Comparative Pharmacokinetics E-Book

• Herausgeber: John Wiley & Sons
• Kategorie: Fachliteratur
• Sprache: Englisch

Seitenzahl: 921

Veröffentlichungsjahr: 2011

Beschreibung

Now in a revised edition, Comparative Pharmacokinetics: Principles, Techniques, and Applications presents the principles and techniques of comparative and veterinary pharmacokinetics in a detailed yet practical manner. Developed as a tool for ensuring that pharmacokinetics studies are properly designed and correctly interpreted, the book provides complete coverage of the conceptual basis of pharmacokinetics as used for quantifying biological processes from the perspectives of physiology and medicine. New chapters have been added on quantitative structure permeability relationships and bioequivalence, and a number of existing chapters have been significantly revised and expanded to provide a current resource for veterinary and comparative pharmacokinetics.

Leseprobe

Table of Contents

Cover

Table of Contents

Half title page

Title page

Copyright page

Coauthors

Preface

1 Introduction

1.1 OBJECTIVES AND PHILOSOPHY

1.2 TARGET AUDIENCE AND APPLICATIONS

2 Principles of Drug Movement in the Body

2.1 AN OVERVIEW OF DRUG DISPOSITION

2.2 THE IMPORTANCE OF MEMBRANE BARRIERS

2.3 DRUG PASSAGE ACROSS MEMBRANES BY DIFFUSION

2.4 EFFECTS OF pH ON MEMBRANE TRANSPORT

2.5 PATHWAYS FOR MEMBRANE TRANSPORT

2.6 INTEGRATION OF MEMBRANE TRANSPORT CONCEPTS

3 Quantitative Structure–Permeability Relationships

3.1 QSPeR MODELING

3.2 APPLICABILITY DOMAIN

3.3 OTHER MODELS AND APPLICATIONS

4 Absorption

4.1 GASTROINTESTINAL ABSORPTION

4.2 TOPICAL AND PERCUTANEOUS ABSORPTION

4.3 RESPIRATORY ABSORPTION

4.4 OTHER ROUTES OF ADMINISTRATION

4.5 BIOAVAILABILITY

5 Distribution

5.1 PHYSIOLOGICAL DETERMINANTS OF DISTRIBUTION

5.2 TISSUE BARRIERS TO DISTRIBUTION

5.3 PLASMA PROTEIN BINDING

5.4 OTHER FACTORS AFFECTING DISTRIBUTION

5.5 CONSEQUENCES OF DISTRIBUTION

6 Renal Elimination

6.1 RENAL PHYSIOLOGY RELEVANT TO CLEARANCE OF DRUGS

6.2 MECHANISMS OF RENAL DRUG EXCRETION

6.3 THE CONCEPT OF CLEARANCE AND ITS CALCULATION

6.4 NONLINEARITY OF TUBULAR SECRETION AND REABSORPTION

6.5 SUMMARY

7 Hepatic Biotransformation and Biliary Excretion

7.1 PHASE I AND PHASE II REACTIONS

7.2 METABOLISM INDUCTION AND INHIBITION

7.3 HEPATIC CLEARANCE

7.4 BILIARY DRUG ELIMINATION

7.5 PHARMACOLOGICAL AND TOXICOLOGICAL SIGNIFICANCE

7.6 THE IMPORTANCE OF EXTRACTION RATIO

7.7 CONCLUSION

ACKNOWLEDGMENT

8 Compartmental Models

8.1 A PRIMER ON THE LANGUAGE OF PHARMACOKINETICS

8.2 THE CONCEPT OF HALF-LIFE

8.3 ONE-COMPARTMENT OPEN MODEL

8.4 ABSORPTION IN A ONE-COMPARTMENT OPEN MODEL

8.5 TWO-COMPARTMENT MODELS

8.6 MULTICOMPARTMENTAL MODELS

8.7 CONCLUSION

9 Noncompartmental Models

9.1 STATISTICAL MOMENT THEORY

9.2 CALCULATION OF MOMENTS

9.3 OTHER RESIDENCE TIMES AND PARAMETERS OF INTEREST

9.4 OTHER MODEL-INDEPENDENT APPROACHES

9.5 AN APPLICATION OF STATISTICAL MOMENT THEORY

ACKNOWLEDGMENT

10 Nonlinear Models

10.1 MICHAELIS–MENTEN RATE LAWS

10.2 PHARMACOKINETIC IMPLICATIONS OF MICHAELIS–MENTEN KINETICS

10.3 THE IMPACT OF CAPACITY-LIMITED KINETICS AND VARIOUS PHARMACOKINETIC PARAMETERS

10.4 OTHER NONLINEAR ELIMINATION PROCESSES

10.5 PROTEIN AND TISSUE BINDING

10.6 NONLINEAR PHARMACOKINETICS: A CAVEAT

ACKNOWLEDGMENT

11 Physiological Models

11.1 INTRODUCTION

11.2 MODEL CONSTRUCTION

11.3 ANALYSIS

11.4 ADVANTAGES

11.5 APPLICATION TO VETERINARY MEDICINE

11.6 AN APPLICATION APPLIED TO A HYBRID MODEL

12 Dosage Regimens

12.1 DOSAGE REGIMEN DESCRIPTORS

12.2 PRINCIPLE OF SUPERPOSITION

12.3 DOSAGE REGIMEN FORMULAE

12.4 SOME COMMENTS ON EFFICACY AND SAFETY

12.5 CONCLUSION

13 Simultaneous Pharmacokinetic–Pharmacodynamic Modeling

13.1 OVERVIEW ON PK/PD MODELING

13.2 THE BUILDING OF PK/PD MODELS

13.3 THE MEANING AND CLINICAL RELEVANCE OF THE DIFFERENT DEPENDENT VARIABLES OF A PD MODEL: ACTION, EFFECT, RESPONSE, BIOMARKERS, AND SURROGATES

