Dopamine D2/3 Receptor Availabilities in Striatal and Extrastriatal Regions of the Adult Human Brain: Comparison of Four Methods of Analysis

Values of binding potentials (BPND) of dopamine D2/3 receptors differ in different regions of the brain, but we do not know with certainty how much of this difference is due either to different receptor numbers, or to different affinities of tracers to the receptors, or to both. We tested the claim that both striatal and extrastriatal dopamine D2/3 receptor availabilities vary with age in vivo in humans by determining the values of BPND of the specific radioligand [11C]raclopride. We determined values of BPND in striatal and extrastriatal volumes-of-interest (VOI) with the same specific receptor radioligand. We estimated values of BPND in individual voxels of brains of healthy volunteers in vivo, and we obtained regional averages of VOI by dynamic positron emission tomography (PET). We calculated average values of BPND in caudate nucleus and putamen of striatum, and in frontal, occipital, parietal, and temporal cortices of the forebrain, by means of four methods, including the ERLiBiRD (Estimation of Reversible Ligand Binding and Receptor Density) method, the tissue reference methods of Logan and Logan-Ichise, respectively, and the SRTM (Simplified Reference Tissue Method). Voxelwise generation of parametric maps of values of BPND used the multi-linear regression version of SRTM. Age-dependent changes of the binding potential presented with an inverted U-shape with peak binding potentials reached between the ages of 20 and 30. The estimates of BPND declined significantly with age after the peak in both striatal and extrastriatal regions, as determined by all four methods, with the greatest decline observed in posterior (occipital and parietal) cortices (14% per decade) and the lowest decline in caudate nucleus (3% per decade). The sites of the greatest declines are of particular interest because of the clinical implications.


Introduction
Dopamine D 2/3 receptors in striatal and extrastriatal regions of the human brain are known to have important roles in the pathophysiology of schizophrenia and other psychiatric disorders [1][2][3][4][5]. Changes of dopaminergic neurotransmission with age have been associated both with normal human aging [6,7] and with impairments of cognitive and motor functions [8][9][10][11]. The evidence of in vivo declines of D 2/3 receptor availability with age is well-established for striatum by studies published in the last more than 30 years [4,5,7,[12][13][14][15], obtained by means of positron emission tomography of the binding of labelled ligands such as N-[ 11 C]methylspiperone and [ 11 C]raclopride to dopamine receptors in striatum. The question remains, however, of how to best characterize these changes. Two characteristics distinguish dopaminergic neurotransmission in vivo, i.e., the density of dopamine receptors and the concentration of dopaminergic ligands. The characteristics are combined in the concept of receptor availability or binding potential, with the availability depending on the affinity of potential ligands to the receptors, as well as on the receptor density. The accumulation of a radioligand therefore is reflected in the binding potential of specific binding relative to non-displaceable binding (hence BP ND ) that by definition is the ratio at true but transient equilibrium of accumulated specifically bound to non-displaceable radioligand molecules in the tissue [16]. Thus, in theory, the binding potential reflects both the density of the receptors and the apparent affinity of the radioligand, as affected by competition from endogenous neurotransmitters and modulators [16,17].
Karrer et al. [18] reported that aging is associated with lower DA transporter and receptor densities in brain of healthy adults, while the DA synthesis capacity is independent of aging [19]. The reported magnitudes of change of D 2/3 receptors in striatum, reflected in the decline of binding potentials, range from 6 to 8% per decade of life after the age of 20 years. The values depend in part on the gender composition of the subject groups, and in part on the use of specific kinetic methods of analysis used in the studies [13]. In extrastriatal regions that include cerebral cortex and thalamus, the density of D 2/3 dopamine receptors is much lower than in striatum. The extrastriatal decline of binding potentials with age has been demonstrated in vivo with radioligands such as [ 11 C]FLB 457 and [ 18 F]fallypride [20][21][22][23] that express much higher affinities to D 2/3 dopamine receptors than [ 11 C]raclopride. The difference of affinities may preclude the application of the high-affinity tracers to D 2/3 dopamine receptors in striatum. In contrast, other studies show that changes of extrastriatal [ 11 C]raclopride binding are associated with brain pathologies such as Parkinson's, Huntington's, and Alzheimer's diseases [24][25][26].
When striatal and extrastriatal binding potentials are obtained with different radioligands, it is in principle unknown to which extent the different striatal and extrastriatal binding potentials reflect differences of density or real or apparent affinities of the different radioligands, as affected by different endogenous dopamine concentrations or different receptor subtype distributions. To avoid this pitfall, Seeman et al. [27] used PET and [ 18 F]fallypride to estimate adult age differences of binding potentials of D 2/3 -like receptor across both cortical and subcortical brain regions. The authors found that the rate and pattern of decline of D 2/3 receptor availability differed among brain regions and from the regional pattern of age-related changes of gray matter volume and white matter integrity [18].
Here, we test the hypothesis that values of BP ND can be determined with [ 11 C]raclopride in extrastriatal as well as striatal regions of the brain of healthy subjects. We test the hypothesis by means of four different methods of analysis of the age-related decline of receptor availability. The methods yield the spatial distribution of the age-related changes both as regional averages and as parametric maps of BP ND in individual voxels. The four methods include the ERLi-BiRD (Estimation of Reversible Ligand Binding and Receptor Density) method, the tissue reference methods of Logan and Logan-Ichise, respectively, and the SRTM (Simplified Reference Tissue Method).

Subjects
Thirty-six healthy volunteers with the average age of 26.9 ± 6 years (mean ± SD, range 20-45 years) were enrolled in the study, approved by the Central Denmark Regional Science Ethics Committee that included 27 men and 9 women. The healthy volunteers included only subjects defined by the authors as non-smoking individuals in good general health, without any mental or physical disorder requiring regular or frequent medication [28]. All subjects gave written informed consent to the participation. All research was performed in accordance with relevant guidelines.

MRI and PET Procedures
T1-weighted MR scans were acquired for each subject with a 1.5 T equipment (GE, Signa Systems, Milwaukee, USA) using a 3D-fSPGR sequence (256 × 256 matrix, slice thickness = 1.5 mm). All subjects were examined using the ECAT EXACT HR (CTI/Siemens, Knoxville, TN, USA) wholebody positron emission tomography. After the intravenous injection of [ 11 C]raclopride (168-364 MBq), dynamic emission recording proceeded for 60 min in 3D mode, divided into 23 frames (6 × 6 × 6.5 mm FWHM). This was followed by a brief attenuation scan using a rotating Ge-68 rod source. Emission frames were reconstructed by employing filtered back projection with a 8 mm Hanning filter (cut-off frequency 0.5 cycle/s), resulting in 47 sections of 128 × 128 pixels per frame.

VOI Based Analysis
The acquired PET images were co-registered to the individual MRI scans. Individual MR images were co-registered to the common stereotaxic space of Talairach and Tournoux [29], as defined by the Montreal Neurological Institute (MNI), using a 12-parameter affined rigid body transformation. Subsequently, dynamic emission recordings were resampled into the MNI space, and templates of regional volumes of interest (VOIs) were drawn on the average MR images on whole cerebellum, caudate nucleus, putamen, frontal, occipital, parietal, and temporal cortices. When necessary, in the elderly subjects, corrected masks of the caudate nucleus and putamen were used because of inadequate segmentation between gray and white matter. We obtained the masks by standard model MRI with the lower threshold set manually and the higher threshold fixed to unity. We used templates with adequate segmentation and size for cerebral cortices. We applied each VOI to the individual resampled MR images and verified an appropriate co-registration. Finally, we extracted the time-radioactivitycurves from the dynamic PET image based on each VOI template. We defined the value of BP ND as the ratio of the maximum receptor binding capacity (B max ) to the apparent dissociation or 50% inhibition constant (K D or IC 50 ) of the radioligand [ 11 C]raclopride for each ROI with four different reference tissue methods. The methods included the Estimation of Reversible Ligand Binding and Receptor Density (ERLiBiRD), based exclusively on the use of integrals [30][31][32], the tissue reference methods of Logan et al. and Logan-Ichise [33,34], and the Simplified Reference Tissue Method (SRTM) [35], all with the cerebellum as reference. We chose the cerebellum as reference to obtain results consistent with the majority of PET studies with [ 11 C]raclopride as the tracer, including previous studies by the present authors, including most recently Winterdahl et al. [36] as well as an earlier comparison of the use of cerebellum and other reference regions [37].
