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Handbook of Pharmacokinetics and Toxicokinetics This fully revised and expanded volume is an effort to blend the common approaches to pharmacokinetics and toxicokinetics. It integrates the principles held in common by both felds through a logical and systematic approach, which includes mathematical descriptions of physical and physiological processes employed in the approaches to pharmacokinetics and toxicokinetics modeling. It emphasizes general principles and concepts and related, isolated applications and case study observations. The systematic compilation of mathematical concepts and methodologies allows readers to decide on relevant concepts and approaches for their research, scientifc or regulatory decisions, or for offering advanced courses/workshops and seminars. Features: ◾ Comprehensive handbook on principles and applications of PK/TK appealing to a diverse audience including scientists and students. ◾ An excellent text fully revised and fully updated for anyone interested in the theoretical and practical pharmacokinetics. ◾ The systematic compilation of mathematical concepts and methodologies allows readers to decide on relevant concepts and approaches for their research. ◾ Incorporates research relevant to SDGs and of interest to industrial and regulatory environmental scientists involved in chemical contamination research and regulatory decision making related to soil, water, and ocean. ◾ Includes sections on applications and case studies. Dr Mehdi Boroujerdi earned his PhD in pharmaceutics and pharmacokinetics from the University of North Carolina at Chapel Hill in 1978. He completed his post-doctoral training at the National Institutes of Health, National Institute of Environmental Health Sciences at Research Triangle Park. He served as professor of pharmaceutics/pharmacokinetics with tenure at Northeastern University, Boston, MA (1982–2002); professor of pharmaceutics and pharmacokinetics at the MCPHS University, School of Pharmacy, Boston, MA (2002–2005); professor of pharmaceutical sciences with tenure at the Albany College of Pharmacy and Health Sciences, Albany, New York (2005–2015); and professor of pharmaceutical sciences with tenure at the College of Health Sciences, University of Massachusetts, Lowell, MA (2015–2017). Dr Boroujerdi has also served as Dean of the School of Pharmacy at Bouvé College of Health Sciences at Northeastern University (1988–1999); as Dean of the School of Pharmacy-Boston at MCPHS University (2002–2005); as Dean of Pharmacy and Vice President for Academic Affairs, Provost, at the Albany College of Pharmacy and Health Sciences (2006–2012); and Founding Dean of the School of Pharmacy and Pharmaceutical Sciences at the College of Health Sciences, University of Massachusetts at Lowell (2015–2017). He also served as the Dean of Research and Graduate Studies at MCPHS (2003–2005), and Director of Graduate Programs in Biomedical Sciences at Northeastern University (1988–1999). Dr Mehdi Boroujerdi has 112 peer-reviewed publications and is the sole author of two books Pharmacokinetics, Principles and Applications (McGraw Hill, 2002) and Pharmacokinetics and Toxicokinetics (CRC Publications, 2015). He has trained many graduate and undergraduate students through his research programs focused on pharmacokinetics and toxicodynamics of anticancer drugs, carcinogenesis, and effux proteins. He also served as consultant to fve pharmaceutical companies. As a professor he taught graduate courses in advanced pharmacokinetics and biopharmaceutics, drug metabolism, advanced pharmaceutics, and drug delivery systems. His teaching of undergraduate courses included drug discovery and development, biopharmaceutics and pharmacokinetics, physical pharmacy and pharmaceutics, and pharmacokinetics in disease states.
Handbook of Pharmacokinetics and Toxicokinetics Second Edition
Mehdi Boroujerdi
Second edition published 2023 by CRC Press 4 Park Square, Milton Park, Abingdon, Oxon, OX14 4RN and by CRC Press 6000 Broken Sound Parkway NW, Suite 300, Boca Raton, FL 33487-2742 © 2023 Mehdi Boroujerdi First edition published by CRC Press 2015 CRC Press is an imprint of Informa UK Limited The right of Mehdi Boroujerdi to be identifed as author of this work has been asserted in accordance with sections 77 and 78 of the Copyright, Designs and Patents Act 1988. This book contains information obtained from authentic and highly regarded sources. While all reasonable efforts have been made to publish reliable data and information, neither the author[s] nor the publisher can accept any legal responsibility or liability for any errors or omissions that may be made. The publishers wish to make clear that any views or opinions expressed in this book by individual editors, authors or contributors are personal to them and do not necessarily refect the views/opinions of the publishers. The information or guidance contained in this book is intended for use by medical, scientifc or health-care professionals and is provided strictly as a supplement to the medical or other professional’s own judgement, their knowledge of the patient’s medical history, relevant manufacturer’s instructions and the appropriate best practice guidelines. Because of the rapid advances in medical science, any information or advice on dosages, procedures or diagnoses should be independently verifed. The reader is strongly urged to consult the relevant national drug formulary and the drug companies’ and device or material manufacturers’ printed instructions, and their websites, before administering or utilizing any of the drugs, devices or materials mentioned in this book. This book does not indicate whether a particular treatment is appropriate or suitable for a particular individual. Ultimately it is the sole responsibility of the medical professional to make his or her own professional judgements, so as to advise and treat patients appropriately. The authors and publishers have also attempted to trace the copyright holders of all material reproduced in this publication and apologize to copyright holders if permission to publish in this form has not been obtained. If any copyright material has not been acknowledged please write and let us know so we may rectify in any future reprint. All rights reserved. No part of this book may be reprinted or reproduced or utilised in any form or by any electronic, mechanical, or other means, now known or hereafter invented, including photocopying and recording, or in any information storage or retrieval system, without permission in writing from the publishers. For permission to photocopy or use material electronically from this work, access www.copyright.com or contact the Copyright Clearance Center, Inc. (CCC), 222 Rosewood Drive, Danvers, MA 01923, 978-750-8400. For works that are not available on CCC please contact mpkbookspermissions@tandf.co.uk Trademark notice: Product or corporate names may be trademarks or registered trademarks and are used only for identifcation and explanation without intent to infringe. British Library Cataloguing-in-Publication Data A catalogue record for this book is available from the British Library
Library of Congress Cataloging-in-Publication Data Names: Boroujerdi, Mehdi, author. Title: Handbook of pharmacokinetics and toxicokinetics / Mehdi Boroujerdi. Other titles: Pharmacokinetics and toxicokinetics Description: Second edition. | Abingdon, Oxon ; Boca Raton, FL : CRC Press, 2023. | Revised edition of: Pharmacokinetics and toxicokinetics / Mehdi Boroujerdi. [2015]. | Includes bibliographical references and index. | Identifers: LCCN 2022054962 | ISBN 9781032197050 (hbk) | ISBN 9781032197470 (pbk) | ISBN 9781003260660 (ebk) Subjects: LCSH: Pharmacokinetics. | Drugs--Toxicology. Classifcation: LCC RM301.5 .B658 2023 | DDC 615.7--dc23/eng/20221214 LC record available at https://lccn.loc.gov/2022054962 ISBN: 9781032197050 (hbk) ISBN: 9781032197470 (pbk) ISBN: 9781003260660 (ebk) DOI: 10.1201/9781003260660 Typeset in Warnock Pro by Deanta Global Publishing Services, Chennai, India
I dedicate this book with much love to my sons Mazy and Bob. –Mehdi Boroujerdi
Table of Contents Preface
xxvii
1 Pharmacokinetics and Toxicokinetics
1
1 1 Introduction
1
1 2 Pharmacokinetics and Pharmacodynamics
1
1 2 1 Clinical Pharmacokinetics/Pharmacodynamics
3
1 2 2 PK/PD Modeling and Pharmacometrics
3
1 2 3 Population PK and PK/PD Modeling
4
1 2 3 1 Infuences of Genetics and Genomics on PK/PD and TK/TD
5
1 2 3 2 Biomarkers
7
1 3 Toxicokinetics and Toxicodynamics
9
1 3 1 TK/TD Modeling, Population Toxicokinetics, and Toxicogenetics
9
