An extended pharmacokinetic/pharmacodynamic model describing quantitatively the influence of plasma protein binding, tissue binding, and receptor binding on the potency and time course of action of drugs

An extended pharmacokinetic/pharmacodynamic (PK/PD) model is presented, in which the effect of binding of the drug to plasma proteins and to tissue binding sites in a peripheral compartment, and nonspecific and receptor binding in the effect compartment are taken into account. It represents an extension of the classical Sheiner model, and the model proposed by Donati and Meistelman. The present model is characterized by the following parameters: ku(e) (exit rate constant of unbound drug from the effect compartment), Pu-e (ratio of the unbound clearances to and from the effect compartment), fu(e) (fraction of drug in effect compartment that is not bound to nonspecific binding sites), K-d (equilibrium dissociation constant of drug-receptor binding), and R(tot) (concentration of receptor binding sites in effect compartment). The rate of association and dissociation of the drug-receptor complex can be incorporated in the model. The influence of the pharmacokinetic parameters (V-1, V-2, fu, fu(2), CLu10, CLu20, CLu12, CLu21) and the PK/PD model parameters (ku(e), Pu-e, fu(e), K-d, R(tot)) on various dynamic parameters is analyzed. These include potency (single dose needed to produce 90% effect, ED(90)), constant infusion dosing rate needed to maintain a constant effect of 90%, time to maximum effect (onset time), and duration to 90% recovery. The neuromuscular blocking agent vecuronium is used as an example. It is shown that both potency and time course of action are strongly dependent on the ratio V-1/fu, CLu10, ku(e), Pu-e (at equipotent doses the time course is not affected by Pu-e), fu(e), K-d, and R(tot) (only if R(tot) is high), whereas they are less affected by the ratio V-2/fu(2), CLu20, CLu12, and CLu21. In general, the model parameters affect the ED(90) and the time course of action in the same direction, e.g., an increase of V-1 results in an increase of ED(90) and an increase of onset time and duration. However, the unbound clearance CLu10, the intercompartmental unbound clearance CLu12 and the receptor affinity K-d have an opposite effect on ED(90) and the time course parameters, e.g., an increase of CLu10 results in an increase of ED(90) and a decrease of onset time and duration. This effect may be responsible for the inverse relationship between onset time and potency of neuromuscular blocking drugs observed in animal experiments and clinical studies. We demonstrate that PK/PD analysis using the traditional effect compartment model (Sheiner model) results in an apparent value of k(eO), which is a function of ku(e), fu(e), K-d, R(tot), as well as the unbound drug concentration in the effect compartment Cu-e. On the other hand, the model proposed by Donati and Meistelman gives correct values of k(eO) (equal to the product fu(e) . ku(e)), but the receptor affinity K-d and the receptor density R(tot) obtained by this method are apparent values, which depend on fu, fu(e), and Pu-e.