± 8	0.96	4.24	0.87 (20)	0.46 (11)	17 ± 14	0.56
OFC	2.94	0.76 (26)	0.24 (8)	15 ± 13	0.81	3.43	0.72 (21)	0.42 (12)	23 ± 20	0.49
ACC	4.27	1.27 (30)	0.23 (5)	11 ± 6	0.94	4.89	0.96 (20)	0.49 (10)	16 ± 10	0.58
SGPFC	4.39	1.45 (33)	0.54 (12)	18 ± 10	0.76	5.05	1.46 (29)	0.57 (11)	23 ± 11	0.74
TC	5.18	1.50 (29)	0.25 (5)	6 ± 10	0.95	5.94	0.83 (14)	0.52 (9)	15 ± 12	0.43
PC	3.09	0.82 (27)	0.20 (6)	11 ± 10	0.89	3.59	0.81 (22)	0.36 (10)	16 ± 14	0.67
OC	2.55	0.56 (22)	0.14 (5)	10 ± 6	0.89	2.96	0.43 (14)	0.24 (8)	15 ± 8	0.53
AMY	4.02	1.27 (32)	0.58 (14)	25 ± 17	0.66	4.77	1.67 (35)	0.59 (12)	25 ± 18	0.78
UNC	5.71	1.23 (22)	0.43 (7)	14 ± 8	0.79	6.59	0.99 (15)	0.29 (4)	8 ± 4	0.84
HIP	4.38	2.32 (53)	0.73 (17)	21 ± 19	0.82	5.16	2.64 (51)	0.78 (15)	30 ± 24	0.84
ENT	6.85	1.94 (28)	0.57 (8)	12 ± 12	0.84	7.09	1.20 (17)	0.85 (12)	21 ± 14	0.33
PHG	5.52	1.80 (33)	0.43 (8)	13 ± 11	0.89	6.35	1.18 (19)	1.03 (16)	25 ± 13	0.14
INS	5.88	1.71 (29)	0.25 (4)	9 ± 5	0.96	6.76	1.36 (20)	0.63 (9)	16 ± 8	0.65
DRN	1.87	0.53 (28)	0.33 (18)	21 ± 22	0.44	2.40	0.44 (18)	0.56 (23)	29 ± 30	−0.24
Mean ± SD				14 ± 6	0.84 ± 0.14				20 ± 6	0.53 ± 0.28

Regional values are mean ± SD of five subjects, with each value measured twice, except for AMY, HIP and ENT (4 subjects), and DRN (3 subjects) because of convergence or identifiability failure. BS, between-subject; WS, within-subject; CV, coefficient of variation; ICC, intraclass correlation coefficient; DLPFC, dorsolateral prefrontal cortex; MPFC, medial prefrontal cortex; OFC, orbito-frontal cortex; ACC, anterior cingulate cortex; SGPFC, subgenual prefrontal cortex; TC, temporal cortex; PC, parietal cortex; OC, occipital cortex; AMY, amygdala; UNC, uncus; HIP, hippocampus; ENT, entorhinal cortex; PHG, parahippocampal gyrus; INS, insula; DRN, dorsal raphe nuclei; CER, cerebellum.

Graphical analysis

Cerebellum. Logan plots achieved linearity after 5 to 10 minutes of scanning, and a linear regression was performed on data from these times until the end of the scan (120 minutes) (Logan et al., 1990). Cerebellum V_T by graphical analysis was 0.85 ± 0.21 mL g⁻¹, a value similar to cerebellum V_T derived by 3CM (0.89 ± 0.27 mL g⁻¹) and larger than cerebellum V_T derived by 2CM (0.64 ± 0.14 mL g⁻¹). Because the graphical analysis does not assume any particular compartmental configuration, the similarity of graphical and kinetic 3CM cerebellar V_T provided additional justification of the use of the 3CM model rather than the 2CM model for kinetic cerebellar analyses. The reproducibility of cerebellum V_T measurements by the graphical method (TRV, 20 ± 9%; ICC = 0.71) was identical to the reproducibility of cerebellum V_T measurements by the 3CM (TRV, 21 ± 9%; ICC = 0.77).

Regions of interest. BP and k₃/k₄ values derived from graphical analysis are shown in Table 6. Regional BPs derived by the graphical method were highly correlated with BPs derived by the kinetic 1B Method (r² = 0.96). Graphical BP values were slightly but significantly lower than kinetic 1B BP values, by an average of 5 ± 9% (repeated measures ANOVA, P < 0.001; Fig. 5). This BP underestimation was mostly detected in small and noisy regions (Fig. 5). For example, the underestimation of BP by the graphical compared to the kinetic 1B Method was 3 ± 3%, 13 ± 6%, and 33 ± 8% in DLPFC, HIP, and DRN, respectively. Graphical k₃/k₄ were highly correlated with kinetic 1C k₃/k₄ (r² = 0.89), and not significantly different from kinetic 1B k₃/k₄ (repeated measures ANOVA, P = 0.12).

FIG. 5.

[¹¹C]WAY 100635 BP in 15 regions of the human brain, derived by kinetic analysis [3CM model unconstrained, indirect, (Method 1B) and graphical analysis (Method 2), both methods using the arterial input function. Graphical BP values were slightly, but significantly, less than the kinetic 1C method BP values by an average of 5 ± 9% (repeated measures ANOVA, P < 0.001). Because this underestimation is caused by a noise dependent bias, this underestimation is noted in small noisy regions such as DRN or ENT, and not in large regions such as DLPFC. Regional values are the mean ± SD of five subjects, with each value measured twice, except for AMY, HIP, ENT (4 subjects), and DRN (3 subjects) because of convergence or identifiability failure. DLPFC, dorsolateral prefrontal cortex; MPFC, medial prefrontal cortex; OFC, orbito-frontal cortex; ACC, anterior cingulate cortex; SGPFC, subgenual prefrontal cortex; TC, temporal cortex; PC, parietal cortex; OC, occipital cortex; AMY, amygdala; UNC, uncus; HIP, hippocampus; ENT, entorhinal cortex; PHG, parahippocampal gyrus; INS, insula; DRN, dorsal raphe nuclei; CER, cerebellum.

TABLE 6.

