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`
`%
`Burger’s Medicinal
`Chemistry and Drug Discove
`
`Page 2 of 44
`
`

`
`BURGER’S MEDICINAL
`
`CHEMISTRY
`AND DRUG DISCOVERY
`
`Fifth Edition
`
`Volume I: Principles and Practice
`
`Edited by
`
`Manfred E. Wolff
`
`lmm
`San
`
`'
`
`harmaceutics. Inc.
`0, California
`
`A WILEY-INTERSCIENCE PUBLICATION
`
`JOHN WILEY & SONS, Inc., New York - Chichester - Brisbane - Toronto - Singapore
`
`Page 3 of 44
`
`

`
`Notice Concerning Trademark or Patent Rights.
`The listing or discussion in this book of any drug in
`respect to which patent or trademark rights may exist
`shall not be deemed, and is not intended as
`a grant of, or authority to exercise, or an
`infringement of, any right or privilege protected by
`such patent or trademark.
`
`This text is printed on acid—free paper.
`
`Copyright © 1995 by John Wiley & Sons, Inc.
`
`All rights reserved. Published simultaneously in Canada.
`
`Reproduction or translation of any part of this work beyond
`that permitted by Section 107 or 108 of the 1976 United A
`States Copyright Act without the permission of the copyright
`owner is unlawful. Requests for permission or further
`information should be addressed to the Permissions Department,
`John Wiley & Sons, 605 Third Avenue, New York, NY
`10158-0012.
`
`Library of Congress Cataloging in Publication Data:
`Burger, Alfred, 1905-
`[Medicinal chemistry]
`Burger’s medicinal chemistry and drug discovery. -- 5th ed. /
`edited by Manfred E. Wolff.
`p.
`cm.
`“A Wiley-Interscience publication.”
`Contents: v. 1. Principles and practice
`Includes bibliographical references and index.
`ISBN 0-471-57556-9
`1. Wolff, Manfred E.
`1. Pharmaceutical chemistry.
`III. Title: Medicinal chemistry and drug discovery.
`RS403.B8
`1994
`615'. 19--dc20
`
`II. Title.
`
`94-12687
`
`Printed in the United States of America
`
`10987654321
`
`Page 4 of 44
`
`

`
`CHAPTER FIVE
`
`Drug Absorption, Distribution
`and Elimination
`
`LESLIE Z. BENET and
`BEATRICE Y. T. PEROTFI
`
`Department of Pharmacy, University of California
`San Francisco, California, USA
`
`CONTENTS
`
`114
`
`1 Overview of Product Development Issues,
`2 Defining Drug Absorption, Disposition and
`Elimination Using Pharmacokinetics,
`114
`3 Important Pharmacokinetic Parameters,Used in
`Defining Drug Disposition,
`115
`J
`3.1 Clearance, 116
`3.2 Bioavailability, 119
`3.3 Volume of distribution, 120
`
`4 Important Pharmacokinetic Parameters Used in
`Therapeutics,
`121
`4.1 Dosing rate, 121
`4.2 Dose adjustment, 122
`4.3 Dosing interval, 122
`4.4 Loading dose, 125
`5 How is Phannacokinetics Used in the
`Development Process?,
`1216
`5.1 Pre-clinical development, 126
`5.2 Pharmacokinetics in initial phase I human
`studies, 126
`5.3 Pharmacokinetics in phases II and III
`studies, 127
`5.4 Late phase I pharmacokinetic studies, 127
`5.5 Pharmacokinetics in phase IV, 128
`6. Applications in Areas Other Than Drug
`Discovery,
`128
`
`Burger’s Medicinal Chemistry and Drug Discovery,
`Fifth Edition, Volume 1: Principles and Practice,
`Edited by Manfred E. Wolff.
`ISBN 0-471-57556-9 © 1995 John Wiley & Sons, Inc.
`
`Page 5 of 44
`
`

`
`114
`
`Drug Absorption, Distribution and Elimination
`
`1 OVERVIEW OF PRODUCT
`DEVELOPMENT ISSUES
`
`Although many compounds come through
`drug discovery every year, only a rare few
`can actually make their way through prod-
`uct development and pass the scrutiny of
`the United States Food and Drug Adminis-
`tration (U.S. FDA). With some ups and
`downs in marketing, these newly approved
`pharmaceutical products eventually land on
`the shelves in pharmacies where they are
`dispensed to patients upon presentation of
`the proper prescriptions.
`Why are so many compounds “killed” in
`the product development stage? Since the
`bottom line question in drug development
`asks, “Is this drug safe and effective in the
`human body?” many of these compounds
`simply do not prove to be safe and effective
`in the human body.
