734 CHAPTEn 36
`
`1,0
`
`oa ~
`
`0.6
`
`X
`M,
`OA
`
`0.2
`
`• Olka • ,.,
`
`~!I.• 10
`ka
`
`Fig 36-10. Tho effoot ot difforonoes In the rote ot abaorpllon of
`drugs on the pet1k concontraUon, time of peak concontrallon e.nd
`sojourn In the body. The rate of ollmlnotlon Is tho somo for 1111 curves.
`The dotted line (len = <») Is approxlmntoly what the concentration
`curve would llo, hod the drug boon given lnlravonously. The d8to
`were colculatod from o one-compartment moao1.
`,.
`
`Flo 36-11 . The efloct of dlfltmmces In the rato of ollmlnatlon of
`drugs en the poak concontrotlon, 1lme of penk concontrallon and
`sojourn In th!l llody. The rote of absorption Is tho soma for all curves.
`Tho dlltn woro calculated rrom a one-compartment model.
`
`treated o.a n alngle phcnomenon if the rllLio of k,/k,1 ia con&id- ·
`ere<l rftlher t h on the ~porote rate consW111tJ1 (Fig .36-12).
`Tho uffects illu~trated in Figs 86-1.0 to 36-12 hnve cerl.ain
`cliuicul implicl\tions:
`l)if/erc11ccs iri t/w rnte "' ,1b~u1·1>Liu11 are of more signi/itunce /<>r
`I.
`slowly /./um for m1,idl,v 11/m,rbed tlru(ts, In Pii( 36·10, the penk blood
`lell1lbiore,1~hiovod whon l,. = 2 hr-• (t111 .. O.Sli hr) i-only 13% lower1Jin11
`wh~o> k. "' 20 hr' ( I 112 = 0.035 hr), bull.he di fference int.he lc•el whnn k.
`,. 0,1 hr··1 (iw"' 0.93 hr) ia49o/.loworLlurn tl1nl whon /1 0 .. 0.5 hr·• (tin,.
`1.39 hr), o,on Lho1•f(h 111 tho luUcr 1-hu rnw difforcnco wne l0111, lhon in tho
`IL lo t-hu~ uppnrcnl lhnL difforo11cos in the rnleo~u
`formor <;11mporito11.
`rnt-Os ,imong difforcnL t>r<,duct.a of tho .nmo drug, or that differences in
`~11Mlroi11\.C~l.i110I mot,il11,y, blovd flow, ate, ll'lll)I be ionpurltml, dopcncliug
`upun k.lkd. ')'his point. hns II spccinl rolevonee t.o ~U8tuined-rclcose ftlld
`deJlOl formulot.lnni, With ti n111111Jor or dru!(e, vepuciolly otnong tho
`,uwroctic dn1gs, tho duse with A S\li;l.lliucd-reln11Ao form oftoll ls a1>r>roxi (cid:173)
`mntoly t.ho u,1111(, ll& thnt of o rnpid-roluuae form; thuA, tho foru\or h119 11
`long durntion in the body but yiold8 low blood lovola whon usod in 11
`einglo d030, Exccpl with t.bc init.iol dciso, tho difforoncos uro of lc8$Cr
`imporumco in ti multiple-dose rt.r,imcn. 8m11ll difforoncos in ~ho rnl.o of
`1tb11orpUon of rapidly 0~01botl dtUl!lJ RtO llRunlly of minur significunco.
`2. Whe11 the rule "f aworpti<m it r(lpid ru/atiue ltt that of elimi,w•
`l illn, 1/i// ere,,ces i11 /.he r(I( e of cl[ 111i1111lion (lo 1Wl-11ruut.ly ulf ect the pe,,lt
`cm1t,mtrati<m c<i11,«flt1<c11/. 10 ll si11J(l11 <los11 (com1>1rn1 t.<>1> two corvo• of
`J?if: :ltl-12). 1'hu11, ln 1lUOh inst1111cCR, t.ho tl<lnk 1Ymr,,nl,rntion i~ rolntivol.v
`in~cnsit.ivc to n<>rmol vurin(.ione In thR rulu of oliminuUon. <.:on~cqucnl•
`ly, wiU1 ~ucl, 11 dru~, tho eizeof tho inltinl doao i11 n mulWpln•cl<llJo rogimon
`
`0
`
`0
`
`~
`
`«.I
`Fig 36-12. The offeot ot dllferencoa In the 1·a110, kolk~ (k,Jk. In
`diagram), on the peak conconlratlon, Ume of peak conco,1tmtlol"I Md
`sojourn In tho body. The ordlnato, XIMo, actually reprosGnt tho
`frectlon of a dose that Is In lh8 body, but they are dlroctly proportlonol
`to conoentratlon and thus serve 10 roprosonl concontrotlon. The
`ousclsso can be converted to tlmo by dividing by le,, tho ellmlnotlon
`rote constant (oourtoey, Goldstein, el nl 6).
`
`often mny noi need lo bo diminishod in \Jiu prc,cucc of ronlll or h(,patJc
`impnir111c:11t: howevor, suba0<1ucnt doscR r(•qulro ndjustment.
`3. A r.lwni:e in /.Jr~ lime of pea/I co11e<mlrot.io11 1,r "/ µeu/1 ,•fleet i•
`mually Ml ir1dicatit.on <,/ a ci1<tt1Rf i11 01111 nf or bl/I.II k« 1111cl k .. ,.
`
`Durnti()n of i\ction--The durot.ion of action of n drug is
`refotr.d t.o ib pharmacokinetics in 11 rather complicutcd wAy.
