Biopharmaceutics and
`Clinical Pharmacokinetics
`
`t
`
`MILO GIBALDI, PH.D.
`Dean, School of Pharmacy
`Associate Vice President,
`Health Sciences
`University of Washington
`Seattle, Washington
`
`F O U R T H E D I T I O N
`
`LEA & FEB1GER
`
`•
`
`Philadelphia
`
`• London
`
`1991
`
`j, I
`
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`f lie
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`li!(f
`ll
`'i'K'l is
`
`SUN - IPR2017-01929, Ex. 1034, p. 1 of 17
`
`

`

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`II .f •
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`Lea & Febiger
`200 Chester Field Parkway
`Malvern, Pennsylvania 19355-9725
`U.S.A.
`'
`(215) 251-2230
`1-800-444-1785
`
`Lea & Febiger (UK) Ltd.
`145a Croydon Road
`Beckenham, Kent BR3 3RB
`U.K.
`
`Library of Congress Cataloging-in-Publication Data
`
`Gibaldi, Mile.
`Biopharmaceutics and clinical pharmacokinetics / Milo Gibaldi.—
`4th ed.
`p.
`cm.
`Includes bibliographical references.
`ISBN 0-8121-1346-2
`1. Biopharmaceutics. 2. Pharmacokinetics. 1. Title
`[DNLM: 1. Biopharmaceutics. 2. Pharmacokinetics. QV 38 G437b]
`RM301.4.G53 1990
`615'. 7—dc20
`DNLM/DLC
`for Library of Congress
`
`90-5614
`CIP
`
`First Edition, 1971
`Reprinted 1973, 1974, 1975
`Second Edition, 1977
`Reprinted 1978, 1979, 1982
`Third Edition, 1984
`Reprinted 1988
`Fourth Edition, 1991
`First Spanish Edition, 1974
`First Japanese Edition, 1976
`Second Japanese Edition, 1981
`Second Turkish Edition, 1981
`
`The use of portions of the text of USP XX-NF XV is by permission of the USP Convention. The Convention
`is not responsible for any inaccuracy of quotation or for false or misleading implication that may arise
`from separation of excerpts from the original context or by obsolescence resulting from publication of a
`supplement.
`
`Reprints of chapters may be purchased from Lea & Febiger in quantities of 100 or more.
`
`Copyright © 1991 by Lea & Febiger. Copyright under the International Copyright Union. All Rights Reserved. This
`book is protected by copyright. No part of it may be reproduced in any manner or by any means without written permission
`from the publisher.
`
`PRINTED IN THE UNITED STATES OF AMERICA
`
`Print no.: 4 3 2 1
`
`SUN - IPR2017-01929, Ex. 1034, p. 2 of 17
`
`

`

`2
`
`A
`
`Introduction to Pharmacokinetics
`
`Compartmental and Noncompartmental
`Pharmacokinetics
`
`Gastrointestinal Absorption—
`Biologic Considerations
`
`Gastrointestinal Absorption—
`Physicochemical Considerations
`
`Gastrointestinal Absorption—
`Role of the Dosage Form
`
`6.
`
`Nonoral Medication
`
`Prolonged-Release Medication
`
`Bioavailability
`
`Drug Concentration and Clinical Response
`
`Drug Disposition—Distribution
`
`Drug Disposition—Elimination
`
`g
`
`9.
`
`10.
`
`11.
`
`Contents
`
`14
`
`24
`
`40
`
`61
`
`80
`
`124
`
`146
`
`176
`
`187
`
`(203
`
`/
`
`ix
`
`SUN - IPR2017-01929, Ex. 1034, p. 3 of 17
`
`

`

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`1\
`
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`
`&
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`I
`
`• 5
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`•p
`
`12.
`
`1 3 .
`
`14.
`
`15.
`
`Contents
`
`Pharmacokinetic Variability—
`Body Weight, Age, Sex, and Genetic Factors
`
`Pharmacokinetic Variability—Disease
`
`Pharmacokinetic Variability—Drug Interactions
`
`Individualization and Optimization of
`Drug Dosing Regimens
`
`Appendix I. Estimation of Area Under the Curve
`
`Appendix II. Method of Superposition
`
`Index
`
`234
`
`272
`
`305
`
`344
`
`377
`
`379
`
`381
`
`SUN - IPR2017-01929, Ex. 1034, p. 4 of 17
`
`

