Pharmacokinetic models for the saturable absorption of cefuroxime axetil and saturable elimination of cefuroxime

European Journal of Pharmaceutical Sciences 21 (2004) 217–223

Pharmacokinetic models for the saturable absorption of cefuroxime axetil and saturable elimination of cefuroxime P. Ruiz-Carretero, M. Merino-Sanjuán∗ , A. Nácher, V.G. Casabó Departamento de Farmacia y Tecnolog´ıa Farmacéutica, Faculty of Pharmacy, University of Valencia, Avda, Vicente Andrés Estellés s/n, 46100 Burjassot, Valencia, Spain Received 28 July 2003; received in revised form 6 October 2003; accepted 13 October 2003

Abstract Since oligopeptidic drugs such as ␤-lactam antibiotics share the same carriers in humans and animals, the absorption and elimination kinetics of cefuroxime (C) were investigated in rats. Plasma C concentrations were measured by liquid chromatography. Pharmacokinetics and bioavailability of C in the rat were examined after intravenous (i.v.) administration at three doses (1.78, 8.9 and 17.8 mg) of cefuroxime sodium and oral administration at two doses (2.02 and 8.9 mg) of cefuroxime axetil (CA). Preliminary fits using data from intravenous administration of C showed that the drug disposition kinetics were clearly nonlinear, with an increase in plasma clearance as the intravenous dose increased. After oral administration of CA, normalized Cmax was higher for smaller dose than for the largest dose. The population pharmacokinetic parameters were obtained by means of nonlinear mixed effect modelling approach according to a nonlinear elimination and nonlinear absorption two-compartment model. The nonlinear elimination could be attributed to a saturable renal tubular reabsorption of the antibiotic and nonlinear intestinal absorption of CA mediated by carrier system. The oral bioavailability of C, calculated by numeric integration of an amount of CA drug absorbed was 22 and 17% for 2.02 and 8.9 mg of prodrug administered orally. © 2003 Elsevier B.V. All rights reserved. Keywords: Cefuroxime; Cefuroxime axetil; Pharmacokinetic models; Nonlinear mixed effects

1. Introduction Cefuroxime (C) is a broad-spectrum, ␤-lactamase-stable cephalosporin, which has well-defined pharmacokinetics after intramuscular and intravenous (i.v.) administration in the form of sodium salt (McEvoy, 2003; Wozniak and Hicks, 1991). When given by oral route, its absorption is lower than 1% of the administered dose, which restricts its use to the parenteral route. After administering the usual dose, C is 33–50% bound to plasma proteins. The apparent volume of distribution in adults is of 9.3–15.8 l/1.73 m2 (McEvoy, 2003). Indeed, ␤-lactam has been shown to be excreted by the renal anionic transport system, and administration of increasing doses of these drugs results in a nonlinearity of ␤-lactam elimination.

∗

Corresponding author. Tel.: +34-6-3544912; fax: +34-6-3544911. E-mail address: [email protected] (M. Merino-Sanju´an).

0928-0987/$ – see front matter © 2003 Elsevier B.V. All rights reserved. doi:10.1016/j.ejps.2003.10.006

The use of C by the oral route requires its administration in the form of prodrug, cefuroxime axetil (CA). Since C is not absorbed orally, the 1-acetyloxyethyl (axetil) ester of C was used to improve its gastrointestinal absorption. CA is used in the treatment of a wide range of infections, but exhibits poor variable bioavailability and thus it is difficult to establish the optimal oral dosage schedule. Accordingly, the pharmacological response of C shows great interindividual variability. In clinical practice, treatment in humans is established in an empirical way by modifying the dose of the prodrug and verifying the pharmacological response. The dosage schedule for C is 1 g twice a day intravenously, and CA is administered 250 mg twice a day orally, despite the fact that the prodrug shows quite variable absolute bioavailability, ranging from 30% in fasted to 50% in fed states (De Sommers et al., 1984; Finn et al., 1987; McEvoy, 2003; Williams and Harding, 1984). After oral administration, esterase in intestinal lumen can hydrolyze CA to the non-absorbable C in the gut lumen

