Abstract
The neuroactive steroid alphaxalone reveals a complex biphasic concentration-effect relationship using the 11.5 to 30 Hz frequency band of the electroencephalogram (EEG) as biomarker. The purpose of the present investigation was to develop a mechanism-based pharmacokinetic-pharmacodynamic model to describe this observation. The proposed model is based on receptor theory and aims to separate the drug-receptor interaction from the transduction of the initial stimulus into the observed biphasic response. Individual concentration-time courses of alphaxalone were obtained in combination with continuous recording of the EEG parameter. Alphaxalone was administered intravenously in various dosages. The pharmacokinetics were described by a two-compartment model, and parameter estimates for clearance, intercompartmental clearance, volume of distribution 1 and 2 were 158 ± 29 ml · min−1 · kg−1, 143 ± 31 ml · min−1· kg−1, 122 ± 20 ml · kg−1 and 606 ± 48 ml · kg−1, respectively. Concentration-effect relationships exhibited a biphasic pattern and delay in onset of effect. The hysteresis was described on the basis of an effect-compartment model with Cmax as covariate. The pharmacodynamic model consisted of a receptor model, featuring a monophasic saturable receptor activation model in combination with a biphasic stimulus-response model. The in vivo affinity (KPD) was estimated at 432 ± 26 ng · ml−1. Unique parameter estimates were obtained that were independent of the dose and the duration of the infusion. In conclusion, we have shown that this mechanism-based approach, which separates drug- and system-related properties in vivo, was successfully applied for the characterization of the biphasic effect versus time patterns of alphaxalone. The model should be of use in the characterization of other biphasic responses.
The sedative-hypnotic and anesthetic properties of a wide range of natural and synthetic steroids were first shown by Selye (1942). This initial work led to the introduction of the synthetic neuroactive steroid alphaxalone (5α-pregnan-3α-ol-11,20-dione) into clinical medicine (Sear, 1996). Alphaxalone exerts its selective action via a specific binding site at the GABAA receptor complex and does not interact with any of the classical cytosolic hormonal steroid receptors (Paul and Purdy, 1992; Lambert et al., 1995). Detailed mechanistic investigations have revealed a dual mechanism of action for alphaxalone. Low concentrations of alphaxalone allosterically modulate the amplitude of GABA-induced ion currents, whereas alphaxalone at higher concentrations (≥1 μM) acts as an agonist, similar to that observed by barbiturates (Cottrell et al., 1987; Paul and Purdy, 1992;Lambert et al., 1995). Recently, there has been a renewed interest in neuroactive steroids in relation to the development of novel strategies for the treatment of anxiety, insomnia, migraine, depression, and seizure disorders (Gasior et al., 1999). However, very few attempts have been made to study neuroactive steroids in vivo on the basis of an integrated PK/PD approach.
In recent years, considerable progress has been made in the elucidation of the PK/PD models of drugs acting at GABAAreceptors (i.e., allosteric modulators such as benzodiazepines and the GABA re-uptake inhibitor tiagabine) using quantitative EEG parameters as pharmacodynamic endpoint (Danhof and Mandema, 1992; Cleton et al., 1999a) . In a preliminary in vivo PK/PD study, alphaxalone was shown to exhibit biphasic EEG effects (Visser et al., 1990). The time-EEG effect profiles showed an increase in effect at low drug concentrations and a decrease in effect at higher drug concentrations. Similar biphasic patterns have been observed for general anesthetics, such as propofol, heptabarbital, amobarbital, and thiopental (Mandema and Danhof, 1990;Ebling et al., 1991; Mandema et al., 1991; Cox et al., 1998b).
Several methods have been proposed to characterize biphasic drug concentration-effect relationships. The most frequently used method is a nonparametric analysis of the concentration-effect data (Ebling et al., 1991). In this method, descriptive pharmacodynamic parameters are obtained on the basis of linear interpolation between the data points. A limitation of this approach is that it is entirely descriptive, with no predictive or explanatory value. Another method to characterize biphasic PK/PD relationships is a biphasic model constructed from various combinations and modifications of the nonlinear sigmoidEmax model, which was first proposed by Paalzow and Edlund (1979) and applied by Mandema and Danhof (1990). This model was based on the observation that biphasic effects were mediated by multiple (two) receptor responses. Although this dual effect model is conceptually simple and relatively easy to parameterize, good parameter estimates can only be obtained if the ratio between the IC50 and the EC50 is at least 300 (Dutta and Ebling, 1997). Furthermore, the mechanistic basis of such a model is not always clear.
