## Abstract

Separate measurements of B_{max}, the density of available receptors, and K_{D}, the equilibrium dissociation constant in the human brain, with PET have contributed to our understanding of neuropsychiatric disorders, especially with respect to the dopamine D_{2}/D_{3} receptor system. However, existing methods have limited applications to the whole striatum, putamen, or caudate nucleus. Improved methods are required to examine B_{max} and K_{D} in detailed functional striatal subdivisions that are becoming widely used. **Methods:** In response, a new method (bolus-plus-infusion transformation [BPIT]) was developed. After completion of a validation study for ^{11}C-raclopride scans involving 81 subjects, age-associated changes in B_{max} and K_{D} were examined in 47 healthy subjects ranging in age from 18 to 77 y. **Results:** The BPIT method was consistent with established reference tissue methods regarding regional binding potential. BPIT yielded time-consistent estimates of B_{max} and K_{D} when scan and infusion lengths were set equal in the analysis. In addition, BPIT was shown to be robust against PET measurement errors when compared with a widely accepted transient equilibrium method. Altogether, BPIT was supported as a method for regional binding potential, B_{max}, and K_{D}. We demonstrated age-associated declines in B_{max} in all 5 functional striatal subdivisions with BPIT when corrected for multiple comparisons. These age-related effects were not consistently attainable with the transient equilibrium method. Irrespective to methods, K_{D} remained unchanged with age. **Conclusion:** The BPIT approach may be useful for understanding dopamine receptor abnormalities in neuropsychiatric disorders by enabling separate measurements of B_{max} and K_{D} in functional striatal subdivisions.

- receptor density
- dopamine D
_{2}/D_{3}receptors - aging
- functional striatal subdivisions
^{11}C-raclopride

Measurements of B_{max}, the density of available receptors, and K_{D}, the equilibrium dissociation constant in humans, with PET have contributed to our understanding of neuropsychiatric disorders, in particular on the role of dopamine D_{2}/D_{3} receptors in schizophrenia (1–3). From the methodologic standpoint, the transient equilibrium method (TEM) (as referred to by Hietala et al. (4)) that was advanced by Farde et al. (5) is of particular significance, being widely used with the reversible radioligand ^{11}C-raclopride. TEM, using the cerebellum as the reference region, yielded B_{max} and K_{D} values in the putamen and caudate nucleus that were indistinguishable from those given by more invasive methods that required metabolite-corrected plasma time–activity curves. However, B_{max} and K_{D} determined with TEM or with plasma input function methods were associated with larger between-subject variability than binding potential (BP_{ND}) as measured with regional SD across subjects: a 26% coefficient of variation (COV) for B_{max} (6), compared with typically less than 10% COVs for BP_{ND} (7) for age- and sex-similar samples. Furthermore, B_{max} determined with TEM or with plasma input function methods showed larger test–retest variability than BP_{ND} (4). The authors ascribed their findings to low signal-to-noise ratio (i.e., due to low counts) of the low-specific-activity (LSA) scans. Another potential contributing factor could be the fact that TEM and other published methods (5) used an instant moment when the change in the bound amount becomes zero to obtain the amount of bound nonradioactive ligand and the bound-to-free ratio to calculate B_{max} and K_{D}.

To overcome this concern, a new method was developed using a formula that predicted regional time–activity curves of the PET experiments using the bolus-plus-infusion (B/I) scheme (8). The formula has been validated for prediction purposes for several PET ligands including ^{11}C-raclopride (9–11). Here, we extend the formula for the derivation of BP_{ND}, B_{max}, and K_{D} for bolus injection PET experiments. The proposed transformation of bolus injection time–activity curves to hypothetical B/I time–activity curves (heretofore referred to as the bolus-plus-infusion transformation [BPIT]) is expected to generate a prolonged steady state (>30 min) on which variables for Scatchard plots are obtained. Therefore, it was anticipated that the proposed BPIT may improve robustness against PET measurement errors over TEM, although it is yet to be examined.

