`
`
`
`Concepts. and Applications
`
`
`
`Clinical Pharmacokinetics:
`
`
`
`
`
`
`
`
`
`Malcolm Rowland, PhD.
`
`Department of Pharmacy
`University of Manchester
`Manchester, England
`
`Thomas N. Tozer, PhD.
`
`School of Pharmacy
`University of California
`San Francisco, California
`
`
`
`Second Edition
`
`
`
`fi’
`
`Lea Es? Febiger
`
`Philadelphia - London - 1989
`
`SHIRE EX. 2030
`KVK V. SHIRE
`
`p. 1 IPR2018—00290
`
`
`
`p. 1
`
`SHIRE EX. 2030
`KVK v. SHIRE
`IPR2018-00290
`
`

`

`
`
`
`
`Lea 8c Febiger
`600 Washington Square
`Philadelphia, PA 19106—4138
`USA.
`
`(215) 922-1330
`
`
`
`
`
`
`
`
`
`First Edition, I 980
`Reprinted, 1982, 1983, 1984, 1986
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`Library of Congress Cataloging-in—Publieation Data
`
`Rowland, Malcolm.
`Clinical pharmacokin‘etics.
`
`Bibliography: p.
`Includes index.
`
`I. Tozer,
`1. Pharmacokinetics. 2. Chemotherapy.
`Thomas N.
`11. Title.
`[DNLM: 1. Drug Therapy.
`2. Pharmacokinetics. QV 38 R883c]
`RM301.5.R68
`1988
`615.5'8
`ISBN 0-8121-1160-5
`
`38-8993
`
`
`
`
`
`
`
`
`
`Copyright © 1989 by Lea 8c Febiger. Copyright under the International Copy-
`right 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 Numberfi 4 3
`
`2
`
`l
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`
`
`
`
`p. 2
`
`

`

`
`
`Objectives
`
`The reader will be able to:
`
`1. Describe the characteristics of, and the differences between, tirst-order
`and zero-order absorption processes.
`
`2. Determine whether absorption or disposition rate limits drug efimination,
`given plasma drug concentration-time data fotlowing different dosage
`forms or routes of administration.
`
`3. Anticipate the effect of altering rate of absorption, extent of absorption,
`clearance, or volume of distribution on the plasma concentration and
`amount of drug in the body following extravascular administration.
`
`4. Estimate the availability of a drug, given either plasma concentration or
`urinary excretion data following both extravascuiar and intravascular ad-
`ministration.
`
`5. Estimate the relative availability of a drug, given either plasma concen-
`tration or urinary excretion data foliowing different dosage forms or routes
`of administration.
`
`6. Estimate the renal clearance of a drug from plasma concentration and
`urinary excretion data following extravascular administration.
`
`7. Knowing the availability, estimate clearance, volume of distribution, and
`elimination half-life from plasma concentration data following extravas—
`cutar administration.
`M
`
` Extravascular Dose
`
`For systemicaliy acting drugs, absorption is a prerequisite for therapeutic
`activity when they are administered extravascularly. The factors that influence
`drug absorption are considered in Chapter 9. In this chapter the following aspects
`are examined: the impact of rate and extent of absorption on both plasma con—
`centration and amount of drug in the body; the effect of alterations in absorption
`and disposition on body level-time relationships; and the methods used to assess
`pharmacokinetic parameters from plasma and urinary data following extravas—
`cular administration.
`Throughout this book, the term availability is used to express the completeness
`of absorption. Thus, availability is defined as the fraction, or percent, of the
`administered dose of drug that is absorbed intact.
`
`33
`
`p.3
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`
`p. 3
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`

