P1: PCX Printer: Yet To Come
9780521704632c06 CUFX213A/Peck 9780521618168 December 27, 2007 14:11
6 Mathematics and pharmacokineticsContext-sensitive half-times
The terminal elimination half-life is a value often cited for comparing the duration
of action of different drugs, but this has little clinical relevance if pharmacokinetic
behaviour follows a multi-compartmental model. Drug action is related to plasma
concentration; in a three-compartment model after a single bolus dose initial distri-
bution between compartments causes a rapid fall in plasma that limits the duration
of pharmacological action more than does the elimination process; re-distribution
will occur at a later stage, but the contribution from peripheral compartments in
maintaining plasma levels is very small and is unlikely to prolong drug effects. On the
other hand, if an infusion has been running for long enough to reach steady-state,
the concentration in the peripheral compartments is the same as that in plasma.
When the infusion is stopped plasma concentration will initially fall due to elimina-
tion, but this creates a concentration gradient between the central and peripheral
compartments so drug in these compartments will be re-distributed to the central
compartment so keeping the plasma concentration higher than would be seen after
abolus dose. For infusions of intermediate duration, concentration in plasma is still
greater than that in the peripheral compartments so distribution will continue after
stopping the infusion. However, the contribution of this initial distributive phase will
be much smaller because concentration gradients between compartments are lower
than at the start of the infusion. The rate at which re-distribution occurs depends
on the inter-compartmental clearance. Fentanyl and propofol have similar com-
partmental volumes, but the inter-compartmental clearances for fentanyl are twice
those for propofol; fentanyl re-distributes much more rapidly than propofol, which
tends to maintain high plasma concentrations following a long infusion.
Thus the time course for the decline in plasma concentration at the end of an infu-
sion depends on the duration of the infusion. The termcontext-sensitive half-time
(CSHT) has been introduced to describe this variability; the termcontextrefers to
the duration of infusion. Context-sensitive half-time is defined as the time for the
plasma concentration to fall to half of the value at the time of stopping an infu-
sion. The longest possible context-sensitive half-time is seen when the infusion has
reached steady state, when there is no transfer between compartments and input
rate is the same as elimination rate. In general terms, the higher the ratio of distri-
bution clearance to clearance due to elimination, the greater the range of context-
sensitive half-time. Fentanyl re-distributes much more rapidly than propofol; in
addition, its clearance due to elimination is about one-fifth that for distribution.
As a consequence the CSHT for fentanyl increases rapidly with increasing dura-
tion of infusion. For propofol the clearance due to elimination is similar to that for
distribution into compartment 2, so plasma concentration falls relatively rapidly
after a propofol infusion due to elimination with a smaller contribution from dis-
tribution. The maximum possible context half-time for propofol is about 20 min-
utes, compared with 300 minutes for fentanyl based on current pharamacokinetic