`

`1
`Introduction to Pharmacokinetics
`
`i
`
`i
`
`)
`
`i
`
`Advancements in biopharmaceutics have come
`about largely through the development and appli­
`cation of pharmacokinetics. Pharmacokinetics is
`the study and characterization of the time course
`of drug absorption, distribution, metabolism, and
`excretion, and the relationship of these processes
`to the intensity and time course of therapeutic and
`toxicologic effects of drugs. Pharmacokinetics is
`used in the clinical setting to enhance the safe and
`effective therapeutic management of the individual
`patient. This application has been termed clinical
`pharmacokinetics.
`
`DISTRIBUTION AND ELIMINATION
`The transfer of a drug from its absorption site
`to the blood, and the various steps involved in the
`distribution and elimination of the drug in the body,
`are shown in schematic form in Figure 1-1. In the
`blood, the drug distributes rapidly between the
`plasma and erythrocytes (red blood cells). Rapid
`distribution of drug also occurs between the plasma
`proteins (usually albumin but sometimes ctj-acid
`glycoproteins and occasionally globulin) and
`plasma water. Since most drugs are relatively small
`molecules they readily cross the blood capillaries
`and reach the extracellular fluids of almost every
`organ in the body. Most drugs are also sufficiently
`lipid soluble to cross cell membranes and distribute
`of various tissues.
`in the intracellular fluids
`Throughout the body there is a distribution of drug
`between body water and proteins or other macro-
`molecules that are dispersed in the body fluids or
`are components of the cells.
`The body can be envisioned as a collection of
`separate compartments, each containing some frac­
`tion of the administered dose. The transfer of drug
`from one compartment to another is associated with
`
`a rate constant (k). The magnitude of the rate con­
`stant determines how fast the transfer occurs.
`The transfer of drug from blood to extravascular
`fluids (i.e., extracellular and intracellular water)
`and tissues is called distribution. Drug distribution
`is usually a rapid and reversible process. Fairly
`quickly after intravenous (iv) injection, drug in the
`plasma exists in a distribution equilibrium with
`drug in the erythrocytes, in other body fluids, and
`in tissues. As a consequence of this dynamic equi­
`librium, changes in the concentration of drug in
`the plasma are indicative of changes in drug level
`in other tissues including sites of pharmacologic
`effect (bioreceptors).
`The transfer of drug from the blood to the urine
`or other excretory compartments (i.e., bile, saliva,
`and milk), and the enzymatic or biochemical trans­
`formation (metabolism) of drug in the tissues or
`plasma to metabolic products, are usually irre­
`versible processes. The net result of these irre­
`versible steps, depicted in Figure 1-1, is called
`drug elimination. Elimination processes are re­
`sponsible for the physical or biochemical removal
`of drug from the body.
`The moment a drug reaches the bloodstream, it
`is subject to both distribution and elimination. The
`rate constants associated with distribution, how­
`ever, are usually much larger than those related to
`drug elimination. Accordingly, drug distribution
`throughout the body is usually complete while most
`of the dose is still in the body. In fact, some drugs
`attain distribution equilibrium before virtually any
`of the dose is eliminated. In such cases, the body
`appears to have the characteristics of a single com­
`partment.
`This simplification, however, may not be applied
`to all drugs. For most drugs, concentrations in
`plasma measured shortly after iv injection reveal a
`
`1
`
`SUN - IPR2017-01929, Ex. 1034, p. 5 of 17
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`

