Piperacillin Population Pharmacokinetics and Dosing Regimen Optimization in Critically Ill Children Receiving Continuous Renal Replacement Therapy

ABSTRACT

We aimed to develop a piperacillin population pharmacokinetic (PK) model in critically ill children receiving continuous renal replacement therapy (CRRT) and to optimize dosing regimens. The piperacillin plasma concentration was quantified by high-performance liquid chromatography. Piperacillin PK was investigated using a nonlinear mixed-effect modeling approach. Monte Carlo simulations were performed to compute the optimal scheme of administration according to the target of 100% interdose interval time in which concentration is one to four times above the MIC (100% fT > 1 to 4× MIC). A total of 32 children with a median (interquartile range [IQR]) postnatal age of 2 years (0 to 11), body weight (BW) of 15 kg (6 to 38), and receiving CRRT were included. Concentration-time courses were best described by a one-compartment model with first-order elimination. BW and residual diuresis (Q_u) explained some between-subject variabilities on volume of distribution (V), where $V_i=V_{\text{pop}\hspace{0.17em}}\times \hspace{0.17em}{(\frac{{\text{BW}}_i}{70})}^1$, and clearance (CL), where ${\text{CL}}_i={\text{CL}}_{\text{pop\hspace{0.17em}}}\times \hspace{0.17em}{(\frac{{\text{BW}}_i}{70})}^{0.75}\hspace{0.17em}\times \hspace{0.17em}{(\frac{{\mathit{Q}}_u}{0.06})}^{0.12}$, where CL_pop and V_pop are 6.78 L/h and 55.0 L, respectively, normalized to a 70-kg subject and median residual diuresis of 0.06 mL/kg/h. Simulations with intermittent and continuous administrations for 4 typical patients with different rates of residual diuresis (0, 0.1, 0.25, and 0.5 mL/kg/h) showed that continuous infusions were appropriate to attain the PK target for patients with residual diuresis higher than 0.1 mL/kg/h according to BW and MIC, while for anuric patients, less frequent intermittent doses were mandatory to avoid accumulation. Optimal exposure to piperacillin in critically ill children on CRRT should be achieved by using continuous infusions with escalating doses for high-MIC bacteria, except for anuric patients who require less frequent intermittent doses.

INTRODUCTION

The main challenge to overcoming bacterial infections in critically ill children is the optimization of the dosing regimen of the administered antibiotic to quickly and sustainably reach an effective concentration (1, 2). Acute renal failure is commonly observed in septic children, and continuous renal replacement therapy (CRRT) can be necessary for the most severe cases. Also, critically ill children who undergo CRRT are likely to develop nosocomial infection given their vulnerability (3, 4). Piperacillin, a beta-lactam possibly combined with a beta-lactamase inhibitor (tazobactam), is commonly prescribed in the pediatric intensive care unit (PICU) given its broad-spectrum antibacterial activity (5, 6), especially for Pseudomonas aeruginosa and multidrug-resistant bacterial infections (7, 8). Piperacillin is mainly eliminated via the kidneys as unchanged drug (68%) and then via biliary excretion as a secondary route (9). Piperacillin is hydrophilic and weakly plasma protein bound with a low molecular weight (10). These properties support an elimination by CRRT (11, 12) depending on blood, dialysate, and/or replacement fluid flow rates (13). Piperacillin pharmacokinetic (PK) studies in adults have shown an impact of at least 25% of CRRT on the clearance of this antibiotic (14). As piperacillin has a maximal efficacy when its concentration is one to four times above the MIC throughout the dosing interval (100% fT > 1 to 4 MIC) (15), there is an increasing amount of literature suggesting the benefit of continuous administration of piperacillin with similar findings in adult patients undergoing CRRT (16–18). Yet, without available guidelines for children in this context, the dosage is usually an extrapolation from children not hospitalized in intensive care or from adult studies (19). Taken together, growth, organ maturation, critical illness features, and CRRT modalities induce large between- and within-subject variabilities in PK parameters, leading to high risk of unpredictable and inadequate exposure to piperacillin. In turn, the risk of treatment failure, toxicity, and emergence of multidrug-resistant bacteria is nonnegligeable when piperacillin conventional dosing is applied for all (20). There is a need to optimize and individualize piperacillin dosing regimens, taking into account critical illness and CRRT modalities (12, 21).

This study aimed to develop a piperacillin population PK model in critically ill children receiving CRRT in order to individualize dosing regimens according to the selected PK target of 100% fT > 1 to 4× MIC.

RESULTS

Patients.

Ninety-three measured plasma piperacillin concentrations from 32 patients receiving CRRT were included. Their main characteristics are displayed in Table 1.

TABLE 1.

Characteristics of the 32 patients^a

Characteristic	Value
No. of patients	32
Age in yrs (median [IQR])	4 (0.6–11)
Male (no. [%])	19 (56)
Wt (median [IQR] [kg])	15 (6–38)
Ht (median [IQR] [cm])	107 (66–145)
Length of ICU stay (median [IQR] [days])	13 (6–19)
PELOD-2 score (median [IQR])	11 (10–20)
No. of organ dysfunctions (median [IQR])	2 (1–4)
Residual diuresis (median [IQR] [mL/kg/h])	0.06 (0–0.3)
Anuria (no. [%])	17 (53)
Vasopressors (no. [%])	17 (53)
Mechanical ventilation (no. [%])	19 (59)
Death (no. [%])	15 (44)
Piperacillin samples
No. of samples	93
Median no. of samples per patient median (min, max)	2 (1, 4)
Amt (median [IQR] [mg/kg/24 h])	300 (293–310)
Concentrations over 1× MIC (no. [%])	87 (93)
Concentrations over 4× MIC (no. [%])	55 (59)
Continuous infusion (no. [%])	18 (19)
RRT type (no. [%])
CVVHDF	60 (65)
CVVH	27 (29)
CVVHD	6 (6)
RRT filter (no. [%])
ST150	49 (53)
ST60	41 (44)
HF20	3 (3)
Anticoagulation used (no. [%])
Heparin	48 (51)
Citrate	36 (39)
None	9 (10)
ECMO	4 (4)
Laboratory data
Albumin (median [IQR] [g/L])	31 (25–35)
CRP (median [IQR] [mg/L])	95 (28–210)

^aICU, intensive care unit; PELOD, Pediatric Logistic Organ Dysfunction score; CRRT, continuous renal replacement therapy; CVVHDF, continuous venovenous hemodiafiltration; CVVH, continuous venovenous hemofiltration; CVVHD, continuous venovenous hemodialysis; ECMO, extracorporeal membrane oxygenation; CRP, C-reactive protein.

Piperacillin median (interquartile range [IQR]) doses infused to patients were 300 (293 to 310) mg/kg/day, and 18 (19%) samples were obtained during continuous infusion. Samples were obtained from 0.1 to 22 h after the dose, with a median (IQR) of 3 (1 to 5) h. The median (IQR) number of piperacillin concentrations per patient was 2 (1 to 4). Four patients had a continuous infusion. In total, 15/32 (47%) had residual diuresis, and 17/32 (53%) were anuric.

The median (IQR) blood flow was 80 (55 to 150) mL/min and 5 (4 to 10) mL/kg/min. Median (IQR) total effluent flow rate (Q_eff) was 1,440 (630 to 4,050) mL/h and 96 (42 to 270) mL/kg/h. For the patients under continuous venovenous hemodialysis (CVVHD) or continuous venovenous hemodiafiltration (CVVHDF), the median (IQR) dialysate flow rate (Q_D) was 2,000 (850 to 3,500) mL/h, corresponding to 91 (59 to 132) mL/kg/h. For the patients under continuous venovenous hemofiltration (CVVH) or CVVHDF, median (IQR) replacement flow rate (Q_RF) was 325 (50 to 738) mL/h, corresponding to 34 (7 to 57) mL/kg/h.

