### Introduction

_{e0}, which is incorporated into the TCI system with various compartmental models of propofol.

_{e0}from the separate pharmacodynamic (PD) model to the different PK models or infusion schemes is undesirable, and fails to predict the time course of the drug effect [3,4]. Struys et al. [5] also revealed that the different k

_{e0}for targeting of effect-site concentration of propofol predicted different time courses for the effect of propofol, as measured by the bispectral index. And Minto et al. demonstrated that the time of maximum effect site concentration could be useful to combine pharmacokinetics and pharmacodynamics [6].

_{e0}s with two different methods in the covariate-adjusted PK model, and compared them to the known PD model.

### Materials and Methods

_{95}. A propofol filled syringe was connected to the 3-channel extension tube with a one-way valve to prevent regurgitation of propofol into the intravenous fluid. The interval for pump control update and data saving was set to 10 seconds, which is the default setting for the STANPUMP. To ensure accurate administration of propofol, the patient was excluded from the study if any alarm on the TCI device was triggered.

_{2}partial pressure between 35 and 40 mmHg.

_{e0}by re-run of the STANPUMP. First, we executed the STANPUMP, inputting data from each subject, such as age, weight, height, and sex. Thus, the covariate-adjusted PK parameters were obtained, and specific external PK files were made for each patient. Each subject file was obtained independently for different k

_{e0}s. The STANPUMP with command line argument of external parameter files was subsequently used to obtain predicted effect site concentrations for LOR with different k

_{e0}. For calculation of effect site concentration, we ran the STANPUMP in real mode with the maximum infusion rate fixing to 1,200 ml/h. In order to obtain the value of k

_{e0}for PK-PD coupling, we used two methods for titration, and compared them with known k

_{e0}.

### Titration of k_{e0} from the link method of 'Concentration-Probability-Time' (Predicted effect site concentration-Probability of LOR-T_{1/2}k_{e0})

_{e0}derived from t

_{1/2}k

_{e0}, which is ln2/k

_{e0}, at which the effect-site concentration becomes half of the target plasma concentration with a certain probability of LOR. When we target a plasma concentration, the effect-site concentration rises slowly, and achieves the half value of the targeted plasma concentration at half-life of t

_{1/2}k

_{e0}, the three quarters (1/2 + 1/4) at twice of half-lives, and seven-eighths (1/2 + 1/4 + 1/8) at triple of half-lives (Fig. 1). As we targeted 5.4, 8.1, and 10.8 µg/ml of plasma concentration in each group, the effect-site concentrations will be 2.7, 4.05, and 5.4 µg/ml at t

_{1/2}k

_{e0}, and 4.05, 6.075, and 8.1 µg/ml at two t

_{1/2}k

_{e0}, and 4.425, 7.0875, and 9.45 at triple t

_{1/2}k

_{e0}.

_{e0}s (ranging 0.2-0.6 with 0.05 intervals). Each analysis proceeded separately, and probabilities of 0.1-0.99 at 0.1-0.5 intervals were attained. Probabilities of LOR at effect-site concentrations that were half, three quarters, or seven-eighths of the target plasma concentration were obtained from probit regression analysis. The link of times to the probability of LOR in each group was obtained from the probit regression analysis curve. These regression curves were used for the link of the 'probability' to 'time' (one, two, and three times of the t

_{1/2}k

_{e0}). Times associated with a given probability of a certain effect-site concentration of the target concentrations were then matched to t

_{1/2}k

_{e0}in each group. If the given effect site concentrations were the value of the 3/4 or 7/8 target plasma concentration, the associated times were divided by 2 or 3, and the k

_{e0}of each group was calculated from t

_{1/2}k

_{e0}(= ln2/k

_{e0}).

_{e0}changed, the k

_{e0}that we inputted and the calculated k

_{e0}from this link of 'concentration-probability-time' showed a discrepancy. Therefore, we sought to determine a k

_{e0}value that could minimize the total discrepancy (TD) between the inputted k

_{e0}and the calculated k

_{e0}. Total discrepancy for each k

_{e0}was the summation of squared differences of the applied k

_{e0}, and the calculated k

_{e0}for a certain probability of the given effect site concentration in each group, and was expressed as follows:

_{e0}was the inputted k

_{e0}for the regression curve of the probability and effect-site concentration, and C

_{ke0-ij}is the calculated k

_{e0}of the effect-site concentration at i times of t

_{1/2}k

_{e0}in the j

^{th}group for the link of time-concentration-probability; and N is the number of the available calculations used for each k

_{e0}. The k

_{e0}for minimal TD was calculated by the nonlinear regression method with curve fitting of a polynominal quadratic equation (Sigmaplot 2001®, 7.0 edition, SPSS Inc.). The following equation was used:

_{e0}+ A*k

_{e0}

^{2}

_{e0}.