Although B_{max} and K_{D} measurements were conventionally limited to whole putamen and caudate nucleus, the recent introduction of functional subdivisions of the striatum, which include 5 motor, affective, and limbic subdivisions per side (12,13), is a new focus in dopamine system research with PET. Subsequent studies demonstrated differential involvements of the subdivisions in various neuropsychologic and substance addiction conditions, including schizophrenia (14,15), Tourette syndrome (7), and alcoholism (16,17). Therefore, methods for B_{max} and K_{D} calculation of dopamine D_{2}/D_{3} receptors have to be validated against smaller subdivisions that are expected to be associated with greater PET measurement errors. The primary aim of this study was to examine whether TEM and BPIT are robust when applied to functional striatal subdivisions.

To this end, we examined age-associated changes in B_{max} and K_{D} in striatal subdivisions. Age-associated decreases in dopamine D_{2}/D_{3} receptors have been established in the human brain in vivo with PET (18,19) and in postmortem studies (20,21). Further, age-associated decreases in BP_{ND} have been reported to differ among striatal subdivisions (22,23). Regarding B_{max} and K_{D}, Rinne et al. (24) showed an age-related decrease in B_{max} on the whole striatum using TEM. When left and right putamen and caudate nucleus were treated separately, the decrease in B_{max} remained statistically significant in the right putamen only. These findings suggested a possibility that TEM was prone to a lower signal-to-noise ratio in smaller volumes. Therefore, examination of age-related changes in B_{max} and K_{D} in striatal subdivisions should serve as a challenging test for the utility of TEM and BPIT in smaller volumes of interest (VOIs). It was anticipated that these methods, when validated for functional subdivisions through this study, would provide useful tools for improving our understanding of the roles of dopamine D_{2}/D_{3} receptors in normal human functions and in neuropsychiatric disorders.

## MATERIALS AND METHODS

### Theory

Carson et al. (8) advanced the following prediction formula for time–activity curves of regions, A_{T}(t) of B/I experiments using observed time–activity curves, and A(t) of bolus injection scans:_{I} is the duration of the PET scan (min) and T_{B} (min) is a time constant, originally denoted by K_{bol} and to be defined for each radioligand. The formula is applicable to time–activity curves in plasma, C(t), of free and bound radioligand in tissue, F(t) and B(T), respectively, and in receptor-free regions, R(t). The original intention of the formula was to obtain a population mean T_{B} for B/I experiments.

Here, we demonstrate mathematically that the B_{max} and K_{D} of receptor systems can be obtained by BPIT via 1 pair of high-specific-activity (HSA) and LSA bolus injection PET scans, as conventionally used (5). In LSA experiments in which the amount of bound ligand is not negligible, we have the following set of differential equations (5):*K*_{1} and *k*_{2} are blood-to-brain and brain-to-blood transport rate constants, respectively; f_{ND} is the tissue-free fraction; SA is the specific activity; and k_{on} and k_{off} are bimolecular association and dissociation rate constants, respectively. B_{max} here denotes the density of receptors that are unoccupied by endogenous ligand and corresponds to B_{avail} proposed by Innis et al. (25). Applying Equation 1 to Equation 2 for A(t) and R(t), we obtain:_{T}(t) of multiple regions, R_{T}(t), and C_{T}(t) approach their plateaus (A_{C}, R_{C}, and C_{C}, respectively) after time t* with optimized T_{B}, Equation 3 guarantees that F_{T}(t) and B_{T}(t) (i.e., A_{T}(t) − F_{T}(t)) also approach plateaus (F_{C} and B_{C}, respectively). For t > t*, the lower portion of Equation 2 is applicable to F_{C} and B_{C}. After rearrangement and dB_{T}(t)/dt = 0, we obtain the Eadie-Hofstee equation (Eq. 4):

