A number of mathematical theories have been developed in an attempt to describe quantitatively the rate of uptake of anaesthetics by the body. Most involve one, two or more exponential processes (see Kety, 1951;Mapleson, 1962;Mapleson, 1963). These same theories have also been used to explain differences between the speeds of induction of anaesthesia by the various anaesthetics as well as the rapidity of recovery from anaesthesia (Kety, 1951;Butler, 1958; Adriani, 1963). However, it is not known whether induction of, or recovery from, anaesthesia follows the single or multiple exponential time-course predicted by these theories. Onset of anaesthesia and recovery from anaesthesia have been described as fast or slow, nothing more. The object of the present experiments was to determine the rates (that is, the kinetics) of anaesthesia more quantitatively. To do so, a simple theory has been formulated such that the existence of one or more exponential components in the onset of anaesthesia could be detected. Three volatile anaesthetics possessing markedly different solubilities in fat and blood were selected for study. These were halothane, ether and methoxyflurane.
THEORETICAL CONSIDERATIONS
Onset of anaesthesiaThe simplest description of the uptake of anaesthetic at its sites of action in the brain is for the situation where uptake is determined by a single exponential process:where x is the concentration of anaesthetic at its sites of action in the brain at a time, t, after exposure to a constant vapour concentration, C, of anaesthetic; k is a rate constant and a is a proportionality constant which includes the blood/air partition coefficient of the anaesthetic.In a series of experiments using different inhaled concentrations of anaesthetic and different times of exposure, we can identify a standard pharmacological effect of the anaesthetic. Let it be assumed that equal concentrations of the same anaesthetic exist at its site of action in the brain when a standard anaesthetic effect is observed, regardless of how these concentrations are achieved. We then have: