Quantitative Analysis for Estimating Binding Potential of the Brain Serotonin Transporter with [ 11 C]McN5652

Abstract

[¹¹C](+)McN5652 is a selective serotonin reuptake inhibitor with subnanomolar potency for the serotonin transporter, and is currently being used for positron emission tomography studies. However, quantification of the regional [¹¹C](+)McN5652 binding potential in vivo is a controversial issue because of its complex characteristics. The authors examined the regional differences in nonspecific binding and proposed simple methods for estimating the binding potential of [¹¹C](+)McN5652. The regional difference in nonspecific binding was evaluated by the activity ratio of the thalamus compared with the cerebellum for inactive-isomer [¹¹C](−)McN5652 and [¹¹C](+)McN5652 saturation studies. The distribution volume of the thalamus was approximately 1.16 times larger than that of the cerebellum. The thalamus-to-cerebellum distribution volume ratio was estimated by nonlinear least square and graphical methods, with and without arterial input function. The graphical method with k₂′ without blood sampling was practical and most applicable for estimation of the distribution volume ratio because this method is more stable than the nonlinear least square method in the simulation study. Binding potential estimated with the distribution volume ratio of [¹¹C](+)McN5652 and the correction with distribution volume ratio of [¹¹C](−)McN5652 represent the most reliable parameters for the assessment of serotonin transporter binding.

The serotonin (5-HT) transporter (5-HTT) is located on the presynaptic terminals of the serotonergic neuron and plays an important role in the regulation of serotonergic neurotransmission by means of reuptake of released 5-HT in the synaptic cleft. It has been suggested that dysfunction of 5-HTT might underlie neuropsychiatric disorders such as mood disorder and Parkinson disease (Stanley et al., 1982; Raisman et al., 1986; Severson et al., 1985). Although several selective serotonin reuptake inhibitors (SSRIs), such as fluoxetine, paroxetine, and citalopram, have been labeled with ¹¹C or ¹⁸F to observe the 5-HTT in vivo (Kilbourn et al., 1989; Hammadi et al., 1993; Hume et al., 1989, 1991, 1992), most ligands are not suitable because of insufficient specific binding in vivo. Trans-1,2,3,5,6,10-β-hexahydro6-[4(methylthio) phenyl] pyrrolo [2,1-a] isoquinoline ([¹¹C]McN5652) has high affinity for 5-HTT and shows relatively high accumulation in high-density regions of 5-HTT, such as the thalamus (Suehiro et al., 1993a,b; Szabo et al., 1995a,b; Shank et al., 1988; unpublished data). McN5652 has optical isomerism, and its pharmacologically active enantiomer (+)McN5652 is at least twice as potent as its pharmacologically inactive enantiomer (−)McN5652 (Shank et al., 1988; Smith et al., 1991; Szabo et al., 1995a).

Recently, several methods have been used to quantify [¹¹C](+)McN5652-specific binding. However, a relatively high fraction of nonspecific binding and the possible differences of nonspecific binding among regions have made it difficult to accurately evaluate specific bindings (Szabo et al., 1995a; Scheffel et al., 1998; Buck et al., 2000; unpublished data). If there were regional differences in nonspecific binding, estimation of transporter occupancy would be unreliable because of the unsettled baseline. Previous studies have overlooked this problem of nonspecific binding. In the present study, we examined regional differences in nonspecific binding and proposed simple methods to estimate the binding potential (BP) of [¹¹C](+)McN5652 using the graphical method with or without arterial plasma input function.

MATERIALS AND METHODS

Radiotracer preparation

[¹¹C](+)McN5652 and [¹¹C](−)McN5652 were synthesized by S-methylation of the corresponding desmethyl precursor with [¹¹C]CH₃I using automated equipment (Sasaki et al., 1996). Each precursor was prepared by demethylation of the corresponding McN5652, stabilized by adding a protecting agent for the thiol group, dithiothreitol (DTT), to the reaction mixture immediately, and purified by HPLC (column, Megapak SIL C18-10 [250 × 7.5 mm, inner diameter]; mobile phase, acetonitrile/0.1-mol/L ammonium formate [pH 4.0, 0.5% DTT]).

Subjects

Fourteen subjects (12 healthy volunteers, mean age 22 years, range 20–24 years; 2 patients with depression, age 30 and 50 years) participated in this study (Table 1). All healthy volunteers were free of any somatic, neurologic, or psychiatric disorders, and had no history of current or previous drug abuse. Two depressed patients receiving high doses of clomipramine were included in this study, but for ethical reasons the healthy volunteers could not take doses high enough to produce full saturation of 5-HTT. The patients met the DSM-IV criteria for major depressive disorder and had received long-term treatment with clomipramine for more than 6 months.

TABLE 1.

Subjects and procedures

Tracer	Dose of clomipramine (mg)	Diagnosis	Blood sampling	Number of subjects
[11C](+) and (−)McN5652	0(+), 0(−)	Normal	With	3
	0(+), 0(−), 50(+)	Normal	With	2
[11C](+)McN5652	50	Normal	Without	1
	100	Depression	Without	1
	250	Depression	Without	1
[11C](−)McN5652	0	Normal	Without	3
	50	Normal	Without	3

0(+) represents that administration dose of clomipramine in [¹¹C](+)McN5652 was 0 mg; 0(−) represents that administration dose of clomipramine in [¹¹C](−)McN5652 was 0 mg.

