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NEUROPHARMACOLOGY

Pharmacokinetic-Pharmacodynamic Modeling of the Antinociceptive Effect of Buprenorphine and Fentanyl in Rats: Role of Receptor Equilibration Kinetics

Leiden/Amsterdam Center for Drug Research, Division of Pharmacology, Gorlaeus Laboratory, Leiden, The Netherlands (A.Y., M.D.); and Department of Anesthesiology, Leiden University Medical Center, Leiden, The Netherlands (E.O., A.D.)

Received December 21, 2004; accepted February 3, 2005.

	Abstract

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The objective of this investigation was to characterize the pharmacokinetic/pharmacodynamic correlation of buprenorphine and fentanyl for the antinociceptive effect in rats. Data on the time course of the antinociceptive effect following intravenous administration of buprenorphine or fentanyl was analyzed in conjunction with plasma concentrations by nonlinear mixed-effects analysis. For fentanyl, the pharmacokinetics was described on the basis of a two-compartment pharmacokinetic model. For buprenorphine, a three-compartment pharmacokinetic model best described the concentration time course. To explain time dependencies in pharmacodynamics of buprenorphine and fentanyl, a combined effect compartment/receptor binding model was applied. A log logistic probability distribution model is proposed to account for censored tail-flick latencies. The model converged, yielding precise estimates of the parameters characterizing hysteresis. The results show that onset and offset of the antinociceptive effect of both buprenorphine and fentanyl is mainly determined by biophase distribution. The k_eo was 0.024 min^–1 [95% confidence interval (CI): 0.018–0.030 min^–1] and 0.123 min^–1 (95% CI: 0.095–0.151 min^–1) for buprenorphine and fentanyl, respectively. On the other hand, part of the hysteresis in the buprenorphine pharmacodynamics could be explained by slow receptor association/dissociation kinetics. The k_off was 0.073 min^–1 (95% CI: 0.042–0.104 min^–1) and k_on was 0.023 ml/ng/min (95% CI: 0.013–0.033 ml/ng/min). Fentanyl binds instantaneously to the OP3 receptor because no reasonable values for k_on and k_off were obtained with the dynamical receptor model. In contrast to earlier reports in the literature, the findings of this study show that the rate-limiting step in the onset and offset of buprenorphine's antinociceptive effect is distribution to the brain.

	Materials and Methods

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Animals. Male Wistar rats were used in all experiments. The animals were housed in plastic cages in groups before surgery and individually after surgery. The animals were housed under laboratory standard conditions at constant room temperature (21°C) and on a 12-h light/dark cycle, with lights turned on at 7:00 AM and off at 7:00 PM. Food (RMH-TM; Hope Farms, Woerden, The Netherlands) and acidified water were allowed ad libitum. The animals were handled and allowed for acclimation to the experimental environment for 10 days prior to the start of the experiment. The protocol was approved by the Ethical Committee on Animal Experimentation of Leiden University.

Surgical Procedure. Surgery was carried out under anesthesia with an intramuscular injection of 0.1 mg/kg medetomidine hydrochloride (Domitor 1 mg/ml; Pfizer, Capelle a/d IJssel, The Netherlands) and 1 mg/kg ketamine base (Ketalar 50 mg/ml; Parke-Davis, Hoofddorp, The Netherlands). Two days before the experiment, indwelling cannulae were implanted, one in the left femoral artery and one in the right jugular vein. The cannula in the right jugular vein was used for administration of the opiate, whereas the cannula in the left femoral artery was used for serial collection of arterial blood samples. The cannulae were made from pyrogen-free, nonsterile polyethylene tubing. One day before surgery, cannulae were disinfected in a 1% benzalkoniumchlorid solution. The venous cannula consisted of 3 cm of polyethylene tubing (0.28 mm i.d.; Portex Limited, Kent, United Kingdom) heat-sealed to 9 cm of polyethylene tubing (0.58 mm i.d.; Portex Limited). The arterial cannula consisted of 3 cm of polyethylene tubing (0.28 mm i.d.) heat-sealed to 21 cm of polyethylene tubing (0.58 mm i.d.). The cannulae were tunneled subcutaneously and fixed at the back of the neck with a rubber ring. The skin in the neck and throat was stitched with normal suture. The skin in the groin was closed with wound clips. To prevent clotting and cannula obstruction, the cannulae were filled with a 25% (w/v) polyvinylpyrrolidone solution (PVP; Brocacef, Maarssen, The Netherlands) in pyrogen-free physiological saline (B. Braun Melsungen AG, Melsungen, Germany) containing 20 IU/ml heparin (Hospital Pharmacy, Leiden University Medical Center, Leiden, The Netherlands).