13.4 HYSTERESIS

13.5 TURNOVER MODELS

13.6 INCORPORATION OF A PD MODEL OF DRUG ACTION INTO A PHYSIOLOGICAL MODEL

13.7 TIME-VARIANT MODELS: TOLERANCE AND REBOUNDS

13.8 POPULATION PK/PD MODELING APPROACHES

13.9 APPLICATION OF THE PK/PD APPROACH TO THE SELECTION OF AN EFFECTIVE DOSAGE REGIMEN

13.10 CONCLUSIONS

14 Study Design and Data Analysis

14.1 INTRODUCTION TO STATISTICAL CONCEPTS

14.2 CURVE FITTING

14.3 COMPUTER CURVE-FITTING EXAMPLES

14.4 GENERAL CONCEPTS

15 Bioequivalence Studies

15.1 BIOAVAILABILITY

15.2 HISTORICAL BIOEQUIVALENCE PERSPECTIVE

15.3 BIOEQUIVALENCE STUDY PROTOCOL CONSIDERATIONS

15.4 PK DATA ANALYSIS

15.5 STATISTICAL ANALYSIS OF BIOAVAILABILITY DATA

15.6 INDIVIDUAL VERSUS POPULATION BIOEQUIVELANCE: ALTERNATIVE STATISTICAL DESIGNS

15.7 ENDOGENOUS COMPOUNDS: PRODUCTS WITH NONZERO BASELINES

15.8 HUMAN FOOD SAFETY

15.9 IN VITRO TESTING AND ANALYSIS OF DISSOLUTION DATA

15.10 IN VIVO/IN VITRO CORRELATIONS

15.11 THE BIOPHARMACEUTICS CLASSIFICATION SYSTEM

15.12 CONCLUSION

ACKNOWLEDGMENT

16 Population Pharmacokinetic Models

16.1 SOURCES OF VARIABILITY

16.2 THE STANDARD APPROACH

16.3 THE POPULATION APPROACH

16.4 POPULATION VERSUS STANDARD APPROACH: AN EXAMPLE

16.5 PHARMACOKINETIC AND PHARMACODYNAMIC BIOLOGICAL VARIABILITY

16.6 PHARMACOKINETIC AND PHARMACODYNAMIC STATISTICAL VARIABILITY

16.7 PHARMACOSTATISTICAL MODELS FOR POPULATION STUDIES

16.8 VALIDATION OF THE RESULTS

16.9 APPLICATION OF POPULATION PHARMACOKINETICS IN VETERINARY MEDICINE

ACKNOWLEDGMENT

17 Dosage Adjustments in Disease States

17.1 RENAL DISEASE

17.2 HEPATIC DISEASE

17.3 OTHER DISEASE STATES

17.4 CONCLUSIONS

18 Interspecies Extrapolations

18.1 PHARMACOKINETIC SCALING

18.2 PROTEIN BINDING

18.3 APPLICATIONS

18.4 THE CONCEPT OF SPECIES-EQUIVALENT TIME AND SPECIES-INDEPENDENT CONCENTRATION-VERSUS-TIME PROFILES

18.5 EXTRAPOLATION PITFALLS

18.6 CONCLUSION

19 Tissue Residues and Withdrawal Times

19.1 ESTABLISHMENT OF A TISSUE TOLERANCE

19.2 ESTIMATION OF A WDT

19.3 PHARMACOKINETICS APPLIED TO WDTS

19.4 LIMITATIONS TO CURRENT WDT DETERMINATIONS

19.5 GUESSTIMATING WITHDRAWAL INTERVALS AFTER EXTRALABEL USE

19.6 CONCLUSION

Index

Comparative Pharmacokinetics

This edition first published 2011 © 2011 by Jim E. Riviere

First edition published 1999 © 1999 Iowa State University Press

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Library of Congress Cataloging-in-Publication Data

Riviere, Jim E. (Jim Edmond), author.

 Comparative pharmacokinetics / Jim E. Riviere, North Carolina State University, Raleigh, North Carolina. – 2nd Edition.

p. ; cm.

 Includes bibliographical references and index.

 ISBN 978-0-8138-2993-7 (pbk. : alk. paper)

 ISBN 978-0-4709-5988-6 (ebk)