`In order to answer this safety and effica-
`cy question satisfactorily, development sci-
`entists must address
`issues
`from many
`areas. Some of the common questions are:
`What route of administration will be used
`
`to deliver the drug? How much of the drug
`gets into the systemic circulation and to the
`site of action? Where in the body will the
`drug distribute? How long does the drug
`remain intact in the body? How does the
`drug get eliminated from the body? Is the
`administered compound metabolized into
`other entities? Is the pharmacological effect
`derived from the administered compound,
`or/ and from metabolites? IIow much drug
`in the body is needed to elicit the pharma-
`cological effect? Can patients develop aller-
`gic or toxic reactions toward the adminis-
`tered compound or its metabolites? How
`much drug in the body is needed to initiate
`such adverse reactions? What is the mecha-
`
`nism for such allergic reactions? Are these
`reactions reversible? Is
`the drug or
`the
`metabolites carcinogenic,
`teratogenic, or
`mutagenic? If so, what
`is the underlying
`mechanism?
`
`2 DEFINING DRUG ABSORPTION,
`DISPOSITION AND ELIMINATION
`USING PHARMACOKINETICS
`
`in product development
`Initial progress
`rests heavily on a thorough understanding
`of the absorption, distribution and elimina-
`tion characteristics of a drug. Absorption,
`distribution
`and
`elimination
`processes
`begin when a dose is administered, and
`may govern the appearance of any thera-
`peutie effect (Fig. 5.1). Pharmacokinetics is
`used to quantitate these processes. Apart
`from its usefulness in explaining the safety
`and toxicity assessment data which will be
`discussed later in the chapter, pharmaco-
`kinetic analysis is used primarily to design
`appropriate dosing regimens, and also to
`quantitatively define drug disposition
`The term pharmacokinetics can be de-
`fined as what the body does to the drug.
`The parallel term, pharmacodynamics, can
`be defined as what the drug does to the
`body. A fundamental hypothesis of phar-
`macokinetics is
`that a relationship exists
`between a pharmacologic or toxic effect of
`a drug and the concentration of the drug in
`a readily accessible site of the body (e.g.,
`blood). This hypothesis has been docu-
`mented for many drugs (3, 4), although for
`some drugs no clear relationship has been
`found between pharmacologic effect and
`plasma or blood concentrations.
`This chapter will focus on the conceptual
`approach to pharmacokinetics, its use as a
`tool
`in therapeutics and in defining drug
`disposition. The more common mathema-
`tical modeling-exponential
`equation-data
`analysis approach to pharmacokinetics will
`not be discussed here. These mathematical
`
`techniques are necessary so as to be able to
`determine the important pharmacokinetic
`parameters that are to be discussed; how-
`ever, for medicinal chemists who need to
`interact with other pharmaceutical scien-
`tists in the drug development process, a
`conceptual approach to pharmacokinetics
`
`Page 6 of 44
`
`

`
`3 Important Pharmacokinetic Parameters Used in Defining Drug Disposition
`
`Dose of drug
`administered
`
`"' " BIOAVAILAHILITY
`
`Drug concentration
`in systemic circulation
`
`Drug metabolized
`M exuemd
`
`Pharmacokrnellcs
`
`r
`CLEARANCE
`
`Ar
`
`Il
`
`Drug in tissues
`oi distribution
`
`DISTRIBUTION
`
`Pharmacodynamics
`
`Drug concentration
`at site of action
`
`Pharmacologic effect
`l
`Clinical response
`
`\E
`
`fficacy
`
`/
`Toxicity
`
`\ /
`Fig. 5.1 A schematic representation of the doseresponse relationship of a drug (1). Reproduced courtesy of the
`author and Appleton & Lange.
`
`_I
`
`will be more useful. Nevertheless, to even
`gain a conceptual understanding of phar-
`macokinetics and its application to drug
`development, some basic simple equations,
`as discussed in this chapter, are necessary.
`This approach should allow the medicinal
`chemist to appreciate why modification of a
`drug molecule may -lead
`to important
`changes in drug disposition.
`
`3 IMPORTANT PHARMACOKINETIC
`PARAMETERS USED IN DEFINING
`DRUG DISPOSITION
`
`Table 5.1 Ten Critical Pharmacokinetic and
`Pharmacodynamic Parameters in Drug
`Development in Order of Importance"
`
`Clearance
`Effective concentration range
`Extent of availability
`Fraction of the available dose excreted
`unchanged
`Blo0d/ Plasma concentration ratio
`Half—life
`Toxic concentrations
`Extent of protein binding
`Volume of distribution
`Rate of availability
`
`Among the many pharmacokinetic parame-
`ters (Table 5.1)
`that can be determined
`
`“Ref. 5. Reproduced courtesy of L.Z. Benet and
`Plenum Press.
