Pharmacology for Anaesthesia and Intensive Care

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Section IBasic principles

for clearance define the removal of drug from the body, which is the product of the

rate constant for elimination k 10 and V 1 , the volume of distribution of the central

compartment. For example, propofol has a k 10 of approximately 0.12, so about 1/8

of the plasma-equivalent volume has drug removed by elimination in unit time. For

propofol, V 1 is about 16 litres and k 10 is approximately 0.12, so the clearance of propo-

fol is 16×0.12, which is about 2 litres per minute. Remifentanil has a much smaller

central compartment volume but a higher k 10 ,sothe clearance of remifentanil is 5.1

×0.5, which is 2.5 litres, quite similar to that of propofol. If we do not know V 1 we

could use Vintialas an estimate but it is often inaccurate due to sampling artefacts at

early times when mixing has not taken place. Instead, clearance is usually calculated

from the area under the concentration–time curve:

Clearance=Dose/AUC.

Elimination of drug from the model represents both metabolism and excretion of

unchanged drug. Metabolism may occur in many sites and be organ-dependent

or independent; a clearance that is greater than hepatic blood flow suggests that

hepatic elimination is not the only route of elimination – either there are other sites

of metabolism or the drug is excreted unchanged, for example through renal or

pulmonary routes. Remifentanil has a very high clearance because it is eliminated

bynon-specific esterase in both plasma and tissue.

Inter-compartmental clearance relates to the movement of drug between

compartments; C 12 and C 13 define drug transfer between compartments 1 and 2 and

1 and 3, respectively. For drugs with comparable compartmental volumes, the higher

the inter-compartmental clearance the more rapidly distribution and re-distribution

takes place.

Time constant and half-life (t1/2)

Inthe single-compartment model there is just a single exponential relationship

between plasma concentration and time. The time constant defines how quickly

the plasma concentration falls with time and is defined as the time it would have

taken plasma concentration to fall to zero if the original rate of elimination had con-

tinued (Figure6.11). Time constantτhas units of time, usually minutes. The half-life

is the time taken for the plasma concentration to fall to 50% of its initial value. In the

mathematics section we saw that half-life is related to time constant by a constant of

proportionality and half-life is ln2.τ, that is, half-life is 0.693.τ; the half-life is shorter

than the time constant. Note that either half-life or time constant may be used to rep-

resent the time dependency of an exponential process. In the multi-compartment

models there are several hybrid time constants each of which relates to one of the

distinct exponential phases of drug elimination. As mentioned above, these do not

relate directly to any one of the individual rate constants in the model.