`

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`34
`
`ABSORPTION AND DISPOSITION KINETICS
`
`KINETICS 0F ABSORPTION'
`
`The oral absorption of drugs in man often approximates first-order kinetics.
`- The same holds true f0r the absorption of drugs from many other extrayascular
`sites including subcutaneous tissue and muscle. As with other first—order proc—
`esses, absorption is characterized by an absorption rate constant, Ru, and a
`corresponding half-life. The half—lives for the absorption of drugs administered
`to man usually range from 15 minutes to 1 hour. Occasionally they are longer.
`Sometimes, most of a drug is absorbed at essentially a constant (zero—order)
`rate. The absorption kinetics are then called zero order, because the rate of ab-
`sorption is proportional to the amount remaining to be absorbed raised to the
`power of zero. Differences between zero-order and first-order kinetics are illus—
`trated in Figure Iii—#1. Zero-order absorption, characterized by a constant rate of
`absorption, is essentially independent of. the amount absorbed. A plot of the
`amount remaining to be absorbed against time on regular graph paper yields a
`straight line whose slope is the rate of absorption (Fig. 4—1A). Recall from
`Chapter 3 that the fractional rate of decline is constant for a first-order process;
`the amount declines linearly with time when plotted on semjlogarithmic paper.
`In contrast, for a zero-order absorption process, the fractional rate of absorption
`increases with time, because the rate is constant but the amount remaining
`decreases. This is reflected in an ever~increasing gradient with time in a semi-
`logarithmic plot of the amount remaining to be absorbed (Fig. 4—1B). A method
`of determining the kinetics of absorption following extravascular administration
`is given in Appendix C.
`For the remainder of this chapter, and for much of the book, absorption is
`assumed to be first order. If absorption is zero order, then the equations de—
`veloped in Chapter 6 (Constant—rate Regimens) apply.
`
`
`
`:3;
`
`E
`
`A. Regular Plot
`
`3. Semllogarlthmlc Plot
`
`
`
`
`
`PercentRemainingtoBeAbsorbed
`
`Zero Order
`
`a:O
`
`3:-D
`
`N0
`
`0
`
`60
`
`Zero Order
`
`1 o
`
`First Order
`
`
`
`
`
`
`Time
`
`Time
`
`B, semilogarithmic plots of the percent remaining to be absorbed against time.
`
`l ll
`
`
`
`
`
`
`
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`
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`
`
`a:C3
`
`
`
`l
`Fig.4-H1. Acomparisonofzero-orderandfirstuorderabsorptionprocesses.Depictedare:A,cartesian,and
`
`
`
`
`
`
`
`
`PercentRemainlngtoBeAbsorbed
`
`p. 4
`
`

`

`" EXTHAVASCULAR DOSE
`
`35
`
`BODY LEVEL-TIME RELATIONSHIPS
`
`k A
`Rate of
`elimination
`
`1
`
`
`
`maewmmr
`
`Comparison with an Intravenous Dose
`Absorption delays and reduces the magnitude of the peak compared to that seen
`following an equal intravenous bolus dose. These effects are portrayed for aspirin
`in Figure 4—2. The rise and fall of the drug concentration in plasma are best
`understood by remembering that at any time
`dA
`dAa
`dt
`dt
`Rate of
`Rate of
`change of
`absorption
`drug in
`body
`where Au is the amount of drug at the absorption site remaining to be absorbed.
`When absorption occurs by a first-order process, the rate of absorption is given
`by kn . Aa.
`Initially, with all drug at the absorption site and none in the body, the rate
`of absorption is maximal and the rate of elimination is zero. Thereafter, as drug
`is absorbed, its rate of absorption decreases, whereas its rate of elimination
`increases. Consequently, the difference between the two rates diminishes. How~
`ever, as long as the rate of absorption exceeds the rate of elimination the plasma
`concentration continues to rise. Eventually, a time is reached when the rate of
`elimination matches the rate of absorption; the concentration is then at a max-
`imum. Subsequently, the rate of elimination exceeds the rate of absorption and
`the plasma concentration declines.
`The peak plasma concentration is always lower following extravascular ad-
`.ministration than the initial value following an equal intravenous bolus dose.
`In the former case, at the peak time some drug remains at the absorption site
`and some has been eliminated, while the entire dose is in the body immediately
`
`p.5
`
`10
`
` Plasma
`
`AspirinConcentration
`
`
`
`(mg!liter)
`
`0
`
`20
`
`40
`
`60
`Minutes
`
`80
`
`100
`
`120
`
`Fig. 4—2. Aspirin (650 mg) was administered as an intravenous bolus (I) and as an oral solution (0) on
`separate occasions to the same individual. Absorption causes a delay and a lowering of the peak concentration.
`(One rag/liter e 5.5 micromoiar.) (Modified from the data of Rowland, M., Riegelman, 5., Harris, P.A., and
`Sholkoff, S.D.: Absorption kinetics of aspirin in man following oral administration of an aqueous solution. I.
`Pharm. Sci., 61:379-385, 1972. Adapted with permission of the copyright owner.)
`
`p. 5
`
`

