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`0022-3565/97/2831-0046$03.00/0
`THE JOURNAL OF PHARMACOLOGY AND EXPERIMENTAL THERAPEUTICS
`Copyright © 1997 by The American Society for Pharmacology and Experimental Therapeutics
`JPET 283:46 –58, 1997
`
`Vol. 283, No. 1
`Printed in U.S.A.
`
`The Prediction of Human Pharmacokinetic Parameters from
`Preclinical and In Vitro Metabolism Data
`
`R. SCOTT OBACH, JAMES G. BAXTER, THEODORE E. LISTON, B. MICHAEL SILBER, BARRY C. JONES,
`FIONA MACINTYRE, DAVID J. RANCE and PHILIP WASTALL
`Departments of Drug Metabolism, Pfizer Central Research, Groton, Connecticut (R.S.O., J.G.B., T.E.L., B.M.S.), and Sandwich, Kent (B.C.J.,
`F.M., D.J.R., P.W.), UK
`Accepted for publication June 23, 1997
`
`ABSTRACT
`We describe a comprehensive retrospective analysis in which
`the abilities of several methods by which human pharmacoki-
`netic parameters are predicted from preclinical pharmacoki-
`netic data and/or in vitro metabolism data were assessed. The
`prediction methods examined included both methods from the
`scientific literature as well as some described in this report for
`the first time. Four methods were examined for their ability to
`predict human volume of distribution. Three were highly pre-
`dictive, yielding, on average, predictions that were within 60%
`to 90% of actual values. Twelve methods were assessed for
`their utility in predicting clearance. The most successful allo-
`metric scaling method yielded clearance predictions that were,
`on average, within 80% of actual values. The best methods in
`which in vitro metabolism data from human liver microsomes
`were scaled to in vivo clearance values yielded predicted clear-
`
`ance values that were, on average, within 70% to 80% of actual
`values. Human t1/2 was predicted by combining predictions of
`human volume of distribution and clearance. The best t1/2
`prediction methods successfully assigned compounds to ap-
`propriate dosing regimen categories (e.g., once daily, twice
`daily and so forth) 70% to 80% of the time. In addition, corre-
`lations between human t1/2 and t1/2 values from preclinical
`species were also generally successful (72– 87%) when used to
`predict human dosing regimens. In summary, this retrospective
`analysis has identified several approaches by which human
`pharmacokinetic data can be predicted from preclinical data.
`Such approaches should find utility in the drug discovery and
`development processes in the identification and selection of
`compounds that will possess appropriate pharmacokinetic
`characteristics in humans for progression to clinical trials.
`
`The process by which new drug candidates are discovered
`and developed is both time consuming and expensive (Di-
`Masi, 1994; DiMasi et al., 1994). This is due in part to the
`high rate of attrition of drug candidates that enter clinical
`development, such that only ⬃10% of drug candidates that
`are selected for clinical development eventually become mar-
`keted drugs. In analyzing the reasons for attrition of drug
`candidates that enter clinical development, it has been re-
`ported that the clinical development of 40% of drug candi-
`dates was discontinued due to unacceptable pharmacokinetic
`properties (Prentis et al., 1988).
`These observations strongly suggest that the process by
`which new drugs are discovered and developed could benefit
`greatly if drug candidates were advanced to clinical develop-
`ment when predicted human pharmacokinetic characteris-
`tics were deemed to be acceptable (e.g., oral bioavailability
`and duration of exposure are projected to be appropriate for
`conducting pivotal efficacy studies). Thus, the development
`
`Received for publication March 4, 1997.
`
`and application of reliable methods to predict human drug
`disposition may decrease the overall attrition of drug candi-
`dates during clinical development by decreasing the number
`of candidates lost due to unacceptable pharmacokinetic char-
`acteristics. Furthermore, the eventual clinical utility as well
`as market success of a newly approved drug could be maxi-
`mized by selecting for development only those compounds
`with optimal, rather than acceptable, pharmacokinetic char-
`acteristics for the intended therapeutic use.
`The best described technique to predict human pharmaco-
`kinetics from in vivo preclinical pharmacokinetic data is al-
`lometric scaling. In its original form, allometry was a tech-
`nique developed to explain observed relationships between
`organ size and body weight of mammals (Dedrick et al., 1970;
`Mordenti, 1986). Additional studies demonstrated further
`relationships between mammalian body weight and physio-
`logical parameters. Considerations of the relationship be-
`tween drug elimination and physiological parameters such as
`hepatic or renal blood flow inevitably led to the application of
`allometric scaling in correlating human pharmacokinetics
`
`ABBREVIATIONS: fut, fraction unbound in tissues; fu, unbound fraction in plasma (or serum); VDss, steady state volume of distribution (in liters/kg);
`Vp, plasma volume (in liters/kg), Ve, extracellular fluid volume (in liters/kg); Vr, “remainder of the fluid” volume (in liters/kg); Re/i, ratio of binding
`proteins in extracellular fluid (except plasma) to binding proteins in plasma; CL, clearance; F, oral bioavailability; MLP, maximum lifespan potential.
