BASICPHARMACOKINETICS

MOHSEN A. HEDAYA

CRC PressTaylor & Francis Croup

Boca Raton London New York

CRC Press is an imprint of theTaylor & Francis Group, an informa business

Table of Contents

Chapter 1Introduction to Biopharmaceutics and Pharmacokinetics 11.1 Introduction 11.2 Application of Biopharmaceutic and Pharmacokinetic Principles

in Biomedical Fields 21.2.1 Drug Formulation Design 21.2.2 Drug Dosage Form Design 21.2.3 Pharmacological Testing 31.2.4 Toxicological Testing 31.2.5 Evaluation of Organ Function 31.2.6 Dosing Regimen Design 3

1.3 Drug Concentration-Time Profile 31.4 Linear and Nonlinear Pharmacokinetics 3

1.4.1 Linear Pharmacokinetics 31.4.2 Nonlinear Pharmacokinetics 4

1.5 Pharmacokinetic Modeling 41.5.1 Compartmental Modeling 41.5.2 Physiological Modeling 41.5.3 Noncompartmental Approach 5

1.6 Pharmacokinetic Simulation 5Questions 5

Chapter 2Drug Pharmacokinetics Following Single Intravenous Administration 72.1 Introduction 72.2 Elimination Rate Constant 8

2.2.1 Rate of Drug Elimination 82.2.1.1 Rate Constant for Drug Elimination 8

2.2.2 Order of Drug Elimination 82.2.2.1 Zero-Order Elimination 82.2.2.2 First-Order Elimination 10

2.2.3 Determination of the First-Order Elimination RateConstant k 13

2.2.4 Mathematical Expressions That Describe the Amountof the Drug in the Body When Elimination ProcessFollows First-Order Elimination 13

2.2.5 Clinical Importance of the Elimination Rate Constant 152.2.6 Summary 16

2.3 Volume of Distribution 162.3.1 Relationship between the Drug Amount

in the Body and Drug Blood Concentration 162.3.2 Drug Protein Binding and Volume of Distribution 172.3.3 Determination of Volume of Distribution 192.3.4 Clinical Importance of Volume of Distribution 192.3.5 Summary 21

2.4 Half-Life 212.4.1 Half-Life during Zero-Order and First-Order Elimination 21

2.4.1.1 Zero-Order Elimination 212.4.1.2 First-Order Elimination 22

2.4.2 Graphical Determination of Half-Life 222.4.3 Clinical Importance of Half-Life 232.4.4 Summary 24

2.5 Total Body Clearance 242.5.1 Relationship between Total Body Clearance,

Volume of Distribution, and the Elimination Rate Constant 242.5.2 Determination of Total Body Clearance 252.5.3 Total Body Clearance and Volume of Distribution Are

Independent Pharmacokinetic Parameters 252.5.4 Clinical Importance of Total Body Clearance 262.5.5 Summary 26

2.6 Area Under the Curve 272.6.1 Factors Affecting Area Under the Curve

after a Single IV Bolus Dose 272.6.2 Calculation of Area Under the Curve after a Single

IV Bolus Dose 282.6.3 Clinical Importance of Area Under the Curve 29

2.7 Factors Affecting the Drug Blood Concentration-Time Profileafter a Single IV Bolus Dose 302.7.1 Dose 302.7.2 Volume of Distribution 312.7.3 Total Body Clearance 31

Practice Problems 31

Chapter 3Drug Absorption Following Oral Administration: BiopharmaceuticalConsiderations 373.1 Introduction 373.2 Physiological Factors Affecting Oral Drug Absorption 38

3.2.1 Nature of the GIT Membrane 383.2.1.1 Passive Diffusion 383.2.1.2 Carrier-Mediated Transport 393.2.1.3 Paracellular 393.2.1.4 Other Mechanisms 39

3.2.2 Gastrointestinal Physiology 39

3.2.2.1 Buccal Cavity 403.2.2.2 Esophagus 403.2.2.3 Stomach 403.2.2.4 Small Intestine 403.2.2.5 Large Intestine 413.2.2.6 Rectum 41