The study of comparison among quantification methods comprised five healthy volunteers (five men, mean age 21 years, range 20–24 years) who were examined with [¹¹C](+)McN5652 and [¹¹C](−)McN5652, and who underwent arterial blood sampling.

In the study of regional differences in nonspecific binding, five subjects (three healthy volunteers, two patients) with [¹¹C](+)McN5652 and clomipramine and 6 healthy volunteers with [¹¹C](−)McN5652 and with or without clomipramine were studied. Two (healthy volunteers) of the five subjects with [¹¹C](+)McN5652 also participated in the previously described study of comparisons among quantification methods, and arterial blood sampling was performed only in these two subjects. In the examination with [¹¹C](+)McN5652, the three healthy subjects were administered 50 mg clomipramine orally 5 hours before the injection, and the two patients were taking 100 and 250 mg clomipramine daily, respectively. In the examination with [¹¹C](−)McN5652, three of the six subjects were administered 50 mg clomipramine orally 5 hours before the injection. The radioactivity ratio of the thalamus and cerebellum of these 11 subjects was compared with that of [¹¹C](+)McN5652 without clomipramine.

The ethics and radiation safety committees of the National Institute of Radiological Sciences (Chiba, Japan) approved the study, and written informed consent was obtained from each subject.

Positron emission tomography

Positron emission tomography (PET) scans were performed using a Siemens ECAT47 system (Siemens, Knoxville, TN, U.S.A.), which provides 47 slices with 3.375-mm (center-to-center) thickness. Radioactivity was measured in two-dimensional mode and the data were reconstructed using a Ramp filter with a cut-off frequency of 0.5 (full width at half maximum 6.3 mm). The subjects were placed in a supine position with eyes closed and ears unplugged. To minimize head movement during each scan, head fixation devices (Fixster Instruments, Stockholm, Sweden) and thermoplastic attachments made to fit the individual subject were used. A transmission scan of 10 minutes with a ⁶⁸Ge-⁶⁸Ga source was followed by a dynamic 90-minute scan with a bolus injection of 707.4 to 758.5 (mean, 728.0 ± 21.0) MBq [¹¹C](+)McN5652. The specific radioactivities were 65.2 to 118.5 (mean, 99.4 ± 20.1) GBq/μmol at the time of injection. A dynamic 90-minute scan with a bolus injection of 455.1 to 728.2 (mean, 625.9 ± 138.2) MBq [¹¹C](−)McN5652 was performed on the same day. The specific radioactivities were 37.1 to 109.9 (mean 63.9 ± 27.3) GBq/μmol at the time of injection. The interval between the [¹¹C](+)McN5652 and [¹¹C](−)McN5652 studies was at least 2 hours, and the studies were performed in random order.

The PET images were coregistered to magnetic resonance images using SPM99 (Wellcome Department of Cognitive Neurology, London, U.K.), and regions of interest were defined over the cerebellum and thalamus based on these coregistered images.

Arterial blood sampling

Arterial blood samples were taken 13 times during the initial 3 minutes after the tracer injection, then 8 times during the next 17 minutes, and then once every 10 minutes until the end of the scan. Each blood sample was separated into plasma and blood cell fraction by centrifugation. To each plasma fraction, at 3.5, 9, 19, 29, 39, 49, 59, 69, 79, and 89 minutes after injection, acetonitrile was added and then centrifuged. The obtained supernatant was subjected to radio-HPLC analysis (column μ Bondapak C18; mobile phase, 50/50 acetonitrile/0.1-mol/L ammonium formate). The plasma time-activity curve was corrected by the amount of unchanged ligand in plasma.

Compartment models

Parameters related to the distribution volume (DV) were estimated for the thalamus and cerebellum using least square fitting and graphical methods. Compartment models (Fig. 1) were used for the analysis of [¹¹C](+)McN5652 and [¹¹C](−)McN5652. The one-tissue compartment model was used for [¹¹C](−)McN5652 data. For data regarding [¹¹C](+)McN5652, the two-tissue compartment model was used for the thalamus, and the one-tissue compartment model was used for the cerebellum. Although the cerebellum has a small amount of 5-HTT (Laruelle et al., 1989), it can be regarded as having negligible specific binding sites for [¹¹C](+)McN5652 in vivo. K₁ was used to describe the uptake of the tracer across the blood-brain barrier, k₂′ was used to represent the back diffusion from tissue to vascular space, and k₃′ and k₄ were included to describe the binding and dissociation of the radioligand at the serotonin transporter site (Koeppe et al., 1991).

FIG. 1.

Kinetic models of the thalamus and cerebellum for [¹¹C](−)McN5652 (upper) and [¹¹C](+)McN5652 (lower).

Estimation of distribution volume with arterial input function

Nonlinear least square fitting method. The total distribution volume (DVtotal) was represented as K₁/k₂′ for the one-tissue compartment model and K₁/k₂′(1 + k₃′/k₄) for the two-tissue compartment model. Each rate constant (K₁, k₂′, k₃′, k₄) was estimated with compartment models as shown in Fig. 1 by the nonlinear least square (NLS) method with iteration of a modified Marquardt method.

Graphical method with arterial input function. Graphical analysis was also performed by the method of Logan et al. (1990). This method yields the distribution volume by the arterial input function and the tissue time-activity curve. Parameters are estimated from the equation

$\frac{{\int }_0^T{C}_t(t)dt}{C_t(T)}=DV\frac{{\int }_0^T{C}_p(t)dt}{C_t(t)}+int$

(1)

where C_p is the radioactivity concentration in plasma, C_t is the radioactivity concentration in tissue, and parameter DV represents the total distribution volume. Because the relation holds only after equilibration time, DV and int were estimated as a slope and an intercept, respectively, by using points between 40 and 86 minutes after injection.