1 4 Basic Concepts and Assumptions of PK and TK
10
1 5 Introduction to the Routes of Administration
12
References
13
2 PK/TK Considerations of Auricular (Otic) – Buccal/Sublingual, and Ocular/ Ophthalmic Routes of Administration
19
2 1 Auricular or OTIC Route of Administration
19
2 1 1 Overview
19
2 1 2 Blood-Labyrinth-Barrier and Auricular Absorption, Distribution, Metabolism, and Excretion
20
2 1 2 1 Syndromes and the Sites of Absorption
20
2 1 2 2 Auricular Distribution, Metabolism, and Excretion 2 1 3 Auricular Rate Equations and PK/TK Models 2 2 Buccal and Sublingual Routes of Administration
21 22 24
2 2 1 Overview
24
2 2 2 Buccal and Sublingual ADME and Related Rate Equations
25
2 2 3 Saliva
27
2 3 Ocular/Ophthalmic Routes of Administration 2 3 1 Overview
29 29
2 3 2 The Blood Aqueous Barrier
29
2 3 3 The Blood-Retinal Barrier
30
2 3 3 1 BRB Effux Transporters
31
2 3 3 2 BRB Infux Transporters
31
2 3 4 Kinetics of BRB Infux Permeability Clearance – Small Water-Soluble Compounds Given Systemically
32
2 3 5 Recommended Ocular Routes for Drug Administration
33
2 3 5 1 Conjunctival Route of Administration
33
2 3 5 2 Subconjunctival Route of Administration
34
2 3 5 3 Intracameral Route of Administration
34 vii
TABLE OF CONTENTS
2 3 5 4 Intravitreal Route of Administration
34
2 3 5 5 Intracorneal Route of Administration
37
2 3 5 6 Retrobulbar, Peribulbar, and Sub-Tenon Routes of Administration
41
References
42
3 PK-TK Considerations of Nasal, Pulmonary and Oral Routes of Administration 3 1 Nasal Route of Administration/Exposure
50 50
3 1 1 Vestibule, Atrium, Valves, and Turbines
50
3 1 2 Mucosal Epithelium
50
3 1 3 Olfactory Epithelium
52
3 1 4 Nasal ADME of Xenobiotics
53
3 1 5 Nasal Rate Equations – PK/TK Models
54
3 1 5 1 A Nose-to-Systemic Circulation PK/TK Model
54
3 1 5 2 An Inclusive Nose-to-Brain PK/TK Model
56
3 2 Pulmonary Route of Administration/Exposure
58
3 2 1 Overview
58
3 2 2 Morphological Differences of Airways Among Species
59
3 2 3 Pulmonary Microbiome
59
3 2 4 ADME of Xenobiotics in the Pulmonary Tract
60
3 2 4 1 Pulmonary Absorption, Deposition, and Clearance
60
3 2 4 2 Transport Proteins of Pulmonary Tract
60
3 2 4 3 Respiratory Tract Metabolic Enzymes – Lung Metabolism of Xenobiotics
61
3 2 4 4 Pulmonary Deposition and Disposition of Particles
62
3 2 4 5 Pulmonary Absorption of Gases and Vapors
63
3 2 4 6 Relevant Pulmonary Kinetic Parameters
66
3 2 4 7 Role of the Lungs in PK/TK of Xenobiotics: Pulmonary First-Pass Metabolism 3 2 4 8 Pulmonary Rate Equations 3 3 Gastrointestinal (Oral) Route of Administration or Exposure 3 3 1 Overview
67 67 73 73
3 3 2 Physiologic and Dynamic Attributes of the GI Tract Infuencing Xenobiotic Absorption 3 3 2 1 Regional pH of GI Tract and pH-Partition Theory
74
3 3 2 2 Absorptive Surface Area
77
3 3 2 3 Gastric Emptying and Gastric Accommodation
78
3 3 2 4 Intestinal Motility: Small Intestinal Transit Time
80
3 3 2 5 Role of Bile Salts
81
3 3 2 6 Hepatic First-Pass Metabolism (Pre-systemic Hepatic Extraction)
81
3 3 2 7 Gastrointestinal Metabolism – Role of CYP450 Isozymes
84
3 3 2 8 GI Tract Infux and Effux Transport Proteins
86
3 3 2 9 Role of Intestinal Microbiotas References viii
74
89 90
TABLE OF CONTENTS
4 PK/TK Considerations of Intra-Arterial, Intramuscular, Intraperitoneal, Intravenous, and Subcutaneous Routes of Administration
50
4 1 Intra-Arterial Route of Administration
107
4 1 1 Overview
107
4 1 2 Intra-Arterial PK/TK Remarks
107
4 2 Intramuscular Route of Administration
107
4 2 1 Overview
107
4 2 2 ADME of Intramuscular Route of Administration
108
4 2 2 1 Rate Equations of Intramuscularly Injected Xenobiotics 4 3 Intraperitoneal Route of Administration 4 3 1 Overview 4 3 1 1 Applications of the IP Route of Administration 4 3 2 Kinetics of Intraperitoneal Transport of Xenobiotics 4 4 Intravenous Route of Administration 4 4 1 Overview
109 112 112 113 114 119 119
4 4 1 1 Intravenous Injection Drawbacks
120
4 4 1 2 Bolus Injection, Continuous Infusion, Intermittent Infusion
120
4 4 2 Intravenous PK/TK Analysis
120
4 5 Subcutaneous Route of Administration
121
4 5 1 Overview
121
4 5 2 Rate Equations of Subcutaneously Injected Xenobiotics
122
4 5 2 1 Subcutaneous Diffusion Rate-Limited Model
122
4 5 2 2 Subcutaneous Dissolution Rate-Limited Model
123
4 5 2 3 Subcutaneous Capacity-Limited Model
123
4 5 2 4 Subcutaneous Models Based on Diffusion Equations
124
4 5 2 5 Other PK Models for Subcutaneous Insulin
125
References
126
5 PK/TK Considerations of Transdermal, Intradermal, and Intraepidermal Routes of Administration
132
5 1 Transdermal Route of Administration
132
5 1 1 Overview
132
5 1 2 Stratum Corneum
132
5 1 3 Epidermis
134
5 1 4 Dermis
135
5 1 4 1 Dermis Cells
135
5 1 4 2 Dermis Appendages
135
5 1 5 Transdermal Absorption, Metabolism, and Disposition
136
5 1 5 1 Transdermal Absorption
136
5 1 5 2 Cutaneous Metabolism of Xenobiotics
138
5 1 5 3 Skin Transport Proteins
139
5 1 6 Mathematical Interpretations of Transdermal Absorption of Xenobiotics
139 ix
TABLE OF CONTENTS
5 1 6 1 Diffusion Models
140
5 1 6 2 Skin-Perm Model
141
5 1 6 3 One-Layered Diffusion Model
142
5 1 6 4 Two-Layered Diffusion Model
143
5 1 6 5 Compartmental Analysis
145
5 1 6 6 Diffusion–Diffusion Model and Statistical Moments for Percutaneous Absorption 5 1 6 7 Physiological Modeling of Percutaneous Absorption of Xenobiotics
153 155
5 1 6 8 Six-Compartment Intradermal Disposition Kinetics of Xenobiotics with Contralateral Compartments 5 2 Intradermal Route of Administration 5 2 1 Overview
156 158 158
5 2 2 PK/TK Parameters and Constants of Drug Absorption from Intradermal Space to Blood 5 3 Intraepidermal Route of Administration 5 3 1 Overview References
159 159 160
6 PK/TK Considerations of Rectal, Vaginal, and Intraovarian Routes of Administration 6 1 Rectal Route of Administration
167 167
6 1 1 Overview
167
6 1 2 Pharmacokinetic Considerations of the Rectal Route of Administration
167
6 2 Vaginal Route of Administration 6 2 1 Overview
169 169
6 2 2 Vaginal Microbiota
170
6 2 3 Pharmacokinetic Considerations of the Vaginal Route of Administration
170
6 3 Intraovarian Route of Administration 6 3 1 Overview References
173 173 173
7 PK/TK Considerations of Absorption Mechanisms and Rate Equations
177
7 1 Introduction
177
7 2 Passive Diffusion
177
7 2 1 Transcellular and Paracellular Diffusion 7 2 1 1 Transcellular and Paracellular Transport Rate Equations 7 2 2 Partition Coeffcient
177 178 180
7 2 2 1 CLOGPcoeff
181
7 2 2 2 MLOGPcoeff
182
7 2 3 Distribution Coeffcient
183
7 2 4 Diffusion Coeffcient
184
7 2 5 Permeation and Permeability Constant
185
7 2 5 1 Estimation of Apparent Permeability Constant Using Caco-2 Cells 7 3 Carrier-Mediated Transcellular Diffusion x
158
187 188
TABLE OF CONTENTS
7 4 Transcellular Diffusion Subjected to P-Glycoprotein Effux
189
7 4 1 Overview
189
7 4 2 Pgp Structure and Function
189
7 4 3 Pgp Computational Equations
192
7 5 Active Transport
194
7 6 Endocytosis and Pinocytosis
196
7 7 Solvent Drag, Osmosis, and Two-Pore Theory
196
7 8 Ion-Pair Absorption
198
References
200
8 PK – TK Considerations of Distribution Mechanisms and Rate Equations
210
8 1 Introduction
210
8 2 Factors Infuencing the Distribution of Xenobiotics in the Body
210
8 2 1 Infuence of Total Body Water on Xenobiotic Distribution
210
8 2 2 Effect of Blood Flow and Organ/Tissue Perfusion on Xenobiotic Distribution
211
8 2 2 1 Perfusion-Limited Distribution and Permeability-Limited Distribution (Transcapillary Exchange of Xenobiotics)
213
8 2 3 Effect of Binding to Plasma Proteins on Xenobiotic Distribution
216
8 2 3 1 Estimation of Protein-Binding Parameters
217
8 2 4 Infuence of Physicochemical Characteristics of Xenobiotics on Their Distribution
221
8 2 5 Infuence of Extent of Penetration Through the Physiological Barriers, and Parallel Removal Processes on Xenobiotic Distribution 8 2 6 Physiological Barriers
221 222
8 2 6 1 Blood–Brain Barrier
222
8 2 6 2 Blood–Lymph Barrier
227
8 2 6 3 Placental Barrier
227
8 2 6 4 Blood–Testis Barrier
228
8 2 6 5 Blood–Aqueous Humor Barrier (BAB) – also Read Chapter 2, Section 232
229
8 2 7 Effect of Body Weight and Composition on Xenobiotic Distribution 8 2 7 1 Ideal Body Weight (IBW in kg)
229 229
8 2 7 2 Body Surface Area (BSA in m )
229
8 2 7 3 Body Mass Index (BMI in kg/m2)
230
8 2 7 4 Lean Body Mass (LBM in kg)
230
2
8 2 8 Impact of Disease States on Xenobiotic Distribution
230
8 2 8 1 Congestive Heart Failure (CHF)
230
8 2 8 2 Chronic Renal Failure (CRF)
230
8 2 8 3 Hepatic Diseases
231
8 2 8 4 Cystic Fibrosis (CF)
231
8 2 8 5 Other Conditions
231
8 3 Applications and Case Studies
231
References
231 xi
TABLE OF CONTENTS
