Two exceptional sets of physiological clearance curves and their mathematical form: test cases?

Amiodarone concentrations y(t) have been measured from 1 min to more than 50 days following 10 min of infusion, with about 40 observations on each of six normal subjects (Tucker et al., 1984, Eur. J. clin. Pharmacol. 26, 655-656). The form of the log-log plots-ln(y) vs ln(t)--is investigated. These appear to show three phases. First there is a rapid decrease of y(t), then a straight line corresponding to a small negative power of t, ca -0.3, and this line changes continuously but quickly at about 0.5 day into a steeper line that is almost straight. For the curve fitting a simple "spline-type" device was successful. Two continuity conditions were imposed at the time of changeover, which was one of the unknown parameters. The results are compared in detail with those from a set of 15 radiocalcium curves obtained during 2 weeks or more from a single injection of 47Ca (Neer et al., 1967, J. clin. Invest. 46, 1364-1379). Again two power functions of time can be seen. The changeover is much more gradual than with amiodarone, and the fits are still better. Both sets of curves are fitted with fewer adjustable parameters than with the usual multiexponentials that are interpreted in terms of homogeneous compartments. Theoretical and practical implications are mentioned. There is much indirect evidence that hundreds of other clearance curves may consist largely of one or two of such power functions of time.