Basic pharmacokinetics (2012)

Basic Pharmacokinetics Basic Pharmacokinetics SECOND EDITION Sunil S Jambhekar BPharm, MS, PhD Professor and Associate Dean, LECOM-Bradenton, School of Pharmacy, Bradenton, Florida, USA Philip J Breen PhD Associate Professor, Department of Pharmaceutical Sciences, College of Pharmacy, University of Arkansas for Medical Sciences, Little Rock, Arkansas, USA London • Philadelphia Published by Pharmaceutical Press Lambeth High Street, London SE1 7JN, UK University City Science Center, Suite 5E, 3624 Market Street, Philadelphia, PA 19104, USA c Royal Pharmaceutical Society of Great Britain 2012 is a trade mark of Pharmaceutical Press Pharmaceutical Press is the publishing division of the Royal Pharmaceutical Society First edition published 2009 Second edition published 2012 Typeset by River Valley Technologies, India Printed in Great Britain by TJ International, Padstow, Cornwall ISBN 978 85369 980 All rights reserved No part of this publication may be reproduced, stored in a retrieval system, or transmitted in any form or by any means, without the prior written permission of the copyright holder The publisher makes no representation, express or implied, with regard to the accuracy of the information contained in this book and cannot accept any legal responsibility or liability for any errors or omissions that may be made The right of Sunil S Jambhekar and Philip J Breen to be identified as the authors of this work has been asserted by them in accordance with the Copyright, Designs and Patents Act, 1988 A catalogue record for this book is available from the British Library Contents Preface About the authors Introduction and overview 1.1 1.2 1.3 1.4 1.5 1.6 Use of drugs in disease states Important definitions and descriptions Sites of drug administration Review of ADME processes Pharmacokinetic models Rate processes xi xiii 1 12 Mathematical review 17 2.1 2.2 2.3 2.4 2.5 2.6 2.7 2.8 2.9 2.10 17 18 18 18 19 20 21 21 24 25 Introduction A brief history of pharmacokinetics Hierarchy of algebraic operations Exponents and logarithms Variables, constants, and parameters Significant figures Units and their manipulation Slopes, rates, and derivatives Time expressions Construction of pharmacokinetic sketches (profiles) Intravenous bolus administration (one-compartment model) 29 3.1 3.2 3.3 3.4 3.5 3.6 3.7 3.8 3.9 29 30 32 36 38 40 41 42 43 Introduction Useful pharmacokinetic parameters The apparent volume of distribution (V) The elimination half life (t1/2 ) The elimination rate constant (K or Kel ) Plotting drug concentration versus time Intravenous bolus administration of drugs: summary Intravenous bolus administration: monitoring drug in urine Use of urinary excretion data vi Contents Clearance concepts 55 4.1 4.2 4.3 4.4 4.5 4.6 4.7 4.8 4.9 Introduction Clearance definitions Clearance: rate and concentration Clearance: tank and faucet analogy Organ clearance Physiological approach to clearance Estimation of systemic clearance Calculating renal clearance (Clr ) and metabolic clearance (Clm ) Determination of the area under the plasma concentration versus time curve: application of the trapezoidal rule 4.10 Elimination mechanism 4.11 Use of creatinine clearance to determine renal function Appendix: Recently developed equations for estimating creatinine clearance and glomerular filtration rate 55 56 58 58 60 61 65 66 67 Problem set 79 Drug absorption from the gastrointestinal tract 95 5.1 5.2 5.3 5.4 95 98 100 101 Extravascular routes of drug administration 6.1 6.2 6.3 6.4 6.5 6.6 6.7 6.8 6.9 6.10 6.11 6.12 6.13 Gastrointestinal tract Mechanism of drug absorption Factors affecting passive drug absorption pH–partition theory of drug absorption Introduction Drug remaining to be absorbed, or drug remaining at the site of administration Determination of elimination half life (t1/2 ) and elimination rate constant (K or Kel ) Absorption rate constant (Ka ) Wagner–Nelson method (one-compartment model) and Loo–Riegelman method (two-compartment model) Lag time (t0 ) Some important comments on the absorption rate constant The apparent volume of distribution (V) Time of maximum drug concentration, peak time (tmax ) Maximum (peak) plasma concentration (Cp )max Some general comments Example for extravascular route of drug administration Flip-flop kinetics 69 69 76 105 106 106 109 110 111 115 116 116 117 118 120 121 126 Problem set 127 Bioavailability/bioequivalence 137 7.1 7.2 7.3 Introduction Important definitions Types of bioavailability 138 138 139 Contents 7.4 7.5 7.6 7.7 7.8 7.9 7.10 7.11 7.12 7.13 157 157 158 159 Factors affecting drug absorption: Physicochemical factors 175 Dissolution rate Dissolution process Noyes–Whitney equation and drug dissolution Factors affecting the dissolution rate Gastrointestinal absorption: Role of the dosage form Introduction Solution (elixir, syrup, and solution) as a dosage form Suspension as a dosage form Capsule as a dosage form Tablet as a dosage form Dissolution methods Formulation and processing factors Correlation of in vivo data with in vitro dissolution data Continuous intravenous infusion (one-compartment model) 10.1 10.2 10.3 10.4 10.5 Introduction Monitoring drug in the body or blood (plasma/serum) Sampling drug in body or blood during infusion Sampling blood following cessation of infusion Use of post-infusion plasma concentration data to obtain half life, elimination rate constant and the apparent volume of distribution 10.6 Rowland and Tozer method 11 145 155 161 9.1 9.2 9.3 9.4 9.5 9.6 9.7 9.8 10 141 141 142 143 Problem set 8.1 8.2 8.3 8.4 Bioequivalence Factors affecting bioavailability The first-pass effect (presystemic clearance) Determination of the area under the plasma concentration–time curve and the cumulative amount of drug eliminated in urine Methods and criteria for bioavailability testing 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 Equivalency terms Food and Drug Administration codes Fallacies on bioequivalence Evidence of generic bioinequivalence or of therapeutic inequivalence for certain formulations approved by the FDA vii 175 175 176 177 187 187 188 188 189 189 191 191 194 203 203 205 205 220 222 225 Problem set 227 Multiple dosing: Intravenous bolus administration 237 11.1 Introduction 11.2 Useful pharmacokinetic parameters in multiple dosing 237 241 viii Contents 11.3 11.4 11.5 11.6 11.7 11.8 12 Multiple dosing: extravascular routes of drug administration 12.1 12.2 12.3 12.4 12.5 12.6 12.7 12.8 12.9 12.10 13 Introduction The peak time in multiple dosing to steady state (tmax ) Maximum plasma concentration at steady state Minimum plasma concentration at steady state ‘‘Average’’ plasma concentration at steady state: extravascular route Determination of drug accumulation: extravascular route Calculation