Drugs and Dosages. Buprenorphine hydrochloride and fentanyl monocitrate were kindly donated by Grünenthal GmbH (Aachen, Germany). Buprenorphine hydrochloride solution was prepared in saline with the aid of 2 drops of polysorbate 80 (Hospital Pharmacy, Leiden University Medical Center, Leiden, The Netherlands). To accelerate solubility, the solution was placed in an ultrasonification bath for 30 min. Fentanyl monocitrate solution was prepared in saline. The doses and concentrations of buprenorphine and fentanyl are expressed as free base.

Measurement of Antinociceptive Effect. A tail-flick analgesia meter (Columbus Instruments, Columbus, Ohio) was used to determine the pain sensitivity in the control and drug-treated rats (D'Amour and Smith, 1941). Radiant heat was applied using a shutter-controlled lamp as a heat source focused on a spot located 6.5 to 7.5 cm from the tip of the tail. The intensity of the beam was set at a level producing basal latency times between 2.5 and 3.5 s. To prevent tissue injury, the cut-off time was fixed at 10 s. A digital response time indicator with a resolution of 0.1 s measured the time between activation of the light beam and the tail-flick.

Drug Analysis. Buprenorphine and norbuprenorphine plasma concentrations were determined by HPLC coupled to tandem mass spectrometry (LC/MS/MS). The chromatographic system consisted of an Agilent HP 1100 HPLC system (Agilent, Waldbronn, Germany) coupled to an API 4000 LC/MS/MS system (Applied Biosystems, Darmstadt, Germany). Chromatography was performed on a precolumn (MetaGuard Polaris 3 µm C18-A 2 mm; Varian Deutschland GmbH, Darmstadt, Germany) guarded Synergi 4 µm Hydro-RP 80A column 75 mm x 2 mm (Phenomenex, Deutschland, Germany) at 40°C and a flow rate of 0.8 ml/min. The mobile phase consisted of water (solvent A) and acetonitrile/tetrahydrofuran (90:10, v/v) (solvent B) both containing 0.1% formic acid. The program started with 90% A for 1 min followed by a linear gradient from 90% A to 25% A ramped up in 4 min. After 2 min with 25% A, the gradient was switched back to 90% A in 0.1 min. The system was equilibrated for 3 min before injecting the next sample. The total run time was set at 10.1 min. A retention time of 3.3 min for norbuprenorphine and 3.8 min for buprenorphine was found for both analytes and their respective deuterated internal standards. A plasma volume of 50 µl was used for the assay of rat samples, standards, and quality control samples. All plasma samples (rat samples, standards, and quality control samples) were spiked with 1 ng (25 µl of 4 µg/100 ml) of the internal standard (²H₄-buprenorphine and ²H₉-norbuprenorphine). After adding 25 µl of concentrated ammonia, the samples were extracted for 15 min by liquid/liquid extraction with 600 µl of methyl tert-butyl ether. After centrifugation at 13,200 rpm for 8 min, the organic phase was transferred to autosampler vials, evaporated to dryness at 40°C under a gentle stream of nitrogen, and reconstituted in 125 µl of 0.1% formic acid in acetonitrile/tetrahydrofuran (90:10, v/v). A volume of 50 µl was injected onto the HPLC column. For the construction of the calibration curve for buprenorphine and norbuprenorphine, the following standard solutions were used: 0.047, 0.092, 0.19, 0.37, 0.73, 1.5, 2.9, 5.9, and 12 ng/ml. The calibration curve was linear in the range from 0.047 to 12 ng/ml for both analytes (r > 0.999). The lower limit of quantification was 0.047 ng/ml for buprenorphine and norbuprenorphine. The accuracy ranged from 99.4 to 102.1% for buprenorphine and from 96.1 to 101.0% for norbuprenorphine. The precision for the determination of buprenorphine, expressed as coefficient of variation, ranged from 2.2 to 6.4% for concentrations between 0.14 and 8.9 ng/ml. The respective values for norbuprenorphine are 2.0 to 3.7% in the concentration range of 0.14 to 8.7 ng/ml.

