& PHARACUKINETIqu
`
`
`
`ANDREW YU
`
`NEUROCRINE1034
`
`, SIXTH ED'TID‘N
`
`LE0N SHARGEL
`
`SUSANNA wu..pflNG
`
`1
`
`NEUROCRINE 1034
`
`

`

`Applied
`Bioph‘armaceutics 8:
`Pharmacokinetics
`
`Sixth Edition
`
`Leon Shargel, PHD, RPh
`Applied Biopharmaceutics, LLC
`Raleigh, North Carolina
`Afliliate 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
`Medical College 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 Afliliation: CDER, FDA“
`Silver Spring, Maryland
`
`*The content of this book represents the personal views of the authors
`and not that of the FDA.
`
`% Medical
`
`New York Chicago San Francisco Lisbon London Madrid Mexico City
`Milan New Delhi 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 base or retrieval 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
`
`171615141312
`
`ISBN 978-0-07-160393-5
`MHID O-O7-160393-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.
`The production manager was Harleen Chopra, 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.
`
`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)
`1. Biopharmaceutics.
`2. Pharmacokinetics.
`1. Yu, Andrew B. C., 1945-
`
`IV. Title: Applied biopharmaceutics and pharmacokinetics.
`111. Title.
`II. Wu—Pong, Susanna.
`[DNLM:
`1. Biopharrnaceutics.
`2. Models, Chemical.
`3. Pharmacokinetics. QV 38]
`RM301.4.SS2 2012
`615’.7—dc23
`
`01 1020446
`
`McGraw-Hill books are available at special quantity discounts to use as premiums and sales promotions, or for use in cor—
`porate training programs. To contact a representative please e-mail us at bulksales@mcgraw~hill.com.
`
`3
`
`

`

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

`

`viii
`
`CONTENTS
`
`Loading Dose Plus IV Infusion—One-
`Compartment Model
`96
`Practice Problems
`98
`
`Estimation of Drug Clearance and V” from
`Infusion Data
`100
`
`Intravenous Infusion of Two-Compartment
`Model Drugs
`100
`Practical Focus
`102
`
`Chapter Summary
`Learning Questions
`Reference
`106
`
`104
`104
`
`Bibliography
`
`106
`
`Drug Elimination and Clearance
`
`107
`
`107
`
`Drug Elimination
`The Kidney
`108
`Renal Drug Excretion
`Clinical Application
`Practice Problems
`
`1 11
`1 14
`114
`
`1 14
`Drug Clearance
`116
`Clearance Models
`1 18
`Renal Clearance
`Determination of Renal Clearance
`
`121
`
`Relationship of Clearance to Elimination
`Half—Life and Volume of Distribution
`
`125
`
`Chapter Summary
`Learning Questions
`References
`129
`
`127
`127
`
`Bibliography
`
`129
`
`Dosage Regimen Schedules
`Practice Problems
`171
`
`169
`
`Chapter Summary
`Learning Questions
`References
`175
`
`173
`174
`
`Bibliography
`
`175
`
`Nonlinear Pharmacokinetics
`
`177
`
`Saturable Enzymatic Elimination Processes
`Practice Problem 180
`
`179
`
`Drug Elimination by Capacity-Limited
`Phannacokinetics: One-Compartment
`Model, IV Bolus Injection
`181
`Clinical Focus
`19]
`
`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
`
`196
`Drug—Protein Binding
`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
`
`131
`Pharmacokinetics of Drug Absorption
`Significance of Absorption Rate Constants
`Zero~0rder Absorption Model
`133
`Clinical Application— Transderrnal
`Drug Delivery
`134
`First-Order Absorption Model
`Practice Problem 142
`
`134
`
`133
`
`Chapter Summary
`Learning Questions
`References
`150
`
`149
`149
`
`Bibliography
`
`151
`
`Multiple-Dosage Regimens
`
`153
`
`153
`Drug Accumulation
`157
`Clinical Example
`Repetitive Intravenous Injections
`Intermittent Intravenous Infusion
`
`158
`163
`
`Estimation of k and VD of Aminoglycosides
`in Clinical Situations
`165
`
`Multiple-Oral-Dose Regimen
`Loading Dose
`168
`
`166
`
`Physiologic Factors of Distribution
`Clinical Focus
`213
`
`205
`
`Apparent Volume Distribution
`Practice Problem 216
`
`213
`
`Protein Binding of Drugs
`Clinical Examples
`221
`Effect of Protein Binding on the Apparent
`Volume of Distribution
`222
`
`219
`
`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
`
`247
`
`Bibliography
`
`251
`
`5
`
`

