Physiologically based pharmacokinetic model of renally cleared antibacterial drugs in Chinese renal impairment patients

Abstract To preliminarily develop physiologically based population models for Chinese renal impairment patients and to evaluate the prediction performance of new population models by renally cleared antibacterial drugs. First, demographic data and physiological parameters of Chinese renal impairment patients were collected, and then the coefficients of the relative demographic and physiological equation were recalibrated to construct the new population models. Second, drug‐independent parameters of ceftazidime, cefodizime, vancomycin, and cefuroxime were collected and verified by Chinese healthy volunteers, Caucasian healthy volunteers, and Caucasian renal impairment population models built in Simcyp. Finally, the newly developed population models were applied to predict the plasma concentration of four antibacterial drugs in Chinese renal impairment patients. The new physiologically based pharmacokinetic (PBPK) population models can predict the main pharmacokinetic parameters, including area under the plasma concentration–time curve extrapolated to infinity (AUCinf), renal clearance (CLr), and peak concentration (C max), of ceftazidime, cefodizime, vancomycin, and cefuroxime following intravenous administrations with less than twofold error in mild, moderate, and severe Chinese renal impairment patients. The accuracy and precision of the predictions were improved compared with the Chinese healthy volunteers and Caucasian renal impairment population models. The PBPK population models were preliminarily developed and the first‐step validation results of four antibacterial drugs following intravenous administration showed acceptable accuracy and precision. The population models still need more systematic validation by using more drugs and scenarios in future studies to support their applications on dosage recommendation for Chinese renal impairment patients.

. Thus, renal impairment with the outcome of a gradual loss of kidney function may have a great effect on the exposure of antibacterial drugs, hence affecting their efficacy or safety (You, Zhang, Yang, & lijun, 2016). For example, as vancomycin has a longer half-life in anephric patients, the dosage reduction is recommended in these patients for safety concerns (US Food & Drug Administration, 2017). Although pharmacokinetic (PK) study in patients with various levels of impaired renal function is recommended by the government of China to provide appropriate dosing recommendations, yet it is challenging to recruit renal impairment patients in clinical trials due to safety risk (National Medical Products Administration, 2012). Consequently, such dedicated PK studies for antibacterial drugs are usually not conducted. It was reported that a dose of 33.6% antibacterial drugs were either unadjusted or adjusted only based on foreign data when applied in Chinese patients with renal impairment (Xu & Wu, 2017). However, it may be risky to directly adopt the dosage recommendation of the Caucasian population due to potential ethnic-related exposure difference. For example, the half-life of ceftazidime, which was eliminated by passive filtration, in Caucasian patients with severe renal impairment was 1.5-fold than that of Chinese patients with severe renal impairment (Zhou et al., 2019). Greater differences in patients may be observed in drugs with complex metabolic pathways and mechanisms.
Physiologically based pharmacokinetic (PBPK) model combines the complex interplay of physiological parameters (demographics, organ size, blood flow, etc.) with drug-related properties (lipid solubility, enzyme, transporter kinetics, etc.) and thus can serve as a mechanistic approach to quantitatively predict the drug PK in different populations (Jamei et al., 2009). Quantitative prediction of the impact of chronic kidney disease (CKD) on drug disposition has become important for the optimal design of clinical studies in patients. PK profiles of 151 compounds under CKD conditions were successfully predicted using a top-down PBPK approach (Sayama, Takubo, Komura, Kogayu, & Iwaki, 2014). In another study by Scotcher et al., the role of various factors in renal disposition of digoxin has been delineated through the application of the PBPK models on renal impairment population, which provided a rational dose adjustment in clinical application (Scotcher, Jones, Galetin, & Rostami-Hodjegan, 2017). Recently, a PBPK model has been used to predict plasma concentration of avibactam, a novel β-lactamase inhibitor, in Caucasian renal impairment patients, with predicted PK parameters within 1.5-fold of the observed values (Hsueh et al., 2018). With a deeper and more refined understanding of the mechanisms, PBPK models verified with clinical study in healthy volunteers could be potentially applied to predict PK profiles and to recommend dose adjustment for CKD patients (Zhou et al., 2019).
However, most models were developed for the Caucasian population whose physiological variables and PK characteristics were not necessarily the same as Chinese, for instance, the physiological characteristics of the kidneys (i.e., kidney weight, kidney blood flow) and the status of the patients with CKD (Cui et al., 2020;Derose et al., 2013).
Thus, the objective of our study is to preliminarily develop physiologically based population models for Chinese renal impairment patients and to evaluate the prediction performance of new population models by renally cleared small-molecule antibacterial drugs in Chinese renal impairment patients. Figure 1 illustrated the approach to develop, verify, and apply PBPK models to predict PK of renally cleared antibacterial drugs in Chinese renal impairment patients using Simcyp (18R1; Certara UK Ltd, Simcyp Division). Briefly, based on the Chinese healthy volunteers' model built in Simcyp, the new PBPK population models were developed and updated with demographic information and serum creatinine concentration values collected from Chinese renal impairment patients. Besides, considering the great effects on drug disposition, the renal volume and blood parameters, which has no sufficient data, were updated by values predefined in Simcyp Caucasian renal impairment population models. Meanwhile, four model drugs were selected and drug-independent physicochemical properties together with clearance (CL) derived from observed PK data were verified by Caucasian healthy volunteers, Caucasian renal impairment population, and Chinese healthy volunteers' models. After verification, the newly developed population models integrated with drug models were applied to simulate the drug concentration in Chinese renal impairment patients. Finally, the main PK parameters, including the predicted area under the plasma concentration-time curve extrapolated to infinity (AUC inf ), peak concentration of drug in plasma (C max ), and renal clearance (CL r ), were compared with the observed data to assess the predictive performance of PBPK population models. CUI ET AL.

