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

Abstract

A simple pharmacokinetic model, incorporating linear plasma protein binding, linear tissue binding, and first order elimination of free (unbound) drug, was studied. If Cl p is the plasma clearance, V f is the “true” volume of distribution of free drug, β is the apparent elimination rate constant, σ 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, k f is the intrinsic elimination rate constant for free drug, and A TB o is the initial amount of drug which is bound to tissues, then the model indicates that the following relationships hold: (1) Cl p = V f σ k f ; (2) β = f k f ; and V dext = (σ/f) V f . Only σ, and not f, can be measured experimentally . Dividing Cl p by σ provides an estimate of the intrinsic clearance of free drug, V f k f . A plot of V dext versus σ has an intercept equal to V f , and the ratio of the slope/intercept is an estimate of A TB o /A f o , where A f o is the initial amount of free drug (equal to V f times initial concentration of free drug in plasma). Thus, an estimate of A TB o may be obtained. Dividing the intrinsic clearance by V f provides an estimate of k f . Thus, theoretically, estimates of V f , k f , A TB o and f may be obtained. The variables are not separated when β is plotted versus σ, and curvature of such plots is expected; no useful information is obtained from such plots.