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Propofol pharmacokinetics in China: A multicentric study Correspondence Address: Objective : A multicenter population pharmacokinetics study of propofol was performed to establish a new population model. Materials and Methods : Three thousand two hundred and fiftynine blood samples of 220 participants were measured by HPLCUV or HPLCFLU or GCMS. Targetcontrolled infusion after single bolus or continuous infusion was applied for propofol anesthesia. The samples were taken from 2 to 1500 min. The concentrationtime profiles were analyzed by nonlinear mixed effect model (NONMEM) with first order estimation method. The interindividual variability and the residual variability were described by exponential model and constant coefficient variation model. The stepwise modeling strategy using PsN was applied for covariate modeling. The criteria of forward addition and backward elimination were (α = 0.01 and α = 0.005, χ^{2}, df = 1). The final model was evaluated by bootstrap using PDx and visual predictive check using PsN. 500 bootstraps and 1000 simulation were run. Result : The propofol population model was described by 3compartment model with interindividual variability of CL, V _{1} , Q _{2,} and Q _{3} describing by exponential model. The interindividual variability of V _{2} , V _{3} were not included because it is reported that the parameter was near its boundary. The typical value of CL, V1, Q2, V2, Q3 and V3 were 1.28 L · min^{1} , 10.1 × (age/44)0.465 × (1 + 0.352 × sex) L, 0.819 L · min^{1} , 36.0 L, 0.405 × (bodyweight/60)1.58 L · min^{1} and 272 L, respectively. Coefficients of interindividual variability of CL, V1, Q2 and Q3 were 30.5%, 35.6%, 43.7% and 66.9%, respectively, and the coefficients of variation of HPLCUV, GCMS and HPLCFLU were 13.3%, 16.9% and 24.2%, respectively. The bootstrap evaluation showed that the final model parameter estimates were within ± 3.39% compared with bootstrap median. The curves of observations percentiles were distributed within the corresponding 95 prediction percentiles by the visual predictive check. Conclusion: The threecompartment model with firstorder elimination could describe the pharmacokinetics of propofol fairly well. The involved fixed effects are age, body weight and sex. The population model was evaluated to be stable by bootstrap and visual predictive check.
Introduction Propofol is widely used in the surgical anesthesia with the characteristics of: Fast induction, rapid elimination, short duration of action, smooth recovery from anesthesia. However, the apparent volume and clearance varied over a huge range because of tremendous body uptakes and rapid elimination. The concentrations were difficult to predict. As a solution the targetcontrolled infusion system (TCI) was introduced into propofol anesthesia. TCI with infusion pump driven by computer meant that the fairly steady concentration in the central or the effect compartment was maintained by presetting the pharmacokinetic parameter. TCI systems require appropriate pharmacokinetics parameters to make sure that a defined concentration could be achieved rapidly and maintained at constant level. In the past 20 years, more than 20 studies about the propofol population pharmacokinetics with different characteristics were retrieved in Medline. But only one by Schuttler [1] was a multicenter study. The benefits of multicenter population research included a large number of participants, a possibility of including a wide range of population group, and a more representative population model. There were several single center studies about propofol population pharmacokinetics in China but no multicenter study. In this study, we performed a multicenter population pharmacokinetic analysis with 220 individual data from anesthesia division of five large hospitals widely located in China to build a more representative population model for Chinese. Our data were analyzed with NONMEM, and a firstorder conditional estimation with interaction [2],[3] was used. Materials and Methods Data Collection We collected data of propofol for anesthesia in department of anesthesiology from four large hospitals [Table 1]. The research was approved by the Hospital Ethics Committee and all patients provided the signed written consent.{Table 1} A mean of 2.58 μg · ml 1 with the standard deviation of 2.33 μg · ml 1 and the range of 0.2 ~ 24.42 μg · ml 1 propofol concentrations from 220 patients were measured from artery. Seventysix participants accepted single bolus dose before TCI infusion for a loading dose which was 34.55% of 220 participants. The rest accepted continuous infusion before TCI. The sampling periods (min) were various among four hospitals, with the 21500 min for Jinling Hospital, 1495 min for Huaxi Hospital, 160 min for First Affiliated Hospital of Xinjiang Medical University, and 2180 min for Third affiliated Hospital of SUNYatSen University. The covariates involved sex, age and body weight, analysing instruments. The blood samples were measured by any of High Performance Liquid Chromatography  Ultraviolet (HPLCUV), Gas ChromatographyMass Spectrum (GCMS) and High Performance Liquid Chromatography  Fluorescence (HPLCFLU) instruments. The lower quantitative