| Development of PBPK population models for Chinese renal impairment patients
Glomerular filtration rate (GFR), incorporating serum creatinine concentration along with demographic data, is the most commonly used index of overall kidney function and used to define the various levels of renal impairment in this study (Stevens, Coresh, Greene, & Levey, 2006) To evaluate if the newly developed population models can adequately describe physiological characteristics in the Chinese renal impairment patients, internal validation was used for height, weight, serum creatinine, and GFR for which 90% confidence interval (CI) of these variables from simulated 4000 subjects (female/total ¼ 0.5; 20 trials, 200 subjects per trial) were compared to observed data.

| Development and verification of drug models
The impact of renal impairment on the non-renal elimination route was not considered and antibacterial drugs that are mainly eliminated by renal excretion were selected in the current study. Based on the drug elimination mechanism and the availability of PK data in Chinese renal impairment patients, four model drugs (i.e., ceftazidime, cefodizime, vancomycin, and cefuroxime) were selected. The literature retrieval strategy was shown in Figure S1. For ceftazidime and vancomycin, the PK data are available in Chinese patients with mild, moderate, and severe renal impairment (Ji et al., 2018;Lin, Wang, & Huang, 1989). For cefodizime and cefuroxime, the PK data are available in Chinese patients with severe renal impairment (Cheng et al., 2010;Li, Song, & Hu, 2000). As the PK data of model drugs in Chinese renal impairment patients were all from clinical studies following intravenous injection (IV) administration, parameters of drug absorption were not involved in our study. For the improvement and comparison of follow-up research, a full PBPK model was used to describe drug distribution.
Depending on drug acid-base properties, the volume of distribution at steady state (V ss ) of ceftazidime, cefodizime, cefuroxime, and vancomycin was initially predicted (Poulin & Theil, 2002;Rodgers & Rowland, 2007). K p scalar was determined by fitting the predicted V ss to observed clinical V ss pharmacokinetic data. For the CL and CL r , the values were derived from the PK studies following a single IV F I G U R E 1 Overall flow diagram of developing, verifying, and applying physiologically based pharmacokinetic models to predict pharmacokinetic characteristics of renally cleared antibacterial drugs in Chinese renal impairment patients with Simcyp 26administration in Caucasian healthy subjects. Detailed input parameters of the PBPK model for each drug were summarized in Table S1.
The drug models were verified using PK data from Caucasian healthy subjects, Caucasian renal impairment patients, and Chinese healthy subjects. For Caucasian mild renal impairment population model that is not available in Simcyp, Yee et al. established a new mild renal impairment model by using Caucasian healthy volunteers' (18-95 years) model built in Simcyp as a template and increasing concentration of serum creatinine by 1.5-fold considering that the GFR lower bound cutoff value of mild renal impairment patients is about 1.5-fold lower than healthy subjects (i.e., 60 vs. 90 ml/min/ 1.73 m 2 ). The other demographic and physiological parameters were kept the same as the Caucasian healthy volunteers' model (Yee et al., 2018).
Trial designs in Simcyp Simulator were set to match the observed clinical studies. The demographic information and study designs for all trials were summarized in Table S2. The simulation was conducted in 10 trials with 10 subjects (effectively used as 100 subjects � 1 trial.) under fasting conditions. The central tendencies were calculated for all virtual subjects. Mean values of simulated and observed data were compared and the rationality of the model was verified when the predicted AUC inf , C max , and CL r were within twofold of the observed values in all studies. The mean absolute prediction error (MAPE) was additionally applied to examine and compare the precision and bias of simulations in PBPK models:

| Application and predictive performance evaluation of the new PBPK population models
In the combination of the verified drug models, the newly developed Chinese renal impairment population models were then applied to predict plasma concentrations of ceftazidime, cefodizime, vancomycin, and cefuroxime, respectively. The methods of simulation setting and assessment were the same as that of drug parameter verification in the above text.
To further confirm the necessity of the newly developed popu-

| Development of PBPK population models for Chinese renal impairment patients
Chinese renal impairment population models were first developed in Simcyp, for which age, body weight, height, and serum creatinine in Chinese patients with mild, moderate, and severe renal impairment were collected. The age limitation and sex ratio were represented by observational data. The summarized data and equation of systemdependent parameters of the population models were shown in Tables 1 and 2, and the age distribution of patients with various renal functions was shown in Figure S2.  Figure S3).

| Development and verification of drug models
The drug models for ceftazidime, cefodizime, vancomycin, and cefuroxime were developed to predict plasma drug concentration following IV administration. The models were then verified with PK data from Caucasian healthy subjects, Chinese healthy subjects, and Caucasian renal impairment subjects. As shown in Figure 3a-c and -27 predicted C max were within 0.8-1.25-fold of the observed values.
For Caucasian renal impairment subjects, as was shown in

| Application and predictive performance evaluation of the new PBPK population models
As was presented in Table S5, the predicted AUC inf for model drugs

