Introduction

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Cocaine, a psychomotor stimulant, is known to produce behavioral activation, to serve as a discriminative stimulus, and to support intravenous cocaine self-administration (Woolverton and Balster, 1982; Johanson and Fischman, 1989). These cocaine-induced effects correlated with plasma cocaine concentrations in humans (Javaid et al., 1978; Cone et al., 1988; Farre et al., 1993; Evans et al., 1996), in rats (Boni et al., 1991; Falk et al., 1991; Lau et al., 1991), in mice (Benuck et al., 1987), and in primates (Lamas et al., 1995). The most apparent reason for studying relations between response and drug concentration is to better understand the mechanisms of drug action. For example, pharmacodynamic (PD) models were developed to demonstrate acute tolerance to the chronotropic and subjective effects of cocaine in humans (Ambre et al., 1988; Noe and Kumor, 1991); however, such modeling often is not performed in animal behavioral research.

In past research, we integrated pharmacokinetics (PK) and PD to study the action of alprazolam and its interaction with caffeine (Lau and Wang, 1996; Lau et al., 1997a). The PD measure used in those studies was performance under the differential reinforcement of low rate (DRL) 45-s schedule, which produces "spaced responding" or "timing" behavior. The DRL 45-s schedule of reinforcement results in low rates of responding, as only those responses that occur after a minimum time interval (in this case, 45 s) after a previous response are reinforced; responses that occur before an interval of 45 s has elapsed are not reinforced, and the timing interval is reset. Interresponse time (IRT) profiles and the number of responses can be recorded throughout the session. There are two measures, the density of reinforcement and the shorter-response (or nonreinforced) rate, for studying drug action. DRL performance satisfies many of the criteria (i.e., objective, continuous, sensitive, and reproducible) proposed as ideal for PD measurement (Laurijssens and Greenblatt, 1996). Drugs can alter the IRT distribution and disturb its sequential patterning. It has been noted that short IRTs are followed by further short IRTs with high probability, and the same is true for the reinforced IRTs as described by the observed sequential dependencies (Weiss et al., 1966). The increased short IRTs is the stimulatory effect herein reported.

Although we have characterized the interaction of alprazolam and caffeine by PK-PD modeling (Lau and Wang, 1996; Lau et al., 1997a), the only PD measure used was the density of reinforcement under the DRL 45-s schedule. By using both the shorter-response rate and the density of reinforcement, we were able to demonstrate that a high dose of a benzodiazepine (alprazolam or midazolam) revealed both stimulatory and sedative components, which are low- and high-concentration effects, respectively, as the drug concentration changed across the 3-h DRL session (Lau and Heatherington, 1997; Lau et al., 1998). The approach of simultaneous PK-PD optimization enabled us to define the DRL performance numerically and to hypothesize the coexistence of stimulation and sedation components for alprazolam and midazolam.

Cocaine increases various aspects of motor function, such as locomotor activity, in a dose-related fashion (Stripling and Ellinwood, 1976; Post and Contel, 1983; Lau et al., 1991). A significant correlation was found between locomotor activity-time profiles and serum or brain cocaine concentration-time profiles in rodents (Benuck et al., 1987; Reith et al., 1987; Falk et al., 1991; Lau et al., 1991), but no explicit PD models were used in these studies. Inasmuch as one can use the DRL 45-s schedule to measure the stimulatory effect as mentioned above, the aim of the present study was to investigate the effects of cocaine on the DRL 45-s performance and the interplay between the shorter-response rate and the density of reinforcement by the integration of PK and PD. The intravenous route was chosen for its rapid onset of action and its reliability without interference from issues of absorption, first pass, bioavailability, and so on. The PD of cocaine under DRL schedules has been characterized in rats only from the standpoint of the dose-effect relation after the extravascular route of administration (Woolverton et al., 1978; Wenger and Wright, 1990), but the concentration-effect relation has not been examined. Rather than viewing drug action as a relation between the dose administered and its PD effect, it is more accurate to relate the drug serum concentration to the effect because this relation permits the partitioning of PK and PD components in drug action. Thus, the PK-PD analysis may allow the identification of the stimulant action of cocaine, which in turn may delineate its consequence on timing performance under the DRL 45-s schedule.