In recent years, an important development in PK/PD analysis has been the design of an entirely new class of mechanism-based PK/PD models (Van der Graaf and Danhof, 1997). A specific feature of these models is that a clear separation is made between a drug-specific part, characterizing the drug receptor interaction in terms of in vivo affinity and intrinsic efficacy, and a system-specific part, characterizing the in vivo stimulus-response relationship (Cox et al., 1998a; Tuk et al., 1999; Van der Graaf et al., 1999; Zuideveld et al., 2001). To date, in this approach both linear and nonlinear (hyperbolic) stimulus-response relationships have been considered. In theory, however, a stimulus-response relationship can take any shape and it can also be biphasic.
In this investigation, we propose a mechanism-based PK/PD model in which the initial receptor activation is monophasic and saturable, whereas the subsequent transduction is biphasic. In the model, the receptor activation is described by a hyperbolic function and the biphasic transduction part by a parabolic function (see Fig.1). To validate the model, we have obtained high resolution concentration and effect data for the synthetic neuroactive steroid alphaxalone in several dosages and infusion rates.
Materials and Methods
Animals and Surgical Procedures.
Male Wistar rats (301 ± 7 g, n = 44; Charles River BV, Zeist, The Netherlands) were used in this investigation. Following surgery, the rats were housed individually in standard plastic cages with a normal 12-h day/night schedule (lights on 7 AM) at a temperature of 21°C. The animals had access to standard laboratory chow (RMH-TM; Hope Farms, Woerden, The Netherlands) and acidified water ad libitum.
Nine days before the start of the experiments seven cortical electrodes were implanted into the skull as described before (Mandema and Danhof, 1990). Briefly, the electrodes were placed at the locations 11 mm anterior and 2.5 mm lateral (Fl and Fr), 3 mm anterior and 3.5 mm lateral (Cl and Cr), and 3 mm posterior and 2.5 mm lateral (Ol and Or) to lambda. A reference electrode was placed on lambda. Stainless steel screws were used as electrodes and connected to a miniature connector, which was insulated and fixed to the skull with dental acrylic cement. The surgical procedures were performed under anesthesia with 0.1 mg · kg−1 i.m. of medetomidine hydrochloride (Domitor; Pfizer, Capelle a/d IJssel, The Netherlands) and 1 mg · kg−1 s.c. of ketamine base (Ketalar; Parke-Davis, Hoofddorp, The Netherlands). After the first surgery, 4 mg of ampicillin (A.U.V., Cuijk, The Netherlands) was administered to aid recovery.
Three days before the start of the experiment, indwelling cannulae were implanted in the right femoral artery for the serial collection of arterial blood samples and in the right jugular vein for drug administration. The cannulae were filled with heparinized 25% (g/v) polyvinylpyrrolidone in saline (Brocacef, Maarssen, The Netherlands) and tunneled subcutaneously to the back of the neck where they were exteriorized and fixed with a rubber ring. The protocol of this investigation was approved by the Ethical Committee on Animal Experimentation of Leiden University.
Drugs and Dosages.
Alphaxalone (5α-pregnan-3α-ol-11,20-dione) was purchased from Sigma-Aldrich BV (Zwijndrecht, The Netherlands). Rats were randomly assigned to six treatment groups of 6 to 8 rats that each received a zero-order intravenous infusion of alphaxalone over 5 or 15 min. A summary of the various infusion regimens is given in Table1. Two different vehicles were used to formulate alphaxalone: 1) 100 μl of dimethyl sulfoxide (DMSO; Baker, Deventer, The Netherlands); and 2) 100 μl of 25% (w/v) 2-hydroxypropyl-β-cyclodextrin (HPβCD; Sigma-Aldrich BV). Vehicle controls were included in all treatment groups.
Pharmacokinetic-Pharmacodynamic Experiments.
All experiments were started between 830 and 930 AM to exclude influences of circadian rhythms. The rats were placed in a rotating drum to control the level of vigilance, thereby avoiding the interference of sleep patterns. During the experiments, the rat was deprived of food and water. Two bipolar EEG leads (Cl-Ol) and Cr-Or) were continuously recorded using a Nihon-Kohden AB-621G Bioelectric amplifier (Hoekloos BV, Amsterdam, The Netherlands) and concurrently digitized at a rate of 256 Hz using a CED 1401plus interface (Cambridge Electronic Design Ltd., Cambridge, UK). The digitized signal was fed into a Pentium III computer and stored on a hard disk for off-line analysis. After recording the EEG baseline for 45 min, a zero-order intravenous infusion of alphaxalone was administered to the conscious and freely moving rats using an infusion pump (BAS Bioanalytical Systems Inc., West Lafayette, IN). The EEG recordings lasted until 120 min after the end of the infusion. For each 5-s epoch, quantitative EEG parameters were obtained off-line by fast Fourier transformation with a user-defined program within the data analysis software package Spike 2 for Windows, version 3.18 (Cambridge Electronic Design Ltd.). Amplitudes in the β-frequency band of the EEG (11.5–30 Hz) averaged over 25-s time intervals were used to quantify the drug effect. Serial arterial blood samples were collected at predefined time intervals in heparinized tubes and centrifuged at 5000 rpm for 15 min for plasma collection. Total volume of redrawn blood samples was kept equal to 2.1 ml during each experiment. Drug samples were stored at −20°C until HPLC analysis.
HPLC Analysis.
Alphaxalone plasma concentrations were determined using HPLC as described before (Visser et al., 2000). Briefly, to 50 μl of plasma, 50 μl of the internal standard (1.5 μg · ml−1 pregnenolone dissolved in acetonitrile) was added. Subsequently, 200 μl of acetonitrile was added to precipitate plasma proteins. After centrifugation, the supernatant was transferred to a clean tube and 50 μl of 2 M NaOH and 25 μl of dansylhydrazine solution (20 mg in methanol acidified with 40 μl of sulfuric acid) were added. After incubation at room temperature for 20 h at a dark place, 500 μl of 1 M NaOH and 5 ml of dichloromethane were added, and the mixture was vortexed for 5 min. The phase system was centrifuged for 15 min at 4500g, and the organic phase was transferred to a clean tube and evaporated under reduced pressure on a vortex vacuum evaporator (Labconco Corp., Kansas City, MO) at 37°C. The residue was dissolved in 100 μl of mobile phase, of which a volume of 50 μl was injected into the HPLC system.
The HPLC system consisted of a Waters 501 solvent delivery pump, a Waters 717plus autosampler (Millipore-Waters, Milford, MA) and a Jasco FP 1520 intelligent fluorescence detector (Jasco Co., Tokyo, Japan). Chromatography was performed on a C18 3-μm cartridge column (100 × 4.6 mm i.d.; Chrompack, Bergen op Zoom, The Netherlands) equipped with a guard column. The mobile phase consisted of a mixture of 25 mM acetate buffer (pH 3.7) and acetonitrile (45:55 v/v). Flow rate was 1 ml · min−1. Fluorescence detection occurred at excitation wavelength 332 nm and emission wavelength 516 nm. Data acquisition and processing was performed using a Chromatopac C-R3A reporting integrator (Shimadzu, Kyoto, Japan). Linear calibration curves were obtained in the range 0.01 to 10 μg · ml−1 (r > 0.990,n = 17), and the limit of quantification was 0.01 μg · ml−1. The intra-assay coefficients of variation for 0.25 and 2.5 μg · ml−1were 6 and 8% (n = 10) whereas the interassay coefficients of variation were 16 and 12% (n = 28), respectively.
In Vivo Protein Binding.
