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Freie Universitaet Berlin, Institute of Pharmacy, Berlin, Germany (N.P., C.B., C.K.); Vienna University School of Medicine, Vienna General Hospital, Vienna, Austria (C.J.); Deutsches Rotes Kreuz (DRK) Kliniken Berlin Westend, Berlin, Germany (S.K.); and Martin-Luther-Universitaet Halle-Wittenberg, Institute of Pharmacy, Halle, Germany (C.K.)
(Received November 29, 2006; Accepted July 12, 2007)
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Abstract |
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). Clinical trials showed that linezolid was generally well tolerated for up to 28 days (French, 2003). Frequent adverse events included headache, nausea, dizziness, and vomiting (Chen et al., 2004). In addition, linezolid therapy frequently led to an increase in transaminases (French, 2003). Especially prolonged treatment caused myelosuppression, which was reversible after discontinuation of therapy (Green et al., 2001). Moreover, optic neuropathy has been observed after long-term treatment (Meyer et al., 2005).
The pharmacokinetics (PK) of linezolid has been subject to various investigations. Linezolid displayed a plasma protein binding of 31% independent of concentration (Slatter et al., 2001). At steady state, the volume of distribution was 40 to 50 liters, which approximates total body water (Diekema and Jones, 2001). Linezolid had a total clearance of 7 l/h and a terminal elimination half-life of approximately 5 h (Perry and Jarvis, 2001). In patients with severely impaired renal function, no significant changes in total clearance were observed; thus, a dose adjustment was reported not to be necessary in this patient population (Brier et al., 2003). Of the total amount of linezolid in the body, only 30% were eliminated unchanged via the kidneys (Moellering, 2003), whereas a major part of the administered linezolid was metabolized by oxidation of its morpholino ring (see Fig. 1), resulting in two metabolites: an aminoethoxyacetic acid metabolite (metabolite A) and a hydroxyethyl glycine metabolite (metabolite B) that was formed by nonenzymatic oxidation in an in vitro setting (Slatter et al., 2001). In urine, 40% of the dose appeared as metabolite B and 10% as metabolite A, whereas 6% and 1.5% were eliminated via feces as metabolite B and A, respectively (Slatter et al., 2001). The formation of metabolite B was found to be optimal under basic (pH 9.0) conditions, which suggests the potential involvement of either an uncharacterized cytochrome P450 enzyme or an alternative microsomally mediated oxidative pathway (Wynalda et al., 2000). In addition, its formation was dependent on NADPH (Wynalda et al., 2000).
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It has been demonstrated that PK characteristics can differ between healthy volunteers and critically ill patients (Gomez et al., 1999; Brunner et al., 2000; Hanes et al., 2000; Joukhadar et al., 2001, 2002; Tegeder et al., 2002). Nevertheless, pharmacokinetic investigations of linezolid in critically ill patients have been scarce (Meagher et al., 2003; Whitehouse et al., 2005) and, concerning the structural pharmacokinetic model as well as pharmacokinetic parameter estimates, yielded controversial results. Moreover, it has been demonstrated that only the unbound fraction of a drug is pharmacologically active (Kunin et al., 1973; Merrikin et al., 1983; Craig and Ebert, 1989). Therefore, more emphasis should be placed on the investigation of unbound linezolid PK in critically ill, e.g., septic patients. To increase the informational value of those studies, informative analysis procedures such as population PK should be adopted. In brief, population PK is a method that is able to analyze concentration-time data of many individuals simultaneously. Moreover, overall variability can be characterized and differentiated in more detail, as, for example, interindividual variability in drug exposure and residual variability (Sheiner, 1984).
The primary objective of this investigation was to analyze data derived from a clinical trial that examined both healthy volunteers and septic patients to thoroughly describe and understand the PK of unbound linezolid in plasma after single and multiple dosing. For this purpose, the population pharmacokinetic analysis technique was applied. Moreover, the developed model was planned to be compared with previously published models and to be evaluated in terms of its predictive performance.