`

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`
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`
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`
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`
`
`
`
`Thus, knowing dose, clearance, and area, availability may be determined.
`
`
`
`
`Increasing the dose, unless this alters the absorption half—life or the availability,
`produces a proportional increase in the plasma concentration at all times. Hence,
`
`
`the time for the peak remains unchanged, but its magnitude increases propor—
`
`
`tionally with the dose. The explanation is readily apparent. Suppose, for ex-
`
`
`ample, that the dose is doubled. Then, at any given time, the amount absorbed
`
`
`is doubled and, with twice as much entering the body, twice as much is elim-
`
`
`inated. Being the difference between the amounts absorbed and eliminated, the
`
`
`amount of drug in the body at any time is, therefore, also doubled. And so too
`
`
`is the total area under the curve. One arrives at the same conclusion by examining
`
`
`Equation 3.
`
`
`
`Changing Absorption Kinetics
`
`
`
`36
`
`ABSORPTION AND DISPOSITION KINETICS
`
`following the intravenous dose. Beyond the peak time, the plasma concentration
`on extravascular administration exceeds that following the intravenous dose
`because of the continual entry of drug into the body.
`Frequently, the rising portion of the plasma concentration—time curve is called
`the absorption phase and the declining portion the elimination phase. As will
`be seen, this description may be misleading. Also, if drug is not fully available
`its concentration may remain lower at all times than that observed after intra-
`venous administration.
`
`Lag time is the deiay between drug administration and the beginning of ab-
`sorption. The lag time can be anywhere from a few minutes to many hours.
`Long lag times have been observed following ingestion of enteric—coated tablets.
`The coating is resistant to the gastric environment to protect an acid~labiie drug
`or to prevent one that produces gastric irritation from doing so. Contributing
`factors are the delay in gastric emptying and the time taken for the protective
`coating to dissolve or to swell and release the inner contents into the intestinal
`fluids. Once absorption begins, however, it may be as rapid as from uncoated
`tablets. Clearly, enteric—coated products should not be used when a prompt and
`predictble response is desired. A method for estimating the lag time is discussed
`in Appendix C.
`Availability and area are also important factors. As discussed more fully in
`Chapters 7 and 9, the completeness of absorption is of primary importance in
`therapeutic situations. The availability, F, is proportional to the total area under
`the plasma concentration-time curve, irrespective of its shape. This must be so.
`Recall from Chapter 3 that:
`
`Total amount eliminated = Clearance - AUC
`
`but the total amount eliminated is the amount absorbed, P - Dose, therefore:
`
`F - Dose : Clearance - ALIC
`Amount
`Total amount
`absorbed
`eliminated
`
`Changing Dose
`
`2.
`
`3
`
`
`
`
`
`
`
`
`
`
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`
`
`
`
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`
`
`
`
`
`Alterations in either absorption or disposition produce changes in the time
`profiles of the amount of drug in the body and the plasma drug concentration.
`
`
`
`p.6
`
`p. 6
`
`