To understand the PD of cocaine in the light of its PK, the PK study must be conducted in animals that are not only of the same species, age, and gender but also exposed to conditions similar to those (e.g., food regimen) used in the behavioral study. These variables can affect the PK parameter or parameters of a drug. We limited the daily access of animals to food to implement a food-reinforced behavioral performance baseline under the DRL 45-s schedule. Thus, the investigation of cocaine and its metabolite concentration-time profiles for cocaine in rats under a food-limited regimen was a secondary aim of this study. It is important to include the active metabolite (norcocaine), if present, in the analysis of the concentration-effect relations. Cocaine disposition after intravenous administration has been characterized in free-feeding rats but not in food-limited rats (Nayak et al., 1976; Barbieri et al., 1992; Booze et al., 1997).

	Materials and Methods

Top Abstract Introduction Materials and methods Results Discussion References

PK

Animals. Four male, albino, virus-free Sprague-Dawley rats from HSD (Indianapolis, IN) were used. They were housed individually in a temperature-regulated room with a daily cycle of illumination from 7:00 AM to 7:00 PM. They were reduced to 80% of their initial, adult free-feeding body weights (mean, 382 g; range, 380-383 g) by receiving limited daily food rations (5 g for the first day, 10 g for the next 5 days) and were then maintained at their 80% body weights by receiving a daily food supplement (range, 14-16 g). They were held at these weights for 3 months before starting the experiment, the time period needed for training, and establishing baseline performance under the DRL 45-s schedule. Water was continuously available in the living cages. Experiments were executed in accordance with the "Guide for the Care and Use of Laboratory Animals" (National Institutes of Health Publication No. 85-23, revised 1985).

Drugs. Cocaine hydrochloride was obtained from the Research Triangle Institute (Research Triangle Park, NC) through the National Institute on Drug Abuse (NIDA). Drug doses of cocaine were expressed in terms of the salt and were corrected to cocaine base for the calculation of the PK parameters. The metabolites of cocaine (norcocaine, benzoylecgonine, and benzoylnorecgonine hydrochloride) also were obtained from the NIDA.

Catheterization. Right jugular vein cannulation was performed under sterile conditions and has been described previously (Lau et al., 1996). The proximal end of the silastic catheter was inserted into the jugular vein; the distal end of the catheter was threaded subcutaneously and exited through a small incision in the back of the animal. The catheter was flushed with 0.9% saline containing 50 U/ml heparin and was sealed with fishing line when not in use.

Reagents and HPLC. Reagents were obtained from standard commercial sources. A rapid and sensitive HPLC microsample (50 µl) method for the determination of cocaine and its metabolites has been described previously (Ma et al., 1997). The separation was performed on a Brownlee C₁₈ column (100 × 2.1 mm i.d., 5-µm particle size) (Perkin-Elmer, Norwalk, CT) with the use of an isocratic mobile phase consisting of methanol/acetonitrile/25.8 mM sodium acetate buffer (adjusted to pH 2.2 with 40% phosphoric acid) containing 1.29 × 10⁴ M tetrabutylammonium phosphate (12.5:10:77.5, v/v). The capacity factors for benzoylecgonine, benzoylnorecgonine, cocaine, norcocaine, and mazindol (as an internal standard) are 2.2, 2.7, 4.4, 7.3, and 10.8, respectively. Cocaine was separated from serum samples by liquid-liquid extraction. The detection limit was 2.5 ng/ml for each agent using a UV detector at 235 nm. The within-day and between-day precisions were high with the coefficients of variation in the range of 1.22-6.1% and 2.98-10.87%, respectively, for all compounds.

Drug Administration and Blood Sampling. Cocaine HCl was dissolved in 0.9% NaCl. The animals were allowed to recover for at least 2 days from the jugular vein catheterization before the drug administration series. The animals received intravenous bolus doses of cocaine (1, 2, and 4 mg/kg) via the jugular vein catheter. Each drug dose was separated by 3 to 5 days in a random order. All injections were given in a volume of 1 ml/kg body weight; cocaine solution was delivered in 15 s and was followed by 0.3 ml of 0.9% saline in 15 s.

Serum Protein Binding. We determined the fraction of free cocaine in 0.5 and 1 µg/ml serum samples by using the ultrafiltration procedure (Amicon, Beverly, MA) with a Micropartition Device purchased from Amicon. The unbound cocaine concentrations in the filtrates were analyzed in quadruplet by HPLC as mentioned above.

PD: DRL 45-s Performance

Animals. Seven male rats of the same strain were placed under the conditions, including a food-limitation regimen, similar to those used in the PK study. The mean initial, adult free-feeding body weight was 382 g (range, 381-384 g).

Apparatus. Four operant Plexiglas chambers were used and have been described previously (Lau and Wang, 1996). Each chamber, equipped with a response lever and a stainless steel food-pellet receptacle into which 45-mg dustless pellets (BioServ, Frenchtown, NJ) could be delivered, was enclosed in a sound-attenuating shell and was controlled by an IBM-type 486X computer. Session contingencies were programmed and data recorded using QuickBasic.

Procedure. Animals were magazine trained initially for 15 min on a noncontingent random-time schedule. Responses on the lever were shaped by successive approximation and were reinforced when IRTs were greater than 3 s. The temporal requirement was slowly increased to an IRT of 45 s over 10 to 20 sessions. Once training was complete, a 3-h operant session was conducted at the same time every day. After intersession performance had stabilized (i.e., the performance did not vary by more than 5% from the baseline for each subject), right jugular vein catheters were implanted as described above. The animals received cocaine i.v. with administration of vehicle, 1, 2, or 4 mg/kg. All injections were given immediately before a session and were separated by 3 to 5 days in a random order.

Data Analyses. The IRT distributions after the administration of vehicle and cocaine doses were analyzed for 3-h sessions. The first 2 min of data, which allowed for the transient effects of handling, were not included in the analysis. Baseline IRT distributions for each session that immediately preceded each injection also were analyzed. For each rat, there were four baseline-day values that were averaged and treated as the mean baseline effect. Responses with IRTs of 45 s (reinforced) and <45 s (shorter or nonreinforced) were derived from the IRT distributions and were calculated as rate (responses per min). The total number of responses consisted of responses with IRTs of 45 s and <45 s. Efficiency was calculated as the ratio of reinforced responses to total responses. For constructing effect-time profiles, the shorter-response rate and density of reinforcement were transformed to mean percent baseline values to compensate for individual differences in DRL performance; that is, the effect is expressed as a function of baseline [E = E_c/E_b)], where E denotes effect, E_b denotes baseline effect, and E_c denotes cocaine effect.

PK-PD Modeling

We used the pooled data (i.e., the full PK data set of 112 concentrations for the four animals and the full two PD data sets of 210 shorter-response rates and 210 densities of reinforcement for the seven animals) to perform PK and PD data analyses using the SAAM II software system (SAAM Institute, 1997). We chose the between-group design for the PK-PD modeling to prevent any effect of blood sampling on DRL 45-s performance. Assessment of the goodness of fit of each proposed model to experimental data was based on Akaike's Information Criterion (AIC), objective function, correlation matrix, residual and weighted residual plots, and precision of parameter estimates (S.D.), which is derived from the covariance matrix. The values of the objective function are a measure of how well the calculated values match the data values, whereas the values of AIC can be used to evaluate model order and perform model discrimination. On an a priori basis, we assigned a 0.1 fractional standard deviation (FSD) to each data set, but for each of the 57 data sets, we estimated a scale factor for its measurement error. The integrator tolerance used for the differential equation integration was 0.1%.

PK Analysis. We analyzed serum concentration-time profiles using compartmental modeling. The cocaine serum concentration-time profile was modeled with an open two-compartment system with elimination from the central compartment after intravenous administration. Three PK models were used (Fig. 1, middle), one for each dosing regimen. Each model contains the same set of PK parameters for the four animals: the volume of distribution at the central compartment (V_c) and the rate constants [k_{(2, 1)}, k_{(1, 2)}, and k_{(0, 1)}]. The PK parameters were estimated by simultaneously fitting all data. These parameter values were used to calculate A, B, , and  by standard formulae for the following equation, which describes the serum drug concentration C_p at any time, t, for cocaine: where the terms A and B are the extrapolated zero intercepts, and  and  represent the apparent first-order distribution and elimination rate constants, respectively. The half-life (T_1/2) for the distribution or elimination phase was calculated by the following equation: T_1/2 = 0.693/ or . The area under the serum cocaine concentration-time curve from time 0 to infinity is called the area under the curve [AUC_(0-)]. The area under the first moment [AUMC_(0-)]curve from time 0 to infinity is the area from 0 to infinity under the product of serum cocaine concentration and time. We calculated AUC_(0-) and AUMC_(0-) by the following formulae: AUC_(0-) = A/ + B/ and AUMC_(0-) = A/² + B/². These values are not PK parameters in themselves but are used to calculate other PK parameters: total clearance (Cl) was then defined as Dose/AUC_(0-), and volume of distribution at steady state (V_ss) was defined as Dose × AUMC_(0-)/AUC²_(0-). The mean residence time (MRT) for intravenous cocaine can be obtained from AUMC_(0-)/AUC_(0-).

View larger version (32K): [in this window] [in a new window]   Fig. 1.   Diagrammatic representation of integrated PK (n = 4; s1-s4, middle) and PD (n = 7; ss1-ss7) models used to describe the shorter-response rate (top) and the density of reinforcement (bottom) after administration of a single intravenous dose of cocaine.

PD Models. A multicompartmental model incorporating two link compartments, representing shorter-response rate and density of reinforcement compartments, was used to describe the data and has been described previously (Lau and Heatherington, 1997; Lau et al., 1998). This effect-link model was based on that proposed by Sheiner et al. (1979) wherein an effect compartment is linked to the central compartment via the first-order rate constant (k1e_st), which is very small relative to the other rate constants (Fig. 1). The general assumption is that mass loss via k1e_st is "negligible" (Sheiner et al., 1979); however, to ensure no loss of mass to the effect compartment, a "dummy" compartment was linked to the central compartment via the rate constant k1e_st. The addition of this compartment did not increase the complexity of the model, as the rate constant was fixed. Drug effect compartment kinetics were defined by the loss rate constant, k_eo.

Shorter-Response Rate (IRT < 45 s). The increase in shorter-response rate after cocaine administration is described by the sigmoidal E_max equation, which is expressed in terms of the serum cocaine concentration in the shorter-response rate compartment (Ce) such that where E₀, E_max, and EC₅₀ are the baseline response, maximal response, and concentration required to produce 50% maximal response, respectively, and n is the Hill factor. The subscript "srr" denotes shorter-response rate. The volume of the hypothetical shorter-response rate compartment (Ve_srr) was calculated by the following equation as described previously (Lau and Heatherington, 1997): Ve_srr = (kle/k_{eo, srr})*V_c. One set of PD parameters (E_max, EC₅₀, E₀, n, k_{eo, srr}, kle) was estimated to describe the shorter-response rate for the seven animals after cocaine administration (1-4 mg/kg).

