Download Man versus Beast: Pharmacokinetic Scaling in Mammals

Man versus Beast: Pharmacokinetic Scaling in Mammals
Joyce Mordenti
Received May 19, 1986, from the School of Pharmacy, University of California, San Francisco, CA 94143-0446.
September 23, 1986.
3000-kg elephant. Despite this 10* range in weight, most land mammals
have similar anatomy, physiology, biochemistry, and cellular structure.
This similarity has allowed interspecies scaling of physiologic properties
such as heart rate, blood flow, blood volume, organ size, and longevity.
The equation that is the basis for scaling physiologic properties among
mammals is the power equation Y = aW, where Y is the physiologic
variable of interest, W is body weight, and log a is the y-intercept and b is
the slope obtained from the plot of log Y versus log W. Animals
commonly used in preclinical drug studies (i.e., mice, rats, rabbits,
mnnkpws anri Hnnsl rin not eliminate druas at the same rate that
with physiologic properties that are well described among species, it
seems reasonable to surmise that drug elimination can be scaled
among mammals. Analysis of drug pharmacokinetics in numerous
species demonstrates that drug elimination among species is predict
able and, in general, obeys the power equation Y = aWb. Early papers
on interspecies pharmacokinetic scaling normalized the x- and y-axes to
illustrate the superimposability of pharmacokinetic curves from different
species. More recently, the x- and y-axes have been left in the common
units of concentration and time, and individual pharmacokinetic varia
bles have been adjusted to predict pharmacokinetic profiles in an
untested species, usually humans.
Two approaches to interspecies phannacokinetic scaling
have emerged, an allometric approach and a physiologic
approach. In the allometric approach, pharmacokinetic pro
files in several animal species are described by a pharmacol r i n o t i p m n r l o l f r n t n n fl r t m p n t fl l n r n n n c n m n a r t r n e n t a l ) . a n d
the pharmacokinetic parameters of the model are scaled by
fV>rt nnmnr Qnnotinn V — nW" An ootimoto fnr onrh nhflrrtlfl.
cokinetic parameter in humans is obtained by solving each
nnwpr pmmrinn fnr 7fl ko- Tn this annrnarh. each soecies is
viewed as a whole entity; no attempt is made to give
Accepted for publication
when organ size and organ function are studied as a function
of species body weight. Huxley1 demonstrated that plots of
organ size (Y) versus body weight (W) produce straight lines,
on log-log paper. The equation for this straight line is log Yi
= 6 log W + log a, where 6 is the slope and log a is'the y-,
intercept. The antilog of this equation is the power equation
Y = aW6, and it has come to be known as the allometric
equation.
Adolph2 compiled 33 equations which related quantitative
quantity (i.e., body weight) are related to one another, h
proposed that mathematical interrelationships could be d«
veloped that equate one physiologic property to another a
follows:
Y- .
=
a-W61
(1)
Y2
=
azW62
(5
log W = (log Y-. - log aj/b!
= (log Y2 - log a2)/62 ('
log Yi = log ai + 61/62 dog Y2 - log ag)
Y-. = a-.(Y2/a2)6l/62
Suppose one needs to calculate urine output is a functio
01 water mtaKe. using tne aata in muxe 1 iui-^iiuc uui
(U) and water intake (I), one calculates IK= C-.46I0-93,'
constant for the output of urine to the exponential ra
co:
means that the rate of urine production is less "than the ra
iffiff-infgjraifii-1^
is established by reducing the pharmacokinetics of a drug in g iled data on the weight of principal organs 6
one animal species to physiologically, anatomically, and
, , , , j'. , other mammals (Fig. 1). All primate data fell on a straig.a
eliminating organs; tissue and fluid volumes; blood-to-plas- ,. .* . , ., r„ . . , :,
Jl*a**>*a1[IKW"J|VA'i
physiologic parameter in humans is then substituted into the
ics of the drug in humans is thus obtained.
«f-J*a»i«J:lii>i-f:lulQjl(lf-4-:-JiJ»):M*l.,/M'*W'KB:itl^^^:j#i<^*a^
Physical similarity, in the engineering sense, is dv
criteria of similarity which are obtained by forming qi
mmimmmmmmimmmm
tion among species, to predict drug disposition in an untested
species, to define pharmacokinetic equivalence in various
species, and to design dosage regimens for experimental
animal models.
Physiologic Basis for Pharmacokinetic Scaling
Despite obvious differences in outward appearance, most
land mammals have similar anatomy, physiology, biochemis1028 /Journal of Pharmaceutical Sciences
Vol. 75, No. 11, November 1986
renal blood flow/cardiac output x 100
= 43.06Wo:77/166W0'79 x 100 = 25.9%
where the units of renal blood flow and cardiac output
milliliters per minute and that of weight is kilograms. T
relationship reveals that renal blood flow is approxims
one-quarter of cardiac output regardless of mammali
0022-3549/86/1100-1028^1.0C
© 1986, American Pharmace'uticarAssocieth
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function of body weight on log-log coordinates, the data for
all species except humans fell on a straight line (Fig. 3).