Plasma protein binding was determined in vivo after administration of 2, 5, and 10 mg kg−1 in 5 min. For each dose level, three rats were used. From each rat, 2-ml blood samples were drawn at 5 and 25 min after administration of alphaxalone and collected in heparinized glass tubes. The tubes were centrifuged for 10 min at 5000 rpm to collect plasma. From each tube, two plasma samples of 50 μl were taken, and the remaining plasma was centrifuged at 37°C (15 min, 2000 relative centrifugal fields) using an ultrafiltrate device (Centrifree; Millipore, Bedford, MA). Two samples of at least 100 μl of ultrafiltrate were taken. After sample preparation, the plasma and ultrafiltrate samples were analyzed on the HPLC. The free fraction (fu ) was calculated by dividing the free concentration in ultrafiltrate by the total (bound and free) concentration in plasma
Pharmacokinetic Data Analysis.
In a population approach, the alphaxalone plasma concentration-time profiles of all individual rats in the different treatment groups were fitted simultaneously while explicitly taking into account both intraindividual variability in the model parameters as well as interindividual variability. A two-compartment model was selected for all compounds on the basis of the Akaike information criterion. The concentration-time courses were modeled according to the following equations.
The interindividual variability of these parameters was modeled according to an exponential equation.
The model was implemented in the ADVAN6 subroutine in NONMEM (version V, NONMEM project group, University of California, San Francisco, CA). The first order estimation method with interaction (FOCE INTERACTION) was used to estimate the population θ, ω2, and ς2. From individual Bayesian post hoc parameter estimates, CL, Q,V1,V2, volume of distribution at steady state (Vdss) and two half-lives were calculated following standard procedures.
After covariate analysis and visual inspection, CL and Qwere modeled as function of body weight.
Hysteresis Minimization.
Hysteresis was characterized on the basis of an effect-compartment model. In the effect-compartment approach, it is assumed that the rate of onset and offset of effect is governed by the rate of drug distribution to and from a hypothetical “effect-site” (Sheiner et al., 1979). Under this interpretation, the effect compartment is linked to the plasma compartment by a first order rate constant k1e
and with a rate constant for drug loss keo
. The rate of change of the drug concentration in the effect compartment can then be expressed by the following differential equation.
The Mechanism-Based Model.
In this investigation, amplitudes in the β-frequency range were used as measure of the drug response. The relationship between drug concentration and pharmacological effect is shown in Fig. 1. The drug, which is present at the effect-site, produces upon binding to the receptor a stimulus that is followed by a cascade of signal-transduction processes leading to the ultimate response. The definition of a drug-mediated response in terms of the occupation theory, first proposed by Stephenson and Furchgott (seeKenakin, 1997), consists of a drug receptor binding part resulting in a stimulus.
In a recent application of this model to characterize the relationshipf between initial stimulus and observed pharmacological effects of benzodiazepines, a natural cubic spline was used, where the knots of the spline were placed at equidistant intervals on the stimulus axis (Tuk et al., 1999). Important characteristics of this relationship were the relatively small increase in effect at low stimulus intensities, the steeper increase in effect at higher stimulus intensities, and that no maximum was observed in this relationship. In this investigation, however, alphaxalone showed a biphasic EEG effect, and the maximal increase in effect was 2 to 3 times higher compared with benzodiazepines. Furthermore, at higher concentrations the effect decreased under baseline toward 0 μV (isoelectric EEG). This implied a physiological maximum of the stimulus (i.e., 0 μV is the maximal stimulus of 1). Therefore, the ePD
of alphaxalone was fixed at 1 in this receptor model (eq. 15). The relationship f between the initial stimulus (S) and the observed EEG effect (E) was characterized by a biphasic function.
Rearranging eq. 16 results in
Statistical Analysis.
Goodness-of-fit was analyzed on the basis of visual inspection and the value of the objective function. Model selection was based on the Akaike information criterion (Akaike, 1974) and assessment of parameter correlation. Statistical analysis was performed using one-way analysis of variance and a Tukey-Kramer multiple comparison test. In case of nonhomogeneity as determined by Bartlett's test, the nonparametric Kruskal-Wallis test was used. Statistical tests were performed using InStat version 3.0 for Windows (GraphPad Software, Inc., San Diego, CA). All data are represented as mean ± S.E.M and p < 0.05 was considered significant.