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Materials and Methods |
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; C. Thallinger, C. Buerger, N. Plock, S. Kljucar, C. Kloft, and C. Joukhadar, manuscript in preparation). In total, 10 healthy volunteers and 24 patients were enrolled in the trial according to previously reported criteria (Buerger et al., 2006). In brief, severe sepsis and septic shock were diagnosed according to the criteria of the ACCP/SCCM Consensus Conference Committee (Bone et al., 1992). Patients were excluded during pregnancy and lactation, if they tested positive for HIV or hepatitis B at the screening visit, received hemodialysis or hemofiltration 3 days before or within the first 4 days of study drug administration, were allergic to linezolid, or were concomitantly given monoamine oxidase inhibitors. Study Protocol. In all subjects, the first dose was 600 mg of linezolid (Zyvoxid; Pharmacia, Erlangen, Germany), administered as a 30-min intravenous infusion. Patients continued to receive 600 mg of linezolid b.i.d. as an infusion. In healthy volunteers, all subsequent doses were given orally as a 600-mg linezolid tablet b.i.d.. The healthy volunteers had to document the actual time of linezolid intake in a diary. In each subject, blood samples were to be collected on two study visits. Visit 1 was conducted beginning with the first linezolid administration. Visit 2 was carried out after multiple dosing, i.e., at least 3 days after continued linezolid administration.
Sampling and Sample Storage. The sampling schedule was the same for both study visits. Samples were collected directly before and 20, 40, 60, 80, 100, 120, 140, 160, 180, 210, 240, 270, 300, 330, 360, 390, 420, 450, and 480 min after the start of linezolid administration. Blood was centrifuged at 2550g for 5 min immediately after sampling and stored at -70°C. Sample transport was carried out using dry ice adhering to a cold chain.
Linezolid Quantification. Total and unbound linezolid concentrations in plasma were measured using a previously described high-performance liquid chromatography method with an RP-18 stationary phase and UV detection (Buerger et al., 2003). In brief, plasma samples were prepared by using a 50-µl aliquot of each sample. Proteins were precipitated with acetonitrile, whereas ultrafiltrate was directly injected after a simple one-step dilution procedure. The method was validated according to U.S. Food and Drug Administration standards (
FDA (2001) Guidance for Industry. Bioanalytical Method Validation. http://www.fda.gov/cder/guidance/4252fnl.pdf) in terms of sample stability, specificity, accuracy, and precision. Linearity was demonstrated in a concentration range of 0.2 to 20 µg/ml. To determine the unbound fraction of linezolid, ultrafiltrate samples (Centrifree; Millipore, Eschborn, Germany, molecular mass cut-off, 30 kDa) were measured according to a previously established method (Buerger et al., 2006).
Pharmacokinetic Data Analysis. PK model building for describing the typical concentration-time profile and characterizing the variability in the population was performed using the nonlinear mixed-effects modeling approach implemented in NONMEM (Version V, Level 1.1, 1998; Globomax, Ellicott City, MD). First-order conditional estimation with interaction was used as the estimation method. In a stepwise approach, first, a structural model was developed. Afterward, interindividual and residual variability was characterized. The model was parameterized in terms of clearances and distribution volumes using the PREDPP subroutine ADVAN 6 supplied in NONMEM. Although the number of included individuals in the data analysis was not very large, it was sufficient to estimate the included number of model parameters because the characteristic of combining data from different sources is one major advantage of the population analysis technique compared with individual PK parameter estimation. The reason for this is that the information of all subjects is interchangeably used to estimate population and also individual parameters.
