sub title author ito, hiroshi(kose, noriko) 巨勢, 典子
TRANSCRIPT
Title Comparative analysis of partition coefficients in linear and nonlinear eliminating organs withoutmeasuring tissue concentrations
Sub TitleAuthor Ito, Hiroshi(Kose, Noriko)
巨勢, 典子(Nakashima, Emi)Deguchi, YoshiharuBenet, Leslie Z.中島, 恵美
Publisher 共立薬科大学Publication year 2007
Jtitle 共立薬科大学雑誌 (The journal of Kyoritsu University of Pharmacy). Vol.3, (2007. 10) ,p.9- 18 Abstract A new method is derived for the determination of partition coefficients (KP) for well-stirred
physiologic models using residence time concepts. The difference in area under the momentcurve (AUMC)/area under the curve (AUC) between inflow and outflow plasma or bloodconcentrations for specific organ is shown to be a function of a tissue distribution volume, bloodflow rate, and extraction ratio. The method allows the investigator to calculate KP of a tissueand/or organ independent of the mode and route of administration without actually requiringtissue concentration measurements. Although the KP determination method described hereworks only for organs in which distribution and elimination follow linear kinetics, nonlinearitiesobserved in other organs will not compromise the accuracy of the determination in an organfollowing linear processes. It is also shown that addition of a second compound, such asantipyrine, relieves the requirement of determination of organ blood flow. The method wasapplied to determine the KP of a drug, thiamylal, in the rabbit leg muscle and brain. Thecalculated KP values were in good agreement with the values of KP at steady-state determined asthe ratio of measured tissue to plasma concentrations.
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Original PaPer
Comparative Analysis of Partition Coefficients in Linear and Nonlinear
Eliminating Organs without Measuring Tissue Concentrations
HirOShi ItOl), NOrikO KOSel), YOShiharU. DegUChi2), LeSlie Z. Benet3), Emi NakaShimal)*
1)Department of Pharmaceutics, Kyoritsu University of Pharmacy,
1-5-30Shiba-koen, Minato-ku, Tokyo l O5-8512, Japan.
2)Department ofDrug Disposition&Pharmacokinetics, School of Pharmaceutical Sciences, Teikyo University
Suarashi 1091-1,Sagamiko, Sagamihara, Kanagawa 229-Ol95, Japan3)Department of Biopharmaceutical Sciences
, University of Califbmia San Francisco 533 Pamassus Avenue, Room
U-68,San Francisco, CA 94143-0446, USA
(Received July 20,2007;Revised August 20,2007;Accepted August 21,2007)
Anew method is derived fbr the determination of partition coefficients(Kp)fbr well-stirred
physiologic models using residence time concepts. The difference in area under the moment curve
(AしIMC)/area under the curve(/望 σq)between inflow and outflow plasma or blood concentrations
fbr specific organ is shown to be a fUnction of a tissue distribution volume, blood flow rate, and
extraction ratio. The method allows the investigator to calculateκp of a tissue and/or organ
independent ofthe mode and route of administration without actually requiring tissue concentration
measurements. Although the飾determination method described here works only fbr organs in
which distribution and elimination fbllow linear kinetics, nonlinearities observed in other organs
will not compromise the accuracy ofthe determination in an organ following linear processes. It is
also shown that addition of a second compound, such as antipyrine, relieves the requirement of
determination of organ blood且ow. The method was applied to determine the Kp of a drug,
thiamylal, in the rabbit leg muscle and brain. The calculated飾values were in good agreement
with the values of Kp at steady-state determined as the ratio of measured tissue to plasma
COnCentrat10nS.
lNTRODUCTION
Physiologically based pharmacokinetic models
have gained increasing attention(1). This is due in
no small degree to the capacity of such models to
combine infbrmation concerning the distribution,
metabolism and elimination of dnlgs and metabolites
as a fUnction of time, together with blood flows to
*Correspondence to Emi Nakashima, Department of
Pharmaceutics, Kyoritsu University ofPharmacy,1-5-30
Shiba-koen, Minato-ku, Tokyo l O5-8512, Japan.