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and is therefore suspected as a possible cause of incomplete bioavailability (Mosher et al., 1992; Ruiz-Balaguer et al., 2002). An in situ study in rat small intestine was developed in order to detect possible nonlinearity phenomena in absorption, that might explain the bioavailability variations of C after oral administration of CA. In turn, the variability in bioavailability obtained could be justified by the existence of interindividual variability in the enzymatic activity of the intestinal esterase responsible for the hydrolysis of the prodrug, as the greater the hydrolyzed fraction, the less the absorbable fraction would be (Ruiz-Balaguer et al., 1997, 2002). The present work was undertaken in rats, to find the processes to which nonlinear phenomena can be attributed in the pharmacokinetic model of intravenous C and oral CA. To allow the estimation of all the kinetic parameters of interest, a nonlinear mixed effect modelling approach was used to analyze data from parallel groups (Karlsson and Sheiner, 1994).

2. Materials and methods 2.1. Animals and surgical preparation All pharmacokinetic studies reported here adhere to the Principles of Laboratory Animal Care. Male Wistar rats weighing 250–300 g were used for all the experiments. Twenty-four hours before drug administration, the rats were subjected to jugular vein cannulation with a 12 cm-long fragment of medical-grade silicon tubing (Silastic, Dow Corning Co.; inner diameter: 0.5 mm; outer diameter: 0.94 mm). The anaesthesia solution administered prior to intervention was prepared by mixing 0.2 ml of a ketamine 50 mg/ml solution, 0.24 ml of a diazepam 5 mg/ml solution and 0.37 ml of an atropine 1 mg/ml solution. 2.7 ml/kg of anaesthesia solution was administered by an intraperitoneal injection. Under anaesthesia, 3.4 cm of the cannula was introduced into the jugular vein toward the heart and the free end was subcutaneously conducted to the dorsal base of the neck, where it emerged; the exteriorized end was closed with a polyethylene plug. The cannula was permanently filled with heparinized (20 IU/ml) saline solution. After surgery and until drug administration, animals were kept on fasting overnight with water freely available. 2.2. Administration and sampling protocol Glaxo Laboratories supplied CA and cefuroxime sodium. The internal standard, cefoxitin, was purchased from Merck Sharp & Dhome (Mollet del Vallés, Spain). Five groups of rats were randomly assigned intravenous or oral administration. In order to facilitate blood sampling

of conscious rats, a 15 cm-long silicon tube (bridge-tubing) was connected to the free end of the cannula. 2.2.1. Oral administration Two groups of seven rats were subjected to gastric intubation under light ether anaesthesia, and one group received 2 ml of solution containing CA, 1.01 mg/ml and the other one 4.45 mg/ml, in 20% propylene glycol isotonic saline solution. 2.2.2. i.v. administration Three groups of rats were administered a bolus of 2 ml of cefuroxime sodium (0.89, 4.45 and 8.9 mg/ml) in isotonic saline solution via the jugular cannula. The cannula was immediately rinsed with 2 ml of heparinized saline solution. Blood samples (0.5 ml) after oral and i.v. administration were withdrawn into heparinized syringes from the jugular vein cannula at 15, 30, 45, 60, 90, 120, 150, 180 and 210 min. After each sampling, the blood volume was replaced with the same volume of saline solution. The number of samples processed to obtain the curve of the plasma level of C was never larger than nine in a 15–210 min period, which corresponds approximately to four times the half-life of the antibiotic. In these conditions, the hematocrite value at the end of the experience had decreased about 19%. The plasma was immediately separated from erythrocytes by centrifugation (2000 rpm for 5 min) and stored at −30 ◦ C until analysis. 2.3. Analytical procedures The plasma samples were assayed for C content by high-performance liquid chromatography (HPLC), which provided excellent separation and quantification of the antibiotic. Previously, C was extracted from plasma samples through Bond Elut® cartridges. Firstly, 200 ␮l plasma were mixed with 25 ␮l of cefoxitin (200 ␮g/ml) saline solution (pH 6.7) as internal standard. The cartridges were rinsed with 2 ml of hexane and 100 ␮l of the prepared sample was immediately transferred to the cartridge. C and cefoxitin were eluted with 1 ml of methanol which contained 0.5% of ammonium acetate, and the elute was collected in a glass tube. The solution obtained was evaporated to dryness under low pressure and replaced with 100 ␮l of mobile phase. After centrifugation, 20 ␮l of the aqueous supernatant was injected into the chromatograph. The mobile phase was a mixture of acetonitrile and aqueous 0.050 M ammonium acetate and 0.050 M acetic acid buffer (pH 4.5), 14:86 (v/v). A flow rate of 2.0 ml min−1 was used. A reversed phase column (Spherisorb S-10 ODS-2, 250 mm × 4.6 mm) in conjunction with a C-130 B precolumn (Tecknokroma C-18) was used. A Perkin-Elmer spectrophotometer, model LC 90 BIO, set at 273 nm, was used to monitor the column effluent. Calibration curves covering the whole range of C concentrations in plasma samples were prepared in triplicate. The peak area ratio of C and the internal standard