`

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`2
`
`Biopharmaceutics and Clinical Pharmacokinetics
`
`Drug at
`Absorption Site
`
`>
`
`^1
`
`Drug in Blood
`
`^2
`
`k_ 2
`
`Drug in
`Other Fluids
`of Distribution
`
`k3
`k_3
`
`, Drug in
`Tissues
`
`k4
`
`^5
`
`^6
`
`Drug in Urine
`
`Metabolite(s)
`
`Drug in Other
`Excretory Fluids
`
`Fig. 1-1. Schematic representation of drug absorption, distribution, and elimination.
`
`distinct distributive phase. This means that a meas­
`urable fraction of the dose is eliminated before
`attainment of distribution equilibrium. These drugs
`impart the characteristics of a multicompartment
`system upon the body. No more than two com­
`partments are usually needed to describe the time
`course of drug in the plasma. These are often called
`the rapidly equilibrating or central compartment
`and the slowly equilibrating or peripheral com­
`partment.
`
`PHYSICAL SIGNIFICANCE OF DRUG
`CONCENTRATION IN PLASMA
`Blood samples taken shortly after intravenous
`administration of equal doses of two drugs may
`show large differences in drug concentration de­
`spite the fact that essentially the same amount of
`each drug is in the body. This occurs because the
`degree of distribution and binding is a function of
`the physical and chemical properties of a drug and
`may differ considerably from one compound to
`another.
`At distribution equilibrium, drug concentrations
`in different parts of the body are rarely equal. There
`may be some sites such as the central nervous sys­
`tem or fat that are poorly accessible to the drug.
`There may be other tissues that have a great affinity
`for the drug and bind it avidly. Drug concentrations
`at these sites may be much less than or much greater
`than those in the plasma.
`Despite these complexities, once a drug attains
`distribution equilibrium its concentration in the
`plasma reflects distribution factors and the simple
`relationship between amount of drug in the body
`(A) and drug concentration in the plasma (C) shown
`in Equation 1-1 applies:
`
`A = VC
`
`(1-1)
`
`The proportionality constant relating amount and
`concentration is called the apparent volume of dis­
`tribution (V). In most situations, V is independent
`of drug concentration. Doubling the amount of
`drug in the body (e.g., by doubling the iv dose)
`usually results in a doubling of drug concentration
`in plasma. This is called dose proportionality; it
`is often used as an indicator of linear pharmaco­
`kinetics.
`The apparent volume of distribution is usually a
`characteristic of the drug rather than of the biologic
`system, although certain disease states and other
`factors may bring about changes in V. The mag­
`nitude of V rarely corresponds to plasma volume,
`extracellular volume, or the volume of total body
`water; it may vary from a few liters to several
`hundred liters in a 70-kg man. V is usually not an
`anatomic volume but is a reflection of drug distri­
`bution and a measure of the degree of drug binding.
`Acid drugs, such as sulfisoxazole, tolbutamide,
`or warfarin, are often preferentially bound to
`plasma proteins rather than extravascular sites. Al­
`though these drugs distribute throughout body wa­
`ter, they have small volumes of distribution ranging
`from about 10 to 15 L in man. A given dose will
`result in relatively high initial drag concentrations
`in plasma.
`On the other hand, many basic drugs including
`amphetamine, meperidine, and propranolol are
`more extensively bound to extravascular sites than
`to plasma proteins. The apparent volumes of dis­
`tribution of these drugs are large, ranging from 4
`to 8 times the volume of total body water (i.e..
`180 to 320 L in a 70-kg man). The frequently small
`doses and large distribution volumes of these drugs
`often make their quantitative detection in plasma
`difficult.
`
`SUN - IPR2017-01929, Ex. 1034, p. 6 of 17
`
`