In practice, B_{max} and K_{D}/f_{ND} are determined using available A_{C} − R_{C} and A_{C}/R_{C} − 1 in place of B_{C} and B_{C}/F_{C}, respectively, in Equation 4. F_{C} is in fact equal to R_{C}, assuming negligible regional differences in nondisplaceable distribution volume, V_{ND} (i.e., *K*_{1}/*k*_{2} = *K*_{1}^{R}/*k*_{2}^{R}) (*25*). BP_{ND} is defined for HSA scans only where B_{C} is negligible:

It appears possible to set T_{I} in BPIT independent of the scan length (T_{S}) for the purpose of data analysis. We theorized that setting T_{I} and T_{S} to equal values (i.e., T_{I} = T_{S}) would yield time-consistent estimates of B_{max} and K_{D}, and that setting T_{I} and T_{S} to unequal values would result in systematic biases. If validated, this would demonstrate that BPIT settings for T_{I} and T_{S} must be equal as originally predicted by the formula in Equation 1 (*8*).

### Subjects

Eighty-one subjects who underwent HSA and LSA ^{11}C-raclopride PET scans are included in this analysis. Subjects were participants of 3 ongoing research projects. One project (26) comprised patients with restless legs syndrome (*n* = 23; mean age ± SD, 59.3 ± 9.3 y; 13 women and 10 men) and healthy subjects (*n* = 32; mean age ± SD, 59.3 ± 8.2 y; 17 women and 15 men). Inclusion and exclusion criteria for restless legs syndrome subjects are described elsewhere (26). Participants of the other 2 projects (*n* = 27; mean age ± SD, 24.2 ± 4.3 y; 14 women and 13 men) were healthy subjects (McCaul and Wand, unpublished data, 2012; (*7*)). Briefly, healthy subjects were without a current or past history of neurologic and psychiatric diseases and substance addiction or dependence and showed no abnormal findings on physical examination at the time of participation. Detailed inclusion and exclusion criteria can be found elsewhere (*7,17,26*). Data of all 81 participants were used for evaluation of analysis methods. All healthy subjects who underwent the 2 scans during the daytime (*n* = 47; age range, 18–77 y; 23 women and 24 men) were included for examination of age-related changes in BP_{ND}, B_{max}, and K_{D}. Subjects gave signed informed consent before their participation. The consent forms were approved by the institutional review board of the Johns Hopkins University.

### PET and MRI Procedures

#### PET Procedures

PET was performed on an Advance scanner (GE Healthcare) with a 14.875-cm axial field of view. Before the scan, a catheter was placed in the antecubital vein of the participant's left arm for the tracer injection. In selected subjects (*n* = 33), another catheter was inserted in the right radial artery to obtain arterial blood samples. Then, the subject was positioned in the scanner with the head lightly immobilized with a custom-made thermoplastic mask to reduce head movement during the scan. After a transmission scan with a ^{68}Ge source for attenuation correction, a 90-min emission scan in 3-dimensional mode was started with a slow bolus injection of ^{11}C-raclopride (714.1 ± 44.4 MBq [19.3 ± 1.2 mCi]). In scans with an arterial catheter, arterial blood was sampled at rapid intervals (<5 s) initially and with prolonging intervals toward the end of the emission scan. Selected samples were analyzed by high-pressure liquid chromatography for radioactive metabolites in plasma using previously reported methods (27). ^{11}C-raclopride was synthesized with minor changes in purification and formulation according to the published procedure (28). In LSA scans, nonradioactive raclopride was added to the ^{11}C-raclopride solution targeting to achieve an SA of 555 MBq (15 mCi)/μmol. The final SA adjusted to the injection time was used for the calculation of B_{max} and K_{D}. Observed SA averaged 383.2 ± 244.2 GBq (10,357.0 ± 6,601.2 mCi)/μmol (range, 60.0–1,330.6 GBq [1,622.8–35,961.0 mCi]/μmol) and 640.1 ± 148 MBq (17.3 ± 4.0 mCi)/μmol (range, 366.3–1,098.9 MBq [9.9–29.7 mCi]/μmol) for HSA and LSA scans, respectively.

