Pharmacokinetics and pharmacodynamics of propofol in children undergoing different types of surgeries

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Original research article

Pharmacokinetics and pharmacodynamics of propofol in children undergoing different types of surgeries Bartkowska-S´niatkowska a, Agnieszka Bienert b, Paweł Wiczling c,*, Marcin Owczarek d, Jowita Rosada-Kurasin´ska a, Małgorzata Grzes´kowiak e, Jan Matysiak f, Zenon J. Kokot f, Roman Kaliszan c, Edmund Grzes´kowiak b

Q1 Alicja

a

Department of Pediatric Anesthesiology and Intensive Therapy, Poznan´ University of Medical Sciences, Poznan´, Poland Department of Clinical Pharmacy and Biopharmacy, Poznan´ University of Medical Sciences, Poznan´, Poland c Department of Biopharmaceutics and Pharmacodynamics, Medical University of Gdan´sk, Gdan´sk, Poland d Department of Anaesthesiology and Intensive Therapy, Collegium Medicum in Bydgoszcz, Bydgoszcz, Poland e Department of Teaching Anesthesiology and Intensive Therapy, Poznan´ University of Medical Sciences, Poznan´, Poland f Department of Analytical Chemistry, Poznan University of Medical Sciences, Poznan´, Poland b

A R T I C L E I N F O

A B S T R A C T

Article history: Received 12 February 2014 Received in revised form 24 April 2014 Accepted 28 April 2014 Available online xxx

Background: Propofol is a commonly used agent in total intravenous anesthesia (TIVA) surgery. However, the link between its pharmacokinetics and pharmacodynamics has not been fully characterized in children yet. Our aim was to determine the quantitative relationship between the venous plasma concentration and bispectral index (BIS) effect in a heterogeneous group of pediatric patients undergoing various surgical procedures (ASA status I–III). Methods: Nine male and nine female patients were anesthetized with propofol–fentanyl TIVA. Sparse venous samples for propofol concentrations assay and dense BIS measurements were collected during and after the end of infusion. Nonlinear mixed-effect modeling in NONMEM was used for data analysis. Results: A three-compartment model was linked with a classical Emax model through a biophase compartment to describe the available data. All clearance and volume terms were allometrically scaled to account for the body mass difference among the patients under study. A typical patient had their PK parameters observed within the range of literature values for children. The pharmacodynamic parameters were highly variable. The EC50 of 2.80 mg/L and the biophase distribution rate constant of 3.33 min1 were found for a typical patient. Conclusions: The BIS values in children are highly correlated with the propofol effect compartment concentrations according to the classical Emax concentration–response relationship. Children had slightly lower sensitivity to propofol and slightly higher clearance, as compared with the adult data available in literature. The intra-patient variations in the BIS require the anesthesiologist’s attention in using BIS values alone to evaluate the depth of anesthesia in children. ß 2014 Published by Elsevier Urban & Partner Sp. z o.o. on behalf of Institute of Pharmacology, Polish Academy of Sciences.

Keywords: Propofol Bispectral index Pharmacokinetic and pharmacodynamics modeling Children Total intravenous anesthesia

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Introduction

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In the past decade the role of total intravenous administration (TIVA) in children increased as many advantages of this technique were reported. For example, postoperative nausea and vomiting are undeniably reduced in the presence of a TIVA anesthetic, as compared with any inhalational anesthetic. Organ toxicity is more

* Corresponding author. E-mail address: [email protected] (P. Wiczling).

likely to occur with inhalational anesthetics rather than intravenous medications [1]. As pharmacodynamic (PD) parameters in children are still debated, up to now there has been no pharmacokinetic/pharmacodynamic (PK/PD) model of propofol available for pediatric anesthesia [2,3]. A pharmacodynamic feedback, such as the bispectral index (BIS), may be useful to counteract interindividual variability in the pediatric population. The technology of BIS monitoring has long been questioned in children [4], however it has become more popular as more research has been done on the subject of relating propofol concentrations with BIS measurements [5–9]. Many factors

http://dx.doi.org/10.1016/j.pharep.2014.04.012 1734-1140/ß 2014 Published by Elsevier Urban & Partner Sp. z o.o. on behalf of Institute of Pharmacology, Polish Academy of Sciences.

