Cl inical Pharmacak inet ics Concepts and Application s third edition
MALCOlM ROWlAND, Ph.D. Depomnenr of Phormocy University of Iv\oncne$ler
fvlonchester, England
THOMAS N. TOZER, Ph.D. School of Pbcrmocv University of California
San Francisco, Cclnormc
A Leu ..v... Febiger Book
.e1~ LI pPINCOTT WILLIAMS & W ILKINS •
A Wollen Kluwef Company
Philadelphia • Ballimore • New York • l ondon Buenos Aires • Hong Kong . Syd ney • Tokyo
f:.w .: uIIH'
f:.I.,,,,, !)""'..l H
11tlO-It'/>f'U" Ud l l.;.[I/.-n Frmu.·#"! I-: li tu, I.L<{;i :'>tnl<1 ' .....1....·' ''',., .u.....lR"...
u. urw.· Ft>¥'$J1h
f 'n:>J«t /-:.111"" J(oh." lJ .1I('1tt,·
Copyright C I99S
lW
~r, lI ..m.
HO ~·01
l!< ~'i u.,; ...
~ .....
Pt"l.Jdrh'" lm yInft .. 1'1101'>-:1021 l ' !>A
All ri¢lt~ re....'rve·d Thi~ h<.. .. i.~ I'rul~-..:1•..J I')' cnpy ril(ht , . .." p;ln (>t lhi~ h•• ok lIu)' I... n.· pr"du...·tI in "n y '.. rm nr tl)' ..n)' rnt~"Il-~. ind ud mjt ph'lIu':OPyinll. 0' ulllll.et.l hy ~n)' infum u lion "" "'-"11<' ~n<.I 1'1.1,...·,..,,1 ~)·", .-n l .....i1huu l ....Titl.-n pemli.,~i"n (ru m lho.- n ,p\.-rixh! . ..... I'll·r An'Ur~l .. inlJiGlli(>n~. ~.h'ff'>t" ll.·oI<.1i< ...~. ~oo J<"..;I!lt' ·hnluk-" fur drull" an.' pt<" i<.k'
f i~ UrwnllO ·it.....' lhe.- p;ld.,.:.lJC" infun1l.llKlf1 wI" ..r II... nunub'1u ...." (lr lho.- mnli<.~ I IIl"'~ rnt'1l1K>nnJ.
I'firllcd in 11M:' l :nit ..-d Sl"l..,.. , rl Anlt"fit'
Ubnry or CAm~ Cata",-"" ln K-ln ·Puh llc a don Dala Itu..... boo. 1t-f.l.kolm, O in i<'f B.."k .~
Ind u<1o:-!< hihli<'Ilf'lphi<.·..1 n..rl·n..I'll~"oo Indo-·" . ISUS ().(1Mj-(J7i(~·O 1 Plunruc" killt1 it'!o l Cho(.-nKJlhlT~J')·, TOIt·r. l1K1flU' S ,
n. nne. lu s U.t 1. Plunrun okllw:iio k.\1~1I .~ .R6K
l .Im..1l Th<.T.. p)·
Q V .\Ii llSK;k 1....,1-11
,~
6 1".7_k lO ' ) ~ L\ L ,() LC
fur lihr~rr .. t CA IOIlft"'"
"Ie.,.,. 10'" I" ..... I " ..1I•."..1 1/lhory-' 1><'/1' ill ·t"Ui' .,· (lm"lRt 'm",,',~ (.1 Iht·fiN o(>(>"rr" "'1l'
Iht- /'"hlu/l<111' ...... 1<. ",.ory .tJi,rr 1'-' Irw.·.. lho-' ·''''.I'tlNbl h.. 'l
>U••
9 10
PREFACE PURPOSE 01 TIXT kt 't' pill~ wtth tilt' fi o t hm ("l;lilions. is a pn nu-r in p harmacokinet ics clhucn l applica tions. 111t' Ix)ok should hl' useful to ilny student. pmc· tulom-r. o r rt'sl'ard lt'r Willi is in f('rt'slt'() o r t 'llga~("ll in til(' dt ·" dopllll'u t , e-....uluutk rn. o r II!\('
The rhin l l"tlitioll. in
\\i th a n
t' llI ph;l~i s 011
of nu-dn-im-s. SIl('h !W n;O Il S illdlldl' ph annac1sts. physicians. vete rinari ans. pharmaccuuca l scn-nt tsts. Im:ieo lo)..,'i sls, al1 al~1 i{Mu1chemists, luoc hennsts. and d ink'al chen us ts. It is a n in-
troduct ory text ami tln-n -fon - pn 'slllllt'S that tilt' n-ader Im." littll' or no t':qx' n t'IIl'(' O f k nowl( '(I~t· i ll lilt , an-a. Previous ('xposnn' 10 certain aspects of physioloK\' and pharmacclogy wo uld ht' 11I·lp(1I1, hilt it is 1101 ('Sst·utia!. SOIllt' kllowlt'( I~(· of calculus is also dt 'Sirab!e . Our intent h to ln-lp tilt' n-ader lenrn to apply plranuacokincncs in therape-utics . To this r-nd. W I ' I'lIlplJit\il l' {,(lIll,('pts t l ln )ll~h problem solving \\i th only til(' essence of requtr ed marlu-nuutcs . In tllis respect. til(' hook is a p ro~r.lI n m {'(II t'am inv; text. AI the bt";ll11i n ~ o f I';u: h d lapll'r, ohjt'(:liH's art' !-pH'n 10 itll'lltif)" lilt' s aln-nt poin ts 10 be learned . T o furt her aid in !e;ln-illl-: tln- man-rial. examples art' \\urkt'(! oul in del ail in tilt' text , At tilt' {'ud o f t·ad. chapter, t'Wl'pt tilt' first. then- an' problems thilt allo..... I!l1' reader to v;r...' p tilt' (,(JJl{" pts o f tilt' chapn-r ,Illd In lnukl 1)1\ man-rial ¢ H'n ill previ ous chapn-rs. nit' u n !t' r of tht, probk-ms in I'a('h cliapter n ·III'(1s cousuh-ratiou of both t1HIi(1111)' and how WI·I\ tlu- problems apply tn chapter principles . TIlt' questions sta rt wi th theless difli tult O Il('S and those thai t·. llplmsi...x- tlu- principh-s.
ORGANIZATION AND CONIINT As in tilt' s('('(md t'(lilioll , 11\1' I)( M)k is t!id t!('(1into fiv(' St,'<.1inllS: AbsUlVlion and Disl'll,).'i itinl\ Kim'lil'S. T ll{'raj'll,'lItil' Hl'¢Illt'nS, I'hysinlo¢ c COII('('pls and Knwttcs . Indhi tluali...at iou. ami SI'!l'(1t, ! Tnpil'S. T lmst' \\i sllinl-: to ~
CHANGES IN TNIRD EDITION T Il(' fl.y('a r ~a p hdw t"('11 tllis thinl ("(filion and tllP st,(,(lIld . puhlish,"(1 ill 19MJ. is shurt t'r tlla" tll(· 9 YI'af1i hd \\l ,,('U til(' st'(u nd alltl firo;l 1, litiol\s. nlis shUl1t·nillJ: o f tilt' Iilllt· spa n
Pl!EfACE
IM'tWl'i 'lI ,·d ilium rd ll'd s tln- l'\ l' r-J,:atl... rill ~ P,I( ~ ' of p" ~n'Ss alld a pplil'atioll of ehnical plla rllla(~lki ll d ics . D,"pill ' IlIi, J,:m\\11i. which Ila,\ n'( lllin "(l Ihe inclusion o f 1I111ch new ruatr-rial. ( '\('1"\' dfort Il,L' IM"( 'II matl(' lu (~lIIlaill tln- over all Si"A' of Ih.. book. This. in 11101, lias meant Ih,;1 SWill' lIlillt' rial llas lIad III Ix' ('o llde llS("(! or dd t'lt'(l. It IIlLs also n's1l11("( 1 ill a muc-h j,(n'all'r u,,' of "hhn ·"ia!ioll' . (·'I)(... · ial l~ for un its . T Ilt' 11I1I1l1M 'r . topn-, alit! S(" IUI'lll'(' of chapters have h('('11 kept ('Sst'lIl iall)" lilt" ~1 1Il (' ,L~ ill 11.1' \('('(Illd , -c Iiiion , IIIMl " I'r, r-ach chapter has b("('11 ('l\lt'nsi\"d )" n-visc..1 am l up(lalt"(! 10 I'IlSUf(' 111;(1 IIII' I',-,unpl,·\ n-lnn- 10 l1IITt'lIlly prescnlx-d dmg) , A part kul,lr (' Ilu rt h,L'; be-en IIMd,· III ind lill.' vtr-n.. It' I I I· lII i~ I T\. n,( ~~l1 i /il l C: Ihal Isomers ma v Imn ' dillen'nl kinet k-s and a(1i\ily. Tl l('n ' h "I"' l ('t>I I ~id('r,~!ioll o r til(" iJl(:n',l~ill~ Il llmh(·~ of IXllyp','pti d, ' am! protein dmj.(s ,·IlII·fJ..,'iIIl! [nun advances ill mol ecular hioJ, ~ and hiol ('('hlloll 'K\-" ' AItI Il)U~h the kiIwl k· (lllll",'ph an' lilt' sallw. 1111' phy, i ll lu'~i ~' halllllilll..:: of macmmoll'(11 lar comp ounds is ' lui'" dislilld from that of I ~pi('al slIIall lllol''(' lIlar \\t·it.:lll dm ~s . TIlt' pn-wutation of lilt' 1M10k h'LSa["'1IM'''II ruar]« .. I1 ~ illlprowd through Ih(' Ust· of (:olo r. TI ll' mort- nuportuut ("Illalions art- IIOW lIil..:lllighl1'd bv means of color. C hapter number ;111.1 ~'('1i' 1I 1 Ilt';\llillg IIlIWalllM 'a r al 1111 ' It Ip 'If ( '01(·11 p'I,l. ::" b~ nu! to assist ill (' mss- rt' fl· n' lIci ll ~ . .-\ lahll' of fn 'lllwnll.\ tN·d '~'llI buls hlL.. IIt·('1l pb( ~ "(II It 'I;lTt . Chapter 1 10 fad lil;lle n"tldillin ~ w mlltlk wln-n IH "~ 'S"IT\ ' . T he ralll.:1' alit! uumla -r of p robk-m-, al Ihe e ud of ('adl chapter and Appendix I (total o f ";7 III'W pruh[('Ill';) Ilan ' 1"'1'11 , " h, tallli,illy extem h-dto itssisl in 1('itm illlJ: p ruh l('m SU "; I1~ ill l)haTlna,~,ki lll 'l i('s , 'I(lsi Ill' lilt, addilillllal problem s an' taken Irmn hterutun-, rather than Sillllltt"'i!. Ib t" , T ilt, thtrd , -c [itiou (1J1llaill\ 102 IWW fig ures anti 20m'w tables, n:'l1('(1 in~, in large P;lrt . Ill,' atklllt'(', ilIad" ill n"t'('111 ~" ;I rs ill 11liT ~'ll lwll'(I~(· o f 111(' pharmacoknu-ttcs uf dn l~s . Tlnmun-rtal 0 11 "S mall \ 'UlllllW u f Di ~ 1 rihlltiull " thut compns,-d tilt' ttsl chapter of tilt' second ,..[itlon II '~~ 11t"('1I illlUTJMlTakti intn C l.aplt'r W . D istrihulioTl , atul :\ppc.·lIdh I-F. \\'1' (~llIlilllll ' 10 adopl a umfonu st'l of svmbols 11m! 10 II...• lIlilli.t.:r.ulIsIliIN (mwLl ,lS tlu vtaudard 1H,'aSl lW of couceutranon. \\'e do rt"l.1lj..'fli7'(·. however. tht· illl'n·,t\i llJl; trend towun ] tilt' atin plillil of 1lI0lM Illlil\ lind haw' pn l\itl'''tl a fad or for conversion ht'!"Wi'('1I tht· two lIllils of nu-acun-uu-nt ill til(' ('ll,'rt iIlPIlI fiWm· captious. \\'t' shall un l~' il(' convtnced of IIII' virt m- of ,,,I,,\y lISi ll~ lilt" molar s~"Sl p lIl of mcasun-ment wln-u dm ~s an' pn-scnlx-d in ~ Ild l Ilnih.
ACKNOWLEDGMENTS \\'1' \,;sh to th ank all tilt· Ulall)" silltipuls lind rea tlt·rs w!lu pn l\itl l"tl inpul thai Ilt'lp' ''lllis sha pt· Ihis Ihinl ("(!ilio n. Their 1·lllhIl Sia.SIIl ami {"m"llll r.t~{"IIWIlI haw ' 11t'('1l lIl,mlillllal st.ltln't· of salisfill1ion . To 111(' 1It'\.\· n·ilde r. Wt· hnpt· that 11... IItMlk \\i ll su('t.'t"("f. 1 in IlI'lpin~ ) U U
San
Fm'irl~('(J .
Calijonl;(/
\l a!t.1,lm H()\,·land l1 Ullll ll'i~ . T oz('r
CONTENTS Definition!> of St:ibols
xi
1. W hy C1inico l P ormocohnerics?
_
1
_
SIOION I. "'SORPTION AND DISPOSITION IINIHCS 2. Basic Ccn stde rcno ns
11
3 . Intravenous Dose
18
4 . Extravascular Dose
34
SlUION II. THIU'IUJI( IIGI.IN5 5 . Therapeutic Response and Toxicily 6 . Constant-Rote Reg imens 7 . M uhiple-Dose Regimens SECTION III.
8. 9. 10 . 11 . 12 .
53 66 83
PHYSIOLOGIC (ON((PTS AND IUUTI(S
I'v'lovement Through MemblOnes Absorption . Distribution Elimina tion Integration With Kinetics
SECTION IY.
10Q 1 19 137 156 184
INDIYIDUALlZATlON
13 . Variab ility 14 . Genetics 15 . AgeandWeighr 16 . Disease 17 . Interacting Drugs 18 . Concennctio n Monito,ing
203 220 230 248 267 290
.
SECTION Y. SEU CTE D TOPICS 19 . 20 . 2 1. 22 . 23 . 24 .
Distribution Kinetics Pharmaco logic Response MetabOlite Kinetics Dose and Time Dependencies TUfnovel Concep's .. , , Dialysis
.
SEUCTED lEADING APPIHDIX I. ADDITIONAL CONUPTS AND DUIYATIONS A . Assessment 01AUe B. Esnmct.on 01Eliminalion Hall·life flam Urine Dote
..
313 340 367 394 424
,44 3 463 469 .47 3
•
CCNTENf5
C . EstimaTion 01 Absorplion Kinetics F,om Plm mo Concentration DolO " .. ,."
478
D. f'.h:Jon Residence Time E. Amount of Drug in Body on Accumula tion
4 85
10 Plateau F. Oislribulion of Drugs Extensively Bound to Plasma Proteins "'
G B!cxxi 1o Plmmo C o oc eollO tjon Rolin H Esllmorion 01C,eohnine Clearance Under Nonsleody-Stote Conditions "rINDII II. IlIIlI.L X
uswn s [0 PlOIUMS
4 90 ,4 Q4
50 2 ..... 504
SOl - "110
586
DEFINITIONS OF SYMBOlS * Amoullt of dnl~ in hody. 1lI~ o r
A...
Amount of dnl ~ ill Ixxl)' at steady state.' during con stant -rate mt rave1I01lS in fusion , mg o r IJIllO]t' ,
A......
A\'erdge amount of dnlg in Ixxl)" during a dosing Interva l at ste ad}' state. mg or umole.
umolo. Atl
Alliount of t1nl~ at ubsorpnou n' m ai lli n~ tu he.' absorbed, 1ll~ o r "UIIO]t' .
sit(·
C UlIlulathl' amount of dnl~ I' Xe.'rd("(,1 U1l('h atl ~('t 1 in th(' urine, Ill~ Of j.tlllo le.
A d (", ) Amount of lllt'ta!xl iite
ellmtnan-d.
umole.
1lI~ or
CUlIllilati\'{' amount of dOl!,!: ex{·rt'h,,( ! ll n{' h;U1~(,,( !
in rlu- urme
A..,......: Mali:imu m and minimum amounts of dnlg in Ixx!y during a dosing Inte rval at sll'lld)" state on administering a fiu'tl dUM" at a fixl-c.1 dosing Interval, m~ o r
A..... ...
IJIIlO!t· ,
A....
dllrin~ a dusill ~ interva l at sh ';ldy
stun-,
111 ~ Of
umok-.
C umulative amount of d m~ ex(: rl"lt-c. I II Ile.·h;U1~t'tl in tilt' urille to lilllt' infinity aftN a ~i ll~!e duse ,
dust, at a fi\I-c.1 t1os in ~ Interval, Ill g O f umole.
AVC
Aft"a under the plasma drug con centration-nm e curve . Total un-a fmm tinll' () to infinity is implied unless the local ('(mt('lt indicates a specific time Interval. e .g,. dosing Interval, mg-hr/l , Of 1J~I . h r.
AVC"
To tal area under the blood dnlg concentrutio n timt· curve , mg-hr! L or p ~ l . hr .
mg or j.tmolt,. A (", )
Amount of md"hulilt ' in Ixx!y. 1Il ~ Of j.tll1ule.'. • TI\(' min imu m umouut o f dm ~ in Ixltly required to obtain " pn-detennim-dh-vcl o f n'spoII ~' , m ~ o r "U Il O!t ' .
A y ...... : ~l ll\i ll1 11 m am i nununum A,\',.."" amou nts of d m ~ in I)(ltly afh' r th e Xtil duSt, of fi.'H't! sin' ,wd ¢\"1'1I at a Iixed dosill~ interval , 1l1 ~ or
A UC(m )An 'illlm l('r tlw plasma rm-tabo-
lite co ncen tra tmn time curve. mg-h r/L or IJl\I ·hr .
AVC..
umoh-. "\\'.,
Amount o f dnl~ in I)(xly at tilllt' t aftN till· Xtli " O\t', 1Il~ Of umole. Amount of t1m ~ (t'maining to he t'xI'n'It-c.! ill umn- arkr a smglc dose-, mg or umole.
· C."..I ""iI' " n ' 10"''' .
Amount of drug in body at lillie t \\ithin a dosing Interval at stt·ady state O il ;u!millish'ring a fin-d
An'a under the plasma drug ( '( )IIcen tranon time cu rve within a dosing interval at steady state,
mg-hr/l . or
IJM -III'.
,\ V.\lC Total an-a under the first momont-time curve . mg-h.-2/L or 1J ~1 -1 1 .-2.
c
Co ncentration of dnl g ill plasma. mwL or j.t ~ 1.
..
.. C (O)
Df fN1X)NS OF
Initial plas ma eoncentratkm,
lISU -
s,r.w!O.S
C_
all)' obtaintod b)' (' d r oiplKdHflll to time 7...-ro. mw'l. or J.l M. C 1:C2 Coefficiellts with units of <:(m('('I1trarjon, m ~'l.nr p M.
lI i~ht', 1 {Im~ ( ' U ll ( 't' u l r.l!illll lll .. ~'nl'tl in plasma follcJ\\ill!{ad-
milli,tralioll of an t'xt m''lL'ol'1lla r
tic .....•• mWl.llr JI\ 1. e l m)..
C Olll't'n l rd lio ll o f a IIIt·l al. llih· al
C.
Ceucentration of t1nl~ in fluitL.. 011 the ;j,~lTptiOIi ,itt·, IIlWi. o r ",\1.
\tt ·;"ly ,t.aft" d urin£: a ('(m..tamrate illt rd'l'IKlU" inf"sinll o f dnl~
C"
C.tllK't·ntrolltnll of dnl ~ in arterial
IIIWI."' J.I\t
C,
('.ou('\'ulmIKlIl of dnl~ in h lood. mWL or J.I \ 1.
CINI
CotK"t"ll lmfinlln( bound d Ol I-:: ill
blood , IIlgfL or J.I \1.
C_ ..
plas ma, IllWI..o r ~~1. C 'J
D nl g l'lIIK"t'n lratinn in c li a l)~I I (' mWl. o r J.i ~ 1.
Ic'a\i n~ d iOllp N .
(;1
CtJlK't'nl rllfiun nf inhibit or of II1t'ta bohsm. 1Il1i!. or ~ \ 1.
CI.
Tot.al clearance of J mg fmm plasma, l A ir.
CI.."
Toeal dt"ar.lIK't' o f Jmg fn)lll hlt:n.1. l A ir .
Cl ..",)
~'5is clt-anuK."'(" ba.~ 'tl Oil dmg l't"K'(·ntr.ttioo in hluu{!. LAir.
CL" II
Hepatic d(~.u-dIKT of dnag from hlnnc.L l A ir.
CI.~
Ht"taI d('llrdlK"t" o f N\·dlillillt-. Illl/min eN" l A ir.
c t.;
Dial)'5is dt'drdlK't' ba.'\t'll 011 dmg couceutrateon in pla.SIlla.. l A ir.
C/,
Clearance a\sudaftoe,l wit h Forma lion of a mt1a!J,olitto fmm a dmg.
l zhr.
c t.;
Hepatic dt'a mnn ' nf d n lg from plasm a. l A ir.
CL""
l nt riuslc ck-aranee of dm~ ill or~an of t'l im inalioll . l A Ir.
"ity o f n~llClIIs(·. mWi . o r J.I \ I. C ,\ _ .: \I.ui lllll lll anduuniunuu ulII<.'(' n C\' ~" tnutons of d rug in plasma afll' r Iht , X III doS{' n n ;td r n i llh ll' ri n~ a fi.\t'tl d o S{' al cquul dos i ll ~ inh'r· vak IIIWL or J.i \ I.
c.;
CUlll't ·ul r.lliun of t1m~ ill Ill'rill.. lll'lll l'a\i f)·, IIIWL nr J.i \ I.
C.
CmK't 'lIlmtiull o f dm~ ill plil-\IU;. al ,11';11.1)" stOlf(' during a n msla nlran- inlr.l\1:"IlCItIS infusion, mWJ. ur J.i \ 1.
C.. _
,\\l' r~{' tln lg conc eutra bcu in
pld.\lIl4/, clu ring a dosill~ i'JlN\~J al stt-....I)· slalt· 011 d(l lII i n isll' ri ll~" fi\t"d diN' a t t'{!ttal dosi ng tnn-rvals, mWJ-,. or I-I \ t.
C..._.: ~ l a'{i lll lll n and nuninuun t'(lIl(,'I1C.. _ Irdfiems of dmg ill pl.tSIIl;& af Slt';lcl)" slaft' em adminis!t'ring;& fi'{{oe,l dust' .II equ a l clus ing int e-rvals, m!ifL o r J.i \1.
C,
J) n l~ ("IJ11c't'lIlmfifn) IIl1hollllcl ill lol al hoc.I)· wate-r. mWI-- or pM.
lAir.
C.",....-
Peritoneal dialysis dC'ardlK"t'
C".......
~1 a.,i Ill U Ill a nd m inimum limits for p la.'lIIa dnl~ ("Ilnn ·n lrdfMms. 1llWI-- or J.I ~ I .
C"
Unbound dm~ (·ollll.'llfr.t tio n ill plasm a, mWJ.. or )1 ~ 1.
C k".u-d1H.,· of unbound drug. l A Ir.
CII,
Unb ound plasma (.'t)lK't'lll mlioll of illilihilllf, mWJ. or 1-1 \ 1.
CAIIK."t'nfrdholl o f ffi(1ahofil t' ill pLaSIila. '"WI. o r 1-1\1.
C,_
C.tIlK"I-utr.lIMlIl of dna,:: ill hlcMII1lIIWl. o r J.i 'l .
plasma. l A ir.
C(m)
courx-utrutjon of d nl ~ ill
JA M.
based o n dOlJl: ("II1K't'llfrdtlon in CI." CI..fl
,\ \'{ ' m~t-
111li,Ls uutshh- plasma, IIlWL o r
Cl'"
CUm ) Tot al d (';\mn("l.' of a rm-t abolitc. CI· ,.u
\ l illi u llI lI l ('1ltK't'nt r.tlin n n"Cluin'tl 10 ohtain a pn'tIt.It'nuint"l! tnten-
Renal clt".uaIK"t' of tlmg.
tAn .
\"(' llt MIS
.~
DEfWlONS Of SV.YaQlS
IJ,.
Luadi ll ~
IJ"
\ laintl'llalln ' dn"", of a f!Wtl.tlOSl' n-WlIll'll. 1Il~ o r ~ullolt"
U
v
__
dose. m~ or ~.IInClI(' .
\ t u i lllll lll mai nft-ll<.IIK,(· du!>(' 10 r-u..un- th .d tiM.' plasma dm~ con('OI'ntrat ~ >II " 'III;UII~ \..ill.in C..,.,,and C.lo ....... Ii mils tillrin ~ a (k)O; i ll~ Interval at st eatl~' ..tat e. 1Il~ or
t".
