Processes involved in pharmacokinetic-dynamic models

As is implicit from all the above, the measured concentration in plasma is directly linked to the observed effect for these simple mechanistic, pharmacokinetic-dynamic models. Accordingly, these models are called direct-link models since the concentrations in plasma can be used directly in (10.6) and (10.7) for the description of the observed effects. Under the assumptions of the direct-fink model, plasma concentration and effect maxima will occur at the same time, that is, no temporal dissociation between the time courses of concentration and effect is observed. An example of this can be seen in the direct-fink sigmoid Emax model of Racine-Poon et al. [418], which relates the serum concentration of the anti-immunglobulin E antibody CGP 51901, used in patients for the treatment of seasonal allergic rhinitis, with the reduction of free anti-immunglobulin E. 

In the direct-link model, concentration-effect relationships are established without accounting for the intrinsic pharmacodynamic temporal behavior, and the relationships are valid only under the assumption of effect site, prereceptor equilibrium H3. In contrast, indirect-link models are required if there is a temporal dissociation between the time courses of concentration and effect, and the observed delay in the concentration-effect relationship is most likely caused by a functional delay between the concentrations in the plasma and at the effect site. 

When a lag time of E (t) is observed with respect to the c (t) time course, the use of a combined pharmacokinetic-dynamic model, the indirect-link model, is needed to relate the drug concentration c (t) to the receptor site drug concentration y (t) (which cannot be measured directly) and the y (t) to the pharmacological response E (t).1 

The effect-compartment model relaxes the assumption H3 and it stems from the assumption of prereceptor nonequilibrium between drug concentration in the blood or plasma c (t) and the receptor site y (t). According to this model, an additional compartment is considered, the effect (or biophase) compartment, and 

Un the classical pharmacokinetic-pharmacodynamic literature, the effect site concentration and the effect site elimination rate constant are denoted by eg and kgq, respectively. Here, the symbols y (t) and ky are used instead. 

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