Pharmacokinetic-Pharmacodynamic Modeling of Stimulatory and Sedative Effects of Alprazolam: Timing Performance Deficits1
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0022-3565/97/2833-1119$03.00/0
THE JOURNAL OF PHARMACOLOGY AND EXPERIMENTAL THERAPEUTICS Vol. 283, No. 3
Copyright © 1997 by The American Society for Pharmacology and Experimental Therapeutics Printed in U.S.A.
JPET 283:1119 –1129, 1997
Pharmacokinetic-Pharmacodynamic Modeling of Stimulatory
and Sedative Effects of Alprazolam: Timing Performance
Deficits1
CHYAN E. LAU and ANNE C. HEATHERINGTON2,3
Department of Psychology, Busch Campus, Rutgers University, New Brunswick, New Jersey (C.E.L.) and Center for Bioengineering, University
of Washington, Seattle, Washington (A.C.H.)
Accepted for publication August 22, 1997
Downloaded from jpet.aspetjournals.org at ASPET Journals on October 10, 2015
ABSTRACT
Alprazolam decreased the reinforcement rate and increased the and high-concentration effects as indicated by the EC50 values
shorter-response rate of contingency-controlled timing behav- of 0.09 and 0.18 mg/ml, respectively. Owing to the rapid onset
ior under a differential reinforcement of low-rate schedule (DRL of i.v. administration, the first peak (a transition phase before
45-s) in rats. An integrated pharmacokinetic-pharmacodynamic the onset of the sedative effect) was absent, with the presence
(PK-PD) model was developed to describe and characterize the of the second peak again coinciding with the offset of the
effects of i.v. and s.c. administration of alprazolam. The onset, sedative effect. The reinforcement rate (IC50 5 0.02 mg/ml)
peak and disappearance of alprazolam effects were evaluated characterized by the indirect response model to account for the
during a 3-hr session. After s.c. alprazolam administration, two initial hysteresis is an index for evaluating the deficit in timing
peak increases in shorter-response rate occurred at moderate performance. Although the effects of alprazolam can be de-
alprazolam serum levels, first in the ascending and then in the scribed in behavioral terms, simultaneous PK-PD optimization
descending limb of the concentration-time profile. We used a numerically defines the performance and hypothesizes the co-
stimulation-sedation PD model incorporating two opposing ef- existence of stimulation and sedation components for alprazo-
fect-link sigmoidal Emax functions to model the two peaks after lam. The stimulation-sedation model may help in delineating
s.c. alprazolam administration. The model suggested that al- the possible mechanisms for adverse rebound side effects and
prazolam possesses both stimulatory and sedative effects in a of tolerance in humans.
continuous but sequential fashion, which corresponded to low-
Benzodiazepines, like many drugs, often exhibit a dose- sponded to receptor in vivo binding of alprazolam for the
related, biphasic effect on behavior in animals. At lower respective doses; the low dose increased, and the high dose
doses, BZs increase response rates for operant or schedule- decreased the binding, although this was not observed for
controlled behavior (Burke et al., 1994; File and Pellow, 1985; other BZs (Burke et al., 1994; Kaplan et al., 1990; Lopez et al.,
Griffiths and Goudie, 1987), as well as for spontaneous ac- 1988; Miller et al., 1987). However, whether the stimulatory
tivity (Flaherty et al., 1996; Lopez et al., 1988); i.e., they and sedative effects of BZs observed under different condi-
produce a “stimulatory” effect. Conversely, at higher doses, tions reflect a common underlying mechanism is not clear,
they typically decrease these rates of responding. “Sedation” especially if inferences are based mainly on time-course data
was observed as the maximum effect after high-dose BZ collapsed into a single point rather than on a complete tem-
administration (e.g., 3 mg/kg s.c. midazolam) with animals poral profile.
maintaining a crouched position without movement (Lau et Inasmuch as pharmacological response often can be pre-
al., 1996). BZs exert their effects through the GABA-BZ
dicted from the respective PK, we chose to investigate the
receptor complex (Haefely et al., 1985). The behavioral end-
effects of low and high doses in light of the corresponding
points observed after alprazolam administration corre-
serum drug concentration profiles instead of the resultant
receptor changes. Integrating PK and PD measures can help
Received for publication December 30, 1996.
1
This research was supported by Grant R37 DA03117, awarded to J. L. define and predict the drug concentration-effect relation. It
Falk, from the National Institute on Drug Abuse.
2
may clarify the relation between the stimulatory and the
Supported by NIH grant NCRR RR02176.
3
Current address: Amgen Inc., 5–1-D, 1840 DeHavilland Drive, Thousand sedative effects observed for BZs; for example, the sequence
Oaks, CA 91320. and the duration of these two effects as functions of BZ
ABBREVIATIONS: AIC, Akaike’s Information Criterion; BZ, benzodiazepine; DRL, differential reinforcement of low rate; EEG, electroencephalo-
gram; IRT, inter-response time; PD, pharmacodynamics; PK, pharmacokinetics; HPLC, high-performance liquid chromatography.
11191120 Lau and Heatherington Vol. 283
concentration. In humans, BZs are used widely for their (Breimer et al., 1991; Mandema and Danhof, 1992; Mandema
therapeutic effects. But they also are associated with a vari- et al., 1991), because it satisfies many of the criteria desirable
ety of adverse side effects, which have been increasingly for such modeling (Dingemanse et al., 1988; Laurijssens and
recognized in recent years, e.g., early-morning insomnia, day- Greenblatt, 1996). DRL performance also satisfies these
time anxiety, tension or panic (Kales et al., 1983; Morgan and same criteria (Lau and Wang, 1996; Lau et al., 1996, 1997);
Oswald, 1982; Vgontzas et al., 1995; Woods et al., 1995). both EEG and DRL measurement are objective, continuous,
Although the therapeutic and adverse side effects of BZs sensitive and reproducible. In addition, although “the phar-
have been described clinically, to our knowledge no explicit macological relevance of the EEG parameters with respect to
PK-PD model has been developed which attempts to describe the clinical effects of [BZs] remains to be established” (Man-
these relations. In past research, we used only one measure dema et al., 1991, p. 476), the DRL performance requires
of DRL 45-s performance, the reinforcement rate, to investi- conduct that fulfills a required and objectively defined behav-
gate its relation to PK (Lau and Wang, 1996; Lau et al., 1996, ioral contingency instead of being limited to a passive mea-
1997). PK-PD-modeling BZ effects with either a single in- sure of an unconditioned drug effect. Although DRL perfor-
creasing function such as an EEG measure (Mandema et al., mance has been used extensively in behavioral pharmacology
1991, 1992) or a single decreasing function such as the rein- to study the dose-effect relation of various drugs from differ-
forcement rate is a simple but perhaps an incomplete proce- ent classes (Richards et al., 1993; Stephens and Voet, 1994;
dure. Simultaneously modeling both increasing and decreas- Sanger, 1980), we do not believe this kind of behavioral mea-
Downloaded from jpet.aspetjournals.org at ASPET Journals on October 10, 2015
ing functions is a complicated task, however. One is required sure has been used outside our laboratory for PK-PD modeling.
not only to use a complex behavioral paradigm but also to We have found previously that the effect-time profiles of the
analyze more than one index of performance. Only then can DRL 45-s schedule correlate well with the respective serum
the relation between the stimulatory and sedative effects be concentration-time profiles for alprazolam, midazolam and caf-
explored and, in turn, provide a useful model for delineating feine (Lau et al., 1996, 1997). The bioavailability values derived
adverse BZ side effects in humans. from these profiles also mirrored those estimated from PK mea-
The present study used a DRL schedule, which produces sures for midazolam following s.c., i.p. and p.o. routes of admin-
“spaced responding” or “timing” behavior. Two distinct istration (Lau et al., 1996).
classes of responding are considered: reinforced and nonre- Alprazolam, a triazolobenzodiazepine, is the most widely
inforced responses. The DRL 45-s schedule of reinforcement prescribed BZ and is used as an anxiolytic, antipanic and
results in low rates of responding, because only those re- antidepressant agent (Dawson et al., 1984; Fawcett and
sponses that occur after a minimum time interval (in this Kravitz, 1982). In humans, the terminal half-life of alprazo-
case, 45 s) after a previous response are reinforced. Re- lam is 6 to 16 hr (Greenblatt et al., 1983; Smith et al., 1984),
sponses that occur before 45 s have elapsed are not rein- whereas it is approximately 30 min in rats (Lau and Wang,
forced, and the timing interval is reset. IRT profiles and the 1996; Owens et al., 1991). Hence, a 3-hr session allows inves-
number of responses can be recorded throughout the session tigation of the onset, peak and disappearance of alprazolam
without prior special physiological preparation of the subject. effects. In a previous study, the effects of alprazolam admin-
The DRL schedule contingency not only entails time discrim- istered s.c. on reinforcement rate were consonant with the
ination but also requires an appropriate inhibition of re- serum alprazolam concentrations, but the relation to shorter-
sponding for reinforcement to occur and involves other mem- response rate (nonreinforced response rate or short IRT rate)
ory, sensory and motor capacities (Kramer and Rilling, 1970). was not evaluated (Lau and Wang, 1996); we use the term
The effect of many drugs is to reduce the inhibition of “shorter-response rate” instead of short IRT rate in the
behavior associated with signals of punishment or nonre- present study to agree with the terminology used in our
ward in DRL behavior (Gray, 1981). Drugs not only can alter previous reports (Lau et al., in press; Wang and Lau, in
the IRT distribution but also can disturb the sequential pat- press). The present study investigated not only the effects of
terning of IRTs. It has been noted that the reinforcing event alprazolam administered s.c. on the reinforcement and short-
can be used as a discriminative stimulus for further rein- er-response rates attained from behavioral analysis but also
forced responding and thus could function as a strategy used modeled the time course relating these changes to the respec-
by animals to maximize their performance (Carter and tive PK. Intravenous alprazolam dosing was chosen to facil-
Bruno, 1968; Farmer and Schoenfeld, 1964; Reynolds, 1964). itate selecting the appropriate PD models. Thus, in this
Drug effects, such as sedation, can distort the timing behav- work, a comprehensive alprazolam PK-PD model was pro-
ior as displayed by the IRT profile, as well as the discrimi- posed to describe and predict the interplay between the
native stimulus effects produced by the occurrence of a rein- shorter-response and reinforcement rates. The implications
forced response. Furthermore, when performance has been of this model for behavioral observations often reported with
disrupted by a drug, even after the drug has disappeared, a respect to tolerance in animals and for adverse side effects
period of transition may be required for the reconditioning of noted in humans after BZ administration will be presented
base-line performance to occur. Consequently, short IRTs under “Discussion.”
may dominate during this phase before reconditioning has
taken place and may cascade because short IRTs are followed
by further short IRTs with high probability, as described by
Methods
the observed sequential dependencies (Weiss et al., 1966). Drug
The result of this increase in short IRTs is the stimulatory Alprazolam was obtained from Upjohn Laboratories (Kalamazoo,
phenomenon reported here. MI). Alprazolam (5 mg) was dissolved in 50 ml of 1.2 N HCl, diluted
The EEG signal has been used as a pharmacodynamic with 0.9% NaCl and administered either subcutaneously or intrave-
measure for the evaluation of BZ effects in PK-PD analyses nously in an injection volume of 1 ml/kg body weight.1997 Alprazolam PK-PD: Stimulation-Sedation 1121
Pharmacokinetics of Alprazolam mediately before a session, and were separated by 3 to 5 days in a
random order within a series.
Animals. Four male, albino, Sprague-Dawley rats from HSD (In-
Data analyses. The IRT distributions after administration of
dianapolis, IN) were used. They were housed individually in a tem-
vehicle and alprazolam doses were analyzed for 3-hr sessions, omit-
perature-regulated room with a daily cycle of illumination from 7:00
ting the first 2 min, which allowed for the transient effects of han-
A.M. to 7:00 P.M. They were reduced to 80% of their initial, adult
dling. Base-line IRT distributions for each session that immediately
free-feeding body weights (mean, 386 g; 380–389 g) during a 2-week
preceded each injection also were analyzed. Responses with IRTs
period by limiting daily food rations: 5 g for the first day, 10 g for the
$45 s (reinforced responses) and ,45 s (shorter or nonreinforced
next 5 days and a food supplement (range, 14–16 g) to maintain their
responses) were derived from the IRT distributions. For each rat,
80% body weights. Water was continuously available in the living
there were four base-line day values that were averaged and treated
cages. Experiments were conducted in accordance with the Guide for
as the mean base-line value for the s.c. injection series; there were
the Care and Use of Laboratory Animals (National Institute of
two base-line day values for the i.v. injection series. These responses
Health Publ. No. 85–23, revised 1985).
were calculated as rates (responses per min) and transformed to
Catheterization. Right jugular vein cannulation was performed
mean percent base-line values to compensate for individual differ-
under sterile conditions and was described previously (Lau et al.,
ences in DRL performance.
