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The samples were placed in an ice-water bath and were left to clot before they were centrifuged at 4°C. After centrifugation, the serum samples were immediately frozen and stored at ?80°C until the analysis. The hip replacement surgery consisted of resection of the femoral head or both the femoral head and the femoral neck and the subsequent implantation of the prosthetic hip joint. 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

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 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: $$mathtex$$\[\frac \mathrm \ \left(\frac \mathrm \mathrm _ >> >>\right)\ \ X1 \frac > >>\ \ X2 \frac _ >> >>\ \ X3\]$$mathtex$$ $$mathtex$$\[\frac \frac > >>\ \ X1 \frac > >>\ \ X2\]$$mathtex$$ $$mathtex$$\[\frac \frac _ >> >>\ \ X1 \frac _ >> >>\ \ X3\]$$mathtex$$ 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 of California, San Francisco) (8) was utilized for population PK modeling.