`

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`
`EXTRAVASCULAF! DOSE
`
`37
`
`This point can be illustrated if one considers the three situations depicted in
`semilogarithmic plots in Figure 4w3, involving changes only in the absorption
`half—life. All other factors (availability, clearance, and volume of distribution,
`and hence elimination half—life) remain constant.
`In case A, the absorption half-life is much shorter than the elimination half—
`life. In this case, by the time the peak is reached, most of the drug has been
`absorbed and little has been eliminated. Thereafter, decline of drug from the
`body is determined primarily by the diSposition of the drug, that is, disposition
`is the rate-limiting step. The half—life estimated from the decline phase is, therefore,
`the elimination half—life.
`
`In case B, the absorption half-life is longer than in case A but still shorter than
`the elimination half-life. The peak occurs later because it takes longer for the
`amount in the body to reach the value at which the rate of elimination matches
`the rate of absorption; the peak amount is lower because less drug has been
`absorbed by that time. Even so, absorption is still essentially complete before
`the majority of the drug has been eliminated. Consequently, disposition remains
`the rate‘limiting step.
`
`Absorption Rate-limited Elimination
`
`Occasionally, the absorption half—life is much longer than the elimination half-
`life and case C prevails (Fig. 445). The peak occurs later and is lower than in
`
`Case A
`
`Case 8
`
`Case C
`
`
`
` i p
`
`..---.....
`
`
`resentswane-w:
`
`
`
`
`Flate(mg/hour)
`
`
`
`PlasmaDrugConcentration
`
`_; OD
`
`2'5
`
`“H““Absorption
`5‘
`;_I
`\
`l
`
`\\
`
`\\\/Eliminaiion
`
`(mg/liter)
`
`
`
`
`
`
`
`
`
`
`
`
`
`Fig. 4—3. A slowing (from ieft to right) of drug loss from the absorption site (lower graphs) delays the
`attainment and decreases the magnitude of the peak plasma drug concentration (top graphs). In Cases A and
`B (bottom two graphs), absorption (llilllll) is a faster process than elimination (-—---). In Case C (third graph on
`bottom), absorption (“Elli”) rate limits elimination so that decline of drug in plasma reflects absorption rather
`than elimination; because there is a net elimination of drug during the decline phase, the rate of elimination
`is slightly greater than the rate of absorption. In all three cases, availability is 1.0 and clearance is unchanged.
`Consequently,
`the areas under the plasma concentration-time curves (top three graphs) are identicai. The
`areas under the curves in the bottom graphs are also equal because the integral of the rate of absorption,
`amount absorbed, equals the integral of the rate of elimination, amount eliminated.
`
`p. 7
`
`

`

`
`
`
`
`
`
`3B
`
`ABSORPTION AND flISPOSiTION KINETICS
`
`the two previous cases. The half—life of the decline of drug in the body now
`corresponds to the absorption half—life for the following reason. During the rise
`to the peak, the rate of elimination increases and eventually, at the peak, equals
`the rate of absorption. However, in contrast to the previous situations, absorp-
`tion is so slow that much of the drug remains to be absorbed well beyond the
`peak time. The drug is either at the absorption site or has been eliminated; little
`is in the body. In fact, during the decline phase, the drug is eliminated as fast
`as it is absorbed. Absorption is now the rate-limiting step. Under these circum-
`stances, since the rate of elimination essentially matches the rate of absorption,
`the following approximation (-3) can be written
`
`that is,
`
`k - A
`
`2 ka - Au
`
`Rate of
`elimination
`
`Rate of
`absorption
`
`Amount ~ kfl
`in body ~ —k-
`
`Amount at
`- absorption
`site
`
`4
`
`5
`
`Accordingly, the amount in the body (and the plasma concentration) during
`the decline phase is directly proportional'to the amount of drug at the absorption
`site. For example, when the amount at the absorption site falls by one—half, so
`does the amount in the body. However, the time for this to occur is the absorption
`half-life.
`
`Absorption influences the kinetics of drug in the body; but what of the area
`under the plasma concentration-time curve? Because availability and clearance
`were held constant, it follows from Equation 3 that the area must be the same
`for cases A, B, and C.
`
`Distinguishing Absorption from Disposition Rate-limited Elimination
`
`Although disposition generally is ratewlirniting, the preceding discussion sug—
`gests that caution may need to be exercised in interpreting the meaning of the
`half-life determined from the decline phase following extravascular administra-
`tion. Confusion is avoided if the drug is given intravenously. In practice, how—
`ever, intravenous dosage forms of many drugs do not exist for clinical use. An
`alternative solution to the problem of distinguishing betWeen absorption and
`disposition rate-limitations is to alter the absorption kinetics of the drug. This
`is most readily accomplished by giving the drug either in different dosage forms
`or by different routes. To illustrate this point, two drugs are considered, the—
`ophylline and penicillin G.
`Food and water influence the oral absorption kinetics of theophylline but not
`the half—life of the decline phase (Fig. 4—4). Here then, disposition rate—limits
`theophylline elimination. In contrast, for penicillin, with a very short elimination
`half—life, intramuscular absorption can become rate-limiting by formulation of a
`sparingly soluble salt (Fig. 4—5).
`
`
`
`
`
`p. 8
`
`