Among the 32 patients, 10 infections were documented in 9 patients. Measurable MICs were available for 10 pathogens. In the cohort, 15 (44%) patients died. A total of four (13%) patients died from a septic condition, including one from a documented clinical failure and three from other reasons. The documented clinical failure concerned a 19-month-old-patient who died from septic shock with an Enterococcus faecalis bacteremia complicated by a hemophagocytic syndrome from a probable digestive translocation on an acute intestinal intussusception. The E. faecalis had a conserved sensitivity to piperacillin (MIC at 3 mg/L), and the patient was well exposed to piperacillin, with residual concentrations that ranged from 70 to 90 mg/L.

Population PK model.

A one-compartment model with first-order elimination best described the data. The between-subject variability (BSV or ω) could be only estimated for clearance (CL). The residual variability was estimated assuming a log-normal distribution. Applying the BW-based allometric rule to volume of distribution (V) and CL decreased the Bayesian information criterion (BIC) by more than 60 units and the ω_CL from 0.84 (base model) to 0.58. Adding the residual diuresis effect on CL did not further decrease the BIC value but significantly decreased ω_CL from 0.58 (base model) to 0.52, so it was retained in the model. The other covariates, including blood flow, CRRT flow rates, pediatric logistic organ dysfunction (PELOD-2) score, and biomarkers (including albumin and C-reactive protein), were not found to be significant. The final PK parameter estimates are summarized in Table 2. When Q_u was undetectable, it was fixed to 0.01 mL/kg/h.

TABLE 2.

Final population pharmacokinetic parameters estimates of piperacillin standardized for a body weight of 70 kg^a

Model	Estimate	Shrinkage	RSE (%)
Structural models
CLpop	6.78		2
Vpop	55.0		12
θQu	0.12		5
Statistical models
ωCL	0.52	0.21	21
σ	0.54	0.105	9

^aThe typical parameters refer to an adult patient weighing 70 kg with a median Q_u of 0.06 mL/kg/h. CL_pop, population clearance in liters per hour; V_pop, population volume of distribution in liters; Q_u, residual diuresis in milliliters per kilogram per hour; θ_Qu, exponent measuring the residual diuresis effect as CL = CL_pop × (BW/70)^0.75 × (Q_u/0.06)^0.12; ω, square root of the between-subject variance (the corresponding shrinkage was 0.21); σ, residual variability (square root of the variance, log normal distribution); RSE, relative standard error.

For the ith patient, the final equations were

$${\text{CL}}_{\text{i}}\left(\text{L}/\text{h}\right)=6.78\times {\left(\frac{{\text{BW}}_i}{70}\right)}^{0.75}\times {\left(\frac{{\mathit{Q}}_{\mathit{u}}}{0.06}\right)}^{0.12}$$

$$\hspace{0.17em}{V}_i\left(\text{L}\right)=\text{\hspace{0.17em}55}.0\times \left(\frac{{\text{BW}}_i}{70}\right)$$

where i denotes the ith individual, Q_u is given in milliliters per kilogram per hour, and BW_i and Q_u are normalized to a 70-kg BW and a median 0.06-mL/kg/h Q_u, respectively.

The goodness-of-fit plots are depicted in Fig. 1. The prediction-corrected visual predictive check (pc-VPC) as a function of time is depicted in Fig. 2.

FIG 1.

Goodness-of-fit plots for the final model. Observation, observed piperacillin concentrations in mg/L; NPDE, normalized prediction distribution error; time in minutes; Cc, piperacillin concentrations in milligrams per liter.

FIG 2.

