Preface xi

About the authors xiii

1 Introduction and overview 1

1.1 Use of drugs in disease states 1

1.2 Important definitions and descriptions 2

1.3 Sites of drug administration 4

1.4 Review of ADME processes 5

1.5 Pharmacokinetic models 7

1.6 Rate processes 12

2 Mathematical review 17

2.1 Introduction 17

2.2 A brief history of pharmacokinetics 18

2.3 Hierarchy of algebraic operations 18

2.4 Exponents and logarithms 18

2.5 Variables, constants, and parameters 19

2.6 Significant figures 20

2.7 Units and their manipulation 21

2.8 Slopes, rates, and derivatives 21

2.9 Time expressions 24

2.10 Construction of pharmacokinetic sketches (profiles) 25

3 Intravenous bolus administration (one-compartment model) 29

3.1 Introduction 29

3.2 Useful pharmacokinetic parameters 30

3.3 The apparent volume of distribution (V) 32

3.4 The elimination half life (t_1/2) 36

3.5 The elimination rate constant (K or K_el) 38

3.6 Plotting drug concentration versus time 40

3.7 Intravenous bolus administration of drugs: summary 41

3.8 Intravenous bolus administration: monitoring drug in urine 42

3.9 Use of urinary excretion data 43

4 Clearance concepts 55

4.1 Introduction 55

4.2 Clearance definitions 56

4.3 Clearance: rate and concentration 58

4.4 Clearance: tank and faucet analogy 58

4.5 Organ clearance 60

4.6 Physiological approach to clearance 61

4.7 Estimation of systemic clearance 65

4.8 Calculating renal clearance (Cl_r) and metabolic clearance (cl_m) 66

4.9 Determination of the area under the plasma concentration versus time curve: application of the trapezoidal rule 67

4.10 Elimination mechanism 69

4.11 Use of creatinine clearance to determine renal function 69

Appendix Recently developed equations for estimating creatinine clearance and glomerular filtration rate 76

Problem set 1 79

5 Drug absorption from the gastrointestinal tract 95

5.1 Gastrointestinal tract 95

5.2 Mechanism of drug absorption 98

5.3 Factors affecting passive drug absorption 100

5.4 pH-partition theory of drug absorption 101

6 Extravascular routes of drug administration 105

6.1 Introduction 106

6.2 Drug remaining to be absorbed, or drug remaining at the site of administration 106

6.3 Determination of elimination half life (t_1/2) and elimination rate constant (K or K_el) 109

6.4 Absorption rate constant (K_a) 110

6.5 Wagner-Nelson method (one-compartment model) and Loo-Riegelman method (two-compartment model) 111

6.6 Lag time (t₀) 115

6.7 Some important comments on the absorption rate constant 116

6.8 The apparent volume of distribution (V) 116

6.9 Time of maximum drug concentration, peak time (t_max) 117

6.10 Maximum (peak) plasma concentration (C_p)_max 118

6.11 Some general comments 120

6.12 Example for extravascular route of drug administration 121

6.13 Flip-flop kinetics 126

Problem set 2 127

7 Bioavailability/bioequivalence 137

7.1 Introduction 138

7.2 Important definitions 138

7.3 Types of bioavailability 139

7.4 Bioequivalence 141

7.5 Factors affecting bioavailability 141

7.6 The first-pass effect (presystemic clearance) 142

7.7 Determination of the area under the plasma concentration-time curve and the cumulative amount of drug eliminated in urine 143

7.8 Methods and criteria for bioavailability testing 145

7.9 Characterizing drug absorption from plasma concentration versus time and from urinary data following the administration of a drug via different extravascular routes and/or dosage forms 155

7.10 Equivalency terms 157

7.11 Food and Drug Administration codes 157

7.12 Fallacies on bioequivalence 158

7.13 Evidence of generic bioinequivalence or of therapeutic inequivalence for certain formulations approved by the FDA 159

Problem set 3 161

8 Factors affecting drug absorption: Physicochemical factors 175

8.1 Dissolution rate 175

8.2 Dissolution process 175

8.3 Noyes-Whitney equation and drug dissolution 176

8.4 Factors affecting the dissolution rate 177

9 Gastrointestinal absorption: Role of the dosage form 187

9.1 Introduction 187

9.2 Solution (elixir, syrup, and solution) as a dosage form 188

9.3 Suspension as a dosage form 188

9.4 Capsule as a dosage form 189

9.5 Tablet as a dosage form 189

9.6 Dissolution methods 191

9.7 Formulation and processing factors 191

9.8 Correlation of in vivo data with in vitro dissolution data 194

10 Continuous intravenous infusion (one-compartment model) 203

10.1 Introduction 203

10.2 Monitoring drug in the body or blood (plasma/serum) 205

10.3 Sampling drug in body or blood during infusion 205

10.4 Sampling blood following cessation of infusion 220

10.5 Use of post-infusion plasma concentration data to obtain half life, elimination rate constant and the apparent volume of distribution 222