`

`I
`
`Introduction to Pharmacokinetics
`
`3
`
`f
`
`,
`
`100
`
`80
`
`60 -
`
`to o
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`o
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`CL
`
`d AA/ d t = d AE/ d t
`
`\ d AA/ d t < d AE :/ d t
`
`C
`
`^ - d AA/ d t = 0
`
`dAA/dt > dAE/dt
`iA
`8
`
`16
`12
`Time (hrs)
`
`4
`
`B
`
`20
`
`Time course"of drug disappearance from the
`Fig. 1-2.
`absorption site (curve A) and appearance of eliminated drug
`in all forms (curve C). The net result is curve B, which
`depicts the time course of drug in the body.
`
`PHARMACOKINETIC CONSIDERATIONS OF
`DRUG CONCENTRATIONS IN PLASMA
`The plasma contains measurable quantities of
`many endogenous chemicals. In healthy individ­
`uals these biochemicals are present in concentra­
`tions that are reasonably constant, and it is appro­
`priate to speak of creatinine or bilirubin levels in
`the plasma. Drug levels or concentrations in the
`plasma are rarely level. One usually finds different
`concentrations of drug in the plasma at different
`times after administration. These changes reflect
`the dynamics of drug absorption, distribution, and
`elimination (Fig. 1-2).
`
`Intravenous Administration
`Absorption need not be considered when a drug
`is given by rapid iv injection. As soon as the drug
`is administered it undergoes distribution and is sub­
`ject to one or more elimination pathways. The
`amount of drug in the body and the drug concen­
`tration in plasma decrease continuously after in­
`jection. At the same time, there is continuous for­
`mation of metabolites and continuous excretion of
`drug and metabolites. Eliminated products accu­
`mulate while drug levels in the body decline.
`Most drugs distribute rapidly so that shortly after
`iv injection, distribution equilibrium is reached.
`Drug elimination at distribution equilibrium is usu­
`ally described by first-order kinetics. This means
`that the rate of the process is proportional to the
`amount or concentration of substrate (drug) in the
`system. As drug concentration falls, the elimina-
`
`tion rate falls in parallel. The proportionality con­
`stant relating rate and amount or concentration is
`called a rate constant. Accordingly, the elimination
`rate is written as follows;
`
`dA
`dt
`
`dAE
`— = kA
`dt
`
`(1-2)
`
`where A is the amount of drug in the body at time
`t, Ae is the amount of drug eliminated from the
`body (i.e., the sum of the amounts of metabolites
`that have been formed and the amount of drug
`excreted) at time t, and k is the first-order
`elimi­
`nation rate constant.
`The elimination rate constant is the sum of in­
`dividual rate constants associated with the loss of
`parent drug. For example, the overall elimination
`rate constant (k) in the model depicted in Figure
`1-1 is given by
`
`k = k4 + kj + k5
`
`(1-3)
`
`•
`
`Dimensional analysis of Equation 1-2 indicates
`that the units of k are reciprocal time (i.e., day
`hr1, or mhr1).
`Since there is a relationship between the amount
`of drug in the body and the drug concentration in
`the plasma (Eq. 1-1), we may rewrite Equation
`1-2 as
`
`d(VC)
`dt
`
`dC
`= -V— = k(VC)
`dt
`
`or
`
`dC
`— = kC
`dt
`
`(1-4)
`
`Integrating this expression between the limits t =
`0 and t = t yields
`
`log C = log C0
`
`kt
`2.303
`
`(1-5)
`
`Equation 1-5 indicates that a plot of log C versus
`t will be linear once distribution equilibrium is
`reached. The term C0 is the intercept on the log
`concentration axis, on extrapolation of the linear
`segment to t = 0.
`Figure 1-3 shows the average concentration of
`a semisynthetic penicillin in the plasma as a func­
`tion of time after an intravenous injection of a 2-g
`dose. The concentration values are plotted on a log
`scale; the corresponding times are plotted on a lin­
`ear scale. The semilogarithmic coordinates make
`it convenient to plot first-order kinetic data for they
`
`I
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`
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`
`SUN - IPR2017-01929, Ex. 1034, p. 7 of 17
`
`