Density of Reinforcement (45-55-s bin). The decrease in density of reinforcement after cocaine administration is described by the classic inhibitory E_max model, the model complementary to the sigmoidal E_max model for the description of an increasing function, which is expressed in terms of Ce such that where E_o, IC₅₀, and Ce are the baseline response, cocaine concentration required to produce 50% inhibition, and concentration in the density of reinforcement compartment, respectively, and i is the Hill factor. The subscript "dr" denotes density of reinforcement. The volume of the hypothetical density of reinforcement compartment (Ve_dr) was calculated as described above. One set of PD parameters (IC₅₀, i, E₀, k_{eo, dr}, kle) was estimated for the seven animals after cocaine administration (1-4 mg/kg).

Integration of PK and PD. After initial PK parameter estimates were obtained as described above, the integrated PK-PD model incorporated the PK model and the PD models for the shorter-response rate and the density of reinforcement after intravenous cocaine administration (1-4 mg/kg). All data (PK and PD) were fitted simultaneously. The principle of parsimony was used to examine whether the parameters could be shared among the three cocaine doses. Only parameters resulting from the integrated model are presented. A diagrammatic representation of the PK-PD models for a cocaine dose is shown in Fig. 1.

	Results

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PK. PK parameters reported in Table 1 (left) describe the serum cocaine concentration-time profiles for the three cocaine doses (Fig. 2A). As an example, Fig. 2B shows the individual observed and predicted profiles after 2 mg/kg cocaine administration. Cocaine was eliminated according to a biphasic process after intravenous administration (Fig. 2A); it was rapidly distributed and eliminated with a distribution half-life (T_1/2) of 1.09 min and a terminal elimination half-life (T_1/2) of 14.93 min (Table 1, left). The V_c and V_ss were 0.69 and 2.24 liters/kg, respectively. Clearance and MRT were 8.31 liters/h/kg and 16.15 min, respectively. Cocaine AUC_(0-) increased linearly as a function of dose.

View larger version (30K): [in this window] [in a new window]   Fig. 2.   Measured and predicted serum cocaine concentration-time profiles after intravenous cocaine administration for (A) 1-4 mg/kg [mean (S.E.)] and (B) 2 mg/kg [individual data (s1-s4)]. C, Mean (S.E.) measured serum benzoylecgonine concentration-time profiles after 1 to 4 mg/kg cocaine intravenous administration.

PD: DRL 45-s Performance. Figure 3 shows the effects of cocaine on IRT distributions for the 3-h sessions. Cocaine increased the shorter IRTs (<45 s) in a dose-related fashion, with two apparent peaks in the bins 1 to 4.9 s and 10 to 19.9 s; the greatest increase occurred in bin 1 to 4.9 s after 4 mg/kg cocaine administration. Cocaine, as a function of dose, decreased the IRTs in bins 40 to 44.9 s and 45 to 49.9 s, bins immediately adjacent to the 45-s criterion. No other reinforced IRTs were affected by cocaine in comparison to those for the vehicle administration.

View larger version (20K): [in this window] [in a new window]   Fig. 3.   Mean effects of intravenous cocaine (0-4 mg/kg) on IRT distributions during 3-h sessions. All responses before the first arrow are nonreinforced (<45 s); others are reinforced (45 s). The region between the two arrows is the 45- to 55-s bin (n = 7).

View larger version (25K): [in this window] [in a new window]   Fig. 4.   Mean (S.E.) effects of cocaine (1-4 mg/kg) for the 3-h sessions on (A) density of reinforcement (inset shows this rate normalized to percent baseline values), (B) shorter-response rate, (C) response rate, and (D) efficiency. B, Baseline. V, Vehicle.

View larger version (40K): [in this window] [in a new window]   Fig. 5.   Mean measured (S.E.) and predicted percent baseline effect-time profiles after intravenous administration of cocaine (0-4 mg/kg, n = 7). A, Shorter-response rate. B, Density of reinforcement. Measured and predicted percent baseline effect-time profiles after 2 mg/kg cocaine intravenous administration for individual animals (ss1-ss7). C, Shorter-response rate. D, Density of reinforcement.

