Pharmacokinetic Model for Cefuroxime Dosing during Cardiac Surgery under Cardiopulmonary Bypass

Cefuroxime (CXM) is an antibiotic recommended for surgical site infection prevention in cardiac surgery. However, the dosing regimens commonly used do not sustain therapeutic concentrations throughout surgery. The aim of this study was to conduct a population analysis of CXM pharmacokinetics (PK), and to propose an optimized dosing regimen. Adult patients undergoing cardiac surgery under cardiopulmonary bypass (CPB) received a 1,500 mg CXM intravenous bolus followed by a 750 mg bolus at CPB priming, then every 2 h thereafter.

ABSTRACT

Cefuroxime (CXM) is an antibiotic recommended for surgical site infection prevention in cardiac surgery. However, the dosing regimens commonly used do not sustain therapeutic concentrations throughout surgery. The aim of this study was to conduct a population analysis of CXM pharmacokinetics (PK), and to propose an optimized dosing regimen. Adult patients undergoing cardiac surgery under cardiopulmonary bypass (CPB) received a 1,500 mg CXM intravenous bolus followed by a 750 mg bolus at CPB priming, then every 2 h thereafter. Model-based PK simulations were used to develop an optimized dosing regimen and evaluate its efficacy in attaining various concentration thresholds, including those recommended in US and European guidelines. In total, 447 CXM measurements were acquired in 50 patients. A two-compartment model best fit the data, with total body weight and creatinine clearance determining interpatient variability in the central and peripheral volumes of distribution, and in elimination clearance, respectively. Using our optimized dosing regimen, different dosing schemes adapted to body weight and renal function were calculated to attain total concentration thresholds ranging from 12 to 96 mg/liter. Our simulations showed that the dosing regimens recommended in US and European guidelines failed to maintain concentrations above 48 mg/liter. Our individualized dosing strategy was capable of ensuring therapeutic CXM concentrations conforming to each target threshold. Our model yielded an optimized CXM dosing regimen adapted to body weight and renal function, and sustaining therapeutic concentrations consistent with each desired threshold. The optimal target concentration and necessary duration of its maintenance in cardiac surgery still remain unclear.

TEXT

Severe postoperative infections constitute a common complication following cardiac surgery under cardiopulmonary bypass (CPB). The incidence of surgical site infections (SSI) of the sternum after coronary artery bypass graft (CABG) procedures ranges from 0.9% to 20% (1). Deep sternal infections, such as mediastinitis, occur with an incidence of 1% to 2% and are correlated with a mortality rate ranging from 22% to 34% (1–3). Cefuroxime (CXM), a second-generation cephalosporin, is one of the first-line antibiotics recommended for the prevention of SSI in cardiac surgery (4, 5), manifesting good tissue penetration and low toxicity (6). Its spectrum of effective antimicrobial activity covers the most common microbiological pathogens responsible for wound infections, namely, coagulase-negative staphylococci or Staphylococcus aureus (60 to 80% of isolates) and aerobic Gram-negative rods (7). Emergence of resistant Staphylococcus have resulted in guidelines for systematic methicillin-resistant Staphylococcus aureus (MRSA) screening and use of vancomycin for antibiotic prophylaxis in cases of positivity. However, the CXM dosing regimens commonly used in cardiac surgery involving CPB appear to be incapable of maintaining plasma concentrations above the therapeutic target throughout the intraoperative period in more than half the patients receiving this antibiotic prophylaxis (8–10). As a result, various alternative dosing regimens have been proposed for CXM administration, but these were all developed empirically. For example, US guidelines recommend a 1,500 mg injection every 4 h up to 24 h postoperation, whereas European guidelines advocate a 1,500 mg injection every 140 min up to 24 h postoperation. It is still unknown whether these regimens are optimal for achieving therapeutic concentrations throughout surgery and which factors are responsible for CXM pharmacokinetic (PK) variability. There is evidence to suggest that CXM administration should be adjusted to patients’ renal function (11), but it is unclear if CXM administration should be adjusted to weight, particularly in obese patients (9).