Fentanyl plasma concentrations were analyzed using HPLC coupled to tandem mass spectrometry (LC/MS/MS). The chromatographic system consisted of an Agilent HP 1100 HPLC system (Agilent) coupled to an API 3000 LC/MS/MS system (Applied Biosystems). Chromatography was performed on a precolumn (MetaGuard Polaris 3 µm C18-A 2 mm, Varian Deutschland GmbH) guarded Atlantis C18 column 3 µm 100 mm x 2.1 mm (Waters, Eschborn, Germany). The mobile phase consisted of water (solvent A) and methanol (solvent B) both containing 0.5% acetic acid. The program started with 98% A for 2 min followed by a linear gradient from 98% A to 10% A ramped up in 1 min. After 3 min with 10% A, the gradient was switched back to 98% A in 0.1 min. The system was equilibrated for 2.5 min before injecting the next sample. The total run time was set at 9.6 min and a retention time of 6.1 min for fentanyl and its deuterated internal standard. A plasma volume of 50 µl was used for the assay of rat samples, standards, and quality control samples. All plasma samples (rat samples, standards, and quality control samples) were spiked with 0.370 ng (25 µl of 14.8 ng/ml) of the internal standard (²H₅-fentanyl). After adding 10 µl of concentrated ammonia, the samples were extracted for 15 min by liquid/liquid extraction with 600 µl of methyl tert-butyl ether. After centrifugation at 13,200 rpm for 8 min, the organic phase was transferred to autosampler vials, evaporated to dryness at 40°C under a gentle stream of nitrogen, and reconstituted in 125 µl of 0.5% acetic acid/methanol (90:10, v/v). A volume of 25 µl was injected onto the HPLC column. For the construction of the calibration curve for fentanyl, the following standard solutions were used: 0.118, 0.24, 0.47, 0.94, 1.9, 3.8, 7.5, 15, 30, 60, and 120 ng/ml. The calibration curve was linear in the range from 0.118 to 120 ng/ml (r > 0.999). The lower limit of quantification was 0.118 ng/ml. The accuracy ranged from 87.0 to 96.1% and the precision from 1.9 to 4.0% for concentrations in the range from 0.4 to 50.2 ng/ml.

Pharmacokinetic-Pharmacodynamic Experiments. To minimize the influence of circadian rhythms, all experiments were started between 9:00 and 9:30 AM. Animals were randomly assigned to the treatment groups. Detailed information regarding experimental design is presented in Table 1. Before administration of drug or vehicle, four consecutive baseline tail-flick latencies were obtained in each animal. The measurements were taken at a 15-min interval. The average of the four baseline latencies was taken as the basal latency time. Upon administration of buprenorphine or vehicle via a zero order intravenous infusion using an infusion pump (BAS Bioanalytical Systems Inc., West Lafayette, IN), tail-flick latency was measured at the following predefined time points: dose I, 0, 5, 9, 14, 19, 24, 30, 40, 50, 95, 105, 125, 155, and 185 min after drug administration; dose II, 0, 5, 10, 14, 19, 24, 30, 40, 50, 65, 70, 95, 105, 125, and thereafter every 30 min until 305 min after drug administration; dose III, 0, 5, 10, 14, 19, 24, 30, 40, 50, 95, 105, 125, and thereafter every 30 min until 215 min after drug administration; dose IV, 0, 5, 10, 14, 19, 24, 30, 40, 50, 70, 90, and thereafter every 30 min until 420 min; and dose V, 0, 5, 10, 14, 19, 24, 30, 40, 50, 70, 90, 150, and thereafter every 30 min until 510 min after drug administration. For fentanyl, antinociceptive measurements were performed at dose I: 0, 3, 7, 13, 17, 23, 33, 45, 75, 105, 150, and 180 min; dose II: 0, 3, 7, 13, 17, 23, 33, 45, 55, 75, 105, and 135 min; dose III: 0, 3, 7, 13, 17, 23, 33, 45, 55, 75, 105, 135, 150, 180, and 210 min; dose IV: 0, 5, 15, 25, 35, 43, 55, 65, 80, 105, 150, and 180 min; and dose V: 0, 3, 7, 17, 23, 33, 45, 55, 75, 95, 135, 150, 210, and 240 min after drug administration. In cases where blood sampling coincided with the tail-flick latency measurement, tail-flick latency measurement preceded blood sampling to minimize stress for the animals. Before the start of the infusion, a blank blood sample (100 µl) was withdrawn. Each blood sample withdrawn was replaced by an equal volume of heparinized 0.9% saline (20 IU heparin/ml). This procedure has minimal effects on the pharmacokinetics. In a separate study, it has been demonstrated that the values of the pharmacokinetic parameters obtained in this manner were identical to those obtained in a separate (pilot) study without replacement of the collected blood (unpublished observations). Serial arterial blood samples were collected in heparinized microtubes. Plasma (50 µl) was separated from the blood by centrifugation at 5000 rpm for 15 min and frozen at –20°C until analysis.

