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6 Mathematics and pharmacokineticsrequired for anaesthesia. Although the CSHT has a maximum value of about 20 min-
utes, during long, stimulating surgery infusion rates will be high and the plasma
concentration when wake-up occurs may be much less than half the plasma con-
centration at the end of the infusion. Thus time to awakening using propofol alone
may be as long as 1 hour.Remifentanil
Unlike most agents used in anaesthesia, remifentanil has a relatively constant
context-sensitive half-time. Remifentanil is a fentanyl derivative that is a pureμ
agonist. It has an ester linkage, which is very rapidly broken down by plasma and
non-specific tissue esterases, particularly in muscle. The metabolites have mini-
mal pharmacodynamic activity. With increasing age, muscle bulk decreases and this
significantly influences the rate of remifentanil metabolism. The context-sensitive
half-time of remifentanil is relatively constant over a wide range of contexts (infusion
duration), from 3 to 8 minutes. Therefore a patient may be maintained on a remifen-
tanil infusion for a long period, without significant drug accumulation as seen with
other opioids. The advantage of this pharmacokinetic profile is that a patient may
be given prolonged infusions of remifentanil for analgesia during surgery, with rapid
offset of action when this is no longer required. The potential disadvantage is that
analgesic effects wear off so rapidly that pain may be a significant problem imme-
diately post-operatively. This must then be anticipated, either by using a regional
technique or by the administration of a longer acting opioid shortly before the end
of surgery.Total intravenous anaesthesia (TIVA) and target-controlled
infusion (TCI)
When using an infusion of propofol or remifentanil there is no ‘point-of-delivery’
measure of the target concentration comparable to the end-tidal monitoring of
inhalational agents. A target-controlled infusion will display acalculatedvalue for
plasma concentration based upon the software model used and the information it
has been given, usually patient weight and, for remifentanil, patient age.TIVA: the Bristol model
The Bristol algorithm, based on a three-compartment model, provides a simple infu-
sion scheme for propofol to achieve a target blood concentration of about 3μg.ml−^1
within 2 minutes and to maintain this level for the duration of surgery. This algo-
rithm was based on plasma concentrations obtained from fit patients premedicated
with temazepam and induced with fentanyl 3μg.kg−^1 followed by a propofol bolus
of just 1 mg.kg−^1 .Induction was followed by a variable-rate infusion of propofol at
10 mg.kg−^1 .h−^1 for 10 minutes, 8 mg.kg−^1 .h−^1 for 10 minutes then 6 mg.kg−^1 .h−^1
thereafter. This ‘10-8-6’ infusion scheme was supplemented with nitrous oxide and