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Antimicrobial Agents and Chemotherapy, May 2009, p. 2074-2081, Vol. 53, No. 5
0066-4804/09/$08.00+0     doi:10.1128/AAC.01056-08
Copyright © 2009, American Society for Microbiology. All Rights Reserved.

Penetration of Moxifloxacin into Bone Evaluated by Monte Carlo Simulation{triangledown}

Cornelia B. Landersdorfer,1,§ Martina Kinzig,1 Friedrich F. Hennig,2 Jürgen B. Bulitta,1,§ Ulrike Holzgrabe,3 George L. Drusano,4 Fritz Sörgel,1,5* and Johannes Gusinde2

IBMP—Institute for Biomedical and Pharmaceutical Research, Nürnberg-Heroldsberg, Germany,1 Department of Surgery, University of Erlangen, Erlangen, Germany,2 Institute of Pharmacy and Food Chemistry, University of Würzburg, Würzburg, Germany,3 Ordway Research Institute, Albany, New York,4 Department of Pharmacology, University of Duisburg-Essen, Essen, Germany5

Received 5 August 2008/ Returned for modification 10 November 2008/ Accepted 2 February 2009


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ABSTRACT
 
Moxifloxacin is a fluoroquinolone with a broad spectrum of activity and good penetration into many tissues, including bone. Penetration of moxifloxacin into bone has not yet been studied using compartmental modeling techniques. Therefore, we determined the rate and extent of bone penetration by moxifloxacin and evaluated its pharmacodynamic profile in bone via Monte Carlo simulation. Twenty-four patients (10 males, 14 females) undergoing total hip replacement received 400 mg moxifloxacin orally 2 to 7 h prior to surgery. Blood and bone specimens were collected. Bone samples were pulverized under liquid nitrogen by a cryogenic mill, including an internal standard. Drug concentrations were analyzed by high-performance liquid chromatography. We used ADAPT II (results reported), NONMEM, and WinBUGS for pharmacokinetic analysis. Monte Carlo simulation was performed to reverse engineer the necessary area under the free concentration-time curve fAUCSERUM/MIC in serum and total AUCBONE/MIC in bone for a successful clinical or microbiological outcome. The median (10% to 90% percentile for between-subject variability) of the AUC in bone divided by the AUC in serum (AUCBONE/AUCSERUM) was 80% (51 to 126%) for cortical bone and 78% (42 to 144%) for cancellous bone. Equilibration between serum and bone was rapid. Moxifloxacin achieved robust (≥90%) probabilities of target attainment (PTAs) in serum, cortical bone, and cancellous bone up to MICs of ≤0.375 mg/liter based on the targets fAUCSERUM/MIC ≥ 40 and AUCBONE/MIC ≥ 33. Moxifloxacin showed high bone concentrations and a rapid equilibrium between bone and serum. The favorable PTAs compared to the 90%-inhibitory MIC of Staphylococcus aureus warrant future clinical trials on the effectiveness of moxifloxacin in the treatment of bone infections.


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INTRODUCTION
 
Quinolones are established in the treatment of osteomyelitis. Most clinical experience has been gained with ciprofloxacin and ofloxacin (28). Oral administration of quinolones was efficacious in surgical prophylaxis, even after a single dose (6, 39), and also facilitates prolonged therapy. In in vitro studies, Staphylococcus aureus penetrates and survives in bone cells, i.e., osteoblasts (25); therefore, quinolones, which penetrate intracellularly, might be of advantage.

Moxifloxacin achieves high concentrations in many tissues. Good penetration into bone has been reported for several quinolones. The average bone/serum concentration ratio in humans at approximately 2 to 5 h postdosing was 0.33 to 0.54 for moxifloxacin (30, 34, 35).

Resistance to the older quinolones has been emerging, and they do not show sufficient microbiological efficacy against S. aureus and coagulase-negative staphylococci and streptococci (28). Moxifloxacin has improved activity against gram-positive and anaerobic pathogens frequently encountered as causative agents in osteomyelitis (28), such as staphylococci, enterobacteriaceae, streptococci, and Haemophilus influenzae (19). Moxifloxacin has lower MICs than do levofloxacin, ciprofloxacin, ofloxacin, and norfloxacin for S. aureus (51), which is the most common pathogen of osteomyelitis. The main causative bacteria for osteomyelitis are S. aureus (methicillin susceptible or resistant), coagulase-negative staphylococci, propionibacteria, streptococci, and Pseudomonas aeruginosa (27). P. aeruginosa can cause osteomyelitis due to nosocomial infections or chronic unresolved middle ear infections in children.