Boxenbaum concluded that the 7-fold difference between
expected antipyrine clearance and reported antipyrine clear
ance for humans made them unique in that they "lacked the
quantitative capacities of other mammalian species," a state
ment which has not been widely accepted.6 When the data
were replotted as unbound antipyrine intrinsic clearance per
maximum lifespan potential (L/MLP) versus body weight on
log-log coordinates (Fig. 4), superposition ofthe pharmacoki
netic data from the different species was achieved.7 Yates
and Kugler8 have presented an alternate hypothesis to
explain why data for humans sometimes appear as outlying
data points on simple allometric plots, specifically, the phe
nomena of neoteny. The effects of neoteny are manifest in
both brain mass and lifespan. As a result of scaling antipy
rine intrinsic clearance of unbound drug across species, using
maximum lifespan potential7 or brain weight,9 the antipy
rine data for humans were brought more closely in line with
that of the other mammals.
For more information on the use of allometry in the
biological sciences, the reader is referred to texts on interspe
cies scaling.610-12
Similarities in Pharmacokinetics
CL .. * 00483 B + 000335
CL ..■ 008I6 B
CL • 008I6
I
02
1
05
I
'
2
1
5
L
I
I
I
I
I
I
12 5 10 20 50 100 200
BOOY WEIGHT (kg)
I
I'll
500 1000
Figure 3—Antipyrine intrinsic clearance in mammals as a function of
body weight. Dashed line is the least-squares fit of nonlogarithmically
transformed data weighted by the factor 1/y2. The solid line is from the
equation fitted using the method of least squares on unweighted,
logarithmically transformed data. Reprinted with permission from ref 5.
Copyright 1980 Plenum Publishing Corp.
1030 /Journal of Pharmaceutical Sciences
Vol. 75, No. 11, November 1986
Goot /f* Mon
20
r = 0.989
10
Monkey
2 2
—
/
.2
/
d .1
•c
=
«
05
-
02
h
01
/
Rabbit %X
i
s
■
s
/ Sheep
/
Dog
p < 0.01
s
f
/
•
Guinea
Rat
(liters
CLum,
=
(0.331
Pig
x
JO
per
«
)
in*
B
MLP)
/
Mouja1/
.005
002
Small mammals can be regarded as true physical models of
large mammals (in the engineering sense ofthe term), and a
formal scheme to describe drug concentration might be
suitable for either. Dedrick et al.13 demonstrated that drug
concentrations in several laboratory animals could be corre
lated as a function of dose and body weight. They plotted
methotrexate plasma (or serum) concentrations from mice,
rats, monkeys, dogs, and humans on one semilogarithmic
plot (Fig. 5a). The pharmacokinetic profiles for the different
0001
01
Pig-/
/
.
■
.. / - '■'■
- «- ■ ■ J- ^
,1
.2
.5
12
5
10
20
50
100
200
Body Weight, B (kg) Y>*-».„
Figure 4—Allometric relationship between intrinsic clearance of r
bound antipyrine per maximum lifespan potential (MLP) and be
weight. Reprinted with permission from ref 7. Copyright 1982 Plenut.
Publishing Corp.
gation ofthe underlying relationships in methotrexate p
macokinetics, the half-life of methotrexate in each sp*
was plotted as a function of body weight on log-log ecu
nates (Fig. 6). The slope of the graph was 0.2 (i.e.,
exponent of W), which is in reasonable agreement with i
value of 0.25 chosen empirically.
These authors were the first to recommend the use
"equivalent time" in the analysis of pharmacokinetic di
obtained from different species. They suggested that cb
elimination could be correlated between species if one ui
an intrinsic biological property (creatinine clearance, bli
circulation velocity, or mean residence time of blood com
nents in the vascular system) as anv equivalent time-scali
factor. This approach is advisable for dynamic systems
cause similarity in these systems does not occur as 1
comparison of simultaneous events. Instead, two dynan
systems are similar at corresponding (but different) instant
of time.15 In other words, two species obeying the sai
dynamics of drug elimination are in a similar temporal sta
at equal instances of intrinsic (biologic) time even though/i
events appear to transpire at unequal rates when measur
with an extrinsic (chronological) time scale.
Boxenbaum7 used data from the same sources as Dedri
et al.13 to calculate the methotrexate plasma .clears
(CLmtx) and volume of distribution (Vdj in five sped
When these pharmacokinetic parameters were plotted aa
function of species body weight on log-log coordinates, bo
were linearly related to body weight. Boxenbaum d
strated the use of engineering dimensional analysis by f<
ing a quotient between the allometric equation for methc
\
<.
v\^"\
v
ft
N
*V
\
^"*-
£ 2 0.081
x\ x
X V \
100
150
200
250
300
350
400
450
TIME AFTER INJECTION, min
0
DIMENSIONLESS TIME (equivalent to minutes in Mon )
200
400
600
800
1000
H
,
1
1
H
'
10
20
30
40
TIME/ (body weight)''**, min/g,/«
Figure 5—-Plasma (or serum) concentrations of methotrexate in the mouse ( ), rat ( ), monkey ( ), dog ( ), and human ( )
after rv or ip injection (the symbols refer to dil °rent dose levels and routes of administration): (a) semilogarithmic plots of methotrexate concentration
versus time and (b) semilogarithmic plot ob ined after normalization of the axes. From ref 13.
