`

`E\·ec11tive Editor.- Do111,a Balado
`Develop111eutal Editors.- Frances Klass, Lisa Stead
`Prod11ctiou Mauage,:· La11rie Forsytb
`Proj ect Edilo1c Robert D. Magee
`
`Cop yright © 1995
`\'(!iJliams & Wilkins
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`of the medicatio ns mentio ned.
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`Printed in the U nited States of America
`
`First Editio n 1980
`
`Library of Congress Cataloging-in-Publication Data
`
`2. Chemothera py.
`
`I. Tozer, Thomas N.
`
`Ro wland, l'vlalcolm.
`Clinical Phannacok inetics : concepts and applicatio ns / iV!alco lm
`Rmvland, Thomas N. Tozer. -
`3rd eel.
`p.
`cm.
`"A Lea & Febiger Book. "
`lnclucles bibliographical references and index.
`ISBN 0-683-07404-0
`1. Pharmacokinetics.
`II. Title.
`[DNLM: 1. Pharmacokinetics.
`RM 301.5.R68
`1994
`615.7-clc20
`DNLM/ DLC
`for Library of Congress
`
`2. Drug Therapy.
`
`QV 38 R883c 1994]
`
`94-26305
`CIP
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`adverte11/~)' overlooked auy, Ibey will be pleased to 111ake tbe necessa,y arra11ge111euts at tbe first opport1111ity.
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`

`

`_ ... ::!..
`
`.
`
`CONTENTS
`
`. . . . . . . . . . .. . . . . . . . . ... . . .. . . .. . .. .
`Definitions of Symbols
`1 . Why C linical Pharmacokinetics?
`. .. . . . .. . . . .. . . . . . . . .. . . . . . . . .. . . . .. . . .. . . . .. .
`
`. . xi
`. 1
`
`SECTION I. ABSORPTION AND DISPOSITION KINETICS
`2. Basic Considerati ons
`................... ... ..... .. .. ........... .. ....... 1 1
`3. Intravenous Dose .. . . . . . . .. . .. . .. . .. . .. . . . . .. . .. . .. .. . . .. . ..
`.. 1 8
`4 . Extravascu lar Dose
`. .. .. . .. . .. . . .. .. . .. . . . . .. . .. . .. . . . . .. . .. . . . . .. . .. . ..
`. ... 34
`
`SECTION II. THERAPEUTIC REGIMENS
`5 . Therapeutic Response and Toxicity
`6. Consta nt-Rate Reg imens .... .. ..... ........ ..
`7. Multiple-Dose Reg imens .......... .. . .
`
`.................................. ..... .. ..... 53
`... ... .... ... ................. .. 66
`.. ... ................. ...... ..... 83
`
`SECTION Ill. PHYSIOLOGIC CONCEPTS AND KINETICS
`8. Movement Throug h Membranes
`. . . . . . . . . . . . . . . . . .. . .. .................... ........ 1 09
`9. Absorption ..... .... . ...................... .... .... .. ... ... ...... ..... ............... ......
`.. . 1 1 9
`.. ... 1 37
`10. Distribution
`. .. . .. . .. . .. . . . . . . . . . . . . . . . .. . . . ..
`. . .. . . . . .. . .. . .. . . .. . .. .. . . . . . .. ...
`.. ..
`1 1 . Eliminati on . . . . . . . . . .
`. ..... ........... ... .. .. .. .. .... ....... .. ... ....... .... . .... ... 156
`12. Integrati on Wi th Kineti cs
`....... ...... ..... ..
`... ... ..
`... . .. .. .. ...
`. . 184
`
`INDIVIDUALIZATION
`SECTION IV.
`1 3 . Variability .............. ... ....
`14 . Geneti cs
`....... ..... .... .. .. .
`15. Age and Weight
`..... .. .
`16. Disease ..... .. ... .. .......... .. .
`17. Interacting Drugs
`....... .
`18. Concentra tion Monitoring
`
`..... .. .... ..
`
`.. ......... 203
`.. ......... 220
`. ... 230
`.... .......... ······· ···· ··· ····· ...... ... ........ .. .. 248
`. .............. ............. .. ... .. ...... .. .. ...... .. 267
`..... . ........................... .... .. ................. .. ...... 290
`
`SECTION V. SELECTED TOPICS
`. ........ ............ ... 313
`............ ... ... .. .... .. ....
`19. Distribution Kinetics
`20. Pharmacolog ic Response
`... ... ..... ... ... ..... ..... ....... ....... .. ........ .... ... .... ... 340
`........................ .. ............... .... .. ... 367
`2 1. Metabolite Kinetics
`22. Dose and Time Dependencies
`.... ... ............. .. ........... .. .... .... ..... .. ...... .. 394
`..... 424
`23. Turnover Concepts
`.. .... .. .. .. ... ...... .... ..... ..... ... .................. 443
`24. Dia lysis
`
`.. .. ........
`
`SELECTED READING
`
`.... .... .. .
`
`··········· ······· •·· •··•· •···•··· ....... ..... .. ....... .. ...... 463
`
`APPENDIX I. ADDITIONAL CONCEPTS AND DERIVATIONS
`... 469
`A. Assessment of AUC
`. .
`. . . . . . . .. ... .. ...... ...... .. ... ....
`B. Estimation of Elimination Half-life From Urine Data
`..... 473
`
`ix
`
`