PK-PD Modeling Procedure. The pharmacokinetic and pharmacodynamic parameters of buprenorphine and fentanyl were estimated using nonlinear mixed-effects modeling as implemented in the NONMEM software version V, level 1.1 (Beal and Sheiner, 1999). The population analysis approach, which takes into consideration both intra- and interanimal variability, was undertaken using the first-order conditional estimation method with - interaction (FOCE interaction) for pharmacokinetic analysis. All fitting procedures were performed on an IBM-compatible computer (Pentium IV, 1500 MHz) running under Windows NT with the Fortran compiler Compaq Visual Fortan version 6.1. An in-house available S-PLUS 6.0 (Insightful Corp., Seattle, WA) interface to NONMEM version V was used for data processing and management (including automated posterior predictive check and bootstrap) and graphical data display.

Pharmacokinetic Analysis. To determine the basic structural pharmacokinetic for buprenorphine and fentanyl, one-, two-, and three-compartment models were tested. Model selection and identification was based on the likelihood ratio test, pharmacokinetic parameter point estimates, and their respective confidence intervals, parameter correlations, and goodness-of-fit plots. For the likelihood ratio test, the significance level was set at = 0.01, which corresponds with a decrease of 6.6 points, after the inclusion of one parameter in objective function value (OFV) under the assumption that the difference in OFV between two nested models is ² distributed. The following goodness-of-fit plots were subjected to visual inspection to detect systemic deviations from the model fits: individual observed versus population or individual predicted values and weighted residuals versus time or population predicted values. On the basis of model selection criteria, two- and three-compartment models were selected for fentanyl and buprenorphine, respectively. The pharmacokinetic analysis for the selected compounds was performed by use of the ADVAN3 TRANS4 and ADVAN11 TRANS4 subroutines in NONMEM. For example, for fentanyl, the pharmacokinetic parameters, clearance (CL), the intercompartmental clearance (Q), and the volumes of distribution of compartments 1 and 2 (V₁ and V₂) were estimated.

The stochastic part of the model was selected to describe interanimal variability in pharmacokinetic parameters and assumed a log normal distribution of all model parameters over the population. Therefore an exponential distribution model was used to account for interanimal variability:

(1)

in which P_i is the individual value of model parameter P, P_tot is the typical value (population value) of parameter P in the population, and _i is the normally distributed interanimal random variable with mean zero and variance ². The coefficient of variation of the structural model parameters is expressed as percentage of the root mean square of the interanimal variance term. Selection of an appropriate residual error model was based on inspection of the goodness-of-fit plots. On this basis, a proportional error model was proposed to describe residual error in the plasma drug concentration:

(2)

in which C_obs,ij is the jth observed concentration in the ith individual, C_pred,ij is the predicted concentration, and _ij is the normally distributed residual random variable with mean zero and variance ². The residual error term contains all the error terms which cannot be explained and refers to, for example, measurement and experimental error (e.g., error in recording sampling times) and structural model misspecification. Individual empirical Bayes estimates of the pharmacokinetic parameters were obtained from the basic pharmacokinetic model and served as input for the pharmacodynamic model.

