Chapter 2

### INTRODUCTION

Clinical pharmacokinetic dosage calculations are conducted using the easiest possible equations and methods that produce acceptable results. This is because there are usually only a few (sometimes as little as 1-2) drug serum concentrations on which to base the calculations. Drug serum concentrations are expensive (typically \$35-100 each), and obtaining them can cause minor discomfort and trauma to the patient. This situation is much different than that found in pharmacokinetic research studies where there may be 10-15 drug serum concentrations used to calculate pharmacokinetic parameters and more complex equations can be used to describe the pharmacokinetics of the drug. Because the goal of therapeutic drug monitoring in patients is to individualize the drug dose and serum concentrations in order to produce the desired pharmacological effect and avoid adverse effects, it may not be possible, or even necessary, to compute pharmacokinetic parameters for every patient or clinical situation.

### ONE-COMPARTMENT MODEL EQUATIONS FOR LINEAR PHARMACOKINETICS

When medications are administered to humans, the body acts as if it is a series of compartments1 (Figure 2-1). In many cases, the drug distributes from the blood into the tissues quickly, and a psuedoequilibrium of drug movement between blood and tissues is established rapidly. When this occurs, a one-compartment model can be used to describe the serum concentrations of a drug.2,3 In some clinical situations, it is possible to use a one-compartment model to compute doses for a drug even if drug distribution takes time to complete.4,5 In this case, drug serum concentrations are not obtained in a patient until after the distribution phase is over.

###### FIGURE 2-1

Using compartment models, the body can be represented as a series of discrete sections. The simplest model is the one-compartment model that depicts the body as one large container in which drug distribution between blood and tissues occurs instantaneously. Drug is introduced into the compartment, distributes immediately into a volume of distribution (V), and is removed from the body via metabolism and elimination via the elimination rate constant (ke). The simplest multicompartment model is a two-compartment model that represents the body as a central compartment into which drug is administered and a peripheral compartment into which drug distributes. The central compartment 1 is composed of blood and tissues that equilibrate rapidly with blood. The peripheral compartment 2 represents tissues that equilibrate slowly with blood. Rate constants represent the transfer between compartments (k12, k21) and elimination from the body (k10).

#### Intravenous Bolus Equation

When a drug is given as an intravenous bolus and the drug distributes from the blood into the tissues quickly, the serum concentrations often decline in a straight line when plotted on semilogarithmic axes (Figure 2-2). In this case, a ...

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