Results
Pharmacokinetics.
Figure 2 shows the observed predicted population and individual alphaxalone plasma concentration time profiles for the six treatment groups. A two-compartment model best described the pharmacokinetic profiles, and pharmacokinetic parameters were found to be dependent on body weight. Population estimates and averaged Bayesian post hoc parameter estimates are summarized in Table 2. An exponential relationship between the values of the parameters CL and Qversus body weight was observed. CL and Q were defined as 158 · BW1.67 and 143 · BW1.67 (ml · min−1 · kg−1), respectively. V1 andV2 were linearly dependent on body weight. For group A, post hoc parameter estimates forV2 were significantly lower. However, for volume of distribution, a coefficient of variation of 48% was observed. Alphaxalone showed a distribution half-life of 0.8 ± 0.1 min and an elimination half-life of 14.2 ± 0.7 min (mean ± S.E.M., n = 44). The dose of 9 mg · kg−1 alphaxalone was administered in two vehicles (DMSO and HPβCD, groups E and F). Parameter estimates were not affected by the vehicle as is shown in Table 2. The free fraction of alphaxalone in plasma was 3.2 ± 0.3% (n = 18). Protein binding was independent of dose, concentration, or time.
In Vivo EEG Time Course of Alphaxalone.
The observed and predicted EEG effect-time course and the predicted concentration time course of alphaxalone is depicted in Fig.3 for representative individuals in each treatment group. The EEG effects, expressed as absolute amplitude in 11.5 to 30 Hz band versus time, revealed a biphasic pattern. Upon the start of the infusion, the amplitude immediately increased, followed by a partial decrease. After the end of the infusion, effect returned to the same height and then gradually returned to baseline. The partial decrease in amplitude appeared to be correlated to a state of unconsciousness of the rats and was deeper with higher dosages. Baseline EEG effect was 10.6 ± 0.3 μV (mean ± S.E.M.,n = 44) and similar for each group. Visual inspection revealed that the initial and second peak reached equal heights in each individual rat and were defined asEtop in the model. The depth of the partial decrease increased with dose and reached amplitudes of only 0 to 3 μV (isoelectric EEG) with the highest dosages (E and F). The first EEG peak was reached within 0 to 2 min during infusion except for the 15-min infusion, where the first peak was reached after ∼5 min. The second peak was reached between 5 and 25 min after stopping the infusion and was later with higher dosages.
The maximal increase in EEG effect upon baseline of alphaxalone (22 μV) was 2 to 3 times higher compared with the monophasic patterns of benzodiazepines, such as for diazepam, which revealed a maximum increase of 9 μV in the same experimental set-up (unpublished observations). Also in contrast to benzodiazepines, alphaxalone showed a biphasic effect-time course in all frequency bands. In control experiments, the vehicles DMSO and HPβCD did not affect the EEG amplitudes (data not shown).
Hysteresis.
All individual plasma concentration-effect relationships were biphasic and showed a hysteresis loop (see Fig.4, left panel). The maximal increase in effect was the same for each individual and dose. At ∼250 ng · ml−1 the amplitudes started to increase andEtop was reached at a concentration of ∼1000 ng · ml−1. Midpoint location for the increasing limb of the concentration-effect relationship was ∼550 ng · ml−1. The decreasing limb, at concentrations higher than ∼1000 ng · ml−1 showed a larger hysteresis loop at higher concentrations, as shown in Fig. 4, left panel.
Hysteresis was minimized both nonparametrically (keo-nonpar) and parametrically (keo-par). With both methods, the hysteresis loop could be successfully minimized, although the parametric approach yielded more accurate parameter estimates. Estimates of keo were lower with increasing concentrations (reflecting the increase in loop with higher dosages) as depicted in Table 3 and in Fig. 5. Estimation ofkeo as a function of the maximal reached concentration (keo,app ) successfully minimized the concentration-dependent hysteresis. Maximal hysteresis with the highest dosages showed that thekeo for alphaxalone is 0.33 ± 0.08 min−1, which corresponds to a half-life ofkeo of 2.1 min. Estimates forkeo,app were not different fromkeo-nonpar andkeo-par, except for group C. Although the plasma kinetics and time course of pharmacological effect varied, the apparent effect-site concentration-effect relationship was consistent between animals (see Fig. 4, right panel).
