HALAL.
`MITTALANArliss
`
`NEUROCRINE 1034
`
`Ome
`
`SUSANNA WU-PONG
`
`Na At
`
`1
`
`NEUROCRINE 1034
`
`

`

`Applied
`Biopharmaceutics &
`Pharmacokinetics
`
`Sixth Edition
`
`Leon Shargel, PHD, RPh
`Applied Biopharmaceutics, LLC
`Raleigh, North Carolina
`Affiliate Associate Professor, School ofPharmacy
`Virginia Commonwealth University, Richmond, Virginia
`Adjunct Associate Professor, School ofPharmacy
`University ofMaryland, Baltimore, Maryland
`Susanna Wu-Pong, PHD, RPh
`Associate Professor
`Director, Pharmaceutical Sciences Graduate Program
`Department ofPharmaceutics
`MedicalCollege of Virginia
`Virginia Commonwealth University
`Richmond, Virginia
`
`- Andrew B.C. Yu, PHD, RPh
`Registered Pharmacist
`Gaithersburg, Maryland
`Formerly Associate Professor of Pharmaceutics
`Albany College ofPharmacy
`Albany, New York
`Present Affiliation: CDER, FDA*
`Silver Spring, Maryland
`*The contentof this book represents the personal views of the authors
`and notthat of the FDA.
`
`Sram Medical
`
`New York Chicago San Francisco Lisbon London Madrid Mexico City
`Milan NewDelhi San Juan
`Seoul Singapore Sydney Toronto
`
`2
`
`

`

` The McGraw-Hill Companies
`
`Applied Biopharmaceutics & Pharmacokinetics, Sixth Edition
`
`Copyright © 2012 by The McGraw-Hill Companies, Inc. All rights reserved. Printed in the United States of America.
`Except as permitted under the United States Copyright Act of 1976, no part of this publication may be reproduced or
`distributed in any form or by any means, or stored in a data baseorretrieval system, without the prior written permission
`of the publisher.
`
`Previous editions copyright © 2005 by The McGraw-Hill Companies, Inc.; © 1999, 1993 by Appleton & Lange; © 1985,
`1980 by Appleton-Century-Crofts.
`
`1234567890 DOC/DOC
`
`17 16 15 14 13 12
`
`ISBN 978-0-07-160393-5
`MHID 0-07-160393-X
`
`This book was set in Times by Cenveo Publisher Services.
`The editors were Michael Weitz and Christie Naglieri.
`The production supervisor was Sherri Souffrance.
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`The design was by Elise Lansdon; the cover design was by Barsoom Design, with cover art © Gregor Schuster/Corbis.
`RR Donnelley wasprinter and binder.
`
`This book is printed on acid-free paper.
`
`Library of Congress Cataloguing-in-Publication Data
`
`Shargel, Leon, 1941-
`Applied biopharmaceutics & pharmacokinetics/Leon Shargel, Andrew
`B.C. Yu, Susanna Wu-Pong.—6th ed.
`p. ; cm.
`Applied biopharmaceutics and pharmacokinetics
`Includes bibliographical references and index.
`ISBN-13: 978-0-07-160393-5 (hardcover: alk. paper)
`ISBN-10: 0-07-160393-X (hardcover: alk. paper)
`|. Biopharmaceutics.
`2. Pharmacokinetics.
`I. Yu, Andrew B. C., 1945-
`Il. Wu-Pong, Susanna.
`Ill. Title.
`IV. Title: Applied biopharmaceutics and pharmacokinetics.
`[DNLM:
`1. Biopharmaceutics.
`2. Models, Chemical.
`3. Pharmacokinetics. QV 38]
`RM301.4.S52 2012
`615’.7—de23
`
`011020446
`
`McGraw-Hill booksare available at special quantity discounts to use as premiumsandsales promotions,or for use in cor-
`porate training programs. To contact a representative please e-mail us at bulksales@mcgraw-hill.com.
`
`3
`
`

`

`Contents
`
`Preface xii
`Glossary
`Xv
`
`Introduction to Biopharmaceutics and
`Pharmacokinetics
`1
`
`cm
`
`One-Compartment Open Model:
`Intravenous Bolus Administration 43
`
`1
`
`4
`
`10
`
`Drug Product Performance
`Biopharmaceutics
`1
`Pharmacokinetics
`3
`Clinical Pharmacokinetics
`Practical Focus
`4
`5
`Pharmacodynamics
`5
`Drug Exposure and Drug Response
`Toxicokinetics and Clinical Toxicology
`Measurement of Drug Concentrations
`Basic Pharmacokinetics and
`Pharmacokinetic Models
`Chapter Summary
`15
`Learning Questions
`17
`References
`17
`Bibliography
`
`18
`
`N
`
`Mathematical Fundamentals in
`Pharmacokinetics
`19
`
`22
`
`Math Self-Exam 19
`Estimation and the Use of Calculators and
`Computers
`20
`Practice Problems
`Calculus
`24
`Graphs
`26
`31
`Units in Pharmacokinetics
`Measurement and Use of Significant Figures
`Units for Expressing Blood Concentrations
`Statistics
`33
`34
`Practical Focus
`Rates and Orders of Reactions
`Chapter Summary
`40
`Learning Questions
`40
`References
`42
`Bibliography
`42
`
`35
`
`45
`
`44
`Elimination Rate Constant
`Apparent Volume of Distribution
`Clearance
`48
`50
`Practical Focus
`53
`Clinical Application
`Calculation of k from Urinary Excretion Data
`Practice Problem 54
`Clinical Application
`Chapter Summary
`Learning Questions
`Reference
`59
`Bibliography
`
`56
`57
`57
`
`59
`
`53
`
`5
`
`6
`
`4
`
`Multicompartment Models:
`Intravenous Bolus Administration 61
`
`63
`
`Two-Compartment Open Model
`Clinical Application
`68
`Practice Problem 68
`Practical Focus
`69
`77
`Three-Compartment Open Model
`Determination of Compartment Models
`Practical Application
`84
`Chapter Summary
`86
`Learning Questions
`87
`References
`88
`Bibliography
`89
`
`79
`
`5
`
`P
`
`Intravenous Infusion 91
`
`91
`One-Compartment Model Drugs
`Infusion Method for Calculating Patient
`Elimination Half-Life
`95
`
`32
`33
`
`vii
`
`4
`
`

`

`viii
`
`CONTENTS
`
`Loading Dose Plus IV Infusion—One-
`Dosage Regimen Schedules
`Practice Problems
`171
`Compartment Model
`96
`Practice Problems
`98
`Chapter Summary=173
`Learning Questions
`174
`Estimation of Drug Clearance and V,, from
`References
`175
`Infusion Data
`100
`Intravenous Infusion of Two-Compartment
`Bibliography
`175
`Model Drugs
`100
`Practical Focus
`102
`Chapter Summary
`104
`Learning Questions
`104
`Reference
`106
`Bibliography
`106
`
`169
`
`9
`
`.
`
`Nonlinear Pharmacokinetics
`
`177
`
`Drug Elimination and Clearance
`
`107
`
`107
`
`Drug Elimination
`The Kidney
`108
`111
`Renal Drug Excretion
`114
`Clinical Application
`114
`Practice Problems
`114
`Drug Clearance
`116
`Clearance Models
`118
`Renal Clearance
`121
`Determination of Renal Clearance
`Relationship of Clearance to Elimination
`Half-Life and Volume of Distribution
`Chapter Summary
`127
`Learning Questions
`127
`References
`129
`Bibliography
`129
`
`125
`
`179
`
`Saturable Enzymatic Elimination Processes
`Practice Problem 180
`Drug Elimination by Capacity-Limited
`Pharmacokinetics: One-Compartment
`Model, IV Bolus Injection
`181
`Clinical Focus
`191
`Drugs Distributed as One-Compartment
`Model and Eliminated by Nonlinear
`Pharmacokinetics
`191
`Chronopharmacokinetics and Time-Dependent
`Pharmacokinetics
`193
`Bioavailability of Drugs that Follow Nonlinear
`Pharmacokinetics
`196
`Nonlinear Pharmacokinetics Due to
`Drug—Protein Binding
`196
`Potential Reasons for Unsuspected
`Nonlinearity
`200
`Chapter Summary
`200
`Learning Questions
`200
`References
`202
`Bibliography
`203
`
`Pharmacokinetics of Oral
`Absorption
`131
`
`10.
`
`Physiologic Drug Distribution and
`Protein Binding
`205
`
`133
`
`131
`Pharmacokinetics of Drug Absorption
`Significance of Absorption Rate Constants
`Zero-Order Absorption Model
`133
`Clinical Application— Transdermal
`Drug Delivery
`134
`First-Order Absorption Model
`Practice Problem 142
`Chapter Summary
`149
`Learning Questions
`149
`References
`150
`Bibliography
`151
`
`134
`
`Multiple-Dosage Regimens
`
`153
`
`153
`Drug Accumulation
`157
`Clinical Example
`158
`Repetitive Intravenous Injections
`163
`Intermittent Intravenous Infusion
`Estimation of k and V, of Aminoglycosides
`in Clinical Situations
`165
`Multiple-Oral-Dose Regimen
`Loading Dose
`168
`
`166
`
`205
`
`219
`
`Physiologic Factors of Distribution
`Clinical Focus
`213
`Apparent VolumeDistribution 213
`Practice Problem 216
`Protein Binding of Drugs
`Clinical Examples
`221
`Effect of Protein Binding on the Apparent
`Volume of Distribution
`222
`Relationship of Plasma Drug—Protein Binding
`to Distribution and Elimination 227
`Determinants of Protein Binding
`231
`Kinetics of Protein Binding
`232
`Practical Focus
`233
`Determination of Binding Constants and
`Binding Sites by Graphic Methods
`233
`Clinical Significance of Drug—Protein
`Binding
`236
`Modeling Drug Distribution
`Chapter Summary
`248
`Learning Questions
`249
`References
`250
`Bibliography
`251
`
`247
`
`5
`
`

`

` Drug Elimination and Hepatic
`
`Clearance
`
`253
`
`265
`
`269
`270
`
`RMoeete of Drug Administration and Extrahepatic
`Dreg Metabolism 253
`Practical Focus
`255
`Hepatic Clearance
`255
`Enzyme Kinetics
`257
`Cimical Example
`261
`Practice Problem 263
`Asatomyand Physiology of the Liver
`Hepatic Enzymes Involved in the
`Biotransformation of Drugs
`267
`Drwe Biotransformation Reactions
`Pathways of Drug Biotransformation
`Farst-Pass Effects
`282
`Hepatic Clearance of a Protein-Bound Drug:
`Restrictive and Nonrestrictive Clearance
`from Binding
`287
`Effect of Changing Intrinsic Clearance and/or
`Blood Flow on Hepatic Extraction and
`Elimination Half-Life after TV and Oral
`Dosing
`288
`289
`Biliary Excretion of Drugs
`Role of Transporters in Hepatic Clearance
`and Bioavailability
`292
`Chapter Summary
`293
`Learning Questions
`294
`References
`296
`Bibliography
`298
`
`Pharmacogenetics
`
`301
`
`Polymorphism 303
`306
`Pharmacogenomics
`Adverse Drug Reactions Attributed
`to Genetic Differences
`308
`Genetic Polymorphism in Drug Metabolism:
`Cytochrome P-450 Isozymes
`310
`Genetic Polymorphism in Drug Transport:
`MDRI (P-Glycoprotein) and Multidrug
`Resistance
`311
`Genetic Polymorphism in Drug Targets
`Relationship of Pharmacokinetics/
`Pharmacodynamics and Pharmacogenetics/
`Pharmacogenomics
`313
`Clinical Example
`315
`Summary
`316
`Glossary
`316
`317
`Abbreviations
`References
`317
`Bibliography
`318
`
`312
`
`CONTENTS
`
`ix
`
`13.
`
`Physiologic Factors Related to Drug
`Absorption 321
`
`Drug Absorption and Design of a Drug
`Product
`321
`321
`Route of Drug Administration
`Nature of Cell Membranes
`324
`Passage of Drugs Across Cell Membranes
`Oral Drug Absorption During Drug Product
`Development
`333
`Drug Interactions in the Gastrointestinal
`Tract
`334
`336
`Oral Drug Absorption
`Methods for Studying Factors that Affect
`Drug Absorption
`348
`Clinical Examples
`351
`Effect of Disease States on Drug Absorption
`Miscellaneous Routes of Drug
`Administration
`353
`Chapter Summary
`355
`Learning Questions
`356
`References
`357
`Bibliography
`359
`
`326
`
`351
`
`14.
`
`Biopharmaceutic Considerations in
`Drug Product Design and In Vitro
`Drug Product Performance
`361
`
`363
`
`376
`
`Biopharmaceutic Factors Affecting Drug
`Bioavailability
`361
`Rate-Limiting Steps in Drug Absorption
`Physicochemical Nature of the Drug
`366
`Formulation Factors Affecting Drug
`Product Performance
`368
`Drug Product Performance, In Vitro: Dissolution
`and Drug Release Testing
`370
`374
`Compendial Methods of Dissolution
`Alternative Methods of Dissolution Testing
`Meeting Dissolution Requirements
`378
`Problems of Variable Control in Dissolution
`Testing
`379
`Performance of Drug Products: In Vitro—In Vivo
`Correlation
`380
`Dissolution Profile Comparisons
`Drug Product Stability
`386
`Considerations in the Design of a Drug
`Product
`387
`Drug Product Considerations
`Clinical Example
`394
`Chapter Summary
`398
`Learning Questions
`399
`References
`399
`Bibliography
`401
`
`386
`
`389
`
`6
`
`

`

`x
`
`CONTENTS
`
`15.
`
`Drug Product Performance,
`In Vivo: Bioavailability and
`Bioequivalence
`403
`
`405
`406
`
`407
`
`418
`
`403
`Drug Product Performance
`Purpose of Bioavailability Studies
`Relative and Absolute Availability
`Practice Problem 407
`Methods for Assessing Bioavailability
`Bioequivalence Studies
`413
`Design and Evaluation of Bioequivalence
`Studies
`414
`417
`Study Designs
`Crossover Study Designs
`Clinical Example
`422
`423
`Evaluation of the Data
`424
`Bioequivalence Example
`Study Submission and Drug Review
`Process
`427
`The Biopharmaceutics Classification System 431
`Generic Biologics (Biosimilar Drug
`Products)
`433
`Clinical Significance of Bioequivalence
`Studies
`435
`Special Concerns in Bioavailability and
`Bioequivalence Studies
`436
`Generic Substitution
`437
`Glossary
`440
`Chapter Summary
`Learning Questions
`References
`448
`Bibliography
`449
`
`443
`443
`
`16.
`
`Impact of Drug Product Quality
`and Biopharmaceutics on Clinical
`Efficacy
`451
`
`451
`Risks From Medicines
`Drug Product Quality and Drug Product
`Performance
`452
`453
`Pharmaceutical Development
`Excipient Affect on Drug Product
`Performance
`455
`Practical Focus
`456
`Quality Control and Quality Assurance
`Risk Management
`459
`Scale-Up and Postapproval Changes (SUPAC)
`Product Quality Problems
`464
`Postmarketing Surveillance
`465
`Glossary
`465
`Chapter Summary
`Learning Questions
`References
`466
`
`466
`466
`
`457
`
`461
`
`17,
`
`Modified-Release Drug Products
`
`469
`
`Conventional (Immediate-Release) and
`Modified-Release Drug Products
`469
`Biopharmaceutic Factors
`473
`Dosage form Selection
`475
`Advantages and Disadvantages of
`Extended-Release Products
`475
`476
`Kinetics of Extended-Release Dosage Forms
`Pharmacokinetic Simulation of Extended-Release
`Products
`478
`480
`Clinical Examples
`Types of Extended-Release Products
`Considerations in the Evaluation of
`Modified-Release Products
`495
`Evaluation of Modified-Release Products
`Evaluation of Jn Vivo Bioavailability Data
`Chapter Summary
`501
`Learning Questions
`501
`References
`502
`Bibliography
`503
`
`497
`499
`
`480
`
`18.
`
`Targeted Drug Delivery Systems and
`Biotechnological Products
`505
`
`514
`
`506
`Biotechnology
`Drug Carriers and Targeting
`Targeted Drug Delivery
`519
`Pharmacokinetics of Biopharmaceuticals
`Bioequivalence and Comparability of
`Biotechnology-Derived Drug Products
`Chapter Summary
`523
`Learning Questions
`524
`References
`524
`Bibliography
`525
`
`S21
`
`322
`
`19.
`
`Relationship Between
`Pharmacokinetics and
`Pharmacodynamics
`527
`
`527
`
`536
`
`Pharmacodynamics and Pharmacokinetics
`Relationship of Dose to Pharmacologic
`Effect
`534
`Relationship Between Dose and Duration of
`Activity (t,,-), Single IV Bolus Injection
`Practice Problem 536
`Effect of Both Dose and Elimination Half-Life
`on the Duration of Activity
`537
`Effect of Elimination Half-Life on Duration
`of Activity
`537
`539
`Clinical Examples
`Rate of Drug Absorption and Pharmacodynamic
`Response
`541
`Drug Tolerance and Physical Dependency
`Hypersensitivity and Adverse Response
`
`542
`543
`
`7
`
`

`

`Drug Distribution and Pharmacologic
`Response
`544
`545
`Pharmacodynamic Models
`Drug Exposure-Pharmacologic Response
`Relationships
`558
`Chapter Summary
`559
`Learning Questions
`560
`References
`561
`Bibliography
`563
`
`20.
`
`Application of Pharmacokinetics to
`Clinical Situations
`565
`
`566
`
`579
`
`580
`
`565
`Medication Therapy Management
`Individualization of Drug Dosage Regimens
`Therapeutic Drug Monitoring
`567
`Clinical Example
`574
`576
`Design of Dosage Regimens
`Conversion from Intravenous Infusion
`to Oral Dosing
`578
`Determination of Dose
`Practice Problems
`580
`Effect of Changing Dose and Dosing
`Interval on. Ce. Cogs and Cy,
`Determination of Frequency of Drug
`Administration
`581
`Determination of Both Dose and Dosage
`Interval
`582
`Determination of Route of Administration
`Dosing of Drugs in Infants and Children
`Dosing of Drugs in the Elderly
`585
`Dosing of Drugsin the Obese Patient
`Pharmacokinetics of Drug Interactions
`Inhibition of Drug Metabolism 594
`Inhibition of Monoamine Oxidase (MAO)
`Induction of Drug Metabolism 596
`Inhibition of Drug Absorption
`596
`Inhibition of Biliary Excretion
`596
`Altered Renal Reabsorption Due to
`Changing Urinary pH 596
`Practical Focus
`597
`597
`Effect of Food on Drug Disposition
`Adverse Viral Drug Interactions
`597
`Population Pharmacokinetics
`597
`Regional Pharmacokinetics
`608
`Chapter Summary
`609
`Learning Questions
`610
`References
`613
`Bibliography
`614
`
`583
`584
`
`588
`590
`
`595
`
`CONTENTS
`
`xi
`
`General Approaches for Dose Adjustment
`in Renal Disease
`618
`621
`Measurement of GlomerularFiltration Rate
`Serum Creatinine Concentration and Creatinine
`Clearance
`622
`624
`Practice Problems
`Dose Adjustment for Uremic Patients
`Extracorporeal Removal of Drugs
`638
`Clinical Examples
`642
`Effect of Hepatic Disease on
`Pharmacokinetics
`645
`Chapter Summary
`651
`Learning Questions
`652
`References
`653
`Bibliography
`655
`
`627
`
`22.
`
`Physiologic Pharmacokinetic Models,
`MeanResidence Time,andStatistical
`Moment Theory 657
`
`Physiologic Pharmacokinetic Models
`Mean Residence Time
`670
`674
`Statistical Moment Theory
`Selection of Pharmacokinetic Models
`Chapter Summary
`689
`Learning Questions
`689
`References
`690
`Bibliography
`691
`
`658
`
`687
`
`Appendix A
`
`Statistics
`
`693
`
`Appendix B
`
`Applications of Computers in
`Pharmacokinetics
`707
`
`Appendix C
`
`Solutions to Frequently
`Asked Questions (FAQs) and
`Learning Questions
`717
`
`Appendix D
`
`Guiding Principles for
`Humanand Animal
`Research 761
`
`Appendix E
`
`Popular Drugs and
`Pharmacokinetic
`Parameters
`767
`
`21.
`
`Dose Adjustment in Renal and Hepatic
`Disease
`617
`
`Index
`
`773
`
`617
`Renal Impairment
`Pharmacokinetic Considerations
`
`617
`
`8
`
`

`

`
`
`Multiple-Dosage Regimens
`
`Chapter Objectives
`Define the index for measuring
`drug accumulation.
`
`>
`
`>
`
`Define drug accumulation and
`drug accumulation t,..
`
`Explain the principle of
`superposition andits
`assumptions in multiple-dose
`regimens.
`
`Calculate the steady-state C_..
`and C,,,, after multiple IV bolus
`dosing of drugs.
`
`Calculate k and V, of
`aminoglycosidesin multiple-
`dose regimens.
`
`Adjust the steady-state C,,.. and
`Cin in the event the last dose
`is given tooearly, toolate, or
`totally missed following multiple
`IV dosing.
`
`Earlier chapters of this book discussed single-dose drug adminis-
`tration. Generally, drugs are given in multiple dosesto treat chronic
`disease such as arthritis, hypertension, etc. After single-dose drug
`administration, the plasma drug level rises above and then falls
`below the minimum effective concentration (MEC), resulting in a
`decline in therapeutic effect. To treat chronic disease, multiple-
`dosage or IV infusion regimens are used to maintain the plasma
`drug levels within the narrow limits of the therapeutic window (eg,
`plasma drug concentrations above the MEC but below the mini-
`mum toxic concentration or MTC) to achieve optimal clinical
`effectiveness. These drugs mayinclude antibacterials, cardiotonics,
`anticonvulsants, hypoglycemics, antihypertensives, hormones, and
`others. Ideally, a dosage regimen is established for each drug to
`provide the correct plasma level without excessive fluctuation and
`drug accumulation outside the therapeutic window.
`For certain drugs, such as antibiotics, a desirable MEC can be
`determined. Some drugsthat have a narrow therapeutic range (eg,
`digoxin and phenytoin) require definition of the therapeutic mini-
`mum and maximum nontoxic plasma concentrations (MEC and
`MTC,respectively). In calculating a multiple-dose regimen, the
`desired or target plasma drug concentration must be related to a
`therapeutic response, and the multiple-dose regimen must be
`designed to produce plasma concentrations within the therapeutic
`window.
`There are two main parameters that can be adjusted in devel-
`oping a dosage regimen: (1) the size of the drug dose and (2) T, the
`frequency of drug administration (ie, the time interval between
`doses).
`
`DRUG ACCUMULATION
`
`To calculate a multiple-dose regimen for a patient or patients,
`pharmacokinetic parameters are first obtained from the plasma
`level—time curve generated by single-dose drug studies. With these
`pharmacokinetic parameters and knowledgeofthe size of the dose
`and dosage interval (tT), the complete plasma level-time curve or
`
`153
`
`9
`
`

`

`154
`
`Chapter 8
`
`the plasma level may be predicted at any time after
`the beginning of the dosage regimen.
`For calculation of multiple-dose regimens,it is
`necessary to decide whether successive doses of
`drug will have any effect on the previous dose. The
`principle of superposition assumesthat early doses
`of drug do not affect the pharmacokinetics of subse-
`quent doses. Therefore, the blood levels after the
`second, third, or nth dose will overlay or superim-
`pose the blood level attained after the (n — 1)th dose.
`In addition, the AUC = (Jf, C,dt) for the first dose is
`e ual
`to the steady-state area between doses,
`ie,
`dc»dt) as shownin Fig. 8-1.
`3 The principle of superposition allows the phar-
`macokineticist to project the plasma drug concentra-
`tion—time curve of a drug after multiple consecutive
`doses based on the plasma drug concentration—time
`curve obtainedafter a single dose. The basic assump-
`tions are: (1) that the drug is eliminated byfirst-order
`kinetics and (2) that the pharmacokinetics of the
`drug after a single dose (first dose) are not altered
`after taking multiple doses.
`The plasma drug concentrations after multiple
`doses may be predicted from the plasma drug con-
`centrations obtained after a single dose. In Table 8-1,
`the plasma drug concentrations from 0 to 24 hours
`are measured after a single dose. A constant dose of
`drug is given every 4 hours and plasma drug concen-
`trations after each dose are generated using the data
`after the first dose. Thus,
`the predicted plasma
`drug concentration in the patient is the total drug
`
`level
`
`Blood
`
`t
`Doses
`
`t
`
`t
`
`Time (hours)
`{
`
`t
`
`: me
`1
`2
`t
`t
`
`Simulated data showingbloodlevels after
`FIGURE 8-1
`administration of multiple doses and accumulation of blood
`levels when equal dosesare given at equal timeintervals.
`
`10
`
`concentration obtained by adding the residual drug
`concentration obtained after each previous dose. The
`superposition principle may be used to predict drug
`concentrations after multiple doses of many drugs.
`Because the superposition principle is an overlay
`method, it may be used to predict drug concentra-
`tions after multiple doses given at either equal or
`unequal dosage intervals. For example, the plasma
`drug concentrations may be predicted after a drug
`dose is given every 8 hours, or 3 times a day before
`meals at 8 AM, 12 noon, and 6 pM.
`in which the
`There are situations, however,
`superposition principle does not apply.
`In these
`cases, the pharmacokinetics of the drug changeafter
`multiple dosing due to various factors,
`including
`changing pathophysiology in the patient, saturation
`of a drug carrier system, enzyme induction, and
`enzymeinhibition. Drugs that follow nonlinear phar-
`macokinetics (see Chapter 9) generally do not have
`predictable plasma drug concentrations after multi-
`ple doses using the superposition principle.
`If the drug is administered at a fixed dose and a
`fixed dosageinterval, as is the case with many multiple-
`dose regimens, the amount of drug in the body will
`increase and then plateau to a mean plasma level
`higher than the peak C, obtained from theinitial
`dose (Figs. 8-1 and 8-2). When the second dose is
`given after a time interval shorter than the time
`required to “completely” eliminate the previous
`dose, drug accumulation will occur in the body. In
`other words, the plasma concentrations following the
`second dose will be higher than corresponding
`plasma concentrations immediately following the
`first dose. However,if the second doseis given after
`a time interval
`longer than the time required to
`eliminate the previous dose, drug will not accumu-
`late (see Table 8-1).
`Asrepetitive equal doses are given at a constant
`frequency, the plasma level-time curve plateaus and
`a steady state is obtained. At steady state, the plasma
`drug levels fluctuate between C*,, and Cri, . Once
`steady state is obtained, C™,, and C™.. are constant
`and remain unchanged from dose to dose. In addi-
`tion, the AUC between (J. C,dt) is constant during
`a dosing interval at steadystate (see Fig. 8-1). The
`Cyax is important in determining drug safety. The
`Cyax should always remain below the minimum
`
`10
`
`

`

`TABLE 8-1 Predicted Plasma Drug Concentrations for Multiple-Dose Regimen Using the
`
`Multiple-Dosage Regimens
`
`155
`
`Superposition Principle*
`
`223,
`19.8
`
`.
`.
`
`22.3
`198
`
`a
`a
`
`5
`35.3
`c
`a
`21.0
`14.3
`C8
`343
`wa ee Se
`a
`29,9
`10.1
`198
`a
`aon.
`46 6 es
`9
`7.15
`143
`21.0
`42.5
`10 a a0 as
`as
`
`3
`
`4
`
`5
`
`:
`
`6
`
`:
`
`2
`
`"
`12
`
`13
`14
`
`5.06
`425
`
`3,58
`3.01
`
`35.0
`:
`10.1
`198.
`8.50 te eS a
`
`
`
`
`7.15
`143
`21.0
`wi Re ee :
`
`46.0
`aa
`
`oa
`10.1
`B06
`253.
`15
`16 ag. se eee - ebasig
`2 Nb
`17 ee beet) 748
`143
`21.0
`iste den Bi aadaes
`1.27
`2.53
`5.06
`10.1
`19.8
`2i3e 425
`850
`«169 0
`1.79
`3.58
`7.15
`143
`210
`dere? 3et eY tad
`223
`1.27
`2.53
`“5.06
`10.1
`19.8
`72 Gas
`Ree
`169
`
`
`
`21
`2
`23
`24
`
`
`
`a
`
`37.5
`<8
`47.8
`44g
`38.8
`32.9
`48.7
`456
`39.4
`33.4
`
`2
`
`2A single oral dose of 350 mg wasgiven and the plasma drug concentrations were measured for 0-24 h. The same plasma drug concentrations are
`assumed to occurafter doses 2-6. The total plasma drug concentration is the sum of the plasma drug concentrations due to each dose.Forthis
`example, Vp = 10 L,t,. =4h, and k, = 1.5 h-’. The drug is 100% bioavailable and follows the pharmacokinetics of a one-compartment open model.
`
`11
`
`11
`
`

`

`156
`
`Chapter 8
`
`is also a good indica-
`toxic concentration. The Cy,,
`tion of drug accumulation. If a drug produces the
`same Cy, at steady state, compared with the (C,, _,)
`max after the first dose, then there is no drug accumu-
`lation. If C=,
`is much larger than (C,, _ ,)max» then
`there is significant accumulation during the multiple-
`dose regimen. Accumulationis affected by the elimi-
`nation half-life of the drug and the dosing interval.
`The index for measuring drug accumulation R is
`
`R=
`
`= CO")cas
`(Char Dye
`
`(8.1)
`
`Substituting for C,,,, after the first dose andat steady
`state yields
`
`p— DolVol-e*)]
`DiIVo
`
`
`
`(8.2)
`
`Equation 8.2 shows that drug accumulation
`measured with the R index depends on the elimina-
`tion constant and the dosing interval and is indepen-
`dent of the dose. For a drug given in repetitive oral
`doses,
`the time required to reach steady state is
`dependent on the elimination half-life of the drug
`and is independentof the size of the dose, the length
`of the dosing interval, and the number of doses. For
`example, if the dose or dosageinterval of the drug is
`altered as showninFig. 8-2, the time required for the
`drug to reach steady state is the same, but the final
`
`
`
`aflv/sIN\si
`
`Max
`Min
`
`steady-state plasma level changes proportionately.
`Furthermore, if the drug is given at the same dosing
`rate but as an infusion (eg, 25 mg/h), the average
`plasma drug concentrations (C;,) will be the same
`but the fluctuations between C=. and C=, will
`vary (Fig. 8-3). An average steady-state plasma drug
`concentration is obtained by dividing the area under
`the curve (AUC)for a dosing period (ie, Pr C,dt)
`by the dosing interval T, at steady state.
`=
`An equation for the estimation of the time to
`reach one-half of the steady-state plasma levels or
`the accumulation half-life has been described by van
`Rossum and Tomey (1968).
`
`Accumulation ¢,,. = t,>(i+3.3 logs Ky4 (8.3)
`
`
`
`a
`
`© 600 mg every 24h
`
`(g/mL)
`
`IV infusion
`(25 mg/h)
`
`
`
`Plasmalevel
`
`Time (hours)
`
`Amountofdruginbody(mg)
`
`FIGURE 8-3=Simulated plasma drug concentration-time
`0
`20
`40
`60
`80
`100
`curvesafter IV infusion and oral multiple doses for a drug with
`Time (hours)
`an elimination half-life of 4 hours and apparent V, of 10 L. IV
`infusion given at a rate of 25 mg/hr, oral multiple doses are
`200 mg every 8 hours, 300 mg every 12 hours, and 600 mg
`every 24 hours.
`
`FIGURE 8-2 Amount ofdrugin the body asa function
`of time. Equal doses of drug were given every 6 hours (upper
`curve) and every 8 hours (lower curve). k, and k remain constant.
`
`12
`
`12
`
`

`

`For IV administration, k, is very rapid (approachesee);
`k is very small in comparison to k, and can be omit-
`ted in the denominator of Equation 8.3. Thus,
`Equation 8.3 reduces to
`
`Accumulation 4,,. = ty(i+3.21og2)
`
`(8.4)
`
`Because k,/k, = 1 and log 1 = 0, the accumulation ¢,,,
`of a drug administered intravenously is the elimina-
`tion ft), of the drug. From this relationship, the time
`to reach 50% steady-state drug concentrations is
`dependenton the elimination f,,. and not on the dose
`or dosage interval.
`As shownin Equation 8.4, the accumulation ¢,,,
`is directly proportional to the elimination t,,.. Table
`8-2 gives the accumulation /,,, of drugs with various
`elimination half-lives given by multiple oral doses
`(see Table 8-2).
`From a clinical viewpoint, the time needed to
`reach 90% of the steady-state plasma concentration
`is 3.3 times the elimination half-life, whereas the
`time required to reach 99% of the steady-state
`plasma concentration is 6.6 times the elimination
`half-life (Table 8-3). It should be noted from Table
`8-3 that at a constant dosesize, the shorter the dosage
`
`Multiple-Dosage Regimens
`
`157
`
`interval, the larger the dosing rate (mg/h), and the
`higher the steady-state drug level.
`The number of doses for a given drug to reach
`steady state is dependenton the elimination half-life
`of the drug and the dosageinterval Tt (see Table 8-3).
`If the drug is given at a dosage interval equal to the
`half-life of the drug, then 6.6 doses are required to
`reach 99% of the theoretical steady-state plasma
`drug concentration. The number of doses needed to
`reachsteady state is 6.6 f,,./t, as calculated in the far
`right column of Table 8-3. As discussed in Chapter
`5, Table 5.1, it takes 4.32 half-lives to reach 95% of
`steadystate.
`
`CLINICAL EXAMPLE
`
`Paroxetine (Prozac) is an antidepressant drug with a
`long elimination half-life of 21 hours. Paroxetine is
`well absorbedafter oral administration andhasa f,,,,,
`of about 5 hours,
`longer than most drugs. Slow
`elimination may cause the plasma curve to peak
`slowly. The f,,,, i8 affected by k and k,, as discussed
`in Chapter 7. The C,,,, for paroxetine after multiple
`dosing of 30 mg of paroxetine for 30 days in one
`study ranged from 8.6 to 105 ng/mL among 15 sub-
`jects. Clinically it is important to achieve a stable
`
`TABLE 8-2 Effect of Elimination Half-Life and Absorption Rate Constant on Accumulation
`
`
`
`Half-Life after Oral Administration?
`
`
`0.0289
`ay
`“Accumulation half-life is calculated by Equation 8.3, andis the half-time for accumulation of the drug to 90% of the steady-state plasma drug
`concentration.
`
`1.00
`
`
` JPcy se
`2 ae
`25.0
`
`13
`
`

`

`158
`
`Chapter 8
`
`TABLE 8-3 Interrelation of Elimination Half-Life, Dosage Interval, Maximum Plasma
`
`Concentration, and Time to Reach Steady-State Plasma Concentration?
`
`2A single dose of 1000 mg of three hypothetical drugs with variouselimination half-lives but equal volumesofdistribution (V, = 10 L) were given by
`multiple IV dosesat various dosingintervals.All time values are in hours; C>,, = maximum steady-state concentration;( Cz) = average steady-state
`plasma concentration; the maximum plasma drug concentration after the first dose of the drug is (C, =,),3, = 100 ug/mL.
`Time to reach 99% of steady-state plasma concentration.
`<Since the dosageinterval, 1, is very large comparedto the eliminationhalf-life, no accumulation of drug occurs.
`
`If t is equal to the dosage interval (ie, the time
`steady-state level in multiple dosing that does not
`“under dose” or overdose the patient. The pharmacist—between the first dose and the next dose), then the
`should advise the patient to follow the prescribed
`amount of drug remaining in the body after several
`dosing interval and dose as accurately as possible.—_hours can be determined with
`Taking a dose too early or too late contributes to
`variation. Individual variation in metabolism rate
`can also cause variable blood levels, as discussed
`later
`in Chapter
`12.
`ater In
`Chapter
`
`Dy = Dye
`
`(8.6)
`
`REPETITIVE INTRAVENOUS
`INJECTIONS
`The maximum amountof drug in the body following
`a single rapid IV injection is equal to the dose of the
`drug. For a one-compartment open model, the drug
`will be eliminated according to first-order kinetics.
`
`Dz = Dye-*
`
`(8.5)
`
`The fraction (f) of the dose remaining in the
`bodyis related to the elimination constant (k) and the
`dosageinterval(t)as follows:
`
`fz Ds =e
`o
`
`(8.7)
`
`With any given dose, f depends on k and 7.If 7 is
`large, f will be smaller because D, (the amount of
`drug remaining in the body) is smaller.
`
`14
`
`14
`
`

`

`Multiple-Dosage Regimens
`
`159
`
`TABLE 8-4 Fraction of the Dosein the Body
`before and after Intravenous Injections of a
`1000-mg Dose?
`
` 2
`
`250
`
`1250
`
`3
`
`4
`
`5
`
`6
`
`7
`
`co
`
`of = 0.25.
`
`312
`
`328
`
`332
`
`333
`
`333
`
`333
`
`1312
`
`1328
`
`1332
`
`1333
`
`1333
`
`1333
`
`Dinax ~ Omnis = Po
`
`(8.8)
`
`In this example,
`
`1333 - 333 = 1000 mg
`D=,, can also be calculated directly by the rela-
`tionship
`
`D”
`max
`
`
`dD,
`ef
`
`(8.9)
`
`Substituting knowndata, we obtain
`
` _ ae
`max —0.25 =1333mg
`
`Then, from Equation 8.8,
`
`Demin = 1333 — 1000 = 333 mg
`
`The average amount of drug in the body at
`steady state, D™ , can be found by Equation 8.10
`or Equation 8.11.F is the fraction of dose absorbed.
`For an IV injection, F is equal to 1.0.
`
`FD,
`o. es
`
`(8.10)
`
`FD,1.44t
`aw (8.11)
`
`15
`
`1. A patient receives 1000 mg every 6 hours by
`repetitive IV injection of an antibiotic with an
`eliminationhalf-life of 3 hours. Assume the drug
`is distributed according to a one-compartment
`model and the volumeofdistribution is 20 L.
`a. Find the maximum and minimum amountof
`drugin the body.
`b. Determine the maximum and minimum
`plasma concentration of the drug.
`
`Solution
`
`a. The fraction of drug remainingin the bodyis
`estimated by Equation 8.7.The concentration
`of the drug declines to one-half after 3 hours
`(ty. = 3 h), after which the amountof drugwill
`again decline by one-half at the end of the
`next 3 hours. Therefore, at the end of 6 hours
`only one-quarter, or 0.25, of the original dose
`remainsin the body.Thusfis equalto 0.25.
`To use Equation 8.7, we mustfirst find the value
`of k from the t,,.
`
`0.693 0.693
`=
`—— =0.231h"'
`ty Fe
`
`k=
`
`The timeinterval t is equal to 6 hours. From Equa-
`tion 8.7,
`
`f = e-(0.23116)
`f=0.25
`
`In this example, 1000 mg of drug is given
`intravenously, so the amountof drug in the body
`is immediately increased by 1000 mg. At the end
`of the dosageinterval(ie, before the next dose),
`the amountof drug remaining in the bodyis 25%
`of the amountof drug presentjust after the previ-
`ous dose,