Effect site: who needs it?
Since the earliest days of i.v. anaesthesia, clinicians have recognized the need to administer the agents judiciously and to allow time for physiological responses to develop. In 1955, John Dundee wrote‘While rapid injection produces a short period of good relaxation, the high concentration of the drug has a profound effect on the blood pressure and cardiovascular system in general. The safety of thiopentone is decreased enormously by a rapid rate of injection’.1The separation of administration and effect is most striking with competitive neuromuscular blockers where up to 3 min is required for full paralysis to develop. A similar but briefer dislocation of arterial concentration and drug effect is seen with i.v. anaesthetics. That is, after a single dose, both compartments (arterial and effect) are in disequilibrium. Arterial drug concentration increases before measurable increased drug effect occurs and, subsequently, the drug effect persists while blood concentration decreases. In 1978, in this journal, Hull first described the concept of the biophase or effect site—a functional space separate from but adjacent to arterial blood and between which a delay occurs accounting for the lag between drug administration and onset of effect.2
Traditionally, and perhaps surprisingly, the disposition of most drugs can be adequately described by polyexponential functions, making up a two- or a three-compartment mamillary model. These models can be adapted to describe drug effect (pharmacodynamics, PD) and drug disposition (pharmacokinetics, PK) by the addition of an effect site (Fig. 1). Because conventional PK models describe the disposition of the whole mass of administered drug, the effect site is attributed a negligible mass, which is superficially a nonsensical idea but one which is mathematically satisfactory and avoids disrupting the underpinning PK model.2
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Plotting arterial drug concentration against effect after a bolus clearly reveals the time lag between arterial and effect-site concentrations in the form of a counterclockwise hysteresis loop. By defining a rate constant Ke0 to characterize the delay between the blood and the site of drug effect, the hysteresis can be explained, and the blood–effect site equilibration half-life (Ke0 half-life) quantified.
In mathematical terms, we consider the observed drug action (effect) to be remote from the measured arterial concentration in two stages. First, the effect is attributed to the concentration at the notional effect site (see above) and, second, the relationship between the effect-site concentration and drug effect is non-linear and typically defined by a sigmoid Emax model (Fig. 2).
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The Emax model is comparatively mechanistic in nature and often describes drug effect data well. It mirrors biological processes in describing a baseline effect (E0) that is maintained until a threshold concentration is reached. Drug effect increases accordingly with an increase in drug concentrations, but is ultimately saturable (Emax). The sigmoidal shape reflects the laws of mass action describing drug–receptor interaction. The Hill coefficient (
) describes the steepness of the linear portion of the drug concentration–effect curve, which is likely to cover the therapeutically important concentration range. As , a dimensionless parameter, increases from a value of one to higher values, the curve becomes steeper and relatively small changes in drug concentration around C50 (the concentration associated with half the maximal drug effect) may result in significant changes in drug effect. At a value of 10 or higher, the model essentially becomes a step function, representing ‘all or nothing’ response. In practice, the dose–response curve is approximately linear in areas of therapeutic interest and, thus, the relationship between predicted propofol concentration and bispectral index (BIS) may reasonably be described by a simple regression line BIS = –12.8[propofol]+93.6.3 We can, therefore, achieve a complete description of the relationship between arterial concentration and drug action, with a delay defined by the rate constant Ke0 and the magnitude governed by the sigmoid Emax curve. It should be noted, however, that the resulting value of Ke0 is highly influenced by the underlying PK model. The effect-site model is widely taught in association with target-controlled, i.v. anaesthesia, and modern target control infusion (TCI) systems typically display a predicted effect-site concentration. It should be borne in mind that TCI systems are programmed with ‘typical’ PK and PD values for the patient population of interest. Because of the (sometimes substantial) between- and within-patient variability in the kinetic and dynamic handling of a drug, the predicted effect-site (and indeed, predicted arterial) concentrations should be interpreted as just that (i.e. predictions based on the best available evidence).
Thus far, effect-site modelling has mainly been confined to the hypnotic effects of i.v. anaesthetics, yet it is well known that haemodynamic effects and hypnosis are de-coupled. When Peacock and colleagues4 induced anaesthesia with different rates of propofol infusion, the patients required smaller induction doses at the lower infusion rates. When a PK–PD model incorporating an effect site is used to simulate these infusions, it is clear that the effect-site concentrations were broadly equivalent at the moment of loss of consciousness, regardless of infusion rate (Fig. 3).
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Despite this, the haemodynamic consequences for induction were strikingly different between the groups, with largest reduction in arterial pressure seen in patients given propofol more quickly. These data suggest, crudely, that the sites of hypnosis and haemodynamic disturbance are separate—hypnosis lies in the brain, whereas haemodynamic disturbance lies within the circulation. Consequently, induction of anaesthesia with rapid propofol infusions achieves high arterial concentrations with concomitant physiological upset.
This description of an apparent separation of hypnotic and haemodynamic effects was usefully explored when Kazama and colleagues5 monitored induction of anaesthesia with target-controlled propofol infusions, and found that the half-times for the plasma–effect-site equilibration for BIS were 2.31, 2.30, 2.29, and 2.37 min in patients aged 20–39, 40–59, 60–69, and 70–85 yr, respectively, whereas the half-times for systolic–arterial pressure changes were 5.68, 5.92, 8.87, and 10.22 min, respectively, and thus demonstrating functionally different effect sites and increasing the possibility that these may be anatomically separate as well. The progressively greater delay in systolic pressure reduction in older patients may reflect longer circulation times or some alternative underlying physiological change.
In this edition of the British Journal of Anaesthesia, Mourisse and colleagues6 7 report experiments that quantified the effect-site dynamics for patients anaesthetized with propofol or sevoflurane. In addition to describing the effects of the two drugs on BIS the investigators also recorded the blink reflex and a limb withdrawal reflex. Thus, three separate measures of drug effect were recorded, although data collection was separated into two phases reflecting the sensitivity of the blink reflex to sedation and light anaesthesia while the withdrawal response to painful electrical stimulation persisted to deeper levels. The characteristics and limitations of the three effect measures are summarized in Table 1.
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In fact, the blink reflex was markedly more sensitive to anaesthesia than BIS and especially sensitive to sevoflurane. In addition, BIS responded to changes in anaesthesia more quickly than the blink reflex (i.e. the effect site for the blink reflex is functionally ‘further’ from the blood than that of the BIS although experimental limitations acknowledged by the authors suggest this finding should be addressed cautiously). The blink reflex is also relatively sensitive to anaesthesia and is completely abolished well before the minimum alveolar concentration (MAC) of sevoflurane is achieved. Thus, the blink reflex is unlikely to be useful either as a measure of anaesthetic depth or to predict responsiveness to surgical incision.
The withdrawal reflex proved difficult to measure and insensitive to propofol and the authors speculate that this is because of differences in the molecular basis of action of the two compounds. The time constant Ke0 for withdrawal is much slower to respond to anaesthesia than BIS, and this may reflect differences in perfusion between the spinal cord and the brain. This difference between spinal and higher sites of anaesthetic action is no surprise and is consistent with findings in goats8 where an anatomical quirk allows experimental perfusion of the brain and spinal cord with different concentrations of anaesthetic agent. Antognini and colleagues9 demonstrated that MAC is determined by spinal cord rather than cortical isoflurane concentration. Similar differential effects have also been proposed for propofol.
Where do the observations of Mourisse and colleagues6 7 leave us?
Neither blink nor withdrawal reflex offers any improvement on BIS for describing the useful range of anaesthetic drug effect; both may also be slower to respond. Spinal reflex may be useful to quantify experimentally in a reproducible way the response to painful stimulation, but is unlikely to find a place in routine clinical practice.
We now know that both passively measured (BIS and arterial pressure) and provoked (blink reflex and limb withdrawal) measures of anaesthetic drug effect are progressively attenuated by increasing anaesthesia, although the sensitivity and delay vary from one measure to another. This diversity of response is further complicated by differences between individual agents—thus, at equi-anaesthetic concentrations (i.e. concentrations producing the same BIS value), the limb withdrawal response may be abolished by sevoflurane, but persist during propofol anaesthesia. Whether this translates into an increased propensity for surgical patients to move during i.v. anaesthesia cannot be determined in a volunteer study and the concept is clouded by the invariable use of analgesia, typically an opioid, during provision of anaesthesia for surgery.
These studies probably do not take us any closer to a usable analgesia monitor or even a ‘ready for surgical incision’ monitor. However, they do illustrate some important underpinning principles that must be addressed by candidate technologies in this area, and suggest that the science inside any usable monitor is unlikely to be simple.
Peninsula Medical School, Plymouth, UK
* E-mail: robert.sneyd{at}pms.ac.uk
References
1 Dundee J. The uses and abuses of thiopentone. Br J Anaesth (1955) 27:203–8.
2 Hull CJ, Van Beem HB, McLeod K, Sibbald A, Watson MJ. A pharmacodynamic model for pancuronium. Br J Anaesth (1978) 50:1113–23.
3 Doi M, Gajraj RJ, Mantzaridis H, Kenny GN. Relationship between calculated blood concentration of propofol and electrophysiological variables during emergence from anaesthesia: comparison of bispectral index, spectral edge frequency, median frequency and auditory evoked potential index. Br J Anaesth (1997) 78:180–4.
4 Peacock JE, Lewis RP, Reilly CS, Nimmo WS. Effect of different rates of infusion of propofol for induction of anaesthesia in elderly patients. Br J Anaesth (1990) 65:346–52.
5 Kazama T, Ikeda K, Morita K, et al. Comparison of the effect-site k(eO)s of propofol for blood pressure and EEG bispectral index in elderly and younger patients. Anesthesiology (1999) 90:1517–27.[CrossRef][Web of Science][Medline]
6 Mourisse J, Lerou J, Struys M, Zwarts M, Booij L. Multi-level approach to anaesthetic effects produced by sevoflurane or propofol in humans: 2. BIS and tetanic stimulus-induced withdrawal reflex. Br J Anaesth (2007) 98:746–55.
7 Mourisse J, Lerou J, Struys M, Zwarts M, Booij L. Multi-level approach to anaesthetic effects produced by sevoflurane or propofol in humans: 1. BIS and blink reflex. Br J Anaesth (2007) 98:737–45.
8 Borges M, Antognini JF. Does the brain influence somatic responses to noxious stimuli during isoflurane anesthesia? Anesthesiology (1994) 81:1511–5.[CrossRef][Web of Science][Medline]
9 Antognini JF, Saadi J, Wang XW, Carstens E, Piercy M. Propofol action in both spinal cord and brain blunts electroencephalographic responses to noxious stimulation in goats. Sleep (2001) 24:26–31.[Web of Science][Medline]
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