Estimation of distribution volume ratio without arterial input function

To estimate BP noninvasively without arterial blood sampling, the DV ratio (DVR) of the thalamus to the reference region (cerebellum) was calculated directly using the graphical method.

Reference method with k₂′. This method expanded the Logan plot described previously for determining the DVR of the target to the reference tissue (Logan et al., 1996). It uses the radioactivity concentration of the reference tissue without specific binding site and the k₂′ value of the reference tissue to approximate the plasma integral of Eq. 1, and it does not require the arterial input function. The equation of this graphical analysis is given by

$\frac{{\int }_0^T{C}_t(t)dt}{C_t(T)}=DVR\left(\frac{{\int }_0^T{C}_r(t)dt}{C_t(T)}+\frac{C_r(T)/k_2^{\hspace{0.17em}\hspace{0.17em}\prime }}{C_t(T)}\right)+int$

(2)

where C_t is the radioactivity concentration in the target tissue with specific binding site, C_r is the radioactivity concentration in the reference tissue devoid of specific binding site, and parameter DVR represents the ratio of the DV in a target tissue to the DV in a reference tissue. The value of k₂′ was determined from the average k₂′ in the cerebellum for [¹¹C](+)McN5652 and [¹¹C](−)McN5652 estimated with the NLS method using the one-tissue compartment model. The mean k₂′ of [¹¹C](+)McN5652 was 0.020 ± 0.0029, and that of [¹¹C](−)McN5652 was 0.026 ± 0.0031.

Reference method without k₂′. If the radioactivity ratio between target and reference tissues became reasonably constant, DVR was also estimated without the use of k₂′ (Logan et al., 1996) by

$\frac{{\int }_0^T{C}_t(t)dt}{C_t(T)}=DVR\frac{{\int }_0^T{C}_r(t)dt}{C_t(T)}+in{t}^{\prime }$

(3)

where DVR, int, and int' (Eqs. 2 and 3) were estimated as a slope and intercepts, respectively, by using points between 40 and 86 minutes after injection.

Estimation of binding potential

We have defined BP as k₃′/k₄ (Mintun et al., 1984). In general, k₃′/k₄ is assessed by the equation

${\mathrm{k}}_3^{\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\prime }/{\mathrm{k}}_4=DVR-1$

(4)

on the assumption that K₁/k₂′ in the target tissue is equal to that in the reference tissue. In this study, we tried to estimate BP even if the amount of nonspecific binding in the target tissue was different from that in the reference tissue. The DV ratio of a target tissue to a reference tissue is given by the following equations for [¹¹C](+)McN5652 and [¹¹C](−)McN5652, respectively, by using the model parameters as shown in Fig. 1:

$DVR(+)=\frac{\frac{K_1^{+}}{k_2^{\prime +}}\left(1+\frac{k_3^{\prime +}}{k_4^{\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}+}}\right)}{\frac{K_1^{\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}r+}}{k_2^{\prime r+}}}$

(5)

$DVR(-)=\frac{\frac{K_1^{\hspace{0.17em}\hspace{0.17em}-}}{k_2^{\prime -}}}{\frac{K_1^{\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}r-}}{k_2^{\prime r-}}}$

(6)

where K₁⁺, k₂′⁺, k₃′⁺ and k₄⁺ are the estimated parameters of [¹¹C](+)McN5652 for the target tissue, K₁^r+ and k₂′^r+ are the estimated parameters of [¹¹C](+)McN5652 for the reference tissue, and K₁⁻, k₂′⁻, K₁^r- and k₂′^r- are those of [¹¹C](−)McN5652. By the NLS or graphical method with arterial input function, DVR is estimated from the DV of the target and reference tissues, whereas by the graphical method without arterial input function, DVR is estimated directly. From Eq. 5, k₃′⁺/k₄⁺ is expressed as

$\frac{k_3^{\hspace{0.17em}\hspace{0.17em}\prime \hspace{0.17em}+}}{k_4^{\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}+}}=\frac{DVR(+)}{\frac{K_1^{\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}+}/k_2^{\prime +}}{K_1^{\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}r+}/k_2^{\prime r+}}}-1$

(7)

If it is assumed that (K₁⁺/k₂′⁺)/(K₁^r+/k₂′^r+) is equal to DVR(−), BP can be derived from Eq. 8.

$\text{BP}=\text{DVR}(+)/\text{DVR}(-)-1$

(8)

This assumption is based on the result of the measurement in which the value of DVR(+) in the saturation study of [¹¹C](+)McN5652 was almost equal to DVR(−). The BP was estimated from Eq. 4 or 8. When BP was estimated from Eq. 8, the mean value of DVR(−) for five studies was used instead of the individual DVR(−). The BP values estimated from these methods were compared with k₃′/k₄ estimated by the NLS method.

Simulation study

Simulated time-activity curves for the thalamus and cerebellum with [¹¹C](+)McN5652 were generated with several noise levels to investigate the reliability of parameter estimates for the NLS and graphical methods. A dynamic tracer concentration for [¹¹C](+)McN5652 was derived from the k values and a measured input function according to the human PET imaging protocol (60 seconds × 4, 120 seconds × 13, 240 seconds × 5, 480 seconds × 5). The true k values (K₁ = 0.46, k₂′ = 0.021, k₃′ = 0.026, k₄ = 0.019 or K₁ = 0.46, k₂′ = 0.021, k₃′ = 0.015, k₄ = 0.019 for thalamus, K₁ = 0.43, k₂′ = 0.022 for cerebellum, respectively) were determined from measured data by using the two-tissue or one-tissue compartment model.

The noise level for each frame was determined according to the collected total count given by

$N(t)=C_t(t)\cdot t_d\cdot exp\left(-\frac{{log}_{e}2}{T}t\right)\cdot factor$

(9)

$Noise(\%)=\frac{\sqrt{N(t)}}{N(t)}\times 100=\frac{1}{\sqrt{N(t)}}\times 100$

(10)

where C_t is the nondecaying tissue radioactivity concentration derived from the k values and the input function, t_d is the data collection time, T is the physical half-life of the radionuclide, and factor is a scaling factor representing the sensitivity of the measurement system and is introduced here to adjust the noise level (Ikoma et al., 1998). The noise was generated with random numbers based on Gaussian distribution and added to the decay-corrected tissue activity for each frame. One thousand simulated data sets were generated for each noise level. The level of the noise for the dynamic data was expressed as the ratio (%) of SD to the count for the last frame (t_last = 86 minutes, mean time point of the last frame). In this simulation study, five data sets with noise levels of 1%, 3%, 5%, 7%, 10% were created.

The rate constants (K₁, k₂′, k₃′ and k₄ for thalamus, K₁ and k₂′ for cerebellum) were estimated by the NLS method with a modified Marquardt method for 1,000 time-activity curves. Parameter estimates were considered invalid if K₁, k₂′, k₃′ and k₄ were outside the range 0.0 < K₁ < 1.0, 0.0 < k₂′ < 0.5, 0.0 < k₃′ < 0.5, 0.0 < k₄ < 0.5, 0.0 < K₁/k₂′ < 100.0, 0.0 < k₃′/k₄ < 10.0. DVtotal and DVR were also estimated by the graphical method. The reliability of the estimates of parameters was evaluated by the mean and SD of the estimates, and the relation between noise and reliability of estimates of parameters was investigated for each analysis method.

RESULTS

Distribution volume of [¹¹C](−)McN5652

Typical examples of tissue time-activity curves of [¹¹C](−)McN5652 for the thalamus and cerebellum are shown in Fig. 2A. Distribution volumes of the thalamus and cerebellum were estimated with metabolite-corrected arterial input function (Fig. 3A) by both the NLS method with the one-tissue compartment model and the graphical method. The DVR estimates of both methods are listed in Table 2. The results show that mean DVR(−) was 1.18 and 1.16 using the NLS and graphic methods, respectively. This means that the DV of the inactive enantiomer was larger in the thalamus than in the cerebellum. The DVR(−) values by means of the NLS and graphic methods were almost the same. The estimated value of DVR(−) ranged from 1.11 to 1.23 for the NLS method and from 1.13 to 1.23 for the graphical method. Coefficient of variance (COV, SD/mean [%]) of five studies was 3.77% and 3.63% for the NLS and graphic methods, respectively. The dispersion of DVR(−) among subjects was not significant.

TABLE 2

Distribution volume ratio of thalamus to cerebellum for [ ¹¹ C](−)McN5652

	Thalamus		Cerebellum		DVR
Subject no.	DVNLS	DVgraphical	DVNLS	DVgraphical	DVRNLS	DVRgraphical
1	11.8	12.8	10.7	11.3	1.11	1.13
2	13.5	14.0	11.6	11.8	1.17	1.19
3	13.9	13.3	11.6	11.8	1.19	1.13
4	17.8	17.1	14.9	15.0	1.19	1.14
5	13.6	14.0	11.1	11.4	1.23	1.23
Mean	14.1	14.2	12.0	12.2	1.18	1.16
COV (%)	15.5	11.9	14.1	12.6	3.77	3.63

DV_NLS, distribution volume estimated by nonlinear least square fitting; DV_graphical, distribution volume estimated by graphical method; DVR_NLS, distribution volume ratio of the thalamus to cerebellum estimated by nonlinear least square fitting with one-tissue compartment model; DVR_graphical, distribution volume ratio estimated by the graphical method; COV, SD/mean (%).

FIG. 2.

Time-activity curves of the thalamus and cerebellum for [¹¹C](−)McN5652 (A) and [¹¹C](+)McN5652 (B). The injected radioactivity was normalized to 370 MBq.

Distribution volume of [¹¹C](+)McN5652

Typical examples of tissue time-activity curves for the thalamus and cerebellum with [¹¹C](+)McN5652 are shown in Fig. 2B. The values of K₁/k₂′, k₃′/k₄ and DVtotal were estimated by the NLS method, and DVtotal was also estimated by the graphical method with metabolite-corrected arterial input function (Fig. 3B). A summary of the comparison of parameter estimates using both methods is presented in Table 3. In the cerebellum, DVtotal ranged from 18.1 to 22.0 using the NLS method and from 17.4 to 22.0 using the graphical method. The COV of five studies was 7.96% and 10.8% using the NLS or graphical method, respectively. The mean DVtotal using the NLS method was 20.5 and that of the graphical method was 19.8, indicating that the values of the two methods were similar. In the thalamus, the mean value and COV of five studies were 19.7 and 17.0% for K₁/k₂′, 1.14 and 34.8% for k₃′/k₄, and 41.7 and 18.2% for DVtotal estimated from the NLS method with the two-tissue compartment model. For the graphical method, the mean DVtotal was 37.2 and COV was 23.8%. The DVtotal estimated from the NLS method was larger than that from the graphical method for all cases, and DVtotal in the thalamus showed variations among subjects.