PK-PD Modeling. The PD parameters for the shorter-response rate and the density of reinforcement for the three cocaine doses are shown in Table 1 (right). The parameter k1e was fixed at 0.0001 min¹ for both effect-link models, a numeric value that has been shown to be of no consequence (Sheiner et al., 1979). For the shorter-response rate, the maximum effect (E_max) and EC₅₀ were 1733% of baseline and 0.467 µg/ml, respectively. For the density of reinforcement, the IC₅₀ was 0.070 µg/ml. The baseline value (E₀) was 101% for both measures. The Hill factor and k_eo for the density of reinforcement (2.83 and 0.379 min¹, respectively) were greater than those for the shorter-response rate (1.58 and 0.142 min¹, respectively). The predicted shorter-response rate- and density of reinforcement-time profiles are shown by solid lines in Fig. 5, A and B; as an example, Fig. 5, C and D, show the individual observed and predicted profiles after 2 mg/kg cocaine administration.

View larger version (34K): [in this window] [in a new window]   Fig. 6.   Mean measured percent baseline shorter-response rate and density of reinforcement versus model-predicted serum cocaine concentration at the effect compartments after intravenous cocaine administration (1-4 mg/kg).

	Discussion

Top Abstract Introduction Materials and methods Results Discussion References

Cocaine was rapidly distributed and eliminated for each of the three intravenous doses used and had a terminal elimination half-life of 14.93 min. This study is the first to integrate cocaine PK and PD using two simultaneous measures of a schedule-controlled behavior across three intravenous doses in rats; others have used the effect of a single intravenous dose on one measure of spontaneous activity (Hutchaleelaha et al., 1997). Cocaine increased the shorter-response rate and decreased the density of reinforcement in a dose- and time-related fashion under the DRL 45-s schedule (Figs. 4, A and B, and 5 A and B). The monotonic effect of cocaine on shorter-response rate-time profiles in the present study resembles the effect of intravenous cocaine doses (1-4 mg/kg) on locomotor activity (unpublished data). The changes in shorter-response rate and density of reinforcement were directly interpretable as functions of cocaine concentration in the respective hypothetical effect compartments with the use of sigmoidal E_max and inhibitory E_max models, respectively. Because the EC₅₀ was greater than IC₅₀, the shorter-response rate began to return toward baseline sooner than did the density of reinforcement (Fig. 6). As cocaine concentration decreased to less than the EC₅₀ value, only then did the density of reinforcement begin to return toward baseline. Thus, the density of reinforcement is an index for evaluating the deficit in timing performance because it rapidly returned to the baseline level after the disappearance of the stimulatory effect (Fig. 6). Although the interplay between the two measures is apparent in effect-time and concentration-effect plots (Figs. 5, A and B, and 6), the latter demonstrated that the intensity of the effects of cocaine depends solely on concentration regardless of the dose. Collectively, the PK-PD analysis allows one to identify the stimulant action of cocaine, which in turn delineates its consequences on timing performance under the DRL 45-s schedule.

Cocaine AUC_(0-) increased linearly as a function of dose (Table 1). During model formulation, we found that the values of V_c for the three PK models were similar across cocaine doses (0.69, 0.73, and 0.71 liters/kg for 1, 2, and 4 mg/kg cocaine, respectively). In addition, the values of V_c were similar across the four animals (0.61, 0.68, 0.61, and 0.76 liters/kg) when V_c was estimated for each animal. Although one value of V_c can be shared for all three dose levels, the rate constants [k_{(2, 1)}, k_{(1, 2)}, and k_{(0, 1)}] were somewhat dose dependent, especially for the lowest dose (1 mg/kg) as reflected in Fig. 2A. It has been reported that cocaine distribution, but not elimination, was dose dependent in rats (Booze et al., 1997). Inasmuch as the major aim of the present study was to obtain a good description of cocaine concentrations for subsequent use in PD modeling, we changed the weight on the terminal portion where there was more noise to 0.2 FSD for the 1 mg/kg dose as opposed to the a priori assigned 0.1 FSD as described in Materials and Methods. As a result, one set of PK parameters was able to describe the serum cocaine concentration-time profiles across the three dose levels (Table 1, left).

