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.