of fluctuation factor ( ) for multiple extravascular dosing Number of doses required to reach a fraction of steady state: extravascular route Determination of loading and maintenance dose: extravascular route Interconversion between loading, maintenance, oral, and intravenous bolus doses 248 249 251 254 254 255 257 257 259 260 261 262 263 264 264 265 266 Problem set 271 Two-compartment model 285 13.1 13.2 13.3 13.4 13.5 13.6 13.7 13.8 13.9 13.10 13.11 14 Designing or establishing the dosage regimen for a drug Concept of drug accumulation in the body (R) Determination of fluctuation ( ): intravenous bolus administration Number of doses required to reach a fraction of the steady-state condition Calculation of loading and maintenance doses Maximum and minimum drug concentration at steady state Introduction Intravenous bolus administration: two-compartment model Determination of the post-distribution rate constant (β) and the coefficient B Determination of the distribution rate constant (α) and the coefficient A Determination of micro rate constants: the inter-compartmental rate constants (K21 and K12 ) and the pure elimination rate constant (K10 ) Determination of volumes of distribution (V) How to obtain the area under the plasma concentration–time curve from time zero to time t and time ∞ General comments Example Further calculations to perform and determine the answers Extravascular dosing of a two-compartment model drug 285 287 292 292 295 296 298 299 300 302 303 Problem set 305 Multiple intermittent infusions 309 14.1 Introduction 14.2 Drug concentration guidelines 14.3 Example: determination of a multiple intermittent infusion dosing regimen for an aminoglycoside antibiotic 14.4 Dose to the patient from a multiple intermittent infusion 14.5 Multiple intermittent infusion of a two-compartment drug: vancomycin ‘‘peak’’ at hour post infusion 309 311 311 313 313 Contents 14.6 Vancomycin dosing regimen problem 14.7 Adjustment for early or late drug concentrations 15 319 Nonlinear pharmacokinetics 323 Introduction Capacity-limited metabolism Estimation of Michaelis–Menten parameters (Vmax and Km ) Relationship between the area under the plasma concentration versus time curve and the administered dose 15.5 Time to reach a given fraction of steady state 15.6 Example: calculation of parameters for phenytoin Drug interactions 341 Introduction The effect of protein-binding interactions The effect of tissue-binding interactions Cytochrome P450-based drug interactions Drug interactions linked to transporters 341 342 348 349 355 Problem set 357 Pharmacokinetic and pharmacodynamic relationships 359 359 361 364 Problem set 10 367 Metabolite pharmacokinetics 369 18.1 18.2 18.3 18.4 18.5 18.6 18.7 18.8 18.9 18.10 18.11 19 332 333 337 17.1 Introduction 17.2 Generation of a pharmacokinetic– pharmacodynamic (PKPD) equation 17.3 Pharmacokinetic and pharmacodynamic drug interactions 18 323 325 327 330 Problem set 16.1 16.2 16.3 16.4 16.5 17 314 315 Problem set 15.1 15.2 15.3 15.4 16 ix Introduction General model Single intravenous bolus of drug conforming to a one-compartment model Single oral dose of drug conforming to a one-compartment model Intravenous infusion of a one-compartment model parent drug Chronic dosing to steady state Study design required to obtain various metabolite pharmacokinetic parameters Computer-aided simulation and fitting of metabolite pharmacokinetic data Case in point: meperidine and normeperidine Active metabolites in renal dysfunction Sample metabolite pharmacokinetics calculations Pharmacokinetic data fitting 19.1 Introduction 19.2 Pharmacokinetic parameter determination 369 370 370 382 384 385 388 388 388 388 393 395 395 395 Index average residence time see mean residence time average total drug concentration at steady state (Css ) protein-binding interactions intravenous route, 344, 345 oral route, 345 tissue-binding interactions, 349 azathioprine, 371 azole antifungal drugs, 349, 354 B (empirical constant), 292 determination, 292, 293 example calculation, 300, 301 bar over a letter, 146 barbiturates, 354 absorption, 184 drug interactions, 354 basiliximab, 420 becaplermin, 414, 417 belimumab, 420 β see post-distribution rate constant bevacizumab (Avastin), 420, 423 Bexxar see tositumomab bile salts, 182 bioavailability, 137 absolute see absolute bioavailability comparative (relative), 139, 440 defined, 138 dosage form ranking by, 188 factors affecting, 141 fallacies, 158 first-pass effect and, 142 formulation and processing factors, 191 particle size and, 178 presentation of data, 152–154 testing, 145 drug product selection, 146 examples, 149 statistical terms used, 146 study designs, 145, 147, 148 types, 139 see also absorption bioequivalence defined, 138, 146 fallacies, 158 FDA approved formulations lacking, 159 FDA codes, 157 studies, 141 terms, 157 testing example, 150, 151 interpreting FDA 90% confidence interval formula, 152 statistical moment theory, 440 study designs, 147 use of confidence intervals, 150, 152 see also equivalence 463 biological half-life see elimination half life biopharmaceutics, Biostrophin, 426 biotechnology drugs, 413 BiovaxID, 424 blood concentration change after extravascular administration, 107 elimination rate and, 58 see also plasma (or serum) concentration blood flow clearance and, 61, 63 see also hepatic blood/plasma flow brain, 287 bromhexine, 371 bupropion, 372 calcium channel blockers, 354 calcium ions, drug complexation with, 182 calcium salts, as diluents, 191 Campath, 420 canakinumab, 420 cancer immunotherapy, 424 capacity-limited (saturable) metabolism, 325 capsules, 189 absorption versus suspensions, 188 diluents, 191 carbamazepine, 372 catumaxomab, 423 Ceclor (cefaclor) suspension, 179 cefazolin, serum half-life and creatinine clearance, 74 cefotaxime, 372 ceftazidime, dosing in renal impairment, 74, 75 central compartment, 286–289 elimination rate constant see elimination rate constant from central compartment mean residence time (MRTC ), 433, 441 volume of distribution see under apparent volume of distribution Cerepro, 426 certolizumab pegol, 420 cetrorelix, 414 cetuximab, 420 chemical modification, to improve absorption, 183 chemically equivalent products, defined, 138 children, creatinine clearance, 70 chloramphenicol palmitate, 181 chlordiazepoxide, 372 chlorpromazine, 372 Christmas factor, 414 Chronic Kidney Disease Epidemiology (CKD-EPI) Collaboration formula, 76 chronic renal failure creatinine clearance, 71 see also renal impairment cimetidine, 356 clearance (Cl), 55 464 Index definitions, 56 hepatic (ClH ) see hepatic clearance intrinsic (Clint ), 63–65 intrinsic free see intrinsic free (unbound) clearance metabolic (Clm ), 66 non-renal (Clnr ), 58 organ, 60, 61 physiological approach, 61 presystemic, 142 rate