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DMD #48819
1
Application of Hybrid Approach Based on Empirical and Physiological Concept for
Predicting Pharmacokinetics in Humans -Usefulness of Exponent on Prospective
Evaluation of Predictability-
Hiroyuki Sayama, Hiroshi Komura, Motohiro Kogayu
Drug Metabolism & Pharmacokinetics Research Laboratories, Central Pharmaceutical
Research Institute, JAPAN TOBACCO INC., Osaka, Japan (H.S., H.K., M.T.)
DMD Fast Forward. Published on December 3, 2012 as doi:10.1124/dmd.112.048819
Copyright 2012 by the American Society for Pharmacology and Experimental Therapeutics.
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Running title: Prediction of plasma concentration-time profiles in humans
Corresponding Author: Hiroshi Komura
Mailing address: hiroshi.komura@jt.com
JAPAN TOBACCO INC.,
Central Pharmaceutical Research Institute, 1-1, Murasaki-cho, Takatsuki, Osaka, 569-1125,
JAPAN
Phone: +81-72-681-9700
FAX: +81-72-681-9725
E-mail: hiroshi.komura@jt.com
Abstract: 250 words
Introduction: 732 words
Discussion: 1375 words
Number of text Pages: 29
Number of tables: 7
Figures: 5
References: 40
ABBREVIATIONS: BrW, brain weight; CL, clearance; P450, cytochrome P450; MLP, mean
life span potential; ROE, rule of exponent; PBPK, physiologically based pharmacokinetics;
afe, average fold error; rsme, root mean square error.
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Abstract
We developed a hybrid method by integrating species differences in in vitro intrinsic
clearance (CLint) into the Dedrick approach based on the allometry concept for predicting
plasma concentration-time curves in humans. With prediction of clearance (CL) by allometric
scaling, taking in vitro CLint into consideration improved the accuracy and reduced the
average fold error from 2.72 to 1.99. With the hybrid approach of applying the same concept
to the Dedrick approach, the predictability of plasma concentration profiles was compared
with the results of the conventional Dedrick approach and the physiologically-based
pharmacokinetic model using 15 compounds with widely ranging physicochemical and
pharmacokinetic profiles. The hybrid approach showed the highest predictability among the
examined methods. For CL and the apparent volume of distribution at the steady state (Vss),
the relationship between the exponent of allometric equation and fold error was also
evaluated with the hybrid approach. The relationship appeared to be a horseshoe curve. Six
compounds with exponents ranging from 0.7 to 1.1 for both CL and Vss (antipyrine, caffeine,
epiroprim, propafenone, theophylline and verapamil) displayed higher predictability. Three
compounds with an exponent ranging from 0.7 to 1.1 for CL showed better predictability for
CL, and other 4 compounds appeared to display similar relationship between the exponent
and predictability for Vss. These findings indicated that the exponent becomes a preliminary
index to speculate on predictability. Combination of the hybrid approach and exponent allows
us to prospectively draw human plasma concentration-time curves, with the implication of
possible prediction accuracy prior to clinical studies.
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Introduction
For pharmaceutical companies, the prediction of human pharmacokinetics has
increasingly become a critical issue, not only to narrow down development candidates to a
development compound with a desirable pharmacokinetic profile in humans, but also to
design first-in-human studies of such a compound including appropriate starting dose and
dose escalation. The nonclinical pharmacokinetics department is required to conduct reliable
prediction of pharmacokinetic parameters such as total body clearance (CL) and apparent
volume of distribution at the steady state (Vss) in humans, and to also describe plasma
concentration-time profiles in humans simulated by the use of those parameters.
A widely utilized methodology for predicting the plasma concentration-time profiles is a
physiologically-based pharmacokinetic (PBPK) model incorporating in vitro intrinsic
clearance (CLint) (Poulin and Theil, 2002; Peters, 2008; Jamei et al., 2009; Jones et al., 2011).
Approximately 50% of all drugs undergo hepatic metabolism by cytochrome P450 (P450)
enzymes (Williams et al., 2004), and some authors demonstrated the usefulness of the PBPK
model in the prediction of human pharmacokinetics, by including this strategy in drug
development (De Buck et al., 2007; Jones et al., 2006). Over the last decade, the advent of in
vitro transporter expression systems revealed that liver uptake and biliary and/or renal
excretion involving transporters are determinant factors in the pharmacokinetics of some
compounds (Shitara et al., 2006; Poirier et al., 2009; Watanabe et al., 2010; Jones et al., 2012).
Retrospective prediction based on the PBPK model including liver uptake mechanisms
successfully described plasma concentration-time curves of a limited number of the
compounds (Watanabe et al., 2009). However, it is difficult to elucidate the mechanisms
governing the pharmacokinetics of development candidates in in vitro studies using chemical
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inhibitors of P450 enzymes and transporters, or their in vitro expression systems, alongside
the relevant in vivo studies within a restricted timeframe due to the labor-intensive and
time-consuming processes.