 1. Pharmacokinetics. 2. Veterinary pharmacology. I. Title.

 [DNLM: 1. Pharmacokinetics. QV 38]

 RM301.5.R58 2011

 636.089′578–dc22 2010047729

A catalogue record for this book is available from the British Library.

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Coauthors

The numbers in parentheses indicate chapters coauthored with Dr. Jim E. Riviere.

Ronald Baynes (7)

Center for Chemical Toxicology Research and Pharmacokinetics

Department of Population Health and Pathobiology

College of Veterinary Medicine

North Carolina State University

Raleigh, NC, USA

[email protected]

James Brooks (Illustrator)

Center for Chemical Toxicology Research and Pharmacokinetics

Department of Population Health and Pathobiology

College of Veterinary Medicine

North Carolina State University

Raleigh, NC, USA

[email protected]

Jennifer Buur (5)

College of Veterinary Medicine

Western University of Health Sciences

Pomona, CA, USA

[email protected]

Jason Chittenden (14 and 16)

Center for Chemical Toxicology Research and Pharmacokinetics

College of Veterinary Medicine

North Carolina State University

Raleigh, NC, USA

Pharsight, Inc.

Cary, NC, USA

[email protected]

Jennifer Davis (17)

Department of Clinical Sciences

College of Veterinary Medicine

North Carolina State University

Raleigh, NC, USA

[email protected]

Teresa Leavens (11)

Center for Chemical Toxicology Research and Pharmacokinetics

Department of Population Health and Pathobiology

College of Veterinary Medicine

North Carolina State University

Raleigh, NC, USA

[email protected]

Sharon Mason (19)

Department of Biological Sciences

Campbell University

Buies Creek, NC, USA

[email protected]

Marilyn Martinez (15)

Center for Veterinary Medicine

US Food and Drug Administration

Rockville, MD, USA

[email protected]

Jim E. Riviere

Center for Chemical Toxicology Research and Pharmacokinetics

Department of Population Health and Pathobiology

College of Veterinary Medicine

North Carolina State University

Raleigh, NC, USA

[email protected]

Pierre-Louis Toutain (13)

UMR181 Physiopathologie et Toxicologie Expérimentales INRA

Ecole Nationale Vétérinaire de Toulouse-23

Chemin des Capelles–31076

Toulouse, France

[email protected]

Xin-Rui Xia (3)

Center for Chemical Toxicology Research and Pharmacokinetics

Department of Population Health and Pathobiology

College of Veterinary Medicine

North Carolina State University

Raleigh, NC, USA

[email protected]

Preface

The second edition of Comparative Pharmacokinetics follows the first edition’s goals of providing the conceptual basis of pharmacokinetics as a tool for quantifying biological processes encountered in comparative medicine.

