Division of Pharmacology, Leiden/Amsterdam Center for Drug
Research, Leiden University, Leiden, The Netherlands (S.A.G.V.,
C.J.G.M.S., B.P.R.R., M.D.); Pfizer Global Research & Development,
Discovery Biology, Sandwich, Kent, United Kingdom (P.H.v.d.G.);
Mathematical Institute, Leiden University, Leiden, The Netherlands
(L.A.P.)
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 · kg1, 143 ± 31 ml · min1
· kg1, 122 ± 20 ml · kg1 and
606 ± 48 ml · kg1, 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 · ml1. 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.
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Introduction |
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 (5
-pregnan-3-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 GABAA
receptors (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 sigmoid
Emax 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.
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Fig. 1.
Schematic view of the mechanism-based PK/PD approach.
The pharmacokinetics describe the disposition of the drug in the plasma
(Cp) and equilibration to the biophase
(effect-site, Ce), where the drug can
activate the receptor. Upon activation of the receptor, a stimulus is
produced which leads to the response via several signal-transduction
processes (pharmacodynamics). The proposed model consists of two parts.
The first part consists of a model for drug receptor interaction (eq.
15), which is a hyperbolic function of the effect-site concentration
producing a stimulus. KPD is the
concentration producing the half-maximal stimulus and
ePD is the maximal stimulus. The
second part consists of a biphasic stimulus-response model, which is
represented by a parabolic function (eq. 19).
E0 is baseline response, the top of the
stimulus-response relationship is located at the value
Etop and is obtained at the value
b1/d and the slope of the parabolic function
is determined by a.
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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 · kg1 i.m.
of medetomidine hydrochloride (Domitor; Pfizer, Capelle a/d IJssel, The
Netherlands) and 1 mg · kg1 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
(5-pregnan-3-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 Table 1. 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-
-cyclodextrin (HPCD; Sigma-Aldrich BV). Vehicle
controls were included in all treatment groups.
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TABLE 1
Six treatment groups (A-F) with their corresponding administered
amount of alphaxalone, infusion time, number of animals, vehicle,
averaged body weight, and dose normalized for body weight (mean ± S.E.M.)
Vehicle was either 100 µl of DMSO or 100 µl of 25% (w/v) HPCD.
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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 -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 · ml1 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 · min1. 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 · ml1 (r > 0.990, n = 17), and the limit of quantification was 0.01 µg · ml1. The intra-assay coefficients
of variation for 0.25 and 2.5 µg · ml1
were 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
kg1 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.
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(1)
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(2)
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in which Cp and
Ct represent the concentration of
alphaxalone in compartment 1 and 2, respectively. The input =
R0 for t 
T and
input = 0 for t > T, where
R0 and T are the zero-order infusion rate and the duration of infusion. In these equations CL is
the clearance, Q is the intercompartmental clearance,
V1 and
V2 are the volumes of distribution of
compartments 1 and 2.
The interindividual variability of these parameters was modeled
according to an exponential equation.
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(3)
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where 
i is the population estimate for
parameter P, Pi is the
individual estimate, and 
i is the random deviation of Pi from P. The
values of i are assumed to be independently
normally distributed with mean zero and variance 
2. The residual error in the plasma drug
concentration was characterized by a constant coefficient of variation
error model.
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(4)
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where Cpij represents the
jth plasma concentration for the ith individual
predicted by the model. Cmij represents
the prediction of concentration, and 
ij
accounts for the residual deviation of the model predicted value from
the observed concentration. The value for was assumed to be
independently normally distributed with mean zero and variance
2.
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 , 2,
and 2. 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 Q
were modeled as function of body weight.
|
(5)
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|
(6)
|
where j was assumed to be the same for CL and
Q. V1 and
V2 were estimated as a linear function
of body weight.
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(7)
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(8)
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Subsequently, the individual Bayesian post hoc pharmacokinetic
parameter estimates were used to calculate the individual alphaxalone
plasma concentrations at the time points of EEG measurements.
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.
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(9)
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where Cp represents the plasma
concentration (see eq. 1 and 2) and Ce
represents the effect-site concentration. Under the assumption that in
equilibrium the effect-site concentration equals the plasma
concentration, this equation can be simplified to
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(10)
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First, the equilibrium rate constant
(keo) was calculated nonparametrically
using the program keo-obj.exe (S. J. Shafer, Palo Alto Veterans
Affairs Medical Center, Stanford University, Stanford, CA).
Subsequently, hysteresis was minimized in a parametric approach. In the
nonparametric approach, a concentration dependence was observed in
keo parameter estimates. Therefore in the
parametric model, keo was expressed as a
function of the maximal observed concentration
(Cmax).
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(11)
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where keo,app is the apparent in
vivo keo, and k is a constant.