`
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`Prediction of Human Pharmacokinetics
`
`47
`
`presents a great challenge to pharmacokinetic prediction
`methods because each method must not only be applicable to
`a close-in homologous series of compounds but also be
`broadly applicable to compounds of all types and physico-
`chemical properties. These data were used in several meth-
`ods, described herein, designed to predict the pharmacoki-
`netics (clearance, volume of distribution,
`t1/2 and oral
`bioavailability) of drugs in humans. The methods include a
`battery of in vitro, in vivo and combined in vivo/in vitro
`approaches both obtained from the scientific literature and
`described for the first time here. A comparison of the pre-
`dicted values to authentic human pharmacokinetic data was
`made to compare the accuracies and uses of these prediction
`methods.
`
`Methods
`Sources of Pharmacokinetic and In Vitro Data
`The original pool of compounds included in this analysis were all
`of those brought into preclinical development at Pfizer over a 14-year
`period from 1981 through 1994 (n ⫽ 83). From this set, those com-
`pounds for which no human data were available were removed (n ⫽
`30). Another three were excluded because they were developed as
`prodrugs. Thus, the data used in this analysis included all available
`preclinical pharmacokinetic and in vitro metabolism data for those
`compounds for which a minimum of a human in vivo t1/2 value was
`available (n ⫽ 50; table 1). The amount of preclinical data available
`for each compound ranged from extensive (in which case, all predic-
`tion methods could be tested) to scant (in which case, only one or two
`prediction methods could be applied). Human in vivo clearance and
`oral bioavailability data used for a given compound were from the
`lowest dose in which sufficient plasma concentration-vs.-time data
`were available to adequately describe the terminal phase. This was
`done to minimize the potential of including CL and F values that
`could be confounded by saturation of CL and/or F or limitations on
`oral absorption at high doses.
`
`Methods for Predicting Human Volume of Distribution
`Four methods were examined for their ability to accurately and
`successfully predict human volume of distribution (table 2): (1) a
`method in which an average fraction unbound in tissue in preclinical
`species is used with human plasma protein binding data to calculate
`human VDss (method V1), (2) a method in which a proportionality is
`established between VDss and fu in dog and human (method V2) and
`(3) allometric scaling without (method 3a) and with (method 3b)
`considerations for interspecies differences in plasma protein binding.
`This yielded a total of four methods, which are further described
`below.
`Average fraction unbound in tissues method (method V1).
`In this method, experimentally determined values for volume of
`distribution (in units of liters/kg) and plasma protein binding for
`each species were used, along with standard values for extracellular
`fluid volumes, plasma volumes and so forth, to calculate the fraction
`unbound in tissues in animal species. The following equation, which
`is a rearranged form of one previously described by Oie and Tozer
`(1979), was used to calculate the fraction unbound in tissues for each
`preclinical species for each compound:
`
`fut
`
`⫽
`
`Vrfu
`
`兲兴 ⫺冋共1 ⫺ fu
`
`关VDss
`
`⫺ Vp
`
`⫺ 共fuVe
`
`Vp册
`
`兲
`
`Re
`i
`
`(1)
`
`Table 3 contains the values used for each of these parameters in
`preclinical species and humans in method V1.
`After fut was calculated for each of the preclinical species, all
`values for a given compound were averaged. This averaged animal
`
`1997
`
`with pharmacokinetic parameters in preclinical species (Box-
`enbaum, 1982, 1984). Allometric scaling of pharmacokinetic
`data typically focuses on interspecies relationships between
`clearance or volume of distribution of unbound drug and
`species body weight; the relationships for these parameters
`established in preclinical species are then extrapolated to
`humans, allowing for predictions of human clearance and
`volume of distribution. Although a number of physiologically
`rather than allometrically based approaches have also been
`developed for interspecies scaling of pharmacokinetic data
`(Iwatsubo et al., 1996; Suzuki et al., 1995), allometry contin-
`ues to be the most widely used approach due to its simplicity.
`In recent years, there has been a resurgence in the use of
`allometric scaling to establish relationships among preclini-
`cal species and humans for both compounds that are meta-
`bolically and nonmetabolically cleared (Boxenbaum and
`DiLea, 1995; Mahmood and Balian, 1995, 1996a, 1996b). The
`major drawback in allometric scaling is its empirical nature.