To refine the stochastic model, correlation between pharmacokinetic parameter estimates was tested by conducting covariance matrix analysis (OMEGA BLOCK option). A significant correlation between two parameters was assumed when the drop in OFV was more than 6.6 points (p < 0.01). Finally, explorative graphical analysis was performed to explore relationships between body weight and pharmacokinetic parameters. The following equation was used to model the pharmacokinetic parameters as function of body weight (BW):

(3)

in which P_i is the individual value of model parameter P and _i and _j are the intercept and slope of model parameter P versus body weight relationship, respectively. To demonstrate the precision and stability of the pharmacokinetic models and to ascertain accurate prediction of concentration-time profiles of fentanyl and buprenorphine, the final population pharmacokinetic models were subjected to an internal validation (Food and Drug Administration, 1999; Ette et al., 2003). The validation procedure consisted of two components: bootstrap validation procedure and a posterior predictive check. For the bootstrap validation procedure, 1000 data sets were generated randomly sampled from the original data set with replacement. Subsequently, the final population PK models were fitted to the bootstrap replicates one at a time. Finally, the mean, standard error, coefficient of variation, and 95% confidence intervals of all model parameters were calculated and compared with parameter values obtained from the original study. To assess the predictive performance of the population PK models, 1000 data sets were simulated from the original data set and the final model parameter estimates. The median outcome and the 2.5 and 97.5% quantiles were calculated from the simulated buprenorphine and fentanyl concentrations at the predefined time points.

Mechanism-Based PK/PD Analysis. In this study, the tail-flick latency is used as a measure of the drug response. The mechanism-based model describing the complex relationship between drug concentration and pharmacological effect is displayed in Fig. 1. The observed hysteresis in concentration-effect data are traditionally explained by incorporation of a link model. In this model, distribution to the biophase is characterized as a first-order process, which is believed to constitute a correct representation of the rate-limiting step in the in vivo pharmacodynamics. Separation of different biological processes, causing hysteresis (i.e., biophase equilibration, receptor association, and transduction), frequently results in the inability to obtain unique parameter estimates expressing the respective rate-limiting steps (Tuk et al., 1997, 1998; Cleton et al., 1999). To explain hysteresis on the basis of two biological processes, the availability of a detailed data set including different doses and infusion schemes is required. Furthermore, with the antinociceptive effect as a pharmacodynamic endpoint the data analysis is complicated by the presence of censored data (tail-flick latencies above the cut-off value). To allow for estimation of the effect above the censoring value, a maximum likelihood parameter estimation approach was used. This approach requires the specification of a probability distribution for the time at which an animal responds to applied radiant heat. In the statistical literature, several distributions have been proposed to describe time-to-event (also called survival) data; factors such as flexibility and practical implementation (i.e., in NONMEM) suggest the log logistic and Weibull distributions as suitable candidates (Cox and Oakes, 1984). The log logistic distribution is characterized by the median time to response (prediction) and a shape factor determining its width (Z). The probability of observing a tail-flick latency >10 s is given by the area under the log logistic curve from 10 s to infinity. So the log likelihood to be maximized is the sum of terms of either:

(4)

or

(5)

View larger version (14K): [in this window] [in a new window]   Fig. 1. A schematic view of the mechanism-based PK/PD model. The model incorporates different processes to explain time dependencies in pharmacodynamics. The pharmacokinetics describe the disposition of the drug in the plasma and equilibration to the biophase site. At the target site, the drug can bind to the receptor. Upon binding to the receptor, a cascade of transduction processes are activated, ultimately leading to a pharmacological response.

(6)

where k_eo is a first-order distribution rate constant describing the rate of change of drug concentration in the effect compartment and [C_p] represents the plasma concentration and [C_e] the effect-site concentration. At the site of action, the drug can bind to the OP3 receptor. Following the law of mass action, the rate of drug-receptor binding (d[C_eR]/dt) is proportional to the drug concentration [C_e] and the free receptor concentration [R]:

(7)

in which k_on is a second-order rate constant describing the rate of association and k_off is a first-order rate constant describing the rate of dissociation of the drug-receptor complex. Under the assumption that the concentration of drug is in excess compared with the free receptor concentration and that the total number of receptors ([R_tot]) is equal to the sum of drug-bound receptors ([C_eR]) and unbound receptors ([R]), eq. 7 can be rearranged into:

(8)

The total amount of receptors ([R_tot]) could not be measured in vivo and therefore was set to one unity. Receptor binding was directly related to the tail-flick latency time according to the following equation:

(9)

The concentration-effect data for fentanyl were analyzed by the following model (Sarton et al., 2000):

(10)

where E₀ is the baseline tail-flick latency, [C₁₀₀] the effect-site concentration causing 100% increase in tail-flick latency, and a slope parameter. This equation follows from the steady-state solution of eqs. 8 and 9 in which case k_on and k_off are not both identifiable (C₁₀₀ = k_off/k_on).