and concentration, 58 renal (Clr ) see renal clearance renal physiology, 56 systemic or total body see systemic clearance tank and faucet analogy, 58, 59 Cockcroft–Gault equation, 70 codeine, 355, 372 coefficient of determination (r2 ), 199 coefficient of variation (cv%), 399, 402 coloring agents, 193, 197 compartment(s) central see central compartment concept, peripheral (tissue) see peripheral compartment compartment models, selection, 8, 295 types, 10 see also one-compartment model; two-compartment model complexation, 182 condition numbers, 400, 402 confidence intervals (CI) bioequivalency testing, 150, 152 defined, 148 interpreting FDA 90% formula, 152 parameter estimates, 402 constants, 19, 20 continuous intravenous infusion, 203 constant rate, 204–206 equations and pharmacokinetic parameters, 205 flow rate, 204 loading dose (DL ), 212 mean residence time, 438, 439, 441 metabolite kinetics, 384–386 steady state, 387 monitoring drug in body or blood, 205, 207 post-infusion data see post-infusion plasma concentration data Rowland and Tozer method, 225, 226 salt form correction factor, 214 sampling drug in body or blood, 205 steady-state plasma concentration, 208 theory, 204 true steady-state, 208 Wagner’s method for attaining steady state, 217–219 see also infusion duration; infusion rates control, defined, 148 controlled-release dosage forms, 138 correlation coefficient (r), 398 correlation matrix, parameter, 399, 400, 402 correlation of in vivo and in vitro studies see in vivo–in vitro correlation creatinine, 69 creatinine, serum concentrations dosing adjustments from, 75 isotope dilution mass spectrometry (IDMS)-calibrated, 76 normal, 69 unstable, Clcr estimation, 71 creatinine clearance (Clcr ), 69 direct measurement, 70 dosing adjustments, 74 indirect measurement, 70 newer estimation methods, 76 normalization, 69 serum half-life and, 72 significance, 72 cross-over designs bioavailability studies, 145, 147 defined, 148 crystalline forms, absorption, 179, 180 curve stripping method see feathering method cyclodextrins, 183 cyclosporine, 349, 354, 372, 414 CYP1A2 interactions, 354 CYP2C9 genetic polymorphism, 354 interactions, 354 CYP2C19 interactions, 355 CYP2D6 interactions, 355 CYP2E1 interactions, 355 CYP3A4, 349 inducers, 354 inhibitors, 349 CYP3A5, 349 CYP3A6, 349 cytochrome P450-based drug interactions, 349–353 cytomegalovirus retinitis, 423 daclizumab, 421 darbepoetin alfa, 414 data fitting, pharmacokinetic, 395 evaluating program output, 401 goodness of fit indices, 398 metabolite kinetics, 388 methods of improving fit, 401 nonlinear regression see nonlinear regression parameter determination, 395, 397, 398 weighting of data points, 408–410 denominate numbers, 22 denosumab, 421 derivatives, 21, 24 Index partial, 403–405 desmopressin, 414, 418 dexamethasone, 354 diazepam, 355, 372 dicloxacillin, 325 dietary components, drug complexation with, 182 diffusion, passive, 7, 11 Fick’s law, 100, 101 gastrointestinal absorption, 98 factors affecting, 100, 101 renal tubules, 56 diffusion layer, 175, 176 solubility of a drug in, 179, 180 digoxin bioequivalence, 158 factors affecting absorption, 183 interactions, 355 intravenous infusion, 210 digoxin immune fab, 414 dihydrostreptomycin, 182 diltiazem, 373 diluents, 191 dipyridamole, 189, 191 disintegrants, 192, 195, 196 disintegration, tablet, 189 disintegration time, 190, 191 disopyramide, 325 disposition, basic pharmacokinetic model, 11 dissociation constant (pKa ), gastrointestinal absorption and, 102 dissolution formulation and processing factors, 191 in vivo–in vitro correlation, 194 Noyes–Whitney equation, 176, 177 process, 175, 176 as rate-limiting step in absorption, 175 time, 50% (t50% ), 200 dissolution rate, 175 factors affecting, 177 dissolution rate constant (K1 ), 176 dissolution tests, 191 fallacy about, 158 paddle method, 193 rotary basket method, 192, 194 USP method 3, 194 dissolution time, mean (MDT), 441 distribution (drug) compartment model selection and, defined, nonlinear, 325 oligonucleotides, 424 rapid and slow, distribution (frequency), 148, 150 distribution half-life ((t1/2 )α ), 292, 300 distribution rate constant (α), 291, 299 465 determination, 292, 294, 295 difference to β, 295 elimination rate constant and, 295 example calculation, 300, 302 distributive phase, 285, 286 disulfiram, 355 DNase (dornase alfa), 415, 417 dosage forms comparative bioavailability, 139 drug development, formulation and processing factors, 191 gastrointestinal absorption and, 187 in vivo–in vitro data correlation, 194 ranking of bioavailability, 188 retention in stomach, 98 see also specific dosage forms dose, adjusted daily, calculation, 76 adjustments in renal impairment, 74, 75 administered amount of drug in body and, AUC and, 144 average steady-state plasma concentration and, 248 calculation, 29 drug absorption and, 155 calculation in multiple dosing, 249 loading see loading dose maintenance see maintenance dose multiple intermittent infusions, 313 dose-dependent pharmacokinetics see nonlinear pharmacokinetics dose-independent pharmacokinetics see linear pharmacokinetics dosing intervals (τ ) average steady-state plasma concentration and, 246, 248 drug accumulation and, 250, 252 drug fluctuation and, 253 multiple intermittent infusions, 309, 310, 314 multiple intravenous boluses, 238, 239, 249 dosing rate (R) estimation, worked example, 330 Vmax and Km estimation from, 329 dosing regimens adjusting for severity of infection, 312 defined, 238 implications of failure to follow, 251 multiple intermittent infusions, 311 multiple intravenous boluses, 248 new drugs, renal impairment, 74, 75 vancomycin problem, 314 Dost ratio (r), 241, 243 doxycycline, 184 drotrecogin alfa, 415 466 Index drug accumulation (R) defined, 238 extravascular route, 263 intravenous route, 238, 249 calculation, 251 dosing interval and, 250, 252 important comments, 250 drug development, in vitro–in vivo correlation, 194 drug interactions, 341 cytochrome P450-based, 349–353 linked to transporters, 355 pharmacokinetic and pharmacodynamic, 364, 365 plasma protein binding, 342 tissue binding, 348 duodenum, 98 duration of action, eculizumab, 421 Eigenvalues, 402 elimination, 6, 55 mechanism, 69 nonlinear, 325 proteins and peptides, 418 elimination half life (t1/2 ), 36 creatinine clearance and, 72 determination extravascular route, 109, 111, 121, 124 graphical method, 37, 38 intravenous bolus, 36, 40, 41 post-infusion data, 222 Rowland and Tozer method, 225, 226 urinary excretion data, 50, 52 as a parameter, 21 parameters affecting, 65 plasma protein binding interactions and, 345, 346 proteins and peptides, 418 route of administration and, 120, 122 selected drugs, 39 steady-state plasma concentration and, 210, 212 tissue-binding interactions and, 348 elimination rate continuous intravenous infusion, 204, 207 drug dosing rate and, 329 first order equation, 14 nonlinear, 324 tank and faucet analogy, 60 true steady-state, 208 zero order equation, 13 elimination rate constant (K or Kel ), 13 absorption rate constant (Ka ) and, 126 determination extravascular route, 109, 112, 121, 123, 124 intravenous bolus, 38, 40 post-infusion data, 222 Rowland and Tozer method, 225, 226 urinary excretion data, 42 distribution rate constant and, 295 flip-flop kinetics, 109, 126 metabolite (k(m)), 381 renal impairment, 72, 73 route of administration and, 120, 122 elimination rate constant from central compartment (K10 ), 289–291 determination, 295, 300 relationship to β, 299 elixirs, 188 enalapril, 373 enzymatic metabolism, 325 epoetin alpha, 415 equilibrium solubility in gastrointestinal fluid, 177 equivalence pharmaceutical or chemical, 138 terms, 157 therapeutic, 138 see also bioequivalence Erbitux, 420 error messages, nonlinear regression, 399, 407 erythromycin, 102, 184, 354 ester forms, 138 etanercept, 415 ethanol, 325 etretinate, 373 excipients bioavailability effects, 191 drug complexation with, 183 excretion, 6, 55 physiology, 56, 57 excretion rate constant (Ku ) calculation from plasma data, 39 calculation from urinary data, 44, 50 experimental design bioavailability testing, 145, 147, 148 metabolite pharmacokinetics, 388, 389 role of simulation, 410 exponents, 18, 19 extraction ratio (E), 61 see also hepatic extraction ratio extravascular administration, 5, 105 absorption rate constant, 110 amount of drug in body/blood, 109, 110 apparent volume of distribution, 116, 121 AUC determination, 144, 146 average steady-state plasma concentration, 248 basic pharmacokinetic model, 11 characterizing drug absorption, 155, 156 comparative bioavailability, 139 drug absorption see absorption drug remaining to be absorbed/at site of administration, 106, 109 flip-flop kinetics, 126 Index general comments, 120 metabolite kinetics, 382, 384 steady state, 387 monitoring drug in blood, 107 multiple dosing see multiple extravascular dosing one-compartment model, 9, 10 absorption rate constant, 111 mean residence time, 434, 441 metabolite kinetics, 382, 384 peak plasma concentration see peak plasma concentration peak time see peak time plasma concentration versus time plot, 3, 207 single dose, 258 two-compartment model, 10, 303, 304 absorption rate constant, 115 mean residence time, 437, 438 worked examples, 121, 123 Exubera, 415, 417 factor VIIa, 414 factor VIII (antihemophilic factor), 414, 418 factor IX, 414 FDA see Food and Drug Administration FDC blue No dye, 194 feathering method α and A determination, 292 initial parameter estimates, 411 (Ka ) determination, 110–112 worked example, 121, 123 ferrous salts, iron content, 216 Fick’s law of diffusion, 100, 101 first-order elimination rate constant see elimination rate constant first-order processes, 7, 13–15 active transport, 100 clearance, 59 passive diffusion, 99 zero-order versus, 14, 15 first-pass effect, 142 flip-flop kinetics extravascular administration, 126 two-compartment model, 295 flow rate, intravenous infusion, 204 fluconazole, 354 fluctuation (φ) extravascular route, 264 intravenous route, 251, 253 fluoroquinolone antibiotics, 354 fluoxetine, 373 follitropin alfa, 415 follitropin beta, 415 fomvirsen (Vitravene), 424 Food and Drug Administration (FDA) approved monoclonal antibodies, 419–422 approved oligonucleotides, 423 bioinequivalent approved formulations, 159 467 codes, 157 definition of bioavailability, 138 definition of in vivo–in vitro correlation, 196 in vitro–in vivo correlation guidance, 195 interpreting 90% confidence interval formula, 152 formulation absorption and, 5, bioavailability effects, 142 bioavailability testing, 146 defined, 148 peak plasma concentration and, 118, 119 fosphenytoin, 373 fraction of drug absorbed (F), 115, 116 absolute bioavailability and, 139 average steady-state plasma concentration and, 248 factors affecting, 121 surviving first-pass effect (F∗ ), 142 fraction of drug traversing GI tract membrane (fGIT ), 341, 345 fraction of drug unabsorbed, 113, 114 fraction of drug unbound in plasma (fup ), 341 average total and free steady-state drug concentrations, 344 elimination half-life and, 345, 346 fraction unbound in tissue (fut ) and, 348 hepatic clearance and, 343, 344 Vss and, 343 fraction of drug unbound in tissues (fut ), 343, 348 fraction of parent drug converted to metabolite of interest (fm ), 370, 382 fraction of parent drug escaping metabolism during a single pass through liver (FH ), 383, 384 fraction of primary metabolite escaping sequential metabolism in liver (FH (m)), 370, 382 fraction of steady-state condition (fss ), 211 number of doses required to reach see number of doses to reach fraction of steady-state time to reach a given, 211, 332, 334 free (unbound) drug concentration nonlinear kinetics, 335 transient changes, 346, 347 free (unbound) drug concentration at steady state ((Cu )ss ) average see average free (unbound) drug concentration at steady state frequency distribution, 148, 150 galsufase, 415 gastrointestinal (GI) tract, 95 drug absorption see also absorption drug complexation within, 182 drug dissolution, 175, 176 drug remaining to be absorbed, 106, 109 fraction of drug traversing (fGIT ), 341, 345 468 Index important features, 95 mean residence time (MRTGIT ), 435, 437 membrane physiology, 98, 99 microanatomy, 96, 97 pH variations, 95, 97 Gauss–Newton method, 405 Genasense, 423 Gendicine, 426 gene therapies, 425, 426 gentamicin flip-flop kinetics, 295 multiple intermittent infusions, 311 glomerular filtration, 56 glomerular filtration rate (GFR), 69 CKD-EPI formula, 76 estimated (eGFR), 76 estimation, 69 Mayo quadratic formula, 76 MDRD study group formula, 76 glucagon, 415 glucocerebrosidase, 415 GM2/KLH immunotherapy, 425 golimumab, 421 goodness of fit indices, 398 goserelin, 415 gp91phox gene, 426 granulocyte colony-stimulating factor (GCSF), pegylated, 417, 419 granulocyte–macrophage colony-stimulating factor (GM-CSF), recombinant human, 417 grapefruit juice, 349 graphs, nonlinear regression, 404, 405 griseofulvin in vivo–in vitro correlation, 200, 201 particle size, 179 growth hormone, recombinant human, 415 gums, natural and synthetic, 192 Gvax, 424 haloperidol, 122 hematocrit (Hct), 344 Henderson–Hasselbalch equation, 102 hepatic blood/plasma flow (QH ), 57 drug interactions and, 342 elimination half-life and, 345 hepatic clearance and, 63, 65 hepatic clearance (ClH ), 57 intrinsic clearance and, 63, 65 parameters affecting, 64 plasma protein binding interactions and, 343, 344 tissue-binding interactions and, 348 hepatic extraction ratio (E), 61–63 selected drugs, 64 hepatitis B vaccine, recombinant, 415, 418 Herceptin, 422 HI-6, 300 