trexate clearance (CLMtx) and the allometric equation for
creatinine clearance (CLCr) as follows:
Vd/TBW = 0.859W°-918/0.703W0-963
= 1.22W-0045 = 1.22 (8)
QWCLc, = 10.9W-/8.2W- = 1.33 (7) where yd ^ TBW „ .„ ^ ^ w., h ^^ ^
'here clearance is in milliliters per minute and W is in analysis suggests that methotrexate Vd is 1.22 times larger
_ ilograms.Thus, CZ-mtx is 1.33CLC„ and this relationship is than tota.1 bo(?v water in all species. The residual mass
independent of species and species size. In a sense, all species exponent in this calculation (-0.045) is small and essentially
are alike, excreting methotrexate from their bodies at a rate zero' indicating that body weight has little or no effect on this
rwhich correlates with their physiology. Similar analysis was ratio[performed for methotrexate volume of distribution (Vd) and
total body water (TBW) as follows. Kallynochrons, Apolysichrons, Dienetichrons,
,000r
Pharmacokinetic
Syndesichrons, and the Concept of
Time
Smaller, short-lived animals generally clear drugs from
*
the.ir
bodies
more
rapidly
(chronological
time)
per
unit
body
I
weight
than
larger,
long-lived
animals.
When
drug
removal
? I00- ^———*~ 1S measured according to each species' own internal (biologi| ^ cal) clock, animals tend to clear drugs at a similar pace.7
I ^ ■ Each species is endowed with a distinctive pharmacokinetic
J^——- . clock in accord with its own particular ideal space-time
continuum. Since pharmacokinetic and physiologic events
I
are
correlated
with
body
weight,
it
is
possible
to
use
body
[? , 0 " w e i e h t a s p a r t o f a c o o r d if nu an tcet i o
s yn s. t e m o n w h i c h t o b a s e a t i m e
Consider antipyrine elimination in the human and the dog
(Fig. 7a) The dog clears antipyrine 9 times faster than the
human. The allometric equation for antipyrine clearance in
> * - ' -■ ^ j t h l s e x a m p l e i s C L = 7 7 . 1 W - 0 1 5 . B o x e n b a u m a n d R o n f e l d "
1000
BOOY WEIGHT , g
SSiSSSSSSSSSSSISSS- ^2—SHSir
Journal of Pharmaceutical Sciences /1031
Human Dose =10 mg/kg
076«i , ,, ,—-0009581
c = 9.8ie"'"" +16.ie
"v.n- 723 min
10
C L l — . j t mi
*—
= / min / i. Scj9 m
/min/lco
^
—
Vi =.386 l/kg Vp =.616 l/kg Vss=.612 l/kg
.4
.3
•
.2
^a>. Dog Dose = 0.1 mg/kg
.1
■ V,. c = .06i5e "9* + .\s7e00t7i'
07
^ ^ * ! ^ f y, p = 7 9 . 2 m i n
05
.04
03
.02
.01
007
\
^S^>*1_
V, = . 4 5 8
VB=.629
Vss=.620
CL
l/kg
=
5.5ml/min/kg
^ S V.
D0ia = 0 1 mU/kg
Dot* = 10 mg/kg
V, =0 4581/1.9
V, =0386l/kg
Vp = 0 629 l/kg
Vg= 0.616 l/kg
V„=0620l/kg
Vss = 0 612 l/kg
Cl= 5 5ml/min/kg Cl = 0 59 ml/.
l/kg
^\^
l/kg
^s.
• ^***
005
004
n) l/j(= 79.2 min (dog)
Time (min)
Figure 7—Antipyrine disposition in dogs and humans after rapid iv injection: (a) biexponential antipyrine concentration-time curves and (b)
elementary Dedrick plot of antipyrine data illustrated in Fig. 7a. "Kallynochron": The first element of this neologism is taken from the word "Kallyno,"
a transliteration of the classical Greek word meaning "to beautify, to look becoming, to make clean." The suffix "-chron" comes from "Cronus".
("Kronos"), a word for the Greek God of time. As such, this neologism refers to the time required to clear drug from the body. Reprinted yrith
permission
from
ref
16.
Copyright
1983
The American
Physiological
S o c i e t y.
(
duced by normalizing the antipyrine data as follows: The
plasma concentrations were normalized by dividing each
concentration by dose per unit body weight. And chronologi
cal time was transformed to pharmacokinetic time (kally
nochrons) by dividing it by W115. Boxenbaum called this
transformation an elementary Dedrick plot in honor of Rob
ert Dedrick's pioneering work in interspecies scaling. When
viewed in this fashion, the antipyrine data were superimposable (Fig. 7b).