Another technique for predicting human plasma concentration profiles is the Dedrick
approach, which is based on the allometric scaling theory (Dedrick et al., 1970; Lave et al.,
1995; Van den Bergh et al., 2011). The Dedrick approach can describe the plasma
concentration-time curves in humans from the relevant profiles in animal species by
transforming the chronological time into the biological time based on the allometric theory
for CL and Vss, which are scaled across the species as a power function of body weight. In
contrast to the PBPK models, the Dedrick approach can be adapted to compounds with
various mechanisms of elimination and distribution. However, allometric scaling tends to
produce over-predicted CLs (Tang and Mayersohn, 2006). Especially, in case of compounds
that display a large species difference in CL dependent on hepatic metabolism, allometric
scaling tends to yield poor prediction accuracy (Lave et al., 1997). This can be ascribed to the
concept of allometry, namely that any difference in pharmacokinetics across species is
defined by body size alone.
How to improve predictability has become a crucial question to be addressed, and much
effort has been made to improve the predictability of allometric scaling (Mahmood, 2002;
Mahmood, 2006; Hosea et al., 2009). Lave et al. (1996a; 1997) proposed allometric scaling
involving CLs corrected by in vitro CLint in the hepatocytes of human and animal species.
Although the same concept was still applied to the Dedrick approach, the predictability of the
plasma concentration profile in humans was only demonstrated by one compound (Lave et al.,
1996b). Therefore, utility of the hybrid approach based on the integration of Dedrick plot and
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the species difference in in vitro CLint has to be evaluated, including comparative analysis
with the PBPK model, for a number of test compounds with widely diverse physicochemical
properties.
In the present study, the predictability of the hybrid approach was evaluated using 15
compounds that had been characterized in vitro and in vivo, and it was compared with the
predictability of the Dedrick method and the PBPK model. Exponents of the allometric
scaling are also regarded as important parameters in the choice of scaling methods such as the
rule of exponent (ROE) method (Mahmood et al., 2006). When the exponents of CL and/or
Vss were found to correlate with the prediction accuracy of the hybrid approach, it was
possible that the exponent became an index for the predictability of human pharmacokinetic
profiles. We evaluated the relationship between the two parameters and the impact of the
exponent on the prospective analysis of predictability of the hybrid method before clinical
studies.
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Materials and Methods
Data Collection
For prediction of CL and Vss by allometric scaling, 92 compounds in total (21 for CL and
86 for Vss) that were reportedly available for intravenous pharmacokinetic parameters and in
vitro CLint in the liver microsomes or hepatocytes were collected from the literature. When
the in vitro CLint was reported as the unit of mg microsomal protein or million cells of
hepatocytes, the value was converted to the unit of mL/min/kg of body weight using 45 mg
microsomal protein/g of liver or 1×106 cells/g of liver and corresponding liver weight for
each species (Barter et al., 2007). These in vivo and in vitro parameters are listed as the
Supplemental Data (Supplemental Table 1). Among these, 15 model compounds, of which the
plasma concentration data in animals and humans after intravenous administration were
reported, were selected and used for the prediction of plasma concentration-time profiles in
humans using the hybrid approach, the Dedrick approach and the PBPK model (Table 1).
Noted that profiles of the lipophilicity (clogP) and CL for 15 model compounds selected were
similar to those in compounds listed in Supplemental Table 1. For prediction using the PBPK
model, additional in vitro data including the unbound fraction in the plasma (fup), and the
blood to plasma concentration ratio (RB) in humans were obtained from the literature, and
clogP, pH-dependent measure of lipophilicity (clogD) and basic and acidic dissociation
constants (pKa) were calculated using CLOGP, version 4.82 (Daylight Chemical Information
Systems Inc., CA, USA) and Pallas, version 4.4.1 (CompuDrug Inc., AZ, USA). The
compounds were divided into acidic, basic and neutral classes based on the difference
between the clogD values at pH 6.5 and 7.4 (∆clogD) as indicated in the following equation.
pH7.4pH6.5 clogDclogDΔclogD −= (Eq. 1)
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The compounds with positive and negative values of ∆clogD were classified as acidic and
basic, respectively. The physicochemical and pharmacokinetic characteristics of the 15 model
compounds are summarized in Table 1.
Prediction of CL and Vss by Allometric Scaling
In vivo CL and Vss of each animal species were plotted against the body weight on a
log-log scale and the conventional allometric equation was used to predict CL and Vss in
humans as shown in the following equations;
xBWaCL ⋅= (Eq. 2)
yss BWbV ⋅= (Eq. 3)
where BW is the body weight, a and b are the coefficients, and x and y are the exponents of
the allometric equation obtained from the animals. The body weight in humans was assumed
to be 70 kg.
In addition, the allometric scaling of CL was integrated with the in vitro CLint in animals
and humans to correct the species difference in CL; namely, the CL in animals was corrected
by in vitro CLint and was plotted against the body weight using the following equation.
x
Animalint,
Humanint, BWa
CL ⋅=⋅
CLin vitro
CLin vitro (Eq. 4)
The subsequent procedure for human CL prediction in the integrated method was the same as
the allometric scaling described above.
