Medical Toxicology
`
`Third Edition
`
`Edited by
`
`Richard C. Dart, M.D., Ph.D.
`
`D irector
`Rocky Mountain Poison and Drug Center
`Denver Health
`Professor of Surgery (Emergency M edicine)
`M edicme and Pharmacy
`University of Colorado Hea lth Sciences Center
`Denver, Colorado
`
`Authors
`
`E. Martin Caravati, M.D., M.P.H.
`Michael A. McGuigan, M.D., C.M., M.B.A.
`lan MacGregor Whyte, M.B.B.S.(Hons), F.R.A.C.P., F.R.C.P.(Edin)
`Andrew H. Dawson, M.B.B.S., F.R.C.P., F.R.A.C.P.
`Steven A. Seifert, M.D., F.A.C.M.T., F.A.C.E.P.
`Seth Schonwald, M.D., F.A.C.E.P., F.A.C.M. T.
`luke Yip, M.D., F.A.C.M.T., F.A.C.E.P., F.A.C.E.M.
`Daniel C. Keyes, M.D., M.P.H., A.C.M.T.
`Katherine M. Hurlbut, M.D., F.A.C.M.T.
`Andrew R. Erdman, M.D.
`Richard C. Dart, M.D., Ph.D.
`
`~~ LIPPINCOTT WILLIAMS & WILKINS
`
`•
`
`A Wolters Kluwer Company
`Philadelphia • Baltimore • New Ymk • London
`Buenos Aires · Hong Kong • Sydney • Tokyo
`
`CFAD Ex. 1032 (1 of 58)
`
`

`
`Acq111sit1DIIS Editor: Anne M. Sydor
`Oe<~elopmelllal [drlor: Raymund E. Reter
`Supervising Editor: Mary Ann McLaughlin
`Produclio11 Editor: Brooke Begin, Silverchair Science+ Communications
`Ma111~(nctur111g Mmrnger: Ben Rivera
`Col•er Desigm'r: Christine jenny
`Compositor: Silvcrchilir Science+ Communications
`Pri11ter: Quebecer World
`
`© 2004 by LJPPINCOIT Wl LLlAMS & W ILKJNS
`530 WaJnut Street
`Philadelp hia, PA 19106 USA
`LWW.com
`
`All rights reserved. This book is protected by copyright. No part of this book may be
`reproduced in any form or by any means, including photocopying, or utilized by Qny
`information storage <md retrieval system withm1t written permission from the copy(cid:173)
`right owner, excep t for brief quotation s embodied in critical articles and reviews.
`Materials appearing in thjs book prepared by individuals as part of their official duties
`as U.S. government employees are not covered by the above-mentioned copyright.
`
`Printed in the USA
`
`Lib rary of Congress Cataloging-in-Pu blication Data
`
`Medical TCl,icology I !edited brl Richard C. Dart.-3rd. ed.
`p. ;em.
`Rev. eel. of: EUenhom's medical to"\.icology I [edited by! Matthew). EUenhClm ... (ct ai.J. c1997.
`lncludes bibliographical references and mdcx.
`ISBN 0-7817-2t45-2
`1. Clinicaltoxicology.l. To>.icologic<ll emergencies. 1. Dart, Richard C. U. EJlenhom':.
`medical toxicology.
`(DNLM: 1. PoisMing--diag.nosis. 2. Poisoning-therapy. 3. Toxicology--method::.. QV
`600 M4888 2003J
`RA 1218.5M·IJ 2003
`615.9-dc22
`
`20030n0574
`
`Care has been taken to confirm the accuracy of the information presented and to
`describe genera Uy accepted practices. However, the authors, editors, and publisher Me
`not responsible for error or umissions or for any consequences from application of the
`information in this book and make no warranty, expressed or implied, with respect to
`the currency, completeness, or accuracy of the contents of the publication. Application
`of thjs information in a particular situation remains the professional responsibilily of
`the practitioner.
`TI1e authors, editors, and publisher have exerted every effort to ensure that drug
`selection and dosage set forth in this te>.t are in accordance with current recommenda(cid:173)
`tions and practice at the lime of publication. However, in view of ongoing research,
`changes in government regulations, and the constant flow of information relating to
`drug therapy and drug reactions, the reader is urged to check the package insert for
`each drug for any change in indications and dosage and for added warnings and pre(cid:173)
`cautjons. This is particularly important when the recommended <~gen t is a new or
`infrequently employed dn1g.