Several population PK studies have been conducted to explain CXM variability, predict CXM concentrations, and propose an optimized dosing regimen for CXM in the context of cardiac surgery under CPB. However, these were either conducted in pediatric populations (12, 13), limited by the small number of patients included (8–10, 14–16), or the characteristics of the sample population made it unlikely to see an effect of weight on CXM exposure. The aim of this study was to conduct a population analysis of CXM PK in adult patients undergoing cardiac surgery under CPB and investigate, using PK simulations, the ability of an optimized dosing regimen to maintain therapeutic concentrations of CXM throughout surgery.

RESULTS

Patients and data sampled.

Fifty subjects were included in the study, with a mean age of 66 years (range 36 to 81), mean total body weight of 80 kg (range 40 to 133), and a mean creatinine clearance (CrCl) according to the Cockcroft-Gault (C&G) formula of 80 ml/min (range 34 to 146). Nine patients presented moderate renal impairment (CrCl 30 to 60 ml/min). Eleven patients were obese (body mass index [BMI] > 30 kg/m²). Four patients (8%) experienced SSI (early infective endocarditis in three patients and superficial SSI in one patient). Patient characteristics are detailed in Table 1. A total of 447 CXM concentrations were measured for the PK analysis, corresponding to a mean of nine measurements per subject distributed from 0.5 to 8.6 h after the first CXM administration.

TABLE 1.

Baseline patient characteristics

Patient characteristica	Number or mean (range)
Age (yrs)	66 (36–81)
Sex
Male	38
Female	12
Total body wt (kg)	80 (40–133)
BMI (kg/m²)	27 (19–52)
CrCl ml/min)	80 (34–146)
ASA physical status
I	1
II	18
III	25
IV	6
CPB time (min)	128 (45–263)

^aBMI, body mass index; CrCl, creatinine clearance according to the Cockcroft-Gault formula; CPB, cardiopulmonary bypass; ASA, American Society of Anaesthesiologists.

Population PK model.

CXM concentrations were best described by a two-compartment model. Interpatient variability was estimated for the following PK parameters: elimination clearance (CL), volume of the central compartment (Vc), intercompartmental clearance (Q), and volume of the peripheral compartment (Vp). A proportional error model best described residual variability.

With regard to the covariates investigated, interpatient variability for parameters Vc and Vp was best explained by total body weight, while interpatient variability for the CL parameter was best explained by CrCl according to the C&G formula. Table 2 presents the PK parameter estimates for the model. Interpatient variability in Vc, Vp, and CL in the final model decreased by 9%, 27%, and 12.5%, respectively, after covariate inclusion compared to the initial values estimated by the model in the absence of covariates. Inclusion of the covariates resulted in a 10.82 point reduction in the Bayesian information criterion (BIC).

TABLE 2.

Estimates of population parameters for model building

Parametera	Estimate (% RSE)a
	Model 1b	Model 2b
CL (liter/h) = ϴ1 x (CrCl/80)ϴ2
ϴ1	5.83 (4.98)	5.94 (4.49)
ϴ2	0	0.36 (37.5)
Vc (liter) = ϴ3 x (TBW/80)ϴ4
ϴ3	4.71 (13.1)	4.97 (12.2)
ϴ4	0	0.79 (63.1)
Q (liter/h)	25.1 (14)	25.1 (13.8)
Vp (liter) = ϴ5 x (TBW/80)ϴ6
ϴ5	9.21 (6.41)	9.01 (5.94)
ϴ6	0	0.7 (37.2)
ΩCL (%)	32 (11.5)	28 (11.6)
ΩVc (%)	58 (18.8)	53 (19)
ΩQ (%)	68 (18)	66 (18.6)
ΩVp (%)	26 (26)	19 (38.5)
Proportional residual variance (%)	16 (9.76)	16 (9.62)
BIC	3,932.68	3,921.86

^aRSE, relative standard error; CL, clearance; TBW: total body weight (kg); Vc, central volume of distribution; Vp, peripheral volume of distribution; Q, intercompartmental clearance; CrCl, creatinine clearance (ml/min) according to the Cockcroft-Gault formula, BIC, Bayesian information criteria.