The allometric scaling was conducted using all of the species (2 to 5 animal species)
listed in the Supplemental Table 1. Since two-species scaling reportedly provided reliable CL
(Goteti et al., 2010; Tang et al., 2007), the prediction based on more than 2 animal species
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would be considered acceptable.
Prediction of Plasma Concentrations: the hybrid and Dedrick Approaches
Prediction of plasma concentration was conducted according to the method reported by
Dedrick et al. (1970) and Boxenbaum and Ronfeld (1983). In brief, assuming that CL is
proportional to BWx and volume of the central compartment (V1), volume of distribution
during the β-phase (Vβ) and Vss are all proportional to BWy (x and y are the exponent of CL
and Vss, respectively, in animals), plasma concentration-time profile of two-compartmental
model can be described by the body weight, compound specific coefficients (intercept in
allometric equation, eg, a and b), and exponents (x and y). Based on this theory, the
chronologic time in humans (thuman) can be derived from the chronologic time in animals
(tanimal) according to the following equation.
xy
animal
humananimalhuman BW
BW−
⎟⎟⎠
⎞⎜⎜⎝
⎛⋅= tt (Eq. 5)
Plasma concentrations in humans (Chuman) were calculated from those in animals (Canimal) as
described below.
y
animal
human
animal
humananimalhuman BW
BW
Dose
Dose⎟⎟⎠
⎞⎜⎜⎝
⎛⋅⋅= CC (Eq. 6)
These Chuman were plotted against thuman and were fitted to a bi-exponential pharmacokinetic
equation. Human pharmacokinetic parameters (k10, k12, k21 and V1) were obtained using
Phoenix WinNonlin, version 6.3 (Pharsight, CA, USA).
To correct the interspecies difference in hepatic metabolism, the in vitro CLint in animals
and humans was incorporated in the following equation to calculate thuman by the hybrid
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approach.
xy
animal
human
humanint,
animalint,animalhuman BW
BW−
⎟⎟⎠
⎞⎜⎜⎝
⎛⋅⋅=
Lin vitro C
Lin vitro Ctt (Eq. 7)
The following processes including the calculation of Chuman and parameter fitting were carried
out in the same manner as with the Dedrick approach described above. The hybrid and
Dedrick approaches were conducted using all of the species listed in the Table 1.
Prediction of Plasma Concentrations: PBPK
A typical PBPK model used to predict plasma concentrations in humans is shown in the
Supplemental Data (Supplemental Figure 2). The model is composed of 11 tissue
compartments, consisting of the lungs, adipose tissue, bones, brain, heart, muscles, kidneys,
spleen, liver, skin and small intestine, which are linked by venous and arterial blood pools.
Perfusion rate-limited kinetics was assumed and each tissue was represented by a single
well-stirred compartment, limited by the blood flow. The liver was considered only on the
elimination site. The principles of mass balance equations for non-eliminating tissues and
eliminating tissue (the liver) are indicated by the following differential equations;
⎟⎟
⎠
⎞
⎜⎜
⎝
⎛−⋅=⋅
pT
TaTT
T
K
CCQV
dt
dC (Eq. 8)
pT
Tint
pT
TaTT
T
K
CCL
K
CCQV
dt
dC⋅−
⎟⎟
⎠
⎞
⎜⎜
⎝
⎛−⋅=⋅ (Eq. 9)
where V is the volume, Q is the blood flow, C is the concentration and subscript T is tissue,
and subscript a is artery. In vitro CLint in humans obtained from the literature was used in the
model, assuming that the unbound fraction in the in vitro system (fuinc) was equal to the
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unbound fraction in blood (fuB) and both parameters were canceled out, as reported by De
Buck et al. (2007). The Kp values of 11 tissues were calculated using the tissue
composition-based equations described by Rodgers et al. (2005; 2006). The respective
equations (Eqs. 10 and 11) used for strong basic compounds with pKa values greater than 7
and for other types of compounds are as follows;
[ ] p
pHp
pHpKaTaPR
NPpHp
logP
NLpHp
logP
IWpHp
pHp
EW
p fu
101
10PR
101
0.7100.3
101
10
101
101
pa
IW
pa
papa
IWa
⋅
⎥⎥⎥⎥
⎦
⎤
⎢⎢⎢⎢
⎣
⎡
+⋅⋅
+⋅+
+⋅+
⋅+
+⋅+++
=
−
−
−
−−
−
KK
KK
K
Kf
fff
K (Eq. 10)
[ ]p
TaPRNPpHp
logP
NLpHp
logP
IWpHp
pHp
EW
p fu
PR101
0.7100.3
101
10
101
101
pa
papa
IWa
⋅
⎥⎥⎥⎥
⎦
⎤
⎢⎢⎢⎢
⎣
⎡
⋅+⋅+
+⋅+
⋅+
+⋅+++
=
−
−−
−
Kf
fff
K
K
KK
K
(Eq. 11)
where f is the fraction tissue volume (subscripts IW, EW, NL, NP refer to intracellular water,
extracellular water, neutral lipids, and neutral phospholipids, respectively) [PR]T is the tissue
concentrations of proteins (acidic phospholipid for strong bases, albumin for weak bases and
acid and lipoprotein for neutral drugs) and KaPR is the affinity constant of the drug for each
protein. Physiological parameters used in the PBPK model and the tissue composition-based
equations are listed as the Supplemental Data (Supplemental Table 2). This PBPK model was
constructed and solved with Phoenix WinNonlin.