Ralio of unbound co ncent ranon in pla.\ lUiI and lotal dru~ (,(JlK,'ntranou in blood. un uni ts .
ft·,
Ralio of unbound and total sih 'S a..'iLil.r.bk fo r bint lill~ nn a pla.\IlU pron-iu, 110 units.
J"ff
Ratio of unhound and a\'('r.t~(' tl.. tal dm~ rono-ntrations in intrat, 'lIl1lar "uids , no units.
f liT
Ratio of IIllhoulltl and to tal dm ~ conccntranons in tissues (o ub idt' plasma). 110 uni ts .
y
Shapl' fact or in conce nt rat ionrt'Srx)IJ ~' n-lanonship. 110 unit s.
GfJl
Glllllwmlar fi ltration rate. 111 11 mill or l;1l1'.
k
Eliminati lln rat e constan t, hr - I.
~Illlllt"
F.
E,tr:.K1illll ratio.
IX :',II
{;onn'ulratioll ~i\i ll~ one-half tiM.' ma"iIl1ll1llI'lT('1. IIlWl. " I' ~ \ I ,
E"
IIt'pal ko l' \ l md iull rutio , TlU units.
f:,.....
\ I,l\ illllllll ('lTl'1 , uutts of re -
1111 units .
SI XlII M' uu-asureuu-ut .
P
H illa\~li bhi li ty fir d m ~. uo units.
h..1
Ratio nr I XIIIIIII til Ini al d m~ conl'Ol'lItmtilllls ill pl.eeu a. nil units .
t"
Di al"''iis cl..aram'e- as a rrd(1io n or tUlal' cleamno- dllrill~ a (Ii al~"is In'a lll MOlIl, no units.
/;
•
ka
Ahso rption rat e co nstant. hr - I. Ehnunatjon r.lIt' constan t whilt' a P"'tiMlt is undergoing tlialrsi' In-aIIlM.'nt.1Ir - I,
fi·
F ract ion of t1nl~ "'~.... te-uuc-ally ...."".liLahlt' 11Iat i", l'uTt'!l,lunt·han!:t'll in urine. lin uuits.
k"
FEV,
Forced (·xp i rdt () ~· \UllInK' in I second. I ~
k.
Frecnou or tlnl~ t'likrill~ tht' live-rtha i Ml'ilp' -s l'limi rlalioll 0 11 singlt' I'la.Ssa~l' t llnlll~h th ai o r-
kJ
"'"
~all ,
110 units.
Jm
F"rad:iull lOr IlnJ!!: sph" Illit-; J I~' ;l\'ailah lt' tha i h t'(lI\\'('r11' ! to a IIl1'l:llx,lilt'. 110 uni ts.
f ill
Fract ion or ..d min i..lt' r,,1do!>(' or dnl ~ that l'nh'f'!i ti ll' J.:t' llt' mlcirl111..-liou us a nu-tabolin-, no un its .
F
•
,
ft·
I"'
Ratio or un!'numlilut! hltal dm R ('OI K'('llt mt ioll~ in pla...ma Ulld("f' t'Uullililll\s or a1tt'n,1 bintlinR- no units.
Hatt' constant ilS-\lldatl'll wit h l1.t ' formatio n of a metabolite, 111' - 1.
/;
Inhihitio n t"fluilibrimn constan t, mWL or ~ ~1.
k (m )
Ralt' constant for th e d ilUina! ioll or a lIll'taholitl' , hr - I.
Am
M k hiU'IiS·\h ·uh 'u coust aut, mWI. o r ~\ I ,
I'm '
\ l ichal.'lis·\le ule n constant. t'Xpres sed in te rms or lot al plasma concentranon. mgIL or p \ l .
Fraction of filn-n-d and !>('(:rt'It't!
Rat io (If unl .Jl.lIltl and toral dm ~ ('OI.IK,'n t r,dion~ in plasma. no umrs .
U rillal)' escn-non rail." constant.
11f - I ,
drug reabsorbe d ill tilt" renal tu bu lc, no units.
AS\lx1ali oll co nstant for tilt' biml · i n~ of dr ug 10 prot ei n. 11 1J1olt' ,
Kp
EqUilibrium dist ribu lion rdtio or
dmg ht1\l.'t ... n tissue and hlc...1 or plasma. no umts.
k, k. )...; )-t
Fr.K1tonal rate at which dm 2
ko""'S tis~ut' , hr - I. Frat.1tomll tUITMI\"t' r r.tle , h I'- ', F.\plnt' lltial coefficit'nls, ltr - I.
OE fNllCl!"iS a S¥MaOlS
. Iv
'"
Slope of Iht' center of It... inten..i~· of n.~polIst· \"t' nus t.. ~ con('t·n l r.d ioll ('1II'H ', units of re-
'."
DumtMlII of a constant-ran- infu sio n, hr .
Tm
~ 1 a.U Ill II Ill rolle of tlm ~ t rolll~pllrt (w't.Tt1 km) into Wllm tnlmM', mwllr ,
'''' "I '
H alf-lift'. hr.
.. 1'11111 ... -.
.\lRT
\ 1t~.I11 tin"" a 1IIC.lI'..,IIt· n -skk-s ill lJ( Jl.~·.
..
1.1. :\ unilk" .. nu mbe-r.
v
:-':1111I1)1;'" o f ( 1tN-~ . no unus.
f
I'I'nnt'abili~' {'tIll·ffi dt·llt . rm/mln 0 1'
V {>"
V/ V..
ws n-m . ml Jmill (II' IAlT. Hall ' of filtm lt·lI11w fmlll ulu-ru ofiltr.tliull S}' h 'm, m l/mi n Ill' l zhr. J le-patu- blond 1l11\\' (port al vetn plus IU'p alk ark !')') , I/ m in or
lA,r.
e
Hiltin of conc eutra nou ill blnnd (, '11 10 thdt IIllhutllltl in plasma.
"-
.\ ("(.'11111111a lio l\ r,olfiu (imlt·'d . 110 uui t...
&I
Ratio o f u nhuulJ(l c k-aran o- of an
Individual patk'Il1 In that or a
~p-
•
I'
•
I'
\'"
",
1("
Itt- nat fUl K.1KIII in .III indi\iftual p;.d it·nl a.~ a fr.K1iun u f n-ual flllK.1iou in a t~'Pkal l);dit·nl. no units. It l le uf l'tlll~tani intr.l\l.'nul!S infll ~ioll , 1IlW'1r.
II,
Tu rm wer rate. 1ll~/1.r.
-'
Salt form factor.
lUI
units.
S/\
Surfaet· urea. m Z,
t
I)o sinv; lnte-rvnl. hr .
'-,
~ 1 ;l'lii Ill U Ill d ns iuv; inh'1"\1ll ln n-lII11i n " i th in (."." .... " Iltl (.'"....... limits , hr.
'_. 'J
Tillie "I which lht' h i ~ht'l>t dnlV; (11IK't·ntr.d ion occurs follu"ill~ al lmini"il r..lioll o f an extravascular cl.l'\ot' , min IIr hr. Duration of ('fTt't.1. hr.
\"ululllt' of (listrilK ltMIIl (a pp a n 'n t) based on ( l rtl~ (1l1l(1'ntm fio n ill
blood . L BlocMI volume, L, " ollllllt' (If d iah'!lall' solutio n (111· It'(1t...1 duri ng ~ helllo(lialp i.s tre-atme-nt , l ; \"Ullllllt'
o f in itial d ilution
( 'lJIIl -
partme-nt. L
\ '".
~1 d.U lll llln rate of IUt' taholi..m I,:,' all r-nzvmati call.., mediated n''''''' lion, 1I~~/hr u r ~mok~lr.
\ '( m )
\"olllnl(' of di strihlliion (ap pan'lI t) o f a Illt1 aholite 00.'\(...1011 ih pb.-una (' "K't' ufrdlkm , r,
KW M panem. IlU units . 1ft'
of ( Ii~t ri htlhon (al'lp .. n 'nl ) tlm l?; (llIK'l"ntrollitlll ill ptl~III'l. L
\"0111111('
ha.' l'll Ull
(:lI VI. r,
Blood flow, 1) lII ill CIT 1.1111'. I>i 'lly~.ah· How in Ilt·lIIullilIJ~ ...is
Turno..er time, hr.
I 'r
PIa.~lIla
\ 're
\"OIIlIlW of dial)"Satt'"ithin lilt' pC'rilulJ(·ll! cavi ty, L.
I'
•
"r
volume-, I ~
Ali"t·tlIlS " U llllll(' of illll'al,'l1nlar fluids. I ~ Pt.)'Sioll~c ..." lu ln(' Clllhic lt·
plll-'mla in ln whi(·h dm~ dtstnbli lt'S.
I ..
of di strihu tiou (appa n ,n l ) uml t'r sn-edv -sta te C't)fuliliom 1~l-'l... 1 o n ll~l~ (.'lJlK't'nlrut!on in p!;lSmOl, 1..
"•
\'I IIIIUl('
\ ' rw
."-q ut·o tls volume oulsklt· pla...ma tuto which dru ~ distrihules , I ~
\
'"
\'olulllt' o f dlSlrihulioll (aPlldn -n u
1Ja.'oC'l1 011 unbound tlnl~ C't.lIK't'UIm hull in pl,uma. L.
WHY CLINICAL PHARMACOKINETICS? T IlOSt' pat ien ts who sufli-r from chronic ailme nts SIICI. as d iaht'h' s and t"pilers), lIlay han ' to lal.:" drugs ( ' \ 1'1)' day for the res t of their li\'l'S. Al the other extreme are tho se who laJ,,(· 01 si ll~l l' duS!.' uf a tlnl)!; 10 n ·!it·\ t' a n occasional headache. 11l(' durattcn of drug therapy is Ilsu ally IM·tWI,,('U till'S(' (·xl n ·lIlt -s. 111(' mann e-r in w hid l a dmg is taken is called a d tutl /!.(· "q~j"U'II . Bot h tI\I' duration of dmg therapy and the dosage regimen depend on the t1W T· apt'utit· ohj('(1iVt's, whith lIlay 1M' t'itlll' f ti l l' cure, the mitigation. or the pn...-e nnon of t1iSt·;L~(, . Bt'('illl'>(' all d m~s ('xhihit undt'simble d T('(1 s, such a.s d ro ws iness, dryness o f the mo u th, )!;;Lstruin lt-sti n.J irritation, 1l<1\ISl.'a , and h)l x)k m ioll, succe ssful dmg therapy is "d li,,\","(1by opti mally halandllg til t' dl·~i mhl(· and tht, un des irahle- ("rTed s. To adli("\'(' opttmul tllt"r.lpy, Ilu- appn ~ui at(' "d rug o f chotec" mu st he select ed. This decision implies an accu rate d iag:uo~i ~ of tlu- disease , a knnw!('tlge of Ihe climcal state o r til(> p atient . and a s(lllml U1u le nlandi ng: of Ilw phartuaeotherapeutk- man agement of thl' disease , T hen tilt' questions How much? How ortl' n? and How long? mus t 1)(· answered. n it' qu est ion 1I0w mudl? n '<.1tgniz('s thai tlw ma gn il\l(les or the the rapeu tic and torte rt'spon St'S an' Iunct lons or tll(, doS(' gin'u. TIl(' qll('stioll Hew oft(' n? ~i7.es the importance uf time, in thai tilt' magn itude o r tilt" effect ("\'('lIluall)' declines with tinll' follo""i ng: a single dose o f drug. Till' fillest ifm lI ow long? n't"tlJ?;lli1A'S that a cos t (in term s of side l' rT('<.'ts, tCl\id l)!, ("(111l1ll1lit'S ) is incu rred with con tinuous d rug urhniui stration. In practice . the se quest ions can not 1)(' dt\lIn1't1 Imm otu- auotln-r, fo r exampk-. thl' convenience or g:h i ng a larger dn"l' k-ss fn" I I I wilily lIIay he mon- than ofTSt't hy all increased incidence of toxicity. In th(' P;l\ I, tilt' an swers to lIlany import ant tln-rapeu tlc questions were obtai ned hy trial and error . TIl(' dose , Interval between do ses. and ro ute of ad ministration wen- 5(,ll"<.1('(1. and tl.l' !lalil'llt's pn~rl'S S followed. TIle desin 'll effeceend an)' S i~IS of toxicity we re ca re fully noted. anti if nec essary. lIlt· c1osaJ?;t· rt>¢nw n w asad jush'll empirically un til an acceptah lt, hallUll"t, 1)('I\\1.'(·n ti ll' desired erred and toxici ty ""~.L~ achieved . Eve nt ually, afte r considembl!:' experinu-ntation n il ,I la~e n umbe r of patients, rt'a.~onabl l· dllsagt· rt-giIllI'1JS were l'sta blisllt'll (Tablt· I-I), hut not without some rt-gi UW llS p nxi lld ll~ excessive toxidt)' or p n J\ing ine rTl'('1 in'. \lon 'lJ\'t 'r, the alxJ\"(' em pmcal app n "ad l left lIlany ques tions ummswr-n-d. \ \1 1)' , for exam ple, doe s tet racyclin e have to be g tcc n l"\"(" )' 6 to H hou rs to I)(! t,rTt'<.1i\"f.', whill' diJ?;o\ in can he Wn' lI on ce dail)'? \\11Y IIIIISt ox)'teK;n Ix· Infused tn trave nously? \ \ 11)' is mo rphine mo re I'fTedive given int ramuscularly thall wht' n giwn orally? Furthe nn nrl', this ('1I1p irical appnJl\('h contribull's litt le , if all)t hing, towa n l estahlishing a saft" I'rTKi in' tlosagt' n-gitllell of lInolhl't (In lg. TIlal is, our hasit' unde rstand ing of dm~ h,L~ not 1)('('11 illCrl"l<;('t1. Tn 1J\·('ft-'UlIll· SIlIIIt' of ti ll' limitatiolJS o f the e llipirical app m;ldl allli to anSWl'r Slllllt' o f ti ll' fllll'stions miSt'll, it i~ fll"(1'SSllI)' to dl'k t· fnrt llt'r into tht' t"\"t'llls thai rollow d mg: ad ministmtio n. III rifm and i 'l ri t:t) studies show thai the ma~lit utll' of the rt'SpOIls(' is a fundion or the l1ml1-'ntralion o f d m g ill the fluid b
2
o f tlwrdpy . II n\"'{."\'t 'r. na n ·I)" is a d n1lo': plat.'t-d at ib silt' of adjoll. Indee-d, lIl(l\1 d m~.. a n '
goen orally, am.! }'('I
tlM:.,.· ad in
fli t" b rain, on t ill' he-art , at the II t 'U n llllllSl'u !ar jUUdHlII. or
t'!........h e re. .\ d Ol!; m u..t th e n- Iore m O\"t" fro m tilt" ..itt>of ou.llllini"lrJotion 10 the sitt" ofaction. SimultiUK'OIls1y. IK,"'"'\·...r. til t· d m g di"lrilmlt~ III all ndK'r ti....1WS i n<,JlIdi ll ~ ttN....• orga ns, nntab~' tht· lh'N ami lIl(' kidneys. that eliminate it from the IlOl. l~·. F igu fl" 1- 1 iIImt ra te-s III(' cwnts occerrtng "ftt'r a tte~· of d nl~ i!'i ar. lmilli..h- n -d or...Jly.
rate at whk·h dm~ init ially enters the bodv ('u't't'tu its rate of eliminat iun ; tilt' (1)11 ('t'nlroltions o f dru~ ill bit..;! ul hN ttssues ri M:. nftt'll ..uffidt·n tl)"hi~h 10 d icillht' dcsi n-d tht-rolpl·utic t' lTl"(:h and sometimes even to pmtlll(,(' to,ilir,'. Ew:·n tu all)". ellt' rod,' of d mg
n it'
and
r Jjmination cxl'l."l"ll, t1.~. roth' uf its eleorption. and t1lt"rt·... In-r. tilt' ('OTK'I.'ntrJ.ti(m of dnJ~ in " "til blood anti t&SIl~'S (1t'Clint"S a nd th e e fTl"(1(s ) slIlxidl'S. To administe r dm~ optilll;lll)'. therefore, knrM·I,'d!{~· is Ilt"l"!t .. l nnt o nly of t h~' 1ll 1.. .han i...ms o f d n l ~ absorption. distrihu -
non, and elimlnanon hilt a1 ~J of till' kineti cs of thl'\(' pnx"l'S<'('S. th 'll is.IJIum llllCl.lkl,U1iN . lIIall;l~I'lI1 t'llt of 1l
TIll' application o f phann'l("l.kindk principles 10 tl.l· tberupeunc
T_~
Trealmenl 01 lnf.ect>onl.
l)go>:;n
ArneIOOfO!oon 01 ~ cc-dcc fo;~
"'" "'"
0<,00<-
Ir.c:I..oon and
"--'-'
""',..,.. .....
'" """"
~e1oe1
rno.ntenonee
01 _ e po,n
250 "'9 ~ 0-8 lit I 5-2"'9 ,ntt>CJly o- 2.4 Iv. li'>e<~ 0 25-0 5 "'9 once 0 cloy o 2-.4 ..........'Ii/rr"n by
....,.,
InIrQI'nuSCuIa<
10 mg ~ ~
"'"
Nor recom....e..d.,d becocse oIleduc ed ~
tl«. 1-1 . PL..".... " "1l' '11!r·' '1I'' ' .J I hn>rh~ tli,... In il.,, 1'i"1 (.. llo... ·h .lt....
unl ,10...,. of a fil. ).n' lt tnulrullo..I·Il"lo'iI-\l' (un llul..liull. Krfof't" lilt' 1"'..1< i\ " •• -I..-d, tI ... r..I, ' ..f "''''''l>lic''' " l ' ('1 h Iha l of t' h minaliu" . Al 11,t' 1 It. tI tv... r..to"f a " I',..]; II..·..... ..firf'. tI ralr of ..Iimi ljun Mt~b 1...., ,/ .u-...''T''jr", IRr<.I/lrOIm fn .... s..ut..... R.. St";ni)""l. \'w.. Dl1rtti. E .• tMhm . A., ilml S-ch"k II U.: f'nov-n l;d'iono( ,",-,k, in
hi<....lui\...-
rD:T_bn.. lnl I . an. f"hann....1
n..-r. TOlicul.. .)'} s;~. IWl.1
o
12
24 Hours
36
46
3
CHAPTf i I
11lt" events f(l ll(J\\i n~ dnl~ admtutstration can he d i\1d("(1 in lo two pluse-s. a IJlwnlulC(Jki"l'I ic IJlww . in which ti ll' 'KljllSta blt." elements of du'l' . dusagt.' fon n . frt"'llIl'II(.')'. am i mute o f udmuu strunou are rt..lated to d nl g k-vel-Hm e rdaliollships in the hudy. and a 1"l lln lw('Ilfl y" mll k pl lfls(·. ill whidl th(· 1"ll1l('t'l1tmt iun of d nlg at tilt' sih'(S) of at.1iou is n-luted to tln- nmgn il mlt· o f lilt' (·fTt"(1(S) pmd ul"('tl (Fi~. 1- 2). Om"(·IM,,1I of these phases han' ),t't'11 dd il\('(l. a dOS;lgt· Tt-W lllt'll ca n 1)(· t!("!iig1lt't1 to a/: hi(...·e Ihe 1!It'T;lI)('utk ohy't.'t in' . I)('spi h ' tilt" grt'a h' r amount of Infonuanon req uired wi th thls upproech. it has several ad va nlag;I'S o\"('r rlu- empiric..tl app n ",l'i l. Flrs t. aml most ull\ i lJus. dis tlnction l'im ht· III;K!(' II(,t\lol't'lI ph am l'K'tl).;illdic allt l Jlll anllal't )(I~llalllit· causes of all unusual dm ~ Tt'SpOIl'l', Se<.'Olld, Il.lt.. IliL\k- concepts o f phannacokiuerics an' co m mon 10 all dmw;; illfon llalioll ~ai l\('ll uh out the plmrm au )l..i nl'l it.,. of 0I1t' linl g 1..11I ls-lp in ;lIl lici pal i n~ tilt' phann;K'tllciul.tit-s of allot lJ('r. Third. Ilnd('rstalld i n ~ tilt' plum naco k tncncs o f a dru g oftl'n expl ains till' manne r of its list·; ()('(';lsio llally snell all 1II1tlt' rstalid ing has savr-d a d nl g th at otl J('rnist' llIay h'l\1;' 1)( '('11 discank-d or lIas 'ill~t''ih'tl a more app ropriate dusa )!;l' re)!;inw n. Lastly, ).;J1(J\\111F; the pilarmal'tl).;illdil"'i I)f a dmg ititl\ tln- clinician ill anlidpiili llg th e op tima! tk)Sit~c n -W lllt'll for 0111 im ih iti llal pal ient am i in prt't:lil1in ~ what may happen when a tlOS:l)!;l' regimen is changed. ;\ llil\ ic tenet uf clinical plumuucekim-tics is th at the- magn itutk·s of hut h tht' tkosin 'tl rt''i!JlIII'>t' amuunt !()'it t,,( plals tile'
Pharmacokinetics
Pharmacodynamics
,, , ,,
~- - -- ---
Dosage Regimen
Plasma ConeenIralion
,
,,, ,
~ - - - - - - - - - - - -~
Site
at
,1_ _ Action ____ _ _
,,, ,
Effects
:, ,,
\~ - - - - - - - - - - - -~
t 'l " , 1_2 . .\ n ~ I'pr"",,'h In tI... ,I." ;!C" fir ~ .I."'"l(t. rt;(i mrn n it, phartn;K'
r,...
•
CHAYlH I
'i('n-ral IIm e's had to he
~n'll
before
d nl ~
uccunurlatkui
Wit..
sufficient
10
product- u ther-
apt'lIlit' concent ranou. Hill! the rapy 1,( '1.'11 stop pe d hefnre 111l'1l. th e dm ~ lIli ~hl have I)('(,u l holl~hl im,(ft"'l1in' ami perhaps ahandoll('(1 pn.·maturt'ly. Altt·Olillin .·'>', larxN closes lIli~hl ha n ' 11('('11 tried , (' .~. , rq~i llll'1I H. Ah holl ~h a th erapeunc rt'SPOIlM' " 11111d ha ve h"'('11 nlu ally p roduced IIl1ilt't..'t· pl;tble loxidly when a dnsill~ rate sllffid t'nlly h i~h 10 he d Tt't..1in ' at'l ltd y "'~.L~ maintained. Only afn-r its ph;tnll;IC.'t)!cillt'lks had 11t'('1I t1t>fillt'(l W lL" Ihis d nl,g Wit'(l sut't.'t..'ssfllll)"·, Q llin is t'l im inaf('(! slm"'!y am! at't..'lllllllb lt-s t>xh >nsi\,(-ly wnh n-pean-d d;uly ad mi nislration . 111t' allSV"t>r ""l'i 10 ¢ \'t> 1 1I ~t' t111'it ' S l"'l'r lilt" firol fl>w days 10 nt pid ly at"ilit'\'t> therapeutic Sll{.'t..'t,.'SS, foll"wt'(l hy small daily clo se-s 10 muintuiu ti lt' p l,L"llIa coucentratiou wn hiu thr- therapeutjc wi ndow. TI lt' plalt'au situation in Fi ~. 1.....1 shows thai ho lh IIIl' widt h of lilt' Ilw ntllt>Ulk window ami lilt' sp' 't"fl o f dm ~ elim ination gm 't'm IIIl' Si7A- of lilt" Illainl t"nann>do~ ' an d 1111' Fn-, qm>IIl'" o f administration. \ \1 lt"1I the \\; fI{!ow is uarm w and the d m ,g is diminatt"tl mpidl)·> small doses mu st 1)(> ,gh l.'!l ofkn 10 ." .'hit'n' therapeutic s m't:'t·s~ . Bo th cvclosponnc- and d i ~o'(ill lIa\'(' a narrow therapeutic \\; m lo\\', hUI hl 't:';IIISf,' t')'{:II)SIX)rillt>is e1iminatt"f!Ill11t·1I num- m pidly than d i ~()\i n . il hils to 1)(' ,gi\1.>11 mon- Frequently. O \)1odn is an ext reme exaruplc: it also h a.s a !l am JW therupe-utic winduw hil i is t,lim inalt'(l wit hin minutes . TIl(' 1I11 1~' nwans o f m!("fillatt'l)" l> llS ll ri n~ a Ilw mlx 'utic concentra tion of oX)1ocin Ihe rt'fort' is 10 illfu ~> it al a p rt'(; ~> am i cousta ut rate d in't(1 1)" into lilt' blood . 111is dt"gTt-'t· of t't llllmi is nol IXJSsih lt>\\; 111 utllt'r Illud!"s of ad mlnis tmtton. Bt·sid t>s. had oX)1odn 11t'i:'n ~\1.>11 o r ally, Ih is I x ,l~lx-p titlt> hc rmom- \\1Juld 1.01\1,' IX'i:>n dt'sl rt'~1,'(1 by tln- p mlt,(,1)"1ic (>UZ)ll1t·S in ti lt" gil'"~ tminn-stinalfhuds . ~t Olllh i ll e , ~Wll orally. is also t1t·s ln ~·t'i:l substantia lly before (>n lt-ring th e gt'lle ral circulation, hu t fo r a reuson r.;landilig pbannacoktue-ucs and coucent ranon- re"I)tlllst>n 'latin nships hilS led in n -cent )"t'il ro 10 the exit-m in> app liC'"dtioll nf sucll in fnnnal io n by tilt' ph arm m.'l>ut ieal ind us try 10 d m g dl'si~ l , Sf,>lt't.1illll, mltl d l'\"t'lopnwlll. Fo r t·xalTlple , a IXIlt-nl t"flm lxl\Il\(l fOIlIlt! to l)t> pno rly alit ! un n >liahly ahso rh('(1 and iu lem lt'1l for oml ad m inislr.\tioll llIay lit' sl1('I\1,'11 ill fa\1,lr o f a sss polt >ut hnl mort' (>xtl'll sh1.' I~· an d rdiahly ahso rl)('(1 t'tllllf'l"lllIld. Also , IImllY of tilt" hll"je p n ll1.>Sst'S l'tilltmllin,g IxlllI phannat"flkind it's alltl n,>sIXJIlst> art· sim ilar at'm ss mam malian slx't.i('S sllcll lhal dala eml II(>..>xInll x llated from animals to p n '(liI1 1Iu:lnl ilalh l.,ly tlte likely he h;t\; or in human s, T his lilian·
" ';!it. 1-3.
