Application of Hybrid Approach Based on Empirical and … · 2012. 12. 3. · Mahmood, 2006; Hosea et al., 2009). Lave et al. (1996a; 1997) proposed allometric scaling involving CLs

DMD #48819

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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.

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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Running title: Prediction of plasma concentration-time profiles in humans

Corresponding Author: Hiroshi Komura

Mailing address: [email protected]

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: [email protected]

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


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Documents

Application of Hybrid Approach Based on Empirical and … · 2012. 12. 3. · Mahmood, 2006; Hosea et al., 2009). Lave et al. (1996a; 1997) proposed allometric scaling involving CLs