The aim of this study was to investigate the independent effect of remifentanil on the approximate entropy (ApEn) in frontoparietal montages. The authors investigated which montages were relevant to assess the remifentanil effect on the electroencephalogram. Spectral edge frequency and the canonical univariate parameter were used as comparators.

Twenty-eight healthy volunteers were enrolled. With recording of the electroencephalogram at the F3, F4, Cz, P3, and P4 montages, remifentanil was infused at the rate of 1-8 mug . kg . min for 15-20 min. The relation between remifentanil concentration and the electroencephalographic parameters were tested by Spearman correlation. Signal-to-noise ratio, artifact robustness, coefficient of variation of the median baseline and maximal electroencephalographic effects, and ratio of average maximal electroencephalographic effect to interindividual baseline variability were measured. The performance of ApEn as an index of remifentanil effect site concentrations was tested by prediction probability.

Approximate entropy showed significant correlation (R = -0.6465, P < 0.0001) with remifentanil concentration. It provided comparable signal-to-noise ratio, artifact robustness, and ratio of average maximal electroencephalographic effect to interindividual baseline variability to 95% spectral edge frequency. The coefficients of variation of the median baseline and maximal electroencephalo graphic effects were smallest in ApEn. Parietal montages showed higher ratios of average maximal electroencephalographic effect to interindividual baseline variability for all electroencephalographic parameters and lower coefficients of variation of the baseline values for ApEn and 95% spectral edge frequency than frontal montages. The prediction probability of ApEn was 0.7730.

Approximate entropy derived from a parietal montage is appropriate for the assessment of the remifentanil effect on the electroencephalogram.

THE electroencephalogram is a useful and sensitive surrogate measure of opioid effect that permits identification of both drug potency and the time course of blood–effect site equilibration.1–3The 95% spectral edge frequency (SEF^{95}) and canonical univariate parameter (CUP) derived from frontoparietal montages are univariate descriptors of the electroencephalogram that have been used to relate the electroencephalographic effect to opioid drug concentration.4,5Approximate entropy (ApEn), which quantifies the regularity of data time series, showed better baseline stability as a measure of the arousal state of the central nervous system than other univariate descriptors.6,7This should improve the predictive ability of this electroencephalographic metric to predict the central nervous system effects of an anesthetic drug.

Approximate entropy derived from the electroencephalographic signals of prefrontal montages has been used to measure the effect of hypnotics on the electroencephalogram and the pharmacodynamic interaction between propofol and remifentanil.8–10However, there is no report regarding to the independent opioid effect on the electroencephalographic ApEn. Two functional magnetic resonance imaging studies showed that the insular cortices were most significantly modulated by remifentanil.11,12For these reasons, it seems to be relevant to measure ApEn at frontoparietal montages rather than prefrontal montages to assess the remifentanil effect on the electroencephalogram.

The primary objective of this study was to investigate whether ApEn derived from the electroencephalographic signals of frontoparietal montages (F3, F4, Cz, P3, and P4; international 10–20 system) were well correlated with the concentration of remifentanil in healthy human volunteers. The secondary objective was to compare the signal-to-noise ratio, artifact robustness, and the ratio of average maximal electroencephalographic effect to interindividual baseline variability of ApEn, which were reported as useful indicators for the electroencephalographic parameter selection, with those of SEF^{95}and CUP.7We also investigated the most relevant montages to assess the electroencephalographic effect of remifentanil on the basis of those selection criteria of electroencephalographic parameters among five frontoparietal montages (F3, F4, Cz, P3, and P4) and compared the performance of approximate entropy as an index of remifentanil effect site concentrations with SEF^{95}and CUP.

## Materials and Methods

### Volunteer Recruitment and Instrumentation

After obtaining the approval of the institutional review board (Asan Medical Center, Seoul, Korea) and written informed consent, 28 volunteers aged 20–79 yr who had no medical problems and abnormal laboratory test results were enrolled. The institutional review board agreed to muscle paralysis in volunteers given remifentanil in doses that may be too low to guarantee unconsciousness. All volunteers were clearly informed and agreed that they might be awake and unable to move or breathe spontaneously.