`

`X
`
`C01'1TENTS
`
`C. Estimation of Absorption Kinetics From Plasma Concentration Doto
`...... 478
`D. Mean Residence Time
`..................................... .............. ... ...... 485
`E. Amount of Drug in Body on Accumulation to Piateou
`. . . ...... ........
`. ........ 490
`F. Distribution of Drugs Extensively Bound to Plasma Protei ns
`. . ....... ..
`. ... 494
`G. Blood to Plasma Concentration Ratio
`....... 502
`H. Estimation of Creotinine C learance Under Nonsteody-Stote Conditions ....... 504
`
`APPENDIX II. ANSWERS TO PROBLEMS
`
`INDEX
`
`..... 507
`
`... 586
`
`

`

`' I , . .
`
`: __ --_
`
`•
`
`.
`
`•
`
`1
`
`MULTIPLE-DOSE REGIMENS
`
`OBJECTIVES
`
`The reader w ill be able to:
`l. Predict the role and extent of drug accumulation for a given regimen of fi xed dose and fixed
`interval .
`
`2. Develop a dosage regimen from knowledge of the pharmacokinetics and therapeutic win(cid:173)
`dow of a drug.
`3. Evaluate the kinetics of a drug given in a multiple-dose regimen.
`4. Evaluate the kinetics of a drug follow ing a multiple-dose regimen of a controlled-release
`formulation.
`
`5. Derive pharmacokinetic parameters for a drug from plasma concentration (or urine) data
`following a multiple-dose regimen.
`
`The previous chapter dealt with constant-rate regimens. Although these regimens possess
`many desirable feahu-es, they are not the most common ones. The more common approach
`to the maintenance of continuous therapy is to give multiple discrete doses . This chapter
`covers the pharmacokinetic principles associated with such multiple-close regimens.
`
`DRUG ACCUMULATION
`Drugs are most commonly prescribed to be taken on a fixed dose, fixed time interval basis;
`e.g. , 100 mg three times a clay. In association with this kind of administration, the plasma
`concentration and amount in the body fluctuate and, similar to an infusion, rise toward a
`plateau.
`Consider the simplest situation of a dosage regimen composed of equal bolus doses
`administered intravenously at fixed and equal time inte1vals. Cmve A of Fig. 7-1 shows
`how amount in the body va1ies with time when each dose is given successively twice eve1y'
`half-life. Under these conditions drug accumulates substantially. Accumulation occurs be 0
`cause _drug from previous closes has not been completely removed.
`
`Maxima and Minima on Accumulation to the Plateau
`
`To appreciate the phenomenon of accumulation, consider what happens when a 100-mg
`bolus close is given intravenously every elimination half-life. The amounts in the body just
`after each dose and just before the next dose can readily be calculated; these values cor(cid:173)
`respond to the maximum (A,,,aJ and minimum (A,,,;,,) amounts obtained within each closing
`inte1val. The corresponding values during the first closing interval are 100 mg (A 1_,,,aJ and
`50 mg (A 1_,,,;,J, respectively. The maximum amount of drug in the second dosing inte1val
`(A2_,,wJ, 150 mg, is the dose (100 mg) plus the amount remaining from the previous dose
`
`83
`
`

