Measurement Error Analysis for the Determination of Dopamine D 2 Receptor Occupancy Using the Agonist Radioligand [ 11 C]MNPA

Abstract

The purpose of this study is to investigate errors in quantitative analysis for estimating dopamine D₂ receptor occupancy of antipsychotics with agonist radioligand [¹¹C]MNPA by numerical simulation, with particular attention to the validity of a quantitative approach based on the use of a reference region. Synthetic data were validated using clinical data combined with a bootstrap approach. Time–activity curves (TACs) of [¹¹C]MNPA were simulated, and the reliability of binding potential (BP_ND) and occupancy estimated by nonlinear least square (NLS) fitting and a simplified reference tissue model (SRTM) were investigated for various noise levels and scan durations. In the human positron emission tomography (PET) study with and without antipsychotic, risperidone, the uncertainty of BP_ND and occupancy estimated by SRTM was investigated using resampled TACs based on bootstrap approach with weighted residual errors of fitting. For both NLS and SRTM, it was possible to have <3% of bias in occupancy estimates of [¹¹C]MNPA by 60 mins. However, shortened scan duration degrades the quantification of very small binding potentials, especially in case of SRTM. Observations were replicated on the clinical data. Results showed that dopamine D₂ receptor occupancy by antipsychotics can be estimated precisely in region of interest analysis by SRTM with a longer than 60-min [¹¹C]MNPA PET scan duration.

Keywords

positron emission tomography occupancy bootstrap reference region

Introduction

The dopamine D₂ receptor exists in both high- and low-affinity states, and the state of high affinity for endogenous dopamine is defined as the functionally active form of the receptor. To determine the binding to the high-affinity state of dopamine D₂ receptors, agonist ligands have been developed (Jones et al, 1984; Neumeyer et al, 1973). It has been reported that [¹¹C]-(R)-2-CH₃O-N-n-propylnorapomorphine ([¹¹C]MNPA), one of the agonist radioligands, is more sensitive than conventional D₂ antagonist radioligands [¹¹C]raclopride to the displacement of binding by endogenous dopamine, thus proposing [¹¹C]MNPA as promising radioligand for positron emission tomography (PET) imaging of the high-affinity state of dopamine D₂ receptors in the primate brain (Seneca et al, 2006).

The dopamine D₂ receptor is a main therapeutic target in schizophrenia, and most antipsychotics have an antagonistic action toward dopamine D₂ receptors. Occupancy of dopamine D₂ receptors evoked by competition from antipsychotic medication can be estimated from the reduction in the observed binding potential (BP_ND) (Farde et al, 1988; Farde et al, 1990). Several quantitative methods have been proposed for estimating BP_ND, and a simplified reference tissue model (SRTM) (Lammertsma and Hume, 1996) has often been used. The SRTM uses as input the time activity of a reference brain region with negligible specific binding and therefore avoids arterial blood sampling. As an occupancy study requires two PET scans, elimination of arterial blood sampling by SRTM method has practical appeal.

Otsuka et al (2009) showed that the SRTM method can be applied to human [¹¹C]MNPA for quantitative BP_ND estimation; however, a precise quantitative evaluation of the SRTM method for occupancy studies with [¹¹C]MNPA has not yet been performed. However, error analysis is important to ascertain whether the variability in occupancy with antipsychotics measured [¹¹C]MNPA is truly biological or generated by the PET measurement system. In this regard, Yokoi et al reported that occupancy levels of the partial agonist aripiprazole, a new antipsychotic a partial agonist for dopamine D₂ receptors without notable extrapyramidal side effects, vary widely, contrasting with the usual presence of extrapyramidal side effects at occupancy levels exceeding 80% for D₂ antagonists (Farde et al, 1988; Kessler, 2007; Yokoi et al, 2002). It is therefore of relevance to perform an error analysis of BP_ND estimation for PET dynamic scanning with [¹¹C]MNPA to quantify the variability induced by the measurement itself to better appreciate the biological variability that may emerge from human bioassays that use this tracer.

In this study, we simulated and evaluated errors in the quantitative analysis for the estimation of dopamine D₂ receptor occupancy when measured with [¹¹C]MNPA with particular attention to the use of SRTM. The effect of scan duration on the error of estimates was also evaluated, because shorter scan duration reduces patient's burden. Tissue kinetics where simulated using a compartmental model and, to assess model validity, we compared the results of the simulations with the errors obtained from clinical data by use of a resampling technique.