Intravenous and intraarterial accesses were established, and volunteers were monitored with electrocardiography, pulse oximetry, end-tidal carbon dioxide concentration, train-of-four, and invasive blood pressure measurement (Datex-Ohmeda S/5; Planar Systems, Inc., Beaverton, OR). The electroencephalographic activity of five monopolar channels (F3, F4, Cz, P3, and P4, referenced by A1 or A2) was recorded by qEEG-8 (LXE3208, Laxtha Inc., Daejeon, Korea). Baseline electroencephalographic activity was recorded for 5 min before the infusion of remifentanil. The electroencephalographic activity, during and after the infusion of remifentanil, was recorded continually up to 170 min after the beginning of remifentanil infusion.

### Drug Administration

The young volunteers (aged ≤ 40 yr, n = 9, male/female = 5/4) received remifentanil for 20 min at a fixed rate that was randomly selected out of 1, 2, 3, 4, 5, 6, 7, and 8 μg · kg^{−1}· min^{−1}.

The middle-aged or elderly volunteers (aged > 40 yr, n = 19, male/female = 9/10) received remifentanil at the rate of 3 μg · kg^{−1}· min^{−1}until the real-time SEF^{95}did not show any further change after it reached maximal suppression. Glycopyrrolate, 0.2 mg, and 4 mg ondansetron were intravenously administered before infusion of remifentanil to prevent bradycardia and nausea/vomiting, respectively. Muscle paralysis was achieved with intravenous injection of rocuronium (0.6 mg/kg) to prevent muscle rigidity. Each volunteer was preoxygenated with 100% oxygen and the lungs were manually ventilated with 100% oxygen *via* facemask, to maintain an end-tidal carbon dioxide concentration of 35–45 mmHg.

At the end of infusion, the muscle paralysis was reversed by intravenous injection of 15 mg pyridostigmine and 0.4 mg glycopyrrolate, and we confirmed that the train-of-four ratio was 90% or greater.

### Blood Sample Acquisition, Handling, and Processing

To prevent hydrolysis of remifentanil by nonspecific blood and tissue esterase,1360 μl citric acid, 50%, was added to the heparinized 5-ml plain tubes 1 day before the trial. Arterial blood samples (3 ml) were taken at preset intervals:

Every 30 s during the first 5 min, every 1 min during the second 5 min, and every 2 min during the third 10 min after the beginning of remifentanil infusion

Every 30 s during the first 5 min, every 1 min during the second 5 min, and every 2 min during the third 10 min after the termination of remifentanil infusion

In addition, 25, 30, 35, 40, 45, 50, 60, 70, 80, 90, 100, 120, 150, 180, 210, and 240 min after the end of remifentanil infusion

The blood samples were vigorously vortexed and stored at −70°C until assay. The concentrations of remifentanil in whole blood were determined by a specific liquid chromatography tandem mass spectrometry method, which was a modification of a previously published method.14The differences were liquid–liquid extraction with dichloromethane and use of alfentanil as an internal standard instead of D4-remifentanil. The lower limit of quantification of remifentanil was 0.1 ng/ml. The calibration curve was linear over the range of 0.1–72.9 ng/ml, with the coefficients of determination (*R* ^{2}) greater than 0.997 for all cases. Overall intraassay and interassay precision values were less than 11% and accuracy values, within 15% of the nominal value, respectively. For measuring samples out of range, a quality control sample, at a concentration of 300 ng/ml, was diluted with water to obtain concentrations falling within the calibration range. These dilution controls were analyzed 15 times within three analytical runs. The overall accuracy values were within 12% of the nominal values.

### Electroencephalographic Analysis

The electroencephalogram was recorded continuously with frontoparietal montages (F3, F4, Cz, P3, and P4). The sampling frequency of the analyzed channels was 256 Hz. The real-time SEF^{95}was obtained by averaging the values of five monopolar channels (F3, P3, F4, P4, and Cz) every 5 s. We used real-time SEF^{95}as a monitor to detect maximal suppression and recovery of electroencephalographic activity and to determine when the infusion of remifentanil should be terminated. To minimize artifacts due to volunteer movement or eye blink, the real-time SEF^{95}was obtained after preprocessing with a band pass filter over 4–30 Hz.

