Taking amoxicillin

The collected bone specimens were immediately frozen on dry ice and stored at ?80°C until analysis.

In cases in which the bone samples included both the femoral head and the femoral neck, these two parts were separated from each other.

The samples were then divided into cortical and cancellous tissues.

The adhering blood was removed from the samples by swabbing for a short time. The bone samples were subsequently pulverized under liquid nitrogen by use of a cryogenic mill (Freezer/Mill). For preparation of calibration standards and spiked quality controls, appropriate amounts of amoxicillin and clavulanic acid standard solutions were added to serum and bone tissue samples that were shown to be free of the study drugs.

For determination of the amoxicillin and clavulanic acid concentrations in serum, 50 ?l of the internal standard solution was added to 100 ?l of each sample. The samples were deproteinized by addition of 300 ?l acetonitrile.

After the samples were thoroughly mixed, they were centrifuged and 50 ?l of the clear supernatant was analyzed by liquid chromatography-tandem mass spectrometry (LC-MS/MS). For analysis of the bone samples, an aliquot of the bone powder was shaken with six times the amount of buffer for 4 h.

The degree of extraction was studied over time to ensure the reproducibility of the results. Amoxicillin and clavulanic acid were stable during the 4-h extraction period. After centrifugation, 50 ?l of the internal standard solution was added to 50 ?l of the aqueous supernatant.

After addition of 175 ?l acetonitrile, the samples were thoroughly mixed and centrifuged.

The clear supernatant was diluted with twice the amount of buffer. For determination of the amoxicillin concentration, 50 ?l of each sample was chromatographed on a reversed-phase column (Ultracarb 5 ODS 30) and eluted by use of an isocratic solvent system consisting of 0.001 M ammonium acetate buffer and acetonitrile (90/10, vol/vol).

The samples were monitored by LC-MS/MS by the selected reaction monitoring method: precursor > product ion for amoxicillin, m/z 366 > m/z 208; precursor > product ion for the internal standard, m/z 350 > m/z 160. Under these conditions, amoxicillin and the internal standard were eluted after approximately 0.8 min. For determination of the clavulanic acid concentration, 25 ?l of each sample was chromatographed on a reversed-phase column (Nucleosil 100 amino) and eluted by use of an isocratic solvent system consisting of 0.01 M ammonium acetate buffer and acetonitrile (40/60, vol/vol).

The samples were monitored by LC-MS/MS by the selected reaction monitoring method: precursor > product ion for clavulanic acid, m/z 198 > m/z 108; precursor > product ion for the internal standard, m/z 232 > m/z 140. Under these conditions, clavulanic acid and the internal standard were eluted after approximately 2 min.

MacQuan software (version 1.4-noFPU; Perkin-Elmer, Toronto, Ontario, Canada) was used for evaluation of the chromatograms.

No interference was observed for the study drugs or the internal standards. The precision and the accuracy of the spiked quality controls for amoxicillin in serum ranged from 1.8 to 10% and 97.3 to 107.8%, respectively, and the precision and the accuracy of the spiked quality controls for clavulanic acid in serum ranged from 0.8 to 4.8% and 96.0 to 100.5%, respectively.

The precision and the accuracy of the spiked quality controls for amoxicillin in bone homogenate ranged from 5.8 to 8.1% and 97.2 to 99.5%, respectively. The precision and the accuracy of the spiked quality controls for clavulanic acid in bone homogenate ranged from 5.0 to 7.8% and 91.7 to 100.0%, respectively. A model with two compartments for amoxicillin and one compartment for clavulanic acid was used to describe the concentrations in serum.

A bone compartment was added to model the concentrations in bone. The drug input into the central compartment was described by a time-constrained zero-order process. Standard diagnostic plots for model evaluation were used, and the predictive performance of the final model was tested by the use of visual predictive checks. For the visual predictive check, serum and bone concentration curves for 10,000 subjects were simulated for amoxicillin and clavulanic acid. We derived the median, the nonparametric 90% prediction interval (5th to 95th percentile), and the nonparametric 50% prediction interval (25th to 75th percentile) from those profiles predicted by validated Perl scripts, as described previously (12).

We compared the median predicted concentrations and the prediction intervals with the observed data and performed a visual assessment to determine whether the median and the predicted intervals adequately mirrored the central tendency and the variability of the observed data. Observations for amoxicillin and clavulanic acid concentrations in serum, cortical bone, and cancellous bone were available.