Phone: ,
FAX:,
e-mail:
particular organs and tissues. However, physiologic
刊ow models are easily simplified into compartmental
systems as demonstrated by Bischoff et al.(2)in
their preliminary analysis of methotrexarate. In this
paper, we combine both physiologic and
compartmental treatments to point out that the
steady-state partition coef且cients between organs
and blood or plasma(Kp), which are required as part
of the physiologic model, can be estimated from
analysis of concentration-time data without actually
requiring a separate measurement of distribution.
Calculations of partition coefficients in organs
exhibiting linear and nonlinear elimination as well as
fbr non-eliminating organs are carried out using
J Kyoritsu Univ Pharm 2007. O Vol.3
ItoHetal.
simulations. Finally, experimental values fbr the
partition of antipyrine and thyamylal into rabbit leg
muscle and brain are examined.
THEORY
With physiological pharmacokinetics, a mass
balance equation in each organ I can be written by
using arterial (Ca) and venous (Ci) plasma
concentration as follows:
K…V…Eli/il・
rRβP・9i・C、 一(RBP・9i+f・ αi。t?・Ci (1)
where it is assumed that the anatomical tissue
volume(玲, the organ blood flow(gi)the organ
tissue to venous plasma concentration ratio(Kpi)and
the organ intrinsic plasma clearance(CLinti)are organ
specific parameters while the blood to plasma
concentration ratio(RB1))and plasma free fraction
ωare organ independent. Note that up to the
present time, physiologic pharmacokinetic models
almost exclusively utilize the venous equilibration
(well-stirred)model to express the relationship
between tissue and venous blood concentrations,
which is the approach we utilize here to estimate
partition coefficients. The approximations required
in utilizing physiologic pharmacokinetics probably
negate any advantages related to the use of other
models relating tissue and venous concentrations, i.e.,
parallel tUbe, dispersion or distributive models.
Taking the Laplace transform of Eq. l yields:
s・Kpi・Vi・ αs,i+XiO
-RBP・9i・ α、,。一(RBP・9i+プ ・CZi。ti)・ α、,i (2)
where aS,、 and aS,i are the Laplace transfbrms of
the equations describing the concentration time
course of drug respectively, in arterial plasma and in
venous plasma from compartment i. Xio is the
amount of drug in tissue i at time O and can be
assumed to be zero fbr an initial dose.
Rearrangement of Eq.2, assuming X io=0, yields:
RBP・9iαs,i= 'αs,a s ・KPi・V
,+RBP・9i+!・C乙i。 、i(3)
Solving fbr area under the curve(Aひ(=)by letting
0 JKyoritsu Univ Pharm 2007. O Vbl.3
s→0
AUCi-lim(、 →o)(a、 ,i)
-lim(・一・)∫》 ・C・dt
Then from Eq.3
㏄GF昭
㎞αヴ君溜ニqσ (4)
The first term on the right hand side of Eq.4is, in
fact, one minus the plasma extraction ratio from the
organ(Ei)
AUCi=(1-Ei)・A UC、 (5)
As we have previously described(3), area under
the moment curve(A UMC)may be determined as
the derivative of as ,i with respect to s,(-as,i)', at the
limit when s apProaches zero:
AUMCi=lim(s→o)(-as,i)'
-lim(・一・)∫♂ ・㍉ ・C・dt
Therefore from Eq.3:
オ㎝鵡
=1'「n(・一・)[(
、.K
RBP・9,・KPi・V,
十 S・KPi・V,+RBP・9,+f・CLi。 、i
Pi・V,+RBP・e,+!・ α
RBP・9i
、。tl)・'as・a
Solving Eq.6as s→0
AUMCi=RBP・9,・KPi・V,
・AUCa
・(一as,a)]
(RBP・2、+f・CL、 。、、)2
RBP・9,十 ・AUMCaRBP・9i+!・ αi
。,i
(6)
(7)
Factoring out a common term from the right hand
side ofEq.7equivalent to、4ひCi, as defined by Eq.4,
yields:
Original paper
AUMCiニRBP・9,・Auc、
・(
RBP・2,+f・CL,。,i
KPi・v,
=AUCi・(
RBP・9i+ノD・ αi。,i
KPi・v,
AUMC十 a
Auc、
AUMC十 a
)
)(8)
measurement of dnlg and antipyrine in arterial and
venous plasma across an organ will yield the organ
tissue to plasma concentration ratio of the drug as
per Eq.12, independent of blood flow and tissue
VOlUme meaSUrementS.