3.2.3 Effect of Food on Drug Absorption 413.2.4 Pathological Conditions Affecting Drug Absorption 41

3.3 Physical Factors Affecting Oral Drug Absorption 423.3.1 Drug Physicochemical Properties 42

3.3.1.1 Drug Lipid Solubility 423.3.1.2 pH Partition Theory 43

3.3.2 Dissolution of the Drug 443.3.2.1 Surface Area 453.3.2.2 Diffusion Coefficient 453.3.2.3 Thickness of the Unstirred Layer 453.3.2.4 Drug Solubility 45

3.4 Dosage Form Characteristics 463.4.1 Types of Oral Dosage Forms 47

3.4.1.1 Solutions 473.4.1.2 Suspensions 473.4.1.3 Capsules 473.4.1.4 Tablets 473.4.1.5 Coated Tablets 483.4.1.6 Sustained-Release Tablets 48

3.4.2 In Vitro Disintegration Test 483.4.3 In Vitro Dissolution Test 48

3.4.3.1 Rotating Basket 493.4.3.2 Paddle Method 493.4.3.3 Other Methods 493.4.3.4 Dissolution Requirements 493.4.3.5 Correlation of In Vitro Drug Dissolution

with In Vivo Drug Absorption 49Questions 50

Chapter 4Drug Pharmacokinetics Following Single Oral Drug Administration:Rate of Drug Absorption 514.1 Introduction 514.2 Drug Absorption after Oral Administration 524.3 Plasma Concentration-Time Profile after a Single Oral Dose 544.4 Determination of Absorption Rate Constant 56

4.4.1 Method of Residuals 564.4.1.1 Lag Time 584.4.1.2 Flip Flop of ka and k 58

4.4.2 Wagner-Nelson Method 60

4.5 Clinical Importance of Absorption Rate Constant 624.6 Summary 63Practice Problems 64

Chapter 5Drug Pharmacokinetics Following Single Oral Drug Administration:Extent of Drug Absorption 675.1 Introduction 67

5.1.1 General Definitions 685.2 Purpose of Bioavailability and Bioequivalence Studies 695.3 Causes for Variation in Drug Bioavailability 69

5.3.1 Factors Related to Drug Formulation and Routeof Administration 695.3.1.1 Route of Administration 695.3.1.2 Dosage Form 695.3.1.3 Excipient 70

5.3.2 Factors Related to the Drug 705.3.2.1 Drug Solubility 705.3.2.2 Drug Partition Coefficient 705.3.2.3 Stability and Drug Interaction 70

5.3.3 Factors Related to the Patient 715.3.3.1 Individual Variability 715.3.3.2 Site of Administration 715.3.3.3 Diseases 71

5.3.4 First-Pass Effect 715.4 Pharmacokinetic Basis of Drug Bioavailability

and Bioequivalence 725.5 Determination of Drug Bioavailability 72

5.5.1 Expected Values for Drug Bioavailability 745.5.2 Clinical Importance of Bioavailability

and Bioequivalence 745.6 Calculation of Area under the Curve

(Linear Trapezoidal Rule) 755.7 Regulatory Requirements for Bioavailability

and Bioequivalence 795.7.1 Design and Evaluation of Bioequivalence Studies 805.7.2 Criteria for Waiver of Bioavailability Requirements 81

5.8 Factors Affecting the Blood Concentration-Time Profileafter a Single Oral Dose 815.8.1 Dose 825.8.2 Bioavailability 825.8.3 Total Body Clearance 825.8.4 Volume of Distribution 825.8.5 Absorption Rate Constant 82

Practice Problems 82

Chapter 6Steady-State Principle and Drug Pharmacokineticsduring Constant-Rate Intravenous Infusion 876.1 Introduction 876.2 Plasma Concentration during Continuous Constant-Rate

IV Drug Administration 886.3 Time Required to Reach Steady State 896.4 Loading Dose 906.5 Determination of the Pharmacokinetic Parameters 92

