BASIC PHARMACOKINETICS AND PHARMACODYNAMICS

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BASIC PHARMACOKINETICSAND PHARMACODYNAMICSAn Integrated Textbook andComputer SimulationsSARA ROSENBAUM WILEYA lOHN WILEY & SONS, INC., PUBLICATION

CONTENTSPreface1xviiIntroduction to Pharmacokinetics and Pharmacodynamics11.1 Introduction: Drugs and Doses, 11.2 Introduction to Pharmacodynamics, 31.2.1 Drug Effects at the Site of Action, 31.2.2 Agonists, Antagonists, and Concentration-ResponseRelationships, 61.3 Introduction to Pharmacokinetics, 91.3.1 Plasma Concentration of Drugs, 101.3.2 Processes in Pharmacokinetics, 111.4 Dose-Response Relationships, l31.5 Therapeutic Range, 141.5.1 Determination of the Therapeutic Range, 161.6 Summary, 182Passage of Drugs Through Membranes2.12.22.32.420Introduction, 20Structure and Properties of Membranes, 21Passive Diffusion, 222.3.1 Transcellular Passive Diffusion, 242.3.2 Paracellular Passive Diffusion, 26Carrier-Mediated Processes: Transport Protei\ls, 272.4.1 Uptake Transporters: SLC Superfamily, 282.4.2 Effiux Transporters: ABC Superfamily, 292.4.3 Characteristics of Transporter Systems, 31vii

viiiCONTENTS2.4.42.4.5Simulation Exercise, 32Clinical Examples of Transporter Involvementin Drug Response, 333 Drug Administration, Absorption, and Bioavailability363.1 Introduction: Local and Systemic Drug Administration, 373.2 Common Routes of Systemic Drug Administration, 373.2.1 Intravascular Direct Systemic Administration, 373.2.2 Extravascular Parenteral Routes, 383.2.3 Other Extravascular Routes, 383.3 Overview of Oral Absorption, 403.4 Extent of Drug Absorption, 413.4.1 Bioavailability Factor, 413.4.2 Individual Bioavailability Factors, 423.5 Determinants of the Bioavailability Factor, 433.5.1 Disintegration, 433.5.2 Dissolution, 433.5.3 Formulation Excipients, 433.5.4 Adverse Events Within the Gastrointestinal Lumen, 443.5.5 Transcellular Passive Diffusion, 463.5.6 Paracellular Passive Diffusion, 473.5.7 Uptake and Efflux Transporters, 473.5.8 Presytemic Intestinal Metabolism or Extraction, 503.5.9 Presystemic Hepatic Metabolism or Extraction, 523.6 Factors Controlling the Rate of Drug Absorption, 533.6.1 Dissolution-ControIIed Absorption, 543.6.2 Membrane Penetration-ControIIed Absorption, 553.6.3 OveraII Rate of Drug Absorption, 553.7 Biopharmaceutics Classification System, 55Problems, 56References, 574 Drug Distribution4.1 Introduction, 614.2 Extent of Drug Distribution, 614.2.1 Distribution Volumes, 624.2.2 Tissue Binding and Plasma Protein Binding: ConcentratingEffects, 644.2.3 Assessment of the Extent of Drug Distribution: ApparentVolume of Distribution, 654.2.4 Plasma Protein Binding, 724.3 Rate of Drug Distribution, 794.3.1 Perfusion-Controlled Drug Distribution, 804.3.2 Diffusion-Controlled Drug Distribution, 824.4 Distribution of Drugs to the Central Nervous System, 83Problems, 86References, 8760