The BP ND measure is the primary outcome of the reference tissue methods [38]. We plotted the values of BP ND for each VOI, determined by the four different methods, against the age of the subjects. We expressed the estimates of ordinate intercept and slope relative to ordinate intercept as mean ± SEM, using the equations listed below. We assessed the correlations between age and regional BP ND values by linear regression analysis and calculation of Pearson's correlation coefficients. We estimated the percentage changes of D 2/3 receptor binding per decade in the age range of 20-45 years, using the linear regression equation, where BP ND (0) is the zero-age intercept, BP ND (A) is the binding potential at age A of the subject, and b is the annual loss of binding potential, relative to the zero-age intercept. We evaluated significant differences of mean BP ND and b among VOIs and methods by two-way ANOVA with Bonferroni posthoc tests. We considered probabilities of less than 5% (P < 0.05) statistically significant. Normalization to a common ordinate intercept used the estimates of the zero-age ordinate intercepts, where R BP is the binding potential normalized to the zeroage ordinate intercept. The calculation of the age of peak binding potential used the second order polynomial regression analysis (quadratic equation), where a and b are parameters of the quadratic equation, A is the age of the subject, and A P is the age at which the binding potential peaks.

Voxelwise Statistical Analysis
The parametric maps of BP ND were obtained by voxelwise analysis with the multi-linear regression version of SRTM [39]. The parametric maps were resampled into the MNI space and smoothed using a 4 mm Gaussian filter. A voxelwise statistical analysis was performed by implementation of BRAINstat. Regional effects of aging were assessed by voxelwise regression analysis, with age as the independent variable. BRAINstat assigned clusters of voxels for significant focal changes (P < 0.05, corrected), based on 3D Gaussian Random Field Theory [40].

Volume-of-Interest Analysis
All four methods demonstrated a decrease with age of the regionally values of BP ND (Fig. 1). We performed secondorder polynomial regressions with Eq. 4 (see Appendix) for BP ND in striatum and cortex as functions of age by four different methods, the Estimation of Reversible Ligand Binding and Receptor Density (ERLiBiRD), the tissue reference methods of Logan and Logan-Ichise, and the Simplified Reference Tissue Method (SRTM). The results of the regressions are listed in Table 1. Both goodness of fit values and best-fit values were very similar in the different regions, showing good consistency by all four methods. We observed a significant difference only in occipital cortex, as shown by SRTM with P < 0.001. Second-order polynomial regressions demonstrated an inverted U-shape with peak binding potentials reached between the ages of 20 and 30 in most regions (Figs. 1 and 2). The correlation between age and the regional estimates of BP ND was significant by linear regression analysis. The quality of the fits provided by the second-order polynomial analysis significantly exceeded those of the linear analysis in parietal cortex by all methods, in caudate nucleus by the Logan analysis, and in occipital cortex by the Logan-Ichise analysis ( Table 2).
The mean values of BP ND in each VOI differed significantly among regions, as summarized in Table 3. Mean BP ND of the putamen significantly exceeded that of the caudate nucleus (P < 0.001), and the mean BP ND value of temporal cortex significantly exceeded the binding potentials of the remaining cerebral cortices (P < 0.001), for all four methods. The mean values of BP ND calculated by the ERLiBiRD method were significantly lower than the binding potentials calculated by the three other methods, in caudate nucleus (P < 0.01) and putamen (P < 0.001). In the cortical regions, the mean values of BP ND estimated by ERLiBiRD tended to be slightly lower than estimates from the three other methods but the differences did not reach significance. Percentage reductions per decade averaged less than 10% for putamen, and more than 10% for the cerebral cortices. The annual loss of receptor availability relative to the zero-age ordinate intercept in occipital and parietal cortices exceeded that of other regions, see Fig. 3. In contrast, the annual loss of binding potential in caudate nucleus was significantly lower than in other regions tested. Visual inspection of the regression suggested that a linear decline of the binding potential values may not be the most appropriate description of the pattern of loss with age.