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Age (  Renal impairment is usually associated with various physiological changes. In Caucasian renal impairment patients, body weight has a nonlinear change that it was stable or slightly increased until cystatin C-based eGFR fell below 35 ml/min/1.73 m 2 ; every 10 ml/min/1.73 m 2 decline in GFR was associated with a mean 2.3 kg (95% CI, 2.1-2.4 kg) weight decline (Ku et al., 2018). Besides, the hematocrit decreased progressively until the estimated creatinine clearance (CL cr ) is below 60 ml/min in men and 40 ml/min in women (Hsu, Bates, Kuperman, & Curhan, 2001). It was also reported that there was a significant decrease in the concentration of serum albumin for moderate and severe renal impairment patients (Amin, El-Sayed, & Leheta, 2016). In contrast, α1-acid glycoprotein showed a significant increase (p < 0.05) (Romao et al., 2006) in patients with severe renal impairment while no significant differences were found in mild and moderate renal impairment patients. Moreover, the kidney volume was shown to decrease with the progress of CKDs (Vegar Zubovic, Kristic, & Sefic Pasic, 2016).
In Chinese renal impairment patients aged 18-85, nearly 50% of the patients were older than 60 years old (Wang et al. 2019a). Among them, the number of men was generally higher than that of women by about 1.5-fold (Tables 1 and 2). Like Caucasian renal impairment patients, the body weights of Chinese renal impairment patients remain stable with GFR > 30 ml/min, and then decrease with the reduction of renal function (Wang et al. 2019b).
Kidney volume, hematocrit, the concentration of serum albumin, and α1-acid glycoprotein were also affected by various renal functions, but have not been reported in Chinese renal impairment patients so far. For kidney size, it was reported that kidney volume decreases significantly in Chinese moderate and severe renal impaired patients, while there were no significant differences between Chinese patients with mild renal impairment and Chinese healthy subjects (Shen et al., 2013, Tian 2015. For hematocrit, human serum albumin, and α1-acid glycoprotein, due to the lack of data, we hypothesized that the values of three blood parameters changed as it did in patients with Caucasian renal impairment population. All of them were changed significantly in severe renal impairment patients, while no significant differences in mild renal impairment patients were found compared with healthy subjects (Amin et al., 2016;Hsu et al., 2001;Romao et al., 2006). Both the hematocrit and concentration of human serum albumin declined significantly in patients with moderate renal impairment patients, while little evidence of changes was found for α1-acid glycoprotein, in consistent with the inbuilt parameter value in Simcyp (Amin et al., 2016;Hsu et al., 2001;Romao et al., 2006). Thus, when the population model was developed for Chinese patients with moderate and severe impairment, these system-dependent parameters are directly adopted from Caucasian patients based on the assumption that the alteration of these parameters is to the same extent between Chinese and Caucasian renal impairment patients.
In this study, the antibacterial drugs ceftazidime, cefodizime, renal tubular reabsorption (Kusama et al., 1998), whereas cefuroxime was suggested to be a substrate of multidrug resistance-associated protein 4 (MRP4) (Akanuma et al., 2011) with 28% (Table S1) of drugs being actively secreted. The evidence implies the importance to incorporate renal transporters (e.g., transport activity data) in the model to better predict the PK characteristics of drugs that have significant active secretion or reabsorption.
Though the predicted PK profiles and parameters for these different drugs were generally in agreement with the observed data, our study had some limitations. First, due to the lack of hematocrit, serum albumin, and kidney volume data in the Chinese population, these data were assumed to be the same as Caucasian renal impairment patients. This assumption requires further verification and confirmation even though our model presented reasonable prediction on the PK of all four drugs in Chinese patients with mild, moderate, and severe renal impairment. Second, for drugs with high degree of active transport, the current model is insufficient to accurately predict their PK profile and parameters, and further development of mechanistic kidney models based on Chinese data is needed (Scotcher, Jones, Posada, Galetin, & Rostami-Hodjegan, 2016). Lastly, apart from the well-recognized effects of kidney disease on renal drug clearance, there is a growing body of evidence demonstrating that renal failure may influence hepatic drug metabolism either by inducing or suppressing hepatic enzymes or by its effects on protein binding, hepatic blood flow, and accumulation of metabolites (Follman & Morris, 2018;Rowland Yeo, Aarabi, Jamei, & Rostami-Hodjegan, 2011;Zhao et al., 2012). In our study, though a minor yet substantial (>25%) route of cefodizime elimination is nonrenal, the predicted results were within 1.25-fold of the observed values. Further studies are needed to consider changes in non-renal clearance by including more drugs with larger non-renal clear proportion for model optimization and validation.

| CONCLUSION
The PBPK population models by employing demographic and physiological parameters of Chinese patients with renal impairment were preliminarily developed and the results of first step toward verification by four antibacterial drugs following IV administration showed acceptable accuracy and precision in Chinese patients with mild, moderate, and severe renal impairment. In future studies, the model should be systematically validated using more drugs with various elimination mechanisms and diverse administrations to support its application in dosage recommendation in Chinese renal impairment patients even in the absence of a dedicated PK study.

ACKNOWLEDGMENT
This study was supported by the Bill & Melinda Gates Foundation (Nos. OPP1204780).