Please cite this article in press as: Bartkowska-S´niatkowska A, et al. Pharmacokinetics and pharmacodynamics of propofol in children undergoing different types of surgeries. Pharmacol Rep (2014), http://dx.doi.org/10.1016/j.pharep.2014.04.012

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influencing the BIS during propofol infusion have not been fully elucidated yet, especially those concerning the time to peak effect and the biophase distribution rate constant [10]. Also, the pharmacokinetics (PK) of propofol requires further studies. High variability in the PK and PD can be observed in children, especially in critical care settings. The PK parameters of propofol change dynamically with age and children of different ages cannot be treated in the same way. Within the first year of the child’s life the body weight-scaled clearance approaches adult values [11]. For older children the weight is mostly used as a covariate to explain the observed inter-patient variability. Several models have already been proposed for children [12–17], with the one by Kataria et al. being the most commonly used. In the model by Kataria et al. the PK of propofol was studied on 53 healthy, unpremedicated children aged from 3 to 11 years. Two administration protocols were used – the first was an intravenous bolus of 3.5 mg/kg, and the other was the same bolus followed by the infusion at a rate ranging from 0.125 mg/kg/min to 0.20 mg/kg/ min. A three-compartment model was used to characterize propofol disposition. In this study weight was found to be an important covariate for all PK parameters. Age improved the fit only moderately. The studies by Rigouzo et al. published in 2010 proved that the Schnider model, which is recommended to adults, may also be useful in pediatrics, in children aged between 6 and 12 years [10,14,18]. Propofol is predominantly metabolized in the liver, mainly by glucuronosyltransferase UGT1A9. The secondary metabolic cascade, mainly mediated by CYP2B6 and to a lesser extent by CYP2C9, leads to the production of 4-hydroxypropofol, which is further metabolized by conjugation. The existence of extra-hepatic metabolism is also taken into consideration. Takata et al. suggested that the organs responsible for its metabolism are the kidneys, small intestine, brain and lungs, where the kidneys were ascribed the most significant role. The high value of the hepatic extraction ratio suggests that the clearance of propofol is flow dependent, so the liver blood flow plays a more significant role in drug elimination than the hepatic enzyme activity [19,20]. In this study we developed the PK/PD model in children undergoing different types of surgeries under propofol–fentanyl TIVA. Due to limited PK sampling the prior literature data obtained by Kataria et al. [14,21] were used to obtain information about the processes that were not supported by our data. The nonlinear mixed-effect approach was utilized to draw conclusions about PK/ PD processes, especially to determine the link between the PK and PD in heterogeneous groups of children, which are encountered in real clinical settings.

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Materials and methods

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Patients

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The study was approved by the local Bioethics Committee (Poznan´ University of Medical Sciences, Poland). A written informed consent was obtained from children and their parents. Eighteen patients aged from 1 to 18 years, ASA status I–III, undergoing elective cardiac catheterization (n = 11), urological operation (n = 4) and inguinal herniotomy (n = 3) were enrolled into the study in two big centers of pediatric anesthesiology. All the patients were scheduled for procedures expected to last more than 1 h. Exclusion criteria included confirmed allergy to propofol, evidence of a severe failure of the hepatic, renal or endocrine system and ASA status IV or higher. Additionally, severe laboratory abnormalities, such as twice higher levels of bilirubin, aminotransferases, BUN and creatinine as well as hipoproteinemia and hypoalbuminemia and abnormal lipid profile excluded patients

Table 1 Demographic data and physiological parameters of patients enrolled in the study. For continuous variables (systolic blood pressure, diastolic blood pressure, body temperature and heart rate) the median value of all records throughout the entire infusion were used for calculations. Parameter, unit

Mean  SD (n = 18); range

Age (year) Body weight (kg) Male/female ASA I/ASA II/ASAIII Total dose of propofol (mg) Infusion duration (min) Systolic blood pressure (mmHg) Diastolic blood pressure (mmHg) Heart rate (bpm)

6.1  4.4; 1.7–16 24.9  17; 10–70 9/9 6/9/3 293  180; 48.4–739 50.3  17.5; 16–73 101.3  15.3; 75–158 58.6  22.1; 25–100 97.1  18.5; 61–177

from the study. Table 1 summarizes the patient characteristics and laboratory data recorded throughout the study.

