`
`
`
`
`
`E
`
`3:7"Wa‘r-‘tm‘ww'hxeam:33:
`v:'::¢ym.m\\\~«:c.\:
`
`i
`
`
`
`i
`
`
`
`
`
`.
`APPLIED
`Bmpharmaceuucs
`WPharmacokinetics
`
`fourth edition
`
`Leon Shargel, PhD
`Vice President and Technical Director
`National Association of Pharmaceutical Manufacturers
`Ronkonkorna, New York
`
`Adjunct Associate Professor
`School of Pharmacy
`University of Maryland
`Baltimore, Maryland
`
`Andrew Yu, PhD
`Associate Professor of Pharmaceutics
`Albany College of Pharmacy
`,
`Albany, New York*
`
`*Present affiliation
`HEB-520 CDER, FDA, Rockvilie, MD.
`(The contents of this book reflect the personal views of the authors and not that of the FDA.)
`
`McGraw—Hill
`
`Medical Publishing Division
`
`NewYork St. Louis San Francisco Auckland Bogota Caracas Lisbon London
`Madrid Mexico City Milan Montreal New Delhi San juan
`Singapore Sydney Tokyo Toronto
`
`SHIRE EX. 2023
`KVK V. SHIRE
`
`
`
`Page 1
`
`SHIRE EX. 2023
`KVK v. SHIRE
`IPR2018-00290
`
`

`

`
`
`
`
`gg
`
`:
`
`
`
`dfivrwswrwwymm
`
`
`
`
`
`li!i|
`
`I
`
`Ly
`
`McGraw-Hill
`A Division of The McGraw-Hill Companies
`
`22
`
`Applied Biopharmaceufics 8c Pharmacokinetics, Fourth Edition
`
`Copyright © 1999 by Appleton 8c Lange. All rights reserved. Printed in the United States
`of America. Except as permitted under the United States Copyright Act of 1976, no part
`of this publication may be reproduced or distributed in any form or by any means, or
`stored in a data base or renievai system, without the prior written permission of the pol}
`lisher.
`
`Previous editions copyright © 1993 by Appleton 8c Lange; copyright © 1985, 1980 by
`Appleton-Century—Crofts.
`
`4567890 HPC/HPC 0987654321
`
`ISBN: 0838502784 (domestic)
`
`Library of Congress Cataloghig—in—Publicafion Data
`
`Shargel, Leon, 194%
`Applied biopharmaceutics and pharmacokinetics / Leon Shargel,
`Andrew Yu. —-4th ed.
`p.
`cm.
`Includes bibliographical references and index.
`ISBN 0-83850278—4 (case : alk. paper)
`1. Biopharmaceutics.
`2. Pharmacokinetics.
`1945— .
`11. Title
`.
`{DNLM:
`1. Biopharmaceutics.
`2. Pharmacokinetics. QV 38 5531a
`7 1999]
`RM301.4.S52
`615'.7—dc21
`DNLM/DLC
`for Library of Congress
`
`1999
`
`1. Yu, Andrew B. C.,
`
`984-9079
`
`Editor—invChief‘. Cheryl L. Mehalik
`Production Service: York Production Services
`Art Coordinator: Eve Siegel
`Cover Design: Aimee Nordin
`Illustrator: Wendy Beth Jackelow
`
`ISBN: 0838503213? (international)
`
`Exclusive rights by The McGraw—Hill Companies, Inc. for manufacture and export. This
`book cannot be reexported from the country to which it is consigned by McGraw-Hill.
`The International Edition is not available in North America.
`
`
`
`
`
`Page 2
`
`