`For example, traditional allometric scaling of plasma clear-
`ance does not allow for an understanding of species differ-
`ences in pathways of metabolic clearance that may have
`significant impact on the ability to accurately extrapolate
`human clearance from preclinical data. However, recent pub-
`lications have proposed novel methods of combining allomet-
`ric scaling with knowledge of species differences in metabo-
`lism derived from in vitro metabolism data to improve the
`utility of allometry for compounds prone to major species
`differences in metabolism (Lave et al., 1995, 1996a, 1996b;
`Ubeaud et al., 1995)
`Methods by which in vivo clearance can be predicted from
`in vitro data were first described ⬃20 years ago (Rane et al.,
`1977). The methodologies and mathematics behind ap-
`proaches to predict in vivo clearance from intrinsic clearance
`data have been summarized in a recent review by Houston
`(1994). Although the data described by Houston are from rat,
`the principles described are applicable to other species, in-
`cluding humans (Iwatsubo et al., 1997). In the seminal work
`by Rane et al. (1977), it was demonstrated that the extent of
`hepatic extraction of several drugs in rats could be estimated
`from enzyme kinetic parameters of the oxidative biotransfor-
`mation of these drugs in rat liver microsomes. The concept of
`an in vitro/in vivo correlation that included data from both
`human and preclinical species was reduced to practice for
`felodipine 10 years later (Baarnhielm et al., 1986). Various in
`vitro systems are available to obtain hepatic intrinsic clear-
`ance data; those most commonly used are liver microsomes,
`hepatocytes and precision-cut liver slices. Each system pos-
`sesses unique advantages and disadvantages in both ease of
`use and accuracy and completeness of the data obtained. In
`general, for kinetic experiments, such as determination of
`intrinsic clearance, the body of data available suggest that
`hepatocytes are a superior method with regard to accurate
`predictions of in vivo data, with microsomes also providing
`good data (Ashforth et al., 1995; Hayes et al., 1995; Vickers et
`al., 1993; Zomorodi et al., 1995).
`In this article, we describe a comprehensive retrospective
`analysis of preclinical pharmacokinetic and in vitro metabo-
`lism data accrued over a 14-year period for Pfizer proprietary
`compounds. The compounds in the data set used for this
`analysis cover a broad range of small-molecule (e.g., molecu-
`lar weight ⬍600) organic compounds designed for therapeu-
`tic use in a variety of disease states. Thus, use of this data set
`
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`Vol. 283
`
`Plasma fu
`
`Urinary
`excretion
`
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`
`%
`
`⬍2
`
`⬍1
`⬍1
`60
`
`⬍1
`
`⬍1
`
`6
`⬍1
`⬍2
`10
`⬍1
`10
`⬍1
`⬍1
`⬍1
`⬍1
`⬍1
`⬍1
`47
`⬍1
`72
`
`⬍1
`20
`59
`65
`61
`1
`⬍1
`8
`⬍1
`
`⬍1
`
`0.01
`
`0.12
`0.03
`0.001
`0.19
`0.51
`0.07
`
`0.09
`0.55
`0.02
`0.01
`0.11
`
`0.60
`0.60
`0.08
`0.07
`
`0.006
`0.93
`0.02
`0.001
`0.007
`0.001
`0.28
`0.005
`0.005
`0.01
`0.08
`0.004
`0.01
`0.16
`0.03
`0.89
`
`0.02
`0.43
`0.02
`0.36
`0.01
`0.04
`0.12
`0.12
`0.001
`0.01
`0.002
`0.08
`
`F
`
`%
`
`20
`
`59
`1.0
`
`4.6
`
`89
`
`70
`
`69
`70
`64
`80
`
`93
`
`83
`
`41
`
`46
`
`48
`
`Obach et al.
`
`TABLE 1
`Summary of pharmacokinetic and physicochemical properties of 50 compounds examineda
`Compound
`Molecular
`Acid, base or
`No.
`weight
`neutral
`
`Lipophilicity
`
`CL
`
`VDss
`
`t1/2
`
`Base
`454
`1
`Base
`241
`2
`Base
`222
`3
`Base
`311
`4
`Base
`412
`5
`Base
`296
`6
`Acid
`404
`7
`Base
`380
`8
`Neutral
`321
`9
`Base
`387
`10
`Acid
`339
`11
`Neutral
`262
`12
`Acid
`291
`13
`Acid
`369
`14
`Neutral
`620
`15
`Neutral
`740
`16
`Base
`329
`17
`Base
`327
`18
`Base
`375
`19
`Base
`414
`20
`Neutral
`236
`21
`Acid
`419
`22
`Base
`749
`23
`Base
`342
`24
`Acid
`320
`25
`Acid
`331
`26
`Acid
`338
`27
`Base
`452
`28
`Acid
`373
`29
`Acid
`428
`30
`Acid
`465
`31
`Neutral
`318
`32
`Base
`299
`33
`Base
`451
`34
`Acid
`283
`35
`Base
`408
`36
`Neutral
`306
`37
`Acid
`283
`38
`Base
`395
`39
`Base
`253
`40
`Base
`376
`41
`Base
`441
`42
`Acid
`399
`43
`Base
`474
`44
`Base
`439
`45
`Base
`418
`46
`Acid
`497
`47
`Base
`582
`48
`Base
`415
`49
`Base
`426
`50
`a A blank entry indicates no data available.