9 PK/TK Considerations of Xenobiotic Metabolism Mechanisms and Rate Equations
237
9 2 Liver
237
9 3 Metabolic Pathways
239
9 3 1 Phase I Metabolism
240
9 3 1 1 Flavin-Containing Monooxygenases
240
9 3 1 2 Flavin-Containing Amine Oxidoreductases
240
9 3 1 3 Epoxide Hydrolases
241
9 3 1 4 Cytochrome P450
241
9 3 1 5 Alcohol Dehydrogenase
245
9 3 1 6 Diamine Oxidase (Histaminase)
246
9 3 1 7 Aldehyde Dehydrogenases
246
9 3 1 8 Xanthine Oxidase
247
9 3 1 9 Carboxylesterases
247
9 3 1 10 Peptidase (Protease/Proteinase)
247
9 3 2 Phase II Metabolism: Conjugation
248
9 3 2 1 Glucuronidation
248
9 3 2 2 Sulfation
250
9 3 2 3 Methylation
251
9 3 2 4 Acetylation (Acylation)
252
9 3 2 5 Glutathione Conjugation
253
9 3 2 6 Amino Acid Conjugation
254
9 3 3 In Vitro Systems for Xenobiotics Metabolism Study 9 3 3 1 Subcellular Fractions
255 255
9 3 3 2 Cellular Fractions – Hepatocytes
257
9 3 3 3 Organ Fractions (Precision Cut Liver Slices)
258
9 3 3 4 In-Situ and Ex-Vivo Liver Perfusion Techniques
258
9 3 3 5 Antibodies Against CYP Proteins
260
9 3 3 6 bDNA Probes
260
9 3 3 7 Pure and Recombinant Enzymes
260
9 3 3 8 Cell Lines
260
9 3 4 In Vivo Samples for Xenobiotic Metabolism Study
261
9 3 4 1 Serum and Plasma Samples
261
9 3 4 2 Urine Samples
262
9 3 4 3 Bile Samples
262
9 3 4 4 Portal Vein Cannulation
263
9 4 Kinetics of In Vitro Metabolism
xii
237
9 1 Introduction
263
9 4 1 Michaelis–Menten Kinetics
263
9 4 2 In Vitro Intrinsic Metabolic Clearance
267
9 4 3 The Catalytic Effciency and Turnover Number
267
9 4 4 Estimation of the Michaelis–Menten Parameters
267
TABLE OF CONTENTS
9 4 4 1 Lineweaver–Burk Plot or Double Reciprocal Plot
267
9 4 4 2 Hanes–Woolfe Plot
268
9 4 4 3 Eadie–Hofstee Plot
269
9 4 4 4 Direct Linear Plot
269
9 4 4 5 Hill Plot 9 4 5 Assimilation of Intrinsic Clearance in Hepatic Clearance Using Liver Models
270 271
9 4 5 1 The Well-Stirred Model (Venous Equilibration Model)
272
9 4 5 2 The Parallel-Tube Model (Undistributed Sinusoidal Model)
273
9 4 5 3 The Dispersion Model
274
9 4 5 4 Physiological PK/TK Organ Model for the Liver
274
9 4 5 5 Zonal Liver Model
276
9 4 6 Inhibition of Xenobiotic Metabolism
276
9 4 6 1 Classifcations of Metabolic Inhibition 9 4 7 Induction of Xenobiotic Metabolism
277 285
9 5 Applications and Case Studies
286
References
286
10 PK – TK Considerations of Renal Function and Elimination of Xenobiotics - Estimation of Parameters and Constants
309
10 1 Introduction
309
10 2 Glomerular Filtration
309
10 3 Tubular Reabsorption and Secretion
309
10 4 Loop of Henle, Distal Tubule, and Collecting Ducts
311
10 5 Estimation of GFR
312
10 5 1 Exogenous Markers of GFR
312
10 5 1 1 Radioisotope-Labeled Compounds
312
10 5 1 2 Inulin
312
10 5 1 3 Iohexol
313
10 5 2 Endogenous Markers of GFR (GFR Biomarkers)
313
10 5 2 1 Creatinine Clearance
313
10 5 2 2 Cystatin C
317
10 6 PK/TK Analysis of Urinary Data
318
10 6 1 PK/TK Analysis of Urinary Excretion of Unchanged Xenobiotic – Intravenous Bolus Injection
320
10 6 1 1 Rate Plot – Intravenous Bolus Dose
321
10 6 1 2 ARE Plot aka Sigma-Minus Plot – Intravenous Bolus Dose
323
10 6 2 PK/TK Analysis of Urinary Elimination of Xenobiotic Metabolites Following Intravenous Bolus Injection
325
10 6 2 1 Amount of Metabolite Remaining to be Eliminated from the Body Following IV Bolus Dose Administration
326
10 6 2 2 Urinary Elimination Rate of Metabolite and Estimation of Metabolic Rate Constant
327 xiii
TABLE OF CONTENTS
10 6 3 PK/TK Analysis of Urinary Excretion of Unchanged Xenobiotic Following Zero-Order Intravenous Infusion
327
10 6 3 1 Urinary Excretion Rate of Unchanged Xenobiotic During Zero-Order Intravenous Infusion and After Attaining the Steady-State Level
327
10 6 3 2 Cumulative Amount of Urinary Excretion of Unchanged Xenobiotic During Zero-Order Intravenous Infusion
329
10 6 4 PK/TK Analysis of Urinary Excretion of Unchanged Xenobiotic Following First-Order Absorption from an Extravascular Route of Administration
329
10 6 4 1 Urinary Excretion Rate of Unchanged Xenobiotic Following FirstOrder Absorption into the Systemic Circulation and Estimation of Absorption Rate Constant
329
10 6 4 2 Amount of Xenobiotic Remaining to be Excreted Unchanged in the Urine Following the First-Order Absorption into the Systemic Circulation from an Extravascular Route of Administration
331
10 6 5 PK/TK Analysis of Urinary Excretion of Unchanged Xenobiotics that Follow the Two-Compartment Model Subsequent to Intravenous Bolus Injection
333
10 6 5 1 Urinary Excretion Rate of Unchanged Xenobiotic Following Intravenous Bolus Injection – Two-Compartment Model
333
10 6 5 2 Amount of Xenobiotic Remaining to be Excreted Unchanged in the Urine Following an Intravenous Bolus Injection – TwoCompartment Model
334
10 6 6 General Equations of PK/TK Multicompartment Analysis of Urinary Excretion Data – First-Order Absorption and Intravenous Infusion
336
10 6 7 PK/TK Analysis of Urinary Excretion Data Using Principles of NonCompartmental Analysis
337
10 7 Renal Metabolism
338
10 8 Renal Mechanistic Models
338
10 9 Estimation of PK/TK Parameters and Constants of Xenobiotics Elimination When Using Renal Replacement Therapy – Dialysis
340
10 9 1 Overview
340
10 9 2 Hemodialysis
341
10 9 3 Peritoneal Dialysis
341
10 9 4 Composition of Dialysate
341
10 9 5 Dialysis Clearance
342
10 9 6 Effects of Dialysis on PK/TK Parameters and Constants
343
10 10 Applications and Case Studies
346
References
346
11 Elimination Rates and Clearances (Excretion + Metabolism)
xiv
352
11 1 Introduction
352
11 2 Rates of Elimination
353
11 3 Extraction Ratio
353
TABLE OF CONTENTS
11 4 Clearances
355
11 4 1 Estimation of Clearance Using Theoretical Models
356
11 4 1 1 Well-Stirred Model
356
11 4 1 2 Parallel Model
358
11 4 1 3 Dispersion Model
358
11 4 2 Clearance Scale-Up in Mammalian Species
359
11 4 2 1 Extrapolation of Clearance from Animal to Human
359
11 4 2 2 Body-Weight Dependent Extrapolation of Clearance in Humans
361
11 4 3 Clearance Estimation in Linear PK/TK
362
11 4 4 Clearance Estimation in Nonlinear PK/TK
363
11 4 4 1 Nonlinear Clearance in Target-Mediated Drug Disposition References
364 364
12 Approaches in PK/PD and TK/TD Mathematical Modeling
368
12 1 Introduction
368
12 2 Physiologically Based PK/TK Models
368
12 2 1 Description
368
12 2 2 Model Development
371
12 2 2 1 Flow-Limited (Perfusion-Limited) Models
372
12 2 2 2 Permeability-Limited (Membrane-Limited) Models
374
12 2 2 3 Variability of Physiological/Biochemical Key Parameters
375
12 2 3 Predictive Capability and Sensitivity Analysis 12 3 Linear PK/TK Compartmental Analysis 12 3 1 Linear Dose-Independent Compartmental Analysis
376 378 379
12 3 1 1 Mathematical Descriptions of a Xenobiotic Administered via an Extravascular Route of Administration: Time Course of the Amount Change at the Site of Absorption in the Body and the Eliminated Amount from the Body
379
12 3 1 2 Mathematical Description of a Xenobiotic Administered Intravenously – Time Course of the Amount Change in the Body, Formation of Metabolite(s), and Elimination from the Body
381
12 3 1 3 Mathematical Relationships of the Central Compartment for an Intravenously Administered Xenobiotic that Follows Multicompartment Model: Use of Input-Disposition Function and General Partial Fraction Theorem
383
12 3 1 4 Mathematical Relationships of the Peripheral Compartment for an Intravenously Administered Xenobiotic that Follows Multicompartment Model: Use of Input-Disposition Function and General Partial Fraction Theorem
385
12 3 1 5 Mathematical Relationships When a Xenobiotic and Its Metabolite(s) Follow Multicompartmental Model – Intravenous Bolus Dose 12 3 2 Dose-Dependent Compartmental Analysis 12 3 2 1 Compartmental Models with Michaelis–Menten Kinetics
386 388 388 xv
TABLE OF CONTENTS
12 4 Non-Compartmental Analysis Based on Statistical Moment Theory
392
12 4 1 Overview
392
12 4 2 Mean Residence Time and Mean Input Time
393
12 4 3 Total Body Clearance and Apparent Volume of Distribution
394
12 5 PK-PD and TK-TD Modeling
395
12 5 1 Overview
395
12 5 2 Xenobiotic–Receptor Interaction and the Law of Mass Action
396
12 5 3 Pharmacodynamic Models of Plasma Concentration and Response
398
12 5 3 1 Linear Pharmacodynamic Model
398
12 5 3 2 Log-Linear Pharmacodynamic Model
399
12 5 3 3 Nonlinear Hyperbolic Emax Model
400
12 5 3 4 Non-Hyperbolic Sigmoidal Model
400
12 5 4 PK/PD and TK/TD Models
402
12 5 4 1 Linking the Nonlinear Hyperbolic Emax Concept to Compartmental Models
404
12 5 4 2 Linking Non-Hyperbolic Sigmoidal Model to PK/TK Models with Different Inputs
406
12 5 5 The Effect Compartment
407
12 5 5 1 PK/TK Models Connected to the Effect Compartment
408
12 6 Physiologically Based PK/TK Models with Effect Compartment