For Cas the value of 1000 was chosen to
position the asymptote, since all Cmax
levels that were reached were higher than 1000 ng · ml1. Replacing keo
in eq. 10 by keo,app we obtain
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(12)
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The Mechanism-Based Model.
In this investigation, amplitudes
in the -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 (see
Kenakin, 1997), consists of a drug receptor binding part resulting in a stimulus.
![S=<FR><NU>∈ · [R<SUB>t</SUB>] · C</NU><DE>C+K<SUB>A</SUB></DE></FR>](/content/vol302/issue3/fulltext/1158/img013.gif)
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(13)
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where S is the stimulus as function of the
concentration C. 
represents the intrinsic efficacy of a
drug to initiate a stimulus from one receptor, which is strictly a
drug-related parameter, [Rt] is the
total number of receptors, KA is the
equilibrium dissociation constant of the drug from the receptor. This
initial stimulus is then propagated into the observed pharmacological
effect through a chain of postreceptor events, which is characterized
by an unknown function f.
![E=f(S)=f<FENCE><FR><NU>∈ · [R<SUB>t</SUB>] · C</NU><DE>C+K<SUB>A</SUB></DE></FR></FENCE>](/content/vol302/issue3/fulltext/1158/img014.gif)
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(14)
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Thus, drug-mediated responses in any given tissue depend on two
tissue factors, [Rt] and f,
an unknown function, and two drug-related factors
KA and intrinsic efficacy . Two
adjustments to this general model were made by Tuk and coworkers (1999)
to apply the model to in vivo systems. First, the total amount of receptors cannot easily be measured in vivo, allowing only the product
of and [Rt] to be estimated
(Black and Leff, 1983). Second, the [Rt] value of the drug reaching the
highest effect must be set to one, to allow an independent estimation
of f and [Rt]. The
relationship between effect-site drug concentration and effect is thus
characterized by the following equation.
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(15)
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where KPD is the in vivo estimated
affinity and ePD is the in vivo estimated
efficacy, relative to 1.
In a recent application of this model to characterize the relationship
f 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.
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(16)
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which is a parabola if and only if d is equal to 1. In this equation, Etop represents the
top of the parabola, a is a constant reflecting the slopes
of the parabola, and b1/d is the
stimulus for which the top of the parabola (i.e., the maximal effect)
is reached. However, in the previous attempt to characterize the
stimulus-effect relationship, Tuk et al. (1999) showed that the
stimulus-effect relationship was defined by a small increase at low
stimulus intensities and a steeper increase at higher stimulus
intensities. This observation required that exponent d
should be greater than 1 to result in a stimulus-effect relationship
that has a shallow increase at low stimulus intensities and a steeper
increase at higher stimulus intensities (see Fig. 1).
Rearranging eq. 16 results in
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(17)
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When no drug is present the EEG is equal to its baseline value
(E0). Equations 16 and 17 then reduce
to
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(18)
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Substituting eq. 18 into eq. 17, and rearranging yields
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(19)
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In this parametric model, individual plasma concentrations were
fitted to the corresponding effects. The parameters
keo,app, KPD,
a, and b were estimated and exponent d
was fixed at 3. It was known that d should be greater than
1, and numerical evaluation revealed that the value of d was
likely to be between 2 and 4. Averaged amplitudes over 40 min of
individual EEG recordings before infusion served as input for
individual baseline values. The interindividual variability in the
pharmacodynamic parameters was modeled according to the exponential eq.
3. Similar to the pharmacokinetics, the residual variability in the
pharmacodynamics was modeled as a constant coefficient of variation
error according to eq. 4. To reduce the run-time, a two-step approach
was applied in which first the individual estimates were obtained for
the pharmacokinetic parameters. In the second step, the pharmacokinetic
parameters were fixed at these values, and the pharmacodynamic
parameters were obtained.
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.
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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 Q
versus body weight was observed. CL and Q were defined as
158 · BW1.67 and 143 · BW1.67 (ml · min1 · kg1),
respectively. V1 and
V2 were linearly dependent on body
weight. For group A, post hoc parameter estimates for
V2 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 · kg1 alphaxalone was administered in two
vehicles (DMSO and HPCD, 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.
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Fig. 2.
Individual alphaxalone plasma concentration-time
profiles for the treatment groups A-F. The observed concentrations
(markers connected with dotted lines), the individual predictions (thin
lines), and population predictions (thick lines) are depicted. The
x-axis represents the time in minutes and the
y-axis represents the plasma concentration of
alphaxalone (ng · ml1) on a logarithmic scale. The
black boxes represent the duration of the infusion.