Assessment of Prediction Accuracy
The plasma concentrations in humans were simulated by 3 different methods: the Dedrick
approach, the hybrid approach and the PBPK model. The Vss, CL and elimination half-life
(t1/2) with each method were estimated by non-compartmental analysis of the simulated
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plasma concentration-time profile using Phoenix WinNonlin. The predictability in individual
drugs was evaluated based on the fold error using the following equations.
( )
( ) predictedobserved valuepredicted
valueobservederrorfold
observedpredicted valueobserved
valuepredictederrorfold
>=
>= (Eqs. 12, 13)
The average fold error (afe) and root mean square error (rmse) were calculated as follows:
nafe∑
=errorfold log
10 (Eq. 14)
( )n
rmse ∑=2observed log-predicted log
(Eq. 15)
where n represents the number of compounds evaluated. In addition, the percentage of
compounds within the 2-fold or 3-fold error was derived from comparison between the
predicted and observed parameters. Comparative assessment of predictability for CL, Vss
and/or t1/2 between the examined methods was performed mainly based on afe and/or the
percentage within 2-fold or 3-fold.
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Results
Allometric Scaling of CL with In Vitro CLint
The human CLs predicted using allometric scaling with or without the correction factor of
in vitro CLint were compared with the observed values (Fig. 1). The relationship between the
observed and predicted CLs was remarkably improved by the introduction of the correction
factor. With the conventional method without in vitro CLint, the afe was calculated to be 2.72,
and 52% of the compounds examined were predicted within 2-fold error of the observed
values (Table 2). The use of in vitro CLint as the correction factor into the allometric scaling
increased the predictability with an afe of 1.99, and 62% of the compounds were predictable
within 2-fold error.
Prediction of Plasma Concentration-time Profiles by Hybrid Approach
The hybrid method based on integration of the Dedrick plot and the in vitro CLint was
applied to predict plasma concentration-time curves in humans, and the obtained profiles
were compared with the corresponding data derived from the conventional Dedrick approach
and PBPK model. We selected 15 compounds of which reported in vitro and in vivo
pharmacokinetic parameters were available, covering a wide range of physicochemical and
pharmacokinetic parameters (Table 1). The plasma concentration-time curves obtained by the
individual prediction method are shown in Fig. 2. The pharmacokinetic parameters, CL, Vss
and t1/2, were estimated based on the plasma concentration-time curves predicted by the
individual method, and the relationship between the observed and predicted parameters is
shown in Fig. 3. The fold-error and/or the afe are also summarized in Tables 3 and 4. The
predictability of CL, Vss and t1/2 was the highest with the hybrid approach using a correction
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factor of in vitro CLint, followed by the conventional Dedrick approach > the PBPK model.
For predictability of CL, Vss and t1/2 with the hybrid approach, the afe was calculated to be
1.74, 1.54 and 2.13, and 67%, 73% and 53% of the compounds were within 2-fold error of
the observed data, respectively. With regard to antipyrine, caffeine, diazepam, epiroprim,
nicardipine, propafenone, propranolol theophylline and verapamil, the hybrid approach
yielded visual plasma concentration-time curves that were close to the observed
concentrations, relative to the PBPK model (Fig. 2).
Relationship between Exponent and Predictability
To find a preliminary index describing the prediction accuracy of compounds with the
hybrid approach, the relationship between the exponent and fold error was evaluated for CL
and Vss projections by allometric scaling (Fig. 4), and the predictability in 3 categories based
on the exponent range (all, 0.7—1.1, or < 0.7 and > 1.1) are summarized in Table 5. With the
allometric scaling of CL using the correction factor, the compounds of which the exponents
ranged from 0.7 to 1.1 exhibited high accuracy such as an afe of 1.53, and predictability was
within 2-fold error for 92% of the compounds, whereas relatively low accuracy was
demonstrated with the other compounds with an exponent of < 0.7 or > 1.1. The predictability
of Vss with allometric scaling using all the examined compounds seemed relatively low, and
predictability was within 2-fold error of the observed values for 65% of the compounds.
However, when compounds of which the exponent ranged from 0.7 to 1.1 were evaluated
with the Vss prediction, the percentage of compounds with predictability within 2-fold error
appeared to increase (Fig. 4), and predictability was within 2-fold error of the observed
values for 80% of the compounds (Table 5). In contrast, low accuracy was observed with
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compounds with an exponent of < 0.7 or > 1.1, as indicated by predictability within 2-fold
error for 19% of the compounds.