Studying the time course and extent of bone penetration before investigating the agent in a clinical trial is important (17, 51). Bone penetration studies most often report the ratio of concentrations in bone and serum. However, the ratio of tissue concentrations to serum concentrations of a drug changes with time, a phenomenon known as system hysteresis, and therefore, the concentration ratio depends on the sampling time. Like in the present study, bone penetration of antimicrobials is most often studied in patients undergoing joint replacement, where only one bone sample can be obtained per subject. Modeling the full serum and bone concentration-time course allows one to evaluate the penetration of antimicrobials into bone and to study the pharmacodynamic profile in bone. We are not aware of any reports about pharmacokinetic-pharmacodynamic (PKPD) modeling of quinolones in bone in humans or animals.

The first objective of our study was to determine moxifloxacin concentrations after oral administration in cortical bone and cancellous bone in subjects undergoing hip replacement surgery in a controlled study. We developed a highly standardized, validated analytical method and quantified moxifloxacin in serum and bone. For the second objective, we intended to develop a pharmacokinetic (PK) model to describe the time course of moxifloxacin concentrations in bone. Our third objective was to calculate the probabilities of target attainment (PTA) for serum, cortical bone, and cancellous bone based on PKPD targets for a successful microbiological and clinical outcome.


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MATERIALS AND METHODS
 
Study participants. The study comprised 24 patients (10 males, 14 females) who were scheduled to undergo total hip replacement. The patients were diagnosed with coxarthrosis and had no inflammation of the joints. Their average ± the standard deviation weight, height, and age were 76.8 ± 13.4 kg, 168.3 ± 9.9 cm, and 63 ± 15 years, respectively. The study was approved by the local ethics committee and performed according to the revised version of the Declaration of Helsinki. All subjects gave their written informed consent prior to starting the study.

Study design and drug administration. Each patient received a single oral dose of 400 mg moxifloxacin (Avalox; Bayer Vital, Germany) 2 to 7 h before surgery. Before surgery, 20 patients received amoxicillin-clavulanic acid, three patients received levofloxacin, and one patient received clindamycin, as intravenous infusions. Since there were no data on the bone penetration of moxifloxacin published prior to initiation of this study, those standard treatments for perioperative prophylaxis were given in parallel to moxifloxacin to assure antibacterial prophylaxis by an established treatment option.

Sampling schedule. Blood samples were collected prior to dosing and at the time of femoral bone resection. The blood samples were cooled in an ice-water bath and allowed to clot before centrifugation at 4°C. After centrifugation, serum samples were immediately frozen and stored at –80°C until analysis. Hip replacement involved resection of the femoral head, or both the femoral head and the femoral neck, prior to implantation of the prosthetic hip joint. Bone samples were immediately frozen on dry ice and stored at –80°C until analysis.

Determination of serum and bone concentrations. Some bone samples consisted only of femoral head, while others included both femoral head and femoral neck. The latter specimens were separated by femoral head and femoral neck. Then, the samples were separated by cortical tissue and cancellous tissue and pulverized under liquid nitrogen by a cryogenic mill. Specified amounts of the resulting powder were shaken with buffer for 24 h. Eluates and serum samples were deproteinized by acetonitrile containing the internal standard (pefloxacin). After thorough mixing, the samples were centrifuged for 5 min at 12,000 rpm, and the supernatant was diluted with ammonium formate buffer.

Moxifloxacin concentrations in bone and serum were determined by high-performance liquid chromatography coupled with fluorometric detection (296/504 nm). All sample handling was done under daylight protection. Twenty microliters of each sample was chromatographed on a reversed-phase column (Spherisorb ODS II [5 µm, 250 by 4.6 mm]) eluted with a gradient elution system consisting of 0.1 M citric acid buffer containing 44 mM ammonium perchlorate and acetonitrile (0 to 2.6 min, 65% ammonium perchlorate and 35% acetonitrile at 1.0 ml/min; 2.6 to 8.0 min, 40% ammonium perchlorate and 60% acetonitrile at 1.3 ml/min; 8.0 to 8.1 min, 65.0% ammonium perchlorate and 35% acetonitrile at 1.0 ml/min). Under these conditions moxifloxacin and the internal standard were eluted after approximately 4.4 min and 3.1 min. The Turbochrom 3 software (version 3.2; PE Nelson, Cupertino, CA) was used for the evaluation of chromatograms.

