Dissociative changes in B_max and K_D of dopamine D2/D3 receptors with aging observed in functional subdivisions of striatum: A revisit with an improved data analysis method

Abstract

Separate measurements of B_max, the density of available receptors and K_D, the equilibrium dissociation constant in the human brain with positron emission tomography (PET) have contributed to our understandings of neuropsychiatric disorders, especially with respect to the dopamine D2/D3 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 [¹¹C]raclopride scans involving 81 subjects, age-associated changes in B_max and K_D were examined in 47 healthy subjects ranging from 18 to 77 years old.

Results

The BPIT method was consistent with established reference tissue methods regarding regional binding potential (BP_ND). 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 to a widely accepted transient equilibrium method (TEM). Altogether, BPIT was supported as a method for BP_ND, B_max, and K_D. We demonstrated age-associated declines in B_max in all five functional striatum subdivisions with BPIT when corrected for multiple comparisons. These age-related effects were not consistently attainable with TEM. 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 striatum subdivisions.

Measurements of B_max, the densities of available receptors and K_D, the equilibrium dissociation constant in humans with PET have contributed to our understandings of neuropsychiatric disorders, in particular on the role of dopamine D2/D3 receptors in schizophrenia (1–3). From the methodological standpoint, 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 [¹¹C]raclopride. The TEM method, using cerebellum as the reference region, yielded B_max and K_D values in putamen and caudate nucleus that were indistinguishable to those given by more invasive methods that required metabolite corrected plasma time-activity curves (TACs). 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 standard deviation (SD) across subjects: A 26% coefficient of variation (COV) for B_max,(6), compared to typically less than 10% COVs for BP_ND (7) for age- and gender-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-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) utilized an instant moment when the change in the bound amount becomes zero to obtain the amount of bound non-radioactive ligand and the bound-free ratio to calculate B_max and K_D.

To overcome this concern, a new method was developed utilizing a formula that predicted regional TACs of the bolus-plus-infusion (B/I) scheme PET experiments (8). The prediction formula has been validated for prediction purposes for a number of PET ligands including [¹¹C]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 TACs to hypothetical B/I TACs (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 plot 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.

While 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 five 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 neuropsychological 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 D2/D3 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 striatum subdivisions.

To this end, we examined age-associated changes in B_max and K_D in striatum subdivisions. Age-associated decreases in dopamine D2/D3 receptors have been established in 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 striatum 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-noise ratio in smaller volumes. Therefore, examination of age-related changes in B_max and K_D in striatum subdivisions should serve as a challenging test for 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 D2/D3 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 (TACs) of regions, A_T(t) of B/I experiments using observed TACs, A(t) of bolus-injection scans:

$${\text{A}}_{\text{T}}(t)=\frac{{\text{T}}_{\text{B}}·\text{A}(\text{t})+{\int }_0^t\text{A}(u)du}{{\text{T}}_{\text{B}}+{\text{T}}_{\text{I}}}$$ (1)

where T_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 TACs 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 B_max and K_D of receptor systems can be obtained by BPIT via one pair of high SA (HSA) and LSA bolus injection PET scans, as conventionally employed (5). In LSA experiments where the amount of bound ligand is not negligible, we have the following set of differential equations (5):

$$\begin{array}{c}\frac{d\text{A}(t)}{dt}=K_1·\text{C}(t)-k_2.\text{F}(t)\\ \frac{d\text{B}(t)}{dt}=f_{ND}·k_{on}·(B_{\mathit{max}}-\text{B}(t)/\text{SA})·\text{F}(t)-k_{\mathit{off}}·\text{B}(t)\end{array}$$ (2)

where K₁ and k₂ are blood-to-brain and brain-to-blood transport rate constants, f_ND is the tissue free fraction, and k_on and k_off are bimolecular association and dissociation rate constants. Note that B_max here denotes the density of receptors that are unoccupied by endogenous ligand, and correspond to B_avail proposed by Innis et al. (25). Applying Equation 1 to the upper equation for A(t) and R(t), we obtain:

$$\begin{array}{l}\frac{{d\text{A}}_{\text{T}}(t)}{dt}=K_1·{\text{C}}_{\text{T}}(t)-k_2·{\text{F}}_{\text{T}}(t)\\ \frac{{d\text{R}}_{\text{T}}(t)}{dt}=K_1^R·{\text{C}}_{\text{T}}(t)-k_2^R·{\text{R}}_{\text{T}}(t)\end{array}$$ (3)

where the subscript T indicates variables after BPIT using Equation 1, and the superscript R denotes variables of the receptor-free region. When A_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, Equations 3 guarantees that F_T(t) and B_T(t) (i.e., A_T(t) − F_T(t)) also approach respective plateaus (F_C and B_C, respectively). For t>t*, the lower Equation 2 is applicable to F_C and B_C. After rearrangement and dB_T(t)/dt = 0, we obtain the Eadie-Hofstee equation:

$$\frac{{\text{B}}_{\text{C}}}{\text{SA}}=-\frac{{\text{K}}_{\text{D}}}{f_{ND}}·\frac{{\text{B}}_{\text{C}}}{{\text{F}}_{\text{C}}}+{\text{B}}_{max}$$ (4)

In practice, B_max and K_D/f_ND are determined by 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. Note that F_C is in fact equal to R_C, assuming negligible regional differences in non-displaceable distribution volume, V_ND (i.e., K₁/k₂ = K₁^R/k₂^R) (25). BP_ND is defined for HSA scans only where B_C is negligible:

$${\text{BP}}_{\text{ND}}=\frac{f_{ND}}{{\text{K}}_{\text{D}}}·{\text{B}}_{max}=\frac{{\text{B}}_{\text{C}}}{{\text{F}}_{\text{C}}}=\frac{{\text{A}}_{\text{C}}}{{\text{R}}_{\text{C}}}-1$$ (5)

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. TI = TS) would yield time-consistent estimates of Bmax and KD, and that setting T_I and T_S to unequal values would results in systematic biases. If validated, this would demonstrate that BPIT settings for TI and TS must be equal as originally predicted by the formula in Equation 1 (8).

Subjects

A total of 81 subjects who had HSA and LSA [¹¹C]raclopride PET scans are included in this analysis. Subjects were participants of three on-going research projects. Participants of one project (26) were patients with restless legs syndrome (RLS; n=23; 59.3 ± 9.3 years; 13 females and 10 males) and healthy control subjects (n= 32; 59.3 ± 8.2 years; 17F/15M). Inclusion and exclusion criteria for RLS subjects are described elsewhere (26). Participants of other two projects (n=27; 24.2 ± 4.3 years; 14F/13M) were healthy subjects (McCaul and Wand, manuscripts in preparation; 7). Briefly, healthy subjects were without current and past history of neurological 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 had the two scans during day time (n=47; Age range: 18 – 77 years; 23F/24M) were included for examination of age-related changes in BP_ND, B_max, and K_D. Subjects gave signed informed consent prior to their participation. The consent forms were approved by the institutional review board of the Johns Hopkins University.

PET and MRI procedures

PET procedures

PET imaging was performed on a GE Advance PET scanner (GE Medical Systems, Milwaukee, WI, USA) 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 reduced head movement during the scan. After a transmission scan with a [⁶⁸Ge] source for attenuation correction, a 90-min emission scan in a 3-dimensional mode started with a slow-bolus injection of [¹¹C]raclopride (19.3 ± 1.2 mCi; mean ± SD). In scans with an arterial catheter, arterial blood was sampled in rapid intervals (<5 seconds) initially and with prolonging intervals towards 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). [¹¹C]Raclopride was synthesized with minor changes in purification and formulation according to the published procedure (28). In LSA scans, non-radioactive raclopride was added to the [¹¹C]raclopride solution targeting to achieve an SA of 15 mCi/μmol. Final SA adjusted to the injection time was used for calculation of B_max and K_D. Observed SA averaged at 10357.0 ± 6601.2 mCi/μmol (mean ± SD; range: 1622.8 – 35961) and 17.3 ± 4.0 mCi/μmol (range: 9.9 – 29.7) for HSA and LSA scans, respectively.