The differential equations for amoxicillin were as follows: $$mathtex$$\[\frac \mathrm \ \left(\frac \mathrm \mathrm _ >> >>\right)\ \ X1 \frac > >>\ \ X2 \frac _ >> >>\ \ X3\]$$mathtex$$ $$mathtex$$\[\frac \frac > >>\ \ X1 amoxicillin & clavulanic acid \frac > >>\ \ X2\]$$mathtex$$ $$mathtex$$\[\frac \frac _ >> >>\ \ X1 \frac _ >> >>\ \ X3\]$$mathtex$$ where compartment 1 is the central compartment, compartment 2 is the peripheral compartment, and compartment 3 is the bone compartment; X 1, X 2, and X 3 represent the amounts of drug in the central, peripheral, and bone compartments; V c entral , V p eripheral , and V b one represent the volumes of distribution in the central, peripheral, and bone compartments.

Initial conditions were 0 for all three compartments. CL is the total clearance from the central compartment, CLic is the intercompartmental clearance between the central and the peripheral compartments, and CLic bone is the intercompartmental clearance between the central and the bone compartments.

The differential equations for clavulanic acid can be obtained from the above equations by setting CLic equal to 0. The observed bone concentrations and initial modeling showed that the rates of equilibration between serum and cortical bone as well as those between serum and cancellous bone were similar. Scale terms were included to describe the equilibrium concentration ratios between cancellous bone and serum ( F cancellous ) and between cortical bone and serum ( F cortical ).

If F cortical is equal to 1, the AUC from time zero to infinity after the administration of a single dose for bone equals the respective AUC for serum. If F cortical is less (greater) than 1, the AUC from time zero to infinity for bone is lower (higher) than that for serum.

Sparse serum concentration-time data were available for the period from 0 to 1.1 h after the end of the infusion.

These data did not allow us to estimate all PK parameters of the population PK model. Therefore, prior knowledge of the structural PK model and the average disposition parameters for the serum concentration profiles and their variability from published studies (4, 5, 29, 30, 49, 51) were incorporated in the present analyses. As those studies were conducted with young healthy volunteers, the amoxicillin clearance reported by Sjovall et al. This was in agreement with the age-related decrease in renal function predicted by the formula of Cockcroft and Gault (13) on the basis of the CL values from the other studies. For clavulanic acid, the age-related decrease in renal function was accounted for according to the formula of Cockcroft and Gault (13). As disposition parameters for amoxicillin and clavulanic acid from the literature were determined in the absence of a bone compartment, the amounts of amoxicillin and clavulanic acid in the bone compartment had to be kept minimal. In our model, the serum PK were not affected by the presence of the bone compartment. This was achieved by choosing a small V b one for the bone compartment.

Between-subject variability (BSV) was described by an exponential variability model, and residual unidentified variability was described by a proportional error model for concentrations in serum and bone. The first-order conditional estimation method with the interaction estimation option in NONMEM (version V, release 1.1; NONMEM Project Group,

University

(vi) Estimation by three-stage hierarchical population approach. To independently confirm the results obtained with NONMEM, PK parameters were estimated by the three-stage hierarchical population approach in S-ADAPT (version 1.55) (7). Priors for population means and BSV of the disposition parameters were obtained from previously published studies (4, 5, 29, 30, 49, 51).

Informative priors were used for the population mean and variability of CL, V c entral , V peripheral , and CLic. Physiologically plausible but uninformative priors were used for the population mean and variability of F cortical and F cancellous and the population mean of CLic bone on the basis of data reported in the literature (36).

The residual unidentified variability was described by a proportional error model.

As only one serum sample and one bone sample were available from each patient, informative priors were used for the residual unidentified variability on the basis of the bioanalytical assay data.

A systematic sensitivity analysis was performed to evaluate the effect of the choice of priors on the extent and the rate of bone penetration. The extent of drug exposure in bone was determined for amoxicillin and clavulanic acid by simulating the AUCs in serum and cortical and cancellous bone.

On the basis of the final estimates from NONMEM, we simulated 10,000 virtual subjects at steady state and calculated the individual ratios of AUC for bone/AUC for serum as well as their BSV.

