Generalizations in linear pharmacokinetics using properties of certain classes of residence time distributions. II. Log-concave concentration-time curves following oral administration

The present approach enables a noncompartmental assessment of log-concave plasma concentration-time profiles following oral drug administration. Observed log-concavity corresponds to a nonparametric class of residence time distributions with the following properties: (1) The fractional rate of elimination kB(t) (failure rate of the distribution) increases monotonically until reaching the terminal exponential coefficient kB,Z. (2) The relative dispersion of body residence times CVB2 (ratio of variance to the squared mean, VBRT/MBRT2) acts as a shape parameter of the curve. The role of the input process in determining the shape of the concentration profile is discussed. In this connection evidence is provided for the importance of log-concave percent undissolved versus time plots, introducing the general concept of a time-varying fractional rate of dissolution. The governing factor for the appearance of log-concavity is the ratio of mean absorption time to mean disposition residence time (MAT/MDRT); this factor exceeds a particular threshold value which depends on the distributional properties of the drug. Generalizing previous approaches which are valid for first-order input processes, the "flip-flop" phenomenon and the problem of "vanishing of exponential terms" are explained using fewer assumptions. Upper bounds for the elimination time (more than 90% eliminated) and the cutoff error in AUC determination are presented. The concept of log-concavity reveals general features of the pharmacokinetic behavior of oral dosage forms exhibiting a dominating influence of the absorption/dissolution process.