The organization of this book remains the same whereby the basic principles of physiology are introduced for systems involved in the absorption, distribution, metabolism, and elimination (ADME) of chemicals and drugs in the body. This is followed by chapters developing the primary approaches used in pharmacokinetic modeling today, namely compartmental, noncompartmental, population, and physiological approaches. Chapters on nonlinear processes, dosage regimen construction, and statistical aspects of data analysis are presented, followed by overviews of pharmacokinetic–pharmacodynamic (PK-PD) modeling and specific applications on bioequivalence, disease effects, interspecies extra­polations, and drug residues in food-producing animals.

As in the first edition, this author has authored or coauthored all chapters for consistency. New additions to this text include extensive revisions of the Distribution chapter coauthored by Jennifer Buur, the Hepatic Biotransformation chapter by Ronald Baynes, and the Physiological Models chapter by Teresa Leavens. Chapters on Study Design and Population Modeling by Jason Chittenden, Dosage Adjustment in Disease by Jennifer Davis, and Tissue Residues by Sharon Mason have been expanded and revised. Pierre-Louis Toutain comprehensively rewrote the PK-PD chapter as PK-PD modeling has become widespread in comparative medicine. A new chapter on Quantitative Structure–Permeability Relationships coauthored with Xin-Rui Xia has been added to illustrate how molecular properties of chemicals and drugs are correlated to membrane transport, the basis of most pharmacokinetic processes. Also, this chapter introduces basic statistical concepts of regression analysis and study validation that are expounded upon later in the book. Finally, the Bioequivalence chapter by Marilyn Martinez of the U.S. Food and Drug Administration offers a complete regulatory perspective on determining product bioequivalence. This chapter demonstrates many of the pharmacokinetic principles introduced in the earlier chapters and adds in the requirements for statistical rigor needed for a regulatory approval. All the remaining chapters have been revised and updated. In addition, cross-referencing topics across all chapters has been expanded to help the reader to make important conceptual linkages between theory and applications.

This comparative and veterinary pharmacokinetics textbook serves as an introduction to this discipline from the perspectives of physiology and medicine. The wide availability of economic but powerful computers with comprehensive software packages can make pharmacokinetic analysis seem automatic. A primary goal of this book is to ensure that studies are properly designed before being conducted, that the proper models are used for the end points in mind, and that resulting pharmacokinetic parameters are interpreted correctly.

Jim E. Riviere

1

Introduction

Pharmacokinetics is best defined as the use of mathematical models to quantitate the time course of drug absorption and disposition in man and animals. With the tremendous advances in medicine and analytical chemistry, coupled with the almost universal availability of computers, what was once an arcane science has now entered the mainstream of most fields of human and veterinary medicine. This discipline has allowed dosages of drugs to be tailored to individuals or groups to optimize therapeutic effectiveness, minimize toxicity, and avoid violative tissue residues in the case of food-producing animals.

What differentiates this discipline from other fields of pharmacology and medicine is its focus on quantitating biological phenomena using various mathematical models and restricting its purview to the movement of drugs and chemicals into, through, and out of the body. The subsequent effects of these drugs on biological processes fall in the realm of pharmacodynamics (PD), which is beyond the scope of the present pharmacokinetic text but is extensively reviewed in Chapter 13 when linkage to pharmacokinetic models is developed. There are numerous applications of pharmacokinetics in clinical practice, some of them unknown to the practitioner as actually being pharmacokinetic modeling exercises since the terminology has become embedded into the lexicon of general medicine.

Since the publication of the first comparative pharmacokinetics text by Desmond Baggot in 1977, there has been explosive growth in all aspects of this discipline. This growth has continued after the publication of the first edition of the present text in 1999 and the release in 2004 of the pivotal UK “PK and PK-PD in Veterinary Medicine” workshop (Lees, 2004). The continued integration of pharmacokinetic concepts into global veterinary drug regulations further fuels this growth, a development that can be appreciated by reading Chapter 15 on regulatory aspects of drug product bioequivalence.

The primary pharmacokinetic models originally utilized by comparative and veterinary pharmacokineticists were the classic open compartmental models. These models, first clearly elucidated by Teorell in 1937, have been the mainstay of pharmacokinetics for much of the last decade. However, the use of noncompartmental models, especially those based on statistical moment analyses, has recently expanded across multiple areas. This popularity can be linked in part to a superb suitability for analysis by digital computers. Paradoxically, many of the properties that make the analysis of serum pharmacokinetic data amenable to exponential equations result from a few mathematical peculiarities in the solution of these compartmental models. Newer noncompartmental approaches to data analysis share many of these attributes and thus also share the same limitations of the classic modeling approaches. These intricacies will be completely explored in this text.