Interindividual variability in model parameters was modeled using an exponential error term according to the equation
 | (1) |
where Pki denotes the value of the parameter k from the individual i (= individual parameter). The model assumed that all Pki values were log-normally distributed. 
k is the typical value of the population parameter k and 
ki is the difference between the natural logarithm of Pki and k. If individual parameters had to be confined to values between 0 and 1, this error model was modified according to the equation
 | (2) |
where k is the typical value of the population parameter k and ki = ln(Pki/(1 - Pki)) - ln(k/(1 - k)). Due to the exponential term, in this equation the numerator can only take values larger than zero. If it approximates values close to zero, Pki will approach a value of 0. In contrast, if the numerator yields values much larger than zero, Pki will approach a value of 1.
Residual variability, that is, the discrepancy between the individual observed (Cobs,ij) and the individual model-predicted (Cpred,ij) plasma concentrations, was expressed as a combined error model with a proportional component, 
1, and an additive component, 2, as follows:
 | (3) |
ij denotes the random deviation between the individual prediction and the observed concentration for each individual i at a certain time point j. The random-effects parameters and were assumed to be symmetrically distributed with zero means and variances of 
2 and 
2, respectively.
The model-building process was guided by analyzing the goodness of fit plots created with Xpose, version 3.104 (Jonsson and Karlsson, 1998), precision of parameter estimates, and the objective function value (OFV) provided by NONMEM. The latter was used for discrimination between hierarchical models in the likelihood ratio test (Bonate, 2005). The addition of a parameter was considered significant if the decrease in objective function value was >3.84, corresponding to a p value of 0.05 (df = 1). Only models that converged successfully were considered and are presented here.
Model Evaluation. For evaluation purposes it was attempted to fit population models to the data that had been described for linezolid in previous reports, i.e., a linear two-compartment model (Whitehouse et al., 2005) and a two-compartment model with parallel linear and Michaelis-Menten elimination (Meagher et al., 2003). The competing models were evaluated using goodness of fit plots. Moreover, the predictive performances of all models were compared by applying a predictive check. For this purpose, 1000 new individual concentration-time profiles were simulated in NONMEM based on the parameter estimates from the final models. The simulation was performed for intravenous dosing only. From all simulated concentrations the median and the 5th and 95th quantile were calculated for each time point using the software S-Plus (Insightful Corporation, Seattle, WA; Version 6.0 Professional Release 2, 2001). Based on these calculations, the 90% prediction interval and the median concentration-time course were presented graphically. All measured unbound linezolid concentrations were then compared with the corresponding 90% prediction intervals.
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Results |
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Concentration-Time Profiles. The semilogarithmic geometric mean concentration-time profiles of healthy volunteers and patients after single and multiple dosing are shown in Fig. 2. In all individual profiles depicting unbound plasma data after intravenous linezolid administration, two disposition phases, i.e., two slopes, could be observed that presumably belonged to an early predominant distribution and a later predominant elimination phase. In contrast, after oral dosing (healthy volunteers), the early distribution phase did not become apparent. When comparing the plots obtained after single and multiple dosing, a change in the disposition of linezolid was visible in both populations studied, i.e., the slope of the elimination phase became shallower over time, which indicated nonlinearity in the PK of linezolid.