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was measured in each sample and correlated with the C concentration. Excellent linear plots relating to the peak area ratios and C concentrations were obtained, and the intercept was not significantly different from zero. The accuracy and precision of the method were established using six concentrations covering the range of the concentrations to be analyzed. The accuracy and precision were evaluated by calculating the relative error and coefficient of variation, which were always less than 6.24 and 8.56%, respectively. The limit of quantification was 0.9 ␮g/ml. The results obtained were considered fully acceptable (Karnes and March, 1993). 2.4. Pharmacokinetic calculations and statistical analysis Non-compartmental preliminary analyzes using data from i.v. and oral administration of the drug separately by means of the WINNONLIN V.2.1 program (Metzler, 1989) was performed. Total area under the curve (AUC), clearance (Cl), volume of distribution at steady state (Vss ), mean residence time (MRT), and half-life in terminal phase (t1/2β ) were obtained in each animal from i.v. groups. After oral administration, Cl/F, Vd/F, tmax , Cmax and Cmax /D were also calculated. Differences in mean parameter values among i.v. groups and between oral groups were assessed by an ANOVA test. Non-proportional increases of the AUC versus doses were detected and compartmental pharmacokinetic models were developed to describe this behaviour. Pharmacokinetic models were fitted to the data from all animals simultaneously, using the NONMEM program (Beal and Sheiner, 1992). First-order (FO) method was used in estimation step. The pharmacokinetic analysis was based on a two-compartment kinetic model with first-order elimination and first-order absorption and degradation in intestinal lumen (basic kinetic model), or with addition of nonlinear processes when indicated. For all models, subroutine ADVAN6 and differential equations were used. The basic model was characterized by the following expressions: dQa = −ka Qa − kd Qa dt

(1)

dQc = ka Qa − k12 Qc + k21 Qp − kel Qc dt

(2)

dQp = k12 Qc − k21 Qp dt

(3)

where Qa , Qc and Qp are the amount of drugs in intestinal lumen, central and peripheral compartment, respectively; (k12 ) forward partition rate constant between blood and tissue; (k21 ) backward partition rate constant between blood and tissue; (kel ) elimination rate constant; (ka ) absorption rate constant of CA; and (kd ) degradation rate constant of CA in intestinal lumen. The population pharmacokinetic parameter (Vc ) volume of central compartment was estimated as scaling factor

