Targeting the effect site
J.G. Bovill. Department of. Anaesthesiology, Leiden University Medical Centre, Leiden, The Netherlands

Computer-controlled or target controlled infusion (TCI) systems for the administration of intravenous anaesthetics have gained considerable popularity in recent years. The pharmacokinetic principles and the mathematical equations needed to rapidly achieve and maintain a constant target drug concentration in plasma or blood have been known since the late 1960s. The equation describing the infusion rate needed to maintain a constant plasma drug concentration (CSS) is:

This equation formed the basis of the B.E.T. (Bolus Elimination Transfer) scheme described by Schwilden in 1981 [1]. This scheme was implemented in the first TCI system developed by Schüttler et al. in 1983 [2]. Subsequently several algorithms have been described and implemented in TCI systems [3,4]. The introduction of a commercially available TCI system (Diprifusor®) has further increased interest in this mode of drug delivery in anaesthesia.

A major advantage of TCI is that drug concentrations can easily be adjusted upwards in anticipation of noxious stimuli and titrated downwards during periods of less stimulation. However, this ability to control plasma concentration does not automatically imply instantaneous control of anaesthetic depth. The primary site of action of anaesthetic drugs is not the plasma but the brain, and it takes a finite time for drugs to cross the blood-brain barrier and reach the site of action, the so-called effect site or biophase. The rate of equilibration of a drug between the plasma and the effect site is characterised by the parameter keo. If a constant plasma concentration is maintained then the time required for the effect site concentration to reach 50% of the plasma concentration is given by the t½keo = 0.693/keo. Drugs such as remifentanil, alfentanil and propofol have short t½keo, with rapid equilibration between plasma and effect site and a fast onset of action. The opioids sufentanil and fentanyl have intermediate values of t½keo while for morphine it is long, i.e. slow onset of action. The hysteresis between plasma and effect site results in a slurring in the rise and fall of drug concentration in the effect site when rapid adjustments are made in the plasma concentration. It would, therefore, be more logical to target the effect site rather than the plasma or blood concentration.

An analytical dosing scheme equivalent to the BET-scheme cannot be derived to control the effect-site drug concentration because there is no closed-form solution for calculating the infusion rate needed to maintain effect site concentrations and this must be solved numerically, as described by Shafer and Gregg [5]. Algorithms have been developed for TCI systems that allow control of a target effect site concentration instead of the more conventional plasma or blood concentration [5,6]. These work by producing an overshoot in the plasma drug concentration to force the drug down a concentration gradient into the effect site. This is analogous to the use of overpressure to increase rapidly the end-tidal concentration of an inhalational anaesthetic. Using these algorithms it is possible to achieve and maintain a specified effect-site drug concentration (CE) as rapidly as possible without overshooting [6]. While very rapid increases in CE can be achieved, this may necessitate large overshoots in the plasma concentration. This would not be a problem if all of the effects of a drug resulted from actions in the targeted effect site. Unfortunately this is seldom the case. Most drugs produce cardiovascular and other side effects that are often directly related to their plasma concentrations rather than the concentration at the site of anaesthetic action. Thus, when targeting effect-site concentrations, one is forced to compromise between speed of anaesthetic action and possible side effects.

Implementation of effect site algorithms produces an oscillation of the infusion rate during maintenance of a constant concentration [5]. This is a consequence of the use of discrete time intervals (typically 10 seconds) rather than continuous time in the iterations. However, once the effect site concentration has become equal to the plasma concentration, it is just as effective, and computationally less demanding, to simply maintain the plasma concentration at the required target. This eliminates the oscillations.

While targeting the effect site is likely to result in the greatest benefit when using drugs with longer t½keo, there is still appreciable benefit for drugs such as alfentanil and remifentanil. While none of the commercially available TCI devices currently provide for effect site targeting, this may change in the future. The latest models, however, do provide the user with information on the predicted effect site concentrations. We may even have future commercial systems that allow for closed-loop control based on, e.g. EEG or evoked potential monitoring. This is likely, however, to present even greater problems with the regulatory authorities than was the case with the simpler TCI devices currently available.

References
1. Schwilden H. A general method for calculating the dosage scheme in linear pharmacokinetics. Eur J Clin Pharmacol 1981;20:279-289.
2. SchüttlerJ, Schwilden H, Stoeckel H. Pharmacokinetics as applied to total intravenous anaesthesia. Anaesthesia 1983;38 (Suppl):53-56.
3. Jacobs JR. Algorithm for optimal linear model-based control with application to pharmacokinetic model-driven drug delivery. IEEE Trans Biomed Eng 1990;37:107-109
4. Bailey JM, Shafer SL. A simple analytical solution to the three compartment pharmacokinetic model suitable for computer controlled infusion pumps. IEEE Trans Biomed Eng 1991;38:522-525.
5. Shafer SL, Gregg KM. Algorithms to rapidly achieve and maintain stable drug concentrations at the site of drug effect with a computer-controlled infusion pump. J Pharmacokinet Biopharm 1992;20:147-169.
6. Jacobs JR, Williams EA. Algorithm to control "effect compartment" drug concentrations in pharmacokinetic model-driven drug delivery. IEEE Trans Biomed Eng 1993;40:993-999.