Reproducibility of [¹¹C]WAY 100635 BP and k₃/k₄ in human brain: kinetic analysis with arterial input function (Method 1B)

Reagion	Graphical BP					Graphical k3/k4
	Mean	BS STD(%CV)	WS STD(%CV)	VAR ± SD%	ICC	Mean	BS STD(%CV)	WS STD(%CV)	VAR ± SD%	ICC
DLPFC	3.17	1.03(32)	0.14 (4)	9 ± 4	0.97	3.78	0.82 (22)	0.41 (11)	18 ± 13	0.60
MPFC	3.67	1.16 (32)	0.18 (5)	10 ± 9	0.96	4.38	0.86 (20)	0.49 (11)	18 ± 16	0.51
OFC	2.81	0.95 (34)	0.31 (11)	23 ± 17	0.81	3.33	0.65 (19)	0.41 (12)	24 ± 23	0.42
ACC	4.19	1.28 (31)	0.27 (6)	11 ± 7	0.92	4.98	0.90 (18)	0.57 (11)	18 ± 11	0.43
SGPFC	4.07	1.31 (32)	0.47(12)	16 ± 11	0.77	4.86	1.20 (25)	0.65 (13)	25 ± 16	0.54
TC	5.14	1.61 (31)	0.25 (5)	6 ± 10	0.95	6.11	0.91 (15)	0.55 (9)	16 ± 11	0.46
PC	3.10	0.86 (28)	0.21 (7)	12 ± 10	0.89	3.74	0.81 (22)	0.36 (9)	16 ± 11	0.68
OC	2.56	0.64 (25)	0.13 (5)	9 ± 7	0.92	3.07	0.35 (12)	0.24 (8)	14 ± 7	0.38
AMY	3.61	1.44 (40)	0.37 (10)	13 ± 11	0.87	4.36	1.37 (31)	0.39 (9)	18 ± 13	0.85
UNC	5.32	1.34(25)	0.50 (9)	18 ± 12	0.76	6.38	1.15 (18)	0.43 (7)	9 ± 10	0.75
HIP	4.01	2.12 (53)	0.61 (15)	26 ± 11	0.85	4.95	2.43 (49)	0.61 (12)	28 ± 23	0.88
ENT	5.85	1.92 (33)	0.60(10)	17 ± 11	0.82	6.87	0.93 (14)	0.75 (11)	17 ± 12	0.22
PHG	5.13	1.90 (37)	0.43 (8)	11 ±9	0.90	6.04	0.94 (16)	0.80 (13)	25 ±8	0.16
INS	5.61	1.62 (29)	0.24 (4)	8 ± 5	0.96	6.68	0.98 (15)	0.69 (10)	17 ± 10	0.34
DRN	1.24	0.30 (24)	0.25 (20)	36 ± 14	0.19	1.65	0.32 (19)	0.39(23)	37 ± 38	−0.19
Mean ± SD				15 ± 8	0.84 ± 0.19				20 ± 7	0.47 ± 0.28

Regional values are mean ± SD of five subjects, with each value measured twice, except for AMY, HIP and ENT (4 subjects), and DRN (3 subjects) because of convergence or identifiability failure. BS, between-subject; WS, within-subject; CV, coefficient of variation; ICC, intraclass correlation coefficient; DLPFC, dorsolateral prefrontal cortex; MPFC, medial prefrontal cortex; OFC, orbito-frontal cortex; ACC, anterior cingulate cortex; SGPFC, subgenual prefrontal cortex; TC, temporal cortex; PC, parietal cortex; OC, occipital cortex; AMY, amygdala; UNC, uncus; HIP, hippocampus; ENT, entorhinal cortex; PHG, parahippocampal gyrus; INS, insula; DRN, dorsal raphe nuclei; CER, cerebellum.

Stability over time. Minimal scanning time required to yield stable outcome measures with graphical analysis are presented for each region in Table 4. The average scanning time needed to yield stable BP was 79 ± 21 minutes, a time not significantly different from kinetic 1B (76 ± 24 minutes, repeated measures ANOVA, P = 0.64), but significantly shorter than kinetic 1C (94 ± 15 minutes, repeated measures ANOVA, P = 0.005). Results were similar for k₃/k₄, with average minimal required scanning time of 80 ± 16 minutes. Figure 4 illustrates the excellent time stability of graphical k₃/k₄ (panel C).

Reproducibility. The reproducibility of regional BP and k₃/k₄ derived by graphical analysis are presented in Table 6. The TRV of BP and k₃/k₄ were 15 ± 8% and 20 ± 5%, respectively, and this difference was significant (repeated measures ANOVA, P = 0.003). The ICC of BP (0.84 ± 0.19) was significantly better than the ICC of k₃/k₄ (0.47 ± 0.38, repeated measures ANOVA, P < 0.001). In contrast, the TRV and ICC of BP and k₃/k₄ were not different between graphical and kinetic 1B analysis (P > 0.05 for all four comparisons).

Kinetic analysis with input function derived from region of reference

Full model. Using the same failure criteria as for Method 1, the FRTM (Method 3A) failed to provide estimates of k₃/k₄ in 58 out of 150 fits (38% failure rate)—15% of the fits did not converge, 11% converged with negative R₁ values, and 12% converged with a positive R₁ value but an error in k₃/k₄ exceeding 30%. Given the high failure rate, no further analyses were performed with this model.

Simplified model. In contrast, the SRTM (Method 3B) provided k₃/k₄ values in all cases, and only in two instances were the errors on k₃/k₄ more than 30% (DRN in both cases). R₁ was 1.04 ± 0.21 (n = 140). The R₁ values derived with Method 3B were correlated to R₁ values calculated from the ratio of K₁ in ROI by Method 1C to cerebellar K₁ provided by 3CM 1C (r² = 0.77; P < 0.05), but the SRTM R₁ values were on average 44 ± 20% higher than the R₁ values provided by kinetic 1C analyses with arterial input function (0.73 ± 0.18; n = 140; repeated measures ANOVA, P < 0.001).

