Abstract
Aim
The simplified reference tissue model (SRTM) is used for estimation of receptor occupancy assuming that the non-displaceable binding in the reference region is identical to the brain regions of interest. The aim of this work was to extend the SRTM to also account for inter-regional differences in non-displaceable concentrations, and to investigate if this model allowed estimation of receptor occupancy using white matter as reference. It was also investigated if an apparent higher affinity in caudate compared with other brain regions, could be better explained by a difference in the extent of non-displaceable binding.
Methods
The analysis was based on a PET study in six healthy volunteers using the 5-HT1B receptor radioligand [11C]-AZ10419369. The radioligand was given intravenously as a tracer dose alone and following different oral doses of the 5-HT1B receptor antagonist AZD3783. Non-linear mixed effects models were developed where differences between regions in non-specific concentrations were accounted for. The properties of the models were also evaluated by means of simulation studies.
Results
The estimate (95% CI) of KiPL was 10.2 ng ml−1 (5.4, 15) and 10.4 ng ml−1 (8.1, 13.6) based on the extended SRTM with white matter as reference and based on the SRTM using cerebellum as reference, respectively. The estimate (95% CI) of KiPL for caudate relative to other brain regions was 55% (48, 62%).
Conclusions
The extended SRTM allows consideration of white matter as reference region when no suitable grey matter region exists. AZD3783 affinity appears to be higher in the caudate compared with other brain regions.
Keywords: caudate, non-linear mixed effects, PET, receptor occupancy, SRTM, white matter
What is Already Known about this Subject
The simplified reference tissue model (SRTM) is a useful and frequently applied method for estimation of binding potential to derive estimates of receptor occupancy in the brain.
What this Paper Adds
This work shows how the SRTM can be extended to account for a difference in non-displaceable binding between brain regions. It is also demonstrated that this can allow estimation of receptor occupancy using white matter as reference.
Introduction
Analyses of positron emission tomography studies (PET) are often performed using the time course of tracer concentration in a reference tissue as input function. The advantage of this approach is that there is no need for invasive arterial blood sampling. Additionally parameter estimation becomes more rapid and stable since simpler models can be applied. Two important assumptions apply to such reference based analyses, 1) that the reference region is void of specific, displaceable binding and 2) that the non-displaceable concentration (CND) in the reference region and in the region of interest (ROI) are identical at equilibrium 1. The second assumption may not be valid if the tissue composition differs between regions, e.g. in terms of lipid content. Also differences in non-specific binding or in transport across the blood–brain barrier could result in differences between brain regions in non-displaceable concentrations. When no grey matter region void of receptors exists fulfilling assumption 1, white matter (WM) has sometimes been considered as a reference region, e.g. for the 5-HT1A ligand [11C]-WAY100635 2,3 and for the GABAA receptor ligand [11C]-flumazenil 4. The tissue composition however differs between white and grey matter 5 and the CND of WM can hence not a priori be assumed to be the same as for grey matter 6.
In the analysis of PET-data, coupled analyses are sometimes used. With this approach several regions of interest are modelled simultaneously sharing common parameters. This can significantly improve precision and improve ability to detect differences 7,8. By simultaneously including data from the whole study, rather than from each PET-experiment separately, it is possible to improve further identifiability of model parameters 9. Non-linear mixed effects modelling, recognizing both inter-individual (IIV) and inter-occasion variability (IOV) is a suitable method for analysis of such data and is also being increasingly used to model PET data 10–12.
In the present work a non-linear mixed effects model is implemented where differences between regions in non-displaceable concentrations can be estimated, hence relaxing the assumption of identical non-displaceable binding in the reference region and regions of interest. The model was developed as an extension to the simplified reference tissue model described by Lammertsma & Hume 1.
The analysis is based on a study which involved PET measurements using the radioligand [11C]-AZ10419369 to evaluate the occupancy of AZD3783 at the serotonin 5-HT1B receptor in human subjects. The cerebellar cortex is a region of negligible density of 5-HT1B receptors in the human brain and is a suitable reference region in PET studies using [11C]-AZ10419369 13.
Data used in the present analysis have been published previously using traditional methods including data for the brain regions thought to be most reliable and relevant 14. Preliminary (unpublished) analyses suggested that occupancy in the caudate differed from that in other brain regions. It was however unclear if this was a result of an actual difference in affinity or if a difference in non-specific binding in the caudate region could explain the finding.