These results demonstrated that the exponent of allometric scaling would possibly be an
advance speculative indicator of the predictability of CL and Vss. Similarly, with the hybrid
approach, the exponent was plotted against the fold error of CL and Vss that was obtained
from the plasma concentration profiles (Fig. 5), and the estimated afe in 3 categories based on
the exponent range as summarized in Table 6. As illustrated in Fig. 5, relatively high accuracy
was found with compounds with an exponent from 0.7 to 1.1, and this trend was more
prominent with the CL data. The 15 compounds were classified into 4 groups based on the
exponent of CL and Vss (Table 7); that is, group 1 was characterized by the exponent ranging
from 7 to 1.1 for both CL and Vss, groups 2 and 3 by the exponent range of 0.7 — 1.1 for CL
and 0.7 — 1.1 for Vss, respectively, and group 4 by the exponent range of < 0.7 and > 1.1 for
both CL and Vss (data not shown). Interestingly, 6 compounds (antipyrine, caffeine, epiroprim,
propafenone, theophylline and verapamil) in group 1 provided the highest level of accuracy
with an afe of 1.29 for CL, 1.40 for Vss and 1.89 for t1/2. Group 2 (felodipine, propranolol,
tolcapone) and group 3 (diltiazem, midazolam, nicardipine, oxazepam) also showed better
accuracy for CL and Vss, respectively.
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Discussion
This study successfully demonstrated that the integration of species difference in in vitro
CLint in the Dedrick approach improved the predictability of plasma concentration-time
curves. It is also of particular note that it is clearly shown that the hybrid approach, which is
based on empirical and physiological concepts, produces better predictability than the PBPK
model, which is based on the metabolic clearance in the liver defined by in vitro CLint and the
tissue distribution defined by plasma protein binding and physicochemical properties (clogP,
clogD and pKa).
Animal scale-up based on the allometry concept has been widely used to predict
pharmacokinetic parameters in humans (Shiran et al., 2006; Tamaki et al., 2011), and there
have been advantages and disadvantages in the predictions by this method. In general,
development of PBPK model needs clarification of elimination mechanisms from the body,
however, in the drug discovery phase, detailed investigation for the major elimination
mechanism of an individual development candidate is practically difficult within the limited
timeframe. One advantage is that allometric scaling can easily be applied to most of the
compounds regardless of their elimination mechanism, which is different from the PBPK
model, which needs modeling of the mechanism after it was elucidated.
Overprediction of CL has been recognized as a disadvantage, and in the worst case, will
generate vertical allometry (Tang and Mayersohn, 2006). This was also understandable by the
CL data predicted in the present study showing that 80% of the compounds with
predictability of over 2-fold error were overestimated by allometric scaling without in vitro
CLint (Fig. 1). Importantly, the application of in vitro CLint obtained from liver microsomes or
hepatocytes with allometric scaling of CL improved the prediction accuracy, as evidenced by
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Lave et al. (1996a; 1997). Similarly, the hybrid method developed using the Dedrick plot and
in vitro CLint in the species provided high accuracy to predict the plasma concentration-time
curves. Noticeably, the predictability of t1/2 derived from their concentration profiles was
higher than with the PBPK model, probably for 11 out of 15 compounds.
There has been a limited number of reports that the predictability of plasma
concentration-time curves was comparatively evaluated between the two different concepts
(empirical approach versus the PBPK model). Yamazaki et al. (2011) demonstrated that a
PBPK model provided better prediction of the maximum plasma concentration and the area
under the plasma concentration-time curves for 2 compounds than a traditional one
compartment model based on CL and Vss predicted by allometric scaling. Comparative
analysis between the Dedrick and PBPK approaches was conducted by Jones et al. (2006),
who employed 19 compounds with a wide range of CL and Vss. The prediction accuracy was
higher with the PBPK model than the Dedrick approach. However, the former study
employed a simplified one-compartment model, which is regarded as a low predictability
model, and the latter study did not utilize any correction factor such as maximum life span
potential (MLP), brain weight (BrW) or in vitro metabolic data with the Dedrick approach.
As an alternative approach with the empirical method, there was the Wajima method in
which plasma-concentration time curves were predicted from pharmacokinetic data in
animals (Wajima et al., 2004; Fura et al., 2008; Van den Bergh et al., 2011); that is, the
plasma concentration-time curves can be normalized by a time axis with mean residence time
and a plasma concentration axis with dose/Vss. Comparative assessment using the
Pharmaceutical Research and Manufacturers of America initiative concluded that the Wajima
method and the PBPK model provided a similar level of accuracy on the intravenous dataset
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(Vuppugalla et al., 2011). However, the Dedrick approach was not utilized in the comparison
study. Our result is the first report demonstrating better predictability with the hybrid
approach than the PBPK model, and this significance in the hybrid method would be
attributable to the use of species difference in in vitro CLint. Our preliminary study also
indicated that the hybrid approach was applicable to compounds that are mainly subject to
biliary excretion in rats, and that it had higher accuracy than the PBPK model used in this
study (data not shown). It should be noted that our findings were derived from 15 compounds
that showed various physicochemical properties (clogP; -0.04—5.30) and pharmacokinetic
profiles in humans (fup; 0.001—1, CL; 0.50—19.23 mL/min/kg, Vss; 124—5731 mL/kg).
One of the major concerns of the physiological approach is underestimation of CL (Ito
and Houston, 2005; Hallifax, 2010). In this study, this trend was also found for the
relationship between the observed and predicted CL obtained with the PBPK model (Fig. 3).
Hence, several pharmacokinetic scientists have gone to much effort to improve the
predictability. For example, an empirical scaling factor to extrapolate the in vitro CLint from
microsomes or hepatocytes to the whole body was employed (Ito and Houston, 2005).
Naritomi et al. (2001; 2003) also developed an animal scaling factor, which was estimated by
comparing in vitro and in vivo CLint in rats or dogs, and using the factor ameliorated the
predictability of in vitro-in vivo extrapolation of CL. However, PBPK models are basically a
rationalized approach. Hence, since the PBPK model yielded lower predictability than the
hybrid method in the present study, mechanistic models to seal the gap between the observed
and predicted data would necessarily be taken into consideration.
The findings in the present study imply that the hybrid approach is a highly predictable
method for many compounds with widely ranging lipophilicity, which is one of the
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determinant factors in pharmacokinetics. For prediction strategy, a preliminary index to
speculate the predictability of plasma concentration profiles would help to consider the risk or
variation range of the predicted data to justify the selection of a development compound or
the design of first-in-human studies. With the allometric scaling of CL, the exponent is
reported to be a key parameter to keep the trend of predictability in perspective, as
demonstrated by the ROE method in which the MLP or BrW approach is selected based on
the exponent in simple allometry (Mahmood et al., 1996). We focused our attention on the
relationship between the exponent and fold-error of CL and Vss in allometric scaling. The
relationship was noticeably described by a horseshoe curve for CL and Vss, and the
compounds for which the exponent ranged from 0.7 to 1.1 showed better predictability
compared to the compounds with an exponent < 0.7 or > 1.1.
With the hybrid method, usefulness of the exponent of CL and/or Vss as an index to
predictability was investigated using 15 compounds. Compounds with both the exponents
ranging from 0.7 to 1.1 yielded the highest level of prediction accuracy. Furthermore, the
predictability of CL appeared to be guaranteed by the exponent from 0.7 to 1.1 for CL, and
similar relationship between the exponent and predictability would be noted for Vss. Based on
these findings, the exponent according to the hybrid approach would become an effective
index to preliminarily evaluate the predictability of the plasma concentration-time curves
prior to clinical studies.
There are hardly any reports in the literature on the relationship between the exponent
and the prediction accuracy in the allometric concept, and only a report by Huh et al. (2011)
illustrated that accuracy was high with an exponent of 0.65 to 0.7 for small-molecular drugs.
However, please note that this result was obtained from single species scaling. Accordingly,
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our study is possibly the first challenge that highlights the utility of exponent to prospectively
evaluate the predictability of human pharmacokinetics by the allometric concept.
In conclusion, we successfully developed a hybrid approach based on the Dedrick
approach and the in vitro CLint in animal species and humans. The hybrid method yielded
better predictability compared to the conventional Dedrick approach and the PBPK method.
We also demonstrated that the exponent in the hybrid approach is an effective index to
preliminarily analyze the accuracy of the predicted human pharmacokinetics prior to clinical
studies. In fact, the plasma concentration-time curves were highly predictable for compounds
with an exponent of 0.7 to 1.1 for both CL and Vss by the hybrid method. The new
combination of the hybrid method and the index of exponent, which is a robust prediction
tool, would allow us to predict the pharmacokinetic profiles in humans as well as to address
the risk assessment.
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Authorship Contribution
Participated in research design: Sayama H, Komura H.
Conducted experiments: Sayama H.
Contributed new reagents or analytic tools: Sayama H.
Performed data analysis: Sayama H. Komura H.
Wrote or contributed to the writing of the manuscript: Sayama H, Komura H, Kogayu M.
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Legends for Figures
Fig. 1
Relationship between the observed and predicted human CLs by allometric scaling without
(A) and with correction factor of in vitro CLint (B). Solid and dotted lines indicate unity and
2-fold errors between predicted and observed values, respectively.
Fig. 2
Comparison of observed and predicted human plasma concentration-time profiles of the 15
model compounds. The bold and thin black lines represent the predicted plasma
concentrations obtained by the hybrid approach and conventional Dedrick approach,
respectively. The gray lines represent predicted the plasma concentrations obtained by the
PBPK model. The observed concentrations are indicated by gray circles.
Fig. 3
Relationship between the observed and predicted human CL (A), Vss (B) and t1/2 (C) of the 15
model compounds. Solid and dotted lines indicate unity and 2-fold errors between predicted
and observed values, respectively.
Fig. 4
A and B, relationship between prediction accuracy and exponent of allometric scaling for CL
prediction using allometric scaling corrected by in vitro CLint (A) and Vss prediction using
conventional allometric scaling (B). Solid and dotted lines represent the range of exponent of
0.7 to 1.1 and 2-fold error, respectively. C and D, relationship between the observed and
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predicted human values for CL (C) and Vss (D). E and F, relationship between the observed
and predicted human values of the compounds with exponent ranged 0.7 to 1.1 for CL (E)
and Vss (F). Solid and dotted lines indicate unity and 2-fold errors between predicted and
observed values, respectively.
Fig. 5
Relationship between prediction accuracy and exponent for CL (A) and Vss prediction (B) in
the hybrid approach using the 15 model compounds.
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TABLE 1 In silico, in vitro and in vivo properties of the 15 model compounds
Compounds Compound
Class / pKa clogP Species
In vitro In vivo
fup RB CLint CL Vss t1/2 (mL/min/kg) (mL/min/kg) (mL/kg) (min)
Antipyrine Neutral 0.20 Human 1 1 0.28 0.62 584 657 Dog 3.95 8.18 738 68
Rabbit 4.07 7.32 903 94
Rat 1.58 3.53 657 135
Caffeine Base: 8.3 -0.04 Human 0.96 1 0.40 1.32 614 329
Dog 0.83 1.83 887 385
Rabbit 1.18 5.03 508 74
Rat 2.55 5.02 763 114
Diazepam Neutral 2.96 Human 0.032 0.58 2.16 0.50 1085 1872
Dog 121.20 21.40 7136 542
Rat 92.23 84.22 4715 71
Diltiazem Base: 8.4 3.65 Human 0.2 1.03 5.86 13.02 3110 190
Dog 10.66 33.33 3581 109
Rat 191.49 89.23 3400 39
Epiroprim Base: 6.9 4.00 Human 0.11 1.1 1.85 3.57 2501 543
Dog 2.76 10.82 8006 571
Monkey 8.45 24.82 3151 231
Rat 45.24 42.30 4122 90
Mouse 38.21 151.48 8356 51
Felodipine Neutral 5.30 Human 0.004 1a 23.13 8.90 3262 318
Dog 56.06 20.73 2559 154
Rat 127.37 90.42 9006 102
Midazolam Base: 5.6 3.42 Human 0.019 0.55 28.68 4.40 713 152
Dog 130.28 48.95 1582 41
Rabbit 73.92 14.23 734 71
Rat 483.12 59.62 1648 21
Nicardipine Base: 7.3 5.23 Human 0.068 0.71 22.51 7.68 489 50
Dog 63.17 38.65 797 17
Rat 118.58 29.77 808 20
Nitrendipine Neutral 3.73 Human 0.02 1a 37.01 19.23 5731 396
Dog 31.98 17.17 1543 83
Rat 105.41 11.28 377 83
Oxazepam Neutral 2.31 Human 0.043 1a 1.23 1.58 861 431
Dog 4.74 4.33 1418 250
Rat 5.71 20.22 1258 57
Propafenone Base: 9.9 3.64 Human 0.024 0.7 5.52 14.63 3492 301
Dog 7.80 28.70 2748 68
Rat 9.83 34.67 1919 34
Mouse 14.16 142.37 3130 18
Propranolol Base: 10.1 2.75 Human 0.068 0.81 12.95 10.15 2421 186
Dog 75.01 40.90 1544 42
Rat 223.99 96.80 4720 42
Theophylline Neutral -0.03 Human 0.51 0.83 0.34 0.82 579 524
Dog 0.59 1.52 710 333
Rabbit 0.89 3.18 923 250
Rat 0.79 1.90 857 352
Tolcapone Acid: 5.1 3.25 Human 0.001 0.6 3.70 1.43 124 87
Dog 5.53 1.45 220 154
Rabbit 16.26 10.82 153 48
Rat 11.42 5.70 98 36
Verapamil Base: 8.3 4.47 Human 0.082 0.84 4.61 11.78 3329 177
Dog 8.36 23.43 3582 186
Rat 5.19 34.22 3016 137 a RB values were assumed to be 1 when literature values were not obtained.