`

`
`
`
`
`.
`l
`
`:
`E
`_g
`g
`.j,
`l:
`
`'
`
`'
`
`
`
`1
`
`INTRODUCTION TO
`BIOPHARMACEUTICS
`
`AND
`PHARMACOKINETICS
`
`BIOPHARMACEUTICS
`
`.
`
`Bithamaceutics considers the interrelationship of the physicochemical properties
`of the drug, the dosage form in which the drug is given, and the route of admin-
`istration on the rate and extent of systemic drug absorption. Thus, biopharma—
`ceutics involves factors that influence the (l) protection of the activity of the drug
`within the drug product, (2) the release of the drug from a drug product, (3) the
`rate of dissolution of the drug at the absorption site, and (4) the systemic absorp—
`tion of the drug. Figure 2—1 is a general scheme describing this dynamic relation-
`ship.
`The study of biopharmaceutics is based on fundamental scientific principles and
`experimental methodology. These methods must be able to assess the impact of
`the physical and chemical properties of the drug; drug stability and large scale pro-
`duction of the drug and drug product on the biological performance of the drug.
`Moreover, biopharmaceutics considers the requirements of the drug and dosage
`form in a physiological environment and the drug’s intended therapeutic use and
`route of administration
`
`Studiesin biopharmaceutics use both 114--vitro and in—viva methods Invitro meth-
`ods are procedures employing test apparatus and equlpment Without involving lab-
`oratory animals or humans. 172—va methods are more complex studies involving
`human subjects or iaboratory animals. Some of these methods will be discussed in
`Chapter 5. Historically, pharmacologists evaluated the relative systemic drug avail-
`ability in viva after giving a drug product to an animal or human and then corn-
`paring specific pharmacoiogic, clinical, or possible toxic responses. For example,
`a drug such as isoproterenol causes an increase in heart rate when given intra«
`venously but has no observable effect on the heart when given orally at the same
`dose level. Therefore, systemic drug availability may differ according to the route
`29
`
`
`
`
`
`
`
`
`
`it
`
`:
`
`
`
`Page 3
`
`

`

`30
`
`CHAPTER 2.
`INTRODUCTION TO BIOPHARMACEUTICS AND PHARMACOKINETICS
`
`
`
`
`Drug release and
`I Absorption"
`Drug in syElemic
`
`dissolution
`circulation
`
`Eiiminatian
`
`Excretion and
`
`metabolism
`
`
`
`
`‘
`
`Figure 2—1. Scheme demonstrating the dynamic relationship between the drug, the drug product.
`and the pharmacologlc effect.
`
`of administration. In addition, the bioavailability (a measure of systemic availabil—
`ity of a drug) may differ from one drug product to another containing the same
`drug. This difference in drug bioavailability may be manifested by observing the
`difference in the therapeutic effectiveness of the drug products.
`
`PHARMACOKINETICS
`
`Pharmacokimtics involves the kinetics of drug absorption, distribution, and elimi—
`nation (ie, excretion and metabolism). The description of drug distribution and
`elimination is often termed drug disposition. The study of pharmacokinetics involves
`both experimental and theoretical approaches. The experimental aspect of phar-
`macokinetics involves the development of biological sampling techniques, analyti—
`cal methods for the measurement of drugs and metabolites, and procedures that
`facilitate data collection and manipulation. The theoretical aspect of pharmacoki—
`netics involves the development of pharmacokinetic models that predict drug dis-
`position after drug administration. The application of statistics is an integral part
`of pharmacokinetic studies. Statistical methods are used for pharmacokinetic pa—
`rameter estimation and data interpretation. Statistical methods are applied to phar-
`macokinetic models to determine data error and structural model deviations.
`Mathematics and computer techniques form the theoretical basis of many phar~
`macokinetic methods. Classical pharmacokinetics is a study of theoretical models
`focusing mostly on model development and parameterization.
`
`CLINICAL PHARMACOKINETIGS
`
`Clinicalpharmawkmetics is the application ofpharmacokinetic methods in drug ther—
`apy. Clinical pharmacokinetics involves a multidisciplinary approach to individu~
`ally optimized dosing strategies based on the patient’s disease state and
`patient-specific considerations. The study of clinical pharmacokinetics of drugs in
`disease states requires input from medical and pharmaceutical research. Table 2.1
`is a list of 10 age—adjusted rates of death from 10 leading causes of death in the
`USA, 1993. The influence of many diseases on drug disposition is not adequately
`studied. Age, gender, genetic, and ethnic differences can also result in pharmaco—
`kinetic differences that may affect the outcome of drug therapy. The study of pharu
`macokinetic differences of drugs in various population groups is termed population
`
`
`
`P
`
`:
`
`
`
`
`
`
`
`
`Page 4
`
`