Voxelwise Statistical Analysis
In the parametric maps of BP ND , analyzed by voxelwise regression against age, we identified five separate clusters of voxels with significant rates of age-related decline of binding potentials (P < 0.05, corrected). These clusters, shown in Fig. 4, included putamen bilaterally, right insula, bilateral temporal cortex (in parts of the superior temporal gyrus and middle temporal gyrus), and parts of the frontal cortex (precentral gyrus).

Discussion
The focus of the present study is the comparison of four methods that previously were not compared directly. The study revealed a method-independent decline with age of the BP ND of D 2/3 receptors in the putamen, occipital, parietal and temporal cortices, determined with tracer [ 11 C]raclopride in all regions. Unlike previous studies, the application of the same radioligand made direct comparison between cortical and subcortical regions possible. The declines determined here slightly exceeded the declines observed in previous studies of cortical regions. Second-order polynomial analysis further revealed a more complex pattern of decline with peak binding potentials being reached between the ages of 20 and 30 in most cortical regions. Some previous studies indicated non-linear or monoexponential decline, with similar declines at all ages [12,20,41]. However, as the present study covers a narrower range of subject ages, it may not be directly comparable to previous studies with wider age ranges.
The dopaminergic system is known to be affected during normal aging with changes of cognitive and motor functions that are keys to investigations into the pathophysiology of neurological and psychiatric disorders [11]. Here, we used [ 11 C]raclopride with PET to quantify the availability of dopamine D 2/3 receptors, both in striatum and cerebral cortices, and we estimated the age-related decline of this measure by means of VOI-based and voxelwise parametric mapping analyses. Previous in vivo studies of the human striatum with the tracer [ 11 C]raclopride showed age-related reduction of the availability of dopamine D 2/3 receptors at the average rate of decrement per decade of 7.9% in the striatum as a whole and 6-8.2% in the putamen [12][13][14]42].
The density of D 2/3 receptors in extrastriatal regions is significantly lower than in striatum [43]. Here, we use the word density as a term for the total number of receptors (B max ). Availability is another word for the term B avail [38] that symbolizes the number of unoccupied receptors that in turn equals the number of remaining receptors when the number of occupied receptors (B) is subtracted from the total number or density of receptors (B max ) as explained by Phan et al. [44].
In cortical regions, previous reports of the decline of dopamine receptors presented the binding potentials of the tracer [ 11 C]FLB 457, a ligand with considerably higher affinity to the D 2/3 receptors than [ 11 C]raclopride [20][21][22][23]. In these studies, the binding potentials declined at rates per decade of 9-13% in occipital, parietal, and temporal cortices.
Previously, [ 11 C]raclopride was not considered ideal for quantification of D 2/3 receptor availability in low-density areas, because of moderate in vivo affinity and a relatively low signal-to-noise ratio, based on measures of specific binding relative to nonspecific binding. High-affinity radioligands such as [ 11 C]FLB 457 and [ 18 F]fallypride instead served to visualize and quantify extrastriatal D 2/3 receptors, although they suffered from other disadvantages. The main disadvantage is the very high affinity of tracer [ 11 C]FLB 457 that causes the clearance of the ligand from the striatum to occur much more slowly than [ 11 C]raclopride, rendering washout of the ligand from the striatum too slow to safely establish a secular equilibrium of binding when coupled to the rapid rate of decay rate of carbon-11. Thus, the use of [ 11 C]FLB 457 may be optimal only for the imaging of extrastriatal regions [45,46]. Tracer [ 18 F]fallypride has been shown to provide quantitative measures of D 2/3 receptor binding to both striatal and extrastriatal regions by prolongation of the imaging session. However, the slow decay of F-18 makes it impossible to complete multiple imaging sessions within the same day, with possible increases of within-subject variability and lower likelihood of detection of subtle changes of BP ND . Although [ 11 C]raclopride may be suboptimal in some attempts to measure extrastriatal dopaminergic transmission, there is evidence that declines of BP ND of [ 11 C]raclopride can be observed in extrastriatal regions after drug or behavioral challenges [45,47].