`

` Drug Elimination and Hepatic
`
`(Durance
`
`253
`
`isle of Drug Administration and Extrahepatic
`Drug Metabolism 253
`Practical Focus
`255
`
`255
`Hepatic Clearance
`257
`Enzyme Kinetics
`261
`(Danica! Example
`Practice Problem 263
`
`Anatomy and Physiology of the Liver
`Hepatic Enzymes Involved in the
`Biotransfonnation of Drugs
`267
`Drug Biotransformation Reactions
`Pathways of Drug Biotransformation
`First-Pass Effects
`282
`
`269
`270
`
`265
`
`Hepatic Clearance of a Protein-Bound Drug:
`Restrictive and Nonrestrictive Clearance
`
`287
`from Binding
`Effect of Changing Intrinsic Clearance and/0r
`Blood Flow on Hepatic Extraction and
`Elimination Half—Life after IV and Oral
`
`288
`Dosing
`289
`Biliary Excretion of Drugs
`Role of Transporters in Hepatic Clearance
`and Bioavailability
`292
`Chapter Summary
`293
`Learnng 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 lsozymes
`310
`Genetic Polymorphism in Drug Transport:
`MDRl (P—Glycoprotein) and Multidrug
`Resistance
`31]
`
`312
`
`Genetic Polymorphism in Drug Targets
`Relationship of Pharmacokinetics/
`Pharmacodynamics and Pharmacogenetics/
`Phannacogenomics
`313
`Clinical Example
`315
`Summary
`316
`Glossary
`316
`317
`Abbreviations
`References
`317
`
`Bibliography
`
`318
`
`CONTENTS
`
`ix
`
`13.
`
`Physiologic Factors Related to Drug
`Absorption 321
`
`Drug Absorption and Design of a Drug
`Product
`32]
`
`321
`Route of Drug Administration
`Nature of Cell Membranes
`324
`
`Passage of Drugs Across Cell Membranes
`Ora] Drug Absorption During Drug Product
`Development
`333
`Drug Interactions in the Gastrointestinal
`Tract
`334
`
`326
`
`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
`
`351
`
`Chapter Summary
`Learning Questions
`References
`357
`
`355
`356
`
`Bibliography
`
`359
`
`14.
`
`Biopharmaceutic Considerations in
`Drug Product Design and In Vitro
`Drug Product Performance
`361
`
`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
`
`363
`
`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
`
`376
`
`379
`Testing
`Performance of Drug Products: In Vitro—In Viva
`Correlation
`380
`
`Dissolution Profile Comparisons
`Drug Product Stability
`386
`Considerations in the Design of a Drug
`Product
`387
`
`386
`
`389
`
`Drug Product Considerations
`Clinical Example
`394
`Chapter Summary
`398
`Learning Questions
`399
`References
`399
`
`Bibliography
`
`401
`
`6
`
`