In the last decade, there has been a greatly increased use of so-called population pharmacokinetic approaches. This growth has been facilitated by the availability of user-friendly software and the implicit recognition that interindividual variability in the physiology underlying pharmacokinetic parameters may overshadow drug-specific parameters. Quantitating this variability using stochastic techniques is becoming widespread.

Pharmacokinetic principles have become widespread in the discipline of toxicology, an application termed toxicokinetics. There are no fundamental differences between pharmacokinetic and toxicokinetic principles except that the latter often deal with higher doses of chemicals, which may saturate metabolizing enzymes and in some cases may damage eliminating organs, thereby altering the disposition of the toxin. However, the principles involved are identical, and the concepts presented in this text are applicable to both fields.

Physiologically based pharmacokinetic (PBPK) models have become routine in many fields of pharmacology and toxicology. These models, unlike the others mentioned, build on the basis of sound anatomical and physiological principles and, although data-intensive, may allow the best opportunity for true mechanism-based interspecies pharmacokinetic extrapolations. Individual organ function is easily scaled across species and in vitro data may be extrapolated to the whole animal. This modeling approach has been increasingly applied to the problem of drug and chemical residues in food-producing animals.

The goal of quantitative pharmacology is always to extrapolate the drug concentration profile in the simpler in vitro experimental environment to that which actually exists in the cells or tissues of whole animals. Such an extrapolation (albeit very crude) is made daily with the use of minimum inhibitory concentrations (MICs) to estimate the efficacy of an antimicrobial drug against a specific bacteria in a human or animal patient. Recent work has focused on quantifying in vitro-to-in vivo correlations, one flavor of which termed IVIVC focuses on predicting oral absorption from in vitro dissolution studies. In vitro studies may be conducted with very simple subcellular, single-cell, or tissue culture systems or more complex perfused organ preparations (also referred to as ex vivo models).

In drug development and biochemical toxicology laboratories, extrapolation is often from a simple receptor or subcellular fraction assay, which detects drug or toxin binding, to the dose of drug that would be required to achieve this effective concentration in vivo. Alternatively, DNA binding or cytotoxicity screens may detect potential adverse events associated with a specific chemical. This defines a hazard in the risk assessment process. However, sufficient exposure in the intact organism is still required for this hazard to be realized as a risk. Pharmacokinetics is often the bridge in this extrapolation. In fact, sophisticated concentration–response relationships, obtained from in vitro bioassay systems, may be defined and then linked to the in vivo dose–response profile using integrated pharmacokinetic–pharmacodynamic (PK-PD) modeling techniques. PBPK models also provide the framework for tying drug delivery to cells in modern systems biology schemes that attempt to model the cellular responses seen after chemical exposure using the tools of genomics, proteomics, and metabonomics.

Work has also exploded in the field of quantitative structure–activity relationships (QSARs) that relates molecular properties to biological activity. From its application to pharmacokinetics, progress has been made to use such techniques to predict oral bioavailability or transdermal delivery. A new chapter in this edition introduces these concepts.

The extrapolation of pharmacokinetic parameters across species is a major focus of research. This is true in laboratory animal medicine and especially so in exotic animal and zoo animal medicine. Many “classic” compartmental pharmacokinetic studies conducted in multiple animal species have been extrapolated using the techniques of allometry. This is often employed when laboratory animal toxicology data must be extended to humans to put into perspective the relationship between the expected toxic dose and therapeutically useful doses. This later concept of a “therapeutic window” framed by a minimal effective therapeutic dose or resultant concentration and maximally safe toxic threshold is found in many areas of medicine and is implicitly based in pharmacokinetic methodology.

The fields of clinical pharmacology have grown in both human and veterinary medicine. Subpopulations of patients based on age or disease processes are routinely defined and dosages of drug appropriately altered. Part of the growth of this discipline was facilitated by the routine application of pharmacokinetics in clinical patients. This was facilitated by the development of population pharmacokinetic approaches mentioned earlier, which merge the estimation of pharmacokinetic parameters with simultaneous clinical estimates of physiological parameters and population variability. Its application to defining disease-induced changes in drug disposition and probing the nature of pharmacokinetic variance are widespread. In veterinary medicine, these same principles are needed to extrapolate dosage regimens for extralabel drug use.

