`
`"
`
`APPLIED
`
`BIOPHARMACEUTICS
`
`AND
`PHARMACOKINETICS "
`
`SEVENTH EDITION ”
`
`‘.- ,..————~
`
`
`
`LEON SHARGEL
`
`ANDREW B.C. YU
`
`1
`
`NEUROCRINE 1033
`
`
`
`1
`
`NEUROCRINE 1033
`
`

`

`Applied
`Biopharmaceutics 8:
`Pharmacokinetics
`
`Seventh Edition
`
`EDITORS
`
`Leon Shargel, PHD, RPh
`Applied Biopharmaceutics, LLC
`Raleigh, North Carolina
`Afi‘iliate Professor, School ofPharmacy
`Virginia Commonwealth University, Richmond, Virginia
`Adjunct Associate Professor, School ofPharmacy
`University ofMaryland, Baltimore, Maryland
`
`Andrew B.C. Yu, PHD, RPh
`Registered Pharmacist
`Gaithersburg, Maryland
`Formerly Associate Professor of Pharmaceutics
`Albany College ofPharmacy
`Albany, New York
`Formerly CDER, FDA
`Silver Spring, Maryland
`
`Mc
`Graw
`Hill
`
`Education
`
`New York Chicago San Francisco Athens London Madrid Mexico City.
`Milan New Delhi Singapore Sydney Toronto
`
`2
`
`

`

`Applied Biopharmaceutics 8: Pharmacokinetics, Seventh Edition
`
`Copyright © 2016 by McGraw—Hill Education. 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 base or retrieval system, without the prior written permission of the
`publisher.
`
`Previous editions copyright © 2012 by The McGraw-Hill Companies, Inc; © 2005, 1999, 1993 by Appleton & Lange;
`© 1985, 1980 by Appleton—Century-Crofts.
`
`1234567890 DOC/DOC 201918171615
`
`ISBN 978’0-07-183093—5
`MHID 0-07-183093-6
`
`This book was set in Times LT Std by Cenveo® Publisher Services.
`The editors were Michael Weitz and Regina Y. Brown.
`The production supervisor was Rick Ruzycka.
`The production manager was Tanya Punj. Cenveo Publisher Services.
`The design was by Elise Lansdon; the cover design was by Barsoom Design, with cover art © Gregor Schuster/Corbis.
`RR Donnelley was printer and binder.
`
`Library of Congress Cataloging-in-Publication Data
`
`Shargel, Leon, 1941- , author.
`Applied biopharmaceutics & pharmacokinetics / Leon Shargel, Andrew B.C. Yu.—Seventh edition.
`p. ; cm.
`
`Applied biopharmaceutics and pharmacokinetics
`Includes bibliographical references and index.
`ISBN 978-0-07-183093-5 (hardcover)—ISBN 0-07-183093-6 (hardcover)
`1. Yu, Andrew B. C., 1945- , author.
`11. Title.
`II]. Title: Applied biopharmaceutics and pharmacokinetics.
`[DNLM:
`l. Biopharmaceutics.
`2. Pharmacokinetics.
`3. DrugAdministration Routes.
`4. Models, Chemical. QV 38]
`RM301.4
`615.7—dc23
`
`2015014810
`
`McGraw-Hil] books are available at special quantity discounts to use as premiums and sales promotions, or for use in
`corporate training programs. To contact a representative please e-mail us at bulksales@mcgraw-hill.com.
`
`3
`
`