The aim of the present work was to extend the previous analysis to
develop a model that could account for differences between regions in terms non-specific concentration,
investigate if the apparent difference between the caudate nucleus and other grey matter regions could be explained by different affinity or differences in non-displaceable concentrations,
investigate, by means of simulation, the ability of the model to detect and distinguish between differences in affinity and non-specific binding between regions as well as the bias when failing to do so and
investigate if white matter could be used as a reference region by accounting for any differences in non-displaceable concentrations.
Methods
Study design and measurements
Occupancy of AZD3783 at 5-HT1B binding sites was investigated using the radioligand [11C]-AZ10419369 (nomenclature according to the British Journal of Pharmacology's Guide to Receptors and Channels 15). Six healthy men, aged between 21 and 34 years, underwent PET examinations with [11C]-AZ10419369. Each of the six subjects were planned to participate in four PET examinations with [11C]-AZ10419369, including one baseline assessment and three subsequent PET examinations performed approximately 3 h after administration of different single oral doses of AZD3783 (pre-treatment). Venous blood samples (4 ml) for determination of the concentrations of AZD3783 and the AZD3783 N-desmethyl metabolite in plasma were drawn regularly before, during and after completion of PET data acquisition.
Brain radioactivity was measured with the Siemens ECAT EXACT HR system in a consecutive series of time frames for up to 93 min. The frame sequence consisted of nine 20 s frames, three 1 min frames, three 3 min frames and 13 6 min frames. The delineations of anatomical brain regions were made manually on the reoriented MR images using in-house image analysis software, Human Brain Atlas 16. The radioactivity concentration in each brain region of interest was calculated for each sequential frame and corrected for radioactive decay. More details on study design and measurements are given in the previous publication 14.
The study was approved by the Medical Products Agency and by the Regional Ethical Review Board in Stockholm, and the Radiation Safety Committee of the Karolinska University Hospital. The study was performed in accordance with the ethical principles of the Declaration of Helsinki that are consistent with ICH/Good Clinical Practice and applicable regulatory requirements and the AstraZeneca policy on Bioethics. Informed consent was obtained from all subjects prior to initiation of the study.
Relationship between AZD3783 plasma concentrations and occupancy
The analysis was based on the simplified reference tissue model (SRTM), which has been previously validated for the analysis of data obtained using this radioligand 13.
The SRTM includes the three parameters R1, k2 and the binding potential (BPND) where k2 is the rate constant for transfer to plasma from the free and non-specific concentration in the region of interest.
BPND corresponds to the ratio of bound concentrations to non-displaceable concentrations at equilibrium as shown in equation 1 where VS and VND are the specific and non-displaceable brain to plasma partition coefficients, respectively.
 |
1 |
R1 accounts for difference in equilibration rate between the target and reference regions and can be derived from
 |
2 |
where k2REF is the rate constant for transfer from the non-displaceable concentration in the reference region to plasma. The SRTM assumes rapid equilibrium in the reference region and the region of interest, such that specific or non-specific binding is not kinetically distinguishable.
The SRTM was implemented in differential form as described previously 11 according to
 |
3 |
where CROI is the brain concentration in the region of interest and CREF is the concentration in the reference region over time.
In order to assess whether any differences between regions in terms of VND influenced the results, the parameter NDREL was added to the model. NDREL corresponds to the non-displaceable brain−plasma partition coefficient of the region of interest (VND) relative to that in the reference region (VREF). Hence VND in the region of interest corresponds to:
 |
4 |
The apparent VS when VREF differs from VND corresponds to the difference between the total partition coefficient (VT) in the region of interest and the VREF (VS,apparent = VT – VREF) as illustrated in Figure 1. Hence the corresponding apparent binding potential (BPAPP) corresponds to
 |
5 |
or by combining equation 1, equation 4 and equation 5:
 |
6 |
Figure 1.
Illustration of brain/plasma partition coefficients VT, VS, VND VREF and VS,apparent
The apparent k2 of the region of interest when the VREF differ from VND is
 |
7 |
By substitution of BPND in equation 3 with BPAPP and k2 with k2APP and simplifying, the following modified version of SRTM in differential form can be derived
 |
8 |
where CROI is the brain concentration in the region of interest and CREF is the concentration in the reference region over time.
Model implementation
The population analysis program nonmem (version 7.2.0), a widely used non-linear regression software package in population pharmacokinetic–pharmacodynamic data analysis, and the first order conditional estimation method (FOCE) were employed (Beal et al. 1989–2006). The post-processor Xpose implemented in R was used for model diagnostic purposes 17.