`

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`4
`
`Biopharmaceutics and Clinical Pharmacokinetics
`
`200 -
`E
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`r 100 ~
`z
`O
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`H
`cn
`h - 50 -
`2
`LU
`o
`2 o
`o
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`(T
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`k
`S l o p e = „
`fcv'
`2.303
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`tl, ' I hr
`'z
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`1 0
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`TIME, hr
`
`Fig. 1—3. Semilogarithmic plot of penicillin concentra­
`tions in plasma after a 2-g intravenous dose. Concentrations
`decline in a first-order manner with a half-life of 1 hr.
`
`avoid the necessity of converting values of C to
`logC.
`According to Equation 1-5, the linear portion
`of the semilogarithmic plot of C versus t has a
`slope corresponding to ~k/2.303 and an intercept,
`on the y-axis (i.e., at t = 0), corresponding to C0.
`If a drug were to distribute almost immediately
`after injection, C0 would be a function of the dose
`and the apparent volume of distribution. Therefore,
`we would be able to calculate V as follows;
`
`V =
`
`iv dose
`C0
`
`(1-6)
`
`For the data shown in Figure 1-3 we can determine
`that C0 = 200 mg/ml and that V = 10 L.
`This approach, however, is seldom useful; Equa­
`tion 1-6 usually gives a poor estimate of V, always
`larger and sometimes substantially larger than the
`true volume of distribution. Equation 1-6 assumes
`that drug distribution is immediate, whereas most
`drugs require a finite time to distribute throughout
`the body space. Other methods to calculate V will
`be described subsequently.
`Although it is possible to calculate the elimi­
`nation rate constant from the slope of the line, it
`
`is much easier to determine k by making use of
`the following relationship;
`k = 0.693/tw
`
`(1-7)
`
`where tw is the half-life of the dmg (i.e., the time
`required to reduce the concentration by 50%). This
`parameter is determined directly from the plot (see
`Fig. 1-3). In a first-order process, the half-life is
`independent of the dose or initial plasma concen­
`tration. One hour is required to observe a 50%
`decrease of any plasma concentration of the semi­
`synthetic penicillin, once distribution equilibrium
`is attained. It follows that the elimination rate con­
`stant of this drug is equal to 0.693/t^ or 0.693 hr'.
`Knowledge of the half-life or elimination rate con­
`stant of a drug is useful because it provides a quan­
`titative index of the persistence of drug in the body.
`For a drug that distributes very rapidly after iv
`injection and is eliminated by first-order
`kinetics,
`one-half the dose will be eliminated in one half-
`life after administration; three-quarters of the dose
`will be eliminated after two half-lives. Only after
`four half-lives will the amount of drug in the body
`be reduced to less than one-tenth the dose. For this
`reason, the half-life of a drug can often be related
`to the duration of clinical effect and the frequency
`of dosing.
`
`Short-Term Constant Rate Intravenous
`Infusion
`Few drugs should be given as a rapid intravenous
`injection (bolus) because of the potential toxicity
`that may result. Many drugs that require intrave­
`nous administration, including theophylline, pro­
`cainamide, gentamicin, and many other antibiotics,
`are given as short-term constant rate infusions over
`5 to 60 min, or longer. The following scheme de­
`scribes this situation;
`
`Drug in
`reservoir
`
`Constant Drug in
`body
`
`rate
`
`k
`
`Eliminated
`drug
`
`The rate of change of the amount of drug in the
`body (A) during infusion is given by
`
`dA/dt = k0 - kA
`
`(1-8)
`
`where k0 is the infusion rate expressed in amount
`per unit time (e.g., mg/min), kA is the elimination
`rate, and k is the first-order elimination rate con­
`stant. This relationship assumes that the drug
`reaches distribution equilibrium quickly. Integrat­
`ing Equation 1-8 from t = 0 to t = t yields
`
`A = k0[l - exp(-kt)]/k
`
`(1-9)
`
`f-m
`
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`
`SUN - IPR2017-01929, Ex. 1034, p. 8 of 17
`
`