human growth hormone (HGH), recombinant, 415 human immunodeficiency virus (HIV) protease inhibitors, 354 Humira, 420 hydration state, 181 hydrophilic drugs, volume of distribution, 34, 35 hydrophobic drugs factors improving dissolution, 179 see also lipophilic drugs hydroquinone, 183 hydroxymethylglutaryl-coenzyme A (HMG-CoA) reductase inhibitors, 349, 354 hydroxyzine, 373 hypoalbuminemia, 323 ibritumomab tiuxetan (Zevalin), 419, 421 rh-alpha-L-iduronidase precursor, 417 imiglucerase, 415 imipramine, 374 immunotherapy, 424 in vivo–in vitro correlation (IVIVC) correlated variables, 200 definitions, 196 examples, 200 levels, 196 systematic development, 198 types of correlation, 199 infliximab, 421 infusion duration plasma concentration and, 208 practical steady-state plasma concentration, 209 infusion rates calculation from post-infusion data, 224 control, 204 elimination rate and, 204, 206, 207 Km calculation from two, 329 loading, 312 multiple intermittent infusions, 314 plasma concentration and, 208 renal impairment, 208 salt value adjustment, 216 steady-state plasma concentration and, 209, 210 true steady-state, 208 Wagner’s method, 217–219 infusions see continuous intravenous infusion; multiple intermittent infusions INGN 241, 426 insulin, human, 415, 417 insulin-like growth factor (IGF-1), 416 insulin-like growth factor 1/insulin growth factor-binding protein complex (IGF-1/IGFBP-3), 416 inter-compartmental rate constants (K21 and K12 ) determination, 295 example calculation, 300 extravascular dosing, 303 interferon alfa 2a, pegylated, 416 Index interferon alpha (IFNα), 416 interferon alpha 2b, 416 interferon beta 1a (IFNβ 1a), 416 interferon beta 1b (IFNβ 1b), 416 interferon gamma 1b (IFNγ 1b), 416 interleukin-1 receptor antagonist (IL-1Ra), 414 interleukin-2, 414 interleukin-11, 417 intermittent intravenous infusions, multiple see multiple intermittent infusions intestine drug absorption, 103 important features, 98 membrane physiology, 98, 99 microanatomy, 97 intravascular administration, 4, characterizing drug absorption, 155, 156 plasma concentration versus time plot, intravenous administration amount of drug in body, drug concentration at steady state, 341 plasma protein binding interactions, 344, 345 intravenous bolus administration AUC determination, 143, 144 loading dose (DL ) see under loading dose multiple dosing see multiple intravenous bolus dosing one-compartment model, 8, 9, 29, 30 ARE method, 430 AUC and AUMC, 430, 431 mean residence time, 429, 431 metabolite pharmacokinetics, 370, 380 pharmacokinetic parameters derived, 30 pharmacokinetic–pharmacodynamic (PKPD) relationship, 362 plasma concentration-derived parameters, 40 protocol, 41 renal clearance, 72 single dose, 238 urinary excretion-derived parameters, 42 two-compartment model, 9, 287, 293 α and A determination, 292 AUC determination, 298 β and B determination, 292 determination of micro rate constants, 295 further calculations, 302 general comments, 299 mean residence time, 431, 433 useful equations and parameters, 288 V determination, 296 worked examples, 300, 301 Vmax and Km estimation, 327 intravenous infusions see continuous intravenous infusion; multiple intermittent infusions intrinsic clearance (Clint ), 63–65 intrinsic free (unbound) clearance (Clint ), 64 469 drug interactions and, 342 hepatic clearance and, 343, 344 inulin, 69 inulin clearance, 69 ipilimumab, 421 iron-containing products, 216 isosorbide dinitrate, 374 iterations, history of, 402 itraconazole, 374 K see elimination rate constant K0 (zero-order rate constant), 12 K10 see elimination rate constant from central compartment K12 see inter-compartmental rate constants K21 see inter-compartmental rate constants Ka see absorption rate constant kanamycin, 182 Kel see elimination rate constant keratinocyte growth factor, 416 ketoconazole, 349, 354 kidney blood flow, 57 cancer, immunotherapy, 424 drug elimination, 6, 55 physiology, 56, 57 protein and peptide elimination, 418 transporter-related drug interactions, 355 Km see metabolic rate constant; Michaelis–Menten constant Ku see excretion rate constant lag time (t0 ) negative, 116 laronidase, 417 lidocaine, 374 lincomycin, 122 linear pharmacokinetics, 7, 323, 324 linear regression, 397 Lineweaver–Burke plot, 328 lipophilic (lipid soluble) drugs absorption, 101, 184 apparent volume of distribution, 34, 35 partition coefficient, 101 lithium, 344 liver blood flow see hepatic blood/plasma flow drug elimination, 6, 55 first-pass effect, 142 intrinsic clearance, 63–65 metabolite formation, 370 protein and peptide degradation, 418 transporter-related drug interactions, 355 loading dose (DL ) defined, 240 extravascular route, 265, 267 intravenous route 470 Index continuous infusion, 212, 215 multiple bolus dosing, 254, 255 salt value adjustment, 216 oral/intravenous interconversions, 266, 268 loading infusion rate, 312 logarithmic transformation (LT), 148 logarithms, 18, 19 Loo–Riegelman method, 115 loperamide, 355 loratadine, 374 losartan, 374 lovastatin, 349 lubricants, tablet, 193, 197 Lucentis see ranibizumab lymphoma, non-Hodgkin’s, 424 MabThera, 422 macrophage colony-stimulating factor (MCSF), 419 Macugen, 423 macular degeneration, age-related, 423 magnesium stearate, 190, 193 maintenance dose (DM ) defined, 240 extravascular route, 265, 267 intravenous route, 254, 255 oral/intravenous interconversions, 266, 268 mammillary model, 287 mass of drug in body/blood see amount of drug in body/blood mathematics, 17 maximum metabolic rate see Vmax maximum plasma concentration see peak plasma concentration maximum velocity of elimination see Vmax Mayo quadratic formula, 76 MDRD (Modification of Diet in Renal Disease) study group formula, 76 mean absorption time (MAT; MRTGIT ), 435, 437, 441 mean dissolution time (MDT), 441 mean residence time (MRT), 427, 428 applications, 440 in body (MRTb ), 435, 437 central compartment (MRTC ), 433, 441 determination, 429 extravascular route: one-compartment model, 434, 441 extravascular route: two-compartment model, 437, 438 gastrointestinal tract (MRTGIT ), 435, 437, 441 intravenous bag (MRTbag ), 438 intravenous bolus: one-compartment model, 429, 431 intravenous bolus: two-compartment model, 431, 433, 441 intravenous infusion: one-compartment model, 438, 439, 441 peripheral compartment (MRTPERI ), 434 mecasermin rinfabate, 416 median, 148 melanoma, immunotherapy, 424 meperidine, 375, 388, 390 metabolic clearance (Clm ), 57, 66 metabolic rate, 326 see also Vmax metabolic rate constant (Km ) determination, 39 see also Michaelis–Menten constant metabolism, drug interactions involving, 349 saturable (capacity-limited), 326 metabolite(s) drugs with active, 371–379 therapeutic activity, metabolite elimination rate constant (k(m)), 381 metabolite pharmacokinetics, 