Basic Pharmacokinetics and Pharmacodynamics

Preface xix Contributors xxi 1 Introduction to Pharmacokinetics and Pharmacodynamics 1 Sara E. Rosenbaum 1.1 Introduction: Drugs and Doses 2 1.2 Introduction to Pharmacodynamics 3 1.2.1 Drug Effects at the Site of Action 3 1.2.2 Agonists, Antagonists, and Concentration–Response Relationships 6 1.3 Introduction to Pharmacokinetics 9 1.3.1 Plasma Concentration of Drugs 9 1.3.2 Processes in Pharmacokinetics 11 1.4 Dose–Response Relationships 12 1.5 Therapeutic Range 14 1.5.1 Determination of the Therapeutic Range 15 1.6 Summary 18 Reference 18 2 Passage of Drugs Through Membranes 19 Sara E. Rosenbaum 2.1 Introduction 20 2.2 Structure and Properties of Membranes 20 2.3 Passive Diffusion 21 2.3.1 Transcellular Passive Diffusion 23 2.3.2 Paracellular Passive Diffusion 25 2.4 Carrier-Mediated Processes: Transport Proteins 26 2.4.1 Uptake Transporters: SLC Superfamily 27 2.4.2 Efflux Transporters: ABC Superfamily 29 2.4.3 Characteristics of Transporter Systems 31 2.4.4 Simulation Exercise 32 2.4.5 Clinical Examples of Transporter Involvement in Drug Response 32 References 33 3 Drug Administration and Drug Absorption 35 Steven C. Sutton 3.1 Introduction: Local and Systemic Drug Administration 36 3.2 Routes of Drug Administration 37 3.2.1 Common Routes of Local Drug Administration 37 3.2.2 Common Routes of Systemic Drug Administration 38 3.3 Overview of Oral Absorption 41 3.3.1 Anatomy and Physiology of the Oral-Gastric-Intestinal Tract and Transit Time 41 3.4 Extent of Drug Absorption 44 3.4.1 Bioavailability Factor 44 3.4.2 Individual Bioavailability Factors 45 3.5 Determinants of the Fraction of the Dose Absorbed (F) 46 3.5.1 Disintegration 46 3.5.2 Dissolution 46 3.5.3 Formulation Excipients 50 3.5.4 Adverse Events within the Gastrointestinal Lumen 50 3.5.5 Transcellular Passive Diffusion 53 3.5.6 Particulate Uptake 53 3.5.7 Paracellular Passive Diffusion 53 3.5.8 Uptake and Efflux Transporters 54 3.5.9 Presystemic Intestinal Metabolism or Extraction 58 3.5.10 Presystemic Hepatic Metabolism or Extraction 60 3.6 Factors Controlling the Rate of Drug Absorption 61 3.6.1 Dissolution-Controlled Absorption 63 3.6.2 Membrane Penetration-Controlled Absorption 63 3.6.3 Overall Rate of Drug Absorption 63 3.7 Biopharmaceutics Classification System 64 3.7.1 Intestinal Reserve Length 64 3.7.2 Biopharmaceutics Classification System (BCS) 64 3.7.3 Biopharmaceutics Drug Disposition Classification System (BDDCS) 65 3.8 Food Effects 65 Problems 66 References 67 4 Drug Distribution 71 Sara E. Rosenbaum 4.1 Introduction 72 4.2 Extent of Drug Distribution 72 4.2.1 Distribution Volumes 74 4.2.2 Tissue Binding Plasma Protein Binding and Partitioning: Concentrating Effects 75 4.2.3 Assessment of the Extent of Drug Distribution: Apparent Volume of Distribution 76 4.2.4 Plasma Protein Binding 82 4.3 Rate of Drug Distribution 89 4.3.1 Perfusion-Controlled Drug Distribution 90 4.3.2 Diffusion or Permeability-Controlled Drug Distribution 93 4.4 Distribution of Drugs to the Central Nervous System 93 Problems 96 References 98 5 Drug Elimination and Clearance 99 Sara E. Rosenbaum 5.1 Introduction 100 5.1.1 First-Order Elimination 101 