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OFV =-447). Because the two models were nested, it was concluded that the model using parallel linear and Michaelis-Menten kinetics was superior to the one using linear elimination only. However, goodness of fit plots revealed that the model using parallel linear and Michaelis-Menten elimination still contained some mis-specifications. Especially small concentrations were overestimated. The mis-specifications were reduced when incorporating a nonmechanistic inhibition of clearance over time; i.e., the decrease in clearance was a direct function of time. Finally, in a last step, this inhibition over time was more mechanistically included in the model by introducing an additional inhibition compartment (OFV = 750, OFV =-726 compared with the model using linear elimination only; models were nested). Depending on the concentration in this empirical compartment, CL from the central compartment was inhibited. In the course of time, CL was allowed to take values between 0 and 100% of the original value estimated for the time of the first linezolid administration. The fraction of CL that could not be inhibited was represented by the parameter RCLF (remaining CL fraction). Thus, a RCLF estimate of 0 corresponded to a clearance inhibition of 100%, whereas a RCLF estimate of 1 represented no clearance inhibition. In addition, to describe the time course of CL inhibition, a rate constant into the inhibition compartment (KIC) and the concentration in the inhibition compartment yielding 50% of CL inhibition (IC50, fixed) were included as additional model parameters. A schematic illustration of the model is presented in Fig. 3. The following differential equations describing the change in amount per time for each compartment (1, absorption compartment; 2, central compartment; 3, peripheral compartment; 4, inhibition compartment) were applied:
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Interindividual variability (IIV) was incorporated for CL, V2, V3, and KA based on eq. 1 and for RCLF according to eq. 2. IIV was moderate to high with coefficients of variation (CVs) of 42% [CL], 40% [V2], 35% [V3], and 72% [KA]. A smaller number of individuals might generally lead to higher interindividual variability (upward bias), but our parameter estimates were not in an unexpected range. As a result of the different individual parameter distributions of RCLF compared with the other PK parameters (U-shaped, Fig. 4) it may not be appropriate to calculate a CV for RCLF. However, its IIV can be described by the 95% confidence interval, which covered the range of 0.00374 to 0.99963. All parameters were estimated with acceptable precision since most relative standard errors were below 50%. Parameter estimates of the final model are presented in Table 1.
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Goodness of Fit. The goodness of fit of the final model and the competing models is presented in Fig. 5. Inspection of the goodness of fit plots of the model with linear elimination (Fig. 5A) showing population predictions against observed concentrations revealed some degree of model mis-specification. Particularly, observed low values were overestimated by the model. This became even more apparent in a plot with log time versus weighted residuals, which showed an explicit trend in the early time phase. Values of the elimination phase after single dosing were overestimated, which further supported the assumption that nonlinearity in linezolid PK was involved, changing its disposition in the course of therapy. The second competing model included both a linear and a Michaelis-Menten elimination pathway (Fig. 5B). The trend that was visible in the model with linear elimination was less pronounced; however, it was still distinguishable. Furthermore, low concentrations at the start of linezolid treatment were overestimated. On the contrary, the goodness of fit plot of the final model (Fig. 5C) revealed that the trend of overestimation, which could be observed in the models with linear elimination and that with parallel linear and Michaelis-Menten elimination was eliminated. Furthermore, in contrast to Fig. 5, A and B, in the plot showing population predictions against observed concentrations, all concentrations were uniformly spread around the line of unity, indicating that the data were well described by the model.
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In one of the patients, extremely high concentration values were observed after multiple dosing (see Figs. 5 and 6). Therefore, it was investigated whether this individual influenced parameter values by case deletion diagnostics. The exclusion of this subject led to acceptable maximum parameter changes of less than 7% compared with the reported final values in Table 1 (maximum change for V3, 6.96%).
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Predictive Check. The predictive check was performed to evaluate which of the investigated models adequately predicted the observed concentration-time profiles of unbound linezolid. After the first dose, an inhibition of clearance developing over time would not be distinctly observable. Therefore, the early median concentration-time course was well captured by all investigated models. However, the best predictions of single dose data were obtained with the inhibition compartment model on the condition that RCLF was set to zero; i.e., under the assumption that clearance would be inhibited to the same extent in every individual: that is, every individual RCLF value would be the same. This assumption had to be implemented in the predictive check because of the special coding for interindividual variability on the parameter RCLF in which individual parameter distribution according to eq. 2 resulted in a U-shape (Fig. 4).
The results of the predictive check after intravenous multiple dosing are presented in Fig. 6. Black lines represent the simulated median concentration-time profile, whereas gray lines represent the 5th and 95th quantile and enclose the 90% prediction interval. The black symbols correspond to the measured concentrations after multiple dosing. Here, the differences in the predictive performance of the models were pronounced. In both the model with linear and the model with parallel linear and Michaelis-Menten elimination, the 90% prediction interval was too wide and the predicted median concentration-time course was highly overpredicted. Again, the best predictions could be obtained by using the inhibition compartment model on the condition that RCLF was set to zero. For this model, the simulated median concentration-time profile as well as the 90% prediction interval closely reflected the observed concentrations.