RBP・9,+f・CLi。,i Auc、
Dividing Eq.8by/A UCi and rearranging yields the
mean transit time of drug in organ i, that is:
AUMCi [(
.4uclKPi= AUMC
i [(
.4UCi
AUCaAUMCa ]drug )・RBP・
.4UCiAUC、
・4σCa・4しηMCa ]antipyrine )・RBP・
.4ひCiAUCa
(12)
AUMC, AUMCa
.4ひCi AUCa
since丘om Eq.4:
AUCi
一 κ…v,.Auq
RBP・2, A UCa
1
RBP・9i・AUC、 RBP・9i+プ ・αi。 、i
(9)
(4a)
The equations described above require
measurements over all time(0→ α○)to obtain accurate
estimates of Kpi. It is also possible to use
incremental A UC measurements to obtain such
estimates as described in the appendix. However,
simulations indicated large errors in such
determinations as will be described.
Solving Eq.9fbr Kpi yields the general equation
fbr predicting the organ tissue to plasma
concentration ratio without actually measuring organ
COnCentratlOnS.
AUMC,KPi=( オ㏄
AUMCa
AUCa )・iiE'Sf'9弓器(1・)
For a non-eliminating organ, where there is no
difference between/A UCa(o→ 。。) and A UCi(o→ 。。), then
Eq.10can be written as:
Kpi=( Auc
,
オしiMq AUMG )・AU(1
RBP・9,
塔(ll)
Thus, if it is possible to measure concentrations
exiting a particular organ, it is theoretically possible
to determine the tissue to plasma concentration ratio
in that organ assuming the venous equilibration
model. Equations lO and ll require the
investigator to determine the organ blood flow rate
(2i)and the tissue anatomical volume(Vli). The
former quantity may be especially difficult to
determine accurately in vivo. Therefbre, we have
chosen to carry out studies using antipyrine as a
reference compound since it is known that tissue to
plasma and blood concentration ratios fbr this
compound are l (i.e., Kpi,antipyirne = 1;
RB1)antipyrine=1). Therefbre, when a drug is
administered simultaneously with antipyrine,
MATERIALS AND MEHODS
Simulations A representative physiologic
pharmacokinetic model containing a plasma
compartment, a non-eliminating organ and eliminating
organs exhibiting linear and nonlinear disposition is
depicted in Fig l. In this model the exit concentration
from plasma compartment is equivalent to the
arterial concentration (Ca) used in the theoretical
derivation and i varies from 2 to 4 for the nonlinear ,
linear and non-eliminating organs, respectively.
Simulated concentrations fbr the model described in
Fig l were estimated by the Runge-Kutta-Gill
methods at 28 time points over lOO min fbr doses of
250,2500,12500mg as depicted in Fig 2.
ChemicaIs Thiamylal sodium (Isozole;
Yoshitomi Pharmaceutical Co. Ltd., Osaka, Japan)
and amobarbital sodium(Isomytal;Nippon Shinyaku
Co. Ltd., Kyoto, Japan)were used as generously
supplied. Antipyrine (Wako Pure Chemical
Industries Ltd., Osaka, Japan) and all other
chemicals were of reagent grade and used without
fUrther purification.