CONTENTS5Drug Elimination and Clearanceix885.1Introduction, 895.l.l First-Order Elimination, 905.1.2 Determinants of the Elimination Rate Constant and theHalf-Life, 915.2 Clearance, 915.2.1 Definition and Determinants of Clearance, 915.2.2 Total Clearance, Renal Clearance, and Hepatic Clearance, 945.2.3 Relationships Among Clearance, Volume of Distribution,Elimination Rate Constant, and Half-Life, 955.2.4 Primary and Secondary Parameters, 965.3 Renal Clearance, 975.3.1 Glomerular Filtration, 975.3.2 Tubular Secretion, 985.3.3 Tubular Reabsorption, 1005.3.4 Putting Meaning into the Value of Renal Clearance, 1015.4 Hepatic Clearance, 1025.4.1 Phase I and Phase 11 Metabolism, 1035.4.2 The Cytochrome P450 Enzyme System, 1045.4.3 Glucuronidation, 1055.4.4 Drug-Drug Interactions, 1065.4.5 Hepatic Drug Transporters, 1075.4.6 Kinetics of Drug Metabolism, 1095.4.7 Hepatic Clearance, 1115.5 Measurement of Clearances, 1155.5.1 Total Body Clearance, 1155.5.2 Renal Clearance, 1175.5.3 Fraction ofthe Drug Excreted Unchanged, 120Problems, 121References, 1246Compartmental Models in Pharmacokinetics6.16.26.36.4Introduction, 127Expressions for Component Parts of the Dose-PlasmaConcentration Relationship, 1276.2.1 Effective Dose, 1276.2.2 Rate ofDrug Absorption, 1286.2.3 Rate of Drug Elimination, 1296.2.4 Rate of Drug Distribution, 129Putting Everything Together: Compartments and Models, 1306.3.1 One-Compartment Model, 1306.3.2 Two-Compartment Model, 1316.3.3 Three-Compartment Model, 131Examples of Complete Compartment Models, 1336.4.1 Intravenous Bolus Injection in a One-Compartment Modelwith First-Order Elimination, 133126

xCONTENTS6.4.2 Intravenous Bolus Injection in a Two-Compartment Modelwith First-Order Elimination, 1346.4.3 First-Order Absorption in a Two-Compartment Model withFirst-Order Elimination, 1356.5 Use of Compartmental Models to Study MetabolitePharmacokinetics, 1366.6 Selecting and Applying Models, 137Problems, 138Recommended Reading, 1387Pharmacokinetics of an Intravenous Bolus Injection in aOne-Compartment Model1397.1 Introduction, 1407.2 One-Compartment Model, 1407.3 Pharmacokinetic Equations, 1427.3.1 Basic Equation, 1427.3.2 Half-Life, 1437.3.3 Time to Eliminate a Dose, 1437.4 Simulation Exercise, 1447.5 Application of the Model, 1457.5.1 Predicting Plasma Concentrations, 1457.5.2 Duration of Action, 1467.5.3 Value of a Dose to Give a Desired Initial PlasmaConcentration, 1477.5.4 Intravenous Loading Dose, 1477.6 Determination of Pharmacokinetic Parameters Experimentally, 1487.6.1 Study Design for the Determination of Parameters, 1497.6.2 Pharmacokinetic Analysis, 1497.7 Pharmacokinetic Analysis in Clinical Practice, 153Problems, 155Recommended Reading, 1578 Pharmacokinetics of an Intravenous Bolus Injection in aTwo-Compartment Model8.1 Introduction, 1598.2 Tissue and Compartmental Distribution of a Drug, 1598.2.1 Drug Distribution to the Tissues, 1598.2.2 Compartmental Distribution of a Drug, 1608.3 Basic Equation, 1628.3.1 Distribution: A, a, and the Distribution tl/2, 1638.3.2 Elimination:B, ß, and the Beta tl/2, 1638.4 Relationship Between Macro and Micro Rate Constants, 1648.5 Primary Pharmacokinetic Parameters, 1658.5.1 Clearance, 1658.5.2 Distribution Clearance, 1668.5.3 Volume ofDistribution, 1678.6 Simulation Exercise, 170158