`

`X
`
`CONTENTS
`
`15.
`
`Drug Product Performance,
`In Vivo: Bioavailability and
`
`Bioequivalence
`
`403
`
`403
`Drug Product Performance
`Purpose of Bioavailability Studies
`Relative and Absolute Availability
`Practice Problem 407
`
`405
`406
`
`Methods for Assessing Bioavailability
`Bioequivalence Studies
`413
`Design and Evaluation of Bioequivalence
`Studies
`414
`
`407
`
`Study Designs 4l7
`Crossover Study Designs
`Clinical Example
`422
`Evaluation of the Data
`
`423
`
`418
`
`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
`Genetic Substitution
`437
`
`440
`Glossary
`Chapter Summary
`Learning Questions
`References
`448
`
`Bibliography
`
`449
`
`443
`443
`
`16.
`
`Impact of Drug Product Quality
`and Biopharmaceutics on Clinical
`Efficacy
`451
`
`Risks From Medicines
`
`451
`
`Drug Product Quality and Drug Product
`Performance
`452
`
`453
`Pharmaceutical Development
`Excipient Affect on Drug Product
`Performance
`455
`Practical Focus
`456
`
`457
`
`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
`
`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
`
`480
`
`Evaluation of In Vivo Bioavailability Data
`Chapter Summary
`501
`Learning Questions
`501
`References
`502
`
`497
`
`499
`
`Bibliography
`
`503
`
`18.
`
`Targeted Drug Delivery Systems and
`Biotechnological Products
`505
`
`514
`
`506
`Biotechnology
`Drug Carriers and Targeting
`Targeted Drug Delivery
`519
`Pharmacokinetics of Biopharrnaceuticals
`Bioequivalence and Comparability of
`Biotechnology-Derived Drug Products
`Chapter Summary
`523
`Learning Questions
`524
`References
`524
`
`Bibliography
`
`525
`
`521
`
`522
`
`19.
`
`Relationship Between
`Pharmacokinetics and
`
`Pharmacodynamics
`
`527
`
`Pharmacodynamics and Pharmacokinetics
`Relationship of Dose to Pharmacologic
`Effect
`534
`
`527
`
`Relationship Between Dose and Duration of
`Activity (rm), Single IV Bolus Injection
`Practice Problem 536
`Effect of Both Dose and Elimination Half-Life
`
`536
`
`537
`on the Duration of Activity
`Effect of Elimination Half-Life on Duration
`
`537
`of Activity
`539
`Clinical Examples
`Rate of Drug Absorption and Pharmacodynamic
`Response
`541
`Drug Tolerance and Physical Dependency
`Hypersensitivity and Adverse Response
`
`542
`543
`
`7
`
`

`

`CONTENTS
`
`Xi
`
`General Approaches for Dose Adjustment
`in Renal Disease
`618
`62]
`Measurement of Glomerular Filtration Rate
`Serum Creatinine Concentration and Creatinine
`Clearance
`622
`Practice Problems
`
`624
`
`Dose Adjustment for Uremic Patients
`Extracorporeal Removal of Drugs
`638
`Clinical Examples
`642
`Effect of Hepatic Disease on
`Pharmacokinetics
`645
`
`627
`
`Chapter Summary
`Learning Questions
`References
`653
`
`651
`652
`
`Bibliography
`
`655
`
`22.
`
`Physiologic Pharmacokinetic Models,
`Mean Residence Time, and Statistical
`
`Moment Theory 657
`
`Physiologic Pharmacokinetic Models
`Mean Residence Time
`670
`
`658
`
`674
`Statistical Moment Theory
`Selection of Pharmacokinetic Models
`
`687
`
`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
`
`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
`
`566
`
`578
`to Oral Dosing
`Determination of Dose
`Practice Problems
`580
`
`579
`
`Effect of Changing Dose and Dosing
`Interval on Cfm, Cumin, and C";
`Determination of Frequency of Drug
`Administration
`581
`
`580
`
`Determination of Both Dose and Dosage
`Interval
`582
`Determination of Route of Administration
`
`Chapter Summary
`Learning Questions
`References
`690
`
`689
`689
`
`Bibliography
`
`691
`
`Appendix A Statistics
`
`693
`
`583
`
`584
`
`595
`
`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
`Human and Animal
`
`Research 761
`
`Appendix E
`
`Popular Drugs and
`Pharmacokinetic
`
`Parameters
`
`767
`
`588
`590
`
`Dosing of Drugs in Infants and Children
`Dosing of Drugs in the Elderly
`585
`Dosing of Drugs in 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
`
`21.
`
`Dose Adjustment in Renal and Hepatic
`Disease
`617
`
`Index
`
`773
`
`617
`Renal Impairment
`Pharmacokinetic Considerations
`
`617
`
`8
`
`

