NONMEM population pharmacokinetic and Monte Carlo dosing simulation of ertapenem in patients with sepsis

An alteration of pharmacokinetics (PK) due to pathophysiological changes in patients with critical illnesses have the impact on the drug levels in plasma, consequently affecting the achievement of pharmacodynamics (PD) targets of antibiotics. The objectives of this study were (i) to determine the population PK, and (ii) to assess the probability of target attainment (PTA) of ertapenem in patients with critical conditions. The study examined the population PK of ertapenem using NONMEM and performed the assessment of the PTAs of achieving 40 and 80% of the time that the free drug level exceeds over the MIC ( f T >MIC ). The central and peripheral volumes of distribution were 49 (with the %CV of 67.10) and 91.90 (with the %CV of 78.90) L, respectively, and total clearance of ertapenem was 15.40 (with the %CV of 46.80) L/h. Our PD analysis for achieving a target of 40% f T >MIC in patients with normal renal function, the dosing of 1 g once daily can cover a MIC of 0.5 mg/L and for a higher minimum inhibitory concentration (MIC) of 1 mg/L, the dosing should be increased to 2 g once daily. Moreover, the achievements of PTAs in patients with lower GFRs were greater than those of PTAs in patients with higher GFRs. In conclusion, higher than maximum recommended dosing of ertapenem may be required for achieving the PD targets in septic patients with critical illnesses; however, in renal impaired patients the required dosage regimens may be lower than recommended dosing.


INTRODUCTION
The worldwide spread of antibiotic-resistant bacteria remain a crucial public health concern resulting in increased mortality and morbidity rates and health care costs in patients with critical illnesses (Manyahi et Santoro et al., 2020;Serra-Burriel et al., 2020). The 2019 antibiotic resistance threats study by Centers for the Disease Control and Prevention of the United States reported that more than 2.8 million patients were infected with antibiotic-resistant pathogens causing more than 35,000 deaths in this year (CDC, 2019). Extended spectrum β-lactamase (ESBL)-producing Enterobacteriaceae has been increasingly found over the last 2 decades in both community and hospital settings and spreading rapidly throughout the world (Doi et al., 2017). ESBLs have been found to be the enzymes responsible for enabling the mechanism of drug resistance of these microorganisms, resulting in resistance to several β-lactam antimicrobial agents such as penicillins, cephalosporins and aztreonam, but not to carbapenems. Therefore, carbapenems are becoming the appropriate antibiotics therapy for these microorganisms (Pitout and Laupland, 2008;Brolund, 2014;Rodríguez-Baño et al., 2018;Gutiérrez-Gutiérrez and Rodríguez-Baño, 2019).
Ertapenem, a carbapenem antibiotic, has a good activity against ESBL-producing Enterobacteriaceae, but poor activity against Pseudomonas aeruginosa and Acinetobacter. This agent can be used via once a day dosing due to its high protein binding, resulting in long elimination half-life. Ertapenem has been licensed in the United States and Europe for several indications. The standard dosage regimen of 1000 mg intravenous of ertapenem has low side effects (Curran et al., 2003;Zhanel et al., 2005;Burkhardt et al., 2007;Doi, 2020). Ertapenem is the time-dependent antibiotic, and the percentage of time that the free drug level exceeds over the MIC (%fT >MIC ) is the pharmacodynamics (PD) index that best predicts the killing effect of drug (Bader et al., 2019). However, an alteration of PK due to pathophysiological changes in patients with critical illness has the impact on the plasma concentrations of antibiotics (Bergen et al., 2017;Chai et al., 2020). The objectives of this study were (i) to determine the population PK, and (ii) to assess the probability of target attainment (PTA) of ertapenem in patients with critical illnesses.

Subjects
This prospective, PK study of ertapenem was undertaken on eleven patients who were admitted to Songklanagarind Hospital during March to December 2019. The inclusion criteria were: (i) patients with sepsis (Singer et al., 2016), and (ii) age >18 years. The exclusion criteria were: (i) pregnancy, (ii) septic shock, (ii) hypersensitivity to β-lactams, and (iv) chronic renal impairment. The severity of illness were assessed by APACHE II and SOFA scores. The study protocol was reviewed and approved by the Ethics Committee of Faculty of Medicine, Prince of Songkla University (Ethical approval: REC 58-372-14-1; Clinical Trials: NCT03859362) and written informed consent was obtained from each participant.

Study design
All participants received treatment with a 0.5 h infusion, 1 g once daily of ertapenem for 10 days. Ertapenem PK studies were carried out on the 3 rd dose of drug administration, and a Monte Carlo simulation (MCS) was performed to assess the efficacy of ertapenem.

Ertapenem assays
The free ertapenem levels were assayed by High Performance Liquid Chromatography (HPLC) with UV detection, at 305 nm (Gordien et al., 2006). The samples were transferred into an ultrafilter and centrifuged at 14,000×g for 10 min at 4°C to separate the unbound drug. A 100 μl aliquot was added with an internal standard (imipenem 25 mg/L in 40 mM phosphate buffer pH 4.0) at a ratio of 1:1. The mixture was vortexed for 30 sec and then 80 μl was injected onto the column. The mobile phase was 10 mM phosphate buffer, pH adjusted to 6.5 with orthophosphoric acid (phase A) and acetonitrile (phase B). A gradient elution program was applied at a flow rate of 1 ml/min as follows: 0-2 min, 94 and 6% for phases A and B, respectively; 2-7 min, 82 and 18%, phases A and B, respectively, and then returned to 94 and 6%, respectively, at 7-10 min. The lower limit of quantitation was 0.25 mg/L. The intra-assay precision values were 1.24, 2.49 and 3.27% for concentrations of 1, 50 and 100 mg/L, respectively. The interassay precision values were 1.24, 2.84 and 3.74% for concentrations of 1, 50 and 100 mg/L, respectively. The accuracy values were 103.26, 97.70 and 95.32% and the recovery values were 102.75, 111.83 and 102.57% for concentrations of 1, 50 and 100 mg/L, respectively.

Population pharmacokinetic analysis
The population PK was analysed using NONMEM ® 7.4.3 (Icon Development Solution, Ellicott City, MD, USA) with the aid of Perl-Speaks-NONMEM version 4.9.0 (Uppsala University, Uppsala, Sweden). Pirana program (Certara, Princeton, NJ, USA) was used to capture and display the model development. R program version 3.6.0 along with R Studio version 1.4.1106 were used for data postprocessing and visualization. The different structural models, including one-, two-and three disposition compartment models with linear elimination, were investigated to find the best fit for ertapenem concentration-time profiles. The PK parameters were estimated using a first-order conditional estimation with interaction between eta and epsilon (FOCE-I) method. The inclusion of an interindividual variability (IIV) on PK parameters was implemented using an exponential error model, and covariances between IIV terms were estimated if they showed any significant correlations. An additive, proportional, or combined additive plus proportional error models were considered for residual variability. The shrinkage for each parameter was also assessed, and values of less than 25% were considered acceptable.
After establishing the appropriate structural model, the effects of age, gender, actual body weight, ideal body weight, body mass index, mechanical ventilation, serum albumin, APACHE II score, SOFA score, creatinine clearance calculated by the Cockcroft-Gault equation (CL CR (CG) ) and Jelliffe equation (CL CR(JEL) ) , and glomerular filtration rate estimated by the Chronic Kidney Disease Epidemiology Collaboration equation (GFR EPI ) and Modification of Diet in Renal Disease study equation (GFR MDRD ) were investigated as potential covariates affecting ertapenem PK parameters. These covariates were incorporated into the structural model using a stepwise covariate modeling algorithm. A covariate was kept in the model if it improved the model fit, as assessed by a reduction in objective function value (OFV) of at least 3.84 units (P <0.05) and an increase of at least 6.64 units (P <0.01) for forward addition and backward deletion procedure, respectively. The model selection was based on the minimum OFV, Akaike Information Criterion (AIC), parameter accuracy, goodness-of-fit plots and various diagnostic plots. A non-parametric bootstrap analysis (n = 2,000) was conducted to ascertain the final model's robustness and to generate confidence intervals of all parameter estimates. In addition, the predictive ability of the final model was also evaluated by a prediction-corrected visual predictive check (n = 2,000).