1996). The proximal end of the silastic catheter was inserted into the
jugular vein and the distal end of the catheter was threaded subcu-
taneously and exited through a small incision in the animal’s back. Pharmacokinetic Pharmacodynamic Modeling
The catheter was flushed with 0.9% saline with 50 U heparin and
PK and PD data analyses were performed on mean data (PK, n 5
Downloaded from jpet.aspetjournals.org at ASPET Journals on October 10, 2015
sealed with fishing line when not in use.
4; PD, n 5 7 and n 5 4 for s.c. and i.v. routes, respectively) by the
Drugs, reagents and HPLC. a-Hydroxyalprazolam and 4-hy-
SAAM II software system (SAAM Institute, 1997). Because PK and
droxyalprazolam were obtained from Upjohn Laboratories. Reagents
PD data were obtained in parallel studies, individual profiles were
were obtained from standard commercial sources. The serum micro-
not used. Fitting models to aggregate data with different doses
sample HPLC method for the determination of alprazolam and its
(Laurijssens and Greenblatt, 1996) is frequently required to estimate
metabolites has been described previously (Jin and Lau, 1994). The
one unique set of parameters (Ekblom et al., 1993; Mandema and
capacity factors for demoxepam (internal standard), 4-hydroxyalpra- Wada, 1995); however, this does not allow analysis of inter- or
zolam, a-hydroxyalprazolam and alprazolam were 2.08, 2.73, 3.37 intraindividual variability. Assessment of the goodness of fit of each
and 4.43, respectively. The two metabolites were not included in the proposed model to experimental data was based on AIC, correlation
PK analysis because their concentrations were either low or not matrix, residual and weighted residual plots, visual plots and error
detected. in parameter estimation (S.D., expressed as CV%) which is derived
Alprazolam administration and blood sampling. Animals from the covariance matrix.
were allowed to recover for at least 2 days from the jugular vein Pharmacokinetic analysis. We analyzed mean serum concen-
catheterization before the alprazolam administration series. The tration time profiles by use of compartmental modeling. The distri-
animals initially received an i.v. dose of alprazolam (1.2 mg/kg) via bution and elimination characteristics were determined after the i.v.
the jugular vein catheter, followed on other days by s.c. administra- 1.2 mg/kg alprazolam dose. Then, i.v. 1.2 mg/kg and s.c. alprazolam
tion into the skin on the back of the neck of 1.25, 4 and 7 mg/kg profiles (1.25–7 mg/kg) were analyzed simultaneously, assuming
alprazolam in a random order. Drug doses were separated by 3 to 5 complete bioavailability of the s.c. administered drug.
days. Blood samples (100 ml) from the jugular catheter were obtained Pharmacodynamic models. Shorter-response rate (IRT , 45 s):
after drug administration at 2, 5, 15, 30, 45, 60, 90, 120, 180, 240 and Stimulation-sedation model. A multicompartmental model, which
360 min postinjection. To maintain the feeding regimen and also incorporated two link compartments representing stimulation and
avoid the effect of food on drug PK, drug doses were given 6 hr before sedation sites, was used to describe the data. This effect-link model
feeding time. was based on the model proposed by Sheiner and colleagues (1979).
To ensure no loss of mass to the effect site, a “dummy” compartment
was linked to the central compartment via a fixed rate constant
Pharmacodynamics of Alprazolam 2k1est. Drug stimulation site kinetic values are defined by the loss
Animals. Seven male rats of the same strain were used under the rate constant, keost, and the effect site concentration (Cest) is defined
conditions and food-limitation regimen similar to that used in the PK as:
study. Their mean initial, adult free-feeding body weight was 383 g
(range, 380–388 g). qe,st
Cest 5 (1)
Apparatus. Four operant Plexiglas chambers were used as de- Vest
scribed previously (Lau and Wang, 1996). Each chamber, equipped
with a response lever and a stainless steel food-pellet receptacle into where qe,st and Vest are the drug mass and the volume of stimulation
which 45-mg dustless pellets (BioServ, Frenchtown, NJ) could be site, respectively, and subscript st refers to stimulation. Assuming
delivered, was enclosed in a sound-attenuating shell and was con- equilibrium conditions, i.e., dqe/dt 5 0, the fluxes between the cen-
trolled by an IBM-type 486 X computer. Session contingencies were tral and the link compartments are equal, that is:
programmed and data recorded by QuickBasic.
k1est z q1 5 keost z qe,st (2)
Procedure. Animals were magazine trained initially for 15 min
on a noncontingent random-time schedule. Responses on the lever
k1est z V z C1ss 5 keost z Vest z Cess,st (3)
were shaped by successive approximation and reinforced when IRTs
were greater than 3 s. The temporal requirement was slowly in- where q1 and C1 are the drug mass and the concentration in the
creased to an IRT of 45 s during 10 to 20 sessions with a 3-hr session central compartment, respectively, and the subscript ss denotes
conducted daily. After performance had stabilized, the drug admin- equilibrium conditions. At steady state, C1ss 5 Cess hence:
istration series began. Animals first received drug subcutaneously
with administration of vehicle, 1.25, 4 and 7 mg/kg alprazolam. After k1est
completion of the s.c. administration, right jugular vein catheters Vest 5 V (4)
keost
were implanted as described above in four of the seven animals.
These animals then received drug intravenously with administration where V is the volume of the central compartment.
of saline and 1.25 mg/kg alprazolam. All injections were given im- The sedation model proposed was based on the acute tolerance1122 Lau and Heatherington Vol. 283
model of Ekblom et al. (1993) wherein sedation acts in opposition to model will be presented. Linear kinetics were assumed after i.v.
stimulation. This was also incorporated as an effect-link model, such dosing between 1.2 and 1.25 mg/kg. A diagrammatic representation
that the sedation site and the equivalent dummy compartment were of the integrated PK-PD model is shown in figure 1.
linked to the central compartment via the rate constants k1esd and
2k1esd, respectively, where the subscript sd refers to sedation. Equa-
tions for the sedation site concentration (Cesd) and the volume of
Results
sedation site (Vesd) were derived as for the stimulation model. Pharmacokinetics of Alprazolam
The stimulatory effect (Est) is described by the sigmoidal Emax
Figure 2 shows the mean serum alprazolam concentration-
equation which is expressed in terms of Cest, such that
time profiles after administration of i.v. 1.2 mg/kg (upper
n
Estmax z Cest panel) and three s.c. doses of alprazolam (1.25–7 mg/kg,
Est 5 n n (5) lower panel). A two-compartment disposition model was most
ECst50 1 Cest
suitable for describing events after i.v. administration of
where Estmax, and ECst50 are the maximal response, and the con- alprazolam; an additional absorption compartment was re-
centration required to produce 50% maximal response, respectively, quired to describe s.c. administration. Parameters, and asso-
and n is the Hill factor. The sedative effect (Esd), which is opposing ciated errors, obtained with the fully integrated model are
and negative, is also described by a sigmoidal Emax model which is
presented in table 1. The volume of the central compartment
expressed in terms of Cesd such that:
was fixed to that obtained when i.v. data were analyzed
Downloaded from jpet.aspetjournals.org at ASPET Journals on October 10, 2015
s
Esdmax z Cesd alone, 0.756 l (2.45 l/kg); this assumes no change in bioavail-
Esd 5 s s (6) ability. As time to peak concentration was not constant for
ECsd50 1 Cesd
the three s.c. doses (1.25 mg/kg 5 5 min, 4 mg/kg 5 12 min,
where Esdmax, and ECsd50 are the maximal sedative effect, and the 7 mg/kg 5 8 min), the absorption rate constant (Ka) differed
concentration required to produce 50% sedation, respectively, and s between doses with 1.25 mg/kg .. 7 mg/kg . 4 mg/kg,
is the Hill factor. The overall shorter-response (srr) rate effect (Esrr) resulting in absorption half-lives of 1.9, 10.3 and 7.1 min,
is the sum of the base-line effect (Eo), the stimulatory effect (Est) and respectively. The intercompartmental rate constants were
the sedative effect (Esd):
similar (0.03 min21, t1/2 25 min) and approximately twice as
Esrr 5 Eo 1 Est 1 Esd (7) slow as Kel (0.06 min21, t1/2 11 min). The return rate con-
stant [k(1,2)] showed the greatest interdose variation. Pre-
For each dose (i.v.1.25 mg/kg and s.c.1.25–7 mg/kg), the stimula- dicted serum concentration-time profiles are shown by solid
tory parameters (k1est, keost, Vest, Estmax, ECst50, n) and the seda- lines in figure 2.
tive parameters (k1esd, keosd, Vesd, Esdmax, ECsd50, s) were esti-
mated by simultaneous optimization of the shorter-response rate Pharmacodynamics of Alprazolam
data.
Reinforcement rate (45–55 s bin): Indirect response model. Rein- After vehicle administration, response rate exhibited a
forcement rate in the 45–55 s bin, instead of total reinforcement rate, function similar to a gamma distribution with the highest
was used in this model (see “Results”). An inhibitory Emax equation response rate occurring in the 40 –50 s bin (fig. 3). As shown
incorporated as an indirect response model (Dayneka et al., 1993) in the figure, IRTs before the first arrow (,45 s) were not
was chosen to describe the data. We proposed that alprazolam in- reinforced and those after the first arrow were reinforced
hibited the production of response, Kin, (Indirect Model I, Dayneka et ($45 s); whereas, the IRTs between the two arrows represent
al., 1993). Hence, the differential equation, describing the response the reinforced IRTs in the 45–55 s bin. Alprazolam decreased
(R) incorporating the inhibition function (Inh) becomes:
the IRTs $45 s and increased the short IRTs , 45 s in a
dR dose-related fashion. We previously found that the reinforce-
5 Kin z Inh 2 Kout z R (8) ment rate in the 45–55 s bin not only was more sensitive to
dt
drug effects but also reached the maximum effect at a lower
where Kout defines the dissipation of the response, and Inh is defined dose than the total-reinforcement rate (Lau and Wang,
as a sigmoidal Emax model of the form: 1996). Thus, the reinforcement rate in the 45–55 s bin, rather
i than total-reinforcement rate, was used to characterize the
Ci
Inh 5 1 2 i i (9) effects of alprazolam. This minimized the possibility of be-
IC50 1 Ci havioral toxicity which might occur if higher doses were
where IC50, Ci, and i are the concentration required to produce 50%
necessary to perform the analysis. Figure 4, upper panel,
inhibition, the concentration in Central Compartment, and the Hill shows the effects of s.c. doses of alprazolam (1.25–7 mg/kg) on
factor, respectively. the shorter-response rate, which increased to the maximum
For each dose (i.v. 1.25 mg/kg and s.c. 1.25–7 mg/kg), the response effect (Emax) with all doses immediately after drug admin-
rate constants (Kin, and Kout) and the PD parameters (IC50, i) were istration (greatest for the 1.25 mg/kg dose), and which then
estimated by simultaneous optimization of the reinforcement rate decreased to near base-line levels. However, the shorter-
data. Ro was set to 100%, the base-line value. PK parameters were response rate again increased in a dose-related fashion in
also estimated. terms of both time to and duration of the second peak. The
Integrated PK-PD model. The integrated PK-PD model incor- second peak occurred at 60, 90 to 120 and 150 min for 1.25, 4
porated the PK model (absorption and two-compartment disposi-
and 7 mg/kg, respectively, and peak duration progressively
tion), the stimulation/sedation model describing the shorter-re-
sponse rate and the indirect response model describing the
increased. For each dose, the second peak lasted longer, but
reinforcement rate. Initial parameter estimates were those obtained was of a lower magnitude than the first peak. In contrast to
after fitting each model separately, as described above. All data (PK the shorter-response rate, alprazolam decreased the rein-
and PD) after i.v. 1.25 mg/kg and s.c. 1.25–7 mg/kg were then fitted forcement rate in the 45–55 s bin (fig. 4, lower panel). The
simultaneously. Only parameters resulting from the integrated maximum effects for the three doses of alprazolam occurred1997 Alprazolam PK-PD: Stimulation-Sedation 1123
Fig. 1. Diagrammatic representation of inte-
grated PK-PD model used to describe both
shorter-response rate (stimulation-sedation
model) and the reinforcement rate in the 45–55
s bin (indirect response model) after s.c. ad-
Downloaded from jpet.aspetjournals.org at ASPET Journals on October 10, 2015
ministration of a single dose of alprazolam.