369 chronic dosing to steady state, 385, 388 chronic meperidine dosing, 388, 390 computer-aided simulation and fitting of data, 388, 389 elimination rate-limited (ERL), 380, 381, 385, 386 formation rate-limited (FRL), 380, 381, 385, 386 general model, 370 intravenous bolus: one-compartment model, 370, 380, 386 intravenous infusion: one-compartment model, 384, 385 oral dose: one-compartment model, 382, 384 renal dysfunction, 388, 392 sample calculations, 393 statistical moment theory, 440 study design for parameter calculations, 388, 389 metoprolol, 253, 355 metronidazole, 375 Michaelis–Menten constant (Km ), 99 dosing rate estimation from, 330 estimation, 327, 411 steady-state plasma concentration from, 330 see also metabolic rate constant Michaelis–Menten equation, 328 Michaelis–Menten kinetics, 325 microcrystalline form, 178 micronized powders, 178, 188, 189 microRNAs (miRNAs), 425 minimization process, 402 minimum drug concentration at steady state see trough drug concentration at steady state minocycline, 74 minoxidil, 375 mixed-order kinetics, 325 models, pharmacokinetic see pharmacokinetic models Index Modification of Diet in Renal Disease (MDRD) study group formula, 76 monoclonal antibodies, 419 morphine, 375 MRT see mean residence time multiple dosing, Vmax and Km estimation, 328 multiple extravascular dosing, 257 average plasma concentration at steady state, 262, 263 drug accumulation, 263 fluctuation factor, 264 intravenous bolus dose interconversions, 266, 268 loading and maintenance doses, 265, 267 maximum plasma concentration at steady state, 260, 261 minimum plasma concentration at steady state, 261 number of doses to reach fraction of steady-state, 264 peak time at steady state (tmax ), 259 plasma concentration at time t after nth dose, 258, 259 multiple intermittent infusions, 309 adjusting for early or late drug concentrations, 315, 317 adjusting for severity of infection, 312 concepts, 309–311 dose to patient, 313 dosing regimen design, 311 drug concentration guidelines, 311 loading infusion rate, 312 two-compartment drug, 313, 314 vancomycin dosing regimen problem, 314 multiple intravenous bolus dosing, 237 assumptions, 240 average plasma concentration at steady state see under average plasma concentration at steady state concepts, 238, 239 definitions, 238 dosing regimen design, 248 Dost ratio (r), 241, 243 drug accumulation see drug accumulation drug fluctuation, 251, 253 loading and maintenance doses, 254, 255 maximum plasma concentration at steady state see under peak plasma concentration at steady state minimum plasma concentration at steady state see under trough drug concentration at steady state number of doses to reach fraction of steady state, 254 oral dose interconversions, 266, 268 steady-state plasma concentration, 238, 240 471 useful pharmacokinetic parameters, 241 muromonab-CD3, 419, 421 myeloma, multiple, 425 nalidixic acid, 375 nanoparticle–aptamer bioconjugates, 424 naproxen, 216 Nelder–Mead (simplex) method, 406 neomycin, 182 nephron, 57 netilmicin, 75 NicVAX, 424 nonlinear pharmacokinetics, 323 administered dose and AUC, 330 capacity-limited metabolism, 325 dose dependence, 323 time to reach given fraction of steady state, 332 Vmax and Km estimation, 327 worked example, 333 nonlinear regression, 396, 397 diagnostics, 403 evaluating program output, 401 goodness of fit indices, 398 methods of improving fit, 401 problems during, 407 settings, 403 simulation, 409 weighting of data points, 401, 408–410 WinNonlin R algorithms, 405 non-steroidal anti-inflammatory drugs (NSAIDs), 354 norethisterone acetate, 178 normeperidine, 390 nortriptyline, 375 novobiocin, 179 Noyes–Whitney equation, 176, 177 number of doses to reach fraction of steady-state extravascular route, 264 intravenous route, 254 number of parameters (NP), 407 obese patients, creatinine clearance, 71 octreotide acetate, 417 OGX-011, 423 oligonucleotides, 423 omalizumab, 421 omeprazole, 216 Oncophage, 424 one-compartment model characteristics, 12 continuous intravenous infusion, 203 extravascular administration see under extravascular administration intravenous bolus administration see under intravenous bolus administration two-compartment versus, 287, 289, 291 onset of action, 472 Index extravascular administration, oprelvekin, 417 oral administration drug absorption after see absorption drug concentration at steady state, 341 first-pass effect, 142 metabolite kinetics, 382, 384, 387 renal dysfunction, 392 plasma protein binding interactions, 345 renal clearance after, 72, 74 see also extravascular administration order of a process, 12 organ clearance, 60, 61 organic anion transporter polypeptide (OATP) transporters, 355 organic anion transporters (OAT), 356 ornithine transcarboxylase (OTC) deficiency, 425 Orthoclone-OKT3, 419, 421 oxytocin, synthetic, 417, 418 P-glycoprotein, 356 inducers, 356 inhibitors, 349, 355, 356 substrates, 356 palifermin, 416 palivizumab, 422 panitumumab, 422 paracetamol, 355 parameters, pharmacokinetic affected by renal impairment, 72–74 correlation matrix, 399, 400, 402 determination, 395, 398, 404 final estimates, 402 improbable results, 399 initial estimates, 402, 406, 411 intravenous bolus dosing, 30 multiple, 241 plasma concentration-derived, 40 two-compartment model, 288 urinary excretion-derived, 42, 43 intravenous infusions, 205 number of (NP), 407 partial derivatives, 403–405 re-expression, 401 redundant, 408 secondary, 403 setting constraints, 401 variance inflation factors (VIFs), 410 see also specific parameters parathyroid hormone, modified, 417 parsimony principle, compartment model selection, 295 partial derivatives, 403–405 particle size, 177, 178 partition coefficient (Km/f ), 101 passive diffusion see diffusion, passive peak plasma concentration ((Cp )max ) bioavailability studies, 146, 149 bioequivalence studies, 138 extravascular dose, 118 determination, 119, 120 worked example, 124 factors affecting, 121, 122 multiple intravenous bolus dosing, 238, 239 significance, 118 peak plasma concentration at steady state multiple extravascular dosing, 260, 261 multiple intermittent infusions, 309–311, 315 multiple intravenous bolus dosing, 243, 246 calculation, 255 fluctuation factor calculation, 252, 253 peak time (tmax ), 117, 118 bioequivalence studies, 141 determination, 117, 121 factors affecting, 121–123 multiple extravascular dosing, 258 multiple extravascular dosing to steady state (tmax ), 259 significance, 118, 119 single extravascular dose, 258 pegaptanib, 423 pegaspargase, 417 pegfilgrastim (pegylated GCSF), 417, 419 pegylation, 418 penicillin V, 200 pentobarbital, 188 pentoxifylline, 376 peptide drugs, 413, 414 period, defined, 148 peripheral compartment, 286, 287 mean residence time (MRTPERI ), 434, 441 multiple, 286 pethidine see meperidine