CONTENTSxi8.7Determination of the Pharmacokinetic Parameters of theTwo-Compartment Model, 1738.7.1 Determination of Intercepts and Macro Rate Constants, 1738.7.2 Determination ofthe Micro Rate Constants: k 12 , k21 ,and k lO , 1758.7.3 Determination of the Primary PharmacokineticParameters, 1758.8 Clinical Application of the Two-Compartment Model, 1768.8.1 Measurement of the Elimination Half-Life in thePostdistribution Phase, 1768.8.2 Determination of the Loading Dose, 1778.8.3 Evaluation of a Dose: Monitoring PlasmaConcentrations and Patient Response, 179Problems, 180Recommended Reading, 1819 Pharmacokinetics of Extravascular Drug Administration1829.19.2Introduction, 183Model for First-Order Absorption in a One-Compartment Model, 1849.2.1 Model and Equations, 1849.2.2 Determination of the Model Parameters, 1869.2.3 Absorption Lag Time, 1929.2.4 Flip-Flop Model and Sustained-Release Preparations, 1929.2.5 Determinants of Tmax and Cmax , 1949.3 Bioavailability, 1959.3.1 Bioavailability Parameters, 1959.3.2 Absolute Bioavailability, 1979.3.3 Relative Bioavailability, 1989.3.4 Bioequivalence, 1989.3.5 Example Bioavailability Analysis, 1989.4 Simulation Exercise, 198Problems, 199Recommended Reading, 20010 Introduction to Noncompartmental Analysis20110.1 Introduction, 20110.2 Mean Residence Time, 20210.3 Determination of Other Important Pharmacokinetic Parameters, 20510.4 Different Routes of Administration, 20710.5 Application of Noncompartmental Analysis to Clinical Studies, 208Problems, 21011Pharmacokinetics of Intravenous Infusion in a One-Compartment Model11.111.2Introduction, 213Model and Equations, 21411.2.1 Basic Equation, 214212

xiiCONTENTS11.2.2 Application of the Basic Equation, 21611.2.3 Simulation Exercise: Part 1, 21611.3 Steady-State Plasma Concentration, 21711.3.1 Equation for Steady-State Plasma Concentrations, 21711.3.2 Application of the Equation, 21711.3.3 Basic Formula Revisited, 21811.3.4 Factors Controlling Steady-State Plasma Concentration, 21811.3.5 Time to Steady State, 21911.3.6 Simulation Exercise: Part 2, 22011.4 Loading Dose, 22111.4.1 Loading-Dose Equation, 22111.4.2 Simulation Exercise: Part 3, 22311.5 Termination of Infusion, 22311.5.1 Equations for Termination Before and AfterSteady State, 22311.5.2 Simulation Exercise: Part 4, 22411.6 Individualization of Dosing Regimens, 22411.6.1 Initial Doses, 22411.6.2 Monitoring and Individualizing Therapy, 225Problems, 22712 Multiple Intravenous Bolus Injections in the One-Compartment Model12.1 Introduction, 23112.2 Terms and Symbols Used in Multiple-Dosing Equations, 23212.3 Monoexponential Decay During a Dosing Interval, 23412.3.1 Calculation of Dosing Interval to Give SpecificSteady-State Peaks and Troughs, 23512.4 Basic Pharmacokinetic Equations for Multiple Doses, 23612.4.1 Principle of Superposition, 23612.4.2 Equations That Apply Before Steady State, 23612.5 Steady State, 23812.5.1 Steady-State Equations, 23812.5.2 Average Plasma Concentration at Steady State, 24012.5.3 Fluctuation, 24212.5.4 Accumulation, 24312.5.5 Time to Reach Steady State, 24412.5.6 Loading Dose, 24512.6 Basic Formula Revisited, 24512.7 Pharmacokinetic-Guided Dosing Regimen Design, 24612.7.1 General Considerations for Selection oftheDosing Interval, 24612.7.2 Protocols for Pharmacokinetic-GuidedDosing Regimens, 24712.8 Simulation Exercise, 251Problems, 253References, 253230