The analysis was based on the following regions of interest: caudate (CAU), occipital cortex (OCC), parietal cortex (PAR), prefrontal cortex (PFC) and thalamus (THA). In the primary analysis the cerebellum (CER) was used as reference region. A model was developed where all PET examinations and regions of interest were included. The radioligand kinetics and the relationship between plasma concentration and saturation of specific binding were assessed simultaneously in the model.
The possibility of using WM as a reference region was also explored. The models with WM as a reference region did not include CAU.
Fixed effects
The relationship between BPND for region of interest i (BPND,i) and AZD3783 exposure was assessed using the saturation function shown in equation 9.
 |
9 |
where KiPL is the plasma concentration corresponding to 50% occupancy, Cp is the average plasma concentration of AZD3783 during the PET experiment. For each region the baseline BPND (BPBL,i) was estimated.
The k2 of the reference region (k2REF) was estimated as a parameter and a separate R1 was estimated for each region of interest. The k2 of region i was then derived from
 |
10 |
The VND relative to the VREF was estimated as the parameter NDREL.
Three different models with CER as reference region were applied to investigate the reason for the initial results which indicated a difference with respect to Ki in CAU.
CER-base: Base model with no difference between brain regions in terms of KiPL or VND.
CER-ND: VND in CAU relative to other regions (NDREL) was estimated.
CER-Ki: KiPL in CAU relative to other regions (KiREL) was estimated.
Random effects
The modelling process included estimation of inter individual variability (IIV) of parameters in a first step. For parameters where IIV was significant, inter-occasion variability (IOV) was tested. After inclusion of IOV (if significant) the importance of IIV was re-evaluated on that parameter. The IIV and IOV were tested on the parameters VND, and BPBL and KiPL with log normal variance models according to the following:
 |
11 |
where Pjκ is the parameter value in the model for subject j at occasion k, θ is the typical parameter value in the population and ηs are zero-mean, normally distributed variables with standard deviation ωP,IIV and ωP,IOV which are estimated as part of the population model.
The following additive residual error model was used:
 |
12 |
in which Cijkl is the model predicted brain concentrations of the ith region of interest, the jth individual at occasion k and time l. Ci,obs are the corresponding observed concentrations. The deviation of the observations from the model predictions are represented by εijkl, and εjkl,joint, where εijkl is the residual error for region i, and εjkl,joint is a common residual error accounting for the correlation between the concentrations in the different regions. The residual errors are assumed to be normally distributed with a mean of zero and variances σi2 and σjoint2. In addition, weighting (WT) was applied to account for the difference in residual error at early time points when the frame duration was less than 3 min and at the very early time points prior to the start of increase in radioligand concentrations.
Model evaluation
Models were evaluated by nonmem objective function values (OFV), goodness of fits plots and standard errors of parameter estimates (when possible). The 95% confidence interval of key parameters was evaluated by means of likelihood profiling in the cases where standard errors of the estimates could not be obtained. The nonmrem OFV is approximately equal to −2 times the log-likelihood of the data, given the model. A difference in OFV between two nested models is approximately χ2-distributed. A difference in the OFV of 3.84 is statistically significant for one parameters' difference of freedom on the 5% level.
Simulation studies
Simulation studies were performed in order to evaluate whether differences between brain regions in VND or KiPL can be detected and to evaluate the consequence of not accounting for such differences. Based on the final models (with either cerebellum or white matter as reference regions), studies of identical design to the executed study were simulated. The simulation model and alternative models were subsequently fitted to the simulated data. Finally, the power to differentiate between the models and the bias when failing to do so were computed. The simulations were performed using the SSE functionality in PsN3.5.3 18. For the evaluation of the type 1 error 500 simulations were performed. Evaluations of the type II error rate (power) and bias were performed using at least 100 simulations per evaluation.