For analysis of the bone samples, calibration standards and spiked quality control samples were prepared by adding appropriate amounts of standard solutions to moxifloxacin-free bone tissue. Concentrations of moxifloxacin were determined using reversed-phase high-performance liquid chromatography with gradient elution and fluorometric detection (296/504 nm). For evaluation of the calibration standards, a weighted linear regression (1/y2) was performed with theoretical concentrations of calibration standards and measured peak height ratios (peak height moxifloxacin/peak height internal standard).

No interferences were observed in serum and bone for moxifloxacin and the internal standard, including in specimens of the three patients who had received a dose of levofloxacin in addition to moxifloxacin. The linearity of moxifloxacin calibration curves was demonstrated from 0.0100 to 5.00 mg/liter in serum and from 0.009 to 4.76 mg/liter in bone homogenate. The interday precision and accuracy of the spiked quality control standards of moxifloxacin in human serum ranged from 1.8 to 5.9% and from 95.1 to 103.8%. The interday precision and accuracy of the spiked quality control standards of moxifloxacin in bone homogenate ranged from 3.7 to 9.2% and from 94.7 to 97.6%.

PK modeling. Models with one or two disposition compartments in addition to bone were tested. Models with or without separate compartments for cortical bone and cancellous bone as well as for samples from femoral head and femoral neck were considered. Informative and noninformative priors for the absorption rate constant, ka, were tested. The predictive performance of our final model was tested via visual predictive checks, the generalized information criterion for maximum a posteriori (MAP) estimation (MAP objective function), plots of observed versus predicted concentrations, and residual plots.

For the visual predictive check, the serum and bone concentration profiles were simulated for 10,000 subjects. From these data, the median, the nonparametric 90% prediction interval (5% to 95% percentile), and the nonparametric 50% prediction interval (25% to 75% percentile) for the predicted profiles were calculated. These prediction interval lines were compared with the original observed data. If the model described the data adequately, 10% of the observed data points should fall outside the 90% prediction interval, and 50% of the data should fall outside the interquartile range. The median predicted concentrations and the prediction intervals were compared to the observed data, and we tested to see whether the median and the prediction intervals mirrored the central tendency and the variability of the raw data for the respective model.

Structural model. Moxifloxacin concentrations were determined in serum, cortical bone, and cancellous bone. Due to the relatively small number of samples from the femoral neck and in order to prevent making the model more complex, our model does not distinguish between samples from the femoral neck and those from the femoral head. A two-compartment disposition model for moxifloxacin in serum and in the peripheral compartment plus one peripheral compartment for each bone matrix was used (Fig. 1). The differential equations for the model are as follows:

Formula

Formula

Formula

Formula

Formula
Compartment 1 is the gut compartment, compartment 2 is the central compartment, and compartment 3 is the peripheral compartment. Compartment 4 is the compartment for cortical bone, and compartment 5 is the compartment for cancellous bone. X1, X2, X3, X4, and X5 denote the amounts of drug in the respective compartments. CL is the apparent total clearance from the central compartment, ka is the absorption rate constant, CLic is the apparent intercompartmental clearance between the central and peripheral compartments, and k24, k42, k25, and k52 are first-order intercompartmental transfer rate constants. VCentral and VPeripheral are the apparent volumes of distribution of the respective compartments. For all apparent clearance and apparent volume terms, the extent of absorption term (1/F) is left out for a clearer presentation of the equations.


Figure 1
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  		FIG. 1. Diagram of the compartmental model.

Scale terms for the concentrations in cortical bone and cancellous bone that describe the equilibrium concentration ratio between cortical bone and serum (Fcortical) and between cancellous bone and serum (Fcancellous) were included. An Fcortical value equal to 1 means that concentrations after a continuous infusion at steady state are the same in cortical bone and in serum; an Fcortical value less (greater) than 1 means that these concentrations are lower (higher) in cortical bone than in serum.

PK modeling approach. We had sparse serum concentration-time data between 2 and 7 h post-oral administration. As the moxifloxacin half-life is approximately 12 h, these data did not allow us to estimate all PK parameters for a two-compartment model. Therefore, MAP-Bayesian estimation based on the disposition parameters of Simon et al. (41) was used, and the average clearance and its standard deviation were derived from previously published studies (41, 45-47, 52). The average age was 46.3 (standard deviation of 10.6) years in the Simon et al. study. Based on those disposition parameters and their standard deviations, we estimated a typical half-life of absorption from our serum data via population PK in NONMEM V (5).

We had no prior information on the rate and extent of bone penetration by moxifloxacin. The raw data and initial modeling showed that the equilibrium between serum and bone was virtually achieved 2 h after dosing, indicating that the rate of equilibration (k42 and k52) was high. Therefore, we could not estimate k42 and k52 and fixed those values to an equilibration half-life of 15 min. The plausibility of this choice was assured via visual predictive checks. A sensitivity analysis was performed using the three-stage hierarchical population approach in S-ADAPT (version 1.55, Monte Carlo parametric expectation maximization algorithm). Initial estimates for absorption half-life, k42 and k52, were systematically perturbed and reestimated using physiologically plausible but uninformative priors.

The disposition parameters of moxifloxacin as described above have been determined in the absence of a bone compartment. As we used MAP-Bayesian estimation (see below), we had to keep the amount of moxifloxacin in the bone compartments minimal so that the serum PK was not affected by the presence of the bone compartments. This can be achieved by choosing a small volume for the bone compartment or an equivalently small value for the rate constants k24 and k25. Therefore, a volume of distribution of 0.5 liter each for the cortical and cancellous bone compartments, which is equivalent to fixing k24 and k25 to 0.022 h–1 in our model, was chosen.

MAP-Bayesian estimation. The individual PK parameters were estimated by MAP-Bayesian estimation as implemented in ADAPT II (13). We used informative priors with prior means and standard deviations and a log-normal distribution to estimate the individual disposition parameters. In the absence of prior information on the bone penetration, noninformative priors (uniform distribution) were used to estimate Fcortical and Fcancellous in the MAP-Bayesian step. The residual unidentified variability was described by a proportional error model for the serum and bone concentrations.

Estimation by the three-stage hierarchical Bayesian approach. To confirm the results from the MAP-Bayesian method, PK parameters were estimated by the three-stage hierarchical Bayesian approach in WinBUGS 1.4 using PKBugs 2.1 (29, 44). For VCentral, VPeripheral, and CLic, priors for population means and between-subject variability were obtained from Simon et al. (41). As described above, the population mean absorption rate constant was estimated to be 1.6 h–1 in NONMEM V, and a between-subject variability of 40% coefficient of variation, which is common for oral absorption parameters, was assumed. The equilibration between bone and serum was assumed to be rapid. Physiologically plausible but uninformative priors were used for the population mean and variability of CL, Fcortical, and Fcancellous based on literature data (26, 41).

Reverse engineering method for PKPD targets. The ratio of the free (non-protein-bound) area under the plasma concentration-time curve to MIC (fAUC/MIC) has been shown to be predictive of the microbiological and clinical outcomes for fluoroquinolones (12, 15). However, there is no PKPD target for moxifloxacin in serum samples of osteomyelitis patients or for quinolones in bone. Therefore, we used a reverse engineering method (7) to propose a PKPD target for moxifloxacin in serum and bone based on studies in osteomyelitis patients.

The reverse engineering method uses the success rate from clinical studies in osteomyelitis patients, the expected areas under the concentration-time curve (AUCs) after the doses given in these studies, and published MIC distributions from the relevant time period to derive the most likely target. The target which best predicts the observed clinical success rate is derived via Monte Carlo simulation (MCS) in an iterative process.

We used published data from four studies (21, 22, 24, 37) on the clinical or microbiological outcome of osteomyelitis caused by S. aureus in patients who obtained 500 mg or 750 mg ciprofloxacin orally every 12 h. Their expected AUCs were derived based on published PK data for ciprofloxacin (2, 54) or based on the AUCs reported by the authors (37). A log-normal distribution was assumed for clearance, and 25% protein binding was used for ciprofloxacin to simulate the expected fAUCs for 5,000 virtual subjects for each osteomyelitis study. We combined these fAUCs with susceptibility data for S. aureus (4, 8-10, 18, 20, 23, 31, 32, 42, 43, 49, 53) from the time period of the osteomyelitis studies to derive the PKPD target in serum, which predicted the observed successful rate. This yielded the PKPD target for S. aureus infections of osteomyelitis patients in serum (fAUCSERUM/MIC). The ratio of total concentration in bone to that in serum (AUCBONE/AUCSERUM) has been reported to be 0.63 for ciprofloxacin (33). We derived the PKPD target in bone (AUCBONE/MIC) based on this ratio. There are no data on protein binding of ciprofloxacin or moxifloxacin in bone. Therefore, the target (AUCBONE/MIC) refers to the total ciprofloxacin concentration in bone. As only the unbound fraction is considered active, application of this target for total concentrations derived for ciprofloxacin to moxifloxacin without further corrections assumes the same binding in bone for both drugs.