Materials and methods

Kinetics of [¹¹C]MNPA

The kinetics of [¹¹C]MNPA in the brain is based on the two-tissue three-compartment model as follows:

\begin{array}{l} \frac{d C_{ND} (t)}{d t} = K_{1} C_{P} (t) - (k_{2} + k_{3}) C_{ND} (t) + k_{4} C_{S} (t) \\ \frac{d C_{S} (t)}{d t} = K_{3} C_{ND} (t) - k_{4} C_{S} (t) \\ C_{T} (t) = C_{ND} (t) + C_{S} (t) \end{array}

(1)

where C_P [Bq/mL] is the radioactivity concentration of unchanged radioligand in plasma (arterial input function), C_ND [Bq/cm³] is the radioactivity concentration of nondisplaceable radioligand in brain, including nonspecifically bound and free radioligand, and C_S [Bq/cm³] is the radioactivity concentration of radioligand specifically bound to receptors. The rate constants K₁ [mL/cm³/min] and k₂ [min⁻¹] represent the influx and efflux rates for radioligand diffusion through the blood–brain barrier. The rate constants k₃ [min⁻¹] and k₄ [min⁻¹] represent the radioligand transfers between the compartments for nondisplaceable and specifically bound radioligand. C_T [Bq/cm³] is the radioactivity concentration in a brain region measured by PET.

Estimation of receptor occupancy

Nonlinear least squares fitting for BP_ND:

K₁, k₂, k₃, and k₄ values in Equation (1) can be determined by nonlinear least squares (NLS) fitting of the time–activity curve (TAC) in the target region. The cerebellum is regarded as a reference region because this brain structure has negligible D₂ dopamine receptor density (Otsuka et al, 2009; Seneca et al, 2008; Tokunaga et al, 2009). K₁^r and k₂^r values in the cerebellum were also determined by NLS using the one-tissue compartment model without the specific binding compartment. The BP_ND can be expressed using the reference region as:

B P_{ND} = \frac{(K_{1} / k_{2}) (k_{3} / k_{4} + 1)}{(K_{1}^{r} / k_{2}^{r})} - 1

(2)

where (K₁/k₂)(k₃/k₄ + 1) is the total distribution volume of the target region and (K₁^r/k₂^r) is that of the cerebellum. In this study, the calculation of BP_ND in Equation (2) was regarded as the standard method for BP_ND estimation (Otsuka et al, 2009). It should be noted that to improve the stability of the NLS fitting for target regions, the K₁/k₂ ratio for the target region was assumed to be the value in the cerebellum (K₁^r/k₂^r) as obtained by NLS using the one-tissue compartment model, meaning that, as a result, BP_ND in Equation (2) is equivalent to k₃/k₄ in this study.

Simplified reference tissue model for BP_ND:

The SRTM yields the binding potential value by eliminating the arterial input function, C_P, arithmetically from model equations by using a TAC from a reference region where specific bindings are negligible, under the assumptions that the distribution volume of the nondisplaceable compartment was equal in the target and reference regions, and that a target region can be described with the one-tissue compartment model shown in Equation (3) (Lammertsma and Hume, 1996).

\begin{array}{l} C_{T} (t) = R_{1} \cdot C_{R} (t) + (k_{2} - \frac{R_{1} K_{2}}{1 + B P_{ND}}) \cdot e^{(\frac{k_{2}}{1 + B P_{ND}} t)} \otimes C_{R} (t) \\ R_{1} = K_{1} / K_{1}^{r} \end{array}

(3)

where C_T and C_R are the radioactivity concentrations in the target and reference regions, respectively. The SRTM estimates three parameters, the delivery ratio of the target region to reference region (R₁), the clearance rate constant of the target region (k₂), and binding potential, referred to as BP_ND by nonlinear least squares.

Receptor occupancy:

Receptor occupancy is calculated from BP_ND of two scans, with and without antipsychotics, as follows:

O c c u p a n c y (%) = 100 \cdot (B P_{control} - B P_{drug}) / B P_{control}

(4)

where BP_control represents the BP_ND value derived from a scan without drug and BP_drug represents that from a scan with drug (Farde et al, 1988).

Simulation study

To evaluate the dependency of the noise level and scan duration for the estimated BP_ND and occupancy, we performed the following simulations. Both NLS and SRTM procedures were performed using in-house software written in the C program with downhill simplex algorithm (Nelder and Mead, 1965) without weighting and without constraints for the range of estimated parameters.