Results
Exposure−occupancy relationship – cerebellum as reference
Initially in the model building process each region of interest was analyzed separately. The results from this analysis suggested that most regions had similar estimated KiPL with overlapping confidence intervals. The estimated KiPL in one of the regions (CAU) was, however, estimated to approximately half of the others. In order to assess whether this difference in KiPL could be better explained by different non-displaceable concentrations, a simultaneous analysis, including all the regions was performed. In the base model (CER-base) all regions were included simultaneously in the analysis assuming the same KiPL and VND in all regions. A plot of the conditional weighted residuals (CWRES) vs. time for CAU based on this analysis revealed a dose-dependent pattern (Figure 2, top panel) indicating model mis-specification. The residuals were generally above zero at the baseline measurement and below zero after pre-treatment with AZD3783, while for other brain regions the CWRES spread more evenly around zero both at baseline and after pre-treatment (not shown). In order to investigate the reason for this pattern, models with estimation of either VND (model CER-ND) or KiPL (model CER-Ki) in CAU relative to the other regions were fitted to data.
Figure 2.
CWRES vs. time for CAU at baseline and after pre-treatment with AZD3783 based on the models CER-base, CER-ND and CER-Ki. The smooth is a loess curve
The parameter estimates of the models are shown in Table 1. The drop in OFV was 75 with CER-ND and 93 with the model CER-Ki compared with the model CER-base suggesting that CAU is statistically significantly different vs. the other regions and that this difference is more likely related to a difference in KiPL than a difference in non-displaceable concentration. Also, the CWRES for CAU suggest that CER-ND (Figure 2, mid panel) is a better model as compared with CER-base and that there is a further slight improvement with the model CER-Ki (Figure 2, bottom panel) in which the residuals are spread around zero both at baseline and after pre-treatment. Individual plots, exemplified by subject 1 data at BL and after pre-treatment (Figure 3), goodness of fit plots (Figure 4) as well as visual predictive checks based on simulation from the model (Figure 5) suggested that the model can describe the data well for all brain regions both at baseline and after pre-treatment.
Table 1.
Parameter estimates of CER-base, CER-ND (VND in CAU relative to other regions estimated) and CER-Ki (KiPL in CAU relative to other regions estimated)
| Parameter | CER-base | CER-ND | CER-Ki |
|---|---|---|---|
| Objective function value | 15612 | 15537 | 15519 |
| Δ OFV vs. base model | 0 | −75 | −93 |
| KiPL (95% CI) ng ml−1 | 10.2 (7.9, 13.4) | 10.3 (8.0, 13.7) | 10.4 (8.1, 13.6) |
| KiREL | 1 FIX | 1 FIX | 0.55 (0.48, 0.62) |
| NDREL | 1 FIX | 0.89 (0.87–0.91) | 1 FIX |
| k2REF | 0.18 | 0.18 | 0.18 |
| BPBL,CAU | 0.736 | 0.98 | 0.80 |
| BPBL,OCC | 1.12 | 1.12 | 1.12 |
| BPBL,PAR | 0.81 | 0.81 | 0.81 |
| BPBL,PFC | 1.10 | 1.09 | 1.09 |
| BPBL,THA | 0.24 | 0.24 | 0.24 |
| R1CAU | 0.75 | 0.75 | 0.75 |
| R1OCC | 0.92 | 0.82 | 0.92 |
| R1PAR | 0.75 | 0.67 | 0.75 |
| R1PFC | 0.80 | 0.71 | 0.79 |
| R1THA | 0.75 | 0.66 | 0.75 |
| IOV in BPBL (CV) | 17% | 17% | 17% |
| IIV in BPBL (CV) | 18% | 18% | 18% |
| IIV in k2REF (CV) | 14% | 14% | 14% |
| σjoint (SD) | 4.1 | 4.1 | 4.1 |
| σCAU (SD) | 7.4 | 6.8 | 6.7 |
| σOCC (SD) | 5.7 | 5.7 | 5.7 |
| σPAR (SD) | 4.5 | 4.5 | 4.5 |
| σPFC (SD) | 2.9 | 2.8 | 2.8 |
| σTHA (SD) | 4.2 | 4.1 | 4.1 |
| Relative change in residual error (SD) first 3 min | 2.7 | 2.7 | 2.7 |
| Relative change in residual error (SD) at initial very low radioligand concentrations | 0.61 | 0.62 | 0.63 |
Figure 3.
Radioactivity concentration vs. time with the CER-Ki model for subject 1 by ROI and dose. (circles are the observed radioactivity concentrations, dashed lines are the population predictions and the solid lines are the individual model predictions). 
, 0 mg; 
, 2 mg; 
, 10 mg; 
, 40 mg. CAU caudate; OCC occipital cortex; PAR parietal cortex; PFC prefrontal cortex; THA thalamus
Figure 4.