`Some drugs and medical devices presented in this publication have Food and Drug
`Administration (FDA) clearance for limited use in restricted research settings. It is the
`responsibility of health care providers to ascertain the FDA status of each drug or
`device p lanned for use In their clinical practice.
`
`10987654321
`
`CFAD Ex. 1032 (2 of 58)
`
`

`
`SECT IO N
`
`7
`Pharmacokinetics
`
`CHAPTER 79
`Principles and Applications
`of Pharmacokinetics
`Michael Mayersohn
`
`This presentation is not intended to be a course in mathematics
`nor, fortunately, does the reader need to be a matJ1ematidan to
`tmderstand and apply the principles of phn.rmacokinetics. Effort
`should be expended in understanding the concepts and princi(cid:173)
`ples, which, hopefully, is facilitated by the shorthand use of
`some selected mathematical relationships. The mat11 provides a
`universal language for developing and discussing the princi(cid:173)
`ples. These relationships must make sense (or they are useless),
`and this occurs if the concepts are understood. That said, it is
`necessary to use equations to represent the ideas and for calcu(cid:173)
`lation purposes. Because one principle or idea draws on tllose
`preceding it, try and .keep clear ''what drives what'' (i.e., which
`is the true indl!pendt!llt variable and which is the depe11de11f vari(cid:173)
`able) and how would a plot of one versus the other appear.
`Being able to graph one variable against another is important
`bec,\llse if one can properly create such a plot, one understands
`tlw principle(s) behind the relationship. A graph represents a
`rapid means of presenting a relationship and often is the starting
`point for a discussion. By convention, there is only one graphing
`rule: the dependent variable appears on they-axis (ordinate)
`and the independent variable appears on the x-axis (abscissa).
`The term pltarmacoki11elics arises from the Greek plum/lacon,
`meaning substance (a drug or toxic agent), and kinetics, meaning
`rate process. Pharmacokinetics is the area of study that exam(cid:173)
`ines lhe rates of those processes associated with entry into, dis(cid:173)
`position through, ciJld exit from the body or a materia l (i.e., drug
`or toxin) presented to the body. Further, such study often
`attempts to relate tlle pharmacologic response or pharmacody(cid:173)
`namk events to the concentration of that s ubstance (or a deriva(cid:173)
`tive, such as a metabolite) as a function of time. The latter gives
`l'ise to useful pharmacokinetic/pharmacodynamic relation(cid:173)
`ships. By extension, toxicokinetics concerns itself with lhe rate
`processes associated with a toxic <~gent (or derivativt') entering
`the body and the consequent concentration and time-related
`toxicodynam ic even ts. One cc1n conh·ast pharmacokinetics to
`pharmacodynamics; the former being what the body docs to tlle
`drug and tlle latter represt>nting what the drug does to the body.
`The processes that are studied and quantified in pharmacoki(cid:173)
`netics are often described by the mnemonic ADME, absorption,
`
`distribution, metabolism, and excretion. The three latter pro(cid:173)
`cesses ~~reassociated with rlisposilio11 (i.e., what happens to the
`drug once in the body, after gaining access to the bloodsh·cam),
`whereas absorption describes the movement of the drug from
`the site of application to the bloodstream. In a more general way,
`these processes may be considered: input (absorption), translo(cid:173)
`cation (distribution), and output (elimi.nation). Critical to out
`w1derstanding, however, is the ultimate expression of the inter(cid:173)
`action between the substance and the body, the biologic outcome,
`which is measured as a response or loXJc event.
`Figure 1 illustrates the important idea of tlle overlap between
`the pharmacoki.netic evt'nts and some corresponding biologic out(cid:173)
`come noted as a pharmacodynamic/toxicodynamic event. The
`driving force for tlle processes shown is concentration of drug in
`the blood. For Utis reason, it is important to Wldcn.tand and char(cid:173)
`acterize the concentration-time profile, as it is criticnl for all subse(cid:173)
`quent events (i.e., distribution, elimination, and response).
`Anotller important aspect of Figure 1 is that all of the evenb. an:
`occurring at the same time, tllough processes are often sequential.
`After drug dosing or environmental exposure (on one or multiple
`occasions), and assuming that the substance is absorbed into t·he
`bloodstream, blood concentrations of the substance are achit>ved.