\ \1..." • •Im )/. i .
~ ...n
in
• 6"'11.10...· .,..1 at Fi",. 1ti nK' inlo'r, ..... 1. (.I.·,.. ot,,,1 l~' II..· .1Tl",,,l. il . .. (~lIl1l1lah ..
"ilhin 110., 1...ly "ntil
Therapeutic Failure
Regimen 8
;t
i. n ·'...~ .... I, Will, n 'Kin..·" A. 11"" "P""Ii<' " KU .... i, . -hit'\,,1 ;U,
pt 'I" " "
' 1....,)1.1, ,..ot inili.J ly. Wil h ..,;""'" H.
II..· lI"' r"I','uli<: "1>;....1;\1' i, ...-I,i,"\.,,1
''''In'
II..• pI..., ,,,,, ,In, l': " .....·" I... titll' i, t1h i n"'I" ~· " •• Itij.:h.
Therapeutic Failure Time
•
CHAPTH 1
titatiw fnllllt"'\~lrk improves rhe chance-s o f sdt't.1i n~ not only tht" most p mmi sin~ (,( 1 1ll 1)( ltl ll{ l~ h ut also tilt" corn-et nmgt· of safe doS('s to first tes t in hu man s. lncorpo ranon
clement wi th the-se t·arly Phase I stud ies, usually in he-althy su bjects, \\i th assessment of any sidt· effec t s produced. helps to define candidate d(Jsa~t· forms and rt'~i ll l('IIS for evalua ttou in Phase II studies conducted in a smal l 1I1111l!Jt'r of patie-nt s. Th e M' ph,l\(' II stud ies aft> aimed at de fining the most likely safe and e ffic-dliolls d()54I~t' rt'WnwllS for use in the subseq uent larger Phase III clinical trials, o lten i ll\ul vi ll~ ll1a n~' t1lollsalld s of patit·nts. Ultimately. some com pou nd s pmvt' to ht· of sul1k i t"llt 1)('llt'fit and safeI)-' to ht· approve-d for a particular clinical iudication hy dmg rt'gu latUfYaut hori ties. Evt-n then tilt' d m~ n ndt'~ot,S \i rtually continuous postm arkt'li ng surveillance to Iu rtlu-r n -fim- its plmnnat'tltlwnlflt·util' profile. This S('tillt' nce of events in d m g dt...-elopmen t and evu huuion is dt pil1t-d sdlt·matim lly in Fig . 1....1. FiK\lrt· 1-5 Illustrates an impo rtant problem idelltifit>
of a
phan ll a('t Jkin('ti(~
h~t'tll(' r
o
PRECLINICAL TESTING
G=v In vitro PKlPD Animal PKlPD
<::::;:7
CLI NICAL (HUMAN) TEST ING Dose (Cone) Response Trials
c;;::::J fi ~
PK-gui• •• Dose escalation
Efficacy
Safety ~ Dosage Assessment Selection
Toxicity
Population PKlPD Characteristicsin Large EfficacyTrials PKlPD in Special Populations
= =
PostMarketing Surveillance
Patient Variables
IAnimalTeSting) PhaseI
"lit. 1- " TIlt' d' '''''~ '1l11 '''llt and ",I lll.'Il1 lIlark.1illll: uf II ,Iruli:. TIll' pn ·lml1lall .lata l...Jp:.lo it"'lI lifnm"ni~! nl:, '''''''I''MIIKL, and h. '''~.'''t "'.,fu l.Ic (; If I"'hlll:, in huma ns. Pha..'S I. II. alld III or human a,""Ssnlt'ut 1:.t'1lt" r...r~· n ,m "p'nK I I" II..· 6"" ",I",iui, tr>lli.lt' I" I,,",, ;tu ri>. ... ...Juah" u I" .. 4.'11.'(1 ;1.11<1 II..• 1a1'):t4" In..ls. """I" '(1i",I~'. I'I"' nm.....l
pot'''''''',
~
25
~
20
~
15
D
"'111:, l ....s. TI,... Iai ~' .Ie...•..f ",oufan n n'(l"in'(l l" p".I".....· , imilar pn>lh rornhin Iim.'S in 2lXl ••dnll p;llUf ,ln' lI: .Ic""lll-'t·. Enr. J. elin, pham...· ....1. 9:1-'l . Il:l7S.1
o '0 10
5
o
N OJ OJ OJ OJ OJ OJ OJ Ol Ol Ol
V ~ ~ ! 1 I ~IJ:~~ Daily Dose (mg)
•
O WTUI
a~lIlalll wa rfariu Iw('(I('d tn p n l(lm."l· a sim ilar pmtlmnnhin ti mt' (an md..-x (If h1()oc:llua~. uJ.,hilily). SUlln:t'lIo of \"" riability ill d m g n "!'r_n!'iot' indmk' tilt" p"titonfs agt". ,wi~llI . t!t"P'''C' (If ol: N.'\it~' , '>1)(> alKI dt-,:n't· o f M"-'{'ri l)' o f tl.t· c.1ist·a'W ', th"'Il;dit'nl's Rt' Jwtk lIlakt'tlp. ut!K'r ( I OI ~' ("II IK' IITt'n l l " adlllinL\ll -c.l. ;,u K.! ("m; nmmt'ut al Iactors. Tl a- n";lIlt is thai a sta ndanl d dOlI{ lIla~' p rtl\'t" tberape-eric ill 'iOIIW patients. itw ff......1i\l.· ill otlH.·n . do ...agt· n ' ;IlH"1l am i tovic ill ..till or hers The Iwt....1 to adjust the (1oY.~(' «'; IIH'II of a dru~ for an indi\;pJrint>, a n illlllllll1o"iupprt"S.'\il1l1 11...... 1 ill lI~an tran"'planta tion , \\i tb tl. t"\(· t l m~ . a nti with rnan~' oebers. variahi lilY ill phannscoktre-ncs Is a majo r "iOlHU.· of total \1Iri:,hili ly in tl m~ n"'p:lI1'it·. It ... hll'l.·Ullli ll~ iIK"1l·a.\in¢y l'Ofll,nOIl to v;ain a.s 'IIIK'I. infonna tion o n va riability a'\ Ixn..ihlt· t1l1riult dm~ tk"'l.·lopllwnt l~' j:!;atht·rillJt. allJt"it lilllitt'ti. ilKIi\idual pla.'IIJd t·olK"t"lItr.lIion ;IIKI n... p:lII.... •tla ta in a t ug,' (lllJlulal it m of patit 'll t", tlllli lll't Ph;......• I I J d ini<"aJ t ria k At lt ' fIlph ;In' tllt'lI 11I.uk· til at'("tltlllt fo r th is \1lriahilil~.. ill te rms of sud, pa t....n t c hardll.1:t·risl in il.\ aV;t· .IIKI wt'i~l1 t , 11k "\( ' IJ>t.1"ulntilm l')h a n nal '01J1K-ticl pI Jdn nal"tKI).T1Clm k shKlin Iorm a Il;,l\i "i fo r tic.....,.... • n-,.,IIII·U recomna-ndatlons in di nit-a! pr.Ktic:t·, Coatllllillidmtitm of \(·n:·r.t.l dm gs til a pa twnt , pn.",a lt·n t in chuk-al prdll.1:kl.·. can IXJ!i(" p mhlt·llI"i. ,\ It l.t M I~' tht· rt"lip lllst· produced by f"'"d('" h dm~ alrnw rna>' ht · pn'tl it1:aIJlt·. that p",tIlK'(..1 I~' tilt' t'(, mhillatinn mOl>' IK' 1l"">S certai n a nd (It,(,"d.\ionall).· 1IIlpn.'tli ctilhlt·, Ketot"(IIIaJ'.ok· . (IIr t·""mpk·, d t....,)jd of iIllIllUlKlSuptln .......llt ac.1i\it)•• plllh'ntia tt'S tt. e dTt"t1: o f t;'l.,It)'l;lx ,rillt·, I't ~ sihle t'UII'it'S uf thi s lind of e !Tt"t1: art' U14U1)" , III th is in.\laIK' ·. il\ in man y o tllt'f'. ti lt' Inn-n....1:iu n iIlH'!\l."S a dw. Il~(" in phamlat-"t)!.;indit:s. SUlllt' t1 nl ~ stilllulatt" drugon
t;r
:\ h l OW, II........ ~ pL..t , p!-""" ,,( 1 ~t, lIin Irt..10 I" i' ~..... ,""It. II"" .I."U'll: r.l,' , II re- I~ ('(......I.-nhlr >...u.tion In I '''' Iwlth .... ,,;&/, (O" r m~ •• 3.Ir. ",M.1 ( Ro.. t1 n fn,m 1.", ,,1. I ~ : t:lT.",'h o( I'hrt,~t•• n in poo' h ,h WIlt. rt"I.,,,y In ~ , Itl it. .""" "('''1...1;'... 111 1'1..."", I n KI" It",.-..I . :fT 1~"( Dn'lt' I" ft,·L. I ;' >II1 In TI lI" r 11.... ".. C.. nn.. ,IM ""'" E.I,I,..II " , D ,S, I).. . ''1M .. ,,, I II , ~ C. I'rlt:l ",..I. M..... li ILu., 1 ~ ""I. IIl' ",.,j 1l"'ll1~I ,,~r. U173 . I'l" 227-2.1.>1 ,)
n it·
1-6,
'~ .......Ir-.I.... ,
•
50
• • • •••
• •• •• •
•
•
•• • ••• . • ••• :!. • •• ••• .!J•••:
·:-. Iot'." ii .~ ..... ~},.;~
•
••
••
• •
• ·1
··.Ii. .'( ~ o
5 DaI ~
10
Dose (mglkgl
15
7
1Ilt"lal x llizi ll.lt (' II7.)lJlt'S and hasn-u lim /{ loss: o t lw TS
Inhilut I ht"~· {' II7.)"Il1l·S a nti slow ('Iillli·
nation. Still others interfere with drug absorption. SUt'1l iutr-ract ious are grad ed. tht' d lilll ~t' in tht, pbe nnaco ktnencs o f 11 elm !!: va r ies ('on li llllc)IIsly \\ilh llit' ph..ma ccncenrration n f tinilltt' nK1i ng dm~ am i IIc'II('(' wil h tum -, Inde-e-d, ~n'll in slIllk-it'nlly high doe-s. almos t allY dm g cau intr-ruct with anot he r. It h al..... I) 'S it questionof dt"grt'l" Ultllt'rstamling t ilt" lilian· lilali\"{' elernents of interact ions ('I\Sl1n'S tlw more rational use of d m~ lhal may ,wl'< llo 1)(· (.,();'ltlm inish'nr-d. Fij..,1l.l rt· 1-6 illust rates a sil lml ilJll in which lI11m itl l ri ll~ of the dmg concent ration Illay ht' bt'lwfid al. Ch'N the narrow mllV;t' of tilt' daily dUSt, of tlu- autu-plleptlc drug p llt'II)1uill, fi ll' plalt·au ptt.~I1l;l t1m ~ l'C lIll't"lItmlio ll varu-s 1ll00rketlly ""i l hi n Ill(' p atient population , Yd till' tlwrspc unc ""indow of pht'n, 1oin is nar r ow. 7 to 20 IIlW[.; 1N." "I1t1 20 Illgll... tln- fn"' llIt'llt~· and the
,
Section I
ABSORPTION AND DISPOSITION KINETICS
BASIC CONS IDERATIO NS
OBJECTIVES The reooe will be able 10: Define rhe following term~: Phatmocokinelio. inkO'oU5Culor cod
ell,lroYo:Iculor odminiS ll"otion, absofphon.
drsco
sirian, distribJllOO, metabolism. excreeon. fif$l-pOSS effect. enteroheparic cycling. com-
IX"""·'"
2 , Disom the limilolionsro interpretation of phormocolinetic dota imposed by ouoys!ho! fo,1 10 diSlinguish berween cceccords odminislefed le.g. R· and 5-isomet'sl Of between drug and melabolite
3. Show the general contribution 01 moss balance concepts to drug ObSOfpliOn and drug OM melobolite disposition _
Phannacoldnencs hit.' mall)' uS{·flll llpp lk liliu llS that skill from ba., il· L'tJlll't'pts. Tht ·~ · concepts a rc dt...·t>!0IX'l! in this ~'Ct iOllllf the !XX)". 111is cha pt e r sllI:'li fieall)' dt·filws ! ('fIll S and dt' S('rillt·s a basic model for d nl~ ahso rp tiol\ and di sposition .
ANATOMIC AND PHYSIOLOGIC CONSIDERATIONS ~ 1 (';l-s u n' 1I 1('1I 1 of 11 dmg in til(' " ud)' is lilll ih'
Sites of Administralioa Then- an' several sites at wh ich d m gs an' I'(JII1 ll1tmly adminisll'n'tl . The-se- sift's lIlay 1)( , d 'ls, ifit.'tl us t'illlt'r int r ava scu lar or extravascular, t ' lt m n I.Sl1l/u ,. administratiul l n'(t' rs ftl tIlt· place ment of a drtl~ t.lin-c:tly into the hllMJfl, t·itllt'r inl 1a\'I'nlJllsly or inlm-arh'rially, Extmnl.';{'u /a,. IIlIMlps of administration indlltll' 1111' oral. sllhlillWml, buccal. int nuuuv cular, subcutaneous. dermal. pulmonary, ant i n -ct ul mull's. To enn-r Iht' hllMJf!. d m g ad 11
CHAYlH 2
BASIC CONSIOU .6.TIONS
12
m in i"II'n'(! e:dJ'
is adm inislen'(l inl ra\"\.s<:llla rly. Dm ~ llIay also hI' atl llli nish'(('(! r('Kinnall)". c.~ .. into IIIl" p le ural o r peritoneal cavi ties or intu tln- l'f:n·hmspi nill ll uid. Ik ¢ o nal mlmuustration includes iutru-artcrial injection inlo tl.e \'t'ssd l('ad ill~ to a tissur- 10 he treated. l' .~. , mu- l'olll"in i ll ~ a ( 'lUll't' nJUS tu mo r. It is 11 pon-utialnwans of ~ai ll i ll~ a sd l'l."lh "(· tllt'ra pt·ul k· advan tage. 111is ad\'allta~l' . ill comparison \\i 11l ut lll' r routes of ad m inistnllio ll. comes alMlllt by i!wn ';lsing d mg ('ll.pm urt· !oe..:Jly. wlw n ' it is lIl'('(lt'(l. a nd dt'1.·n ·ilsin ~ o r p lll(lnd np; tittle or 110 d MIlp;t· in (-'l)( ls lI n' tllm up;lu lIll til(' n-st of the IMltly. wlll'r(' i t is not wanted.
Disposition O lin ' ubsorbed. a t1m ~ is d ist rihllt t'tl to tb l' various o rgallS of tlu- IKltly, D isl rihlllioll is iullueuc......! hy how w('11 ('at'l. organ is pt' rfllS('t1 \\;111 bloo d. orgall sizt'. hilJ(li ll~ of d n l~ wi thin blood am! in tissue s, ami pl.'rnlt'ahility of liSS1U' 1llt' lllhr.ul('s. T Il(" two prtm-ipal O ~;lIl S of elimiuatiou. tln- livt'r and Il.e kidlleY". a n.' sl.t M11 sc purately in Fi ~. 2- 1, Tlu- k i d n(~ 'S a n.' III(' pri ma ry sih' for excretion of thr- dwmi t'al ly unaltered, O f III l("han ~t " l. d m~. Tlu- lin 'r is the- us ua] orgall for d m~ lIlt'tilIK,!iSIll; l.uWt'\"t 'r. ti lt' kidneys am! other n f~a ns can also play un im portant metabolic 011(" for {..-rt ain dnl j.,"S. nil' IIl('lah. oltn-s ~, Io rnu-d art' elther furt her lIlt'f ahnliZt'{1 or t'x("rt.'lt'{ l ll ndl;Ul~t'{ l . Tilt' lin'f lIlayal."" St't'n'\(' llll{'ha ll,l!;t'{l d nl~ illtn lilt' hi ll' . 111(' h lll ~s an'. or llIay be. au important route for
t·'R, 2-I . (),K" a/ N ,rilt',J fnom .IlIY of 1111' (lI;UI~ )i h'~ "f ...h"i"i,lr"I'''Il. ,Iml.! i. t' '''\1~.'tI I~' hle...I ,,, all ' ilo'" "irl ,i ll
1I,,·I ly i' K'hlllill lt ,I..• ..(i ",ill.,li ll ("f)(..Il• . Sil .""
" f ... [mi"i' I ,,,.., i'Kl " .Ie,: a , ..,1" 1)": h , 1"·" pl..·....I -..ill ' c. 111" ·1..· " ,III '111>..,I" ' II't..I ' II..."" , ,f,l ll "~' "",I ",1:"" lro: """ I "" t! 1.-...1. 11..· .Ltrk_ " ,111 li~I'I .... ,l..,". 1 li'K'"
Heart
II.., ", ,,,, """·,'n,,·,,1 "f ,In'lt in 1"Ie,. " ...I.....1i"·I).·. 11... """" ",,·,,1 "f vrr-
" i l h "m","" n'f"r I "
hle . "I .tI,,1 in
n., ..
I" ... ,,~' .Im( .".." h., f"ll.."" ..1 fru", ~i l,' uf ...l",in i. · Ir.d i" " I" " I,' " f ,·lim i" ,,'" ''''
.c •a
•b
Other Tissues
.. Site of Administration
U •
Kidney
Enterohepatic Cycle Routeof Elimination
Renal Excretion
Gut Wall
Gut Lumen
Fecal Excretion and Decomposition
Metabolism
13
dilllilliltilllt \ulalile substa nces, fo r e xample, ~a.<;{,,(JIIS anesthetics . Another pot ential route of elimination is via a motln-r 's milk. Ahhough an i llsi~ni f1 call l route of elimination ill the mot lu-r. d nl K in till' mi lk ", a~' lit, {"Il1lSU Ill('( ! in suffkit"1l1 tlua ntit}" to alTl"<.1 tilt" slIc kling infant.
CHIMICAl PURITY AND ANAL YTlC SPICIFICITY A gt'lll' ml stah'lI ll'll l 111"('(1... to lit, miltll' about th t" dll'mical pu r itj-of prescnbedmedicnes aud t ill' spt·t:ifki ly of cln-nucal 'lsSilyS. Ove r tilt' years , a major thru st of till' pharmace utical indu stry has been to produce tlll'rapt'llli e agents that art' not on ly as safe and dTt,(:t i\'t· as poss ible hut also an' well e!la rat'leri7.l.'() to ('lISure rcproducibk- qualities. n it' majority o f admtntste red drugs today art' tlwrt·fon· ('sM'llliaJly pun' materials. and coup led wit h specific analytic techniques for their det ermination in bi tJlo~ic fluids. dcfinitjve infomlalio n about their phurmacoktnetics mil 1)(· ~ai llt'tl. II 0wt' \'('r, a la~t' numbe-r of d m~ substa nces art' not si n~le c hemical e ntities bul rather uux tun-s. This particularly ap plies to ste reoi soun-rs am i protein s. TIlt' most com mon stereotsomers found tc~d lwr in medicines are optical isomers, o r compounds for which their struct ures an' mirror images: tilt' drug subs tance is usually a r acemate, a 50 :50 nuxrun- of tll(' H- and S-iSCllllt'T'S, Soim- d mg suhs ta nces contain gpOIl1t'lric Isomers . and still others. especially proll'Ins o f h i ~, molecular weight dl'ri\'t.-d from natural products or Ihmu~h fermentation , lIlay IN.' a mixture of struct urally n-lated . hut d ll' Jllieally disttnct, l'tIIllI'N IUmk Each dWIllil"a]l'ntity wit hin the dnl~ subs tance ean haw a d ifTl'n'nt pharmal'tllowe, toXil'tl]o¢ e, am! pimnnal'tlkilll'lic profile. Somethnes Iht,Sf.' dilTen'll('('s an' small ant! inl-'tmsc·cl" elltial. utlil'r tunes Ihe difTl'n'IIl-,('S l'lUi ht' therapeutically important. Fo r t'xample , dext roamphetamine (S. jso mer) is a pOle nt central nervous stimulant, when-as the R-('nan tiollwr is alm os t d t'\uiclof such activity. Desptte such differences , mall)' commonly ('mplll)'('ti clu-mtca l :L\sayS do 1IC11 d istinguish [x-twee-n stereotsome rs. Oll\iously, und er Illest· cirx-umstauces, alk mpting 10 ' lu,lIltify the various pnx'('SSf.'S anti to n-late plasma coucentrunon to respClIIM' has llIallY p roblems with no simple solutions, Notwit hstandin~ Ihest:' problems. spc.'(.i fk Informat ion about eac h chemical ellt ity should he Sf.)u ~h l whenever possihlt·, h ll·n·'L\i ll ~]Y, sten-oisonu-rs an' hei ng produced as smgle chemical t'nt itil' S, such as S-nslrcJ>·t't l in lhe ga.stroinlestinal tml1 , fm m whil·h t hl~ dt'gnulatinn pn ll!ul1s c'IIIN Iht' hoch' alld an ' ('\'t'nhtallv t'.\cn·!t'tl illllrint'. A b:tsic lesson is leanlt"(l liNe. D islinK\lish l"lll't·full)' ht'I\\'('t,u dnl~ ami IIIt·taholile(s), ~l allY lIIt'laholilt'San' of in!t'n'Sl. l'S{X'(.; a1 ly if tl.ey art' ad!\(' or toxic. Each d\{' mi(-d1 !;'util) ' lIlust lit' ("Cmsitle rt"d Sf.'par,ltt'ly for kine·tic dat a lu he nlt'anin ~flli.
CHAPTE R2
14
DIFINITIDNS " h htlu ~h the- p rnn ·s ~t·s of aleorption ami e-linunation l ift' dt·M·rip ti\'(· and their II1t·allillj.,~ an.' app an'll! at fi.....t !{hUll...-. it is n nly wit hin lilt' context of expc-rtun-n tal o h'I: I"';llio ll tha i
th"y (~UI ht· '1IIillltirit'd (Chaps. 3. 4. a lld 6). G t'llt' ral dcfiuutous of tht' P OIl"-'"St·s follow.