Piperacillin prediction-corrected visual predictive check versus time. Lines depict the 10th, 50th, and 90th percentiles of observed data, and the blue and lighter areas represent the 90th confidence intervals of the 10th, 90th, and 50th percentiles of simulated data.

Dosing regimen optimization.

We used our final model to perform Monte Carlo simulations to determine the probability of attaining the target of 100% fT of >1 to 4× MIC (Fig. 3), and the most appropriate dosing regimens were tested using population simulations curves over time among different BWs and residual diuresis for MICs ranging from 0.25 to 128 mg/L. Four typical patients with different BWs (10 kg, 20 kg, 30 kg, and 40 kg) were defined among the following residual diuresis (Q_u): 0 mL/kg/h (A), 0.1 mL/kg/h (B), 0.25 mL/kg/h (C), and 0.5 mL/kg/h (D) (Fig. 4). The piperacillin dosing regimens were studied as previously described in Materials and Methods with intermittent and continuous administrations. We suggested the best scheme to attain the target of 100% fT > 1 to 4× MIC at steady state according to MICs, BWs, and residual diuresis (Q_u) (Tables 3 and 4) According to Monte Carlo simulations, for all patients with residual diuresis of >0.1 mL/kg/h, continuous. infusion was more adequate to attain 100% fT > 1 to 4× MIC, with higher doses for high MICs over or equal to 8 mg/L or for low BW less than 10 kg. A high risk of accumulation was described in anuric patients (with residual diuresis < 0.1 mL/kg/h) where the neurotoxicity threshold corresponding to 361 mg/L was attained around 72 h of treatment for both 200 and 300 mg/kg/24 h, either by intermittent or continuous infusions (Fig. 4). Less frequent intermittent infusions of 70 mg/kg every 12 h as a 30-min infusion after a loading dose of 140 mg/kg and 200 mg/kg every 12 h as a 30-min infusion after a loading dose of 100 mg for MIC over or equal to 8 mg/L permitted attainment of 100% fT > 4× MIC with limited risk of accumulation.

FIG 3.

Probability of target attainment for a target defined as 100% fT > 1 to 4× MIC for a 15-kg patient. PTA, probability of target attainment (%); q8h, intermittent administration every 8 h; CI, continuous infusion; vertical blue line, 1× MIC; vertical red line, 4× MIC.

FIG 4.

Piperacillin population simulation curves over time. The piperacillin dosing regimens as follows. (A) Intermittent infusion of 70 mg/kg every 6 h as a 30-min infusion and 100 mg/kg every 6 h as a 30-min infusion. (B) Intermittent infusion of 70 mg/kg every 8 h as a 30-min infusion and 100 mg/kg every 8 h as a 30-min infusion. (C) Continuous infusion of 200 mg/kg per day after a loading dose of 75 mg/kg and 300 mg/kg per day after a loading dose of 100 mg/kg. (D) Intermittent infusion of 70 mg/kg every 12 h as a 30-min infusion after loading dose of 140 mg/kg and 100 mg/kg every 12 h as a 30-min infusion after loading dose of 200 mg/kg. For each panel, the simulations were done for different range of residual diuresis (Q_u) with, respectively, from left side to right side, 0.01 mL/kg/h, 0.1 mL/kg/h, 0.25 mL/kg/h, and 0.5 mL/kg/h. For each panel, each color of the lines corresponds different weight, as follows: black for 40 kg, red for 30 kg, green for 20 kg, and blue for 10 kg. Dotted lines represent superior line corresponding to neurotoxicity threshold at 361 mg/L and inferior line at four times the EUCAST MIC breakpoint for Pseudomonas aeruginosa, corresponding to 64 mg/L.

TABLE 3.