### Titration of k_{e0} for the minimal discrepancy between the median effect site concentrations of each group

_{e0}s (ranging 0.2-0.6 with 0.05 intervals) that could minimize discrepancy between the groups. The predicted effect site concentration was obtained by a dry run of the STANPUMP with a previously described patient specific external PK file. Total discrepancies (TD) for each k

_{e0}were obtained using the following equation:

_{e0}) = [(C

_{e1}- C

_{e2})

^{2}+ (C

_{e2}- C

_{e3})

^{2}+ (C

_{e3}- C

_{e1})

^{2}]

^{1/2}

_{e1}, C

_{e2}, and C

_{e3}were the median predicted effect-site concentrations for LOR of the 5.4, 8.1, and 10.8 µg/ml targeted groups. The k

_{e0}for minimal TD was calculated using the nonlinear regression method described above.

### Comparison with Schnider's PD model

_{e0}s obtained from our two analytical methods were compared with Schnider's pharmacodynamics [7]. Using a previously described simulation of the STANPUMP, the predicted effect site concentrations for each subject (n = 90) from these three k

_{e0}were obtained all over again. We compared mean effect site concentrations for LOR, and also found effect site concentrations of propofol that could represent LOR in 50% (C

_{e50}) and 95% (C

_{e95}) of subjects for each k

_{e0}s. The times to peak effect of the TCI system for these k

_{e0}s were furthermore calculated using the STANPUMP.

### Results

_{e0}(0.4/min) in patients who received propofol to 8.1 µg/ml of the target plasma concentration is shown in Fig. 3. Calculated k

_{e0}s (C

_{ke0}) for a differently inputted k

_{e0}(I

_{ke0}) and the probabilities (P

_{LOR}) of LOR at given effect site concentrations of 1/2, 3/4, and 7/8 of the target plasma concentration (C

_{p}) in each group are listed in Table 4. Because the effect site concentration of highest probability (P

_{LOR}= 0.99) was lower than predicted in group II and III, times to the predicted effect site concentration could not be calculated when we applied k

_{e0}for 0.2 and 0.25/min. Likewise the C

_{ke0}could not be calculated when the predicted concentration was lower than 1% of probability or higher than 100% of probability. These unavailable data were expressed as 'NA' in Table 4. TD of the inputted k

_{e0}and the calculated k

_{e0}for different k

_{e0}is shown in Fig. 4. Coefficients ± SE for the regression curve were 0.0310 ± 0.0043 for y0, -0.158 ± 0.0199 for A, and 0.2145 ± 0.0220 for B (R

^{2}= 0.9906, P < 0.001), respectively. The k

_{e0}for the minimal TD was 0.3692/min. TD of the median predicted effect site concentration for different k

_{e0}is shown in Fig. 5. The coefficients ± SE for the regression curve were 2.6624 ± 0.1750 for y0, -9.4815 ± 0.9360 for A, and 12.5145 ± 1.1584 for B (R

^{2}= 0.9568, P < 0.001), respectively. The k

_{e0}for the minimal TD was 0.3788/min.

_{e0}. Predicted effect site concentrations of LOR in 50% and 95% of subjects for three different k

_{e0}s are shown in Table 5. Time to peak effect from Schnider' PD was nearly identical with that of our results.

### Discussion

_{e0}of propofol for the optimal link of pharmacodynamics to a specific PK model for the TCI. This method of link between 'Concentration-Probability-Time' could provide the optimal k

_{e0}for the PK-PD model of propofol. A similar result was also obtained from the method for the minimal discrepancy between the median effect site concentrations; however, our results were lower than the previously published value of k

_{e0}.

_{e0}of propofol was 0.316/min using the 'connect-the dots' model of plasma concentration, and 0.456/min using the covariate-adjusted PK set. Results of this study were different from those of Schnider's k

_{e0}, and the calculated effect-site concentration of LOR from Schnider's k

_{e0}was significantly higher than the effect-site concentration from our results, and the times to peak effect was slightly longer. The reasons for these differences could be attributed to the following: First, monitoring of the central nervous system is a continuous measure of the drug effect of propofol. However, our study used LOR as the primary measure of the time course of the drug effect. Even though this measurement is useful in routine clinical settings, it required 10 second intervals. Therefore, it could be possible that some subjects could have lost responsiveness prior to assessment of the pharmacodynamic profile. As a result, the regression curve for 'concentration-probability' could be shifted to the right side; however, the regression curve for 'probability-time' also shifted to the right side. These consequences would be reflected in the influence on the final outcome of the k

_{e0}. Second, the influence of gender on pharmacokinetics and pharmacodynamics could be considered as a significant cause for the difference of k

_{e0}. Gan et al. [9] reported that gender proved to be a highly significant independent predictor for recovery time, and that women woke significantly faster than men. All subjects in our study were female. If gender differences in the sensitivity of propofol at the effect site exist, the k

_{e0}could be different. Thus, gender might be considered as one of the important variables in PD studies of propofol, even though the gender difference with regard to pharmacokinetics could not be completely excluded.