`

`Contents
`
`Contributors
`
`xi
`
`xv
`Preface
`Preface to First Edition
`
`xvii
`
`1.
`
`Introduction to Biopharmaceutics and
`Pharmacokinetics
`1
`
`Drug Product Performance
`Biopharmaceutics
`1
`Pharmacokinetics
`4
`
`4
`Pharmacodynamics
`Clinical Pharmacokinetics
`Practical Focus
`8
`
`1
`
`5
`
`10
`Pharmacodynamics
`10
`Drug Exposure and Drug Response
`10
`Toxicokinetics and Clinical Toxicology
`11
`Measurement of Drug Concentrations
`Basic Pharmacokinetics and Pharmacokinetic
`Models
`15
`
`Chapter Summary
`Learning Questions
`Answers
`23
`References
`
`25
`
`21
`22
`
`Bibliography
`
`25
`
`2. Mathematical Fundamentals in
`
`Pharmacokinetics
`Calculus
`27
`
`27
`
`29
`Graphs
`Practice Problem 31
`
`33
`Mathematical Expressions and Units
`Units for Expressing Blood Concentrations
`Measurement and Use of Significant Figures
`Practice Problem 35
`Practice Problem 36
`Rates and Orders of Processes
`
`40
`
`34
`34
`
`Chapter Summary
`Learning Questions
`Answers
`46
`References
`
`50
`
`42
`43
`
`3. Biostatistics
`Variables
`51
`
`51
`
`Types of Data (Nonparametric Versus Parametric)
`Distributions
`52
`
`51
`
`Measures of Central Tendency
`Measures of Variability
`54
`Hypothesis Testing
`56
`Statistically Versus Clinically Significant
`Differences
`58
`
`53
`
`Statistical Inference Techniques in Hypothesis
`Testing for Parametric Data
`59
`Goodness of Fit
`63
`
`Statistical Inference Techniques for Hypothesis
`Testing With Nonparametric Data
`63
`Controlled Versus Noncontrolled Studies
`
`66
`
`66
`Blinding
`Confounding
`Validity
`67
`68
`Bioequivalence Studies
`Evaluation of Risk for Clinical Studies
`
`66
`
`68
`
`Chapter Summary
`Learning Questions
`Answers
`72
`References
`
`73
`
`70
`70
`
`One-Compartment Open Model:
`Intravenous Bolus Administration 75
`Elimination Rate Constant
`76
`
`Apparent Volume of Distribution
`Clearance
`80
`
`77
`
`85
`Clinical Application
`Calculation of k From Urinary Excretion Data
`Practice Problem 87
`Practice Problem 88
`
`86
`
`Clinical Application
`Chapter Summary
`Learning Questions
`Answers
`92
`Reference
`96
`
`89
`90
`90
`
`Bibliography
`
`96
`
`Multicompartment Models:
`Intravenous Bolus Administration 97
`Two-Compartment Open Model
`100
`Clinical Application
`105
`
`4
`
`

`

`vi
`
`CONTENTS
`
`Practice Problem 107
`Practical Focus
`107
`Practice Problem 110
`Practical Focus
`113
`
`Three-Compartment Open Model
`Clinical Application
`115
`Clinical Application
`116
`Determination of Compartment Models
`Practical Focus
`117
`
`114
`
`116
`
`118
`Clinical Application
`Practical Problem 120
`
`121
`121
`122
`123
`124
`
`Clinical Application
`Practical Application
`Clinical Application
`Chapter Summary
`Learning Questions
`Answers
`126
`References
`128
`
`Bibliography
`
`129
`
`6.
`
`131
`Intravenous Infusion
`131
`One-Compartment Model Drugs
`Infusion Method for Calculating Patient Elimination
`Half—Life
`135
`
`Loading Dose Plus IV Infusion—One-Compartment
`Model
`136
`Practice Problems
`
`138
`
`Estimation of Drug Clearance and VD From Infusion
`Data
`140
`
`Intravenous Infusion of Two-Compartment Model
`Drugs
`141
`Practical Focus
`
`142
`
`144
`144
`
`Chapter Summary
`Learning Questions
`Answers
`146
`Reference
`148
`
`Bibliography
`
`148
`
`7. Drug Elimination, Clearance, and
`Renal Clearance
`149
`Drug Elimination
`149
`Drug Clearance
`150
`Clearance Models
`152
`
`157
`The Kidney
`162
`Clinical Application
`163
`Practice Problems
`163
`Renal Clearance
`Determination of Renal Clearance
`Practice Problem 169
`Practice Problem 169
`
`168
`
`Relationship of Clearance to Elimination Half-Life
`and Volume of Distribution
`170
`
`Chapter Summary
`Learning Questions
`Answers
`172
`
`171
`171
`
`References
`
`175
`
`Bibliography
`
`175
`
`Pharmacokinetics of Oral
`
`Absorption 177
`Introduction
`177
`
`Basic Principles of Physiologically Based
`Absorption Kinetics (Bottom-Up Approach)
`Absoroption Kinetics
`182
`(The Top-Down Approach)
`182
`Pharmacokinetics of Drug Absorption
`Significance of Absorption Rate Constants
`Zero-Order Absorption Model
`184
`Clinical Application—Transdermal Drug
`Delivery
`185
`First-Order Absorption Model
`Practice Problem 191
`
`185
`
`178
`
`184
`
`Chapter Summary
`Answers
`200
`
`199
`
`Application Questions
`References
`203
`
`202
`
`Bibliography
`
`204
`
`9.
`
`Multiple-Dosage Regimens
`Drug Accumulation
`205
`Clinical Example
`209
`Repetitive Intravenous Injections
`Intermittent Intravenous Infusion
`
`205
`
`210
`214
`
`216
`Clinical Example
`Estimation of k and VD of Aminoglycosides in
`Clinical Situations
`217
`
`Multiple-Oral-Dose Regimen
`Loading Dose
`219
`Dosage Regimen Schedules
`Clinical Example
`222
`Practice Problems
`222
`
`218
`
`220
`
`224
`225
`
`Chapter Summary
`Learnng Questions
`Answers
`226
`References
`228
`
`Bibliography
`
`228
`
`10.
`
`229
`Nonlinear Pharmacokinetics
`Saturable Enzymatic Elimination Processes
`Practice Problem 232
`Practice Problem 233
`
`231
`
`Drug Elimination by Capacity-Limited
`Pharmacokinetics: One-Compartment
`Model, IV Bolus Injection
`233
`Practice Problems
`235
`Clinical Focus
`242
`Clinical Focus
`243
`
`Drugs Distributed as One—Compartment
`Model and Eliminated by Nonlinear
`Pharmacokinetics
`243
`
`5
`
`

