Population Pharmacokinetics of Propofol: A Multicenter Study

We analyzed 4,112 concentrations of 270 individuals. Two-hundred fifty-six were patients undergoing surgery; 14 were volunteers (table 1). Propofol (Disoprivan or Diprivan; Zeneca Pharmaceuticals, Macclesfield, United Kingdom) was administered as a bolus or using continuous infusion, with the infusions computer-controlled in groups 2 and 4–8. The sampling period was in the range of 0.25–24 h. Propofol concentrations were measured from arterial (groups 1, 2, 3, and 6) and venous samples (groups 4, 5, and 7–9). Propofol concentrations were measured in whole blood (groups 1–8) and plasma (group 9) using high-pressure liquid chromatography (groups 1–6 and 9) and gas–liquid chromatography (groups 7 and 8) with fluoreometric or electrochemical detection. 28 

The propofol concentration data were analyzed with NONMEM (version V, double precision). 29NONMEM allows multiple nonlinear regression of population data simultaneously, which means that not only the mean kinetic parameters but also inter- and intraindividual variability can be estimated. In addition, it is possible to quantitate the influence of covariates such as body weight, age, and gender. Another advantage of the population approach is that the number of observations per individual can be kept relatively small.

Pharmacokinetics were assumed to be linear with two- or three-compartments and elimination from the central compartment. The elimination clearance (Cl¹), the intercompartmental clearances (Cl², Cl³), and the volumes of the central compartment (V¹), the shallow peripheral compartment (V²), and the deep peripheral compartment (V³) were chosen as pharmacokinetic parameters to be estimated. To investigate the effect of covariates, additional parameters were successively included in the model (see Regression Procedure).

One major advantage of NONMEM is that interindividual and intraindividual variability can be quantified. The interindividual variability describes the variance of a pharmacokinetic parameter among different subjects. We estimated the variability of all clearances and volumes using a log-normal model. This means for the i  th individual

in which θⁱis the individual value of the parameter θ, θis the mean population value of this parameter, and ηⁱis a random variable with mean zero and variance ω^η2. For the intraindividual variability that describes the residual errors resulting from assay errors, time-recording inaccuracy, model misspecification, and so forth, we used a constant coefficient of variation model:

in which c^ijis the j  th measured concentration of the i  th individual and cp^ijis the corresponding predicted concentration. Again, ε^ijis a random variable with mean zero and variance ς^ε2. NONMEM estimates the mean pharmacokinetic parameters of the population, the interindividual variances ω^η2, and the intraindividual variances ς^ε2, including estimates of the standard errors and correlation coefficients for all parameters.

The complete data set was randomly divided into two subsets containing 135 individuals each. The subjects of each subset were comparable with respect to age, weight, gender, sampling site, and administration mode. The first subset was used for the development of the model as described subsequently. The predictive accuracy of the model was then tested with the second subset. In a first step, individual Bayesian estimates of the pharmacokinetic parameters of each individual were obtained using a three-compartment model without any covariates. The estimated parameters were plotted independently against body weight, age, and gender to identify the influence of the covariates and the shape of the parameter–covariate relationships. Subsequently, we performed a population analysis of all data, beginning with a simple model without any covariates and successively incorporating additional parameters. The effects of covariates were tested for statistical significance using the NONMEM objective function (which is −2 · log-likelihood) and the standard errors of the additional parameters. An additional parameter was included in the model if the decrease of the objective function was at least 7.8 (P < 0.005) and the 95% confidence interval of the additional parameter (mean ± 2 · SE) did not include zero (null hypothesis value). In addition, the inter- and intraindividual variabilities should decrease as an additional covariate parameter explains the difference between individuals. To exclude covariate correlations, we tested whether deletion of any additional parameter from the full model resulted in a decreased goodness of fit. To estimate the accuracy of the model we calculated the weighted residual (WR) and the absolute weightedresidual (AWR) for each sample:

in which c^ijis the j  th measured concentration of the i  th individual and cp^ijdenotes the corresponding predicted value. The median population values of WR (median weighted residual, MWR) and AWR (median absolute weighted residual, MAWR) were used as overall measures for goodness of fit.

Finally, we calculated MWR and MAWR for the remaining subset of individuals who were not included during model development, using the estimated parameters of the full model. This gives additional information about the ability of the final model to predict propofol concentrations.