Mechanism-Based PK/PD Modeling.
In the mechanism-based PK/PD approach, the plasma concentrations and EEG effects were fitted using the mechanism-based model and the link model. All the individual plasma concentration-effect profiles were successfully described using the mechanism-based PK/PD model, yielding estimates forkeo,app , KPD ,a and b. The pharmacodynamic parameter estimates are depicted in Table 4. Figure 3 shows the predicted effect versus time profile, and Fig. 4 shows the predicted plasma concentration and predicted effect-site concentration versus effect relationship for representative rats. The relationship for the effect-site concentration versus stimulus for all rats (n = 44) is shown in Fig.6A. PopulationKPD was estimated at 432 ± 26 ng · ml−1, whereasePD was fixed at 1, due to the fact that the effects at maximal stimulus reached a physiological maximum. The mean parameter estimates for KPD did not significantly differ between the groups, although groups A and F were slightly outside the 95% confidence interval of the population estimate. In Fig. 6B, the biphasic stimulus-effect relationship for all individual rats (n = 44) is shown. The stimulus-effect relationship was described using eq. 16: E = 32 ± 0.8 − 108 ± 6 · (S3− 0.44 ± 0.01)2. CalculatingEtop from individualE0 using eq. 18 and averaging resulted in the value for Etop: 32.0 ± 0.8 μV (mean ± S.E.M., n = 44). Mean post hoc parameter estimates for a and bwere not significantly different between the groups. The intraindividual residual variability was 16%. The drug-receptor interaction and the following stimulus-effect relationship were consistent for all animals and treatment groups.
Discussion
Alphaxalone Pharmacokinetics.
Alphaxalone pharmacokinetics were successfully described by a two-compartment model. The observed alphaxalone distribution and elimination half-life (0.8 and 14 min, respectively) are in agreement with a previous investigation, reporting a half-life of 7 min (Child et al., 1972). The clearance of alphaxalone (158 · BW1.67 ml · min−1 · kg−1) was approximately equal to the rat liver blood flow (∼20 ml · min for a rat weighing 300 g). Blood flow-dependent elimination can explain that body weight was an important covariate of the clearance. It has been shown that alphaxalone is rapidly metabolized to inactive metabolites by the hepatic mixed function oxygenase system (Sear and McGivan, 1981). A fast hepatic clearance and low oral bioavailability was also reported for humans (Sear, 1996). The volume of distribution (V2) for the lowest dose (group A) was significantly lower than for the other groups. An explanation might be that the mean protein-binding is different in this group or alternatively, that there is a dose-dependent (fat) tissue distribution. It has been reported that alphaxalone exhibits a uniform distribution throughout the body, except for a slight accumulation in the fat and brain tissue (Pastorino et al., 1979). A Michaelis-Menten type of pharmacokinetic elimination was unlikely, since in this investigation the maximum in vivo concentrations (Cmax) of alphaxalone only exceeded the in vitro Km for cytochrome P450 (∼8.3 μg/ml; Sear and McGivan, 1981) at dosages higher than 9 mg · kg−1.
In this investigation, the plasma protein-binding of alphaxalone was ∼97% and no dose, concentration, or time dependence was observed.Child et al. (1972) reported a protein-binding between 35 and 44% in rats. However, it cannot be excluded in that study that unbound metabolites of alphaxalone were a masking factor, since protein-binding was measured using radioactive-labeled alphaxalone in contrast to our sensitive and selective HPLC method. A qualitative determination showed that alphaxalone binds to albumin and β-lipoprotein in rats (Jones, 1972).
Hydroxypropyl-β-cyclodextrin did not alter alphaxalone pharmacokinetic and pharmacodynamic parameter estimates (groups E versus F). This was also reported for the bioavailability and onset of effect of pregnanolone and pregnenolone (Brewster et al., 1995).
Alphaxalone Pharmacodynamics and Hysteresis.