^bModel 1: model without covariates; model 2: final model including covariates.

The prediction-corrected visual predictive check (VPC) showed that the observed data were fully included in the 90% prediction interval of the simulated data, indicating a good predictive capacity of the model (Fig. 1). The goodness of fit plots showed no apparent bias in model prediction (Fig. 2).

FIG 1.

Prediction-corrected visual predictive check for the pharmacokinetic model. The 5^th, 50^th, and 95^th prediction intervals from the simulated concentrations of CXM are plotted against time, with the observed data superimposed.

FIG 2.

Goodness of fit plots. The black line represents the identity line, the orange line represents the regression line.

PK simulations.

Using the formulae specified in the Materials and Methods section and estimates of the population PK parameters, we developed different dosing regimens adapted to body weight and renal function to maintain total CXM concentration above various target levels ranging from 12 to 96 mg/liter. Figure 3 displays graphs illustrating the optimized dosing regimen estimated by our model to maintain total CXM concentrations above 48 mg/liter throughout antibiotic prophylaxis for 80% of patients. The graphs indicate that the required loading dose increases with increasing body weight and that the maintenance dose decreases with renal impairment.

FIG 3.

Optimized dosing regimen estimated to obtain total CXM concentrations above 48 mg/liter. Loading dose depended on body weight and continuous maintenance dose depended on creatinine clearance. Intermittent bolus maintenance dose depended on creatinine clearance and body weight (yellow dashed line: patient weighing 50 kg; solid blue line: patient weighing 80 kg; red dashed line: patient weighing 110 kg). The loading dose increased with increasing body weight, the maintenance dose decreased with renal impairment.

We then investigated the capacity of the dosing regimens recommended in US and European guidelines, as well as that of our proposed regimens, to maintain total CXM concentrations above different threshold values ranging from 12 to 96 mg/liter. Table 3 presents for each regimen the median duration for which CXM concentration remained above the desired threshold with 24-h antibiotic prophylaxis and Table 4 presents the total CXM dose administered over 24 h. Our simulations showed that the CXM dosing regimen recommended in US guidelines is sufficient to maintain concentrations up to 24 mg/liter (2× MIC), and that the regimen recommended in European guidelines is sufficient to maintain concentrations up to 48 mg/liter (4× MIC), with the regimen advocated in European guidelines being more effective owing to the higher doses used. In contrast, for target concentrations above 48 mg/liter, the regimens recommended in US and European guidelines both failed to reach the threshold concentrations. PK simulations using our model show that our individualized dosing strategy was capable of maintaining therapeutic CXM concentrations above each of the target threshold values considered.

TABLE 3.

Estimated times above the threshold value for each target concentration threshold using PK simulations with different dosing regimens

Target total plasma concn threshold (mg/liter)	Time above threshold during 24 h, median (IQR)a ,b
	US guidelines	European guidelines	Optimized dosing regimen (intermittent bolus injections)	Optimized dosing regimen (continuous infusion)
12	24.0 (24.0–24.0)	24.0 (24.0–24.0)	24.0 (20.76–24.0)	24.0 (21.70–24.0)
24	23.0 (17.5–24.0)	24.0 (24.0–24.0)	24.0 (20.76–24.0)	24.0 (21.70–24.0)
36	16.9 (12.1–22.2)	23.9 (23.1–24.0)	24.0 (20.76–24.0)	24.0 (21.70–24.0)
48	12.2 (8.5–17.0)	22.9 (19.6–23.6)	24.0 (20.76–24.0)	24.0 (21.70–24.0)
60	8.7 (5.8–12.7)	21.3 (14.9–22.8)	24.0 (20.76–24.0)	24.0 (21.70–24.0)
72	6.0 (3.9–9.3)	17.4 (11.2–21.7)	24.0 (20.76–24.0)	24.0 (21.70–24.0)
84	4.1 (2.7–6.8)	13.5 (8.5–19.9)	24.0 (20.76–24.0)	24.0 (21.70–24.0)
96	2.9 (1.9–4.8)	10.4 (6.3–16.5)	24.0 (20.76–24.0)	24.0 (21.70–24.0)

^aIQR, interquartile range.