Animals Male albino rabbits(2.5-3.5 kg
from Sankyo Laboratory Company, Toyama Japan)
were used fbr intravenous infusion stUdies without
fasting.
a)Rabbit hind leg:The left femoral artery was
cannulated with polyethylene tubing(type No.15;
J Kyoritsu Univ Pharm 2007. O Vol.3
ItoHetal.
Plasma Compartment
Vl 25・mL
RBP 1
50 mL/min
N・nlin・ar-elimin・ting・rg・n 10 mUmin
15 mL
(兀int 2001(10+C2) mL/min
Lmear-eliminating organ
V315・mL
Kp3 3
CLint 2.O mLlmin
Non-eliminating organ
V4200・mL
Kp4 0・2
Fig l
A schematic compartment model for drug and the various elimination processes. Symbol are in the text.
15mI」1min
25ml/min
:i。 。P1-C・mp・ ・tm・nt 1,。 Nonlinea「'elimination o「gan 目 (
警1・・ .._、5..㎎ 甚1・ ,9 糟 )
這 as。。¶9 屋 り 一 目 儒
ゆ り く 、1
5・ es。.。 1 窪 ・el δ ・。1 器 =
・o。1 ・ool
O 20 40 60 ヨ0 100 0 20 40 60 E〔】 100
Time(min) Time(min)
Non-elimination organ Linear-elimination organ
臼 日
量 10。 量 1㎝ ⇔の ◎9 =し =L
) 10 )
目 目 10 0 0
1昌 眉 6 爵
ニロ レ
葛 .. 基 り リ ロ コ
δ 。1 δ
.OO1 .01 0 20 40 巨o 巳0 100 0 20 40 60 so loo
Time(min) Time(min)
Fig 2
Time courses ofconcentration ofthe drug in the fbur compartments. Three different doses were used in the simulation:250,2500, and l 2500 mg.
2 JKyoritsu Univ Pharm 2007. O Vbl.3
Igarashi Ika Kogyo Co. Ltd., Tokyo, Japan)and the
right femoral vein was punctured with a 23 G needle
(Terumo Corporation, Tokyo, Japan) via the
abdominal wall. Thiamylal sodium(10 mg/kg)and
antipyrine(50 mg/kg)were simultaneously infUsed
through a right ear vein fbr lO min. Blood samples
(lmL)were simultaneously withdrawn from the left
femoral artery and the right femoral vein through the
cannula and needle, respectively, at 2,4,7,10,15,20,
30,45,60,90,120min after the start of infUsion.
Plasma samples were separated and frozen at-80℃
until analyzed.
b)Rabbit brain:Catheters were placed in the left
femoral artery and the left internal j ugular vein fbr
blood sampling. PE l O polyethylene tubing(Clay
Adams, Becton Dickinson Company, Parsippany, NJ)
was used fbr the catheterization of the intemal
jugular vein and apProximately O.5 mL blood
samples were collected at the appropriate times. All
other experimental conditions were identical to that
described fbr the hind leg measurements.
Determination of tissue-to-plasma partition
coefficients at steady state(Kpss)
Arep The conventional method was also used fbr
the determination of Kps、 in rabbit hind leg muscle
and brain tissue in each of the animals studied. The
thiamylal solution was infUsed at a rate of 9 mg/hr to
achieve a steady state plasma concentration of lO
μg/mL. After 4 hr, the rabbits were sacrificed and
the tissue from the hind leg muscle and the brain
were quickly excised, rinsed with saline, and blotted.