`

`Introduction to Pharmacokinetics
`
`5
`
`Z
`o
`H
`<
`cc
`H
`Z
`ui
`O
`Z
`O
`O
`(D
`D
`oc
`a
`
`c
`O
`c
`o
`o
`O)
`o
`
`time
`
`i
`6
`
`i
`8
`
`2
`
`4
`T I M E
`
`Fig. 1-4. Drug concentration in plasma during and after
`a 1-hr constant rate intravenous infusion. The inset shows
`the same data, plotted on semilogarithmic coordinates.
`
`or
`
`(1-10)
`C - k0[l - exp(-kt)]/kV
`According to Equation 1-10, drug concentration
`in plasma increases during infusion. When the en­
`tire dose has been infused at time T, drug concen­
`tration reaches a maximum given by
`(1-11)
`Cmax = k0[l - exp( —kT)]/kV
`and thereafter declines. The declining drug con­
`centration is described by
`C = Cmax exp(-kt')
`
`(1-12)
`
`or
`
`(1-13)
`
`log C = log Cmax - (kt72.303)
`where t' = t —T. Equations 1-12 and 1-13 apply
`when distribution equilibrium is essentially reached
`by the end of the infusion. A semilogarithmic plot
`of C (post-infusion drug concentration in plasma)
`versus t' yields a straight line, from which the half-
`life and elimination rate constant can be estimated.
`The entire drug concentration-time profile during
`and after a short-tenn infusion is shown in Figure
`1-4.
`Equation 1-11 may be arranged to calculate V,
`
`since all other terms are known. This estimate may
`be less than accurate but it is always better than
`that provided by Equation 1-6.
`The maximum or peak drug concentration in
`plasma is always lower after intravenous infusion
`than after bolus injection of the same dose. The
`more slowly a fixed dose of a drug is infused, the
`Consider a rapidly dis­
`lower the value of C
`tributed drug with a half-life of 3 hr. A given dose
`administered as an iv bolus results in an initial
`plasma level of 100 units. The same dose, infused
`over 3 hr (T = tw) gives a Cmax value of 50 units
`(Cmax/2); infused over 6 hr (T = 2tw), it gives a
`concentration of 25 units (Cmax/4). Also, since C
`is a linear function of k0, doubling the infusion rate
`and infusing over the same period of time (i.e.,
`doubling the dose) doubles the maximum concen­
`tration.
`
`max1
`
`max
`
`Extravascular Administration
`A more complex drug concentration-time profile
`is observed after oral, intramuscular, or other ex­
`travascular routes of administration because ab­
`sorption from these sites is not instantaneous, nor
`does it occur at a constant rate. As shown in Figure
`1-2, the rate of change of the amount of drug in
`the body (dA/dt) is a function of both the absorption
`rate (dAA/dt) and the elimination rate (dAE/dt); that
`is,
`
`dA
`dt
`
`dAA
`dt
`
`dAE
`dt
`
`(1-14)
`
`or
`
`(1-15)
`
`dAE
`dAA
`dC _
`dt
`dt
`dt _ V
`where V is the apparent volume of distribution.
`When the absorption rate is greater than the elim­
`ination rate (i.e., dAA/dt > dAF/dt), the amount of
`drug in the body and the drug concentration in the
`plasma increase with time. Conversely, when the
`amount of drug remaining at the absorption site is
`sufficiently small so that the elimination rate ex­
`ceeds the absorption rate (i.e., dAE/dt > dAA/dt),
`the amount of drug in the body and the drug con­
`centration in the plasma decrease with time. The
`maximum or peak concentration after drug admin­
`istration occurs at the moment the absorption rate
`equals the elimination rate (i.e., dAA/dt = dAE/dt).
`The faster a drug is absorbed, the higher is the
`maximum concentration in plasma after a given
`
`•
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`I
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`SUN - IPR2017-01929, Ex. 1034, p. 9 of 17
`
`

`

`i
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`11 [
`
`I
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`>r
`
`6
`
`Biopharmaceutics and Clinical Pharmacokinetics
`
`dose, and the shorter is the time after administration
`when the peak is observed.
`
`First Order In—First Order Out
`Many drugs appear to be absorbed in a first-
`order fashion and the following scheme often ap­
`plies;
`
`Drug at
`absorption site
`
`Drug in
`body
`
`^ ^ Eliminated
`drug
`
`Under these conditions
`
`(1-16)
`
`kaAA - kA
`dA/dt
`where ka is the apparent first-order absorption rate
`constant, k is the first-order elimination rate con­
`stant, A is the amount of drug in the body, and AA
`is the amount of drug at the absorption site. Inte­
`grating Equation 1-16 from t - 0 to t = t and
`converting amounts to concentrations results in the
`complicated equation shown below:
`C = kaFD[exp( - kt)
`
`(1-17)
`
`- exp( —kat)]/V(ka - k)
`where F is the fraction of the administered dose
`(D) that is absorbed and reaches the bloodstream,
`V is the apparent volume of distribution, and C is
`the drug concentration in plasma any time after
`administration. Equation 1-17 is often used to de­
`scribe drug concentrations in plasma after extra-
`vascular administration.
`The absorption rate constant of a drug is fre­
`quently larger than its elimination rate constant. In
`this case, at some time after administration, the
`absorption rate term in Equation 1-15 approaches
`zero, indicating that there is no more drug available
`for absorption, and Equation 1-17 simplifies to
`(1-18)
`C = kJFD[exp( — kt)]/V(ka - k)
`
`or
`
`and
`
`C = C0* exp(-kt)
`
`(1-19)
`
`log C = log C0* -
`
`kt
`2.303
`
`(1-20)
`
`Equation 1-18 assumes that distribution equilib­
`rium is essentially reached by the end of the ab­
`sorption phase.
`When absorption is complete, the rate of change
`of the amount of drug in the body equals the elim-
`
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`CJ> 50 -
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`ct
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`z
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`O
`o
`o
`ZD
`cc
`Q
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`1 0 -
`
`T
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`T
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`T
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`Start of po»t-
`abtorptive phase
`
`\
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`S l 0 P' "
`IS*/
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`k— 11 —>1
`'l
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`i
`4
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`i 1
`20
`16
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`12
`8
`TIME, hr
`
`Fig. 1-5. Typical semilogarithmic plot of drug concentra­
`tion in plasma following oral or intramuscular administra­
`tion of a slowly absorbed form of the drug.
`
`ination rate, and Equation 1-15 reduces to Equa­
`tion 1-4. The portion of a drug concentration in
`the plasma versus time curve, commencing at the
`time absorption has ceased, is called the postab-
`sorptive phase. During this phase, the decline in
`drug concentration with time follows first-order-
`kinetics. A semilogarithmic plot of drug concen­
`tration in the plasma versus time after oral or other
`extravascular routes of administration usually
`shows a linear portion that corresponds to the post-
`absorptive phase. A typical plot is shown in Figure
`1-5; the slope of the line is equal to -k/2.303.
`The intercept of the extrapolated line (C0*) is a
`complex function of absorption and elimination
`rate constants, as well as the dose or amount ab­
`sorbed and the apparent volume of distribution. It
`is incorrect to assume that the intercept approxi­
`mates the ratio of dose to volume of distribution
`unless the drug is very rapidly and completely ab­
`sorbed, and displays one-compartment character­
`istics (i.e., distributes immediately). This rarely
`occurs.
`Occasionally, the absorption of a drug is slower
`than its elimination, a situation that may be found
`with drugs that are rapidly metabolized or excreted
`and with drugs that are slowly absorbed because
`of poor solubility or administration in a slowly
`releasing dosage form. When this occurs, a semi­
`logarithmic plot of drug concentration versus time
`
`SUN - IPR2017-01929, Ex. 1034, p. 10 of 17
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`