`

`84
`
`MULTIPLrnOSE REGIMENS
`
`CHAPTER 7
`
`(50 mg). The amount remaining at the end of the second dosing interval (A2,m;n) , 75 mg,
`is that remaining from the first dose, 25 mg (100 mg X 1/ 2 X 1/ 2, because two half-lives
`have elapsed since its administrat10n) plus that remaining from the second dose, 50 mg.
`Alternatively, the value, 75 mg, may simply be calculated by recognizing that one-half of
`the amount just after the second dose, 150 mg, remains at the end of that dosing interval.
`Upon repeating this procedure, it is readily seen (curve B, Fig. 7-1) that drug accumulation,
`viewed in terms of either maximum or minimum amount in the body, continues until a
`limit is reached. At the limit, the amount lost in each interval equals the amount gained,
`the dose. In this example, the maximum and the minimum amounts in the body at steady
`state are 200 mg and 100 mg, respectively. This must be so since the difference between
`the maximum and minimum amounts is the dose, 100 mg, and since at the end of the
`interval, one half-life, the amount must be half that at the beginning.
`Following a constant rate input, the plateau is reached when rate of elimination matches
`rate of input. Then the level of drug in the body is constant. With discrete dosing, the level
`is not constant within a dosing interval, but the values at a given time within the interval
`are the same from one dosing interval to another, that is, when the amount lost equals the
`amount gained within the interval. The term plateau is also applied to this interdosing
`steady-state condition.
`The foregoing considerations can be expanded for the more general situation in which
`a drug is given at a dosing interval, ,, which may differ from the half-life. The general
`equations deiived in Appendix 1- E for the maximum and minimum amounts in the body
`after the Nth dose (AN,max; AN.min) and at plateau (Ass.max; Ass.min) are
`
`Maximum amount in
`body after N th dose, A N ,max
`
`Dose ·
`
`[
`
`1 _ e-NKr]
`
`_ e -kr
`
`1
`
`Minimum amount in
`body after Nth dose, AN
`.
`, min
`
`_ A
`-kt
`N ,max · e
`-
`
`Maximum amount in
`body at plateau, A ss, max
`
`Dose
`
`Fig. 7- 1. Dosing frequency controls the de(cid:173)
`gree of drug accumulation. Curve A, i.v. bolus
`dose (100 mg) administered twice eve1y half(cid:173)
`life; curve B, same bolus dose administered
`once eve1y half-life. Note that time is ex(cid:173)
`pressed in half-life units.
`
`-Cl)
`
`E
`>,
`"'CJ
`0
`co
`C
`
`300
`
`200
`
`2
`
`3
`
`A
`
`B
`
`Cl)
`
`2
`0
`
`0 -C
`
`:::,
`0
`E
`<(
`
`100
`
`0
`
`0
`
`2
`
`4
`Ti me/Half-life
`
`6
`
`8
`
`

`

`CHAPTER 7
`
`MULTIPLE-DOSE REGIMENS
`
`Minimum amount in
`.
`body at plateau, A
`ss, min
`
`= A
`-kr _ A
`ss,max e
`-
`ss,max
`
`_ D
`ose
`
`85
`
`4
`
`Recall from Chap. 3 that the function e-kt is the fraction of the initial amount remaining
`in the body at time t. Similarly, the amount in the body at the end of a dosing interval ,
`of a multiple-dose regimen, (AN.min) , is obtained by multiplying the corresponding maxi-
`-kr tit·A
`-A
`-kr.A
`-A
`t b
`-kr
`lilU111 arnoun y e
`' 1a 1S , N, niin -
`.
`N,max e
`ss,max e
`Ss;m.in -
`Ol
`To further appreciate the phenomenon of accumulation, consider an oral dosage regi(cid:173)
`men of 0.1 mg daily of digitoxin, used in the treatment of certain cardiac dysfunctions.
`Although not as widely used as the more popular drug, digoxin, digitoxin nicely illustrates
`many of the aspects of accumulation and design of dosage regimens. Given that absorption
`is complete and virtually instantaneous, oral administration can be simulated using i.v. bolus
`doses.
`·
`The average half-life of digitoxin is 6 days; therefore, from Eq. 3 the maximum amount
`at plateau is 0.92 mg, and from Eq. 4 the minimum amount at plateau is 0.82 mg. Digitoxin
`clearly undergoes considerable accumulation when given daily.
`These calculations of the maximum and minimum values at plateau strictly apply only
`to intravascular bolus administration. They are reasonable approximations following extra(cid:173)
`vascular administration, when absorption is complete and virtually instantaneous. The fol(cid:173)
`lowing discussion deals with a less restrictive view of accumulation, which applies to all
`routes of administration.
`
`Average Amount and Concentration at Plateau
`In many respects the accumulation of drugs, administered in multiple doses is tl1e same as
`that observed following a constant-rate i.v. infusion. The average amount in the body at
`steady state, plateau, is readily calculated using the steady-state concept: Average rate in
`must equal average rate out. The average rate in is F · Doseh. The average rate out is
`k · Ass.av, where Ass.av is the average amount of drug in the body over the dosing interval
`at plateau. Therefore,
`
`or
`
`F · Dose
`
`k · A
`
`55,0V
`
`F · Dose
`
`CL · C
`ss,ov
`
`5
`
`6
`
`where Css,av is the average plasma concentration at the plateau. Since k = 0.693/t112, it also
`follows that
`
`and
`
`A ss,av
`
`1.44 · F · Dose· 1112/r;
`
`F Dose
`Css,av =. CL . - t-
`
`7
`
`8
`
`These are fundamental relationships; they show how tl1e average amount in the body at
`
`