The biphasic pattern and counter clockwise hysteresis, observed for the concentration-effect relationship of alphaxalone, are common for general anesthetics (Mandema and Danhof, 1990; Ebling et al., 1991;Mandema et al., 1991; Cox et al., 1998b). In all these reports hysteresis has been minimized by postulating a hypothetical effect-compartment. For propofol and thiopental, the values for the half-life keo were between 1 and 3 min (Ebling et al., 1991; Cox et al., 1998b), which is the same range as alphaxalone. In these investigations, the resolution of concentration-effect data was not always sufficient to be able to detect concentration-dependent hysteresis. Some indication for similar concentration dependence of keo might be that Mandema and Danhof (1990) have reported that two equilibration rate constants existed for dual effects of heptabarbital. And in another report nonsteady-state conditions for equilibration rate constants have been assessed by the estimation of a biophase equilibrium time (Mandema et al., 1991).
An explanation for the concentration dependence ofkeo may be the occurrence of concentration-dependent cardiovascular or hemodynamic side-effects. Administration of alphaxalone has been shown to affect heart-rate and aortic pressure in the rat and man in a concentration-dependent manner (Sear, 1996). Other i.v. anesthetic agents such as thiopental and propofol in most conditions also cause a drop in cerebral blood flow and consequently diminish their own rate of transport to the brain assuming that this transport is perfusion rate-limited (Upton et al., 2000). Another explanation for the concentration-dependent hysteresis might be a saturable transport to the site of action, to the brain. However, to date, no specific neuroactive steroid transporters have been demonstrated at the blood-brain barrier. Calculation of polar surface area indicated that alphaxalone should be able to pass the blood-brain barrier easily by the transcellular route (Kelder et al., 1999).
Mechanism-Based PK/PD Modeling.
Although several methods have been described to characterize biphasic drug concentration-effect relationships, all these approaches are rather empirical (Mandema and Danhof, 1990; Ebling et al., 1991; Dutta and Ebling, 1997). In the present investigation we have developed a mechanism-based PK/PD approach to describe the biphasic concentration-effect relationship of alphaxalone. Although the parabolic stimulus-response function is an empirical equation, the separation of the drug-receptor interaction from the biphasic stimulus-response relationship is an important feature of this mechanism-based PK/PD model. In principle the drug-specific properties (i.e., receptor affinity and intrinsic efficacy) can be determined in in vitro test systems. The system-related properties (related to transduction processes) on the other hand can only be obtained in vivo. The latter are unique in the sense that they are identical regardless of the drug that is administered.
An important example of a mechanism-based model is the operational model of agonism (Black and Leff, 1983). This model is based on the assumption that the unique stimulus-effect relationship is hyperbolic in nature. Recently, this model has been successfully applied in in vivo investigations to predict tissue selectivity for low efficacy adenosine A1 receptor agonists (Van der Graaf et al., 1999), receptor reserve for μ-opioid receptor agonists (Cox et al., 1998a) and to explain functional adaptation in epilepsy models (Cleton et al., 1999b). In another mechanism-based modeling approach, based on the occupancy receptor theory, a stimulus-effect relationship was found for benzodiazepines, which was a nonparameterized monotonously increasing function without a maximum (Tuk et al., 1999).
In the present investigation, alphaxalone revealed a 2 to 3 times higher increase in absolute EEG effect relative to benzodiazepines, which indicated a system maximum of the EEG. Furthermore, a decrease in amplitudes at high concentrations was observed which decreased under baseline and reached isoelectric EEG (i.e., physiological minimum). Based on literature, a biphasic stimulus-EEG effect relationship upon binding was proposed, which should be unique for this system. In this investigation, this biphasic stimulus-response relationship was characterized, whereas in subsequent investigations, the mechanism-based PK/PD model is validated. Other neuroactive steroids, like alphaxalone, show all biphasic concentration-response relationships in vivo (unpublished observations).
