A novel method of deriving the effect compartment equilibrium rate constant for propofol

T. A. Lim

Anaesthesiology Unit, Faculty of Medicine and Health Sciences, Universiti Putra, Malaysia E-mail: limta@hotmail.com

Accepted for publication: June 25, 2003


    Abstract
 Top
 Abstract
 Introduction
 Methods and results
 Comment
 References
 
Background. Calculation of the effect compartment concentration (Ce) in non-steady-state conditions requires the equilibrium rate constant, keo. Most studies of propofol derive the keo using EEG measurements. This study investigated an alternative method. Starting from a predicted concentration–time profile, a keo value was included so that the predicted Ce at a specific pharmacodynamic end-point was the same when using three different methods of injection.

Methods. Seventy-five patients were given propofol for induction of anaesthesia. Twenty-five patients received a single bolus, 25 patients received an infusion, and 25 patients received a bolus followed by an infusion. Computer simulation was used to derive the central compartment concentration. The keo that brought about the same value for Ce at loss of the eyelash reflex using the three methods of injection was derived.

Results. Keo was found to be 0.80 min–1. Mean (SD) Ce at loss of the eyelash reflex was 2.27 (0.69) µg ml–1.

Conclusions. The effect compartment equilibrium rate constant and concentration at loss of the eyelash reflex can be derived without the use of electronic central nervous system monitors.

Br J Anaesth 2003; 91: 730–2

Keywords: anaesthetics, i.v., propofol; model, computer simulation; pharmacokinetics


    Introduction
 Top
 Abstract
 Introduction
 Methods and results
 Comment
 References
 
It has been shown previously that the predicted effect compartment concentration (Ce) of thiopental at loss of the eyelash reflex was independent of the method of injection.1 While the use of thiopental is generally confined to induction of anaesthesia, propofol has established itself as an i.v. agent suitable for both induction and maintenance of anaesthesia.

A previous study demonstrated that plasma propofol concentrations after bolus injection are fairly well described by infusion pharmacokinetics, while the pharmacokinetics are linear during infusion.2 These conditions are necessary if infusion algorithms are to accurately predict target concentrations.

Prediction of the concentration at the effect site requires an additional parameter, the effect compartment equilibrium rate constant (keo). This parameter is highly influenced by the pharmacokinetic model, making it unwise to mix the keo derived from one study with the pharmacokinetic data from a different study.3

Most studies derive the keo using EEG measurements taken either during an infusion, or after a bolus dose of the drug. The method used in this study differs from the methods used previously, as it does not require any EEG measurements. In addition, as the keo value was derived using a combination of infusion and bolus dosing, the value derived should be applicable to both methods of injection.


    Methods and results
 Top
 Abstract
 Introduction
 Methods and results
 Comment
 References
 
The study was approved by the local clinical research ethics committee. Seventy-five patients, ASA physical class I or II, undergoing elective surgical operations gave informed consent for the study. Patients with a body weight above 80 kg, patients with evidence of cardiovascular disease, or a history of sensitivity to propofol were excluded. On arrival in the operation theatre, routine monitoring was set up and an i.v. cannula was inserted into a forearm vein for infusion of drugs and fluid. Patients did not receive premedication or any other sedative drug before induction of anaesthesia.

Patients were randomized to one of three groups:

1. Group 1. Patients received a single bolus dose of propofol 2 mg kg–1 injected over 10 s. If loss of the eyelash reflex was not achieved after 60 s, an additional dose of 0.5 mg kg–1 was given.

2. Group 2. Patients received a continuous infusion of propofol at 25 mg min–1 until loss of the eyelash reflex was demonstrated.

3. Group 3. Patients received a bolus of propofol (30, 40, or 50 mg), followed by a continuous infusion at 25 mg min–1.

The eyelash reflex was tested every 2.5 s, and the time at which the reflex was lost was recorded (Table 1). After induction of anaesthesia was successfully achieved, patients were maintained using a standard anaesthetic technique.


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Table 1 Patient data (mean (range or SD)), induction characteristics and predicted propofol concentrations at loss of the eyelash reflex (mean (range)). *P<0.05 when comparing between groups. {dagger}No significant difference between Groups 2 and 3.
 
Central compartment concentrations of propofol were initially predicted using the model reported in Marsh and colleagues.4 Ces were then calculated numerically. This methodology has been described previously.1

For each group of patients, the mean Ce at loss of the eyelash reflex was calculated for any particular value of the keo. The sum of the squared differences of the mean effect compartment concentrations was then calculated using the formula:

sum of squared differences =(Ce gp1 – gp2)2 + (Ce gp2 – gp3)2 + (Ce gp1 – gp3)2

where, (Ce gpx – gpy)2 is the squared difference between the mean effect compartment concentrations of groups x and y. Microsoft Excel Solver, which uses the Generalized Reduced Gradient non-linear optimization codesolver function, was used to derive the keo value that minimized the sum of the squared differences. This value was taken as the keo for propofol.

In order to determine the variability of the keo, each of the three treatment groups were divided into two sub-groups. Combinations of three sub-groups, each sub-group being from a different treatment group, were made. This gave a total of eight combinations. A keo value was then derived for each combination. The mean and SD of the keo obtained using this ‘two-stage’ method was calculated.

Differences between means were tested using ANOVA. A value of P<0.05 was considered significant.

A keo value of 0.80 min–1 gave the least difference between the mean predicted Ces of propofol at loss of the eyelash reflex using the three different methods of injection. Using the ‘two-stage’ method, the mean (SD) keo was 0.81 (0.25) min–1.

Ce at loss of the eyelash reflex, calculated using the derived keo value, was not significantly different between groups (Table 1). After combining data from all three groups, mean (SD) Ce at loss of the eyelash reflex was 2.27 (0.69) µg ml–1. Figure 1 shows the relationship between the keo and the Ce at loss of the eyelash reflex in the three groups.



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Fig 1 Relationship between effect compartment equilibrium rate constant (keo) and mean predicted effect compartment concentration of propofol at loss of the eyelash reflex.

 

    Comment
 Top
 Abstract
 Introduction
 Methods and results
 Comment
 References
 
The concentration at the effect compartment has a hysteresis-free relationship with the pharmacological effect. Estimation of the Ce usually requires some monitor of central nervous system electrical activity. This study illustrates a new method of estimating the Ce at a pharmacodynamic end-point without the use of such monitors. One advantage of this method is the reduction in cost. In addition, when different methods of analysis arrive at the same result, the confidence in such results is enhanced.

A wide range of keo values has been reported by previous investigators. Schnider and colleagues, using a value of 0.456 min–1, reported a time to peak effect of 1.7 min after a bolus dose of propofol.5 Struys and colleagues, using this time to peak Ce, calculated a keo of 1.21 min–1 when applied to the pharmacokinetic parameters reported by Marsh and colleagues.6 Struys went on to show that this keo more accurately predicted the time of peak EEG effect. The value obtained in this study is between both these values, and is close to the value reported by Wakeling and colleagues.7 Using the ‘two-stage’ method, the 95% confidence interval of the keo was found to be 0.32–1.30 min–1. This wide confidence interval mirrors the range of previously reported keo values.

One way of assessing the accuracy of the derived keo value is to compare the predicted Ce with previous reports. The Ce reported in this study is similar to that reported in a previous study using a similar end-point.8 In addition, the value derived is similar to the median pseudo-steady-state concentration at loss of eyelash reflex reported by other investigators.9 10

The computer simulation used in this study relies on a compartmental pharmacokinetic model, which unfortunately does not deal well with the rapid changes in blood concentrations following a bolus dose. Furthermore, the model assumes that the pharmacokinetic parameters and the keo are not affected by the rate of drug administration. However, any inaccuracy caused by propofol affecting its own pharmacokinetics is likely to be much less than that introduced when a compartmental model is used to describe the concentration–time profile after a bolus dose. In spite of all this, it is generally accepted that a single set of pharmacokinetic parameters is sufficient for predicting blood propofol concentrations after a bolus injection and during infusion.

Most manual dosing regimens and target controlled infusion systems rely on a series of bolus injections and infusion rates to achieve a desired plasma or Ce. In the absence of real time estimation of the drug concentration, real time prediction of the concentration offers a reasonable alternative. The values of the parameters used for predicting such concentrations must be applicable equally well to bolus doses and infusions. The keo value derived in this study used both these methods of drug injection, and should be able to predict drug concentrations adequately in both situations.

In conclusion, this study reports a new method of deriving the effect compartment equilibrium rate constant. However, as this method uses data pooled from the entire sample, the keo derived is a population value. For propofol, the keo was found to be 0.80 min–1.


    Acknowledgement
 
The author wishes to thank the Director-General of Health, Malaysia, for his permission to publish this article.


    References
 Top
 Abstract
 Introduction
 Methods and results
 Comment
 References
 
1 Lim TA, Inbasegaran K. Predicted effect compartment concentration of thiopental at loss of the eyelash reflex. Br J Anaesth 2001; 86: 422–4[Abstract/Free Full Text]

2 Schnider TW, Minto CF, Gambus PL, et al. The influence of method of administration and covariates on the pharmacokinetics of propofol in adult volunteers. Anesthesiology 1998; 88: 1170–82[ISI][Medline]

3 Gentry WB, Krejcie TC, Henthorn TK, et al. Effect of infusion rate on thiopental dose-response relationships. Assessment of a pharmacokinetic-pharmacodynamic model. Anesthesiology 1994; 81: 316–24[ISI][Medline]

4 Marsh B, White M, Morton N, Kenny GNC. Pharmacokinetic model driven infusion of propofol in children. Br J Anaesth 1991; 67: 41–8[Abstract]

5 Schnider TW, Minto CF, Shafer SL, et al. The influence of age on propofol pharmacodynamics. Anesthesiology 1999; 90: 1502–16[ISI][Medline]

6 Struys M, De Smet T, Depoorter B, et al. Comparison of plasma compartment versus two methods for effect compartment-controlled target-controlled infusion for propofol. Anesthesiology 2000; 92: 399–406[ISI][Medline]

7 Wakeling HG, Zimmerman JB, Howell S, Glass PS. Targeting effect compartment or central compartment concentration of propofol: what predicts loss of consciousness? Anesthesiology 1999; 90: 92–7[ISI][Medline]

8 Leslie K, Sessler DI, Smith WD, et al. Prediction of movement during propofol/nitrous oxide anesthesia. Performance of concentration, electroencephalographic, pupillary, and hemodynamic indicators. Anesthesiology 1996; 84: 52–63[ISI][Medline]

9 Vuyk J, Engbers FHM, Lemmens HJM, et al. Pharmacodynamics of propofol in female patients. Anesthesiology 1992; 77: 3–9[ISI][Medline]

10 Forrest FC, Tooley MA, Saunders PR, Prys-Roberts C. Propofol infusion and the suppression of consciousness: the EEG and dose requirements. Br J Anaesth 1994; 72: 35–41[Abstract]