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Discussion |
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), most pronounced for Cmax values. Using a linear two-compartment model, the obtained PK parameters were not in accordance with any other investigations, e.g., the distribution volume was estimated to be 284 liters (Whitehouse et al., 2005), whereas others reported a volume of distribution of 40 to 50 liters (Diekema and Jones, 2001). This led to the conclusion that both a classical linear one- and two-compartment model were not sufficient to describe linezolid PK, although this was stated otherwise by the authors (Whitehouse et al., 2005). This conclusion was confirmed by our own investigations. Fitting a two-compartment model with linear elimination to the data resulted in model mis-specifications that became apparent when plotting weighted residuals against the logarithm of time. As a result of the underlying assumption of a constant CL for single- and multiple-dose data, concentrations were distinctly overestimated in the drug elimination phase of the first dose. Examination of the individual concentration-time profiles revealed a change in the disposition of linezolid when comparing concentration-time profiles obtained after single dosing to those obtained after multiple dosing, suggesting PK nonlinearity, which might presumably be attributed to CL.
Antal et al. (2000) reported a one-compartment model with parallel linear and Michaelis-Menten elimination. Clearance estimation resulted in values of 10.99, 6.96, and 4.51 l/h for concentrations of 1.02, 5.86, and 13.94 µg/ml, respectively. Meagher et al. (2003) developed a two-compartment model with parallel linear and Michaelis-Menten elimination. A combination of linear and nonlinear elimination resulted in a mean average total clearance of 6.85 l/h/65 kg. A model using only a Michaelis-Menten process for the description of linezolid clearance was presented by Beringer et al. (2005) for the description of single-dose data. Its performance was compared with that of a linear model. The maximum metabolic rate Vmax and the Michaelis-Menten constant Km were in the same range as those estimated before (Meagher et al., 2003), resulting in a clearance between 4.5 and 22.1 l/h for concentrations between 0 and 14 µg/ml. In the linear model, clearance was estimated to be 11.2 l/h (Beringer et al., 2005).
Although the presented studies all reported to have successfully described the PK of linezolid, the results indicated that the use of Michaelis-Menten elimination might not be suitable. In such a case, one would expect a decrease in clearance with increasing doses. However, in the study performed by Antal et al. (2000), a plot showing weight-normalized clearance against weight-normalized dose revealed that clearance varied randomly with differing doses. Meagher et al. (2003) reported that clearance seemed to change with an increasing number of doses. Unfortunately, they did not report whether the change in clearance also became apparent in subjects who had similar concentrations after single dosing and at steady state. However, they described an apparent change in Vmax and Km with increasing doses when applying a model with sole Michaelis-Menten elimination. This might also indicate that this type of model still contained some mis-specifications. Finally, the model presented by Beringer et al. (2005) was based on single-dose data and every subject was given the same dose. The authors concluded that the model with linear elimination and the one with Michaelis-Menten elimination performed equally well. However, because the model did not include multiple-dose data and different drug amounts, the performance of the two competing models might not have been completely assessable. Finally, our own investigations based on the total data set described in this investigation and on reduced data sets containing only one population subgroup (healthy volunteers or patients) revealed that linezolid disposition changed over time even if Cmax values after single and multiple dosing were almost equal, as seen in 26.5% of the subjects (total data set). These observations cannot be explained by saturable Michaelis-Menten kinetics. When fitting a model with parallel linear and Michaelis-Menten elimination to the available data, the model mis-specification became apparent when plotting weighted residuals against logarithm of time (Fig. 5). Although the trend was reduced in comparison to the model with linear elimination, concentrations were overestimated in the drug elimination phase of the first dose. Thus, a direct concentration dependence could be excluded from further consideration.