5.1.2 Determinants of the Elimination Rate Constant and the Half-Life 102 5.2 Clearance 102 5.2.1 Definition and Determinants of Clearance 102 5.2.2 Total Clearance, Renal Clearance, and Hepatic Clearance 104 5.2.3 Relationships among Clearance, Volume of Distribution, Elimination Rate Constant, and Half-Life 105 5.2.4 Primary and Secondary Parameters 106 5.2.5 Measurement of Total Body Clearance 106 5.3 Renal Clearance 108 5.3.1 Glomerular Filtration 109 5.3.2 Tubular Secretion 110 5.3.3 Tubular Reabsorption 113 5.3.4 Putting Meaning into the Value of Renal Clearance 114 5.3.5 Measurement of Renal Clearance 115 5.3.6 Fraction of the Dose Excreted Unchanged 118 5.4 Hepatic Elimination and Clearance 119 5.4.1 Phase I and Phase II Metabolism 120 5.4.2 The Cytochrome P450 Enzyme System 121 5.4.3 Glucuronidation 122 5.4.4 Metabolism-Based Drug–Drug Interactions 122 5.4.5 Hepatic Drug Transporters and Drug–Drug Interactions 125 5.4.6 Kinetics of Drug Metabolism 127 5.4.7 Hepatic Clearance and Related Parameters 128 Problems 139 References 142 6 Compartmental Models in Pharmacokinetics 145 Sara E. Rosenbaum 6.1 Introduction 146 6.2 Expressions for Component Parts of the Dose–Plasma Concentration Relationship 146 6.2.1 Effective Dose 146 6.2.2 Rate of Drug Absorption 147 6.2.3 Rate of Drug Elimination 148 6.2.4 Rate of Drug Distribution 148 6.3 Putting Everything Together: Compartments and Models 149 6.3.1 One-Compartment Model 149 6.3.2 Two-Compartment Model 150 6.3.3 Three-Compartment Model 150 6.4 Examples of Complete Compartment Models 152 6.4.1 Intravenous Bolus Injection in a One-Compartment Model with First-Order Elimination 152 6.4.2 Intravenous Bolus Injection in a Two-Compartment Model with First-Order Elimination 153 6.4.3 First-Order Absorption in a Two-Compartment Model with First-Order Elimination 154 6.5 Use of Compartmental Models to Study Metabolite Pharmacokinetics 155 6.6 Selecting and Applying Models 156 Problems 157 Suggested Readings 157 7 Pharmacokinetics of an Intravenous Bolus Injection in a One-Compartment Model 159 Sara E. Rosenbaum 7.1 Introduction 160 7.2 One-Compartment Model 160 7.3 Pharmacokinetic Equations 162 7.3.1 Basic Equation 162 7.3.2 Half-Life 163 7.3.3 Time to Eliminate a Dose 163 7.4 Simulation Exercise 163 7.5 Application of the Model 165 7.5.1 Predicting Plasma Concentrations 165 7.5.2 Duration of Action 166 7.5.3 Value of a Dose to Give a Desired Initial Plasma Concentration 167 7.5.4 Intravenous Loading Dose 167 7.6 Determination of Pharmacokinetic Parameters Experimentally 168 7.6.1 Study Design for the Determination of Parameters 168 7.6.2 Pharmacokinetic Analysis 169 7.7 Pharmacokinetic Analysis in Clinical Practice 173 Problems 174 Suggested Reading 176 8 Pharmacokinetics of an Intravenous Bolus Injection in a Two-Compartment Model 177 Sara E. Rosenbaum 8.1 Introduction 178 8.2 Tissue and Compartmental Distribution of a Drug 179 8.2.1 Drug Distribution to the Tissues 179 8.2.2 Compartmental Distribution of a Drug 180 8.3 Basic Equation 181 8.3.1 Distribution: A, α, and the Distribution t1/2 182 8.3.2 Elimination: B, β, and the β t1/2 182 8.4 Relationship Between Macro and Micro Rate Constants 183 8.5 