Pharmacodynamics assessment
Crystal Ball program (version 11.2, Oracle Corporation, Denver, CO, USA) was used for Monte Carlo simulations (MCS) analysis to determine the PTAs of several dosing regimens and duration of infusions of ertapenem. The PK parameters, IIV (including covariance terms), and the uncertainty of each parameter were used for simulating drug levels. As GFR was found to influence ertapenem clearance, the simulated subjects were divided into three different renal function groups (GFR 0-29.99, 30-59.99, 60-120 ml/min). Thereafter, 10,000 virtual subjects were simulated for each dosing regimen and %fT >MICs (40% and 80% fT >MIC ) were used as the PK/PD targets for ertapenem.

RESULTS
The important characteristics of patients are summarized in Table 1. The average unbound plasma concentrationtime profiles are displayed in Figure 1. Concentrations below the LLOQ value, which represented only 1.7% of the dataset, were imputed with LLOQ/2 value. A total of 119 free plasma concentrations were used for population PK analysis. A two-compartment model with first-order elimination best described the ertapenem concentrationtime profiles. A combined additive plus proportional error model were selected to characterize the residual variability. An IIV was assigned to all parameters. However, the IIV of intercompartment clearance (Q) was very low, therefore it was not estimated and was fixed to Jaruratanasirikul et al. 73 zero. There were moderate to high correlations between several of the random effects, and therefore covariance terms between the IIV on total clearance (CL), central volume of distribution (V C ) and peripheral volume of distribution (V P ) were estimated, resulting in an 11.3-unit decrease in the Akaike Information Criterion (AIC) compared with the initiating model. After covariate testing, GFR EPI was the only significant covariate describing the clearance of ertapenem. The inclusion of GFR EPI for CL significantly improved the model fit (ΔOFV = -15.2) and reduced the IIV of CL from 68.0% to 46.8%. Of note, GFR MDRD , CL CR (CG) and CL CR(JEL) also improved the model fit, but the OFV reduction was less than GFR EPI . There was no significant covariate that explained V C and V P . The final population PK parameters of ertapenem are shown in Tables 2, 3 and Supplementary  Table 1. All final parameters were estimated with acceptable precision, and the percentages of eta and epsilon shrinkage were low (<10%). The parameters estimated from the final model were similar to the median value and all were within the 95% confidence interval obtained from the bootstrap analysis, indicating the robustness of the final model. The goodness-of-fit plots for the final model showed no apparent bias in model predictions ( Figure 2). The pcVPC (Figure 3) also confirmed the good predictive performance of the model, as the observed 5 th , 50 th , and 95 th percentiles were within the 80% confidence intervals for the simulated 5 th , 50 th , and 95 th percentiles at every time point. The PTAs of ertapenem in patients with various ranges of GFR on the 1 st and 3 rd dose of drug administration are shown in Supplementary Table 2 and Table 4. The PTAs of ertapenem in patients with GFR 60-120 ml/min are shown in Figure 4.