Different rates of change in regions of the cerebral cortex may also depend on differences of affinity of the D 2/3 receptors for [ 11 C]raclopride and [ 11 C]FLB 457, but previous studies did not reveal age-related changes of the apparent affinity constant IC50 of the D 2/3 receptors in the striatum, tested in vivo or postmortem [48][49][50]. Thus the present rates of decline of BP ND are more likely to be related to changes of receptor density than to changes of endogenous ligand concentration in these regions.
In the present study, the value of BP ND in the temporal cortex significantly exceeded the averages observed in other cortices, in agreement with the distribution of receptor densities demonstrated in a previous study with [ 11 C]FLB 457 [43]. The value of BP ND of the caudate nucleus was no more than 80% of the value of the putamen (Table 4), in agreement with findings of other studies by investigators who compared estimates of the maximum binding capacity (B max ) of the caudate nucleus with the value determined in the putamen in vitro [27,51]. A previous in vitro study also indicated no difference of estimates of the apparent K D between the caudate nucleus and the putamen [51]. The present study documented proportions of binding in putamen of 5.5-6% of the values in frontal cortex, 5.6-6.7% in the occipital cortex, 5.3-5.7% in the parietal cortex, and 7.1-7.6% in the temporal cortex (Table 4).
Other studies revealed the percentages of receptor density compared to the putamen in the frontal, occipital, parietal, and temporal cortices to be approximately 3%, 2%, 3%, and 5%, respectively, as expressed by the calculated values of the B max of the regions measured with [ 11 C]FLB 457, and of the striatum, measured with [ 11 C]raclopride in vivo [43,52]. Similar values of K D in striatum and frontal and temporal cortices have been reported in vitro [51,53], and in vivo, and the values of K D were not significantly different across cortices in a previous study [43].
As dopamine diffuses freely in the extracellular fluid, a difference of dopamine concentrations of two closely neighboring subdivisions of the striatum is improbable, except for partial volume effects (PVE). The PVE reflects the limited spatial resolution of a PET device with negative effect on the quantitative accuracy of the analysis of PET images. Several methods have been suggested to compensate for this complication [54]. Although PVE correction methods may improve the quality and quantitative accuracy of PET images, limitations include prolonged computations that are impractical in clinical settings, increases of the image noise, and incomplete accounting for the spill-over effect.
The issue of whether the binding of [ 11 C]raclopride reflects the true levels of specific binding to D 2/3 receptors in the cortical areas has not yet been fully resolved. Stokes et al. used a tomograph with lower resolution (∼ 5 mm), the whole-body ECAT HR + 962 device (CTI/Siemens Medical Solutions, Knoxville, TN, USA), and reported cortical BP ND values of close to 0.2 in right middle frontal and superior temporal gyri, in good agreement with the present study [47].
Alakurtti et al. used a high resolution tomograph (HRRT; Siemens Medical Solutions, Knoxville, TN, USA) to examine long-term reliability of striatal and extrastriatal dopamine D 2/3 receptor binding estimates with [ 11 C]raclopride [45]. The authors reported values of BP ND of close to 4 in putamen and caudate nucleus, and an order of magnitude lower (i.e., 0.3-0.7) in thalamus, dorsolateral prefrontal, orbitofrontal, and temporal cortices, applying the same SRTM method used in the present study.
Generally, PET is very sensitive to motion during image acquisition, especially in small structures or areas with low signal-to-noise ratio and this greatly biases BP ND estimates. In addition to the use of a tomograph with higher spatial resolution, Alakurtti et al. [45] corrected for head displacement that may otherwise have prevented the determination of higher BP ND values compared to the present study (see Table 3). Notably, the subjects had a mean age of 24 years, not too different from the subjects of the current study with a mean age of 27 years. The difference in age is not likely to result in significantly lower BP ND estimates, as predicted by the known decline of receptor availability with age. Alakurtti et al. thus showed that it is possible to improve the reliability of cortical measurements of [ 11 C]raclopride binding with protocol optimization [45].
