Linear pharmacokinetic equations allowing direct calculation of many needed pharmacokinetic parameters from the coefficients and exponents of polyexponential equations which have been fitted to the data

Abstract

It is shown that if the numerical values of the coefficients and exponents of the polyexponential equation describing the whole blood (plasma or serum) concentration after administration of a drug by bolus intravenous injection, or during or after termination of a constantrate intravenous infusion, are known, then many needed pharmacokinetic parameters may be obtained directly. Parameters readily calculated by simple arithmetic are as follows: plasma or serum clearance, Cl_p; volume of plasma compartment, V_p; volume of distribution at steady state, V_dss; V{darea} or V_β, extrapolated volume of distribution, V_dexr; half-life of elimination, t_1/2; amount metabolized and/or excreted to time t, (A_e); amount in the body at time t, A_b; amount in the plasma (reference) compartment at time t, A_p; and amount in other compartments at time t, A_o. Simulations have shown that the equations yield the correct answers for an n-compartment mammillary model with central compartment elimination only, when rate constants, dose, and a value of V_p have been assigned. Since whole blood (plasma or serum) concentrationtime data always lead to ambiguities as to which specific model is involved, the equations are most appropriate.