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Study design

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One hour before arrival at the operating room all the patients received premedication with oral midazolam at age-dependent doses: 0.5 mg/kg (1–5 years or <25 kg b.w.), 0.3 mg/kg (6 years or 25–40 kg b.w.) and 7.5 mg for older children. In the operating room, before induction, a venous catheter was introduced to administer fluids, propofol and other drugs. Another catheter was placed into the contralateral arm for blood sampling after the induction of anesthesia. Standard noninvasive monitoring, including the heart rate (HR), non-invasive blood pressure (NBP), peripheral oxygen saturation (SpO2), capnometry (ETCO2) and temperature (TEMP), was performed for every patient. Additionally, before the induction of anesthesia and after the acceptance of the child Pediatric BisSensor leads (Aspect Medical Systems, GE) were applied to assess the depth of anesthesia. The skin on every patient’s forehead was prepared according to the manufacturer’s instructions. Propofol was administered with a standardized syringe pump Alaris TIVA (1000LBO1539 Iss2, CareFusion). All the children received 0.5 or 1.0 or 2.0% Propofol (Braun) at agedependent doses. The scheme of TIVA-propofol administration included the loading dose followed by a continuous infusion at three decreasing dosage intervals. The induction in the children from group I (1–5 years) was performed at a dose of 4 mg/kg, and then it was followed by an infusion of 17 mg/kg/h at the first interval, 12 mg/kg/h at the second interval, and the final 10 mg/kg/ h for the last 10 min, before the end of the procedure. The induction in the children from group II (6–12 years) was performed with propofol at a dose of 3 mg/kg, followed by an infusion of 15 mg/kg/ h, and 10 mg/kg/h and 8 mg/kg/h for the last 10 min before the end of the procedure. During the induction the children from group III (older than 12 years) received a dose of 2 mg/kg of propofol, followed by 10 mg/kg/h, 8 mg/kg/h, and finally – 8 mg/kg/h, respectively. A single dose of mivacurium (0.2 mg/kg) was administered before the endotracheal intubation. A fentanyl dose of 1–1.5 mg/kg was routinely used to ensure proper analgesic effect during the procedure. The children were mechanically ventilated with a mixture of oxygen and air (40%/60%) to an end-tidal carbon dioxide tension (ETCO2) between 35 and 45 mmHg. After the end of the procedure the infusion of propofol was stopped and the children were continuously monitored and given supplementary oxygen (100%) until they were awake and extubated. All monitored data were continuously recorded at 5-min intervals, including the HR, SpO2, ETCO2, BP, TEMP and BIS. At the beginning and at the end of propofol infusion the BIS values were recorded at 0.5 min intervals. There were nine venous blood samples (3 mL) collected from each patient during and after the

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Please cite this article in press as: Bartkowska-S´niatkowska A, et al. Pharmacokinetics and pharmacodynamics of propofol in children undergoing different types of surgeries. Pharmacol Rep (2014), http://dx.doi.org/10.1016/j.pharep.2014.04.012

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infusion of propofol and then they were immediately centrifuged. The plasma was stored at 4 8C until analysis. The concentration of propofol in the plasma was measured for 8 weeks with a fluorescence detector by means of high-performance liquid chromatography [22–24]. The limit of quantification was estimated at 50 ng/mL. The within-day coefficients of variation were less than 10%.

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PK/PD model

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The collected data were analyzed with the nonlinear mixedeffect modeling approach in NONMEM (Version 7.2.0, Icon Development Solutions, Ellicott City, MD, USA). NONMEM was compiled with the Intel Fortran Compiler 9.0. The runs were executed with Wings for NONMEM (WFN703, http://wfn.sourceforge.net). The data were processed and plotted with Matlab1 Software version 7.0 (The MathWorks, Inc., Natick, MA, USA). In this study the propofol concentrations were described by means of a three-compartment model with ADVAN6, where CP denoted the propofol concentrations in the central compartment, CT denoted the concentration in the peripheral compartment; VC and VT1 and VT2 are the volume of the central and peripheral compartments, Cl is the total systemic clearance, and Q1 and Q2 are distribution clearances. The sparse nature of our PK data did not enable us to make a reliable estimation of all parameters of the model. To overcome this limitation the Kataria et al. dataset [14,21] was pooled with our data. It contained dense PK data obtained from healthy children with comparable demographic characteristics and infusion parameters to our patients. An effect compartment was added to the three-compartment PK model to better account for the delay between the propofol concentrations and the observed effect. The change in the effect compartment concentration (Ce) was defined by the following expression: dC e ¼ ke0 C P  ke0 C e ; dt

