Basic Pharmacokinetics and Pharmacodynamics

Sara E. Rosenbaum, PhD, is Professor of Biomedical and Pharmaceutical Sciences at the University of Rhode Island, where she teaches courses in pharmacokinetics and pharmacodynamics. Her research interests concentrate on the development and application of pharmacokinetic and pharmacodynamic models to better understand the drug dose-response relationship.

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