^bFor the optimized dosing regimens, the time above threshold was the same for each threshold value owing to PK linearity and adjustment of the dosing according to the target threshold.

TABLE 4.

Total cefuroxime dose received for each target concentration threshold using PK simulations with different dosing regimens

Target total plasma concn threshold (mg/liter)	Total CXM dose (g) received over 24 h (median, IQR)a
	US guidelines	European guidelines	Optimized dosing regimen (intermittent bolus injections)	Optimized dosing regimen (continuous infusion)
12	9.0	16.5	3.7 (3.3–4.1)	2.3 (2.1–2.5)
24	9.0	16.5	7.3 (6.7–8.2)	4.7 (4.3–4.9)
36	9.0	16.5	11.0 (10.0–12.3)	7.0 (6.4–7.4)
48	9.0	16.5	14.7 (13.3–16.3)	9.3 (8.6–9.9)
60	9.0	16.5	18.4 (16.7–20.4)	11.7 (10.7–12.3)
72	9.0	16.5	22.0 (20.0–24.5)	14.0 (12.9–14.8)
84	9.0	16.5	25.7 (23.3–28.6)	16.4 (15.0–17.2)
96	9.0	16.5	29.4 (26.6–32.7)	18.7 (17.1–19.7)

^aIQR, interquartile range.

Figure 4 shows CXM concentration-time courses in the simulated population based on the dosing regimens advocated in US and European guidelines and on our optimized intermittent and continuous dosing regimens designed to maintain total CXM concentrations above 48 mg/liter. With the optimized regimens, the administered dose was individually adapted to patients’ total body weight (TBW) and CrCl. For the average patient of the study with a TBW of 80 kg and a CrCl according to the C&G formula of 80 ml/min, the CXM rounded doses provided by our model were a 900 mg loading dose followed by additional 1,200 mg boluses every 2 h for the optimized intermittent dosing regimen, and a 900 mg loading dose followed by an additional continuous infusion of 400 mg/h for the optimized continuous dosing regimen. These curves show that our dosing regimen was capable of maintaining therapeutic concentrations above the target level throughout antibiotic prophylaxis.

FIG 4.

Concentration-time courses of CXM in the simulated population based on the dosing regimen recommended in US guidelines (1,500 mg every 4 h), European guidelines (1,500 mg every 140 min), and the optimized dosing regimens designed to maintain total CXM concentrations above 48 mg/liter. The optimized regimens were given either as an intermittent administration or as a continuous administration. Blue solid lines correspond to the mean CXM concentrations. Blue shaded areas correspond to the 95% prediction interval.

DISCUSSION

We conducted a population PK study to quantify CXM exposure in adult patients undergoing cardiac surgery and to propose a dosing regimen capable of maintaining therapeutic concentrations.

Our final model was a two-compartment model with total body weight best describing interpatient variability in the volume of distribution, and creatinine clearance best describing interpatient variability in clearance. The PK parameter values estimated in our model were in accordance with the results of a previous PK parametric study conducted with CXM in adult patients undergoing cardiac surgery (11).

However, estimation of the elimination clearance in our study was likely more accurate owing to the larger number of patients included, the number of CXM concentrations measured, and the higher proportion of subjects with renal impairment (18%). Moreover, our study was the first population PK study to identify the effect of weight on CXM concentrations. This can be explained by the inclusion of patients with extreme body weights in our study (range 40 to 133 kg with 22% of patients with BMI > 30 kg/m²), permitting a robust and accurate estimation of the PK parameters in our model.