CONTENTS13Multiple Intermittent Infusionsxiii25413.113.2Introduction, 254Steady-State Equations for Multiple IntermittentInfusions, 25613.3 Monoexponentia1 Decay During a Dosing Interval:Determination of Peaks, Troughs, and EliminationHalf-Life, 25913.3.1 Determination of Half-Life, 25913.3.2 Determination of Peaks and Troughs, 26113.4 Determination of the Volume of Distribution, 26113.5 Individualization of Dosing Regimens, 26413.6 Simulation Exercise, 265Problems, 26514 Multiple Oral Doses26714.114.2Introduction, 267Steady-State Equations, 26814.2.1 Time to Peak Steady-State Plasma Concentration, 26914.2.2 Maximum Steady-State Plasma Concentration, 27014.2.3 Minimum Steady-State Plasma Concentration, 27114.2.4 Average Steady-State Plasma Concentration, 27114.2.5 Overall Effect of Absorption Parameters on aSteady-State Dosing Interval, 27214.3 Equations Used Clinically to Individualize Oral Doses, 27214.3.1 Protocol to Select an Appropriate Equation, 27314.4 Simulation Exercise, 274References, 26515 Nonlinear Pharmacokinetics15.115.2Linear Pharmacokinetics, 277Nonlinear Processes in Absorption, Distribution, Metabolism,and Elimination, 28015.3 Pharmacokinetics of Capacity-Limited Metabolism, 28115.3.1 Kinetics of Enzymatic Processes, 28215.3.2 Plasma Concentration-Time Profile, 28315.4 Phenytoin, 28415.4.1 Basic Equation for Steady State, 28515.4.2 Estimation of Doses and Plasma Concentrations, 28715.4.3 Inftuence of Km and Vrnax and Factors That AffectThese Parameters, 28915.4.4 Time to Eliminate the Drug, 29015.4.5 Time to Reach Steady State, 29115.4.6 Individualization of Doses of Phenytoin, 292Problems, 295References, 296277

xiv16CONTENTSIntroduction to Pharmacodynamic Models and IntegratedPharmacokinetic-Pharmacodynamic Models29716.1 Introduction, 29816.2 Classic Pharmacodynamic Models Based on TraditionalReceptor Theory, 29916.2.1 Receptor Binding, 30016.2.2 Response-Concentration Models, 30216.3 Empirical Pharmacodynamic Models Used Clinically, 30716.3.1 Sigmoidal E max and E max Models, 30816.3.2 Linear Adaptations of the E max Model, 31016.4 Integrated PK-PD Models: E max Model Combined witha PK Model far Intravenous Bolus Injection in aOne-Compartment Model, 31216.4.1 Simulation Exercise, 31416.5 Hysteresis and the Effect Compartment, 31516.5.1 Simulation Exercise, 318Problems, 319References, 32117Mechanism-Based Integrated Pharmacokinetic-Pharmacodynamic Models 32317.1 Introduction, 32417.2 Alternative Models for Drug-Receptor Interaction: OperationalModel of Agonism, 32517.2.1 Simulation Exercise, 32917.3 Physiological Turnover Model and Its Characteristics, 32917.3.1 Points ofDrug Action, 33017.3.2 System Recovery After Change in Baseline Value, 33017.4 Indirect Effect Models, 33117.4.1 Characteristics of Indirect Effect Drug Responses, 33317.4.2 Characteristics of Indirect Effect Models IllustratedUsing Model I, 33417.4.3 Other Indirect Models, 34017.5 Transduction and Transit Compartment Models, 34017.5.1 Simulation Exercise, 34317.6 Tolerance Models, 34417.6.1 Counter-regulatory Force Model, 34517.6.2 Precursor Pool Model of Tolerance, 34817.7 Irreversible Drug Effects, 35017.7.1 Application of the Tumover Model to Irreversible DrugAction, 35017.7.2 Model for Hematological Toxicity of Anticancer Drugs, 35217.8 Disease Progression Models, 35617.8.1 Generation of Drug Response, 35617.8.2 Drug Interaction with a Disease, 35617.8.3 Disease Progression Models, 356Problems, 360References, 365