To illustrate the pharmacokinetic findings, various simulations were carried out. Using the estimated parameters we calculated the time for a 50% decrease in concentration after continuous infusion (context-sensitive half-time). 30To show the effect of age on dosing we computed the infusion rates necessary to maintain a defined concentration. The interindividual variability was illustrated by calculating the context-sensitive half-time for a population of 100 subjects whose pharmacokinetic parameters were log-normally distributed with means and variances as estimated for the full model. To demonstrate the influence of the administration mode (bolus vs.  infusion) we simulated the concentration course after a bolus dose using the kinetic parameters for bolus and infusion, respectively. All simulations were performed with software written by the authors.

The individual estimates revealed an influence of body weight and age on all clearances, V¹, and V²; V³was almost constant in all subjects. As an example, figure 1shows the individual estimates of Cl¹as a function of body weight. The shapes of the relationships suggested that body weight should not be incorporated into the model in a linear fashion but as a power function with a positive exponent smaller than one. V¹was almost constant in adults but decreased in children. If divided by the body weight, V¹showed a clear relationship with age, which could be described by a power function with negative exponent. The effect of age on Cl¹was a linear decrease for patients older than 60 yr. The predictive accuracy of the individual Bayesian estimates was quite high (MWR =−1.5%, MAWR = 9.6%;fig. 2).

In the subsequent population analysis, these effects were modeled by incorporating additional parameters. The results of this procedure are shown in table 2, in which −2LL  denotes the value of the objective function (−2 log-likelihood), describing the goodness of fit. As mentioned previously, a decrease of −2 log-likelihoods means an improvement of fit. Significant effects were retained in the subsequent regressions. The pharmacokinetic parameters of the final model are shown in table 3.

Initially, a simple two-compartment model was assumed, but the resulting fit was quite poor. A three-compartment model markedly improved the fit, because of the long sampling period in some groups (1, 4, and 5).

As suggested from the individual estimates, we found effects of body weight on Cl¹, Cl^2,Cl³, V¹, and V². The influence was best modeled by a power function with an exponent smaller than 1. As an example, table 2shows the results for a simple weight normalization of Cl¹(model 3) and the power function (model 4). This means that the weight-normalized parameter (parameter divided by body weight) increases with decreasing weight (e.g. , for children). V³did not vary with age and body weight. The elimination clearance decreased linearly in individuals older than 60 yr. The volume of the central compartment decreased with age if divided by body weight. This led to a worse fit if V¹was modeled weight-proportionally (model 9, table 2). Inclusion of age and weight as a power function, however, improved the model (model 10, table 2). No influence of gender could be found for the analyzed subjects.

An influence of different sampling sites was found only for Cl², which was smaller for venous samples; no other parameter was altered significantly.

Nearly all parameters with the exception of Cl¹and V³were found to be altered with bolus administration compared with infusion data. Whereas V¹, V², and Cl²were larger than after infusion, Cl³was decreased.

The estimates of all parameters and their standard errors are summarized in table 3. Fixing of any additional parameter to zero led to a significant decrease in goodness of fit (increase of −2 log-likelihood), indicating that all additional parameters were required. Calculation of the weighted residuals revealed median values of −3.4% (MWR) and 24.9% (MAWR) for the first subset. The prediction errors for the second subset calculated with the estimated kinetic parameters were similar (MWR =−0.4%, MAWR = 25.5%). Figure 3shows the predicted concentrations, as calculated with the parameters derived from the first subset, plotted against the measured concentrations of the second subset. The ratio of measured:predicted concentration was calculated for each sample and plotted against time for each individual (fig. 4).

We performed several simulations for five typical individuals (child, lean adult, average adult, obese adult, and elderly) using the estimated pharmacokinetic parameters of the full model (table 4). Figure 5shows that the propofol infusion rate maintains a propofol concentration of 1 μg/ml for 2 h. The total doses, including the loading dose, were 3.7 mg · kg⁻¹· h⁻¹for the child, 2.6 mg · kg⁻¹· h⁻¹for the lean adult, 2.3 mg · kg⁻¹· h⁻¹for the average adult, 1.9 mg · kg⁻¹· h⁻¹for the obese adult, and 1.5 mg · kg⁻¹· h⁻¹for the elderly individual. The context-sensitive half-times for these five individuals are depicted in figure 6. The half-times are nearly the same for the child and the adults but markedly increased for the 80-yr-old subject. Figure 7depicts the context-sensitive half-times for 100 individuals, calculated with kinetic parameters that were log-normally distributed with the mean values of a 30-yr-old adult with average weight (table 4) and variances as estimated for the full model (table 3). Figure 8shows the effect of the administration mode. The concentration course after a bolus dose of 100 mg propofol was calculated using the kinetic parameters obtained from bolus and infusion data, respectively. Use of the infusion kinetics leads to an overestimation of the concentration during the first 10 min and an underprediction during the following 4 h.