Time-activity curves for [¹¹C]MNPA:

A dynamic tracer concentration for [¹¹C]MNPA was derived from the kinetic parameters listed in Table 1 with a dynamic frame (20 secs × 9, 1 min × 5, 2 mins × 4, 4 mins × 11, 5 mins × 6, total 90 mins) and a measured arterial input function (10 secs × 12, 30 secs × 2, 60 secs × 7, 120 secs × 1, 180 secs × 1, 300 secs × 3, 600 secs × 6, total 90 mins) of a single subject obtained by Otsuka et al (2009). These K₁, k₂, and k₄ were estimated based on the two-tissue three-compartment model using NLS fitting of region of interests (ROIs) in the putamen at baseline (the number of subjects (n) = 10) (Otsuka et al, 2009). Furthermore, three k₃ values, 0.015, 0.075, and 0.15, were arbitrarily chosen to investigate the occupancy of antipsychotics with [¹¹C]MNPA. During a loading study with a drug, the observed binding potential (BP_ND) is reduced mainly due to the suppression of the radioligand transfers from the compartments for nondisplaceable to specifically bound radioligand, k₃. Therefore, we varied k₃ values while covering the practical range of occupancy from a likely level at 50% to the extreme scenario of a 90% occupancy. A measured arterial plasma input function of a single subject according to human PET imaging protocols and noise-free simulated TACs (three target curves and a reference) are shown in Figure 1A and B.

Table 1

Kinetic parameters for the simulation study of [¹¹C]MNPA

	K ₁	k ₂	k ₃	k ₄	BP _ND	Occup. (%)
Target regions	0.44	0.067	0.015	0.18	0.0833	90
			0.075		0.417	50
			0.15		0.833	—
Reference region	0.44	0.067	—	—	—	—

Figure 1

(A) Metabolite-corrected plasma input function of a single normal subject for simulation study. (B) Noise-free simulated TACs of three BP_ND values and reference TAC. (C) Noise-added TACs in the case of BP_ND = 0.417.

Noise was generated with random generator based on Gaussian distribution and added to the decay-corrected target TACs. The noise ratio for each time frame was determined (Ikoma et al, 2008) according to the collected total count given by

\begin{array}{l} N O I S E_{i} (%) = (\sqrt{N_{i}} / N_{i}) \cdot 100 \\ N_{i} = \int_{t_{i} - \frac{Δ t_{i}}{2}}^{t_{i} + \frac{Δ t_{i}}{2}} C_{T} (t) \cdot e^{- λ t} d t \cdot F \end{array}

(5)

where i is the frame number, C_T is the decay-corrected tissue radioactivity concentration derived from the k-values and the input function, t_i is the midpoint time of the i-th frame, Δt_i is the data collection time, γ is the radioisotope decay constant, and F is a scaling factor representing the sensitivity of the measurement system and is introduced here for adjusting the noise level.

Noise level dependency:

Target TACs of [¹¹C]MNPA with several noise levels were generated to investigate the bias and variation of parameter estimates caused by the statistical noise for NLS and SRTM. The bias and variation were calculated as %bias of estimated BP_ND against the true BP_ND value and coefficient of variance (COV) by the mean and s.d. of the estimates excluding the outliers, respectively.

In this simulation study, the noise level for dynamic data was expressed as the mean of percentage noise described in Equation (5) from 1 to 90 mins, and it was chosen so that the mean of percentage noise would be 1%, 3%, 5%, 7%, and 10%, with 500 noisy data sets being generated for each. An example of noise-added simulated TAC with BP_ND = 0.417 is shown in Figure 1C.

In these noise-added TACs, each kinetic parameter including BP_ND was estimated by NLS and SRTM with a noise-free reference TAC. For both NLS and SRTM, initial parameters varied by ± 25% from the true value (Ichise et al, 2003; Ikoma et al, 2008), and parameter estimates were considered invalid outliers if estimated parameters were negative or more than three times the true value (Ichise et al, 2003; Ikoma et al, 2008). Occupancy was also calculated from Equation (4) by using estimated BP_ND with assumed k₃ = 0.15 as BP_control and with assumed k₃ = 0.015 or 0.075 as BP_drug.