This proliferation of pharmacokinetics throughout these diverse fields has been propelled by the explosive growth in analytical methodologies using principles of both chromatography (high-performance liquid and gas chromatography) and immunology (radioimmunoassay, enzyme-linked immunosorbent assay [ELISA]). Not only has the cost per sample of these procedures plummeted but their availability and sensitivity have also increased tremendously. For many drugs, simple disposable card-type assays are being developed that will provide the clinician instantly with estimates of drug concentrations. In veterinary medicine, such assays are available to monitor milk and urine for the presence of violative drug residues.

With the drug concentration data now readily available, complex mathematical modeling that was once restricted to the esoteric and truly “user-unfriendly” and even “user-adverse” mainframe computers can now be routinely done on nearly any available personal computer using one of a myriad of simple-to-use pharmacokinetic software packages including Win-Nonlin and other packages (e.g., CONSAAM and SAAM, PK-Analyst, P-Pharm). In fact, the proliferation of these automated software packages is one of the developments that highlighted the need for this text because, parallel to this proliferation of tools to conduct pharmacokinetic analyses, many workers have failed to study its basic principles and often inappropriately apply models to experimental and clinical situations.

1.1 OBJECTIVES AND PHILOSOPHY

The purpose of this book is to provide an introduction of the discipline of pharmacokinetics for the student, researcher, and comparative medicine clinician. The text presents an overview of the basic processes of drug absorption and disposition and then details how these processes can be quantitated using different pharmacokinetic approaches. The book is directed toward both the individual responsible for doing the analysis and the user of the pharmacokinetic information generated. To properly employ pharmacokinetic information, the limitations of the specific model that generated the pharmacokinetic parameter estimates must be appreciated. Are the parameters compatible with the model in which it will be used to make predictions? Many pharmacokinetic parameters are model-dependent, and serious errors may occur if the inappropriate parameters are used. A pharmacokinetic model is simply an artificial mathematical link to the underlying interaction of a drug’s pharmacology with an animal’s physiology (Fig. 1.1). The nature of the link will determine the types of parameters calculated.

Fig. 1.1 Conceptual framework of how a pharmacokinetic model links the observed data to the underlying biology controlling drug disposition.

A common misconception is that if one specific model fails to adequately predict the data or experimental scenario, then the process being studied is assumed to not be amenable to pharmacokinetic analysis. Often, the fault is that insufficient data have been collected to properly define the model and its so-called inference space. The “links” were not properly constructed. In other cases, incomplete understanding of the disposition processes involved resulted in construction of a woefully inadequate model in the first place. The limitations of specific models and techniques must be appreciated before extrapolations can be made.

This book is also written for the individual who never plans on actually doing a pharmacokinetic study but desires to understand more about the time course of drug movement throughout the body. The primary goal of pharmacokinetics is to generate parameters that are mathematical abstractions that quantitate physiological processes as an aid to better understanding drug disposition. Mathematical modeling generates parameters that may vary as the physiology varies as a result of disease, age, sex, or drug-induced toxicity. The parameters are mathematical constructs that reflect changes in underlying physiology. There is no absolute value of any parameter that exists independent of the model; parameters are defined by the model and reflect the nature of the mathematical links to the physiology.

Models may be classified as mechanistic (e.g., compartmental and physiological), which represent some abstraction of the underlying physiologic reality, or as empirical (e.g., noncompartmental, neural-net analysis), which are restricted to predicting observed data. Alternatively, models may be classified as deterministic and thus purport to have exact predictability; or stochastic, which incorporate a level of statistical uncertainty in the predictions. An understanding of how models and links are derived is necessary for a thorough understanding of drug disposition and, ultimately, drug efficacy or toxicity.

There are many misconceptions as to what a pharmacokinetic study actually entails. Many workers in veterinary medicine believe that measuring drug concentrations in plasma or blood and plotting the resulting concentration–time profile comprises such a study. Similarly, some feel that if parameters such as peak concentration (Cmax), time to peak concentration, and the area under the concentration–time curve (AUC) are recorded, a pharmacokinetic analysis has been performed. In fact, to determine product bioequivalence, this does comprise a complete study. A new Chapter 15 has been added to this edition to overview the use of such approaches and present appropriate statistical techniques used in determining product bioequivalence by regulatory authorities. As will be stressed throughout this book, the problem with such analyses is that they are descriptive only for the experiment performed and are difficult to use for extrapolation to another animal or clinical conditions.