Piperacillin dosing regimens suggestions for PK target of 100% fT > 1× MIC under CRRT^a

MIC (mg/L)	Dosing regimen for Qu (mL/kg/h) of:
	<0.1	0.1–0.25	0.25–0.5
0.125	140 mg/kg, then 70 mg/kg q12h	70 mg/kg, then 200 mg/kg/day CI	70 mg/kg, then 200 mg/kg/day CI
0.25	140 mg/kg, then 70 mg/kg q12h	70 mg/kg, then 200 mg/kg/day CI	70 mg/kg, then 200 mg/kg/day CI
0.5	140 mg/kg, then 70 mg/kg q12h	70 mg/kg, then 200 mg/kg/day CI	70 mg/kg, then 200 mg/kg/day CI
1	140 mg/kg, then 70 mg/kg q12h	70 mg/kg, then 200 mg/kg/day CI	70 mg/kg, then 200 mg/kg/day CI
2	140 mg/kg, then 70 mg/kg q12h	70 mg/kg, then 200 mg/kg/day CI	70 mg/kg, then 200 mg/kg/day CI
4	140 mg/kg, then 70 mg/kg q12h	70 mg/kg, then 200 mg/kg/day CI	70 mg/kg, then 200 mg/kg/day CI
8	140 mg/kg, then 70 mg/kg q12h	70 mg/kg, then 200 mg/kg/day CI	70 mg/kg, then 200 mg/kg/day CI
16	140 mg/kg, then 70 mg/kg q12h	70 mg/kg, then 200 mg/kg/day CI	70 mg/kg, then 200 mg/kg/day CI

^aDosages are for any body weight. PK, pharmacokinetic; Q_u, residual diuresis; CI, continuous infusion; BW, body weight; q12h, every 12 hours; light gray shading, lower dosing; dark gray shading, higher dosing.

TABLE 4.

Piperacillin dosing regimens suggestions for PK target of 100% fT > 4× MIC under CRRT^a

MIC (mg/L)	Dosing regimen for Qu (mL/kg/h) of:
	<0.1	0.1–0.25	0.25–0.5
0.125	140 mg/kg, then 70 mg/kg q12h	70 mg/kg, then 200 mg/kg/day CI	100 mg/kg, then 300 mg/kg/day CI
0.25	140 mg/kg, then 70 mg/kg q12h	70 mg/kg, then 200 mg/kg/day CI	100 mg/kg, then 300 mg/kg/day CI
0.5	140 mg/kg, then 70 mg/kg q12h	70 mg/kg, then 200 mg/kg/day CI	100 mg/kg, then 300 mg/kg/day CI
1	140 mg/kg, then 70 mg/kg q12h	70 mg/kg, then 200 mg/kg/day CI	100 mg/kg, then 300 mg/kg/day CI
2	140 mg/kg, then 70 mg/kg q12h	70 mg/kg, then 200 mg/kg/day CI	100 mg/kg, then 300 mg/kg/day CI
4	200 mg/kg, then 100 mg/kg q12hb	100 mg/kg, then 300 mg/kg/day CI	130 mg/kg, then 400 mg/kg/day CIc
8	200 mg/kg, then 100 mg/kg q12hb	100 mg/kg, then 300 mg/kg/day CI	130 mg/kg, then 400 mg/kg/day CIc

^aPK, pharmacokinetic; Q_u, residual diuresis; CI, continuous infusion; BW, body weight; q12h, every 12 hours; light gray shading, lower dosing; dark gray shading, higher dosing.

^bDosage is for BW of <20 kg.

^cDosage is for BW of <10 kg.

DISCUSSION

This population PK study of piperacillin in critically ill children undergoing CRRT highlighted the critical need to individualize dosing based on individual characteristics, as these vulnerable patients must be well exposed throughout the course of antibiotic therapy.

Although the estimated PK parameters were similar to those previously reported, the influencing covariates vary widely (18, 22–28). The V was high in our study, which was expected in critically ill patients, whereas other studies mostly concerned patients with less severe illness.

The present study is the first population PK study to point out the residual diuresis’s impact on piperacillin PK in critically ill children receiving CRRT. This result highlights the importance of considering residual renal elimination pathways even when patients are on CRRT, especially for piperacillin, which is mainly eliminated by the kidneys.

The CRRT parameters were not significant, although some adult studies found some effects of nonrenal clearance or type of membrane (22, 24). A recent study that included 32 critically ill children (19 without CRRT and 13 with CRRT) showed that piperacillin PK was best described with a two-compartment model, and renal, nonrenal, and hemofilter clearances were found to be influenced by glomerular filtration rate, height, weight, and filter surface, respectively (28). The absence of a significant effect of CRRT parameters in our study may be explained by the higher RRT flow rates, with a potential CRRT plateau effect on piperacillin elimination (29–32). Yet the details of Q_D were not available in the Butragueño-Laiseca et al. study, and only 3 patients showed residual diuresis, which may explain the difference with our study, where an increased residual diuresis was associated with a lower variability of concentration model prediction (33).

Optimal piperacillin exposure in critically ill children under CRRT and with residual diuresis was attained with continuous infusions with increasing doses according to MIC and BW. For anuric patients, we observed a risk of accumulation, so for them, there is a need to space intermittent doses with an initial loading dose. The loading dose increase was necessary due to the increase of V in these critically ill patients.

The threshold of toxicity was not reached with either intermittent or continuous administration during the first days, but it is mandatory to adjust the dose during the following days, especially if the CRRT is interrupted or the corresponding effluent flow is decreased, in order to avoid accumulation with a risk of toxicity. This supports therapeutic drug monitoring and prospective recording of adverse effects with our suggested dosing regimens to ensure both efficacy and safety exposure. Usual dosing recommendations are given considering the residual renal function of the patient and the MIC for the isolated bacteria without CRRT (22), while the PK model suggests tailoring piperacillin dosing according to BW and residual diuresis under CRRT.

Our study has some limitations. First, since unbound concentrations were not measured, analyses were performed on total concentrations, and a theoretical protein binding of 30% was assumed to derive the unbound drug concentration. Second, because of insufficient data on tazobactam, the population PK of tazobactam could not be studied, whereas the combination of piperacillin and tazobactam should suggest a decrease in tazobactam dose to prevent accumulation (34). Third, given the small size of our cohort, we were unable to describe the association between piperacillin concentrations and clinical or bacterial outcomes. However, the limited number of samples was sufficient to build a population PK model and estimate accurate parameters; all relative standard errors (RSEs) were below ~20%. Fourth, given the high mortality rate of patients, our study may have a bias in the dosages performed. Finally, the suboptimal exposure rate observed with the actual dosing was probably overestimated since some MIC values were not available. Conversely, this study improved knowledge of piperacillin PK in critically ill children undergoing CRRT, highlighting the need to tailor dosing regimens by considering residual diuresis and BW.

Conclusion.

Optimal exposure to piperacillin in critically ill children on CRRT was achieved using continuous infusions with escalating doses for high MIC bacteria except for anuric patients who require intermittent and less frequent doses.

MATERIALS AND METHODS

Patients and setting.

This study was conducted in a 32-bed pediatric intensive care unit (PICU) center and high-dependency unit at the Necker Hospital (Paris, France) from September 2015 to July 2020. All children aged less than 18 years old receiving piperacillin and CRRT were included. Baseline patient characteristics, including severity of illness of the patients, residual diuresis, CRRT modalities, and biological data, were collected. The Ethics Committee of Necker Hospital approved the study, which was registered at ClinicalTrials.gov under registration no. NCT02539407. Before any inclusion, consent was obtained from the children’s parent(s).

Clinical and microbiological success criteria were defined as (i) no escalation of therapy (change of antibiotic) for the treatment of the same infection, and (ii) disappearance of obvious infectious signs. For bacteremia, this meant negative blood cultures at the supposed end of treatment (conventional duration, 7 to 10 days) without recurrence within 14 days of stopping treatment. For pneumonia, this meant no relapse within 14 days of stopping treatment. For deep infection, this meant negative deep samples (if available) and no relapse within 21 days.