`

`Introduction to Pharmacokinetics
`
`7
`
`(see Fig. 1-5) after oral administration cannot be
`used to estimate k or half-life because the slope is
`related to the absorption rate constant rather than
`the elimination rate constant. The drug must be
`administered in a more rapidly absorbed form or
`given intravenously.
`
`Patient-To-Patient Variability
`The time course of drug in the plasma after ad­
`ministration of a fixed dose may show considerable
`intersubject variability. The variability after intra­
`venous administration is due to differences between
`patients in distribution and elimination of the drug.
`These differences may be related to disease or con­
`comitant drug therapy or they may be genetic in
`origin. Variability is greater after intramuscular ad­
`ministration because, in addition to differences in
`distribution and elimination, absorption may be
`variable. Differences in absorption rate after intra­
`muscular injection have been related to the site of
`injection and the drug formulation. Still greater
`variability may be found after oral administration.
`The absorption rate of a drug from the gastroin­
`testinal tract varies with the rate of gastric emp­
`tying, the time of administration with respect to
`meals, the physical and chemical characteristics of
`the drug, and the dosage form, among other fac­
`tors. Similarly, the amount of an oral dose of a
`drug that is absorbed depends on biologic, drug,
`and dosage form considerations. Many commonly
`used drugs are less than completely available to
`the bloodstream after oral administration because
`of incomplete absorption @)presystemic metabo­
`lism.
`"""""
`""""
`"
`'
`
`Absorption Rate and Drug Effects
`The influence of absorption on the drug concen­
`tration-time profile is shown in Figure 1-6. Ad­
`ministration of an equal dose in three different dos-
`age forms results in different time courses of drug
`in the plasma. The faster the drug is absorbed, the
`greater is the peak concentration and the shorter is
`the time required after administration to achieve
`peak drug levels.
`Many drugs have no demonstrable pharmaco­
`logic effect or do not elicit a desired degree of
`pharmacologic response unless a minimum con­
`centration is reached at the site of action. Since a
`distribution equilibrium exists between blood and
`tissues, there must be a minimum therapeutic drug
`concentration in the plasma that corresponds to,
`though may not equal, the minimum effective con-
`
`A
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`c
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`B
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`MEC
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`c
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`J
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`L
`T i m e
`
`Fig. 1-6.
`The effects of absorption rate on drug concen-
`tration-time profile. The same amount of drug was given
`orally with each dosage form. The drug is absorbed most
`rapidly from dosage form A. Drug absorption after admin­
`istration of dosage form C is slow and possibly incomplete.
`The dotted line represents the minimum effective concen­
`tration (MEC) required to elicit a pharmacologic effect.
`
`centration (MEC) at the site of pharmacologic ef­
`fect. Thus, the absorption rate of a drug after a
`single dose may affect the clinical response. For
`example, it is evident from Figure 1-6 that the
`more rapid the absorption rate, the faster is the
`onset of response. The drug is absorbed so slowly
`from dosage form C that the minimum effective
`level is never attained. No effect is observed after
`a single dose, but effects may be seen after multiple
`doses.
`The intensity of many pharmacologic effects is
`a function of the drug concentration in the plasma.
`The data in Figure 1-6 suggest that administration
`of dosage form A may evoke a more intense phar­
`macologic response than that observed after ad-
`ministration of dosage form B since A produces a
`higher concentration of drug. When dosage form
`C is considered, it is clear that an active drug may
`be made to appear inactive by administering it in
`a form that results in slow or incomplete absorp­
`tion.
`
`BIOAVAILABILITY
`The bioavailability of a drug is defined as its rate
`and extent of absorption. Rapid and complete ab­
`sorption is usually desirable for drugs used on an
`acute or "as needed" basis for pain, allergic re-
`
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`SUN - IPR2017-01929, Ex. 1034, p. 11 of 17
`
`