A pharmacokinetic study in the context of this book is defined as an experiment in which some type of mathematical model is fitted to the drug concentration–time profile in blood, tissue, and/or excreta. This opens the possibility of correlating model parameters to physiological processes or using them for interspecies extrapolation. In these types of analyses, parameters such as half-life (T½), volume of distribution (Vd), and clearance (Cl) are calculated in addition to the descriptive parameters mentioned above. A separate chapter will be devoted to the physiology underlying each type of parameter. Similarly, the major types of modeling paradigms adopted will be developed and compared. Whatever type of model is employed (linear vs. nonlinear, compartmental vs. noncompartmental), a model is only a tool to estimate drug concentrations and generate parameters that are useful for further analyses and quantitating the biological process under investigation. Models are neither correct nor incorrect, but should be judged only as to how accurately drug concentrations are predicted under new exposure conditions.

The selection of a model relative to its use for prediction of future events is an important decision. Fig. 1.2 depicts how three radically different mathematical models may fit the same limited data set. The three models are statistically equivalent in terms of their ability to describe the observed data, and thus all are mathematically appropriate. However, only the exponential model has a relatively direct link to biological reality. All three predict very different drug concentrations for times beyond the actual data collected. Within the observed time interval, all models accurately interpolate drug concentrations at times between collections. This is defined as the inference space of the model. However, extrapolation outside of the observed time window requires knowledge that the model has biological reality at these time points. Collection of as few as one or two additional data points would expand the model’s inference space and help select the more predictive model. It is surprising how often this simple limitation of fitting equations to data is overlooked.

Fig. 1.2 Illustration of how three very diverse mathematical models may adequately describe the same limited set of data yet result in very different values when predictions are extrapolated beyond the models’ inference space. Linear (—); sinusoidal (– –); exponential (— — —).

Completely independent of the model selected, it is the fitting of the model to the data, for the purposes of the investigator, that must be optimized. This is where statistics interfaces with pharmacokinetics. For example, three different approaches and sets of sampling intervals are used in studies to estimate a peak drug plasma concentration, to determine a dosing interval for chronic treatment, or to estimate the tissue residue withdrawal time in a food-producing animal. Although the underlying models may be very similar, or even identical, these three cases require optimizing estimates of different components of the model, and thus the experimental time frame may be very different, ranging from minutes to hours to days. The drug concentration ranges for these three applications are also likely to differ by three to four orders of magnitude. Failure to select a specific model appropriate to the proper experimental frame of reference may lead to serious errors in extrapolation. These aspects of experimental design and data analysis will be extensively reviewed at the end of the text.

Semantics plays a very important role in this interface between statistics and pharmacokinetics. Serious errors have occurred when the same term in both disciplines refers to two different items. Examples include the use of the Greek letter β, which in statistics may refer to the probability of a type II statistical error or the slope of a regression line, but in pharmacokinetics may specifically refers to the terminal exponential slope of the plasma drug concentration versus time data from a two-compartment model following intravenous drug administration. Standard practices for fitting mathematical models to the same data set in both disciplines may be very different. For example, the modeling approaches used in pharmacokinetics often are based on additive exponential functions simply because the resulting parameters then have physiological meaning; that is, they can be linked back to the animal. Such exponential functions are but a subset of those available to the statistician and may not even be the best for fitting to a specific curve. Nevertheless, they are used because they are interpretable and have physiological meaning, and thus can be incorporated into models that physiologically and pharmacologically make sense. Even if exponential equations are used by both disciplines, pharmacokinetic analysis often employs the principle of superposition and thus curve “stripping” to analyze the data, a restriction not present in a pure statistical model. Neither approach is right or wrong as each has its merits. Problems arise only when parameters from one model are mistakenly used as input into another.

Recent advances in in vitro technology and the ease of conducting large-scale pharmacokinetic trials have resulted in a plethora of readily available data that would appear to span all levels of biological organization. This is especially true in comparative pharmacology and risk assessment. The combination of such diverse data requires that certain assumptions be fulfilled and the limits of the mathematical bridges employed to link the data sets be strictly defined. Even when done properly, some combinations of diverse in vitro and in vivo model systems result in the generation of so-called emergent properties, the hallmark of complex system behavior. In other cases, nonlinear systems dynamics or “chaotic behavior” may take hold, making extrapolations possible but difficult unless the behavior is clearly understood. Thus, as will become evident throughout this text, pharmacokinetics and other forms of mathematical extrapolations may be used in many scenarios, but they must be applied in the proper context and the assumptions and defining rules inherent to each system closely tested and followed.

