Introduction

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As other nonsteroidal anti-inflammatory drugs (NSAIDs), naproxen has been extensively used during the past decades in the treatment of rheumatoid arthritis, febrile syndrome, and pain (Davies and Anderson, 1997). Naproxen inhibits both cyclooxygenase 1 (COX-1; constitutive) and cyclooxygenase 2 (COX-2; induced in settings of inflammation) and thereby the synthesis of prostaglandins (PGs) and thromboxanes (Vane, 1971; Ehrich et al., 1999; Langenbach et al., 1999).

Limited insight on the in vivo pharmacodynamic (pd) properties of NSAIDs, based on plasma/biophase levels and drug effect relationships, have been published. Recently, clinical protocols characterizing the antipyretic effects of ibuprofen in children related to biophase concentration (Kelley et al., 1992; Brown et al., 1998) or to plasma concentration by an indirect response model (Garg and Jusko, 1994; Trocóniz et al., 2000), have been proposed. Preclinical studies are useful alternatives to investigate different pharmacokinetic/pharmacodynamic (pk/pd) models to get insight into the "in vivo" mechanism of drug action. To our knowledge pk/pd modeling of the antipyretic effects of NSAIDs has not been performed in experimental models. Moreover, only few studies dealing with the time description of the anti-inflammatory effects of these agents (Castañeda-Hernández et al., 1995; Landoni and Lees, 1996; Landoni et al., 1999) have been published.

The injection of a wide range of doses of lipopolysaccharide (lps) into animals induces fever (Kluger, 1991; Yirmiya et al., 1994; Wachulec et al., 1997). It is known that lps-induced fever is driven by enhanced formation of cytokines such as interleukin-1, interleukin-6, interferons  and , and tumor necrosis factor-. The cytokines increase the synthesis of PGE₂ in circumventricular organs and near to the preoptic hypothalamic area. There PGE₂, via cyclic AMP increasing, triggers the hypothalamus to elevate body temperature (T^a). NSAIDs suppress this response by inhibiting the synthesis of PGE₂ (Ruwe et al., 1985; Oka et al., 1997; Zhang et al., 1997).

On the other hand, a time-dependent inflammatory reaction is observed following diverse doses of carrageenin injected to the paw of rats (Di Rosa et al., 1971; Castañeda-Hernández et al., 1995). In this model, COX-2 levels are elevated with a concomitant increase in prostaglandin production. Although these mediators do not appear to have direct effects on vascular permeability, both PGE₂ and PGI₂ markedly enhance edema formation and leukocyte infiltration by promoting blood flow in the inflamed region. Systemic inhibition of COX leads to a decreased production of PGs at sites of inflammation, and in the spinal cord (Coderre et al., 1990; Seibert et al., 1994). Vane and Botting (1994) suggested that PGs play an important role in promoting the signs and symptoms of inflammation. Nonetheless, as in the case of antipyretic effect of naproxen, the kinetics of its anti-inflammatory action is yet to be characterized.

Therefore, the goal of the current study was to develop a suitable pk/pd model for the antipyretic and anti-inflammatory effects of naproxen. To estimate its pd properties, experimentally induced pyresis or inflammation models were required. Thus, baseline variations within the time span of the experiments, as occurs with the adjuvant-induced alterations, represent an additional complexity, which should be included into the models.

	Materials and Methods

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This work includes results from the pk/pd modeling of the antipyretic (study I) and anti-inflammatory (study II) effects of naproxen in the rat.

Chemicals

The (S)-6-methoxy--methyl-2-naphthaleneacetic acid (naproxen) was supplied by Syntex S.A. (Madrid, Spain; study I) and by Syntex S.A. (Mexico City, Mexico; study II). Bayer (Madrid, Spain) and Novartis (Mexico City, Mexico) kindly supplied ibuprofen and sodium diclofenac (used as internal standards), respectively.

Lipopolysaccharide from Escherichia coli, serotype 0111:B4 was purchased from Sigma (Barcelona, Spain). Carrageenin was purchased from Sigma (St. Louis, MO). All reagents and solvents used were purchased from commercial sources and were of analytical grade.

Animals

Male Wistar rats, weighing 180 to 270 g were used in studies I and II. Animals were kept under laboratory standard conditions on a 12-h light/dark cycle with light from 8:00 AM to 8:00 PM, in a temperature (22°C)-controlled room, and were acclimatized for a minimum of 2 days before experiments were performed. They were housed in individual cages after the surgical procedures, with free access to water. Food was withheld for 12 h before the start of experiments. The protocols of the studies were approved by the Committee of Animal Experimentation of the University of Navarra and of the Centro de Investigación y Estudios Avanzados del Instituto Politécnico Nacional (Mexico City), respectively.