411
12 7 Hysteresis Loops in PK/PD or TK/TD Relationships
412
12 8 Target-Mediated Drug Disposition Models
413
12 8 1 One-Compartment TMDD Models
414
12 8 2 Two-Compartment TMDD Models
415
References
417
13 Practical Applications of PK/TK Models: Instantaneous Exposure to Xenobiotics Single Intravenous Bolus Injection
423
13 1 Introduction
423
13 2 Linear One-Compartment Open Model – Intravenous Bolus Injection
423
13 2 1 Half-Life of Elimination
425
13 2 2 Time Constant
425
13 2 3 Apparent Volume of Distribution
425
13 2 4 Total Body Clearance
426
13 2 5 Duration of Action
426
13 2 6 Estimation of Fraction of Dose in the Body at a Given Time
427
13 2 7 Estimation of Fraction of Dose Eliminated by All Routes of Elimination at a Given Time
427
13 2 8 Determination of the Area Under Plasma Concentration–Time Curve after Intravenous Bolus Injection
427
13 3 Linear Two-Compartment Open Model with Bolus Injection in the Central Compartment and Elimination from the Central Compartment xvi
428
TABLE OF CONTENTS
13 3 1 Equations of the Two-Compartment Model
429
13 3 2 Estimation of the Initial Plasma Concentration and Volumes of Distribution, Two-Compartment Model 13 3 3 Estimation of the Rate Constants of Distribution and Elimination 13 3 4 Half-Lives of the Two-Compartment Model
432 433 433
13 3 4 1 Biological Half-Life – Two-Compartment Model
434
13 3 4 2 Elimination Half-Life – Two-Compartment Model
434
13 3 4 3 Half-Life of α – Two-Compartment Model
434
13 3 4 4 Half-Life of k12
434
13 3 4 5 Half-Life of k 21
434
13 3 5 Determination of the Area Under the Plasma Concentration–Time Curve, Volumes of Distribution, and Clearances – Two-Compartment Model
435
13 3 6 Assessment of the Time Course of Xenobiotics in the Peripheral Compartment – Two-Compartment Model
436
13 4 Linear Two-Compartment Open Model with Bolus Injection in the Central Compartment and Elimination from the Peripheral Compartment
438
13 5 Linear Three-Compartment Open Model with Intravenous Bolus Injection and Elimination from the Central Compartment
440
13 6 Linear Three-Compartment Open Model with Intravenous Bolus Injection in the Central Compartment and Elimination from a Peripheral Compartment
442
13 7 Model Selection
444
13 8 Applications and Case Studies
444
References
444
14 Practical Applications of PK/TK Models: Continuous Zero-Order Exposure to Xenobiotics Intravenous Infusion
446
14 1 Introduction
446
14 2 Compartmental Analysis
447
14 2 1 Linear One-Compartment Model with Zero-Order Input and First-Order Elimination
447
14 2 1 1 Estimation of the Time Required to Achieve Steady-State Plasma Concentration Using a Single Long-Term Infusion
449
14 2 1 2 Administration of Loading Dose with Intravenous Infusion to Achieve the Steady-State Level Without a Long Delay
450
14 2 1 3 Estimation of Plasma Concentration after Termination of Infusion
452
14 2 1 4 Estimation of Duration of Action in Infusion Therapy
453
14 2 2 Linear Two-Compartment Model with Zero-Order Input and First-Order Disposition
454
14 2 2 1 PK/TK Equations of Zero-Order Input into the Central Compartment with First-Order Elimination from the Central Compartment
454
xvii
TABLE OF CONTENTS
14 2 3 Simultaneous Intravenous Bolus and Infusions Administration into the Central Compartment of a Two-Compartment Open Model with First-Order Elimination from the Central Compartment
456
14 2 4 Linear Two-Compartment Model with Two Consecutive Zero-Order Inputs, as Loading and Maintenance Doses, with First-Order Elimination from the Central Compartment
456
14 2 5 Three-Compartment Model with Zero-Order Input into the Central Compartment and First-Order Elimination from the Central Compartment
458
14 2 6 Three-Compartment Model with Zero-Order Input into the Central Compartment and First-Order Elimination from a Peripheral Compartment
459
14 3 Applications and Case Studies
459
References
459
15 Practical Applications of PK/TK Models: First-Order Absorption via Extravascular Routes Oral Administration
461
15 1 Introduction
461
15 2 Compartmental Analysis
461
15 2 1 Linear One-Compartment Model with First-Order Input and First-Order Elimination
461
15 2 1 1 Initial Estimates of the Overall Elimination Rate Constant, K and Absorption Rate Constant, k a
464
15 2 1 2 Estimation of Time to Peak Xenobiotic Concentration – Tmax
473
15 2 1 3 Estimation of Peak Concentration (Cp max)
474
15 2 1 4 Estimation of the Area Under Plasma Concentration–Time Curve
476
15 2 1 5 Estimation of Total Body Clearance and Apparent Volume of Distribution
476
15 2 1 6 Fraction of Dose Absorbed (F) – Absolute Bioavailability
478
15 2 1 7 Duration of Action
479
15 2 2 Linear Two-Compartment Model with First-Order Input in the Central Compartment and First-Order Elimination from the Central Compartment
479
15 2 2 1 Equations of the Model
479
15 2 2 2 Interpretation of ka , α , and β
481
15 2 2 3 Parameters and Constants of the Two-Compartment Model with First-Order Input
482
15 2 2 4 Estimation of First-Order Absorption Rate Constant of a TwoCompartment Model – Loo–Riegelman Method
485
15 2 3 Linear Two-Compartment Model with First-Order Input in the Peripheral Compartment and First-Order Elimination from the Peripheral Compartment
487
15 2 4 Linear Three-Compartment Model with First-Order Input in the Central Compartment and First-Order Elimination from the Central Compartment
xviii
490
15 3 Applications and Case Studies
491
References
492
TABLE OF CONTENTS
16 Practical Application of PK/TK Models: Multiple Dosing Kinetics
495
16 1 Introduction
495
16 2 Kinetics of Multiple Intravenous Bolus Injections – One-Compartment Model
495
16 2 1 Equations of Plasma Peak and Trough Levels
496
16 2 2 Estimation of Time Required to Achieve Steady-State Plasma Levels
496
16 2 3 Average Steady-State Plasma Concentration
498
16 2 4 Loading Dose vs Maintenance Dose
499
16 2 5 Extent of Accumulation of Xenobiotics Multiple Dosing in the Body
500
16 2 6 Estimation of Plasma Concentration After the Last Dose
500
16 2 7 Design of a Dosing Regimen
501
16 2 7 1 Dosing Regimen Based on a Target Concentration
501
16 2 7 2 Dosing Regimen Based on Steady-State Peak and Trough Levels
502
16 2 7 3 Dosing Regimen Based on Minimum Steady-State Plasma Concentration
502
16 3 Kinetics of Multiple Oral Dose Administration
502
16 3 1 Peak, Trough, and Average Plasma Concentrations Before and After Achieving Steady-State Levels 16 3 2 Extent of Accumulation in Multiple Oral Dosing
503 504
16 3 3 Oral Administration of Loading Dose, Maintenance Dose and Designing a Dosing Regimen
505
16 4 Effect of Changing Dose, Dosing Interval, and Half-Life on the Accumulation in the Body and Fluctuation of Plasma Concentration
505
16 5 Effect of Irregular Dosing Interval on Plasma Concentrations of Multiple Dosing Regimen 16 6 Multiple Dosing Kinetics – Two-Compartment Model
505 505
16 6 1 Peak, Trough, and Average Plasma Concentrations Before and After Achieving the Steady-State Levels for Two-Compartment Model Xenobiotics Given Intravenously
506
16 6 2 Estimation of the Time Required to Achieve Steady-State Plasma Levels of Two-Compartment Model Xenobiotics Given Intravenously
510
16 6 3 Estimation of Fraction of Steady State, Accumulation Index, and Relationship Between Loading Dose vs Maintenance Dose 16 6 4 Evaluation of Plasma Level after the Last Dose
510 511
16 6 5 The Concept of Half-Life in Multiple Dosing Kinetics of Multicompartmental Models
512
16 7 Multiple Intravenous Infusions
513
16 8 Applications and Case Studies
513
References
514
17 Biopharmaceutics Provisions, Classifcations and Mechanistic Models
545
17 1 Introduction
515
17 2 Infuence of Physicochemical Properties on Absorption of Xenobiotics
515 xix
TABLE OF CONTENTS
17 2 1 Polymorphism
515
17 2 2 Partition Coeffcient
516
17 2 2 1 Rule of Five
516
17 2 3 Infuence of Particle Size, Porosity, and Wettability on Dissolution Rate at the Site of Absorption
517
17 2 3 1 Absorption of Particles
517
17 2 3 2 Infuence of the Particle Size on the Solubility/Dissolution at the Site of Absorption 17 2 3 3 Infuence of Wettability and Porosity on the Dissolution Profle 17 3 Formulation Factors
518 518
17 3 1 Solutions and Syrups
518
17 3 2 Suspensions
518
17 3 3 Emulsions
519
17 3 4 Soft and Hard Gelatin Capsules
519
17 3 5 Compressed Tablets (Uncoated and Coated)
519
17 3 6 Dosage Form Tactics for Poorly Soluble Compounds
519
17 4 Disintegration and Dissolution
520
17 4 1 Mathematical Models of Dissolution
520
17 4 1 1 Noyes–Whitney Model
520
17 4 1 2 Hixson–Crowell “Cube Root” Model
521
17 4 1 3 First-Order Kinetics Model
521
17 4 1 4 Kitazawa Model
522
17 4 1 5 Higuchi “Square Root of Time Plot” Model
522
17 4 1 6 Weibull–Langenbucher Model
523
17 4 1 7 Korsmeyer–Peppas Model
523
17 4 1 8 Nernst–Brunner Model
523
17 4 1 9 Baker–Lonsdale Model
524
17 4 1 10 Hopfendberg Model
524
17 4 2 In Vitro–In Vivo Correlation (IVIVC) of Dissolution Data
524
17 4 2 1 Level A Correlation
524
17 4 2 2 Level B Correlation
525
17 4 2 3 Level C Correlation
525
17 4 2 4 Multiple-Level C Correlation
525
17 5 Biopharmaceutics Classifcation System
xx
517
525
17 5 1 Absorption Number
525
17 5 2 Dissolution Number
525
17 5 3 Dose Number
526
17 5 4 Classes of Biopharmaceutics Classifcation System
526
17 5 4 1 Class I: Compounds with High Permeability and High Solubility
526
17 5 4 2 Class II: Drugs with High Permeability and Low Solubility
526
17 5 4 3 Class III: Drugs with Low Permeability and High Solubility
526
TABLE OF CONTENTS
17 5 4 4 Class IV: Drugs with Low Permeability and Low Solubility
526
17 5 5 Biowaivers
526
17 5 6 Biopharmaceutics Drug Disposition Classifcation System
527
17 6 Other Factors Infuencing Absorption of Xenobiotics
527
17 6 1 Chirality and Enantiomers
527
17 6 2 Effects of Food and Drink on Absorption of Xenobiotics
528
17 6 3 Effects of Disease States
529
17 6 4 Infuence of Genetic Polymorphism
529
17 6 5 Effects of Release Mechanisms from the Solid Dosage Forms
529
17 6 6 Infuence of Drug Administration Scheduling
529
17 6 7 Presence of Other Substances
529
17 6 8 Other Factors
529
17 7 Mechanistic Absorption Models
529
17 7 1 Absorption Potential Models
530
17 7 2 Dispersion Models
530
17 7 3 Compartmental Absorption and Transit Model
531
17 7 4 Gastrointestinal Transit Absorption Model
532
17 7 5 Advanced Compartmental Absorption and Transit Model
535
17 7 6 Advanced Dissolution, Absorption, and Transit Model
535
17 7 7 Grass Model
536
References
537
18 Bioavailability, Bioequivalence, and Biosimilarity
545
18 1 Introduction
545
18 2 Defnitions
546
18 2 1 Bioavailability
546
18 2 2 Pharmaceutical Equivalents
546
18 2 3 Pharmceutical Alternatives
546
18 2 4 Bioequivalent Drug Products (Bioequivalence)
546
18 2 5 Therapeutic Equivalents
546
18 2 6 Generic Drug Products
547
18 2 7 Absolute and Relative Bioavailability
547
18 3 Peak Exposure, Total Exposure, and Early Exposure 18 3 1 Estimation of Absolute Bioavailability from Plasma Data – Single Dose
547 548
18 3 2 Estimation of Absolute Bioavailability from Amount Eliminated from the Body – Single Dose 18 3 3 Estimation of Relative Bioavailability from Plasma Data – Single Dose
548 549
18 3 4 Estimation of Relative Bioavailability from Total Amount Eliminated from the Body – Single Dose
549
18 4 Bioavailability and First-Pass Metabolism
549
18 5 Linearity Validation of Relative or Absolute Bioavailability During Multiple Dosing Regimen
550 xxi
TABLE OF CONTENTS
18 6 Bioequivalence Evaluation
552
18 6 2 Overview of Statistical Analysis of PK/TK Data for Bioequivalence Study
553
18 6 3 Required PD/TD Data
553
18 7 Biosimilar (Biosimilarity and Interchabgeability)
553
18 7 1 Introduction
553
18 7 2 Comparability of Biosimilar and Application of PK/PD Parameters
554
References
555
19 Quantitative Cross-Species Extrapolation and Low-Dose Extrapolation 19 1 Cross-Species Extrapolation 19 1 1 Introduction: Interspecies Scaling in Mammals 19 1 2 Allometric Approach
561 561 561 561
19 1 2 1 Allometric Approach and Chronological Time
564
19 1 2 2 Application of Allometric in Converting Animal Dose to Human Dose
565
19 1 3 Application of PBPK or PBTK in Cross Species Extrapolation 19 1 3 1 Toxicogenomics
566 566
19 2 Low-Dose Extrapolation
567
19 2 1 Introduction
567
19 2 2 Threshold and Non-Threshold Models
568
19 2 2 1 The Probit Model
568
19 2 2 2 The Logit Model
569
19 2 2 3 The One-Hit Model
569
19 2 2 4 The Gamma Multi-Hit Model
569
19 2 2 5 The Armitage-Doll Multi-Stage Model
570
19 2 2 6 Statistico-Pharmacokinetic Model
570
References
570
20 Practical Application of PK/TK Models: Population Pharmacokinetics/Toxicokinetics
xxii
551
18 6 1 Required PK/TK Parameters and Other Provisions in Bioequivalence Study
574
20 1 Introduction
574
20 2 Fixed Effect and Random Effect Parameters
575
20 2 1 Fixed Effect Parameters
575
20 2 2 Random Effect Parameters
575
20 2 3 Linear and Nonlinear Mixed-Effect Models
575
20 2 3 1 Linear Mixed-Effects Model
576
20 2 3 2 Nonlinear Mixed-Effects Model
576
20 2 3 3 Partially Linear Mixed-Effect Model
578
20 2 3 4 Naïve-Pooled Data Approach
578
20 2 3 5 Naïve Average Data Approach
579
20 2 3 6 Standard Two-Stage Approach
579
20 2 3 7 Global Two-Stage Approach
579
20 2 3 8 Iterative Two-Stage Approach
579
TABLE OF CONTENTS
20 2 3 9 Bayesian Approach
579
20 3 Computational Tools for popPK/TK
579
References
580
21 Practical Application of PK/TK Models: Preclinical PK/TK and Clinical Trials
586
21 1 Introduction
586
21 2 Preclinical PK/TK
586
21 2 1 Estimation of the First Dose in Humans 21 2 2 PK/TK Preclinical Requirements
586 587
21 2 2 1 Safety Pharmacology and Toxicity Testing
588
21 2 2 2 Metabolic Evaluations in Preclinical Phase
589
21 3 PK/TK and Clinical Trials
590
21 3 1 Phase I-a Clinical Trial
590
21 3 2 Phase I-b Clinical Trial
590
21 3 3 Phase II-a Clinical Trial
591
21 3 4 Phase II-b Clinical Trial
591
21 3 5 Phase III Clinical Trial
591
21 3 6 Phase IV Clinical Trial
591
References
591
22 Adjustment of Dosage Regimen in: Renal Impairment, Liver Disease and Pregnancy
595
22 1 Renal Impairment
595
22 1 1 Introduction
595
22 1 2 Dosage Adjustment for Patients with Renal Impairments
595
22 1 2 1 Estimation of the Overall Elimination Rate Constant or Half-Life of a Therapeutic Agent Based on the Estimated GFR
595
22 1 2 2 Adjustment of Multiple Dosing Regimen Using the Adjusted Elimination Rate Constant, K 22 1 2 3 Dosage Adjustment Based on the Steady-State Peak and Trough Levels 22 1 3 Applications and Case Studies 22 2 Liver Diseases 22 2 1 Introduction 22 3 Pregnancy
599 602 602 602 602 604
22 3 1 Introduction
604
22 3 2 Changes Impacting Oral Absorption during Pregnancy
604
22 3 3 Changes Infuencing Drug Distribution during Pregnancy
604
22 3 4 Changes in Drug Metabolism during Pregnancy
604
22 3 5 Changes in Renal Excretion during Pregnancy
604
22 3 5 1 Estimation of GFR during Pregnancy
604
22 3 6 Role of the Placenta
605
22 3 7 PK/TK Models
605
References
605
xxiii
TABLE OF CONTENTS
Addendum I – Part 1: Standard Terminologies for Routes of Administration
609
Addendum I – Part 2: Relevant Mathematical Concepts
615
Addendum I – Part 3: Abbreviation – Glossary – PK/TK Constants and Variables
626
Addendum II – Part 1
627
Addendum II – Part 1
629
Addendum II – Part 1
630
Addendum II – Part 2
631
Addendum II – Part 2
632
Addendum II – Part 2
635
Addendum II – Part 2
635
Addendum II – Part 2
636
Addendum II – Part 2
639
Addendum II – Part 2
640
Addendum II – Part 2
641
Addendum II – Part 2
643
Addendum II – Part 3
644
Addendum II – Part 3
647
Addendum II – Part 3
649
Addendum II – Part 3
650
Addendum II – Part 3
652
Addendum II – Part 3
654
Addendum II – Part 3
654
Addendum II – Part 3
655
Addendum II – Part 4
658
Addendum II – Part 4
659
Addendum II – Part 4
661
Addendum II – Part 4
662
Addendum II – Part 4
663
Addendum II – Part 4
665
Addendum II – Part 4
666
xxiv
TABLE OF CONTENTS
Addendum II – Part 4
668
Addendum II – Part 4
672
Addendum II – Part 5
674
Addendum II – Part 5
675
Addendum II – Part 5
676
Addendum II – Part 5
677
Addendum II – Part 5
678
Addendum II – Part 5
680
Addendum II – Part 5
682
Addendum II – Part 5
684
Addendum II – Part 5
685
Addendum II – Part 6
686
Addendum II – Part 6
691
Addendum II – Part 6
694
Addendum II – Part 6
697
Addendum II – Part 6
699
Addendum II – Part 6
701
Addendum II – Part 7
704
Addendum II – Part 7
705
Addendum II – Part 7
707
Addendum II – Part 7
708
Addendum II – Part 7
710
Addendum II – Part 7
714
Addendum II – Part 7
716
Addendum II – Part 7
717
Addendum II – Part 7
718
Addendum II – Part 8
720
Addendum II – Part 8
721
Addendum II – Part 8
722
Addendum II – Part 8
723 xxv
TABLE OF CONTENTS
Addendum II – Part 8
724
Addendum II – Part 8
725
Addendum II – Part 8
726
Addendum II – Part 8
727
Addendum II – Part 8
728
Addendum II – Part 9
729
Addendum II – Part 9
730
Addendum II – Part 9
731
Addendum II – Part 9
732
Addendum II – Part 9
733
Addendum II – Part 9
733
Index
735
xxvi
