Mean time concept and component analysis in pharmacokinetics

In 1958, F.H. Dost [1958] defined the mean life-span ("mittlere Lebensdauer") of a total number of N molecules as the arithmetic mean of all times "z(i)" of any one of the N molecules residing in a pharmacokinetic system. This pharmacokinetic characteristic did not attract special interest for several years. Almost simultaneously Yamaoka et al. [1978], Cutler [1978], van Rossum [1978], Benet and Galeazzi [1979], and von Hattingberg and Brockmeier [1979] recommended the mean residence time (MRT) or mean time (MT) as a useful summarizing characteristic for complex pharmacokinetic systems. One of the most useful properties of the statistical analysis (also called "moment analysis" or "statistical moment analysis") of concentration-time data and in vitro dissolution profiles using moments is the additivity of mean times [von Hattingberg and Brockmeier 1978, 1979]. The very simple and compelling logic of additivity can be explained by the following example: considering an oral administration of a readily available dosage form, the distribution of each individual molecule within the body and the elimination from the body must be preceded by absorption of this molecule, which is trivial. However, as a consequence, the total transit time of an individual molecule through this system is the sum of its time up to absorption into the central circulation z(i).abs and the time the molecule spends in any part of the volume the molecule can reach z(i).vss. Therefore, the total mean time of all drug molecules available is the sum of the mean absorption time MT(abs) and the mean time in the steady-state volume of distribution MTvss. It is obvious that we can estimate the two components of the total mean time, i.e. MTabs and MTvss, by an appropriate experimental setting giving the drug once intravenously and determining MTvss and once giving the drug as an oral solution and deducing MTabs = MTtotal - MTvss. Because of this very useful property of the statistical analysis of concentration-time data by moments, this approach has been entitled "component analysis" [von Hattingberg et al. 1984].