BJA Advance Access published online on August 5, 2007
British Journal of Anaesthesia, doi:10.1093/bja/aem212
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Estimation of the plasma–effect-site equilibration rate constant (ke0) of rocuronium by the time of maximum effect: a comparison with non-parametric and parametric approaches
Departamento de Anestesiología, Facultad de Medicina, Hospital Clínico U.C., Pontificia Universidad Católica de Chile, PO Box 114-D, Marcoleta 367, Santiago, Chile
* Corresponding author. E-mail: licorti{at}med.puc.cl
Accepted for publication June 14, 2007.
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Abstract |
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Background: The first order plasma–effect-site equilibration rate constant (ke0) links the pharmacokinetics (PK) and pharmacodynamics (PD) of a given drug. For the calculation of the ke0, one method uses a single point of the response curve corresponding to the time to peak effect of a drug (tpeak); however, it has not been validated. This study compares the ke0 calculated with the method of tpeak and the ke0 calculated with traditional non-parametric and parametric methods.
Methods: Fifteen adult patients receiving total intravenous anaesthesia (TIVA) were studied. All patients were monitored with an NMT Monitor 221 (GE Healthcare, Helsinki, Finland) to obtain the evoked compound EMG of the adductor pollicis to a train-of-four stimuli at 10 s intervals. During TIVA, rocuronium 0.15 mg kg–1 was given i.v. as a bolus, and the neuromuscular response was recorded until recovery from block. Using the tpeak and the complete response curve, ke0 of rocuronium was calculated with the three methods using the predicted plasma concentrations of rocuronium from a PK model. Values of ke0 are median (range).
Results: The ke0s obtained were 0.19 min–1 (0.09–0.72) with the ‘tpeak’ method, 0.20 min–1 (0.14–0.44) with the non-parametric method, and 0.19 min–1 (0.11–0.38) [typical value (range)] with the parametric method (NS).
Conclusions: If the tpeak can be adequately estimated from the data, the ‘tpeak method’ is a valid alternative to traditional methods to calculate the ke0.
Keywords: neuromuscular block, rocuronium; pharmacokinetics; pharmacology, rocuronium
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Introduction |
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The pharmacodynamics (PD) of a drug can be studied during non-steady-state conditions through the application of an effect-compartment model.1 For this, the first-order plasma–effect-site equilibration rate constant (ke0) needs to be estimated and incorporated in the pharmacokinetic (PK) model. The traditional approaches to calculate the ke0 are the parametric or sequential PK–PD method developed by Hull and colleagues,2 and Sheiner and colleagues1 and the non-parametric PD modelling also developed by the group of Sheiner and colleagues.3 4 The disadvantage of these methods is that a wide range of drug effect, starting at baseline, achieving a maximum effect, and then returning to the baseline state is needed.5 This very often results in an ethically questionable situation or is impossible to obtain in the clinical setting.
An alternative method to calculate the ke0 is based on the time to maximum effect (tpeak) after a bolus dose.6 7 This concept, introduced by Shafer and Gregg,8 has the advantage that it does not require the complete effect curve. However, it has not been validated by the traditional methods.
Thus, the objectives of this study are: (i) to compare the ke0 of rocuronium estimated with the tpeak method with those obtained by the traditional methods and (ii) to determine which percentage of the complete response curve is the minimum needed to calculate the ke0 accurately with the traditional methods.
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Methods |
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After institutional ethics committee approval (Facultad de Medicina, Pontificia Universidad Católica de Chile, Santiago, Chile) and obtaining informed consent, 15 adult patients, undergoing surgery under general anaesthesia were studied. All were ASA physical status I, did not receive premedication, and were within ±20% of the ideal body weight for height. Exclusion criteria included pregnancy, chronic, or acute (within the last 48 h) intake of any drug known to interact with non-depolarizing neuromuscular blockers and any known adverse reaction to the study drugs. In the operating room, routine non-invasive monitoring of arterial pressure, ECG, and pulse oximetry were initiated. Anaesthesia was induced with fentanyl 3–5 µg kg–1 and propofol 2 mg kg–1, and tracheal intubation was accomplished without neuromuscular blocking drugs. Anaesthesia was maintained with propofol 120 µg kg–1 min–1 without inhaled agents and E'CO2 was kept between 30 and 35 mm Hg. Before the start of surgery, neuromuscular block monitoring was started on the arm contra-lateral to the i.v. line using the evoked compound EMG of the adductor pollicis to a train-of-four (TOF) stimuli at 10 s intervals (NMT Monitor 221, GE Healthcare, Helsinki, Finland). A bolus dose of rocuronium 0.15 mg kg–1 administered in <5 s was then given to the patients followed by a flush of saline. The TOF response was manually recorded every 10 s until full spontaneous recovery occurred. Thereafter, the study was finished and anaesthesia continued according to the attending anaesthesiologist.
From the recorded data, the time to maximum effect and the entire response curve were obtained for determination of the ke0. No plasma concentration levels of rocuronium were measured in this study, instead the mean values of the pharmacokinetic parameters reported in Saldien's study9 were used to describe the changes in rocuronium plasma concentration during the study period in each patient.
‘tpeak’ method
The time to maximum effect (tpeak) was first estimated by visual inspection of the response curves of each patient and then corroborated using the ‘minimum’ function of Excel (Microsoft Corporation, Redmond, WA, USA) to determine the minimum value of the TOF data (Fig. 1).
As an example, Figure 2 shows the measured TOF response vs time data after a bolus dose of rocuronium in one subject (Fig. 1A). The minimum value of TOF recorded (maximal effect) determined by visual inspection and by the use of the ‘minimum’ function of Excel allowed us to determine the time ‘tpeak’, which in this case is 130 s and simply corresponds to the time elapsed from the start of the bolus dose until the moment where the maximum effect was observed. At tpeak, the PK–PD model used assumes that the effect-site concentration (Ce) of rocuronium is maximal and that, at this point, the plasma concentration (Cp) curve crosses the Ce curve (Fig. 2B). Then, knowing that Ce equals Cp at tpeak, Ce (tpeak) can easily be calculated with the parameters reported by Saldien9 using the classical polyexponential equation that describes the plasma concentration of a drug after a bolus dose:
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are known pharmacokinetic parameters published by Saldien and colleagues.9
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Then, knowing the value of Ce (tpeak) from equation (1) and using the same pharmacokinetic parameters,9 equation (2), which represents the concentration in the effect site resulting from a bolus dose, can be easily solved for ke0 at tpeak:
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Traditional methods
Two traditional approaches, one non-parametric and the other parametric, were used to model the electromyographic effect of rocuronium. In both approaches, the concentration in the effect compartment was assumed to be linearly linked to rocuronium's Cp1 and was estimated with:
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,10 assuming that the plasma concentrations over time were those predicted by the pharmacokinetic parameters reported by Saldien and colleagues.9 ke0 was then estimated by minimizing the area of the hysteresis loop of the electromyographic effect vs Ce.3 4 This was done in each patient separately minimizing the non-parametric ‘ke0 Objective function’ of the PK–PD Tools for Excel© program developed by Charles Minto and Thomas Schnider (www.pkpdtools.com). The computations were performed with the Solver tool of Excel (Microsoft Corporation, Redmond, WA, USA).