MCS. We studied a range of MICs from 0.125 to 16 mg/liter. The protein binding of moxifloxacin has been reported to range between 47% and 55% (3, 40, 45, 54). Therefore, an average protein binding of 50% was assumed for moxifloxacin in serum. Between-subject variability was not included for protein binding, as the between-subject variability for protein binding is already included in the estimated variability for total clearance and for volume of distribution. For moxifloxacin in bone, it was first assumed that it has the same binding as ciprofloxacin. Other extents of binding (free fraction of 75%, 50%, 25%, or 10% of the free fraction of ciprofloxacin in bone) were also assessed.

We simulated the serum and bone concentration-time curves for 10,000 patients after an oral moxifloxacin dose of 400 mg every 24 h (q24h) at steady state in the absence of residual error. The PTA was derived by calculating the fraction of subjects who attained the PKPD target at each MIC. The PKPD breakpoint was defined as the highest MIC for which the PTA was at least 90%.


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RESULTS
 
Concentrations of moxifloxacin in serum and cortical and cancellous bone are shown in Fig. 2. Moxifloxacin concentrations in cortical and cancellous bone were similar to those found in serum. In cortical bone, moxifloxacin concentrations were similar in the femoral head and femoral neck, whereas in cancellous bone, concentrations were slightly higher in the femoral neck. Moxifloxacin was stable during the 24-h extraction period.


Figure 2
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  		FIG. 2. Concentrations in serum and bone of subjects undergoing hip replacement surgery after a single oral dose of 400 mg moxifloxacin.

PK analysis. The absorption half-life (ln 2/ka) was estimated to be 26 min by NONMEM V. A sensitivity analysis showed that absorption half-lives between 8 and 34 min yielded similar log-likelihoods (differences of <1) and that the mean (individual) bone-to-serum AUC ratio was affected by <3% (<7%) for this range of absorption half-lives. A sensitivity analysis for k42 and k52 (Fig. 1) showed that mean equilibration half-lives below 30 min yielded similar objective functions. The considered range of initial equilibration half-lives was 4 to 415 min. For mean equilibration half-lives between 4 and 30 min, the mean bone-to-serum AUC ratios differed by less than 9% under all studied conditions.

Final parameter estimates from the MAP-Bayesian estimation in ADAPT, from WinBUGS, and from S-ADAPT (results not shown) were similar, as shown in Table 1. Figure 3 shows the extent of moxifloxacin penetration into cortical and cancellous bone and its between-subject variability, calculated from the ratios of AUCcortical/AUCserum and AUCcancellous/AUCserum for 10,000 subjects that we simulated at steady state. The median penetration (10% to 90% percentile) was 80% (51% to 126%) for cortical bone and 78% (42% to 144%) for cancellous bone.


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  		TABLE 1. Median parameter estimates (coefficient of variation) and range of individual PK parameter estimatesa


Figure 3
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  		FIG. 3. Penetration of moxifloxacin into cortical and cancellous bone (based on the estimates from ADAPT II [Table 1]), determined by the ratio of AUCs in bone and serum at steady state.

The visual predictive checks showed an acceptable predictive performance of the final model for all three matrices (Fig. 4). The central tendency of the concentrations in bone was slightly underpredicted between 2.5 and 3.5 h, whereas it was predicted adequately in serum. The variability was well predicted for all three matrices. This supported the use of our model in the MCS. Concentration-time profiles in serum and bone predicted by the final estimates from WinBUGS (Table 1) were comparable to the predicted profiles shown in Fig. 4.


Figure 4
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  		FIG. 4. Predictive check for serum and bone concentrations after oral doses of 400 mg moxifloxacin based on the estimates from ADAPT II (Table 1). The plots show the raw data, the 90% prediction interval (5 to 95% percentile), and the interquartile range (25 to 75% percentile). Ideally, 50% of the raw data points should fall inside the interquartile range at each time point, and 90% of the raw data should fall inside the 90% prediction interval.