`That (driving force) concentration causes movement from the
`blood to other tissues, including the organs thilteliminate the drug
`(e.g., liver and kidney) .1s well as the tissues that contain receptors
`or regions of potential toxicity. Thus, while the drug i::; being
`absorbed into the bloodstrl'<lm, it is s imultaneously being dlsh'ib(cid:173)
`uted to site of action or to'\icity, Jnd It is undergoing elimination.
`Whereas a response tends to be reversible (increasing or decreas(cid:173)
`ing in some manner related to blood concentration; often directly),
`elimination processes arc almost a lways irreversible.
`A more comprehensive view of the Plcmentary scheme (Fig. 1)
`IS illustrated in Figure 2. The banner cites the b:~sic pmceS'>i!::.,
`input-translocation-output, which are f·urther divided into more
`spccit1c events. Thus, the processes on the left side of the scheme
`describe the transition steps of disintegration tn dissolution to
`absorption that a solid form of a drug Wldergocs on ingestion.
`The dissolution step is often critical because it can rate-limit the
`overall absorption process, especially for poorly water-soluble
`
`CFAD Ex. 1032 (3 of 58)
`
`

`
`Pharmacoklnetic Events
`
`pharmacodynamic Events
`
`Figure 1. Sr.hC'mMit illustration of the overl<~p between pharmacokinelic
`c>vcnt~ and biologic outcome noted as pharmacodynamic:/toxicodynamic
`evt>nl,. Bloorl concentration is the driving force lor all of the events shown.
`All of the processes are dynamic as they are constantly changing with time.
`~r rom M. MayerS(Ihn, unpublished, '' ith permission I rom Saguaro Techni(cid:173)
`cal Press, Int., Tuc~on, AZ, 1002.1
`
`compounds. Absorption, or the process of passing acmss one or
`more biologic membran~ into the bloodstream, is a function of
`U1c pl'lmeability of the molecule (which is related to the oil/water
`pAr~ition coefficient of the chemical). As the molecule moves
`through the intestinal epitht;!lial cells into the bloodstream, it may
`undergo metabolism (especially by the CYP-450 oxidative system
`,,z. well as by conjugation reactions) or encounter efflux transport(cid:173)
`er:. (P-glycoprotein), which move the compound from the cell
`back into the gut lumen. Any absorb!:!d dntg then moves via the
`portal circulation into the liver. Because the latter is the major site
`of metabolism, the compound could undergo further chemical
`alteration as it passes through the liver. The first-pn::s effect, also
`kntlWn as pre>y!'lemic metnboli!im, refers to the movement of com-
`
`79: PI<INCIPI FS A!\.'0 APPLICAIIONS Of PHJ\R\IIACOI<..INliil" 283
`
`pound through the gut wall and liver and its metabolic alteration.
`The first-pass effect can b~ quite important in modulating the
`response to a drug. As noted later, i~ is the magnitude of metabolic
`clearance that determines the significance of the first-pass effect
`(see Nonvascular Input: Absorp~ion and Bioavailability. Once
`past the liver, the compound (and metabolites) gains access to the
`bloodstream (the body).
`Numt•rous other routes of administration (pulmonary, rectal,
`s ubcutaneous, intramuscular, dermal, nasa l) may provide alter(cid:173)
`native and perhaps more efficient modes of adm1inistration com(cid:173)
`pared to the oral route (Fig. 2). ln each instance, just as with oral
`dosing, the drug mus t traverse biologic membranes to gain
`access to the bloodstream. Each route has its own advantages
`and disadvantages. The absorption pmcess can be completely
`bypassed by use of a vascular route, such as intr.wenous admi11~
`istration. The latter involves either bolus (all at once) do!>ing or
`infusion {Wer a specified time. In either approach, the entire
`absorbed dose enters the body.
`Once in the bloodstream, the compound has access to 1:1Ll tis(cid:173)
`sues and organs in the body. During this time the drug distrib~
`utes to the sites of action or toxicity and it undergoes elimination
`by the primary eliminating organs, the liver and kidney. Metab(cid:173)
`olites may form during this time and they in tmn distribute to
`tissues and organs, possibly produce an effect Ot' toxicity, and
`undergo fmther elimination from the body. TI1e scheme in Fig(cid:173)
`ure 2, although appearing somewhat complex, i!> a considerable
`simplification of rea lity.
`Recall that all of the events previously described arc occur(cid:173)
`ring at thl:! same time. One needs to understand and relate dose
`to blood concentration, blood con~ntration to r'esponse, and all
`of these e,·ents with time. This is the challenge .and the purpose
`of pharmacok.inetic::. and toxicokinetics.