pH dissolution of drugs and, 179 gastrointestinal absorption and, 103 gastrointestinal tract, 95, 97 urine, 56 pH–partition theory of drug absorption, 101 pharmaceutical alternatives, 138 pharmaceutically equivalent products, 138 pharmacodynamics, 359 biotechnology drugs, 413 drug interactions, 362 pharmacogenetics, 349 pharmacokinetic data fitting see data fitting, pharmacokinetic pharmacokinetic models, basic, 11 compartment concept, fitting data to, 396–398 types, 10 Index pharmacokinetic parameters see parameters, pharmacokinetic pharmacokinetic–pharmacodynamic (PKPD) relationships, 359 drug interactions, 364, 365 equations, 361 models, 360–363 pharmacokinetics defined, history, 18 sketches (profiles), 25 phenacetin, 179, 376 phenobarbital, 183 phenobarbital sodium, 215 phenytoin administered dose and AUC, 331 calculation of parameters for, 330, 333 drug interactions, 354 particle size variations, 189 salt value, 215 saturable metabolism, 325 (pKa ), gastrointestinal absorption and, 102 plasma/blood drug concentration ratio (Cplasma /Cblood ), 344 plasma (or serum) concentration (Cp or Cs ) average, drug accumulation from, 249 elimination rate and, 58 free and total, nonlinear kinetics, 335 initial, determination, 36, 38, 40, 41 maximum (peak) see peak plasma concentration post-infusion see post-infusion plasma concentration data sampling protocol, 41 steady state see steady-state plasma concentration therapeutic effect and, 359, 360 time of maximum (tmax ) see peak time time to decline from initial to specific value, 334 toxic effects and, 359, 360 two-compartment model, 292, 303 plasma concentration at time t intravenous bolus dose, 30 intravenous infusion, 208 multiple extravascular dosing, 258 multiple intermittent infusions, 311 multiple intravenous bolus dosing, 241 single extravascular dose, 109 two-compartment model, 292 plasma concentration–effect–time relationships three-dimensional plots, 361 plasma concentration–time plots area under the curve see area under the plasma concentration–time curve bioavailability studies, 146, 149 characterizing absorption from, 155 comparative bioavailability determination, 139, 140 473 compartment models, different formulation, 5, extravascular route multiple dosing, 258, 259 two compartments, 303 initial plasma concentration determination from, 38, 40, 41 intravascular route, 4, intravenous bolus multiple dosing, 238, 239 one compartment, 31, 32 parameter determination from, 40, 41 single dose, 238 two compartments, 292 intravenous infusion cessation, 220 extravascular route versus, 207 loading intravenous bolus dose, 214 K determination from, 38, 40, 41 nonlinear kinetics, 324, 325 steady-state, 212, 213 t1/2 determination from, 38, 40, 41 V determination from, 40 plasma flow clearance and, 61 see also hepatic blood/plasma flow plasma protein binding interactions, 342 average total and free steady-state drug concentrations, 344, 345 elimination half-life, 345, 346 hepatic clearance, 64, 343, 344 transient changes in free drug concentration, 346, 347 Vss , 343 worked calculations, 346, 348 platelet-derived growth factor (becaplermin), 414, 417 polymorphism, 180, 181 post-distribution half-life ((t1/2 )β ), 292, 300 post-distribution rate constant (β), 291 determination, 292, 293 difference to α, 295 example calculation, 300, 301 relationship to K10 , 299 post-distributive phase, 286, 287 post-infusion plasma concentration data, 221, 222 examples of use, 222 t1/2 , Kel and V determination, 223–225 prazepam, 376 predicted data, 403 prednisone, 376 presystemic clearance, 142 primidone, 376 probenecid, 356 procainamide metabolism, 377 474 Index salt value, 216 Wagner’s method, 219 prodrug, 370 profiles, pharmacokinetic, 25 proguanil, 377 ProMune, 424 propafenone, 377 proportionality constant (K), nonlinear elimination, 325 propranolol, 377 prostate cancer, immunotherapy, 424 protein drugs, 413, 415 Provenge, 424 quantitative correlation, 199 quinidine, 216, 377 radioimmunotherapy drugs, 419 ranibizumab (Lucentis), 422 ranitidine, 122 rank, 402 rank-order correlation, 199 rate of excretion method, 48, 51 characterizing absorption, 156, 157 frequency of urine sampling, 53 non-exclusive renal excretion, 53 rate processes, 12 rates, 21, 24 reabsorption, passive renal, 56 receptor-mediated endocytosis, 418 redundant parameters, 408 regression linear, 397 nonlinear see nonlinear regression Remicade, 421 renal clearance (Clr ), 57 calculation, 66 intravenous bolus, 72 metabolite, 391 nonlinear, 325 orally administered dose, 72, 74 rate, 58 renal function, measurement, 69 renal impairment adjusted daily dose, 76 dosing adjustments, 74, 75 infusion rate adjustment, 208 loading intravenous bolus dose, 214 metabolite kinetics, 388, 392 multiple intravenous bolus dosing, 248 pharmacokinetic parameters affected, 72–74 renal clearance and, 72 ReoPro (abciximab), 419, 420 reparameterization, 401 residence times, 428 frequency distributions, 438 mean see mean residence time residuals curve-fitting, 396 estimating goodness of fit, 398, 400 method of see feathering method Resten-CP, 423 Rexin-G, 426 rifampin, 356 risperidone, 377 ritonavir, 354 rituximab (Rituxan), 422 routes of drug administration, effects on absorption, 121 see also specific routes Rowland and Tozer method, 225, 226 salbutamol see albuterol salicylic acid, 192, 193 salt form correction factor (S) (salt value), 214 salt forms, 138 sargramostim, 417 saturable (capacity-limited) metabolism, 326 scale-up and post-approval changes (SUPAC), 195 secondary parameters, 403 semilogarithmic (SL) plot, 8, sequence group, defined, 148 serum concentration see plasma concentration severe combined immunodeficiency disease (SCID), 425 sigma minus method see amount remaining to be excreted (ARE) method significant figures, 20 sildenafil, 354 simplex, 406 simulation, 409 metabolite kinetics, 388, 389 Simulect, 420 simvastatin, 378 singular value decomposition (SVC), 406 sipuleucel T, 424 sites of drug administration, sketches, pharmacokinetic, 25 slopes, rates, and derivatives, 21, 24 slow disposition rate constant see post-distribution rate constant sodium lauryl sulfate, 193, 197 solid dispersions, 178 solid dosage forms see capsules; tablets Soliris, 421 solubility in diffusion layer, 179, 180 equilibrium, in gastrointestinal fluid, 177 solutions (as dosage forms), 188 somatotropin, recombinant, 415 spironolactone, 187 SSE see sum of squares error St John’s wort, 354 standard deviation (s), 408 Index standard error (SE), 150, 402 starch concentrations, 192, 195 types, 193, 196 statins, 349, 354 statistical moment theory applications, 439 see also mean residence time steady-state condition defined, 240 fraction of (fss ) see fraction of steady-state condition metabolites, 385, 388 multiple intermittent