limits of HPLCUV, GCMS and HPLCFLU were 20 ng · ml 1 , 10 ng · ml 1 and 5 ng · ml 1 . Base Model Propofol concentrationtime data were analyzed using NONMEM [4] (double precision, Version VI, Level 2.2) integrated with PD × 3.1 (version for trial, Icon developmental solutions, Hanover, MD, USA). The complier was G77 Fortran under environment of Window XP® . Two and threecompartment pharmacokinetic models were compared. The interindividual variability was described by an exponential [3],[5] (EXP) model and for the residual variability, we used a constant coefficient of variation [3],[5] (CCV) model. By the instructions of NONMEM manuals, [4],[6] the covariate analyzing instrument (INST) was analyzed as a potential influence on random error (Eq.1), and therefore the codes ε 1, ε2, ε3 were residual error of HPLCUV, GCMS and HPLCFLU instrument The first order conditional estimation method with interaction [2],[3] method was applied as an estimation algorithm for model fitting. The subroutine ADVAN11 TRANS4 in PREDPP was chosen. [INLINE:1] In which, Y was the measured concentration and F was the corresponding predicted concentration. ε1, ε2, ε3 were the residual errors which obey the normal distribution with mean of zero and variances of [INSIDE:1]. The code 1, 2 and 3 represented HPLC, GCMS and HPLCFLU. Stepwise Covariate Modeling The stepwise covariate modeling tool of PsN [7] implements Forward Selection and Backward Elimination of covariates to a model. In short, one model for each relevant parameterrelationship was tested in a univariate manner. The relationship of continuous covariates such as age, bodyweight was was: [INLINE:2] where P j was the model predicted value of a pharmacokinetic parameter P in the jth patient for a given covariate valueCovj. represented a scaling factor for the influence of that covariate. Cov j /Cov m was the normalized transformation for Covj where Covm was the median of covariate. TVP represented the typical parameter value. The relationship of categorical variates such as sex was [INLINE:3] where Covj was the numeric index value of the covariate, the θcov represented a multiplicative factor for the influence of that covariate. For example, if the θcov is negative, the effect was a decrease in the typical value, and an increase if the was θcov positive on the other hand. The rest codes were the same as the corresponding one in the continuous expression. The covariates selected by PsN [7] were based on the maximum of drop of objective function value. In first step, the model that gives the most drop of objective value is retained and taken forward to the next step. However, we added the criteria that the interindividual variabilities and residual variabilities should decrease. After a forward modeling run finished, we selected the qualified models whose drop of objective function valuewas larger than 6.64 (a = 0.01, c2, df = 1) and made a comparison. Only the model which gives the most decrease in interindividual variabilities could be taken forward to the next step. The forward selection step stopped when there were not any increased interindividual variabilities even a forward model give the qualified drop of objective function value which was larger than 6.64. An increase in the objective function valueof at least 7.87 (α = 0.005, χ2 , df = 1) was used as a criterion for retaining relationship during the backward elimination. The final population model was the one which contained all significant covariate after backward elimination process. Model Evaluation The shrinkage value was calculated in the final model using PsN. [7] The final model was evaluated by bootstrap and visual predictive check (VPC) to check its accuracy and p robustness. VPC were executed using PerlspeakNONMEM (PsN 3.1.0, Uppsala University, Uppsala, Sweden) under the environment of Perl language (ActiveState Software Inc.). Xpose [8] 4.1.0 (Uppsala University, Sweden) was used for data visualization under the environment of the R [9] 2.9.0 (The R Development Core Team). A total of 1000 replicates of the original dataset were simulated using the final model to generate the expected concentrations and 90% prediction interval. The percentile of the observations was plotted with the 90% prediction interval. Those plots were separated by four hospitals. Bootstrap which was internal evaluation assessed the model reliability by the 95% confidence interval. Five hundred bootstraps were executed using PD × 3.1 (version for trial, Icon developmental solutions, Hanover, MD, USA) and the result was reported in the form of 95% CI and the bias (%) between the median and the final value. Results Base Model The minimal objective function value (OFV) was  1485.73 when the 2compartment was adopted, and  2585.06 of 3compartment, respectively. The 3compartment model which was parameterized in terms of the elimination clearance (CL), intercompartmental clearances (Q2, Q3), the volume of central compartment (V1), the shallow peripheral compartment (V2) and the deep peripheral compartment (V3) was selected as the base model according to the comparison as well as the suggestion from the correlated references. [1] The results of base model were displayed in [Table 2]. The interindividual variabilities of V2 and V3 were not considered into the base model because the parameter was near its boundary according the NONMEM report. The largest interindividual variability among parameters was 72.2% (Q3), and the least one was 30.9% (CL). As shown in the [Table 2], the residual variability of three measuring instruments was different in which HPLCUV of 13.2% was the smallest and the most precise.