Similar transformation of chlordiazepoxide pharmacoki
netic data obtained for a dog and a human did not produce
superimposable profiles, indicating that these data are illconditioned for such a plot (Fig. 8a). Further analysis re
vealed that the dog has a greater relative volume of distribu
tion than the human. To account for this difference, the
allometric equation for volume of distribution (W058) needed
to be included in the transformation of each- axis. The
inclusion of W068 in the transformation of the y-axis is
straightforward (i.e., plasma concentration/dose per W^58),
For the transformation of the x-axis, Boxenbaum and Ronfeld16 introduced another unit of pharmacokinetic time, the
apolysichron, which they defined as iVW6' " 6, in which b' and
6 are the allometric exponents relating volume of distribu
tion and clearance to body weight, respectively. In one apoly
sichron, species have eliminated the same fraction of drug
from their bodies and have cleared the same volume of
plasma per kilogram b' of body weight. Obviously, the kallyn
ochron and the apolysichron are equivalent when b' = 1 or
£
Dog - 10 5 kg
Hu non - 89 4 kg
Dow =10 mg/kg
Do * = 0 2 9 9 m g / k g
V, =0 497 l/kg
Vi
01851/kg
= 0330l/kg
V0 =0 762 l/kg
Vo
Vss-0 714 l/kg
V4V = 0 321 l/kg
Cl = 6S 5B°"°
Cl
Cl = 43 9ml/min
Cl
30 5ml/min
Cl = 4 IB ml/mm/kg
Cl
0 34lml/m,n/k»
-65 5B°"°
?j 7 ■
Is
4
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0
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o
3
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"
ca
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0
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0 1
0
07
Cl = 65.5B-0"
a a
V, =1.48B05<
Vp. =191B0<"
OS
VSS=1.72B063
O
10
JO
30
*0
5.0
60
70
Apolysichrons (Tim«/B07S)
Dog lime (minj
Dog Jim. (m,n)
400
loo
Human Time (min)
^!^^^e^^^x
S&5?^^
*£*
ff
ofchtordiatepoxide
plasm*
neologism is from the word "apolysis/a transliteraL oA/h^S^ The ftrst element of thi
release or deliverance from (a thing).". The suffi
1032 /Journal of Pharmaceutical Sciences
Vol. 75, No. 11, November 1986
tion is directly proportional to
f weight. This double transformation, or complex Dedrick
ot, produced pharmacokinetic profiles that were superim>sable (Fig. 8b).
Boxenbaum has defined two additional pharmacokinetic
lace-time continua: dienetichrons17 and syndesichrons.18
lese units of pharmacokinetic space—time are similar to
▶olysichrons except that maximum life potential (MLP,
g. 9) and brain: weight (BW; Fig. 10) are incorporated in
e scaling paradigms.
• Human './,= 723 min B = 70kg
002
.001
0007
•■ Ral 1.4= 70 min B = 0.25 kg
V^***"
"^V^^
■
y
-
=
0.963
X
t'/,=
156min
B
=
50kg
^""""""^""S^-a
=
—i
10
0001
Interspecies Pharmacokinetic Scaling
Sheep
^ " ^ > - ^ \
0005
0002
°
1.039
i
20
i
30
i
40
--^^^
i
m
i
*n
i
Dienetichrons
The collapse of pharmacokinetic profiles from different
animal species into a unique species-independent profile
demonstrates the similarity of pharmacokinetics among spe
cies, introduces the concept of biologic (or equivalent) time in
interspecies pharmacokinetic comparisons, and provides the
foundation for interspecies pharmacokinetic scaling. Two
approaches to interspecies pharmacokinetic scaling have
lometric equations which represent individual pharmacoEaerged,
an allometric
(based
the formulationo.-.of
*iAtir nnrarno+orcA
ariA approach
O TiVi\-air«lnrrif»
(nron
»-a»liinfi«-i--.i'o4-\
, rach (based on the scale-up of physiologic flow models).
Allometric Approach
j The allometric approach to interspecies scaling is a black
Human Time (min)
Sheep Time (min)
Ral Time (min)
Figure 9—Semilogarithmic dienetichron plot for antipyrine disposition in
t*Ji:liNil^/iTitJiBBWIIiumiie^m:it-niun)m^miil,
neologism is from the word "dienec," a transliteration of the classical
Greek word meaning "continuous, unbroken." The suffix "-chron"
comes from "Cronus" ("Kronos"), a word for the Greek God of time. The
prefix comes from the view that space experience and temporal
seauence form an intp.nratpii nnntiniium ArmrHinn in thie \iiaiu tho
entire organism is merely a section of a certain magnitude from birth to
the pharmacokinetic parameters. Frequently, there is no
ed to know the details of drug distribution in many tissues.
t is sufficient to know and be able to control the concentra-
_ ,.._.,„„ ..,„ i.nnmiinaii rnv f/uiv-uiiui l^u-l iiyvi ICI nj.j I icuillll
permission from ref 17. Copyright 1983 Marcel Dekker, Inc.
&
_ •»
. 0 0 3 r*
\ j» 002
-
5 ft
I
^L>
— OOI
« 0005 .
i
Syndesichrons
B295xBW-6'5 x time xlO"2
. 0) 0003
*-*•*>
°»'^
0002
B Baboon
D Dog
C Cynomolgus Monkey
P Pig
S Sheep
{J\ CQ .000071
Q .00005
R Rat
Z Human
F Cow (Friesian Breed)
M Rhesus Monkey
E Horse (Equine)
H Rabbit (Hare)
c
,
Syndesichrons
.
,
-*
JU
5*.
60
B295xBW-6,sx time xlO2
BP /"fc-r^n^o-i Si 'ZS' J transllter3tion of the classical Greek word mea,
Journal of Pharmaceutical Sciences /1033
tion of drug in the plasma. In these instances, the allometric
approach is the method of choice and can be applied to the
data, provided that the pharmacokinetics are first order in
each species, the percentage of protein binding is similar and
linear over the concentration range of interest, the elimina
tion processes are physical (i.e., renal or biliary), and enough
data are available for satisfactory linear regressions.