Unlike the real-time SEF^{95}, the raw electroencephalographic signal was filtered between 0.5 and 30 Hz for the off-line calculation of SEF^{95}, ApEn, and CUP used in this analysis. To calculate SEF^{95}and CUP, the raw electroencephalographic signal was divided into epochs of 10 s without overlap. For the calculation of ApEn, the length of epoch (*N* ) was 2,056. No smoothing technique was applied to the calculation of ApEn, SEF^{95}, and CUP. Serious artifacts were excluded by checking the maximum amplitude for each epoch; if the amplitude was greater than 200 μV, the epoch was excluded. The appropriateness of artifact rejection was manually confirmed. Artifact rejection and analysis of each electroencephalographic parameter was performed by a single, blinded, experienced analyst.

The following electroencephalographic parameters were calculated from each epoch:

For the calculation of ApEn, the number of previous values (

*m*) used to predict the subsequent values was 2, and a filtering level (*r*) was 10% of the SD of the amplitude values (see appendix).SEF

^{95}was the 95th percentile of the power distribution.CUP was calculated as reported.5For the calculation of CUP, the power spectrum from 0.5 to 30 Hz was divided into 10 frequency bins of 3 Hz each. The power in each bin was converted into a natural log, and each of the 10 bins was multiplied by a previously validated weighting factor for remifentanil.5The sum of the 10 weighted bins was the CUP.

### Correlation between Electroencephalographic Parameters and Measured Concentrations of Remifentanil

To calculate the correlation coefficients by Spearman correlation, we selected measured concentrations of remifentanil and three electroencephalographic parameter values within 60 min after the beginning of remifentanil infusion, which were relatively free of noises due to volunteer movement or eye blink. The time delay between remifentanil concentrations and three electroencephalographic parameters was within 10 s. To show the trends of changes in the electroencephalographic parameters, curves were generated using the coarse locally weighted scatterplot smoothing (LOWESS) function in Prism 4 for Windows (version 4.03; Graphpad Software Inc., San Diego, CA). This allowed fitting a curve without selecting a model and can be helpful when the data progresses monotonically.15

### Signal-to-noise Ratio, Artifact Robustness, and Ratio of Average Maximal Electroencephalographic Effect to Interindividual Baseline Variability

Before calculating these parameter values, the region showing maximal electroencephalographic effect was selected out of the individual electroencephalographic data by visual inspection. Then, the selected 5-min segment including maximal electroencephalographic effect was analyzed.

The ratio of average maximal electroencephalographic effect to interindividual baseline variability, which was originally stated as interindividual baseline stability, was calculated as the difference between median individual baseline value and median individual maximum effect averaged over all volunteers, divided by the SD of all individual median baseline values.7This ratio represents the factors by which the average maximal electroencephalographic effect exceeds interindividual baseline variability. In addition, we measured the coefficient of variation (CV) of the median baseline values of each electroencephalographic parameter.

We measured the artifact robustness of each electroencephalographic parameter by obtaining the ratio of signal-to-noise ratio with artifact rejection to that without artifact rejection.7Signal-to-noise ratio, which was stated as baseline variability in previous report,7was calculated as the difference between the median baseline value and the median maximum effect (signal) divided by the SD of the baseline values (noise).

The ratio of average maximal electroencephalographic effect to interindividual baseline variability, CV of the median baseline values, signal-to-noise ratio, artifact robustness of ApEn, SEF^{95}, and CUP were calculated for each montage used.

### Pharmacodynamic Modeling

For pharmacodynamic modeling by NONMEM® V level 1.1 (GloboMax LLC, Ellicott City, MD), 1,581 points of ApEn, SEF^{95}, and CUP values of the P4 montage were selected. Unlike previous data selection for the calculation of correlation between electroencephalographic parameters and measured concentrations of remifentanil, the selection criteria for pharmacodynamic modeling were the same as blood sampling interval for 40 min after the beginning of remifentanil infusion, and thereafter, every 5–10 min until 170 min after the beginning of remifentanil infusion. The number of electroencephalographic data per individual was 59 ± 6.

The relation between remifentanil effect site concentration and the electroencephalographic parameters was analyzed using a sigmoid Emax model:

where Effect is the electroencephalographic effect being measured (ApEn, SEF^{95}, or CUP), E0 is the baseline measurement when no drug is present, Emax is the maximum possible drug effect, Ce is the calculated effect site concentration of remifentanil, Ce^{50}is the effect site concentration associated with 50% maximal drug effect, and γ is the steepness of the concentration-*versus* -response relation. Model parameters were estimated using first-order estimation.