Similar models were used for s.c 1.25, s.c. 4,
s.c. 7 and i.v. 1.25 mg/kg.
during the 15- to 45-min period, and these decrements grad-
ually recovered to base-line level at the end of the session in
a dose- and time-related fashion, although the rate remained
below base line for the s.c. 7 mg/kg dose.
To further investigate the relationship between the two
successive peaks for the shorter-response rate produced by
s.c. doses of alprazolam, an i.v. 1.25 mg/kg alprazolam dose
was chosen. Figure 5 shows the effects of i.v. 1.25 mg/kg
alprazolam and vehicle on the shorter-response rate and on
the reinforcement rate in the 45–55 s bin (n 5 4). For com-
parison, the effect of s.c. 1.25 mg/kg alprazolam on the two
response rates is shown for the seven animals (fig. 4). Vehicle
administration by each route had negligible effects on the
two rates of responding, which remained approximately at
base line. The effect of i.v. 1.25 mg/kg alprazolam on the
shorter-response rate closely followed that for the s.c. dose
between 45 and 180 min; however, a below-base-line rate was
observed during the first 30 min of the session, as opposed to
an initial stimulation peak in the s.c. dose. It is interesting
that the second peak produced by alprazolam was route-
independent in terms of peak time, magnitude and duration
of the peak (fig. 5, upper panel). After the i.v. 1.25 mg/kg
dose, there was no reinforced response in the 45–55 s bin at
the 5-min time point, and the reinforcement rate remained
low for up to 45 min, whereas for the s.c. 1.25 mg/kg dose the
reinforcement rate started to recover after 15 min (fig. 5,
lower panel). Therefore, because both curves were equal at Fig. 2. Mean (S.E.) measured and predicted serum concentration time
the 150-min time point, the recovery between 45 and 150 min profiles after i.v. (1.2 mg/kg, upper panel) and s.c. (1.25, 4 and 7 mg/kg,
for the i.v. dose was faster than the s.c. dose. The shorter- lower panel) administration of alprazolam (n 5 4).1124 Lau and Heatherington Vol. 283
TABLE 1
Pharmacokinetic and pharmacodynamic parameters estimated by simultaneous PKPD modeling of serum concentration,
reinforcement rate in the 45–55 s bin and shorter response rate after administration of alprazolam (i.v. 1.25 or i.v. 1.2, s.c. 1.25, 4 and
7 mg/kg)
Parameters (as defined in text) with estimation error expressed as CV%.
Dose (mg/kg)
Parameter Units
s.c. 1.25 s.c. 4 s.c. 7 i.v. 1.2 (1.25 PD)
Pharmacokinetic parameters
Ka min21 0.364 (18.8) 0.067 (5.6) 0.097 (10.0) N/A
Kel min21 0.057 (9.6) 0.060 (2.3) 0.066 (10.3) 0.084 (3.9)
21
k(2,1) min 0.037 (55.3) 0.038 (18.0) 0.032 (34.5) 0.064 (5.2)
k(1,2) min21 0.062 (45.8) 0.032 (12.6) 0.015 (24.6) 0.026 (18.7)
Va l 0.756 0.756 0.756 0.756
Shorter response rate parameters: Stimulatory effect (effect link model)
k1estc min21 0.0001 0.0001 0.0001 0.0001
keost min21 0.046 (25.4) 0.070 (15.2) 0.037 (20.6) 0.054 (14.5)
Vest ml 1.64 (25.4) 1.08 (15.2) 2.02 (20.6) 1.41 (14.5)
Estmaxc % 800 800 800 800
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ECst50 mg ml21 0.079 (17.5) 0.098 (7.6) 0.091 (10.8) 0.030 (7.2)
n 1.41 (23.4) 1.49 (12.5) 1.36 (18.7) 2.24 (11.2)
Shorter response rate parameters: Sedative effect (effect link model)
k1esdc min21 0.0001 0.0001 0.0001 0.0001
keosd min21 0.021 (15.2) 0.051 (6.9) 0.027 (15.7) 0.125 (68.4)
Vesd ml 3.64 (15.2) 1.49 (6.9) 2.80 (15.7) 0.60 (68.4)
Esdmaxd % 2800 2800 2800 2800
ECsd50 mg ml21 0.083 (15.7) 0.177 (6.7) 0.180 (11.5) 0.027 (31.6)
c
s – 10.43 3.52 (7.2) 2.90 (17.2) 5.28 (37.5)
Reinforcement rate parameters (indirect I model)
Kinb %min21 26.2 (24.3) 40.2 (24.5) 23.9 (14.0) 232.9
Kout min21 0.262 (24.3) 0.402 (24.5) 0.239 (14.0) 2.33
c
Ro % 100 100 100 100
IC50 mg ml21 0.022 (32.8) 0.024 (48.1) 0.028 (31.7) 0.012 (13.0)
I – 0.928 (22.2) 1.25 (28.6) 1.78 (20.7) 4.03 (12.7)
Summary statistics
50 adjustable parameters
14 pairs of parameters had correlation coefficients $0.9 (range, 0.907–0.971)
Weighted residual sums of squares: 1170
a
Fixed according to that obtained for i.v. 1.2 mg kg21.
b
Kin 5 Ro z Kout.
c
Fixed.
d
Fixed equal and opposite to Est max.
Pharmacodynamic Models
Shorter-response rate (IRT < 45 s): Stimulation-se-
dation model. In the hypothetical stimulation-sedation
model, the parameters k1est and k1esd were both fixed at
0.0001 min21, numeric values that have been of no conse-
quence (Sheiner et al., 1979). The value of Estmax was fixed
at 800%. This experimentally reasonable value was chosen so
that the maximal effect observed (565%) could be accommo-
dated. Esdmax was set equal to 2Estmax (i.e., 2800%), be-
cause the sedation was capable of totally negating the stim-
ulatory effect so that the measured effect was approximately
equal to Eo (base-line value 5 100%).