C e ð0Þ ¼ 0

(1)

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The time course of the electroencephalographic (EEG) spectral frequency index (BIS) was directly linked to the effect compartment concentrations through the Emax model:   ðC e =EC 50 Þ þ MID BIS ¼ BIS0 1  Emax (2) ðC e =EC 50 Þ þ MID þ 1

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where BIS0 denotes the baseline BIS score (fully awake) that was fixed to 100. The Emax is the maximal effect fixed to 1 and EC50 is the concentration for the 50% decrease in the BIS score caused by propofol. The initial (at time zero) BIS value was variable and lower than 100 (86.9 on average). Most likely it was a consequence of midazolam premedication that was shown to have additive effect on the depth of anesthesia [25–27]. This effect was included in the model assuming the constant concentration of midazolam for a short (less than 1 h) period of time [24]. The parameter MID = CMid/ EC50,Mid equals to the ratio of midazolam concentration and EC50,Mid value of midazolam. Thus, Ce/EC50 + MID denotes the virtual effect concentration, which is defined as the sum of the normalized effect-site concentrations of propofol and midazolam assuming the additive interaction of these drugs [28]. Any jth observation of propofol concentration for the ith individual, Cij and any BIS value for the ith individual, BISij measured at time tj, was defined by the following equation: C i j ¼ C P ðP i ; t j Þð1 þ eC;i j; pro p Þ BISi j ¼ BISðP i ; t j Þ þ eBIS;i j;add

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(3)

where CP and BIS denote the basic structural population model (Eq. (1)). Pi stands for the pharmacokinetic parameters for the ith

3

individual (Cl, VC, VT1, Q1, VT2, Q2, EC50, MID, keo), and eC,ij,prop, eBIS,ij,add represent the proportional residual intra-individual random errors. It was assumed that e is symmetrically distributed around a mean of 0, with variance denoted by s 2pro p . Inter-individual variability for the Cl, VC, VT1, VT2, Q1, Q2, keo, MID, EC50 was modeled with the following exponential error model: Pi ¼ uP expðhP;i Þ

(4)

where Pi is the set of PK/PD parameters for the ith individual, uP is the population estimate of PK/PD parameters, hP,i is a random effect for a particular parameter with mean 0 and variance v2P . The effect of body weight on all of the volume and clearance parameters was predicted on the basis of allometric scaling as follows [29]: Pi ¼ uP



BW i 70

K

expðhi Þ

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(5)

where Pi denotes the individual value and uP stands for the population estimates of volume and clearance terms (Cl, VC, VT1, VT2, Q1, Q2); BWi is the individual body weight, 70 denotes the body weight of a standard healthy adult, and K is the exponent equal to 0.75 for clearance and 1 for volumes of distribution. Recent studies have demonstrated the validity of this type of allometric scaling to predict propofol disposition in subjects of different weight [30]. The minimum of the NONMEM objective function value (OFV), typical goodness-of-fit diagnostic plots, and an evaluation of the precision of pharmacokinetic parameters and variability estimates were used to discriminate between various models during the model-building process. The shrinkage was evaluated for all model parameters to assess if and to what extent the individual parameters ‘shrink’ toward the population values. It was calculated as follows: Shrinkage ðhÞ ¼ 1 

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SDðEBEh Þ

v

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(6)

where v is the estimated variability for the parameter in the population and SD is the standard deviation of the individual values of the empirical Bayesian (individual) estimates (EBE) of h [31]. The shrinkage of inter-individual parameters which is lower than about 20–30% suggests that the data are highly informative about the individual-predicted parameters [31]. To assess the potential relationships between the parameters and covariates an exploratory analysis was made by plotting the empirical Bayesian (individual) estimates of each parameter and the covariates tested (age, body weight, study, gender). Then, the covariates which were identified as important were tested on the basis of the likelihood ratio. The likelihood ratio was determined as the difference in the OFV of a full model (with covariate) and reduced model (without covariate) after refitting the data. The OFV difference of 7.9 between the models for one degree of freedom was considered to be statistically significant (at p < 0.005) for the equation to be included into the model.