{Table 2} Final Population Model The expression of final model was expressed as follow: [INLINE:4] After stepwise covariate modeling process, covariates which remained significant in the final population model were the body weight on Q3, and the age, sex on V1. The final model had a decrease in OFV of 58.95 points compared with base model. The interindividual variability decreased from 30.9% to 30.5% for CL, from 41.0% to 35.6% for V1, from 44.2% to 43.7% for Q2, from 72.2% to 66.9% for Q3. The final parameter estimates were presented in [Table 3].{Table 3} The whole process of establishing the final model including stepwise forward addition and backward elimination was displayed in [Table 4]. None was excluded from the final model after the backward elimination because the minimum increase of OFV was 21.19 which was larger than 7.87.{Table 4} The final model indicated that covariate of body weight had a positive affect on Q3, instead of CL which was reported by Schuttler. [1] The covariate bodyweight was excluded during the forward selection because it made the interindividual variabilities an increase from 41.0 to 41.6% for V1, from 44.2 to 44.4% for Q2 and from 72.2 to 72.5% for Q3 although a decrease from 30.9 to 26.7% for CL. V1 in males were higher than those in females at 35.2%. The coefficients of variation of HPLCUV, GCMS and HPLCFLU were 13.3%, 16.9% and 24.2% which were square roots of the variances 0.0176, 0.0285 and 0.0590, respectively, in the final model. Model Evaluation The weighted residuals were homogeneously distributed over individuals [Figure 1]. The estimates of shrinkage for CL, V1, Q2, Q3, were 8.83%, 8.92%, 15.15%, and 21.34%, respectively.{Figure 1} Four hundred bootstraps were minimized successfully from 500 runs. The final model parameter estimates were within ± 3.39% compared with bootstrap median. Parameter estimates were within their 95% confidence interval which was displayed in [Table 3]. The percentiles of the observation were plotted with the corresponding percentiles of the prediction s over the whole time courses separated by hospitals are shown in [Figure 2]. Because the sampling time was not regular, a small part of the percentile line of observations were located outside of the 95 percentile predictive interval of simulations. Most part of percentile lines of observations were within the predictive interval of simulations.{Figure 2} Discussion A multiplicative equation instead of a linear equation was applied to describe the relationships between the continuous covariates and parameters because of the large size of data, covariate age, and bodyweight. The clearance (Q3) was estimated to be most influenced by body weight obviously, which was the different with other published literature. [10],[11],[12],[13] Some of sampling data that we reanalyzed have been analyzed in the published literatures. [11],[12],[13] But those literatures reported that the residual variability was described by exponential model and the first order estimation was used. It was proven to be not a proper choice for population analysis because of the Taylor expansion. [2] Though the model including the affect of bodyweight on clearance (CL) had a significant drop on OFV, the interindividual variability of V1, Q2, and Q3 increased. After comparison with the model including the bodyweight affect on Q3, we abandoned the covariate bodyweight on CL. The normalized transformation BW/60 could be put into practise simply. The body weight had an increasing affect on Q3, which was confirmed through the published literature. [1],[13] Although both of the two studies discovered the affect of age on V1, this is a limitation that the patients' age ranged from 19 to 77 in our study, when compared to those ranged from 2 to 88 in Schuttler [1] study. The phenomenon mentioned by Schuttler [1] that the model resulted in a underestimation (observed > predicted) when concentration >8 μg × ml 1 still appeared in our analysis, for a high concentration caused a reduced blood flow in liver, and a decreased clearance as a chain reaction. And also, to be mixed instantaneously was a little difficult for high concentrations. [14] Therefore, high concentrations were still unable to predict ideal values. Maybe propofol at high concentration may follow nonlinear pharmacokinetics. [15],[16] The difference of the precision among the three measuring instruments was discovered during the NONMEM analysis when including the instrument as an indicator variable for residual variability. The limitation of this study, when compared to the one by Schuttler et al. is that no children and elderly patients were included in present study. However, our study represents the Chinese population. The data collected from four hospitals which were widely located in main land of China are more representative than any paper reported before. [10],[11],[12],[13],[17] References