Regional values of k₃/k₄ derived by Method 3B are provided in Table 7. Regional k₃/k₄ values derived by Method 3B were well identified (error of 4.7 ± 4.9%) and highly correlated with k₃/k₄ values derived by the kinetic 1B Method (r² = 0.95). However, Method 3B k₃/k₄ were significantly lower than kinetic 1B k₃/k₄ by an average of 17 ± 8% (repeated measures ANOVA, P < 0.001; Fig. 6). Figure 7 provides examples of fits of the anterior cingulate with Methods 1C and 3B. Despite the appropriate fits provided by both methods, the k₃/k₄ returned by Method 1C (7.35) was 28% more than the k₃/k₄ value returned by Method 3B (5.72).

FIG. 6.

[¹¹C]WAY 100635 k₃/k₄ in 15 regions of the human brain derived by kinetic analysis (3CM model, Method 1B), graphical analysis (Method 2), and simplified reference tissue model (SRTM, Method 3B). Graphical k₃/k₄ values were similar to kinetic 1C k₃/k₄ values except in small and noisy regions like the DRN, in which graphical k₃/k₄ was underestimated. SRTM k₃/k₄ values were significantly less than kinetic 1C k₃/k₄ values by an average of 17 ± 8%. Because this underestimation is more pronounced in regions with high receptor density and is noise independent, it is more pronounced in regions such as TC compared with regions such as DRN. See legend of Fig. 5 for abbreviations and number of subjects per regions.

FIG. 7.

[¹¹C]WAY 100635 activity in the anterior cingulate. Points are measured values, dotted line represents values fitted to a 3 compartment model using the arterial input function with K₁/k₂ constrained to cerebellum V_T (Method 1C). Solid line represents values fitted to the simplified reference tissue (cerebellum) model (Method 3B). Although both methods provided appropriate fit to the data, the k₃/k₄ returned by Method 1C (7.35) was 28% higher than the k₃/k₄ value returned by Method 3C (5.72).

TABLE 7.

Reproducibility of [¹¹C]WAY 100635 k₃/k₄ measurements in human brain: simplified reference tissue analysis (Method 3B)

Region	Mean	BS STD(%CV)	WS STD(%CV)	VAR ± SD%	ICC
DLPFC	3.17	0.68(21)	0.34(11)	19 ± 13	0.59
MPFC	3.64	0.70 (19)	0.36 (10)	17 ± 13	0.58
OFC	2.88	0.50 (17)	0.33 (11)	21 ± 22	0.40
ACC	4.20	0.73 (17)	0.38 (9)	15 ± 9	0.58
SGPFC	4.14	0.97 (23)	0.41 (10)	20 ± 10	0.69
TC	4.75	0.72 (15)	0.37 (8)	14 ± 11	0.58
PC	3.22	0.72 (22)	0.29 (9)	15 ± 12	0.72
OC	2.71	0.41 (15)	0.19 (7)	13 ± 5	0.66
AMY	3.83	1.14 (30)	0.34 (9)	19 ± 15	0.83
UNC	4.93	0.79 (16)	0.23 (5)	9 ± 5	0.85
HIP	4.24	1.98 (47)	0.54 (13)	26 ± 21	0.86
ENT	5.18	0.74 (14)	0.60 (12)	20 ± 13	0.21
PHG	4.85	0.86 (18)	0.58 (12)	21 ± 8	0.37
INS	5.45	0.98 (18)	0.51 (9)	16 ± 8	0.57
DRN	2.33	0.54 (23)	0.69 (30)	44 ± 34	−0.25
Mean ± SD				19 ± 8	0.55 ± 0.29

Regional values are mean ± SD of five subjects, with each value measured twice, except for AMY, HIP and ENT (4 subjects), and DRN (3 subjects) because of convergence or identifiability failure. BS, between-subject; WS, within-subject; CV, coefficient of variation; ICC, intraclass correlation coefficient; DLPFC, dorsolateral prefrontal cortex; MPFC, medial prefrontal cortex; OFC, orbito-frontal cortex; ACC, anterior cingulate cortex; SGPFC, subgenual prefrontal cortex; TC, temporal cortex; PC, partietal cortex; OC, occipital cortex; AMY, amygdala; UNC, uncus; HIP, hippocampus; ENT, entorhinal cortex; PHG, parahippocampal gyrus; INS, insula; DRN, dorsal raphe nuclei; CER, cerebellum.

The regression of Method 3B k₃/k₄ values to Method 1B k₃/k₄ values had an intercept of 0.65 and a slope of 0.68 (Fig. 8, left panel). The fact that the slope was different from unity and that the intercept was positive indicated that the SRTM method underestimates k₃/k₄ more in regions with high 5-HT_1A receptor density compared with regions with low 5-HT_1A density. This phenomenon was confirmed by plotting the underestimation of k₃/k₄ by SRTM relative to Method 1B as a function of the value of k₃/k₄ derived from Method 3B. This plot, presented in Fig. 8 (right panel), shows a scattered (r² = 0.43), but significant (P < 0.001) relationship between the relative underestimation of k₃/k₄ by SRTM and k₃/k₄ returned by Method 1B. For example, the underestimation of k₃/k₄ by Method 3B relative to Method 1B was 10.1 ± 5.7% in parietal cortex (1B k₃/k₄ of 3.8 ± 0.8) and 26.6 ± 3.1% in ENT (1B k₃/k₄ of 7.1 ± 1.2).

FIG. 8.

Relation between k₃/k₄ as derived with kinetic analysis and arterial input function. (left panel) Regression of kinetic 1B k₃/k₄ (Method 1C, × axis) and simplified reference tissue model k₃/k₄ (SRTM, Method 3B, y axis). The full line represents the line of identity. The dotted line represents the linear regression between k₃/k₄ as derived by each method (slope of 0.68). (right panel) Underestimation of k₃/k₄ by Method 3B relative to Method 1B (y axis) as a function of the value of k₃/k₄ derived by Method 1B (× axis). This significant relationship (P < 0.001) indicates that SRTM underestimates k₃/k₄ more in regions with high 5-HT_1A densities than in regions with low 5-HT_1A densities. However, the scattered aspect of the relationship (r² = 0.43) suggests that other factors are implicated in this phenomenon.

Stability over time. The average scanning duration needed to yield stable k₃/k₄ estimates was 83 ± 12 minutes, not significantly different than the duration required for kinetic 1B (79 ± 21 minutes) and graphical (80 ± 16 minutes) methods, but significantly shorter than for the kinetic 1C method (93 ± 12 minutes, repeated measures ANOVA, P < 0.001; Table 4). Figure 4 (panel D) illustrates that SRTM analyses of shorter data sets were associated with a bias towards underestimation of k₃/k₄, but with a minimal error. For scan duration of 60 minutes, k₃/k₄ was underestimated by 14 ± 16%.