Interindividual random variability was modeled using a log-normal distribution:

where *P ^{i}* is the parameter value (E0, Emax, γ, or Ce

^{50}) in the

*i*th volunteer,

*P*is the typical value of the parameter in the population, and η is a random variable with a mean of 0 and a variance of ω

^{TV}^{2}. Interindividual random variability is reported as ω

^{2}, the variance of η in the log domain. To compare the distribution of ηs to the normal distribution, we calculated the correlation of the points in the normal probability plot, in which the null hypothesis of the test is that the data come from a normal distribution.16,17If we obtain a

*P*value greater than 0.05, we cannot reject and conclude that normality is a reasonable assumption.

Residual random variability was modeled using an additive error model. Residual random variability is reported as σ^{2}, the variance of ϵ.

Model parameters were evaluated by comparing the NONMEM® objective function values (minus twice log likelihood), with improvement of 3.84 in objective function value with the addition of a single parameter considered statistically significant.18

We used the median absolute residual and its percentage of pharmacodynamic range (E0 − Emax) of the final models to describe the quality of prediction for the population.

A nonparametric bootstrap analysis was performed as an internal model validation, using the software package Wings for NONMEM® (N. Holford, version 404, June 2003, Auckland, New Zealand).19This process was repeated 3,000 times. The final model parameter estimates were compared with the median parameter values and the 2.5–97.5 percentiles of the nonparametric bootstrap replicates of the final model.

### Statistics

The correlation between the remifentanil concentration and electroencephalographic parameters was tested by Spearman correlation (Prism 4 for Windows, version 4.03; Graphpad Software Inc.). We compared the ratio of average maximal electroencephalographic effect to interindividual baseline variability, signal-to-noise ratio, and artifact robustness of electroencephalographic parameters by Friedman repeated-measures analysis of variance on ranks or one-way repeated-measures analysis of variance as appropriate (SigmaStat for Windows, version 3.10; Systat Software Inc., Point Richmond, CA). All pairwise multiple comparisons (Tukey test) were performed.

The correlation between the calculated effect site concentrations of remifentanil and electroencephalographic parameters was tested by Spearman correlation.

A *P* value less than 0.05 was considered statistically significant.

Prediction probability (P^{K}) was assessed as described by Smith *et al.* 20We calculated P^{K}using the Somers’ d cross-tabulation statistic on SPSS (version 11; SPSS Inc., Chicago, IL), which was then transformed from the −1 to 1 scale of the Somers’ d to the 0 to 1 scale of P^{K}as P^{K}= 1 − (1 −|Somers’ d|)/2. The ApEn, SEF^{95}, and CUP were set as the dependent variable for the Somers’ d cross-tabulation statistic, and the calculated remifentanil effect site concentration was set as the independent variable. The prediction probability was calculated on the full set of measurements. The SE of P^{K}was calculated as (SE of Somers’ d)/2.

## Results

The characteristics of patients are described in table 1.

### Correlation between Electroencephalographic Parameters and Measured Concentrations of Remifentanil

Even though the real-time SEF^{95}did not include the power spectrum below 4 Hz, it showed close similarity to off-line SEF^{95}, except the degree of maximum suppression of electroencephalographic activity (fig. 1). Therefore, we could successfully determine whether SEF^{95}was maximally decreased and when to stop the remifentanil infusion.

All of the volunteers showed maximal suppression of electroencephalographic activity during remifentanil infusion. The mean (SD) values of ApEn, SEF^{95}, and CUP calculated from 5-min segments of electroencephalographic signal from the P4 montage (including maximal electroencephalographic effect) were 0.48 (0.05), 6.97 (1.60), and 3.24 (0.47) Hz, respectively. Their CVs were 11.0%, 23.0%, and 14.4%, respectively. Therefore, SEF^{95}showed higher variability of maximal electroencephalographic effect. The CVs of ApEn, SEF^{95}, and CUP at their maximal effect calculated from other montages showed similar results.

Remifentanil infusion led to electroencephalographic changes from the high-frequency, low-voltage pattern to the low-frequency, high-voltage pattern, culminating in the prominent increase of delta power.

