PK and PD Modeling

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Pharmacokinetics (PK) may be defined as what the body does to the drug, as opposed to pharmacodynamics (PD) which may be defined as what the drug does to the body [4].

The site of action of a pharmacological substance might be restricted to certain tissues or cells, which is why a quantitative estimate of the amount of administered substance that is available at the site of action is required. This question is the subject of pharmacokinetics and different modeling techniques are well- established in pharmaceutical research to support its investigation. So far, the most widely used approach is to establish descriptive and comparatively simple compartmental PK models that can be well identified based on available data. Often these models are applied to population PK data using nonlinear mixed-effect techniques (NLME), e.g. to quantify sources of population variability or covariate effects. Besides PK, such models may also include a description of a compound's effects (PD), for example, in the form of a simple hyperbolic or sigmoid concentration-effect relation (Michaelis-Menten, Hill, or Emax type).

Thus, in classical pharmacokinetic modeling, the aim is to fit a comparatively simple model to experimental data in order to determine pharmacokinetic parameters from the fitted concentration-time-course. These parameters are then used to characterize and quantify the behavior of the investigated substance in general or in a certain clinical trial and, potentially, to make extrapolations to situations that have not been already investigated.

In contrast to the rather phenomenological consideration of drug PK in compartmental models, physiologically–based pharmacokinetic (PBPK) models aim for a detailed representation of physiological processes as will be summarized in the following. Consequently, PBPK-modeling is based on the mathematical description of physical and physiological processes and in the framework of PBPK modeling a genuine simulation of the pharmacokinetic behavior using this description is performed. Also, the pharmacodynamics can be represented in more mechanistic detail as briefly discussed in Modeling Concepts - PD and Reaction Network Modeling. A good starting point for further reading can be found in [65].

Structure of compartmental PK model (A) and PBPK model (B)