Numerous examples in the literature demonstrate the
suitability of the allometric equation for predicting pharma
cokinetic parameters in humans. Sawada et al.19 predicted
total body clearance, renal clearance, hepatic clearance,
volume of distribution, intrinsic clearance of unbound drug,
volume of distribution of unbound drug, and elimination
half-life for six /3-lactam antibiotics in humans. Data from
mice, rats, rabbits, dogs, and monkeys were used in the
extrapolations. Discrepancies between the observed and pre
dicted values for volume of distribution and hepatic clear
ance were attributed to differences in the plasma-free frac
tion in each species and uncertain hepatic clearance (the
observed hepatic clearance was calculated as the difference
between plasma clearance and renal clearance, and it may
have included some extrahepatic metabolism).
Sawada et al.20 investigated the effect of species differences
in the extent of protein binding of 10 basic drugs on the
apparent volume of distribution (after distribution equilibri
um) and the ratio of distributive tissue volume to unbound
fraction in the tissue (VT/fuT). Small differences in tissue
distribution of the drugs between animals and humans were
detected, suggesting that uptake by the tissues and binding
to tissue components did not display significant interspecies
variation. Despite this similarity in the tissues, it was not
possible to predict volume of distribution in humans from the
animal data unless the plasma-free fraction was included in
the analysis. Interspecies differences in binding to plasma
proteins were variable and appeared to coincide with the
variable distribution of binding constituents in plasma (i.e.,
albumin, ax-acid glycoprotein, and ^-lipoprotein).
The postdistribution half-lives (ty2) of 10 cephalosporin
and 2 monobactam antibiotics in humans were predicted
from data obtained from mice, rats, rabbits, monkeys, and
dogs.21 This forecasting was accomplished with the allome
tric equation tyz = aWb (Fig. 11). Only one antibiotic,
Observed
(tronge)-
cefotetan, did not scale well among the smaller animals
humans. The disparity between the predicted and observ
half-life values for cefotetan may be the result of tl
antibiotic's existence in tautomeric forms.
The allometric equation was used to establish an empiric
relationship between the pharmacokinetic parameters '
macrolide antibiotics (erythromycin, oleandomycin, and tyl
sin) and body weight.22 Despite agreement between t"
observed and predicted human pharmacokinetic values fi.
erythromycin and oleandomycin, the allometric model di
not discriminate between the pharmacokinetics of these tw
antibiotics in humans. For some compounds, the usefulnea
of the allometric relationship may reside in predictin,
whether large interspecies differences in animal pharmacc
kinetics will translate to meaningful differences in humans
Another area in which the allometric equation may proij|
valuable is the prediction of toxicologic endpoints. Althoug
limited data are available, log-log plots of minimally^ toxi
dose (lethal dose in 10% of small animals and maximui
tolerated dose in large animals) versus weight for man
anticancer agents are linear, meaning that these data ai
well described by the allometric equation23 (Fig. 12). I
general, small animals require larger doses to approximat
the lethal dose in humans. If toxicity is due to a metaboliti
the converse may be true24; however, without some inform'
tion about the bioactivation and degradation process in eac
species, it is more difficult to extrapolate toxicity data f(
compounds that undergo metabolism. |
The allometric approach can be used to predict entii
pharmacokinetic profiles for humans from animal dati
These predictions are obtained as follows:
1. Determine discrete pharmacokinetic parameters fc
the drug in young adult animals of four or mca
species (compartmental or noncompartmental metl
ods can be used).
2. Perform linear regression analysis on the relatioi
ship log pharmacokinetic parameter versus log, we;gi
to obtain allometric equations for each parameter .(.
necessary, longevity, brain weight, or other signif
cant physiologic parameters can be incorporated int
the regression).
3. Solve each allometric equation for the average youn
adult human, that is, substitute 70 kg for weight i
predict average pharmacokinetic parameters. ■'4. Use the predicted pharmacokinetic parameters t
write pharmacokinetic equations for drug dispositio
in humans.
5. Check the prediction by administering the drug t
young adult humans or obtain experimental dat
from the literature.
Swabb and Bonner25 used a one-compartment model an
MAXIMUM TOLERATED DOSE
Swiss mouse
f o>
c oj 1
oE
BODY WEIGHT (kg)
Figure 11—Log-log plot of half-life versus body weight for ceftizoxime.
The solid circles represent the values reported in the literature for each
species. The solid line is the least-squares linear regression line for the
animals, excluding humans. The prediction for antibiotic half-life in
Weight (kg)
ttlUlmth
bars represent the range of values from the literature. Numbers in
from ref 21. Copyright 1985 American Society for Microbiology.
1034 /Journal of Pharmaceutical Sciences
Vol. 75, No. 11, November 1986
a^/^lM3a8//7K-^
Wff»aaT>'«ra*a*f«Jl
llffr'ff.'f"!
) LD10; (■) maximum tolerated dose. Reprinted with permission fro
Vlti'JltillimKI.l^±Ttit:lit»KliM2ikUtik7s!:iViilttWLlAJJ^uT\TWFl>.
from ref 53.
Dose Predicled Observed
CEFTIZOXIME, 4 GRAM I.V. INFUSION
1000 hund
f Infuaio
TIME (hours)
Time, hr
Figure 14—Comparison between predicted and observed serum con
centrations for ceftizoxime given as a 4-g, 30-min iv infusion to healthy
male subjects. Key: ( ) Method I; ( ) Method II; ( ) Method
| centrations for aztreonam given as 500- and 1000-mg iv infusions over 3
mm io neanny mate suujttuis. vettuos aiv means iui mu yiuuLia ui
I■subjects.
with permission from ref 25. Copyright 1983 Plenum
PublishingReprinted
Corp.
data from four species to predict aztreonam pharmacokinet
ics-in humans (Fig. 13). These predictions were helpful in
choosing doses and serum sampling times for the first kinetic
study in healthy male volunteers and agreed well with
subsequently measured concentrations in humans.