Our model generated an optimized dosing regimen by taking into account certain parameters implicated in PK variability, corresponding to the covariates included our final model (TBW and CrCl). The simulations showed that our proposed CXM dosing regimens, administered either as intermittent bolus injections or as a continuous infusion, provided sustained therapeutic concentrations consistent with each desired threshold value. Lower total doses were necessary with the continuous infusion regimen compared to the intermittent bolus injections (9 g over 24 h for a target defined as 4× MIC throughout antibiotic prophylaxis versus 15 g over 24 h). This is in accordance with recent data (17). Our simulations (Fig. 4) indicated that European guidelines fit better than the US guidelines, and were similar to our optimized intermittent dosing regimen to target a 48 mg/liter concentration threshold. However, the optimized regimen can provide an adjustment to extreme values of creatinine clearance and total body weight, and is more convenient (bolus every 2 h versus 140 min). Thus, the optimized regimen can avoid over dosing in cases of renal insufficiency or under dosing in cases of severe obesity. It can also provide an individualized dosing if the target threshold was to be changed.

In our study, we evaluated attainment of various total concentration thresholds ranging from 12 to 96 mg/liter. Based on the results of in vitro studies, the maximum bactericidal effect of beta-lactam antibiotics is obtained at 4- to 8-fold their MIC against the target bacteria (18, 19). The most common pathogens responsible for wound infections after cardiac surgery are coagulase-negative staphylococci and Staphylococcus aureus (7), with the MIC of CXM against these bacteria being 8 mg/liter (8). Unbound CXM is the active form with regard to antimicrobial effect, and the MIC is based on this form. Multiplication of this MIC by a factor of 4 gives a concentration threshold of 32 mg/liter with regard to free CXM, equivalent to 48 mg/liter in terms of total CXM concentrations when you take into account a protein binding rate of 33% (20). This threshold concentration has already been used in PK and PK/PD studies to investigate the efficacy of CXM prophylaxis in cardiac surgery and is known to allow good bone penetration of the antibiotic (21, 22). Nevertheless, some authors have chosen different efficacy thresholds, ranging from 2 to 64 mg/liter based on unbound concentrations (8, 9, 11–14, 16, 23). Alqahtani et al. performed a PK/PD analysis of CXM prophylaxis in cardiac surgery using MIC as an outcome for CXM efficacy (11). However, in fine, the relationship between CXM concentrations and the incidence of postoperative infections after cardiac surgery has never been demonstrated. Moreover, it is not known whether the efficacy threshold for antibiotic prophylaxis should be the same as for antibiotic treatment. In addition, use of an efficacy threshold corresponding to 4 to 8 times the MIC is based principally on a citation in a minireview concerning the effect of beta-lactam antibiotics on Gram-negative bacilli (18). Reaching an 8× MIC target could lead to high exposures, especially if the intermittent optimized dosing regimen is used. Aiming for lower thresholds, such as 4× MIC, could avoid overdosing and antibiotic neurotoxicity. A PK/PD analysis needs to be conducted to evaluate the relationship between CXM concentrations and postoperative infections.

We showed that our dosing strategy was capable of maintaining CXM concentrations above the desired target. However, the optimal duration of CXM prophylaxis is still unclear. CXM is known to be a time-dependent antibiotic (24), and various durations of its use have been proposed for cardiac surgery, ranging from the perioperative period up to 80 h postoperation. Data suggest that the longer time above the MIC, the better the outcome in infected patients (25). Yet a relationship between the duration of prophylactic CXM administration and the incidence of postoperative infections has never been demonstrated.

Another limitation of this study is that we performed CXM measurements only during CPB, so we could not evaluate CPB in our covariate analysis and could not identify CPB as a factor capable of explaining CXM PK variability. However, in a previous study, CPB was not shown to affect CXM concentrations (26). Moreover, Aalbers et al. evaluated the effect of CPB on CXM concentrations during CABG (9), reporting that PK parameters remained unchanged during CPB compared to values recorded before CPB, with no hemodilution effect. These authors concluded that the use of CPB during CABG was not a significant covariate in terms of explaining CXM PK variability and that CPB did not necessitate any dosing modification. In consequence, CXM doses for antibiotic prophylaxis in cardiac surgery do not need be adjusted in the context of CPB.

We did not measure unbound drug concentrations in this study. Instead, we measured total CXM concentrations and calculated free serum concentrations according to the published value of the unbound fraction (20). Previous studies have shown that the use of this strategy is acceptable for drugs with low to moderate levels of protein binding, such as CXM (27).