`

`
`
`EXTRAVASCULAFI DOSE
`
`39
`
` Plasma
`
`
`
`TheophyilineConcentration(mglliter)
`
`Fig. 4—4. Two tablets, each containing 130 milli-
`grams theophylline, were taken by 6 healthy volun-
`teers under various conditions, Absorption of the the-
`ophylline was most rapid when the tablets were
`dissolved in 500 milliliters water and taken on an
`empty stomach (D). Taking the tablets with 20 milli-
`liters of water on an empty stomach (0) resulted in
`slower absorption than taking them with the same
`volume of water immediately following a standard—
`ized high carbohydrate meal (0). Despite differences
`in rates of absorption, however, the terminal half-life
`(6.3 hours) was the same and, therefore, it is the elim-
`ination half-life of theophylline. (One mgfliter = 5.5
`micromolar.) (Modified from Welling, P.G., Lyons,
`L.L., Craig, W.A., and Trochta, G.A.: Influence of
`diet and fluid on bioavailability of theophylline. Clin.
`Pharmacol. Ther., 7:475—480, 1975.)
`
`
`Hours
`
`
`
`Changing Disposition Kinetics
`What happens to the plasma concentration-time profile of a drug when the
`
`absorption kinetics remain constant, but modifications in disposition occur?
`
`When clearance is reduced, but availability remains constant, the area under
`
`the plasma concentration—time curve must increase; so must both the time and
`
`magnitude of the peak concentration. These events are depicted in Figure 4—6.
`
`With a reduction in clearance and, hence, elimination rate constant, a greater
`
`amount of drug must be absorbed, and the plasma concentration must be greater
`
`prior to the time when the rate of elimination equals the rate of absorption.
`
`As shown in Figure 4—7, the events are different when an increased volume
`
`of distribution is responsible for a longer elimination half-life. Under these cir—
`
`cumstances, if availability and clearance remain unchanged, so does the area
`
`under the curve. The peak occurs later and is lower, however. With a larger
`
`volume of distribution, more drug must be absorbed before the plasma concen—
`
`tration reaches a value at which the rate of elimination (CL - C) equals the rate
`
`
`
`
`Fig. 4u5. Penicillin G (3 mglkg) was administered to
`the same individual on different occasions. An aque-
`ous solution was given intramuscularly (I.M,) and
`orally (P.O.); procaine penicillin was injected intra-
`muscularly in oil (P-l.M.) and in oil with aluminum
`monostearate (AP-1.M.). The differing rates of decline
`of the plasma concentration of penicillin G point to
`an absorption rate-limitation when this antibiotic is
`given orally in aqueous solution and intramuscularly
`as with the procaine salt in oil. Distinction between
`rate-limited absorption and rate-limited disposition
`following intramuscular administration of the aque-
`ous solution can only be made by giving penicillin G
`intravenously. (One rag/liter : 3.0 micromelar.)
`(Modified from Marsh, D.F.: Outline of Fundamental
`Pharmacology. Charles C Thomas, Springfield, IL,
`1951.)
`
`(mg!
`
`
`
`
`liter)
` SerumPenicillinConcentration
`
`
`
`
`p. 9
`
`

