Applications of a recirculatory stochastic pharmacokinetic model: limitations of compartmental models

General equations for the time integral on [0, infinity) of the venous drug concentration-time function after intravenous and oral drug administration are derived. A physiologically realistic stochastic recirculating model is applied in the derivations. The quotient of the intravenous drug dose and the integral on [0, infinity) of the resulting venous blood drug concentration function is equivalent to a summation of organ clearances only provided that drug elimination does not occur in the pulmonary system, and in general it is not equivalent to "total body clearance." In general, mammillary compartmental models are not isomorphic with recirculating models. A necessary condition for isomorphism is that the pulmonary system be conservative toward the drug. Equations for the pulmonary "first-pass" effect derived via the compartmental analysis are invalid. A valid expression for the pulmonary "first-pass" effect is derived. General equations derived via compartmental analysis for the extent of hepatic metabolism and the hepatic first-pass" effect are shown to be valid. A generally applicable expression for the advantage of close intraarterial drug administration is derived. The limitations of compartmental models for representing drug distribution and elimination are discussed, and the advantages of recirculating models are emphasized.