PKPD Modeling of Biomarkers

PK/PD modeling and simulation tools have continued to develop to a high level of sophistication over the past 20 years. Mechanism-based PK/PD modeling involves a set of techniques using mathematical and mechanistic models derived from quantitative pharmacology. The simplest compartmental PK model can be described as a one- compartment model following intravenous administration of a drug. A schematic representation of the compartmental model is presented in Figure 1. In this example, the removal of

Figure 1 Pharmacokinetic modeling and equations.

drug from the central compartment (i.e., systemic circulation) was described using a first-order elimination rate constant. Compartmental analyses can be performed routinely by fitting the data to a model using a PK/PD software package such as WinNonlin (Pharsight, a Certara Company, St. Louis, Missouri), Kinetica (ThermoFisher, Waltham, Massachusetts), S-AD APT (University of Southern California,) or NONMEM (University of California at San Francisco). The PK of drugs can be described using more advanced compartmental models and can be customized to describe any type of PK behavior. Case studies in which different types of compartmental models were used in preclinical and clinical drug development are presented later in the chapter.

Modeling the concentration-effect relationship on the biomarker is very dependent on the mechanism of action of the drug. In vitro studies that may elucidate this mechanism are very important in the early stage of drug development. For example, drug-induced changes in biomarkers of interest are often modeled using classical drug receptor theory following the law of mass action. This theory predicts that as receptors in the target organ interact with the drug, the biomarker levels will increase with increasing interaction until all receptors have been occupied, at which time no further change in bio-marker will occur. In its simplest form, the effect on the biomarker will be driven by the measured drug concentration over time, Ctime- assuming that drug concentrations in the systemic circulation is at equilibrium with the effect site. The classic and most commonly used PD model under these conditions is the Emax model, which is an empirical function for describing nonlinear concentration-effect relationships. It has the general form illustrated in Figure 2, where Emax represents the maximum effect on the biomarker, Ctime the concentrations of a drug predicted over time with a PK model, and EC-0 the concentration of the drug that produces half of Emax. The PD model can be

Equation Pharmacodynamics

Equation Pharmacodynamics

Drug Concentration

Figure 2 Pharmacodynamic modeling and equations.

Drug Concentration

Figure 2 Pharmacodynamic modeling and equations.

Pharmacokinetics

Pharmacodynamics

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