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Model evaluation

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The model performance was assessed by means of Visual Predictive Check (VPC). The VPC was calculated on the basis of 1000 datasets simulated with the final parameter estimates. In this study the 10th, 50th and 90th percentile were used to summarize the data and VPC prediction. The VPC enabled us to compare the confidence intervals obtained from prediction with the data observed over time. When the corresponding percentile from the observed data falls outside the 95% confidence interval derived from predictions, it indicates misspecification of the model. Since

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the PK/PD data deviated from nominal times to some extent, binning across time was done [32]. A non-parametric bootstrap method (n = 200) was used to study the uncertainty of all PK parameter estimates. 90% confidence intervals (5th–95th percentile) were obtained from the bootstrap empirical posterior distribution, as described previously [33].

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Results

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The PK and PD measurements were obtained from 18 pediatric patients (Table 1) during and after the discontinuation of propofol infusion that ranged from 16 to 73 min (mean 50.3  17.5). The patients’ age ranged from 1.7 to 16 years (mean 6.1  4.4) and their body weight ranged from 10 to 70 kg (mean 24.9  17). The experimental data comprised 119 venous concentrations of propofol and 1031 BIS measurements. Due to ethical restrictions it was not possible to obtain dense samples that would fully characterize the PK of propofol. Most of the PK samples (79%) were derived from the pseudo-plateau phase before the end of infusion. The mean post-dose PK sampling duration was 8 min (range 1–30 min). The dataset alone did not enable us to correctly characterize the pharmacokinetics of propofol. The parameter estimates resulted in comparable values with those in the literature only for the total systemic clearance, whereas all volume-of-distribution parameters and distribution clearances were considerably biased. To overcome this inherent limitation of our PK model our data were combined with the freely available Kataria dataset [14,21]. The use of priors reported by Kataria et al. [14,21] (instead of data pooling) was also tested in Nonmem with essentially identical results. The

data pooling enabled more reliable estimation of the PK parameters of propofol in children and assessment of the link between the PK and PD. Furthermore, the PK and PD measurements were analyzed together. Since the pharmacodynamic model of propofol (Emax-type relationship) is well established, both datasets were simultaneously analyzed to extract more information. The BIS data were collected every 0.5 min at rapidly changing phases and every 5 min in the plateau phase up to the point where it was feasible in a particular patient. The mean post-infusion BIS measurements lasted 22.2 min on average and ranged from 10 to 41 min, till the patient was transferred to the post-operative room, where BIS monitoring was discontinued. For one subject (ID = 3) the instrument was not working properly and the data were not collected. Also for some subjects (ID 1–2, 5, 6) the initial BIS measurements were not taken due to technical problems with signal transmission and disturbed skin resistance. Figs. 1 and 2 present the experimental data, along with the population and individual model predictions of propofol concentrations and BIS measurements. These plots show that the final PK/ PD model accurately described the data. However, some propofol predictions (ID: 5, ID: 14) are considerably biased from the experimental measurements. Also, some BIS measurements (ID: 15, 16, 17) show substantial intra-patient variability around model predictions. The goodness of fit plots was stratified with respect to the origin of the data, which can be seen in Fig. 3. The individual and population predictions versus the observed concentrations are relatively symmetrically distributed around the line of identity. The individual weighted residuals (iWRES) versus individual predicted concentrations, and conditional weighted residuals (CWRES) versus time, do not show any trend and are relatively

Fig. 1. A plot of the observed (gray circle), population-predicted (dotted line) and individual-predicted (solid line) propofol concentrations versus time for the final PK/PD model.

Please cite this article in press as: Bartkowska-S´niatkowska A, et al. Pharmacokinetics and pharmacodynamics of propofol in children undergoing different types of surgeries. Pharmacol Rep (2014), http://dx.doi.org/10.1016/j.pharep.2014.04.012

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Fig. 2. A plot of the observed (gray line), population-predicted (dotted line) and individual-predicted (solid line) BIS values versus time for the final PK/PD model.

