non compartmental pharmacokinetics

8/19/2019 Non Compartmental Pharmacokinetics

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NON-COMPARTMENTAL PHARMACOKINETIC

MODELLING APPROACH

Submitted by:Rajpreet Kaur Sandeep Kaur M. Pharm. Sem.1st


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PHARMACOKINEICS

Pharma!"#ineti!s is a dis!ip$ine "% s!ien!e dea$in& 'ith the bi"$"&i!a$ %ate "% dru& and("r its metab"$ites inside the b"dy"% man "r anima$ durin& its m")ement 'ithin the b"dy usin& mathemati!a$ m"de$in&.

M"de$ is a hyp"thesis based "n s"me s"und assumpti"ns t"e*p$ain either numeri!a$$y and("r dia&rammati!a$$y the %ate"% dru& inside an anima$ "r human b"dy.

'" imp"rtant aspe!ts "% pharma!"#ineti! studies are:

Drug analysis

Data analysis


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MEHO+S ,OR ANA-SIS O,

PHARMACOKINEIC +AA

MO+E- +EPEN+EN APPROACH

MO+E- IN+EPEN+ENAPPROACH

COMPARMENA-MO+E--IN/

MAMI-AR MO+E-

CAENAR MO+E-

PHSIO-O/ICA-

MO+E-

PER,0SION -IMIE+MO+E-

+I,,0SION -IMIE+MO+E-

NON COMPARMENA-ANA-SIS


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KE PI,A--S O, COMPARMENA-

ANA-SIS

-a!# "% ri&"r"us !riteria t" determine the n". "%!"mpartments ne!essary t" des!ribe the disp"siti"n "% dru&

Hi&h$y sensiti)e t" samp$in& %reuen!y be!ause the n". "%e*p"nentia$s reuired t" des!ribe disp"siti"n depends "n

b"th the timin& and %reuen!y "% samp$in&.

-a!# "% meanin&%u$ phsi"$"&i!a$ basis %"r deri)ed parameters.

M"de$ identi%i!ati"n and parameter estimati"n is %urther

!"n%"unded by )anishin& e*p"nentia$s.


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Need statisti!a$$y s"und estimates "% ea!h s$"pe andinter!ept 'hi!h s"metimes be!"me t"" !"mp$e* %"rdata at hand in mu$ti!"mpartmenta$ ana$ysis.

he same dru& in eua$ d"ses and administered bysame r"ute may need di%%erent m"de$ stru!ture indi%%erent patients be!ause m"de$ used is "ne 'hi!h %itsthe data best.

he same dru& in eua$ d"ses and in the same patientadministered by di%%erent r"utes may need di%%erent

m"de$ stru!ture t" des!ribe their pharma!"#ineti!s.

C"ntd2


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S"3 !"rre!t identi%i!ati"n "% m"de$ be!"mes di%%i!u$tas m"re than "ne m"de$ "% !"mparab$e !"mp$e*ity is!"nsistent 'ith the a)ai$ab$e data.

he basi! assumpti"n under$yin& !"mpartmenta$ana$ysis that b"dy !"nsist "% %e' #ineti!a$$yh"m"&en"us !"mpartments seems t" be unrea$isti! anddi%%i!u$t t" justi%y %r"m phsi"$"&i!a$ rea$ity.

C"mpartmenta$ m"de$$in& ma#e use "% di%%erin& n". "%e*p"nentia$ terms in empiri!a$ mathemati!a$

e*pressi"ns.

C"ntd2


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In hi&her !"mpartmenta$ m"de$s3 !"mp$e*ity "%

mathemati!a$ euati"ns ma#es them di%%i!u$t t"!"mprehend.

+i%%i!u$ty in !"mparis"n "% pharma!"#ineti! parameters'ithin sin&$e studies and bet'een studies "% same dru&.

P"ssibi$ity "% %$ip %$"p phen"men"n %"r dru&s 'ith sh"rter

ha$% $i%e %"$$"'in& n"n4instantane"us administrati"n.