Figure 2shows approximate entropy and waterfall plot derived from the raw electroencephalographic data of the P4 montage, and concentrations of remifentanil in volunteer 1. The time lag between peak remifentanil concentration and minimum ApEn was less than 2 min (time 25 and 27 min, respectively). ApEn recovered promptly when the remifentanil concentration decreased.

All of three electroencephalographic parameters showed statistically significant correlation with the concentrations of remifentanil (fig. 3). Compared with SEF^{95}and CUP, ApEn showed a similar degree of correlation with remifentanil concentration. It is noticeable that there were nine negative values of CUP in four volunteers, which were observed only during the recovery period. The median concentration of remifentanil corresponding to negative CUP was 1.7 (0.6, 6.8) ng/ml.

### Signal-to-noise Ratio, Artifact Robustness, and Ratio of Average Maximal Electroencephalographic Effect to Interindividual Baseline Variability

The normalized ratio of average maximal electroencephalographic effect to interindividual baseline variability in five montages after artifact rejection is shown in table 2. This normalized ratio was consistently higher in P4 than in F3, F4, Cz, and P3, irrespective of the electroencephalographic parameters. The ratio was highest in SEF^{95}and lowest in CUP. The actual values of the ratio of average maximal electroencephalographic effect to interindividual baseline variability of SEF^{95}in F3, F4, Cz, P3, and P4 were 3.15, 3.44, 3.98, 4.66, and 5.69, respectively. Values for ApEn were 3.18, 3.9, 4.23, 4.15, and 5.34, and values for CUP were 2.36, 2.48, 2.83, 3.00, and 3.26, respectively. The ratio of average maximal electroencephalographic effect to interindividual baseline variability before artifact rejection showed similar findings.

The CVs of the median baseline value of ApEn, SEF^{95}, and CUP after artifact rejection are shown in table 3. The CV of ApEn was consistently smaller than those of SEF^{95}and CUP for every montage. The CVs of ApEn and SEF^{95}derived from the P4 montage were consistently smaller than those from other montages. The CV of CUP was smallest in Cz and highest in the P4 montage.

The distribution of the median baseline values of ApEn, SEF^{95}, and CUP is shown in figure 4, which suggests that the between-subject variability of the median baseline value of each electroencephalographic parameter was smallest in P4 for ApEn and SEF^{95}.

The signal-to-noise ratios (median and 25th, 75th percentiles) of ApEn, SEF^{95}, and CUP in P4 before artifact rejection were 5.7 (2.5, 8.4), 5.1 (3.4, 7.0), and 3.9 (2.5, 6.2), respectively (*P* = 0.005). All pairwise multiple comparisons showed significant differences between SEF^{95}and CUP, and between ApEn and CUP (*P* < 0.05, respectively). The signal-to-noise ratios of ApEn, SEF^{95}, and CUP in P4 after artifact rejection were 10.9 (5.6, 16.0), 9.8 (7.9, 13.4), and 6.9 (4.2, 10.7), respectively (*P* < 0.05). All pairwise multiple comparisons showed significant differences between SEF^{95}and CUP (*P* < 0.05). These findings suggest that the signal-to-noise ratio of ApEn was comparable to SEF^{95}and better than CUP. Similar results were obtained in other montages.

The artifact robustness values of ApEn, SEF^{95}, and CUP in P4 were 1.7 (1.5, 2.1), 1.8 (1.6, 2.3), and 1.8 (1.6, 2.1), respectively, and did not show statistically significant difference.

### Pharmacodynamic Modeling

Spearman correlation coefficients (SE, 95% confidence interval) of ApEn, SEF^{95}, and CUP *versus* effect site concentrations of remifentanil were −0.7145 (0.0122, −0.7385 to −0.6887), −0.7621 (0.0105, −0.7826 to −0.7400), and 0.7088 (0.0134, 0.6826 to 0.7332), respectively. P^{K}values (SE, 95% confidence interval) of ApEn, SEF^{95}, and CUP were 0.7730 (0.0055, 0.7622 to 0.7834), 0.7880 (0.0045, 0.7792 to 0.7968), and 0.7600 (0.0045, 0.7492 to 0.7708), respectively. These findings suggested that the performance of SEF^{95}as an index of remifentanil effect site concentration was best and ApEn was comparable to SEF^{95}, with 5% level of significance.