`
`Page 7 of 44
`
`

`
`116
`
`when delining a new drug substance, clear-
`ance. (CL) is the most important for defin-
`ing drug disposition. Bioavailability (F)
`and volume of distribution (V) are also of
`primary in1poi'tant:e when pharm:u:okin-
`ctics are used to deline drug disposition.
`
`3.1 Clearance
`
`the
`the measure of
`is
`Clearance (CL)
`ability of the body to eliminate a drug.
`Initially, clearance will be looked at from a
`physiological point of view. Figure 5.2
`depicts how a drug is removed from the
`systemic circulation when it passes through
`an eliminating organ. The rate of presenta-
`tion of a drug to a drug elimination organ is
`the product of organ blood [low (Q) and
`the concentration of drug in the arterial
`blood entering the organ (CA). The rate of
`exit of a drug from the drug eliminating
`organ is the product of the organ blood
`flow (Q) and the concentration of the drug
`in the venous blood leaving the organ (CV).
`By mass balance, the rate of elimination (or
`extraction) of a drug by :1 drug eliminating
`organ is the difference between the rate of
`presentation and the rate of exit.
`
`Drug Absorption, Distribution and Elimination
`
`Rate of presentation = Q - CA
`
`Rate of exit = Q - CV
`
`(5.1)
`
`(5.2)
`
`Rate of elimination = Q - CA — Q - CV
`
`= Q ' (CA — CV)
`
`(5.3)
`
`Extraction ratio (ER) of an organ can be
`defined as the ratio of the rate of elimina-
`tion to the rate of presentation.
`
`Extraction ratio = (Rate of elimination/
`
`Rate of presentation)
`
`(5.4a)
`
`ER:AQ'(CA'CV)/QICA
`
`ER = (CA - CV)/CA
`
`(5.4b)
`
`The maximum possible extraction ratio
`is 1.0 when no drug emerges into the
`venous blood upon presentation to the
`eliminating organ (i.e., CV = 0). The low-
`est possible extraction ratio is zero when all
`the drug passing through the potential drug
`eliminating organ appears in the venous
`blood (i.e., CV = CA). Drugs with an ex-
`traction ratio of more than 0.7 are by
`convention considered as high extraction
`ratio drugs, while those with an extraction
`ratio of less than 0.3 are considered as low
`extraction ratio drugs.
`‘
`
`-u—|ntravenous
`dose
`
`Remainder
`of the body
`
`Fig. 5.2 A schematic representation of the concentration—clearance relationship.
`
`Page 8 of 44
`
`

`
`117
`3 Important Pharmacokinetic Parameters Used in Defining Drug Disposition
`occurring in the liver, the kidney. and other
`The product of organ blood [low and
`organs. The total systemic clearance will be
`extraction ratio of an organ represents a
`the sum of the individual organ elezirauccs.
`rate at which a certain volume ol' blood is
`completely cleared of a drug. This expres-
`sion defines the organ clearance (CTLUWH)
`of a drug.
`
`CLtotal : CLhepatic + CLrenal + Cl‘other
`
`(5.10)
`
`CL
`
`organ
`
`=Q-ER=Q-(CA—C\,)/CA
`
`(5.5)
`
`From equations 5.3 and 5.5, one can see
`that clearance is a proportionality constant
`between rate of elimination and the arterial
`drug concentration.
`At steady ‘state, by definition, rate in
`equals rate out. Rate in is given by the
`dosing rate (Dose/1-, i.e., dose divided by
`dosing interval 1-) multiplied by the drug
`availability (F), whereas rate out is the rate
`of elimination (clearance multiplied by the
`systemic concentration (C)).
`Rate In = Rate Out
`
`(5.6)
`
`F-Dose/~r=CL-C
`
`(5.7)
`
`When equation 5.7 is integrated over time
`from zero to infinity, equation 5.8 results.
`
`F-Dose = CL-AUC
`
`(5.8)
`
`where AUC is the area under the con-
`centration time curve, and F is the fraction
`of dose available to the systemic circulation
`(see Bioavailability in section 3.2).
`the
`Clearance may be calculated as
`available dose divided by the area under
`the systemic drug concentration curve.