Inabi$ity t" predi!t the per%"rman!e "% !"ntr"$$ed re$easedru& pr"du!ts.

C"ntd2


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N"t suitab$e %"r e*trap"$ati"n bet'een spe!ies "utsidethe measured d"main as the m"de$s are empiri!a$.

N"t suitab$e %"r 5uantitati)e Stru!ture

Pharma!"#ineti! Re$ati"nship 65SPR7 studies.

edi"us dru& !"mputati"n %"r dru&s e*hibitin& n"n$inear pharma!"#ineti!s.

Ca$!u$ated pharma!"#ineti! parameters are hi&h$ym"de$ dependent.

C"ntd2


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A+8ANA/ES O, NONCOMPARMENA-ANA-SIS

Ease "% deri)ati"n "% pharma!"#ineti! parameters by simp$e

a$&ebrai! euati"ns.

he same mathemati!a$ treatment !an be app$ied t" a$m"st

any dru& "r metab"$ite pr")ided they %"$$"' %irst "rder

#ineti!s.

Pharma!"#ineti! !"mparis"n 'ithin studies and bet'een

study is easier as same mathemati!a$ treatment is app$ied t"

a$$ data sets3 and thus3 it is spe!ia$$y use%u$ in bi"eui)a$en!e

studies.


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C"ntd2

A detai$ed des!ripti"n "% dru& disp"siti"n

!hara!teristi!s is n"t reuired.

Easy dete!ti"n "% n"n$inearity.

imin& "% samp$e is n"t as !riti!a$ as in !"mpartmenta$ m"de$ ana$ysis.


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NEED TO DEVELOP NONCOMPARTMENTAL METHODS

Due to criticisms of compartmental approach.

To e!elop a methos of estimatin"pharmaco#inetic parameters that o not

re$uire teious an some%hat su&'ecti!emetho of nonlinear re"ression.


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NONCOMPARMENA-

MO+E--IN/ APPROACH

N "n !"m par t ment a$ m"d e$in& a p pr "a!h pr ") id es a means "% "bt ainin& pr imar y phar ma!"# inet i! par amet er s "% d r u& ' it h"ut usin& n"n$inear r e& r essi"n and p"st u$at

in& unr ea$ist i! assum pt i"ns inher ent t " !"m par t ment a$ ana$y sis.


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9ASIC ASS0MPIONS:System !"ntains at $east "ne a!!essib$e p""$ that is a)ai$ab$e %"r

input and data !"$$e!ti"n.

Other parts "% system are n"t a!!essib$e %"r input and("r data!"$$e!ti"n.

his di)ides the system int" a!!essib$e and n"n4 a!!essib$e p""$.

he 'ay in 'hi!h n"n4a!!essib$e system is des!ribed!hara!teries the n"n !"mpartmenta$ m"de$.

A$$ input and a$$ irre)ersib$e $"sses "!!ur %r"m a!!essib$e

!"mpartment.


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Accessi&le pool

(naccessi&lepool

(nput )enerali*eElimination

Recirculation

Samplin"

)ENERAL +MODEL, -OR THE

NONCOMPARTMENTAL ANALS(S


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he %$u*es "% materia$ in the system that !an depart %r"mthe a!!essib$e p""$ be%"re irre)ersib$y $ea)in& the systemare des!ribed by re!ir!u$ati"n "r e*!han&e arr"'.

here is n" input "r $"ss a$"n& re!ir!u$ati"n arr"'.

Any number "% e*!han&es !an "!!ur %r"m any number "%tissues 'ith"ut reuirin& the identi%i!ati"n "% any

physi"$"&i!a$ stru!tures "r 'ith"ut the need t" assi&n anynumber "% !"mpartments "r any number "% e*p"nentia$st" e*p$ain the p$asma !"n!entrati"n4time data.

C"ntd2


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Central

Accessi&lepool

/ 0

1 n

INPUT ELIMINATION

2

E*!han&e bet'een tissues and

a!!essib$e p""$


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he dru& %"$$"'s $inear( %irst "rder pharma!"#ineti!s.

Superp"siti"n: A!!"rdin& t" this assumpti"n3 'hen t'"

inputs are &i)en simu$tane"us$y then the resu$tant resp"nse'"u$d be the sum "% t'" separate resp"nses. his prin!ip$e is

used t" determine the resp"nse a%ter mu$tip$e d"ses.

ime In)arian!e: A!!"rdin& t" this assumpti"n3 the resp"nse"btained sh"u$d be the same %r"m the d"ses &i)en at di%%erent

times e.&. "ne d"se in m"rnin& and the "ther &i)en in thee)enin& sh"u$d pr"du!e same resp"nses. In "ther '"rds3

pharma!"#ineti!s "% a system d"es n"t )ary ")er the time"% data !"$$e!ti"n.

C"ntd2


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NON COMPARMENA-MEHO+S

Statisti!a$ m"ment appr"a!h

-inear system ana$ysis6-SA7

he re!ir!u$at"ry m"de$


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NON COMPARMENA-

PARAMEERSA!!essib$e p""$ parameters:

8"$ume "% +istributi"n3 8

C$earan!e Rate3 C-E$iminati"n Rate C"nstant3 #

Mean Residen!e ime3 MR

• System parameters:

"ta$ eui)a$ent 8"$ume "% +istributi"n3 8t"tSystem Mean Residen!e ime3 MRs

Mean Residen!e ime Outside the A!!essib$e p""$6Re!ir!u$ati"n ime73 MR"


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ERMINO-O/MOMEN: A!!"rdin& t" Kar$ Pears"n3 M"ment is a

mathemati!a$ des!ripti"n "% dis!rete distributi"n data. In pharma!"#ineti!s 3m"ment is a true estimate "%

pharma!"#ineti! %un!ti"n des!ribin& the entire time pr"%i$e "% p$asma dru& !"n!entrati"n.


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C"ntd2SAISICA- MOMEN: is use%u$ in studyin& the

time re$ated !han&es in ma!r"s!"pi! e)ents. Ama!r"s!"pi! e)ents is !"nsidered as the ")er a$$ e)ent

br"u&ht ab"ut by the !"nstituti)e e$ements in)"$)ed.he !han&e in p$asma !"n!entrati"n "% a dru& 'ithtime is a ma!r"s!"pi! e)ents.

MEAN RESI+ENCE IME: his !an be de%ined asthe a)era&e time spent by the dru& m"$e!u$e in the

b"dy be%"re bein& irre)ersib$y e$iminated %r"m the b"dy.


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C"ntd2MEAN A9SORPION IME: e!hni!a$$y3 MA is the

mean arri)a$ time; that is3 the a)era&e time it ta#es %"r

dru& m"$e!u$es t" enter a #ineti! spa!e 6su!h as the

systemi! !ir!u$ati"n7. H"'e)er3 sin!e the m"st !"mm"n !"nditi"n under 'hi!h MA is determined is a%ter "ra$

administrati"n3 !"mm"n$y re%er t" it as the mean

abs"rpti"n time3 'hi!h is the time dru& m"$e!u$es spend

at the site "% abs"rpti"n.


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C"ntd2

• MEAN RANSI IME 6M7 :

he a)era&e time3 that m"$e!u$es "% a &i)en d"se spend in

#ineti! system.


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MERIS O, SAICICA-

MOMEN APPROACHie$ds simp$isti! m"de$in& 'ith %e'er3 $ess

restri!ti)e3 easi$y )eri%iab$e and rea$isti!

assumpti"ns.

ie$ds simi$ar pharma!"#ineti! euati"ns %"r

dru&s thus %a!i$itatin& !"mparis"n.

Can be used t" dete!t n"n$inearity in the data.


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-IMIAIONS O, SAISICA-

MOMEN APPROACH


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HEOR

he !"n!ept "% statisti!a$ m"ment 'as %irst app$ied inn"n!"mpartmenta$ pharma!"#ineti!s by ama"#a et al. and Cut$erin 1>?@.

Statisti!a$ m"ment the"ry pr")ides a uniue 'ay t" study time4re$ated !han&es in ma!r"s!"pi! e)ents.

A ma!r"s!"pi! e)ent is !"nsidered as the ")era$$ e)ent br"u&htab"ut by the !"nstituti)e e$ements in)"$)ed.

In pharma!"#ineti!s3 !"nstituti)e e$ements are the dru& m"$e!u$es administered int" a!!essib$e p""$ and the ma!r"s!"pi! e)ents are

6residen!e times7 e*it time shared by &r"up "% dru& m"$e!u$es.


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• Ea!h dru& m"$e!u$e is mi*ed 'e$$ and distributes n"n4

intera!ti)e$y and rand"m$y in the b"dy.

• A!!"rdin& t" the statisti!a$ m"ment the"ry3 the dru& m"$e!u$es inthe b"dy are rand"m$y distributed3 and ea!h m"$e!u$e has a !ertain

pr"babi$ity t" be e$iminated at a !ertain time t.

• A mathemati!a$ %"rmu$a des!ribin& the pr"babi$ity "% a dru&m"$e!u$e e*ited at any time is a Pr"babi$ity +ensity ,un!ti"n

6P+,7.

• P+, des!ribes the $i#e$ih""d "% e*it "% dru& m"$e!u$es6residen!e time pr"babi$ity "% a m"$e!u$e in a p"pu$ati"n7 t"

ta#e p$a!e "n a &i)en time.

C"ntd2


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• he pr"babi$ity %"r the e*it "% m"$e!u$es 6rand"m )ariab$e7 t" %a$$ 'ithin&i)en time ran&e is &i)en by inte&ra$ "% m"$e!u$e 6)ariab$es7 density i.e.

C6t7 Bp$asma dru& !"n!. ")er the &i)en time ran&e.

C6t7 in &enera$ 'ritten as %6t7 'hi!h is a!tua$$y e$iminati"n %$u* 6#D"7 here.

9e!ause in %irst "rder rate pr"!ess e$iminati"n %$u* is !"nsidered

pr"p"rti"na$ t" p$asma dru& !"n!entrati"n C6t7 s"3 C6t7 is ta#en as)ariab$es density.6but it may be disad)anta&e in s"me !ases 'heree$iminati"n %$u* is n"t pr"p"rti"na$ t" C6t7.

In this te!hniue er"3 %irst and se!"nd m"ments "% statisti!a$ distributi"n!ur)e are "btained.

In n"n!"mpartmenta$ pharma!"#ineti!s3 p$asma dru& !"n!entrati"n4time!ur)e is !"nsidered as statisti!a$ distributi"n !ur)e.

C"ntd2


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• A0C3 MR 6Mean residen!e time7 and 8R68arian!e "% mean

residen!e time "% dru& in b"dy7 are termed the er"3 %irst andse!"nd m"ment3 respe!ti)e$y3 "% dru& !"n!entrati"n4time !ur)e.

he area under er" m"ment !ur)e 6C"n!. 8s time7 is termed as

A0C.

•he area under !ur)e "% a p$"t "% the pr"du!t "% !"n!entrati"nand time 6%r"m er" time t" in%inity7 )ersus time is "%ten re%erred

t" as the area under the 6%irst7 m"ment !ur)e3 A0MC.

•On$y er" and %irst m"ments are used in pharma!"#ineti!ana$ysis be!ause the hi&her m"ments are pr"ne t" anuna!!eptab$e $e)e$s "% !"mputati"na$ err"r.

C"ntd2


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STAT(ST(CAL MOMENTSIn pharma!"#ineti!s3 a m"ment is true estimate "%

pharma!"#ineti! %un!ti"n des!ribin& the entire time pr"%i$e "% p$asma dru& !"n!entrati"n 6C p7.

Irrespe!ti)e "% r"ute "% administrati"n3 the %irst three 6er" t"

se!"nd7 m"ments are:

En.617

En.67

En.6F7


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,r"m euati"n 13GF A0C3 MR G 8R!an be !a$!u$ated

En.67

En.67

En.6J7


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)RAPH SHO4(N) 5ERO AND -(RSTSTAT(ST(CAL MOMENTS

,r"m: R"'$and M3 "erN. Clinical Pharmacokinetics –

Concepts and

Applications3 Frd editi"n33 p. @?.

5eromoment cur!e

-irstmoment cur!e


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Statistical istri&ution cur!e

The time course of ru" concentration in plasmacan usuall6 &e re"are as a statistical istri&utioncur!e.

• The *enith of fre$uenc6

cur!e 789 represents MRT.

• The s$uare of the hori*ontal

istance &et%een therespecti!e &ases of the*enith an the in:ectionpoints 7σ;9 is VRT.


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C"n!ept "% MR

20

A !"n!eptua$ understandin& !an be &ained %r"m the

%"$$"'in& e*amp$e: Assume a !hi$d re!ei)ed dimes %"rhis birthday and immediate$y p$a!es them in his pi&&y ban#.O)er the ne*t m"nth3 he peri"di!a$$y rem")es 1 "r m"redimes %r"m the pi&&y ban# t" pur!hase !andy. Spe!i%i!a$$y3

F days a%ter p$a!in& the !"ins in his ban# he rem")es dimes3 "n day 1 he rem")es dimes3 "n day 1 herem")es J dimes and "n day F he rem")es dimes. At theFth day a%ter p$a!in& the !"ins in his ban#3 a$$ "% the !"ins

ha)e been rem")ed. Hen!e3 the elimination "% the dep"siteddimes is !"mp$ete. he MRT "% the dimes in the pi&&y

ban# is simp$y the sum "% the times that !"ins spend in the ban# di)ided by the number "% dimes p$a!ed in the ban#.


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C"ntd2

S.no. No. of dimes removed(frequency) Day of removalafter placing Residence time(time spent y

t!e coins in t!epiggy an"#

1 F FLFLFLFLF "r 6F7=1

1 1L1L1L1 "r 617=

F J 1 1L1L1L1L1L1 "r61J7 = 1J

F FLFLFLFLF "r 6F7 =1

"ta$ n". "% dimes =


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/raph I$$ustratin& MR

In n"n!"mpartmenta$ pharma!"#ineti!s3 p$asma dru& !"n!. C6t7 Is ta#en asre$ati)e %reuen!y and !"n!. mu$tip$ied by time 6Ct7 is ta#en as residen!e time.hen t"ta$ residen!e time 6A0C "% Ct )s t p$"t7 di)ided by t"ta$ %reuen!y6A0C "% C )s t p$"t7

C d


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C"ntd2S"3 MR !an be determined %"r any &i)en number "% dru&

m"$e!u$es Ai3 'hi!h spend a &i)en am"unt "% time in the

b"dy3 ti3 as %"$$"'s:


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SI/NI,ICANCE O, MRMean Residen!e ime "% dru& a%ter intra)en"us b"$us

administrati"n pr")ides a use%u$ estimate "% the persisten!etime in the b"dy and thus it is re$ated t" ha$% $i%e.

MRi.). = 1(# G t1( = .J>F(# 3 s" as ha$% $i%e te$$s us ab"ut the

time reuired t" e$iminate "% the d"se; here MRi.). te$$s usab"ut the time reuired t" e$iminate JF. "% the i.). b"$us d"se.

Mean Residen!e ime is a %un!ti"n "% h"' 'e administer the dru&.

MRn.i. 'i$$ a$'ays be &reater than that MRi.)..

S" MRi.). !an be estimated %"$$"'in& "ther r"utes "% dru&administrati"n as %"$$"'s:

MRi.). = MRin% 6(7


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-or urinar6 e


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)RAPH PRED(CT(N) >R(NARE?CRET(ON O- A DR>)


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Methos to etermineNon@NumericNumeric

MEHO+S O +EERMINE A0C


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NON N0MERIC MEHO+S

1./raphi!a$ meth"d

./ra)imetri! meth"d

F.P$animeter meth"d


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N0MERIC MEHO+S

-inear trape"ida$ meth"d

-"& trape"ida$ meth"d Cubi! sp$ine meth"d

Parab"$a thr"u&h the "ri&in

Hybrid meth"d-a&ran&e meth"d


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NON4N0MERIC MEHO+S 1./RA8IMERIC MEHO+: Ca$ibratin& %"r 'ei&ht "% !ur)e

)ersus A0C

+isad)anta&es1. ime !"nsumin&.

. Err"ne"us resu$ts i% !uttin& n"t d"ne a!!urate$y a$"n& !"nt"ursand i% paper is n"t "% uni%"rm thi!#ness.

./RAPHICA- MEHO+: C"untin& "% suares and re$atin& t" A0C.

+isad)anta&es:/i)es "n$y a r"u&h estimate "% A0C.

here is a hi&h p"ssibi$ity "% human err"r


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P-ANIMEER MEHO+A p$animeter is a me!hani!a$ de)i!e that y"u

!an use t" !"mpute the area "% an irre&u$ar %i&urea%ter tra!in& the perimeter "% a s!a$e dra'in& "%

the %i&ure 'ith the tra!in& p"int "n the p$animeter. Ca$ibrati"n is reuired.

he m"st !"mm"n$y used instrument is !a$$ed

the p"$ar p$animeter.


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P-ANIMEER


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N U M E R I C M E T H O D S


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N0MERIC MEHO+S

(I). -INEAR RAPEOI+A- MEHO+:,"r a &i)entime inter)a$ 6t1 t73 the A0C !an be !a$!u$ated as

%"$$"'s:


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C"ntd2 Ad)anta&es:

Simp$i!ity in !"n!ept.

+isad)anta&es:

-inear intrap"$ati"n bet'een data p"ints 'i$$ tend t"underestimate the area 'hen the data %"rm a !"n)e*!ur)e and t" ")erestimate 'hen the !ur)e is !"n!a)e.

Ma&nitude "% err"r depend "n the "s!i$$at"ry nature"% !ur)e3 "r the $a!# there "%3 bet'een data p"ints.

/reater the time inter)a$3 &reater '"u$d be the err"r.

C td


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C"ntd2

7((9 -O/ RAPEOI+A- MEHO+:his meth"d ism"re a!!urate 'hen !"n!entrati"ns are de!reasin&

be!ause dru& e$iminati"n is e*p"nentia$ 6'hi!h ma#es it$inear "n a $"&arithmi! s!a$e7.

,"r a &i)en time inter)a$ 6t1 t73 the A0C !an be

!a$!u$ated as %"$$"'s:

C d


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C"ntd2 Ad)anta&es:

M"st appr"priate 'hen app$ied t" data 'hi!h appear t" de!$inee*p"nentia$$y.

Err"r pr"du!ed is independent "% the time inter)a$.

A!!ura!y is &""d as R""t Mean Suare Err"r 6RMSE7 is sma$$.

+isad)anta&es:

Pr"du!e $ar&e err"rs 'hen in an as!endin& !ur)e3 near a pea#3"r in a steep des!endin& p"$y4e*p"nentia$ !ur)e.


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SP-INE MEHO+

,"r !ubi! sp$ine meth"d:


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C"ntd2 Ad)anta&es:

C"mp$ete sm""thness "% the %itted !ur)e 6as !"mpared t"-a&ran&e Meth"d7.

C$"se t" rea$ity.

Sma$$ a$&"rithmi! err"r s" area !a$!u$ated $ess dist"rtedand m"re suitab$e %"r %urther data ana$ysis.

+isad)anta&e:

Has $ar&e e*!ess )arian!e .

PARA9O-A HRO0/H HE


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PARA9O-A HRO0/H HE ORI/IN MEHO+

Here3 &= aLbtL!tLdtF 6Cubi! p"$yn"mia$7 %"r inter)a$s t" n4 &= aLbtL!t 65uadrati!7 %"r inter)a$s 1 t" n41

Ad)anta&es: Simp$e t" !"mpute 6as !"mpared t" Sp$ine Meth"d7

-ess biased.

/i)es better appr"*. than a sin&$e strai&ht $ine in midd$einter)a$s.

+isad)anta&e:

Has $ar&e e*!ess )arian!e.


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C"ntd2..

App$ied %"r n"n4instantane"us "r e*tra )as!u$ar r"ute "n$y

be!ause in )as!u$ar r"utes there is a de%inite inter!ept.


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H9RI+ MEHO+

rape"ida$ and -"& rape"ida$: In this up t"as!endin& !ur)e $inear trape"ida$ meth"d isapp$ied and then t" des!endin& !ur)e $"&trape"ida$ meth"d is app$ied.

Sp$ine and -"& rape"ida$: In this up t"as!endin& !ur)e $inear sp$ine meth"d is app$iedand then t" des!endin& !ur)e $"& trape"ida$meth"d is app$ied.


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MEHO+S O +EERMINE A0MC

1. -inear rape"ida$ Meth"d

. -"& rape"ida$ Meth"dF. -a&ran&e Meth"d. Hybrid Meth"d

. Parab"$a hr"u&h he Ori&inJ. Sp$ine Meth"d


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EDRAPO-AION O, A0C:

It is uite unpra!ti!a$ t" determine areas under !ur)e and m"ment

!ur)es ti$$ in%inity. Hen!e e*trap"$ati"n is ad)isab$e %r"m the $astsamp$in& time up'ards ti$$ in%inity as per the %"$$"'in&re$ati"nships:

∞−∞ += MM t t AUC AUC AUC λ (

M

M

C AUC t =∞−

∞−∞ += MM t t AUMC AUMC AUMC

EMMM ((M λ λ C t C AUMC t +=∞−

t* is the $ast samp$in& timeC* represents the $ast samp$ed p$asma !"n!entrati"nλ is the s$"pe "% the termina$ $inear p"rti"n "% $"& Cp )ersus time !ur)e


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C d


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C"ntd2Re$ati"n bet'een MR and e$iminati"n rate !"nstant3# %"$$"'in&

i.). b"$us administrati"n %"r dru&s that distribute rapid$y: MRi.). = 1(#

• ,"r dru&s 'hi!h distributes s$"'$y3 MR is a re$ated as:

MRi.). = 1(#Q


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C"ntd2 Apparent )"$ume "% distributi"n at steady state %"$$"'in&

!"nstant rate i.). in%usi"n

Sin!e the in%used d"se is eua$ t" # then ab")e euati"n!an be e*pressed as:

C"ntd


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C"ntd2 Mean Residen!e ime %"$$"'in& !"nstant rate i.). in%usi"n


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C"ntd2 Steady state !"n!entrati"n:

Steady state !"n!entrati"n is a %un!ti"n "% n"n!"mpartmenta$ parameters as %"$$"'s:

Mean Abs"rpti"n ime %"$$"'in& er" "rder input:

Abs"rpti"n ha$% $i%e is &i)en by:

Css#Cl

MA=6(7

t1( = .J>F6MA7

C $ $ ti % MA MI d M+


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Ca$!u$ati"n "% MA3MI and M+

MA6 Mean abs"rban!e time7: B,"$$"'in& n"n4

instantane"us r"ute. MAT = MRT n.i. – MRT i.v.

MI6 Mean input time7: B ,"$$"'in& i.). in%usi"n.

MIT = MRT in. – MRT i.v.

M+ 6Mean diss"$uti"n time7:

M!T = MAT solid – MAT solution

M+ and MA !an e)entua$$y be used %"rin)esti&atin& the in"vitro"in"vivo !"rre$ati"ns.

he Mean Abs"rpti"n ime 6MA7


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he Mean Abs"rpti"n ime 6MA7 MA6 Mean abs"rban!e time7: B,"$$"'in& n"n4

instantane"us r"ute.