Reverse engineering method for PKPD targets. We used data from published clinical studies with ciprofloxacin in osteomyelitis patients and assumed a protein binding level of 25% for ciprofloxacin and of 50% for moxifloxacin in serum. The resulting PKPD targets for successful clinical or microbiological outcome were fAUCSERUM/MIC ≥ 15 (21), fAUCSERUM/MIC ≥ 36 (37), fAUCSERUM/MIC ≥ 43 (24), and fAUCSERUM/MIC ≥ 66 (22). The respective targets for total bone concentrations were AUCBONE/MIC ≥ 13 (21), AUCBONE/MIC ≥ 30 (37), AUCBONE/MIC ≥ 36 (24), and AUCBONE/MIC ≥ 55 (22). As the targets calculated in the studies by Nix et al. (37) and Hoogkamp-Korstanje et al. (24) were very similar, we used the average from these two studies investigating clinical or microbiological outcome, i.e., fAUCSERUM/MIC ≥ 40 and AUCBONE/MIC ≥ 33 for MCS. In one of these two studies PK parameters were reported for several subjects and could be used for calculation of the AUCs. The resulting targets from these two studies (fAUCSERUM/MIC ≥ 40 and AUCBONE/MIC ≥ 33) fall between the targets calculated from the other two studies (Table 2).


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  		TABLE 2. PKPD breakpoints for moxifloxacin in serum, cortical bone, and cancellous bone and various PKPD targets for fAUC/MIC after oral moxifloxacin doses of 400 mg q24h at steady stateb

MCS. The PTA-versus-MIC plots are shown in Fig. 5. The PKPD breakpoints for serum, cortical bone, and cancellous bone are listed in Table 2 for the assumption that the extent of moxifloxacin binding to bone matrix is the same as that of ciprofloxacin binding to bone. The breakpoints were similar in serum and bone. The PKPD breakpoint was about 0.375 to 0.5 mg/liter for the median PKPD target in serum and bone for a dosage regimen of 400 mg moxifloxacin q24h at steady state. For a moxifloxacin binding level in serum of 47%, the breakpoint is 0.375 mg/liter, and for 55% protein binding, the breakpoint is 0.25 mg/liter for the target fAUCSERUM/MIC ≥ 40. Table 3 reports breakpoints in bone for various extents of moxifloxacin binding to bone.


Figure 5
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  		FIG. 5. Probabilities of target attainment for serum, cortical and cancellous bone after oral doses of 400 mg moxifloxacin q24h at steady state (based on the estimates from ADAPT II [Table 1]). fAUC/MIC values for serum and bone, respectively, are as follows: 15 and 13 for target calculated from Gentry and Rodriguez (21) (asterisks); 40 and 33 for target calculated from Nix et al. (37) for bacterial eradication and from Hoogkamp-Korstanje (24) (open squares); and 66 and 55 for target calculated from Greenberg et al. (22), for successful clinical outcome in osteomyelitis patients.


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  		TABLE 3. PKPD breakpoints in cortical and cancellous bone for the target AUC/MIC ≥ 33 after oral moxifloxacin doses of 400 mg q24h at steady state, depending on the free fraction of moxifloxacin in bone compared to ciprofloxacina


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DISCUSSION
 
It is important to study the penetration properties of a drug before investigating the agent in a clinical trial. Knowledge about how fast moxifloxacin reaches effective levels in bone is important for choosing the adequate time period between moxifloxacin administration for perioperative prophylaxis and surgery. The maintenance dose in treating bone infections should be selected based on the AUC in bone. Average bone/plasma concentration ratios for moxifloxacin in bone ranged from 0.3 to 0.54 between 1 h and 5 h after the end of infusion in various patient groups (30, 34, 35).

The complexities of determination of drug concentrations in bone might be a reason for widely different results between studies, even for the same antimicrobial agent. Malincarne et al. (30) report that bone samples were hand minced into 20- to 30-mg pieces and then extracted. Manual slicing of bone samples into small pieces resulted in a lower recovery after extraction than that resulting from pulverization by a cryogenic mill (38). We developed a highly standardized, validated method for sample preparation and analysis and tested the degree of extraction over time to ensure reproducible results. Our calibration standards were prepared in moxifloxacin-free bone tissue, whereas other studies often prepared standards in buffer or serum (26, 30) or did not report the matrix (34).

Most tissue penetration studies (26), including previous studies of moxifloxacin (30, 34, 35), only report the concentration ratio between tissue and serum for PK analysis and compare concentrations in tissue to MICs of pathogens. Mouton et al. (36) criticized this method of analysis and cited a bone penetration study as an example. The bone/serum concentration ratios may change over time, and therefore, ratios at a single time point are difficult to interpret. Some authors fitted the time course of bone concentrations by naïve techniques which ignore the between-patient variability. Drusano et al. analyzed the penetration of levofloxacin (17, 16) by use of population PK and MCS. This approach considers the full time course of penetration, estimates between-patient variability, and allows one to calculate the extent of penetration by the ratio of AUCs in tissue and serum.

A three-stage hierarchical Bayesian population PK approach additionally offers the advantage of borrowing information on mean PK parameters and between-patient variability with uncertainty based on previous studies. Borrowing of information from a study with frequent sampling is particularly important for analysis of very sparse data, as in this study and in most other bone penetration studies.

Population PK and MCS may then be used to estimate PTA for the desired pharmacodynamic endpoint (e.g., successful microbiological outcome) in serum and tissue. The ratio of AUC/MIC is the most predictive surrogate for microbiological success of treatment with quinolones (1, 14). To the best of our knowledge, population PK and MCS have not been used for analyzing bone penetration studies with antibiotics, and a full Bayesian population PK approach has not yet been applied to tissue penetration studies with antibiotics.

The limitations of our study with only 24 patients are the rather narrow range of sampling times of between 2 and 7 h and the sampling of only one blood and bone sample postdosing. Optimal design methodology should be applied in future studies to select several informative blood sampling times per patient. For bone, it is usually not feasible to obtain concentrations at more than one time point; and even in case this was done, the blood circulation to the bone would be impaired, and this could bias the observed time course. While these limitations apply to the vast majority of published bone penetration studies, we applied the latest modeling approaches to derive as much information as possible from the available data.

Like most bone penetration studies (26), our study was performed with patients with noninfected bone. In osteomyelitis patients, the rates and extents of bone penetration might differ. Blood flow into bone might be increased due to reactive hyperemia or decreased due to pus, ischemic regions, and sequester. Some studies (26) show higher concentrations in infected bone than in noninfected bone. The PK in bone might also be influenced by a potentially decreased bone density in elderly patients.

Our study with hip replacement patients was a single-dose trial. This reflects the common practice for surgical prophylaxis in which a single dose is usually given before surgery, which might be followed by additional doses afterwards. As moxifloxacin displays linear PK after single and multiple doses (48), we simulated the drug concentrations after multiple dosing to predict the PKPD profile in serum and bone for treating osteomyelitis.

As another limitation of our study, we measured total concentrations after extraction of bone homogenate. Bone is not a homogenous tissue and consists of blood vessels, extracellular fluid, bone cells, organic matrix (mainly collagen fibrils), and inorganic matrix (mainly hydroxyapatite crystals). Quinolones bind to hydroxyapatite (53a). It seems possible that neither antibiotics nor bacteria distribute uniformly in bone tissue as discussed previously (26).

In general, only the free antibiotic concentration is considered active, as molecules bound to the bone matrix might not contribute to bacterial killing. Determination of total concentrations in bone homogenate is a limitation of virtually all bone penetration studies. Analytical techniques to determine unbound drug concentrations in bone would provide further insights and may allow better predictions of the effectiveness of different antibiotics in bone infections.

To address this potential limitation we reverse engineered the required PKPD targets in serum and bone based on clinical trials in osteomyelitis patients. This reverse-engineered PKPD target for bone from clinical trials accounts for the potentially inhomogeneous distribution of bacteria and quinolones in bone. This approach assumes that ciprofloxacin and moxifloxacin have similar binding and distribution properties due to their structural similarity. Additionally, we calculated the PKPD profile of moxifloxacin in bone for various values for the free fraction.

We studied the concentrations of moxifloxacin in bone and serum between 2 and 7 h after the oral dose of moxifloxacin. The average concentration ratio between serum and bone showed no obvious change with time during our observation period. The observed data and initial modeling showed that the rate of bone penetration in our study was higher than expected, and equilibrium between serum and bone was virtually achieved 2 h after dosing. Therefore, the bone and the central compartment were in pseudoequilibrium during our observation period (from 2 to 7 h postdosing), and the bone concentrations declined in parallel to the serum concentration. A fast distribution equilibrium of moxifloxacin between plasma and bone is in agreement with the data of Malincarne et al. (30) and Metallidis et al. (34).

Our data could be adequately described by a model with first-order distribution. A rapid equilibrium between serum and bone might have been caused by an active transporter from bone tissue to serum. Transporters involved in tissue distribution have been found for quinolones in other tissues. High flow rates of interstitial fluid of up to 600 µl/g/h have been calculated based on in vivo studies (11). For an antimicrobial with similarly high rates of absorption and bone penetration compared to moxifloxacin, antibacterial prophylaxis should be achieved within 2 h in both cortical and cancellous bone after an oral dose. Due to the risk of emergence of resistance, moxifloxacin was not recommended for use in surgical prophylaxis (50).

