By JOHN G. WAGNER
Semilogarithmic plots of amount (or per cent) not excreted against time will be curved either if (a) the wrong asymptote is used, or (b) absorption is still proceeding during the interval observations are made. Factor (a) causes "convex decreasing" type of curvature, whereas factor (b) causes "concave decreasing" type of curvature. If both factors are operative, it is possible to obtain an apparently linear semilogarithmic plot; however, the rate constant estimated from the linear segment is meaningless. Models and actual data from the literature are used to illustrate these points. Using a simple model, it is shown that rate constants estimated from terminal segments of semilogarithmic plots of amount not excreted or of blood levels may be appreciably lower than the true values. The implications of these factors in making in vitro-in vivo correlations are discussed.
AN LIEW (1) indicated that concavity' of a Vsemilogarithrnic curve may result from operation of one of four types of systems. Application of the "backward projection" technique to "convex decreasing" semilogarithmic plots of blood level and urinary excretion data can lead to linear components from which rate constants between assumed independent compartments may be estimated. Van Liew showed that another interpretation may be the operation of a continuum of exponential processes.
Assuming the independent compartment model applies to blood level and urinary excretion data, this report will discuss (a) other causes of curvature of semilogarithmic plots, (b) possible errors in plotting and interpreting such data, and (6) the implications of these factors in making in vitroin vioo correlations.
Several types of semilogarithmic plots are commonly utilized. In these, time is plotted as the abscissa and the ordinates plotted on the logarithmic scale are (A) urinary excretion rate (amount/unit time or per cent of dose/unit time),