Effect site equilibration

This chapter answers parts from Section B(v) of the 2017 CICM Primary Syllabus, which (among other things) expects the exam candidate to "describe the concepts of effect-site and context sensitive half time". Presumably, in the pursuit of a certain economy of their language, by this statement the college meant that the trainees should be able to describe the concept of effect-site and effect-site half-time (which is a concept distinct from context-sensitive half time).

In brief :

• Effect site concentration is the concentration of drug at the site of its biological activity, eg. bound to the receptors
• Effect site concentration is proportional to pharmacological effect, whereas plasma concentration may not be
• The rate of effect onset is determined by the rate of distribution of the drug from other compartments (i.e. central compartment) into the effect site.
• Equilibration between the central and the effect-site compartment follows first-order kinetics, described by the constant k^e0. 
• t_½k^e0 is a value which describes the time taken to achieve 50% effect-site concentration when the plasma levels are maintained at steady state. 

The official college pharmacology text  (Birkett et al, Pharmacokinetics Made Easy - 2009)  does not have anything specifically about this term, but around page 26-28 a discussion takes place of the different rates at which drugs distribute into tissues, and what relevance this has to the onset of action. Diazepam distribution into brain (rapid onset) and digoxin distribution into heart (slow onset) are used as examples in Figure 2.3, and cautions are issued for use of drugs which are slow to distribute into their effect site.

If one were for whatever reason disinclined to pay a pittance to Birkett and The Australian Prescriber, one may be able to find good answers in anaesthetics literature. This is the main stage for effect-site concentration pharmacokinetics because anaesthetists have some significant interest invested in being able to control a timely onset and offset of effect. For one, it is important in terms of case turnover. One such anaesthesia-centric article is the 2007 editorial by Sneyd and Rigby-Jones, titled "Effect site: who needs it?". This article by itself is enough to inform and entertain the time-poor exam candidate. If one wishes to see some classical graphs representing the effect site distribution of opiates, one might wish to explore the extensively referenced paper by Shafer and Varvel (1991) - their graphs have been adapted into every anaesthetics textbook since the nineties.

Effect site distribution

Behold Substance X.

Substance X is a drug with extensive tissue distribution, which takes place at different rates depending on the tissue. which makes sense, because brain is better perfused than muscle, and both are better perfused than fat. 

Substance X is also a dirty drug, which means that it has some sort of pharmacological effect at every site. Let's say that these effect is sedation (in the brain), neuromuscular junction blockade (in the muscle) and increased lipolysis (in fat).

So, the effects will be chronologically spaced out following a bolus of Substance X. CNS effects will be seen almost immediately, and by the time these start wearing off the NMJ blockade will become apparent. In summary, the rate of distribution of the drug into the tissue of interest determines the rate of effect onset, which has implications for dosing and therapy. This phase of distribution into the "clinically interesting" compartment is known as effect site distribution, or distribution into the "biophase" (i.e. the biologically active phase of distribution). 

In summary, drugs are going to differ in terms of how rapidly their plasma concentration equilibrates with their concentration at the compartment where they exert their biologically relevant effect, and this determines the onset of their effect.

Plasma-effect site equilibration rate constant (k^e0)

The effect site compartment is a virtual compartment which is in some way linked to the central compartment into which you inject your drugs. Because the movement of drugs between compartments is a concentration-driven affair, the rate of drug movement between the central compartment and the effect-site can be described as a first-order constant. That constant is k^e0.

The k^e0 is calculated based on plasma concentrations and clinical effect. For instance, the clinical effect of propofol is sleepiness. Measuring this effect - previously somewhat subjective - is now possible with the aid of such things as the EEG. One can measure the effects of the drug on EEG at the same time as one measures the plasma concentration and plot these on the same graph. One cannot do this assuming that the drug's concentration at the effect site is 100% correlated with the magnitude of its effect - rather, a sigmoid E_max curve is applied to modify the predicted effect site concentration.

In summary, equilibration between the central and the effect-site compartment follows first-order kinetics, described by the constant k^e0. Using this constant, it is possible to generate a value for "k^e0 half-time" or t_½k^e0. Like half-life, using the natural logarithm of 2 we can produce the equation, 

t_½k^e0 = 0.693 / k^e0 

This value represent the time required for the effect-site compartment to reach 50% of the plasma concentration as an infusion of the drug is running to maintain a constant plasma concentration.

That graph, of course, has the benefit of some sort of magical infusion which reaches its plasma concentration immediately. The following table is paraphrased from Miller's Anaesthesia; it is impossible to know precisely where their data was derived from because there is no reference for it.

Time to Peak Effect and t_½k^e0, in Minutes

Drug	Peak effect onset time	t½ke0
Morphine	19	264
Fentanyl	3.6	4.7
Alfentanil	1.4	0.9
Remifentanil	1.8	3.0
Propofol	90-100 seconds	1.7
Ketamine	-	3.5
Thiopentone	1.6	1.5
Midazolam	2.8	4.0

The interaction of peak onset time and t_½k^e0 is clinically important. The slower the t_½k^e0, the more drug needs to be given as a bolus dose. For example, the rapid distribution of alfentanil into the effect site means that by the time of the peak effect (at 1.4 minutes) only 60% of the total drug has been distributed into the tissues. With fentanyl, effect site distribution is relatively slow (3-4 minutes), and by the time peak effect is seen, 80% of the drug has already disappeared from circulation. 

The graphs above are from Shafer and Varvel (1991), frequently seen in anaesthetics textbooks. Also included is a chart from Hull (1978), who was  was the first to use the term "biophase" when discussing the pharmacokinetic modelling of pancuronium.  It was in fact Furchgott (1955) who first discussed the drug bound to receptors as occupying its own sort of pharmacokinetic compartment, and to him go the mad props for coming up with this concept. 

Clinical utility of the plasma-effect site equilibration rate constant

What's the point of all this? Basically, the fascination with this concept stems from the fact that we typically measure (and adjust our doses) on the basis of plasma drug concentrations, while remaining mainly interested in drug effects on something other than plasma. From this, it follows that we should be more interested in the concentration of the drug at the effect site rather than in the plasma. Thus, bolus dose and infusion kinetics calculations should probably be geared to take this into account.

In fact this is what good automated TCI pumps do. Rather than calculating the infusion dose according to plasma concentrations (who cares what the plasma concentration of propofol is) they calculate the infusion rate according to predicted effect site concentration, which they are programmed to maintain in within some pre-defined therapeutic window. This is described very well in an excellent editorial by Cortinez (2014).