With the parametric method, the relationship between the Ce and the electromyographic effect was mathematically modelled. The PD model used to fit the electromyographic effect data was the sigmoid Emax model:
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is the steepness of the concentration–response curve. The model parameters were estimated using a population fit with NONMEM (Globomax LLC, Hanover, MD, USA).11 Interindividual variability was modelled using a log-normal distribution:
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, or Ce50) in the ith patient, PTV the typical value of the parameter in the population, and 
a random variable with a mean of 0 and a variance of 
2. Individual variability is reported as , the SD of in the log domain, which is approximately the coefficient of variance in the standard domain. Residual intraindividual variability was modelled with a standard additive error model. To explore the accuracy of the non-parametric and parametric methods to estimate the ke0 in data sets with an incomplete recovery phase, first, the ke0 estimation was made using the entire response curve. Then, each recovery phase was progressively amputated by arbitrary 20% decrements, thus leaving 80%, 60%, 40%, 20%, and 0% of the recovery phase for data analysis. In each of these shortened recovery periods, the ke0 was again calculated with both traditional methods until no data of the recovery phase were used (i.e. only data from drug administration to tpeak were used).
Statistical analysis was carried out with one-way ANOVA and ANOVA for repeated measurements followed by the Dunnett method for post hoc comparisons. Agreement between methods was assessed with Bland–Altmann analysis. The prediction probability (PK) between Ce and TOF was calculated using the PKMACRO, developed by Smith and colleagues.12 The PK can range from 0.5 to 1. A PK value of 0.5 means no predictive ability (50% chance) and a PK of 1 means that the Ce always correctly predicts increments or decrements in the level of TOF. A P-value of <0.05 was considered significant. Values are mean (SD) or median (range).
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Results |
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Patient characteristics and general data are shown in Table 1. Individual response curves over time are shown in Figure 3. Median measured tpeak was 4.5 min (2.0–7.7). In 13 of the 15 patients, the recordings of TOF response exhibited one single point having a minimum TOF value. In two patients, two and three consecutive minimum TOF values were observed. The first of these consecutive values was considered the tpeak.
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The ke0s obtained were 0.19 min–1 (0.09–0.72) with the ‘tpeak’ method, 0.20 min–1 (0.14–0.44) with the non-parametric method, and 0.19 min–1 (0.11–0.38) [typical value (range)] with the parametric method (NS).
The relationship of Ce to TOF modelled with NONMEM (parametric method) is shown in Figure 4. Diagnostic plots of this model are shown in Figure 5. The typical parameter values for the population model including the coefficient of variance (as a measure for interindividual variability in the standard domain) are found in Table 2. The SD of the model (as a measure of the intraindividual variability in the log domain) was 5.23. A good agreement was found between the ke0s estimated with all methods, especially between the non-parametric and parametric approaches (Fig. 6).
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When the ke0s determined with the full and the amputated responses were compared, ANOVA for repeated measures found a statistically significant difference (P<0.01) only with the parametric approach. With this method, paired comparisons found a significant difference (P<0.01) only between ke0s estimated using the full response and those derived from curves with no recovery phase (i.e. from drug injection until tpeak) (Fig. 7).
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Discussion |
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The main findings of this study are: (i) the ke0 of rocuronium calculated with the method of tpeak is similar to those calculated with the non-parametric and parametric methods and (ii) accurate ke0 estimations are possible with either the non-parametric or parametric methods even when a considerable portion of the recovery phase is not used.
The tpeak method to calculate the ke0 offers some advantages over the traditional methods such as the requirement for only a portion of the effect data instead of the complete course of drug effect,13 and the fact that no assumptions are needed on the degree of equilibration between plasma and biophase after a bolus, an infusion,10 or step modifications of plasma concentrations.14 Additionally, it does not require mathematical iterations that can lead to increased inaccuracies.10 13 14 An argument against using this method is its lack of validation with ‘traditional’ methods, and that it is not intended to replace them when the full response curve is available.6 15 When a response curve after a dose of rocuronium producing a submaximal neuromuscular block followed by 98% recovery was used with the tpeak and two traditional methods, the median ke0 calculated with all methods was the same.