TABLE 3.

Distribution volume of the thalamus and cerebellum for [ ¹¹ C](+)McN5652

	Thalamus				Cerebellum
Subject no.	K1/k2′	k3′/k4	DVtNLS	DVtgraphical	DVtNLS	DVtgraphical
1	16.3	0.98	32.3	27.9	18.1	17.8
2	22.2	1.36	52.2	47.6	21.9	21.7
3	17.8	1.41	43.0	40.6	20.2	20.2
4	18.0	1.44	44.1	41.9	22.0	22.0
5	24.3	0.51	36.7	27.9	20.1	17.4
Mean	19.7	1.14	41.7	37.2	20.5	19.8
COV (%)	17.0	34.8	18.2	23.8	7.96	10.8

DVt_NLS, distribution volume estimated by nonlinear least square fitting with the two-tissue compartment model for the thalamus and with the one-tissue compartment model for the cerebellum; DVt_graphical, distribution volume estimated by the graphical method.

FIG. 3.

Time curve of the ratio of nonmetabolite ligand to plasma concentration for five studies in [¹¹C](−)McN5652 (A) and [¹¹C](+)McN5652 (B).

Nonspecific binding of [¹¹C]McN5652

The time-activity curves of [¹¹C](+)McN5652 in the thalamus did not reach the same level as those in the cerebellum in the patient taking 250 mg clomipramine per day (Fig. 4). The ratio of the area under the time-activity curve of the thalamus to cerebellum from 40 to 86 minutes was approximately 1.12. The ratios of the areas under the time-activity curves for 11 subjects are listed in Table 4. The mean ratio of [¹¹C](−)McN5652 of three subjects with 50-mg clomipramine pretreatment was almost the same as that of [¹¹C](−)McN5652 without clomipramine. The ratios of the thalamus to cerebellum using [¹¹C](+)McN5652 after pretreatment with 50 mg clomipramine and the patients taking 100 or 250 mg clomipramine were very similar to that of [¹¹C](−)McN5652.

TABLE 4.

Accumulated activity ratio of the thalamus to cerebellum

	Dose of clomipramine (mg)	Ratio
[11C](+)McN5652	0	1.34
	50	1.15
	100	1.13
	250	1.12
[11C](−)McN5652	0	1.14
	50	1.13

Ratio represents the ratio of the area under the time-activity curves of the thalamus to cerebellum from 40 to 86 minutes.

FIG. 4.

[¹¹C](+)McN5652 time-activity curves of a patient taking 250 mg clomipramine. The injected radioactivity was normalized to 370 MBq.

Correlation between graphical method with and without arterial input function

The DVR estimated from the graphical method with arterial input function was compared with that estimated from the graphical method without arterial input function (reference method) with or without k₂′, and the correlation is shown in Fig. 5. A strong correlation was found between the graphical methods with and without arterial input function. The slope of the regression curve for [¹¹C](+)McN5652 with k₂′ was 0.96, whereas that without k₂′ was 0.16. The DVR estimated from the reference method without k₂′ was smaller than that estimated with the arterial input function.

FIG. 5.

The relation between the DV ratio of the thalamus to cerebellum estimated from the graphical method with and without arterial input function and with and without k₂. (A) The relation for [¹¹C](−)McN5652, and (B) for [¹¹C](+)McN5652.

Binding potential of the thalamus

The DVR was derived from the DV of the thalamus and cerebellum, which was estimated individually by the graphical method with arterial input function; BP was calculated from Eqs. 4 and 8 by using individual DVR(−) or mean DVR(−) values. Figure 6 shows BP estimated by the graphical method using Eq. 4 (without DVR(−)), Eq. 8 (with individual DVR(−) and with mean DVR(−)) compared with k₃/k₄ estimated by the NLS method. As a matter of course, BP estimated from the conventional method using Eq. 4 was larger than that estimated from our new method using Eq. 8. The BP from Eq. 4 ranged from 0.57 to 1.20, the mean value was 0.86, and COV was 31.3%; BP from Eq. 8 by using individual DVR(−) values ranged from 0.31 to 0.85, the mean value was 0.60, and COV was 39.7%. The BP from Eq. 8 by using mean DVR(−) ranged from 0.35 to 0.89, the mean was 0.60, and COV was 38.5%. The BP values estimated from Eq. 8 with individual or mean value of DVR(−) were almost the same.

FIG. 6.

The relation between k₃′/k₄ estimated from the nonlinear least square method and the binding potential estimated from the graphical method with arterial input function for the thalamus with [¹¹C](+)McN5652. In the graphical method, binding potential was estimated by DVR(+)-1 (without DVR(−), closed circles), DVR(+)/DVR(−)–1 (with individual DVR(−), closed squares), and DVR(+)/DVR(−)_mean-1 (with mean DVR(−), open triangles).

The regression lines were estimated for these three methods (Fig. 6). The intercepts of two regression lines obtained by the new method (with individual and with mean DVR(−)) were near zero (−0.01 and 0.08), whereas the intercept of the regression line by the conventional method (without DVR(−)) was 0.25.