Each emission scan was reconstructed to 35 transaxial images of 128 by 128 voxels by a back projection algorithm using the manufacture-provided software correcting for attenuation, scatter, and dead-time. Resulting resolution was approximately 6 mm at full-width-half-maximum (FWHM) (29).

MRI procedures

On a separate occasion, a spoiled gradient (SPGR) sequence MRI was obtained on 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 cm2; image acquisition matrix, 256 × 192, reformatted to 256 × 256.

PET Data analysis

Volumes of interest

VOIs for putamen, caudate nucleus, and cerebellum were defined on MRI using the 3-D interactive-segmentation mode of a locally developed VOI defining tool (VOILand) (30). Then, striatal VOIs were subdivided to the ventral striatum, and anterior/posterior putamen and caudate nucleus (5 subdivisions per side; 13) using a semi-automated method (30) that incorporated anatomical guidance based on post-mortem human materials (31). Anterior putamen, and anterior and posterior caudate nucleus were classified as associative striatum, while posterior putamen represented motor striatum, and ventral striatum consisted of limbic striatum (12). VOIs were transferred from MRI to PET space according to MRI-to-PET coregistration parameters obtained with a SPM5 module for this purpose (32, available at www.fil.ion.ac.uk/spm5), and applied to PET frames to obtain regional TACs.

Optimization of TB

First, T_B was optimized by minimizing the sum of SDs of A_T(t), R_T(t), and C_T(t) across PET frames from t* to 90 min for 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 nRRS 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 biological 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 results), 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: Setting both T_I and T_S at 80 or 90 min (T_I = T_S), and setting T_I at 80 or 100 min with T_S fixed at 90 min (i.e., TI≠TS), as explained in the Theory section.

Following methodological 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 (R²) was used to evaluate correlations between methods and approaches. Pearson’s correlation coefficients (r) and p values were reported to evaluate correlations of B_ND, B_max, and K_D to age using a Matlab function ‘corr’ (Mathworks, Natick, MA). Analysis of variance (ANOVA) was used to compare methods across regions (two-way ANOVA) using a 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 when compared to MRTM2 (Table 1) (Main effect: F=848.78; df=1; p<10⁻¹⁰). Significant region effects were observed (F=83.7; df=9; 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 (14.7 ± 8.6 nCi/mL) that were similar to ventral striatum (t-test; t=1.735; df=370; p>0.05) for 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 that F_T(t), 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; R²=1.00; pooling HSA and LSA scan values). Therefore, remaining analyses were conducted using A_T(t) and R_T(t) alone. The best estimates of T_B averaged at 105 ± 25.8 min and 125 ± 30.3 min for HSA and LSA scans, respectively.

Figure 1.

Observed and transformed regional time activity curves (TACs) of anterior putamen, A(t) and A_T(t), respectively and cerebellum, R(t) and RT(t), respectively of HSA (Panel A) and LSA (Panel B) [¹¹C]raclopride scans. Both A_T(t) for all striatal subdivisions and R_T(t) became stable by 30 min in all cases. Assumed plateaus (A_C and R_C) are shown by horizontal solid lines.

Table 1.

Volumes and normalized residual sums of squares (nRSS) in functional striatum subdivisions

	Anterior putamen	Posterior putamen	Anterior caudate nucleus	Posterior caudate nucleus	Ventral striatum
	Volume (mL)
Left	1.93 ± 0.29	1.88 ± 0.39	2.10 ± 0.34	0.67 ± 0.20	0.87 ± 0.21
Right	2.00 ± 0.29	1.76 ± 0.33	2.19 ± 0.33	0.66 ± 0.19	0.85 ± 0.16
Merged	3.93 ± 0.53	3.65 ± 0.69	4.29 ± 0.64	1.22 ± 0.37	1.72 ± 0.34
	nRSS (nCi/mL)
BPIT	3.0 ± 2.1	3.3 ± 2.4	3.4 ± 2.7	12.9 ± 9.1	10.4 ± 9.0
MRTM2	15.1 ± 11.8	16.5 ± 14.8	17.8 ± 15.6	60.1 ± 40.6	57.6 ± 59.9

For HSA scans, BPIT (=x) yielded essentially identical BP_ND values as MRTM2 (=y1) and RTGA (=y2): y1 = 1.02·x − 0.014; R²=0.996; y2 = 1.00·x − 0.066; R²=0.998. The findings validated BPIT for BP_ND for HSA [¹¹C]raclopride scans. BPIT yielded time-consistent estimates of B_max as well as 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 T_S of 90 min, respectively, compared to setting T_I and T_S at 90 min (Table 2). Estimates of BP_ND remained unchanged (R² = 1) when T_S was set at 90 min.