Absorption i I.' III(' pm<:t'SS lIy "bid l Illlt:h;IIll-tI'l! d nl~ pnM.,,'tls fru m stn- of ad lIlin isl m t io n 10 silt ' of IIW;lSlIrt'lllt'nl wi thin till" hutly. To illm l mlt· why llhscllVti ll1l is dt·61\('(1 ill Ihi'. Wot)', 11l1ls itll' r the- ,'wills dt'p itkd in Fi ~. 2-2 ;L" a t1 m~. ~\'t" ll mall)" moves fm m IIn- :0;111- o f ad m in ist rati u n tn 1111" !{t'llt" m l ci rculation. Then- a n" S(-"\'(' m l pnssih lt' s ilt's Ill' los s. {)111' sill ' is l ilt' !{'lst miute-st uml lunu-n whe n - d t'l"lllllpns il io ll lIlay oc cur. SlIp pllst·, however, that a t l m ~ sll "in'~ dt ost n l(:tiun ill IIIl' lunu-n n llly III1M' ('(lIllplt,!t,ly 1I1l't aIM,li:l.t't1by t'liZ)1 I1t'~ :lS it p;lSst'S 11J",u ~h till' me-mb ranes uf l ilt' ~,lstmill!t's l i nlll tract . One \\'lIl1ld as k. h tilt' dm ~ ahsorl wd ? E n ' n I llo ll~h lilt' d m~ k-aves lilt' ~;lst nJi n lt'st i ll al Ira ti , it would lIu t t11'1t'{,It'd in t ilt' gencml circulation. I1t'J1{1.', tln- d rug is nul absorbed sysh 'm im Ily, Taktng Ih is a r~"' I IIlt' nt (lilt' ~ II'P fu rt her. h tlu- d rug ahsnnM't ) if all of the orally atllll inistt,rt't I t1n l ~ wen- til 1l t'j);tm ld y, tln- answer \\lII llt1 IJ(' IM)sil in ' , If, how t'\1.'r, ,lS is ('(IIll IllO II , h lond or plasrna ill all arm vein is lilt' silt" of me-asun-me-u t, tlu-u. IJ(,{",III"l' nu dm g: wfJllltl lM' detec t ed. tlu- a llw, 't'r \\1Iu ll! 1M' III"gillin', IlIdt't't1. 10'S ut allY silt' p rior 10 lilt' sitt' of measurement contri butes to ;1 d l'{"rt',l'il' ill tlu- ~ystt ' lTlk' ahso rp tiou. 11\1' ~;I' lnJ i nlt'sti llal tissllt 's and ti lt' liver. in particula r. a n ' o fIt · II silt 'S o f d im ina lioll. 111t, n ''1ui n 'lllt-nl for a n orally adlllin ist l' rt "<1 d n l ~ In ll;l'S l " nJtl~h Iht,"l' liss\lt,S, p rio r 10 rt'al,:hillg: tbl' silt' o f rm-asun-nu-m . makes Ihe extent o f
AbsOIvt iull is dd il\l'il
"t'
Gut Wall
Portal
Liver
Vein To Site01 Measurement
Metabolism
Metabolism
To Feces HR. 2-2. " tlnJ~ "" " 11 a.. .....I..\, ,'rK~""'''''' ",,,"-r.J h...rri<·n ..", I " I... .. f ...., ill ih "'~ I'H'" li;d " " " 1'T,,,·,,1thlli ul: R.."o-"""..'j" ,01 "1""'1lti..,,. 1"' ." "'1'1.1,' ~ " li.. n. 10M' hll"I I', ·n''' ·''''ihl~·. "",I ""1.. in II..· "' 111" ""'11 " r I,y ""~ ........ ill tI.., ", ll w.. 11 ..,... (.,.,,, f PO'''' ..t......p li" " . H,' ",,,, -..I "f ,1",1:.... it 1"'"' .... 11In..,!:I, II.., 1M "
"j
f"rllo .', n ~ I,,<~, . ..l""'1ltit",
' 'Io...
fi,,'
1>,.".",
"
CHA.PTER2
ahsorption dcpondeut on d iminalion. T Il(' loss as d Ol ~ pa~S(·s . for the firsl time . th rull~h sites of d illlinatioll. sll(:h as tln- ~:l~t mi n lt'sti nal membranes and the liver, d ll ri n~ abso rption is knowu us Ill('jin t-IHlu t1Ji.'l1 . Absorption is nol res tricted to oral admiuistruno n . It occ urs as w.:-II follouing tnt ramus<'11Iar. slll)(:lItall('tllls, and other extra vascula r routes of ud mi uist r ation . ~Ion itori ng Intact d Ol ~ in hl(1l 1l1 or plasma olTers a IIst'flll nwan s of a..sess illg the ('ntf)' o f d m g into the syste mic circulation .
Disposition As absorption and d imillatio ll of d Ol~ art' juterrelated for pl l)'Si (ll~c ami anato mic n -aso too art' distrihutioll and elhmnanon. O nce absorbed . a d m g is delivered sim uha Il('tlllsly hy arterial hl()()(1 to all tissue s. incl lldin~ organs o f elimination. D i still~uish in ~ lx-twec-n e-huuuution and drstrthutfon llS a ('U II st' for a decluu- ill concent ration in blood o r phsma is nfh'n t1iffil11l!. lJisIXA\·ltioli is tilt" term IIS('(! to em brace both pnx'(·§.·i('S. Dispo.~it itm lIlay 1)(· defiued as all Ill(' pn x'('Sses that occur subsequent to the absorption o f a d m ~. By d t·finitioll, lIlt' l11mpu m'Ilts o f disposition art' d istrihu tion and elimination. D ist ribu tion. Distrih utio n is the pn x't"ss of rt's"ersiblt" transfe r of u d m ,; 10 .md frnm the sih' of measurement . usually Ihe blt)()(1o r plasma. An exemple is dis tri bution !Jt'h\1't'n blood ;llld musek-. Th e pa thway fo r ret urn o f d r ug 11("('1.1 not he the sann- lLS that !t'a\; lIg tln- circulation. Fur example, dm~ llIay he excreted in Ihe bill'. sto red in and rt.·lt·.l.....-d From tilt' ~all hl :l( !l lt·r . t mllS i t into tln- small intes tine, ami bt· rea bsorhl'tl int o the circulation. B, · doing so, til(' t1m~ complet es a (")"(:11', the l'tl tf'mlu1H1tk C1Jcle (S('t. Fig. 2- 1). If all tilt' dm ~ is rt'absm !J('t1 in this manner. hiliar:v sccn-ttou is not a m ute of e liminatio n: till' ()t·ling is then a component of dist ribunon. n i l' situa tion is analogo us 10 Ollt· in whic h water is plllllpl'1.l from om- n -senotr into unotln-r, only 10 drain hack into rln- origi nal n -w rvot r. Biliary v -crenon is tr uly a mu te of climmntion only 10 tilt' extent that the t1mg fails 10 lit, ft·ahsur llt'1.l. Th is Iailurt- llIay result fmm dcc omposttion in IIIl' intestine, p' xJr absorption d Jar.K1('ri stit'S, or otln-r complica tions. Uncha nged drug in hilt' thai is nei ther n -ahsorl x-d nor dt'l'(,ml)()St1.1 ill tilt' intest inal tract is t'\"("l1tllull)"excret ed in tilt' feces . E limina tio n , Elim ination is ti lt' Irreve rsible los.~ of d Ol ~ fm m tilt" site of meas urem e nt . Elimination occurs hy two p nx"l;'sS('5. excretion and meta bolism. 1':xcn1io/l is ti lt' im...ersihle Inss of d lt'lIlkall" IIl1d lltllgt"t1 d rug. •\ln aboli.'01II is tht' conwrslou of one l'ht' mit'lll ,!)("{1t·S to anothe-r. Ck,(';lsionally. rm-tabolites are conve rted hack to the drug. As with euI('mlll'pal k l.,"(:ling, Illis nu:ttllxuic illlrmml'f'nitm is a rou te of d imination only to the t·\ tt'llt Ihat rln- I1lt'l al)( llill' is excreted or oth("m;S(' im"'1:'rsih ly lost from Iht' body. SOilS,
BASIC MODEL FOR DRUG ABSORPTION AND DISPOSITION TIlt' complexiu... ~ of hu man anato my am i phrsi o10r0' "'11111d ap pt'a r 10 make it difficult, if not impo \sihll'. to 1II1)(ld !low Iht·I)(IlI)' handles a dOl ~. I't'rhaps surprisingly then, il is a simp lt· ph armlll'()I...;nt'tit· !Il()(lt,l, depil1:t'1.l in Fig. 2--3 whit'll ha~ pm \'("{1 use ful in 1Il.1II) ' applieatiolls ami is t' mplla\i7.l.'(l lhm ug!lnul IImd l of Ihis " t)(lk. ~I on' ('()mple x 1Il(IlIl'1s art:' IIt'('('ssaly 10 t!(·St:rihl· till' pha rmiK1Ikint'til-s of SO lnC dmgs. Examplt·s of sud l llltlllt·ls an'
or
..
CHAPTER2
Tln- Illudd is h..L\t "{1 U ll a mo unts o ( dnJ~ a nd nu-tabolue. lI uwt,\'(' r. t1H' amounts of dnl ~ ilm l lllt' t.thnhlt' ('l UI nlJ l~' lit, measured in urin e din'C:tl)'. '111' tnt"I IUIllMlIlf of dm/;t 11K-tal... n lil.l.'1! illdmlt... IIlt'hthnl itc'!i in , a.\ ",..J I as el inunated fro m. !II(" I..dv. nit" a UK)U1l1 in the h()d~· is mll.llly dt"lt>mlint"(! {nlln measure ment o f Iht> hlond o r ph, ;na ('U IK't ' n l ratiu lI . F~\· lilllah'~ of t lm~ ill III(" ahsurvtiull l"Olu pal1 mc'n t art" ..tso mually mad. · int lin't11y from either hle. .. I IIT urne - (Lila. DnJ ~ at d lt' aho,()rptio n sill- inC'llldc", that w hidl is IIt"'-'t"r absorbed. for ,·u-m pl.·. d nJ ~ th ai is 1I 1 I i lllah'~' de c omposed in tilt· ga.\lminh"s lirwl trolC.1 or 1m! in th e (c"(1;"S .Ifh"r oml .\lJ lIlinbt rJ.tiun . n it' mod.·' is rt·;" lil,"visuahzcd from mass haliUK't' ('(lIIsick· rdfto lls. 11 It' clu!>t" ts al'l'Ul.llllro fo r 01.1 au)' O Ut ' trme- ~: til(" molar amo un t o f suhslall(.,\' in ( ' al-ll of Ill(' ('u m pa r1nwn h : Amounlof drug 0 1
Dose ..
o ~ ,ite
Amount
+
of drug in body
Amounlof
Amount +
of drug
+
excreted
rnelobo!ile in body
Amounlof +
rnetobo! ile el iminated
11M' ma.'I.'I. haldfK'f' nf dm~ a mi related mat erial \00; 111tum- is SIM"' 11 in Fi ~. 2..... . SiJl('\' tlie SIIIII o f ti l(· 11K"''' a llMllm h of d rug in transfer anti dM'mie-
n it' n ·latiu lI'l.h ip'" (·\ p n...._
1 in (-:'1'" I am i 2 apply
lIIKIN
Role
of
2
el imination
all ti n.' llUstarK'l'S. n~anlk'Ss of
IIJI' narun- uf tilt' absorpnon and eliminatio n p nx'-~'S . 111l')' an" part in lldrly 115(·flll in dl·n ·llIpi ll ~ mon- o unplex IIl(Mk-1s for clua ntil).i ll!2: drug absorption ami deposition . Phar-"llln,1.:I Ilf1 ;c~¥ is tiM' quant ttanou of the- tune- (, )UI'1'e of a d nJ~ am i its llH'talxllilt'S in tt.(·IMKly
Drug at Absorption Site
Drug in Body
Excreted Drug
Metabolite in Body
Eliminated Metabolite
nil:. 1-.1 , ,\ ,lrull. ,. "m"II"' I.... a1 orf....I"'lo II t...h · ..."d ..Ii"'" rn .", II to. ._""....., nort ,l,..... n p" '""" .,r ...t"'''I'h''ro ~ 1 .....'tal n' ~ i....Iil. ",It. anuoo,:....t , <:t ,poort "'ilt. t n " 1""" ,10 n-pn--.__ dtffi-n.nf 10 ohrf..n.nl d "'il. c. _ ~a1.oLl..). \1t1...t..",I I"''''
, n.....·.. ....., t".· f,,,"h.... ~..t.oL .. n tn<Jt oh<...n l .... ("\("ft'f.", .
17
CHAPTER '1
100
Filt. 2-4. Till..• t~"l"" of tln1lit "' ..\ ".... ""li'.. i" ......., "f tI... mlTlp"rfn"'llh .t.o.. I" Flit 2--.1, n ..· .. rnc"lllt .~ d , '~""I rtn ll Ii ...1' 1i1.. .. 1"·n~·"I..~· 1..
/ Drug at Absorplioo Site
75
Eliminated Metabolite
~
8
/ Drug in
'0 50
Bod~
" ~
,I Excreted
u ~
~
i., .•
of,
,1c
lOIl
i"i."·
..II'
,1<
I
" •.,rl
l. In "'i' M.ilrnl,k·.
I,
DrlJ9
0-
25
o
4
8
12
16
Time (Arbitral)' Units) .uu l tilt' ck-velopment (If appn lpriah ' lIlotl.·]s In dt·S(.'ri! ll· ohservatious and p rt'1lil1 out comes in otln-r situatio ns.
STUDY PROBLEMS (Answers to Srvdy Problems ore in Appendix 11 .1 I . Defino' 1111' tenns lish ..1 in th p fi" t o" jt'('fiw at tlU' Ill;;nning uf thi s chapter. di slill~ui sh IX'h\1't'1I n· and S·i· SUIlI,'rs can I" atl lu pruhl" lIls in ti lt' interpretution uf plasma data follo\\inJ: admtntstr at iuu of a met 'llIk mixtu n-. 3. U...illJ: F iJ:s. :2-.1 aud 2- t slx'(1Ib l(' 011 how an .LSSilY thai measures tilt' ...11 111 of d m~ and illat'fin' 1Ilt'lal ll)lift, llIi ~h l inllllt'I\('(' a cc rrela tton I)('t wt't'll p!'lsma concentrauon am) tlwm p' ·lItit· n·s lxlIlsI·. .1. Follf)\\ill ~ oral ad millist ratioll of a t1 m g lalx-led with a nlditl
2. Brit·lIy sia l(' why an unalyncalmethod thai do!;'s nol
v
INTRAV ENOU S DOSE OIJlCTIVES The leader will be able 10: 1 Deline rhe meaning of holl~ife, eliminatiOn rcie ccoscot, li/$I-Older prOCMS. volume 01 dislffbutiOn. clearance. renal clearance. and f'ocllon excreed unchanged 2 Estimore the vo~ 01 holf·liIe, elimination rote ccoscot volume 01 di!>tribJtion. and clearance
from plasma Of blood ccecerecnons 01 0 drug following on intravenous dose. 3. Esllmote Ihe vo~ of half-life, eliminatiOn rOle conslon'. ond frocliOn excreted unchanged f10m ulinory excretion dolO following on inllovenous dose . .4 Estimate The value01 !he reoclclearance of a drug from conbioed plasma and Vfine dcrc. 5 Cokulole rhe concentration of drug in the plasma and the amounl 01 d".'9 in the body With lime following on inlToveoous dose. given -..alUM 101 the phormocokinehc pClfOme!ers,
:\d lll i ll i ~h'ri ll !!
a d nl ~ illtrd\1l-"C:11Iar ly ensures that 1111 of till" d OM' enters ti ll' ~l·Ilt'm.1 d R.·\!larion. Uy rapid injection . ele vated co nce ntrations of dnJJ,?; in tile hloo d can I){' promptly adl;t'\l'(1: bv infusion at a coutrolh-d ra te. a constant eoncentratton can hI.' rnalntalned. \ \ 'ith /ltl ot lw r r oute- of aduuuist ratton can blood co ncentruncn Ill.' as prolllptly am i {'mO('IIt1,. conr mlled. of tln- two illtm\';L..culur rou tes. tilt' intravenous [ t.v.) one is the most Fre-quently (omp lo}'("tl. Intra-arterial administration. which 11a_" gIl'ah'r Inherent lllanipu lat h'(' dange rs. is n ·S(·....·("(1 fur situatio ns in wh i(:h dm ~ locahza non in a spt"t-; fic o~all o r tissue is desired. T ill.' (iispos itiull charactcristlcs of a dmg lift' ch-fi ucd hy allalFjng tilt' tem po ral changes of t1mg and meta bolites in blood. plasma . am i ot.'(-d..\ ionally u rine follo\\; ng i.v. ad m tnist ra-
non. lI uw thi s infonnation is ubtaillC"tl fol h""'i ng a rapid injection of tilt" d rug for ms the IllL~is (If thi s cl.epn- r. The- rt' lIlaini ng chapte-r in this Sf.'<.1in ll d('als wi th (...-ents folloy,; ng an e xt ra\1l-<;1:1IIar tlmI.'. 111(' pliarmacokim-tic informatio n so dt'ri \'("tlfon ns a bll-..is for maki ng ra tfoual c!c"(; sic)IJs in tl ll·rap(·utks. til(" sllhj('t.1 of sllhsc'tlllt' nt se-ctions.
DISPOSITION VIEWEO FROM PLASMA St"n· m l ult't hocl.. an' t·lJlp lu)l."tl for grllphkally d ispla}i ng p llL'ma conce nt ratton- u uu- data. O m' t'(IIII IIIOII method. shown wit h t11l't lpl.)'lIill(' ill Fig. 3-1A, ts to p lot concentration again..t tilllt' nn rt':'llar (C llTIPsian) gra ph Illlpt·f. D l'pit1("t1 in th is manner, tilt' plasma {'o n('('u ! rat io n is nhst ·....·('t l to fall rap idly imm("tliat d y aft e r a 500-mg bolus. in th is <:a 'i(' [rom appm\illllltd~' 2~J to 18 IIIw'L wi thin 3n min . Th ereafte r. ti lt' ra te of t!1"(,lint' become s 11111<.'h slower. tilki ll~ almos t a nother oj 11I's bc fo n- th e ('()11('('ntriitiflil falls 50% to 9 mWl.. Anotl lt' r 111t'!I1od u f d isplay is a p lot of the sanu- dat a o n M·m iIOKdritlulli<.' f'
19
S ol il't· t il(' sha rp hn-ak at ahoul I hr wln-n tilt' plasma conce-utrut tou is ubout 16 IllWL. Bf·fon· lhi ~ tune, tilt' fall is ra pid . Then-afte r, tilt, d l 'i ...hm- is s IOWN and . Oil thi s wnulo gan thmic plot, appt,';m; 10 l'tmtilllll" lim·urly. 111t' ea rly phase is l'll llllll(m ly r..llIl'() the tlhtrl· Imtion plum· an d the latter, th e e!im;Flo titlll I,"ast'. 111is di stinct ion i.. sometimes flot clearcut . an ' <'' 1)('(1 more compk-n-ly d ist"IIS'i('(! in Chap. 19, Distrib ution Kinetics .
Distn'bution Pfluse TIlt' distrihutioll p!l;l'i(' is so ea llt'l l be cause distribution primarily dct emnnes tilt, (·arl), rapid
Elimination Phase D urilll-: till' dtstnhunon
phil~" changes in tilt' concentration o f tim )!; in plasma ft'fI("('t pri marily movement of drug within. ruther IhlUI loss from. tht' hnt ly. Howeve r, with time . di stribut ion ("fltlilih rim n of drug ill ttssuc with that in plllSJlla is t'sla1J1ish('t1 in mon- and
mon- tisslles. and t'\"t'lIhmlly, dlan,l!;t's in plasma concentrat ion rd lt"('t a proportional dJan~t' ill tlu- (UlI("('ntmtiollSof tim ,!!; in all otilN tissues and , hence . in lilt' amou nt of d mg in the IMM.I)'. D lI ri ll ~ th is propo rtionality phase tilt' IMXly ad s kin('ti('ally a.s il sill,l!;le containe r OT ('(Impartlllellt . As dt't'lillt' of tln- plasma coucentranon is 1J(J\\l due on ly 10 elimination of dOl~ {nun tilt' 111M(1)' . this phil'>t' is ofn-n called t ill' elimination pllll"l.' . E lim inati un lI a lf· Life. n it' elimination phase is d,ar.Il't('ri7.(""I IJ)· h ' 11 p
A
40 ~-
~og, >-E
30
~~ c 00
... - 20 ~
~
.-
~
}
~
c
"- .., -
0
~-
~og, >' E_ ~ -~
••
••
~ -
E ~ ~ u
8
100
~ c -
~ 2 !1 10 ..... e g
E " ~ • • • • • • • a:8
\ . .............. ...........................
~-
~u
10
0 0
2
4 Hours
6
8
0
2
4
6
8
Hours
.'1 ". 3-1. ,\, I'L"" "" "" Il~· "l r"t il " ' (If tl..~ '1"I~lli .......uh Ii" ... aft..r a 5ln-mJo: 1.\-. 1.,,1,,\ 1";'''''1i1111 into a 7O-l~ 1);lh"lIl, H, l11(' ,Lila ill" an' " "" li'rla~.~1 a' .. "'",i~'lo:"r1II""k r~ >t . S ,>t.. lhr .t .nrt .li'lnl>" tilll' p1w.,,' (I "'WI_ .. .';,5 /1 \ 1). ( \I , " Ii fi.~ 1 (" ' 111 tl..· .L.ta "f \1110"111.. .. PoO' " 111111 ( ~"w. RI .: Phanll;lll~>kin.'tK" o( i"I""""II'''' t lw.~'1,h . yll ulI·. el i", l 'II;<",l;II"" ~ ' l1...r., f.I .'\U\h "i13. 1l1i3.)
INTIlA'/ENOUS rose
20
lift' is til(' time taken for the plaxmu concentration, a.s well as tbe amount of thl' d rug in Illl' IMM ly. In fall by OIlt··half. TI lt' half·life of th eophyllilll" determined by the time taken to fall (m ill I fi to " 1Ilw'L- is 5.11 !In; ( Fig. 3- 1B). l 1lis is tilt' s am e tmu- that it lakes for the (1111{'(' n t ra t io Tl 10 fall Im m 12 10 fi IlIWL. In otln-r words, for theophylline at till" dost" ad m illish ·rt"tl. tilt' r-hnunution half-lift' is illtlt ,!lt'IIt1t'nl of lilt" a mo unt of lim p; in the hody. It follo w .., tln-nfon-, tha t k-ss dn l~ is l'Iim inah 't ! in each su('(.'t"t·d ing haIr· lift,. In itially thenare SOlllllg in Ihl' hody. AflN I half-Iif.· (5 hr ), 250 IIlg rem.un. Afh 'r :2 half-lives ( Ill hr ], 12.') lllg n-nnuu. am i after 3 lla lr· lin·s (1.'5 hr). 62 .5 lllP; remain. In pratiil,('. all the dmp; (H7%) lIIil)" I~ · n-gMd t't! as "
/1
v - Ale Volume of .. di~lribu lion
Amount in body P1a~ma d rug ccocentrcfico
Volunu- or d istrih llliOll i.. IIst·rul ill c'stimatill/{ plols ma concent ra tion when a known amo u nl or dOl ~ is ill till' IMllly or, l'()IJ\'C 'rlit.'!y, in c'stimal ill ~ lilt' dost, reqnin-d to uchicve a ~\l '1l ph\lIla e uu vntranou. Calt'u b liollllf \'C IIUlIll' or d islrilmt inn n-qui n-s that di strihutiou equilihruuu hc' adlie\l'll ht'twc'('u cln l/{ ill tis'llit'S alll! thut in ph~llla . Tilt' amount uf c lm~ in tilt' hCIl!)' is kmJ\'11 illllllt'(liall'ly afte-r un l.v. ho lus: it is the dost, admlntstr-red. Ilcl\\·t,\·l'r, d istribution t'f!lIilihrimu ha s nnt yl'1 11l'l'1I adlit'\ '/'l!, All t'stimall' is Ilt,('l lc'l! or III(' ph~Ill;l concentration tlmt wuu ld h;l\'(' n -sulted had all d rug spontaneously c1htriblllt'll int o its final volume or distri b ulioll. To dn th is, list' is madC' o r till' linear c!C'l:lillt' d ll ri n~ the t'!iminalicm plul-"l' st'('n ill till' sl' m i lo~a ri t i ll n ic plol (Fi~. 3-1B). !>C'l.'IiIU ' in plasma roncent r at ton dunng tbe diminal io ll ph a.o;t;, ca n II(' d mra<1t' rin'l! hy thl' linear t'fj1lalio n
InC _ lnqO) _h
2
wlU'rt, k is thl' J>lopC' or tlU' lillt, ill Fi/{. 3-- 18 am! C (ll ) is till' n mn' ut mtioll /lIlC' wu u lel dt'lC'nJlint , rru m this t'filialiou at ...c'm tilll(', 111t' nq.~ati\"(' s i ~ 1 aris c's Ilf'l.'UlSt' ('C lIK'C 'ntra lio n dc'(,1illc's \\ill. tilllt' , TI.t, te rm C (l l) is an t'xtrapn !llh '(l \"alm' lind is all t'stimatt' of tlU' (1 )Jl t1'lIt m!ioll wllil'h whl'll llHlltiplic'll hy th l' \"ulllllll' It'nll , \ ', al'l.'C lllllt s ro r Iht' duSt, mlm ini stt 'rt'll. i.l' .,
Do.. - V · qOj
3
In tl)(' c':\
2.
nanon phase. For esamph-, w hen tilt' 'hNt' art' 140 m,.-:; in tilt" IXKk
{'1II 11'l'n l m t iull
of th ' 'l'phyllint' in pWTJliI is 5 mWI..
VnlUlIIt" of w stribllHoll is 'il Jin"'(:t IIWClSUnc- o f tht" ('" II'nl of Ib~t rilllltjon. II ran-ly, ' It,"'· t"I1·r. corre-sponds 10 a real volu me , such as plasma \ulu nM:' (3 1.). n.t rdCt"lIula r water ( 16 L), o r total hod). wate r (42 L ). DnJ j?; tli\trilHltion ma~'lrll ' to al l)" utlt' o r a comb ination of tht- tissues and fluids o f tilt ' bud)" F urtbe rmon-, himhng 10 lissm' l'Om porwn ts rna)" till' ....:, gn-at thai tbe \'olunlt' of (Lst rilm tion is mall)" t illlt"S tht· total l...~· ..i7.t".