`

`
`
`Multiple-Dosage Regimens
`
`Chapter Objectives
`
`i
`
`D
`
`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
`and Cmin after multiple IV bolus
`dosing of drugs.
`
`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
`IV dosing.
`
`Earlier chapters of this book discussed single-dose drug adminis-
`tration. Generally, drugs are given in 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 efiective 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 may include 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 drugs that 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) 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
`levelrtime curve generated by singlevdose drug studies. With these
`pharmacokinetic parameters and knowledge of the size of the dose
`and dosage interval (T), 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 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 — l)th dose.
`In addition, the AUC-— (I:Cpdt) for the first dose1s
`eual to the steady--state area between doses,
`ie,
`( Cpdt) as shownin Fig 8-1
`' 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 obtained after a single dose. The basic assump—
`tions are: (1) that the drug is eliminated by first-order
`kinetics and (2) that the pharrnacokinetics 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— l,
`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
`
`Blood
`
`level
`
`l
`
`’l
`
`l
`
`l
`
`l
`
`l‘
`
`t
`
`Simulated data showing blood levels after
`FIGURE 8'1
`administration of multiple doses and accumulation of blood
`levels when equal doses are given at equal time intervals.
`
`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 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 dosage interval, 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 Cp obtained from the initial
`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 dose is given after
`
`longer than the time required to
`a time interval
`eliminate the previous dose, drug will not accumu-
`late (see Table 8—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 Cmax and C3,. Once
`steady state is obtained, Cmx and CE“ are constant
`and remain unchanged from dose to dose In addi-
`tion the AUC between (I: Cpair)
`is constant during
`a dosing interval at steady state (see Fig. 8-1). The
`CS?“ is important in determining drug safety. The
`CS“ should always remain below the minimum
`
`10
`
`10
`
`

`

`Multiple-Dosage Regimens
`
`155
`
`TABLE 8-1 Predicted Plasma Drug Concentrations for Multiple-Dose Regimen Using the
`Superposition Principle'l
`
`
`
`1
`
`3
`I
`
`'4
`
`21.0
`
`_19.8
`
`I
`
`"169
`
`7 0
`
`5
`6
`7 V
`
`;
`
`8
`9
`
`10
`
`1 1
`12
`
`14.3
`12.0
`10.1
`
`'
`
`8.50 'i
`7.15
`
`H 6.01 V
`
`5.06
`4.25
`
`21.0
`223
`19.8
`
`16.9-
`14.3
`
`12.0
`
`10.1
`8-50
`
`3
`
`4
`
`,
`
`
`I U
`
`_
`
`_
`
`I
`
`I
`
`‘
`
`1
`
`:2
`
`-
`
`7
`
`o
`21.0
`
`22.3
`
`19.8
`16.9
`
`" “
`
`5:7-
`
`‘
`
`'
`
`3‘
`
`7
`
`_
`
`-
`
`I
`
`_
`
`
`‘0
`
`21.0
`
`21.0,
`
`19.8
`
`16.95:
`
`35.3
`34.3 .:
`29.9
`
`25.4 I
`42.5
`
`40.3:
`
`35.0
`29-7
`
`46.0
`
`3.58
`
`3.01
`
`7.15
`
`14.3
`
`6.01
`
`'
`
`.120
`
`13
`
`14
`
`15
`'16
`17
`
`
`
`18
`
`
`
`19
`
`20
`21
`
`5
`
`_
`
`6
`
`22.3
`
`19.8
`5 16.9
`14.3
`
`12.0
`
`10.1
`
`8.50
`7.15
`
`-
`
`.
`
`0
`21.0
`
`223
`
`19.8
`
`16.9
`14.3
`
`_,
`
`0
`- 21.0
`
`
`.
`
`43.3
`
`37.5
`31.8
`47.8
`
`44.8
`
`38.8
`
`32.9
`48.7
`
`'_
`
`I.
`
`45.6 2
`122.3
`12.0
`6.01
`f 3.01
`:151
`2222
`39.4 '
`19.8
`10.1
`'5.06
`2.53
`1.27
`23
`33.4;f
`{If-16.9
`8.50
`1
`"24.25
`.
`2.13
`1.07,‘
`24
`“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, 11,2 = 4 h, and ka = 1.5 h-‘.The drug is 100% bioavailable and follows the pharmacokinetics of a one-compartment open model.
`
`5.06 2
`4.25
`3.58
`
`3.01
`
`2.53
`
`_
`
`2.13.
`1.791 1
`
`10.1
`8.50'
`7.15
`
`l
`
`6.01
`
`7
`
`7
`
`5.06
`
`'425
`3.58
`
`'
`
`‘
`
`_
`2.53
`7 2.13 75..
`1.79 V
`
`7
`
`1.51"
`
`127
`
`
`
`11
`
`11
`
`