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uniformly distributed around zero, indicating acceptable performance of the model in quantifying the PK/PD data. Supplemental Fig. 3S shows the VPC plots for the propofol concentration and BIS. The plots indicate that both the central tendency of the data and the variability at a particular sampling time were recaptured well. The observed misspecifications are mostly the consequence of a relatively small dataset used to build the population model. Table 2 shows the parameter estimates and interindividual variability obtained after the population modeling. The parameters were estimated reasonably well, with lower precision than 51%. The interindividual variability was estimated on all parameters, except the peripheral volume of distribution, where it tended to amount to zero during the model building process. It was also reported to amount to zero in the original analysis by Kataria et al. [14]. As far as our data are concerned, the shrinkage was acceptable for most PK parameters ranging from 7.4 to 39.5%, whereas it was very high (about 60%) for the PD measurements, indicating that the data did not have enough power to support the covariate search. Thus, the present analysis did not enable us to assess the influence of age on the EC50 and keo. Additionally, no other covariates (age, body mass, gender, heart rate, systolic and diastolic blood pressure) were identified during the model building process. Supplemental Figs. 2S and 3S show the individual estimates of the ETA (the difference between the patient-specific value and the population mean) for all of the PK and PD parameters in relation to the patients’ body weight and age. Pediatric patients differ in their body mass considerably. In our approach this difference was accounted for by standard allometric scaling of all clearance and volume terms, as previously explored by Knibbe et al. [30]. The original Kataria dataset was analyzed

with weight-proportional relationship for all volume and clearance terms. In order to assess the influence of our data on the parameters obtained from the Kataria dataset, the model was refitted by means of allometric relationships. The parameter estimates obtained from the modeling of the Kataria data (without our data) are given in Table 2. The pooled data led to essentially identical parameter estimates. Almost no shift (less than 5%) was noted for the typical values of Cl, Q1, and Q2; whereas for VC and VT1 and Q3 the parameters were lower by about 20–30%. Some increase in inter-individual parameters was also observed with the highest value (about 30%) for Vc and VT1. Those differences were not statistically significant. Fig. 4 shows the individual estimates of the ETA (the difference between the patient-specific value and the population mean) for all the PK parameters related with the study. The baseline BIS value was lower than 100 for almost all the patients. The MID parameter equaled 0.121, indicating that a typical patient had been sedated before the propofol infusion started with typical BIS values of 89.2. The MID value suggests that the midazolam EC50 exceeded its concentration by a factor of 8.

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Discussion

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Despite the fact that total intravenous anesthesia (TIVA) is gaining popularity among pediatric anesthesia practitioners, there are still limitations to the current use of TCI in children. There are no integrated PK/PD studies on children, partly due to the lack of consistent effect measures [11]. The high interindividual variability of anesthetic requirements in the pediatric population is frequently a function of growth and maturation. Thus, it is difficult to predict the PK/PD of propofol in a given child. Recently Rigouzzo et al. [34] examined the bias of TCI systems of propofol in children

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Fig. 3. Goodness-of-fit plots: the observed concentrations versus the population-predicted concentrations; the observed concentrations versus the individual populationpredicted concentrations; individual weighted residuals (iWRES) versus individual-predicted concentrations; and conditional weighted residuals (CWRES) versus time. Closed symbols represent BIS measurements, open symbols represent propofol concentrations obtained in this study, and gray symbols represent propofol concentrations from the dataset by Kataria et al. [14].

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and young adults and they noted that the measurements of propofol concentration were generally underestimated by the target plasma concentration (as predicted by the Kataria and Schnider models). The bias was higher in children than in adults. The authors concluded that the predictability of plasma concentrations of propofol by means of classical pharmacokinetic/ pharmacodynamic models is limited in children. The authors examined healthy, ASA I and II children undergoing middle ear surgeries. In severely ill children or in obese patients the TCI inaccuracy may be even higher [35]. In this study we evaluated the PK and PD of propofol during TIVA in children undergoing different types of surgeries (ASA I/II/III of 6/9/3) to better characterize the relationship between the venous plasma concentration and BIS effect. The pharmacokinetics of propofol is usually described by a three-compartment model. However, it is difficult to obtain reliable parameter estimates in children due to sampling difficulties, especially at the beginning of infusion and at late postinfusion times. The data pooling approach was used in this study to stabilize the part of the model that was not supported by our data. The use of prior information, especially pharmacokinetics-related, is a common practice in pediatric anesthesia [36–38]. As can be seen in Fig. 4, the parameters obtained in this study are in good agreement with the parameters from Kataria et al. The CL scaled to 20 kg obtained in this study (0.82 L/min) is in good agreement with