To appnocialt" th e dTt"(1 of ti' SUt· hindill~. ('o nsid(' r the di'!>trilmlion of 100 mg o f a {Inag in II I· L system com posed o f ....-ate-r and 10 R o f al1i\'ah'll d lan 'o al and ....iw.>n.. 9'9'1- of dm~ is lIlL'il,rbe.-d ont o the cha rcoal. \\l l('n til(" charcoal has !\t.·ttlt-cJ. lhl' roncentratson of tl n l ~ in tht· ;l(]lIt·ous pha..... would ht, I mWI..: th us, 100 L I)f tilt" a1 11lt"lK'S phasot' ....,ou ltJ hI' n "l lnin'll to lK,('CIu llt for all lIlt' dnl~ in tilt' ~ ...te-rn, a vnluun- IIIl1t'h Jtn'alN tha n that uf tilt' total 5)";h 'lII. Vohmu-s o f di..tnbunon fo r M,II"C.1 t't! dnl~" an' ..h U\\11 ill Fi ~, 3-2. nit, l'
c -qol ·.-"
4
A _ Dc». . • _ b
5
"------'-
silK'l' C ' " and C(O) , " art· tlK" illll(KlIlt in th t· IJ(JtI)' allli tbe t!tlst' ad mmlstered. n ""'I'M "l·· th't"I, ·, Equanons -I a nd 5 t'nahle the concentranon and amull nt ill tlte hod)' at ioUl" h lllf.' tn Iw.' esti mated . \ \11t'1I tlt'(..lim' in tilt' pl asma tUIt(.'('n trdholl or amount in tbe btJti)· l'Wl lit, tlt~I'M"'I1 h,· a sinJtlt' MpOlIt·ntiai n-rrn a... ~\l'1I II)' Etl s. -I anti 5 , it is sait! til ht· (1lI0IK)K'xporw ll tial. SilM.'l' ti lt· dimimll io ll half·lift· (frl2) is the time taken fo r t he ('(lIlt't' n · tration a nd th e amount in tilt' IKJti)' to fall by OI1(".lIalf, I' .~ .• fn JIII C (O) to 112 C(O), it fol1..,"""\ from Efl_-I that :
6
o r, on ill\l' rsioll
TakinR the natural Ic~aritlllll o f buth side-s, ~ Oi l«'
. 'In - In 2 - 0 .693
nh taill5 t he important relanonsbip.
0 .693
'In - -,-
7
constant k is i ll tilt· t'\ pollt'n t in F.,+ -I and <-.III II(' calculated fmm F.cl' 7. ih 1M.' ht1tt'r uncL'nttoo lJ)' ex.a.mi n i ll~ tl H' rat e a l ",nil''' the a mou nt in tilt, 1.0,1,., A , is dlan~ll~ with time. ntis is ohtaint"ll ll)' t1ifft'n'lltioltin~ 1':'1. 5. Alt"ou~ t he lIlt"a.llin~ may
22
CHAPTH J
INTRAVEf'..0U5 D05[
dA
8
di but ~i nl't ·.\ = D cl'il,' , ., - h , it (nllnw
9
Tln- term 0 11 lilt' left-hand sid e of Eel. 9 is rln- ra il' (If (:hanKe' uf lilt" amount i ll tilt" hud)'. T his is also tlU' mit' of clnninatkm o f dnt~ fm m tht· heMl)'. Pn xx-sses such as this, in which
Volume 01 Distribution
liters/70 kg
Drug
liters/Kg
50.000 Quinacrine
20.000
Chloroquine
500 200
10.000 100 5000
AmiodalOOlI
Doxorubicin
50
Onipr~mine
2000 1000 n Jt. 3-2. 11..• "'I'I>;U'O'nl ".I""". mt" "'~,kll ,Inol:' ,Ih ln h" k , ...rit~ "'itlo·I~·_
ChlOrpromwne
20
Nortriptyline
MlfIoxi
10 500
200
0'001.111
Qiltlaum
5
Verapamil Morphine Raflllidine
2
100 50
20
DiazePim EryUlromycin Phenytoin Theophylline
0.5
Ampicillin
0.2 10
tbupreten Warfarin
5
Erythropoill'1in
3
0.1 0.05
23
INaAVINOUS DOSE
CHAPTER3
Ih", r ate of rt'ac:1:iu ll is pr oportional to ti l(' amount pn-se-nt, art' known as ji n tofmler li me· The pm pmtiollality const an t is know n 1L~ Ih(·ji n'-t,,.,/f'r rate n llu to " t with dinn-nsions o f tuue - I . Bec ause I.: cha racn-nzes till' eliuuuation pnl('t'ss. it is known us t!J<> r [i mi llotil m rate n m_~t(m t . Sill(:t' ti l(" rute consta nt can also he denllt'1.l hy ft'arnUl~ n/;!; Eq. 9 to yk-ld l'_n~',~ .
k _ Ra te of elimination Amovn t in body
10
til(' eii nuuatjou rate L't mstanl lIlity sim ply 1",-' ft1!1lfll('t11ls 111(' jmctiOllfl1 m re {if dn,1!. w/JI onl!, Fo r e xample. sint't' Ih(· half·li ft· o f IIlt'uphylliJlt' is 5 hr . tile va lut' o f its e limination ranconstant is 0 .14 h r - I . II t,IIt" . lilt" sp('('1.l u f tilt' d im illati,," pm('t'Ss n f theophylline- c-an ht" dlamd eri 7...('(! ('itl wr by its half-Iif(', S hr. o r hy sa~ i ll ~ thnt tlte Fructional mil' o f r-limlnatton is C),I " (o r '4% ) o f l l l(' d Ol ~ ill III(' bo(ly p('r hour. Fruction of Do<;(' Remaining. Another view of tln- kin etics of dru~ e ln nln anou lIIay I I(~ ,::ai,wd by l''tlUnillill'::how tilt" fraction of tlu- do ">(' n' lIlai n i ll~ ill the body (NOose ) varies "'i tlJ tiun-. By (('ft,rt:'lll't.' 10 Eq . 5.
of dose A remaining in the body - Dose -
Frac tion
11
111t" [ruct ion of tiu- doS(' (('Illai ll i ll~ is. llwrt'fo ((', ~\1 '1I hy {, - lr. Sorncumcs. it is !I'w ful ln ( ':
12
re ma ining in the body -
Fracti on of dose
re ma ining in the body = I
1/ In
13
2
1/ 2 o r SOli u f tjn- doS(' remains afte r ' ha lf-lift', % n-nuuns afte-r 2 Imlf-Ii\1's. and SCJ on . Total C le a rance . Jml .lS the pa(;mlt'l('r vnl uuu- (If t1istrihulioTl is 11('('(1('1.1 10 n-lanconcentrat ion to amount ill th t' 1)(1(1)', so 111("((' is 11 Ill't't l to ha\1' a p ararm-tcr to n-late rmrce-nt m tion to rate o f dnl ~ t>l imillalioll . Cleumue- (Iotal). dt'(Jot('t1 hy CT. , is that p ro po rtionalit y f'Ki m . Tlltl s,
111l1S,
""'
", o, .." o e '''el imino tion - CL· Conce""' .,o,Ii,O,,". .
....
14
111(' uut ts o f eleanmce, like Iho ">(' o f [low, 01(( ' colunn- I)('r unit tune. Fu r example, if the d ('amn('(' \111ue is I l zhr , then al a concentratiou o f I IIlWl.. tilt' rate of dmg d illlina tiull is I JlI ~/hr . Ortlillllrily, us the- conccut renon of 11 dm ~ i1wn '11.S('S, so dot'S its mit' of dillli1I111iull ; ch-amuce rvmafn s ti l(' s ame. F r om EII- mil.' o f r-lhrnnatton :::: k . A . Sillt't, A :::: v C; From Ell. I. il follow~ that
».
Rate of e limina tion - k · V · C
C omp arison o f Eqs . 14 and 1.'5 !('lI<1 ~ 10 tlw n-lattousbi p
15
2.
CHAPTER3
Clecrc oce • k . V U sill~
16
ElJ. 16, tlu- Itolal) dl·amll(:t· of t1lt'ophyllint' is calculated to lit· -I l Air o r 67 flit /min.
So 11m! at a (11,'-\ 111<1 coucentranou nf I mJil .. t· .~ .• t jn- ra lt' of d ill1inatioll (If tht'oph)1Iillt" (mill t ill'
hO: Nly is -I
III Whr.
C learance and E lim inatio n lIa lf-life . It is mo re l "Ollll ll O Il to refer to tilt" lI a](·Ii f(· ruther than III thc elumnatton rail' cons tan t uf a t1nl ~. Hccallthut ' \12 "" 1I.69.Vk . so tha t half-lift· is n-lan-d to d t·;lr.lflc(' by: 0 .693 • Volume of distribution ,1/ 2 - """''---'-;'C''''::''' ==== Clearance
17
Equation 17 is p Ulvosd y arr.Ul ~t '(l in Iln- abo\'(' 1lI,U1Ilt'f to stn-ss th ;11 hillf·)if(' {and d illli· mlli on ra il' constant } rt'llt'(1s rat her than contro l.. \, IIUIIlI' of d islrihut inn ami cleara nce. two ill(l" I)I:II(I"nl pammdt·rs. To show lilt' app lil'< llioll o f Eq. 17, l111lsidt' r the lise of creatinine, a product of ruusch- cnrubohsm. as a marker of n-nal fum-non. C n 'alln!IIt' !la\ 11 clearance of -:.2 1)111" am i is t-n 'nly , listrillllh>il t hmll~hullll h,' 42 L o f total hudy water. As t'X))('(.'tt>i1 hy calculatlon m inl-t E' I. 17, its half-Iif,' is .. h r. Inulin, a pn lysal'd mrid,' also 1I.\t"t1 to a\M'SS n-nal fUlld inll, has lilt"sault' t.,lt·;lr.1IIt.1' ;\-\ creatinine, I!OWt"\'N , inu lin hlL\ a half·lift· of nu ly 1.5 lrr !1(>i';lIh" il is n...tri(1,'(1 to Ih,' )6 L u f exlm' 1'Iluiar wa ter. C lt.· arance. Arc" . a n d Volum" o f Distrihution. 11l11s far , cleurunce has )1('('11 ..-slimalt,) Fnnn !lalf· life alltl volunn- of d isiri butiu li. Clearaue - can he better t'slilllaftotl iu OilillthN way. H)' n'arr.U1¢ n~ Eq. l-t. it lV,lII be seen th at d \l rill~ a small interva l of time, tit, Am ount elim inated in interval dt _ Clearance ' C · d,
18
whe-n- tln- product C ' tit is tilt, l, )m'sl)( md i n~ small an-a under the plasma co ncentrattonlim!' t-urve-. For r-xuu ph-, if the- d,'amllt" of II , I m~ is I l z min and lilt' lIn';t IIl1d r-r IIIl' l'll r.,' 1)(,t\\"' '('11 flO and 6 1 mill h I 1ll ~-m i l\/ l ~ tlu-n tht, a mo unt Ilf d Olg r-lhnlnat cd ill th ill mhnnv is I m ~. 11w lulal amount of d Olg ('n 'lIll1a11y ('lim ina l('(I, wllid l for an i.v . bolus ("(Iuals the do \(' atllllinisl...n-d. is ;l\st'ssc'(l hy m ld ill~ "p 111" inftogmtillg tlu- alllllllnh ,'!illlina!t'() in each finu- Interval, Fnun limt' 7.t'm 10 infinite tim..., and therefore.
Dose - Cl ' AUC
19
when- A L'C is li lt' lolal a n-a und er th r- concenr rutton- unu- curve. 11111s, mu-e AVe is KIUJ\\ 11 (Ap!)('mlix I·A1, clearance is rt';ulily ralculated . ;-';u!t' th ai IlwIT' is lUI needto \..110\\' til,' half· lif,' or vnlunn of t1ist rih ulilln 10 calcnlan- clearance. Furthermore, th is l,;,!t"ulatillll of d ear unce is imlt'!w lltlt'lIt o f the shape' o f lilt' coucentranou-tinu- pmfil(-. Ti ll' rdatillllsiJip !K'I\\'t'('n are-a lind ehmluntiou ran II(' applied al auy linw fll!lo\\i ng d mg mllllinisimiion , as Illust r ated in Fig. 3-.1. Thus , IIm llipl)illl-t tilt' an-a up 10 a giwn rinu-, [A L'e (f), t JI hy dt'amlll1' ~\'t's lilt' amount of , Inag that has 11('('11 ...hnunan-d up to that lillit'. :\l lt'mati\"...Iy, wlu-u lilt' area is ('xp n 'ssc'll a~ a fr.tt1iull of II.... tnt al AVe . IIIit' o!'taillS 111(' fral'tion o f tlw d oS(' d imina lt'll. :\ml th... fr.it"tion of til(' Inial art'il hl')uud a g1wn lilll(' is a 1ll, 'a.~lI n' IIf tilt" fmt1 inn o f dllst, n 'lIIain ing In l)t, ,'!illlill;llt'(l. Fllr t·X;llllp lt·, in tilt' eoL'it- uf tll' 'l)pllyllillt'. hy ,1.6 11 1" tile an'a is 4U% of lilt' tul al AVe , allt l lll:'lIl't" 4O'.t, o f th ... mlmillistt.·f('(l 5()()-lllg lIost,. or 2()O mg. h;l~ 11('('11 ...Jiminalt'll fn uu Iht'! I(KI)'; 3lXl mg ha~ )'('t 10 ht, t'lim illah 'l l. \ 'nl ulIl,' o f d islri lm lio ll { \1 is IIst'() 10 n '!alt' p t l\lII;1 l1ml'('llt mlioll to amoull I of dmg in Iht, IItKly d uring Iht, dilllillalio ll pha-"" , of"'''11 111(' \, ,JIl" obtail l(,(! by ,'xtr.tpolalioll (1': '1' 3 )
CHAPTE ~
3
INTRA-Vi NOUS
oose
2'
is a rt"L\(mahlt, t'slinm!l' of this \u11l1l1l' tcnn. Ot't'l.LSiOmllh·. when t'slt'lIsin' r-lunmntkm occurs in tln- dislrihlltillll ph'N" it is not . The lM."st 1I1("IIIoc1 of t'ak'lIlatin~ \1IIUIII(' of distrihutlou is to d h id(· d l'anllll,(' bv r-lunmauon run- con stant
v .Cl . Dose 1 AUC ·l
20
Unhke extrapolation, this method of t'stilll atill ~ \ ' is not restrit1t... l m the l.v. bolus situation hilt l',1Il hc' usc... 1unde-r a \'ari dy of conditions, t' . ~. , long-tt"nn i.v. infusions . Cm lsc'C!IU'n tly, lilt' valuc' of \ ', t·stimafe... 1 n sill~ Eel' 20. is app!it...1throughout th ... n-nuunder of thi s hook, alt holl)!;h olhl'r voluuu- n-nus are t·x.ullint't! in Chap. 19 . Distrihution Kiuet k-s.
RlNAl ClEARANCE Elilll ina!iull
CI('(· U ""
hy n-nal excn-t ion ,md extmn-nal piltl l\\1I)'S, n.sllally IWpiltit: IJlt'lall(llism .
~(JI onl., · is n-nal r-xcn-non an important route of t'limillalioll for lIIany d m gs, bul IIsc'ful
p llanllal'llkil1t'l k iuformutiou run iJ,t' ohtaillt'tl [roru analysis o f urinarv dat a. C""lllml lo this analysis is lilt' t'l)JIl'!.'pl (If ",.,IIlJ f'!nlnlmY' . "\ l1 a l0l-~lI ll s 10 to lal <'I t·arall('!.'. n-ual d t'a nlllt1.' (CI. R ) is d l'fill(...1 as th(' proportiouahty n-nu l)('t"'I"1I urinarv excn-rion rate- ami plasma l'Ulll'('lIlmliull:
bcretion role • Cl// . C
21
lh-na l d t'a nllll'l', lilt· total dl·ar'U1l't·, h,ls nnits of flow. usually m illilil(·rs!lIlinnlt· or hn-rs/ hour. Pnldil'al pnJb le'ms ari se, howt'\"t'r. ill t's timalill)!; renal d t';tf"d llt'l'. Urine- is l u llt-c1l't! cvt-r a finite IX'n od , I· . ~ .• -I hr. t1l1rin~ wllk-II tilt' plasma conce ntration is dmll~lI~ l'o lilinllu llsly. SI.(lrtt ·lI ilJ~ II.t· (u llt'1.1iI1ll pt 'rind reduces tln- dmll~l' ill. Jl1;l~ma coucentr anou h' ll iu(·n·, tst·s till' IIIlt't·rtainly in tln- t'Stimat e u f excre-tion mit, o\\ill~ 10 incomplete hladdt' r t·lIlpl)ill ~. Tlus is l·sl)(-c·ially trm- fur urine- (u l1t'l1in rl inn-rcals of Il'SS thau (,') min . 1 ,(' lIhrt l lt' n i ll~ tilt'
t'l ~. 3-1.
I,LL, ,,,;c
A
li".·;O]" pi". "r,.... sa,,,,'
(~ "K ~·"lr..' k"H jl!"·
,LoI;c rfl r 'I"'0 l'''~ lt i ll'' ..s .lhl'l..~ .·c1 ill t"i" . :J-I,'l. n it·......" lip In 3 6 Itr i . 411'. "i tl..• ,"• ..I .U·C i,.. lin alilll: IlwI 411'. of II.., .Ie · "'lmini...·rt..1 ha.' 1" '1'11 .·1i1rlin;ct
I I ~' 1I,, ·n .
n ..· ;crt·;( 1 "~lJ'MI
.1.6 hr rtllrt... ·nh ,I..· fill'l- or ""Imin. i'lI .r"I II....'1II,~·Il; , ... n·,,,;cininj( In I ...
,·li", ;n;cl<..1
o
2
4 Hours
6
8
2.
C HAJ'T E ~
3
collection inte-rval, 10 avoid t ilt" problem of iuce mpk-n- t·lll pl~;lI g . rt'(juin's II II1 fl(lifit '(! ap p reach for tht' estimat ion of renal clearance. 111is app roach is analogous In th at tak('n with to lal clearau ce-. By rt"arrdnJ.,tj ll~ F.A!. 2 1, duri ng a \"t'f)' small int erval of Ii me, tlt.. Amount excreted '" CLI/ . C .. df
22
when' C . (Jt is the l,(JlTt-'sp:m
'lee,'
Amoun t excre ted , in .: CLI/ " ( A ' t
co
Of\ In
efV(]
uc
lth In l mle rvo I)
WI
23
Th e p roblem in ca I('ulalill~ n-nal dt'am.I1(1.' then-Ion - n -sts with t's l ill1 atiu~ tilt, AUe withi n ti lt' ti nlt' int erval ( St"t' Appt'mli \ I-A ). TIlt' a\·I'rl.l~t' plasma drug conceutratfon du ri n ~ the (1.1Ilt'('!ion interval is !-?WII by «AUC wit hin inlt'mt! )lN ). 111is awmgt' plasm a (1.)II{1.'IItration is neit he r the value at tln- ht' w nnill g nor at tht, t' nd o f Ill(' (d lt"('!ion tum- hut at some inlenl\('tl iat e po int. By asslllllillR that IIII' p h SlIli' rmu-eut rution dl;lllgt'S lillearly with time , ti l l' ap p mpriatl' concenrranon is that at tht, midpo int of the (d ll'('!iull interval . Ix" cause the plasma conce ntra non of drug is in faet dlan!-?Ilg t'Xpo lll'lltially with titue, thi s assumption of linear change is reasonable oll l~' when los.s d uring tilt' tnn-rvnl ts small. In practice, til(' Int erval sho uld ht, lt,ss than an elim ina tion hal f-lift' . EXlt'liding E(I. 23 11\ " 1' all t tn«- Intervnls, [rruu zem to infin ity, 1I1ll' obnuns tilt' useful
relationship ,
ena c ecro nce "
Total a mount excreled unchang ed
AUC
24
when- AUe is the total area 1I11dl'r tilt' rl.lsma t!rtl g concentratiou- ttuu- ('U I'\'(' , T o apply Eq. 24, can - mu st hi' taken to eusu re thut allurine is colh-cn-d an d for a su ffidt 'u t ('Jt'rind of tilllt' til gain a ROIIlI es timale of tilt' total amount excrcn-d u nd langt'tl. In pruet ice, the pe-riod of tune 1I111s1 1)(' at lt'il-st 5 to 6 elimination half·li n 's of tilt' d m~ (st'(· Appt·nd ix I- B), 1111I"', if the Ilal f·lift" of it drug b in till' unlt'r of it fl:'\\' hOlln. , IlIJ p ract ical t1ifTk ·ultit·... t'xb l in t' mllri n ~ urine collections taken 11\ '('1' an at!t'(lllah ope-riod of tum-, St·\'('rt' t1iffit'ulti l'S wi th {1.lInp li'lI\l't, in unli t' collect km occu r. however. for d ru w; such ,l\ plwllolml'hil,(1 with ;l half· Iifl' of abo ut a week, si ll{"t' all uri ne formed on'T a I)('rillli uf at 1I',l\ 1 1 mon th must lxcollec t ed.
DISPOSITION VIEWED FROM URINE ONLY Lac ]; o f sll ffidt~n t l)' sensitive ilnal)tic tec hniques cau and prt '\illllsly has prewu n-dme.eurement o f the- couceutrauon of lIIall)" d m gs in plasma. In tln- ahst' lIl't' o f plasma tueusu rements. neuber \ UIIIIlI(' of dist rtlmttou nor d ('amn('(' can 1)(' d('It'nnillt'll. :'\om-tln-le-ss. useful tnformanon can still ht, ohlailJ('(l Irom u rine data alone, wllt'n sud l i.~ 1ll '("t' SSiU) ·.
TI lt' dilllinalioll half·li ft" o f lilt' ft'\1.'rsihlt, l'!IOIiIlt'sh' r.lSto inhi bitor, galallihamil u', l"itll I., l'slimah't l fmlll Urillt' data. TIlt' apprtliK'h is to plot ti lt' an'mgt' t'w n' lilm mit' agaillSt the midpoi nt of tilt' (,(lllt'('!ioll tim e Sl' lll i l(~a ri t h Illi<.'lilly and . fmill t11(' slope o f t lit' stl'ili~h t Iilit' ,
(!-\APTER 3
INTRAVE NOUS DOSE:
27
obtain an es timate o f till' half-lift" I ll t ll i livt'1~·, tilt" approach is ('asy to see. Assullling that renal d t'a r.Ull't' is constant . lilt, uri nal) ' excret ion rate is proportional to p lasm a con ce ntra non, and pl ott in~ uri nal)' excre tion rate a~.tillS t tune is likt" plotting plasma eoncent runon a~aill s t ttnu-. TIll' half-life is then taken as the time for the urinaryexcretion rate (or plasma l'(Jm't·lltr.ltio n) to fall by ollt··halr. For ~aJant ham iJw this is approximatt'1y 6 hr in a ht·alt hy subject ( Fi ~, ,~ ) , COII,·t'~' ly . wlu-n a st r.ti ~h t lille is obtaillt'(l h)' plotting the urin al) ' ewreuou run - a~ain s t tlu- mid poi nt tune , l'tlllsta nl'" o f renal clearance is Inferred. '111e 11('('(1 for using midpoint tune follows fm m the previous diSl1lssiou; the measured u rinary excrclion r ate n -fh-cts till' ;l\·l'r.l~{, p lasma conce ntration duri ng; the collect ion inte rval. Formal pmo f uf till' fu rt'going diSl11ssion is !'in'n ill Appendu I- B,
Renal Excretion as a Fraction of Total Elimination :\n impo rtant phan nal'(,killt'lit., paranlt'tl'l"is tln- fract ion of the amount enter mg the V;t' ne rdl cm-ulunon that is exc reted U1ll'haug('(l.fi', II is a quantitative measure of the cont rihntion of renal I·XI'n·tinn to (lw r:lll dmg eltm tnatron. KIltJ\\ing f e ajds in t'stablishing uppmpriatrlIlod ifil'atiolis in tIL(' IIsual dusa~(' rl";u\('n u f a d n lg for pa th-uts with \1u) i n,l1; degn "t's o f reuul fUl1(1ioll, AIIlUll ~ d m~s , tilt' value offi ' mn gt's het\' 't't'u 0 and l.O. \\l w ll the \ 11111l' is low, excretion is a minor path\\N .lYof dmg ehnunauon. Ol"l-d-sionaJly. n-nal excre-tion is the on ly rout e of eliminat ion , in whic h l'a<;t' the value o f fe is 1.0. By ddinition the difT('f'('lIl't', I - ft'. is 1111' fract ion (If II\(' amount (' n t(' ri n ~ the o rr-Illation that is elhnlnan-d hy extra re nal mecluuustus. usually me-tabolism . :\n ('st ima tl' offi· is most readily ohtalm-d [rom cumulative urinal)' excretion data Iol1 U\\i n~ i.v. admintstrutkm, since by defiuitlou. Totcl d,ug
Ie _ excreted unchanged
25
Do.. In pract ice, ca n- should
alw;I~-s
lx- ta ken to ens ure complete urinal)' rt"t,,(J\'('l) ' (i.e., collect
.'R,dn3--1,nn i/: ";ot.·h ,..