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between the amount in the central compartment (Qc ) and plasma concentration (Cp ) of the drug. The POSTHOC function of NONMEM enabled estimation of the individual pharmacokinetic parameters using a Bayesian approach taking both individual observations and population effects into account. Several kinetic models, including nonlinearities in absorption and/or disposition processes were tried. Saturable absorption was modelled using both an absorption rate constant for each oral dose administered and a mechanistic Michaelis–Menten equation. The elimination process was characterized as a glomerular filtration, represented by first-order kinetics, and a process of active tubular reabsorption, represented by the Michaelis–Menten equation, considering that concentration of the drug in tubular lumen was equilibrated with plasma drug concentration. In this case, the following differential equations for remaining amounts in intestinal lumen and central compartment were used: dQa Vma (Qa /Vc ) =− − kd Q a dt Kma + (Qa /Vc ) Vma (Qa /Vc ) dQc =− − k12 Qc + k21 Qp dt Kma + (Qa /Vc )
 Vm (Qc /Vc ) − kel Qc − Km + (Qc /Vc )

(4)

(5)

where Vma is the maximal absorption rate expressed in amount per unit time, Kma the concentration at which the absorption rate is half-maximal, Vm the maximal tubular reabsorption capacity, expressed in amount per unit time, Km the concentration at which the tubular reabsorption rate is half-maximal; in this case kel denotes the first-order rate constant of glomerular filtration. All other symbols are described above. Differential equation for peripheral compartment was Eq. (3). Both interindividual variability in pharmacokinetic parameters and residual error in plasma concentration was modelled as exponential according to Eqs. (6) and (7): Pi = Ppop exp(ηi )

(6)

Cobs = Cpred exp(εi )

(7)

where Ppop is the population parameter value, η a normally distributed zero-mean variable with the standard deviation ω; Cobs the observed concentration; Cpred the predicted concentration by individual parameter Pi , and ε a normally distributed random variables with zero-mean and standard deviation σ. In the selection of the model, the objective function value provided by NONMEM was used. For hierarchical models, the difference in objective function value is distributed approximately Chi-squared and formal testing between models can be performed. A P level 0.01 was chosen for accepting a more complex model over a reduced one. For hierarchical models differing by one or two parameters, the corresponding differences in the objective function values were

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6.63 and 9.21, respectively. Precision in the estimation of the parameter values, quantified as the relative standard error (R.S.E.%), was also evaluated to select the final model. The graphical goodness of fit analysis was evaluated through the use of SPSS for Windows, version 11 (SPSS Inc., Chicago, IL). Bioavailability was obtained by numerical integration of the amount of drug absorbed using the following expression:  Qa∞   ∞ dQa Vma (Qa /Vc ) f = 0 = dt (8) D Kma + Qa /Vc 0 Both Qa and D were expressed as C active.

3. Results The observed C average plasma concentration-time profiles obtained after i.v. administration of C and after oral administration of CA are shown in Fig. 1. The average and standard error of the pharmacokinetic parameters of C calculated after i.v. administration by non-compartmental analysis of the experimental data are given in Table 1. Statistical comparison of the pharmacokinetic parameters as a function of the dose administered was performed using a one-way ANOVA test. The results of the statistical analysis are also shown in Table 1. No significant differences between mean values of terminal phase disposition half-life and terminal rate constant were found. Table 2 gives non-compartmental pharmacokinetic parameters of C after administration of CA by oral route. The

statistical results are also listed in Table 2. The tmax values were similar for the two doses administered by oral route. One-way ANOVA test showed that the rest of the pharmacokinetic parameters analyzed were statistically different (P < 0.05). In the description of the data, entering a saturable component, either as saturable absorption or saturable excretion, offered significant improvement over assuming linear models (linear model: MOF = 1175.42, saturable tubular reabsorption: MOF = 1077.43 and saturable absorption and saturable tubular reabsorption: MOF = 1023.99). The best model assuming saturable absorption and saturable renal reabsorption process using mixed effects model is shown in Table 3. Bioavailability values calculated are also given. Fig. 2 shows the correlation between individual and population predicted versus observed C plasma concentrations for the model selected. 4. Discussion Non-compartmental analysis was carried out to obtain the individual pharmacokinetic parameters of C after i.v. and CA oral administration. Through a one-way ANOVA test, significant differences were assessed in Cl and normalized AUC associated with the dose of C administered i.v., which indicates that nonlinearity in the elimination process exists. Parameters obtained after CA administration by oral route indicate that normalized Cmáx and normalized areas decrease as the administered dose of the prodrug increases. This

Fig. 1. Mean plasma levels and standard deviations of C after intravenous administration of C and after oral administration of CA. Lines represent population predictions based on final NONMEN model.