the pediatric literature data, which range from 0.56 to 0.83 L/min [12–17]. When scaled to 70 kg, the clearance in children is slightly higher (2.10 L/min) than in healthy adults (1.23–2.05 L/min) [15,16,39–41], although some higher clearance values were noted in ASA III surgical patients 2.64 L/min [42]. Our study proves that for a typical patient there is an Emaxtype relationship between the propofol effect concentrations and BIS, which proves the usefulness of BIS in monitoring the depth of anesthesia in children. The biophase distribution rate constant was found to be high (3.33 min1), with considerable variability of 223%. The possible correlation with age and other covariates could not be assessed in this study due to the lack of power. Munoz et al. reported the values which were a few times smaller, where the median ke 0 in children amounted to 0.41 min1 with the Kataria model and where it amounted to 0.91 min1 with the Paedfusor model [43]. Jelsacov et al. [44] used a two-stage pharmacodynamic analysis with BIS monitoring and they revealed an age-dependency of the ke 0 value for propofol, where the ke 0 decreased as the age increased. There are some limitations to ke 0 quantification in children, especially when out of critical care. First, it is highly unlikely to obtain arterial blood samples and to obtain the data describing the full concentration of the drug versus the effect profile. Therefore, the current commercially available TCI systems for children do not include the ke 0 [45].

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Table 2 Summary of the final population PK/PD parameters, inter-subject and residual error variance estimates and bootstrap results for propofol and BIS measurements. The parameter estimates obtained from the modeling using only Kataria et al. data (19) are shown for comparison. Parameter, unit

Fixed effect (PK) uVC (L) uCL (L/min) uVT1 (L) uQ1 (L/min) uVT2 (L) uQ2 (L/min)

Final PK/PD estimates

Kataria data

Estimate (% CV) [shrinkage]

Bootstrap median [5th–95th CI]

Estimate (% CV) [shrinkage]

25.6 (15.5)  (BW/70) 2.10 (5.0)  (BW/70) 0.75 46.6 (10.1)  (BW/70) 3.16 (10.8)  (BW/70) 0.75 377 (13.1)  (BW/70) 1.15 (8.0)  (BW/70) 0.75

22.8 [13.1–30.8] 2.10 [1.71–2.40] 48.3 [36.1–65.0] 3.27 [2.64–4.40] 376 [202–877] 1.14 [0.998–1.48]

32.9 (11.6)  (BW/70) 2.14 (5.0)  (BW/70) 0.75 59 (10.3)  (BW/70) 3.01 (10.9)  (BW/70) 0.75 389 (14.1)  (BW/70) 1.89 (8.5)  (BW/70) 0.75

Fixed effect (PD)

uMID uke0 (1/min) uEC50 (mg/L)

0.121 (30.6) 3.33 (44.1) 2.77 (18.8)

0.119 [0.0603–0.180] 1.63 [0.683–10.12] 2.87 [2.11–3.85]

– – –

Inter-individual variability

v2Vc (%) v2Cl (%) v2Vt1 (%) v2Q1 (%) v2Vt2 (%) v2Q2 (%) v2BIS;0 (%) v2ke0 (%) v2EC50 (%)

83.2 (28.8) [18.2] 31.9 (25.9) [7.4] 71.3 (31.4) [12.9] 42.1 (44.5) [39.5] – 39.0 (37.9) [33.9] 93.4 (50.8) [63.9] 223 (47.0) [66.7] 68.8 (31.9) [52.3]

86.4 30.7 64.0 49.1

[63.1–120] [24.8–39.0] [38.8–86.2] [20.5–74.9]

39.2 [25.9–58.3] 87.5 [36.9–136] 179 [104–310] 65.4 [47.1–82.1]

56.4 26.3 42.8 46.1 – 31.8 – – –

(29.5) (26.1) (42.6) (49.3)

[23.0] [5.93] [20.9] [28.3]

(35.0) [28.9]

Residual variability

s 2pro p;C; Kataria (%) s 2pro p;C; Our data (%) s 2add;BIS

19.2 (5.3) [7.12] 33.4 (20.2) [13.2] 8.72 (10.3) [2.70]

19.2 [17.6–21.0] 31.7 [22.7–50.3] 8.56 [7.42– 9.92]

19.8 (5.4) [12.4] – –

Fig. 4. The individual posterior Bayes estimates of the ETA (the difference between the patient-specific value and the population mean) for the PK parameters of propofol in relation to the origin of experimental data. No statistically significant differences were noted for our or Kataria et al. [14] patients.