Figure 6 shows the predicted stimulatory effect (Est), sed-
ative effect (Esd), resultant predicted effect and observed
effects for each dose. The estimated parameters and associ-
Fig. 3. Mean (S.E.) effects of s.c. alprazolam on IRT distributions dur- ated errors, with the integrated model, are shown in table 1.
ing the 3-hr session. All responses before and after the first arrow are The parameters describing the stimulatory effect after s.c.
nonreinforced (,45 s) and reinforced ($45 s), respectively, and be- administration changed little across doses, which indicated a
tween the two arrows are the 45–55 s bin responses (n 5 7). lack of dose dependence, with the estimated values for
response rate increases produced by s.c. alprazolam occurred ECst50 and n at 0.09 mg/ml and 1.4, respectively; whereas
at the onset and immediately after the maximum effects for those values for the i.v. 1.25 mg/kg dose were 0.03 mg/ml and
the reinforcement rate. Owing to the rapidity of the i.v. dose 2.2, respectively. The parameters describing sedation were
effect, the onset transition phase was lacking, and thus the similar for the s.c. 4 and 7 mg/kg doses (ECsd50 5 0.18 mg/ml,
first peak did not occur. s 5 3); however, the ECsd50 and s values were two to three1997 Alprazolam PK-PD: Stimulation-Sedation 1125
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Fig. 5. Response rate-time profiles, expressed as % baseline (S.E.)
after s.c. (n 5 7) and i.v. (n 5 4) administration of alprazolam (vehicle
and 1.25 mg/kg). Upper panel, shorter-response rate; lower panel,
reinforcement rate in the 45–55 s bin.
Fig. 4. Response rate-time profiles, expressed as % base line (S.E.)
after s.c. administration of alprazolam (vehicle, 1.25, 4 and 7 mg/kg,
n 5 7). Upper panel: shorter-response rate; lower panel: reinforcement
rate in the 45–55 s bin.
times greater for the s.c. 1.25 mg/kg dose than for the i.v. 1.25
mg/kg dose. Both site volume (Vest, Vesd) and elimination
rate (keost, keosd) were similar for the stimulatory and seda-
tive effects with less than a 2-fold variation across doses and
routes. The half-life of equilibration for stimulation and se-
dation (t1/2 keost 5 ln2/keost; t1/2keosd 5 ln2/keosd) ranged
from 9.9 to 18.7 min and 5.5 to 33 min, respectively, for the
four doses.
The difference in values for the two reference concentra-
tions (ECst50 and ECsd50) and the Hill factors (n and s) for
the two opposing effects accounted for the two peaks ob-
served in the shorter-response rate. For the two higher s.c.
doses, both the ECsd50 and s values were two times greater
than for the ECst50 and n values; this implied that the onset
of the stimulatory effect preceded that of the sedative effect,
and resulted in the appearance of the first peak for the
shorter-response rate (fig. 6). On the other hand, for the s.c.
1.25 mg/kg dose, the first peak was mainly attributed to the
large Hill factor value for the sedative effect (s 5 10.43) in Fig. 6. Measured shorter-response rate, predicted stimulatory, seda-
comparison with that for the stimulatory effect (n 5 1.41). tive and resultant effects versus time with the proposed model after i.v.
(1.25 mg/kg, n 5 4) and s.c. (1.25, 4 and 7 mg/kg; n 5 7) administration
The disappearance of the first peak occurred immediately of alprazolam.
after the onset of the sedative effect for the three s.c. doses.
The time that the shorter-response rate remained at base- peak arises from a faster offset of the sedative effect because
line level, and the time for the second peak to appear, and the of its greater Hill factor value. For the i.v. dose, owing to the
duration of the peak, were alprazolam dose-dependent for the rapidity of onset of the sedative effect, the first peak of the
s.c. route. The model described and predicted that the second shorter-response rate was negated by the sedative effect; the1126 Lau and Heatherington Vol. 283
second peak was similar to the one observed for the s.c. 1.25 which it rapidly and progressively recovered in a dose-related
mg/kg dose. fashion for both routes of administration.
Reinforcement rate (IRT 45–55 s): Indirect response
model. The effects of alprazolam on the reinforcement rate
were described well in terms of delay in attaining the maxi-
Discussion
mum effect and the recovery of the disruptive performance to The two measures of DRL 45-s performance, the shorter-
base line by the indirect response model for the three s.c. response rate and the reinforcement rate in the 45–55 sec
alprazolam doses (fig. 7). Table 1 shows that the parameters bin, exhibited time- and dose-related changes, which were
were all estimated with a high degree of confidence, as indi- readily interpretable as functions of serum alprazolam con-
cated by low estimation errors. As before, the reference con- centration during 3-hr sessions. This study presents the first
centration, IC50, remained similar across the three s.c. doses attempt to characterize the effects of alprazolam by use of a
(0.022–0.028 mg/ml), whereas both the production rate (Kin) steady state base-line performance of contingency-controlled
and the Hill factor (i) varied by less than 2-fold. For the i.v. behavior in PK-PD modeling. The stimulation-sedation and
1.25 mg/kg dose, the onset and the dissipation effects of the indirect models presented describe and predict the short-
alprazolam on reinforcement rate were faster than the s.c. er-response and the reinforcement rate changes, respec-
1.25 mg/kg dose (i.e., large i and Kout values, table 1 and fig. tively. The stimulation-sedation model accounts for the two
7). peaks in the shorter-response rate after s.c. dosing. There-
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Predicted serum alprazolam concentration and its fore, we propose that alprazolam produced both stimulatory
relation to shorter-response and reinforcement rates. and sedative effects in a continuous but sequential fashion,
Both the shorter-response and reinforcement rates remained which were low- and high-concentration effects as reflected
low at a predicted serum concentration of approximately by their respective EC50 values, approximately 0.09 and 0.18
0.025 mg/ml for the i.v. 1.25 mg/kg alprazolam dose (fig. 8). As mg/ml. Not only did the stimulatory effect endure longer with
the concentration subsequently decreased, the shorter-re- a smaller Hill factor, but its onset preceded the sedative
sponse rate increased yielding the second peak (predicted effect. In comparison with the i.v. dose, for the s.c. alprazo-
serum concentration, 0.019 mg/ml), after which the reinforce- lam dose series the disappearance of the first peak in the
ment rate recovered rapidly to base-line level. For the short- shorter-response rate resulted from the slower onset of the
er-response rate, an initial clockwise hysteresis was evident sedative effect, rather than from other mechanisms, e.g.,
for the two higher doses (s.c. 4–7 mg/kg) but not for the s.c. acute tolerance (fig. 5). The reinforcement rate had the low-
1.25 mg/kg dose. It is interesting that the second peak for the est reference concentration with an IC50 of approximately
shorter-response rate occurred at almost the same predicted 0.02 mg/ml, and was used as an index for evaluating the
serum alprazolam concentrations: 0.037, 0.043 and 0.045 timing performance on the DRL 45-s schedule. It is sensitive
mg/ml for s.c. 1.25, 4 and 7 mg/kg doses, respectively. At these to both the stimulatory and sedative effects, as the rate
concentrations, the reinforcement rate in the 45–55 s bin was recovered rapidly to base-line level during the disappearance
also similar and ranged from 22 to 36% of the base-line level. phase of the two effects (figs. 6 and 8). The model dissociates
The decreases in reinforcement rate in the 45–55 s bin cor- the behavioral components of stimulation and sedation in the
related well with the predicted serum alprazolam concentra- DRL performance, which might serve as a useful screening
tion, except an initial lag was observed for the three s.c. function for drug development. For example, midazolam, a
doses. It is evident that reinforcement rate generally re- BZ agonist, is similar to alprazolam in that it has both the
mained low until the appearance of the second peak, after stimulatory and sedative components (Lau et al., unpub-
lished data). Other agents, such as novel anxiolytic or hyp-
notic drugs, may exhibit primarily one or the other of the two
components.