A time that the non-protein-bound drug concentration remained above the MIC ( fT > MIC ) of ?50% of the dosing interval was shown to be the PK-PD target for near-maximal bactericidal activity, and an fT > MIC of ?30% was shown to be the PK-PD target

for

We studied a range of MICs from 0.25 to 64 mg/liter and used a protein binding of 18% for amoxicillin in serum (27).

In the absence of data on the protein binding in bone, we assumed a protein binding of 18% for amoxicillin in bone. Additionally, we provided the expected PK-PD breakpoints for various potential scenarios of the distribution of drug and bacteria in bone.

A 30-min infusion of 2,000 mg amoxicillin every 4 h (q4h), q6h, or q8h was studied at steady state. We simulated 10,000 virtual subjects in the absence of residual error. The probabilities of target attainment (PTAs) were derived by calculating the fraction of subjects who attained the PK-PD target at each MIC.

The PK-PD breakpoint was defined as the highest MIC for which the PTA was at least 90%.

To determine the clinical relevance of the differences in the PTAs between the dosage regimens, the PTA expectation value was calculated on the basis of several published MIC distributions for amoxicillin-clavulanic acid. The PTA expectation value (also called the cumulative fraction of response [46]) was calculated by multiplying the PTA at each MIC with the frequency of how often this MIC occurs in the selected MIC distribution. The individual products at each MIC were summed, and the sum yielded the PTA expectation value for the selected MIC distribution. The PTA expectation value is the PTA in a specific patient population for the treatment of infections caused by bacteria from a specific MIC distribution (ideally, the MIC distribution of each local hospital). Figure 1 shows the concentrations of amoxicillin and clavulanic acid observed in serum and cortical and cancellous bone. For both drugs, the concentrations were lower in cortical and cancellous bone than in serum.

The concentrations in the femoral neck samples were similar to those in the femoral head samples. Figure 2 shows the high correlation of the ratio of the concentration in bone to the concentration in serum within the individual patients. Concentrations in serum and bone of subjects undergoing hip replacement surgery after administration of a single intravenous dose of 2000 mg amoxicillin and 200 mg clavulanic acid as a short-term infusion.

Bone concentration-to-serum concentration ratios of amoxicillin versus clavulanic acid in cortical bone (A) and cancellous bone (B).

The population PK parameter estimates from NONMEM and the three-stage hierarchical approach in S-ADAPT were comparable (Table 1). The average estimated drug AUCs for bone relative to that for serum ( F c ortical and F c ancellous ) ranged from 19 to 21% for amoxicillin and from 12 to 19% for clavulanic acid.

The half-life of equilibration between bone and serum was rapid for both drugs (Table 1).

Averages and between-subject coefficients of variation (percent) calculated from individual PK parameter estimates a.

Figure 3 shows the simulated extent of amoxicillin and clavulanic acid penetration into cortical and cancellous bone and the BSV of penetration, calculated from the ratios of AUC cortical /AUC serum and AUC cancellous /AUC serum at steady state for 10,000 virtual subjects on the basis of the results obtained with NONMEM. The median AUC ratios for amoxicillin were 20% (10th to 90th percentile, 16% to 25%) for cortical bone and 18% (10th to 90th percentile, 11% to 29%) for cancellous bone.

The median AUC ratios for clavulanic acid were 15% (10th to 90th percentile, 11% to 21%) for cortical bone and 10% (10th to 90th percentile, 5.1% to 21%) for cancellous bone. Therefore, for both drugs the AUC ratio for cancellous bone was more variable (see also the variability for F c ortical and F c ancellous in Table 1) and (slightly) lower than that for cortical bone.

Simulated ratios for the AUC between bone and serum for amoxicillin (A) and clavulanic acid (B) during one dosing interval at steady state (based on the results obtained with NONMEM [Table 1]).

The visual predictive checks showed a highly sufficient predictive performance of the final NONMEM model for both drugs (Fig. This qualified our model for use in the Monte Carlo simulation. Visual predictive check after treatment with 2,000 mg amoxicillin and 200 mg clavulanic acid.

The plots show the observed data, the 90% prediction (P) intervals (5th to 95th percentiles), and the interquartile ranges (25th to 75th percentiles). 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. Visual predictive checks are based on the results obtained with NONMEM. The PTA-versus-MIC plots based on the estimates from NONMEM are shown in Fig.

5; and the respective PK-PD breakpoints for serum, cortical bone, and cancellous bone are listed in Table 2.