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

Summary

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 ^o_TB is the initial amount of drug which is bound to tissues, then the model indicates that the following relationships hold: (1) Cl_p = V_fσ k_f; (2) β = f k_f; and V_dext = (σ/f) V_f. Only σ, and not f, can be measuredexperimentally. Dividing Cl_p by σ provides an estimate of the intrinsic clearance of free drug, V_fk_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 ^o_TB /A ^o_f , where A ^o_f is the initial amount of free drug (equal to V_f times initial concentration of free drug in plasma). Thus, an estimate of A ^o_TB 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 ^o_TB and f may be obtained. The variables are not separated when β is plottedversus σ, and curvature of such plots is expected; no useful information is obtained from such plots.