Surgical Procedure

The day before the experiments, rats were anesthetized i.p. with 100 mg/kg ketamine (Ketolar; Parke-Davis, Madrid, Spain) and 15 mg/kg xylazine (Rompun; Bayer, Mexico City, Mexico) for studies I and II, respectively.

In study I, two polyethylene (0.5 mm i.d., 11-cm-long; 0.3 mm i.d., 21-cm-long; Vygon, Ecouen, France) catheters were implanted in the right femoral artery and in the left jugular vein for blood sampling and drug administration, respectively. Rats in study II were surgically implanted with polyethylene catheters into the caudal artery as described previously (Granados-Soto et al., 1995). All catheters were filled with heparinized saline solution (20 IU/ml) to prevent clotting.

Experimental Protocol

Study I. Figure 1, left, represents the dosing and pk and pd data collection schedules used for study I. 

View larger version (13K): [in this window] [in a new window]   Fig. 1.   Experimental design carried out in the current study for the analysis of the antipyretic (left) and anti-inflammatory (right) effects.

Induction of fever and pd data measurements. Animals (n = 30) were randomly divided into five groups. Sterile saline solution (0.5 ml) containing 0.1 mg/kg lps was given i.p. to groups II to V, whereas the group I (baseline) only received 0.5 ml of sterile saline solution i.p. The lps solution was prepared at the beginning of the experiment and was injected at 37°C to animals. T^a was monitored in the rectum once every 30 min for 11 h just before and after the injection of the lps with a rectal thermometer (Panlab model 0331; Barcelona, Spain).

Drug administration and pk data collection. Naproxen was administered as an aqueous solution neutralized with NaOH and filled up to the administered volume with a phosphate-buffered solution (Lauroba et al., 1986). The pH of the administered solution was 7.6 and the maximum infused volume was 0.7 ml.

Drug analysis. Briefly, plasma samples (50-100 µl) were spiked with 50 µl of methanol containing the internal standard (ibuprofen) at a concentration of 200 µg/ml followed by acidification with 0.3 ml of 2 N HCl. After the double addition of 2 ml of tert-butylmethylether, samples were shaken on a vortex mixer for 1 min and centrifuged for 5 min at 3500 rpm. The organic phase was transferred to a 10-ml tube and evaporated to dryness at vacuum in a vortex evaporator at 40°C. The dried residues were reconstituted with 500 µl of mobile phase and 100 µl were injected into the chromatographic system. This consisted of a Hewlett Packard high performance liquid chromatograph HP 1100 equipped with a quaternary pump, an autosampler, and a diode-array detector set at 229 nm.

Study II. Figure 1, right, depicts the dosing and pk and pd data collection schedules used for study II.

Induction of paw inflammation and pd data collection. Animals (n = 24) were randomly allocated into four groups. To induce inflammation all animals were injected s.c. into the right hind paw with 0.1 ml of a 1% carrageenin suspension in 0.9% saline. Induced inflammation was measured by plethysmography as it has been described before (Winter et al., 1962). Paw swelling was determined once just before and during the following 6 h to carrageenin and drug administration.

Drug administration and pk data collection. Animals were treated orally with naproxen 1.7 mg/kg (group II), 3.2 mg/kg (group III), and 10 mg/kg (group IV), suspended in 0.5% carboxymethyl cellulose solution. The drug was given in a volume equal to 4 ml/kg and was simultaneously administered with the injection of carrageenin. Group I (control) received only carrageenin and blood samples were taken to study the influence of sampling on the time course of paw swelling.

Drug analysis. Measurements of naproxen in plasma were carried out using the method previously described by Borgå and Borgå (1997) with some modifications. Briefly, plasma samples (10 µl) were spiked with 20 µl of methanol containing the internal standard (diclofenac) at a concentration of 50 µg/ml. This mixture was diluted to 500 µl with phosphate buffer (pH = 7) and stirred until homogenization. Then, 20 µl was injected into the chromatograph.

Data Analysis

The time course of the drug concentration and antipyretic/anti-inflammatory effect were analyzed with a population approach using the first order method implemented in NONMEM (version V) software (Beal and Sheiner, 1992). This approach makes it possible to simultaneously fit data from all individuals, describing both mean population tendencies and individual profiles, and provides estimates for the interindividual variability and residual (intraindividual) error. Data for study I and II were analyzed separately.