6.5.1 Total Body Clearance 926.5.2 Elimination Rate Constant 926.5.3 Volume of Distribution 92

6.6 Effect of Changing the Pharmacokinetic Parameters on Steady-StatePlasma Concentration during Constant-Rate IV Infusion 946.6.1 Infusion Rate 946.6.2 Volume of Distribution 946.6.3 Total Body Clearance 94

Practice Problems 95

Chapter 7Steady State during Multiple Drug Administrations 997.1 Introduction 997.2 Drug Plasma Concentration-Time Profile during Multiple Drug

Administrations 1007.3 Average Plasma Concentration at Steady State 1027.4 Time Required to Reach Steady State 1047.5 Loading Dose 105

7.5.1 Intravenous Drug Administration 1057.5.2 Extravascular Drug Administration 105

7.6 Drug Accumulation 1057.7 Controlled-Release Formulations 1067.8 Effect of Changing the Pharmacokinetic Parameters on

Steady-State Plasma Concentration during Repeated DrugAdministration 1077.8.1 Dosing Rate 1077.8.2 Total Body Clearance 1077.8.3 Volume of Distribution 1077.8.4 Absorption Rate Constant 107

7.9 Dosage Regimen Design 1077.9.1 Factors to Be Considered 107

7.9.1.1 Therapeutic Range of the Drug 1077.9.1.2 Required Onset of Effect 1087.9.1.3 Drug Formulation 1087.9.1.4 Patient Disease State 108

7.9.2 Estimation of Patient Pharmacokinetic Parameters 1087.9.2.1 Lack of the Patient's Medical History 1087.9.2.2 Information Available about the Patient's

Medical History 1087.9.2.3 Patient with History of Using the Drug 108

7.9.3 Selection of Dose and Dosing Interval 1097.9.3.1 Controlled-Release Oral Formulation 1097.9.3.2 Fast-Release Oral Formulations and IV Bolus

Administration 1097.9.4 Selection of Loading Dose 110

Practice Problems 111

Chapter 8Renal Drug Elimination 1158.1 Introduction 1158.2 Mechanisms of Renal Excretion of Drugs 116

8.2.1 Glomerular Filtration 1168.2.2 Tubular Secretion 1168.2.3 Tubular Reabsorption 116

8.3 Determination of Renal Excretion Rate 1178.3.1 Experimental Determination of Renal Excretion Rate 1178.3.2 Renal Excretion Rate-Time Profile 118

8.4 Renal Clearance 1198.4.1 Creatinine Clearance as a Measure of Kidney Function 120

8.5 Cumulative Amount of the Drug Excreted in Urine 1218.5.1 Determination of Renal Clearance from

the Cumulative Amount Excreted in Urine 1228.6 Determination of Pharmacokinetic Parameters from Renal

Excretion Rate Data 1238.6.1 Elimination Rate Constant and Half-Life (k and t]/2) 1238.6.2 Renal Excretion Rate Constant ke 1238.6.3 Volume of Distribution Vd 1238.6.4 Renal Clearance CLR 1238.6.5 Fraction of Dose Excreted Unchanged in Urine 1248.6.6 Bioavailability 124

8.7 Effect of Changing the Pharmacokinetic Parameterson Urinary Excretion of Drugs 1278.7.1 Dose 1278.7.2 Total Body Clearance 1278.7.3 Renal Clearance 127

Practice Problems 128

Chapter 9Metabolite Pharmacokinetics 1319.1 Introduction 1319.2 Simple Model for Metabolite Kinetics 133

9.2.1 Elimination Rate Limitation 1359.2.2 Formation Rate Limitation 1369.2.3 Mathematical Description of Elimination Rate-

and Formation Rate-Limited Metabolites 1379.2.4 Time to Achieve Maximum Metabolite

Concentration 1379.3 General Model for Metabolite Kinetics 1389.4 Estimation of Metabolite Pharmacokinetic Parameters 140

9.4.1 Metabolite Elimination Rate Constant 1409.4.1.1 Elimination Rate-Limited Metabolites 1409.4.1.2 Formation Rate-Limited Metabolites 140