1000
,~.f'aI;:t"
u rin.' ,og:n 't;on {·UII."'1ion m1"''''''/ afl.. r lU' 1,\'. I• .tll. J. of 10 ml/:of1/:;cl.."Ih>imi l"'lt> .. I lth~, subj ..d . (R..,lr,,"'·n rm m 8i .·~ ..I, U., n ,,"n....'. T .. W,'h" T, W.. n..-Iwr, J .... 801("' no, R., S ilT. ),1.. ..,,,1 11:....,il7., II . I'han ll... ulj",,'t~ or ~;u" Ih;omi...· in I"",,,. ns ..n
f:
100
-"
~ a:
10
~
Unlit'
Ph..rm",'ol . TI,,' r .. 1Y91.1
"
;u; w"
I
0.1 0
12
24
36 Hours
48
60
72
,S fl : 4 :W- 4 2~,
2.
OW1H3
\II;m' fllr 011 It'll" 5 t'limillatiull h;Jf-liv('s), I" lilt' (~lW of ~al all t hillll il lt',fi' is app m"imah.ly 0 .2.'5 in sllhjt"t1s with normal n-ual Imu-t ion . AI any inslanL t llt' fr..u:lioTlfi' Illay II(' d l,fjl\("tl ilS th e fatiu o f Illl' rate (If ewn-tion til till' mil' of elim inatio n. 11: 0 16 of excretion
26
I!:ole of elimination Appmpriatt>l~· s ll "st it ll!ill~ (or IU.IIIN ato r am i ch-nouuuator ill
Eq . 26 , it is Sl."t'll that
27
Thus. fi· liMy "lSI , II(' t!,·fillt't ! llmi l'sti lllah·d ,lS tll(' mi lO ()f n-nal am i total
dt 'ar.tlll '(' s . l'lis is pa rtit'ulany useful in Il lOSl' situation s in whit-Ii totul u n l it' l '(IIII't:IiOIl is lint po ssihlt·. III p r act ice, estimates of e l . and CJ.x ;In.' u h tililll't i di n -ctly, w!lt' n ';"->; ex t run-ual t..lt";tr;llil't' is dt 'h ' n uilll'l! hy d ilTl'T('!It't·. 11 111s, extran-nal dear-lIlt't' is ( I - Je) . CI..
ESTIMATION OF PHARMACOKINETIC PARAMETERS To apprr-cian- how lilt' p hann
,.We 3-001 .
Pl._ .IMI UrI_ ..... 0W-1...4 ••II.wI.., •• I.. . . .1• • 0._ TI1MMEM C# Dolo'' '
08Sf N AOClN
1'\.A.S.Y.A (),Io.' '''
lJRf",((),Io.'''' TWf 1NTf1V"I
..,..... I
3 5 7 10 18
CO
"'roN
o ccec
' 2'1.13 '0" ''''(}-2 ~,
2-4
010 0 43 0 20 0 0 25
, -<>
.>-8 8- 12 12- 2.1
"""" o ... "" 120 180
BO
340 178 ' 50
CCN:f:NTU ,~ '"
'NO.N
="",,,,0
"VCWlT~
""" N " "
Im ....Tf lll,'A!. ("'\J"/ll
"'''' 133 50 63 10 18 2
" (tfIl D
C UYU./l 11VI
N"" ....J!NA!.
~""-'" H C91flO
...
'
' 00 226 14 0
'6 0 00 56
0 66 0 80 0 43
34
32
"
...
160 250 30 6 34 0 372 391
Plasma Data Alone A p lot o( p!;Lsma concentranon versus lime illdi("lill' s that IIII' \·alll('s an- dmppin~ p n ~n's sin,l)", hilt o nly a(h'r tln- da ta an' ploltt'( l S<' lIIi l()~ari tl ll n it."lllly (Fi ~ . 3-.5 ) 1·1111 til(' !tal(· li(t' and elimination r.lt(' constant 1M.' n-adtl v de!t'rmilll,(1. 111<' Ital (-li( ', 1;I)(('1l a\ Ill(' tiul(' (or til(' l'lIl('('n lr.tt ion to fall in hal( ( '.~.' from I .U to U.S 1lI""'1. ( I f U.2 to U. I mwL), is 2.S hr . so that k is 0.25 Ilf - I. Clear-lII('(' is t1t'lt-n nillt'(l by t1 i\itli n~ doS!:' hy AL'C. 111(' Intal.U : C , esli llllt1I,(!lIsi n~ Ihe trapczoldal m il' (Appe nd ix I- A), is 10.2 1Il ~.ll r/L and wlu-n di\itlt'(! into the dos<' \idds a value of 4 .9 lA ir for clennme-. \ 'olulIlI' of distrihutiou. ,'sl im a!('(1 From CU I. (E:I. 20) , is Ihe n -(on' 19 .6 L. Tht s value is \irtll;lll)" id, 'utiedllo Ihal calouluted hy ((hi d iug duS(' h)" till' Intercept l'tJ!l('('utmtin lJat IA'n l ti llle. !M.'(.'allw no t1i \t ill('1 tlislrilJ1tlitlll phase is appa n 'ut.
Plasma and Urine Data Bntlt p (,L'ima anduri ue data an' n 't illirt't! tn ('slimalt' rennl dl',mUl(" . T his pamnlt'h'r can I" , nIJl:lim'(! {rom tilt' sln j'" of a plnl o( Ihl' amoun t e-xcreted \\il ltin a " 11l('(1inu interval
CHAPTH 3
INT RAVE NOUS DOSE
a~aill \t ..\ L'C within tilt' sann- tim!' i llft·...... 11 (Fig:, 3--fi), TIl(' \t r.ug:ht Iiiit' implit'S thai n-nal dt·ar.lll('t· i\ con stan t and illtlt'pt'ndpllt (If plasma concentration . TIlt" stolx>o f tilt>liue indican-s that tilt' n-nal d t'ilr.U1{,(· of thi s dOl ~ is -I IJhr, ES.\I."lItialty the sann- \lllllt' is o!Jt
Urine Data Alone TIlt" elimination Ilalf.lift>of tilt' dOl~ (';1Il ht· ohtatncd from either excretion mit' or latin' cxcn-t ton data. TI lt' app r opriate nu-thods an ' dt'all wi th in Aplx'llflix I -H,
3.0 2.0
....§.z: ~
H It, :J.-..5·
<'1 1111 11-
St,,,,il"Kantlullit' r~>t u(I Il. , rt.....ltlat" " .
n '"lralilM,· li n M· , Lola
Ki'n , in TaM" .1-- 1.
1.0 0.5
g
e c 0.2 ~
y
~
0
u 0 0
C5
0.1 0.05
~
E
~
0.02
" 0.01
c,
0
8
4
12
16
20
Hours
HK .3-4>. n... an MM",1 f"un 1... 1i. ,liW<1h· r" '1M.Ifl i1Moal In fiM' ,-\l 'e: ""·.... un.. l " "'f"T 11M' ""'M' tulJ..-c1i<M' in l....\;a] . 1"" ,,;
o
1
2
3
Area Under Curve Within Sampling Interval (mg-hrlll
4
30
lNn AVfNOUS DOSE
Cl-W"TE fl J
A Question 01 Predsioa Had vnu , tilt, re-ader, p lolh-d li lt' sa m,' data and eak u lalt'( I III,' phurmacokine-nc parunu-ters, ~' lll lIIay ha\"l' ohtaillt"tl a nswers that d ilTN Irom t!loS{' ~\"l·11. Thi s is 1101 unusual and " i ll
U('(1Ir in llIa llY case-s when }llll
dWl"k }llu r uu swers 10 l ilt" problems a l tilt, ('11(1 o f ('adl
l"h
of a Iilli' th mll!-:h data. aflN 111(')" ha\'(' lx-en plolh'd. alld in roll lldi ll~-Orr numbers . In addition . all 1IlI' ;LSUrt'II\I' UIs han' errors lLs s.od a l l't ! \\i th all al~ t ie methods. t l lTlllitium (If , t(J"'~I' . ;ull l l l;U1d li ll ~ of ....mpk-s prior to iUla l}1iis . :\l sc ), 11ilt! tilt' sl udy ju st ('o llSidl'I't '( I IJ("('1I rl'pt'ah '1) suh">("(llIl'ntly ;n the "lllll l' indtvtduul, tilt' ,",limah'1,l half-lift' ilia)· haw ht'f 'n :U hr instr-ud of 2.S hr. For almust all d illiC'lll situatiolls. IIIis t1t-grt·'t· of illinum li\i tlual variat ion is
¢ \l'!1 to ! \\11 or 11 10"" Sij.,'11ifica nl p lace s. III this chupte r. mall Y s~lu hols an- ck-Hned. ll\ it is the firsl tune tlmt ti lt')"an- 1I ~,,(1. 11 1t'~' s)1llho l\ a n - rt' u ~'t l ft>pt ·aft'tll)· I llft lll~hoU I Ilu- hook. To
Measurement Fluid So far, lilt' phartuacokinetk-s of tilt' t1 m~ wi thin Iht, INltl,. han ' lx-eu t1t'fillt'(l \\id l n 'f('n'II('(' 10 d m !!: ill p l;l\llla. SUlIll'l illll'S tlu' fl.'ft,rt'lIt'(' is t1nJ~ ill serum Of wholt' blo od. TIlt' majuf d aTt' f('II('t' " t'IWt'('1I p l'l-sm
Use of Computers Tt ltla)' (um putt'r.- an.' \ISl'lllo all'IIF.t' p IJilnll1lt.'t,killt't i<' data alltl makt' prt'C.lidin ns. B,N .'l1 upnn slalistit'lll ('rilt' ria, Ihe.' pharma('tlki lll.'fit' l'ardlllt'It'r \·alm' s art' adjllslt'( l lo J:i\'t' llw I~'st fil of Ih(' appmpri;lft' t'(lllalion 10 Iht' ('.\ I)('rinlt' lltal da ta . 11lis appmad l 1101 (111)' pnJ\itl(,s the IN'sl t'\limalt' of Ilitf1l11wlt 'r.; b ut also in('f(';lst'S Out··... l'tlllfidt'!l<-"C ill t1lt'IIl. Alstl, appli('atioll of tilt' ~I m(' t'o lllp ult 'r p n J!.,'T;ulI fl.'sn lts in tll(' Sll lllt' all\"\o\"(' r.; inclt'pt 'llllt'1I1 of Ihe 0lwflit uf. This ('flllsistc'Il('''' (Mdllllnt h(' ad lit'\ '('t l h)' fitlill~ ~rdphi<-,
"
C HAP1f ~3
t'l!u atinm; that cannot ht· hm-anzed. 111('11, ohta inillg a lx-st fit hy 1')'(' 11l"<.'Olllto:; \i rt ilall~' impm sihll' , 11lis limitatiuu does 1I0t ari se lISin~ a compute r: any equa tion can Ill' filtt 'l! di rt"<.-tly In thl' 1'\I)('rill ]('lIlal datil. Xoucthek-ss. a ~n'ul d eal aillmi (Lila is lea rned by di spla~ ill g " W ill gm phil'ally, 0 11(' gains a f('t·ling for tln- quality o f the dat a and thl' ('(!lIation that is I11l l' 1 lil.t>ly til dt'S('ril ll' them app ropriatdy, 111l' pa mTllt' IN \11111t'S nhtailwd by t')'t· also gt·'ll'r.tlly M'r\l' ;L~ su itabl t· slarting \'1III1(' s in a l'lJlIIputer pm~rmn. Because of IIIl' ~n'al 11l'llt' fih lu I( 'an l ill~ ph anllaml.int't il'S gaillt'l! by plntling data, tht s r-h-ment is Inco rpo rated inl n lIl 'Ul~· p r obh-ms thnmglumt tln- book.
IFIICT OF 0051 An adj m tnlt' 1l1 in dOM' is ofh-n 1\t'('(' sSilry to achil' \'l' optimal d m g therapy. :\ dj llsl lllt'nt is mad t, mon- n 'ud i l~' when tilt' \·alllt·s of tilt' plllln mu.'likillt·tit, p'lr.l.Il1l'h ·1'!i u f a dnlg dn lint \'ar:' \\i lh IIm l' or \\i lll concenrra tiou.Tln- possibilif>' for a dJallgt· \\i lll dOM' exists . howt·ve r, fo r ma ny reasons. and thes e an' dealt with in C ha p, 22 under th e utle of D UM' and Tim e Dl'pl·IJ(Il'll eit·s. Tl m mg!1011t tlu- majority of till' book, huwt"\...r , pharmac okmc tic pa r.tl1ll'n-rs an' aSMIIllI'l! llllt to (.'hungl' wt th either dOM' or ume.
STUDT PROBllMS (Answen to Stvd y Problems ore in Append ix n.)
1. G in 'lI IIlat till' t1isposilion l.int'l it's of a dm~ is t1I'Sl'riht'l l h~' a one-compartment Illtxlt'l , whid l O1I1'(S) of tilt· follO\\i ng statements is co rrect? 11.t· hal f-lift· of a t1 m~ follf)\\in~ tlw r apent ic doS('s in humans is oJ h r. the-refore, a. 111(' t·lim inatillll run- con stan t o f this dm ~ is O.l i 3 hr - I. h. It takes Hi hr for S' "S'.f of an i.v. holm dUM' to hI' clnninated. c. It takt ·s ~\in ' ;~s long to t'l imina!t· 0.3.5 g fllll c J\\i n~ a O.5-g holm tIClS(' a.s it doe -s 10 t'lillli llalt· ll..'i g folltl\\i llg a I .~ tIUM·. d. Co m pll'll' unnc ('lIIlI"l:lion np to 12 hr is 11('1"111"1110 pn l\itl l' a good t·slilllalt· of Ill(' ulttman- amount of d n lg ewn-n-dunchangcd. e . T ht· fr;tl'li oll o f the admi nistt'n "ll tloS(' elhmnated by it gin'n tillle is ilJ(lept'nde llt o f rlu- si....t· of til(' tIusl', 2. Cuk-ulan- tlu- foltfl\\ing: a. Tht' f"'ll-tiol\ of all i.v. tluS(' rell lajniu~ ill the Ixxly at 3 hr. when lilt" half-lift· is 6 hr. h. 111t' half-Iifl' of a d r ug, when IS% of th e dose re mains in till' hl xl)' -I hr aftN all l.v. bolus dost·. 3 , l'n-pu n - a st' milngari llunk pint uf till' f{)lIf l\\i n~ plasm a conceutratlou-ttnx- relationship :
C '" 0.9 e - 0 3.. 71 where C is in IIl WL and tinn- is in hours . 4 . A t1 m g tha i di splays OIlI··l'l Jlllpa rt lllt'1I1 disposition kmet tcs is adnuniste-n-d OLS a singll' !MIIIiS dust,. 1>t'pi(-tt'll ill tln- left -hand graph of Fig. 3--. are the plas ma con centrations o f d m g ohst'!yt'tl initially ( 10 IIIWL ) and 60 min later (2.5 IIIW!. ). Depicted ill till' ri ~h l hand j?;rdp h of Fig. 3--. is the tot al uri na ry excretion of unchanged d r ug IAt'" "" 60 mg]. Complete tilt" fig un- by drawtng continllum lint'S thai t!t-pil1 Iht' fall of d m R t1111('('lltmlioll in plasma ;lIld tilt' at."<.11Illulalioll of d m g ill u rillt' \\i lll tilllt' . ,S. F ru m 0 10 3 h r af!t'r a ,,)(l. mg ix . boills doS(' of dmg. lilt' Ave is 5 . 1 II1g- h rll ~ 111t' lotal :\ l'C is 2:1,4 mg.hr/L and tilt' (11I11 ulati\l' amollnl l'"l'n·It"lllln(:h an~t'll. :\r " . is II m~. a_ \\1lal I)('r<"t' nl o f 11.1' atl1l1i nisll'H'l1 tIoS!' rt'mains in th l' l x xl~' a<; t1 m g ill 3 hr?
"
CHAPTU J
II. Ca l("ulafto total clearance. c. Calculate tilt' renal clearance of Hu- drug. d. \\lmr's the fnl11ioll of till' dost" tlml is dilllill
C . 7.14 6- 0. 173 '
10
9 8
~
7
2- 6 .~ 5
°E
c;Eo;
~ " c -c.. ~
~
y
c 0 u
4
3
c.
2
o o
0.5
1.5
2
2.5 3 Hours
3.5
4
60
4.5
5
~
50
<> _E c _ o~ o ~
40
~go ~2 > y
~
c:;:
30
-" => o~
E ~
0,"
u~
y
20
"
~
10 0
o
2
3 Hours
4
5
CHAJ'ff R3
Call,dah' : 3. VOIIIIIK' of tli..lrihllhou h . ElimiJl
Pharmecol. n
,.we 3-02 •
Wf, _ 3 ;:522--52'\ , I g.~') , )
..... _
C
1•• -.1.0 -.lkw) h . Time lhrl
~lmg/lj
s.
I 137
I - . .. c.fhoIw 6 120
12 103
AffMo I•• • &4.1
24 76
48 42
1_".
n
Qo
23
12
144 37
a. J'n -p.tn· a ~ ' Ill i~ui llllnk pk Jl o f Ihc' plasma l11IK" lltr.llion of l't.· ftru.\OIIl- \I'nll" tin K'. E..tilll;ltt" Iln - !aoLlf·lift· of I.... d m~. h. Est ill\,;llc' ti ll' total A (:C of l1·ftria.\lJIll", C , C.ak·t1lalt' lotal clearance. d . C.ak' ilatc· tilt' , ,,Imllt." of d i'\t rilmtin n . n il' tlata !{i' 't"u in T abk- ~ .tn· lhc· plasma l1 111l"t-n tnd iuIlS of l'K.~IIl· a.\ a flll"-1ie llluf tillW aftt"r I." . ;tllm iui..tr.lliou of 3.1 m~ cocaine h~tt m('l.loride· In a subjt't1 . (Mnlt, 'u lar w.-i~th l o f cocaine h)tlrn t'b1oritle' := 340 Wmn1e·; IUo lt" llar ""t'i~ 1 o f ('(Il'UiIW := 31).1 Wmo 1c',) (Adapt t"C1 fn un C IItJ\\', \I.J.. Amlin ' . J.J.. RUIl, T ,I" Alli nson. A,J.. B ow..la-r . D.J., allli Fi'\(:luTlitll. ~I ,\\'. : Kitll'ttl'S of coc aine d istribution. •-liminatjou. al KI dlnmotrupk' d Tc'1". C lin . Ilh;.oIl."-'u l. Tl ...r., 38 :31S-.124, 1 9-~,) . )
,.we~.
"-- c •• _IJ.U. . . . . c.e.I_ a ..... 11. .lel•• . 0.-" 33 . .
Time lhrl ConcenIrahOn ~/U
01 6 170
0.5 122
10 74
15 45
20 28
25 17
30 10
Ol. l' n-pan - a '\('lIl i lu,.~a ri l " lIlil' p lo l of plasma lt ml"t' u l raliu ll versus lirllt',
b. E!otimah' ti ll' 1J1lIf·l ift' am] lolal clcaruncc of cocaine. c. G i\,c'n tl lal lilt' bud y wl'i~" 1 o f Ill(' slIhjt'l1 is ; ,'i k~, m ll'IIOI h' Ihc' \'Ullllllt' uf d isl ri· h utillll IIf l"tJl-ainc' ill l A Jt.
EXTRAVASCULAR DOSE OBJECTIVES The leader will be able 10: 1. Describe me choroderi5liCS 01, and the di!felences between, lirS/"Ol'der and
oZel'O'OIde1
ob-
5Ofption processes
2 . Oeiermine wherher obsorpll()O 01 disp<»ilion role limil!. drug e1,minohon, given plasma (orr
following d;/ferenl dosage lcems Of roulE!S 01 administrotlOn. 3. Anhcipolelhe effect 01 oflefing loleof absorptiOn, e'denrol absorption, clearance, 01 volume ofdislr'bution on the pIo:.ma cceceoectco and crrooet ofdnJg in the body ioIbMng eeo ceoecrcenee 0010
vascular odminislrohon .
4. EsllRlOle!he biOOYailobilityoi a drug. given ei!her plasmaccoceoncrco 01 ullncllyeXClehon
dolofo/bMng boIh exlt(M)SCUlo, and inlroYOSC\JlOI odmlni~ohon _ 5. EstllTlOle the relolive bioa.ooilobillty of 0 dll.'9. given ei!hef plasma cceceotctce Of urinary exclelion dolo following differenl 005096 forms OIIOUIeS of administration , 6 . E~,male!toe renal clearance 01 a drug From plasma ccoceoecrce and Ullraory e>lCleloon dolo IoIIowing exfrovo5CUIo, administration.
Fu r sys h ·mie.llly ad i ll~ dmhrs. abso rp tion is a pn-requisin- for t1l(' mr~ 'lIt i c adhity wln-n Iher an' a
n it"
imp,,(:t o f rate and extent o f absorptton o u lJott. plasma ouux-ntration andamount u f dm~ ill tilt' hody; tl.t' d Tt'\.1 of a!tt'mthllls ill ahsmpliull alltl d isposition 011 hull y k-vel-ttunn -lationshlps; ami Ihe methods used to assess plmrn \;t(:okindil' paramet e rs fmlll p lasma undurinary (Llta foll()\\in~ e xt rava scula r udnuulstrat ion. The term IJ;{I(I lA'lilaIJllity is l'CJlIllllollly appliloO to IX)jh rate ,lilt! exh-ut u f t!0l ~ inp ut int o tilt' sys te rmc em ulation. 11mm glJollt thi s book the term will ht· Iilllih'(l to tilt' extent of drug input and can 1M.' conslden-d as the Fraction, ur pcrwnt . of tht, aduuntsn-nd dust-, abso rh{'(1 int act .
KINITICS Of ABSORPTION 1111' oral ahso rp tion of dm~s ufit 'li approxiruutr-s first-o nlt 'r kiru-ucs . {'spt"li;llly when Wn 'lI in solution. Th e sam e holds true for the absorption of dmw; from llIany other extravascular sill'S i nd \l(li ll~ subcuta neous tiss ue and 1Il1lS(·II'. Unde r these ci rcumstances. uhsorptiou is d l' rdllR{' fmm 15 min til 1 lrr. OI"l"il-si'. tilt')" an ·lflllgt'r .
OWTE ~ 4
Souu-tinu-s, 11 dmg; is ahso rll("(l al t"s<;t'n lially a constant rail', 111(' absorption kinet ics an' tiu-u ('
B. 8emilogarithmic Plot
A. Regular Plot u
100
u
~
..."
80
'"s
60
0
~
D
"... 0
'"s
Zero Order
~
E
40
0
~
·E
First Order
.~
E o:
"" ~
20
FirstOrder
5
"Il ~
~
c,
10
~
~
'"
Zero Order
~
0
.~
50
~
D
~
·E
100
~
II:
0 Time
Time
t"lII:, "-I. ., " "" I'-In" ", .. f " ,",...",Io'r and li"t-<""Io'r al"" 'l l(inn I'I'"l......" .". ,, 'mik'l{>Ili thmk I,k~ ...f II.., 1" 'rn'Tll n '",,,i,,i"lI: In h.. ..1......."..1 ~ ',.I tllTll".
n.,.1<-.1an', ..\ . Il,~nlar .u,,1 H.