`

`
`INTRODUCTION TO BIOPHARMACEUTICS AND PHARMACOKINETICS CHAPTER 2.
`,
`J
`
`31
`
`Ratio of Age-Adjusted Death Rates, by Male/Female Ratio from the to
`TABLE 2.1
`
`Leading Causes of Death in the USA, I993
`DISEASE
`
`RANK
`
`MALE:FEMALE
`
`
`
`
`
`
`‘
`
`
`
`
`
`
`
`
`
`
`
`
`
`
`
`
`
`
`
`
`
`
`
`
`
`
`
`
`
`
`
`
`
`Disease of heart
`Malignant neoplasms
`Cerebrovascular diseases
`Chronic obstructive pulmonary diseases
`Accidents and others"
`Pneumonia and influenza
`Diabetes meilitus
`HIV infections
`Suicide
`
`
`L9
`I
`LS
`2
`[2
`3
`L6
`4
`2.6
`5
`L6
`6
`i.2
`7
`6.3
`8
`4.4
`9
`Homicide and legal intervention 3‘8 10
`
`
`*Death due to adverse effects suffered as defined by CDC
`Source: CDCMMWR (Morbidity and Mortality Weekly Report], March 1, 45:8, I996.
`
`phamacokimtics (Sheiner and Ludden, 1992). Another important aspect of phar-
`macokinetics is therapeutic drug monitoring (TDM). When drugs with narrow thera~
`peutic indices are used in patients,
`it
`is necessary to monitor plasma drug
`concentrations closely by taking periodic blood samples. The pharmacokinetic and
`drug analysis services necessary for safe drug monitoring are generally provided by
`the clinical pharmacokinetic service (CPKS). Some drugs frequently monitored are the
`aminoglycosides and anticonvulsants. Other drugs closely monitored are those used
`in cancer chemotherapy in order to minimize adverse side effects (Rodman and
`Evans, 1991).
`
`PHARMAC ODYNAMICS
`
`Pharmacodynamics refers to the relationship between the drug concentration at the
`site of action (receptor) and pharmacologic response, including biochemical and
`physiologic effects that influence the interaction of drug with the receptor. The in«
`teraction of a drug molecule with a receptor causes the initiation of a sequence of
`molecular events resulting in a pharmacologic or toxic response. Pharmacokinetic-
`pharmacodynamic models are constructed to relate plasma drug level to drug con-
`centration in the site of action and establish the intensity and time course of the
`drug. Pharmacodynamics and pharmacokinetic-pharmacodynamic models are dis-
`cussed more fully in Chapter 19.
`
`TOXICOKINETICS AND CLINICAL TOXICOLOGY
`
`Toxicokz'netics is the application of pharmacokinetic principies to the design, con-
`duct and interpretation of drug safety evaluation studies (Leal et al, 1993) and used
`in validating dose related exposure in animals. Toxicokjnetic data aids in the in—
`terpretation of toxicologic findings in animals and extrapolation of the resulting
`data to humans. Toxicokinetic studies are performed in animals during preclini—
`cal drug development and may continue after the drug has been tested in clinical
`trials.
`
`-...._.._--—r......+mm~—.—~s~v
`
`
`
`
`':
`
`
`
`Page 5
`
`