Reproducibility. The reproducibility of k₃/k₄ by Method 3B (Table 7) was similar to Method 1B (Table 5) and Method 2 (Table 6).

DISCUSSION

The aim of the current investigation was to evaluate and compare different data analysis strategies to derive regional 5-HT_1A receptor parameters after a single bolus injection of high specific activity [¹¹C]WAY 100635. To address this issue, a comprehensive data set was collected (that is, with arterial input function and long scanning times), and each experiment was repeated to determine reproducibility.

Outcome measures, models, and methods

Independent measures of receptor density (B_max) and affinity (1/K_D) cannot be derived in experiments conducted at tracer doses. These experiments potentially provide BP, that is, the B_max/K_D ratio. At tracer dose, BP is mathematically equal to the equilibrium ratio between the specifically bound and the free radiotracer (Laruelle et al., 1994a). However, the free radiotracer is only a fraction of the total concentration present in the plasma (f₁) or in a brain region devoid of receptors (f₂). Thus, when the specific binding is expressed relative to the plasma radiotracer concentration, BP is in fact equal to f₁B_max/K_D. When expressed relative to the brain tissue concentration in a region devoid of receptors, BP is in fact equal to f₂B_max/K_D. In the current article, we use the term BP to designate the first (Eq. 11) and k₃/k₄ to designate the latter (Eq. 12). Without a reliable experimental method to measure f₁, one is reduced to choose between BP as defined here or k₃/k₄. Both outcome measures are potentially biased, one by potential between-subject differences in binding to plasma proteins (f₁), and the other by potential differences in nonspecific binding to the reference (cerebellar) tissue (f₂).

Three general analytical methods were evaluated using this data set. The first, and most comprehensive method, was the kinetic analysis of regional brain uptake as related to the measured arterial input function (Method 1). This method assumed a given compartmental model, and had the potential to yield estimates of the rate constants governing the transfer of the radiotracer between these compartments and the distribution volumes of these compartments. The second and third methods were mathematically derived from the first method. The graphical analysis (Method 2) was introduced as a generalization of the compartmental model in that this method did not assume a given compartmental configuration (Logan et al., 1990). The third method, the reference tissue method (Method 3), was initially developed for rodent studies in which the measurement of the arterial input function is technically difficult (Hume et al., 1992). Like the graphical method, the reference tissue model was mathematically derived from the first method. Thus, the first method could be considered as the “parent” method from a mathematical point of view. In a perfect (noise free) world, in which radiotracers would strictly behave according to a particular compartmental model, all three methods should provide similar outcome measures.

Several points are important to recognize regarding the choice of outcome measures and analytical methods. The first point is that the use of Method 3 restricted the choice of outcome measures to k₃/k₄ and implied that between-subject differences in nonspecific binding are not significant. In contrast, Methods 1 and 2 enabled derivation and comparison of both outcome measures. Thus, five outcome measures were evaluated in this study—BP by Methods 1 and 2, and k₃/k₄ by Methods 1, 2, and 3.

The second point is that, in the absence of a “gold standard”, the comparison between analytical methods was based on various operational criteria. The first criterion used was the success rate. Although it was expected (and possibly desirable) that a given method fail on some particularly noisy regional data set, too high of a failure rate was not practical. Second, the answer must be determined with a reasonably low error term, that is, the identifiability should be acceptable. Third, the answer should not depend on the duration of the scan (after a given time). Fourth, the answer should be reasonably reliable when the same measurement is performed twice (low TRV) and reveal true between subject differences (high ICC).

A third consideration was whether mathematically equivalent methods return the same results. Because Methods 2 and 3 were mathematically derived from Method 1, one should expect outcome measures derived by Methods 1,2, and 3 to be highly correlated and not significantly different from each other. If this is not the case, the reasons for these discrepancies must be determined because these reasons often reveal either particular susceptibilities to noise or effects of model assumption violations.

Before comparing in detail the performance of the three Methods, we should first discuss the difficulties encountered with [¹¹C]WAY 100635 in measuring both the arterial input function and the reference tissue region (cerebellum).

Measurement of plasma input function

[¹¹C]WAY 100635 was rapidly metabolized (90% of the dose was metabolized within the first 10 minutes). This factor, combined with the rapid decay of C-11, prevented measurement of the unmetabolized fraction after 60 minutes. Unmetabolized fraction after 60 minutes were extrapolated by curve fitting (one exponential plus one constant). The use of this function over this interval (0 to 120 minutes) was supported by the observation that after 20 minutes the rate of decrease of the total plasma activity (that is, parent and metabolite activities) was nearly identical to the rate of decrease of the cerebellum activity. We should also note that fitting the unmetabolized [¹¹C]WAY 100635 fraction to a sum of two exponentials resulted in a second exponential of exponent zero in nearly all cases. In essence, our approach here was similar to the one used by Gunn et al. (1998), who used a sigmoidal curve to fit the unmetabolized [¹¹C]WAY 100635 fraction. Inspection of Fig. 3 of Gunn et al. (1998) reveals that the unmetabolized [¹¹C]WAY 100635 fraction values at later times are practically constant, a finding we confirmed in our data set (fitting our data to the same function resulted in a metabolite fraction change of less than 0.0003% from t = 50 minutes to t = 120 minutes).

Despite these difficulties, [¹¹C]WAY 100635 plasma clearance was measured with good reproducibility (TRV of 7 ± 4%) and high reliability (ICC = 0.83).

Cerebellum distribution volume

The nonspecific binding of [¹¹C]WAY 100635 in brain tissue was low (cerebellum V_T values less than unity). Cerebellum V_T values reported in this study (0.89 ± 0.27 mL g⁻¹) were in good agreement with values of 0.9 ± 0.2 mL g⁻¹ reported by Farde et al. (1998) and 0.58 ± 0.12 mL g⁻¹ reported by Gunn et al. (1998) (all values corrected for the vascular contribution).