Primary Pharmacokinetic Parameters 183 8.5.1 Clearance 184 8.5.2 Distribution Clearance 184 8.5.3 Volume of Distribution 186 8.6 Simulation Exercise 188 8.7 Determination of the Pharmacokinetic Parameters of the Two-Compartment Model 191 8.7.1 Determination of Intercepts and Macro Rate Constants 191 8.7.2 Determination of the Micro Rate Constants: k12 k21 and k10 193 8.7.3 Determination of the Primary Pharmacokinetic Parameters 193 8.8 Clinical Application of the Two-Compartment Model 194 8.8.1 Measurement of the Elimination Half-Life in the Postdistribution Phase 194 8.8.2 Determination of the Loading Dose 195 8.8.3 Evaluation of a Dose: Monitoring Plasma Concentrations and Patient Response 197 Problems 197 Suggested Readings 199 9 Pharmacokinetics of Extravascular Drug Administration 201 Dr. Steven C. Sutton 9.1 Introduction 202 9.2 First-Order Absorption in a One-Compartment Model 203 9.2.1 Model and Equations 203 9.2.2 Parameter Determination 205 9.2.3 Absorption Lag Time 210 9.2.4 Flip-Flop Model and Sustained-Release Preparations 212 9.2.5 Determinants of Tmax and Cmax 212 9.3 Modified Release and Gastric Retention Formulations 214 9.3.1 Impact of the Stomach 214 9.3.2 Moisture in the Gastrointestinal Tract 215 9.4 Bioavailability 215 9.4.1 Bioavailability Parameters 215 9.4.2 Absolute Bioavailability 217 9.4.3 Relative Bioavailability 217 9.4.4 Bioequivalence 217 9.4.5 Single-Dose Crossover Parallel and Steady-State Study Designs 219 9.4.6 Example Bioavailability Analysis 219 9.5 In Vitro-In Vivo Correlation 219 9.5.1 Definitions 219 9.5.2 Assumptions 220 9.5.3 Utility 220 9.5.4 Immediate Release IVIVC 220 9.5.5 Modified Release IVIVC 221 9.6 Simulation Exercise 222 Problems 223 References 224 10 Introduction to Noncompartmental Analysis 225 Sara E. Rosenbaum 10.1 Introduction 225 10.2 Mean Residence Time 226 10.3 Determination of Other Important Pharmacokinetic Parameters 229 10.4 Different Routes of Administration 231 10.5 Application of Noncompartmental Analysis to Clinical Studies 232 Problems 234 11 Pharmacokinetics of Intravenous Infusion in a One-Compartment Model 237 Sara E. Rosenbaum 11.1 Introduction 238 11.2 Model and Equations 239 11.2.1 Basic Equation 239 11.2.2 Application of the Basic Equation 241 11.2.3 Simulation Exercise: Part 1 241 11.3 Steady-State Plasma Concentration 242 11.3.1 Equation for Steady-State Plasma Concentrations 242 11.3.2 Application of the Equation 242 11.3.3 Basic Formula Revisited 243 11.3.4 Factors Controlling Steady-State Plasma Concentration 243 11.3.5 Time to Steady State 244 11.3.6 Simulation Exercise: Part 2 245 11.4 Loading Dose 246 11.4.1 Loading-Dose Equation 246 11.4.2 Simulation Exercise: Part 3 248 11.5 Termination of Infusion 248 11.5.1 Equations for Termination Before and After Steady State 248 11.5.2 Simulation Exercise: Part 4 249 11.6 Individualization of Dosing Regimens 249 11.6.1 Initial Doses 249 11.6.2 Monitoring and Individualizing Therapy 250 Problems 252 12 Multiple Intravenous Bolus Injections in the One-Compartment Model 255 Sara E. Rosenbaum 12.1 Introduction 256 12.2 Terms and Symbols Used in Multiple-Dosing Equations 257 12.3 Monoexponential Decay During a Dosing Interval 