Mordenti26 used three methods of pharmacokinetic scaling
and data from mice, rats, monkeys, and dogs to predict
biexponential disposition profiles for ceftizoxime in humans.
Method I scaled the coefficients (A,B) and exponents (a,/3) of
the biexponential equation from each species; Method II
scaled the microconstants (ki2, k2\, k\$) and volume of distri
bution (Vdi) from the two-compartment model; and Method
HI scaled' volume of distribution (Vd*., Vdss, Vdarea) and
clearance. Irrespective of the method chosen to produce the
biexponential equations, there was close agreement between
CHRONOLOGICAL CLOCK
human'
dog
monkey
rat
Ceftizoxime
Half-Life
(Minutes)
from ref 26. Copyright 1985 American Pharmaceutical Assoc.
the predicted concentrations of ceftizoxime in human serum
and the concentrations in serum reported in the literature
(Fig. 14). This finding is important because it means that the
pharmaceutical scientist is at liberty to choose any method of
pharmacokinetic m< :eling and still obtain reasonable esti
mates in humans w.th che allometric approach.
Dimensionless criteria of similarity are obtained from the
ceftizoxime data by allometric cancellation as follows:
ceftizoxime half-life/time for heartbeat
= 30.1Wa248/4.15 x 10"3W0'25 = 7253 (!
where ceftizoxime half-life and time for heartbeat are mea
sured in minutes. In other words, 50% of a dose of ceftizoxime
is eliminated in -7,300 heartbeats, regardless of animal
BIOLOGICAL CLOCK
human
dog
monkey
Ceftizoxime
Half-Life
(Heartbeats)
Society for Microbiology.
Journal of Pharmaceutical Sciences /1035
\ / r s l 7 / - M r s 11 M r s s e c s r r s h r s r 1 0 Q £
species. This quantity, -7300 heartbeats, represents a unit
of interspecies equivalent time. To forecast each half-life of
ceftizoxime in other animal species, multiply the time for one
heartbeat (in minutes) by 7300. The similarity in ceftizoxime
half-life in different animal species is not apparent when the
reference time is extrinsic, chronological time (minutes; Fig.
15a); however, the similarity is apparent when the reference
time is intrinsic, biologic time (heartbeats; Fig. 15b).
The complexity of the scheme depends on the pattern of d
distribution, available data, and the insight ofthe investiga
tor. The mathematical pharmacokinetic model is obtained by
writing mass balance equations for the sum of the processes
occurring in each compartment, and the resultant differen
tial equations are solved simultaneously. Once the pharma
cokinetics of the drug are defined in one animal species,
predictions for humans are obtained by replacing the values
for the physiological, anatomical, and biochemical parame-ters of the test species with the values for corresponding
parameters
of humans. These values can be obtained from
4 . 1 l ' A J - J - J * J C * _ _ ' _ •■_ _ _ _ / ' • •
Physiologic Approach
The physiologic approach is based on physiologic flow
• i i w u > ~ i o " i i i v. i i a i c o u a i u i u i t i u i v, c " - * V o i \ J l \ l g l \ . a i i y, C U 1 U U i U -
estim
chemically correct.27-29 One must consider blood flow to
The physiologic approach is the method of choice when the
binding; and enzyme kinetics. The models are drawn as a
connected via the circulatory system as in the body (Fig. 16).
netic data can be obtained from only one animal species.
In formulation of a physiologic flow model for species fo:
which few physiologic data are known, allometric relation
ships can be used to provide reasonable estimates of these
data. In an illustration of this concept, physiologic parame
ters for seven animal species, representing a IO3 range of
weights, were taken from the literature27 (Table II). Allome
tric equations were fitted to the physiologic data by using t^he
method of least squares on unweighted, logarithmically
transformed data (Table III). In all cases, statistically signifi
cant associations were obtained. Predictions of theae physio*
logic parameters in an unlisted species can be obtained by
substituting the weight of the unlisted species into the
allometric equation. Allometric equations for tissue volumeB
and flow rates can be incorporated directly into the flow
model.
Physiologic flow models are developed in laboratory ani
mals, then scaled up (in the engineering sense) to make
a priori predictions of drug disposition in humans. The
anticancer agent methotrexate has been the most extensive
ly studied drug, and details of the development of the physio
logic model for methotrexate can be found in major review
articles.27-29 The physiologic model for methotrexate is multicompartmental and includes linear protein binding, strong,
saturable protein binding, and enterohepatic circulation.;
-x Blood flow
Figure 16—Schematic of a physiologic flow model.
Table II—Physiologic Parameters"
Parameter
Mouse
Body weight, g
22
Compartment volumes, mL
Plasma
Muscle
Kidney
Liver
Gut
Gut lumen
Heart
Lungs
Spleen
Marrow
1.0
10
0.34
1.3
1.5
1.5
0.095
0.12
0.1
0.6
Plasma flow rate, mL/min
Plasma
Muscle
Kidney
Liver
Gut
Heart
Lungs
Spleen
Marrow
a Data from ref 27.