`

`Clinical Focus
`
`244
`
`Chronopharmacokinetics and Time-Dependent
`Pharmacokinetics
`245
`Clinical Focus
`247
`Bioavailability of Drugs That Follow Nonlinear
`Pharmacokinetics
`247
`
`Nonlinear Phannacokinetics Due to Drug—Protein
`Binding
`248
`Potential Reasons for Unsuspected
`Nonlinearity
`251
`Dose-Dependent Pharmacokinetics
`Clinical Example
`253
`Chapter Summary
`254
`Learning Questions
`254
`Answers
`255
`References
`257
`
`252
`
`Bibliography
`
`258
`
`1 1. Physiologic Drug Distribution and
`Protein Binding 259
`Physiologic Factors of Distribution
`Clinical Focus
`267
`
`259
`
`Apparent Volume Distribution
`Practice Problem 270
`
`267
`
`273
`
`Protein Binding of Drugs
`Clinical Examples
`275
`Effect of Protein Binding on the Apparent Volume
`of Distribution
`276
`Practice Problem 279
`
`280
`Clinical Example
`Relationship of Plasma Drug—Protein Binding to
`Distribution and Elimination
`281
`
`282
`Clinical Examples
`284
`Clinical Example
`Determinants of Protein Binding
`Clinical Example
`285
`Kinetics of Protein Binding
`Practical Focus
`287
`
`286
`
`285
`
`Determination of Binding Constants and Binding
`Sites by Graphic Methods
`287
`Clinical Significance of Drug—Protein
`Binding
`290
`299
`Clinical Example
`300
`Clinical Example
`Modeling Drug Distribution
`Chapter Summary
`302
`Learning Questions
`303
`Answers
`304
`References
`306
`
`301
`
`Bibliography
`
`307
`
`12. Drug Elimination and Hepatic
`Clearance
`309
`Route of Drug Administration and Extrahepatic
`Drug Metabolism 309
`
`CO NTE NTS
`
`Vli
`
`Practical Focus
`
`311
`
`311
`Hepatic Clearance
`Extrahepatic Metabolism 312
`Enzyme Kinetics—Michaelis—Menten
`Equation
`313
`317
`Clinical Example
`Practice Problem 319
`
`321
`Anatomy and Physiology of the Liver
`Hepatic Enzymes Involved in the Biotransformation
`of Drugs
`323
`Drug Biotransformation Reactions
`Pathways of Drug Biotransformation
`Drug Interaction Example
`331
`Clinical Example
`338
`First—Pass Effects
`338
`
`325
`326
`
`Hepatic Clearance of a Protein-Bound Drug:
`Restrictive and Nonrestrictive Clearance From
`
`346
`
`344
`Binding
`Biliary Excretion of Drugs
`Clinical Example
`348
`Role of Transporters on Hepatic Clearance
`and Bioavailability
`348
`Chapter Summary
`350
`Learning Questions
`350
`Answers
`352
`References
`354
`
`Bibliography
`
`355
`
`13. Pharmacogenetics and Drug
`Metabolism 357
`358
`Genetic Polymorphisms
`Cytochrome P-450 Isozymes
`Phase [I Enzymes
`366
`Transporters
`367
`Chapter Summary
`Glossary
`369
`369
`Abbreviations
`References
`370
`
`368
`
`361
`
`14. Physiologic Factors Related to Drug
`Absorption 373
`Drug Absorption and Design
`of a Drug Product
`373
`374
`Route of Drug Administration
`Nature of Cell Membranes
`377
`
`Passage of Drugs Across Cell Membranes
`Drug Interactions in the Gastrointestinal
`Tract
`389
`
`378
`
`390
`Oral Drug Absorption
`Oral Drug Absorption During Drug Product
`Development
`401
`Methods for Studying Factors That Affect Drug
`Absorption
`402
`Effect of Disease States on Drug Absorption
`Miscellaneous Routes of Drug Administration
`
`405
`407
`
`6
`
`