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TABLE 2
Population pharmacokinetic parameter estimates for CL, Q,
V1, and V2 with corresponding
interindividual coefficient of variation (CV) and 95% confidence
interval (CI)
Below the population estimates, the averaged individual Bayesian post
hoc pharmacokinetic parameter estimates are given for treatment groups
A through F (mean ± S.E.M.). The intraindividual residual error
was 26.5%.
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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 as
Etop 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.
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Fig. 3.
Changes in amplitude in the frequency range in
time following administration of alphaxalone. For each treatment group
(A-F) a representative observed (dots) and predicted (thick line)
effect-time profile is shown. The black boxes represent infusion
duration. Time (min) is given on the x-axis and the
amplitude in the b frequency range (µV) is given on
the left y-axis. The corresponding plasma concentration
(ng · ml1, dotted line) in time is depicted on the
right y-axis on a logarithmic scale. The individual dose
is depicted in the graph.
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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 HPCD 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 · ml1 the amplitudes started to increase and
Etop was reached at a concentration of
~1000 ng · ml1. Midpoint location for
the increasing limb of the concentration-effect relationship was ~550
ng · ml1. The decreasing limb, at
concentrations higher than ~1000 ng · ml1 showed a larger hysteresis loop at higher
concentrations, as shown in Fig. 4, left panel.
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Fig. 4.
Left panel, observed and predicted alphaxalone
plasma concentration versus EEG effect in the b
frequency range for three representative rats that differ in maximal
plasma concentrations (Cmax). The value for
Cmax is depicted in the graphs. In each
graph the increasing effect at low concentrations (<1000 ng · ml1) shows a similar profile independent of dose, whereas
at high concentrations (>1000 ng · ml1) the
hysteresis loop increases with increasing maximal concentrations. Right
panel, observed and predicted alphaxalone effect-site concentration
versus EEG amplitude in the frequency range after minimizing
hysteresis.
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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 of
keo as a function of the maximal reached
concentration (keo,app) successfully
minimized the concentration-dependent hysteresis. Maximal hysteresis
with the highest dosages showed that the
keo for alphaxalone is 0.33 ± 0.08 min1, which corresponds to a half-life of
keo of 2.1 min. Estimates for
keo,app were not different from
keo-nonpar and
keo-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).
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TABLE 3
Mean parameter estimates of keo for groups A through
F
The value of keo was estimated nonparametrically
(keo-nonpar), parametrically
(keo-par), and parametrically
(keo,app) with maximal plasma concentrations
(Cmax) as covariate. The concentration-dependent
hysteresis was defined as
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Fig. 5.
Nonparametric (squares) and parametric (triangles)
keo estimates and
keo,app as a function of
Cmax (filled circles):
keo,app = 0.325 ± 0.08 + ((1150/(Cmax 1000)). The maximal
plasma concentration measured for each individual
(Cmax) is depicted on the
x-axis and values for
keo and
keo,app on the
y-axis.
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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 for
keo,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. Population
KPD was estimated at 432 ± 26 ng · ml1, whereas
ePD 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. Calculating
Etop from individual
E0 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 b
were 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.
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TABLE 4
Population pharmacodynamic parameter estimates (groups A-F) for
KPD, a, and b with
corresponding coefficient of variation (CV) and 95% confidence
interval (CI)
E0 was 10.6 ± 0.3 µV and
Etop was 32 ± 0.8 µV (mean ± S.E.M.,
n = 44). Exponent d was fixed at 3. Below
the population estimates, the averaged individual Bayesian post hoc
pharmacokinetic parameter estimates are given for treatment groups A
through F (mean ± S.E.M.). Intraindividual residual variation was
16%.
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Fig. 6.
Panel A, drug-receptor interaction. The
relationship between effect-site concentration and stimulus for
alphaxalone for all individuals (n = 44).
Effect-site concentration (ng · ml1) is depicted
on the x-axis, and the stimulus is depicted on the
y-axis. Panel B, stimulus-effect
relationship. The predicted biphasic stimulus-effect
relationship for all individuals (n = 44) is shown.
Dots represent the observed amplitudes, and the thin lines represent
the best-fitted individual lines by the parabolic stimulus-effect
model. Intraindividual variability is 16%.
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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 · min1 · kg1) 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 · kg1.
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 -lipoprotein in rats (Jones,
1972).
Hydroxypropyl--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 of
keo 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 · ml1 is in the
range of values reported for the (indirect) inhibition of
35S-t-butylbicyclophosphorothionate
binding by alphaxalone, for which the IC50 varied
between 110 and 180 ng · ml1 (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 · ml1 (Hill Venning et al., 1996). Using this
mechanism-based PK/PD approach for the determination of the in vivo
KPD 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.
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
Pharmacol 129:81].
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;
HPCD, 2-hydroxypropyl--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.
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Abstract
Introduction