9.4.2 Fraction of the Parent Drug Converted to a SpecificMetabolite (or Amount of Metabolite Formed) 141

9.4.3 Metabolite Clearance 1429.4.4 Metabolite Volume of Distribution 1429.4.5 Metabolite Formation Clearance 142

9.5 Effect of Changing the Pharmacokinetic Parameters on Drugand Metabolite Concentration-Time Profiles after a SingleIV Drug Administration 1459.5.1 Drug Dose 1459.5.2 Drug Total Body Clearance CLp 1469.5.3 Drug Volume of Distribution Vd 1469.5.4 Fraction of Drug Dose Converted

to Metabolite fm 1469.5.5 Metabolite Total Body Clearance CL^ , 1479.5.6 Metabolite Volume of Distribution Vd(m, 147

9.6 Steady-State Metabolite Concentration during RepeatedAdministrations of Parent Drug 147

9.7 Effect of Changing the Pharmacokinetic Parameters on theSteady-State Drug and Metabolite Concentrations duringRepeated Drug Administrations 1509.7.1 Drug Dose 1509.7.2 Drug Total Body Clearance CI^ 1519.7.3 Drug Volume of Distribution Vd 1519.7.4 Fraction of Drug Dose Converted to Metabolite fm 1519.7.5 Metabolite Total Body Clearance CL^,, 1519.7.6 Metabolite Volume of Distribution Vd,m, 151

9.8 Metabolite Kinetics after Extravascular Administrationof the Parent Drug 151

9.9 Kinetics of Sequential Metabolism 152Practice Problems 153

Chapter 10Disease State and Drug Pharmacokinetics 15910.1 Introduction 15910.2 Patients with Kidney Dysfunction 159

10.2.1 Factors Affecting the Change in Drug Pharmacokineticsin Patients with Kidney Dysfunction 15910.2.1.1 Fraction of Dose Excreted Unchanged in Urine 15910.2.1.2 Degree of Kidney Dysfunction 160

10.2.2 Dosage Adjustment in Patients with Renal Dysfunction 16010.2.2.1 Determination of Kidney Function 16010.2.2.2 Determination of the Fraction of Dose Excreted

Unchanged in Urine 16110.2.2.3 Determination of Dosage Requirements in Patients

with Reduced Kidney Function 16110.3 Patients with Liver Diseases 163

10.3.1 Child-Pugh Score 164Practice Problems 165

Chapter 11Nonlinear Pharmacokinetics 16911.1 Introduction 169

11.1.1 Causes of Nonlinear Pharmacokinetics 16911.1.1.1 Saturable Drug Absorption 16911.1.1.2 Saturable Protein Binding 16911.1.1.3 Saturable Renal Elimination 17011.1.1.4 Saturable Drug Metabolism 17011.1.1.5 Others 170

11.1.2 Evidence of Nonlinear Pharmacokinetics 17011.2 Michaelis-Menten Enzyme Kinetics 170

11.2.1 Pharmacokinetic Parameters 17211.2.2 Plasma Concentration-Time Profile after a Single Intravenous

Dose of a Drug Eliminated by a Metabolic Pathway ThatFollows Michaelis-Menten Kinetics 17311.2.2.1 After a Single Drug Administration 17311.2.2.2 After Multiple Drug Administrations 174

11.3 Determination of the Pharmacokinetic Parameters 17511.3.1 Total Body Clearance 17511.3.2 Half-Life 176

11.4 Effect of Changing the Pharmacokinetic Parameters on PlasmaConcentration-Time Profile 17611.4.1 Dose 17611-4.2 Vmax 17611.4.3 Km 176

11.5 Oral Administration of Drugs Eliminated by a Michaelis-MentenProcess 177

11.6 Pharmacokinetic Parameter Determination and DosageRecommendation 17711.6.1 Mathematical Method 17711.6.2 Direct Linear Plot 17811.6.3 Linear Transformation Method 180

11.7 Multiple Elimination Pathways 180Practice Problems 181

Chapter 12Multicompartment Pharmacokinetic Models 18512.1 Introduction 18512.2 Two-Compartment Pharmacokinetic Model 18612.3 Two-Compartment Pharmacokinetic Model Parameters 189