We defined clinical failure as the persistence of clinical/biological infectious signs at the end of treatment and microbiological failure as the persistence of germs in the sterile sites at the end of treatment and/or the recurrence of infection with the same germ within the delay as mentioned above.

Study design.

According to local protocol, piperacillin-tazobactam (4 g/0.5 g powder; Mylan, France) or piperacillin (4 g powder; Panpharma, France) were diluted (in glucose 5%; freeflex; Fresenius Kabi, France) to obtain 36/4.5- or 80-mg/mL standard solutions, respectively, and were prescribed in most cases at 75/9.375 or 75 mg/kg every 6 h over 20 min, respectively, or in continuous infusion using a programmable electronic syringe pump (Orchestra DPS; Fresenius Kabi). Syringes were changed every 6 h for continuous infusion. Final prescriptions could differ at the discretion of the treating physician. Blood samples were collected before the entry line of CRRT (prefilter) during routine laboratory tests and as part of the patient’s routine clinical care. Samples were centrifuged (4,000 × g, 5 min) to yield plasma, which was stored at −20°C before analysis. The dosages were sent directly to the lab of Cochin Hospital and were performed day by day. If it was during working days, it was immediately considered for dosing. If not, the samples were buffered with 3-(N-morpholino)propanesulfonic acid (MOPS) before storage to minimize degradation of antibiotics allowing sensitive quantification.

Assays.

Piperacillin concentrations were quantified by high-performance liquid chromatography (HPLC) with UV detection, using a chromatographic system (Thermo Scientific; Dionex UltiMate 3000). One hundred microliters of plasma sample was mixed with 400 μL acetonitrile using 3′-O-acetyl thymidine as the internal standard. After centrifugation at 14,000 rpm for 10 min, the supernatant was mixed with 200 μL ammonium formate buffer (100 mM, pH 4.8) and 1,400 μL dichloromethane and then centrifuged at 4,000 rpm for 10 min. Twenty microliters of supernatant was injected into the chromatographic system. Separation was carried out on a Kinetex C₁₈ column (5 μm, 150 by 4.6 mm; Phenomenex; Le Pecq, Cedex, France) using a mobile phase composed of ammonium formate buffer (50 mM, pH 3.8, adjusted with formic acid) and methanol at a flow rate of 1 mL/min. The column temperature was set at 26°C, and the detection wavelengths were set at 258 nm for both piperacillin and the internal standards. The method was validated according to the U.S. FDA guideline for bioanalytical method validation (35) and the European Medicines Agency (EMA) guidelines for bioanalytical method validation (36). The lower limit of quantification was 2.5 mg/L, and the coefficients of variation for the piperacillin assay, as well as the intra- and interassay bias, were all <10%.

MIC determination.

MICs were determined in the microbiology laboratory of Necker Hospital. MICs for piperacillin were evaluated by a diffusion method on a solid-state culture, using the Etest methodology (Etest; bioMérieux, France). When the MIC was not available, clinical breakpoints were used for identified pathogens according to the European Committee on Antimicrobial Susceptibility Testing (EUCAST) recommendations (37). The breakpoint for Pseudomonas aeruginosa, one of the most common bacteria encountered in ICUs, was 16 mg/L, which was taken for simulations.

Continuous renal replacement therapy.