Reliability of parameter estimates

In the NLS method, the dispersion of K₁/k₂′, k₃′/k₄ and DVtotal became large as the noise increased, as shown in Fig. 7. The SD of parameter estimates for the thalamus with the two-tissue compartment model was much larger than that for the cerebellum with the one-tissue compartment model. When the noise level was 5%, COV of DVtotal for the cerebellum was 2% (Fig. 7A). However, for the thalamus, COV of K₁/k₂′, k₃′/k₄ and DVtotal was approximately 30%, 95%, and 80%, respectively, when BP was 0.79; COV of K₁/k₂′, k₃′/k₄ and DVtotal was approximately 30%, 65%, and 60%, respectively, when BP was 1.37. The mean value of K₁/k₂′ estimates for the thalamus became smaller (Fig. 7B), whereas k₃′/k₄ and DVtotal became larger (Figs. 7C and 7D) as noise increased.

FIG. 7.

The relation between the noise and reliability of parameter estimates for the nonlinear least square method. Shown are the mean value and SD for the simulation data with noise at 0%, 1%, 3%, 5%, 7%, and 10%. (A) The relation for the cerebellum with the one-tissue compartment model. (B–D) The relation for the thalamus with the two-tissue compartment model. Dotted lines represent true values. For the thalamus, a two-parameter set (k₃′/k₄ = 0.79 [closed circles] or 1.37 [open squares] was investigated. The DVtotal of the cerebellum means

The relations between noise and reliability of parameter estimates using the graphical method with arterial input function are shown in Fig. 8. In the thalamus, the DVtotal estimates became small as noise increased (Fig. 8B). At a 5% noise level, mean DVtotal was 32.4 and COV was 9% when BP was 0.79, and mean DVtotal was 40.3 and COV was 12% when BP was 1.37. The tendency of underestimation became stronger as noise increased and BP became larger. When the noise level was 10%, the mean of DVtotal estimates was 28.1 and COV was 15% for the simulated data in which BP was 0.79, and the mean DVtotal was 31.5 and COV was 19% for the simulated data in which BP was 1.37; the mean DVR of these two cases was very similar. In the cerebellum, although the DVtotal became smaller as noise increased, the deviation was much less than that in the thalamus (Fig. 8A).

FIG. 8.

The relation between noise and reliability of DVtotal for the graphical method with arterial input function. Shown are the mean value and SD for simulation data with noise at 0%, 1%, 3%, 5%, 7%, and 10%. Dotted lines represent true values. DVtotal was estimated as the slope of the regression line by using points between 40 and 86 minutes. Relation for the (A) cerebellum and (B) thalamus of two parameter sets (k₃′/k₄ = 0.79 [closed circles] or 1.37 [open squares]).

In the reference method with k₂′, the mean of DVR estimates became smaller and SD became larger as noise increased (Fig. 9A), the same pattern as with the graphical method with arterial input function. At a noise level of 5%, mean DVR was 1.64 and COV was 12% when BP was 0.79, and mean DVR was 2.02 and COV was 15% when BP was 1.37. However, in the reference method without k₂′, the mean DVR estimates did not change and SD did not increase as the noise level increased (Fig. 9B). At a 5% noise level, mean DVR was 1.35 and COV was 3% when BP was 0.79, and mean DVR was 1.51 and COV was 3% when BP was 1.37. As for the reference method without k₂′, the DVR estimates were smaller than the true value even if the noise level was low.

FIG. 9.

The relation between noise and reliability of parameter estimates for the graphical method without arterial input function with k₂′, k₂′ = 0.022 (A) and without k₂′ (B). Shown are the mean values of DV ratio (DVR) and SD for simulation data with noise at 0%, 1%, 3%, 5%, 7%, 10%. Dotted lines represent true values. DVR was estimated as the slope of the regression line by using points between 40 and 86 minutes. Two parameter sets (k₃′/k₄ = 0.79 [closed circles] or 1.37 [open squares]) were investigated.

DISCUSSION

Effect of nonspecific binding on binding potential

The radioactivity concentration in the target region such as the thalamus includes the radioactivity of both nonspecific and specific binding. In dopamine D2 receptor studies, the amount of nonspecific binding is usually estimated from activity in a region without specific binding, such as the cerebellum. If the distribution of nonspecific binding is uniform or if the amounts of nonspecific binding for both specific and nonspecific regions are the same, BP is calculated using the conventional method of Eq. 4. In the [¹¹C](+)McN5652 study, however, the time-activity curve of the thalamus did not meet that of the cerebellum with negligible specific binding sites for [¹C](+)McN5652 in vivo either in healthy volunteers taking 50 mg clomipramine or in patients taking 100 or 250 mg clomipramine (Fig. 4). The thalamus-to-cerebellum ratio of [¹¹C](−)McN5652 saturated with clomipramine did not differ from that of [¹¹C](−)McN5652 without pretreatment (Table 4), suggesting that [¹¹C](−)McN5652 has no specific binding component in vivo and the thalamus-to-cerebellum ratio of [¹¹C](+)McN5652 saturated with clomipramine was similar to that of [¹¹C](−)McN5652. The BP estimated by Eq. 4 does not become zero when k₃′ equals zero, as shown in Fig. 6. This fact indicates that K₁/k₂′ in the thalamus is not equal to that in the cerebellum, and that the distribution of nonspecific binding of [¹¹C](+)McN5652 may not be uniform in the brain.