`

`tt
`t.t
`
`3
`
`ABSORPTJON AND DISPOSITION KINETICS
`
`40
`
`
`
`PlasmaDrugConcentration
`
`(mg/liter)
`
`1 000
`
`500
`
`Fig. 4—6. A twofold reduction in clearance increases
`the area under the plasma concentration—time (stip-
`pied line, top graph) twofold compared to that of the
`centre! (solid line) after a single extravascular dose.
`With no change in absorption kinetics (and hence
`absorption rate profile) (-—--, bottom graph), the rate
`of elimination is observed to be lower at first but to
`increase to a value greater than that of the control
`(solid line, bottom graph), as the area under these
`rate curves must be equal to the dose (see Fig. 4—3).
`The decrease in clearance causes the peak concentra—
`tion to be greater and to occur at a later time (only
`slightly different here). The peak time occurs when
`the rate of elimination equals the rate of absorption
`(bottom graph). The terminal slope reflects the in—
`
`
`
`
`
`
`
`
`
`
`
`
`
`
`
`
`
`
`
`
`Hours
`
`of absorption,- the absorption rate is lower then and so is the plasma concen-
`tration.
`
`Predicting Changes in Peak
`
`Qualitative changes in peak concentration and the time of its occurrence, when
`absorption or disposition is altered, are difficult to predict. To facilitate this
`prediction, a memory aid has been found to be useful. The basic principle of
`the method (Fig. 4—8) is simple; absorption increases and elimination decreases
`the amount of drug in the body. The faster the absorption process (measured
`by absorption rate constant) the greater is the slope of the absorption line, and
`the converse. The faster the elimination process (elimination rate constant) the
`steeper is the decline of the elimination iine.
`the new point of intersection
`If the absorption rate constant is increased,
`indicates that the peak amount is increased and that it occurs at an earlier time.
`If the etimination rate constant is increased, the new point of intersection occurs
`at an earlier time, but at a lower amount.
`The graph is designed for predicting changes in peak time and specifically in
`peak amount in the body. It applies as well to peak plasma concentration with
`the exception of when the volume of distribution is altered. An increase in the
`volume of distribution causes a decrease in the peak concentration, and the
`converse, as explained under Changing Disposition Kinetics.
`
`
`creased elimination half—life.
`
`
`200
`
`100
`
`50
`
`
`
`Rate(mg/hour)
`
`Elimination
`
`
`
`
`
`
`
`
`
`p. 10
`
`

`

`.4 I3
`
`(J1
`
`
`
`PlasmaDrugConcentration Ungfifien
`
`
`
`Rate{mgihoun
`
`EXTRAVASCULAR DOSE
`
`Fig. 4—7. A twofold increase in the volume of dis-
`tribution causes an increase in the elimination half—
`life and delays the time at which the peak plasma
`concentration occurs (stippled line, top graph) com»
`pared to the control observation (solid line) after a
`single extravascular dose. With no change in clear
`ance, the area is unchanged and the peak concentra—
`tion is thereby reduced. Because of a lower concen—
`tration,
`the rate of elimination is initially slowed
`(stippled line, bottom graph), but since the amount
`eliminated is the same (the dose), the rate of elimi—
`nation eventually is greater than that of the control
`(solid line, bottom graph).
`
`limiaaiion
`
`p.11
`
`Fig. 4—8. Memory aid to assess changes in peak time
`and peak amount in the body after extravascular ad-
`ministration of a single dose when absorption or dis—
`position is altered. The relative peak time and the
`relative peak amount are indicated by the intersection
`of the absorption and elimination lines (A) with slopes
`representing the absorption and elimination rate con-
`stants, respectively. The predictions for an increased
`absorption rate constant (dashed line, B) and an in-
`creased elimination rate constant (dotted line, C} are
`shown. (Modified from Qie, S. and Tozer, T.N.: A
`memory aid to assess changes in peak time and peak
`concentration with alteration in drug absorption or
`disposition. Am. I. Pharm. Ed, 46:154—155, 1982).
`
`ASSESSMENT OF PHARMACOKINETIC PARAMETERS
`
`How some parameter values are estimated following extravascular adminis-
`tration can be appreciated by considering both the plasma concentration-time
`curves in Figure 4—9, obtained following intramuscular and oral administrations
`of 500 milligrams of a drug, and the additional information in Table 4—1.
`
`
`
`
`
`{AmountinBody}/(AbsorbedDose)
`
`p. 11
`
`