4.38
0.5
0.8
1.1
0.9
0.28
4.38
0.05
0.17
1036 / Journal of Pharmaceutical Sciences
Vol. 75, No. 11, November 1986
Hamster
150
6.48
1.36
6.89
12.23
0.63
0.74
0.54
40.34
5.27
6.5
5.3
0.14
28.4
0.25
Monkey
500
2330
19.6
245
3.65
19.55
11.25
8.8
1.15
2.1
1.3
70
1350
15
100
120
84.6
22.4
12.8
4.7
14.6
1.6
2.25
0.95
520
155
6
•4 T
17
1
47
flfl
177
111
16
520
9.0
■i«
Human
5005530
Kl!al
480
480
■—
120
120
36
120
512
138
90
60
81.5
60
512
13.5
20
3000!
.-35000'
280
1350
21002100
300
—
160
1400
3670
420
700
800
700
150-
—
240
120
imimtm
1
•
METHOTREXATE, --g/g
1"
■:
;
to
Ol CO CO KJ
«
-4 co en -*•
c?S|l
_ CD co a
1 .-* *«• o N
I 8 I' 8 | 3 ;2L B- i
{DpEJ.Q- ▶*5it*j'-»'t';
*™~* i-*• i**"I ifa »-- ,
3 CD
1 -o £
ro°J 5=
rourompoiurjip
UQ-^'--bb(*l(DCO
(O ^UCOUKDOOU
-r^ en co co co ro co ro
•-*. -»•-' -» ro en co j».
ojcopcop^cop-vjco
mcoco-->jJ».co----^--g--g
ocDcococncnrococno)
S, o' 3 aq
3r;cD
o s-cd
-* j3-^ <» Co -a.
METHOTREXATE, u,g/ml
CO S. cB CU S-. -^
!*3 2 co =■ ,3 I
]_^ CD ^CQ |
METHOTREXATE. Mg/g
alffiSa
-», - • r- _ O CD
I ooati- t> 1
'
Q. ?\ tu OJ
O
O
'o»
o» -»*■ ?i i
O CD co 3*
3 -^ CD CD
OO CO 'O ~°>o
/
equivalent time between species by viewing the methotrex
ate plasma concentrations for mice and stingrays in two
ways. When the time scale (x-axis) was an extrinsic time
scale (minutes), the concentration profiles appeared dissimi
lar (Fig. 18a). When the time scale was made proportional to
the blood circulation velocity for each species, the concentra
tion profiles were superimposable (Fig. 18b). These figures
emphasize the importance of using intrinsic clocks for mea
suring pharmacokinetic events.
For drugs that are metabolized, physiologic models can be
combined with in vitro estimates of intrinsic clearance33 or in
vitro estimates of enzyme activity (Vmax and Km) to obtain
reasonable estimates of drug disposition in different species.
The anticancer drug cytarabine hydrochloride (Ara-C) is
converted to uracil arabinoside (Ara-U) by pyrimidine nucle
oside deaminase. This enzyme is distributed differently in
each species, and it is highly variable in kinetic characteris
tics (Vmax and Km). A physiologic model for Ara-C disposition
was developed for humans by using in vitro values for
enzyme activity and Michaelis constants.34 The model pre
dicted the plasma concentrations of Ara-C and Ara-U in
humans after a single intravenous dose of the parent com
pound (Fig. 19). Using enzyme kinetics determined in vitro,
this model was extended to mice, monkeys, and dogs to
produce accurate pharmacokinetic profiles for each species.35
The model was then expanded for the mouse to include the
intracellular metabolism ofthe drug to the active metabolite,
arabinoside cytosine triphosphate.36 The variable distribution
and kinetic activities of the deaminase enzymes make direct
scale-up of Ara-C among species difficult unless in vitro data
are available for each tissue.
The anticancer agent ds-dichlorodiammineplatinum (cisplatin) binds irreversibly to low molecular weight nucleophiles and macromolecules to form mobile and fixed metabo
lites at rates which are tissue specific. Biochemically, cis-
dichlorodiammineplatinum is an unusual di*ug because
rates of its biotransformation do not appear to be enzyma
cally mediated. A physiologic flow model for the dispositio
of cis-dichlorodiammineplatinum and its biotransformation
products was developed for female rats bearing Walker 256
carcinoma.37 The model was scaled up to rabbits, dogs, and
humans by using an interesting set of assumptions, approxi
mations, in vitro estimations, and allometric extrapolations
to provide the necessary biochemical and physiologic param
eters.38 Accurate predictions ofthe plasma concentrations, of
cis-dichlorodiammineplatinum, the total filterable platinum,
and the total platinum in humans were obtained (Fig. 20).
Ethoxybenzamide is oxidized to salicylamide primarily by
liver microsomal enzymes. A good correlation between in
vitro and in vivo drug metabolism rates has been demon
strated . for the rat.39 The physiologic flow model for
ethoxybenzamide in the rat was successfully scaled up for the
rabbit40 by incorporating the in vitro Michaelis-Menten
constants for ethoxybenzamide de-ethylation into the model
(Fig. 21).
