Classical Pharmacodynamics

Pharmacokinetics is closely related to pharmacodynamics, which is a recent development of great importance to the design of medicines. The former attempts to model and predict the amount of substance that can be expected at the target site at a certain time after administration. The latter studies the relationship between the amount delivered and the observable effect that follows. In some cases the observable effect can be related directly to the amount of drug delivered at the target site [2]. In many cases, however, this relationship is highly complex and requires extensive modeling and calculation. In this text we will mainly focus on the subject of pharmacokinetics which can be approached from two sides. The first approach is the classical one and is based on so-called compartmental models. It requires certain assumptions which will be explained later on. The second one is non-compartmental and avoids the assumptions of compartmental analysis. 

II.e.5.1. Background. The most important drug interactions result from pharmacokinetic (PK) phenomena. Pharmacodynamic (PD) interactions are poorly understood in humans (receptor level interaction potentiation of effect by action on different targets). Classically, PK interactions occur at the enzyme level. Careful attention to this factor should help limit the incidence of adverse effects, make it easier to maintain plasma levels within the therapeutic range, and demonstrate the benefit of certain therapeutic combinations. Clinical trials on add-on regimens are needed. It should be noted that the clinical relevance of certain PK interactions remains to be established. 

Although little is known about the pharmacodynamics of hypericum, even less is known about its metabolism or its potential to affect the metabolism of other drugs. However, hypericum has recently been shown to produce substantial induction of CYP 3A3/4 such that a warning has been issued about its ability to decrease the levels of protease inhibitors to less than effective concentrations. Thus, physicians will likely need to prescribe higher doses of CYP 3A3/4 substrates when a patient is taking hypericum just as in patients on carbamazepine, a classic CYP 3A 3/4 inducer. 

A traditional isostere, or classical isostere, is an atom or group of atoms with similar spatial requirements (Table 11.4, page 281).10 Exchanging one for another imparts little change on the shape and volume of the molecule and therefore should not affect the binding (pharmacodynamics) of a compound. Changing one isostere for another, however,... 

Fig. 1.3 Pharmacokinetic/pharmacodynamic (PK/PD) modeling as combination of the classic pharmacological disciplines pharmacokinetics and pharmacodynamics (from [5]).

Pharmacokinetic studies are in general less variable than pharmacodynamic studies. This is so since simpler dynamics are associated with pharmacokinetic processes. According to van Rossum and de Bie [234], the phase space of a pharmacokinetic system is dominated by a point attractor since the drug leaves the body, i.e., the plasma drug concentration tends to zero. Even when the system is as simple as that, tools from dynamic systems theory are still useful. When a system has only one variable a plot referred to as a phase plane can be used to study its behavior. The phase plane is constructed by plotting the variable against its derivative. The most classical, quoted even in textbooks, phase plane is the c (f) vs. c (t) plot of the ubiquitous Michaelis-Menten kinetics. In the pharmaceutical literature the phase plane plot has been used by Dokoumetzidis and Macheras [235] for the discernment of absorption kinetics, Figure 6.21. The same type of plot has been used for the estimation of the elimination rate constant [236]. 

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. 

An important outcome of these studies is the opportunity that it offers to discuss the implications of the presence of nonlinear dynamics in processes such as the secretion of cortisol. Based on the aforementioned discussion it is evident that the concepts of deterministic nonlinear dynamics should be adopted in pharmacodynamic modeling when supported by experimental and physiologic data. This is valid not only for the sake of more detailed study, but mainly because nonlinear dynamics suggest a whole new rationale fundamentally different from the classical approach. Moreover, the clinical pharmacologist should be aware of the limitations of chaotic models for long-term prediction, which is contrary to the routine use of classical models. 

The area of clinical pharmacology that first directed attention to the consequences of stereoisomerism on therapeutic and pharmacokinetics was that of drug interactions, particularly those of the anticoagulant warfarin. Not only may drug interactions be stereoselective, but there is a potential for one stereoisomer to alter the pharmacokinetics and pharmacodynamics of the other. A classical example is the interaction with achiral phenylbutazone, which inhibits the metabolism of active 5-warfarin but stimulates the metabolism of the less active R isomer. Other stereoselective drug interactions include the induced elimination of misoni-dazole by phenytoin. Phenytoin enhances the clearance of (4—)-misonidazole by 56%o, which is higher than the increase in clearance of 33%o noted for (—)-misonidazole. 

Pharmacodynamics describes the time course and the magnitude of pharmacological response of drugs. Based on the classic receptor-occupancy theory, after drug molecules reach the target biophase, it binds to the receptors to form the drug-receptor complex to exert pharmacological response (Fig. 2). 

Biopharmaceutical research often involves the collection of repeated measures on experimental units (such as patients or healthy volunteers) in the form of longitudinal data and/or multilevel hierarchical data. Responses collected on the same experimental unit are typically correlated and, as a result, classical modeling methods that assume independent observations do not lead to valid inferences. Mixed effects models, which allow some or all of the parameters to vary with experimental unit through the inclusion of random effects, can flexibly account for the within-unit correlation often observed with repeated measures and provide proper inference. This chapter discusses the use of mixed effects models to analyze biopharmaceutical data, more specihcally pharmacokinetic (PK) and pharmacodynamic (PD) data. Different types of PK and PD data are considered to illustrate the use of the three most important classes of mixed effects models linear, nonlinear, and generalized linear. 

---