`

`viii
`
`CONTENTS
`
`Chapter Summary
`Learning Questions
`Answers to Questions
`References
`411
`
`408
`409
`410
`
`Bibliography
`
`414
`
`15. Biopharmaceutic Considerations in
`Drug Product Design and In Vitro Drug
`Product Performance
`415
`Biopharmaceutic Factors and Rationale for Drug
`Product Design
`416
`418
`Rate-Limiting Steps in Drug Absorption
`420
`Physicochemical Properties of the Drug
`Formulation Factors Affecting Drug Product
`Performance
`423
`
`Drug Product Performance. In Vitro: Dissolution
`and Drug Release Testing
`425
`429
`Compendial Methods of Dissolution
`Alternative Methods of Dissolution Testing
`Dissolution Profile Comparisons
`434
`Meeting Dissolution Requirements
`436
`Problems of Variable Control in Dissolution
`
`431
`
`437
`Testing
`Performance of Drug Products: In Vino—In Viva
`Correlation
`437
`
`Approaches to Establish Clinically Relevant Drug
`Product Specifications
`441
`Drug Product Stability
`445
`Considerations in the Design of a Drug
`Product
`446
`
`450
`
`Drug Product Considerations
`Clinical Example
`456
`Chapter Summary
`461
`Learning Questions
`462
`Answers
`462
`References
`463
`
`Bibliography
`
`466
`
`16. Drug Product Performance, In Vivo:
`Bioavailability and Bioequivalence
`Drug Product Performance
`469
`Purpose of Bioavailability and Bioequivalence
`Studies
`471
`
`469
`
`Relative and Absolute Availability
`Practice Problem 474
`
`472
`
`Methods for Assessing Bioavailability and
`Bioequivalence
`475
`In Vivo Measurement of Active Moiety or Moieties
`in Biological Fluids
`475
`Bioequivalence Studies Based on Pharmacodynarnic
`Endpoints—In Vtvo Pharmacodynamic (PD)
`Comparison
`478
`Bioequivalence Studies Based on Clinical
`Endpoints—Clinical Endpoint Study
`In Vitm Studies
`481
`
`479
`
`Other Approaches Deemed Acceptable
`(by the FDA)
`482
`Bioequivalence Studies Based on Multiple
`Endpoints
`482
`482
`Bioequivalence Studies
`Design and Evaluation of Bioequivalence
`Studies
`484
`
`490
`Study Designs
`Crossover Study Designs
`Clinical Example
`496
`Clinical Example
`496
`Pharmacokinetic Evaluation of the Data
`
`491
`
`497
`
`499
`
`The Partial AUC in Bioequivalence
`Analysis
`498
`Examples of Partial AUC Analyses
`Bioequivalence Examples
`500
`Study Submission and Drug Review Process
`Waivers of In Vivo Bioequivalence Studies
`(Biowaivers)
`503
`The Biopharmaceutics Classification System
`(BCS)
`507
`Generic Biologics (Biosimilar Drug
`Products)
`510
`Clinical Significance of Bioequivalence
`Studies
`51 1
`
`Special Concerns in Bioavailability and
`Bioequivalence Studies
`512
`Generic Substitution
`514
`
`517
`Glossary
`Chapter Summary
`Learning Questions
`Answers
`525
`References
`526
`
`520
`520
`
`502
`
`I7. Biopharmaceutical Aspects of the
`Active Pharmaceutical Ingredient and
`Pharmaceutical Equivalence
`529
`Introduction
`529
`Pharmaceutical Alternatives
`Practice Problem 534
`
`533
`
`Bioequivalence of Drugs With Multiple
`Indications
`536
`
`Formulation and Manufacturing Process
`Changes
`536
`Size, Shape, and Other Physical Attributes of
`Generic Tablets and Capsules
`536
`Changes to an Approved NDA or ANDA 537
`The Future of Pharmaceutical Equivalence and
`Therapeutic Equivalence
`538
`Biosimilar Drug Products
`539
`Historical Perspective
`540
`Chapter Summary
`541
`Learning Questions
`541
`Answers
`542
`References
`542
`
`7
`
`