`

`s §’
`
`5.
`
`§ai
`
`
`
`32
`
`CHAPTER 2.
`
`INTRODUCTION TO‘ BlOPHARMACEUTiCS AND PHARMACOKINETICS
`
`Clinical toxicology18 the study of adverse effects of drugs and toxic substances
`(poisons) in the body. The pharmacokinetics of a drugin an over—-medicated (in—
`toxicated) patient may be very different from the pharmacokinetics of the same
`drug given in therapeutic doses. At very high doses, the drug concentration in the
`body may saturate enzymes involved in the absorption, biotransformation, or ac
`tive renal secretion mechanisms thereby changing the pharmacokinetics from lin—
`ear to nonlinear pharmacokinetics. Nonlinear pharmacokinetics is discussed in
`Chapter 16. Drugs frequently involved in toxicity cases include acetaminophen, sal-
`icylates, morphine and the tricylic antidepressants (TCA). Many of these drugs can
`be assayed conveniently by fluorescence immunoassay (FIA) kits.
`
`MEASUREMENT OF DRUG CONCENTRATIONS
`
`Sensitive, accurate, and precise analytical methods are available for the direct mea—
`surement of drugs in biologic samples, such as milk, saliva, plasma, and urine.
`Measurements of drug concentrations in these biological samples are generally val-
`idated so that accurate information is generated for pharmacokinetic and clinical
`monitoring. In general, chromatographic methods are more discriminating since
`chromatography separates the drug from other related materials that may cause
`assay interference.
`
`Sampling of Biologic Specimens
`
`Only a few biologic specimens may be obtained safely from the patient to gain in—
`formation as to the drug concentration in the body. Invasive methods include sam—
`pling blood, spinal fluid, synovial fluid, tissue biopsy, or any biologic material that
`requires parenteral or surgical intervention in the patient. In contrast, noninvasive
`methods include sampling of urine, saliva, feces, expired air, or any biologic ma-
`terial that can be obtained without parenteral or surgical intervention. The mea—
`surement of drug concentration in each of these biologic materials yields different
`information.
`
`Drug Concentrations in Blood, Plasma, or Serum
`
`Measurement of drug concentration (levels) in the blood, serum, or plasma is the
`most direct approach to assessing the pharmacokinetics of the drug in the body.
`l/Wzole blood contains the cellular elements including red blood cells, white blood
`cells, platelets, and various other proteins, such as albumin and globulins. In gen~
`eral, serum or plasma is used for drug measurement. To obtain serum, whole blood
`is allowed to clot and the serum is collected from the supernatant after centrifu—
`gation. Plasma is obtained from the supernatant of centrifuged whole blood to
`which an anticoagulant, such as heparin, has been added. Therefore, the protein
`content of serum and plasma is not the same. Plasma perfuses all the tissues of the
`body inciuding the cellular elements in the blood. Assuming that a drug in the
`plasma is in dynamic equilibrium with the tissues, then changes in the drug con-
`centration in plasma will reflect changes in tissue drug concentrations.
`
`Plasma LevelmTime Curve
`
`The plasma level-«time curve is generated by measuring the drug concentration in
`plasma samples taken at various time intervals after a drug product is administered.
`
`
`
`Page 6
`
`

`

`
`
`[NTRODUCTION TO BIOPHARMACEUTICS AND PHARMACOKINETICS CHAPTER 2.
`
`33
`
`The concentration of drug in each plasma sample is plotted on rectangular coor—
`dinate graph paper against the corresponding time at which the plasma sample
`was removed. As the drug reaches the general (systemic) circulation, plasma drug
`concentrations will rise up to a maximum. Usually absorption of 'ardrug is more
`rapid than elimination. As the drug is being absorbed into the systemic circulation,
`the drug is distributed to all the tissues in the body and is also simultaneously being
`eliminated. Elimination of a drug can proceed by excretion or biotransformation
`or a combination of both.
`
`The relationship of the drug level—time curve and various pharmacologic param-
`eters for the drug is shown in Figure 2-2. MEG and MTG represent the minimum
`efierifiive concentration and minimum toxic concentration of drug, respectively. For some
`drugs, such as those acting on the autonomic nervous system, it is useful to know
`the concentration of drug that will just barely produce a pharmacologic effect (ie,
`MEC). Assuming the drug concentration in the plasma is in equilibrium with the
`tissues, the MEC reflects the minimum concentration of drug needed at the re“
`ceptors to produce the desired pharmacologic effect. Similarly, the MTG represents
`the drug concentration needed to just barely produce a toxic effect. The onset time
`corresponds to the time required for the drug to reach the MEC. The intensity of
`the pharmacologic effect is proportional to the number of drug receptors occu~
`pied, which is reflected in the observation that higher plasma drug concentrations
`produce a greater pharmacologic response, up to a maximum. The duration of drug
`action is the difference between the onset time and the time for the drug to de—
`cline back to the MEC.
`
`In contrast, the pharmacokineticist can also describe the plasma level—time curve
`in terms of such pharmacokinetic terms as peak plasma level, time for peak plasma
`levei, and area under the curve, or AUG (Fig. 2—3). The time of peak plasma level
`is the time of maximum drug concentration in the plasma and is a rough marker
`of average rate of drug absorption. The peak plasma level or maximum drug con-
`
`
`
`————————————————————————— MTC
`Peak concenlrntion
`
`7;
`i
`E
`n.
`_3
`
`T:
`a
`E
`D.
`L6
`
`Onset
`“me
`
`Time
`
`Fault
`"me
`
`Time
`
`Figure 2-2. Generalized plasma levelatime
`curve after oral administration of a drug.
`
`Figure 2-3.
`Plasma levelfitime curve showing
`peak time and concentration. The shaded por-
`tion represents the AUC (area under the curve).
`
`ig
`
`
`E
`..
`g
`
`t\'n\K\K.rnA\k:71rrr
`
`Page 7
`
`