AnalyticaI procedures Hゆ 緬 ㎜ce
liquid chromatography (LC-6A system;Shimadzu
Co叩oration, Kyoto, Japan)was used to determine the
concentrations of thiamylal and antipyrine in
biological samples. For thiamylal in plasma, a
portion(0.2 mL)of the plasma sample was added to l
mL of pH 5.0, I M phosphate buffer solution
containing 60μg/rnL of amobarbirtal as an internal
standard and vigorously mixed with 2 mL of ethyl
acetate. The mixture was spun in a cenUifUge fbr 5
min at 3500叩m. A l.5 mL portion of the
supemLatant organic layer was separated and
evaporated to dryness under nitrogen. The residue
was reconstitUted with mobile phase, and a 20 FL
aliquot was i功ected onto the HPLC colu㎜
Original paper
(Shim-pack CLC-ODS,6mm×150 mm;Shimadzu).
The HPLC conditions used were:flow rate,1.O
mL/min;wavelength UV 230 nm:mobile phase:60%
methanol in O.OI M NaH2PO4. Peak area
measurements(model CR-3A recorder;Shimadzu)
yielded good linearity over the concentration range
l-50μg/rnL(r=0.999).
For measurement of thiamylal in muscle tissue, a
modification of the method of Stout and De Vane(4)
was utilized. A l g portion of the tissue sample was
homogenized with O.34 M perchloric acid(4 mL).
AO.5 mL portion of the homogenized sample was
mixed with l mL of pH l l.4 phosphate buffer,0.15
mL of O.34 M perchloric acid,0.5 mL of the intemal
standard solution, and 4 mL of ethyl acetate. The
organic layer(3 mL)was evaporated to dryness and
then reconstituted with mobile phase(acetonitrile:
0.4mM KH2PO4=2:3)and inj ected onto an ODS
colu㎜. The HPLC conditions were:flow rate, l
mL/min;UV wavelength 254 nm. Good linearity
was obtained over the concentration range l.56-25
μg/mL(r=0.997).
Antipyrine plasma concentrations were determined
by a modification of the method of Teunissen et al.
(5).AO.l mL portion of the plasma sample was
vigorously mixed fbr l5-30 second with lOμL of
the intemal standard solution,0.4 mg/rnL phenacetin
in ethanol, and 2 mL of dichloromethane:n-pentane
(1:1).After centrifUgation at 4000 rpm for 5 min,
the organic layer(1.5 mL)was evaporated under
nitrogen fbr lO min at room temperatUre. The
residue was reconstituted with mobile phase
(acetonitrile:0.05 M phosphate buffer=1:3)and a
20μLaliquot was inj ected onto an ODS HPLC
colu㎜. The HPLC conditions were:刊ow rate l.O
mL/min;wavelength UV 245 nm. Good linearity was
obtained over the concentration range 3.125 - 100
μ9/mL(r=0.999).
RESULTS
Calculated Kpi values from Eqs.10 and l l fbr the
simulations using the model depicted in Fig l are
given in Table l fbr the 3 different doses utilized.
Excellent
estimates of the Kp values fbr the non-eliminating
(compartment 3)were obtained. The estimate ofKp
f()rthe nonlinear eliminating organ(compartment 2)
was within 2.2%of the theoretical value fbr the low
J Kyoritsu Univ Pharm 2007. O Vol.3 3
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Table l Estimation ofKp values for compartments 2,3and 40f the model depicted in Fig l.
κ
Dose(mg)
Compartment 250 2500 12500 Theoretical
2(Nonlinear)
3(Linear)
4(Noneliminating)
4.89
3.30
0.200
3.34
3.30
0.201
2.45
3.30
0.201
5.0
3.0
0.200
dose(250 mg)simulation. Significant error in the
Kp estimate for this compartment was observed as the
dose increased(Table l). Note in Fig 2 that the
nonlinearity resulting from compartment 2
elimination at the higher doses, causes the
concentration time curves fbr each of the fbur
compartments to exhibit nonlinearities, yet accurate
estimates ofKp for compartments 3 and 4 can still be
obtained. Reasonable Kpi estimates also were
obtained using the incremental area equations
presented in the Appendix but only fbr concentration
measurements obtained very early in the sampling
schedule when arterial-venous di fferences were
relatively large. For the 250 mg dose, estimates of
Kp exhibited less than 5%error using measurements
up to 20 min post dosing fbr compartments 3 and 4,
while up to 5 min fbr the nonlinear eliminating
compartment 2. In contrast fbr the l 2500 mg dose,
estimates of Kp exhibiting less than 5% error
necessitated use of measurements within 5 min of
dosing fbr compartments 3 and 4, while only
measurements in the first 3 min post dosing yielded
accurate estimates ofKp for compartment 2.