View larger version (22K): [in this window] [in a new window]   Fig. 2. Individual buprenorphine concentration-time profiles for the treatment groups I–V. The observed concentrations (closed circles) and population predictions (thick line) are depicted. The black boxes represent the duration of infusion.

View larger version (22K): [in this window] [in a new window]   Fig. 3. Individual fentanyl concentration-time profiles for the treatment groups I–V. The observed concentrations (closed circles) and population predictions (thick line) are depicted. The black boxes represent the duration of infusion.

	Results

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Finally, to validate the pharmacokinetic models, a bootstrap validation and a posterior predictive check were conducted. The final population pharmacokinetic estimates for buprenorphine and fentanyl were nearly identical to the estimates obtained by fitting 1000 data sets to the final population PK models. Also, the estimated interanimal variability for the final pharmacokinetic parameters was supported by the bootstrap validation (Tables 2 and 3). The results of the posterior predictive check showed that the population PK models could well predict the time course of buprenorphine and fentanyl concentration after intravenous administration (Fig. 4).

View larger version (27K): [in this window] [in a new window]   Fig. 4. Results of the posterior predictive performance of the population PK models of buprenorphine (left panel) and fentanyl (right panel) for the different treatment groups. The observed concentration (closed circles), 2.5% quantile (bottom solid line), median value (dashed line), and 97.5% quantile (top solid line) are presented. The black boxes represent the duration of infusion. The influence of body weight on the pharmacokinetics of buprenorphine and fentanyl was also taken into account. Body weight was simulated for each animal assuming interanimal variability of body weight is 3.5% (normal distribution) and mean body weight is 0.300 kg.

View larger version (28K): [in this window] [in a new window]   Fig. 5. Changes in tail-flick latency in time following administration of buprenorphine. For each treatment group (I–V), the observed (closed circles) and predicted (solid line) time course of antinociceptive effect is shown.

View larger version (29K): [in this window] [in a new window]   Fig. 6. Changes in tail-flick latency in time following administration of fentanyl. For each treatment group (I–V) the observed (closed circles) and predicted (solid line) time course of antinociceptive effect is shown.

View larger version (17K): [in this window] [in a new window]   Fig. 7. A, concentration-receptor binding relationship. The relationship between effect-site concentration and receptor binding for buprenorphine for all rats. Effect-site concentration (nanograms per milliliter) is depicted on the x-axis on a logarithmic scale, and receptor binding is expressed as fractional receptor occupancy on the y-axis. The closed circles represent the predicted receptor binding. B, receptor binding-effect relationship. The receptor binding versus effect relationship as described by eq. 9 for buprenorphine for all rats. The closed circles represent the predicted tail-flick latency. C, fentanyl concentration-effect relationship. The fentanyl effect-site concentration versus tail-flick latency relationship as described by eq. 10. The closed circles represent the predicted tail-flick latency. The solid line displays the cut-off tail-flick latency time.

	Discussion

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A population PK/PD model for semisynthetic opiates is proposed, which allows separate characterization of the kinetics of target site distribution and the receptor association/dissociation kinetics as determinants of the time course of the antinociceptive effect. It is shown that for buprenorphine, both the target site distribution and the receptor binding kinetics contribute to the observed hysteresis between plasma concentration and effect, whereas for fentanyl, hysteresis is determined by target site distribution only. The pharmacokinetics of buprenorphine and fentanyl were successfully described by a three- and two-compartment model, respectively. All pharmacokinetic parameters, including the estimated stochastic model parameters, were estimated precisely as indicated by the obtained standard errors. Both compounds share similar pharmacokinetic characteristics, with moderate to large steady-state volumes of distribution (0.6 to 1.5 l) and high hepatic clearance values (15 to 20 ml/min for rats weighing 300 g). The high clearance values found for buprenorphine and fentanyl approximate the rat hepatic blood flow and support blood flow limited clearance of fentanyl and buprenorphine found in humans (Bullingham et al., 1980; Stanski, 1987). Finally, PK model validation demonstrated the accurateness and precision of the developed population PK models.