`

`18.
`
`Impact of Biopharmaceutics on
`Drug Product Quality and Clinical
`Efficacy
`545
`Risks From Medicines
`Risk Assessment
`546
`
`545
`
`Drug Product Quality and Drug Product
`Performance
`547
`
`2].
`
`Pharmaceutical Development
`Example of Quality Risk
`550
`Excipient Effect on Drug Product
`Performance
`553
`Practical Focus
`554
`
`547
`
`Quality Control and Quality Assurance
`Practical Focus
`555
`
`554
`
`557
`Risk Management
`Scale-Up and Postapproval Changes (SUPAC)
`Practical Focus
`561
`
`558
`
`561
`562
`
`Product Quality Problems
`Postmarketing Surveillance
`Glossary
`562
`Chapter Summary
`Learning Questions
`Answers
`564
`References
`565
`
`563
`564
`
`Bibliography
`
`565
`
`I9. Modified-Release Drug Products and
`Drug Devices
`567
`Modified-Release (MR) Drug Products and
`Conventional (Immediate-Release, IR)
`Drug Products
`567
`572
`Biopharmaceutic Factors
`575
`Dosage Form Selection
`Advantages and Disadvantages of Extended-
`Release Products
`575
`
`577
`Kinetics of Extended-Release Dosage Forms
`Pharmacokinetic Simulation of Extended-Release
`Products
`578
`
`580
`Clinical Examples
`Types of Extended—Release Products
`Considerations in the Evaluation of
`Modified-Release Products
`601
`Evaluation of Modified-Release Products
`
`581
`
`Evaluation of In Vivo Bioavailability Data
`Chapter Summary
`608
`Learning Questions
`609
`References
`609
`
`604
`
`606
`
`Bibliography
`
`613
`
`20.
`
`Targeted Drug Delivery Systems and
`Biotechnological Products
`615
`Biotechnology
`615
`Drug Carriers and Targeting
`Targeted Drug Delivery
`627
`
`624
`
`CONTENTS
`
`ix
`
`Pharmacokinetics of Biopharmaceuticals
`Bioequivalence of Biotechnology-Derived
`Drug Products
`631
`Learning Questions
`632
`Answers
`632
`References
`633
`
`630
`
`Bibliography
`
`633
`
`Relationship Between Pharmacokinetics
`and Pharmacodynamics
`63S
`Pharmacokinetics and Pharmacodynamics
`Relationship of Dose to Pharmacologic Effect
`Relationship Between Dose and Duration of
`Activity (rm), Single IV Bolus Injection
`Practice Problem 643
`Effect of Both Dose and Elimination Half—Life on
`the Duration of Activity
`643
`Effect of Elimination Half-Life on Duration of
`
`635
`640
`
`643
`
`644
`Activity
`Substance Abuse Potential
`
`644
`
`Drug Tolerance and Physical Dependency
`Hypersensitivity and Adverse Response
`Chapter Summary
`673
`Learning Questions
`674
`Answers
`677
`References
`678
`
`645
`646
`
`Application of Pharmacokinetics to
`Clinical Situations
`681
`68]
`Medication Therapy Management
`lndividualization of Drug Dosage Regimens
`Therapeutic Drug Monitoring
`683
`Clinical Example
`690
`Clinical Example
`692
`692
`Design of Dosage Regimens
`Conversion From Intravenous Infusion to
`
`682
`
`694
`Oral Dosing
`Determination of Dose
`Practice Problems
`696
`
`696
`
`Effect of Changing Dose 0nd Dosing Interval on
`CL” sz. and c;
`697
`Determination of Frequency of Drug
`Administration
`698
`
`Determination of Both Dose and Dosage
`Interval
`698
`Practice Problem 699
`Determination of Route of Administration
`
`699
`
`Dosing Infants and Children
`Practice Problem 702
`
`700
`
`Dosing the Elderly
`Practice Problems
`
`702
`703
`
`704
`Clinical Example
`705
`Dosing the Obese Patients
`Pharmacokinetics of Drug Interactions
`Inhibition of Drug Metabolism 710
`
`706
`
`8
`
`

`

`X
`
`CONTENTS
`
`712
`
`Inhibition of Monoamine Oxidase (MAO)
`Induction of Drug Metabolism 712
`Inhibition of Drug Absorption
`712
`Inhibition of Biliary Excretion
`713
`Altered Renal Reabsorption Due to Changing
`Urinary pH 713
`Practical Focus
`713
`
`713
`Effect of Food on Drug Disposition
`Adverse Viral Drug Interactions
`714
`Population Pharmacokinetics
`714
`Clinical Example
`722
`Regional Pharmacokinetics
`Chapter Summary
`725
`Learning Questions
`725
`Answers
`728
`References
`731
`
`724
`
`Bibliography
`
`732
`
`23.
`
`Application of Pharmacokinetics to
`Specific Populations: Geriatric, Obese,
`and Pediatric Patients
`735
`Specific and Special Populations
`735
`Module 1: Application of Pharmacokinetics t0 the
`Geriatric Patients
`736
`
`749
`Summary
`Learning Questions
`Answers
`750
`References
`751
`
`749
`
`754
`Further Reading
`Module II: Application of Pharmacokinetics to the
`Obese Patients
`754
`
`760
`Summary
`Learning Questions
`Answers
`761
`References
`761
`
`760
`
`Module III: Application of Pharmacokinetics to the
`Pediatric Patients
`763
`
`769
`Summary
`Learning Questions
`Answers
`771
`References
`773
`
`770
`
`General Approaches for Dose Adjustment in Renal
`Disease
`777
`Measurement of Glomerular Filtration Rate
`Serum Creatinine Concentration and
`Creatinine Clearance
`780
`Practice Problems
`782
`
`779
`
`Dose Adjustment for Uremic Patients
`Practice Problem 787
`Practice Problem 792
`Practice Problems
`793
`Practice Problem 795
`
`785
`
`Extracorporeal Removal of Drugs
`Practice Problem 799
`
`796
`
`800
`Clinical Examples
`Effect of Hepatic Disease
`on Pharmacokinetics
`Practice Problem 805
`
`803
`
`809
`810
`
`Chapter Summary
`Learning Questions
`Answers
`811
`References
`813
`
`Bibliography
`
`815
`
`25. Empirical Models, Mechanistic
`Models, Statistical Moments, and
`
`Noncompartmental Analysis
`Empirical Models
`818
`Mechanistic Models
`822
`
`817
`
`835
`Noncompartmental Analysis
`Comparison of Different Approaches
`Selection of Pharmacokinetic Models
`
`842
`844
`
`845
`845
`
`Chapter Summary
`Learning Questions
`Answers
`846
`References
`847
`
`Bibliography
`
`848
`
`Appendix A Applications of
`Software Packages in
`Pharmacokinetics
`851
`
`24. Dose Adjustment in Renal and Hepatic
`Disease
`775
`775
`Renal Impairment
`Pharmacokinetic Considerations
`
`775
`
`Appendix B Glossary 875
`
`Index
`
`879
`
`9
`
`