BODY lIYIl·TlMI RIlATIONSHIPS Comparison With an Intravenous Dose Absorpt iull t1, 'lilY~ ilnd ll'(lul."·" tllO' "1lIJ:,/Iit l/ dl ' eif Ow Il1.'ak {'OIIlIl;Irt"(1 to tha t s('("1I follel\\ill~ all t'(lua l i.v. bol us dost·. TIlt'S(' 1·0'1'(15 are portrayed for aspiri n in Fig. 4-2, 111l' rise awl fall of till' dOl~ couceutrutiou in plusma art' be s t understood by n'lIlt'III I I('ri n~ (C hap. 2, Ell. 2, p . 16) that at any ti me
dA d'
I·A
Rate of
Rate of
Role of
change of
o b$Orption
elimination
drug in body
CHAPIfI! 4
when- A" is 11M' amoun t of dm~ ,II rln-
ah~)'11ti ull ~ il l' n.' lIl ili n i n~ III Ill.' absorbed. \ \ 1lt'1l
h~' a first-onk-r p R ll't' S" ,
tilt' rate of abso rp tion i.. ~n'n hy kn-Au. Initially, wi th al l dm~ al the ahS()'11Iioll silt' and nOll(' in Iln- hOlly, rate of ah~)'11tiul\ is mamual an d rail' o f elim ina tiuu i.. zem, The-n-efter. ;l" d Ol~ is ahsorht'll. ito; r an- of ah<,uq llinn dt'1·n'il<'(~ , ",1Iert'a<, its ra te o f r-luntuatfon tncrc.ea-s. CUII''l'( plt'lIl l~'. tilt' di ITl'rt'IIl'(, Ilt.,· IWI'l'n lilt' I\\'U nm-s diminid lt's. If nwt'\"('r, u-.. ltlll~ il" tht' rate of OI!JSC IIVlitJIl C,\ ('t'l'(L.. thut of t'li millatioll lht' plasma concentr atkm cont inues to nw. E\"('l1tually. a tum- I ....... is rt'adll'll wllt"n tilt' mt(' o f t'lim inalioll matcht'li tilt' ran - of ah..u rplioll; ti lt' ("l)1l('t'ntmliou is theu .11 a maximum, C....... Suhst.'qu e ntly, lhe mil' of elhntnatton e:\('t'1'1I.. thl' rats- u f ubsor ptfon and tl u- p lil..lua conceutra uon dl,t:lim's. 111t' pe-ak pla...ma concent runon i.. always ICI\\'t'r folle l\\i n ~ ('\tm\"il"!11Iar ad ministral io ll than lilt' initial value fn lln\\i ll~ all ('lillal is. holus (lelSt'. In Iht' Iomu-r (' ''-'it' . at Ihe Ilt.'ak lilllP ~ ltllt' d m~ n-m.uus at lilt' nhso rp tion silt' alltl <,(llllt' lms been t'l im illalt'l l. whilt' ti lt' entin- c!US( ' i.. ill ti lt" hudy illllllt'1lialt,ly fol\(l\\i lll' rlu- Lv. di N' . Ht, u llcl lhe ()I'ak tune, tilt' pLt..ma ronce-ntration t'X('t't'lls that f(JII( J\\i ll~ L\". ;ulm illisi ml iull uf till' sallll' do...' hl ,('
absorption IIl'CU O
10
~
0
~
"
8
~ ~
0
-
';;~ .;:; E .5. -
.::>
6 4
~
E ~
'"
2
0.
0 0
20
40
60
80
100
120
Minutes
""ti""
t"iJl:.4-2. '-\' I" rin (6.''10 "'It) w.... ,.Imini'kn'ti ll.' all ;nl r..... 1.. ",. I M~ Il. ,.1 . ,,,1a' all ur,.] ... (OJ" n .. " ..."1.. in.ln" I,,..). " ' '''' '''11111 >11ca,,_ '" ,,,.l.t~ . lUlIl .. \c... .-rilti/: {If II""I",·ak l". Il, ·nlr..tio mII rnlo1I. .. .5,.5 j.I~ l l . ( ~ I , ..lifin l frum ,I... tLI... of Re... L,,"!. ~I " 1\;."·I,,,all. S., I I..m •. 1', .-\.. ;.... 1s l...Il"lT. S I)., ...I""'1>1io" l i,....Il...
,,,!:
A,Lq>tI'tI..1t1, p"' n n i"
it ll l
,i ,h., ("I~~J I '....' ItT )
EXTiAVASCl.J.AR OOSE
"
TIl(' h iua\Oiilahilil)', F, is proportional to the-t otal urea lImlt'r the plasma couceut ratiou-time curve (r\ Ce ) irn'sl)("(1in' of its shape. T lns must la- so . Heeall From C hap . 3 th at :
T0101 a mount eliminaled .. Clearance ' AUC hul tl.t' lul,ll a mollnl t·!illlinatt'ti is
2
tilt' <\111011111 ah so r])('(I, F . Dust" tllt' rt'fo1l':
F . Dose - Clearance ' AUC Amount Total amounl absorbed elimina ted
3
Thus. liIl n\\ill~ tlo,,-', ch-arance. and un-a. hioa\1lilahi 1i I~' llIa~' l lt, den-mum-d.
Changing Dose Unless ah"-''llt ion half·lift' or h io
po rtional ill(:n:',l"-' in phlsllla coucemrauon ut all tunes . TIll" value of ' "",. n 'maim unchaugcd. hilt C"",. increases p roportionally with dust·,
Changing Absorption Kinetks A!tt' ml iolls in t' illlt' r 'lhS()'lllion or di spositioll produce changes in 111l' ti me profiles of tl uamou nl ill IllI' h(ltly am i tilt' pl.l-sma co nce ntration, Thi s poinl is iUmt rolh"tI I,:,' tilt' tlm 't' situations dl'pi(1("t) in tilt' o;( 'lJlilo~~arit l\lll il- plots of Fig:, 4--3 tnvolvtug only a dlal\~t' in tilt'
Case A
'00
300 100
CaseS
CaseC
Absorption Elimination
o
,
8
'2
o
,
8
'2
o
,
8
'2
16
Hours t "i l(. ~1. A .1'''''''1:: (fn nn \o.'ftt" ri" ht l ..f ,lmlt Jo.·di,... at til<' a1"""llCi"" .il.. (It""..., !t"".apI" l ,I..~., I...· ;ollllin n"'n l " 'MI ,1. ~ TO 'a...... tI ", " "' l(Tli'n, lr"or tI,,· I..;ok l'u"TllI dro it l~"'Il" I , ;o1o"" l'liou (IoLoo.·1< lmd io .. f.., II'r pnll~,," tI..." ('hmll Ii,," (cul..,..IIi.... ). In CoIL'" C (Ihin l ",>r..pl, on lilli""" I, al....''1" ioll' II,Loo.·1< li'''' l r.." , h",i l' ..h", i"" lio." "" 1"" 1, I.·di 'l<· Il( .In ti( in pt..,,,,,, " .fI."t1$ a1""orpt"." r..tl,•-r ,·Ii," inat io •., ; l. ~"",, , tla-n- i. a ''' '! ,' h", inati.... nf dniK (!llrinlt tht' ,Wi,,,, pt..u... t...• r"l(' o( d imi,...lioll is ,h"",t ~· j..'n"oat,'r t ]..... 11 K" r..It' .. f ;o1""'1" i..." In all II,,,.., (.......-s. hitl\(·n liLJ.ilily i$ 1,0 ;0,><1 (.I.';or",,,"t" ~. ll!1l·h"n!:,,,!. c.''' '' ~ I"."n l l~-. tl,,' ;on'" , ,,,,,1.' 1' 11"' 1,1.," ";0 (~.""' '' Indit m · li nlt' ('\/1'\'0', k.. m~r- "Mli r>l( li",,,,r 1'10" o( II... I''f' 11m..' ~pl" ) an ' itl.'nli, ,.1 n M "..H ·C. Ilr tI.., Ii'''';or pit" . or tI,,· n" I.. d..t,, ;oll' 1lI.. , "'-1"llIl .."t'au't' II inl' V .,] or th.. ....1(' of ah" ''1" '''lIl, ;0""""" ,,1....,..+....1. '''I'''''' II,,· inh V ,,] o( I...· ra,....f r h",inatio", """..",t ..Ii"'i, I•..I.
,I,w,
3.
fKlRAVASCUAR 005£
CHAPTER 4
ah sorptio n half.llfe. All other fat1nr.; (hio' l\1Iil
Altsorpliol Rat,.Umited Uiminatio" Occasionally. ab sorpuon h:M-lift· is 11111<:1. IO Il ~(,( th an elim inalion half-lift·, and Cl<;t' C prevails ( Fi ~. 4-3). TIlt' pe ak occ urs lan-r and is lo"', N tha n in till' two p n '\1ous l'lN·S. T ilt· half-l ift, of dechnc o f d nlg ill tilt' hotly lIOW corre s ponds to tilt' ahMlrptioll half-lift'. 1> 1I ri ll ~ tht· rtw 10 llll" peek. lilt, ra te o f eliruiuation increases ami t'\'t'n lllall~', al tht· peak. e-quals lilt' rate of abso rption. Ilnwt,\"(·r. in con trast In tilt' pn.'\10 IlS situations, ubsorpttou is so slow that much of 111(" d m~ remains to lx- ahM,rflt'(l well Ix-yond tlu- peak tune. T Ill' d m~ is either al till' abso rption site o r has be en 1·!imin:I!<'(!; htt le is in rlu- I)(KI)'. In f.ll"t, d ll ri ll~ the decline pbaw, tt.l· d m p; is e limi na ted a'i fast ,LS it is ahsurllt'(1. ,VJ,\'OfJJtiorl ~~ fllJU: tlw ratelimit/'l l! slt?J. Under t111'SC circumstances. since the rate of elnninatiou ('sM'lItiall)' matches Ihe rate of absorpnou . tilt' f(JIl(J\\1 n~ approximancu (... ) ( "lUI 1)(' written
I·A Role of eliminotion
-
ia ' Aa Role of a bsorpl ion
thai is.
A mount a . . . body - (I) -I . remaining A~" '
In
10
be absorbed
5
A(1.,(lnling::ly, amount in till' Iltltly (am i p lasma ('()m'('lltmlifln ) du rinp; tln- dr-cltm- phase is
Distinguishing Absorption From Disposition Rate-Limited Elimination .\ 11 1.0 111-:1. d ispm il io ll 1-:1'lIt'mlly is m lt · · li lllit i ll~. tht' pr('('I"tlilll-: d i<;(.'u.\siun Sll~t"lil s tl llIl e d. ll-
lilill II lay Ilc,('f l h i lit, c'sl'rd '\t'(1in ill!l"llrdi ng tilt, II lt 'a ni ll ~ of Ilalf-lill· del('mlillt't ! fmlll the t11·diIW pha",' fo llowi ll~ t'\tr.i\'a\('lllar adminh lralion . ( :o llfu\ inn is a\~lidt'tl if lhe d n lg is
,.
CHAP1H A
al~l ~\"en intnl\"{'llollsly. III pml1k'-'.IIIl\\·I·\"{·r, i.v. dusa~c' forms of Illany
fur eliuical IISl' . Distin"..nishi nF; ht'l Wl'C'1\ ah sorptioll ami d isposition rate -limitation s is aeh il'wtl by altt'rillF; the ab sorption kiuet fcs of lilt' t1nl ~. This is most n'adily accoruphdn-d hy ~h i ll ~ the t1mJ{ t'itlll'T in diffen'llt do sa!?:t' fo rm s or hy d iITen'nt mutt's. To i11l1stmte thi s po int , l'ulisitiN data fur t1wuphylline ami pC'nidllill (; . FIMMI nnd wate-r inHuc'nl't' tilt ' oral ah"': lIv tion kinetics of thc'tlp hyllinl' hut nul t "c~ ha lflife elf tht, dc't.'lilll' pl.llw (Fi~. 4-4 ). li e n ' then, dispnsitioJl rute-linuts theophylline eliminauon. In contrust, fur penicilhn. \\ith a \"('l)' sho rt d iminalinnllillf,life , Intrur nuscular (LIII.) ahsOIVlioll eanlk,(11lllt' mk·limitin j!; hy fonllllialion of a sparingl)' solnhle salt (F ig. -1 ~5 ) .
10
1-"11/,. +-4. t h'. 'l>l l~
8
~
51111 ",I. " f ",...k r . 'MI ,..k-n on lU I " ln l>l~' _t" m,.d , (0), T akin1/: tiM' ,..ltJ.'!, "'; 111 2lJ mL of .....w. ' "' "" " "'Ilty ,1" tI ", (0) ~ull ...1 in "'.... ·r ..h""'l'h,," tha" t.,k",!: tI ", "ith Itw Il&mt' " >1"" ,,.
4
e
~
u c 0 U
",...Iia"·~· li>llo...i nll: .. .tantLordiD..1 hill:h {1lrhnhy-
2
, I',d. - tlM·..l (el. D' ''' 1'il '' rlifT.. 1'f'fK'M In roll", nf a!>...,rl'li"l1. I.."",·....r. th., It'n niruoJ h;Jf·lif,· w~ II.., ..."... 1".3 h.."n) tl...n-f", e . il l. tI..· .-li miu "li,, " 1....lf·lif.· lh''''l,h yili"t- ( I mWl • .5.5 f.l\l l. ( " ,..d . 1". ..1 (nUll \\'..Il l1l~ P.G .• l.yo I_I ~ , enliJt. \\".A . of.1ire a,Ml IIniel un an,l Trudo!a. G .A , l" fI" hi"""".;I,,1>11;1,- of 111......,11) 111ne . C h n. I'h" rUl;U'11. nM'r " ; ,475--4'jll. I~~.)
~
s
~
~
0
~
~ ~
E
."ttI.
or
'" ~
"'I:
,,"';llO
§.
.~
c<M'I.unin]( 1.111
tiN , .. rio.. " .",.. Iilin'" _ i\ IKC oq>tlo n .,f 1I"''1>1,., lIi,,.· " ,. . .1 r~>i, 1 .. ~ ..·n tI... ,,,h it.., "" ' 1'1 ' di. ...>1""11 ill
6
c
T" ., lal.l<1'. .-;00;-1,
m,",.'''' 1'1' ,..k.... I,> 6 1"...Jlh;o-,. ,jun" ~· n "11 '
0.5
~
.ss c,
0.3
4
0
8
12
Hours
5
c 0
~ e 8c 0
P·I.M.
1
f"ri""
_
';; ~ ~E
"
u-
.~
0.1
t:----..
I.M.
c,
E J
~
J!
HI!:, t--S . "' '' li<:illin c: (3 1fW\l() ......, ... Iminio· h,,,,..1 intTII.mmn,Larl" to I 'u iI" lni1;'''' "fIo, 1 raI e- Ii "';t~ th'l"lSilk'" f,~"",,1111: i,,tnun " .....' wr ...Iml"i.t ratif", trl tI......1'.......... "" Iio-It, t'ltIl '''lly t... m...It· by K*'i"!t l""..iMllin (; intr. ' .. """.Iy. ( I mWI. - 3 .0 "M ). ( Mod ili,·,1 f ru m M"",,,. I> F .: o"tli"" ..f Fu lld..,..... 'I"" 11"mll......1-
0.Q1 0
6
12 Hours
18
24
or
h.",
or
I'..,
' ~'.
e h" n... C. Th..rn...... SprinKfir1t1.
II ~
19.-') 1.)
n n AVASCULAl1 rose
CHAPTH
~
0
10
",,,I.., tl,,' I,l"",;/' .. ",n'nl.a, ~
Fill:_4-fi. .\ ,,,,, (,,I.l •.0: ... ...... tl..· .on-..
" ~ I ' M1 " " , in (,I.-Mall'" j " .
,..,"-,''',,, 1,. .."....11"..·. 1,,1' Io:r"1',/, ),... . .("lel, ••", · p.......II" ,1,.,1 ,,( tl..· .. ml n~ 11>I...1Ii",-) ..f" ·r .. " "l:I, · .·\lr..' ....."1..1 .1. \ \ ';111 ''', d ~Ul~" ill "I>. ""!,h",, Li'", tin 1... " 11 ",, , ah"''l'Ii'' '' r.lt,!' rnhl.· wit l,
l li,..·. I. ,tt u lIl l::r..I'IoI.
lo",,· ) (, .. "'
110." ".It<- .. f ,·I""i".di" ,,
<
1 Ii'..-. I..,n"",
l" I..· 1<",,-• .,t Ii". 1"'1 ,,, I...... " ..· C.. ·.,I<-, Ih.... "f tI,,· .. 'IIln,I II,I...1
1:'''1,11 \
j, ,~ .... ·... , .. I
tI,."
'" 8-a,
5
0"
2
~
u
~ -
=E 0 _ ~
E ~ ~
1",,·. I.. ~ Ic " " 1:'-"1",1, .., II..· Mo' " ","I.., II..· nor" "'1" ,,,.1"'1:: h,..·". f ' I"....· ....10· (.,n ,... """.
p"."..
1000
h." '''1".,1 I" tl,,· .10 · (" F;( . "~1 1. 11..· ,10·· ,·rt·.....· in "!.-,...",,, " , 11.., I'O"', L '''' '''' ll l r~ · 'M'" ,,, I.· I:"'~r,'r ,,,..I'n ' ..... r ,,' " 1;'10" h UH" h ,,,l~ , hl:h' l ~ ,MT" n'''! h,·",). 11..• I" ·,,l li UH" '1( ' . " ' ''' " I..·" ,I.., r'l" '''( , 'loU"'~'!" """'I,,~l. ' h, ' r.." , .,f " I"" ,!' I " '" 11" '11" 11I l:'''l'h l. T Il<' 1,' rn,;" ..1 , I" ..• n·II...1- 11..· ;,,,·n·..,.. I,·I""",,
500 -
~
Absorption
200
§. 100 ~
'"'"
/ ' / Elimination
50 20 10 0
4
8
12
Hours n"t lm ·lio u ill dl'ilf;llln' und. IWIll, '. ('!illlinal ilm run- coustaut , a gn-a h' r a mo u nt of t1 nlg IIHlst hi' a h\ll rlll "ti. am i lI lt' ptl\lIIa l'lIll" lIl ra tillll 1I1mt Ill' gn'alt' r pri o r 10 till' li lllt' wheu th,' rutr- of dilllillalioll ("tillais 11.(· rate o f ah\l)'l)liuli . As SI.(I\\11 ill Fig. ·1-'j , tl.,' t,\('nls a n' d in-I'n 'nl wln-n an illl' I'(',I-\( 'l! volunu- (If di st rihulilm b n 'sl'NlI\sihl(' fur a IUllg(' r (,Iilllinalioll l.a1f·li f(,. Um ll' r 11ll'\(' r-i rcumv tances tilt ' t\ UC is til l' s.uue if h iu;l\"ailahilily and ('(1'011'.1111" a n ' 11II(·ha ngl,,(1. 1111' peak IJ('('11rs late-r ancl i~ 10w('I', htlwt '\I 'r , \\'itl. u b r):t,1' \'UIIlTlIt' tlf distnbutton. 11I0 1'(' d m~ IIIU\I IN;' ahsorlN;"t1 (,('fo n ' 11.(' p l.l-s lIM{,(lIIl"('lll ra tioll n-acin-s a vulue al which Iht , rate- o f eli nunution ((.'1. ' C ) (,,( plills tlumit' u f all ,mplio n: the- ubsorption run- is 10\\ 1'1' tlu-u ilTltI so is ti lt, plaouu 1'lllll" lIlralioll .
PreetKting Changes in Peak Qll alil"lin- d l a l\~(,s ill C".... am l t...... •rn - diffu-ult 10 pn-du-t whr-n ab sorpnon or d ispositioll is nhr-n-d. T o f..l'i litalt' t h is pn'll idiulI , u IIII'mlll)' aid h,l-s hl"t'li foun d to IN;' 1I<;('fl1l . Til(' h..stc prtnciplr- o f IIJ(' lIw tl uMI ( Fi~, ,,--Ii) is silllpl("; 1l11\(11"])tion iUl'rt' ;L",-'S <111I1 dilllimition " ('('n ',l-\('<; li lt' amount uf t1 m~ in lilt" 1'N'Nly. Tlt l' f;lslt' r III(' ahSl:I'l)liu lJ p n ll' '<;s (ant';Lsllrt"t1 hy ah "'ll'lltion ran- ("(lIIsIOlIlI), tilt ' g rt';ah-r is till' slop" of till' ah\ll'l)tin u lim' , ;\1J(1 111t' rou ve-rw-. 1111' fasn-r tln- ('!illl ill;llioll P",I'l'SS ((,Iim iualillu ra n- 1"(lmt.lI1 t), tIll' sh"('I)«'1' is till' t1.'('!im ' uf tilt' ('Iillli llalioll lim '. If a h\lI'l)lioll raft- constant is illl·n·.lSt't1,Ihl' 111'\\' poi nt of inlt' N'('tiflu iml it'a!t's t hat Iw ak anmuut is illl·n "lSl,,1 und thut it lll'('ur; at ,111 carln-r lillit' . If t'l illlill
t_.
CMAP 1E ~
.,
A
">I"",,.
I-l K. " _7. .\ f\>.,,(,,1cI i'K.,.,·.....· III ,I.., tlf ,1I'l ril..,h.." (."'" ........ ,,,,,fuM ;'Il1'1·.....· ill tlo.,·!im j" ..ti .. " I...I(·l i(. - ;on<1 ,I••l",~ . tl". Ii "", .. I
"foid, tI..· 1" 'oIL pI..,,,... ""..H ,lr.dio", tI(U,I' ... 01<,0.11".... "'I' j(ml>l,\ .... "1..." ..1til 11... (. ,u· I n ,l , 01",,' n d lil m
",Lt.{ li".. l ;tll.'r .. ,i"I:'" ,'\I r..·
"IM,J,....·. With "" d,.."\,,,· ill ,-I.·at,nM. ....n'" ' ,ullk" I",. ' ar Il.·"tr"'Ii.. "·fj"... 1,10.. 1 ;. " " .
,;t...
li""
'~'''''I:', l .m.t p l nllK""tr.. i, 11,, ·n·I ~· n-. ,I"n'd ISo ....,,"'· "I" .. " ...." , , ·.,lr.ll ...I1. •" t.' "f o-li,,,i,,.oIic,,, i, i ",tial~' . 1. ,..1 (I,.I.,n..1 [illl ' , I....' ..m I(r"I", >. I",1,i,,,, -,I..· .." ...." '1 ,·]i"';II"I., 1 ;, II..· ...." III ,,· ,L",·I. " f •.fi"'I".lIiI.......·,,· ,,,..I~ i. " " •., II."" ,I.", "f ,I..· ',lI.l,,>I lill.. ,l IUN', h"tt"", 1(,,,,,11 1.
1000
,.1,·
500 _ Absorption
~
200
S- 100 ~ a:
/ / Elimination
50
r
20 10
0
4
12
8 Hours
. '11:. 4-8.
B,'
,
,
,
,,
,
, ,.
,
,
,
,
Me mu ry aid to ;u... u du. np:l'l in pt'a k
Iim.. . nd prak a moun l in the body. ftl'rnlravalMIla r ad m lni l tnatlon o f ;0 IrinKJe ,) n . b. m rpt lo n or di~i1iun " . It..red. n... tiYr pt'u 11m.. anU Ih<- I't'l.o.tiw' ["'a le amount art' tn-
,
dicalNl by lhoe Inlerwctlon of the ahwrp hon and
..limlnaU,m lin... (A) with .Iopo-. n-p....... nlinp:the
A
a h....pbon a nd ..lImi l1.lllio n rale conttanll.~' 11\~ly. p....Jic.1lo nJ (OT a n IIKTt'aord a hso rp-
n...
l ion ral e:' co nsta nt (colored dashed line and poi nt Bl and an Incn-.ur
C
10 a. Sf'lt duo nKM In pralc ti me and pt'aIc COlKTn-
Time
lra lion wi th aheratlo n in druJl: .hoorpuon or
pm iUo n. Am. J. Pharm .
duo
ea.. 46:154-155, 1~2. )
vnlunu- o f distrihut ion v..111M'S a d('('n ' ;l<;(' in pea k concentration , and the cnuus e-xplained under Ch'UlWI\~ Dhpusitinl\ Kinet ics . Spt"<.ifil· rt'l aliu llst.ips for t'stiIl l
!IIe l'l'il'" i ll \"(' I"!\(' ,
ASSESSMENT Of PHARMACOKINETIC PARAMETERS lI ow sonu- paralllt"h-r vuhu-s art · t'stimalt'tl follo",i ll~ t'xtm\ll-"l."olilr ad ministra tion ran lit, a pprt'('iatt'(l hy {"Iln si dt' ri ll~ ho tll tllt' pl.t\ lIIa conceutratkm -tun e (·U ....es in Fi~. 4--9, ohtaillt'(l
CHAPTER.4
42
2.0 Fl~ . ~9 .
,e- .,
\ 51"'" ""
, ~ ...... i. 1/;i"'" ;,,' r"""'''-~ II...I~·
"'K IIIr.J I~ (0- .
"-",,m'h' ,
" ..1", ,.1
·0) h. tI..· '
1.0
;,,,... 11,,· t1nlj( i. It·•• loi.w..."il..IoI.· 01",1 1 ",,, n ' fn ,m .1..· ",,,,-' l,,,i nh.. ti ,,..l
.1<""1:-
In.d , A l'.mJ Io·1 ,10...·li'.... 1.."" "H"r, inopll<" lilA ,Ii., ,,," il ;' ''' i. ' oI!t". ]im ih " l: ill
""d, i n,f..lln '• .