Preface The principles and methodologies of pharmacokinetics and toxicokinetics (PK/TK) have undergone steady growth and intricacy during the past fve decades. A cursory glance at the current publications reveals the increasing utility and recognition of PK/TK principles and methodologies in diverse scientifc research projects, regulatory decision-making processes and guidelines, and the multitude of applications in various medical felds. I undertook the writing of this handbook to provide a useful reference resource for research and a teaching text for graduate and undergraduate students. I have presented a substantial portion of the materials contained in this handbook in graduate and advanced undergraduate courses at the various universities and colleges at which I have had the pleasure of working with students of different disciplines and post-doctoral fellows. I have observed that the PK/TK subjects enthuse students, even those without a strong background in mathematics showing a keen interest in the subject, many of whom then undertook PK/TK studies at the research bench. This handbook is comprehensive enough to cover many areas of interest and permit integration of the methodologies in different research projects. The main emphases of the book are how the body deals with xenobiotics and how the xenobiotics interact with the elements of the body in vitro, in vivo, and in situ settings. I use the word ‘xenobiotics’ here and throughout the book as a general term for all natural and manufactured substances with therapeutic, toxic, and nontoxic properties. The frst chapter is an overview of PK/TK signifcance as it relates to other scientifc felds. Chapters 2–6 examine 19 essential routes of administration, highlighting their uniqueness and reviewing their PK/TK principles. Chapters 7–11 aid in understanding the kinetics of absorption, distribution, metabolism, and excretion (ADME) of xenobiotics and their related mathematical descriptions. Chapter 12 discusses various approaches and methodologies in PK/TK modeling and their important parameters and constants. Chapters 13–22 are about the practical applications of the models and their assumptions and concepts. The book includes two addendums: Addendum I includes the list of recognized routes of administration, selected mathematical topics relevant to the chapters of the book, and the abbreviations/glossary of acronyms, variables, and constants; Addendum II consists of case studies and the practical application of PK/TK principles. The book covers a wide range of basic concepts, and the focus is on the understanding of these concepts and the governing principles of their mathematics and kinetic interconnectivity. Therefore, I avoided topics like neural networks, advanced stochastic modeling, descriptions of statistical and numerical analysis of computer software, and computer-generated curves of published data. Finally, the editors and publisher deserve the author’s gratitude for their efforts toward the goal of producing a book of utility to researchers, educators, and students. Mehdi Boroujerdi
xxvii
1 Pharmacokinetics and Toxicokinetics 1.1 INTRODUCTION The word xenobiotic, a combination of two Greek words (xenos and biōtkós), literally means “foreigner or stranger to life” and refers mostly to an exogenous organic or inorganic chemical compound foreign to the human body or other living organisms. Xenobiotics, in small or large molecules, may act as therapeutic agents, food additives, toxins, carcinogens, pollutants, pesticides, etc., which upon direct or indirect interaction with various components of the body produce favorable or unfavorable biological response(s). The interaction occurs during the physiological and biochemical processes of absorption, distribution, metabolism (biotransformation), and excretion (ADME). The ADME processes facilitate the delivery and interaction of a xenobiotic with its receptor site or target tissues, the eventual outcome, and its removal from the body. The pharmacokinetics (PK) and toxicokinetics (TK) disciplines are the quantitative science of the processes of ADME for a given xenobiotic and the corresponding pharmacological and/or toxicological responses (Figure 1.1). The fundamental goals of both disciplines are to understand how the body handles the administered or exposed xenobiotic as a foreign substance and how to predict and measure the magnitude of its pharmacological or toxicological response or outcome. The result of pharmacokinetic/toxicokinetic (PK/TK) analysis is establishing appropriate criteria and approaches to avoid undesirable outcomes of the xenobiotics interaction with the body and to safeguard human life. The attainment of an acceptable outcome from interaction of a xenobiotic with the body can be as practical as: ◾ developing appropriate dosage forms or a dosage regimen for the purpose of achieving optimum therapeutic outcome or pharmacological response, or ◾ establishing regulatory guidelines/policies for consistency of the outcomes through bioequivalence and biosimilar evaluations, or ◾ as challenging as a low-dose extrapolation of toxicants, chemical carcinogens, and understanding of a safe dose in hazardous environmental pollutants or a new therapeutic entity in drug discovery and development. PK and TK use the same mathematical principles of kinetics, differential equations, statistical methodologies, and numerical analysis in data exploration, interpretation, and deduction or prediction. The difference between the two disciplines may be only their biological outcomes. 1.2 PHARMACOKINETICS AND PHARMACODYNAMICS The time course of xenobiotics in the body has been studied since 1927 (Widmark and Tandberg, 1924; Widmark, 1932; Widmark and Elbel, 1937 ; Teorell, 1937a; 1937b), but the term pharmacokinetics was frst introduced in 1953 (Dost, 1953). The history of the frst 50 years of pharmacokinetics is well chronicled in a paper published by John Wagner, another pioneer of pharmacokinetics in 1981 (Wagner, 1981). The following defnitions have gained wide acceptance in the scientifc feld: Pharmacokinetics is the study of the time course (i.e., kinetics) of ADME of drugs and their metabolites in the body (Figure 1.1) and the corresponding infuence(s) on the intensity and time course of the pharmacological response. Pharmacodynamics (PD) is the quantitative study of the pharmacological response and the therapeutic outcome of a drug and its mechanism of action in a biological system, with emphasis on the dose–response or drug concentration–effect relationships. In essence, pharmacokinetics and pharmacodynamics (PK/PD) are two integrated subjects that, in combination, elucidate how the body handles drug molecules and what therapeutic outcome results from their interaction with target tissue(s). PK/PD are studied using in vivo (animal or human whole body), ex vivo (using cells or tissues previously exposed to a drug), in vitro (on isolated cells and tissues), and/or in silico (computer modeling and simulation) methods, utilizing a wide range of analytical methodologies and computer programs. There are factors that can infuence the PK/PD of xenobiotics. The most notable ones are: ◾ genetic predisposition ◾ routes of administration DOI: 10.1201/9781003260660-1
1
1.2 PHARMACOKINETICS AND PHARMACODYNAMICS
Figure 1.1 Schematic illustration of the physiological processes of absorption, distribution, metabolism, and excretion (ADME); the arrows represent the direction of physiological or biochemical processes or fow, and the routes of administration include direct entry into the systemic circulation by intravenous injection (IV) or access after the absorption process that requires permeation of a compound through an absorption barrier; included examples in the fgure are gastrointestinal absorption (PO), intramuscular injection (IM), subcutaneous injection (SC), sublingual absorption (SL), rectal administration (PR), transdermal absorption (TD), and inhalation; biological samples of experimental animals are identifed by , and the noninvasive biological samples for human subjects include serum, plasma, whole blood, urine, saliva, sweat, milk, and hair; the biophase represents the target/receptor sites associated with organs, tissues, whole blood, or other milieus. ◾ physicochemical factors related to drug and administered dosage form (i.e., pharmaceutics and biopharmaceutics) ◾ drug–drug interaction, drug–occupational exposure interaction, and drug–herbal interaction ◾ age (including gerontology and pedology) ◾ gender (including hormonal infuence) ◾ body weight ◾ exercise ◾ nutrition and dietary factors and food–drug interaction ◾ alcohol intake ◾ tobacco or marijuana smoking ◾ pregnancy and lactation ◾ disease states that infuence renal, hepatic, gastrointestinal, cardiovascular, and immunological functions 2
PHARMACOKINETICS AND TOXICOKINETICS