_{e0}by about 0.5 µg/ml. Similarly, the C

_{e50}and C

_{e95}from our results appeared to be different from that of Schnider's k

_{e0}; however, these differences are believed to originate from the different value of k

_{e0}.

_{p50}and C

_{p95}of propofol for loss of eye reflexes were 2.07 and 2.78 µg/ml and for loss of consciousness were 3.40, 4.34 µg/ml. Kazama et al. [11] also found that the plasma concentration for loss of response to verbal command in 50% and 95% were 4.4 and 7.8 µg/ml. In a study of the drug interaction of propofol and fentanyl, Smith et al. [12] showed that C

_{p50}and C

_{p95}for propofol alone were 3.3 and 5.4 µg/ml. The differing results of these concentrations would also be due to differences in the study population, methodology, and PK models. A post-hoc power analysis conducted for determination of power revealed that total sample sizes of 90 and 90 achieve 93.1% power for detection of a difference of -0.51 between the null hypothesis stating that both means are 4.57 and the alternative hypothesis stating that the mean of effect-site concentration from 0.456/min of k

_{e0}is 5.08, with estimated group standard deviations of 0.84 and 0.83, and with a significance level (alpha) of 0.01, using a two-sided two-sample t-test.

_{e0}for propofol in the conventional three-compartment model of Marsh et al. [14], and found that the value of k

_{e0}was 0.80/min. This study compared the three infusion patterns without using the TCI system, and the methodology was quite similar to the second method used in this study. Our previous research [15] also confirmed that the k

_{e0}of propofol was 0.77/min for the minimal difference of the median effect site concentration in the PK model of Gepts et al. [16].

_{e0}in each patient. In the simulation mode of the STANPUMP, initial maximum flow rate was higher than in the real mode (1,200 ml/h), and the amount of propofol until LOR was different from the actual amount administrated during the study. Therefore, effect-site concentrations were calculated differently. For example, if we simulate the predicted effect site concentration of one patient (e.g. female, age 34 years, weight 55 kg, height 150 cm, k

_{e0}0.4/min) targeted to 10.8 µg/ml of plasma concentration, and time to LOR is 80 sec, the pump speed is 1,798 ml/h during the first 10 sec, and then decreases to 259 ml/h, and the predicted effect site concentration is 4.25 µg/ml, and 98 mg of propofol is infused at LOR in simulation mode. However if we run in real mode by dry run, the predicted effect site concentration will be 4.09 µg/ml at LOR. This overestimation of the concentration will shift the 'concentration-probability' curve to the right side. Eventually the t

_{1/2}k

_{e0}decreases, and the calculated k

_{e0}increases.

_{e0}plays an important role in the TCI system. When we target the plasma concentration, the time course of the effect site concentration is the predicted convolution of the concentration of plasma over time for k

_{e0}e

^{-ke0t}, with the disposition function of the effect site [17,18]. If inadequate values of k

_{e0}were applied, the effect site concentrations would be predicted as either higher or lower than the 'real' concentration of the effect site. However, this could occasionally be just a passive reference guideline on the time course of the effect of the drug, because even though we apply a higher value of k

_{e0}, if we wait for a longer period of time (4-5 times of t

_{1/2}k

_{e0}for the smallest possible k

_{e0}), the plasma and the effect site concentration will reach equilibrium in the end. However, when we target the effect site concentration, k

_{e0}plays a more important role by determining the amount of drug rapidly achieving the targeted effect site concentration of the drug. If we applied a lower value than the 'real' k

_{e0}, more amount of drug would be administrated; hence, overshooting the effect of the drug could occur, and the likelihood of side effects would increase. The computer simulation shown in Table 6 demonstrates the different doses and patterns of infusion of propofol targeted to 5.4 µg/ml of the effect site concentration when a different k

_{e0}is applied during TCI. Initial bolus dose for rapid achievement of the targeted effect site concentration increased as we applied smaller values of k

_{e0}. Therefore, titration of the optimal k

_{e0}for the adequate link of pharmacodynamics and pharmacokinetics during TCI is essential.

_{e0}for any population could be easily calculated. Moreover, the first method could be used for investigation of k

_{e0}for a wide range of possibilities, and for the effect site concentration for various levels of sedation during the process of analysis. However, in order to confirm the validity of the k

_{e0}from this study, we should assess the TCI of effect site targeting with the k

_{e0}under monitoring of the central nervous system. Doufas et al. [19] tested the TCI of propofol with the PK model of Schnider with 0.456/min of k

_{e0}for the targeting of the effect site concentration, and demonstrated the validity and stability of this constant during mild to moderate sedation.

_{e0}of propofol. Optimal k

_{e0}should be obtained for the proper link of pharmacokinetics and pharmacodynamics during TCI. Adequate k

_{e0}for a specific PK model will predict an accurate time course of concentration, and will be used for better control of the effect site concentration during targeting of the effect site.