Introduction

Pharmacokinetics is a study of drug and metabolite kinetics in the body: drug absorption, distribution, metabolism, and excretion. Pharmacokinetic models and mathematic models are used to calculate drug dosage regimens, perform dosage adjustments in patients, predict food–drug and drug–drug interactions, design and test drug formulations and novel drug delivery systems, and evaluate the quality of pharmacologic products. The most common pharmacokinetic model is the mammillary model. It is an abstract model, in which one or more compartments represent the whole body or group of tissues and where the movement of drug molecules from one compartment to another, as well as drug excretion and metabolism, follows first-order kinetics.

Keywords

Compartmental models; duration; mammillary model; onset time; pharmacokinetic model; population pharmacokinetics; therapeutic index

Chapter Outline

Although the concept of drug absorption, distribution and elimination has been known for over 150 years [1] the term “pharmacokinetics” was first introduced in 1953 by Friedrich Hartmut Dost in his book “Der Blütspiege: Kinetic der Konzentrationsabläufe in der Krieslaufflüssigkeit” [2,3]. Later Perl [4], Nelson [5], Krüger-Thiemer [6], Wagner [7,8], Garrett [9,10], Rowland [11], Gibaldi [12,13], Riegelman [14], Levy [15], and numerous other scientists introduced the various pharmacokinetic methods and terms, giving us the science of pharmacokinetics as it is today [1].

1.1 Some Basic Concepts

A drug proceeds through a distinct pathway from mixing the active pharmaceutical ingredient (API) with excipients to forming the drug product to the therapeutic effect (Figure 1.1). For example, a propranolol tablet is formed by compressing a mixture of the API (i.e., propranolol hydrochloride) and various excipients such as lactose into a tablet. Tablets are one of several different propranolol drug products. Other known propranolol products include oral solutions and solutions for parenteral injection. Following oral administration (sometimes referred to as per os or per oral [PO] administration), the tablet disintegrates, and solid propranolol dissolves in the aqueous fluid of the gastrointestinal (GI) tract. The dissolved propranolol molecules are then absorbed into the general blood circulation and distributed throughout the body. The drug is partly metabolized and excreted from the body, but a small fraction of the drug, which is a β-blocker, reaches the target site, where its binds to receptors (e.g., β-adrenergic receptors), causing vasodilatation (which is the pharmacologic response) that leads to lowering of blood pressure (which is the therapeutic effect). Pharmacokinetics is the kinetics of drug absorption, distribution, metabolism, and excretion (ADME). All of these four criteria influence the levels and kinetics of drug exposure to tissues and thus influence the performance and pharmacologic activity of the compound as a drug. ADME profiling and toxicology screening are some of the most important research activities in the drug discovery and development process. ADME and toxicologic (ADME/Tox) properties determine the “druggability” of new chemical entities (NCEs). Biopharmaceutics describes how the physicochemical properties of drugs, the pharmaceutical dosage forms, and the routes of drug delivery affect the rate and extent of drug absorption into the body. Pharmacodynamics is the science that describes the relationship between the drug concentration at the receptor and biological activity (i.e., pharmacologic response or drug effect).

After oral administration, the drug is absorbed from the GI tract into the body (Figure 1.2). In general, some fraction of the drug is then metabolized and the metabolites excreted through urine, but a fraction of the drug may also be excreted unchanged through urine.

Bioavailability represents the drug fraction that reaches the systemic blood circulation after, for example, oral administration. Bioavailability can be divided into pharmaceutical availability and biologic availability. If propranolol is completely released from a tablet and dissolved in the aqueous GI fluid, the drug is said to have 100% pharmaceutical availability. Aqueous propranolol solution has 100% pharmaceutical availability (Fpharm). However, propranolol undergoes first-pass metabolism and thus its biologic availability (Fbio) after oral administration is frequently about 75%. Consequently, the bioavailability (F) of propranolol solution will be only about 75%:

=Fpharm×Fbio=1.00×0.75=0.75 (1.1)

If the pharmaceutical availability of propranolol in a tablet is 50% and the biologic availability is 75%, the bioavailability of the propranolol tablets will be 37.5%:

=Fpharm×Fbio=0.50×0.75=0.375 (1.2)

Drugs have 100% bioavailability when they are administered through intravenous (IV) injection, that is, the entire drug dose enters the general blood circulation. Minimum effective concentration (MEC) is the minimum plasma concentration of a drug needed to achieve sufficient drug concentration at the receptors to produce the desired pharmacologic response, if drug molecules in plasma are in equilibrium with drug molecules in the various tissues (Figure 1.3). Minimum toxic concentration (MTC) is the minimum drug plasma concentration that produces a toxic effect. Onset time is the time from administration that is required for a drug to reach its MEC. Duration of drug action is the difference between the onset time and the time when the drug concentration declines below MEC (Figure 1.3).

After oral administration, the drug is absorbed from the GI tract into the general blood circulation, where it reaches maximum plasma concentration (Cmax) at time (t) equals tmax. Then the concentration declines as a result of metabolism and excretion of unmetabolized drug. The therapeutic concentration range (or therapeutic window) of a drug is the concentration range from the MEC to the MTC. In animal studies, the therapeutic index (TI) is the lethal dose of a drug for 50% of the animal population (LD50) divided by the minimum effective dose for 50% of the population (ED50). In humans, TI is frequently defined as the ratio of the dose that produces toxicity in 50% of the population (TD50) divided by ED50 (Figure 1.4):

animals:TI=LD50ED50 (1.3)

humans:TI=TD50ED50 (1.4)

1.2 Pharmacokinetic Models

Various types of pharmacokinetic models are used to describe drug absorption, distribution, metabolism, and elimination from the body (i.e., ADME). There are three basic types of pharmacokinetic modes: (1) compartmental models, where a compartment represents a group of tissues that have similar affinity to the drug; (2) physiologic-based pharmacokinetic models, which apply physiologic parameters such as blood flow and drug partition into tissues; and (3) noncompartmental models, which use time and drug concentration averages. In compartmental models, groups of tissues that have similar blood flow and drug affinity are represented as single compartments. The compartments do not represent any specific anatomic region within the body. Uniform drug distribution is assumed within each compartment, and simple first-order rate equations are used to describe the transport of drug into and out of the compartment. Since the drug can enter and leave the body, the models are characterized as “open” models. The caternary model, in which the compartments are arranged like train wagons, and the mammillary model, which consists of one central compartment connected to peripheral compartments, are examples of compartmental pharmacokinetic models. The most common pharmacokinetic model in humans, and the only one discussed in this book, is the mammillary model.

Ideally, each and every tissue and body organ should be represented by one compartment, but the complexity of the human anatomy and physiology makes it virtually impossible. However, in physiologic-based pharmacokinetic models, some organs or tissues are represented by single compartments, whereas others are grouped into paired compartments (Figure 1.5). The blood...