◾ infection and infammation and diabetes ◾ stress, psychiatric status, behavior, and depression ◾ circadian and seasonal variation ◾ environmental factors, culture, and occupation ◾ trauma, surgery, etc. 1.2.1 Clinical Pharmacokinetics/Pharmacodynamics An applied feld of PK/PD is the clinical pharmacokinetics that focuses on the application of PK/ PD principles to the safe and effective therapeutic management of patients and individualized optimization of drug dosage and response. Clinical Pharmacokinetics/Pharmacodynamics (CPK/ PD) is achieved by using drug concentrations, pharmacokinetic principles, and pharmacodynamic criteria. CPK/PD is also called “therapeutic drug monitoring.” It is worth noting that not all CPK/ PD clinical or research projects involve patients, but their end goal is to optimize the therapeutic outcome and minimize the probability of toxicity. Ordinarily, the drugs that are monitored are those with a narrow therapeutic range that trigger a toxic response at plasma levels close to the maximum therapeutic level. Furthermore, all factors that can infuence the PK/PD of xenobiotics as noted in Section 1.2, especially the disease states, impact the ADME of many therapeutic agents, which necessitates the application of CPK/PD practice, and the safe and effective therapeutic management for the individual patient. Noteworthy disease states are those that signifcantly impair the organs and physiological processes involved in ADME. 1.2.2 PK/PD Modeling and Pharmacometrics The mathematical approaches of PK and PK/PD modeling with the related assumptions, logics and methodologies will be discussed in detail in forthcoming chapters of this book (Chapter 12). The PK/PD modeling links the ADME kinetics (PK) of a xenobiotic to its pharmacological response (PD). The kinetics and dynamics of optimum response are usually decided based on individual or collective observations of in vivo, in vitro, in situ and/or in silico studies. Over the last few decades, PK/PD modeling has continued to develop, offering higher levels of intricacy in order to: ◾ provide a quantitative ADME portrayal of a xenobiotic in the body ◾ summarize the observed data ◾ provide a useful framework that is founded on relevant observations and trustworthy for prediction ◾ develop mathematical relationship(s) that defne the connection between the magnitude of a xenobiotic exposure and its measurable response. The term “predication” applies to a whole host of benefts from the modeling, which include the following: ◾ extrapolation to a higher or lower input ◾ extrapolation from experimental animals to human ◾ predication of in vivo response from in vitro observations ◾ predication of response and ADME profle in disease states ◾ selection and optimization of a lead compound in drug discovery and development ◾ assessment of human health risk from exposure to environmental toxicants, or preclinical and clinical trials in drug discovery and development, and others. The PK/PD modeling has also grown into an advanced mathematical feld of pharmacometrics (PMX) that streamlines interpretation of complex physiological/pharmacological processes and conveys them in a quantitative manner. Pharmacometrics deals mostly with population PK/PD models and mechanistic models. It employs advanced graphical methods and computer programing, using statistical analysis and stochastic simulation to further clarify and quantify the complex PK/PD models and associated parameters and constants. The generated data from PMX analyses are most useful and practical in: 3
1.2 PHARMACOKINETICS AND PHARMACODYNAMICS
◾ drug discovery and development ◾ planning, conducting, and analyzing clinical trials and clinical data analysis (Williams and Ette, 2006; Koch et al., 2020; Akacha et al., 2021) ◾ quantitative expression of system pharmacology ◾ applied in silico models for drug development (Musuamba et al., 2020; Musuamba et al., 2021) ◾ regulatory review and decision-making (Garnett et al., 2011) ◾ drug approval and labeling decisions (Bhattaram et al., 2005), etc. 1.2.3 Population PK and PK/PD Modeling It has been proven that certain physiological, pathophysiological, biochemical, and demographical factors can alter the therapeutic outcome of a drug in specifc group(s) of patients. Consequently, the feld of population pharmacokinetics (popPK) has advanced and been applied in many areas, including drug discovery and development and pharmacogenetics (PGT) in recent years. PopPK helps to defne the PK variability among individuals in a target population sharing the same attributes, such as gender, age, race, disease, etc. and to study the impact of variability of drug behavior in the body (Aarons, 1991; FDA, 1999, 2022). Population PK and PK/PD analyses and modeling provide valuable quantitative assessment of the incorporated PK and PK/PD parameters and constants, including inter- and intraindividual and residual variability in drug concentration. The calculated data are then used to evaluate, validate, and optimize the dose, dosage regimen, or dosage adjustment of therapeutics agents (Kawaguchi et al., 2021; Stillemans et al., 2021; Krzyzanski et al., 2021) and biologics (Ogasawara et al., 2019; Wang et al., 2018). The popPK analyses are usually carried out in the following three phases: ◾ exploratory data analysis ◾ model development, and ◾ model validation. The interindividual variability in gene-encoding protein transporters, drug-metabolizing enzymes, some receptors, ion channels, immune molecules, etc. infuences the PK/PD of xenobiotics (Evans and Relling, 1999; Eichelbaum et al., 2006; Daly, 2010). Specifcally, genetic differences in drug metabolism (Evans and Relling, 1999), toxicity, and response have direct impact on metabolic clearance and formation of active or toxic metabolites. A pharmacogenetic polymorphism (Yang et al., 2013) occurs in a subgroup of a population when the mutated allele occurs at a level that causes different responses and/or different ADME outcomes. For example, when there is a drug metabolism polymorphism, the interindividual inconsistency manifests itself with greater variation compared to the rest of the population. Poor metabolizers will be at higher risk for toxicity when enzyme-mediated inactivation is failing, and fast metabolizers may reduce the drug concentration to a level below the therapeutic range, which will reduce effcacy of the therapeutic agent. It is essential to consider a large sample size for popPK studies when the goal is to identify slow and fast metabolizers. Various guidelines have been developed by working groups, regulatory agencies, and academic/ research institutions, conveying the signifcance of pharmacogenomics and pharmacogenetics in PK and PK/PD modeling and analyses. Notable among them are: ◾ US Food and Drug Administration (FDA) • https://www.fda.gov/regulatory-information/search-fda-guidance-documents/pharmacogenetic-tests-and-genetic-tests-heritable-markers) • https://www.fda.gov/drugs/science-and-research-drugs/table-pharmacogenomic -biomarkers-drug-labeling ◾ Clinical Pharmacogenetics Implementation Consortium (CPIC) • https://cpicpgx.org/guidelines/ ◾ Dutch Pharmacogenetics Working Group (DPWG) • https://www.pharmgkb.org/page/dpwg 4
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◾ European Medicine Agency (EMA) • https://www.ema.europa.eu/en/use-pharmacogenetic-methodologies-pharmacokinetic -evaluation-medicinal-products ◾ German Federal Institute for Drugs and Medical Devices (BfArM) • https://www.bfarm.de/EN/BfArM/Tasks/Research/Pharmacogenomics/_node.html ◾ and numerous related books and publications (Shekhani et al., 2020; Becquemont et al., 2011). Advances in PGX and PGT in combination with sophisticated PK/PD modeling and analysis will provide guidance for the practice of personalized medicine. 1.2.3.1 Infuences of Genetics and Genomics on PK/PD and TK/TD An important element infuencing the variability of PK/PD or toxicokinetics and toxicodynamics (TK/TD) analyses is the genetic makeup of the target population. The study of how humans respond to xenobiotics due to their genetic inheritance and the infuence of internal and external factors on their genetic makeup and PK/PD variability are explored in pharmacogenomics and pharmacogenetics. The infuence of genetics and genomics on PK and PD processes and the distinctions between PGX and PGT are presented in Figure 1.2. The following are very brief descriptions of the included titles in Figure 1.2, just to shed some light on their role in PK, PD, PGX, and PGT. For more comprehensive information on the titles, the relevant references and publications should be consulted. 