Basic goodness of fit by region for CER-Ki (The final model with KiREL estimated). CAU caudate; OCC occipital cortex; PAR parietal cortex; PFC prefrontal cortex; THA thalamus
Figure 5.
Visual predictive check, prediction corrected with observed median and 95% CI based on simulations from the model CER-Ki (KiREL estimated)
The KiPL was estimated to 10.4 ng ml−1 (95% CI 8.1, 13.6) with the final model (CER-Ki). The KiPL in the CAU was estimated to be 55% of that in the other regions (95% CI 0.48, 0.62). A model, where both KiREL and NDREL were estimated resulted in an estimate of NDREL of 0.96, i.e. close to 1 and an estimate of KiREL of 0.65, with a limited, albeit statistically significant, drop in OFV of 5.7.
Exposure−occupancy relationship – white matter as reference
In order to assess the possibility to estimate occupancy using WM as reference region, the model was also fitted to the data using WM as the reference region. The base model (WM-base) assumed the same VND in regions of interest and in WM. An alternative model (WM-ND) where the VND in regions of interest relative to WM (NDREL) was estimated was also fitted to data. The goodness of fit when WM was used as reference region appeared acceptable, although the model under-predicted the observed values slightly in the time-range 10–40 min at the baseline PET measurement (Figure 6).
Figure 6.
Radioactivity concentration vs. time with the WM-ND model for subject 1 by ROI and dose. (circles are the observed radioactivity concentrations, dashed line are the population predictions and the solid lines are the individual model predictions). 
, 0 mg; 
, 2 mg; 
, 10 mg; 
, 40 mg. OCC occipital cortex; PAR parietal cortex; PFC prefrontal cortex; THA thalamus
The main results from these analyses are shown in Table 2. The estimated KiPL based on the WM-ND model was 10.2 ng ml−1 which is very similar to the estimate obtained using CER as the reference region. The NDREL was estimated to 0.94 with a relative standard error (RSE) of 3% showing that NDREL could be estimated with a high degree of precision. The NDREL estimate was however close to 1 explaining why the estimate of KiPL only changed marginally with NDREL fixed to 1.
Table 2.
KiPL and NDREL estimates based on white matter (WM) as reference region
| Model | ΔOFV | KiPL | RSE | 95% CI | NDREL | RSE | 95% CI |
|---|---|---|---|---|---|---|---|
| WM-base | – | 11.7 | 19% | 7.3, 16.1 | 1 FIX | – | – |
| WM-ND | −45 | 10.2 | 24% | 5.4, 15.0 | 0.94 | 3% | 0.89, 0.99 |
The kinetics in WM were also estimated, including only WM data using CER as reference, assuming no specific binding in WM (or in CER). The NDREL, expressed as VND,CER/VND,WM, was then estimated to 0.91 (RSE = 6%), hence agreeing well with the estimate of 0.94 obtained with the WM-ND model which did not include CER.
Thus in the present case, WM appears to be an acceptable reference region and it is possible, albeit not necessary, to account for differences in non-displaceable binding in the reference region compared with the region of interest.
Simulations with cerebellum as reference
In order to assess the ability of a model-based approach in detecting and correcting for differences between regions in non-displaceable concentrations or KiPL a simulation experiment was performed. Three models (base, AltND and AltKi) with parameters based on the final model (CER-Ki) were used. In the base model, KiREL and NDREL were fixed to 1. In the AltND model, the NDREL was set to 0.9 (non-fixed) while KiREL was fixed to 1 and in the AltKi model, KiREL was set to 0.55 (non-fixed) while NDREL was fixed to 1.
The simulation experiment included:
Simulation with the base model followed by estimation of the simulated data using the models base, AltND and AltKi,
Simulation with AltND followed by estimation using base, AltND and AltKi and
Simulation with AltKi followed by estimation using base, AltND and AltKi.
The type 1 error rate determined based on simulation experiment 1 above was estimated to 6.6% and 4.6% for AltND and AltKi respectively, i.e. close to the nominal value of 5% for a ΔOFV of 3.84. The power to identify the true model was near 100% both vs. the base model and the incorrect alternative model (Table 3). The KiREL was biased by −33% when the VND was 10% lower in the CAU compared with the other regions if not accounted for (Table 4). In the converse situation where the KiPL in the CAU was 0.55 of that in the other regions (KiREL = 0.55) while NDREL was 1, the NDREL was biased by −9%. No bias was seen when estimating using the simulation models.
Table 3.
Power* to detect the true model and mean change in OFV. Based on simulation and estimations assuming either different CND (AltND) or different Ki (AltKi) in caudate relative to other regions. Power is also calculated vs. a model assuming no difference between regions (base)
| Power* (mean ΔOFV) to identify the simulation model as the true model | |||
|---|---|---|---|
| Simulation (True) models | vs. base | vs. AltND | vs. AltKi model |
| AltND | 100% (−64) | – | 99.6% (−32) |
| NDREL = 0.9, KiREL = 1FIX | |||
| AltKi | 100% (−106) | 100% (−58) | – |
| NDREL = 1 FIX, KiREL = 0.55 | |||
Drop in OFV > 3.84 when using the simulation model for estimation vs. alternative estimation models.
Table 4.
Bias and precision of NDREL and KiREL based on simulations with cerebellum as reference, assuming either different CND (Alt1) or different Ki (Alt2) in caudate relative to other regions
| Simulation models | Estimation models | ||||||
|---|---|---|---|---|---|---|---|
| AltND* | AltKi† | ||||||
| Parameter | NDREL | KiREL | |||||
| values | Mean | RMSE | Bias | Mean | RMSE | Bias | |
| AltND | NDREL = 0.9 | 0.90 | 1.4% | 0% | 0.67 | 33% | −33% |
| KiREL = 1 FIX | |||||||
| AltKi | NDREL = 1 FIX | 0.91 | 9.0% | −9.0% | 0.55 | 5.9% | 0% |
| KiREL = 0.55 | |||||||
NDREL estimated and KiREL fixed to 1.
KiREL estimated and NDREL fixed to 1.
Simulations with white matter as reference
A simulation experiment was performed to investigate whether it was possible to identify and account for a different VND in the reference region relative to regions of interest. Simulations were performed where VND in the reference region was 90% of that in regions of interest (NDREL = 0.9). Based on the simulated data, estimations of model parameters were performed using the simulation model where NDREL was estimated as well as with an alternative model where NDREL was fixed to 1.
Simulations were performed based on the final estimates of the WM-ND model which included four regions of interest. The KiPL was however set to 10, 30 or 100, to mimic situations in which the highest doses in the study induced occupancy of around 45% (KiPL = 100) up to 89% (KiPL = 10). In order to assess whether inclusion of a brain region with low BPND improved the precision in the KiPL, the BPND of THA was set to either much lower than the other regions of interest at 0.2 or at 0.8 which was similar to the other regions included in the analysis.
As shown in Figure 7 and Table 5, it was possible to identify and account for a different non-displaceable uptake in the reference region relative to the region of interest. The bias in the KiPL estimate, when accounting for the difference in VND, was negligible in all the cases, while it was 19–32% when not doing so.
Figure 7.
Bias and RMSE of the KiPL estimate plotted vs. occupancy of the highest dose in the study based on a simulation where VND in the reference region is 90% of that in regions of interest. Results shown with NDREL estimated (left) or fixed to 1 (right). One scenario with similar BPND in all regions (BPND∼0.8) and one scenario where BPND was low (BPND = 0.2) in one of the regions of interest and 0.8 in the others. 
, RMSE, High + Low BPND; 
, RMSE, only high BPND; 
, Bias, High + Low BPND; 
, Bias, only high BPND
Table 5.
Bias and precision of KiPL and power to detect the true model based on a simulation where VND in reference region is 90% of that in regions of interest. One scenario with similar BPND in all regions (BPND∼0.8) and one scenario where BPND was low (BPND = 0.2) in one of the regions of interest
| Estimation model = Simulation model (NDREL estimated) | Alternative model (NDREL fixed to 1) | ||||||||||
|---|---|---|---|---|---|---|---|---|---|---|---|
| ΔOFV mean | NDREL | KiPL | KiPL | ||||||||
| Simulation model | Power | mean | Mean | RMSE (%) | Bias (%) | Mean (ng ml−1) | RMSE (%) | Bias (%) | Mean (ng ml−1) | RMSE (%) | Bias (%) |
| One region with low BPND | |||||||||||
| KiPL = 10 (Omax = 89%)* | 100% | 84 | 0.90 | 1.03 | −0.15 | 9.9 | 4.69 | −0.7 | 12.6 | 27.5 | 26 |
| KiPL = 30 (Omax = 73%)* | 100% | 36 | 0.90 | 1.62 | 0.11 | 30.4 | 6.06 | 1.2 | 37.6 | 26.7 | 25 |
| KiPL = 100 (Omax = 45%)* | 93% | 14 | 0.90 | 2.93 | −0.42 | 99.8 | 8.59 | −0.2 | 119 | 20.9 | 19 |
| Similar BPND all regions | |||||||||||
| KiPL = 10 (Omax = 89%)* | 100% | 75 | 0.90 | 1.12 | −0.06 | 9.9 | 5.68 | −0.6 | 13.2 | 33.7 | 32 |
| KiPL = 30 (Omax = 73%)* | 100% | 32 | 0.90 | 1.50 | −0.03 | 30.3 | 6.30 | 1.1 | 38.6 | 30.1 | 29 |
| KiPL = 100 (Omax = 45%)* | 83% | 10 | 0.90 | 3.58 | −0.23 | 100 | 10.41 | 0.3 | 122.2 | 25.0 | 22 |
Occupancy of the maximum dose in the study.