`
`-
`
`CL = F-Dose/AUC
`
`(5.9)
`
`The maximum value for organ clearance is
`limited by the blood flow to the organ, i.e.,
`extraction ratio is 1. The average blood
`flow to the kidneys and the liver is approxi-
`mately 66 L/ h and 81 L/h,
`respectively.
`Clearance can occur in many sites in the
`body and is generally additive. Elimination
`of a drug may occur as a result of processes
`
`Among the many organs that are ca-
`pable of eliminating drugs,
`the liver,
`in
`general, has the highest metabolic capa-
`bility. Drug molecules in blood are bound
`to blood cells and plasma proteins such as
`albumin and alpha‘-acid glycoprotein. Yet
`only unbound drug molecules can pass
`through hepatic membranes into hepato-
`cytes where
`they are metabolized by
`hepatic enzymes or transported into the
`bile. Thus in order to be eliminated, drug
`molecules must partition out of the red
`blood cells, and dissociate from plasma
`proteins to become unbound or free drug
`molecules. Because unbound drug mole-
`cules are free to partition into and out of
`blood cells and hepatocyles,
`there is an
`equilibrium of free drug concentration be-
`tween the blood cells, the plasma, and the
`hepatocytes. The ratio between unbound
`drug concentration and total drug concen-
`tration constitutes the fraction unbound
`(f\l)'
`Fraction unbound = Unbound drug con-
`centration/ Total drug concentration
`
`f.=C;/C
`
`(5.11)
`
`Since an equilibrium exists between the
`unbound drug molecules in the blood cells
`and the plasma,
`the rate of elimination of
`unbound drugs is the same in the whole
`blood as
`in the plasma at steady state.
`Thus,
`
`(5.12)
`CLP -.cp : CL, - C, = CL“ - cu
`where the subscripts p, b, and u refer to
`plasma, blood and unbound, respectively.
`From the material ]’Jl‘I3SC1llBl'_l so far, one
`may intuitively imagine that hepatic drug
`clearance will be
`inlhienced by hepatic
`
`Page 9 of 44
`
`

`
`118
`
`blood flow, fraction unbound, and intrinsic
`clearance; that is, the intrinsic ability of the
`organ to clear unbound drug. The simplest
`model
`that describes hepatic clearance in
`terms of these pliysiolngic parameters is the
`well-stirred mode] ('6'). Assuming instanta-
`neous and complete mixing, the well-stirred
`model states that hepatic clearance (with
`respect to blood concentration) is
`CLhep = Qhep . fu I CLint/(Qhep +fu . CLint)
`(5.13)
`
`Note that f“ is calculated from unbound
`and total concentration in whole blood.
`Equation 5.5 advises that hepatic clear-
`ance is the product of hepatic blood ilow
`and hepatic extraction ratio. 'l'herefore_. as
`shown in equation 5.13, hepatic extraction
`ratio is
`,
`
`ERhep =f.. ' CLim/(Qiep +fu ' CLint)
`(5.14)
`
`Exainining equations 5.13 and 5.14, one
`finds that for drugs with a high extraction
`ratio (i.e., ER approaches 1.0), f“ -CLIM is
`much greater
`than QM, and clearance
`approaches QM. In other words. the clear-
`ance for a high extraction ratio drug,
`imi-
`pramine for example,
`is perfusion rate
`limited. For drugs with a low extraction
`ratio (i.e., ER approaches zero), QM,
`is
`much greater than fu - (TIMI, and clearance
`is approximated by fu - CLIM. An example
`of a low extraction ratio drug is acetamino-
`phen.
`The intrinsic ability of an organ to clear
`a drug is directly proportional to the activi-
`ty of the metabolic enzymes in the organ.
`Such metabolic processes. both in vi'.'ro and
`in vivo, are characterized by Michaelis—
`Menten kinetics:
`
`Rate of metabolism = VMAX - C/(KM + C)
`
`(5.15)
`
`the maximum rate at
`in which VMAX,
`which metabolism can proceed, is propor-
`
`Drug Absorption, Distribution and Elimination
`
`tional to the total concentration of enzyme.
`KM is the Michaclis-Menten constant corre-
`sponding to the drug concentration which
`yields 112 of the maximum rate of meta-
`bolism. Dividing both sides of equation
`5.15 by the systemic concentration (C)
`yields:
`
`Rate of metabolism/C = CL,nm,m,i5m
`
`= VMAX/(KM + C)
`
`(5.16)
`
`Since ‘identification of a saturable process
`only occurs for low extraction ratio com-
`pounds (1.e., CL.mm,m“5_“ = -__-(..‘Li,,,),
`the
`relationship
`between
`classical
`enzyme
`kinetics and pharmacokinetics is revealed:
`
`fu . CLint : MAX/(KM +
`
`As VMAX and KM can be obtained from
`in vitro metabolism experiments, develop-
`ment scientists may reasonably predict the
`in vivo clearance parameter of a low or
`intermediate extraction ratio drug from in
`vi'.n'o data. using equations 5.13 and 5.17.