`

`lr
`
`
`
`
`
`
`
` E
`
`i:
`
`%
`
`
`
`
`
`
`
` 34 CHAPTER 2. lNTRODUCTlON to BIOPHARMACEUTECS AND PHARNLACOKlNETlCS
`
`centration is related to the dose, the rate constant for absorption, and elimination
`constant of the drug. The AUC is related to the amount of drug absorbed system-
`ically. These and other pharmacokinetic parameters are discussed in succeeding
`. chapters.
`
`Drug Concentrations in Tissues
`
`Tissue biopsies are occasionally removed for diagnostic purposes such as the ver—
`ification of a malignancy. Usually, only a small sample of tissue is removed, malt-i
`ing drug concentration measurement difficult. Drug concentrations in tissue
`biopsies may not reflect drug concentration in Other tissues nor drug concen~
`tration in the tissue from which the biopsy material was removed. For example,
`if the tissue biopsy was for the diagnosis of a tumor within the tissue, the blood
`flow to the tumor cells may not be the same as the blood flow to other cells in
`this tissue. In fact, for many tissues, blood flow to one part of the tissues need
`not be the same as the blood flow to another part of the same tissue. The mea—
`surement of the drug concentration in tissue biopsy material may be used to as_
`certain if the drug reached the tissues and obtained the proper concentration
`within the tissue.
`
`Drug Concentrations in Urine and Feces
`
`Measurement of drug in urine is an indirect method to ascertain the bioavailabil—
`ity of a drug. The rate and extent of drug excreted in the urine reflects the rate
`and extent of systemic drug absorption. The use of urinary drug excretion
`measurements to establish various pharmacoltinetic parameters is discussed in
`Chapter 10.
`Measurement of drug’in feces may reflect drug that has not been absorbed after
`an oral dose or may reflect drug that has been expelled by biliary secretion after
`systemic absorption. Fecal drug excretion is often performed in mass balance stud—
`ies in which the investigator attempts to account for the entire dose given to the
`patient. For a mass balance study, both urine and feces are collected and their drug
`'content measured. For certain solid oral dosage forms that do not dissolve in the
`gastrointestinal tract but slowly leach out drug, fecal collection is performed to re-
`cover the dosage form. The undissolved dosage form is then assayed for residual
`drug.
`
`Drug Concentrations in Saliva
`
`Saliva drug concentrations have been reviewed for many drugs for therapeutic drug
`monitoring (Pippenger and Massoud, 1984). Because only free drug diffuses into
`the saliva, saliva drug levels tend to approximate free drug rather than total plasma
`drug concentration. The saliva/plasma drug concentration ratio is less than 1 for
`many drugs. The saliva/plasma drug concentration ratio is mostly influenced by
`the pKa of the drug and pH of the saliva. Weak acid drugs and weak base drugs
`with pKa significantly different than pH 7.4 (plasma pH) generally have better cor~
`relation to plasma drug levels. The saliva drug concentrations taken after equilib-
`rium with the plasma drug concentration generally provide more stable indication
`of drug levels in the body. The use of salivary drug concentrations as a therapeu~
`tic indicator should be used with caution and preferably used as a secondary indi-
`CfltOF.
`
`
`
`
`
`Page 8
`
`