`

`
`
`Multiple-Dosage Regimens
`
`Rodney C. Siwale and Shabnam N. Sani
`
`Chapter Objectives
`
`b
`
`b
`
`Define the index for measuring
`drug accumulation.
`
`Define drug accumulation and
`drug accumulation rm.
`
`Explain the principle of
`superposition and its
`assumptions in multiple-dose
`regimens.
`
`Calculate the steady-state Cmax
`mill
`and C
`after multiple iv bolus
`dosing ofdrugs.
`
`Calculate k and VD of
`aminoglycosides in multiple
`dose regimens.
`
`Adjust the steady—state Cmax and
`Cmin in the event the last dose
`is given too early, too late, or
`
`totally missed following multiple
`lV dosing.
`
`Earlier chapters of this book discussed single-dose drug and
`constant—rate drug administration. By far though, most drugs are
`given in several doses, for example, multiple doses to 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 eflective 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
`minimum toxic concentration or MTC) to achieve optimal clinical
`effectiveness. These drugs may include antibacterials, cardioton—
`ics, 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. For drugs that have a narrow therapeutic range
`(eg, digoxin and phenytoin), there is a need to define the therapeu—
`tic minimum and maximum nontoxic plasma concentrations
`(MEC and MTC, respectively). In calculating a multiple-dose regi-
`men,
`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
`developing a dosage regimen: (1) the size of the drug dose and
`(2) r, 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 knowledge of the size of the dose
`and dosage interval (r), the complete plasma level—time curve or
`
`205
`
`10
`
`10
`
`

`

`206
`
`Chapter 9
`
`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 assumes that 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 = ( I: Cp a't) for the first dose is
`equal to the steady—state area between doses, that is,
`(I:2 C], dt) as shown in Fig. 9-1.
`I The principle of superposition allows the pharma-
`cokineticist to project the plasma drug concentration—
`time curve of a drug after multiple consecutive doses
`based on the plasma drug concentration—time curve
`obtained after a single dose. The basic assumptions are
`(1) that the drug is eliminated by first-order kinetics
`and (2) that the pharmacokinetics of the drug after a
`single dose (first dose) are not altered after taking mul-
`tiple doses.
`The plasma drug concentrations after multiple
`doses may be predicted from the plasma drug con-
`centrations obtained after a single dose. In Table 9-1,
`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 con-
`centrations 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
`
`Blood
`
`level —q
`
`l
`Doses
`
`l
`
`l
`
`l
`
`l
`
`l
`
`’2
`l
`
`Simulated data showing blood levels after
`FIGURE 9-1
`administration of multiple doses and accumulation of blood
`levels when equal doses are given at equal time intervals.
`
`11
`
`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.
`There are situations, however,
`
`in which the
`
`In these
`superposition principle does not apply.
`cases, the pharmacokinetics of the drug change after
`multiple dosing due to various factors,
`including
`changing pathophysiology in the patient, saturation
`
`of a drug carrier system, enzyme induction, and
`enzyme inhibition. Drugs that follow nonlinear phar-
`macokinetics (see Chapter 10) 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 dosage interval, as is the case with many mul-
`tiple-dose regimens, the amount of drug in the body
`will increase and then plateau to a mean plasma level
`higher than the peak Cp obtained from the initial
`dose (Figs. 9-1 and 9—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 dose is given after
`a time interval longer than the time required to elimi-
`nate the previous dose, drug will not accumulate
`(see Table 9-1).
`
`As repetitive 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 C23, and C32,". Once
`steady state is obtained, Cg“ and C3," are constant
`and remain unchanged from dose to dose. In addi-
`tion, the AUC between (
`:2 Cp dt) is constant during
`a dosing interval at steady1 state (see Fig. 9-1). The
`no
`C3“ is important in determining drug safety. The
`should always remain below the MTC. The 0’“
`lelX
`max
`
`11
`
`