`

`86
`
`MULTIPLE-DOSE REGIMENS
`
`CHAPTER 7
`
`steady state depends on rate of administration (Doselr), bioavailability, and half-life, and
`how the corresponding average concentration depends on the first two factors and clear(cid:173)
`ance.
`Drug accumulation is not a phenomenon that depends on the property of a drug, nor
`are there drugs that are cumulative and others that are not. Accumulation, in pmticular
`the extent of it, is a result of the frequency of administration relative to half-life (t 11/ , or
`1/h) as shown in Figs. 7-1 and 7-2.
`Notice that the average amount of digitoxin (0.87 mg), calculated from Eq. 7, lies midway
`between the maximum 0.92 mg and the minimum 0.82 mg. Since calculating the average
`value is the much simpler procedure, under these circumstances the maximum and mini(cid:173)
`mum values can easily be calculated by adding and subtracting one-half the maintenance
`dose absorbed, respectively, to the average value. With digitoxin, for example, Ass,,,wx is
`0.87 + 0.05 = 0.92 mg; Ass,min is 0.87 - 0.05 = 0.82 mg. This simple method is a
`reasonable approximation as long as the dosing interval does not exceed the half-life.
`
`Comparison of Maximum, Average, and Minimum Amounts at Plateau
`Fluctuation in the amount of drug in the body, like accumulation, depends on both fre(cid:173)
`quency of drug administration and half-life. Fluctuation also depends on rate of absorption;
`it is greatest for i.v. bolus administration. Figure 7-2A illustrates how maximum, minimum,
`and average amounts in the body at plateau depend on the frequency of i.v. bolus admin(cid:173)
`istration. Several observations are pe1tinent: (1) The average amount increases in direct
`proportion to frequency of administration (inverse of the dosing interval) . (2) The maximum
`amount is not much greater than dose if drug is administered less frequently than once
`0.33 or less. Then most of the drug from all previous doses has
`every 3 half-lives, t 112!,
`
`A
`
`5
`
`4
`
`3
`
`0
`~
`a:.
`
`2
`
`0
`
`0
`
`2
`3
`Half-life /Dosing Interval
`
`4
`
`B
`
`i;
`+✓;,;,
`~0
`
`5
`
`4
`
`3
`
`0
`~
`a:.
`
`2
`
`1
`
`0
`
`0
`
`2
`3
`Half-life /Dosing Interval
`
`4
`
`Fig. 7-2. More frequent administration results in a greater degree of drng accumulation and hence smaller
`relative differences among the maximum (A,s,uwJ, average (A,,, 00 ) and minimum (A,,,,,,; ,, ) amounts of chug in the
`body at plateau. Note that frequency is the reciprocal of the dosing interval expressed here in half-life units. A,
`Ratios of the maximum, average (colored line), and minimum amounts of drug at plateau to the maintenance
`dose following chronic Lv. bolus administration, as a function of the dosing frequency. B, Ratios of maximum to
`average ( colored line), and minimum to average amounts of drng in the body as a function of the dosing frequency.
`
`

`

`CHAPTER 7
`
`MULTIPLE-DOSE REGIMENS
`
`87
`
`been eliminated before the next dose is administered. (3) Defining fluctuation as the ratio,
`Ass,ma/Ass,mi,v given by ekr (Eq. 4), the greater the relative frequency of administration (1/
`h) the smaller is the fluctuation. Figure 7-2B demonstrates how fluctuation at plateau
`depends on frequency of administration. The maximum and minimum amounts are each
`compared with the average amount in the body. Note that the average is arithmetically
`closer to the minimum than to the maximum value. This is particularly evident for low
`frequencies of administration.
`
`Rate of Accumulation to Plateau
`
`The amount in the body rises on multiple dosing just as it does following a constant-rate
`i.v. infusion (Chap. 6). That is, the approach to the plateau depends solely on the drug's
`half-life. The data for digitoxin, in Table 7-1 which show the ratio of the minimum amount
`during vaiious dosing intervals to the maximum amount at plateau, illustrate this point.
`Observe that it takes 1 half-life (6 days), or 6 doses, to be at 50% of the value at plateau,
`2 half-lives (12 days), or 12 doses, to be at 75% of the plateau value, and so on.
`Accumulation of digitoxin takes a long time because of its long half-life. The degree of
`accumulation is extensive, because of relatively frequent administration. The frequency of
`administration also determines the small fluctuation in the amount of drug in the body at
`plateau; 0.1 mg is lost every dosing interval, when there is about 0.9 mg in the body.
`The approach to steady state, observed for the minimum amounts of digitoxin in the
`body, also holds true for the maximum (proof in Appendix 1- D), and average amounts,
`that is,
`
`AN,av
`AN max
`-----'---'-'= = -
`-
`Ass,max
`Ass,av
`
`AN,min
`= - - = 1 - e - Nkr
`Ass,min
`
`9
`
`where AN.av is the average amount in the body in the dosing interval after the Nth dose.
`
`Accumulation Index
`
`If the amounts at steady state are compared to the corresponding values at time 'C after the
`first dose, then
`
`-
`A
`A
`A
`ss,m,n
`ss,av
`ss max
`Amax, l = Aav, l = Amin, l = ( 1 - e - h)
`
`10
`
`The quantity, 1/(1 - e-h), is an index of the extent of accumulation. For digitoxin (le
`0.116 day- 1, 'C = 1 day), the accumulation index (Rae) is 9.2. Thus, the maximum, average,
`and minimum amounts (and for that matter the amount at any time within the dosing
`interval at plateau) are 9.2 times the values at the corresponding times after a single dose.
`
`Table 7-1. Approach to Plateau on Daily Administration of Digitoxin
`
`Time (days)0
`Number of doses IN)
`
`0
`
`2
`2
`
`3
`3
`
`6
`6
`
`12
`12
`
`18
`18
`
`24
`24
`
`30
`30
`
`CX)
`
`CX)
`
`[ M;o;m,m omoocT
`Minimum amount
`at plateau
`
`0
`
`0.1 l
`
`0.21
`
`0.29
`
`0.5
`
`0.75
`
`0.875
`
`0.94
`
`0.97
`
`1.00
`
`°Time oher first dose
`6AN:min/A55,min = l - e~O.l l bN
`
`

`

`88
`
`MULTIPLE-DOSE REGIMENS
`
`CHAPTER 7
`
`Change in Regimen
`
`Suppose that the decision is made to halve the amount of digitoxin in the body at plateau_
`The need for a twofold reduction in the rate of administration, to 0.05 mg/day, follows
`from Eq. 7.
`As with i.v. infusion, it takes 1 half-life to go one-half the way from 0.90 to 0.45 mg, 2
`half-lives to go three-quarters of the way, and so on. For digitoxin it would take about 12
`days to go 75% of the way to the new plateau. (The same principle applies to an increase
`in the rate of digitoxin administration.) The fastest way to achieve 0.45 mg would be to
`discontinue drug for 1 week (approximately 1 half-life) before initiating the reduced rate
`of administration.
`
`RELATIONSHIP BETWEEN INITIAL AND MAINTENANCE DOSES
`
`It might be therapeutically desirable to establish the required amount of digitoxin in the
`body on the first day. When the first or initial dose is intended to be therapeutic it is
`referred to as the priming or loading close. In this case, the patient would require 0.9 mg
`initially, followed by 0.1 mg daily. For digitoxin the initial dose is often administered in
`divided doses. Several procedures are followed, but the divided dose is commonly given
`every 6 hours until the desired therapeutic response is obtained. In this way each patient
`is titrated to the initial therapeutic dose required.
`Instead of determining the loading dose when the maintenance dose is given, it is more
`common to determine the maintenance dose required to sustain a therapeutic amount in
`the body. The initial dose rapidly achieves the therapeutic response; subsequent doses
`maintain the response by replacing drug lost during the dosing interval. The maintenance
`dose, DM, therefore, is the difference between the loading dose, Dv and the amount
`remaining at the end of the dosing interval, DL · e-kr_ That is,
`
`Likewise, if the maintenance dose is known, the initial dose can be estimated:
`
`_ Ma intenance dose
`d
`.
`L d
`oa ing ose -
`(l _ e-kr)
`
`11
`
`12
`
`Thus, for digitoxin, a daily maintenance dose of 0.1 mg requires a loading dose of 0.9 mg.
`The similarity between Eqs. 3 and 11 should be noted. From the view point of accu(cid:173)
`mulation, Eq. 3 relates to the maximum amount at plateau on administering a given dose
`repetitively. If the maximum amount were put into the body initially, then Eq. 11 indicates
`the dose needed to maintain that amount. The relationships are the same, although they
`were derived using diffE)rent logic. These equations form the hea1t of multiple-dose drug
`administration and might well be called the "dosage regimen equations."
`The ratio of loading to maintenance doses depends on the dosing interval and the half(cid:173)
`life and is equal to the accumulation index, Rae· For example, tetracycline has approximately
`an 8-hour half-life in man, and a dose in the range of 250 to 500 mg is considered to provide
`effective antimicrobial drug concentrations. Therefore, a reasonable schedule is 500 mg
`(two 250-mg capsul~s) initially, followed by 250 mg every half-life, as shown in Fig. 7-3.
`A dosage regimen consisting of a priming dose equal to twice the maintenance dose and a
`dosing interval of one half-life are convenient for drugs with half-lives between 8 and 24
`hr. The frequency of administration for such drugs vaiies from 3 times a day to once daily,
`
`

`

`CHAPTER 7
`
`MULTIPLE-DOSE REGIMENS
`
`89
`
`respectively. For drugs with very short to sho1t half-lives, less than 3 hr, or with very long
`half-lives, greater than 24 hr, this regimen is often impractical.
`Although a loac.i.ng or initial dose greater than the maintenance dose seems appropriate
`for drugs with half-lives longer than 24 hr, such is often not the case. There are a vaiiety
`of reasons why this is so. For piroxicam, an analgesic/antipyretic with a half-life of 48-hr,
`the most common adverse effects are gastrointestinal reactions. Such reactions may be
`increased if the loading dose is three to four times the maintenance dose (DL = D~/(1 -
`e-kr), , = 1 day). Another example is that of warfa1in (half-life = 37 hr), for which the
`anticoagulant effect develops slowly with time. A third example is that of protiiptyline (an
`antidepressant with a half-life of 78 hr), for which larger doses slow gastiic emptying and
`gastrointestinal activity (anticholinergic effect), resulting in slower and more erratic ab(cid:173)
`sorption of this and other drugs. Furthermore, for protriptyline, the development of ther(cid:173)
`apeutic effects is also delayed, usually for 2 to 3 weeks.
`
`MAINTENANCE OF DRUG IN THE THERAPEUTIC RANGE
`Dosage regimens that achieve therapeutic concentrations are listed in Table 7-2 for drugs
`with both medium to high and low therapeutic indices and with various half-lives.
`
`Half-Lives Less Than 30 Min
`
`Great difficulty is encountered in trying to maintain therapeutic concentrations of such
`drugs. This is particularly true for a drug with a low therapeutic index, e.g., heparin, which
`has a half-life of approximately 30 min. Such a drug must be either infused or discarded
`unless intermittent concentrations are permissible. Drugs with a high therapeutic index
`may be given less frequently, but the greater tl1e dosing interval, the greater is the main(cid:173)
`tenance dose required to ensure that drug in the body stays above a minimum effective
`value. Penicillin is a notable example of a drug for which the dosing interval (4 to 6 hr) is
`many times longer than its half-life (approximately 30 min). The dose given greatly exceeds
`that required to yield plasma concentrations of antibiotic equivalent to tl1e minimum in(cid:173)
`hibitory concentration for most microorganisms.
`
`Half-Lives Between 30 Min and 8 Hr
`
`For such drugs, the major considerations are therapeutic index and convenience of dosing.
`A drug with a high therapeutic index need only be administered once every 1 to 3 half(cid:173)
`lives, or even less frequently. A drug with a low tl1erapeutic index must be given approxi(cid:173)
`mately every half-life, or more frequently, or be given by infusion. Lidocaine, for example,
`
`500
`
`a.,
`C
`c3
`» -c.., O>
`~ E
`1i, -
`I- >, 250
`_-o
`O
`0
`....... co
`C
`::::, ·-
`C
`0
`E
`<(
`
`0
`
`Fig. 7-3. Sketch of the amount of tetracy(cid:173)
`cline in the body with time; simulation of the
`i.v. admin istration of 500 mg initially and 250
`mg eveI)' 8 hr thereafter, curve A. When the
`initial and maintenance doses are the same,
`cmve B, it takes approximately 30 hr (3 to 4
`half-lives) before the plateau is practically
`reached. Thereafter, curves A and B are essen(cid:173)
`tially the same.
`
`0
`
`8
`
`16
`Hours
`
`24
`
`32
`
`

`

`90
`
`MULTIPLE-DOSE REGIMEl'-15
`
`CHAPTER 7
`
`has a half-life of 90 min, and the range of plasma concentrations associated with the treat(cid:173)
`ment of cardiac arrhythmias is only about threefold. This drug must be given by infusion
`to ensure prolonged suppressiou of arrhythmias and minimal toxicity.
`
`Half-Lives Between 8 and 24 Hr
`Here, the most convenient and desirable regimen is one in which a dose is given every
`half-life. If immediate achievement of steady state is desired, then, as previously mentioned,
`the initial dose must be twice the maintenance dose; the minimum and maximum amounts
`in the body are equivalent to one and two maintenance doses, respectively.
`
`Half-Lives Greater Than 24 Hr
`For drugs with half-lives greater than l day, administration once daily is convenient and
`promotes patient compliance. If an immediate therapeutic effect is desired, a therapeutic
`dose needs to be given initially. Otherwise the initial and maintenance doses are the same,
`in which case several doses may be necessary before the drug accumulates to therapeutic
`levels. The decision whether or not to give larger initial doses is often a practical matter.
`Side effects to large oral doses (gastrointestinal side effects) or to acutely high concentra(cid:173)
`tions of drug in the body may necessitate a slow accumulation.
`
`Table 7-2. Dosage Regimens for Continuous Maintenance
`of Therapeutic Concentrations
`
`RATIO Of INITIAL
`DOSE TO
`MAINTENANCE
`DOSE
`
`RATIO OF
`DOSING
`INTERVAL TO
`HALF-LIFE
`
`THERAPEUTIC
`INDEX0
`
`Medium to
`High
`
`HALHIFE
`
`<30 min
`
`30 min to 3 hr
`
`3-8 hr
`8-24 hr
`
`>24 hr
`
`1-2
`2
`
`>2
`
`3-6
`
`1-3
`
`<l
`
`Low
`
`<30 min
`
`30 min to 3 hr
`3-8 hr
`
`1-2
`
`-1
`
`8-24 hr
`>24 hr
`
`2-4
`>2
`
`0.5-1
`<l
`
`DRUG EXAMPLES
`
`Nitroglycerin
`
`Cephalosporins
`
`Tetracycl ine
`
`Sulfamethoxazole
`
`Chloroquine
`(suppression of
`malaria)
`
`GENERAL CO/v'MENTS
`
`Condidote for constant-rate
`administration a nd/ or
`short-term therapy.
`To be given any less often
`than every 3 half-lives,
`drug must have very high
`therapeutic index.
`
`VeJ common and
`esirable regimen.
`Once daily is eactical.
`Occasional y given once
`w eekly, or less
`frequently. Initial dose
`may need to be much
`greater than main-
`tenance dose.
`
`Not a candidate except
`
`under ved closely
`
`infusion.
`controlle
`O nly by infusion.
`Reduires 3-6 doses per
`ay, but less frequently
`with controlled-release
`form ulation.
`
`Requires careful control;
`once toxicity is produced
`drug concentration and
`toxicity decline slowly .
`
`Nitroprusside
`
`Lidocaine
`
`Theophylline
`
`Clonid ine6
`Digitoxin
`
`0 Usually toxic maintenance dose/usual therapeutic maintenance dose .
`bAs with many other drugs. in this categof'y, rather than administering a loading dose, dosage is progressively elevated until the desired response is
`achieved.
`
`

`

`CHAPTER 7
`
`MULTIPLE-DOSE REGIMENS
`
`91
`
`To summ arize the foregoing discussion, conside r th e antibiotic drug tetracycline, the
`nasal conges tant phenylpropanolamine, and th e antiepileptic agent phenobarbital, and their
`dosage regimens given in Table 7-3. Listed in Table 7--4 are the corresponding fractions
`of the initial amount remaining at the e ncl of a dosing inte rval, the average amounts at
`steady state, and the maximum and minimum values. Instantaneous and complete absmv(cid:173)
`tion is assumed.
`Dosing intervals for all three drugs are identical. The closes of phenylpropanolamine
`and phenobarbital are also the same, but the amounts of them in the body with time are
`certainly not. The explanation is readily visualized with a sketch.
`As with any graph, conside ration should first be given to scaling the axes. The amount
`of drug in the body should be scaled to th e maximum am ount at steady state. The time
`axis should be scaled to 4 to 5 half-lives, by which time plateau is achieved.
`F or tetracycline the amount in the body immediately after the first close is 500 mg. At
`the encl of th e closing interval, th e fraction re maining is 0.5, and the amount the refore is
`250 mg. A maintenan ce dose of 250 mg returns th e level to 500 mg and so on. Figure
`7-3, curve A, is thus readily drawn. Now consider the sketch had no loading close been
`given. The initial amount, 250 mg, would then decline to 125 mg at the encl of the first
`interval. The amount in the body immediately after the next close would be 375 mg. At th e
`end of the second inte rval, 187 mg would remain , and so on (curve B of Fig. 7-3) .
`F or phenylpropanolamine the maximum and minimum amounts in th e body at plateau
`are 40 mg and 10 mg, respectively, and a period of 4 hal f-lives is 16 hr. The fraction
`remaining at the encl of each closing inte rval is 0.25; therefore, the values of Ass, rnax and
`A ss, 111i11 are:
`
`Dose
`1
`
`2
`
`3
`
`Time (hr)
`0
`8
`8+
`16
`16+
`
`A ss, 11wx (mg)
`30
`
`A ss, 111 i11 (mg)
`
`37.,5
`
`39.4
`
`7.5
`
`9.4
`
`By the third dose (24 hr), the plateau is virtually achieved. Being given every two half-lives,
`the accumulation of phenylpropanolamine is minimal. Figure 7--4 is a sketch of the amounts
`of phenylpropanolamine in the body with time.
`
`Table 7 - 3. Dosage Regimens and Half-lives of Three Drugs
`
`DRUG
`
`Tetracycline
`Phenylpropanalamine
`Phenobarbital
`
`lOADING
`DOSE 1mg)
`500
`30
`30
`
`MAINTENANCE
`DOSE 1mg)
`250
`30
`30
`
`DOSING
`INTERVAl
`1hr)
`8
`8
`8
`
`HAlf·llFE
`1hr)
`
`8
`4
`100
`
`Table 7-4. Amount of Drug in Body (mg) on Regimens Given in Table 7-3
`
`DRUG
`
`Tetracycline
`Phenylpropanalamine
`Phenobarbital
`
`OGiven by e ~ h
`bl .44 · l11, · D,,/ r.
`
`FRACTION
`REMAINING
`AT END OF
`ll~TERVAl0
`0.5
`0.25
`0.946
`' F · DMI I - e-l,I
`dA.u,mo, - F . DM-
`
`AVERAGE AT
`STEADY
`STATEb
`360
`22
`540
`
`MAXIMUM AT
`STEADY
`STATE'
`500
`40
`556
`
`MINIMUM AT
`STEADY
`STATEd
`250
`10
`526
`
`

`

`92
`
`MULTIPLE-DOSE REGIMENS
`
`CHAPTER 7
`
`The same dosage regimen for phenobarbital produces a dramatically different result. At
`the end of each closing interval , the fraction remaining is 0.946. Accumulation then occurs
`until the 5.4% lost in each interval is equal to the dose, and th e amount in th e body at
`steady state is therefore about 19 times the dose. From the calculated value of the maximum
`amount at plateau (556 mg) and the half-life, it is apparent that a sketch must be scaled to
`600 mg and to about 15 clays (Fig. 7-5). The curve is similar to that obtained with constant(cid:173)
`rate infusion. The amounts in th e body at 100 hr is one-half of the steady-state amount,
`and at 200 hr the level is 75% of the plateau amount, and so on. Practically, the re is little
`need to consider the minor Auctuations.
`The clinical implications of these regimens are manifold. The tetracycline regimen is
`designed to attain and maintain therapeutic levels. The phenylpropanolamine regimen gives
`rise to large fluctuations that may be desirable. Tolerance to the drug develops readily; the
`maintenance of high , effective, decongesting concentrations is questionable. \Vith pheno-
`
`Fig. 7-4. Sketch of th e amount of phenyl(cid:173)
`propanolamine in the body "~th tim e; simu(cid:173)
`lation of 30 mg given i.v. eve,y 8 hr. Because
`the half-life , 4 hr, is short relative to the dosing
`interval, the degree of accumulation is small
`and the flu ctuation is large.
`
`40
`
`Q)
`C
`E
`ro
`0
`~- 30
`Cl. Cl
`2 E
`a . -
`~-6' 20
`Q) 0