Typical femoral artery and venous plasma
concentration profiles of thiamylal fbllowing a l O
(日目\。ω二言
。遍
ち5
昌
。り
儒目
の三自
100
1・筋
1
Artgrv
Ψ口舶 囎
,f
O 60 120
Time(min)Fig 3
Typical femoral artery (口)and venous(■)plasma
concentration profiles ofthiamylal in a rabbit(2.7 kg)following
intravenous infusion of thiamylal(10mg/kg)and antipyrine(50
mg/kg)for lOmin.
min intravenous infUsion to a rabbit are shown in Fig
3.The arterial concentrations fbr the first 20 min
were much higher than the arterial levels. These
results indicate that thiamyhlal is rapidly taken up by
rabbit hind leg muscle tissue and that the drug
exhibits marked arterial-venous plasma concentration
differences. Fig 4 illustrates typical femoral artery
and venous plasma profiles of antipyrine also shows
marked arterial-venous plasma concentration
differences in rabbit hind leg.
Figs 5 and 6 exhibit typical femoral artery and
intemal jugular vein concentration profiles of
thiamylal and antipyrine, respectively. In contrast
to the results shown in Figs 3 and 4, no marked
arterial-venous plasma concentration differences
exist, indicating that pseudo-steady-state is rapidly
achieved in brain tissue.
The experimental parameters fbr thiamylal and
antipyrine necessary fbr the determination of Kp
using Eq.12, as well as the caluculatedκp value and
measuredκp value at steady state fbr thiamylal in
rabbit hind leg are listed in Table 2. The mean
values fbr.∠ ひCa/.4σCi of thiamylal and antipyrine
were slightly lower than unity although not
statistically different from unit》1. Mean transit times
(目目\⇔。ユ言
。嘱驚
ち唱8
ぎ
9
儒目
の儒=
1000
100
10
彊日■■
Arieiy
Venovs
1
0 60 120
Time(min)
Fig 4
Typical femoral artery (口)and venous(■)plasma
concentration profiles of antipyrine in the same rabbit studied in
Fig.3.
JKyoritsu Univ Pharm 2007. O Vbl.3
Original paper
(目目\b幻ユ)昌o欝
』省
8
唱oり
儒∈
器=
100
10
1
Artery
距 船 雌
¶1
0 60 12a
Time(min)
Fig 5
Typical femoral artery(□)and intemal jugular venous(■)
plasma concentration profiles of thiamylal in a rabbit(2.8 kg)
f()llowing intravenous infusion of thiamylal(10 mg/kg)and
antipyrine(50 mg/kg)for l O min.
(目目\⇔⑳ユ)唱o眉捻』芒
8
琴
9
帽目量
店
1000
100
10
Artar)t
Venovs
1
0 60 120
Time(min)
Fig 6
Typical femoral artery(口)and intemal jugular venous(■)
plasma concentration profiles of antipyrine in the same rabbit
(2.8kg)studied in Fig.4.
in hind leg were 21.7±4.5 min fbr thiamylal and
24.1±2.7min fbr antipyrine. The Kp value
estimated using Eq.12(0.62±0.02)was slightly
larger than the measured KpsS value(0.52±0.ll), but
there is no significant difference between them(p<
0.05)fbr this limited set of experiments.