Cocaine PK has been characterized in humans (Barnett et al., 1981; Inaba, 1989; Jeffcoat et al., 1989) and in animals (Nayak et al., 1976; Benuck et al., 1987; Lau et al., 1991; Booze et al., 1997) after different routes of administration. The present study is the first, to our knowledge, in which dose-response cocaine PK and metabolite profiles in a within-subject design after intravenous administration were investigated in rats under a food-limited regimen. For free-feeding rats, cocaine dose-response PK was investigated in a between-subject design (Booze et al., 1997). The values of MRT and the distribution and elimination half-lives were somewhat larger with venous blood sampling in the present study in comparison to those obtained with arterial blood sampling (Booze et al., 1997). Collectively, after intravenous cocaine administration, cocaine PK in rats under the food-limited regimen was in large part not different from that in rats under the free-feeding regimen except for the metabolite profile; norcocaine was not detected in the present study.

The effect-time and concentration-effect profiles (Figs. 5, A and B, and 6) indicated that the effect of cocaine on shorter-response rate or density of reinforcement exhibited two distinct characteristics: first, the E_max was attained, and second, the effect was at baseline when cocaine concentration was not present; that is, the curve starts at the origin, increases or decreases monotonously, and approaches E_max asymptotically for high concentrations. These properties can be characterized by the hyperbolic E_max model, which has been extensively used in research in enzyme kinetics and protein binding. Simultaneous optimization of the PK-PD pooled data revealed that neither the linear model nor the usual hyperbolic E_max model predicted the two measures well (objective function = 6.97 and 6.32, respectively; AIC = 4.52 and 4.22, respectively). However, when operational slope factors were added to the E_max model and its complementary inhibitory E_max model, the effects of cocaine on the shorter-response rate and the density of reinforcement were described and predicted well by the respective sets of PD parameters for the three cocaine dose levels (Table 1 and Figs. 5, A-D).

We have used the effect-link model (Sheiner et al., 1979) and an indirect response model (Dayneka et al., 1993) to account for the delays observed in the effects of s.c. alprazolam or s.c. midazolam on the shorter-response rate and the density of reinforcement under the DRL 45-s schedule (Lau and Heatherington, 1997; Lau et al., 1998). After a single intravenous infusion dose of cocaine, the effect-link sigmoidal E_max model was used to describe the relation between locomotor activity and plasma cocaine concentrations (Hutchaleelaha et al., 1997). On the basis of no apparent delay in effects on the DRL performance (Fig. 5, A-B), the rapid distribution for cocaine (T_1/2 = 1.09 min, Table 1), as well as studies showing that cocaine plasma or serum concentrations paralleled brain concentrations in rodents (Benuck et al., 1987; DeVane et al., 1989; Lau et al., 1991; Robinson et al., 1994), we tested the feasibility of linking the two PD models directly to the serum cocaine concentrations in the central compartment. For the shorter-response rate, that the ensuing PD parameters (i.e., E_max, and EC₅₀) were found to be dose dependent indicated that the concentration-effect relation in the central compartment was inappropriate for describing the in vivo pharmacology of cocaine despite its lower AIC value. One possible explanation is that a brief hysteresis occurred during the first 2 min of the session, for which data were not included in the behavioral analysis to exclude the transient effects of handling. For the density of reinforcement, the fitting did not optimize when the inhibitory E_max model was directly linked to the central compartment in the integrated PK-PD model. Thus, the two PD models were linked to the respective hypothetical effect compartments as shown in Fig. 1.