12.3.1 Definition of the Pharmacokinetic Parameters 18912.3.2 Mathematical Equation That Describes the Plasma

Concentration-Time Profile 19012.4 Determination of Two-Compartment Pharmacokinetic

Model Parameters 19112.4.1 Method of Residuals 19112.4.2 Determination of Model Parameters 192

12.4.2.1 Volume of Central Compartment Vc 19312.4.2.2 Area under the Curve (AUC) 19312.4.2.3 Total Body Clearance CL[. 19312.4.2.4 First-Order Elimination Rate Constant

from Central Compartment k3 19312.4.2.5 First-Order Transfer Rate Constant from

Peripheral Compartment to CentralCompartment k2 193

12.4.2.6 First-Order Transfer Rate Constant fromCentral Compartment to PeripheralCompartment k, 194

12.4.2.7 Volume of Distribution at Steady State Vdss 19412.4.2.8 Volume of Distribution in Elimination Phase Vdg 194

12.5 Effect of Changing the Pharmacokinetic Parameters on DrugConcentration-Time Profile after a Single IV Dose 19612.5.1 Dose 19612.5.2 Volume of Distribution 19612.5.3 Hybrid Distribution Rate Constant a 19712.5.4 Hybrid Elimination Rate Constant P 197

12.6 Oral Administration of Drugs That Follow the Two-CompartmentPharmacokinetic Model 197

12.7 Constant Rate IV Administration of Drugs That Follow theTwo-Compartment Pharmacokinetic Model 198

12.8 Multiple Drug Administrations 19912.9 Renal Excretion of Drugs That Follow the Two-Compartment

Pharmacokinetic Model 19912.10 Effect of Changing the Pharmacokinetic Parameters on Drug

Distribution between Central and Peripheral Compartments 20012.10.1 Dose 20012.10.2 First-Order Transfer Rate Constant from

Central to Peripheral Compartment k, 200

12.10.3 First-Order Transfer Rate Constant fromPeripheral to Central Compartment k2 200

12.10.4 First-Order Elimination Rate Constant fromCentral Compartment k3 201

12.11 Three-Compartment Pharmacokinetic Model 201Practice Problems 202

Chapter 13Drug Pharmacokinetics Following Administration by IntermittentIntravenous Infusion 20513.1 Introduction 20513.2 Drug Concentration-Time Profile during

Intermittent IV Infusion 20613.2.1 After First Dose 20613.2.2 After Repeated Administration before Reaching

Steady State 20813.2.3 At Steady State 209

13.3 Effect of Changing the Pharmacokinetic Parameters onSteady-State Plasma Concentration during RepeatedIntermittent IV Infusion 21013.3.1 Dose 21013.3.2 Infusion Time 21013.3.3 Total Body Clearance 21013.3.4 Volume of Distribution 210

13.4 Application of Pharmacokinetic Principles for Intermittent IVInfusion to Therapeutic Use of Aminoglycoside 21013.4.1 Pharmacokinetic Characteristics 211

13.4.1.1 Absorption 21113.4.1.2 Distribution 21113.4.1.3 Excretion 211

13.4.2 Guidelines for Aminoglycoside Plasma Concentration 21113.4.3 Extended-Interval Aminoglycoside Dosing Regimen 212

13.5 Individualization of Aminoglycoside Therapy 21213.5.1 Determination of Initial Dosing Regimen Based

on Population Parameters 21213.5.2 Determination of Patient-Specific Pharmacokinetic

Parameters 21313.5.2.1 If the Patient Is to Receive the First

Aminoglycoside Dose 21313.5.2.2 If the Patient Received Aminoglycosides before

but the Steady State Was Not Achieved 21513.5.2.3 If the Patient Received Aminoglycosides

and Steady State Has Been Achieved 21613.5.3 Determination of the Dosing Regimen Based

on the Patient's Specific Parameters 217

13.5.3.1 Selection of Dosing Interval x 21713.5.3.2 Selection of Dose 21713.5.3.3 Selection of Loading Dose 217

Practice Problems 221

Chapter 14Noncompartmental Approach to Pharmacokinetic Data Analysis 22514.1 Introduction 22514.2 Noncompartmental Approach in Data Analysis 22614.3 Mean Residence Time 227