`
`Pharmacologic
`or Toxicologic
`effect
`
`L---->
`
`Translocation
`(Distribution)
`
`PharmacoloQiC
`or Toxicologic
`effect
`
`n....--"'---~~;;;;;;;;~~BIIo
`
`Feces
`Pulmonary
`L------'~ PersplratJon
`
`Figure 2. Conceptualized lAte of a
`drug in an clnim,ll bodv aiter dostng
`hy one or mort:' r-outes of .1dministra·
`tlon. The left side· or the schcn1,1 rep(cid:173)
`resents proce:.s•~s <~ssociated wl1 h
`oral absorption (input). The> center
`portion reflects drug mo,ement aiter
`g.1ining aCl.e~s tn the body \lrJn~lo ­
`cn tion). Tlw righ t-htmd side o l the
`srhema illuslrillc•; elimination by var(cid:173)
`iou' organs IOUipuU. (From M MJyer·
`sohn, unpuiJiisherl weth pC'rmi~ston
`irom Saguartl T<•chntGll Prto~s. Inc,
`Tuc~on, AZ. I 'J9;B.)
`
`CFAD Ex. 1032 (4 of 58)
`
`

`
`284
`
`l: GENERAL APPROACH TO THE POISO ED PATII:NT
`
`KINETIC PROCESSES
`
`First-O rder (linear) Kinetic Processes
`The best phm.? to begin a discussion of pharmacokinetic princi(cid:173)
`ples is by fir~:ot discussing the elimination (or ou tput or Joss) pro(cid:173)
`et•s::. and by making a number of limiting assumptions. To
`de,·elop a Fundamental principle, that of first-order or lillt'ar pllar(cid:173)
`IIUICOkini!ltcs, one first assumes that the drug is given as an intra(cid:173)
`venous (TV) bolus dose (the e ntire dose is placed into the
`bloodstream at one time). Second, one assumes that the drug
`distributes instantaneously from the blood to the res t of the
`tissues of tht! body. That assumption gives rise to the so-~Called
`one-compartment mtJrlcl. Although the idea of compartments is
`developed later, for the purpose her~. one assumes the sim(cid:173)
`plest possible model (i.e., the one-compartment model).
`As long as the body receives doses of the subs tance that do
`not exceed the ability of the eliminating processes to hnndle
`those doses, one ob:;ervcs a process of elim ination referred to as
`first-urder or linear pharmacokinetics. Some important excep(cid:173)
`tion:; to lhis assumption exist (e.g., ethanol), and there are s ignif(cid:173)
`icant pharmacologic and toxicologic implications when they
`occur. The principle of first-order kinetics, simply stated, is that
`tile ralt' aj a11y Frace:;.; rs directly rdated to the concentratio11 or
`amormt of that s11/Jslmrce nt n11y given time. Thus, the driving force
`for the rate of that prt.)ccss is simply the concentration or amount
`present at that time. After an lV bolus dose o f drug <md given the
`assumptions, the rate of elimination from the body is directly
`related to the blood concentration or amou nt present in the
`body, as shown in equation 1:
`
`rate"" concentration
`
`fEq. 1l
`Double the bl0od concentration (by doubling the dose), and the
`rate of elimination will double. Halve the concentration (by
`halving the dose), and the rate w ill hnl ve. The proportionality
`sign can be replaced with a constiln t of proportionality and an
`equ<~l sign to give
`rate = K ·concentration OR
`
`rate = K · C
`in which Cis conc~nh·ation (in blood or plasma or seru m), and
`K is the constant of proportionali..ty. To have a final correct eq ua(cid:173)
`tion, a minus sign needs to be added to one side of the eqLta lion
`to indicate loss or elim ina tion of drug from the body.