The estimates of population pharmacodynamic parameters and their median values (2.5–97.5%) of the nonparametric bootstrap replicates of the final model for three electroencephalographic parameters are found in table 4. All of the ηs except those of Emax of SEF^{95}and CUP were normally distributed. k^{e0}, Ce^{50}, and γ of all electroencephalographic parameters and Emax in SEF^{95}showed high interindividual variability. The differences between structural parameter estimates and their median values of the nonparametric bootstrap replicates of the final models were small, whereas those between statistical parameter estimates between their median values of the nonparametric bootstrap replicates of the final models were high. In general, for sparse data and even with dense data, estimating the variance component is difficult, and this degree of bias may reflect this difficulty or may be due to the relatively small sample size.21

Age was a significant covariate for k^{e0}and Ce^{50}in all population models in this study. The objective function values were decreased by 22.32 for ApEn, 69.82 for SEF^{95}, and 88.30 for CUP, compared with basic models without covariate by adding two parameters (θ^{2}and θ^{4}in table 4) into the structural model for k^{e0}and Ce^{50}(*P* < 0.001, respectively).

Figure 5shows the relations of typical values of blood–brain equilibration half-time (t^{1/2}k^{e0}) and Ce^{50}*versus* age. Although the change of t^{1/2}k^{e0}of SEF^{95}was not as much as those of other electroencephalographic parameters, the incorporation of age into the final model as a covariate reduced the objective function value by 15.08. The *post hoc* Bayesian predicted values of ApEn, SEF^{95}, and CUP *versus* calculated effect site concentrations of remifentanil and the typical population effect site concentration–response curves of ApEn, SEF^{95}, and CUP are shown in figures 6 and 7, respectively.

Median absolute residuals and their percentage of the pharmacodynamic ranges (E0 − Emax) of the final models were 0.04, 13.5% for ApEn; 2.12 Hz, 13.0% for SEF^{95}; and 0.52, 25.1% for CUP, respectively.

## Discussion

Remifentanil infusion caused a decrease in ApEn, which reflects the increasing regularity and the decreasing randomness of the electroencephalographic activity. It has been known that ApEn has a strong correlation with the effects of desflurane, isoflurane, and propofol.22–24In this study, we demonstrated that ApEn was also well correlated with the remifentanil concentration as were SEF^{95}and CUP, and the performance of approximate entropy as an index of remifentanil effect site concentration was comparable to SEF^{95}, which was supported by good correlation and prediction probability of ApEn with remifentanil effect site concentrations.

The decrease in ApEn and SEF^{95}could be related to the large increase of the power of delta band and hence the increase of total power caused by remifentanil, as shown in figure 2. Although SEF^{95}, ApEn, and CUP showed similar correlation with remifentanil concentration and similar artifact robustness, the signal-to-noise ratio of ApEn was comparable to that of SEF^{95}but better than that of CUP, especially before artifact rejection. After artifact rejection, the signal-to-noise ratio of CUP was similar to that of ApEn but still worse than that of SEF^{95}. These results are inconsistent with those of Bruhn *et al.* , 7in which CUP showed better signal-to-noise ratio than SEF^{95}when propofol was used instead of remifentanil. Remifentanil caused a tremendous increase (up to 856.3 μV^{2}, 92.2% of total power) in the power of the electroencephalographic delta band and hence total power, but this was not the case for propofol.25SEF^{95}is a percentile of the total power, and the filtering level *r* of ApEn is calculated as a percentage of the SD of the amplitude values.6Therefore, the increase of the total power is reflected on the calculation of SEF^{95}and ApEn. However, the calculation of CUP does not take the total power into account. This may contribute to the reason that SEF^{95}and ApEn showed better signal-to-noise ratio, the normalized ratio of average maximal electroencephalographic effect to interindividual baseline variability, and prediction probability (P^{K}) than CUP in this study.

We observed some negative CUP values at low concentrations of remifentanil during the period of recovery. The CUP involves five negative coefficients in the frequency ranges of 9.5–18.0 and 21.5–27.0 Hz.5For the negative values of CUP, the power in these bands was large enough for their log transforms to be positive, and hence the products of the coefficients and log transforms of the power in these bands surpassed the sum of these values in the other frequency bands with positive coefficients.