Scan duration:

The effect of scan duration on BP_ND and occupancy estimates was investigated for both NLS and SRTM methods. In the 90-min simulated TACs of 3% noise level corresponding to the noise level of human ROI analysis, the duration of the scan used for the parameter estimation was progressively reduced from 90 to 32 mins (32, 44, 60, 75, and 90 mins) for [¹¹C]MNPA.

Human study

Subjects and positron emission tomography procedure:

[¹¹C]MNPA PET studies were performed before and after antipsychotic drug administration of risperidone (0.5 and 2.0 mg) on separate days for each two healthy male volunteers (20 to 21 y.o.). Scan start time after antipsychotic administration was 4h. The study was approved by the ethics and radiation safety committees of the National Institute of Radiological Sciences, Chiba, Japan. Written informed consent was obtained from each subject.

The PET acquisitions were performed on the ECAT EXACT HR+ (CTI-Siemens, Knoxville, TN, USA). A 10-min transmission scan with 3-rod source of ⁶⁸Ge–⁶⁸Ga was performed. Dynamic PET scans of [¹¹C]MNPA were performed for 90 mins in three-dimensional mode with a bolus injection of 208.0 to 234.0 MBq. Frame intervals were the same as this simulation study. The specific radioactivity was 245.1 to 313.8 GBq/μmol at the time of injection. Arterial blood sampling was not performed. All emission data were reconstructed by filtered-back projection using a Hanning filter with a cut-off frequency of 0.4.

Data analysis:

The summed PET images for all frames were coregistered to individual MR images, and ROIs were drawn manually over the putamen, caudate, and cerebellum. Especially, R₁, k₂, and BP_ND in the putamen were estimated by SRTM using the cerebellum as reference region.

Human data were used to check model validity for the simulation studies. Given that an occupancy is measured only once (two scans for subject) and that repetitive measurements are not usually available, the reliability of parameter estimates can be evaluated by a bootstrap approach with weighted residual errors of fitting as published earlier (Rosso et al, 2009; Turkheimer et al, 1998). For each ROI in each individual subject data, 500 replication TACs were generated using bootstrap approach, and then parameters were estimated by SRTM and the COV of these 500 estimates was calculated to produce an accurate estimate of the statistical variability of the parameters. The weighted residual, ξ, using model-predicted tissue TAC, C_T, and the measured tissue TAC, X, were calculated as follows;

\begin{array}{l} ξ_{i} (X (t_{i}) - C_{T} (t_{i})) \cdot \sqrt{N_{i}} \\ N_{i} = \int_{t_{i} - \frac{Δ t_{i}}{2}}^{t_{i} + \frac{Δ t_{i}}{2}} C_{T} (t) \cdot e^{- λ t} d t \end{array}

(6)

Then the residuals, {ξ_i} (i = 1,…,k), were randomly resampled with substitution into a new set of the residuals

{ξ*_i}. As an example with k = 5, [ξ₁, ξ₂, ξ₃, ξ₄, ξ₅] were randomly selected [ξ₅, ξ₁, ξ₄, ξ₁, ξ₃] as a new residual set [ξ*₁, ξ*₂, ξ*₃, ξ*₄, ξ*₅]. The bootstrapped residuals were used to generate a new data X* defined as,

X^{*} (t_{i}) - C_{T} (t_{i}) + \frac{ξ_{i}^{*}}{\sqrt{N_{i}}}

(7)

In keeping with the simulation study, the relationship between the scan duration and COV of estimates and between the scan duration and bias was investigated by shortening the interval of fitting of the bootstrap replication TACs from 90 to 32 mins. The bias of BP_ND and occupancy was defined as the difference between the mean of these calculated for each truncated fitting interval and that of the 90 mins. Parameter estimates based on bootstrap approach were considered invalid outliers if estimates from X* were negative or more than three times that of the 90 mins.

Results

Simulation study

Noise level dependency:

In the NLS method, the bias of BP_ND was small especially at a low noise level. However, COV of BP_ND became larger as the noise level increased (Figure 2A). In the SRTM method, the bias of BP_ND was observed even though TACs were free from noise and both the bias and COV of BP_ND became larger as the noise increased, which is typical in the case of small BP_ND (Figure 2B). For both NLS and SRTM methods, these bias and COV values of occupancy were smaller compared with BP_ND. The tendency that COV with 90% occupancy was smaller compared with that with 50% occupancy was a common observation for NLS and SRTM.

Figure 2

Noise level dependency. (A) Bias and COV of BP_ND and occupancy estimated by NLS (K₁/k₂ = 6.6 fixed), (B) estimated by SRTM.