Table 2.

Effects of T_I in Equation 1 and assumed scan length for BPIT (T_S) on B_max and K_D estimates

TI (min)	TS (min)	Correlation equations (R2: Coefficient of determination)
		Bmax	KD
80	80	y = 1.00·x + 0.46 (R2 = 0.989)	y = 1.00·x + 0.17 (R2 = 0.968)
80	90	y = 1.05·x − 0.04 (R2 = 1)	y = 1.05·x − 0.025 (R2 = 1)
100	90	y = 0.96·x − 0.003 (R2 = 1)	y = 0.96·x − 0.02 (R2 = 1)

x: B_max or K_D estimates with both T_I and T_S set to 90 min. y: Estimates obtained with T_I and T_S set as indicated.

Regional B_max as well as K_D correlated between BPIT and TEM when left and right VOIs were merged (Figure 2). When compared to 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). Using TEM, correlations were not supported when left and right sides were treated separately (R²=0.062 for B_max; R²=0.0012 for K_D) mainly due to an increased number of outliers.

Figure 2.

Scatter plots of regional values of B_max (Panel A) and K_D (Panel B), TEM (=y) versus proposed BPIT (=x). Data from all subjects (n=81), 5 subdivisions per subject with left and right VOIs merged are shown (a total of 405 points). Linear regression Equations and coefficients of determination (R²) are shown in each panel.

When left and right VOIs were analyzed separately, regional B_max decreased as a function of age in 9 out of 10 regions (excluding right posterior caudate nucleus) by BPIT whereas only 4 regions showed correlations by TEM after Bonferroni correction (Table 3). When left and right VOIs were combined, BPIT revealed that Bmax in all five subdivisions was inversely correlated with age where as TEM failed to identify age differences in Bmax 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 above findings, plots of B_max against age were shown in Figure 3 for ventral striatum with left and right VOIs merged.

Table 3.

Correlations of B_max to age in healthy subjects

	Left		Right		Merged
	BPIT	TEM	BPIT	TEM	BPIT	TEM
Anterior putamen	−0.477 (0.000701)* 0.49%	−0.424 (0.00298)* 0.48%	−0.417 (0.00361)* 0.45%	−0.338 (0.0201) n.s.	−0.433 (0.00239)* 0.47%	−0.375 (0.0095)* 0.47%
Posterior putamen	−0.453 (0.00137) * 0.51%	−0.463 (0.00105)* 0.54%	−0.437 (0.00214)* 0.50%	−0.414 (0.00386)* 0.49%	−0.461 (0.0011)* 0.51%	−0.416 (0.00363)* 0.49%
Anterior caudate nucleus	−0.508 (0.000268)* 0.62%	−0.363 (0.0121) n.s.	−0.483 (0.000579)* 0.60%	−0.428 (0.00267)* 0.53%	−0.508 (0.000264)* 0.61%	−0.476 (0.000719)* 0.58%
Posterior caudate nucleus	−0.34 (0.0196) n.s.	−0.227 (0.126) n.s.	−0.452 (0.00141)* 0.73%	−0.285 (0.0519) n.s.	−0.411 (0.00407)* 0.66%	−0.258 (0.0801) n.s.
Ventral striatum	−0.415 (0.00377)* 0.62%	−0.0261 (0.862) n.s.	−0.454 (0.00134)* 0.68%	−0.224 (0.130) n.s.	−0.471 (0.000844)* 0.67%	−0.0694 (0.643) n.s.

Each cell lists Pearson’s correlation coefficient (upper row), p values (middle row) with denoted by an asterisk when statistically significant after a Bonferroni correction, and rates of declines per year relative to B_max value at 20 years old (lower row, when significant).

Figure 3.