`

`hN
`
`ABSORPTION AND DISPOSITION KINETICS
`,.
`
`(mglllter)
`BloodDrugConcentration
`
`
`Hours
`
`Fig. 4J9. A SUD—milligram dose was given intramus-
`cularly (H) and orally (0- - -0) to the same subject
`on separate occasions. The drug is less available and
`is absorbed more slowiy from the gastrointestinal
`tract. A parallel decline, however, implies that in both
`instances disposition is rate-limiting.
`
`Table 4—1. Data Obtained Following Administration oi 500 milligrams of a Drug In Solution
`by Different Routes
`
`
`
` Plasma Data Urine Data
`
`Cumulative Amount
`Hall-life;
`Area
`Excreted Unchanged
`Decay Phase
`(mg—hour!
`(mg)
`(minutes)
`liter)
`Route
`i 52
`1 90
`7.6
`intravenous
`147
`185
`7.4
`Inlramuscular
`70
`193
`3.5
`Oral
`MW..—
`
`Plasma Data Alone
`Availability. Supplemental data from intravenous administration allow cal—
`culation of the availability, F. The, total area under the concentration—time curve
`following extravascular administration is divided by the area following an in—
`travenous bolus, appropriately correcting for dose. The basis for this calculation,
`which assumes that clearance remains constant, is as follows:
`
`Intravenous (i.v.) dose
`
`Dose”, = Clearance - ALICE”,
`
`Extravascular (e.v.) dose
`PM,
`
`- Doseem = Clearance - ALICM.
`
`which upon division yields
`
`F
`
`H ALICE,“
`e.v. _
`ALICLV.
`
`Dose”,
`Dose”,
`
`6
`
`7
`
`*
`
`8
`
`For example, appropriately substituting the area measurements in Table 4.4 into
`Equation 8 indicates that the intramuscular availability of the drug is 97 percent.
`This value is sufficiently close to 100 percent to conclude that all drug injected
`into muscle is absorbed. In contrast, only 46 percent is absorbed when it is given
`orally in solution.
`An alternative method of estimating the availability, which gives the same
`answer, is to substitute the value for clearance directly into Equation 7. Clearance
`
`p. 12
`
`
`
`.~\".‘:t*i:<e:eez:we
`
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`
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`
`p. 12
`
`

`

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`EXTHAVASCULAH DOSE
`
`43
`
`can be estimated from blood (or plasma) data following either an intravenous
`bolus dose or a constant—rate intravenous infusion (Chap. 6).
`Relative availability is determined when there are no intravenous data. Cost,
`stability, solubility limitations, and potential hazards are major reasons for the
`lack of an intravenous preparation. Relative availability is determined by com—
`paring different dosage forms, different routes of administration, or different
`conditions (e.g., diet, disease state). As with the calculation of availability, clear-
`ance is assumed to be constant.
`Thus, taking the general case:
`
`Dosage form A
`
`Dosage form B
`
`So that,
`
`PA - DoseA = Clearance - ALICA
`Amount
`Total amount
`absorbed
`eliminated
`
`PH ~ Doseg = Clearance - ALICE
`
`Relative
`availability
`
`
`= E : AUCA
`Doses
`F3
`ALICB
`DoseA
`
`9
`
`10
`
`*
`
`11
`
`The reference dosage form chosen is usually the one that is most available, that
`is, the one havingthe highest area-to~dose ratio. In the example considered,
`this would be the intramuscular dose; the relative availability of the oral dose
`would be 46 percent. If only two oral doses had been compared, they may have
`been equally, albeit poorly, available. it should be noted that all the preceding
`relationships hold, irrespective of route of administration, rate of absorption, or
`shape of the curve. Constancy of clearance is the only requirement.
`Other Pharmacokinetic Parameters. Given only extravascular data, it is some—
`times difficult to estimate pharmacokinetic parameters. Indeed, no pharmaco—
`kinetic parameter can be determined confidently from observations following
`only a single oral dose. Consider: Area can be calculated without knowing
`availability, but clearance cannot. Similarly, although a half-life can be ascribed
`to the decay phase, without knowing whether absorption or disposition is rate-
`1imiting, the value cannot be assigned as the absorption or the elimination half«
`life. Without knowing any of the foregoing parameters, the volume of distri—
`bution clearly cannot be calculated.
`Fortunately, there is a sufficient body of data to determine at least the elim—
`irration half«life of most drugs. Failure of food, dosage form, and, in the example
`in Figure 4M7, route of administration to affect the terminal half-life indicates
`that this must be the elimination half-life of the drug. Also, a drug is nearly
`always fully available (P = 1) from the intramuscular or the subcutaneous site.
`Hence, clearance can be calculated knowing area (Eq. 3), and the volume of
`distribution can be estimated once the elimination half~life is known. Consider,
`for example, just the intramuscular data in Table 4...1_ Clearance, obtained by
`dividing dose (500 mg) by area (7.4 mgwhour/liter), is 1.1 liters/minute. Dividing
`clearance by the elimination rate constant (0.693/185 minutes) gives the volume
`of distribution, in this case 300 liters.
`
`Ei
`gr;l
`
`
`
`
`
`p. 13
`
`