Because of the low radiotracer uptake in the cerebellum, cerebellum activity was significantly contaminated by activity present in the vascular compartment. Without an input function measurement and correction for vascular contribution, k₃/k₄ would be underestimated and affected by between subject differences in plasma activity. Thus, vascular correction was important for this ligand and provided additional justification for the measurement of the input function, even if k₃/k₄ was the intended outcome measure. Because the vascular contribution to the total regional activity was high in the cerebellum, we investigated the effect of errors in blood volume assumptions on the outcome measures. Brain data was simulated using a typical input function, typical cerebellar and cingulate cortex kinetic parameters, and a blood volume of 7.5%. The data were then analyzed assuming a blood volume of 5%. The resulting curves yielded BP and k₃/k₄ values that were 101% to 104% of the true values used to generate the curves. Thus, errors in blood volume assumption would affect k₃/k₄ more than BP. We should also note that for the vascular correction we used the total plasma activity rather than the total blood activity, thus assuming that the plasma to cells partition coefficient was close to unity and constant over time. In fact, comparison of plasma and blood activities revealed that the plasma to cell partition coefficient was close to 2 but constant over time (data not shown). The impact of assumption violations regarding the plasma to cell partition coefficient was expected to affect k₃/k₄ more than BP.

As previously observed in baboons (unpublished data) and in humans (Gunn et al., 1997; Farde et al., 1998), a 3CM was needed to fit the cerebellum uptake of [¹¹C]WAY 100635. The 2CM provided an obviously poor fit. Compared with cerebellar V_T derived by 2CM, cerebellar V_T derived by 3CM was more identifiable, equally stable, more reproducible, and closer to the graphical V_T. The observation of a better fit by 3CM compared with 2CM for a region of reference is the rule rather than the exception in neuroreceptor imaging (Frost et al., 1989; Logan et al., 1990; Lammertsma et al., 1996; Ito et al., 1998). This second tissue compartment may correspond to a slow component of nonspecific binding or to a progressive buildup of metabolites in the brain (Osman et al., 1996; Farde et al., 1998). Because our HPLC conditions were optimized to separate unmetabolized [¹¹C]WAY 100635 from metabolites, but not to identify the different metabolite peaks, further investigation of this later explanation was not possible in this data set. We also evaluated the cerebellum fit under various assumptions used to construct the input function (for example, by constraining the unmetabolized [¹¹C]WAY 100635 fraction to a significant terminal half-life) or to perform vascular correction (such as under different blood volumes assumptions). In all cases, a 3CM was required to model the cerebellum. Thus, the need for a 3CM in the cerebellum was unlikely because of inaccuracies in measurement of the tail of the input function.

This additional compartment in the cerebellum was unlikely to represent binding to 5-HT_1A receptors. The presence of 5-HT_1A receptors in the cerebellum has not been demonstrated in vitro in humans (Hall et al., 1997) or in vivo in primates (Farde et al., 1997). We recently confirmed in humans that pretreatment with the 5-HT_1A partial agonist pindolol (30 mg dose) did not affect the distribution volume of [¹¹C]WAY 100635 in the cerebellum (Martinez et al., 2000). However, we should point out that 5-HT_]A receptors have been detected in postmortem cerebellar tissue in patients with schizophrenia (Slater et al., 1998). Therefore, the use of the cerebellum to define nonspecific binding might not be appropriate in some pathologic conditions.

We should also note that it is likely that the nondisplaceable uptake in regions with 5-HT_1A receptors would also be best described by a 3CM. This uptake was assumed to follow a 2CM in Method 1. Precise elucidation of the nature and configuration of these nonsaturable compartments would be required to develop a four compartment model to evaluate the effect of this assumption violation. However, since the total distribution volume of the cerebellum was used to define the nondisplaceable distribution volume in all methods (but 1A), this factor will affect k₃/k₄ to the same extent in all methods.

Impact of analytical methods on receptor parameters

Kinetic analysis with arterial input function (Method 1). For ROI analysis, three different strategies were used to derive BP and k₃/k₄. The indirect (1B) and constrained (1C) methods produced equivalent results, but the direct (1A) method resulted in a large underestimation of the nondisplaceable compartment distribution volume (V₂), which had a marked impact on k₃/k₄; values of k₃/k₄ were twice as high by Method 1A compared with Methods 1B and 1C. This observation demonstrated that the unconstrained 3CM was appropriate to derive ROI V_T, but failed to differentiate the respective contribution of V₂ and BP to V_T, as previously shown for [¹¹C]raclopride or [¹²³I]β-CIT (Laruelle et al., 1994d; Lammertsma et al., 1996). Because Farde et al. (1998) used this direct unconstrained model, the reported kinetic k₃/k₄ values were about twice the values reported for graphical analysis. In contrast, the k₃/k₄ (and BP) values derived here by Methods 1B and 1C were much closer to the outcome measures derived by graphical analysis.

Graphical analysis with arterial input function (Method 2). The graphical analysis BP and k₃/k₄ values were slightly, but significantly, lower than values from kinetic Methods 1C and 1B by an average of 5 ± 9%. With [¹¹C]NNC 112, we observed that the graphical V_T were lower than kinetic V_T by an average of 14 ± 3% (Abi-Dargham et al., 2000). This phenomenon is due to a noise dependent bias (Abi-Dargham et al., 2000). When mean zero noise (that is, values are randomly increased or decreased by the same amount) is added to simulated data, the slope (V_T) of the graphical analysis decreases (see also Carson, 1993; Slifstein and Laruelle, 2000). In this study, we observed a significant relationship between the noise in the regional data as measured by the residual sum of squares of kinetic fit (Method 1C) and the underestimation of BP by the graphical method (r² = 0.59; P < 0.001). This relation explains why the DRN, the noisiest region, was also the region whose BP was most underestimated by graphical analysis compared with the fit with Method 1C (average underestimation of 33 ± 8%).

Kinetic analysis with input function derived from reference region (Method 3). The FRTM model (Method 3A) provided k₃/k₄ values in only 62% of the regional curves. Although this model is mathematically equivalent to 3CM, the parameter identification associated with the operational equation of the model is poor. This problem led to the development of the simplified version of the model (SRTM) in which the second and third compartments are collapsed into a single compartment (Lammertsma and Hume, 1996).