259 12.3.1 Calculation of Dosing Interval to Give Specific Steady-State Peaks and Troughs 260 12.4 Basic Pharmacokinetic Equations for Multiple Doses 260 12.4.1 Principle of Superposition 260 12.4.2 Equations that Apply Before Steady State 261 12.5 Steady State 262 12.5.1 Steady-State Equations 263 12.5.2 Average Plasma Concentration at Steady State 264 12.5.3 Fluctuation 267 12.5.4 Accumulation 267 12.5.5 Time to Reach Steady State 269 12.5.6 Loading Dose 270 12.6 Basic Formula Revisited 270 12.7 Pharmacokinetic-Guided Dosing Regimen Design 270 12.7.1 General Considerations for Selection of the Dosing Interval 270 12.7.2 Protocols for Pharmacokinetic-Guided Dosing Regimens 272 12.8 Simulation Exercise 276 Problems 277 Reference 278 13 Multiple Intermittent Infusions 279 Sara E. Rosenbaum 13.1 Introduction 279 13.2 Steady-State Equations for Multiple Intermittent Infusions 281 13.3 Monoexponential Decay During a Dosing Interval: Determination of Peaks Troughs and Elimination Half-Life 284 13.3.1 Determination of Half-Life 284 13.3.2 Determination of Peaks and Troughs 286 13.4 Determination of the Volume of Distribution 286 13.5 Individualization of Dosing Regimens 289 13.6 Simulation 289 Problems 290 14 Multiple Oral Doses 293 Sara E. Rosenbaum 14.1 Introduction 293 14.2 Steady-State Equations 294 14.2.1 Time to Peak Steady-State Plasma Concentration 295 14.2.2 Maximum Steady-State Plasma Concentration 296 14.2.3 Minimum Steady-State Plasma Concentration 296 14.2.4 Average Steady-State Plasma Concentration 296 14.2.5 Overall Effect of Absorption Parameters on a Steady-State Dosing Interval 297 14.3 Equations Used Clinically to Individualize Oral Doses 298 14.3.1 Protocol to Select an Appropriate Equation 298 14.4 Simulation Exercise 300 References 301 15 Nonlinear Pharmacokinetics 303 Sara E. Rosenbaum 15.1 Linear Pharmacokinetics 304 15.2 Nonlinear Processes in Absorption, Distribution, Metabolism, and Elimination 306 15.3 Pharmacokinetics of Capacity-Limited Metabolism 307 15.3.1 Kinetics of Enzymatic Processes 307 15.3.2 Plasma Concentration–Time Profile 309 15.4 Phenytoin 310 15.4.1 Basic Equation for Steady State 311 15.4.2 Estimation of Doses and Plasma Concentrations 313 15.4.3 Influence of Km and Vmax and Factors That Affect These Parameters 314 15.4.4 Time to Eliminate the Drug 316 15.4.5 Time to Reach Steady State 317 15.4.6 Individualization of Doses of Phenytoin 318 Problems 321 References 322 16 Introduction to Pharmacogenetics 323 Dr. Daniel Brazeau 16.1 Introduction 324 16.2 Genetics Primer 324 16.2.1 Basic Terminology: Genes Alleles Loci and Polymorphism 324 16.2.2 Population Genetics: Allele and Genotype Frequencies 326 16.2.3 Quantitative Genetics and Complex Traits 327 16.3 Pharmacogenetics 328 16.3.1 Pharmacogenetics of Drug-Metabolizing Enzymes 330 16.3.2 Pharmacogenetics of Drug Transporters 333 16.4 Genetics and Pharmacodynamics 334 16.4.1 Drug Target Pharmacogenetics 334 16.5 Summary 335 Reference 335 Suggested Readings 335 17 Models Used to Predict Drug–Drug Interactions for Orally Administered Drugs 337 Sara E. Rosenbaum 17.1 Introduction 338 17.2 Mathematical Models for Inhibitors and Inducers of Drug Metabolism Based