The effect-time profiles, which reflected the respective PK, provide a better understanding of drug action than do time course data collapsed into a single point. For example, alprazolam, a triazolobenzodiazepine, is used as an anxiolytic, antipanic, and antidepressant agent. Under the DRL 45-s schedule, alprazolam increased the shorter-response rate and decreased the density of reinforcement after intravenous administration, as did cocaine (Fig. 4, A and B), according to 3-h collapsed data (Lau and Heatherington, 1997). Although the densities of reinforcement-time profiles were similar for both classes of drugs, the shorter-response rate-time profiles differed distinctly (Fig. 5, A and B). After intravenous drug administration, cocaine increased the shorter-response rate immediately, whereas alprazolam increased the shorter-response rate only after the offset of the sedative effect. This is not surprising because cocaine is a putative psychomotor stimulant, whereas alprazolam is a sedative agent, although the two drugs have a similar pattern of disappearance in serum drug concentration after intravenous drug administration. Nevertheless, the density of reinforcement is an index for evaluating the deficit in timing performance for both drugs. Thus, the PK-PD approach allows one to examine apparently similar behavioral effects and uncover differences in these effects, which in turn correspond to their different pharmacological properties. Another distinct difference between the two classes of drugs was their effects on longer IRTs (>55 s), characteristic of their putative actions. Benzodiazepines (e.g., alprazolam, midazolam) increased the longer IRTs as a function of dose (Lau et al., 1997a, 1998), whereas cocaine did not (Fig. 3), which corresponded to the results observed for cocaine under DRL schedules in rats (Woolverton et al., 1978; Wenger and Wright, 1990).

It is best to determine a drug dose-response relation under conditions in which a preceding dose has no residual effect on the succeeding dose for both PK and PD studies. By using the steady state performance under a DRL 45-s schedule, we found that no mutual interference (e.g., tolerance, sensitization) occurred between doses for midazolam, alprazolam, and caffeine when these doses were separated by 3 to 5 days (Lau et al., 1996, 1997a, 1998). Furthermore, the drug action and interaction paralleled the respective PK in these studies. We performed cocaine PK-PD modeling using two parallel groups of animals as in our previous studies; these animals not only were of the same species, age, and gender but also were under the same feeding regimen. The major reason for the between-subject design was to prevent any possible effect of blood sampling on the DRL performance. The concentration-effect plots indicated that the effect of cocaine was directly proportional to cocaine concentration (Fig. 6). Thus, it is unlikely that residual effects were present during the cocaine dose-response determination under the DRL 45-s schedule.

Free, unbound drug concentration is closely related to pharmacological response, yet it is only occasionally measured. Although it was not the major aim of the present study to investigate the serum protein binding of cocaine, the free fraction of cocaine in serum samples was determined for archival purposes because such information is lacking with regards to rodents. We found that the free fraction of cocaine (31.3-33.1%) in the serum samples was independent of cocaine concentrations in the range of 0.5 to 1 µg/ml. In contrast, only 33.4% of cocaine was plasma protein bound in free-feeding rats (Nayak et al., 1976). Thus, the free fraction of cocaine may depend on variables such as species, age, gender, food regimens, and so on.

Cocaine dose-response PK and PD were conducted within a narrow range of doses (1-4 mg/kg) because the LD₅₀ for intravenous cocaine is 1.4 mg/100 g b.wt. in rats (Smith et al., 1991). The effects of cocaine on the two measures are purely concentration dependent and can be predicted by the two sets of PD parameters. That the effect in the concentration-effect relation reported herein was expressed as percent baseline values after normalization of actual data values implies that the predicted concentration-effect relation is not just limited to the DRL 45-s schedule but can be generalized to other values of the DRL schedule. However, careful considerations are needed in choosing optimal experimental variables, such as session length, to maintain a reinforced behavior.