In conclusion, we developed a PK model of CXM for patients undergoing cardiac surgery under CPB, with TBW and CrCl identified as factors affecting CXM exposure. Our PK simulations showed that our dosing strategies were better than those recommended in current guidelines in terms of maintaining bactericidal concentrations of CXM against the pathogens most frequently encountered in cardiac surgery. Yet the optimal CXM concentration to target and the period of time during which this concentration should be maintained for antibiotic prophylaxis remain unclear. A PK/PD study needs to be conducted to evaluate the relationship between CXM exposure and postoperative infections after cardiac surgery.

MATERIALS AND METHODS

Patients.

This prospective, open-label, observational, routine medical care clinical study was conducted in the teaching hospital of Saint Etienne, France following approval of the study protocol by the hospital Ethics Committee (Institutional Review Board number IRBN012016/CHUSTE) [28]). The need for informed written consent was waived by the Ethics Committee on the understanding that the study did not require any supplementary procedure compared with standard care. All consecutive patients undergoing cardiac surgery under CPB from February to April 2016 were included if they were over 18 years old and were scheduled to receive CXM for antibiotic prophylaxis. Every subject was screened for methicillin-resistant Staphylococcus aureus (MRSA). Patients diagnosed with MRSA were decolonized with mupirocin and chlorhexidine and were excluded from the study because they received vancomycin for antibiotic prophylaxis.

Study protocol.

Anesthesia was conducted according to the institutional standards of care in cardiac surgery. CXM was administered according to the French guidelines for antibiotic prophylaxis in patients undergoing cardiac surgery (29). Subjects received a direct intravenous bolus injection of 1,500 mg of CXM at anesthesia induction, followed by a 750 mg bolus at CPB priming and then a further 750 mg bolus every 2 h until surgical skin closure. The priming volume used for CPB was standardized at 1,500 ml, consisting of 1,000 ml crystalloid solution and 500 ml hydroxyethyl starch solution (Voluven, Fresenius Kabi, France). A nonpulsatile pump flow was maintained at a rate ranging from 2.0 to 2.4 liters/min/m². Myocardial protection was ensured either by use of a cold cardioplegic solution (Custodiol; Eusa Pharma, Limonest, France) or by normothermic blood cardioplegia. Anticoagulation during CPB was ensured with unfractionated heparin (UFH, Panpharma, Fougères, France) and monitored by repeated blood measurements of the activated clotting time (ACT). Patient blood management with regard to blood product transfusion was accomplished according to the international standards of care applicable to cardiac surgery (30).

Sample collection and drug assay.

Blood samples for CXM concentration measurements were drawn into EDTA-containing blood collection tubes via a radial artery catheter during CPB every time a blood sample for ACT measurement was required. The samples were stored at −80°C until analysis. Total plasma CXM concentrations were measured using an Acquity ultra performance liquid chromatography (UPLC) system coupled with a Xevo TQD triple quadrupole mass spectrometer (Waters, Saint-Quentin-en-Yvelines, France). The analyses were performed in negative ionization mode both for CXM in plasma samples (mass/charge [m/z] 423.17→207.07) and for the internal standard ([²H₃]-CXM; m/z 426.2→321.08). The mobile phase was a mixture of (A) 0.1% formic acid in water and (B) 0.1% formic acid in acetonitrile, applied as a gradient to a BEH C₁₈ column (50 mm × 2.1 mm × 1.7 μm) (Waters). Samples were prepared by dilution of 50 μl of the plasma sample with 300 μl of [²H₃]-CXM in methanol. The method was linear over the concentration range of 5 to 200 mg/liter. The lower limit of quantification was 5 mg/liter. The inter- and intraday precisions were evaluated at three quality control levels and the coefficients of variation were under 10%.

Model development and evaluation.