The metabolism of diazepam in various rat tissues was
determined in vitro using microsomal fractions from each
tissue.41 The resultant values were incorporated into a phys
iologic flow model and used to predict diazepam pharmacoki
netics in a 10-compartment physiologic rat model. When the
model was scaled up to humans by using literature values for
the metabolism of diazepam in humans, an accurate assess
ment of diazepam plasma disposition was obtained.-4.2
Other examples ofthe successful scale-up of animal physio
logic models to humans include digoxin (rat to dog to hu
man),43 doxorubicin (rabbit to human),44-45 lidocaine (mon
key to human),46 mercaptopurine (rat to human),*7 pentazo
cine (rabbit to human),48 and hexobarbital, phenytoin,
phenobarbital, and quinidine (rat to human).49 Scale-up of
u 0.8
o
O
20
40
60
80
100
120
140
TIME (minules)
Figure 19—Prediction of cytarabine (Ara-C) and uracil arabinoside
(Ara-U) plasma concentrations in humans, using a physiologic model
that included in vitro values for enzyme activity and Michaelis-Menten
with permis
[}fflMM!\Wtmmlffii
1038 / Journal of Pharmaceutical Sciences
Vol. 75, No. 11, November 1986
TIME HOURS
Figure 20— Prediction of cisplatin (DDP), total filterable platinum (total
filterable Pt), and total platinum (total Pt) in humans fnllnwihn sn iv/*«■«■
Was
Wmmmmmmm
i. Reprinted with.
100.0
ATD=4.33 B-°A12
(r=0.985)
*U I
monkey
rabbit
w
.
30
60
90
120
TIME,min
Figure 21—Prediction of ethoxybenzamide plasma concentrations in
rabbits based on scale-up of a rat physiologic model. The symbols
mnmsnnt ohsfin/fid snnim concentrations fnllnwino iv doses of 10
mg/kg (O), 20 mg/kg (■), and 80 mg/kg (•). Reprinted with permission
from ref 40. Copyright 1982 Plenum Publishing Corp.
Body weight, B (kg)
Figure 22—Apparent threshold dose (ATD) of nipradilol in mammals as
Copyright 1985 Pharmaceutical Society of Japan.
spectively. The B- and y-globulin concentration terms did not
i
pam was not successful (rat to human).49
Oral Drug Administration
i Although the prediction of intravenous pharmacokinetics
has been successful, predicting the plasma concentration
curves for humans after oral dosing is more difficult. One
application of interspecies scaling that may prove useful for
orally administered drugs is the estimation of the apparent
threshold dose, that is, the dose of a high extraction ratio
drug necessary to saturate elimination pathways, allowing
drug to reach the systemic circulation. This application is
illustrated by nipradilol, an antihypertensive and antian
ginal agent. Nipradilol is metabolized by different mecha
nisms and to different extents in the rat, rabbit, monkey, and
dog.60 In spite of complete absorption of orally administered
doses, first-pass metabolism leads to low bioavailability, and
thfi svstftmic* availahilitv fnr all snppips inrrsasoe wif-V» rlnoo
Marked species difference is seen in the apparent threshold
dose, with the larger animals requiring smaller doses to
saturate presystemic drug metabolizing enzymes (Fig. 22).
The apparent threshold dose (ATD) of nipradilol relates to
species body weight (B) as follows: ATD (mg/kg) =
4.33B-0472.
Protein Binding
Although binding to plasma proteins seems unpredictable
across species, interspecies scaling ofthe extent of camptothcally determined plasma protein fraction concentrations as
independent variables.51 Data from 24 species were used to
produce the equation that describes the percent of camptothecin which is unbound in plasma [fu(%)]. This equation is
written as follows:
log fu (%) = 2.12 + 0.0628 log (a{) + 0.895 log (a2)
- 3.30 log (albumin) - 0.651 log (albumin) log (ax)
- 1.93 log (albumin) log (a2) (1())
where albumin, a-, and a2 refer to albumin, a--globulin, and
a2-globulin protein fraction concentrations (g/100 mL), re-
aigim-uani-iy uu'imuuLt: lu explaining tne variance Ol tne
dependent variable and were not included in the equation.
Equations such as this one may prove helpful when protein
binding has a significant impact on interspecies pharmacoki
netic scaling.
Conclusions
Animal data may be used to predict pharmacokinetic and
toxicologic endpoints in humans. Two approaches are pre
sented in this paper: the allometric approach and the physio
logic approach. The approach that one selects to scale up
animal data to humans depends on the nature of the com
pound and the desired mathematical output. The allometric
approach is empirical, but easy, and best suited for renally
excreted compounds or linear pharmacokinetic data. The
physiologic approach is detailed, but difficult, and best suited
■ui lucbctuuiiz-eu (jump-juiius ur numinear pnarcnacoKineuc
data. Both approaches allow us to extrapolate outside the
range of data with some confidence if the dominant mecha
nisms of transport are sufficiently well understood. A priori
predictions are possible for many drugs, based on limited
available data.
Animals live in different pharmacokinetic space-time continua. Use of an internal, or biological, clock in pharmacoki
netic data analyses removes the superficial differences im
posed by an external, or chronological, clock.
In general, small animals require more drug, administered
scaling can guide us in selecting equivalent dosage regimens.
References and Notes
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l.-l
noHrfot
R
T ■
THc.~Ur.tF
V
TJ
.
-7-1
i__
t-»
r.
s~,
„'.
Rep., Part 1 1970, 54, 95-101.
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11 0 3 - 11 2 7 .
'
'
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