However, Parsey et al. (2000) reported that the DVtotal of [¹¹C](+)McN5652 was significantly higher than that of [¹¹C](−)McN5652 in the cerebellum; we obtained a similar result (Tables 2 and 3). Moreover, the shapes of the time-activity curves of the cerebellum were different between [¹¹C](−)McN5652 and [¹¹C](+)McN5652 (Fig. 2), but similar between [¹¹C](−)McN5652 and [¹¹C](+)McN5652 with clomipramine (Fig. 4). The washout was quicker for [¹¹C](−)McN5652 and [¹¹C](+)McN5652 with clomipramine, as if there were specific binding in the cerebellum. However, we evaluated the DVtotal of [¹¹C](+)McN5652 in the cerebellum both with and without clomipramine, and the values of the DVtotal of [¹¹C](+)McN5652 in the cerebellum before and after the pretreatment with clomipramine were not changed (unpublished data). The change in the shape of the time-activity curves of the cerebellum may be attributed to the change in plasma input due to the high uptake of [¹¹C](+)McN5652 in the lung (Suhara et al., 1998; unpublished data). In vitro binding studies with [³H]paroxetine have reported that the cerebellum has a small amount of 5-HTT (Laruelle et al., 1989) and that its density is approximately 27 fmol/mg protein, approximately 10% of that of basal ganglia (Backstrom et al., 1989). Because there was no difference between [¹¹C](+)McN5652 distribution volumes with and without clomipramine, the cerebellum could be used as a practical reference region in vivo. However, it is still not an ideal reference region because of the regional differences of nonspecific binding. The difference of DVtotal in the cerebellum between [¹¹C](−)McN5652 and [¹¹C](+)McN5652 might be explained by the stereo-specificity for drug binding to plasma proteins and for transport across membranes (Lawrence et al., 1984; Jian et al., 1997; Farde et al., 1988). These data indicated that the absolute DV value of [¹¹C](−)McN5652 was not desirable for determining the derivation of BP. However, the binding condition was assumed to be physiologically much closer within the brain tissue. Therefore, although DVtotal based on the plasma concentration cannot be used directly, the reference tissue method and DVR could be used to estimate the nonspecific binding in vivo.

Instead of the conventional method used in Eq. 4 in which the regional difference of the nondisplaceable distribution volume is not considered, the difference of K₁/k₂′ between target and reference regions is taken into account in Eq. 8 (Fig. 6). Based on the finding that the thalamus-to-cerebellum ratio of [¹¹C](+)McN5652 under the saturated condition was almost the same as that of [¹¹C](−)McN5652 (Table 4), the regional difference of nonspecific binding can be corrected with the parameter of [¹¹C](−)McN5652. The DVtotal of the thalamus for [¹¹C](−)McN5652 was 1.16 times larger than that of the cerebellum (Table 2) and was similar among all subjects. Moreover, the DVtotal ratio of the thalamus to cerebellum for [¹¹C](−)McN5652 was almost equal to that of [¹¹C](+)McN5652 saturated by clomipramine. Assuming that the K₁/k₂′ ratio of the thalamus to cerebellum in Eq. 7 is equal to the DVR of [¹¹C](−)McN5652, the BP is calculated from Eq. 8 as DVR(+)/DVR(−)–1. In the conventional method, the ratio of target K₁/k₂′ is regarded as equal to the reference K₁/k₂′. However, we found that K₁/k₂′ may differ between the target and reference regions. Using Eq. 8, BP will become zero when the value of k₃′ is zero (i.e., without specific binding). In the human study, the intercept of the regression line between k₃′/k₄ estimated with the NLS method and BP estimated from Eq. 8 approached zero, as shown in Fig. 6.

In the simulation study, the DVR(+) estimated using the graphical method was smaller than the true value (Fig. 8), whereas k₃′/k₄ estimated using the NLS method became larger as noise increased (Fig. 7C). In the simulation study with a 3% noise level, mean DVR(+) was approximately four fifths of the true value by the graphical method, and mean k₃′/k₄ was approximately 1.5 times larger than the true value estimated using the NLS method. Therefore, the underestimation of BP is considered to be due to the effect of noise and the properties of the graphical method. Although BP estimated by the conventional method does not become zero when k₃′ is zero, a relative evaluation of BP could be performed as a qualitative analysis because the regression curves obtained from Eqs. 8 and 4 are parallel to each other. However, this bias—the nonzero intercept—will introduce an error in some cases, such as in the evaluation of transporter occupancy.

Expanding our method for BP estimation, the occupancy of [¹¹C](+)McN5652 can be estimated more precisely with the DVR of [¹¹C](−)McN5652 by the following equation:

$\begin{array}{lll}occupancy(\%)\hfill & =\hfill & \left(1-\frac{\frac{k_3^{\prime drug}}{k_4^{\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}drug}}}{\frac{k_3^{\prime +}}{k_4^{\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}+}}}\right)*100(\%)\hfill \\ \hfill & =\hfill & \frac{DVR(+)-DVR(drug)}{DVR(+)-DVR(-)}*100(\%)\hfill \end{array}$

(11)

where k₃′⁺ and k₄⁺ are parameter estimates of [¹¹C](+)McN5652 for target tissue under control conditions, k₃′^drug and k₄^drug are parameter estimates of [¹¹C](+)McN5652 with the competitor of the 5-HT transporter, DVR(+)/DVR(−) is the distribution volume ratio of target tissue to reference tissue for [¹¹C](+)McN5652 and (−)McN5652 under control conditions, and DVR-(drug) is the distribution volume ratio of target tissue to reference tissue for [¹¹C](+)McN5652 with the competitor of the 5-HT transporter.