CRRT was performed using the Prismaflex (Gambro, Deerfield, IL) using either continuous venovenous hemofiltration (CVVH), hemodialysis (CVVHD), or hemodiafiltration (CVVHDF). CRRT was performed using either a 0.2-m² polyarylethysulfone filter (HF20; Gambro) or a 0.6-m² or 1.5-m² polyacrylonitrile filter (AN69 ST60 or ST150; Gambro) through a double-lumen catheter inserted into the femoral or internal jugular vein. Heparin or regional citrate anticoagulation was used either through the pre-blood pump or using a 3-way stopcock attached to the arterial line. All flow rates, including dialysate fluid flow (Q_D), filtration replacement fluid flow (Q_RF), and ultrafiltration flow (Q_UF), were recorded from the Prismaflex machine during the study. These flow rates were added to obtain the total effluent flow rate (Q_eff), resulting in the equation Q_eff = Q_D + Q_RF + Q_UF.

Population PK model.

Piperacillin time courses were analyzed using nonlinear mixed-effects modeling software (Monolix; 2019R2 version) using the stochastic approximation expectation maximization (SAEM) algorithm. Both one- and two-compartment structural models with first-order elimination were tested. The between-subject variability (BSV or ω) was ascribed to an exponential distribution. The residual variability (σ) was tested for additive, proportional, combined normal, or log-normal distributions.

Several covariates were tested, including BW, sex, postnatal age, C-reactive protein, albumin level, residual diuresis rates either in milliliter per hour or in milliliter per kilogram per hour, mechanical ventilation, catecholamines, extracorporeal membrane oxygenation (ECMO) use, pediatric logistic organ dysfunction (PELOD-2) score, and number of organ dysfunctions (38). The effects of the CRRT parameters on clearance (CL) were tested, i.e., Q_eff, Q_D, Q_RF, Q_UF, and blood flow rates in mL/h or mL/kg/h and CRRT set sizes on both CL and volume of distribution (V).

Categorical covariates were assessed as follows:

$${\text{θ}}_i={\text{θ}}_{\text{pop}}\times {\text{θ}}^{\mathrm{cov}}$$

where θ_i is the individual PK parameter for the ith patient, θ_pop is the median population value for the parameter of the group for which the covariate is equal to 0, θ is the covariate parameter, and cov is category 0 or 1 for covariate. Continuous covariates were associated using the power function

$${\text{θ}}_i={\text{θ}}_{\text{pop}}\times {\left(\frac{{\text{cov}}_i}{\text{med}\left(\text{cov}\right)}\right)}^{\text{β}}$$

where cov_i is the covariate value for the ith patient, med(cov) is the median value of the covariate, and β is the exponent.

The BW effect was assessed according to the allometric rule, and β values were fixed to 0.75 for CL and 1 for V. The Bayesian information criterion (BIC) was used to test different hypotheses regarding the final model, covariate effect on PK parameters, residual variability model, and structure of the variance-covariance matrix for the BSV parameters. PK parameters were properly estimated if the relative standard errors (RSEs) were <50%. The effect of a covariate was retained if it caused a decrease in the BIC and reduced the corresponding BSV. The goodness-of-fit plots (observed-predicted concentration scatterplots and normalized prediction distribution error [NPDE] versus time-predicted concentration scatterplots) of each model were evaluated by visual inspection. From the final model, 1,000 Monte Carlo simulations per patient were performed to compute the prediction-corrected visual predictive check (pc-VPC) to evaluate the model (39).

Dosing regimen simulations.

Using our final model, 1,000 Monte Carlo simulations were performed using R software to identify the appropriate dosing regimen for the probability of attainment of the PK target of 100% fT>1 to 4× MIC. Typical patient dosages were derived according to the significant covariates identified in the final PK model. The dosing regimens were as follows: 75 mg/kg every 12 h, 8 h, or 6 h as a 30-min infusion, 100 mg/kg every 12 h, 8 h, or 6 h as a 30-min infusion, 200 mg/kg per day as a continuous infusion with a loading dose of 75 mg/kg, and 300 mg/kg per day as a continuous infusion with a loading dose of 100 mg/kg. We used the EUCAST clinical breakpoint for Pseudomonas aeruginosa corresponding to 16 mg/L (37) and the neurotoxicity threshold corresponding to 361 mg/L (40).