The greater range in ke0 values observed with the tpeak method was mainly explained by two outlier values (ke0=0.63 and 0.72). Without these two subjects, the ke0 range would have been (0.09–0.26). These outlier values were significantly higher than those ke0s obtained in the other 13 patients and also higher than the values estimated for these same patients with both traditional methods (Figs 8 and 9). This suggests that the traditional methods better estimated the ke0s in these patients. In addition, in these two patients, the PK values calculated from the Ce estimated with each ke0 and the corresponding degree of neuromuscular block were higher with the non-parametric method (0.96 and 0.97) than with the tpeak method (0.92 and 0.93), suggesting that the traditional methods might be more reliable that the tpeak and that artifacts in the EMG recording during the peak effect portion of the curve might explain these discrepancies between methods (Figs 8 and 9).
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One of the advantages of the tpeak method is that it only requires the portion of the curve that allows an accurate estimation of the time of the maximum effect to calculate ke0. In the case of the non-parametric method, Stanski5 states that the complete response curve (i.e. starting from zero effect and returning to zero effect) is needed; however, this requirement is not evident from the articles that first described the method.3 4 Although in these two articles the degree of return towards zero effect required to calculate ke0 accurately is not mentioned, the figures in the study by Fuseau and Sheiner3 show that response curves with 75–100% recovery were utilized to calculate ke0. The possibility, however, that the use of response curves with incomplete recovery of the effect can lead to inaccurate estimations of ke0 was not evaluated. From the analysis of the amputated recovery curves, we assessed how much of this recovery phase is needed to obtain reliable ke0 estimates with these methods. Interestingly, we found that the progressive amputation of the recovery phase results in median ke0 values similar to those obtained with full recovery (Fig. 7). Sheiner and colleagues1 used a parametric approach to calculate ke0 of d-tubocurarine and found that the use of response curves with 10% or less recovery resulted in ke0s able to predict the effect several hours later, although with less precision than with ke0s determined with the complete data set. If our results are confirmed for other drugs, the relative advantage of using only a small portion of the response curve with the tpeak method might not be necessarily a real one since, the detection of tpeak, by definition, needs an important part of the recovery phase for a reliable estimation.
The absence of differences found in the comparison of ke0s between methods might be explained by insufficient power (type II error) and this is a limitation of the study. The ke0 variability with the tpeak method was higher than expected (74%), and a post hoc power analysis with 
of 0.05 and ß of 0.80 showed that 142 paired measurements (i.e. 142 patients) would be needed to find as significant a 25% difference between the ke0 measured by tpeak and any of the other methods. The Bland–Altman analysis, however, adds very relevant information to these comparisons between methods. How well (or badly) the three methods agree is probably better answered with this last analysis than with more traditional comparison of mean or medians. In addition, from a clinical point of view, we are mainly interested in the median value of the ke0. This is the single value that is incorporated in a PK model to predict the typical response time profile of the population. In our results, the median ke0 values of the three methods are almost identical (0.19, 0.20, and 0.20 min–1).
The fact that we used predicted concentrations of rocuronium by a PK model, rather than actually measuring the arterial drug concentrations is also a limitation of the study. However, in our opinion, since we are using the same PK model, the same patients and the same predicted plasma concentrations with all three methods, this is not a critical issue in the results for the purposes of this study.
It is important to consider that this study is limited to rocuronium's response data which can be accurately and easily measured in real time with an EMG monitor. General applicability of the current results to other types of responses, such as the level of hypnosis estimated with EEG monitors, needs further validation. Finally, all the methods used for ke0 estimations require that the effect can be adequately measured. However, since the ‘tpeak method’ relies on an accurate estimation of only one value (the time of maximum effect), it is very sensitive to the time intervals used to measure the effect and probably will be less reliable than traditional methods in the presence of noisy data in this portion of the curve.
In conclusion, if the tpeak can be adequately estimated from the data, the ‘tpeak method’ is a valid alternative to calculate the ke0 compared with the non-parametric and parametric methods. These last methods, in turn, might also result in reliable ke0 estimations even when a considerable portion of the recovery phase cannot be obtained.
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Acknowledgement |
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Departmental funding supported this study.
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References |
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