`

`Multiple-Dosage Regimens
`
`207
`
`TABLE 9-1 Predicted Plasma Drug Concentrations for Multiple-Dose Regimen Using the
`Superposition Principle"
`
`N31151:”
`1
`
`Time (h)
`0
`
`" Plasma Drug Ctmcent'ratio‘n (IQ/ml.)
`Dose1
`Dosez
`Dose 3’
`F
`Dose4
`Doses -
`Doses
`Total
`0
`0
`
`1
`
`2
`
`3
`
`4
`
`5
`
`6
`
`7
`
`8
`
`9
`
`10
`
`11
`
`12
`
`13
`
`14
`
`21.0
`
`22.3
`
`19.8
`
`16.9
`
`14.3
`
`12.0
`
`10.1
`
`8.50
`
`7.15
`
`6.01
`
`5.06
`
`4.25
`
`3.53
`
`3.01
`
`0
`
`21.0
`
`22.3
`
`19.8
`
`16.9
`
`14.3
`
`12.0
`
`10.1
`
`8.50
`
`7.15
`
`6.01
`
`2
`
`3
`
`4
`
`0
`
`21.0
`
`22.3
`
`19.8
`
`16.9
`
`14.3
`
`12.0
`
`10.1
`
`0
`
`21.0
`
`22.3
`
`19.8
`
`21.0
`
`22.3
`
`19.8
`
`16.9
`
`35.3
`
`34.3
`
`29.9
`
`25.4
`
`42.5
`
`40.3
`
`35.0
`
`29.7
`
`46.0
`
`43.3
`
`37.5
`
`5
`
`5
`
`15
`
`16
`
`17
`
`18
`
`19
`
`20
`
`21
`
`22
`
`23
`
`24
`
`2.53
`
`2.13
`
`1.79
`
`1.51
`
`1.27
`
`1.07
`
`0.90
`
`0.75
`
`0.63
`
`0.53
`
`5.05
`
`4.25
`
`3.58
`
`3.01
`
`2.53
`
`2.13
`
`1.79
`
`1.51
`
`1 .27
`
`1.07
`
`8.50
`
`7.15
`
`6.01
`
`5.06
`
`4.25
`
`3.58
`
`3.01
`
`2.53
`
`2.13
`
`15.9
`
`14.3
`
`12.0
`
`10.1
`
`3.50
`
`7.15
`
`6.01
`
`5.06
`
`4.25
`
`0
`
`21.0
`
`22.3
`
`19.8
`
`16.9
`
`14.3
`
`12.0
`
`10.1
`
`8.50
`
`0
`
`21.0
`
`22.3
`
`19.8
`
`16.9
`
`31.8
`
`47.8
`
`44.8
`
`38.8
`
`32.9
`
`48.7
`
`45.6
`
`39.4
`
`33.4
`
`"A single oral dose of 350 mg was given and the plasma drug concentrations were measured for 0—24 h. The same plasma drug concentrations are
`assumed to occur after doses 2—6. The total plasma drug concentration is the sum of the plasma drug concentrations due to each dose. For this
`example, VD = 10 L, rm = 4 h, and k, = 1.5 h-‘.The drug is 100% bioavailable and follows the pharmacokinetics ofa one-compartment open model.
`
`12
`
`12
`
`