`

`
`
`44
`
`ABSORPTiON AND DISPOSITION KINETICS
`
`Previously, a range of likely absorption half-lives was quoted. The values were
`estimated indirectly from plasma concentration—time data. Direct measurements
`of absorption kinetics are impossible because plasma is the site of measurement
`for both absorption and disposition. To calculate the kinetics of absorption, a
`method must therefore be devised to separate these two processes. One simple,
`graphic method for achieving this separation is discussed in Appendix C.
`
`Urine Data Alone
`
`Given only urine data, neither clearance nor volume of distribution can be
`calculated. if the renal clearance of drug is constant, the rate of drug excretion
`is proportional to its plasma concentration, and under these circumstances,
`theoretically, excretion rate data can be treated in a similar manner to the plasma
`data. In practice, during the first collection of urine, usually 1 or 2 hours after
`drug administration, absorption of many well—absorbed drugs is complete. Uri-
`nary excretion rate data are then of little use in estimating the absorption kinetics
`of the drug.
`Cumulative urine data can be used to estimate availability. The method as—
`sumes that the value of fe remains constant. Recall from Chapter 3 that fe is the
`ratio of the total amount excreted unchanged (Aew) to the total amount absorbed.
`*1:
`
`Ag”
`f8 3 F-Dose
`
`12
`
`Then, using the subscripts A and B to denote two treatments, it follows that
`
`FA ' DOSeA : Aem‘AffE
`
`PB - DoseB = Aem,B/fe
`Amount.
`Total amount
`absorbed
`eliminated
`
`which upon division gives:
`
`
`
`g _ (AemlA) ' (DoseB)
`
`PB
`
`Aem‘B
`
`DoseA
`
`13
`
`14
`
`i“
`
`15
`
`The ratio of the cumulative amount excreted unchanged is therefore the ratio
`of the availabilities. When dose B is given intravenously, the ratio is the avail-
`ability of the drug. Otherwise the ratio gives the relative availability. For example,
`from the cumulative urinary excretion data in Table 4—1, it is apparent that the
`intramuscular dose is almost completely available; the corresponding value for
`the oral dose is only 46 percent [(70 mg/152 mg) X 100]. Notice that this value
`is the same as that estimated from plasma data.
`Urine data alone can be particularly useful for estimation of availability when
`the fraction excreted unchanged approaches 1. Under this condition, changes
`in renal clearance (and hence total clearance) affect the AUC, but not the amount
`excreted, which is a direct measure of the amount absorbed. The major problem
`here is in ensuring complete urine collection for a sufficiently long period of
`time.
`
`
`
`p. 14
`
`

`

`ita
`is
`ia
`
`iisa
`
`:
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`
`
`EXTRAVASCULAR DOSE
`
`45
`
`Plasma and Urine Data
`
`.~,
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`
`
`wammwmwWm:
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`When both plasma and urine data are available, in addition to the other
`pharmacokinetic parameters, the renal clearance of a drug can be estimated. The
`approach is identical to that taken for an intravenous dose (Chap. 3). Since no
`knowledge of availability is required, the estimate of renal clearance from com—
`bined plasma and urine data following extravascular administration is as accurate
`as that obtained following intravenous drug administration.
`
`
`Study Problems
`
`(Answers to Study Problems are in Appendix G.)
`
`1. Depicted in Figure 4—10 are curves of the plasma concentration and of the amount
`in the body with time following the oral ingestion of a single dose of drug. Draw
`five pairs of curves identical to those in Figure 440. Draw another curve on each
`pair of these curves that shows the effect of each of the following alterations in
`pharmacokinetic parameters.
`
`
`
`PlasmaDrugConcentration
`AmountofDrugInBody
`
`
`Fig. 4—10.
`
`(a) V increased, it decreased
`
`(b) Jul increased
`
`(c) CL increased, it increased
`
`(d) CL decreased, k decreased
`
`(e) F decreased
`
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`