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Table 1 Noncompartmental pharmacokinetic parameters of C after different intravenous administration (mean value (S.E.)) Parameter β (h−1 ) t1/2β (h) MRT (h) Cl (l/h) Vss (l) AUC0−∞ (mg h/l) AUC0−∞ /D (h/l)

Intravenous dose of cefuroxime

P

1.69 mg

8.45 mg

16.9 mg

0.518 (0.069) 1.43 (0.12) 2.02 (0.10) 0.0328 (0.0012) 0.0659 (0.0035) 52.02 (2.01) 30.78 (1.19)

0.539 (0.059) 1.39 (0.14) 1.67 (0.10) 0.0468 (0.0018) 0.0770 (0.0030) 182.4 (7.10) 21.59 (0.84)

0.682 (0.101) 1.24 (0.27) 1.30 (0.15) 0.0483 (0.0017) 0.0615 (0.0055) 352.7 (13.02) 20.87 (0.77)

NS NS 0.0017 0.0001 0.033 0.0001 0.0001

Table 2 Non-compartmental pharmacokinetic parameters of C after oral administration of CA (mean value (S.E.)) Parameter

(h−1 )

β t1/2β (h) MRT (h) Cl/F (l/h) Vβ /F (l) tmax (h) Cmax (mg/L) Cmax /D (1/D) AUC0−∞ (mg h/l) AUC0−∞ /D (h/l)

Oral dose of cefuroxime axetil

P

1.69 mg

8.45 mg

0.4777 (0.036) 1.49 (0.09) 2.42 (0.09) 0.1383 (0.0078) 0.2940 (0.0168) 0.75 (·) 5.303 (0.278) 3.138 (0.164) 12.436 (0.654) 7.359 (0.387)

0.5968 (0.0253) 1.17 (0.05) 1.99 (0.06) 0.2481 (0.0180) 0.4185 (0.0323) 0.7857 (0.0357) 15.40 (0.809) 1.823 (0.096) 35.224 (2.722) 4.169 (0.032)

0.0191 0.0096 0.0022 0.0001 0.0001 NS 0.0001 0.0001 0.0001 0.0001

NS: not significant.

suggests that the absorption process of CA is nonlinear for the range of dose administered. However, this behaviour could be attributed to the increase in Cl observed, to the decrease of fraction of dose reaching systemic circulation or both. Nevertheless, the interpretation of the non-compartmental analysis was complicated by the inability to perform successive administrations of C by i.v. and CA by oral routes, in the same animals. Moreover, in some animals a flip-flop phenomenon occurs in CA kinetics. The flip-flop phenomenon made it difficult to attribute the terminal slope of the kinetic curve to β or ka , while the inability to perform a crossover study precluded the estimation of individual F-values. The population approach, at least in part, alleviated the above mentioned problems. Combining data for rats receiving the drugs by the i.v. and oral routes in the analysis was likely to constrain the estimation of the pharmacokinetic parameters so that they were consistent across groups, because minimization of the objective function forces the individual estimates of the parameters toward the mean value in the population. Since the data of i.v. administration provided information about the “true” values of distribution and elimination parameters, these parameters could be estimated properly from the oral data, even though the flip-flop phenomenon occurred in rats. Treating the data for all groups together allowed the evaluation of the processes responsible for the nonlinearities. In this respect, the population analysis made it possible to obtain the population kinetic parameters

corresponding to C i.v. administration and CA oral administration. Several models were developed in order to describe the characteristics of the absorption of CA and elimination of C observed previously. In the model building, saturable absorption and saturable elimination processes were taken in account. The saturation of C bound to serum proteins could justify the increase of Cl but, simultaneously, a change in the distribution parameters should be observed. In accordance

Table 3 Population pharmacokinetics and statistical values for C Parameter

Estimate (S.E.)