`

`156
`
`Chapter 8
`
`is also a good indica-
`toxic concentration. The C3,,
`tion of drug accumulation. If a drug produces the
`same C32“ at steady state, compared with the (Cnfl)
`max after the first dose, then there is no drug accumu—
`lation. If C3“ is much larger than (C =1)mx, then
`there is significant accumulation during the multiple-
`dose regimen. Accumulation is affected by the elimi-
`nation half—life of the drug and the dosing interval.
`The index for measuring drug accumulation R is
`
`R — (C°°)mx
`— (anl )max
`
`(8.1)
`
`Substituting for Cmax after the first dose and at steady
`state yields
`
`R
`
`2 DO/VDU/(l - e'h )1
`00er
`
`
`(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 independent of the size of the dose, the length
`of the dosing interval, and the number of doses. For
`example, if the dose or dosage interval of the drug is
`altered as shown in Fig. 8-2, the time required for the
`drug to reach steady state is the same, but the final
`
`§§
`
`a.8
`
`
`
`Amountofdruginbody(mg)
`
`too88 O
`
`O
`
`20
`
`40
`
`60
`Time (hours)
`
`80
`
`100
`
`FIGURE 8-2 Amount of drug 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.
`
`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 (C3,) will be the same
`but the fluctuations between Cg“ and Cgin 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, ItZder)
`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 t],2 = r1,2 (I + 3.3 log k k: k]
`
`8
`
`
`
`(8.3)
`
`. 600 mg every 24 h
`
`(A)C
`
`N0:
`
`Plasma
`
`level(ug/mL) MO
`
`Time (hours)
`
`FIGURE 8'3 Simulated plasma drug concentration—time
`curves after IV infusion and oral multiple doses for a drug with
`an elimination half-life of4 hours and apparent VD 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.
`
`12
`
`12
`
`

`

`For IV administration, k3 is very rapid (approaches co);
`k is very small in comparison to ka and can be omit-
`ted in the denominator of Equation 8.3. Thus,
`Equation 8.3 reduces to
`
`Accumulation ’1/2 = [”2 [1+ 3.3 log12—3]
`
`(8.4)
`
`Because ka/ka = l and log 1 = 0, the accumulation rm,
`of a drug administered intravenously is the elimina-
`tion 11,2 of the drug. From this relationship, the time
`to reach 50% steady-state drug concentrations is
`
`dependent on the elimination t],2 and not on the dose
`or dosage interval.
`
`As shown in Equation 8.4, the accumulation 11,2
`is directly proportional to the elimination [1/2- Table
`8-2 gives the accumulation rm 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 dose size, 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 dependent on the elimination half-life
`of the drug and the dosage interval 1 (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
`
`reach steady state is 6.6 t1,2 /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
`
`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 [max
`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 7. The me 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 Administrationa
`
`
`
`1.50
`
`_
`
`,
`
`
`
`
`
`
`0.0239
`
`1.00
`
`25.0
`
`”Accumulation half-life 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.
`
`13
`
`
`8,6,7.
`
`
`
`
`
`24.7
`
`
`
`.559
`' 8.99
`
`
`
`13
`
`