Table 31ists the variable moment parameters and the
estimated and observed Kp values fbr thiamylal and
antipyrine in brain tissue. Mean transit time in brain
tissue was 6.32±2.35 min fbr thiamylal and 7.13±
3.41min fbr antipyrine. These values are much
smaller than those fbund in hind leg. The mean
estimated Kp value using Eq.12(0.96±0.43)was in
good agreement with the mean measured Kpss value
(0.94±0.23),however, the mean value exhibited a
larger coe箭cient ofvariation(45%vs.24%).
DISCUSSION
In physiological pharmacokinetic analysis, the
estimation of Kp values is usually based on tissue
sampling at steady-state in various animal species.
Since the sampling of human tissue is limited, animal
scale-up to humans is the most popular method
utilized to predict Kp values in man. Experimentally,
Kp is determined by measuring tissue and plasma
concentrations at steady-state (6,7)and also under
non-steady-state conditions(8). Gallo etα1.(9)
demonstrated that.4ひC measurements of tissue
concentrations may provide a reasonable estimate of
the partition coefficient. However, in all of these
methods(6-9)an animal must be sacrificed fbr each
tissue-sampling time point. Moreover, many
difHculties arise in correctly assaying drug
concentrations in various tissue samples. In the
Table 2 Estimationκb values using Eq.12 qnd Qbserved KpsS values at . steady state. for thiamylal in rabbit hind legs, together withthe moment parameters of thiamylal afid antipyrine used for the estimation ofKp values.
Parameters 1
Rabbit Number
2 3 mean 土 SD
Thiamylal
R、BP
AしwrCi/AひCi-A UMC、IA UC、(min)
AひC。/AUCi
0.651
16.8
1.05
0.684
25.5
0.841
0.801
22.8
0.863
0.712土0.079
21.7土4.46
0.918±0.116
Antipyrine
AしiMCi/A UCi一4 UMCa/A UCa(min)
AUC。/A UCi
gi略(min'1)
21.6
0.879
0.0527
23.6
1.Ol
O.0420
27.0
0.911
0.0407
24.1土2.71
0.932±0.066
0.0451±0.0066
KPss
0.603
0.619
0.617
0.400
0.641
0.536
0.620土0.019
0516±0.107
J Kyoritsu Univ Pharm 2007. O Vol.3
ItoHetal.
Table 3 Estimated飾values using Eq.12 and observed Kpss value at steady state fbr thiamylal in rabbit brain tissue, and moment
parameters ofthiamylal and antipy'rine'used for the estimation ofKp values.
Parameters 4
Rabbit Number
5 6 mean 土 SD
Thiamylal
RBP
A UMCi/A UCi-AUMC。IA UC。(min)
AUC。/A UCi
0.929
8.99
0.992
0.87
4.56
0.995
0.720
5.41
0.962
0.841±0.108
6.32土2.35
0.983±0.Ol9
Antipyrine
A UMCi/A UCi-AUMC、/A UC、(min)
AUC。/A UCi
gi/Vi(min-1)
8.03
0.878
0.142
3.36
0.952
0.313
10.0
0.814
0.123
7.13土3.41
0.881±0.069
0.192土0.105
路
飾
飾
1.18
0.674
1.24
1.04
㈱
沮
α
1
0.959±0.434
0.940±0.234
method presented here, tissue-sampling is not
necessary and thus the development of an appropriate
tissue sampling technique and the corresponding
standard curve is not necessa「y.
Kety and Schmidt(10)determined cerebral blood
flow rates in man using nitrous oxide. However, this
determination required the fbllowing assumptions:a)
the brain is a homogeneous tissue;b)Kp of nitrous
oxide between tissue and blood is unity, and c)
nitrous oxide is taken by the tissue via a blood flow
limited process. Using Eq.13 developed by Kety
and Schmidt, Kp values in particular organ could be
determined independent of nonlinear disposition
processes which may occur in other organs of the
body.
RBP・9、 ・(AUC。(。 →,)-AσC、(。 →,))KPi= V
i・Ci(13)
Where Ci is the measured concentration of the
drug in the venous outflow from organ i at time t.