The median baseline values of ApEn showed the narrowest distribution (fig. 4) and the lowest CV (table 3). Although the scale of ApEn, SEF^{95}, and CUP was not normalized, this lesser interindividual difference in the baseline values of ApEn implied the higher stability than SEF^{95}and CUP. This can be supported by the finding that the CV of CUP, which has a much smaller scale than SEF^{95}, was larger than the other two electroencephalographic parameters. The baseline values of an electroencephalographic parameter should be stable for pharmacodynamic modeling of centrally acting drugs.

The lower interindividual variability of electroencephalographic parameters at their maximal effects is as important as that of baseline values for pharmacodynamic modeling. In this study, the CV of SEF^{95}calculated from 5-min segments including maximal electroencephalographic effect was higher than those of ApEn and CUP. ApEn showed the lowest CV at its maximal effect.

It is noticeable that the ratio of average maximal electroencephalographic effect to interindividual baseline variability was higher in parietal montages (P3 and P4) than in frontal montages (F3 and F4) for all electroencephalographic parameters in this study. In addition, CVs of the baseline values of ApEn and SEF^{95}in parietal montages were consistently smaller than those in frontal montages. This trend can also be seen in figure 4. Functional magnetic resonance imaging studies of steady state infusion of remifentanil showed pain-related activity to be robust in the insular cortices.11,12The insular cortex lies deep to the brain’s lateral surface, within the lateral fissure which separates the temporal and inferior parietal cortices. μ-Opioid receptors have been shown to be present in the insular cortex as well as in other regions of the pain matrix, including the anterior cingulate cortex and medial thalamus.11Lorenz *et al.* 26demonstrated that remifentanil markedly increased regional cerebral blood flow in μ-opioid receptor–rich regions. On the basis of these findings, it can be speculated that remifentanil has more profound electroencephalographic effect on parietal montages than on frontal montages.

Of the parietal montages, P4 showed a higher ratio of average maximal electroencephalographic effect to interindividual baseline variability for all electroencephalographic parameters and lower CVs of the baseline values of ApEn and SEF^{95}. According to the investigation of Autret *et al.* ,27a clear right spectral dominance in the θ, α, and β spectral bands were observed in right-handed subjects at rest. Grabow *et al.* 28also reported that α activity in the medium and high range was significantly decreased in the left central and parietal areas in right-handed women during resting state. On the basis of these findings, we speculated that the difference between P3 and P4 might be related to the interhemispheric asymmetry in electroencephalographic activity, which was supported by the fact that all volunteers in this study were right-handed.

It is well known that the absolute value of ApEn is influenced by three parameters: the length of the epoch (*N* ), the number of previous values used for the prediction of the subsequent value (*m* ), and a filtering level (*r* ). In many studies, the parameter set of *N* = 1,024, *m* = 2, *r* = 0.2 (20% of the SD of the amplitude values) was commonly used.7,22In this study, the sampling frequency was 256 Hz, the time window was 10 s, *N* was 2,560, and *r* = 0.1. With *N* = 1,000–3,000 and *m* = 2, the average differences of ApEn between *r* = 0.1 and *r* = 0.2 were estimated as less than 2%.29Therefore, there seemed to be little difference in the absolute values of ApEn compared with other reports in which *r* was 0.2.

Age is a significant covariate for t^{1/2}k^{e0}and Ce^{50}, which is similar to a previous report.4With increasing age, t^{1/2}k^{e0}increased and Ce^{50}decreased. However, unlike the previous report,4the interindividual variabilities of t^{1/2}k^{e0}, Ce^{50}, and γ were high. The good predictive probability and correlation of the electroencephalographic parameters for remifentanil effect site concentrations as well as the small median absolute residual and its percentage of the pharmacodynamic range (E0 − Emax) suggest that the pharmacodynamic models in this study were optimal.

There were several issues to be considered as limitations of this study.

First, it might be assumed that the change of electroencephalographic parameters in this study was induced by a hypnotic effect of high-dose remifentanil. There have been no reports determining whether clinical and higher doses of remifentanil induce a similar change of electroencephalographic activity. In a preliminary study in which electroencephalographic activity was recorded for 10 min after intravenous bolus administration of 1 μg/kg remifentanil, ApEn, SEF^{95}, and CUP showed close similarities to the pattern of electroencephalographic change in this study (figs. 1 and 8). The subject in this preliminary study was conscious, and no other drugs were administered for 10 min of electroencephalographic recording. Although we could not observe whether the volunteers in this study were conscious or unconscious, it is hardly assumed that the electroencephalographic activity mainly reflected the hypnotic effect of high-dose remifentanil, because a subject who received 1 μg/kg remifentanil and was conscious showed a similar pattern of electroencephalographic activity.