`

`
`
`
`
`35 gINTRODUCTION TO BIOPHARMACEUTICS AND i’HARMACOKlNETlCS CHAPTER 2.
`
`
`Forensic Drug Measurements
`
`Forensic science is the application of science to personal injury, murder, and other
`legal proceedings. Drug measurements in tissues obtained at autopsy or in other
`bodily fluids such as saliva, urine, and blood may be useful if the person has taken
`an overdose of a legal medication, has been poisoned, or has been using drugs of
`abuse such as opiates (eg, heroin), cocaine or marijuana. The appearance of so—
`cial drugs in blood, urine, and saliva drug analysis show short~term drug abuse.
`These drugs may be eliminated rapidly, making it more difficult to prove that the
`subject has been using drugs of abuse. The analysis for drugs of abuse in hair sam-
`ples by very sensitive assay methods, such as gas chromatography coupled with mass
`spectrometry, provides infonnation regarding past drug exposure. A recent study
`(Cone et a], 1993) showed that the hair samples from subjects who were known
`drug abusers contained cocaine and B—acetyimorphine, a metabolite of heroine (di«
`acetylrnorphine).
`
`Significance of Measuring Plasma Drug Concentrations
`
`The intensity of the pharmacologic or toxic effect of a drug is often related to the
`concentration of the drug at the receptor site, usually located in the tissue cells.
`Because most of the tissue cells are richly perfused with tissue fluids or plasma,
`checking the plasma drug level is a responsive method of monitoring the course
`of therapy.
`Clinically, individual variations in the pharmacokinetics of drugs are quite com~
`mon. Monitoring the concentration of drugs in the blood or plasma ascertains that
`the calculated dose actually delivers the plasma level required for therapeutic ef-
`fect. With some drugs, receptor sensitivity in individuals varies so that monitoring
`of plasma levels is needed to distinguish the patient who is receiving too much of
`a drug from the patient who is supersensi'tive to the drug. Moreover, the patient’s
`physiologic functions may be affected by disease, nutrition, environment, concur-
`rent drug therapy, and other factors. Pharmacokinetic modeis allow more accurate
`interpretation of the relationship between plasma drug levels and pharmacologic
`response. In the absence of pharmacokinetic information, plasma drug levels are
`relatively useless in dosage adjustment. For example, suppose a single blood sam—
`pie from a patient was assayed and found to contain 10 ,LLg/inL. According to the
`literature, the maximum safe concentration of this drug is 15 ug/InL. In order to
`apply this information properly, it is important to know when the blood sample
`was drawn, what dose of the drug was given, and the route of administration. If the
`proper information is available, the use of pharmacokinetic equations and models
`may describe the blood level—time curve accurately.
`Monitoring of plasma drug concentrations allows for the adjustment of the drug
`dosage in order to individualize and optimize therapeutic drug regimens. In the
`presence of alteration in physiologic functions due to disease, monitoring plasma
`drug concentrations may provide a guide to the progress of the diseased state and
`enable the investigator to modify the drug dosage accordingly. Clinically, sound
`medical judgment and observation are most important. Therapeutic decisions
`should not be based solely on plasma drug concentrations.
`In many cases, the pharmacodynamic response to the drug may be more im—
`portant to measure thanjust the plasma drug concentration. For example, the elec—
`trophysiology of the heart including an electrocardiogram (ECG) is important to
`
`mamwmmmm
`
`
`
`
`
`zsawwwnrmsmswxmwe:imwmzswmwwmwswsmmwutwWswwwwwwymmmssswwwmuwwmwnasutgxmanv
`
`
`
`
`Page 9
`
`