The PK/PD correlation of buprenorphine and fentanyl was determined in the rat using the effect of radiant heat on tail-flick withdrawal as a pharmacodynamic endpoint. Characterization and prediction of the time course of drug effect was complicated by the presence of censored time to response values, which is an inherent limitation of the applied tail-flick rat model. To integrate censored data (latencies above 10 s) in the PK/PD analysis, tail-flick latencies were assumed to be log logistically distributed, and a maximum likelihood parameter estimation approach was used. A similar approach had been successfully applied in other studies (Luks et al., 1998; Sarton et al., 2000). An alternative for the log logistic distribution is the Weibull distribution, which is also often used to describe time-to-event data. From the better performance of the log logistic distribution in comparison with the Weibull distribution, it is concluded that the former better matches the actual distribution of the observed tail-flick latencies.

The present study provides novel information on the pharmacokinetic/pharmacodynamic relationship of buprenorphine and fentanyl. Considering the time course of drug action, usually a combination of different processes is involved in time delays of the biological effect intensity relative to plasma concentration. However, it is often difficult to extract and discriminate those processes from the available PK/PD data (Jusko et al., 1995; Verotta and Sheiner, 1995; Cleton et al., 1999). In this study, the separation of biophase kinetics from the in vivo receptor kinetics is an important feature of the mechanism-based PK/PD model. It is shown that with values of the half-life of biophase equilibration (t_1/2,keo) and the receptor dissociation (t_1/2,koff) of 29 and 9 min, respectively, the rate of onset and offset of antinociceptive effect is predominantly determined by distribution of buprenorphine to the effect site, as is also the case with fentanyl. However, in contrast to fentanyl, the contribution of the slow association/dissociation of buprenorphine to the OP3 receptor is not negligible. The half-life of biophase equilibration (t_1/2,keo) for fentanyl was 5.6 min. These results are consistent with the idea that time dependencies in fentanyl effect can be attributed to blood-brain concentration equilibration. The value of the half-life for biophase equilibration of fentanyl is remarkably similar to values reported by Scott et al. (1991) and Cox et al. (1998) who showed that the half-life of blood-brain equilibration is 6.6 and 2.2 min in rats and humans, respectively, using electroencephalogram effect as pharmacodynamic endpoint. Remarkably, the similarity of these values in humans and rats suggests that the rate constant of biophase equilibration of fentanyl is independent of species similar for the electroencephalogram effect and for antinociception. Due to its high lipophilicity, it is believed that fentanyl readily penetrates the blood-brain barrier (Henthorn et al., 1999). It is reasonable to assume that after blood-brain barrier passage, fentanyl distributes into the brain tissues before it is released to bind to the OP3 receptor. Since both compounds are highly lipophilic, it is likely that buprenorphine distributes to the OP3 receptor in a similar manner, albeit the values of the rate constants can be different.

The association/dissociation kinetics of buprenorphine at the OP3 receptor have also been determined in vitro (Villiger and Taylor, 1982; Boas and Villiger, 1985). Based on those receptor binding studies, two binding affinity sites for buprenorphine have been identified. Dissociation of buprenorphine was characterized by an initial rapid phase (t_1/2,koff = 5.6 min) followed by a slower phase (t_1/2,koff = 166.4 min). The estimated in vivo dissociation half-life for buprenorphine of 9.5 min is in the range of the reported value for the initial rapid phase of the dissociation from the buprenorphine-OP3 receptor complex in vitro. More important, the estimated in vivo equilibration constant K_D for 3.20 ng/ml buprenorphine corresponding to 6.85 nM is in the same range as the in vitro dissociation equilibration constant, for which the values of 0.12 nM for the high-affinity binding site and 1.38 nM for the low-affinity binding site in the spinal cord and 1.0 nM for the binding site in the brain have been reported (Villiger and Taylor, 1982). It should be noted that the estimated in vivo K_D is calculated on the basis of total plasma concentrations. Correction for the free fractions in plasma will result in an even greater similarity of the K_D values. For buprenorphine, no information on the free fraction is available, which can be explained by the physicochemical properties of buprenorphine. Notably, the lipophilicity of buprenorphine complicates accurate measurement of the free fraction (sticking of buprenorphine to the membrane filter).