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) observed a clearance of 7.38 l/h after multiple administration of 625 mg of linezolid. To correctly interpret the observed higher clearance value, one has to consider that the clearance estimated by the model presented here was the maximum possible value. It would only apply to the first dose of linezolid when inhibition was negligible. Considering this factor, the estimated value of 11.1 l/h corresponded well to, e.g., the value of 11.2 l/h estimated by a linear model after single-dose administration (Beringer et al., 2005). The decrease in clearance was triggered by the parameter RCLF. The estimate of RCLF revealed that clearance could be inhibited to 76.4% of its original value. Consequently, population clearance changed to 8.48 l/h over time. This value was higher than some of the other values mentioned above. Nevertheless, this model also led to some individual clearance values in the range of 4 l/h in the course of time. Moreover, the presented value was a result of clearance not being a direct function of concentration as in the Michaelis-Menten model. The resulting values thus might not be directly comparable. Finally, the best predictions were obtained by using the inhibition compartment model, whereas the other models tended to overpredict concentrations after multiple dosing. Although the predictive check for the inhibition compartment model was performed using a model simplification by assuming the same extent of clearance inhibition in every individual, the results indicate that the presented model was superior to those that have been presented in the literature before.
From a mechanistic perspective, the inhibition of linezolid clearance might result from changes in linezolid metabolism. One of the major linezolid metabolites is the hydroxyethyl glycine metabolite (see Fig. 1). It is produced via formation of its precursor hydroxylinezolid (Feenstra et al., 1998). The production of hydroxylinezolid was demonstrated to be dependent on NADPH (Wynalda et al., 2000). Next, it was hypothesized that linezolid inhibited mitochondrial activity (Palenzuela et al., 2005), and only recently it was confirmed that linezolid induced a dose- and time-dependent decrease of mitochondrial respiratory chain enzyme activity at therapeutic concentrations (De Vriese et al., 2006). The formation of NADPH is connected to the respiratory chain enzyme activity by glycolysis and the pentose phosphate pathway. The ATP required for glycolysis is a product of the citric acid cycle and oxidative phosphorylation, which account for 95% of all energy used by aerobic human cells (Berg et al., 2003). In consequence, the hypothesis can be generated that linezolid inhibits its own metabolism via inhibition of the mitochondrial respiratory chain enzyme activity (Fig. 7). It has been reported that 40% of the administered linezolid dose is eliminated as the hydroxyethyl glycine metabolite via the formation of hydroxylinezolid (Slatter et al., 2001). The final model estimated an inhibitable clearance fraction of 23.6%. The metabolic capacity of this pathway would thus be inhibited by slightly more than 50%. It is highly probable that the observed PK nonlinearity resulted from the clearance inhibition, which was due to the inhibition of the formation of the major linezolid metabolite. This hypothesis offers a mechanistic explanation for the presented empirical PK model.
Further modeling activities might aim at using an indirect response model (Mager et al., 2003). After identifying covariate relations, the developed model might be used for practical purposes in clinical treatment, i.e., for an individualized antimicrobial therapy, which might also prevent further development of antimicrobial resistance.
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Acknowledgments |
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Footnotes |
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ABBREVIATIONS: PK, pharmacokinetic(s); KA, absorption rate constant; CL, clearance; Q, intercompartmental clearance; OFV, objective function value; ALAG1, lag-time after oral dosing; RCLF, remaining CL fraction (i.e. noninhibitable fraction of CL); IIV, interindividual variability; KIC, rate constant into the inhibition compartment; IC50, concentration in the inhibition compartment yielding 50% of CL inhibition; Vmax, maximum elimination rate; Km, Michaelis-Menten constant.
Address correspondence to: Prof. Dr. Charlotte Kloft, Martin-Luther-Universitaet Halle-Wittenberg, Institute of Pharmacy, Dept. Clinical Pharmacy, Wolfgang-Langenbeck-Str. 4, 06120 Halle, Germany. E-mail: charlotte.kloft{at}pharmazie.uni-halle.de
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