`

`$tat M
`
`enu-waste...._:_‘_r.,,.....
`«soa,\'\x\1\\mvz\l":>’.‘swi\\\v'
`
`
`
`36
`
`CHAPTER 2.
`
`lNTRODUCTlON TO BiOPHARMACEUTlCS AND PHARMACOKINETICS
`
`assess in patients medicated with cardiotonic drugs such as digoxin. For an anti—
`coagulant drug, such as’dicumarol, prothrombin clotting time may indicate whe ther
`proper doSage was achieved. Most diabetic patients taking insulin will monitor their
`own blood or urine glucose levels.
`For drugs that act irreversibly at the receptor site, plasma drug concentrations
`may not accurately predict pharmacodynamic response, Drugs used in cancer
`chemotherapy often interfere with nucleic acid or protein biosynthesis to destroy
`tumor cells. For these drugs, the plasma drug concentration does not relate di-
`rectly to the pharmacodynamic response. In this case, other pathophysiologic pa—
`rameters and side effects are monitored in the patient to prevent adverse toxicity.
`
`BASIC PHARMACOKINETICS AND
`PHARMACOKINETIC MODELS
`
`Basic pharmacokinetics involves the quantitative study of various kinetic processes
`of drug disposition in the body. The biological nature of drug distribution and dis-
`position is complex, and drug events often happen simultaneously. Basic pharma—
`cokinetics requires (1) a thorough knowledge of anatomy and physiology and
`(2) an understanding of the concepts and limitations of mathematical models.
`Drugs are in a dynamic state within the body. A model is a hypothesis using math—
`ematical
`terms to concisely describe quantitative relationships. Simplifying as-
`sumptions are made to describe a complex biologic system concerning the
`movement of drugs. Various mathematical models can be devised to simulate the
`rate processes of drug absorption, distribution, and elimination. These mathemat-
`ical models make possible the development of equations to describe drug con-
`centrations in the body as a function of time.
`The predictive capability of a model lies in the proper selection and develop-
`ment of mathematical function(s) that parameterize the essential factors govern-
`ing the kinetic process. The key parameters in a process is commonly estimated by
`fitting the model to the experimental data known as variables. A pharmacokinetic
`function relates an independentvariable to a dependentvariable. For example, a model
`may predict the drug concentration in the liver 1 hour after an oral administra—
`tion of a 20 mg dose. The independent variable is time and the dependent vari-
`able is the drug concentration in the liver. Based on a set of time versus drug
`concentration data, a model equation is derived to predict the liver drug concen»
`tration with respect to time. The drug concentration depends on the time after the
`administration of the dose.
`A model may be empificalhi or physiologically based. The model that simply inter-
`poiates the data and allows an empirical formula to estimate drug level over time
`is justified when limited information is available. Empirical models are practical
`but not very useful in explaining the mechanism of the actual process by which the
`drug is absorbed, distributed and eliminated in the body.
`Physiologically based models also have limitations. Using the example above and
`apart from the necessity to sample tissue and monitor blood flow to the liver in
`viva, the investigator needs to understand the following questions. What does liver
`drug concentration mean? Should the drug concentration in the blood within the
`tissue be determined and subtracted from the drug in the liver tissue? What type
`of cell is representative of the liver if a selective biopsy liver tissue sample can be
`collected without contamination from its surroundings? Indeed, depending on the
`
`
`
`
`
`Page 10
`
`