The parametric mapping (see Appendix) demonstrated significant foci of age-related decline bilaterally in putamen, in the right insula, and in regions of the temporal cortex (superior temporal gyrus, middle temporal gyrus) and regions of the frontal cortex (precentral gyrus). In the   present study, we observed significant declines of values in insula and frontal cortex in the VOI analysis, as well by the parametric mapping analysis.
In the putamen of patients with early Parkinson's disease, D 2/3 receptors undergo up-regulation [55], whereas in the prefrontal cortex of individuals with advanced Parkinson's disease, D 2/3 receptors appear to decline [22]. The combination of increased receptor density in the caudate nucleus and decreased values of BP ND in the cortex has been reported for patients with schizophrenia [56,57]. In patients with Parkinson's disease and schizophrenia, estimates of BP ND with [ 11 C]raclopride may therefore reveal changes of dopamine concentrations in the cerebral cortex, as well as in the striatum. Another interesting aspect to investigate would be the comparison between genders, of whom Fazio et al. found a negative correlation between BP ND and age, and an effect of gender with higher values of BP ND in females [58].
However, estimates of BP ND were 10-20% lower in thalamus, hippocampus, and insular and temporal cortex of alcohol dependent (AD) patients (P < 0.05). Agedependent declines in BP ND were very small in control subjects, but more pronounced and widespread in the AD group. Striatal and thalamic BP ND increased by 30% in four patients with long-term abstinence or reduced alcohol consumption. VOI-based [ 18 F]fallypride PET analyses revealed group differences of D 2/3 receptor availability primarily in extra-striatal regions. Age-related loss of dopamine D 2/3 receptors was more pronounced in AD patients. VOI-based [ 18 F]fallypride PET analyses revealed group differences in D 2/3 receptor availability primarily in extra-striatal regions. Age-related loss of dopamine D 2/3 receptors was more pronounced in AD patients [59].

Conclusion
The present study with tracer [ 11 C]raclopride revealed age-related declines of D 2/3 receptor availability in striatum, and in the cerebral cortices where the density of D 2/3 receptors is low, as determined by four common methods of analysis that revealed no significant differences. Values of BP ND were determined for individual voxels from regional averages of VOI from dynamic PET using [ 11 C] raclopride, The parametric maps of the BP ND estimates confirmed the spatially distinct patterns of age-related decline of binding potentials of the regions. In comparison with previous PET studies investigating extrastriatal D 2/3 receptors with the high-affinity ligand FLB 457 of D 2/3 receptors, the present results suggest that the significant regional differences of dopamine D 2/3 receptor availabilities across human brains are not consistent with differences of extracellular dopamine concentrations between the cerebral cortices and the striatum.

Appendix
The possible mechanism of the inverted-U changes of binding potentials as functions of age determined in the present study can be ascribed to at least two factors that include the receptor density and the availability of receptors as reflection of the concentration of the endogenous ligand (dopamine). We may ascribe the observation that the ratios of BP ND of cortices to putamen differ somewhat from the ratio of receptor densities to differences of extracellular dopamine concentrations between the cerebral cortices and striatum. Major differences of the dopamine concentration can be estimated by the formula for the concentration of a competitor, derived from the definition of the binding potential and maximum binding capacity, where V T is the total distribution volume of the tracer, C i and K i the steadystate and half-inhibition concentrations of endogenous ligands or other competitors, respectively, and α the availability of the receptors, defined as the fraction of un-occupied receptors. Availability can then be described by following equation, where is the degree of occupancy of the receptors by all competing ligands. The combination of the approximately linear decline of the maximum binding capacity as a function of age, and the inverse U-shape of the relationship between the actual binding potential and age, suggests that two reciprocally active factors are in operation, as also expressed by the rearrangement of Eqs. 1 and 2, where BP 0 is the theoretically highest achievable binding potential, i.e., the binding potential in the absence of competitors, equal to B max ∕(V T K D ). It is possible to assess the concentration of competitors as function of age by regression of Eq. 6 to the inverted U-shape of the relationship between binding potential and age, on the basis of three claims: The maximum binding capacity declines linearly with age [60], the inverted-U shape of the binding potential as function of age dictates a linear increase of the availability of the receptors with age-associated loss of dopamine [55,61], and the average occupancy by dopamine is 10% at the age of 30 [62], consistent with an availability of 90%. In another study [63], the authors estimated D 2/3 receptor occupancy by dopamine to be 21% at an average age of 25, with the assumption that it might be even higher due to an incomplete depletion of synaptic dopamine, after administration of the tyrosine hydroxylase inhibitor alpha-methyl-para-tyrosine (AMPT). Here, we set the occupancy level at the age of 25 at 50% corresponding to an availability of 50%. The resulting regression equation rearranges to, where BP 0.25 is the value of BP 0 at age 25, b the rate of increase of availability as function of age, A the age of the subject, and b BP the rate of decline of the maximum binding capacity ( BP 0 ) as function of age. The regression parameter b was chosen to be 0.1, providing the optimal R 2 values for the regression to be fitted to the data (see Fig. 5).