Scan duration:

The relationship between the reliability of BP_ND and occupancy estimates and the scan duration was investigated as shown in Figure 3. The bias of BP_ND and occupancy estimated by NLS was small despite short scan durations (Figure 3A); however, more than 10% outliers was caused with BP_ND = 0.0833 at 32, 44, 60, 75, and 90 mins (Table 2). As scanning time became shorter, BP_ND for all three conditions was overestimated by SRTM (Figure 3B) and its bias magnitude was larger than that of NLS. More than 10% outliers was seen with BP_ND= 0.0833 at 32 and 44 mins, BP_ND = 0.417 at 32 mins and 0.833 at 32 mins. Bias was under 3% at a 3% noise level with occupancy estimates by SRTM method with scan duration longer than 60 mins (Figure 3B).

Table 2

Scan duration dependency on the percentages of outliers of BP_ND at 3% noise level estimated by NLS and SRTM

	BP _ND	Scan duration (min)

		32	44	60	75	90
NLS	0.0833	27.4	22.8	22.6	12.8	10.8
	0.417	5.8	3.4	1.4	2.6	1.2
	0.833	3.8	1.8	0.2	0	0
SRTM	0.0833	40.4	19.8	3.4	0.2	0
	0.417	29.2	0.6	0	0	0
	0.833	26.0	0.2	0	0	0

NLS, nonlinear least square; SRTM, simplified reference tissue model.

Figure 3

Scan duration dependency of bias and COV of BP_ND and occupancy at a 3% noise level estimated by (A) NLS and (B) SRTM methods.

Human study

Time–activity curves:

As shown in Figure 4, the shape of the TACs was similar between before and after antipsychotic administration in the cerebellum, whereas the accumulation of radioactivity in the postantipsychotic scan decreased at late times in other regions. In Figure 4A and B, estimated BP_ND in putamen of a subject before and after administration of Risperidone 2 mg were 0.968 and 0.437, then its occupancy resulted in 54.8%. For the other subject shown in Figure 4C and D, estimated BP_ND in putamen of a subject before and after administration of Risperidone 0.5 mg were 0.866 and 0.496, then its occupancy resulted in 42.7%.

Figure 4

TACs for a single subject with baseline (A), and 2 mg administration of Risperidone (B), TAC for the other subject with baseline (C), and 0.5 mg administration of Risperidone (D). ROIs were drawn on putamen, caudate, and cerebellum.

Scan duration:

On the basis of the bootstrap approach, the relationship between the reliability of BP_ND and occupancy estimates and the scan duration was investigated as shown in Figure 5.

Figure 5

Scan duration dependency of bias and COV of BP_ND and occupancy in the putamen estimated by SRTM method for a single subject with 0.5 mg administration (A) and the other subject with 2 mg administration (B).

As scanning time became shorter, BP_ND in both before and after antipsychotics administration for two volunteers was overestimated. However, the bias of occupancy was small despite short scan durations. The COVs of both BP_ND and occupancy also became larger with shorter scan durations. These observations are consistent with the simulation results especially in the case of occupancy shown in Figure 3B, even though a small difference of magnitude of bias in BP_ND was still observed.

Discussion

In this study, we evaluated the effect of noise and scan duration of dynamic PET [¹¹C]MNPA studies on the BP_ND estimates obtained with NLS and SRTM for a range of BP_ND values, a range that is likely to be encountered in occupancy studies with antipsychotic medication. Error analysis was performed using artificial datasets. The validity of the simulations was assessed by using the bootstrap on a small cohort of human data to calculate ‘real variances’ that resulted in good agreement with those obtained from the artificial datasets.

Reliability of estimated parameters

In the case of NLS, the larger number of parameters introduced instability and, even though we introduced a fixed K₁/k₂ ratio, the variability of BP_ND was still significant as shown by the percentage of outliers by NLS (Table 2). K₁/k₂ for both target and reference regions were same in this simulation study; however, in clinical situation, sometimes K₁/k₂ values may vary from regions to regions (Ginovart et al, 2007) and these difference may introduce errors in BP_ND when the ratio K₁/k₂ is fixed.