`By using appropriate scaling factors, the in
`viva clearance parameter in humans can be
`approximated from in virm metabolism
`data from other species (7, 8).
`The kidneys are also important drug
`eliminating organs. Renal clearance (CL,)
`is a proportionality term between urinary
`excretion rate and systemic concentration.
`Integrating equation 5.18a over time from
`zero to infinity, renal clearance is the ratio
`of the total amount of drug excreted un-
`changed to the area under the systemic
`concentration curve. The total amount of
`drug excreted unchanged can be measured
`experimentally or can be calculated from
`the close if the fraction of the available dose
`excreted unchanged (fe) is known.
`
`(5.18a)
`CL, = Urinary excretion rate/ C
`= Total amount of drug excreted
`
`unchanged/AUC (5.18b)
`
`=fe - F-Dose/AUC
`
`(5.18c)
`
`Page 10 of 44
`
`

`
`3 Important Pharmacokinetic Parameters Used in Defining Drug Disposition
`
`119
`
`It is obvious above that the conceptual
`approach to clearance requires measure-
`ments
`of
`blood
`concentrations. Yet,
`bioanalytical measurements are often car-
`ried out
`in plasma due to the ease of
`sample handling. However, measuring the
`blood to plasma ratio allows one to convert
`clearance values determined in plasma, to
`their corresponding blood values using
`equation 5.12.
`
`3.2 Bioavailability
`
`The bioavailability of a drug product via
`various routes of administration is defined
`as the fraction of unchanged drug that is
`absorbed intact and then reaches the site of
`action; or the systemic circulation following
`administration by any route. For an in-
`travenous dose of a drug, bioavailability is
`defined as unity. For drug administered by
`other routes of administration, bioavail-
`‘ability is often less than unity. Incomplete
`bioavailability may be due to a number of
`factors
`that
`can
`be
`subdivided
`into
`categories of dosage-form effects, mem-
`brane effects and site of administration
`
`effects. Obviously, the route of administra-
`tion that offers maximum bioavailability is
`the direct
`input at the site of action for
`which the drug is developed. This arrange-
`ment may be difflcult to achieve because
`the site of action is not known for some
`
`disease states, and in other cases, the site
`of action is completely inaccessible even
`4 when the drug is placed into the blood-
`stream. The most commonly used route is
`oral administration. However, orally ad-
`ministered drugs may decompose in the
`fluids of the gastrointestinal lumen, or be
`metabolized as they pass through the gas-
`trolntestinal membrane. In addition, once a
`drug passes into the hepatic portal vein, it
`{nay be cleared by the liver before entering
`Into the general circulation. The loss of
`drug as it passes through drug eliminating
`
`organs for the first time is known as the
`first pass effect.
`The fraction of an oral dose available to
`the systemic circulation considering both
`absorption and the first pass effect, can be
`found by comparing the ratio of AUCs
`following oral and intravenous dosing.
`
`F = Aucm,/A UC,_,_
`
`(5.19)
`
`If an assumption is made that all of a drug
`dose is absorbed through the gastrointesti-
`nal tract intact, and that the only extraction
`takes place at the liver, then the maximum
`bioavailability (Fmx) is
`
`Fm, = 1 — ER
`
`hep
`
`(5.20)
`
`From equations 5.5 and 5.20, one can
`derive the following relationship for Fmax:
`
`Fmax = 1 _ (CLhep/Qhep)
`
`(5.21)
`
`For high extraction ratio drugs, where
`CLhep approaches Qhep, Fm“ will be small.
`For
`low extraction» ratio drugs, Qhep is
`much greater than CLMP, and Fm“ will
`approximate one.
`Recently, bioavailability and clearance
`data obtained from a cross-over study of
`cyclosporine
`kinetics before
`and after
`rifampin dosing,
`revealed a new under-
`standing of drug metabolism and disposi-
`tion of this compound (9). Healthy vol-
`unteers were given cyclosporine, intraven-
`ously and orally, before and after their
`CYP3A (P450 3A) enzymes were induced
`by rifampin. As expected, the blood clear-
`ance of cyclosporine increased from 0.31 to
`0.42 L/h/kg due to the induction of the
`drug’s metabolizing enzymes (i.e., an in-
`crease in VMAX in equation 5.15). There
`was no change in volume of distribution,
`but there was a dramatic decrease in bio-
`availability from 27% to 10% in these
`individuals.