MAT = MRT n.i. – MRT i.v.e!hni!a$$y3 MAT is rea$$y the mean arrival time; that is3 thea)era&e time it ta#es %"r dru& m"$e!u$es t" enter a #ineti! spa!e6su!h as the systemi! !ir!u$ati"n7.

he m"st !"mm"n !"nditi"n under 'hi!h MAT is determined isa%ter administrati"n thr"u&h n"n4instantane"us r"ute3 many 6perhapsm"st7 auth"rs "% te*ts and j"urna$ arti!$es re%er t" it as the mean

a#sorption time.

I% it is )ie'ed as abs"rpti"n time3 "ne is !"nsiderin& the time dru&m"$e!u$es spend at the site "% abs"rpti"n. he pr"b$em 'ith thisn"ti"n is that rare$y is this measured. Instead 'hat is measured is

the appearance "% dru& in the systemi! !ir!u$ati"n


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STOCHAST(C

APPROACH

S h i h


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St"!hasti! appr"a!h

Pharmaco#ineticall6= the moment of ini!iualru" molecules throu"h &o6 compartment is"o!erne &6 pro&a&ilit6.

As illustrate= some ma6 hit the tar"et 7Stocha9as all ma6 not "et a&sor&e 7or meta&oli*e oristri&ute or e


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C0 O,, ERROR

he ris# "% err"r in m"ment ana$ysis in!reases 'ith thema&nitude "% e*trap"$ati"n reuired.

,"r a !ase "% 1C9M3'ith "ra$ %irst "rder abs"rpti"n the

p"tentia$ !ut "%% err"rs are indi!ated in the %"$$"'in& tab$e:

Percent of

$ last % $ ma&

Potential Errors in Parameters

AU$MRT 'RT

) * ) *+,) *-,)

+) *+) *.) *+,)

Soft%are reports on noncompartmental pharmaco#inetic


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Soft%are reports on noncompartmental pharmaco#ineticata anal6sis usin" statistical approach

Soft%are Lan"ua"e Applications Auth"r6s7 ear

MO+MOM--- Meth"d %"r statisti!a$ m"ments Chan G @F

-A/RAN ‑‑‑ E*aminati"n "% A0C and m"ments usin&-a&ran&e3 $inear3 $"&4 trape"ida$ "r!"mbinati"n meth"ds

R"!!i G us#" 1>@F

‑‑‑ ‑‑‑ Pharma!"#ineti! ana$ysis based "n the

statisti!a$ m"mentsReitber& et al 1>@

MOM ‑‑‑ Ca$!u$ati"n "% statisti!a$ m"ments in pharma!"#ineti! studies

E%thymi"p"u$"s 1>@>

M IN+‑ ‑‑‑ E)a$uati"n "% pharma!"#ineti! parameters by the m"de$4independent meth"d "%statisti!a$ m"ments

A&a%"n") G Pi"tr")s#ii 1>>1

NCOMP ,ORRAN >>

-inear system appr"a!h


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-inear system appr"a!h

App$ies &enera$ $inear prin!ip$es $i#e de!"n)"$uti"n and

!"n)"$uti"n.

It des!ribes the entire time !"urse "% dru& !"n!entrati"n in b"dy inm"re !"mprehensi)e and dynami! manner.

Appr"a!h !an be used %"r:

Predi!ti"n "r simu$ati"n "% systemi! dru& !"n!entrati"n by!"n)"$uti"n.

Estimati"n "% time !"urse "% dru& abs"rpti"n by de!"n)"$uti"n.

Estab$ishin& in vitro" in vivo !"rre$ati"ns.


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Re!ir!u$at"ry m"de$s

end t" des!ribe dru& disp"siti"n in terms "%repeated !y!$es thr"u&h the b"dy !ir!u$at"ry

systems.

S"metimes ar&ued t" be better than e)en s"!a$$ed physi"$"&i!a$$y based !"mpartmenta$ m"de$s.


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non compartmental pharmacokinetics

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