These results demonstrate the usefulness of this mechanism-based PK/PD model to explore in vitro-in vivo K_D correlations. Similar correlations have been reported for calcium channel antagonists using a receptor association/dissociation model (Shimada et al., 1996) and also for A₁ adenosine receptor agonists and GABA_A receptor modulators using a different mechanism-based PK/PD model based on receptor theory (Van der Graaf et al., 1999; Visser et al., 2003). Moreover, the ability to estimate an in vivo K_D allows a strict quantitative comparison with the antinociceptive effect of other compounds. An important issue is the potency and intrinsic activity of buprenorphine relative to fentanyl. Interestingly, estimates of in vivo potency of buprenorphine and fentanyl are in close agreement and show that both compounds display equiantinociceptive potency (3.20 versus 3.51 ng/ml). The estimated C₁₀₀ for fentanyl is obtained from eq. 10. This equation follows from the steady-state solution of eqs. 8 and 9, in which case k_on and k_off are not identifiable. Under steady-state conditions, C₁₀₀ equals k_off/k_on = K_D and therefore K_D and C₁₀₀ can be used to compare in vivo potency of buprenorphine and fentanyl. In addition, the relative in vivo potency of drug and metabolite or drugs exhibiting enantiomeric isoforms can be explored using an integrated mechanism-based PK/PD modeling approach (Zuideveld et al., 2002). For instance, it is postulated that buprenorphine's major metabolite, norbuprenorphine, possesses a 50-fold weaker antinociceptive activity than the mother compound (Ohtani et al., 1995). In the present study, the plasma concentrations of buprenorphine's major metabolite, norbuprenorphine, were also measured. However, the norbuprenorphine plasma concentrations were far below the concentration range, reflecting buprenorphine's antinociceptive effect (Fig. 8). Therefore, it was assumed that the contribution of norbuprenorphine to the overall analgesic effect is minimal. An important question is whether buprenorphine acts as a full agonist (i.e., displays full antinociceptive effect). Mechanism-based PK/PD models provide a unique basis to characterize the effects of drugs in terms of in vivo potency and intrinsic activity (E_max). In recent years, this approach has been successfully applied to explore the concentration-effect relationships of several compounds belonging to different drug classes (Van der Graaf et al., 1999; Visser et al., 2002). In the present investigation, maximal antinociceptive effect could not be estimated from the concentration-effect relationships. We relate this to the fact that in this tail-flick rat model, stronger stimuli lead to a higher response, ultimately leading to complete antinociception. Consequently, no E_max is observed, and no distinction can be made between partial and full antinociceptive response during analysis. Furthermore, drug efficacy estimation is hampered by the fact that above the cut-off value only a probability distribution-based prediction of the antinociceptive behavior is provided. For some animals receiving the highest buprenorphine dose (0.1 mg/kg), the maximal predicted tail-flick latency time is equal to or lower than the maximal predicted tail-flick latency time resulting from 0.06 mg/kg administration. This seems consistent with data derived from previous animal studies supporting the concept of ceiling effect for antinociception (Cowan et al., 1977a,b; Dum and Herz, 1981). However, on the basis of the present results, no conclusions can be drawn regarding an eventual difference in the intrinsic efficacy of buprenorphine relative to fentanyl.

View larger version (20K): [in this window] [in a new window]   Fig. 8. Representative individual concentration versus time profiles for buprenorphine and its metabolite norbuprenorphine. The observed buprenorphine concentrations (closed circles), norbuprenorphine concentrations (closed triangles), and individual predicted buprenorphine concentrations (dashed line) are depicted.

	Acknowledgements

 
We gratefully acknowledge the technical assistance of S. M. Bosvan Maastricht. We thank Dr. Michael Gautrois and Dr. Rolf Terlinden as well as Nicole Kohl, Klaus Malmendier, and Jürgen Weiher for skillful support with the bioanalytical measurements performed in the frame of this work.

	Footnotes

 
Financial support by Grünenthal GmbH, Aachen, Germany is gratefully acknowledged.

doi:10.1124/jpet.104.082560.

ABBREVIATIONS: PK/PD, pharmacokinetic/pharmacodynamic; HPLC, high-performance liquid chromatography; LC/MS/MS, liquid chromatography/mass spectrometry/mass spectrometry; BW, body weight; CI, confidence interval; OFV, objective function value.

Address correspondence to: Dr. Meindert Danhof, Leiden/Amsterdam Center for Drug Research, Division of Pharmacology, Gorlaeus Laboratories, P.O. Box 9502, 2300 RA Leiden, The Netherlands. E-mail: m.danhof{at}lacdr.leidenuniv.nl

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