14.3.1 Calculation of AUC and AUMC 22814.3.1.1 Area Under the Plasma Concentration-Time Curve...22814.3.1.2 Area Under the First Moment-Time Curve 228

14.3.2 Mean Residence Time after Different Routesof Administration 23114.3.2.1 Mean Residence Time after Extravascular

Administration 23114.3.2.2 The Mean Residence Time after Constant-Rate

IV Infusion 23314.4 Other Pharmacokinetic Parameters That Can Be Determined

Using the Noncompartmental Approach 23314.5 Determination of Mean Residence Time for Compartmental Models....234Practice Problems 235

Chapter 15Physiological Approach to Hepatic Clearance 23715.1 Introduction 23715.2 Organ Clearance 23715.3 Hepatic Extraction Ratio 23815.4 Intrinsic Clearance (CLint) 23915.5 Systemic Bioavailability 23915.6 Effect of Change in Intrinsic Clearance and Hepatic

Blood Flow on Hepatic Clearance, Systemic Availability,and Drug Concentration-Time Profile 24015.6.1 Low Extraction Ratio Drugs 24015.6.2 High Extraction Ratio Drugs 243

15.7 Protein Binding and Hepatic Extraction 250Practice Problems 250

Chapter 16Pharmacokinetic-Pharmacodynamic Relationship 25316.1 Introduction 25316.2 Pharmacodynamic Models 254

16.2.1 Fixed-Effect Model 25516.2.2 Linear Model 25516.2.3 Log-Linear Model 256

16.2.4 Emax Model 25716.2.5 Sigmoid Emax Model 259

16.3 Link between Pharmacokinetic and PharmacodynamicModels 260

16.4 Application of Pharmacodynamic Models 26016.4.1 Duration of Drug Effect 26016.4.2 Dosing Regimen 261

Practice Problems 261

Chapter 17Therapeutic Drug Monitoring 26317.1 Introduction 26317.2 General Principles of Initiation and Management

of Drug Therapy 26317.3 Drug Blood Concentration versus Drug Dose 26417.4 Therapeutic Range 26517.5 Variability in Drug Pharmacokinetics and Response 267

17.5.1 Body Weight 26717.5.2 Age 267

17.5.2.1 Pediatrics 26717.5.2.2 Geriatrics 267

17.5.3 Drug-Drug Interactions 26817.5.4 Genetic Factors 26817.5.5 Pregnancy 26817.5.6 Diseases 26817.5.7 Other Factors 269

17.6 Advantages of Therapeutic Drug Monitoring 26917.6.1 Facilitate Rapid Achievement of an Appropriate

Dosing Regimen 26917.6.2 Evaluate Existing Dosing Regimen 26917.6.3 Prophylaxis against Toxicity 26917.6.4 Distinguish between Pharmacokinetic and Pharmacodynamic

Causes of Therapeutic Failure 26917.6.5 Cost-Effectiveness 269

17.7 Candidate Drugs For Therapeutic Drug Monitoring 27017.7.1 Drugs with Low Therapeutic Index 27017.7.2 Drugs with Great Variability in Their Pharmacokinetic

Properties 27017.7.3 Drugs Used in Patients Who Are at High Risk

of Toxicity 27017.8 Methods for Measuring Drug Blood Concentrations 27017.9 Establishing a Therapeutic Drug Monitoring Service 271

17.9.1 Major Requirements 27117.9.2 Procedures 271

17.9.2.1 Determination of Initial Dosing Regimen 271

17.9.2.2 Determination of the Patient's SpecificPharmacokinetic Parameters 271

17.9.2.3 Calculation of Dosage Requirements Basedon the Patient's Specific PharmacokineticParameters of the Drug 272

Questions 272

Chapter 18Solutions to Practice Problems 273

Index 285