1.2.3.1.1 Metabolomics and Metabonomics Metabolomics is the all-inclusive analysis of all metabolites in the body. The reason behind this undertaking is that certain metabolites are commonly associated with specifed pathogenic conditions and associated mechanisms (Gerszten and Wang, 2008). The scope of metabolomic analysis is way beyond the typical medical laboratory measurements and techniques. It includes very hydrophilic to very hydrophobic metabolites of endogenous and exogenous substances metabolism and enzymatic activities encoded by the human genome (Kuehnbaum and Brits-McKibbin, 2013) as well. This comprehensive metabolic enterprise provides opportunities for assessment of the complex nature of normal and abnormal chemical, physiological, and genetic factors and processes. The metabolomic knowledge provides valuable clues for discovery and development of new drug entities and forecasts the infuence of external factors on a system. The external factors also include the effect of xenobiotics on a system and their handling by the system after exposure. The term metabonomics is often used in conjunction with metabolomics. Metabonomics describes the time-dependent changes in metabolomics due to the involvement of pathophysiological conditions or genetic modifcations (Nicholson et al., 2007). 1.2.3.1.2 Proteomics Proteomics, in the same way as metabolomics, refers to the comprehensive study and identifcation of proteins and protein levels in a biological system/human body – those that correspond and correlate with the normal physiological state and those that can be used as biomarkers of disease states. The role of proteomics, in addition to acting as biomarkers, is to reveal and validate drug targets, identify toxicity markers, and clarify drug modes of action. The science of proteomics plays a signifcant role in drug discovery and development, environmental stressors like toxic chemicals, disease prevention and treatment, and many areas in biomedical science research, like apoptosis-related proteins and biomarkers in cancer research (Bai et al., 2011). 1.2.3.1.3 Transcriptomics As the title indicates, transcriptomics, is the omics of transcripts and the expression of gene regulation and provides principal understanding on gene structure, expression, and regulations (Lowe et al., 2017; Casamassimi et al., 2017). Transcriptomics offers information on RNA transcribed by the genome in a specifc organ or tissue or cell type under normal physiological conditions or pathophysiological states. The information reveals critical changes that initiate disease states and the molecular diagnosis that ultimately assists in providing a more effective therapeutic outcome (Byron et al., 2016).
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Figure 1.2 Interconnection between pharmacokinetics and pharmacodynamics with the collective infuence of genetic polymorphism, proteomics, metabolomics, epigenomics, and transcriptomics under the provisos of pharmacogenetics and pharmacogenomics. 1.2.3.1.4 Epigenomics The control and function of the genome are closely associated with the physical confguration of genomic DNA. This includes the way it is bundled into chromatin, encompassing histones, its binding sites, protein complexes, and noncoding RNAs (Kouzarides, 2007; Bernstein et al., 2007; Fraser and Bickmore, 2007). Chromatin is subject to alteration of its DNA and protein components that cause functional and structural changes. The distribution of the alteration and functional changes across the genome of a given system is called “epigenome,” and epigenomics is the study of characteristic alterations of gene expression, DNA methylation, and changes in chromatin that are associated with disease states (Jaenish and Bird, 2003; Jones and Baylin, 2007; Feinberg, 2007; Kabekkodu et al., 2017; Ushijima et al., 2021). 6
PHARMACOKINETICS AND TOXICOKINETICS
1.2.3.2 Biomarkers The defnition of biomarkers has been evolving over the past two decades by various agencies and working group such as the Committee on Qualifcations of Biomarkers and Surrogate Endpoints in Chronic Disease from the Institute of Medicine (Micheel and Ball 2010) and the FDA-NIH Biomarker Working Group (FDA-NIH, 2016–2017) that offered the basic defnition for a biomarker as: “A defned characteristic that is measured as an indicator of normal biological processes, pathogenic processes to an exposure or intervention.” This defnition embodies the idea that biomarkers are molecular, physiologic, histologic, and radiologic traits of an intervention that can be assessed objectively, validated analytically, and appraised as an indicator of a normal biological process or a pathogenic manifestation. Furthermore, a pharmacological and/or toxicological response to a xenobiotic may generate endogenous or exogenous molecule(s) that can be considered a biomarker. In PK/PD and TK/TD modeling, the quantitative measurement of biomarkers is used to monitor the response and conceivably quantify the effect. When a biomarker is used to quantify the effect, instead of a clinical or medical endpoint, it is called a “surrogate endpoint.” A surrogate endpoint is expected and must be validated to predict beneft, harm, or no effect; and the validation must be based on scientifc, pathophysiologic, and/or population verifcation (Biomarkers Defnitions Working Group, 2001). Furthermore, a biomarker can only be identifed as a surrogate endpoint if it is correlated with the clinical outcome assessment, and any fuctuation in the measurements of the biomarker must correspond and refect variation in the measurements of the clinical endpoint. It is essential to differentiate between clinical outcome assessment and biomarkers. Clinical or medical outcome assessment, which is often associated with the clinical endpoint, is an important measurement for the therapeutic management and outcome. Whereas, the measurements of a biomarker, as the surrogate, is linked only to a projection of the clinical endpoint and exists between the infuence of therapeutic agent and therapeutic outcome. To rephrase it, a measurable biomarker may or may not refect the medical state of a patient as is determined by the medical endpoint. However, in the absence of an approved clinical outcome assessment, a validated biomarker can be used in drug discovery and development to accelerate the FDA approval process (FDA, 2018). Clinical endpoint measurements refect directly how a patient functions, endures, or survives the treatment. For example, for cancer patients, the endpoint is the disease-free period between the treatment or surgery and undetectable sign of the disease, or the improvement in quality of life, such as absence of pain and negative side effects of the therapeutic agent. A surrogate endpoint is laboratory or physical data such as cholesterol levels, bone density measurement, blood pressure, hemoglobin A1C measurement, etc. In ecotoxicological terms, surrogate endpoint biomarkers would be most valuable if they were linked to adverse effects in an individual as well as to population and ecosystem effects. It is common that a biomarker may represent the intermediate step between exposure and response. Biomarkers are used routinely in clinical practice and drug development to describe risk, select the appropriate dose, achieve maximum therapeutic effciency and minimum toxicity, and monitor the therapeutic outcome. Often, PK/TK parameters and constants associated with analysis of serum drug levels, e.g., area under the plasma concentration time curve, maximum plasma concentration, and time to achieve the maximum concentration are also considered biomarkers. The suggested (Califf, 2018; FDA-NIH, 2017) biomarker categories are: ◾ Diagnostic – reveals or confrms a disease or identifes patients with a disease. ◾ Monitoring – detects the effect of medical products/biologic agents for measuring pharmacodynamic response (e.g., measuring blood pressure). ◾ Pharmacodynamic/response – its measurements refect the response to administration of or exposure to a xenobiotic; useful in drug discovery and development. ◾ Predictive – indicates that its presence, absence, or change forecasts a favorable or unfavorable response in an individual or group of individuals; useful in the design and conduct of clinical trials in drug discovery and development. ◾ Prognostic – identifes the probability of disease progression or recurrence in patients with a given disease or medical condition. ◾ Safety – reveals the presence or extent of a toxic outcome or any harmful occurrence before or after exposure to a medical procedure or an environmental element/xenobiotic. ◾ Susceptibility/risk – indicates the possibility for an emerging disease or medical condition in an individual who does not have the condition/disease. 7