10.6 Rowland and Tozer method 225

Problem set 4 227

11 Multiple dosing: Intravenous bolus administration 237

11.1 Introduction 237

11.2 Useful pharmacokinetic parameters in multiple dosing 241

11.3 Designing or establishing the dosage regimen for a drug 248

11.4 Concept of drug accumulation in the body (R) 249

11.5 Determination of fluctuation (Φ): intravenous bolus administration 251

11.6 Number of doses required to reach a fraction of the steady-state condition 254

11.7 Calculation of loading and maintenance doses 254

11.8 Maximum and minimum drug concentration at steady state 255

12 Multiple dosing: extravascular routes of drug administration 257

12.1 Introduction 257

12.2 The peak time in multiple dosing to steady state (t′_max) 259

12.3 Maximum plasma concentration at steady state 260

12.4 Minimum plasma concentration at steady state 261

12.5 "Average" plasma concentration at steady state: extravascular route 262

12.6 Determination of drug accumulation: extravascular route 263

12.7 Calculation of fluctuation factor (Φ) for multiple extravascular dosing 264

12.8 Number of doses required to reach a fraction of steady state: extravascular route 264

12.9 Determination of loading and maintenance dose: extravascular route 265

12.10 Interconversion between loading, maintenance, oral, and intravenous bolus doses 266

Problem set 5 271

13 Two-compartment model 285

13.1 Introduction 285

13.2 Intravenous bolus administration: two-compartment model 287

13.3 Determination of the post-distribution rate constant (β) and the coefficient B 292

13.4 Determination of the distribution rate constant (α) and the coefficient A 292

13.5 Determination of micro rate constants: the inter-compartmental rate constants (K₂₁ and K₁₂) and the pure elimination rate constant (K₁₀) 295

13.6 Determination of volumes of distribution (V) 296

13.7 How to obtain the area under the plasma concentration-time curve from time zero to time t and time ∞ 298

13.8 General comments 299

13.9 Example 300

13.10 Further calculations to perform and determine the answers 302

13.11 Extravascular dosing of a two-compartment model drug 303

Problem set 6 305

14 Multiple intermittent infusions 309

14.1 Introduction 309

14.2 Drug concentration guidelines 311

14.3 Example: determination of a multiple intermittent infusion dosing regimen for an aminoglycoside antibiotic 311

14.4 Does to the patient from a multiple intermittent infusion 313

14.5 Multiple intermittent infusion of a two-compartment drug: vancomycin "peak" at 1 hour post infustion 313

14.6 Vancomycin dosing regimen problem 314

14.7 Adjustment for early or late drug concentrations 315

Problem set 7 319

15 Nonlinear pharmacokinetics 323

15.1 Introduction 323

15.2 Capacity-limited metabolism 325

15.3 Estimation of Michaelis-Menten parameters (V_max and K_m) 327

15.4 Relationship between the area under the plasma concentration versus time curve and the administered dose 330

15.5 Time to reach a given fraction of steady state 332

15.6 Example: calculation of parameters for phenytoin 333

Problem set 8 337

16 Drug interactions 341

16.1 Introduction 341

16.2 The effect of protein-binding interactions 342

16.3 The effect of tissue-binding interactions 348

16.4 Cytochrome P450-based drug interactions 349

16.5 Drug interactions linked to transporters 355

Problem set 9 357

17 Pharmacokinetic and pharmacodynamic relationships 359

17.1 Introduction 359

17.2 Generation of a pharmacokinetic- pharmacodynamic (PKPD) equation 361

17.3 Pharmacokinetic and pharmacodynamic drug interactions 364

Problem set 10 367

18 Metabolite pharmacokinetics 369

18.1 Introduction 369

18.2 General model 370

18.3 Single intravenous bolus of drug conforming to a one-compartment model 370

18.4 Single oral dose of drug conforming to a one-compartment model 382

18.5 Intravenous infusion of a one-compartment model parent drug 384

18.6 Chronic dosing to steady state 385

18.7 Study design required to obtain various metabolite pharmacokinetic parameters 388

18.8 Computer-aided simulation and fitting of metabolite pharmacokinetic data 388

18.9 Case in point: meperidine and normeperidine 388

18.10 Active metabolites in renal dysfunction 388

18.11 Sample metabolite pharmacokinetics calculations 393

19 Pharmacokinetic data fitting 395

19.1 Introduction 395

19.2 Pharmacokinetic parameter determination 395

19.3 Nonlinear regression 397

19.4 Goodness of fit indices 398

19.5 Ways to improve fit 401

19.6 Evaluation of program output 401

19.7 How are the values of the parameters determined? 404

19.8 Problems that may occur during a nonlinear regression run 407

19.9 Weighting of data points 408

19.10 Simulation 409

19.11 Initial estimates 411

19.12 Conclusion 412

20 Pharmacokinetics and pharmacodynamics of biotechnology drugs 413

20.1 Introduction 413

20.2 Proteins and peptides 413

20.3 Monoclonal antibodies 419

20.4 Oligonucleotides 423

20.5 Vaccines (immunotherapy) 424

20.6 Gene therapies 425

Appendix: Statistical moment theory in pharmacokinetics 427

A1 Introduction 427

A2 Statistical moment theory 428

A3 Applications 439

Glossary 443

References 453