Simple model to explain effects of plasma protein binding and tissue binding on calculated volumes of distribution, apparent elimination rate constants and clearances.

A simple pharmacokinetic model, incorporating linear plasma protein binding, linear tissue binding, and first order elimination of free (unbound) drug, was studied. If Clp is the plasma clearance, Vf is the "true" volume of distribution of free drug, beta is the apparent elimination rate constant, sigma is the fraction of the drug which is free in plasma, f is the fraction of the drug which is free in the entire body, kf is the intrinsic elimination rate constant for free drug, and AoTB is the initial amount of drug which is bound to tissues, then the model indicates that the following relationships hold: (1) Clp = Vfsigma kf; (2) beta = f kf; and Vdext = (sigma/f) Vf. Only sigma, and not f, can be measured experimentally. Dividing Clp by sigma provides an estimate of the intrinsic clearance of free drug, Vfkf. A plot of Vdext versus sigma has an intercept equal to Vf, and the ratio of the slope/intercept is an estimate of AoTB/Aof, where Aof is the initial amount of free drug (equal to Vf times initial concentration of free drug in plasma). Thus, an estimate of AoTB may be obtained. Dividing the intrinsic clearance by Vf provides an estimate of kf. Thus, theoretically, estimates of Vf, kf, AoTB and f may be obtained. The variables are not separated when beta is plotted versus sigma, and curvature of such plots is expected; no useful information is obtained from such plots.