Each emission scan was reconstructed to 35 transaxial images of 128 ×128 voxels by a backprojection algorithm using the manufacturer-provided software corrected for attenuation, scatter, and dead time. The resulting resolution was approximately 6 mm in full width at half maximum (29).

#### MRI Procedures

On a separate occasion, a spoiled-gradient-sequence MRI scan was obtained for each subject using the following parameters: repetition time, 35 ms; echo time, 6 ms; flip angle, 458; slice thickness, 1.5 mm with no gap; field of view, 24 × 18 cm; and image acquisition matrix, 256 × 192, reformatted to 256 × 256.

### PET Data Analysis

#### VOIs

VOIs for the putamen, caudate nucleus, and cerebellum were defined on the MR image using the 3-dimensional interactive-segmentation mode of a locally developed VOI-defining tool (VOILand) (30). Then, striatal VOIs were subdivided to the ventral striatum and anterior and posterior putamen and caudate nucleus (5 subdivisions per side (*13*)) using a semiautomated method (30) that incorporated anatomic guidance based on postmortem human materials (31). The anterior putamen and anterior and posterior caudate nucleus were classified as associative striatum, whereas the posterior putamen represented motor striatum and the ventral striatum consisted of limbic striatum (12). VOIs were transferred from MRI to PET space according to MRI-to-PET coregistration parameters obtained with an SPM5 module for this purpose ((*32*); available at www.fil.ion.ac.uk/spm5) and applied to PET frames to obtain regional time–activity curves.

#### Optimization of T_{B}

First, T_{B} was optimized by minimizing the sum of the SDs of A_{T}(t), R_{T}(t), and C_{T}(t) across PET frames from t* to 90 min for a t* of 30, 40, and 50 min for each scan for subjects with arterial blood samples. Values of A_{C}, R_{C}, and C_{C} were obtained as respective means of A_{T}(t), R_{T}(t), and C_{T}(t) between t* and 90 min. To evaluate achievement of plateaus in BPIT quantitatively, normalized residual sums of squares (nRSS) across t*- to 90-min frames were compared between BPIT and the multilinear reference tissue method with 2 parameters (MRTM2 (*33*)). Calculation formulas for nRSS are Σ(A_{T}(t) − A_{C})^{2}/A_{C} for BPIT and Σ(A(t) − eA(t))^{2}/A_{C} for MRTM2, where eA(t) stands for model-predicted A(t) given by MRTM2. MRTM2 was applied to LSA scans for this evaluation after confirming small differences in nRSS between HSA and LSA scans, although the biologic significance of estimated parameters are unclear for LSA scans. After confirming that A_{T}(t), R_{T}(t), and C_{T}(t) reached respective plateaus at least at 40 min on visual inspection and by means of nRSS (see the “Results” section), BPIT was applied to all subjects, setting t* at 40 min without including C(t) in the analysis.

#### Evaluation of BPIT

Regional estimates of BP_{ND} were compared between BPIT, MRTM2 (33), and reference tissue graphical analysis (RTGA (*34*)) for HSA scans. Then, estimates of B_{max} and K_{D} were compared among the following conditions: both T_{I} and T_{S} set at 80 or 90 min (T_{I} = T_{S}) and T_{I} set at 80 or 100 min with T_{S} fixed at 90 min (i.e., TI ≠TS), as explained in the “Theory” section.

After methodologic evaluations, age-associated changes in B_{max} and K_{D} were examined in functional subdivisions of the striatum using TEM and BPIT.

#### Statistical Approaches

Data were summarized as means and SD. The coefficient of determination (*R*^{2}) was used to evaluate correlations between methods and approaches. Pearson correlation coefficients (*r*) and *P* values were reported to evaluate correlations of B_{ND}, B_{max}, and K_{D} to age using the Matlab (The MathWorks) function “corr.” ANOVA was used to compare methods across regions (2-way ANOVA) using the Matlab function “anova2.”

## RESULTS

Plots of A_{T}(t) and R_{T}(t) approached respective plateaus by 30 min in all HSA and LSA scans, as shown in Figure 1. In cases with arterial plasma samples, C_{T}(t) also remained unchanged after 40 min. BPIT showed about 5 times less nRSS than MRTM2 (Table 1) (main effect, *F*_{1} = 848.78; *P* < 10^{−10}). Significant region effects were observed (*F*_{9} = 83.7; *P* < 10^{−10}), probably because of smaller volumes of posterior caudate nucleus and ventral striatum. For the cases with plasma blood samples, C_{T}(t) showed nRSS (543.9 ± 318.2 Bq [14.7 ± 8.6 nCi]/mL) that were similar to those of the ventral striatum (*t*_{370} = 1.735; *P* > 0.05) for a t* of 40 min. These findings confirmed that A_{T}(t), R_{T}(t), and C_{T}(t) reached respective plateaus at 40 min and consequently that F_{T}(t) and then B_{T}(t) also approached respective plateaus in this time frame. Accordingly, regional BP_{ND} values were identical between the plasma input method (i.e., using A_{T}(t), R_{T}(t), and C_{T}(t) for estimation of T_{B}; =*y*) and the reference tissue method (i.e., using A_{T}(t) and R_{T}(t) alone; =*x*) (*y* = 1*x* + 0; *R*^{2} = 1.00; pooling HSA and LSA scan values). Therefore, the remaining analyses were conducted using A_{T}(t) and R_{T}(t) alone. The best estimates of T_{B} averaged at 105 ± 25.8 and 125 ± 30.3 min for HSA and LSA scans, respectively.

For HSA scans, BPIT (=*x*) yielded BP_{ND} values essentially identical to those ofMRTM2 (=*y*1) and RTGA (=*y*2): *y*1 = 1.02*x* − 0.014, *R*^{2} = 0.996, and *y*2 = 1.00*x* − 0.066, *R*^{2} = 0.998. The findings validated BPIT for BP_{ND} for HSA ^{11}C-raclopride scans. BPIT yielded time-consistent estimates of B_{max} and K_{D} when both T_{I} and T_{S} were set at 80 or 90 min (Table 2). Conversely, BPIT yielded 5% higher or 4% lower values of B_{max} and K_{D} when T_{I} was set at 100 min or 80 min for a T_{S} of 90 min, respectively, than when T_{I} and T_{S} were set at 90 min (Table 2). Estimates of BP_{ND} remained unchanged (*R*^{2} = 1) when T_{S} was set at 90 min.

Regional B_{max} and K_{D} correlated between BPIT and TEM when left and right VOIs were merged (Fig. 2). When compared with BPIT, TEM yielded slightly higher B_{max} and K_{D} values and suffered some outliers (e.g., B_{max} > 60 pmol/mL; K_{D} > 50 pmol/mL). Correlations were not supported using TEM when left and right sides were treated separately (*R*^{2} = 0.062 for B_{max}; *R*^{2} = 0.0012 for K_{D}), mainly because of an increased number of outliers.

When left and right VOIs were analyzed separately, regional B_{max} decreased as a function of age in 9 of 10 regions (excluding right posterior caudate nucleus) by BPIT, whereas only 4 regions showed correlations by TEM after Bonferroni adjustment (Table 3). When left and right VOIs were combined, BPIT revealed that B_{max} in all 5 subdivisions was inversely correlated with age, whereas TEM failed to identify age-effect in B_{max} posterior caudate nucleus and ventral striatum. BPIT and TEM showed similar rates of decline in B_{max}, ranging from 0.47% per year to 0.73% per year in regions. No correlations of K_{D} with age were observed in any region by BPIT (0.421 < *P* < 0.829, across left and right subdivisions) or by TEM (0.251 < *P* < 0.915). To exemplify these findings, plots of B_{max} against age are shown in Figure 3 for ventral striatum, with left and right VOIs merged.

## DISCUSSION

This study demonstrated that BPIT yielded robust estimates of B_{max} and K_{D} of dopamine D_{2}/D_{3} receptors for functional subdivisions of the striatum using HSA and LSA ^{11}C-raclopride PET. However, the widely used TEM (5), also using the cerebellum as the reference region, showed more unstable estimates when applied to striatal subdivisions than did conventional, larger VOIs for which the method has been validated. Therefore, the current findings support application of BPIT for the newly emerged anatomic demand (*7,12–17*). The improved robustness of BPIT over TEM can be ascribed to the different approaches that the 2 methods assumed to overcome the challenging point (i.e., the equation of dB(t)/dt in Eq. 2) of B_{max} and K_{D} measurements: Farde et al. (5) advanced a solution by focusing on an instant moment when dB(t)/dt became zero in Equation 2. Accordingly, the method was referred to as TEM by Hietala et al. (4). In contrast, we devised a simple solution without use of the complicated equation. This study demonstrated that steady-state for BPIT is achieved for ^{11}C-raclopride scans when t* and T_{I} were set at 40 and 90 min, respectively. In other words, BPIT uses averages between 40 and 90 min, whereas TEM uses the instant time point. The limited time resolution of PET may be a disadvantageous factor for TEM.

BPIT is a graphical method for model parameter estimation. A close analogy would be RTGA (34): the Logan lot of calculated variables, namely ∫A(t)dt/A(T) (=*y*) versus ∫R(t)dt/A(T) yields BP_{ND} as a slope of the asymptote less 1. RTGA requires an assumed value for *k*_{2} of the reference region (*k*_{2}^{R}, 0.163 min^{−1} for ^{11}C-raclopride (*34*)). Similarly, the BPIT plot (Fig. 1) uses a calculated variable (Eq. 1) as *y* variable and yields BP_{ND} (Eq. 5). BPIT estimates 1 value of T_{B} for all regions in each experiment. Techniques for estimating a variable that is assumed to be common across regions was also advanced by Wu and Carson (*35*) for *k*_{2}^{R} for the simplified reference region method (36) and by Ichise et al. (*33*) for *k*_{2}^{R} in an independent linear solution. BPIT yielded regional values of BP_{ND} that were indistinguishable from established RTGA and MRTM2 for HSA ^{11}C-raclopride scans. Thus, we concluded that BPIT is validated for HSA ^{11}C-raclopride scans.

Because of the time-consistent estimates of B_{max} and K_{D} obtained with equal values of T_{I} and T_{S} and systematic biases seen with unequal T_{I} and T_{S} (Table 2), we concluded that T_{I} must be set at T_{S} in BPIT as it was verified for the prediction purpose (8).

An age-dependent decline of BP_{ND} of dopamine D_{2}/D_{3} receptors has been repeatedly confirmed, predominantly using ^{11}C-raclopride. To our knowledge, Kim et al. (23) was the first to examine age-dependent declines in BP_{ND} in the functional striatal subdivisions. The authors found significant decreases bilaterally in the posterior putamen alone, probably because of the relatively narrow age range and smaller sample size (24–54 y; 13 women and 10 men). This study showed significant decreases in all subdivisions in a population sample, with larger age ranges and larger sample size (18–77 y; 20 women and 22 men). Interestingly, the findings of the 2 studies agreed in that posterior putamen (i.e., motor striatum) showed larger rates of decline than associative striatum and limbic striatum.

Rinne et al. (24) reported a rate of decline in B_{max} to be 0.5% per year using ^{11}C-raclopride, whereas Wong et al. (37) reported a rate of 1% per year using an irreversible radioligand ^{11}C-*N*-methylpiperone and a distinctive analysis method (38). Compared with their previous report (24), Pohjalainen et al. (39) replicated a significant decrease in B_{max} in the right striatum but not in the left striatum, despite a larger number of subjects and inclusion of a wide age range (19–82 y; 21 women and 33 men). Putamen and caudate nucleus were not evaluated independently in this study. The authors did not find any age-associated change in K_{D}, in agreement with earlier reports (24,37). To our knowledge, these 3 studies appeared to be the only reports that examined B_{max} and K_{D} with respect to age in the human brain. Therefore, this study using proposed BPIT is the first to report age-associate decreases of B_{max} in functional striatal subdivisions. Weaker correlations were observed with TEM.

There are several limitations of the study. First, the radioactivity in the vascular volume within a region was omitted from the equations to simplify presentation of the theory (e.g., A(t) = B(t) + F(t) + v_{0}·C(t) to be precise, where v_{0} is the vascular volume). However, because of the linear nature of Equation 1, it is self-evident that the inclusion of v_{0} does not change the findings. BPIT may suffer degrees of biases in BP_{ND}, B_{max}, and K_{D} similar to other established tissue reference methods. Second, observed SA averaged 640.1 MBq (17.3 mCi)/μmol in LSA scans (target SA = 555 MBq [15 mCi]/μmol). The measure was taken to reduce the chances of adverse effects such as akathisia with pharmacologic doses of the dopamine antagonist raclopride (5). TEM was validated with significantly lower SA levels (88.8–114.7 MBq [2.4–3.1 mCi]/μmol; (*5*)). Rinne et al. (24) also used lower SA levels (92.5–418.1 [2.5–11.3 mCi]/μmol) to examine age-dependent changes in B_{max}. In theory, lower SA levels in LSA scans bring LSA points toward the *y*-axis in the Eadie-Hofstee plot (Eq. 4) and contribute to increasing the accuracy of B_{max}. Therefore, it should be clarified that the accuracy of TEM estimated in this study cannot be directly compared with these earlier studies. Conversely, BPIT could be applicable to studies even with relatively modest SA in LSA scans.

The most difficult point in the validation of BPIT could be to prove achievement of plateaus. Linear regression may appear appropriate for this purpose. To evaluate achievement of plateaus in an unbiased manner, we used an approach that applies RSS of model fitting. RSS is considered to be composed of errors originating from PET measurement errors and the systematic bias due to disagreement between the model and reality. The results indicated that systematic biases observed with BPIT (i.e., steady increases or decreases of A_{T}(t), R_{T}(t), and C_{T}(t)) were significantly lower than systematic biases that were associated with MRTM2, provided PET measurement errors were relatively similar to each other. For this reason, we concluded that plateaus were achieved for PBIT. Further validation may be obtained by actually performing HSA and LSA B/I experiments, as has been reported in animal studies for the opiate receptors (40).

## CONCLUSION

This study demonstrated that BPIT is a valid method for measurements of BP_{ND}, B_{max}, and K_{D} of dopamine D_{2}/D_{3} receptors using ^{11}C-raclopride PET scans. The method yielded more robust estimates of B_{max} and K_{D} in smaller striatal subdivisions than the widely used TEM. Age-dependent declines in B_{max} were observed in functional striatal subdivisions, except for the posterior caudate nucleus, using BPIT. Therefore, BPIT may be useful for detecting changes in B_{max} and K_{D} in small functionally uniform regions in various neuropsychiatric and substance abuse disorders.

## DISCLOSURE STATEMENT

The costs of publication of this article were defrayed in part by the payment of page charges. Therefore, and solely to indicate this fact, this article is hereby marked “advertisement” in accordance with 18 USC section 1734.

## Acknowledgments

We thank the Johns Hopkins Hospital PET Center and Biomedical Cyclotron staff. This work was supported by PHS grants R01 AA012837, R01 AA010158, PO1 AG21190, R01 NS42857, and R01 MH078175. No other potential conflict of interest relevant to this article was reported.

## Footnotes

Published online Apr. 9, 2012.

- © 2012 by the Society of Nuclear Medicine, Inc.

## REFERENCES

- Received for publication September 12, 2011.
- Accepted for publication January 3, 2012.