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TABLE 2
Statistics for the predicted human CL using allometric scaling
Method n afe rmse r Within 2-fold
error (%) Within 3-fold
error (%) Allometric Scaling 21 2.72 0.61 0.43 52 67 Allometric Scaling (in vitro CLint) 21 1.99 0.37 0.63 62 76
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TABLE 3
Prediction accuracy for pharmacokinetic parameters of the 15 model compounds using the hybrid, Dedrick approach and PBPK model
Compound Exponent Fold Error
CL Vss CL Vss t1/2 Dedrick Hybrid PBPK Dedrick Hybrid PBPK Dedrick Hybrid PBPK
Antipyrine 0.972 1.042 22.84 1.27 2.21 1.48 1.51 1.01 14.75 1.95 2.19 Caffeine 1.062 1.019 1.07 1.23 3.35 1.52 1.51 2.37 1.68 1.92 7.91 Diazepam 0.555 1.112 18.66 1.75 2.32 6.79 1.46 1.11 2.11 2.11 2.26 Diltiazem 1.516 1.014 1.44 3.55 2.75 1.09 1.04 1.51 1.21 3.10 4.38 Epiroprim 1.036 0.948 1.60 1.19 1.25 2.79 2.36 10.01 2.46 2.39 12.47 Felodipine 0.823 0.659 1.07 1.53 1.47 2.52 2.31 3.68 2.05 1.10 3.08 Midazolam 1.256 0.911 3.63 2.78 1.45 1.39 1.13 2.52 2.59 1.86 2.91 Nicardipine 1.242 0.996 5.74 2.85 3.84 1.71 1.71 6.24 3.40 1.69 3.55 Nitrendipine 1.437 1.382 1.26 2.73 1.55 1.13 1.13 1.31 1.29 2.80 1.67 Oxazepam 0.633 1.032 1.24 2.21 1.37 1.79 1.42 1.98 1.43 2.92 1.58 Propafenone 0.851 0.988 1.25 1.27 4.92 1.02 1.14 1.12 1.24 1.47 3.60 Propranolol 1.063 0.697 2.68 1.21 1.65 2.54 2.54 1.19 5.97 1.83 1.68 Theophylline 1.034 0.957 2.11 1.35 2.93 1.12 1.06 1.57 1.87 1.27 1.78 Tolcapone 0.856 1.217 1.36 1.60 1.29 3.94 3.15 1.11 4.72 5.25 1.99 Verapamil 0.768 1.047 1.58 1.48 2.50 1.17 1.16 1.66 1.17 2.74 5.71
afe 2.42 1.74 2.12 1.81 1.54 1.95 2.36 2.13 3.09
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TABLE 4
Statistics for the predicted human CL, Vss, and t1/2 of the 15 model compounds using the hybrid,
Dedrick approach and PBPK model
Parameter Methods afe rmse r Within 2-fold
error (%) Within 3-fold
error (%) CL
Dedrick 2.42 0.57 0.55 60 73 Hybrid 1.74 0.29 0.78 67 93 PBPK 2.12 0.37 0.41 47 80
Vss Dedrick 1.81 0.34 0.49 67 87 Hybrid 1.54 0.24 0.77 73 93 PBPK 1.95 0.41 0.38 67 80
t1/2 Dedrick 2.36 0.48 0.52 47 73 Hybrid 2.13 0.37 0.95 53 87 PBPK 3.09 0.55 0.14 33 53
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TABLE 5
Relationships of exponent and accuracies in prediction of CL and Vss using allometric scaling
Parameter Exponent n afe rmse r Within 2-fold
error (%)
Within 3-fold
error (%)
CL
All 21 1.99 0.37 0.63 62 76
0.7 – 1.1 13 1.53 0.23 0.89 92 92
< 0.7 and > 1.1 8 3.04 0.53 0.71 13 50
Vss
All 86 2.11 0.50 0.41 65 81
0.7 – 1.1 65 1.56 0.26 0.78 80 94
< 0.7 and > 1.1 21 5.32 0.89 -0.01 19 43
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TABLE 6
Relationships of exponent and accuracies in prediction of CL, Vss, and t1/2 of 15 model
compounds using the hybrid approach
Parameter Exponent n afe rmse r Within 2-fold
error (%)
Within 3-fold
error (%)
CL
All 15 1.74 0.29 0.78 67 93
0.7 – 1.1 6 1.29 0.12 0.99 100 100
< 0.7 and > 1.1 9 2.13 0.36 0.88 44 89
Vss
All 15 1.54 0.24 0.77 73 93
0.7 – 1.1 6 1.40 0.19 0.77 83 100
< 0.7 and > 1.1 9 1.64 0.27 0.88 67 89
t1/2
All 15 2.13 0.37 0.95 53 87
0.7 – 1.1 6 1.89 0.30 0.71 67 100
< 0.7 and > 1.1 9 2.30 0.41 0.97 44 78
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TABLE 7
Prediction accuracies of CL, Vss, and t1/2 of 15 model compounds in each group using the
hybrid approach
Groupa n Exponent afe
CL Vss CL Vss t1/2
1 6 0.7 – 1.1 0.7 – 1.1 1.29 1.40 1.89
2 3 0.7 – 1.1 < 0.7 and > 1.1 1.44 2.64 2.20
3 4 < 0.7 and > 1.1 0.7 – 1.1 2.81 1.30 2.31 a Group 1: Antipyrine, caffeine, epiroprim, propafenone, theophylline, verapamil
Group 2: Felodipine, propranolol, tolcapone
Group 3: Diltiazem, midazolam, nicardipine, oxazepam
This article has not been copyedited and formatted. The final version may differ from this version.DMD Fast Forward. Published on December 3, 2012 as DOI: 10.1124/dmd.112.048819
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