`A decrease in bioavailability is to be
`expected, because cyclosporine undergoes
`some
`first—pass metabolism as
`it goes
`
`Page 11 of 44
`
`

`
`120
`
`through the liver following oral dosing. But
`if one predicts on the basis of pharma-
`cokinetics what
`the maximum bioavail-
`ability (as calculated by Eq. 5.21) would be
`before and after rifampin dosing, the maxi-
`mum bioavailability would decrease from
`77% to 68%. Thus,
`there would be an
`expected cyclosporine bioavailability de-
`crease of approximately 12% just on the
`basis of
`the clearance changes resulting
`from inducing CYP3A enzymes in the liver.
`In fact, there was a bioavailability decrease
`of 60%. Furthermore, bioavailability was
`significantly less than would be predicted at
`maximum. While some of that lower bio-
`availability was due to formulation effects,
`the discrepancy between the theoretical
`maximum bioavailability and the achiev—
`able bioavailability of cyclosporine
`re-
`mained a question.
`However, on the basis of new findings
`during the last several years about the high
`prevalence of CYP3A isoxymcs in the gut,
`significant metabolism of cyclosporine in
`the gut as well as in the liver was specu-
`lated. This hypothesis can consistently ex-
`plain the sigmfzcrmtly lower bioavailability
`than would be predicted even if all of the
`drug could be absorbed into the blood
`stream. This finding, particularly quantifi-
`cation of the magnitude of gut metabolism
`(more than 2/ 3s of the total metabolism for
`an oral dose of cyclosporine occurs in the
`gut), would not have been realized had
`pharmacokinetics not been utilized in the
`analysis of the given data.
`
`3.3 Volume of Distribution
`
`The volume of distribution (V) relates the
`amount of drug in the body to the con-
`centration of drug i11 the blood or plasma,
`depending upon the fluid nteasured. At its
`simplest,
`this
`relationship is defined by
`equation 5.22:
`
`V: Amount of drug in body/C (5.22)
`
`Drug Absorption, Distribution and Elimination
`
`the plasma
`For a normal 7U-kg man,
`volume is 3L. the blood volume is 5.5 L.
`the extracellular linid outside the plasma is
`12L and the total body water is approxi-
`mately 42 L. However. many classical drugs
`exhibit volumes of distribution far in excess
`of these known liuid volumes. The volume
`of distribution for digoxin is about 700 L,
`which is ztpproximately "ill
`times greater
`than the total body volume of a 7t)—kg man.
`This example serves to emphasize that the
`volume of distribution does not represent :1
`real volume. Rather.
`it
`is an apparent
`volume which should be considered as the
`size of the pool of body fluids that would he
`required if the drug were equally distribut-
`ed throughout all portions of the body.
`in
`fact, the relatively hydrophobic digoxin has
`a high apparent volume of distribution
`because it distributes predominantly into
`muscle and adipose tissue,
`leaving only a
`very small amount of drug in the plasma in
`which the concentration of drug is mea-
`sured.
`a
`the distribution of
`At equilibrium,
`drug within the body depends upon binding
`to blood cells, plasma proteins, and tissue
`components. Only the unbound drug is
`capable of entering and leaving the plasma
`and tissue compartments. A memory aid
`for this relationship can be summarized by
`the expression:
`
`V: Vp + V'rw ' fu/fu,T
`
`(5.23)
`
`where VP is the volume of plasma, VTW is
`the aqueous volume outside the plasma, f“
`is the fraction unbound in plasma, and fu‘T
`is the fraction unbound in tissue. Thus, a
`drug that has a high degree of binding to
`plasma proteins (i.e., low fa) will generally
`exhibit
`a
`small volume ol‘ distribut'io_n.
`Unlike plasma protein binding, tissue bind-
`ing of a drug cannot be nteasurerl directly.
`Generally, this parameter is assumed to be
`constant unless indicated otherwise.
`in equation 5.22. the body is considered
`:1 single homogeneous pool of body
`
`as
`
`Page 12 of 44
`
`

`
`4 Important Pharmacokinetic Parameters Used in Therapeutics
`V55 = Dose“ - AUMC/AUC2
`
`121
`(5.24)
`
`fluids as described above for digoxin. For
`most drugs, however, two or three distinct
`pools of distribution space appear to exist.