We analyzed a quite unhomogeneous population with different modes of administration (bolus dose and continuous infusion), different sampling sites (venous and arterial), and a wide range of ages and weights. Therefore we had to incorporate additional parameters to describe all effects of covariates on the pharmacokinetics of propofol. The final model was able to describe the pharmacokinetics of the population with sufficient precision, as indicated by the values of MWR and MAWR for both data subsets. A precision of about 25% is typical for pharmacokinetic models. 31–33The plot of predicted versus  measured concentrations (fig. 3), however, shows a good correlation for concentrations up to 8 μg/ml, but a lack of fit for higher concentrations in which the model underestimates the measured concentration. Consideration should be given to the fact that the model for intraindividual variability assumes that the error increases with increasing concentrations, but this error should be centered around zero, whereas we observed only a positive deviation (measured > predicted). This underestimation may indicate nonlinear pharmacokinetics of propofol, in the sense that the total body clearance decreases with increasing concentration. Nonlinear pharmacokinetics of propofol have been investigated previously, with controversial results. Coetzee et al.  31and Vuyk et al.  32suggested that propofol may have nonlinear kinetics; Bailey et al.  34and Schnider et al.  35did not find any indication of nonlinearity. It is known that propofol reduces liver blood flow, particularly at high concentrations such as are found shortly after bolus administration. 36The very high concentrations in our data were achieved with continuous infusion, which also may cause a reduced blood flow and therefore a reduction of clearance. One general problem with compartment models is that they assume instantaneous mixing in the central compartment, which is obviously a simplification. Major et al.  found considerable differences between venous and arterial samples during the first 60 s after administration of a propofol bolus dose, indicating that instantaneous mixing does not occur. 37Therefore, it is possible that incomplete mixing in case of high infusion rates causes unexpectedly high propofol concentrations.

Whereas there was only a slight effect of the sampling site, the mode of administration (bolus vs.  infusion) did significantly affect the pharmacokinetics (fig. 8). Similarly, Schnider et al.  reported an overestimation of the early concentrations after bolus administration, followed by an underprediction using kinetic parameters evaluated from infusion data. 35A possible reason for this phenomenon may be model misspecification, because the conventional compartment model assumes instantaneous mixing and does not consider recirculation effects. On the other hand, it must be taken into account that the sampling in bolus studies is quite different from that used in infusion studies, in which there are not so many samples in the very early time and therefore less information about the initial distribution process. At least the bolus data that were included in our analysis were characterized by a very long sampling time. Therefore, it is quite reasonable that Cl³was reduced compared with infusion pharmacokinetics, which means a slowed transfer back from the deep third compartment and in consequence higher concentrations in the terminal phase as shown in figure 8.

In addition, it should be considered that differences in the propofol assays may be a source of intraindividual error. All propofol concentrations were measured with assays based on the same method, 28but with some modifications. In groups 7 and 8, propofol was analyzed with gas–liquid chromatography rather than high-pressure liquid chromatography, which was used for all other data. Analysis of group 9 used propofol plasma concentrations; the propofol concentrations of the remaining groups were measured in whole blood. Fan et al.  did not find significant differences between propofol concentrations measured with high-pressure liquid chromatography and gas chromatography, respectively, but the plasma concentrations during infusions were higher than those from whole blood. 38 

The estimates of the pharmacokinetic parameters for an adult as revealed in this study are similar to those found by other investigators, 5,8–11,15with the exception of V¹, which was smaller in our analysis. The central volume is more difficult to determine than the clearance, because it depends on the mode of administration, the sampling site, and the number of compartments. The very first concentration values after the start of administration are essential for the consistent estimation of the central volume. Because we had only few data from the first minutes, and because these were mainly from bolus administration, there might be a model misspecification.