`
`[Eq. 2]
`
`rate= -K · C
`
`[Eq. 3]
`
`The sign simply indicates the direction t.lf movement of the sub(cid:173)
`stance; in this case, movement out of the body (by elimination)
`and, therefore, concentrations in the blood arc declining wtth
`time. The const<mt of proportionality, K, is referred to as the
`nppomrl overall firsf--orda climinntio11 role co11sflmt, and it refl ects
`the unchanging relationship between rate and C. Thus,
`K =rate c
`
`lEq. 41
`
`Double the concentration, and the ratl' will double, and K will be
`unchanged. Halve the concentration, and the rate will be halved
`and, K w ill be tmchanged . The units of K can be foLtnd by :.ub(cid:173)
`slituting the appropriate units for rate and C:
`K = rate (concentration/time) = _ 1 _ OR t - 1
`C (concentration)
`time
`The units of a first-order rate constan t are a lways reciprocal
`time. The mt'aning of K is described later; however, every com(cid:173)
`pound h as a specific nverage value and range of values forK in
`a given subject group (or anjmal species). The pt'oblem with lhe
`pn.:vlous rate t-qu<'ltions is that tht•y relate concentration and rate
`
`[Eq. S]
`
`rather than what is more useful, concentration and time. To
`obtain that more useful relationship, it is necessary to integrate
`equation 3 over the interval, time %ero to infinity. Perfurming
`that operation gives
`
`fo rate = -fo"K·C.dt
`
`[Eq. 61
`
`!Eq. 7J
`Equation 7 is a clilssic relationship describing an exponential pro(cid:173)
`cess, in this case a declining exponential. In conh·ast, microbio(cid:173)
`logic growth ca n be described by nn identica l but positive
`ex-ponentia l equation. Blood concentration, C. at any time after an
`IV bolus dose is equal to an initial (at Hme zero) blood concentra(cid:173)
`tion, CO, which is multiplied by some number whose value is
`declining over time. Tilat number is given by the base, e, raised to
`il negative t!xponent, which is formed by the product of the first(cid:173)
`order elimimttion rate constant, K, and time (t), after the lV bolus
`injection. Because the product of Kandt increases as ~ime goes on,
`the base raised to an increasing n~gative numbt!r results in
`smaller and sma ller values, which, when multiplied by C1, gives
`decreasing numerical values for blood concentration. Blood con(cid:173)
`centration is declining exponentially according to the valu!! of K:
`The !atger the value of K, the more rapidly the compound is lost
`from the body; the smaller the value of K, the slower it is lost from
`the body. A plot of blood concentration versus time on a linear
`(Carte:.;ian coord inate) graphic sca le results in a curved line
`whose concentration values d ecli ne exponentially. The initial
`time zero concentration, C'1, is the result of the lV dose being dis~
`tributed into some apparent space nr volume, generally referrt!d
`to as the apparent mlume vf distribution, V .~·This somewhat con(cid:173)
`fusing term is d iscussed in Distribution.
`Scientists go through almost any contortion to be able to
`express data in the form of a straight line (which is easy to ana(cid:173)
`lyze). It is not surprising, therefo re, that equation 7 is most often
`presented in one of the two following transform ations, w hich
`are in the form of straight-line equations.
`InC = In C0 - K · t
`(Eq. 8J
`Equation R is obtained by taking the natural logarithm (In; base
`e) of both sides of equation 7. Using the more familiar and com(cid:173)
`mon logarithmic form (log; base 10), one obtains tJ1e following
`useful equation:
`
`o K
`loge = loge - -
`2.3
`
`t
`
`u u u u
`
`IEq. 9)
`
`Y =b - m · X
`Thus, as long iiS all of the assumptions a re correct, n plot of log
`C versus time results i.n a log-linea r straight line w hose slope (m)
`is given by - K/2.3 ,md whose y-intcrcept (b) is equal to the time
`zero concentration, C0. ln contrast to a graphic plot o n linear
`axes, which results in an exponentially curved line, a plot of the
`same data on a semilogarithmic scale results in a straight line.
`1l1e latter has far more useful i.nfonnation compared to the lin(cid:173)
`ear scale plot. The data are either transformed to logarithmic
`values nnd those plotted on a linear scale or, and the more likely
`method, semilogarithmic graph paper is ust.>d jn which the
`numerical vnlues fo r concentrations a re placed onto the loga(cid:173)
`ritlunic y-axis. In fact, what is most often done today is to form
`a data set in a &oftware program (such as L'<CEL), and the data
`are plotted according to the method of choice. The latter
`approach often gives the choice of selecti11g between a linear
`scale or a JogarHhmic scale on the y·axis.
`Semilogan thmic graph paper has a lso been called ratio pnper.
`ScmiJogarithmic scales are best suited to the plotting of d,tta Lh<~t·
`
`CFAD Ex. 1032 (5 of 58)
`
`

`
`ell
`
`e-Vl E
`2.5
`}!t» 2.0
`Q.C
`CD c"
`... -0 c
`c 0 1.5
`o-
`.~:iii
`Q.'- 1.0
`E~ 0.5
`0 c
`... 0
`"g.o 0.0
`:I:
`
`0
`
`79: PHJNUPI.a. ANIJ API' I I< A TI{)N::, Of l'llARMt\COKJNITill5 285
`
`A
`
`1
`
`ell e-
`~~~e
`~Ole 10
`l
`Q.
`CD C 4 •
`a.2
`2 ~-~
`
`B
`
`~~ 1r .
`! ~11121
`
`2
`
`6
`4
`Time, hr
`
`8
`
`10
`
`~() 0.1 -
`0
`
`'I
`
`2
`
`6
`4
`Time, hr
`
`8
`
`10
`
`Figure 3. A: Plasma concentration-time profile after ;-tn Intravenous bolus dose of h)dromorphunt' to nor·
`mal human subjccts Tiw data are plotted on lineM (c-art~Sian) scales, and the resuhing c.urvlhncanly IS an
`indication of an exponential decline in concentration~ with time. 8: Graph olthl' s.1me data illustrated in
`(A) but plotted t>n ,1 ~emilogarithmic scalc. The data ,1re represented bv a single log-l1near relationship.
`con~istent with Jn e~ponential (i.e., first-orciN) process to desuibe drug loss from the hody. The initial
`(hypothetical) lime zero conu·ntration of this chug, hilsed on extrapolation of the line back to they-axis,
`is appro>.im.ltely 4 nglml. The slope of the line is given by -K/2. ~. Th12two arrows inrlic ate the time needed
`for the hyprotlwtical initial concentration (4 nglml) to decline by 50% to a value of 1 mg/L. The t..urrespond(cid:173)
`ing intercept on thE' x-axis (approximately J hou~>) 1epr1?scn1s the half-life (1 111) of tht' drug. Any other pair
`of conc..entr,llion values in the ratio of l:l gives the ~am<:> value for half-life. Not all1>f the data have been
`reploued for th1~ illustration, Js discussed later (Sl'f! Fig. 12). (0Jta recoverE-d and replotted from Parab PV,
`Ritschel WA, Co~ le DE, et al. Pharmacokinetics of hydromorphont> dftc•r intr<~venous, peroral and rectal
`administration to human subjL'Ct~- BiophMm Drug 01 pos 198a;9:1 87-199. FromM. Mayersohn, unpub(cid:173)
`ltshed, "ith pt>rmission irom Saguaro Technical Press. Inc.., Tuc.on, AZ, 2002.)
`
`change in an exponential fashion, such as the concentrat11 . .>n·
`time data obtained in pharmacokinctic investigations. The term
`rntio wa5 used to indicate thai numbers in Lhe same ratio to each
`other are the same distance apart on the logarithmic scale. Thus,
`1·he following pairs of numbers, which arc in the same ratio (of
`5:1 ), are separated by the same distLince: 10/2, 100/20, 600/120,
`and so forth. Similarly, numbers that represent the same per(cid:173)
`centage increase or decrease are separated by the same distance
`on the logarithmic scale. The followtng pairs of numbers, which
`represent a lO~o decrease, are the same distance apart: 100/ 90,
`10/9, and 20/ 18. Another charLicteristic of semi log scales is the
`number of cycles that they represent. Each cycle is an order of
`magmtude (or a factor) of ten. Two-cycle log axis encompasses a
`100-fold range (or two orders of magnitude of ten) from, for
`example, l to 10 to 100 or 0.01 to 0.1 to 1.0.
`K, U1e apparent overa ll first-order elimination rate constant,
`represents a fractionaJ rate of loss of drug from the body. Thus, for
`example, if a drug has a value of K of 0.1 hour-I (or 0.1/hour), it
`is nppntnmnlcly correct to say that at U1e end of any hour npproxi(cid:173)
`matt'ly 10°·o of d.ntg that was there at the beginning of the hour ha::.
`now been eliminated. For example, at time zero after giving an IV
`bolus dose nf dn•g the plasma concentration is 100 mg/ L. One
`~our later, U1e bod) has lost ai'Proximatdy 10% of 100 mg/ L, gi\'(cid:173)
`mg a concentration of90 mg/Lat 1 hour. One hour after that (at 2
`hours), another 10°'o has been lost and the plasma concentration
`at 2_ ho~r-. is now approxi11mtcly 81 mg/L. At 3 homs, the concen(cid:173)
`tratiOn ts nppro:ril/lntrly 73 mg/ L; at4 hours, npproximntely 67 mg/
`L; and so forth.lfthtc> rate constant had .1 value ofO.OS year t (0.05/
`year), npprnXilllntdlj 5% of the drug present al U-,e beginning of the
`year would be !oM by the end of that year. There is a more useful
`~nd simpler way to express drug Joss from the body and it
`·~v~lv:S the idea of Tlalf-li(e, t1 2; a term commonly used in many
`dt<;c•plint><. (i l'., radioacti\ e decay in physics and i11uitro degrada(cid:173)
`hon ~eactions in chemistry).
`F1gurc 3 illustrates two plasma concentration-time graphs or
`hydromorphone after IV bolus dosing to a group of normal
`human subjects (1). For a reason that is explained in Disposition:
`~odcls, not c11l of the data have been replotted in these graph5.
`hr graph on the left (Fig. 1/\) is plotted on linear (caJtesian)
`
`coordina te axes. The data and U1c corresponding line are curvt(cid:173)
`linear, consistent with expcmenlial decline in concentration w 1th
`time. JJ1 contrast, the g raph on the right (Fig. 3B) is a plot of th~
`same data on semilog axes. This graph, ttn.l.ike the one using a
`linear seale, contains usdul information and is the starting point
`for any pharmacokinctic data analysis. It is absolutely essential
`to plot a data set before beginning any analysis Lo visuali;!e the
`behavior of the drug and the system. There are several points
`U1at need to be made about Figure 3B. The data are represented
`by a single, log-linear line, which is expected for any simple (i.e.,
`single) exponential, first-order kinetic process. There is no cun i(cid:173)
`linearity in the graph for the dalcl plotted, which is consistent
`w ith the assumption of instantaneous distribution fH1m the
`blood to all body tissues (i.e., a one-compartment model). The
`slope of the line is given by - K/2.3, from which one can estimate
`the value for the apparent overall first·-order elimination ra te
`constant, K. The intercept on they-axis represents the (hypothet(cid:173)
`ica l) time zero plasma concentration, which is never (lctually
`measured (it is always estimated by extrapolation of the straight
`line back to they-axis).
`An important concept illustrated on the semilog graph is the
`useful and practical idea or J 111~. Unlike a value forK, it is easy
`to understand the concept of a t112• By definition, t112 is the time
`necessary for any given va lue of concentration to decline by one(cid:173)
`half or by 50'Y.o. This is illustrated in Figure :m by the horizontal
`arrow indicating where a plasma concentration valtte of 2 ng/
`ml is seen on the line and the vt!rtical arrow tha l ind icates the
`time at which that concent•·ation ib achieved Because the drug
`level declined 50% (4 to 2 ng/ml) at the 3-hour time point, 3
`hours is the value for t 1 1~ fM hydromorphone. However, any
`other pair of concentration valut>5 in the ratio of 2:1 could have
`been used (e.g., 2 to 1 ng/ ml) and U1e same value for t1, would
`h;JYe been obtained.
`Although it does not have meaning at this point, it is good
`pr.Ktice to refer to t 112 as the termmal tt 12.lnfact,although Ll van(cid:173)
`ety of different words arc used to qualify the term tt/l' includmg
`/liologk, eliminnlio11, and disposition, the one term that is always
`correct is terminLII t1 1~. Biologic L112 is not a good expre!>Sil1n
`because it can be confused with the decline in pharmacody-
`
`ftz
`
`CFAD Ex. 1032 (6 of 58)
`
`

`
`286
`
`l : GENERAL APPROACH TO T HE POISONED P ATIENT
`
`namic activity rather than characterization of drug loss from the
`body. Elimirmtion t11~. although commonly used, is only correct
`when dealing with a one-compnrlmcnt model, ns discussed
`Inter. Disl'osil imt t 112 is often a correct usC~ge; however, it may be
`incorrect when characterizing plasmCI concentration-time data
`after nnnvascular dosi ng (e.g .• oral rQlltt::).