`This condition results in a time—dependent
`decrease in the measurable blood or plasma
`concentration, which reflccts distribution
`into other body pools independent of the
`body’s ability to eliminate the drug. Figure
`5.3 describes mean serum IFN-oz concen-
`trations after a 40 min intravenous infusion
`as well as after intramuscular and subcuta-
`neous injections of the same dose. Note the
`logarithmic biphasic nature of the mean
`plasma concentration time curve following
`the intravenous infusion. This biphasic na-
`ture represents both the distribution and
`elimination processes.
`Generally, comparisons of volume of
`distribution are made using a parameter
`designated as the volume of distribution at
`steady state (V55), which refleets the sum of
`the volumes of all the pools into which the
`drug may distribute. V55 can be calculated
`from the area under the moment curve
`(AUMC) and the area under the curve
`(AUC) as defined by Benet and Galeazzi
`(11):
`
`AUMC can be calculated from areas
`under a plot of concentration - time vs time.
`Both AUC and AUMC may be calculated
`from the coeilicients and exponents of the
`equations utilized to described the multi-
`eompartnient nature of drug kinetics as
`depicted in Figure 5.3. These concepts will
`be revisited following a discussion of halt‘-
`life.
`
`4 IMPORTANT PHARMACOKINETIC
`PARAMETERS USED IN
`'1‘HERAPEUTICS
`
`In addition to the three parameters, clear-
`ance (CL), bioavailability (F), and volume
`of distribution (V) discussed previously, a
`fourth parameter, half-life (rm),
`is also
`crucial
`in therapeutics. The decreasing
`order of importance of these four parame-
`ters are clearance, bioavailability, half-life
`and volume. Clearance defines the dosing
`rate, bioavailability defines dose adjust-
`ment, and half-life defines the dosing inter-
`val. Volume of distribution defines
`the
`loading dose.
`
`4.1 Dosing Rate
`
`As discussed in equation 5.6 in section 3. I,
`rate of presentation equals rate of exit at
`steady state. Whereas rate of presentation
`is the product of bioavailability and dosing
`rate, rate of exit is the product of clearance
`and average (steady state} concentration.
`By replacing the average concentration
`with the target concentration,
`the dosing
`rate can be computed with known values of
`bioavailability and clearance.
`
`Rate in = Rate out
`
`(5.6)
`
`
`
`Meanplasmaeoncn(pg/mt)
`
`
`
`
`
`I._ _I_
`10
`Time tn)
`
`l"ll£- 5.3 Mean serum lFN—n concentrations after a
`"l"R.|e 3:‘) r. til" l_| dose as an inlravenntts infusion (O)
`III‘ an itttrantttscttliir (X) or subeutilneotts (A) injection
`UU). Reproduced eotlrtcsy of the author and Clin.
`Pharmacol. Ther.
`
`Bioavailability >< Dosing rate = Clearance
`
`>< Average concentration
`
`(5.7a)
`
`F - Dosing rate = CL - Cmge,
`
`(5,7b)
`
`Page 13 of 44
`
`

`
`122
`
`Drug Absorption, Distribution and Elimination
`
`4.2 Dose Adjustment
`
`Table 5.2 Percentages of Dose Lost as a Func-
`tion of Number of Half-Lives
`
`There is often a therapeutic concentration
`range of drug in the blood that is necessary
`to elicit a clinical effect without causing
`drug toxicity. The boundaries of this range
`are set by the minimum effective concen-
`tration (MEC) and the minimum toxic
`concentration (M TC ). For example,
`in
`order to maintain a steady rate of presenta-
`tion of 100 mg/min, one can either ad-
`minister a completely bioavailable i.v. infu-
`sion at 100 mg/min, or a sustained release
`oral dosage form with 50% bioavailability
`at 200 mg/min. As shown in equations 5.7a
`and 5.7b, the actual dosing rate depends on
`the bioavailability of the dosage form. For
`proper dosing adjustment,
`the bioavail-
`ability (F) of a given dosage form stands as
`a must-know parameter in therapeutics.