CONTENTSxvAppendix A Review of Exponents and LogarithmsAl Exponents, 368A2 Logarithms: log and In, 369A3 Performing Calculations in the Logarithmic Domain, 370A3.l Multiplication, 370A3.2 Division, 371A3.3 Reciprocals, 371A3.4 Exponents, 371A.4 Calculations Using Exponential Expressions and Logarithms, 371A5 Decay Function: e- kt , 373A6 Growth Function: 1 - ekt , 374A7 Decay Function in Pharmacokinetics, 374Problems, 375368Appendix B Rates of ProcessesB.l Introduction, 377B.2 Order of a Rate Process, 378B.3 Zero-Order Processes, 378B.3.1 Equation for Zero-Order Filling, 378B.3.2 Equation for Zero-Order Emptying, 379B.3.3 Time for Zero-Order Emptying to Go to 50%Completion, 379B.4 First-Order Processes, 380B.4.1 Equation for a First-Order Process, 380B.4.2 Time for 50% Completion: The Half-Life, 381B.5 Comparison of Zero- and First-Order Processes, 382B.6 Detailed Example of First-Order Decay in Pharmacokinetics, 382B.6.l Equations and Semilogarithmic Plots, 382B.6.2 Half-Life, 383B.6.3 Fraction or Percent Completion of a First-Order ProcessUsing First-Order Elimination as an Example, 384B. 7 Examples of the Application of First-Order Kinetics toPharmacokinetics, 385377Appendix C Creation of Excel Worksheets for Pharmacokinetic AnalysisC.1 Measurement of AUC and Clearance, 387C.l.l Trapezoidal Rule, 388C.1.2 Excel Spreadsheet to Determine AUC o-- oo andClearance, 389C.2 Analysis of Data from an Intravenous Bolus Injection in aOne-Compartment Model, 393C.3 Analysis of Data from an Intravenous Bolus Injection in aTwo-Compartment Model, 394C.4 Analysis of Oral Data in a One-Compartment Model, 398C.5 Noncompartmental Analysis of Oral Data, 399387Appendix D Derivation of Equations for Multiple Intravenous Bolus Injections 403D.l Assumptions, 403

xviCONTENTSD.2D.3Basic Equation for Plasma Concentration After MultipleIntravenous Bolus Injections, 403Steady-State Equations, 406Appendix EAppendix FSummary of the Properties of the Fictitious Drugs Usedin the Text407Computer Simulation Models409Glossary of Abbreviations and Symbols410Index415

PREFACEThe behavior and characteristics of therapeutic drugs vary enormously. For example, dosesdiffer more than a thousandfold. Some drugs must be taken three times a day, othersonce daily, and some every month. The response to some therapies occurs immediately,whereas for others it may take days or even weeks for the response to be apparent. Somedrugs must be taken with food; others must be taken on an empty stomach. Concurrentmedications interact with some drugs but not with others. The study of pharmacokinetics(the dose-concentration relationship) and pharmacodynamics (the concentration-responserelationship ), which have been referred to as the pillars of clinical pharmacology, unlocksthe mystery of this behavior and brings clarity to diverse patterns of drug action. The goalof this book is to provide straightforward, uncomplicated, but comprehensive coverage ofthe essentials of pharmacokinetics and pharmacodynamics. I hope the book will enable alarge and diverse group of students to develop an interest in this subject and gain a betterunderstanding of the properties and behaviors of drugs.Basic Pharmacokinetics and Pharmacodynamics: An lntegrated Textbook and ComputerSimulations is an introductory textbook suitable to accompany courses in pharmacokinetics, pharmacodynarnics, and clinical pharmacology in pharmacy and medical schools. Itis also directed toward people in the pharmaceutical field who want to gain an understanding of this area through self-study. The book is organized and written with severalobjectives in mind. First, as an introductory textbook, the intent is to present the material in as simple a way as possible, without compromising the accuracy and scope ofthe material. I think it is important that students not be overwhelmed during their initialexposure. Interested students can always find more advanced literature. Second, simulations are integrated into the text to allow students to visualize important concepts and topromote understanding. Pharmacokinetics and pharmacodynamics are subjects that mustbe approached with the goal of understanding, not memorizing, the material. The textprovides exercises to guide readers through simulations, but readers are also encouragedto experiment with simulations on their own. A third goal is to balance the qualitativeside of pharmacokinetics with the quantitative side, or equations. Although only a fractionxvii

BASIC PHARMACOKINETICS AND PHARMACODYNAMICS An Integrated Textbook and Computer Simulations SARA ROSENBAUM WILEY A lOHN WILEY & SONS, INC., PUBLICATION . CONTENTS Preface 1 Introduction to Pharmacokinetics and Pharmacodynamics 1.1 Introduction: Drugs and Doses, 1 1.2 Introduction to Pharmacodynamics, 3

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