Interanimal variability was fitted using exponential models. Residual variability was modeled by using a constant-coefficient variation model for plasma drug concentrations, and an additive model for effect measurements.

Model selection was based on the exploratory analysis of goodness-of-fit plots performed with Xpose package (Jonsson and Karlsson, 1999), the estimates of the parameters, and their confidence intervals. The minimum value of the objective function provided by NONMEM was also used as a criterion for model selection. The difference in the objective function between two hierarchical models is approximately chi square distributed; p < 0.05 was used as the level of significance. Results from data analysis are presented as estimated values and their relative standard error. Estimates of the interanimal and residual variability are expressed as coefficients of variation (%).

Pharmacokinetic Models. Naproxen disposition properties were characterized by compartmental models. In the case of study II, different absorption models were tested: first order, zero order, and Michaelis-Menten absorption models; the presence of a lag time was also explored.

Pharmacodynamic Models. Figure 2 shows the models fitted to the data for studies I and II.

View larger version (13K): [in this window] [in a new window]   Fig. 2.   Schematic representation of the pharmacodynamic model used to describe the data for study I (top) and study II (bottom). IR(t), input rate function of fever or inflammation mediators; KIN, first order rate constant of release of inflammation mediators into the inflammation compartment; Ksyn, zero order rate constant of formation of basal fever or inflammatory response; Kout, first order rate constant of degradation of fever or inflammatory response.

Study I: antipyretic effect. After injection of lps control group showed a time-varying response, which was modeled using the following model:

(1)

where dR/dt represents the rate of change in response (T^a); K_syn is the zero order rate constant of response formation and K_out is the first order rate constant of response degradation. IR(t), the input rate function representing the increase in the formation of fever mediators accounting for the temporal increase in response, was modeled nonparametrically using a linear spline. A linear spline is characterized by a number of real numbers called breakpoints and a number of polynomials, which simply join at the breakpoints (DeBoor, 1978). In this study the breakpoints were located at the times of observations. The number and location of the breakpoints were selected as a part of the model-building process. The heights of the spline at each of the breakpoints were parameters to be also estimated during the model-building process together with the rest of the pharmacodynamic parameters, and were constrained to be non-negative.

(2)

Study II: anti-inflammatory effect. Although previous equations were suitable for describing T^a data when applied to inflammation data, the model predictions obtained were not satisfactory. Thus, a more complex model was built to account for the delayed increase in inflammation in naproxen-treated groups in comparison with control. This model assumes that 1) carrageenin injection elicits a transient formation of inflammatory mediators (M), which is described by the input rate function IR(t) (see above); 2) the mediator-induced inflammatory response is governed by a first order rate constant (K_IN), which can be inhibited by naproxen in plasma; and 3) in absence of carrageenin and/or drug in the body, a certain degree of inflammation (baseline level) is maintained by the balance between the production (represented by the zero order rate constant, K_syn) and the degradation (represented by the first order rate constant, K_out) of inflammatory response. The model is represented by the following set of differential equations:

(3)

(4)

where dM/dt represents the rate of change of inflammatory mediators, dR/dt is the rate of change of inflammatory response, and DRUG is the effect of naproxen on the system. Different models were tested for DRUG: lineal, E_max, and sigmoidal E_max models.

Statistical Analysis. Results from studies I and II after injection of lps or carrageenin are showed as mean data with their corresponding standard deviations. Within each study, comparisons of the observed responses between the different groups were made by one-way ANOVA followed by a Tukey's posteriori test. Statistical significance was set at p < 0.05.

	Results

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Study I

Pharmacokinetics. A three-compartment model was used to describe the kinetics of naproxen in plasma. Estimates of the typical pk parameters and their values of interanimal variability are listed in Table 1. Mean observed and typical model-predicted plasma concentration versus time profiles are shown in Fig. 3. Mean observed plasma concentrations at the time the infusions were stopped were 46.22 ± 2.11, 55.45 ± 6.39, and 52.85 ± 2.72 µg/ml for the 30- and 15-min infusions, respectively.

View larger version (12K): [in this window] [in a new window]   Fig. 3.   Time course of plasma concentrations of naproxen in study I. Symbols represent mean observed data, lines represent typical model predictions, and vertical lines represent standard deviations.

Pharmacodynamics. Figure 4 shows the mean observed T^a versus time profiles for all groups injected with lps in study I. Baseline group showed a constant basal body T^a over a 12-h period with a mean ± S.D. value of 37.2 ± 0.06°C. Basal T^a recorded at the time of lps injection did not differ statistically among groups I to V (p > 0.05). In addition, at the times T^a were recorded between lps injection and the start of the drug infusions no statistical differences in T^a (p > 0.05) were found among groups II to V. A mean maximal increase in body T^a of 38.27 ± 0.15°C located at 5.3 ± 0.4 h after lps injection was found for group II; T^a then returned gradually to baseline; 11 h after lps injection mean observed T^a was 37.92 ± 0.33°C. Mean times to baseline were 8 ± 1.5, 11 ± 1, and 4.5 ± 1.6 h for groups III, IV, and V, respectively. The onset of the antipyretic effects was fast in the three groups. However, T^a returned to baseline with a 2- to 3-h delay with respect to time to peak plasma concentrations, indicating that observed effects and plasma drug concentrations could not be related directly.

View larger version (21K): [in this window] [in a new window]   Fig. 4.   Time course of rectal Ta after lps injection and naproxen administration (symbols, mean observations; lines, typical model predictions). Vertical lines represent standard deviations.

Pharmacokinetic/Pharmacodynamic Modeling Results. Figure 4 shows the typical model-predicted time course of T^a in all groups on the basis of the model described in Fig. 2 (top) and by eqs. 1 and 2. It can be observed that model predictions for groups III and IV are almost superimposable; the fact that plasma drug concentrations for both groups at early times after the end of the infusion were 9 to 11 times higher than the estimated value of IC₅₀, together with the high interindividual variability, could explain this issue. Figure 5 shows in solid line the selected shape for the linear spline representing the input rate of fever mediators responsible for the temporal increase in body T^a. The breakpoints were selected at times 0, 2, 6, and 11 h after lps injection. It can be observed that IR(t) has a value different from zero at t = 0. This result should be interpreted as an almost instantaneous increase in the synthesis of fever mediators after the lps injection. The effect of naproxen plasma concentrations on the inhibition of IR(t) was described by an inhibitory E_max model. Table 2 lists the estimates of the parameters of the linear spline and pd parameters and their estimates of interanimal variability; all parameters were estimated with an adequate precision. During the model building process E_max was estimated close to 1; for that reason, its value was fixed (Table 2). At times before lps injection dT/dt = 0 = K_syn  K_out · E₀, where E₀ is the basal T^a; then K_syn = K_out · E₀. The typical value of K_syn computed using the estimates of K_out and E₀ was 29.76°C/h.

View larger version (9K): [in this window] [in a new window]   Fig. 5.   Profiles of the selected input rate functions of fever (solid line) and inflammation (dashed line) mediators.

Study II

Pharmacokinetics. A one-compartment model was enough to describe the disposition of naproxen in plasma when the drug was given orally. The typical values of the estimates (and their associated interanimal variability) for plasma clearance (CL) and apparent volume of distribution (V), which in the case of the three-compartment model is the sum of the initial volume of distribution, and shallow and deep compartment volumes of distribution (V₁, V₂, and V_3, respectively; Table 1), were very similar between the two studies. Table 3 lists the typical pk parameters and their values of interanimal variability for naproxen obtained from study II; the mean observed and typical model-predicted plasma naproxen concentration versus time profiles are shown in Fig. 6. Relative bioavailability for the group receiving the lowest dose was fixed to 1, and bioavailability for groups receiving 3.2 and 10 mg/kg were estimated with a value significantly lower than 1 (p < 0.05); a 25% reduction of bioavailability was found in the highest dose group. Mean maximum plasma concentrations of naproxen were observed 20 min after drug administration in all groups and with values of 9.1 ± 0.8, 14.4 ± 0.7, and 39.3 ± 3.1 µg/ml for the 1.7-, 3.2-, and 10-mg/kg dose groups, respectively.

View larger version (14K): [in this window] [in a new window]   Fig. 6.   Time course of plasma concentrations of naproxen in study II. Symbols represent mean observed data, lines represent typical model predictions, and vertical lines represent standard deviations.

Pharmacodynamics. Figure 7 shows the mean observed paw swelling versus time profiles. Mean basal swelling values did not differ significantly between groups (p > 0.05). A maximum paw swelling of 46.55 ± 2, 48.7 ± 2.5, 44.5 ± 2.3, and 40.5 ± 2.4 ml was found for groups I-IV, respectively. These maximums were observed at 3.3 ± 0.8, 4.8 ± 0.26, 5.5 ± 0.55, and 5.9 ± 0.2 h, after the injection of carrageenin, respectively. No statistical differences were found between groups at the end of the experiment (p > 0.05). In groups III and IV paw swelling remained at basal levels for 2 ± 0.89 and 3 ± 0.52 h after the start of the experiment, respectively.

