Modelling the delay between pharmacokinetics and EEG effects of morphine in rats: binding kinetic versus effect compartment models

Drug–target binding kinetics (as determined by association and dissociation rate constants, k(on) and k(off)) can be an important determinant of the kinetics of drug action. However, the effect compartment model is used most frequently instead of a target binding model to describe hysteresis. Here we investigate when the drug–target binding model should be used in lieu of the effect compartment model. The utility of the effect compartment (EC), the target binding kinetics (TB) and the combined effect compartment–target binding kinetics (EC–TB) model were tested on either plasma (EC(PL), TB(PL) and EC–TB(PL)) or brain extracellular fluid (ECF) (EC(ECF), TB(ECF) and EC–TB(ECF)) morphine concentrations and EEG amplitude in rats. It was also analyzed when a significant shift in the time to maximal target occupancy (Tmax(TO)) with increasing dose, the discriminating feature between the TB and EC model, occurs in the TB model. All TB models assumed a linear relationship between target occupancy and drug effect on the EEG amplitude. All three model types performed similarly in describing the morphine pharmacodynamics data, although the EC model provided the best statistical result. The analysis of the shift in Tmax(TO) (∆Tmax(TO)) as a result of increasing dose revealed that ∆Tmax(TO) is decreasing towards zero if the k(off) is much smaller than the elimination rate constant or if the target concentration is larger than the initial morphine concentration. The results for the morphine PKPD modelling and the analysis of ∆Tmax(TO) indicate that the EC and TB models do not necessarily lead to different drug effect versus time curves for different doses if a delay between drug concentrations and drug effect (hysteresis) is described. Drawing mechanistic conclusions from successfully fitting one of these two models should therefore be avoided. Since the TB model can be informed by in vitro measurements of k(on) and k(off), a target binding model should be considered more often for mechanistic modelling purposes. ELECTRONIC SUPPLEMENTARY MATERIAL: The online version of this article (10.1007/s10928-018-9593-x) contains supplementary material, which is available to authorized users.