Data were analyzed using MONOLIX modeling software (version 4.3, release 3, Lixoft). CXM concentrations were analyzed using the following nonlinear mixed-effect model framework:

$$\mathit{Ob}{s}_{\mathit{ij}}=F(t_{\mathit{ij}},{\varphi }_i)+(a+b\times F(t_{\mathit{ij}},{\varphi }_i))\times {\epsilon }_{\mathit{ij}}$$ (1)

where Obs_ij denotes the observed data measured for patient i at time j; the function F(t_ij, ϕ_i) corresponds to the concentration predicted by the model for patient i at time j with individual PK parameters ϕ_i, parameters a and b being the constant and proportional components, respectively, of the error model with ε_ij ∼N (0, 1).

We used the stochastic approximation expectation maximization algorithm to estimate the maximum likelihood of the model (31). The model parameters were assumed to be log-normally distributed. The model was built according to a stepwise procedure, with initial identification of the best structural model for CXM PK, in the absence of covariates, by estimation based on 1-, 2-, and 3-compartment PK models.

We then evaluated the effect of covariates on CXM exposure. The covariates tested were selected according to the chemical and pharmacological properties of CXM (32). They included age, various body size descriptors such as total body weight (TBW), body mass index (BMI), and lean body weight (LBW), then creatinine clearance (CrCl) according to the Cockcroft-Gault (C&G) formula (33), sex, and ASA score. Covariates were tested using a stepwise procedure, and were kept in the model if they improved the goodness of fit, reduced interindividual variability, and decreased the Bayesian information criteria (BIC) in comparison to the previous model. Covariates were tested with allometric scaling according to the following equation (using clearance [CL] as an example):

$$C{l}_i=C{l}_{\mathit{POP}}\times {\left(\frac{\mathit{CrC}{L}_i}{80}\right)}^{{\theta }_{\mathit{CrCl}}}\times e^{{\eta }_i}$$ (2)

where $C{l}_i$ and $\mathit{CrC}{L}_i$ are the individual values of CL and CrCL, respectively, for patient i, $C{l}_{\mathit{POP}}$ is the estimated typical population value of Cl, ${\theta }_{\mathit{CrCl}}$ is the estimated effect factor for CrCL, and ${\eta }_i$ is the random effect for patient i, assumed to be normally distributed with a mean of zero and a variance equal to ${\omega }_{\mathit{Cl}}^2$ (N[0,${\omega }_{\mathit{Cl}}^2$]).

Model evaluation and selection were based on inspection of the prediction-corrected visual predictive check (pred-corrected VPC) and the goodness of fit, using the data set used to build the model. The pred-corrected VPC was obtained by generating 1,000 simulations of the subject’s PK parameters using the final model. The capacity of the model to predict the observed data was evaluated by comparing the distribution of the simulated concentrations with the observations. The goodness of fit was determined by plotting the observed values versus the population predictions of the model, the normalized prediction distribution errors (NPDE) versus time, and the NPDE versus predictions (34).

Optimized dosing regimen.

Unbound plasma CXM is the active form in terms of antibiotic effect. As we measured total plasma CXM concentrations, we took into account a 33% rate of protein binding when calculating concentration thresholds on the basis of total plasma concentrations (20). The MIC of CXM for the most common bacteria responsible for wound infections after cardiac surgery is acknowledged to be 8 mg/liter (7, 8). We evaluated unbound concentration thresholds ranging from 1 to 8 times the MIC (8 mg/liter to 64 mg/liter with respect to free CXM concentrations, equivalent to 12 mg/liter to 96 mg/liter in terms of total CXM concentrations). For each threshold, we evaluated the efficacy of different regimens of intravenous CXM administration in maintaining plasma concentrations above the desired targets for 24 h. The regimens tested were: (i) the regimen defined in US guidelines (1,500 mg every 4 h); (ii) the regimen defined in European guidelines (1,500 mg every 140 min); and (iii) two individualized regimens derived from our PK model, comprising continuous infusion of CXM preceded by a loading dose and intermittent CXM administration.