Second, the values of the electroencephalographic parameters at maximal effects might be influenced by different rates and durations of remifentanil infusion assigned for each volunteer. However, it can be assumed that the effects of different rates and durations of remifentanil infusion were equally reflected on the three electroencephalographic parameters, and therefore, the comparison should not be biased.

Third, neuromuscular blockade reduces the value of the Bispectral Index or A-Line autoregressive index by reducing electromyographic activity.30–32These effects of neuromuscular blockade on the electroencephalographic activity might be negligible, because the duration of these effects was reported to be short (2.5 min).32

In summary, ApEn showed a significant correlation with remifentanil concentration. It yielded a comparable signal-to-noise ratio, artifact robustness, and ratio of average maximal electroencephalographic effect to interindividual baseline variability to SEF^{95}, but the baseline values of ApEn were more stable than those of SEF^{95}and CUP. The values of ApEn at its maximal effect were more stable than those of SEF^{95}. The performance of approximate entropy as an index of remifentanil effect site concentrations was comparable to that of SEF^{95}.

Of five frontoparietal montages (F3, F4, Cz, P3, and P4), parietal montages (P3 and P4) showed higher ratios of average maximal electroencephalographic effect to interindividual baseline variability for all electroencephalographic parameters and lower CVs of the baseline values than frontal montages (F3 and F4) for ApEn and SEF^{95}. The difference between P3 and P4 in these measurements might be related to the interhemispheric asymmetry in the electroencephalogram.

We conclude that ApEn derived from parietal montages is an appropriate univariate descriptor for the assessment of the electroencephalographic effect of remifentanil.

The authors thank Jung-Mi Choi, Ph.D., and Ki-Seong Kim, Ph.D. (Laxtha Inc., Daejon, Korea), for the analysis of the electroencephalograms; and Sook-Kyung Seo, M.P.H. (Research Associate, Asan Medical Center, Seoul, Korea), and Yoo-Mi Kim, M.P.H. (Research Associate, Korea Health Industry Development Institute, Seoul, Korea), for the preparation of data used in this study. The authors also thank Ae-Kyung Hwang, B.S. (Technician, Clinical Research Center, Asan Medical Center, Seoul, Korea), for the measurement of remifentanil concentration.

#### Appendix: Approximate Entropy

Approximate entropy (ApEn) quantifies the predictability of subsequent amplitude values of the signal based on the knowledge of the previous amplitude values present in the time series33:

The normal procedure to calculate ApEn is the following. First, we start with the only data that we have, the discrete time series of electroencephalogram, denoted by equation 1, where *T* is the sample period and *n* is the number of samples of the electroencephalogram. The delay embedding vectors as usual are denoted by equation 2:

Here, *L* is the number of sampling intervals between successive components of an embedding vector, and *j* is the number of sampling intervals between the first components of multiple successive vectors. Then, the correlation sum is defined by C^{i}^{m}(r):

where Θ is the Heaviside unit-step function and the norm “∥∥” defines the distance between two vectors, which is taken as the maximum distance between their components defined by equation 4. In this study, the length of the epoch (*N* ) was 2,560, the number of previous values used for the prediction of the subsequent value (*m* ) was 2, and a filtering level (*r* ) was 10% of the SD of the amplitude values. The summation in this formula counts the number of pairs of vectors *x* (*i* ) and *x* (*j* ) for which ∥*x* (*i* )−*x* (*j* )∥^{1}is less than the chosen distance *r* :

The parameter given by equation 5is a simple normalization factor:

Approximate entropy is then defined by equation 6, which can be considered as an approximation of the Kolmogorov-Sinai entropy33:

The electroencephalographic signals were processed with the following steps:

Step 1: A moving window of 10 s was applied to the five channels at the same time.

Step 2: The data inside the window were used for reconstruction of a phase space following the Takens34delay theorem.

Step 3: The Grassberger and Procaccia35algorithm was used for the point in the phase attractor to compute the correlation sum and then ApEn following the aforementioned algorithm.