The SRTM provided reliable estimates although variability increased for low BP_ND values even with favorable noise levels (Gunn et al, 1997; Ikoma et al, 2008). As shown in Figure 2B, both bias and COV with small BP_ND = 0.0833 were larger than those with BP_ND = 0.417 or 0.833. The small bias of BP_ND estimates in noise-free TACs (Figure 2B) may originate from the two-tissue model of the target tissue. In the SRTM method, even when the one-tissue model for target tissue is not appropriate, the apparent rate constant (=k₂/(1+BP_ND) in Equation (3) could be used to fit the curves well and bias in BP_ND is negligible (Wu and Carson, 2002). In this study, as shown in Figure 2B, the bias of BP_ND was small and the error propagation of biased BP_ND to occupancy in the SRTM method was also small. Errors of both estimated BP_ND and occupancy by SRTM were small at a low noise level, indicating that ROI analysis of SRTM will be useful for a quantified BP_ND and occupancy study with [¹¹C]MNPA.

In the simulation study, the reference TAC was assumed as noise free; however, noise may affect the reference TAC depending on the size of ROI (Ogden and Tarpey, 2006). For SRTM, the use of a 1% noise on the reference TAC increased %COV of the BP_ND estimates for the target regions (where noise was 3%) by 20% to 30%. However, the noise in the reference TAC did not change the profile of BP_ND %COV in the target TAC according to scan duration nor changed the biases in the estimated occupancies that remained similar.

Effects of scan duration

In the simulation study, a 60-min scan duration gave unbiased and reliable BP_ND and occupancy estimates by NLS with [¹¹C]MNPA both at baseline and with drug load (Figure 3A). Conversely, the results of SRTM method showed that at least 60-min scan duration would be required for the quantification of occupancy; bias was under 3% at a 3% noise level with scan duration longer than 60 mins (Figure 3B). Shorter scan duration caused larger bias of BP_ND estimated by SRTM. Note that the sampling rate of the reference input function is inherently lower than the one of the plasma input function and this may introduce errors with SRTM although in this instance, kinetics in tissue are not particularly fast.

The use of the bootstrap approach on clinical data validated most of the observations obtained from simulations for the SRTM method, such as the overestimation of BP_ND and underestimation of occupancy at shorter scan durations. It is important to remark that the variability considered here is the one associated with the measurement error only. Further variability of biological origin (between subjects and/or associated with age, gender, etc. (Inoue et al, 2001; Kaasinen et al, 2001)) should be taken into account and possibly controlled at the design stage.

We can therefore conclude that, for both NLS and SRTM methods, reliable and unbiased occupancy estimates of [¹¹C]MNPA could be obtained by 60 mins, with COV of 50% occupancy remaining at 11.0% and 10.1%, respectively (Figure 3). In the case of lower occupancy than 50%, COV at 60-min scan duration may be >11% but no bias should be expected.

Conclusion

The effects of bias, variance, and scan duration in PET quantitative analysis of dopamine D₂ receptor occupancy using [¹¹C]MNPA were evaluated in a simulation study and validated using a bootstrap approach on clinical data. The results suggest that a reference approach with SRTM applied to ROI data with a scan duration of at least 60-mins PET scan duration represent a valid bioassay for the task.

Footnotes

Acknowledgements

This study was supported in part by Grants-in-Aid for Young Scientists (B) (No. 19700395) and by a consignment expense for the Molecular Imaging Program on ‘Research Base for PET Diagnosis’ from the Ministry of Education, Culture, Sports, Science and Technology (MEXT), Japanese Government and by the Royal Society, International Project Grant no. JP0871550, UK. We thank Dr Hiroshi Watabe for his valuable advice.

The authors declare no conflict of interest.

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Measurement Error Analysis for the Determination of Dopamine D 2 Receptor Occupancy Using the Agonist Radioligand [ 11 C]MNPA

Abstract

Keywords

Introduction

Materials and methods

Kinetics of [11C]MNPA

Estimation of receptor occupancy

Nonlinear least squares fitting for BPND:

Simplified reference tissue model for BPND:

Receptor occupancy:

Simulation study

Time-activity curves for [11C]MNPA:

Noise level dependency:

Scan duration:

Human study

Subjects and positron emission tomography procedure:

Data analysis:

Results

Simulation study

Noise level dependency:

Scan duration:

Human study

Time–activity curves:

Scan duration:

Discussion

Reliability of estimated parameters

Effects of scan duration

Conclusion

Footnotes

Acknowledgements

References

Kinetics of [¹¹C]MNPA

Nonlinear least squares fitting for BP_ND:

Simplified reference tissue model for BP_ND:

Time-activity curves for [¹¹C]MNPA: