Pharmacokinetic modeling of P-glycoprotein function at the rat and human blood–brain barriers studied with (R)-[11C]verapamil positron emission tomography
© Müllauer et al.; licensee Springer. 2012
Received: 30 August 2012
Accepted: 26 September 2012
Published: 16 October 2012
This study investigated the influence of P-glycoprotein (P-gp) inhibitor tariquidar on the pharmacokinetics of P-gp substrate radiotracer (R)-[11C]verapamil in plasma and brain of rats and humans by means of positron emission tomography (PET).
Data obtained from a preclinical and clinical study, in which paired (R)-[11C]verapamil PET scans were performed before, during, and after tariquidar administration, were analyzed using nonlinear mixed effects (NLME) modeling. Administration of tariquidar was included as a covariate on the influx and efflux parameters (Q in and Q out) in order to investigate if tariquidar increased influx or decreased outflux of radiotracer across the blood–brain barrier (BBB). Additionally, the influence of pilocarpine-induced status epilepticus (SE) was tested on all model parameters, and the brain-to-plasma partition coefficient (V T-NLME) was calculated.
Our model indicated that tariquidar enhances brain uptake of (R)-[11C]verapamil by decreasing Q out. The reduction in Q out in rats during and immediately after tariquidar administration (sevenfold) was more pronounced than in the second PET scan acquired 2 h after tariquidar administration (fivefold). The effect of tariquidar on Q out in humans was apparent during and immediately after tariquidar administration (twofold reduction in Q out) but was negligible in the second PET scan. SE was found to influence the pharmacological volume of distribution of the central brain compartment V br1. Tariquidar treatment lead to an increase in V T-NLME, and pilocarpine-induced SE lead to increased (R)-[11C]verapamil distribution to the peripheral brain compartment.
Using NLME modeling, we were able to provide mechanistic insight into the effects of tariquidar and SE on (R)-[11C]verapamil transport across the BBB in control and 48 h post SE rats as well as in humans.
KeywordsNonlinear mixed effects modeling Positron emission tomography (R)-[11C]verapamil P-glycoprotein Tariquidar Pilocarpine-induced epilepsy Species differences
About one-third of patients with epilepsy are pharmacoresistant and do not respond adequately to antiepileptic drug therapy . The blood–brain barrier (BBB) has a major role in regulating the transport of antiepileptic drugs to their target site of action. Drug penetration across the BBB is influenced by several mechanisms, such as passive diffusion, active influx, and active efflux. Regional overactivity of efflux transporters at the BBB is thought to contribute to drug resistance by impeding therapeutically effective concentrations of antiepileptic drugs at their sites of action . P-glycoprotein (P-gp), which is physiologically located at the luminal membrane of brain capillary endothelial cells, is currently one of the most widely studied efflux transporters at the BBB. Positron emission tomography (PET) with carbon-11-labeled P-gp substrates, such as (R)-11C]verapamil or 11C]-N-desmethyl-loperamide, has been evaluated as a tool for in vivo imaging of P-gp function in different species [3–6]. However, these radiotracers are high-affinity P-gp substrates and consequently display very low brain concentrations, limiting their suitability as PET tracers [5, 7, 8]. This drawback can be overcome by modulation of P-gp with the third-generation P-gp inhibitor tariquidar, which leads to increased brain uptake of these radiotracers. After partial inhibition of P-gp with 3 mg/kg tariquidar, regional differences in P-gp expression and functionality between naïve and status epilepticus (SE) rats become evident [9, 10]. Additionally, P-gp at the BBB has been found to be upregulated after acute seizure activity like SE or in chronic epilepsy [11–15]. Further, species-dependent differences in P-gp expression and functionality at the BBB have been described and discussed in literature [16–18], including the P-gp mediated interaction between (R)-11C]verapamil and tariquidar at the human and rat BBB studied by Bauer et al. . Despite several published studies, there is still an ongoing debate, whether P-gp inhibition with tariquidar or other inhibitors is enhancing the brain uptake of substrate radiotracers by increasing the influx or decreasing outflux across the BBB of the radiotracer .
In PET research, pharmacokinetic (PK) modeling (compartment modeling) is used for detailed quantitative analysis of PET data. Each individual is analyzed separately, and group averages and variability are subsequently based on the individual estimates. An alternative way to analyze PK-pharmacodynamic (PD) data is nonlinear mixed effects (NLME) modeling, often referred to as population modeling. This modeling approach is routinely used in pharmaceutical research and has also found to be suitable for PET research [19–29]. A population approach analyzes data from all subjects simultaneously and gives a description of the PK in the typical subject as well as the variation in the study population. Syvänen et al.  analyzed data from a (R)-11C]verapamil PET study in naïve and post SE rats (seven days after kainate treatment) with both a PET PK-modeling approach and a NLME-modeling approach and concluded that both approaches produced similar PK parameter estimates, but that NLME modeling provided more precise parameter estimates.
Preclinical data set
The preclinical dataset was recently published by Bankstahl et al. , and the study setup is illustrated in Figure 1A. The study was approved by the Institutional Animal Care and Use Committee, and all study procedures were performed in accordance with the European Communities Council Directive of November 24, 1986 (86/609/EEC). All efforts were made to minimize both the suffering and the number of animals used in this study.
Number of animals ( n ), weight at time of PET, injected doses (average ± standard deviation) of ( R )-[ 11 C]verapamil for baseline and post-inhibition scans in naïve and 48-h post SE rats and different treatments with 3 or 15 mg/kg of tariquidar
Naïve and 3 mg/kg tariquidar treated
Naïve and 15 mg/kg tariquidar treated
48-h post SE and 3 mg/kg tariquidar treated
48-h post SE and 15 mg/kg tariquidar treated
Body weight (g)
260 ± 5
307 ± 18
234 ± 14
247 ± 16
260 ± 28
Baseline (R)-[11C]verapamil (MBq)
97 ± 27
88 ± 17
84 ± 20
94 ± 25
91 ± 22
I.V. injection time (sec)
18 ± 7
39 ± 10
19 ± 2
25 ± 11
24 ± 11
Post-inhibition (R)-[11C]verapamil (MBq)
93 ± 27
101 ± 28
91 ± 9
92 ± 16
94 ± 21
I.V. injection time (sec)
18 ± 6
36 ± 5
16 ± 2
32 ± 18
24 ± 13
Clinical data set
The clinical dataset has been described in detail by Wagner et al. . The study setup is illustrated in Figure 1B. The study protocol was approved by the local Ethics Committee and was performed in accordance with the Declaration of Helsinki (1964) in the revised version of 2000 (Edinburgh), the Guidelines of the International Conference of Harmonization, the Good Clinical Practice Guidelines, and the Austrian Drug Law (Arzneimittelgesetz). All subjects were given a detailed description of the study, and their written consent was obtained before they enrolled in the study.
Number of human volunteers ( n ), weight at time of PET, injected doses (average ± standard deviation) of ( R )-[ 11 C]verapamil for baseline, and post-inhibition scans after tariquidar (2 mg/kg) treatment
Healthy volunteers and 2 mg/kg tariquidar treated
Body weight (kg)
Baseline (R)-[11C]verapamil (MBq)
I.V. injection time (sec)
Post-inhibition (R)-[11C]verapamil (MBq)
I.V. injection time (sec)
For modeling, (R)-11C]verapamil concentration-time curves before and after tariquidar administration, expressed in kBq/ml, were extracted from a WB gray matter region as described previously .
PK modeling: PET approach
PET PK modeling parameters for rats and human were taken from Bankstahl et al.  and Wagner et al. , respectively. Individual profiles from each animal or human were analyzed using the common data analysis approaches for PET (PK modeling of individual profiles) [33, 34]. In both studies, a two-tissue-4-rate constant (2T4K) compartment model was applied to estimate the brain-to-plasma partition coefficient, referred to as the volume of distribution in PET literature (V T-2T4K), and the rate constants describing exchange of radioactivity between the plasma and the two brain tissue compartments. To further obtain a model-independent estimate of the brain-to-plasma partition coefficient, Logan graphical analysis  was used (V T-Logan). Data obtained during and immediately after tariquidar treatment, i.e., the last part of the baseline scans, were not included when estimating V T- 2T4K and V T- Logan.
where θ i is the parameter in the i th animal, θ pop is the parameter in a typical animal, and η i is the inter-animal variability, which is assumed to be normally distributed around zero with a standard deviation ω, to distinguish the i th animal from the typical value as predicted from the regression model. Inter-animal variation was studied on all parameters and was included if the model was improved significantly (OFV > 3.83). To test the significance of the covariate inclusion, e.g., effect of tariquidar and SE, a stepwise forward addition and backward deletion approach was applied, and covariates were only kept in the model if they significantly improved the model. Finally, proportional error models were included for the residual variability, i.e., variability that remained unexplained after inclusion of inter-animal variability and covariates. More comprehensive description of NLME modeling can be found elsewhere, for example in the paper by Pillai et al. .
The model development was carried out using the rat dataset (WB region) and the model was built in sequential steps. The first step was to develop a PK model for (R)-[11C]verapamil plasma concentration-time profiles. Two and three compartment models were evaluated. Treatment (tariquidar-treated or tariquidar-untreated) and rat group (control or 48-h post SE) were defined as covariates (Efftariquidar and EffSE) and their effects on the parameter estimates were studied. Next, a PK model of (R)-[11C]verapamil concentration-time profiles in brain was developed. Two and three compartment models were evaluated, and again treatment and rat group were defined as covariates. Finally, in the last step of the model development, the PK models for (R)-[11C]verapamil kinetics in plasma and brain were merged.
Differences between groups were analyzed by 2-way ANOVA including Bonferroni correction using PRISM 5 software (GraphPad Software, La Jolla, CA). The level of statistical significance was set to p < 0.05.
NLME modeling of plasma and brain PK with and without tariquidar administration
Population parameter estimates and relative standard errors (%) of the ( R )-[ 11 C]verapamil plasma model using mixed effects modeling of the WB region of interest of rats and humans
V c (ml)
V p1 (ml)
V p2 (ml)
Q 1 (ml·min−1)
Q 2 (ml·min−1)
Residual error plasma
Population parameter estimates and relative standard errors (%) of ( R )-[ 11 C]verapamil brain model are shown for all investigated brain regions
V br1 (ml)
V br2 (ml)
Q in (ml·min−1)
Q out (ml·min−1)
Q br (ml·min−1)
Residual error brain
Effect of pilocarpine induced SE
Effect of tariquidar
Efftariquidar (3 mg/kg or 2 mg/kg)d
Efftariquidar (15 mg/kg)d
Effect of scan on tariquidar induced P-gp inhibition
Influence of tariquidar on (R)-[11C]verapamil transport across the BBB
Efftariquidar3 and Efftariquidar15 are the estimated effects of tariquidar for the 3 and 15 mg/kg doses, respectively. The exponent, cov, was assigned to a value of 0 when no tariquidar was administered or 1 when tariquidar was administered. Effscan describes the difference in tariquidar effect between baseline and post-inhibition scans. The exponent, cov, of Effscan was assigned to a value of 0 and 1 for the baseline and post inhibition scan, respectively. The total effect of tariquidar inhibition, D, was therefore the fractional change in transport caused by tariquidar while also taking into account changes of tariquidar-induced P-gp inhibition occurring between the two scans (baseline or post-inhibition) as it is likely that the inhibition is changing due to the elimination of tariquidar from the plasma and brain.
Volume of distribution (V T-NLME)
V T-NLME (Q in/Q out) values at baseline and after tariquidar administration are shown in Figure 8A,B,C,D for rats and humans. Tariquidar increased V T-NLME by approximately 6.2-fold after 3 mg/kg dose and 7.4-fold after 15 mg/kg dose in the whole brain region when all data were analyzed (Figure 8C). V T-NLME increase was lowest in EC (fourfold) and highest in CS (ninefold) for the 3 mg/kg tariquidar treated group. Also, for the 15 mg/kg tariquidar group, V T-NLME increase was lowest in EC (fivefold) and highest in CS (tenfold). V T-NLME was slightly decreased when the data acquired during and immediately after tariquidar administration (scan 1, 60 to 140 min) was excluded. This was the result of a slightly decreased Efftariquidar in the second scan compared to the first scan. In humans, a twofold increase in V T-NLME relative to baseline was observed during and after tariquidar administration (Figure 8D). In contrast, V T-NLME was unchanged in the post-inhibition scan as compared with baseline (Figure 8D).
The influence of rat group (status epilepticus)
where EffSE is the estimated influence of pilocarpine-induced SE on V br1 (Equation 6) and implies a fractional difference between control and 48-h post SE rats. Hence, the exponent, cov, in Equation 6 was assigned to a value of 0 for the control rat group, while it was assigned to a value of 1 for the 48-h post SE group.
EffSE was found to be a significant covariate that increased V br1 in 48-h post SE rats as compared with control rats (see Figure 2, Table 4) in all brain regions except Cer. The largest increase in V br1 in the 48-h post SE group was observed for FMC (+130%, EffSE = 2.3) and in THipp (+121%, EffSE= 2.21) (Table 4). In Cer, a small decrease in V br1 for 48-h post SE rats as compared with naïve rats was found (−8%, EffSE = 0.92). EffSE was not considered for the analysis of the human data set due to the fact that only healthy subjects participated in the clinical study.
In the present study, we used NLME modeling to study the PK of (R)-[11C]verapamil in plasma and brain, and the influence of tariquidar on (R)-[11C]verapamil brain PK to gain better insight into the mechanism of P-gp modulation by tariquidar. Moreover, our goal was to evaluate if the increase in brain activity induced by tariquidar during the first PET scan is better suited to describe regional and species differences and differences between control and post SE rats in cerebral P-gp function/expression as compared with using data from the post-inhibition scan alone. The developed model described the rat data well (Figure 6) and was then used to model the clinical data set. The small number of human subjects made it difficult to obtain estimates of the inter-individual variation in the human data set, but the model converged and, although the fit was not perfect, provided estimates of all structural model parameters. However, the variation in the human PK data set between the five subjects was rather large, and in combination with the few subjects, the results should be interpreted with some caution.
Comparison of volumes of distribution ( V T ) values of naïve, 48-h SE rats, and humans obtained with Logan analysis, PK modeling, and nonlinear mixed effects modeling, respectively
Logan analysis a
PK modeling a(2T4K)
Nonlinear mixed effects modeling
Increase after 3 mg/kg tariquidarb
48-h post SE rats
Increase after 3 mg/kg tariquidarb
Increase after 2 mg/kg tariquidarb
The major findings of this study are as follows: First, it has been debated whether inhibition of P-gp affects the transport of substrates across the BBB into the brain (K 1, Q in) or the transport out of the brain (k 2, Q out). Two models have been suggested, i.e., influx hindrance and efflux enhancement. Influx hindrance can be described by the ‘gatekeeper’ model, where substrates are transported back from the lipid layers of the luminal cell membrane into the blood before they reach the cytoplasm. Efflux enhancement can be described by the ‘vacuum cleaner’ model  which suggests that substrates can be transported from the endothelial cells or brain parenchyma back into the blood. Thus, the question remains if tariquidar enhances brain distribution of (R)-11C]verapamil by increasing the influx (K 1, Q in) or decreasing the efflux (k 2, Q out) of the tracer. Our model clearly indicated that tariquidar enhances brain uptake of (R)-11C]verapamil by decreasing Q out of the radiotracer. P-gp inhibition led to an on average sevenfold reduction in Q out in rats (3 mg/kg tariquidar), while in humans (2 mg/kg tariquidar) a twofold reduction in Q out was observed when all data were included into the model. When data during and immediately after tariquidar administration were excluded, an average fivefold reduction in Q out was observed in rats. Thus, the reduction in Q out when including the data obtained during and after tariquidar administration was more pronounced than when this part was excluded. This indicates that the effect of tariquidar on P-gp function is already declining at 2 h after tariquidar administration. In humans, the tariquidar effect on Q out was apparent only during and after tariquidar administration and had completely disappeared in the post-inhibition scan. This highlights the importance of designing appropriate study protocols when investigating active transporters at the BBB as the onset and decline of inhibition is very rapid. Also, important to point out is that the analysis showed that Q out and Q in estimates were very similar regardless of whether the data from the tariquidar administration period were included or not, i.e., this confirms that the model is reliable and that only parameters that are expected to vary over time, e.g. the effect of tariquidar, are indeed changing.
Second, the study also indicated some regional and species differences in P-gp inhibition; large tariquidar-induced decreases in Q out (CS, Th, and Hipp) indicated strongly enhanced brain uptake of (R)-11C]verapamil, while small decreases in Q out (Cer, EC) indicated a weak enhancement in brain uptake of (R)-11C]verapamil as compared with baseline scans (Figure 8). A decrease in Q out leads to an increased V T-NLME as V T-NLME is defined as the ratio between Q in and Q out. Thus, the developed NLME model indicated that, after P-gp inhibition, V T-NLME was significantly increased both in naïve and 48-h post SE rats. Inhibition with 3 mg/kg tariquidar resulted in regionally different enhancement of brain activity distribution, with weakest enhancement (low V T-NLME) in Cer and strongest enhancement (high V T-NLME) in CS and Th, similar to the findings of Kuntner et al. , who reported lowest V T-2T4K increases in Cer and highest V T-2T4K increases in Th of naïve rats after administration of 3 mg/kg tariquidar. (R)-11C]verapamil WB V T-NLME was about threefold lower at baseline in humans than in rats (0.51 vs. 1.6±0.3) (Table 5). This is also in good agreement with findings from Bauer et al.  reporting twofold lower V T-2T4K values in humans than in rats (Table 5). These observed differences could be due to different expression and transport capacity of P-gp.
Third, SE (EffSE) was found to increase V br1 in most regions leading to an increase in brain exposure time of (R)-11C]verapamil in 48-h post SE rats compared with controls. This is mainly because an increase in V br1 indicates increased distribution of (R)-11C]verapamil to the slow equilibrating brain compartment (V br2). This in turn will slow down the elimination of (R)-11C]verapamil from the brain. The difference between the two groups was largest in FMC (EffSE = 2.3, Table 4). This is in line with results reported by Syvänen et al. , which showed that V br1 in WB was increased 1.3-fold in kainate-induced post SE rats. In contrast to all other regions, exposure time was decreased in Cer in 48-h post SE rats compared with controls (EffSE = 0.924, Table 4). In line with these findings, Bankstahl et al. reported an increase of V T-2T4K in FMC, while Cer showed the largest decrease of V T-2T4K in 48-h post SE rats compared with controls . The decrease in V T-2T4K in Cer of 48-h post SE rats was presumably caused by a twofold upregulation of P-gp as compared with control rats as revealed by post-mortem immunohistochemical analysis of the brain tissue . Opposite to the findings presented in this paper, Bankstahl et al. also reported decreases or non-significant differences between controls and 48-h post SE rats in CS, Hipp, and Th. However, when ranking the regional SE-induced differences reported in the present study and by Bankstahl et al., the order is the same: FMC > CS > Hipp > Th > Cer. Bankstahl et al. found these regional differences only after partial inhibition of P-gp with 3 mg/kg. In the present study, all data were analyzed simultaneously including data from rats administered with 3 and 15 mg/kg tariquidar. This may, at least in part, be a reason for the differences in magnitude of regional differences between the present study and the study by Bankstahl et al. The present study showed that the effect of SE was mainly influencing the distribution of (R)-11C]verapamil within the brain (V br1) and not the actual transport across the BBB (Q in, Q out). It was possible to make this distinction by parameterization of the model using distribution volumes (the pharmacological term) and clearances instead of rate constants which depend on distribution volumes and clearances. Again, the effect of SE was the same when including and excluding data from the tariquidar administration period which indicated that the model parameter estimates are robust and do not change when adding or deleting some of the data set.
This study showed that tariquidar enhances brain uptake of (R)-[11C]verapamil by decreasing the outflux (Q out) of the tracer across the BBB. Pilocarpine-induced SE did not directly influence (R)-[11C]verapamil transport across the BBB but had an indirect influence on the (R)-[11C]verapamil exposure time in brain by influencing the pharmacological volume of distribution in the brain (V br1). For the quantitative analysis of PET data, the NLME modeling approach used in this study is an interesting supplemental tool to standard PET PK modeling approaches on individual level to increase mechanistic knowledge of radiotracer transport across the BBB.
JM is a post-graduate student developing new methods for analyzing PET data. CK, SS, and JPB are senior researchers focusing on preclinical and translational PET including pharmacokinetic modeling. MB is a senior researcher focusing on clinical PET. Professor RAV is an expert on animal models in epilepsy research. Professor MM is an expert in clinical pharmacology, and Professor OL specializes in the development of radiotracers for the imaging of CNS targets.
Two tissue compartment model
Corpus striatum region
Entorhinal cortex region
- Effscan :
Effect of scan 2 as a fractional change from scan 1
- EffSE :
Effect of pilocarpine-induced SE as a fractional change from control
- Efftariquidar :
Effect of tariquidar treatment as a fractional change from no treatment
Frontal motor cortex region
Nonlinear mixed effects
Objective function value
Positron emission tomography
- Q 1 :
Clearance from central compartment to first peripheral compartment
- Q 2 :
Clearance from central compartment to second peripheral compartment
- Q in :
Clearance from plasma to brain
- Q out :
Clearance from brain to plasma
Septal hippocampus region
Standardized uptake value
Temporal hippocampus region
- V br1 :
Pharmacological distribution volume in first brain compartment
- V br2 :
Pharmacological distribution volume in second brain compartment
- V c :
Pharmacological distribution volume in central compartment
- V p1 :
Pharmacological distribution volume in first peripheral compartment
- V p2 :
Pharmacological distribution volume in second peripheral compartment
- V T-Logan :
The brain-to-plasma partition coefficient obtained with Logan analysis
- V T-NLME :
The brain-to-plasma partition coefficient obtained with NLME
- V T-2T4K :
The brain-to-plasma partition coefficient obtained with 2T4K
Whole brain region.
The authors thank Johann Stanek, Thomas Wanek, Thomas Filip, and Maria Zsebedics (Austrian Institute of Technology GmbH), and Marion Bankstahl (University for Veterinary Medicine, Hannover, Germany) for their skillful assistance during the performance of this study as well as the staff of the radiochemistry laboratory (Seibersdorf Laboratories GmbH) for their continuous support. This work was supported by funding from the European Community's Seventh Framework Programme (FP7/2007-2013) under grant agreement number 201380 (‘Euripides’) and from the Austrian Science Fund (FWF) project ‘Transmembrane Transporters in Health and Disease’ (SFB F35).
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