on In Vitro Data 340 17.2.1 Reversible Inhibition 340 17.2.2 Time-Dependent Inhibition 341 17.2.3 Induction 345 17.3 Surrogate In Vivo Values for the Unbound Concentration of the Perpetrator at the Site of Action 345 17.3.1 Surrogate Measures of Hepatic Inhibitor and Inducer Concentrations 346 17.3.2 Surrogate Measures of Intestinal Inhibitor and Inducer Concentrations 346 17.4 Models Used to Predict DDIs In Vivo 347 17.4.1 Introduction 347 17.4.2 Basic Predictive Models: R Values 348 17.4.3 Predictive Models Incorporating Parallel Pathways of Elimination (fm) 350 17.4.4 Models Incorporating Intestinal Extraction 354 17.4.5 Models Combining Multiple Actions of Perpetrators 358 17.5 Predictive Models for Transporter-Based DDIs 359 17.5.1 Kinetics of Drug Transporters 359 17.6 Application of Physiologically Based Pharmacokinetic Models to DDI Prediction: The Dynamic Approach 362 17.7 Conclusion 362 Problems 363 References 364 18 Introduction to Physiologically Based Pharmacokinetic Modeling 367 Sara E. Rosenbaum 18.1 Introduction 368 18.2 Components of PBPK Models 369 18.3 Equations for PBPK Models 369 18.4 Building a PBPK Model 373 18.5 Simulations 377 18.6 Estimation of Human Drug-Specific Parameters 378 18.6.1 Tissue Plasma Partition Coefficient 379 18.6.2 Volume of Distribution 379 18.6.3 Clearance 380 18.7 More Detailed PBPK Models 381 18.7.1 Permeability-Limited Distribution 381 18.7.2 Drug Transporters 383 18.7.3 Models for Oral Absorption 386 18.7.4 Reduced Models 387 18.8 Application of PBPK Models 387 References 388 19 Introduction to Pharmacodynamic Models and Integrated Pharmacokinetic–Pharmacodynamic Models 391 Drs. Diane Mould and Paul Hutson 19.1 Introduction 392 19.2 Classic Pharmacodynamic Models Based on Receptor Theory 393 19.2.1 Receptor Binding 394 19.2.2 Concentration-Response Models 395 19.3 Direct Effect Pharmacodynamic Models 402 19.3.1 Emax and Sigmoidal Emax Models 402 19.3.2 Inhibitory Imax and Sigmoidal Imax Models 404 19.3.3 Linear Adaptations of the Emax and Imax Model 404 19.4 Integrated PK–PD Models: Intravenous Bolus Injection in the One-Compartment Model and the Sigmoidal Emax Model 406 19.4.1 Simulation Exercise 409 19.5 Pharmacodynamic Drug–Drug Interactions 410 19.5.1 Simulation Exercise 410 Problems 411 References 412 20 Semimechanistic Pharmacokinetic–Pharmacodynamic Models 413 Drs. Diane Mould and Paul Hutson 20.1 Introduction 414 20.2 Hysteresis and the Effect Compartment 416 20.2.1 Simulation Exercise 419 20.3 Physiological Turnover Models and Their Characteristics 419 20.3.1 Points of Drug Action 421 20.3.2 System Recovery After Change in Baseline Value 421 20.4 Indirect Effect Models 422 20.4.1 Introduction 422 20.4.2 Characteristics of Indirect Effect Drug Responses 424 20.4.3 Characteristics of Indirect Effect Models Illustrated Using Model I 426 20.5 Other Indirect Effect Models 432 20.5.1 Transit Compartment Models 435 20.5.2 Model for Hematological Toxicity of Anticancer Drugs 439 20.5.3 Alternate Parameterizations of Transit Models 442 20.6 Models of Tolerance 442 20.6.1 Introduction to Pharmacologic Tolerance 442 20.6.2 Counter-Regulatory Force Tolerance Model 444 20.6.3 Precursor Pool Model of Tolerance 447 20.7 Irreversible Drug Effects 450 20.7.1 Application of the Turnover Model to Irreversible Drug Action 450 20.8 Disease Progression Models 452 20.8.1 Drug Pharmacokinetics 452 20.8.2 Pharmacodynamics 452 20.8.3 Disease Activity Models 453 20.8.4 Disease Progression Models 453 Problems 459 References 465 Appendix A Review of Exponents and Logarithms 469 Sara E. Rosenbaum A.1 Exponents 469 A.2 Logarithms: Log and Ln 470 A.3 Performing Calculations in the Logarithmic Domain 471 A.3.1 Multiplication 471 A.3.2 Division 472 A.3.3 Reciprocals 472 A.3.4 Exponents 472 A.4 Calculations Using Exponential Expressions and Logarithms 472 A.5 Decay Function: e−kt 474 A.6 Growth Function: 1 − e−kt 475 A.7 Decay Function in Pharmacokinetics 475 Problems 476 Appendix B Rates of Processes 479 Sara E. Rosenbaum B.1 Introduction 479 B.2 Order of a Rate Process 480 B.3 Zero-Order Processes 480 B.3.1 Equation for Zero-Order Filling 480 B.3.2 Equation for Zero-Order Emptying 481 B.3.3 Time for Zero-Order Emptying to Go to 50% Completion 481 B.4 First-Order Processes 482 B.4.1 Equation for a First-Order Process 482 B.4.2 Time for 50% Completion: the Half-Life 483 B.5 Comparison of Zero- and First-Order Processes 484 B.6 Detailed Example of First-Order Decay in Pharmacokinetics 484 B.6.1 Equations and Semilogarithmic Plots 484 B.6.2 Half-Life 485 B.6.3 Fraction or Percent Completion of a First-Order Process Using First-Order Elimination as an Example 485 B.7 Examples of the Application of First-Order Kinetics to Pharmacokinetics 487 Appendix C Creation of Excel Worksheets for Pharmacokinetic Analysis 489 Sara E. Rosenbaum C.1 Measurement of AUC and Clearance 489 C.1.1 Trapezoidal Rule 490 C.1.2 Excel Spreadsheet to Determine AUC0→∞ and Clearance 491 C.2 Analysis of Data from an Intravenous Bolus Injection in a One-Compartment Model 494 C.3 Analysis of Data from an Intravenous Bolus Injection in a Two-Compartment Model 496 C.4 Analysis of Oral Data in a One-Compartment Model 498 C.5 Noncompartmental Analysis of Oral Data 501 Appendix D Derivation of Equations for Multiple Intravenous Bolus Injections 505 Sara E. Rosenbaum D.1 Assumptions 505 D.2 Basic Equation for Plasma Concentration After Multiple Intravenous Bolus Injections 505 D.3 Steady-State Equations 508 Appendix E Enzyme Kinetics: Michaelis–Menten Equation and Models for Inhibitors and Inducers of Drug Metabolism 509 Sara E. Rosenbaum and Roberta S. King E.1 Kinetics of Drug Metabolism: The Michaelis–Menten Model 510 E.1.1 Overview 510 E.1.2 Assumptions for Validity of Michaelis–Menten Model 510 E.1.3 Km and Vmax 511 E.1.4 Derivation of the Michaelis–Menten Equation 511 E.1.5 Summary, Practical Considerations, and Interpretations 513 E.1.6 Relationship Between Intrinsic Clearance and the Michaelis–Menten Parameters 514 E.2 Effect of Perpetrators of DDI on Enzyme Kinetics and Intrinsic Clearance 515 E.2.1 Reversible Inhibition 515 E.2.2 Time-Dependent Inhibition 518 E.2.3 Enzyme Induction 524 References 526 Appendix F Summary of the Properties of the Fictitious Drugs Used in the Text 527 Sara E. Rosenbaum Appendix G Computer Simulation Models 529 Sara E. Rosenbaum Glossary of Terms 531 Index 537