The disadvantage of this new method is that it requires [¹¹C](−)McN5652 in addition to [¹¹C](+)McN5652. However, in the present study with normal volunteers, the value of DVR(−) was very similar among subjects (1.16 ± 0.042), and the mean value can be used as that of DVR(−) for calculating BPs.

In this study, we used the thalamus as the target region because the uptakes of cortical regions were similar to that of the cerebellum, and the signal of specific binding was not enough for reliable quantification (Parsey et al., 2000; unpublished data).

Reference method without arterial blood sampling

The DVR estimated using the reference region with the k₂′ value was compared with that obtained using the graphical method with arterial input function, and good agreement was observed between these two methods (Fig. 5). The reference method with k₂′ needs the k₂′ value of the reference tissue as an input parameter, and usually mean k₂′ of the reference tissue is used in Eq. 2. Logan et al. (1996) investigated the variations in DVR with the change of k₂′ value in a [¹¹C]dMP study with simulation, and reported that variations of ±25% from the original k₂′ value resulted in a change in DVR of 3% to 4%. In our simulation study with [¹¹C](+)McN5652, the input k₂′ varied between ±25% from the true k₂′ value (k₂′ = 0.022) and the change in DVR was 2% to 5%. This result indicates that the error in k₂′ value does not significantly affect the DVR value. The SD of parameter estimates in the simulation study was under 15% at 5% noise, a reliability level almost the same as that of the thalamus with plasma input. However, DVR came to be underestimated as noise increased. This tendency was similar to the results with the plasma input.

Although the DVR estimated from the reference method without k₂′ had good correlation with the results with plasma input, the value obtained was smaller than that obtained with plasma input (Fig. 5). In the simulation study, DVR without k₂′ was also underestimated, even though the noise level was low (Fig. 9). The reference method without k₂′ depends on the assumption that (DVR/k₂′)Cr(T)/Ct(T) is small or reasonably constant (Logan et al., 1996, 2000). In this study with [¹¹C](+)McN5652, (DVR/k₂′)Cr(T)/Ct(T) was not small enough [(DVR/k₂′)Cr(T)/Ct(T) >50], which could be the reason for the underestimation (Logan, 2000). However, there was good correlation between the graphical method with arterial input function and the reference method without k₂′. Moreover, in the simulation study, the SD of parameter estimates for this method without k₂′ was smaller than that for other methods, and the mean DVR did not become smaller when noise increased (Fig. 9). Therefore, the reference method without k₂′ can also be useful for comparing the values of BP.

Reliability of estimated parameters

Regarding the analysis model of [¹¹C](+)McN5652, some groups recommended the one-tissue compartment model (Szabo et al., 1999; Parsey et al., 2000) and others suggested the two-tissue compartment model (Buck et al., 2000). Although k₃′ and k₄ can be estimated individually by the NLS method with the two-tissue compartment model, these parameter estimates are very sensitive to noise. Deducing the noise level from residual error, the noise level of region-of-interest analysis for human data was 3% to 5%. At this noise level, the mean difference between the parameter estimate and true value of k₃′/k₄ was more than 50% and DVtotal was approximately 30% (Fig. 7). Moreover, the mean value of K₁/k₂′ estimates became smaller and k₃′/k₄ became larger than the true value as noise increased (Fig. 7). To improve the reliability of parameter estimates, parameter coupling is often used (Buck et al., 2000; Kegekes et al., 1997), though deciding on a fixed value is difficult with human data in which the true value is not known. Therefore, the NLS method with the two-tissue compartment model does not seem to be practical for the analysis of [¹¹C](+)McN5652. In comparison with the two-tissue compartment model, parameter estimates with the one-tissue compartment model are more robust and less affected by noise. However, the one-tissue compartment model does not apply to the regions with specific binding. Goodness of fit of the one-tissue and two-tissue compartment models was evaluated in the thalamus using F test statistics, and the mean F value of five studies was 5.91. Because F > 3.35 means improvement of the fit, the two-tissue compartment model was considered suitable for the thalamus (Buck et al., 2000).

The graphical method is simpler than the NLS method, and the slope of the regression line represents DVtotal. However, DVtotal estimates became smaller with increasing noise (Fig. 8), and this tendency became more obvious as the value of k₃′/k₄ became larger. Nonetheless, dispersion was far less than that with the NLS method. Taken together, the graphical method appears to be a good method for [¹¹C](+)McN5652 because parameter estimates are robust and little affected by noise.

CONCLUSIONS

We have presented a method for the quantification of [¹¹C]McN5652 binding in which the regional difference of nonspecific binding was considered. The graphical method with k₂′ without blood sampling is practical and most applicable for estimation of the DVR, because this method is more stable than NLS and does not need blood sampling. The BP estimated with the DVR of [¹¹C](+)McN5652 and the correction with DVR(−) represents the most reliable parameter for the assessment of 5-HTT binding, but BP without correction with the DVR(−) value can also be used for the comparison of groups. However, to evaluate the transporter occupancy, the DVR(−) value is essential. 5-HTT occupancy can only be measured accurately using both (+)McN5652 and (−)McN5652, and the selective loss of 5-HTT can be measured by this method. However, if there were any changes in nonspecific binding in the disease process, interpretation of the estimated change of 5-HTT would require some caution.