In addition to MAP-Bayesian estimation, we performed a three-stage hierarchical Bayesian analysis in WinBUGS. The parameter estimates from WinBUGS were comparable to the results from MAP-Bayesian estimation (Table 1). Contrary to MAP-Bayesian estimation in ADAPT, WinBUGS allows the population PK parameter estimates and their between-subject variability to deviate from their prior values based on the uncertainty of the priors. This is potentially the main reason for the differences in PK parameter estimates between both methods. However, predictions from both sets of parameter estimates were similar.

Overall, the concentrations in our hip bone samples were about twice as high as those found in the other studies in knee and sternum. Possible reasons could be that different types of bone were studied and different methods of sample preparation were employed. In knee replacement surgery, most often a tourniquet is applied which restricts blood flow to the leg that is operated on and this could influence bone concentrations. Also, inflammation in and around the joint which was not present in our study could potentially affect bone penetration.

Secondary to the high extent of bone penetration for moxifloxacin, MCS showed robust (≥90%) PTA for MICs up to 0.375 mg/liter in serum and in cancellous bone for the targets fAUCSERUM/MIC ≥ 40 and AUCBONE/MIC ≥ 33, and up to 0.5 mg/liter in cortical bone for 400 mg moxifloxacin q24h at steady state (see Table 2). We used a protein binding level of 50% for moxifloxacin in serum and assumed the protein binding in bone to be the same for moxifloxacin and ciprofloxacin, because of the absence of reports on protein binding in bone. Assuming twice as high (protein) binding of moxifloxacin in bone compared to ciprofloxacin, breakpoints would still be 0.125 mg/liter in both cortical and cancellous bone for all calculated targets (Tables 2 and 3).

An MIC90 of 0.125 mg/liter has been reported for moxifloxacin against S. aureus (51). If one simplifies the PTA versus MIC profile by assuming a PTA of 100% for all MICs that are ≤0.125 mg/liter and a PTA of 0% for all MICs that are ≥0.25 mg/liter, it is possible to calculate that the overall probability of target attainment will be ≥90% for moxifloxacin against S. aureus based on an MIC90 of 0.125 mg/liter. Therefore, a high (>90%) probability for successful clinical and microbiological outcome would be predicted for S. aureus infections up to a target AUCBONE/MIC ≥ 55 and protein binding in bone of 50%.

In conclusion, we found a good penetration of moxifloxacin into bone. Based on AUC ratios, the median penetration (10% to 90% percentile for between-subject variability) was 80% (51% to 126%) for cortical bone and 78% (42% to 144%) for cancellous bone. We found a short equilibrium half-life (<60 min) between serum and cortical bone as well as between serum and cancellous bone. The PKPD breakpoint for moxifloxacin doses of 400 mg q24h at steady state was 0.375 mg/liter in serum and cancellous bone, and 0.5 in cortical bone, based on the target AUCBONE/MIC ≥ 33 (fAUCSERUM/MIC ≥ 40) for successful microbiological outcome and assuming a protein binding level of 50% for moxifloxacin in serum and the same extent of binding as ciprofloxacin in bone. As the MIC90 of moxifloxacin is 0.125 mg/liter against S. aureus, moxifloxacin was predicted to have a high probability (≥90%) for successful microbiological outcome. This provides the required basis for a larger study of the clinical effectiveness of moxifloxacin against bone infections.


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ACKNOWLEDGMENTS
 
We thank Stephen B. Duffull and Venkata V. Pavan Kumar for helpful comments about the use of WinBUGS.


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FOOTNOTES
 
* Corresponding author. Mailing address: IBMP—Institute for Biomedical and Pharmaceutical Research, Paul-Ehrlich-Str. 19, D-90562 Nürnberg-Heroldsberg, Germany. Phone: 49-911-518290. Fax: 49-911-5182920. E-mail: ibmp{at}osn.de Back

{triangledown} Published ahead of print on 17 February 2009. Back

§ Present address: Department of Pharmaceutical Sciences, State University of New York at Buffalo, Buffalo, NY 14260. Back


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Antimicrobial Agents and Chemotherapy, May 2009, p. 2074-2081, Vol. 53, No. 5
0066-4804/09/$08.00+0     doi:10.1128/AAC.01056-08
Copyright © 2009, American Society for Microbiology. All Rights Reserved.



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