If PET measurements at high occupancy were included in the study, the power to detect a difference in VND was increased and the precision of the KiPL and NDREL was improved. When NDREL was fixed to 1, however, the bias increased with increasing occupancy.
Inclusion of a region with low BPND in the analysis also improved the power to detect a difference and the precision of NDREL to some extent. The bias when NDREL was fixed to 1 was reduced by inclusion of a region with low BPND.
Discussion
In the present analysis it was shown how the SRTM can be extended to allow different VND in the reference region and other regions of interest. Variability between individuals and regions was accounted for using a non-linear mixed effects approach.
A statistically significant difference for CAU relative to the other regions was identified in the analysis. The analysis suggests that this difference is more likely related to KiPL than to VND. Inter-regional differences in KiPL could theoretically be a result of differences in transport of AZD3783 across the blood−brain barrier resulting in higher free brain concentrations and hence higher AZD3783 receptor occupancy in CAU compared with other brain regions. Another possibility is that AZD3783 competes with the radioligand at different binding sites and that the binding site with high AZD3783 affinity is more abundant in CAU relative to other regions. Differences in endogenous ligand concentration can also influence the apparent KiPL value. The possibility that methodological factors such as a partial volume effect influences the observed concentration in CAU, cannot be ruled out since it is a relatively small region close to a ventricle. We are not aware of studies supporting these hypothesis and additional investigations would be needed to confirm the mechanism behind the difference in CAU relative to other regions. The simulation experiment based on CER further supported that it can be possible to discriminate between different reasons for interregional differences and to account for this difference.
The estimate of KiPL of 10.4 ng ml−1 (22 nm) in the present analysis concurs with the previously reported results 9 where the KiPL was estimated to 11 ng ml−1 (24 nm) and 8.4 ng ml−1 (18 nm) for occipital cortex and ventral striatum, respectively.
When using WM as a reference region it was possible to estimate KiPL accounting for the difference in VND between reference and regions of interest and the estimate of KiPL was very similar to the estimate obtained with CER as reference.
The simulation experiments illustrate that the KiPL will be biased when not accounting for a difference in VND between the reference region and regions of interest and that it is possible to identify and account for this difference using the proposed extension to the SRTM.
The simulation also shows that the parameter precision and the power to detect a difference between the reference region and regions of interests in VND can be improved by inclusion of PET measurements in the presence of high displacer concentrations and inclusion of ROIs with low BPND in the analysis. This is expected since inclusion of experimental data from ROIs with little specific binding (i.e. with predominantly non-displaceable radioligand concentrations) should be informative on the VND parameter.
The simulations were all performed based on the (extended) SRTM. More extensive simulations would be needed to investigate the sensitivity of the present approach to violations of the assumption that the tracer kinetics are described by a single tissue compartment in both the reference region and regions of interest.
In the present work, we have shown that the proposed extension to the SRTM model can improve understanding of differences between brain regions. Perhaps more importantly the extended SRTM can be useful in situations where the non-displaceable concentration cannot a priori be assumed to be the same in the reference region and the brain regions of interest opening up the possibility to use white matter as a reference region in PET receptor occupancy studies.
Competing Interests
All authors have completed the Unified Competing Interest form at http://www.icmje.org/coi_disclosure.pdf (available on request from the corresponding author) and declare Matts Kågedal is an employee of AstraZeneca, Mats O. Karlsson receives grants and personal fees from AstraZeneca, outside the submitted work. Andrew C. Hooker and Katarina Varnäs have nothing to disclose.
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