Scatter plots of B_max versus age for ventral striatum of healthy subjects (n=47) with left and right VOIs merged, given by BPIT (Panel A) and TEM (B). Linear regression Equations and coefficients of determination (R²) are shown in each panel.

DISCUSSION

This study demonstrated that BPIT yielded robust estimates of B_max and K_D of dopamine D2/D3 receptors for functional subdivisions of the striatum using HSA and LSA [¹¹C]raclopride PET. However, the widely used TEM (5), also using cerebellum as the reference region, showed more unstable estimates when applied to striatum subdivisions, when compared to conventional, larger VOIs for which the method has been validated. Therefore, the current findings support application of BPIT for the newly emerged anatomical demand (7, 12–17). The improved robustness of BPIT over TEM can be ascribed to the different approaches that the two methods assumed to overcome the challenging point (i.e., the equation of dB(t)/dt in Equation 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 [¹¹C]raclopride scans when t* and T_I were set at 40 and 90 min, respectively. In other words, BPIT utilizes averages between 40 and 90 min, while TEM utilizes the instant time point. The limited time resolution of PET maybe a disadvantageous factor for TEM.

It should be clarified that 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 slope of the asymptote less 1. RTGA requires an assumed value for k₂ of the reference region (k₂^R, 0.163 min⁻¹ for [¹¹C]raclopride; 34). Similarly, the BPIT plot (Figure 1) utilizes a calculated variable (Equation 1) as y variable and yields BP_ND (Equation 5). BPIT estimates one 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 k₂^R for the simplified reference region method (36), as well as by Ichise et al. (33) for k₂^R in an independent linear solution. PBIT yielded regional values of BP_ND that were indistinguishable from established RTGA and MRTM2 for HSA [¹¹C]raclopride scans. Thus, we conclude that BPIT is validated for HSA [¹¹C]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 conclude that T_I must be set at T_S in BPIT as it was verified for the prediction purpose (8).

Age-dependent decline of BP_ND of dopamine D2/D3 receptors has been repeatedly confirmed, predominantly using [¹¹C]raclopride. To our knowledge, Kim et al. (23) was the first to examine age-dependent declines in BP_ND in the functional striatum subdivisions. The authors found significant decreases in bilateral posterior putamen alone probably due to the relatively narrow age range and smaller sample size (24 – 54 years; 13F/10M). This study showed significant decreases in all subdivisions in a population sample with larger age ranges and larger sample size (18–77 years; 20F/22M). Interestingly, the findings of the two 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 [¹¹C]raclopride while Wong et al. (37) reported a rate of 1% per year using a irreversible radioligand [¹¹C]N-methylpiperone and a distinctive analysis method (38). 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 (Age range: 19–82;21F/33M), compared to their previous report (24). 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 three 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 employing proposed BPIT is the first to report age-associate decreases of B_max in functional striatum subdivisions. Weaker correlations were observed with TEM.

There are several limitations of the study to discuss. First, the radioactivity in the vascular volume within a region was omitted from Equations to simplify presentation of the theory (e.g., A(t) = B(t) + F(t) + v₀·C(t) to be precise where v₀ is the vascular volume). However, because of the linear nature of Equation 1, it is self-evident that the inclusion of v₀ does not change the findings. BPIT may suffer similar degrees of biases in BP_ND, B_max, and K_D as other established tissue reference methods. Second, observed SA averaged at 17.3 mCi/μmol in LSA scans (target SA = 15 mCi/μmol). The measure was taken to reduce the chances of adverse effects such as akathisia with pharmacological doses of the dopamine antagonist raclopride (5). TEM was validated with significantly lower SA levels (2.4 – 3.1 mCi/μmol; 5). Rinne et al. (24) also employed lower SA levels (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 towards y-axis in the Eadie-Hofstee plot (Equation 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 to 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 employed an approach utilizing RSS of model fitting. RSS is considered to be composed of errors originated 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 conclude 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 D2/D3 receptors using [¹¹C]raclopride PET scans. The method yielded more robust estimates of B_max and K_D in smaller striatum subdivisions than widely used TEM. Employing BPIT, age-dependent declines in B_max were observed in functional striatum subdivisions except for posterior caudate nucleus. 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.