The SRTM method (Method 3B) provided well identified estimates of k₃/k₄ in all cases. Method 3B k₃/k₄ values were well correlated with Method 1C k₃/k₄ values but were significantly lower by an average of 19 ± 7%. Similar results were reported by Gunn et al. (1998). Comparing k₃/k₄ values derived from the indirect kinetic method in Table 2 of Gunn et al. (1998) with the SRTM derived k₃/k₄ values presented in Table 4 of Gunn et al. (1998) shows that SRTM values underestimate kinetic 1B values by 32 ± 15%. The larger underestimation in the data of Gunn et al. (1998) compared with data reported here might be caused by two factors. First, SRTM data from Table 4 were not corrected for the vascular contribution. Second, the data of Gunn et al. (1998) were collected over 90 minutes as opposed to 120 minutes in the current study. Figure 4 demonstrates that an additional 10% underestimation of k₃/k₄ is present at 90 minutes with the SRTM method compared with the 120-minute value.

If the SRTM method was associated with a relative underestimation of k₃/k₄ that was independent of k₃/k₄ values, one could argue that this phenomenon is not of major concern (all values would be scaled down by a given factor). Unfortunately, this was not the case. The regression of Method 3B k₃/k₄ to Method 1C k₃/k₄ had a slope far from unity (0.67) and a positive intercept (0.65, Fig. 8). Similar results were reported by Gunn et al. (1998). The regression of SRTM k₃/k₄ values (without vascular correction) to k₃/k₄ derived with indirect kinetic modeling (the equivalent of Method 1B in this paper) had a slope of 0.54 and a positive intercept (0.99) (Fig. 7 of Gunn et al., 1998). The positive intercept and the slope lower than unity (0.67 here and 0.54 in Gunn et al., 1998) indicates that SRTM underestimates k₃/k₄ more in regions of high receptor density than in regions with low receptor density (Fig. 8). Thus, the underestimation of k₃/k₄ by SRTM was not just a scaling factor, but will significantly affect between subject comparisons.

This observation was unexpected to the extent that the RTM methods were mathematically derived from the differential equations governing Method 1 (Eq. 2 and 3). In contrast to the underestimation of BP by the graphical Method, the underestimation of k₃/k₄ by SRTM was not a noise dependent phenomenon; the analyses with SRTM of a “perfect” noise free data set returned k₃/k₄ values lower than the k₃/k₄ used to create the data set. This observation is illustrated in Fig. 9. A cerebellum time-activity curve was created by convolving a typical [¹¹C]WAY 100635 arterial input function with a 3CM model with typical cerebellar rate constants (K₁ = 0.130 mL g⁻¹ min⁻¹; k₂ = 0.351 min⁻¹; k₅ = 0.030 min⁻¹; k₆ = 0.029 min⁻¹, with k₅ and k₆ being the rate constants for the radiotracer transfer between the second and the third compartment). Similarly, an anterior cingulate curve was created with typical cingulate [¹¹C]WAY 100635 parameters: K₁ = 0.130 mL g⁻¹ min⁻¹; k₂ = 0.171 min⁻¹; k₃ = 0.096 min⁻¹; k₄ = 0.013 min⁻¹). Note that, in this simulation, R₁ was 1, cingulate k₃/k₄ was 7.25, and the cingulate K₁/k₂ ratio was equal to the total cerebellum total distribution volume. These parameters (R₁ = 1, k₂ = 0.171 min⁻¹, k₃/k₄ = 7.31) were then entered in the SRTM operational equation to derive the expected anterior cingulate values using the cerebellum as input function. As shown in Fig. 9, the cingulate time-activity curve derived by SRTM using the true parameters overestimated true cingulate values. The SRTM model was then allowed to adjust the values of the parameters to improve the fit and the model converged with R₁ = 1.28, k₂ = 0.102 min⁻¹ and k₃/k₄ = 5.72. Thus, to optimize the goodness of fit, the SRTM model had to increase the value of R₁ (from a true value of 1 to an estimated value of 1.28, that is, 28% overestimation) and to decrease the value of k₃/k₄ (from a true value of 7.31 to an estimated value of 5.72, that is, 21% underestimation). This overestimation of R₁ and underestimation of k₃/k₄ were consistent with the errors observed in the real data set (overestimation of 44 ± 20% for R₁, underestimation of 19 ± 7% for k₃/k₄). Because the error was replicated on a noise free data set, this error was intrinsic to the SRTM model applied to [¹¹C]WAY 100635 data and was not caused by a particular bias because of experimental noise (as in the case of the graphical analysis).

FIG. 9.

Demonstration of the difference between the simplified reference tissue method and the kinetic method based on arterial input function. Typical [¹¹C]WAY 100635 cerebellum (open circle) and cingulate (closed circle) regions were created by convolving a typical [¹¹C]WAY 100635 input function with 3CM model (cerebellum rate constants: K₁ = 0.130 mL g⁻¹ min⁻¹; k₂ = 0.351 min⁻¹; k₃ = 0.030 min⁻¹; k₄ = 0.029 min⁻¹; cingulate rate constants: K₁ = 0.130 mL g⁻¹ min⁻¹; k₂ = 0.171 min⁻¹; k₃ = 0.096 min⁻¹; k₄ = 0.013 min⁻¹). Note that, in this simulation, R₁ was equal to 1, cingulate k₃/k₄ was 7.25, and the cingulate K₁/k₂ ratio was equal to the cerebellum total distribution volume. These parameters (R₁ = 1; k₂ = 0.171 min⁻¹; k₃/k₄ = 7.31) were then entered in the SRTM operational equation to derive the expected anterior cingulate values using the cerebellum as input function. The cingulate time-activity curve derived by SRTM using the true parameters (solid line) overestimated true cingulate values. The SRTM model was then allowed to adjust the values of the parameters to improve the fit, and the model converged with R₁ = 1.28; k₂ = 0.102 min⁻¹; and k₃/k₄ = 5.72 (dotted lines). Thus, to optimize the goodness of fit, the SRTM model had to increase the value of R₁ (from a true value of 1 to an estimated value of 1.28, that is, 28% overestimation) and to decrease the value of k₃/k₄ (from a true value of 7.31 to an estimated value of 5.72, that is, 21% underestimation). This example, based on noise free data, demonstrates that estimates of k₃/k₄ derived by both methods are not equivalent.