We used a 3-hr session based on the serum alprazolam
concentration-time profiles to evaluate the onset, peak, and
disappearance of alprazolam effects (fig. 2). Figure 3 shows
that alprazolam increased the IRTs , 45 s and decreased
those in the 45–55 s bin in a dose-related fashion. As a result,
the shorter-response rate-time and reinforcement rate-time
profiles were constructed for the investigation of the effects of
alprazolam on DRL 45-s performance during 3-hr sessions
(figs. 4 and 5). Put in behavioral terms, the decreases in
reinforcement rate and the increases in the shorter-response
rate produced by alprazolam may be attributed to the dis-
ruption of the discriminative stimuli determining the rein-
forced behavior and the sequential dependency phenomenon
(Carter and Bruno, 1968; Farmer and Schoenfeld, 1964;
Reynolds, 1964; Weiss et al., 1966; see the introduction). The
reinforcement rate did not start its major recovery until after
the appearance of the second peak of the shorter-response
Fig. 7. Measured reinforcement rate in the 45–55 s bin and predicted
rate, which can be considered a transition phase during
effect versus time with the proposed model after i.v. (1.25 mg/kg, n 5 which reconditioning was occurring. The effects of the i.v.
4) and s.c. (1.25, 4 and 7 mg/kg; n 5 7) administration of alprazolam. 1.25 mg/kg alprazolam dose identified that the second peak1997 Alprazolam PK-PD: Stimulation-Sedation 1127
Fig. 8. Measured shorter-response and reinforcement
rates (% base line, mean) versus model predicted se-
rum concentration after i.v. (1.25 mg/kg, n 5 4) and s.c.
(1.25, 4 and 7 mg/kg; n 5 7) administration of alprazo-
lam. Arrows indicate the time sequence.
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produced by alprazolam was not only route-independent but studying drug dose-effect relations in behavioral pharmacol-
also independent of the first peak (fig. 5, upper panel). Thus, ogy, limited attention has been given to effect-time profiles
the disappearance of the first peak was not a result of acute and their relation to PK. These results, as well as our previ-
tolerance. ous studies, demonstrated that the effect-time profile rather
Although effect-time profiles provide a better understand- than the use of data temporally collapsed into a single point
ing of drug action than time-course data collapsed into a is the method of choice for investigating the effects of drugs
single point, integrating PK and PD offers more. PK-PD on behavior, as it describes and reflects the on-going behavior
modeling not only relates the time course of drug concentra- and PK (Lau and Wang, 1996; Lau et al., 1996, 1997). Taking
tion to the time course of pharmacological effect but also all these rationales together, a high alprazolam dose pro-
permits the prediction of the effects for other drug doses in duces predominantly a sedative effect; but when it undergoes
the linear range. Consequently, various effect measures can absorption and disposition, a stimulatory effect emerges
be plotted against the same independent variable, predicted whenever the serum alprazolam concentrations reach a level
serum or effect-site drug concentration, to investigate the similar to that produced by a low dose. In turn, both kinds of
interplay between these measures. Furthermore, the phar- effects were detected after the administration of a high dose.
macological effects are defined by mathematical functions, Thus, it is reasonable to assume that the effects of low and
rather than by the experimenter’s descriptions, which facili- high BZ doses mentioned in the introduction (Burke et al.,
tates the exploration of the possible mechanism(s) of drug 1994; File and Pellow, 1985; Griffiths and Goudie, 1987)
action involved in the complex behavioral paradigm used. resulted from the effects of the low and high concentrations,
Put in PK-PD terms, the PD parameters define the effects of which accounted for the observed stimulatory and sedative
alprazolam on the two rates of responding; the second peak effects, respectively. Alprazolam produces both nonspecific
occurred when the predicted serum alprazolam concentration increases in motor activity as well as anxiolytic effects (Bar-
had decreased to 0.037 to 0.045 mg/ml for each of the s.c barito et al., 1996; Hascoet and Bourin, 1977; Lopez et al.,
doses, after which the reinforcement rate rapidly and pro- 1988); whether the effect of alprazolam on increases in short
gressively recovered in a dose-related fashion (fig. 8). These IRTs in the present study was caused by either one or both
results suggest that reconditioning depends on serum con- effects requires further clarification.