`

`8
`
`Biopharmaceutics and Clinical Pharmacokinetics
`
`sponse, insomnia, or other conditions. As sug­
`gested in Figure 1-6, the more rapid the absorp­
`tion, the shorter is the onset and the greater is the
`intensity of pharmacologic response. The efficacy
`of a single dose of a drug is a function of both the
`rate and extent of absorption. In such cases, there
`is no assurance of the bioequivalence of two dosage
`forms of the same drug simply because the amount
`of drug absorbed from each is equivalent; the ab­
`sorption rate of drug from each drug product must
`also be comparable. Rapid absorption may also
`reduce the frequency and severity of gastrointes­
`tinal distress observed after oral administration of
`certain drugs, including aspirin and tetracycline,
`by reducing the contact time in the gastrointestinal
`tract.
`Usually, a useful estimate of the relative ab­
`sorption rate of a drug from different drug products
`or under different conditions (e.g., with food or
`without food) can be made by comparing the mag­
`nitude and time of occurrence of peak drug con­
`centrations in the plasma after a single dose.
`
`Estimating the Extent of Absorption
`The extent of absorption or relative extent of
`absorption of a drug from a product can be esti­
`mated by comparing the total area under the drug
`concentration in plasma versus time curve (AUG),
`or the total amount of unchanged drug excreted in
`the urine after administration of the product to that
`found after administration of a standard. The stand­
`ard may be an intravenous injection, an orally ad­
`ministered aqueous or water-miscible solution of
`the drug, or even another drug product accepted
`as a standard. When an iv dose is used as the
`standard and the test product is given orally (or via
`some other extravascular route), we determine ab­
`solute bioavailability. If, following equal doses of
`the test product and the iv standard, the AUG values
`are the same, we conclude that the drug in the test
`product is completely absorbed and not subject to
`presystemic metabolism.
`Frequently, however, the standard is an oral so­
`lution or an established product. If, following equal
`doses of the test product and standard, the AUG
`values are the same, we conclude that the test prod­
`uct is 100% bioavailable, relative to the standard;
`we need use the word relative because we do not
`know a priori that the standard is completely ab­
`sorbed or completely available. When two products
`produce the same peak concentration of drug in
`
`T
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`T
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`T
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`Area = I
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`^.g-hr
`ml
`
`W- 1 hr-H
`
`ct t* -
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`1
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`CT 4 -
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`Z
`O
`1— 3 -
`<
`cr
`h-
`LU 2 -
`O
`Z o
`0 I -
`(S)
`a:
`Q
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`I
`
`2
`3
`TIME, hr
`
`4
`
`Typical rectilinear plot of drug concentration in
`Fig. 1-7.
`the plasma following an oral dose. The area under the con­
`centration-time plot from t = 0 to t - 4 hrs is denoted by
`shading.
`
`plasma and the same AUG, the p