This error could be derived from two violations of assumptions associated with SRTM. First, the RTM model (whether full or simplified) assumed that the region of reference (cerebellum) was appropriately modeled by a 2CM model. As discussed above, this condition was not met for [¹¹C]WAY 100635. Second, the simplified RTM assumed that the ROI was also appropriately modeled by a 2CM, which was not the case (data not shown). However, when it converged, the full RTM also underestimated k₃/k₄ by 19 ± 18% (n = 69). Because the full RTM did not make the second assumption, we would propose that the violation of the first assumption was the most important factor. This proposition was reinforced by examination of previously published [¹¹C]raclopride data (Table 3 in Lammertsma et al., 1996). [¹¹C]raclopride k₃/k₄ values (n = 8) derived with full RTM (Method 3A here, Method C in Lammertsma et al., 1996) were 14 ± 9% lower than k₃/k₄ values derived with indirect 3CM model (Method 1B here, Method Ab in Lammertsma et al., 1996). [¹¹C]raclopride cerebellar uptake also required a 3CM fit rather than a 2CM fit. This factor alone should not disqualify the RTM as an interesting alternative for deriving k₃/k₄ when arterial plasma data are not available. However, additional research is needed to define the factors that influence the magnitude of this error.

Time stability

A basic requirement of any analytical approach used to derive BP or k₃/k₄ is that after a given time, the outcome measure should be nonsignificantly affected by acquisition of additional data. Regions significantly differed in the scan duration needed to yield stable outcome measures. Everything else being equal, it would be expected that required scan duration would be longer for regions with higher receptor density. This relationship was not observed in this data set (relation between duration to reach stability and BP, r² = 0.05; P = 0.38). However, the size of the region was a significant factor. Large neocortical regions (such as TC) became stable first, followed by small limbic regions, then by the DRN which, in fact, never met the stability criteria. This observation suggested that the noise in the regional measurement was the determining factor for the required scan duration. Indeed, we observed a significant relationship between the regional noise (as measured by the residual sum of squares of the 1C fit) and the minimal scan duration needed to achieve stable BP with Method 1C (r² = 0.65; P < 0.001; Fig. 10).

FIG. 10.

Relation between the noise measurement in each region (as estimated by the residual sum of squares of the Method 1C fit) and the minimal scan duration needed to achieve stable k₃/k₄ with Method 1C (r² = 0.84; P < 0.001). This relation indicates that regions with larger noise (that is, smaller size regions) require longer scan duration to yield stable outcome measures.

Significant between method differences were also noted. The kinetic 1B, graphical, and SRTM methods required about 10 minutes less data to reach stability criteria compared with the kinetic 1C method. In addition, the error and the bias associated with shorter scans were much greater for kinetic 1C compared with the three other methods, as can be appreciated in Fig. 4. Kinetic 1B and graphical analysis presented only negligible bias, even at scan durations as low as 60 minutes, whereas SRTM was associated with a bias towards lower k₃/k₄ values. Finally, the error associated with graphical analysis was less than the error associated with kinetic 1B. Thus, from the point of view of scan duration, the graphical analysis offered the best analytical method (no bias, small error), followed by kinetic 1B (no bias, larger error), SRTM (small bias, small error), and kinetic 1C (large bias, large error).

Reproducibility

The reproducibility of the outcome measures was affected by the region size and the nature of the outcome measure (BP vs. k₃/k₄), but not by the method of analysis (Table 5). It was not surprising that 5-HT_1A receptor parameters were measured with higher reproducibility in large regions such as TC or DLPFC compared with smaller regions such as UNC or ENT. Smaller regions have inherently lower counting statistics and are more vulnerable to head movement or coregistration errors. Nevertheless, with the exception of the DRN, all regional BP had acceptable (>0.50) to excellent (>0.75) ICCs, suggesting that BP can reliably be estimated in small regions of the medial temporal pole.

Usually, the TRV of BP is higher than that of k₃/k₄ (see Abi-Dargham et al., 2000). Because k₃/k₄ was essentially BP normalized to the cerebellum distribution volume, this measure should have been less vulnerable to experimental errors affecting plasma measurement and cross calibration between the gamma counter and PET camera. Typically, this normalization comes at the expense of losing some information regarding true between subject differences and, despite higher variability, the ICC of BP is frequently higher than the ICC of k₃/k₄. Thus, the data reported in the current study were unusual in that BP was superior to k₃/k₄ both in terms of TRV and ICC. This situation arose from the fact that the [¹¹C]WAY 100635 cerebellum tissue concentration was very low (see above), that the measurement of cerebellum V_T was associated with significant lack of reproducibility (TRV of 21 ± 9%), and that the error in cerebellum V_T impacted more on k₃/k₄ computation (cerebellum V_T was the denominator of k₃/k₄) than on BP computation (cerebellum V_T was only a subtraction term in BP). This result is in agreement with the data reported by Gunn et al. (1998). Table 8 presents the TRV and ICC of BP and k₃/k₄ (Method 1B) in medial temporal cortex, insular cortex, and cingulate cortex reported here and in Gunn et al. (1998). In both studies, BP performs better than k₃/k₄ in terms of TRV and in terms of ICC values.

TABLE 8.

Comparison of [¹¹C]WAY 100635 reproducibility parameters in three large regions between the current study and Gunn et al. (1998)

Outcome measure	Study	BP	k3/k4
		Kinetic analysis (Method 1B)	Kinetic analysis (Method 1B)	STRM analysis (Method 3B)
TRV	Current study	9% ± 3%	16% ± 1%	15% ± 1%
	Gunn et al. (1998)	20% ± 7%	26% ± 3%	13% ± 3%
ICC	Current study	0.95 ± 0.01	0.55 ± 0.11	0.57 ± 0.01
	Gunn et al. (1998)	0.81 ± 0.10	0.56 ± 0.11	0.87 ± 0.07

Values for Gunn et al. (1998) are calculated from data presented in Table 2 (kinetic method using arterial input function, indirect derivation of BP and k₃/k₄, equivalent to Method 1B) and Table 4 (simplified reference tissue model, equivalent to Method 3B here, with the exception that no vascular correction was applied). Values are averages of medial temporal cortex, insular cortex, and cingulate cortex from Gunn et al. (1998), and of three comparable regions (temporal cortex, insula and anterior cingulate) from this study. Values are derived from 90-minute scans for Gunn et al. (1998), and 120-minute scans in the current study. Note that BP in the notation of Gunn et al. (1998) is equivalent to k₃/k₄ here. BP, binding potential; TRV, test-retest variability; ICC, intraclass correlation coefficient.