It is known that neuroactive steroids are general anesthetics, which act by selective binding on ligand-gated ion channels, specifically at the GABAA receptor (Yamakura et al., 2001). Neuroactive steroids, but also barbiturates, show biphasic EEG effects in vivo. Although much has been reported about the cause of biphasic effects, still no definite consensus has been reached. One explanation, which can be ruled out, is the formation of a metabolite that acts as an antagonist on the EEG effect at higher concentrations. It has been shown that alphaxalone is rapidly metabolized only into metabolites that are pharmacologically inactive (Child et al., 1972; Sear and McGivan, 1981).
An explanation that suggests the involvement of several receptor systems with opposite effects (Paalzow and Edlund, 1979) is unlikely. Although brain region-dependent variation in binding and function of GABAA receptor has been reported (Lambert et al., 1995; Yamakura et al., 2001), it appears that the biphasic effects of neuroactive steroids are not related to receptor heterogeneity but that in various tissues the efficacy of GABAA receptor modulators varies due to the dual actions that they have on GABAA receptor channels: i.e., the allosteric modulation of GABA binding and direct channel activation at higher concentrations (Srinivasan et al., 1999). It has been shown that neuroactive steroids can produce biphasic responses via single neurons (MacIver and Roth, 1987; Dallwig et al., 1999), (recombinant) receptors (Lambert et al., 1995; Hill Venning et al., 1996), and in hippocampal CA1 pyramidal cell (Burg et al., 1998). This is in agreement with another report that suggested that GABAA receptor response may change from inhibitory to excitatory, depending on the frequency (i.e., intensity) of stimulation (Archer and Roth, 1999). The fact that other GABAA receptor ligands such as barbiturates showed biphasic EEG effects supports the suggestion that the transduction cascade leading to the effect which follows the receptor activation is biphasic.
The estimated in vivo KPD for alphaxalone of 432 ± 26 ng · ml−1 is in the range of values reported for the (indirect) inhibition of35S-t-butylbicyclophosphorothionate binding by alphaxalone, for which the IC50 varied between 110 and 180 ng · ml−1 (Hill Venning et al., 1996; Anderson et al., 1997) and values reported for in vitro functional studies with recombinant receptors, for which the EC50 was ∼730 ng · ml−1 (Hill Venning et al., 1996). Using this mechanism-based PK/PD approach for the determination of the in vivoKPD will allow comparison between biphasic EEG effects of other compounds, but also between these biphasic EEG effects and other pharmacodynamic endpoints in vivo and in vitro studies.
In conclusion, in this mechanism-based PK/PD approach, in vivo biphasic concentration-effect relationships have been successfully described. The in vivo affinity of alphaxalone was estimated and a biphasic stimulus-effect relationship was parameterized. This mechanism-based biphasic PK/PD model can be further extended in the investigation of GABAA receptor modulation by other neuroactive steroids and benzodiazepines.
Acknowledgments
We gratefully acknowledge Erica Tukker for excellent technical assistance.
Footnotes
-
Preliminary results were presented at the British Pharmacological Society meeting January 2000 [Visser SAG, Smulders CJGM, Van der Graaf PH, and Danhof M (2000) Biphasic and dose-dependent in vivo time course of GABAA-receptor-mediated EEG effects of the neurosteroid alphaxalone, in rats. Br J Pharmacol129:81].
- Abbreviations:
- PK/PD
- pharmacokinetic-pharmacodynamic
- EEG
- electroencephalogram
- HPLC
- high pressure liquid chromatography
- CL
- total body clearance
- Q
- intercompartmental clearance
- V1 and V2
- volumes of distribution of compartment 1 and 2
- Vdss
- volume of distribution at steady state
- Cmax
- maximal concentration reached in plasma
- DMSO
- dimethylsulfoxide
- HPβCD
- 2-hydroxypropyl-β-cyclodextrin
- fu
- fraction unbound
- keo
- equilibration rate constant for hysteresis
- E0
- baseline EEG
- Etop
- maximal EEG effect
- ePD
- in vivo drug efficacy
- KPD
- in vivo drug affinity
- a
- coefficient determining steepness of the parabola
- b
- stimulus intensity where the top of the parabola is reached
- d
- exponent determining the asymmetry of the parabola
- Received December 26, 2001.
- Accepted May 10, 2002.
- The American Society for Pharmacology and Experimental Therapeutics