centration, and hence is closely linked to PK; it occurred at For the three s.c. doses, the increases in the shorter-re-
twice the concentration of the IC50 value (table 1). Owing to sponse rate occurred both before the onset and after the offset
the different durations of action of the four alprazolam doses, of the sedative effect; whereas, the increase occurred only in
the interplay between the reinforcement rate and shorter- the latter phase for the i.v. 1.25 mg/kg dose. This reveals that
response rate shown in effect-concentration profiles (fig. 8) is the stimulatory effect becomes visible only at lower serum
more apparent than that shown in effect-time profiles (figs. 4 alprazolam concentrations in comparison with the higher
and 5). The stimulation-sedation model further suggests the concentrations associated with the sedative effect. This coin-
coexistence of stimulation and sedation components for al- cides with the ascending and descending limbs of the alpra-
prazolam, whereas the reinforcement rate defined by the zolam PK profile after s.c administration. After chronic BZ
indirect response model was an index for evaluating timing administration, tolerance develops rapidly to the sedative or
performance under the DRL 45-s schedule. depressant effect of high doses but does not develop to the
Although behavioral endpoints have been used widely for stimulatory effect of low doses (File and Pellow, 1985; Fla-1128 Lau and Heatherington Vol. 283
herty et al., 1996; Griffiths and Goudie, 1987). In addition, proteresis (clockwise hysteresis) observed was attributable to
repeated low-dose administration can even enhance the stim- the onset of the sedative effect. This can be seen by compar-
ulatory effect (Sansone, 1979). To our knowledge, no mecha- ing it with the effect after the i.v. 1.25 mg/kg dose (fig. 8);
nism has been proposed for these observations, hence our many other mechanisms have been suggested, such as acute
interest in promulgating the stimulation-sedation model. If, tolerance (Ekblom et al., 1993; Laurijssens and Greenblatt,
indeed, stimulatory and sedative effects are concurrently 1996; Porchet et al., 1988). Modeling the effects of alprazolam
present and both exhibit sigmoidal Emax functions but are on shorter-response rate was a more complex task because no
opposed components, then stimulation would become evident simple function can simultaneously account for the two ob-
and progressively enhanced as tolerance to sedation devel- served peaks. The stimulation-sedation model described the
oped. shorter-response rate by using two effect-link, sigmoidal
If one uses the above rationale and considers that the Emax models representing different hypothetical sites but
second peak in the DRL performance represents the transi- having actions opposite in direction (fig.1).
tion phase for recovery from the sedative effect, then it is It is best to determine a drug dose-response relation under
perhaps not surprising that adverse “rebound” side effects conditions where a preceding dose has no residual effect on
are observed (e.g., early-morning insomnia) as special fea- the succeeding dose for both PK and PD studies. By using the
tures during chronic BZ use in humans, intruding sooner and steady state performance under a DRL 45-s schedule, we
becoming stronger. Furthermore, the violent behavior asso- have found that no mutual interference (e.g., tolerance) oc-
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ciated with flunitrazepam (“Roches”) reported recently may curred between doses for midazolam, alprazolam and caf-
also be attributed to the stimulatory component of the drug feine when these doses were separated by 3 to 5 days (Lau et
(Wesson et al., 1996). The rebound period in humans resem- al., 1996, 1997, in press). Therefore, learning and experience
bles many aspects of the second stimulation peak in DRL do not play a role in the observed alprazolam effects even
performance. For example, behaviorally, it is the transient though the sequence of the route of administration was fixed
rebound (i.e., stimulatory or agitated) phase for returning to for both the PK and PD studies. Furthermore, alprazolam PK
base line; pharmacokinetically, it is associated with decreas- was not altered by repeated alprazolam dosing separated by
ing BZ concentrations. Thus, the stimulation-sedation model 3 to 5 days even in the presence of caffeine (Lau et al., 1997).
and DRL performance may serve as a laboratory model for In conclusion, we have demonstrated, by using three PD
studying human rebound agitated behavior and tolerance. models in the context of PK-PD modeling, that the two mea-
Although BZs commonly are prescribed for chronic use, sures of DRL performance, the reinforcement and shorter-
single dosing is also used in anesthesia, and in hypnotic and response rates, are valid, clinically relevant PD measures for
anxiolytic therapies. In single-dose PD studies, a delay is the investigation of the effects of alprazolam. There were two
often observed between drug serum concentrations and drug serum alprazolam concentration-dependent peaks in the
effect. This so-called hysteresis is generally treated by as- shorter-response rate for the s.c. doses, whereas only the
suming an effect compartment in an effect-link model (Shei- second peak was observed for the i.v. 1.25 mg/kg dose. This
ner et al., 1979), although other models, including indirect dose helps to identify the first peak as the transition phase
response models, also have been applied (Dayneka et al., before the onset of the sedative effect and the second peak as
1993; Jusko and Ko, 1994). The decrease in reinforcement a transient, rebound phase in the recovery from the sedative
rate produced by alprazolam was best described by an indi- effect. The reinforcement rate is an index for evaluating the
rect response model, because the peak effect (i.e., maximum deficit in timing performance. Although the effect of alprazo-
inhibition) occurred during a longer period (5– 45 min); the lam can be described in behavioral terms, PK-PD modeling
effect-link model requires that all dose levels produce a max- not only outlines the performance and its relation to alpra-
imum effect at the same time (Dayneka et al., 1993). During zolam serum concentration but also hypothesizes the coex-
model formulation, three other models were tested, an indi- istence of stimulation and sedation components for alprazo-
rect response model incorporating stimulation of Kout (ade- lam. The stimulation-sedation model may help in delineating
quate description but higher AIC), an effect-link model the possible mechanisms for the adverse rebound side effects
linked to the central compartment (good description for indi- and of tolerance observed in humans.
vidual doses, however large variation and higher AIC value)
and an effect-link model linked to the peripheral compart- Acknowledgment
ment (this did not optimize). In humans, the delay to the The authors thank Dr. J. L. Falk for his helpful suggestions and Y.
onset of the effect has been observed with alprazolam and Wang and F. Ma for their meticulous skills in catheterization of the
has been attributed to a distributional delay (Smith et al., jugular vein, HPLC and data analyses. We also thank Dr. B. E.
1984). However, no hysteresis was observed between mida- Williams of the Upjohn Co., Kalamazoo, MI, for generous supplies of
zolam blood concentrations and EEG effect in rats (Mandema alprazolam and its two metabolites.
et al., 1992). For the three s.c. doses in the present study, the
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