Vc (l) k12 (h−1 ) k21 (h−1 ) kel (h−1 ) Vm (mg/h) Km (mg/l) Vma (mg/h) Kma (mg/l) kd (h−1 ) Residual variability σ 2 Objective function value F(1.69 mg) F(8.45 mg)

0.0446 (0.0013) 0.734 (0.00214) 1.79 (0.00642) 1.28 (0.0112) 0.887 (0.0194) 27.4 (6.48) 4.09 (0.984) 116 (39.3) 2.56 (0.172)

Interindividual variability ω2 (S.E.) 0.0975 (0.0645) 0.0975 (0.0645) 0.0056 (0.00171)

0.0249 (0.0147)

0.0261(0.00524) 1024.103 22 17

Bioavailability values obtained for each dose of CA administered orally are also shown.

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Fig. 2. Population (up) and individual predicted (down) versus observed C plasma concentrations ((䊊), i.v. and (), p.o.) for selected model. Identity lines are also given.

with the literature, C is 30–50% bound to serum proteins (McEvoy, 2003). This low value does not justify the increase of Cl of C at doses administered. Observable saturable active tubular reabsorption is a much rarer phenomenon. Some authors (Inui et al., 2000; Groneberg et al., 2002) demonstrated the existence of tubular reabsorption of peptide-like drugs such as ␤-lactam antibiotics across the brush-border

renal membranes. Saturation of tubular reabsorption could explain the increase of the C renal Cl when the dose administered increases, resulting in the increase in total Cl. On the other hand, it is well known that following oral administration, CA is rapidly hydrolyzed to C by non-specific esterases in the intestinal mucosa and blood (Ruiz-Balaguer et al., 1997, 2002; Ruiz-Carretero et al., 2000). The axetil

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moiety is metabolized to acetaldehyde and acetic acid, while C is not metabolized and is excreted unchanged, principally in urine by both glomerular filtration and tubular secretion (McEvoy, 2003). Indeed, comparison of the Cl of C from blood (varies from 0.0328 to 0.0483 l/h, when the dose of C administered increases from 1.69 to 16.9 mg) to C glomerular filtration Cl (which is the product of fu and the glomerular filtration rate, i.e. 0.5 l/h × 0.6 l/h = 0.30 l/h (Padoin et al., 1998)) indicates that some reabsorption process is in action. Taking into account the chemical properties of the C passive reabsorption process is not the most probable mechanism. Therefore, an active tubular reabsorption was considered in the population analysis to characterize the elimination of C in rats. Nonlinear absorption process was modelled by means of a first-order absorption rate constant for each dose administered; bearing in mind that degradation of CA in intestinal lumen is well characterized by first-order kinetics. Nevertheless, the best model to assess absorption process was by using Michaelis–Menten equation kinetics to describe saturable intestinal absorption of CA and a first-order kinetics to describe degradation of prodrug in intestinal lumen. For the two doses of CA administered, few bioavailability values have been obtained (Table 3). The loss of absorbability and enzymatic activity of the intestinal esterase responsible for the hydrolysis of the prodrug has a significant effect on drug bioavailability. On the other hand, the increase of CA dose is associated with a reduced bioavailability (<22%). A decreased bioavailability could be attributed to absorption mediated by a carrier system and/or if absorption took place is in a limited portion of the intestine. For CA these characteristics have been recently reported (Ruiz-Balaguer et al., 2002). In the rat, the biological half-life obtained is 1.43(0.12)– 1.24(0.27) h, and the reference value in humans is 1.2–1.6 h (McEvoy, 2003). In both cases, the drug is eliminated from the body in a short period of time. Taking into account that in humans the regimen schedule for CA is 250 mg twice a day, and the biological half-life of C is about 1.4 h, there is no accumulation of the drug in the body between doses. Therefore, the results obtained in rats after single dose administration can be considered as representative of the multiple dose schedules in humans. The methods developed in

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the investigation, described here, provide an example of a way by which nonlinearities in drug pharmacokinetics can be manifested using rats as an animal model.

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