Pharmacokinetic-Dynamic Modeling

In the mid-1960s, G. Levy [412,413] was the first to relate the pharmacokinetic characteristics with the in vivo pharmacological response of drug using 

1 are not necessarily incorporated in the final model used in practice. Almost always, one of these steps is considered to be the limiting one, and the model reduces to one of the basic models described below. 

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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. 

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... 

Numerous applications of pharmacokinetic-dynamic models incorporating a biophase (or effect) compartment for a variety of drugs that belong to miscellaneous pharmacological classes, e.g., anesthetic agents [419], opioid analgesics [420-422], barbiturates [423,424], benzodiazepines [425], antiarrhyth-mics [426], have been published. The reader can refer to a handbook [427] or recent reviews [405] for a complete list of the applications of the biophase distribution model. 

Ariens [432] was the first to describe drug action through indirect mechanisms. Later on, Nagashima et al. [433] introduced the indirect response concept to pharmacokinetic-dynamic modeling with their work on the kinetics of the anticoagulant effect of warfarin, which is controlled by the change in the prothrombin complex synthesis rate. Today, indirect-response modeling finds extensive... 

All the above-mentioned pharmacokinetic-dynamic models are characterized by reversibility of the drug-receptor interaction. In several cases, however, drug action relies on an irreversible bimolecular interaction thus, enzyme inhibitors and chemotherapeutic agents exert their action through irreversible bimolecular interactions with enzymes and cells (bacteria, parasites, viruses), respectively. 

Using the approach of Sheiner and Verotta [452], a large number of pharmacodynamic models can be considered as hierarchical models composed of a series of submodels. These submodels are linear or nonlinear, static or dynamic input-output, elementary models. Several possible combinations of such submodels have been considered, but they have systematically associated the linear with dynamic features, and the nonlinear with static ones. Is there hesitation or fear of using nonlinear dynamics in the traditional pharmacokinetic-dynamic modeling context ... 

The fundamental assumption and equations governing the effect-concentration relationship for each one of the models considered are listed in Table 10.1. The presence or not of an hysteresis loop in the effect-plasma concentration plot of each model is also quoted in Table 10.1. At present, the methodology for performing efficient pharmacokinetic-dynamic modeling is well established [405,456,457],... 

Table 10.1 Assumptions and operable equations for the pharmacokinetic-dynamic models. The hysteresis column Hyster refers to the graph of the effect-concentration plot.

We need to know something about the distributions of the deviations of individual patient pharmacokinetic-dynamic model parameters from their population average values, and how these deviations correlate with one another. The deviations are population parameters of a different type random individual effect parameters random because individual deviations are regarded as occurring according to chance mechanisms. 

Nonlinear mixed-effects modeling methods as applied to pharmacokinetic-dynamic data are operational tools able to perform population analyses [461]. In the basic formulation of the model, it is recognized that the overall variability in the measured response in a sample of individuals, which cannot be explained by the pharmacokinetic-dynamic model, reflects both interindividual dispersion in kinetics and residual variation, the latter including intraindividual variability and measurement error. The observed response of an individual within the framework of a population nonlinear mixed-effects regression model can be described as... 

The model described above has been successfully applied to characterize the in vivo concentration effect relationships of several 5-HT1A agonists including flesinoxan and buspirone [558,559]. This model has also linked with the operational model of agonism into a full mechanism-based pharmacokinetic-dynamic model [560]. 

These studies show that it is possible to predict the time course of drug effects in vivo in situations in which complex homeostatic control mechanisms are operative. As such, they form the basis for the development of an entirely new class of pharmacokinetic-dynamic models. These models are important for the development of new drugs and the application of such drugs in clinical practice. For example, on the basis of this kind of model, it becomes possible to predict whether withdrawal symptoms will occur on cessation of (chronic) drug... 

Paalzow, L., Integrated pharmacokinetic-dynamic modeling of drugs acting on the CNS, Drug Metabolism Reviews, Vol. 15, 1984, pp. 383-400. 

Type of endpoint. The type of endpoint recording is essential for the application of different types of mixture toxicity models. Endpoints measured at only 1 point in time may only be used to derive concentration-response-related parameters, such as ECx or LCx or NOECs. Continuous recording or at least repeated recording of responses may allow for time series analysis. Time-related responses may, for example, be used for the derivation of kinetic parameters by applying pharmacokinetic/dynamic models (like the PBPK models in human toxicology see, e.g., Krishnan et al. 1994) or... 

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