`

`1 58
`
`Chapter 8
`
`TABLE 8-3
`
`Interrelation of Elimination Half-Life, Dosage Interval, Maximum Plasma
`Concentration, and Time to Reach Steady-State Plasma Concentration"
`
`
`
`
`
`aA single dose of 1000 mg of three hypothetical drugs with various elimination half-lives but equal volumes of distribution (VD = 10 L) were given by
`multiple IV doses at various dosing intervals. All time values are in hours; C“max
`= maximum steady—state concentration; ( C; ) = average steady-state
`plasma concentration; the maximum plasma drug concentration after the first dose of the drug is (anl)m, = 100 ug/mL.
`bTime to reach 99% of steady-state plasma concentration.
`cSince the dosage interval, 1, is very large compared to the elimination half—life, no accumulation of drug occurs.
`
`steady-state level in multiple dosing that does not
`“under dose" 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
`variation. Individual variation in metabolism rate
`
`can also cause variable blood levels, as discussed
`
`later in Chapter 12.
`
`REPETITIVE INTRAVENOUS
`
`INJECTIONS
`
`The maximum amount of 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.
`
`DB = Doe-k1
`
`(8.5)
`
`If 1: is equal to the dosage interval (ie, the time
`between the first dose and the next dose), then the
`
`amount of drug remaining in the body after several
`hours can be determined with
`
`DB = Doe-hr
`
`(8.6)
`
`The fraction (1‘) of the dose remaining in the
`body is related to the elimination constant (k) and the
`dosage interval (1:) as follows:
`
`-2; e-k‘r
`0
`
`f
`
`(8-7)
`
`With any given dose, f depends on k and I. If 1: is
`large, f will be smaller because DB (the amount of
`drug remaining in the body) is smaller.
`
`14
`
`14
`
`

`

`Multiple—Dosage Regimens
`
`159
`
`TABLE 8-4 Fraction of the Dose in'the Body
`before and after Intravenous Injections of a
`1909-?19 Dose“
`
`7'
`H
`'
`
` 2
`
`I
`
`1000
`1250
`
`1
`
`_
`
`0
`250
`
`3
`
`4
`
`5
`7
`
`m
`
`”f: 0‘25-
`
`312
`
`328
`
`333
`333
`
`333
`
`1312
`
`1328
`
`1333
`1333
`
`1333
`
`Dmax - Dmin = D0
`
`(8.8)
`
`In th'5 example,
`
`1333 - 333 = 1000 mg
`
`0:” can also be calculated directly by the rela-
`tionship
`
`I; = 0°
`1‘ f
`
`(39)
`
`Substituting known data, we obtain
`
`... _ 1000 _
`max ’1_0.25 “1333'“9
`
`Then,from Equation 8.8,
`
`Dzin =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 8.1 LP is the fraction of dose absorbed.
`For an IV injection, F is equal to 1.0.
`
`a _fD_o
`3"
`k1:
`
`D°° _ FD01.44tV2
`aV——
`T
`
`(8 10
`'
`
`)
`
`(8.11)
`
`15
`
`1 . A patient receives 1000 mg every 6 hours by
`repetitive IV injection of an antibiotic with an
`elimination half—life of 3 hours.Assume the drug
`5 is distributed according to a one—compartment
`model and the volume of distribution is 20 L.
`a. Find the maximum and minimum amount of
`
`drug in the body.
`.
`.
`.
`.
`b. Determine the maxrmum and minimum
`
`plasma concentration of the drug.
`
`a. The fraction of drug remaining in the body is
`estimated by Equation 8.7.The concentration
`
`of the drug declines to one-half after 3 hours
`(t1,2 = 3 h), after which the amount of drug will
`again