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425 In the literature, the PK/PD relationships of propofol in children 426 were mostly based on predicted propofol concentrations [46–48], 427 for which much higher EC50 values were observed. All the three 428 studies confirmed the correlation of BIS with the predicted 429 propofol concentrations. However, Park et al. [47] found that 430 the correlation in preschool children was weaker than in adults. 431 Munoz et al. noted that the EC50 of propofol in children was 432 comparable to adults [46]. However, the second study by the same 433 group [48] examining auditory evoked potentials (AEP) following a 434 submaximal bolus dose of propofol suggested that children may be 435 more sensitive to propofol than adults, because there were higher 436 EC50 values calculated in adults than in children (3–11 years). The 437 conflicting results from such studies may be partly related with the 438 choice of the monitor of the depth of anesthesia and differences in 439 the pharmacokinetic models used to administer propofol and/or to 440 predict the effect site concentrations [45]. Tirel et al. [5] noted that 441 there was some difficulties interpreting the BIS value in children 442 (3–15 years) because of the absence of significant changes for 443 higher plasma concentrations of propofol or because of the link 444 with age for lower concentrations of propofol. 445 On the contrary, our study was based on the measured 446 concentration. The observed sensitivity to propofol hypnosis in 447 children tends to be lower than in adults. The obtained EC50 value 448 of 2.77 mg/L is slightly higher than the value for healthy adults – 449 2.55 mg/mL [36], or surgical ASA III patients – 2.19 mg/L [38]. Thus, 450 higher doses of propofol may be required to achieve the same 451 depth of anesthesia. Rigouzzo et al. [30] obtained similar results in 452 their study, where they compared the relationship between the 453 measured concentration of propofol and BIS in children and young 454 Q2 adult patients. The obtained EC50 value was higher in children than 455 in adults (4.0 mg/L versus 3.3 mg/L). Both EC50 values of propofol 456 were slightly higher than in our study. However, this may have 457 been caused by the age characteristics. In the study by Rigouzzo 458 et al. [34] the patients’ age in the children group ranged from 6 to 459 13 years (mean 10 years), whereas in the adult group the patients’ 460 age ranged from 14 to 32 years (mean 18 years). In our study the 461 patients’ age ranged from 1.7 to 16 years (mean 6.1 years). It is 462 known that age may influence the BIS response to propofol [5]. 463 The time dependence of measured BIS values around individual 464 model predictions was noted for some subjects (i.e. for ID-15). It 465 may have been the consequence of co-administration of opioids 466 and other drugs, the influence of surgical procedures and the 467 patients’ state of health. The study by Jeleazcov et al. [44] showed a 468 moderate impact of fentanyl on the BIS values. However, a more 469 detailed study would be necessary to confirm the exact mechanism 470 of those variations. 471 A typical patient was sedated prior to the initiation of propofol 472 infusion. Brosius et al. showed that the median pre-induction BIS 473 was significantly lower in the group of pediatric patients receiving 474 midazolam (92; range, 67–98) than in the control group (97; range, 475 89–98) [49]. These results are in perfect agreement with our 476 observations. 477 This study has several limitations as the propofol concentra478 tions were derived from venous samples. However, it is very 479 difficult to obtain arterial blood samples from children outside 480 critical care units and due to the restrictions of the local ethics 481 committee. Also, the sparse sampling did not enable us to fully 482 characterize the PK of propofol, especially at the beginning and 483 after the end of infusion. The potential propofol–opioid interac484 tions and surgical procedures were not included in the analysis. 485 Nevertheless, the proposed approach was successful in character486 izing the PK/PD of propofol in children. Our own data combined 487 with the literature data enabled us to recover the PK/PD 488 parameters from the limited sampling design and to obtain 489 information about the link between propofol concentrations and 490 BIS measurements in real routine clinical patients.

Conclusions

491

In conclusion, not only the pharmacokinetics but also the pharmacodynamics of propofol in children is different than in adults and it is highly variable. Thus, to optimize the dosage of propofol to the pediatric population a PK/PD analysis is required with due consideration of different age groups. Also, the use of measured plasma concentrations of propofol seems to indicate that children are more likely to be less sensitive to propofol hypnosis than adults. The intra-patient variations in BIS values require the anesthesiologist’s attention in using BIS values alone to measure the depth of anesthesia in children.

492 493 494 495 496 497 498 499 500 501

Conflict of interest

502

None declared. Funding This study was supported solely from departmental sources.

503 504 505

Appendix A. Supplementary data

506

Supplementary material related to this article can be found, in the online version, at doi:10.1016/j.pharep.2014.04.012.

507 508

References

509

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