Ideally, optimization of the CXM dosing regimen would necessitate the estimation of individual pharmacokinetic parameters using a Bayesian estimation procedure. In this work, individualization is not possible as it would necessitate quantifying CXM concentration during the surgery, which is not realistic in practice. Without doing Bayesian individualization, it is only possible to calculate doses based on covariate-adjusted typical values. However, this would not guarantee that most of the subjects would be adequately exposed. For example, if covariate-adjusted typical value of the clearance is used to calculate an infusion rate, this rate would only be sufficient to maintain the CXM concentration in 50% of the subjects with the same covariate level. This is due to the unexplained intersubject variability. Therefore, the proposed optimized dosing regimen includes a scaling factor in order to ensure that the target is reached for a desired percentage of subjects (greater than 50%).

For both individualized regimens, the loading dose (LD) required to achieve the desired plasma CXM target concentration (TC) was calculated using the following equation (35):

$$\mathit{LD}=\left(V_C\times e^{{\omega }_{V_C}\times \kappa }+V_P\times e^{{\omega }_{V_P}\times \kappa }\right)\times \mathit{TC}$$ (3)

Where $V_C,\text{and}{V}_P$ correspond to covariate-adjusted typical values (TV) of the central and peripheral volumes of distribution, respectively. Parameters ${\omega }_{V_C}$ and ${\omega }_{\mathit{Vp}}$, respectively, correspond to the standard deviation of the random effects of $V_C\hspace{0.17em}\text{and}\hspace{0.17em}{V}_P$ parameters. The constant $\kappa$ corresponds to a correction factor that allows interindividual variability to be taken into account. This correction factor constrains the loading dose to be adequate in terms of target concentration achievement for a desired percentage of patients. As random effects ($\eta )$ are supposed to follow a normal distribution, the constant $\kappa$ corresponds to the quantile of the normal distribution, including the desired percentage of patients. For example, if we want a loading dose that is adequate for at least 50% of patients, $\kappa$ will be equal to 0. If we want a loading dose that is adequate for at least 80% of patients, $\kappa$ will be equal to 0.84. The latter value is employed in the following sections of this article.

For the continuous infusion regimen, the maintenance dose (MD) was calculated using the equation:

$$M{D}_{\mathit{Infusion}}=\mathit{CL}\times \mathit{TC}\times e^{{\omega }_{\mathit{Cl}}\times \kappa }$$ (4)

Where $\mathit{CL}$ corresponds to the covariate-adjusted typical values of clearance parameters and $\kappa$ denotes the correction factor as explained above.

For the intermittent dosing regimen, the maintenance bolus dose was determined using the following equation:

$$M{D}_{\mathit{Bolus}}=\frac{\mathit{TC}}{C_{1mg}(\mathit{TV},\tau )}$$ (5)

The quantity $C_{1mg}(\mathit{TV},\tau )$ corresponds to the concentration obtained at time $\tau$ after injection of a 1 mg bolus at steady state assuming an interdose interval of $\tau$ h. The vector $\mathit{TV}$ corresponds to the covariate-adjusted typical values of the PK parameters:

$$\mathit{TV}=\left(V_C\times e^{{\omega }_{V_C}\times \kappa },\hspace{0.17em}{V}_P\times e^{{\omega }_{V_P}\times \kappa },\hspace{0.17em}Q,\hspace{0.17em}\mathit{CL}\times e^{{\omega }_{\mathit{Cl}}\times \kappa }\right)$$ (6)

PK simulations.

Finally, we performed simulations using the main CXM dosing regimens proposed for cardiac surgery, to evaluate whether their use would maintain total CXM plasma concentrations above the therapeutic target value throughout surgery. Time above the CXM concentration threshold was estimated by simulation using the Monte Carlo method with R software (version 3.2.2) based on our population PK model. In order to incorporate realistic patient characteristics into our simulations, we integrated the TBW and CrCl values of 255 consecutive patients who had undergone cardiac surgery in the teaching hospital of Saint Etienne from February to July 2017. PK profiles (1,000) were generated according the patient characteristics of this population. Then, we performed simulations using our optimized dosing regimen to evaluate its ability to reach target concentrations.

Graphs of the results were generated by means of R software (version 3.2.2) using the ggplot2 package (version 2.1.0).