`
`4.3 Dosing Interval
`
`Half-life (rm) is an extremely useful kinetic
`parameter in terms of therapeutics, since
`this parameter,
`together with therapeutic
`index, helps define the dosing interval at
`which drugs should be administered. By
`definition, half—life is the time required for
`50% of the drug remaining in the body to
`be eliminated. In three and one third half-
`lives, 90% of the dose would have been
`eliminated. Table 5.2 shows the percentage
`of dose lost in different numbers of half-
`lives. If the dosing interval is long relative
`to the half—life,
`large fiuctuations in drug
`concentration will occur. On the other
`hand, if the dosing interval is short relative
`to half—life,
`significant accumulation will
`occur. The half—life parameter also allows
`one to predict drug accumulation within the
`body and
`quantifies
`the
`approach to
`plateau that occurs with multiple dosing
`and constant rates of infusion. Convention-
`ally, three and one third half-lives are used
`as the time required to achieve steady state
`under constant infusion. The concentration
`
`Number of
`Half-Lives
`
`Dose Lost, %
`
`50
`75
`87.5
`90
`93.8
`96.9
`
`level achieved after this time is already
`90% of the steady state concentration, and
`clinically, it is difficult to distinguish a 10%
`difference in concentrations.
`After determining the extent of oral
`drug bioavailability, half—life is probably
`the next most important parameter in terms
`of deciding the appropriateness of a drug
`for further development. Drugs with very
`short half—lives create problems in main-
`taining steady-state concentrations in the
`therapeutic range. Thus, a successful drug
`product with a short half—life will require a
`dosage form which allows a relatively con-
`stant prolonged input. Drugs with a very
`long half—life are favored in terms of effica-
`cy considerations; however, this long half-
`life may be a negative characteristic in
`terms of toxicity considerations. Figure 5.4
`illustrates the importance of half—life in
`defining the dosing interval.
`This figure depicts the relationship be-
`tween the frequency of theophylline dosing
`and the plasma concentration time course
`when a steady-state theophylline plasma
`level of 15 p.g/mL is desired. The smoothly
`rising curve shows the plasma concentra-
`tions achieved with an intravenous infusion
`of 43.2 mg/h to a patient exhibiting an
`average theophylline clearance of 0.69 mL/
`min/ kg. The steady-state theophylline plas-
`ma level achieved is midway within the
`therapeutic concentration range of 10-
`20 ,u.g/mL. The figure also depicts the time
`courses
`for 8-hourly administration of
`
`
`
`
`
`
`
`
`
`
`
`....-.—._-i._.-_.=.-‘sag—".1' ',::;-L“'—--;'4a-3=I'Ii.._4:._-.-.-:~_«.F-;_-—--‘-+‘:-:.._.—r-.:Jo—-£-
`
`Page 14 of 44
`
`

`
`4 Important Pharmacokinetic Parameters Used in Therapeutics
`
`4'0
`
`0.) O
`
`R)O
`
`24~h dosage
`
`8—h dosage
`
`3E\b
`
`N-
`
`e1\—
`:...
`3-e
`3‘
`§“\Q
`2'Q
`'43o
`
`1:eUQ:QQ
`(JoN
`9.:
`
`oE‘
`
`8
`
`16
`
`24
`
`32
`
`40
`Time (h)
`Fig. 5.4 Relationship between frequency of dosing and maximum and minimum plasma concentrations when a
`steady—state plasma level of 15 uglinl.
`is desired. The time course of plasma concentrations for 43.2 mg/h
`intravenous infusion, an Bvltourly 34l.l mg oral dose, and a 24 hourly 1020 mg oral dose are depicted. Reproduced
`courtesy of the author and Appleton S: Lange.
`
`48
`
`56
`
`64
`
`72
`
`80
`
`340 mg and 24-hourly administration of
`1020 mg, assuming that
`these doses are
`administered in an immediate release dos-
`age l’orm. in each case the mean steady-
`state concentration is l5 ugfml... However,
`the peak to trough ratio and the concert-
`trations acliicved with the once daily dosing
`(i.e., 1.020 mg) of a rapidly released formu-
`lation would result in concentrations in the
`toxic range,’ exceeding 20 ,u.gfmL for cer-
`tain periods of time, as well as concen-
`trations expected to not yield eflicaey, i.e.,
`less than 1U p.glmL, for signilicant periods
`during each dosing interval. In contrast, the
`8-hourly dosing, which is approximately
`equivalent
`to the half—lit'e of theophylline.
`shows :1 2-fold range in peak to trough, and
`theophylline levels stay within the thera-
`peutic plasma concentration range.
`Although half-life is a very important
`p{lt':.tlTtClCl‘
`in therapeutics for detining the
`dosing interval,
`half—|il'e can he
`a very
`inislcnding parameter when one is attempt-
`
`in
`ing to use pharmacokinetics as a tool
`defining drug disposition. As depicted in
`equation 5.29, half-life varies as a function
`of the two physiologic-related parameters,
`volume and clearance.
`
`t1,2 = 0.693 ~ V/CL
`
`(5.29)
`
`Half-life has little value as an indicator
`of