`

`208
`
`Chapter 9
`
`is also a good indication of drug accumulation. If a
`drug produces the same CE“ at steady state, com-
`pared with the (C—l)max after the first dose, then
`max
`thereis no drug accumulation. If C‘”
`is much larger
`max, then there is significant accumulation
`than (CH)
`during the multiple—dose regimen. Accumulation is
`affected by the elimination half-life of the drug and
`the dosing interval. The index for measuring drug
`accumulation R is
`
`R =
`
`(C°°)
`
`max
`(Cn=l )max
`
`(9 1)
`
`Substituting for Cmx after the first dose and at steady
`state yields
`
`R =
`
`D0/VD[1/(l —e"”)]
`DOIVD
`
`
`(9.2)
`
`Equation 9.2 shows that drug accumulation mea—
`sured with the R index depends on the elimination
`constant and the dosing interval and is independent
`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 inde-
`pendent of the size of the dose, the length of the
`dosing interval, and the number of doses. For exam-
`ple, if the dose or dosage interval of the drug is
`altered as shown in Fig. 9-2, the time required for the
`drug to reach steady state is the same, but the final
`steady-state plasma level changes proportionately.
`
`
`
`0
`
`20
`
`N>O~8§8880c: Amountoidruginbody(mg)
`
`40
`
`60
`Time (hours)
`
`80
`
`l 00
`
`Plasma
`
`u 600 mg every 24 h
`
`levelLug/ml)
`
`Time (hours)
`
`Simulated plasma drug concentration—time
`FIGURE 9-3
`curves after N infusion and oral multiple doses for a drug with an
`elimination half-life of 4 hours and apparent VD of 10 L IV infusion
`given at a rate of 25 mg/h, oral multiple doses are 200 mg every
`8 hours, 300 mg every 12 hours, and 600 mg every 24 hours.
`
`Furthermore, if the drug is given at the same
`dosing rate but as an infusion (eg, 25 mg/h), the aver—
`age plasma drug concentrations will (C°“) be the
`same but the fluctuations between CL“ and C31“ will
`vary (Fig. 9-3). An average steady--state plasma drug
`concentration is obtained by dividing the area under
`the curve (AUC) for a dosing period (ie, I? Cp dt) by
`the dosing interval 1', 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 t1,2-t“2 [1+3.310g
`
` 4‘)
`
`k
`ka
`
`(9.3)
`
`FIGU RE 9-2 Amount ofdrug in the body as a function of
`time. Equal doses of drug were given every 6 hours (upper curve)
`and every 8 hours (lower curve). ka and k remain constant.
`
`For IV administration, ka is very rapid (approaches no);
`k is very small in comparison to ka and can be omitted
`
`13
`
`13
`
`

`

`in the denominator of Equation 9.3. Thus, Equation 9.3
`reduces to
`
`Accumulationt1,2 =1.‘1,2[1+3.3log%]
`
`(9.4)
`
`Since ka/ka = 1 and log 1 = 0, the accumulation rm of
`a drug administered intravenously is the elimination
`rm of the drug. From this relationship, the time to
`reach 50% steady—state drug concentrations is depen-
`dent only on the elimination t1 ,2 and not on the dose
`or dosage interval.
`As shown in Equation 9.4, the accumulation
`rm is directly proportional to the elimination ’1/2-
`Table 9—2 gives the accumulation rm of drugs with
`various elimination half-lives given by multiple
`oral doses (see Table 9-2).
`
`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 9-3). It should be noted from Table 9-3 that at
`
`a constant dose size, the shorter the dosage 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 dependent on the elimination half—life
`
`Multiple—Dosage Regimens
`
`209
`
`of the drug and the dosage interval I (see Table 9-3).
`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
`
`reach steady state is 6.6t1 ,2/1', as calculated in the far
`right column of Table 9—3. As discussed in Chapter 6,
`Table 6-1, it takes 4.32 half—lives to reach 95% of
`
`steady state.
`
`
`CLINICAL EXAMPLE
`
`Paroxetine (Prozac) is an antidepressant drug with a
`long elimination half-life of 21 hours. Paroxetine is
`well absorbed after oral administration and has a tmax
`of about 5 hours,
`longer than most drugs. Slow
`elimination may cause the plasma curve to peak
`slowly. The tmax is affected by k and ka, as discussed
`in Chapter 8. The Cmax 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
`steady-state level in multiple dosing that does not
`“underdose” or overdose the patient. The pharmacist
`should advise the patient to follow the prescribed
`dosing interval and dose as accurately as possible.
`Taking a dose too early or too late contributes to
`
`TABLE 9-2 Effect of Elimination Half-Life and Absorption Rate Constant on Accumulation
`Half-Life after Oral Administrationa
`
`Elimination
`Half-life (h)
`
`Elimination Rate
`constant (11h)
`
`Absorption Rate
`Constant (1/h)
`
`Accumulation
`Half-life (h)
`
`4
`
`8
`
`1 2
`
`24
`
`4
`
`8
`
`1 2
`
`24
`
`0.1 73
`
`0.0866
`
`0.0578
`
`0.0289
`
`0.1 73
`
`0.0866
`
`0.0578
`
`0.0289
`
`1 .50
`
`1 .50
`
`1 .50
`
`1 .50
`
`1 .00
`
`1 .00
`
`1 .00
`
`1 .00
`
`4.70
`
`8.67
`
`1 2.8
`
`24.7
`
`5.09
`
`8.99
`
`1 3.0
`
`25.0
`
`aAccumulation halfrlife is calculated by Equation 8.3, and is the half-time for accumulation of the drug to 90% of the steady-state plasma drug
`concentration.
`
`14
`
`

`

`210
`
`Chapter 9
`
`TABLE 9-3
`
`Interrelation of