One major aim of the present study was to quantitate the effect of covariates on the pharmacokinetics of propofol. Body weight was obviously the covariate that influenced all parameters with the exception of V³. Interestingly, the influence of weight was best described by a power function; in most previously published models the pharmacokinetic parameters were weight-proportional. 5,6,21The combination of children and adults in our data may explain these results, because other authors analyzed more homogenous groups of only adults or children. The power function for weight may therefore describe not only the influence of body weight but also partly the effect of age. This is supported by the fact that for nearly all parameters for which the influence of body weight was modeled as a power function (Cl¹, Cl², Cl³, and V²), no additional parameters for children were necessary. All estimated exponents of the power functions were smaller than 1, which means that the corresponding parameters were higher for children if normalized for body weight, as reported by other authors. 18,20,21For the central volume of distribution (V¹), a power function for weight and age revealed the best results. This also means an increase of the weight-normalized V¹for children. In subjects older than 60 yr, we found a marked linear decrease of the elimination clearance Cl¹and a slight decrease of V¹, which was best described by a power function with a negative exponent. The reduction of the elimination clearance and V¹in elderly have also been observed in other studies. 17Although weight and age are correlated, inclusion of both covariates improved the fit significantly compared with inclusion of only weight or age. Particularly for V¹, simple weight normalization led to a worse fit, but the inclusion of weight and age improved the fit. In several studies on population pharmacokinetics, lean body mass was found to be a significant covariate for pharmacokinetics. 35,39Unfortunately, we could not model the effect of lean body mass, because we had not the heights of all subjects. Furthermore, a formula for lean body mass of children is not available. For those adults whose heights were known, the individual pharmacokinetic parameters did not correlate better with lean body mass than with body weight. The power function of weight, however, may reflect in part the influence of height, because the absolute dose for an obese adult, for example, is increased compared with an adult of average weight, but the weight-normalized dose is smaller than for an average adult (table 4). Generally, one has to consider that the estimated effects of age are valid only for that range investigated in our study (2–88 yr). For patients older than 90 yr, Cl¹would become almost zero or negative, and V¹increases toward infinity the younger the patient is (the effect of body weight on V¹, however, may compensate for this).

For clinical practice, the effects of body weight and age allow the dosing to be adjusted to the individual patient. The different infusion schemes necessary to maintain a propofol concentration of 1 μg/ml in three adults who are thin, of average weight, and obese, an 80-yr-old patient, and a 5-yr-old child of 20 kg body weight are plotted in figure 5. If normalized to weight, the total doses required for a period of 120 min are quite higher for children and smaller for elderly individuals. Because an obese adult needs less than an average adult, simple weight-normalization of the dose (as it is used for example in the common target-controlled infusion pumps) would lead to overdosing for such a patient. To evaluate the effect of covariates on recovery, we estimated the time required for a 50% decrease in propofol concentration after a constant infusion of variable length (fig. 6). This context-sensitive half-time is clearly prolonged in elderly individuals and nearly identical for children and the adults of different weights. It should be emphasized that this prolonged half-time for elderly individuals does occur, although the kinetic parameters were adjusted for age and weight. This means that the adjustment of pharmacokinetics can help to avoid misdosing, but differences with respect to the recovery cannot be overcome.

Even with inclusion of covariates, the interindividual variabilities remained relatively large, indicating a large variance of pharmacokinetics among patients. This leads to a broad range of context-sensitive half-times (fig. 7), which masks the small differences between children and adults but not the differences between adults and elderly. The relatively large interindividual error may be considered a limiting factor for target-controlled infusion and open-loop control of anesthesia, which are based on pharmacokinetic models. Clinical practice, however, has shown that effective and safe anesthesia can be achieved with infusion schemes based on pharmacokinetic models, because titration of the target concentration may help to overcome the problem of interindividual variability of pharmacokinetics and pharmacodynamics. 2–6The use of population-based pharmacokinetic parameters is likely to further improve the accuracy of target-controlled drug-delivery systems. Moreover, the field for target-controlled infusion may be broadened using our results for application in children and elderly patients.

Participants of the multicenter study: Ian D. Cockshott, Ph.D., Zeneca Pharmaceuticals, Macclesfield, United Kingdom; Peter S. Glass, M.D., Professor, Department of Anesthesiology, Duke University Medical Center, Durham, North Carolina; Jürgen Schüttler, M.D., Professor and Chairman, Department of Anesthesiology, Friedrich-Alexander-University of Erlangen-Nuremberg, Erlangen, Germany; Steven L. Shafer, M.D., Professor, Department of Anesthesiology, Stanford University School of Medicine, Palo Alto, California; and Martin White, Ph.D., Staff Anesthesiologist, Department of Anaesthesiology, Academisch Ziekenhuis Leiden, Leiden, The Netherlands.