`

`
`
` 2gi9
`
`,t
`fr:
`
`INTRODUCTION TO BIOPHARMACEUTICS AND PHARMACOKENETICS CHAPTERZ.
`,.
`
`37
`
`n of the liver tissue from the hepatic blood vessels, tissue drug con-
`spatial locatio
`centrations can differ. Moreover, changes in the liver blood perfusion will alter the
`tissue drug concentration. If the heterogeneous liver tissue is homogenized and as
`sayed, the homogenized tissue only represents a hypothetical concentration that
`matches no real liver tissue. Most generated pharmacokinetic information depends
`on the method of tissue sampling, timing of the sample, drug analysis, and the pre-
`dictive model selected. The need to approximate the real system (assuming uni-
`formity within a given space or region) with a model is necessary and rational.
`Assumptions are inherent in all pharmacokinetic models even when a physiologic
`model is considered. A detailed physiologic model is more difficult but can reveal
`organ—specific or suborgan-regional information. In general, most pharmacokinetic
`models assume that the plasma drug concentration reflects drug concentrations
`globally within the body. Based on knowledge of the physiologic and biochemical
`composition of the body organs, the drug concentration in the liver may be esti-
`mated by knowing the liver extraction ratio for the drug.
`A great number of models have been developed to estimate regional and global
`information about drug disposition in the body. Some physiologic pharmacokinetic
`models are discussed in Chapter 20. Pharmacokinetic processes are discussed in
`separate chapters under the topics of drug absorption, drug distribution, drug elim-
`ination, and pharmacokinetic drug interactions involving one or all the above
`processes. Theoretically, an unlimited number of models may be constructed to
`describe the kinetic processes of drug absorption, distribution, and elimination in
`the body depending on the degree of detailed information considered. Practical
`considerations have limited the growth'of new pharmacokinetic models.
`For example, assume a drug is given by intravenous injection and that the drug
`rapidly dissolves (distributes) in the body fluids. A pharmacokinetic model that de-
`scribes this situation is a tank containing a volume of fluid that is rapidly equili—
`brated with the drug. In the human body, a fraction of the drug would be continually
`eliminated as a function of time (Fig. 2-4). The concentration of the drug in the
`tank after a given dose is governed by two parameters: (1) the fluid volume of the
`tank that will dilute the drug, and (2) the elimination rate of drug per unit of time.
`In pharmacokinetics, these parameters are assumed to be constants. If a known set
`of drug concentrations in the tank is determined at various time intervals, then the
`volume of fluid in the tank and the rate of drug elimination can be estimated.
`Because drug concentrations is dependent on time, the two variabies in this ex-
`ample, drug concentration and time, are called dependent and independentvariables,
`respectively. In practice, pharmacokinetic parameters are determined experimen—
`tally from a set of drug concentrations collected over various times known as data.
`The number of parameters needed to describe the model depends on the com-
`plexity of the process and on the route of drug administration. In general, as the
`number of parameters that need to be evaluated increases, accurate estimation of
`these parameters becomes increasingly more difficult. With complex pharmacoki—
`netic models, computer programs are used to facilitate parameter estimation.
`
`
`
`
`
`
`
`
`
`
`
`
`
`
`
`
`
`
`
`
`
`
`
`
`
`
`
`
`
`
`
`
`
`
`
`
`
`
`
`
`
`
`
`
`
`
`volume constant
`
`Fluid replenished
`dulomoticuly to keep
`
`Fluid
`0‘1“”
`
`Figure 2-4. Tank with a constant volume of fluid
`equilibrated with drug. The vofume of the fluid is l.0 L.
`The fluid outlet is 10 mL/min. The fraction of drug re-
`moved per unit of time is 10/1000, or 0.0? min".
`
`
`
`Page 11
`
`

`

`38
`
`CHAPTERZ.
`
`INTRODUCTION TO BIOPHARMACEUTECS AND PHARMACOKINETICS
`
`However, for the parameters to be valid, the number of data points should always
`exceed the number of parameters .in the model.
`Pharmacokinetic models are used to:
`1. Predict plasma, tissue, and urine drug levels with any dosage regimen.
`2. Calculate the optimum dosage regimen for each patient individually.
`3. Estimate the possible accumulation of drugs and/or metabolites.
`4. Correlate drug concentrations with pharmacologic or toxicologic activity.
`5. Evaluate differences in the rate or extent of availability between formulations,
`(bioequivalence).
`physiology or disease affect the absorption, distribu-
`6. Describe how changes in
`tion, or elimination of the drug.
`’7. Explain drug interactions.
`Because a model is based on a hypothesis and simplifying assumptions, a certain
`11y on the pharmacoltinetic model to
`degree of caution is necessary when relying tota
`predict drug action. For some drugs, plasma drug concentrations are not useful in
`predicting drug activity. For other drugs, disease state and compensatory response
`from the body may modify the response of a drug. If a simple model does not fit ac-
`curately all the experimental observations, a new, more elaborate model may be pro
`posed and subsequently tested. Since limited data are generally available in most
`kinetic data should be interpreted along with clinical
`clinical situations, pharmaco
`observations rather than replacing sound judgment by the clinician. Development
`of pharmacomeuic, statistical models may help to improve prediction of drug levels
`among patients in the population (Sheiner and Beal, 1982; Mallet et al, 1988).
`However, it will be some time before these methods become generally accepted.
`
`Compartment Models
`d as a series, or systems, of compartments that com“
`The body can be represente
`h other. 'A compartment is not a real physiologic or
`municate reversibly with eac
`anatomic region but is considered as a tissue or group of tissues that have similar
`blood flow and drug affinity. Within each compartment, the drug is considered to
`be unifome di