`1112 and K are related. Taking equation 9 and specifying that
`Cis one-half of the starting value, C11 (which by definition OCClii'S
`after one t 112) and rearranging,
`
`K · t
`II
`It,~C -loge=-
`2.3
`o K · ttr
`o
`,., •
`logC - log[0.5C ] = -
`2
`
`.;)
`
`Co J K . tin
`log-- =---
`[
`0.5Co
`2.3
`
`IEq. 101
`
`,
`K·t
`logl 2l =~
`2.3
`[0.30101·[2.31
`K
`
`-
`t
`112 -
`
`- 0.693
`t
`112 - ~
`
`t112 and K are inversely related; the greater the K, the smaller the
`t112, and thesmaUcr the K, the greater the t1 ·~ ·Furthermore, notice
`that t112 (a.nd K) is i11rlept'11denl of dose or plasma concentration.
`TI1is is what is meant by dose-indcpendl?lz/ pharmacokinetics; the
`parameters describing the disposition of ad rug are 11ot dependent
`on dose (thi~ statement also applies to other pharmacokinetic
`parameters. such as apparent volume of distribution and clear(cid:173)
`ance). ln the example cited in Figure 3B, the terminal t112 val ue of
`npproximatcly 3 hours for hydromorphone has a tenninal rate
`constant of 0.693/3 hours, Qr 0.231 hour1.
`ln contrast to the pMameters being iwkpc11rfen/ of dose,
`plasma concentration docs dellt'lld on dose; double the dose and
`plasma concentrations will double, with no change iJ.1 t112. These
`two sta tements are illustrated in Figure 4. l.n Figure 4A, three
`different TV bolus doses ha\ e been administered: doseD, dose
`2D. and dose 50. A plot of the concentration-time data on semi(cid:173)
`log axes gives lines that are parallel to each other, because there
`is only one value for K or t112 for that drug. However, the lines
`
`c 10 l
`0
`;: 5 ...
`~
`E
`T '
`
`.... ....,..._
`
`A
`
`. --------, ____ ,
`
`intercept they-axis gi,•ing 6mc zero concenh'ations in lhe same
`ratio as the doses: concentration of one u nit, concentration of
`two units, and concentration of five units. As noted above, and
`as shown in Fig ure 4B, a plot of t1, 2 (or K) as a function of dose
`gives a flat line; there is no dependence of t112 on dose.
`Whereas t112 is i11dt>pt'11dcnt of dose, the resulhng plasma con(cid:173)
`centrations (as noted in Fig. 4A) are directly dependl'lll on dose,
`as shown in Figure SA. This is often referred to as dose-propor(cid:173)
`tionality. The idea illustrated in Figur~ 4A can also be repre(cid:173)
`sented by the principle of supcrposilicm, which s tates that
`because doubling the dose results in doubling of plilsma concen(cid:173)
`tration, a plot of concentration/ dose should give rise to one line
`thill represents the superposition of all concentration and dose
`pairs. This principle is illustrated in Figure SB.
`One of the most important aspects of first-order or linear
`kinetics is that everything about the disposition or behavior of a
`drug is predictable, as can be surmised from the relationships
`illush·ated in Figures 4 and 5. Because parameters I'Cn1flin con(cid:173)
`stant w ith dose and because concentrations are directly depen(cid:173)
`dent on dose, one is able to predict a concentration-time profile
`for any given IV dose. ln such a linear sy::.tern, doubling the
`i.nput resu lts in an exact doubling of the output (e.g .• double the
`dose, double the plasma concentration). When first-order
`kinetic principles do not apply, all predictabi lity is ~one and one
`faces significant problems in, for example, drug dosing and
`extrapolating from a subtoxie dose to a toxic dose.
`
`Non-First-Order (Nonlinear) Kinetic Processes
`Many physical and biologic processes cannot be simply charac(cid:173)
`terized by first-order kinetic or linear S)'Stems behavior. l.n fact,
`the world is a nonlinear one in which doubling the input often
`results in something other than a doubling of the output (less
`than or more than double the output). The assumption is often
`made that the system (e.g .. the body) behaves i11 a li11ear way, or
`at least that approximation is believed to be correct. ln fad, it is
`true that many of the drugs and toxins that arc dealt wi th
`behave in a linl;!ar ma11J1er, at least at medically relevanl doses.
`Bu t, th.is may not be a reasonable approximation for some doses
`or Le\'Cis of exposure, especially at the h.igh end of the range in
`which the toxicologist becomes involved. All pharmacokinetic
`processes (absorption, distribution, elimination) may exhibit
`nonlinear behavior, and there are drug and toxin examples of
`such behavior fur cnch of those processes.
`
`41
`... 31
`.c.
`i
`i
`..J 2 .
`