The results of the non-linear regression with Eq. 3 shown in Figs. 1 and 2 include the estimates of dopamine concentrations, calculated from Eq. 3, the decline of BP 0 , and the estimation of availability as function of age. The values calculated by the ERLiBiRD method were the lowest among those tested by all four methods in all regions, explained by the inclusion of the contents of the vascular (7) BP ND = 0.5BP 0. 25 1 + b A 1 + 25b volume into the calculation of the quantity of non-displaceable tracer. It is known that the ratio of precision to accuracy of the ERLiBiRD method is higher than in the reference tissue methods of Logan and SRTM [30], as also revealed by the coefficient of variation determined in the present study, but the accuracy is not directly quantifiable without consideration of the volume of the vascular bed and the partition coefficient of the radioligand raclopride. With a partition coefficient of 0.5 [29] and a vascular volume of 5% of the whole-brain volume, inclusion of the radioactivity in the vascular bed in the calculation of the binding potential with ERLiBiRD accounts for 10% in the steady-state, enough to explain the lower binding potentials obtained with the ERLiBiRD method.
The parametric mapping demonstrated significant foci of age-related decline bilaterally in putamen, in the right insula, and in regions of the temporal cortex (superior temporal gyrus, middle temporal gyrus) and regions of the frontal cortex (precentral gyrus). In the present study, we observed significant declines of values in insula and frontal cortex in the VOI analysis, as well by the parametric mapping analysis. In the putamen of patients with early Parkinson's disease, D 2/3 receptors undergo up-regulation [55], whereas in the prefrontal cortex of individuals with advanced Parkinson's disease, D 2/3 receptors appear to decline [22]. The combination of increased receptor density in the caudate nucleus and decreased values of BP ND in the cortex has been reported for patients with schizophrenia [56,57]. In patients with Parkinson's disease and schizophrenia, estimates of BP ND with [ 11 C]raclopride may therefore reveal changes of dopamine concentrations in the cerebral cortex, as well as in the striatum. Another interesting aspect to investigate would be the comparison between genders, in whom in a recent study, Fazio et al. [58] found a negative correlation between BP ND and age, and an effect of gender with higher values of BP ND in females [58], perhaps related to period phases. In the present study, because of the comparatively low number of women investigated (one quarter of all subjects tested), exclusion of women from the analysis did not significantly change the results.
Author Contributions AG: conceived the study, collected the subjects to be analyzed and received the permission to do the experiments. JK: critically evaluated and revised the manuscript. YN: conducted the initial analysis. NHSC: assisted the analysis and contributed to drafting the article. DFW: critically revised the manuscript. AM: supervised the tomography and critically revised the manuscript. All authors have given their final approval to the version to be published.

Fig. 5
Mean R 2 values as a function of b α . The R 2 is coefficient of determination, which determines convergence of model with experimental data and the higher value of R 2 results in higher accuracy, which is seen b α equal 0.1. Abscissa: Log10 rescaling of b values, the rate of increase of availability as function of age