`It is usually shorter thnn the s;ojoum of I.he drug in the body,
`because ll Uireshold, or minimal effective, concentration
`mt1st be reMhed beforo the effect occurs (seo l~ig :36-9), oncl
`the effoct usually ceases when tho p l asmn c:onconiral.ion falls
`bolow the threshold level. In 8 ono-compartment. syst.cm,
`durntion of acLion tends to ho proporl.ionol to log-dose. Jn a
`two-cornpArtment sys tom, it tends to be pro1)ori.iolllll t.o k>g(cid:173)
`dose only when tho site of action is in the cent.ral comport(cid:173)
`ment and tho effective concentrat.ion~ (minimum to muxi•
`mum) are entirely within (.he conc(.\ntrotions found durinu
`the el imination phase. In Fig 36-9, Lhe durotkm of l\ction i6
`3.26 hr with dose D, 4.6 hr with 1.l'>D om! 5.4 hr with 2D; wero
`tho t.hroshold at 6 (dotted line), in~t.ead of 4 (dnahed line),
`the rcapcctivo durntion11 would havo b(ien I.5, :l.25 ond 4.25
`hr. Alt.hough the example in which the thl'oshold fa 6 pro(cid:173)
`vides that the d u ration of action would be displ'oportionate•
`ly prolonged as the doso is increnRed , lhe contrary ia seen
`when tho threshold is ii. Corn1oquontly, im:re<1s1:ng the dos(cid:173)
`age i.~ usually not a f em1ible. way of increasing the durnticm
`of actimi and toxic co11centraU1)11s ore often renched more
`predict.obly thun duration is prolongod.
`With o few drugs, there is 110 1nathcmatically definable
`rolotionuhip between durntion of action Md poreiat.enco of
`tho plnsmu concontrntion, With rcser1>ine, for oxnmpl(l, tho
`effect. outlasts tho sojourn uf the dr.ug, bccou1,e of the deple(cid:173)
`tion of n 11lowly replaceable biologlcnl mediator.•
`Multiplo-Doso Admiulstration- 'l'his refers t.o the ad(cid:173)
`ministration of a succession of doRee ot intervah1 such thnt
`the drug doe.a not leavo the body completoly in each intorvol
`bet woon do11ee. The usual procoduro in a multiple-dose
`regimon is to administer ti drug 1·cpetitively with o const11nl:
`dose intorvul, designotad 'T , with both dose and r chose11 so 99
`t<> maintain the plaenia concen\.r11tion ill U1c thcrapeut:ic
`
`• Careful $tud ice ijhow tJu1l tr11c~ an101mw of ro~c11>l11c In tho hody
`ouLIHsL tho nff~cL and tlu1eluru1.lo11 (Jf net.ion mov bo reln1-<:<I 1.0 t.lui~c t.r11ce
`omount11.
`'rhe~e reKiclunl nom,unt~, howovor, 1\rc much ~mnllor t:hn11 a.ro
`r<iquirl'd tn init.i~to tho CJ1tocholn111i110,dc1>lot.ing oct,icm.
`
`FRESENIUS EXHIBIT 1013
`Page 180 of 408
`
`

`

`13ASIC PMARMACOl{INlfflCS
`
`735
`
`?.O
`
`•
`I
`I
`D• ~I)•~/)• ~l>
`1>, ·k10.im 0 0
`
`{J
`
`--v Aiyn1r,1otc,
`
`/Jl1nu1l
`
`o~-~' - ~ ,.~~w,)
`
`Fig 36·· 13, The accumulation ol drug in tho body during ii regime of mulllt)lo dosing. Dose, 0, Is admlniston .. ><I lntrnvenoosly al intervals. ·, ,
`tiqOOf to the hall-Ille. tlf2, Thu:;, ,iflor i,ncll dos1➔• 1111,i amount in the body. Do, h11s docreusod to holf tho previous peak amount at the time each
`dosa 18 ndmlnlstorod. Whon 1110 cumul1\lod 11mount 111 tho l>otly utter fn)oGtlon reachos 20, tM bocty content will fl11cwuto from 20 to 1/)during
`each dosa lntorval thoroafter. Approximately 6 half .. llvos nro rnqulrnd l>ef(>re this luvollog off (ploleau) Of the:, body content occurs. Tho
`stippled aro~ Is tho m·eo undllr 1110 elimination curve of a single Injection, If no second rloso had be0n givrm. The eross•hfllCllell nre11 is th0 mcu
`under the 011rve during a :ainglo•close Interval. Tho two aroas are eq11al.
`
`fir
`
`7r
`
`nmge. Some feuturcH of H\t('.h rcpet.itivt1 doi1inv. may lrn IHWll
`from t.he cons(.J'U(:t.ion reprntluced in Vir, :16· l!l.
`Acrnmululion<md Plateau. Principfo ..... ff t.hc novice mac\ ..
`er will make hi,; own congtnidion, iL will nid gr(,a(.)y his
`J n tho constrnctfon, {.he
`understnncling of (.h i: i;ubjt\cl..
`amount of dr\1g in t.h(! body, IJ11, is nlou.r.d 11g11in~t t.i me.
`Dose, D, is given rc1wf.il;i11oly, int.r11vono11sly, at intc1rv11I~
`such t:hnt r = t 112, in ol'Cler to focilit,1t.e t he const.ruct.ion,
`'l'he first dose is given al, r = 0; since ii. is given int.rnvenously,
`I.he ntnO\tllt i1.1 I.he b(>dy ri1;es t<> D11 = l essentfolly inst.i1111.11-
`neoualy. lnnneclil.\tely, Dn f'nlls oxponent:iolly wit:h the fir$t•
`orclc1· ldMtfos of Eq I , exc:(ipt. t.h11l whole-body conl.cmt., rnth(cid:173)
`cr thnn Cp, i:qilot-.t.cd. Since r = /,1n ,at:7·, Du'' 1hl); when t he
`next. du~c, D, ill added, it brings the body content, up 1.0 L) +
`1M ) , During coch dose intervi\l, Dll foll:;; (!;,;poMn1,ially t.o
`one-hillf the pi·ovious post.inject.ion pouk. As D11 l'ises nfu,r
`<!flch ndmiuisf,1•ntlon, the rnte (not th<, r11to cmrnt:nnt) of nlim(cid:173)
`illlltion ri:1es proportionately, unt.il event.uully t.hc ;immmt
`eliminatnd during .,. cs:,mnlially c<1u11hi the amo11nl inj<ic:t.cd.
`'l'he maximum und minimum val.ues of D,i, D111mu.1> and
`IJll(,>,i1,J, during r, 1\J)J>roach respedive I\Sym1>tote~. shown on
`tht~nraph. As 1. ·-~ ,o, Dm11101·> .... 2D and nm,,,;111 ... ~ D, Thul;,
`although D,, l111ctuntes bctwocn J)/l(m11xi ,rnd nll(mill), OllCP, t h0
`irnympt:Cltci; me npprm.:imotod cl<>s1ily, Du c.in ho t;hour,h t of
`as having rc:nc:hed u qu11lificd .~/.ect<ly-~ta/.e C<>nclit.ion, nnd
`I.Ju~ pharma<:okinet,ics are s<>met-.imcn called st.ca<ly,st.ate
`l)harmacoki11eUcs. Also, Dh i~ suid t.o huvll reached a pln(cid:173)
`t.iiau. It is important. t.o note t.Jwt thli rote ut which the1
`plote11u is 1·cv.ched ie v.t. exactly the some rilt.e at. which drn11 is
`eliminowd from the borly aft.er n single! d.osc.
`'l'hu$, !,he
`expommtinlly foiling line for I.he elimin11lfon of D {;ivon 11t r
`"'() (hnd no further doses hecn given) is t.lH! mit·t<>r imn1~e tif
`the lim, connecting the scq11enU11I D1w11.,,>s· The! principle
`Uint when the l'Qte of absorption is f os/. c:ompnr<id to the ra/.e
`of 1:.limination (h0 > 511,,1) th<' rat(/ at whid1 ihe multipl{!.·
`drMq #eady statc1 is approaclir.d is d11ter1111'.1wd only /,y II,,/,
`nnd is known as the plateau principle. T his is t.he funda(cid:173)
`mentnl feature of 011e-comp11rt.ment'. mult.iplo-dt>S(l kin <:!t.ics,
`h. obw.1i11s irrm,pe.ctivc of l:he value of r. However, t.hc pla•
`tcnu cooc:1mt.rntim1s do depend upon ·r (!:lee below).
`In l•'il{ :.16-1 :~. the drt.11{ was ndminfattu·ed int.n1v(111ously, so
`tbnt. no t.ime-dc:1>ond<!nt. 11bsorptjon hCld !.o hi; r.,msidored.
`When abisorption is involved, the c,,(11,..., 1 i~ not ni; hi{{h 11~
`
`wit.h in(.rt1VH$(!ular ad1ninistr11tion, but is hlunt:ed nnd occurs
`with 11 lntc,n<:y af1.(,r ndministration that. i,; determi1llicl by h.,I
`h,.,,jwit. os in ~in1Ile-dol!C admini!Strl\l.i(,n. 'f'hli tif)pelH',tncl!. of
`c.he C,,-t.inw cm·vo with multiplc,-do;;(, udmi,iist.rat.ion i"
`shown in l•'ig 3G- l 4. The value of' C1, 1,1i. nny Lime d1JrinR
`mult.iple-dv8e adminisLrnt.ion cnu be calc:ulat.t1d n(:C<>rding t:o
`l◄:q :IO.
`
`wlwre n is the n{.h do~e, 1 i~ t:ll</. do:m,intervnl, t i~ t.lw 1,inrn
`$inlic, the IO$L dose, l) i~ t.he m11i11t<rn1111ce do~u, JY is 1.lw .
`initial m· loaclinu dos~: (sc,e lH:low) 1111d / iii the f'ruct,ion nb(cid:173)
`:ml'lmd (bionvailnhility f1u~tor). WiU1 t.his 1iq1Jnl.ion, C1,.
`rather tlian IJ11, ii; calculatod; howovcr, it. will lw rci1:111led I.lull..
`
`,,.
`I(· ..
`'
`fr)\~f
`
`..
`
`('-.
`'--
`~\.ff
`<·-~L
`
`0 ,•,• ,m >+• - • -• H < ~ - . . . -••"•-·-~•• .. ••••·•"""HO Y '>
`• '-•- ••• .. • .. ~••-••• - • "'•• ••rn ••rn • - -•-•' ·• -•• ••• ....... ~ •--•
`t,
`I
`Fig 36• 14, Tlino course of the I>li1&111a concontratlon of a drug
`adn'1l11istciro<I according to a Mlllliple-dose schodulo. C' (ordinate);
`con<:ontratlon: f (111.)sclssa): Um11: D': inlll11I do\\tJ: D : ,nni,Henanci>
`doso; r : dOS(l•intorvul (equal l o 1112 In this llluMrullon); C' """: mini•
`mum c:oncoi1trntlon uflor i,ach doso (smno as Cp(mmi In loxt) (co111'losy.
`Kr(~Jer .. Thlornor 1
`).
`
`I
`
`FRESENIUS EXHIBIT 1013
`Page 181 of 408
`
`

`

`736 CHAl>TER 36
`
`c:: = Dl\111 , nnd similal'ly, C,, '" O,i/V,1, so t.hnt tho (l(Jlll\tion
`Msily is modified to c11lculnt.o either C,, or LJ1, nml Uw snmc
`pl'inciplc:i npply in cit.hur form.
`lt is import.uni. to knuw how milny ha lf-lives lllll8I. t.l'l\n(cid:173)
`spiro b<!fol'e t.ho plntcsiu i,:; l\))pro11ched <:loi;cly Cll(►l.lgh to be
`considm·od complct~i for prncticnl 1n11·poi1cs.
`'l'h<.! v11luc of
`Di,1111, 111 is approxi11111t<ily 9:1% comphite al-. 4T nnd 9'7% at. 5,-;
`D11im•xl i~ B7% 111. 4r and 08.5'1'~ at fir. T hus, it. mny be stnted
`\.hat, for prn<:tical 1>11rposcs, the platunu 11tut.u is rear.hod in
`ll))J)l'oximat.oly f) lrnlf-livcs, provided h., > M,.,. This is nn(cid:173)
`othor form of tlm plc1frnu pri11<:iple. The pri.nciple applies
`whcmever /.lw st.eady .~I.a Lt! c:ondi.lion~ arc perturbed; that is,
`5 lwlf-limes will bc1 rnquir<!d to read1 a 11.cm, plateau., wheth(cid:173)
`er tho 1>lt1sma eo11c1mtralio11 is rising or foiling to n new
`plnteou ($CO Vi1{ :m-1'1).
`Mo.rimum ond Minimum Conum.t1·a1.fo11s---During mul(cid:173)
`tiple dosing, cj>(IIWY ) 11nd c ,,imin) are cles<:l'ilrnd by Eqs :u and
`32:
`
`whcr() n is t.hc nth dose, C~; is thll concent.rntion Uiot would
`hnvc occurrnd from inst.mt.nneous .ih11orptio11 11nd distribu,
`tion (obtained by <~xtrapolntion of the elimination curvo t.o
`wro Lime) 111l<I t 0 is the absorr>ti<>n time. The t.cmn C): mny
`be r(iploced by /DIV'J. During I.he platcm1 ~t.nt.~, I -· e11k,,,
`hccomci; e··k,,,,, nnd c,,1,,,,,,J and c,,(mi"l tll'll d<lsi{(llll\.(id c~;.,,
`and c;,;1,,, re~pect:ivcly. '!'he cqunl.ion is v11lid only whon h" >
`Mi,,;, It.can be seen that. C,,1m«.,> iii cl<?t~rmined by bot.h h,. and
`h,,1 (h,, shows it8l'lf only indirect.ly, in / . .,) anti C,11,,.,,,, by '1,,1.
`'l'hc ,~rM\.est. diffel'(lllet\ bHWC(!ll c,,1m1t.d and c ,,tmi11l (}C<:tlr$
`whcm t.lw drul( i;; giv,m int rnvenously; when r "' t 1n, uftor
`illl:)'I\VOnou~ injocUon, c,,111mx,/C1,1miuJ t;heo1·ot.icolly i~ cqunl
`to 2. WiUi cxtrnvnsc:ulnr udminii;l.rntion, the rnl:io i~ nlwnyi.
`les!I Lhnn that wiLh intravenoos 11dminist.l'lltio11, (.he rntio
`bc;,inf~ det.0r111ined by 1<1111<,•r• As h,.///,.1 decreases, C//,.,,0_./
`C1,1mi111 cltHW<ln6as.
`Aor.ra11e Goncenf.rntirm ,md 13ody Cont.ent.--.. Thc avcrogc
`concontrotion dudng UlC\ plotcau sta te is d<ii,(!ribed hy Eq 3:3.
`"' . ...l!? ..... = .1
`4
`('
`~ .. ~Y~!l!_
`• ..
`v,,r
`V,i/1,,,T
`The co<ifficicnt IA~ is the rnciprocal of 0.69a in Eq 3. Th0
`t.erm C1, 1,,..,, is 11 timo-nvcrat;ed concent.rntion nnd thcrnf<►l'll
`i3 rNtlly n mean conccntr11tion. Sinc<i C,,"' D11/V,1, it follows
`t.hnl
`
`[wt • vo1- 1]
`
`(:l3)
`
`' f>(av,•)
`
`_ JfJ .. "' 1:.1~ .. ~!ttf I!,
`D
`111,,,,,,) - h,,1•
`T
`
`lw1.1
`
`(34)
`
`It is salf-cvidcml. Uiat the plMmu conc~mtru t:ion, or amount
`of drug iii t ho body, is dirnctly proportioirnl to the fra ction of
`drug nbsorhcd (/, hioavailt1bilit.v fuclo r).
`'l'he appcarn nc~ of
`/ in tlwse equ:1tions nnd Rq 30, howevel', sc,rves as II remind or
`thnt a change from ono druR product. Lo another with a
`d ifferent bio1wnilabilit.y, f, will b~ a<:<:<,mpanied by c,hanges
`in C,,c,w,') und D11(1m..i, Mi well ns in the moxima nnd minimn.
`'J'bc l,quuti(ms nl!:lo renmphosi%c that o change in t112 (01· Ii,,)
`will affect c,,(mw) 01ul D111t11«!)> 111.l other fnctOl'll being held
`eonstnnt.. Sinr.e II.,;/ uml I (und 11ometimes V(, in rnlntion to
`woight.) vor.v from 1>atient. to J)al.it:nt, t.he do~age of certain
`d l'11gs 11lw11ys needs to be ascort11ined wil,h lnbomt.ory na~h,(cid:173)
`tunce mid acumen. The efiocti; ofchonges in,,. ore discu$Bed
`belc)w.
`lmportm1c11 of Dose- l11 t:1'1'1ml ..... .'J'lrn 1·111.io C,,111w.,,/G1,cmi11l
`depend~ on the doi;u .. intcrval, ·,, If tho interval is illl\l'ensed
`
`0
`
`6
`
`9
`
`Minimun, F.fleo.liWl Concc,1t,ot1Qn
`.. ·-··1t-· ...... JIO ....... ,;:i
`I?.
`Time \hours l
`Fig 36-15 . TllO offcct of the doso lntorvnl on the tlme coursa of tho
`plasma concootrat!on of a drug administered In II multlple-do!\o regi(cid:173)
`men. o• = 4, D = 3 nnd k•lk~, = 3. The oose intervo.l is 1. 7 hr in
`Curve 1, 7. 7 tu in Curwl 2 nnct 3.ll hr in Curve 3 (courtesy, Notarl9).
`
`. 24
`
`nnd tha dose is unchonged, c ,,tuwr ), c,,c, ... ·,,, 1)1ld C;,(tw,•J nil
`d!lcrM$C, but C1,(umxi/C,,tmiu) is incronscd. If T is (k!Creasod,
`then C,,1,,, •. ,,, c,,1mit1) 1111d C,,1,,,,,•J incrcnRC, but. c,,(11wxJ/C,,(111i11)
`is dccro11sed. This is i1hown in Fig 36-15. To uvnid n change
`in c,,1. ,,,., consciqmint to II change in 1, Lhe close mny he
`chan1;ed nppr(lpriot.<,ly, in accordance with gqs 32 and :i:1.
`Nevm·Uwlr.ss, (.ho wider fl uc:l.uut.iorn; bat.ween C"tmo,1 tllld
`C,,tmM, wh(ln T ii; lrmgt.licmcd, cannot. be avoided simply by
`adjust ing th e dos,i (see Vig :~6-16, hrokcn lines). If C1,v.,;,,J ,
`rather Llum Cp111,,,;)t is held con~tnnt, the fluctuntfons hccome
`lW81l l11rgc1· (Vil{ :16-16, solid lines), 1111d the hmmrd of the
`
`31+---...\-----1----4----+----I
`&
`
`·~ ! I.) .r 2
`
`0
`cii n:
`
`,. '
`
`I
`I
`
`I
`
`, ,.
`'-..... , ,....
`
`I
`
`t
`'·, ... :
`·,
`
`' •
`' ·,J
`
`1J m,a
`....~j C1
`
`'
`
`\
`',.
`',, ;
`,.
`
`6"''"
`
`2
`
`3
`
`4
`
`5
`
`6
`
`7
`
`Time
`Flo 36-16. FluctuatlO>lS hl tho plruima concontl'atlon ol a drug when
`the ctoso Interval is ch11ngod but the doso Is altel'Od to maintain the
`sarne minimal (solid lines) or 11v0ri19.; (broken lines) concentration
`durfng mi1l11ten911ce. C ':"'' is the minima! conctintration (corre~pond(cid:173)
`lnQ 10 Cll(mll>l In tho tOlCt) ond c;• ts lhll ovorogll concontrotlorl during
`malntooaoco (corresponding to c,.<•••l ln tho toxt). Time Is In multl(cid:173)
`ptos of the half.life (couI1esy, KrOoer•Tl1lomor.1 ndoploel),
`
`FRESENIUS EXHIBIT 1013
`Page 182 of 408
`
`

`

`(:f11)e(;t11.l'ation rcu(:hin1{ the: toxic 1·1rn1t<: i:; intr<?Oiieid. C\111-
`vc1-scly, /./w 1:Jrm1f r!r UH: 1111m.lJer of diui<fod do.~e.~, Lite s1)Wl/11r
`l•'or d1·u1:., wi t h a
`t he fluc/iwl i1m., in plas111<1 cm1r<•11t.rt1Lim1.
`narrow ~hcrnprml.ic 1·11111{(?, it. is u:mully inn<lvi~ahle ~o dni;t• tll
`inuwvol~ lonfror than l-1h• W i l.h digiU,x in, .,-
`is mm:h snrnllur
`thnn L111, ,wd Wio fluct.11111.icms in pl:1~m1\ ccmcen1.,•utio11 ,,re
`consoquunt.ly I<•~ t.han .I 0%. H,)wc,1r.r, for dru({S wit h ll hi1:h
`t.h<1nlJ)l;lll,ic ind<?x und wh ich do nol. n.,quirc II st.ci1<ly plasnrn
`c(Hl(:enl.rntion for tlll odeq11111.c th<1rn p1rnl.i c act.i,rn, dose in-
`1.1:wvolH much larger Limn I-th may Ul' U!!c<l convcnicnUy.
`Pcnici llin G it1 $l1Ch n drug; ii. is more <:un vl'nit?n(. tc) 11ivc lnr,ill
`dosm; nt. 1-hr inl.ul'vals , or longer, l-hun a1. :lO· (.o (lO,min
`inl~rv!llR (t 1t1 ° :10 Lo GO mil)).
`C1111111/r,f.i<m. lfo/.i-u n11<l Am1islenc11 Factor .. - J?rom t.he
`nhovc, i~ b1 evident. ~hot t he cl1·uc( c111n 11l11l.<)<I
`i11 ~he ltocly
`cllu·in!{ I.he rc pel.iliv(! t1clministrnt.ion npjll'Oachcl! difrc1·(,nt.
`onrn11nts (ntiylllp(,)1.os) in t lrn ph11cau sl~1Lc; according t.o the
`nrngnitu<lc of r in roln1.ion W l 112 (or /1,,1). T he dos<,-int.m·val
`must h (i u l=•:inv1mie11t. inl.tffval l.hu(. 111)\. only if! 011:<;y f or Urn
`pnl.il•nt. or mcclicol and piH:1mmlic:1l per1;01111t1l Lo keep t.rn\:lt
`of hut. 11li;o on!l whid1 d1ws no(. s11hj1,ct. the pol i~11 t lo nu
`nnnoyinl{ or difficult. num bm ,,f do~l!ll par dny. Fwt hor(cid:173)
`morc, /,in varies from pti t.ient 10 p11t.ic11t. Cmrnequonl.ly, ii i,;
`rorc when r = I 1r1 , altJ1011gh i i is ,;011rnt.i111cs d ose Oll(lUgh I hnt
`the diffo r~:Jll~(! ir; incons1Jq uonU nl.
`'l'h() rr.f'oro, ii. is importan t
`(.o bu a ble, l.o ,~~Limnl.11 t.he e ~tenl. of cumulRtion wit.h a ny do:tt!
`intcrvol in (Illy palienl- T his 1:.c111 he done wi\.h informal.ion
`derivori from n sin1{lci dc~e. by mc11ns of t.lrn w·c111111tloli1J11
`f11ct.01-, r,,.
`
`r = ·-
`l - e~,,,,.,
`u
`The co1111>mH,nt. l'nc!.o r, e-·I,,.,,, i!! t.he p<•1·siste11cr. fnc;l<,r, r ,
`which ir, t.hc fr11ctio11 by which C,, or nu fa lls durin11 t.he <loi;c
`inu,rvnl. When the pl11(.(im1, m· s lcacly :;l.11L11, is 1·t1111:hod !,Im
`cumulated plasnrn con,:l!nl.rat.ion 0 1· body conl 011(. will bo
`lnri:cr tlum (.hat from t he first dose hy a f11cto1· known as the
`c1m111 /nt.ioll rfllio (or drug lmwun t r<iliv) , R,..
`U,. = ... !- = ~~~.hfl "'.~t (or:'?:!l!)
`IJ,i;1
`Jl,.JT
`( ;
`'7
`whl\re (~~-' is t.hn nrnun conc1m t.ri1t.ion dul'inr, 01m dos111{(! int.er•
`vol du rinr, t ho su,ndy st.111.r. nn(I t•;;· is W111 mci.ln Mlll'.ent.rnt.ion
`from I = 0 tot •~ <» 11rtcr n single: dos1~; Di,, irn,J DiJ,1 i~re l lrn
`C01To8po11ding 1·c,,1)1)ct.ivo body cout.tintl!. Sinco hoth c;~· and
`C;' can be esl.imni.ed frnm t.ho AUC, it Is npproprial.<! W
`discu:;.<; t.his f\1 rthnr.
`Ar1,11 nmi<lr Cu.n:C! (A UC)-···•'l'ho lll'l!ll unclor 1.h11 mononx-
`1>onc,11t.1;1lly fotling, ~in1:lc-dos(! plnsmn conccntrnUon-(.imc,
`curve is the inl<Jt~rnl or ~hu rliffcrcnl.ial form of g<1 I, from t .,.
`0 t.o I .. m;
`
`lno units) {;lG)
`
`,,
`t1 UC"' .... =- <}1 .... == Cllt L
`
`AILho111{h 1.IH1 unit.s nre conccmtrnLion l imes t.ime, (.Im v.iluo i11
`(,qua I t.o t.h(: l,i1no-ov<ir11gr.d co11ctt1\l.1·1ttion 1111d lwncc is calloct
`t lw r,11em,:e concr.ntrntion C;1·, al l.hough it. is moro appropri(cid:173)
`ill.<lly (t log-m e1111 (:onccnlrnl ion. Ir t.lw rmH>1m1. oJ drnfi in
`t.h(i I.Jody ir. used, instMd of' pl(1:;mn co1.1ccnt.rut.ion, t.h(! A UC'
`is C!Q\llll to thC:! li1ne-no11r<1J1ed l>ody v1111t,ml. The avm·u~c
`body r.onlent. COttld, c)f r..1ursCJ, he cnlc:ulnt.(!(l r)'c)m <5; hy
`mnltiplyi nR by l/,1.
`g ve11 when two or more cx1)oncnt.ial proctisses ud. Mldi(cid:173)
`t.ively on t.hc pl1111m11 r.onccnLrnt.ion {or body cont.mil}, £11\ in
`uhsm·pt.ion phtH (!limiM(fon, t.hc-. AUC0 ' " cqt1o l11 <:,.; (M D,'i).
`Tho int.crC!~t,,,.t !!Utdr.n t. m11y verify t.hi~ by intc:14r11t./11g any or
`
`BASIC l'MAHMACOKINl:TIGS
`
`'/37
`
`gqs 28--30. In t.h(, Lwo-<:ompa1·t.1110nl sy,;t.em ( sec; huluw),
`II 11c11 · "" for a plllHll\a COIIC(llltratioll··l.i11rn 1:1,n'V(\ COJ:)'l!Ct.ly
`eq uals <:;;: howtwor, Oj1 c1111not he cnl<;uh*'" from t:;;, he•
`<:011sc 1.hu 1,li1s n111 co11i:en1.rutinn cliffors from 1.hc ,wc:rngl!
`bod.v wncont.ral.ion.
`S i11c(! A UC"'· ••.. "' c;:1k,:1 iii ( he Oll tl •<:ompai· t.m cnt H)'ilklll,
`it h; obvious thn!. AU(, does not. provide ,iny n(•w i11fom111l ion
`t.h,11. o1.hcirwis<: c1111111Jt be:, ,1ht nined, as by bm:k •<?xl.!·npul11t i,m
`(II' rcj!rnimion a nnly:clis. Nevcrt.hel1J~~. I\ UC f'HJ(JUClll,ly is
`w;ed in liou of C¼fh.,. For <Jxumple, in tho rt utJ,nninnt.io n of
`1.lw hio1wnilnhilit,v frwt.or, / , 1.hu A UC'> ·••, art.er ex£rava~('lllar
`udministrnLion (Al.IC~!.,·'•), divided hy the AUC nil.or inlrn •
`va1,cular ndministrntion (AUCR, ''") is Hq uu l l.u / .
`'J'he turm A l /C'<l · ~ is not I.he only A UC th11t mny he: ll!,(!(I
`in phnnnacokim1tics. Thr. A UC dmi111c diff!!rcnt timo int.er(cid:173)
`vnlfi, under i;Up p1)se;dly st.m1dy-s U1t.e condit,ion~, could ho Cll\·
`1>loycd Lo delJ.,cL i.imc• or CCJ11cent.r111:ion-rnlal:od (shnnf(CI. in
`clcu1:unce (Cf(, flCll gqs 11 und 27). During 1.Jw 1>h1l,lllll), <ll'
`sl,l<t1dy ,sl.ut.<1, t.hci A UC du ring (11lt11lol\o int.ervid (A UC" ) ii- of
`,;pcriul inll:rcst. 'l'l> evaluol,e A uc~• .... rcquire$ mnny mim·
`plo!\ tnkon ovur 11 Ion~ 1>ol'iocl of tim(t, which i$ on inrnnvu-
`11im11:e ~o the t>Ub;ic<:t. or pnt.icnl.
`'l'hc vnhw of AUC" c:rn
`p rovido t.lw Sl\ll\Cl dci·ivecl inform1\t.km wit h fowu1· snl\l))l<,s
`and le,;s t in,e_ Thfa is het1n11,c AU<~• •' A UC" ..... Thus, in
`Vil! :l6-1:-I, U\O sUpplt!d arM, w hich ii; AUC11 · - , wou ld he
`l!lllH)l t.o tho cro,;s-hi1ld1ed nrcn, A U(?·' , uxcl1pl. for t.lrn nngli·
`/\t.t "" '" , t he r.wo
`1;iblc ;;t.i1>pfod arnn !,hut r<:mllins a ftci· f>r.
`nr<ms would hci 1li!sa11tinlly iclcnt.ica l.
`ln I.his comparison of
`1 1./Cs, I.ho idr.11t.icnl arnm; do not. nw1111 1.hftt: c;; is iden l i1'nl to
`<.~;, but it. d<111A Clllnhlr. A UC" LO hlHIAl~cl t.o cnl1:ul11t.e valur.s of
`sint:le-dosc• pnrnmcl.crs a nd (lice 1;e1•.~n.
`Ccm.sL<ml I nfusio11 c,nd 811.~t.niiwd lkfoast?-···/\ l,111ist,ml..
`in(usion or nw1tai1wd n1l~i11s<, of n drug moy !)(', i·~i.::nrdc.d as 11
`series of m inido.ws 1iivon nl inf'inil.o)~, sh<ll't, clm,<l inl.lirvals.
`Whm1 inft1Hi<,ll is int.rovai;c11lar, t.h(' plosma conct•nt.ru1i,.,n
`will risll jJ) l<)l(fll'it.hmic fo11hi on wi~h the Ranrn l.inl(! conrsr.
`and t'lU)1 ulol.io11 fnctm· m; wit.11 mul1.iplc dosing, ic, wil.h a rate
`cnnsl.1mt of'//,.,. T hus, thr~ 1>lnt.eou prindple applie-; <•((lt/111,v
`t.o const.nnl. infusion und n,ult.iple d()Ring. After lli:;conl.inu-
`11t.ion 1>f i111'11sion, I.ho pl11sm11 com:entral.ion fnl 1,, (!Xj)c)111<n(cid:173)
`t.ially with :I rnt:<! Mnsumt /1,,1, in m•cordunc!! with g<l I.
`'l'IH!.ijr. pri nciples nm illust.r:1Lud in Pi1.: :!/i-1 7.
`
`r········· --....... ···-·-..
`
`.. _____ ................... --- .. .. .
`
`i :.:: ((_.,.-, ....... ,·---
`
`\
`
`'
`\
`'
`\
`
`..:!·
`Ii
`•,;:
`.,
`0
`~
`...
`& 01•
`~
`,Q
`Q.
`
`\
`K
`'
`\(--··7.303
`
`\
`' \
`\
`\
`
`\
`
`oo,L ___ , .. . ~:-,--- ~- - ~~-..,.--
`
`20
`
`2!.
`
`tO
`\::">
`Time lhrt
`Fi!J 3G• 17. Somllogurltllmlc plot of plosmn conconlral1011 during aml
`ofter <:GtiSlltion of a constant intravenous tnr~r1 of n drng 111 a cno(cid:173)
`co1npor11no11t syijt(!m. Whothor lnlusion Is stoppod prior to lhe at•
`talnn,ont of n 1>l1111mu or ofler, tht! pla$11\II conco11tr111ion will f;.111 IO[I•
`llneady wilh ,, slopo ol ·-0.<13~k.,,.
`In tho fl9uro. I( is k,.,an<I '112.303
`., 0.43'1. c,. Is ,tie steucJy-slntfl cor1centr«ti(1n. C:: (courto$y, (;!(cid:173)
`
`!)
`
`lmlc.11 {ill(! PorrlorO),
`
`I I
`! I
`
`FRESENIUS EXHIBIT 1013
`Page 183 of 408
`
`

`

`738 CHA.PTl:A 36
`
`[wt.• voJ··•]
`
`(38}
`
`The 11tcady-~tate pl11smu c<mc<mtrnLion, C~,'. iH tiqual 1.o the
`infusion ruto divided by the whole body denmncc:
`C" = -uv · "'
`,ro
`Vc1l1,.1
`'' C/1,,,
`where R11 is the iofusion rate. The tel'ln Vt1 111u!lt be t,x(cid:173)
`prci;8ed in t.hu snmc volume unit.fl ns U11; Cl"'' ,rnd N" mu~t. be
`in t.he sntnC! tim() unil-8 u:. /1.,.1•
`Wit.h Sl!Gtllincd-rnlcuse do:mgi, fonm;, in which thll rnlcn,;o
`is approximately c:onstnnt for Jong 1>mfod11 of Limo, the ph11r(cid:173)
`m11cc)ki11el:ici, urc lilrn those of conshmt infui,ion.
`T,uaditl/1 and M(li11,te11<mce.--Jn Pi~ 36-13, Dmm,rxl · • 'lD;
`conscqucnUy, had 2D bcwn given for I.lit< first do:10 and l)
`thereafter, the pl11t1111u condition would h11ve been rcnchnd
`immodiately. This illunrates the pri11dple u/ loading.
`'fhe same effect. of loading is shown hy curve a in Fig 36-14;
`in both (;1\01;(! figures, r ,., t 1ri, The initinl do,;e iB (!Ulled t.Jrn
`loacli11!! dose, D•, and enr.h $Ubsequent do~e ii; culled the
`maini.encmcc dose, D. Since it t-0kes about ii hnlf-liv!ls to
`re1wh the 1>lat.cn11 suite, ii, is vm·y import.illlt to use n loading
`dose with drugs t.hot h11vu long h11Jf.Jivos or in situntio11s in
`which it is dcsirnble t hat. (,he opt.imnl thel'llpcut.ic t,oncent.J'll·
`t.ion be readied rapidly.
`'l'he l011ding dose, D*, sh<,uld t1pproximntc t.he nmount of
`drug in Uw body which will be, contnincd durin(/ mninte(cid:173)
`nnnce {ic, t.he 1>latem1 slate). 1'he moi;t. dirnct wuy to cnl(\\I·
`1.at.e D• is with the equation
`('"
`V
`o· e --.!!..:.~~)
`lwt.J
`I
`assuming thnt v:t and c:;:;{!,wxJ are both known. A firnt doKe
`so cok:ulat.cd achieve~ a t:1, 1..,11, 1 l:hnt is eql11,1 1.0 I.hat. at the
`~tmidy suite only for iMrav1u;cul11r administration. Aller
`<1xlravof\culu1· 11dmini~t.rot.io11 C,,c,,wt) ii; less thnn t.hat. ufuir
`inlravosculnr 11dminist.rntio11 cmd hentie the lo11dior, dose is
`propo1·tioni1l.cl,v smaller. With som(! intrnvasculn1·ly admin(cid:173)
`ist.cred drugM, t.he l011din1t dose is cnlculnled (Mibemtcly to
`be lCf>S t.lum thnt cnlculnted by Bq 39. Among renllons fo1•
`choosing a lower do~o lhnn 1.h11t. c11lcul11tcd by g<l :J9 i:1 that
`the effects of U1e fir11tof' n Aeries of dc,seK ofttm clici1~~ gte1Her
`re~ponacs t.han do subsequent dO$C?-S, becm1ae reflex, hormo•
`nnl and other counter-rngulotory offecl,8 hnve n(lt had
`emrngh time to come 1111.o full piny. This practice applies
`even to some l'.ttrnvaaculnrly t1dminiRtcred drugi;, imch as
`prn:w:,in. Consequently, 75;;'. 01· evtm c;:i,,.,,,1, mny bt\ used i.n
`Ihm of c;:1..,,,,1• lt must be rcmombcred that. with sudi un•
`derloading t.he steady stut.c is nol. achieved fully wi(;h the
`loading dose. With drugs which hove o very low und crrotic
`thernpeutic index and potentially fatnl loKidt.y, the loading
`dose moy be divided into small.er doses, w hll givm111L variouR
`inter\'nls before the first mnint.enance dose; t.hi8 permits
`monit.orinK ofhoth C,, and clinical effects during Jonding nud
`allow~ an asso!l~ment of whothor the intended muinl.cmmco
`dosu ii; cot·roct. J<'ructionnl louding nls(l hi used when n drug
`with n low t.hC!-l'!lf)e11ti(! ind1>x has n 11ignificn11t distribution
`phase, lluch t.hot toKir. plasma concentrat.ions o<,ct1r b(!fol"c
`distribution cquilihl'ium occurs. With some drngs, till up•
`proprinw v:f i8 not known, t.hu1:1 makinl! lsq 39 ino1>Plic11blc,
`With Mich drngn, I)• can be calcul11t.ed i'rnm t:r11dWc111nl,
`empirical maint.enancc do~es by mcons of the equation
`D• "'. - .... ___ n ________ ,
`[wq
`
`c~o)
`
`(1 - e·-lr.,)(l -
`l!-1,,,,,)
`The equotion corrcr.tly applies only when h., > :3h01• Ahm,
`D• can bll cnlcu)nted according t.o
`o~ "' !DIR, = 1A4/l>t112/r
`[wt.)
`where/(, is the cumulntion 1·11tio (8ce J5q a6).
`'l'he tirne com·sc of the plmmltl t\Oncont.rat.ion oft.er d iffer-
`
`{41)
`
`en(. !om.ling do~es is shown in J<'ig ar,. H. When D• "" 2D, the
`1>lat.e,n1 tn11inUmonr.o conccntrntion is 11pp1·oximutcd dos«Jy
`when -r '" t 11~ but is smollcr thun 2 when r < t 1/'l. 1\11d greater
`when r > liti,
`In li'iit 36- I ,J, it. 11houlcl he noted that if I.he loading dose fa
`not optimal, eit.her too low m· ton high, the 1>late11u st.ate is
`n1>1>ronchcd wit.h the sanw time c:our.le ns when no loading
`dO$C ii; given.
`When ll conKtnnt. int.ravenot111 infusion is U$ed, the 1>1-inci(cid:173)
`ple of 101\ding 11111<> npplici;, because the plnt0t1u principln
`01>plies; londing may hcaccompli~hecl with one or more l't\!)id
`intruvcnous doso11, culled bolus<!s m· slugs, or by nn init.ial
`period of rn1>id infusion to bring t.ho p)m,m« concentl'lltion to
`tJ1<1 maintennnce l<!vel. 'J'he londing dos~ 1)1\1\ b(1 colculnt:ed
`from fi:q 30 or the infuf;ion rate and half-1.ime, ns
`,
`Uot112
`D, .. -
`----·· ·
`'
`0A34 log2
`
`!wt.I
`
`(42l
`
`Open Two-Compartment Model
`
`'l'hc <m<.!-cOmp11rtmcnt model adcqua(.(\Jy describ(i~ tho
`pharmocokinctics of mony drugs. Howr.vcr, with nn even
`lm·ger number of drugs, after in1J•11.vM0118 11clmi11ifltmt.ion,
`u,~ decline in plnsm11 co11ccntr11tion is not monO<!Xp<mcnLinl
`but rn ther manifests t.wo or more m<>11oexponcntiol compo(cid:173)
`nent.<; which are disc<lrnible in Urn semilog11rilhmic plol. of C1,
`ver~us time. The most common i~ 11 decline which mnnifost.s
`two components; the op1m t.wo-compartnrnnt model mo~t
`ndc<1u11tllly describes such phormacokintltics. Other models
`hnving morn com1rnrtment.s or other com1>lexitiee will be
`mentioned lat.er briefly.
`Dt:!l!criptic)n of tho ModeJ.--- In thr. open t.wo-compart·
`ment model, t:hc body is considered to com1>rist! t;wo com•
`Pllrl.mcnls in d:vnomic cquilihri\tlll, a~ depicted in l~iK 36-18.
`ThH conwartmcnt inl.o which Uw drug is directly abwrbcd
`,md from which the drul( is t•limi1111tcd i6 called compartment.
`1, or the ccmtrC1l c11111p<ll'/.m.ent.. The blood i11 a pm't of this
`compartment. is the trani;pot'Linl{ and distributing modium
`1md is the modium oct.1111lly snmplcd for chomicnl and phnr(cid:173)
`mncokinctic 1rn11lysi!\; commqucnt.ly, c:ompnrt.mcnt l is some-
`
`Comf)Orlrr,ent 2
`(p~•ipl,~,o1 compo,tmt"t}
`~'?2--.
`iC,
`i
`
`; >
`k11
`0--.,__-,_,t..lJ1 --·
`c, ~·,,..
`
`OUTPUT
`(tWminoHo,d
`
`ComportmeAI I
`(1:qf\fiol tO"'J>Orlml'nH
`Flo 30-10. Diagram ol open two-compartmont pharmacoklnetlc
`modol. An amount of drug, ID, is absorbed lrorn the admlnls tored
`dose, D, with o llrst-ord&r roto coost1mt of k• Into compar1ment 1 ol
`volumo v,. Somo ol the obsorlled dr110 enters comportment 2 with a
`1trst-or<10r rato constant 01 IC,~ ond Is roturnod Into com1,wtmel'II 1 with
`a flrst-ordor ralo constant or k2 ,. o, Is 11\e amount or dr1,1g In
`comportment 1 ancl Dt In compartment .?.; C, (Ind c,. aro mo respec(cid:173)
`tive (.'OncontraUons In compnrtmenls 1 ond 2 (C, ., C,J. Drug Is
`ollminotod lrom compa,tmont 1 with a first-order r11Ie constant, "••
`which, howovor, Is obscurod by tho log In tra,1sfor of drug from
`compartment?. to compartment 1. D., ls lhe amount oJ<croted into
`urine, locos, explrod air, swoot, milk, etc; D., Is the t1mount ol drug
`motabollzod. Tho rotative volumos of V, and V2 may Yary oroolly, V1
`sometimes being the laroer ancl other limes the smallor.
`
`FRESENIUS EXHIBIT 1013
`Page 184 of 408
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`- •rTif' ·--·---;·- m ft7T 111T T WT'T ' :S-WtT'.)"'f['f 'fr ~
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`BASIC PHARMAGQKINETICS
`
`730
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`Limes mhilendingly called t.he hlood or plasma ,~ompmt.mm1t,
`even t.hou1:h t.lw orythrncytmi 01· p)a;;nrn prot.cil)H may ijOfllt!·
`t.iOW$ bd1nve kineLically as tho111{h t.lwy l\'(!r(, Jifll'I. of com ..
`In (.\w simp)