In the current study, the reproducibility of [¹¹C]WAY 100635 outcome measures was independent of the analytical approach used. For example, the TRV and ICC of k₃/k₄ were similar whether derived with (Method 1B and 2) or without (Method 3) arterial input function. This result was at variance with Gunn et al. (1998), who reported significantly better reproducibility of k₃/k₄ by SRTM compared with the kinetic 1B Method (Table 8). This observation suggests more within-subject variability in arterial input function measurements in the Gunn et al. (1998) data compared with data reported here, although the impact of a shorter scanning time (90 vs. 120 minutes) and the absence of vascular correction may also contribute to this different result.

Comparison between methods and outcome measures

Overall, method 1B appeared as the method of choice. Two methods (1A and 3A) were found clearly inappropriate; the direct kinetic method (1A) provided inaccurate values of B P and k₃/k₄, and the full RTM method (3A) provided values in only 62% of the cases. Method 1C should be used with caution because of the marked instability associated with shorter scan duration. Methods 2 and 3B were associated with underestimation of binding parameters, but for very different reasons. The underestimation of BP by Method 2 was moderate, a noise dependent phenomenon, and affected only the small and noisy regions (the DRN was the region most affected). The underestimation of k₃/k₄ by Method 3B was more pronounced. This underestimation was not noise dependent, but was dependent on regional 5-HT_1A receptor density and affected regions with high k₃/k₄ more than regions with low k₃/k₄ (the DRN was the region least affected).

In this data set, a clear advantage was associated with BP as opposed to k₃/k₄, strongly suggesting that if an arterial input function is available, BP should be the outcome measure of choice. If an arterial input function is not available, Method 3B provides a useful method, if one keeps in mind the following limitations: (1) underestimation of k₃/k₄ by this method is significant and will vary across regions and across subjects as a function of 5-HT_1A density, (2) this underestimation is accentuated for shorter data sets, (3) the cerebellum activity is contaminated by the activity in the blood, (4) cerebellum distribution volume may vary across subjects and across conditions.

Comparison with in vitro data

Figure 11 shows regional [¹¹C]WAY 100635 BP values derived by Method 1B and regional [³H]WAY 100635 binding values reported by Hall et al. (1997) in autoradiographic studies of human brains (n = 3). A significant correlation was observed (r² = 0.57; P < 0.001) between in vivo and in vitro values. Both studies identified ENT as the region of the human brain with the highest density of 5-HT_1A receptors.

FIG. 11.

Comparison of in vivo [¹¹C]WAY 100635 BP and in vitro [³H]WAY 100635 binding (r² = 0.57; P < 0.001). Autoradiography values are from Hall et al. (1997) (total binding of [³H]WAY 100635, 2 nmol/L). Regions: 1, cerebellum; 2, caudate; 3, thalamus; 4, putamen; 5, dorsal raphe nuclei; 6, occipital cortex; 7, amygdala; 8, parahippocampal gyrus; 9, insula; 10, dorsolateral prefrontal cortex; 11, parietal cortex; 12, anterior cingulate; 13, temporal cortex; 14, hippocampus; 15, uncus; 16, entorhinal cortex.

Dorsal Raphe 5-HT1A receptors

The visualization of 5-HT_1A autoreceptors in the dorsal raphe nuclei is a fascinating aspect of [¹¹C]WAY 100635 PET scans. Because these receptors control the firing rate of 5-HT neurons, potential alterations of these receptors might have widespread consequences for 5-HT function. Unfortunately, the almost evanescent quality of this signal precludes accurate quantification. We are not referring here to the partial voluming effect, which is admittedly major in this structure, and quite difficult to correct for given the absence of anatomical boundaries detectable on the MRI. The noise associated with this measurement hinders even appropriate quantification of the primary signal. The noise of the DRN measurement, as assessed by the residual sum of squares of the 1C fit, was the highest of all regions. The average identifiability of DRN BP was marginal (error of ± 26.4 ± 4.8% with the kinetic 1C method, after deleting two values with errors higher than 30%). With most methods, the time stability of DRN outcome measures could not be demonstrated even with 120 minutes of data. The TRV of DRN BP by the kinetic 1B method was ± 21 ± 22%, with an ICC of 0.44. Worse, the TRV of the kinetic 1B DRN k₃/k₄ was ± 29 ± 30%, with a negative ICC value of −0.24 (a negative ICC indicates that larger differences were observed within-subjects than between-subjects). The reproducibility was equally limited with the other methods. Thus, irrespective of the method, a significant error was associated with measurement of 5-HT_1A receptor density in the DRN, and this factor should be taken into account in power analysis for investigations comparing between- or within-subject DRN [¹¹C]WAY 100635 BP.

In conclusion, the results of this study indicated that 5-HT_1A receptor parameters can be measured with high reliability with [¹¹C]WAY 100635 in the human brain, even in small regions such as the hippocampal formation or the entorhinal cortex. The DRN was the major exception, given the high noise associated with the measurement of [¹¹C]WAY 100635 concentration in this region. Because of the low nonspecific binding of [¹¹C]WAY 100635, the distribution volume of the reference region (cerebellum) was small (less than unity) and associated with a significant error. As a result, the normalization of BP by the cerebellum (that is, k₃/k₄) was associated with a larger error than BP itself. The 3CM kinetic analysis with indirect derivation of BP was the most satisfying approach. Derivation of BP by graphical analysis performed equally well, with the caveat of a noise dependent underestimation detected only in small and noisy regions. Both methods required careful measurement of the arterial input function and at least 90 minutes of data acquisition. If the input function was not available, the SRTM method provided an alternate method of analysis, limited by the nature of the outcome measure (k₃/k₄) and by the fact that multiple factors—intrinsic assumption violations, absence of vascular correction, and possibly inadequate data set length—will conspire towards a significant and variable underestimation of k₃/k₄. Additional work is warranted to better understand the factors that determine the magnitude of k₃/k₄ underestimation by SRTM and to evaluate other methods for deriving k₃/k₄ in the absence of an arterial input function.