Since small Ci value may result in large errors in Kp
determination, Eq.13 is most accurate during the
initial sampling Phase.
Statistical moment theory has been used fbr many
years to determine tissue transit times(ll). Kakutani
et al.(12)applied moment theory to determine Kp for
the in situ perfused hind leg of rabbits using outflow
measurements fbllowing single pass drug perfUsion
of the leg. In the present study, we demonstrate
that Kp values can be determined independent of the
mode of administration using Eq.12, as long as no
drug is present in the system from a previous dose.
Lassen and Perl(ll)defined the"mean transit time
of system"as given in Eq.14 when both inflow and
outflow for the system can be measured over time.
mean transit time of system=∬q。・4弔c諺
熊 ㎝4'熊 ・4'
(14)
We previously showed in a reversible mammillary
model with a single input site, but independent of the
site of input or the type of input process, that the
difference in.4σMCZ4ひC ratios between the central
and a peripheral compartment will yield a measure of
the sum of exit rate constants from that peripheral
compartment(3). For example, consider the
model depicted in Scheme l from reference 3.
For such mammillary models, where there are no
restrictions on site of input or exit, then:
1
万
-
AUMC, A UMC,
Auc, Auc, (15)
where i is a peripheral compartment into which
input does not occur(i.e.1<i≠pin Scheme l)and
thus the mean transit time of system(Eqs.9and l4)
in the physiologic model is equivalent to the sum of
the exit rate constants(Eq.15)in a compartmental
model.
Although the method proposed here to determine
Kp values has many advantages over previous direct
(measure Kpss as in reference 6 and 7)or indirect
JKyoritsu Univ Pharm 2007. O Vbl.3
Original paper
Input into Central
Compartment(i)
\
Input into Peripheral
Compartment(P)
\
/
.-,■■■■
/Scheme l
methods (Eq. 13 and references 8-10), the
calculations are subj ect to the errors inherent in
determining .4 UMC (13). That is, the
extrapolation ofA UMC to time infinity is much more
sensitive to errors in calculating the terminal
disposition rate constant as compared to the AUC
extrapolation. However, it is our belief(although
not exhaustively tested as yet) that calculations
involving a difference in AUMC/A UC measures
versus a single measure as used by Kakutani(12)
may be less influenced by errors in the terminal rate
constant.
In summary, the Kp value in a physiologic model
employing the traditional well-stirred assumptions
can be calculated using Eq.12. A great advantage of
use of Eq.12 is the Kp values can be then calculated
independent of mode of administration.
AUC。(。 →、)RBP・9、+!・ α 、。,、
オ ㏄ 、(。→、) RBP・9,(A2)
Appendix A=Derivation of Eq.13
1ntegrating Eq. l between times O and tl(where Ci
=Oat time=Oand Cl>Oat time=のto obtain
incremental areas under the curve from O to time tl,
AUC(o→tl)・yields:
KPi・V,・Ci-RBP・9i・A UC、(o→t1)
一(RBP・9i+!・ α}inti)・A UCi(o→9)(A l)
Since Cl is also zero at t=oO, it fbllows that:
Dividing both sides of Eq. Al by Vi・Ci and
substituting the ratio of areas over all time fbr the
extraction ratio related te㎜(Eq. A2)yields
K,1ニ V,・Cl・!1ひq(σ→。。)
For a non-eliminating organ where A UCa(o→ 。。)
=AUCi(o →。。), Eq. A3 reduces to Eq.13.
RBP●(鉛(A uc,(o -…)' A uc・(o→・「AUCa(o-…)●Auc,(〔b・))(A3)
ACKNOWLEDGEMENT
This study was supported in part by a Grant-in-Aid
fbr Scientific Research from the Ministry of
Education, CultUre, Sports, Science and Technology
(MEXT), Japan, the Science Research Promotion
Fund from the Promotion and Mutual Aid
Corporation fbr Private Schools of Japan.
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