0.5
00 0 0 0 0
0 0
0.2 0.1 0
4
2
6
Hours
y.w
hlvll
1. D.ttI 0Ith It)' Dlfte_,,'
newl... &tI.I.I........... SOO _ . . . . . . . . . hi
. ~(),t.I"
l'\A.'.M.Il. o,.o..l'"
Cl,Wl.U..1N( AAlOJll
!'WJ~(
eon InIlO.-enou~
Intromuscular
0 01
"""
DECAT PI-t.o.Sl:
'....A>
,-,
76 74 35
190 185 193
E lC tn1DLNC ~O
l""!ll
152 147 70
r(lllm\in~ i.m . and u ra l adm inist rat ions ,,( SOl) mv; of a dnl ~. and in Tahh- -I- I.
tln- mld itin ll"l tnformatton
P10sma Data AIon. Hinn n.i1l1h ilit,... Sup plt'lIlt'ntal dill•• [mtn L\'. ad lllilli"tmtioll allow ('a l('u lal iclll nf hiu;wailah ility. f . n il" tol ot! Ace fullo\,;nv; extravascular adminis tration is d i\itlt'1l by ti lt' are a fnlllJ\\ill~
whk-h ass tlllWS that
d n lnlllCf' rrm atnx olllMtm t , is .l\ fullows :
In tr.t\"(·l\ou s (i.\,,) (10<;(' Do~, , ~ .
= Clearance ' A UCj ~ ,
6
E,l m\·'l\t'u la r (I'.'·.) ill, S(' F. ~ _
. Dose. ~ .. Clearance '
AUC. ~
7
8
Fo r ('xa rnpll', app m priatt'iy SlJ ltstit ut i ll~ till' an-a 1II(',l' urt'lIlt'n b ill Tahl(· -1-- 1 illto ECJ . S
intl it-,Ilt's tha t the- bioavaila hility of tilt' LIlI . doso is 97'l . Virt ually all dm ~ illjP<.1I"{1 into 11111Sd t, is abs orbed s~~tt' lIlitM.tIly. III contrast. only -16% is btoavailable w hen drug ts ~'1.'1l ondlv in so ilitioll, A'II alll'nlalin ' method of ('stilllatill~ bioavailabthty. w htch ~vt's the- same answer, is to subs titute tilt' vahu- fo r clearance di l1."(1:ly into Ell. 7, Clearance can lx- es tunan-d fmm bloo..1 (or pb,sllla ) data foll()\';I1~ euher an i.v. bolus dose or a constant-rate is . infus ion (C hap . 6 1. Rl'1ut it t, hitl(lt"fli!"I,il ity is dl'l enllille..l w hen the re art' 110 i.v. (lila. Cost, slahility, solu. hility limitations. am i polt'lltial hazards art' major n-asons for the leek of an i.v. p rep aration. Hdati\"l' hi();1' 1tilah ility is det emuued hy ccmp an ng different dosage fon ns . difh-reut routes of admillistrati oll. o r tliffl'n'llt condutons (e .g.. diet. di ~·a...e state ]. As with th e calcula tfou of hi();l\"ailahility. d t'am lll'(' is ;\.ssUIIll'd to I)f.' constant. T hus . I ;lkill ~ the ~1'1U' rall'l'it· :
F" . Dose"
=
Clearance ' AUC"
Amou nl
Totolo mounl
absorbed
ellmlnoted
9
Fe ' Dose e s Clecrcoce . AUCe
10
fA •
11
Relotive _ bioovoilobility Fe
(AUC6XDoseB) AUCB Dose6
TIll' n ·f('n 'II('l' d nsap;l' fnn n d lO'i('lI is uSllall>' th e om' with the highest hioavai lahil it>·, th ai is, tilt' on..' h· o f till' oral doS(' is the n -16%. If on l)" two oral doses had I ~ '(' II ('fllllpart... 1. Ihey nmy havebe... ·11 e-qually, ullx-it poorl y, hio;l\'ail ah lc·. It should I)f.' 1I0h'i.! that all th e p rt'l'l,
CHAPTH 4
Fort unat e ly. tl u-n- is a su ffid l"lll hod y o f dat a to determuu- a t Il'lLst till' I'limi na tio ll halflift· of most drugs. Failure o f food. dosa~t" form , and. in till' I' \iullplt, in Fi~. 4-7. route of ad minist ra tio n to arTt'(.1: Iht· lNlIlillil1hillf-lift' indicatethut th is must ht ' tilt' r-lhmnation halflift". Also . a d nl~ is "ftt'l\ fully bin,lva il,lh l!' (1" = I ) From i.lII. or sllll(.'uta nt't ills silt'S, Ih·m"{·. t'!t·a r.lllt"{· can II(.' (:ak11Iah 'tl k lJ(,,\i ll~ an-a (Efl. 3 ). am lt lw vulunn- o f d ist rih ution t";1II lx' t"sli malt'tl tlIwt,t ht' t·limina tioll Illllf·l ift' is known. Consider. fo r t.xalllp lt-. just tilt' i.lII. dat a in Tahlt, -I-I. C k -arane-, uhlaillt"{l hy t1i,i din~ dost, ( 501l 1ll ~) hy Aue (7.... 1Il ~- hr/L) . is 1.1 Lznun. Di \ldi ll~ dt'amll<."{' by tht, el im inat io n mit ' cous taut ( U. 69.1I 1 ~,) min ) ~\'t 'S tlu- \1111IIIlt' of dhi rih utitlll. in t his t' LSI' :JOll L. Pn...i ons!y. a r.lIlKt· o f likt'!)"ahso rp tioll llillf-livt's W,LS II\lokt l. TI lt' v,llm's wt' n ' t'Sl imalt'l l imlin'(.1:I)· fn nn ptLSlllll t'tlllt'(·nt mtio ll·tilllt' data. Dtn -ct I1lt',LSUn 'llIt'lits uf llhso rp liOlI ktrwt tcs an' illlpos sihlt, ll(.'l.H dllst' p!,Lsma is l ilt· sitt' (If n u-asun-rueut fo r both ilhst lT))tioli a nd di spos itio ll. To calculate til(' kim-tics of absorpnon. a nu-thodmust tllt'n 'fn n ' 1M' dt...i st'(! to Sl'!l;Ir.lh' t hr-se two p n l(.'('sst's. T \\11 n ,lal in ·I>' sim plt, IIlt'tll1Mls for ad lit'\l nK this Sl·llilr.lliflll an' dtscusscd ill Appl,IItIi.\ I-G
Urine Dot. AIoM G in'lI o nl)" uri ne data, m-i tln-r ch-umnce nor \Ullllll(' of drstnbunon l '1lI1 1M' calc ulated. If n-unl c k-anmrx- of t1mK is constant , mi t' u f d m K l'xc n 'titJII is I' ml'urt ion a l 10 its pt L\ llla concentration, ami IIndt' r Ihl 'st' circum stances . thco n-tunllv. excn-tiou mit' dat a can II(.' rrea ted in 1I IlIl11111t'r sim ilar III Iha! fOT pl.uuur dat a. In l' r.tl1:'k t " dllnll~ l ilt' firs t t'tl llt'l 1: io ll o f urme-, usllally I or 2 hr a ftN drug administratinn, ahst lT)ll ioll o f lll,lIIy \\"t'II-a llsm IJt"t1 t1 n lJ.,'S is \irtllillly fiuislll,(1. A shurter t'()IlI'l.1:inn Inn-nul is Ilt't't lt'l] 10 d larat1:e ri v:e- ah st lrp tioll kiuelit."!i hil l is tmpracnca l bl'l.";I1ISt· uf ill('O lllplt'tt, (' lIl pt~i ll ~ o f tilt' hladd t' r and a ll inahility o f it sllhjl'l.i: til p mdll('t' a uriru- s ampk- 1111
1-, ,,. ....
B
'n
10. 11,,· ,\ ["C "p t.."" . II..• tim.· "I" ",:t~lm ·Il,-,· ..f tl ..· I 'i~ ""'1 .." ..., ." . Ir..li< .." c....... n 'Wi", h . ,I,,· 'nl..! .,\ t·C " 1"""""" tl..· .."...."' t .·li ",in...h, 1at I ......
n·I••t,,", h' II,,· l<Jlal .." " ..,,,t ,·l""inat,,1("''t' t' il:. ......1 ).
/ C_
ult i",.d.·~,
6 c
.~
;;;
E 4 u c ~
0
" 2
o
o
3
6 Hours
9
12
CHAJ'T£ ~
os
4
Fe _
Aex F · Dose
12
T1lt'II, Ilsing: lilt' SUhSt'ripts :\ and B to d('noll' IWII treatments, il follows thai Ae,,-•.Jfe
13
Fe ' Doses = A• •.elf•
14
F... • Dose... =
Amount absorbed
t, Fs
g
Ictcl amount elimina ted
(A•..A) . (~) Ae"" s
Dose,.,
15
1111' ",tioof till' dO<;(·-lIonnalir.("I1('u mulatin' mnouut (,:lOl'n '!l"ll um:lmuK("I1is 111t'n·fnn· tilt' ralio uf tilt' hio
mwl ,52 l ll~ ) X IOU], :\o!it" that . ,t~ l'Xpt't11"l1ifJe is con stant, thi s \ -al i li' is th(' S
f'tasma and Urine Dota T Ill' n 'nal dt·;lr.II1(,(· u f a d m g: r-an 1)(· es tilllit!("(1 when bolh plasma an d urine da ta exist. TIlt' app" );\l'h is idt 'nti l";lllo thai taken fur an i.v. dose- (C hap , 3 ). Sinn.' no kllowlt"lI~(· nf hi();,\"ailability is n-qui n-d. til(' ('stimatl' of n 'nal ch-arunce From combhu-d pl.l~lI1a and umndala fol1()\\; ug: t·:l.lm\·;L"l'ular udmitu strunon is us accu rateas that obla illl,(! fnll(}\\; n~ i.v. dmg: ;u Inunivt rollion.
BIOIQUIVAIINCI 1..IWS lIl,mda!! ' th at nt 'W tlnlg: product s ht· Slife and (·IT('l.'lin', If a IlI'W pmt.lul1 of;l t.In1g: lilt' Sl IIl1\ ' Illolar tlo....• and is of sim ilar fonllulat ion to mn- aln-adv sIJO\\1l to 1)(' S
..
C HAPTU 4
In p ml"liet·, C...... um l I ...." a rt" ('slimill("(l [mm till' I li~lu 'sl ('UlIt'\'utm!iull measured and
rlu- linn' uf its occurrence . As till' plasma coucontratiou-time curve is fluitt· flat near thept·ak a ll tl h t"(';lUW uf assay variability. til(> vahn- of t...... dlll'O(' 1I 1ll;1~' nul lx- a ~ull(l "·(In·· v-nta tiou of II\(" act ual value. Furt hermore , thl' iK't.' lr.ll·~" o f tln- t""'. ('s lima!t· is Iilllih.J hy silln plt·s II(' i ll~ o hla illt"tl o nly at d iM-'n'h- times. nillt '(llI j val (,Il('t 'I ('still ~ usually urtses when a pa l(' l\! (Ill an Innovator's dnlJ' ex pi re-s. O ther
manuflu-tun-rs lIlay tlu-u wis h to ma rket tln- sam!' formulanou of tilt ' dnl ~. Formulations thut are hio('(llIi\'a lt'1I1 wuh that of ti lt" innovator a nd ht'ari ll~ till' 1!( 'II t' rit' name o f till' ( I nI~ an' ( -;1111'( 1 ~l'/lI'ric products. Bil)l"(iuiva lt'll t'(, tl"slin~ is also rfomu-d dllrill~ the t'(IIIN' of d t"\t'!"pIlIt'1l1 n f new drugs. wh en a foruurlation is d mll~t'1 l. or wln-n tilt· sitt- n r I1 wlllOtl of tuaunfact un- is a lk n't!.
r"..
STUDT PRDllfMS (Answers to Study Prob lems ore in Appe ndix II .) I dt 'lI ti ~v t'"el. of Iht' stateme nts below tl mt an' corn-et (see- Fi~. 4--.')). For Iht, one. n r mere, that is lint t'OITt't1, st,,!c' wb y it is no l or su pp ly a llualifit'a!inll, a . All utllt'r paramdt,rs n ' ma ini llg tllw hallgt't l. li lt' s!IJ\\'l'r tlu- ahsorpl iull p n l(' '''''s , lilt' h i ~l 1t' r is lilt' peak pl. l.s ma concentration afk r a s i n~lt· oral d n....-. b. :\ fiN a siug!t' oral close. 1II 1 illt'n 'lLS(' in hin; lvlliiahilily t'tlltst'" the pe ak ti me In sllOrtt'll. e. Fur a ~\l' 1I dnl~ in a sllbjt"t'I, ..\ UC is p m)'nrt itllla l to tilt' amount of t1 n l~ abso rbed. d . If kll < < lc , 111t'1I the- terminal slo pt, of tilt' p!;LSIIl'1t'llllt"lltralinll \l 'rsliS tum- t11rVt' n-th-cts «leorpnou . lil lt cluntnatlon. 2. (:ralTlIl'r d al. (( ; m lTllt' r, c., Juhnsso ll. ( ; ., a nti Sji~n' n , J.: I'ha r m;l('l,kill t'l i("S (If prot"1till;llIlitlt' lut ravr-uonslv am i omllv as conventional a nd slow- n-h-asetable-ts. e lin. Pharmacol. 11 1t'r. , / ;'":-114-12.3 . 19 • .'» ), in l'\ltlua ling tlifTt' n 'lI1 dosagt' forms n f p n ){'ltinm nid t', uhla iTlt'11 the fnlt()\\; lIg ,.\ l:C and ('u lIlu lat i\'{' u rine {'u'n..tion {la ta Hste-d in Tahlt' -1- 2 .
I.
T.~"4-2.
eccn .0 0' FOIm,,101>Otl 1 f Ol m,,10110'l '2
cos
-o:
t .«:t HlO 10-48 "'I to-gl
IWOJ'{I
'" 500
("'9"'/1)
13 1
332
1000 1000
200 10 0
586 554
u. E ~ l i llmh' " olh hioi.t\1tilahility a m i rt,lali\"(' hioa ntilability of Iomudatton 2
Irom hnth t', tilt' t!uS!' "t!mi nislt'n'tl ;Int! a ll n tllt'r IMmll ll'h ' n; ( a"ll lll~ f", ktl , \ ', ami C /. ) n ' ma in \l llel.a l\~t"l. l . ptl\lII
.7
Time
Time
a. F dl'('n ',l'>("(l
h. h, Incn-ased c. CI. mcn-av-d. k Increav - dhy ~1I 1l(' (idor d . C l. ck-cn-ased. k d t'('T!,it'>t't ! hv same Iactor r-. v i1wrt'a.'>t'd , k /l; j.( nil st'Il;lrah' O('(;:L"io ns . Tahl(· 4--.1 lists lilt' saltent fi lld in~ o f t ht"w studn-s. Tlu- nu-an wt"ighl uf ti ll:' pa tie uts wa... 60 kg:. T.It•• 4-3. M_.. AU~ Maxi• • • PI. . . . CeIK Iryth p.I I S el DI _ _ a..... I..I .
_.",
I"'!ravenous
3010
Scbcccrecos
1372
'--...::I _
~
"'"""'"
«c
~S!~"TO-'
0
f~
( U
•
~"""""""I'QhfI"'"~nglo _ ., _ ...... I,." I>oc<j ~
wa> "' ''''
COt<EN1lA10'1 .....",
4 17 40 ,5 ><'* H C
~ "'"
~~
C ,
t~
_ ••1HI ' ....1...1H.If·I'" ef 'onowl I.•• olld •.c. A
CO'-.a NTV.!lON
' ''''''' ..,
5 mm b 17.
16,1
" "
"",a,
(>
"""""
8 . .,... 5ctooooalo . M
_
67 ....... col
_~
'--
<>
a. Dd l'0I 1ine tilt' d l'arann ' am i vclunu- o f distribntjon of this d r ug. h . Calt-ulaft· tilt' hill;l\'ailOlhility of ('l)1 hropclic'li n aflN s.c. atl minisl mli o ll in tl.t'....· patk-uts. lI ow lIl i ~hl }UU exphdu }ullr answer? C', Tln- muxin... rn ( 'o ll l '(' ni m tillll o h.st' r\"t"(! wus uun-h Iuw('r after tlw s.c. do...-. II nw dn )',," l" plaill lhis " h >;l: 'I"\'alioll? .5. Clnunn-r uud Holx-rts ( W ~51 stud ic'(l lllt' t'fft '1. 't of del ayt't) (osoplmgt·al trans it O il tluabsor pt iou of ;\c'{·!,"nil lllplwlJ. Ead. o f 20 pati ents ;1\\1Li ti ll~ (~.lR.li 'K· I·llt l.dt·ri7..at iou swalloWt..t1 a single' tahld ('(m ia illilll?: acetaminopla-n ( 5()(). m~) and bari um sulfan-. T Ilt" fin-t J I sllhjt'(:b swa l1ow(... J tll(' lahlt,t while I)i ll ~ t1l 1\\11: in III of these subjects. t ra nsit IIf lilt' ta bid W ,l S d t,la) l,(1. ; l S \i.slIaIi7J'(1 hy lluorosco py. In th e ot he r 9 sllbje<.1: s who swullowt't1 tht' lahlt'! wh ilt' sta lld i n~, it ent er ed the stomach imllll'(liatdy. III both ~rnll p~ tilt' ta bid was ta ken with a snffid t'llt \~ )l tl llw o f wa ter to past" swalltl\\i ll ~. Table 4-1 Ih ts Ih t, a\"t'r.lJ.(t' ph sllla ao-cuutncphen dat a obtatncd ove r 6 lrr a ftl' r s, m lluwi llJ.( tilt"
tahlt'!.
••
CHAPTU 4
T."I.~ .·
o
20 30
40 50
o
50 58 03 47
03 I 1
01 19
28 32 39 31
00
4.1
Q()
3.5 28 22
29
17
18
18 15 075
15
120 150 180 210
"-..c_ _
o
2.1
10
240 300 o--
~ ~ _ ~-..
CJC
17
07
f-'d~~ _ .,..,..-_""'--"""""
n..
~
n- .l7n_
10. 10 85
"l:>.. "'9Jl .. 0
(I .....
a . \ \ "hat d Tt'(.1: do('~ dd ay('(I l's()pl. a~t·al t ransit havl' 0 11 the slx"{'(1 a nd extent ( If ahsorptiou of of this d m~? fl. Bt·sllyah d ul. ( Bt'shya h. S.A., Anyanku . V.• S ilhthya lliUllhiln. n., Sharp , P.• and Joh n. ston . D .( ;.: 111l" d Tt'(:t o f SlIht'ula lU'()IJS injec t ion sitt' o n ah smp tio ll of hu man ~rn\\1 h
hormone: Abdomen \,(' fSUS t hi~lJ . Clin. Endocnnol.• J .5:40H- H 2, H~Jl ) examined the l' lTt"(:1 of s.e. illjl"<.1in!l site Oil III(' absOIvtioli of lm mun ~n)\'1 h hormone. T ah le 4-5 lists till' meun seru m rmrcentrutlons ill I I subjects ohserved dunug the first 12 h r a fle r thr- adnnmstration of ", IU (illte m alio llal u llits ) of bios~l lt ht't i t' hu man ~n)\'1 h hormone. T Ill' t1 nl~ wa.s inj' 't.1t'(I, 011 Sl,'!l
-
AIHI._
1w.E il'-1 "'C!lCNSllf
n "9 h
0
<2 <2
34 10
1
J
55
92
27
27
_
o-wth M_ _ " , 12 .., ,.11.wI.., 1111...
4 ~ 6 J 8 SoIR\.w. CONCf"ITlA l1ONl""""""";
Q
10
II
11
75
74
24
20
28
28
19
14
12 12
10
84 37
"
23
31
20
8
a. Is there informat ion ill l"t'Sl,' data, ~lt'am"(l From graphical llllalysis. 10 SUAAt's l wln-thr-r ab sorpnon or d ispositio n of gn )\\1h ho m lollt' rute-linuts tilt' terminal de. d im'? Brit·lI), d iM-·nss. II. \l allYp n ueiu... Kin 'lI sllIK'uliUlI'llllslynr intramuscula rly a n ' partially d{'g mdt 'tl wi thin Illt· lylIlp ha lit· syste lll bcfon- ft'ad lillg tilt' S~1i h' lll i<: ctreulu tion. C a lt11la te tilt' n-lanvt' hioavu i1ilbility of lilt' dmg aftt'r Sot' . inject ion inlo lilt' Illigli (ft,latiw to ahd olllt"n ). c. T"t' dearmlt't' o f gnJ\\1h honnouc hits been rt1x lr1t'tl in the literatun- 10 a\"{'m~(' about .5 I Jh r. Houghly es tima te tilt' hioil\1ub hility o f tln- dmg fnlll)\\i llg alxlominal s.c. illjt"(1io ll.
4'
CHAPTH 4
;,
I'l ll 'Il~ I t'lhyllll alllll id(' ( I' F. ~ I A ) is Ont' of til(' majo r me-tabolite-s of t ln- anlit'p ilt'plk (In l!!: prtnudom-. As part o f il p r ogr am to ,lSSl'SS the potential use of PEM:\. as an autk-pileptic tim!!: ilst'lL its phannacokine-ncs wert ' stud ied foll(l\\i n~ L\'. and oral adnunistrut lon of :Jon Ill)'!;. Table 4-6 b"l ow lists till' resultan t plasma concentration s in om' suhjt"(1. Also . " I'l- o f till' i.v. doSt" wa.s recovered i llllri1lt' u n ('h'Ul~t,(1.
III' at HMA
eo..c
T.It•• 4-4. PI••_
tI••• f.II_I.,
to .. s.ltl~
on
TWf(lY] , ~
F'Iom'la conc enlrahon
(mg/ll
14 7
o c!
·~""""P'>
O"d ~<"""
...
"""'010 .... 8 272,276 IQ83
0$
007
12 6 24
11,0
I
0-1 a".I. 1
1$
4
6
I.trwtt•• at
10
16
500
J2
24
48
QO 82 7 Q 66 6 2 46 32 23 1 2 3.8 4 2 4 6 8 1 5 8 5. 1 4 I 3 0 2 3 1,3
~.......,.<J~tp[ lMIa1w<:o'Qlatd-.our.cn-_
C"" Pto-
a , From a sl'lIIilogarillullk plol of 111l' p lasma concentrations. estimate till' ehmtnanon hal f-lift· of I' E~ l:\ in lilt· subje-ct . II. Cal{'nlah' tilt' total Av e f()lIo\\ill ~ i.v. and oral administration, c. F ro m tlu- i.v. datu, ('st imalt' Ilu- dt'amm'(' and VO ! U Il l(' o f di slrihutioll of P E ~ I A , d . Cak'ulah ' till' ora l hit);l\"ailahility o f lIlt' dm)?;. e. Cak-ulatt' tlu- n-ual dt'ar.lIll,(' . ,"i. Umdam l ("/ til. (Howbud . ~ I .. Epstein. \ \ '.. and R i {'~t'lman , S.: Ahsorption kinetics o f ).!;rist'o ful\i n in man . J. Phu rm. Sci...57:WH-9S9. 1968 ) ga\'t· grtscofulvtu om lly, 0.5 g: o f a mk'rtllliz("l.1 d mg: fo rmulation and . on anotln-r occ asion intr.t\'('nously. ]lX) 1Il~, III volunte-ers. T I](' ph..ma concentra tkm-tlnu- data ohtaim-d in mn - sllhjt"(1 art' W\'('l1 in T able -t-; lx-low,
T.ltl.4-7. eon rm
""'""
0
" "
OQ8 000 0 80
o
0 4 OQS
'" '"
G<,~""~ Conce
Img/tt
, , , ,
0
11'01
00'
'OJ
r
,. • " " 0"" " 0 . 8 035 OJ'
" "
.. 0 "
000 I OS 090 0 85 080 050
Frmn appmpriatt' plots and cak'ulations, what can lit, {,mdlltlt"l.l [n un tl ll' St,' data with n 'slx'{1 10 : a, Halt· tlf ahslIIvl ioll of griSt"llfuhin with tiuu- 011 orul administrutiou ill this ind hidllal? II, ( ;olllplt,!t·!lt,SS of ahStlrptio n? 9 . l\usl l'llhalldt 'r r-t al. ( 19• .'5) measured plasma phcnytom coucentruttous ufh-r tilt, ad lIl illi ~t ration of St lllium pl J('I\~1 n in inl r.UlluSt.·lIlarly (5(XI 111~) and inlmn 'llollsly (2.'50 lll ~) . Tln- :1\'(·r.I)?;t' data obtahu-d ill 12 Sllhjl'<.1S. each o f \,1IOm rt"('('i\'('{llxJth trcat nn-uts. art' lislt'(l ill Tahl" -t...s'
,.ltl.4-a.1MI"1 Pb"""~",,,~ Conce<>MO'oOf'l
Img/lf
"'""
1~IrO"'lI1(:uIoI~M~
""'W«to
..
He
~
JO
e
~ 0 ...' "
3J
38
ce 08
JQ
H ."Io:G:o.<"',JP
oo.'.,O"d~~oIo"""",.<J~~
'0--0"'\l/l
.
, • e • n " " , o 3. " 0"88 oa " " ,. s a " " " " n... 0
... DG 1liod"-,l"' M >u,.. we . O"d . ..... IB u~'>O. 1075 0.. F'Ion-o
F~.l~.Pooo-
~w
""
oa
......
a. Estimale tl.t' hif