1.2 TARGET AUDIENCE AND APPLICATIONS

The focus of this book is to present the basic concepts of pharmacokinetic principles to the scientist or practitioner with a strong biological background. The mathematics should be tolerable to such an individual as it will not go much beyond what he or she has already encountered in related disciplines. The most obvious user of pharmacokinetic principles is the basic scientist studying drug or chemical disposition in animals. Simple pharmacokinetic studies are often used to describe the blood or tissue concentrations seen after drug administration. These parameters provide the basis for determining differences in the rate and extent of drug absorption, distribution, or elimination, as well as permitting the calculation of safe and efficacious dosage regimens. They allow for the development of simple mathematical models to interpret the time-dependent nature of numerous biological phenomena. These strategies will be completely developed.

Pharmaceutical scientists use pharmacokinetics in many industrial and regulatory settings. Parameters are derived to define the shape of an efficacious drug’s blood concentration versus time profile (AUC, Cmax) so that other products may be formulated to “copy” this profile or, in pharmacokinetic jargon, to be “bioequivalent.” Similarly, drug absorption is assessed in simple model systems to select candidate drugs for development and determine the purity of a drug formulation. Pharmacokinetic parameters are calculated to extrapolate from preclinical and clinical trial results. Toxicologists in these environments must use pharmacokinetic principles to interpret the dose that produces a toxicological “event” in an animal study relative to its potential to do the same in a clinical setting at therapeutic doses. Many practices of risk assessment use similar extrapolations.

The field of pharmacokinetics and its concepts has become especially important as a consequence of the dramatic and almost radical changes that are presently occurring relative to the regulations surrounding drug use in veterinary medicine. For most of the recent past, the operative concept was that a single dose of drug listed on a product label was optimal for all therapeutic uses. The legal concept of “flexible or professional labeling” and the passage by the US Congress in 1994 of the Animal Medicinal Drug Use Clarification Act (AMDUCA) legalizing extralabel drug use forever eradicated this fallacious ideal of a single optimal dose. The veterinarian must now select a drug dose based on numerous factors inherent to the therapeutic scenario at hand to maximize therapeutic efficacy and minimize the likelihood of drug-induced toxicity or induction of microbial resistance. Unlike human medicine and companion animal practices, food animal veterinarians face the further restriction that proper withdrawal times must be determined to ensure that drug residues do not persist in the edible tissues or by-products (milk, eggs) of treated animals long after they have left the care of the veterinarian (Fig. 1.3). As will be demonstrated, the withdrawal time is in reality a pure pharmacokinetic parameter since it can be calculated solely from knowledge of the legal tissue tolerance and the drug’s half-life or rate of decay in that tissue.

Fig. 1.3 Illustration of the food animal veterinarian’s dilemma in optimizing the dose of a therapeutic drug.

Yet it is not only the food animal veterinarian who faces these challenges. The laboratory animal and exotic/zoo animal worker must often extrapolate drug dosages across species with widely differing body sizes and physiology since there are very few approved drugs for the treatment of such animals. Pharmacokinetic principles and techniques are ideally suited for this application. Practitioners are often faced with disease processes (e.g., renal failure) that are known to affect the disposition of a drug. Knowledge of how such a pathological process affects a drug’s clearance or volume of distribution is sufficient to adapt a dosage regimen appropriate for this condition.

Other scientists who deal with drugs in both in vitro and in vivo systems may not be interested in constructing complex pharmacokinetic models but rather in the relationship between the administered dose and the effect. The link between dose and effect, however, is the drug concentration at the site of action (the so-called biophase), which is the essence of a pharmacokinetic study. These data are necessary to link these different systems in order to determine whether a drug concentration threshold exists for drug action or toxicity, or to study the time course of drug effect. Pharmacokinetics provides the parameters to serve as experimental end points and to extrapolate beyond the individual experiment to the target population.

To pursue these varied goals, this book starts with the biology and progresses to the presentation of the different modeling approaches used in pharmacokinetics. The book concludes with elements of experimental design and data analysis, followed by some specific applications to select fields.

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