View larger version (16K): [in this window] [in a new window]   Fig. 7.   Time course of inflammation after carrageenin injection and naproxen administration (symbols, mean observations; lines, typical model predictions). Vertical lines represent standard deviations.

Pharmacokinetic/Pharmacodynamic Modeling Results. Figure 7 shows the typical model predicted time course of the inflammation response using the model described by eqs. 3 and 4 and Fig. 2 (bottom). In this case the shape of the selected linear spline was similar to the profile of a constant input rate function that could be characterized by K₀ (zero order rate constant) and T_syn, (duration of the input rate function). Figure 5 shows in dashed line the profile of the input rate function of inflammation mediators. The effect of naproxen was described by an inhibitory sigmoidal E_max model. The estimates of the pd parameters and their estimates of interindividual variability are listed in Table 4. E_max was also fixed to 1, since in the case of groups III and IV, plasma drug concentrations were able to block completely the onset of inflammatory response for 2 and 3 h, respectively. K_syn, computed as in study I, had a value of 19.2 ml/h.

	Discussion

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Study I

Pharmacokinetics. The estimates of V₁ (45.2 ml/kg) and CL (32 ml/h/kg) obtained from the fit of i.v. data were in agreement with those published previously in rats (Lauroba et al., 1986; Castañeda-Hernández et al., 1995), and also in humans where the estimates of CL and V reported by Davies and Skjodt (2000) were 42 ml/h/kg and 100 ml/kg, respectively. The fact that a three-compartmental model was selected, when, in general, most authors have used the two-compartmental model to describe the kinetics of naproxen in plasma, could be related to the i.v. infusion design used here and the extensive sampling.

Pharmacodynamics. To describe the time course of the antipyretic effects of naproxen, estimating at the same time reliable pd parameters, we induced fever experimentally by i.p. injection of lps (0.1 mg/kg) from E. coli (Wachulec et al., 1997). Several authors have used the same design to study the physiological factors influencing fever response (Cao et al., 1997; Matsumura et al., 1998; Molina-Holgado et al., 1998). Our results were very similar to those obtained by Wachulec et al. (1997), using rats of the same strain, sex, and age, and receiving the same dose of lps; the authors found a maximum mean increase of 38.6°C located 6 h after lps injection. In our study those values were 38.3°C and 5.5 h, respectively. At the time the experiment ended, 11 h after lps injection, mean observed T^a was 37.92°C, a reduction of almost 40% on the maximum achieved.

Study II

Pharmacokinetics. When the area under plasma drug concentrations corrected by mean dose versus time curves (AUC_dose) was computed, the value of AUC_dose obtained from the 1.7-mg/kg oral dose was comparable with the value of AUC_dose from study I (29 and 30 mg · h/ml, respectively), but AUC_dose from the 3.2- and 10-mg/kg oral dose groups tended to be lower (23 and 22 mg · h/ml, respectively). On the basis of these preliminary results we assumed complete F for the lowest oral dose group and allowed the estimation of F for the higher oral dose groups. Previous studies have also shown that naproxen has a high but not complete F (Lauroba et al., 1986). The reason for a decrease in F when the dose is increased is not clear but it could be the case that there is a limited time for the drug to be absorbed in the gut, and that time limitation could cause the fraction of dose absorbed to be lower for the highest doses.

Pharmacodynamics. The carrageenin-induced edema model has long been used to evaluate the anti-inflammatory activity of NSAIDs (Seibert et al., 1994; Smith et al., 1998). The time profile of the paw swelling found for the baseline group in the current study was very similar to the one published by Castañeda-Hernández et al. (1995), using rats of the same strain, sex, and age, receiving the same dose of carrageenin. They found a maximum paw swelling increase of 38% located after 4 h after carrageenin injection, whereas we observed corresponding values of 46.2% and 4 h, respectively. By the time the experiment was stopped, average paw volume had been declined to 34.3% in our study and 35% in Castañeda-Hernández et al. (1995) study. On the other hand, Davies and Skjodt (2000) indicated that plasma naproxen concentrations of 50 µg/ml or doses between 3.5 and 22 mg/kg were needed to achieve an adequate anti-inflammatory response in humans, which are values very close to the ones reported in the current study.