DISCUSSION
A change in pathophysiological condition in patient with sepsis can occur which can also result in PK changes for antibiotics (Taccone et al., 2011;Bergen et al., 2017;Chai et al., 2020). The shifting of fluid used for resuscitation of sepsis from blood vessels into the extravascular space can lead to a greater total volume of distribution (V) compared to those from healthy subjects (Taccone et al., 2011;Varghese et al., 2011). Moreover, end-organ dysfunction, particularly renal impairment due to sepsis, can occur, resulting in decreased renal clearance of antibiotics (Bergen et al., 2017;Chai et al., 2020). Therefore, changes of V and CL of antibiotics for management of sepsis result in unpredictable plasma concentrations and, consequently, unacceptable outcomes. A previous study with burn patients examining PK changes of ertapenem (Dailly et al., 2013) found that the mean values of V were higher than that from normal subjects (Wiskirchen et al., 2013). In our study, the V of ertapenem was also found to be higher than that from normal subjects (Wiskirchen et al., 2013). This finding may be explained by noting that our patients had severe illness. In our study, a twocompartment model was the best model for describing the ertapenem concentration-time profiles, which was in accordance with other studies (Zhou et al., 2014;Goutelle et al., 2018). In addition, the binding of a drug to the plasma protein plays a crucial role in antimicrobial activity due to the binding effect on the PK and PD of an antibiotic. The unbound drug is the only fraction of an antibiotic that can penetrate into the infection sites in interstitial tissues or body fluids and correlates with the efficacy of the agent. Changes in plasma protein binding can alter PK parameters, consequently affecting the achievement of PD targets of antibiotics (Zeitlinger et al., 2011;Heuberger et al., 2013;Shah et al., 2015;Onufrak et al., 2016). An in vivo microdialysis study found that the free fraction of ertapenem in extravascular space were much lesser than the total drug levels in plasma (Burkhardt et al., 2006). Another study in obese patients found that the average free fraction of ertapenem in interstitial tissues were variable and approximately 50.7 and 75.4%, respectively, of the free drug exposure in plasma (Wittau et al., 2017). Moreover, this drug has been found to have near-linear PK and high protein binding with a range from 92 to 95% (Majumdar et al., 2002;Curran et al., 2003;Zhanel et al., 2005;Burkhardt et al., 2007;Zusman et al., 2015). Recent studies have reported that the clinical  breakpoint of ertapenem against Enterobacteriaceae was 0.5 mg/L (CLSI, 2020; EUCAST, 2020). The standard dosing of 1 g once daily of ertapenem has been prescribed for coverage of ESBL-producing Enterobacteriaceae in several disease situations. A previous study in morbidly obese patients on this dosing found that the free fraction of ertapenem achieved the PTA of 40% T >MIC for MICs of ≥0.5 mg/L in plasma (Wittau et al., 2017). Previous studies in animal found that for antimicrobial killing effect of β-lactams, the target of 100% T >MIC was unnecessary (Vogelman et al., 1988;Craig, 1995) and bactericidal killing activities of carbapenems were found at the target of 40% T >MIC (Drusano, 2003). Moreover, several clinical studies showed that an extended infusion of β-lactam antibiotics for the treatment of patients with severe infections had lower mortality (Lodise et al., 2007;Shabaan et al., 2017;Vardakas et al., 2018;Yu et al., 2018) and higher rates of clinical improvement (Abdul-Aziz et al., 2016;Shabaan et al., 2017;Yu et al., 2018) and microbiologic eradication (Shabaan et al., 2017) than short-term infusion. Our MCS analysis found that the achievement of the PTAs by the extended infusion of ertapenem were higher compared to the short infusion, findings which were similar to previous studies with other β-lactam antibiotics (Masich et al., 2018;Thabit et al., 2019). Therefore, we believe that a prolonged infusion time of drug administration for this drug should be a good strategy to augment the probability of achieving PK/PD targets and therapeutic outcomes. Our PD analysis for achieving a target of 40% fT >MIC in patients with normal renal function, the dosing of 1 g once daily can cover a MIC of 0.5 mg/L and for a higher MIC of 1 mg/L, the dosing should be increased to 2 g once daily. In immunodeficiency host, the PD targets for achieving the optimal therapeutic outcomes of βlactams should be nearly 100% fT >MIC . A previous study in this patient population found that the achievement of the optimal clinical response of meropenem was occurred when the %T >MIC were >75% (Ariano et al., 2005). The dosing of 1 g once daily achieved the PTAs for only a MIC of 0.25 mg/L. An increase in ertapenem dosage up to 2 g every 24 h for the treatment of tuberculosis was safe with few adverse effects (Zuur et al., 2018). In addition, we found that the achievements of PTAs in patients with lower GFRs were greater than those of PTAs in patients with higher GFRs.
Therefore, the use of ertapenem for treatment of severe infections associated with renal end organ dysfunction requires lower dosage regimens than in patients without end organ dysfunction. The current study had a notable strength, in that the measured drug concentrations in this study were the free form of ertapenem which is the fraction of drug that correlates to the efficacy of antimicrobial activity. However, the study also had a few notable limitations. First, our study was conducted with the small number of patients. Second, the low-bodyweight patients may affect the values of PK, therefore, the results of the study should be extrapolated with caution for using in the general population.
In conclusion, an increased V of ertapenem was observed in this study on the pathophysiological changes in septic patients with multiple comorbidities, therefore higher than maximum recommended dosage regimens may be required in this patient group. However, patients with renal end organ dysfunction may require lower-thanrecommended dosing. A prospective well-designed study