infusions, 309 peak time in multiple extravascular dosing to (tmax ), 259 practical, 209 true, 208 steady-state plasma concentration ((Cp )ss ) average see average plasma concentration at steady state fluctuation, 251, 255 infusion rate and, 209, 210 instantaneous and continuous, 212 Km calculation from two, 329 maximum see peak plasma concentration at steady state Michaelis–Menten parameters for estimating, 330 minimum see trough drug concentration at steady state multiple intravenous bolus dosing, 243, 244 nonlinear kinetics, 324 post-infusion data for calculating, 224 practical time required to reach, 209, 210 time required to attain 90%, 333, 334 true, 209 Vmax and Km estimation, 328 Wagner’s method for attaining, 217–219 stomach dissolution of weak acids, 179, 180 drug absorption, 98 important features, 98 membrane physiology, 98, 99 microanatomy, 96 streptomycin, 182 study design see experimental design sulfadiazine, 178 sulfameter, 181 sulfathiazole, 193, 197 sulfonamides, 354 sulindac, 378 sum of squares error (SSE) Gauss–Newton method, 406 local and global minima, 407, 408 475 Nelder–Mead method, 406 summary table, nonlinear regression, 403, 404 surface-active agents, 179 surface area (of a solid drug) dissolution rate and, 177, 179 particle size, 177 wetting agent to increase, 179 suspensions, 188 Synagis, 422 syrups, 188 systemic clearance (Cls ), 57, 58 average steady-state plasma concentration and, 248 estimation, 65 intravenous infusion, 208 statistical moment theory, 440 t statistic, 150 t0 see lag time t1/2 see elimination half life tablets, 189 absorption versus suspensions, 188 coloring agents, 193, 197 crushing, 190 diluents, 191 disintegrants, 192, 195, 196 disintegration, 189 disintegration time, 190, 191 lubricants, 193, 197 steps in dissolution and absorption, 190 talc, 193 tank and faucet analogy, 58, 59 targeted drug delivery, 424 tenectelplase, 417 terfenadine, 354, 378 teriparatide, 417 termination of action, tetracycline, 183, 184 theophylline bioavailability data, 152 interactions, 354 salt value adjustment, 216 therapeutic effect, 359, 360 therapeutic equivalence defined, 138 FDA codes, 157 therapeutic range, maintaining drug concentration within, 204 multiple intravenous bolus dosing regimen design, 248 thiazide KCl, 158 thioridazine, 378 time expressions, 24, 25 time for 50% of drug to dissolve (t50% ), 200 time of maximum drug concentration (tmax ) see peak time 476 Index time to reach 90% of true steady-state plasma concentration, 334 time to reach given fraction of steady-state, 211, 212, 332, 334 time to reach practical steady-state plasma concentration, 209, 210 timolol, 355 tissue-binding interactions, 348, 349 tissue plasminogen activator (tPA), 417 tmax see peak time TNFerade, 426 tobramycin, dosing in renal impairment, 75 tocilizumab, 422 tolbutamide chemical modification, 184, 185 disintegrating agents, 192 toll-like receptor (TLR) agonists, 423 tositumomab (Bexxar), 422 total body clearance (TBC) see systemic clearance total drug concentration, nonlinear kinetics, 335 total drug concentration at steady state (Css ) average see average total drug concentration at steady state toxic effects, 359, 360 transfer rate constants see inter-compartmental rate constants transporters, drug interactions linked to, 355 trapezoidal rule, AUC determination, 145 example calculation, 68 statistical moment theory, 428 two-compartment model, 298 trastuzumab, 422 tricyclic antidepressants, 355 trimethoprim/sulfamethoxazole, 188 trough drug concentration at steady state multiple extravascular dosing, 261 multiple intermittent infusions, 309–311, 315 multiple intravenous boluses, 243, 246 calculation, 255 fluctuation factor calculation, 252, 253 TroVax, 425 tubular secretion, active, 56 two-compartment model, 285 concepts, 285–289 extravascular administration see under extravascular administration intravenous bolus administration see under intravenous bolus administration multiple intermittent infusions, 313, 314 one-compartment versus, 287, 289, 291 selection, 295 types, 287, 290, 291 see also central compartment; peripheral compartment unbound drug concentration see free (unbound) drug concentration United States Pharmacopeia (USP) definition of in vivo–in vitro correlation, 196 dissolution tests, 191 units, 21, 23 urinary excretion one-compartment intravenous bolus model, 42, 43 parameter derivation from, 43 see also amount remaining to be excreted method; kidney; rate of excretion method urine amount (mass) of drug in, absorption rate constant determination, 113 cumulative amount of drug eliminated absolute bioavailability from, 139 changes over time, 42, 44, 45 characterizing absorption from, 155 comparative bioavailability from, 140, 141 determination, 143 frequency of sampling, 53 pH, 56 ustekinumab, 422 V see apparent volume of distribution vaccines, 424 vancomycin adjusting for early or late drug concentrations, 316 dosing regimen problem, 314 multiple intermittent infusions, 309, 310 “peak” at h post-infusion, 313, 314 variables, 19, 20 variance/covariance matrix, 403 variance inflation factors (VIFs), 410 vascular endothelial growth factor (VEGF) antagonist, 423 Vectibix, 422 Veegum, 192, 195, 196 venlafaxine, 378 verapamil, 378 vitespen, 424 Vitravene (fomvirsen), 423, 424 Vmax , 325 dosing rate estimation from, 330 estimation, 327, 411 steady-state plasma concentration from, 330 volume of distribution, see also apparent volume of distribution Wagner–Nelson methods mass of drug in urine data, 113 plasma drug level data, 111 Wagner’s method for attaining steady state, 217–219 warfarin, interactions, 354 washout, 150 weak acids Index dissolution in stomach, 179 gastrointestinal absorption, 102, 103 renal excretion, 56 weak bases gastrointestinal absorption, 102 renal excretion, 56 weighted sum of squares residual (WSSR), 403, 409 weighting of data points, 401, 408–410 wetting agents, 179 WinNonlin R program, 396, 397 algorithms, 405 evaluating output, 401 metabolite kinetics, 383 477 Wolf’s plot, 328 xenobiotics, Xolair, 421 Zenapax, 421 zero-order processes, 12, 13 active transport, 100 first-order versus, 14, 15 intravenous infusion at constant rate, 204, 205 zero-order rate constant K0 , 12 Zevalin see ibritumomab tiuxetan zidovudine, 379 .. .Basic Pharmacokinetics Basic Pharmacokinetics SECOND EDITION Sunil S Jambhekar BPharm, MS, PhD Professor and Associate... were learned once but perhaps have been forgotten 18 Basic Pharmacokinetics 2.2 A brief history of pharmacokinetics The mathematics of pharmacokinetics strongly resembles, and arises from, the... of equations in clinical practice Since pharmacokinetics is basically mathematical in nature, a chapter has been included to provide the reader with a basic review of the mathematical principles