`
`clogP
`6.99
`2.91
`1.48
`3.90
`4.42
`3.46
`0.91
`4.10
`5.10
`5.97
`4.80
`0.62
`2.67
`1.56
`4.31
`1.83
`0.19
`1.81
`4.37
`5.50
`0.64
`2.35
`1.83
`5.35
`4.69
`2.70
`4.84
`⫺0.56
`5.59
`5.53
`4.61
`2.06
`6.09
`3.82
`2.04
`2.78
`⫺0.11
`4.02
`4.00
`1.69
`1.53
`1.58
`0.18
`2.28
`2.03
`3.08
`7.21
`5.22
`5.44
`3.66
`
`ml/min/kg
`
`liter/kg
`
`4.0
`
`12
`15
`
`0.7
`
`2.3
`6.6
`
`21
`16
`
`1.5
`5.5
`
`0.1
`
`0.1
`
`1.2
`7.6
`7.0
`0.3
`
`8.0
`3.2
`5.9
`4.3
`2.3
`9.8
`
`5.9
`
`1.0
`0.4
`21.0
`0.7
`
`15.1
`1.5
`9.0
`2.8
`3.4
`1.5
`
`2.1
`
`hr
`16
`0.9
`3.5
`3.8
`2.8
`4.7
`1.9
`7.4
`1.2
`30
`1.3
`40
`5.5
`2.3
`1.5
`45
`1.1
`4.3
`41
`1.0
`43
`27
`68
`26
`26
`45
`45
`11
`25
`400
`30
`2.3
`1.0
`11
`0.6
`35
`26
`0.9
`27
`5.4
`2.4
`7.6
`1.6
`4.0
`3.2
`4.1
`16
`2.5
`33
`3.0
`
`value for fut is assumed to be equal to fut in humans and, along with
`the value experimentally determined for human fu (fraction unbound
`in human serum/plasma), was used in the prediction of human VDss
`(in units of liters/kg) using the following equation (rearranged ver-
`sion of equation 1) and using appropriate human values for Vp, Re/i
`and so forth:
`
`䡠 Vp冎
`
`Re
`i
`
`VD(human prediction)
`
`⫽ Vp
`
`⫹ 关fu共human兲 䡠 Ve
`
`兴 ⫹再冋1 ⫺ fu共human兲册 䡠
`
`(2)
`
`⫹ Vr
`
`䡠
`
`fu共human兲
`fut共average兲
`
`Proportionality (method V2). This method simply states that a
`proportionality could be set up between the free-fraction of drug in
`
`plasma in dog and human and the volume of distribution in these two
`species. [In other words, free VD(human) ⫽ free VD(dog).] Implicit to
`this method was the assumption that tissue binding of drugs is
`similar in dogs and humans and that physiological parameters, such
`as extracellular fluid volumes, are similar between the two species
`on a per-weight basis. Solving for the human volume of distribution
`(in units of liters/kg) yielded the following equation:
`
`VD(human prediction)
`
`⫽
`
`fu共human兲 䡠 VD(dog)
`fu共dog兲
`
`(3)
`
`where the term fu designated the fraction of drug unbound in the
`plasma (or serum) of dog or human, and VD(dog) represented the
`volume of distribution at steady state in dog (in units of liters/kg).
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`1997
`
`TABLE 2
`Summary of pharmacokinetic prediction methods
`Method
`Abbreviation in text
`
`Prediction of Human Pharmacokinetics
`
`49
`
`Data required
`
`Underlying assumptions
`
`Plasma protein binding in two or more species
`and human
`Intravenous pharmacokinetics in two or more
`species
`
`Plasma protein binding in dog and human
`Intravenous pharmacokinetics in dog
`
`Average fut(preclinical species) ⫽ fut(human)
`Re/i is uniform across species and is the same for
`all binding proteins
`
`fut(dog) ⫽ fut(human)
`
`Intravenous pharmacokinetic data in two or
`more species
`
`No intrinsic differences in plasma protein or tissue
`binding across preclinical species and human
`
`Intravenous pharmacokinetic data in two or
`more species
`Plasma protein binding in two or more species
`and human
`
`No intrinsic differences in tissue binding across
`preclinical species and human
`
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`
`Invitrorates and activities are representative of those that
`occur invivo
`Liver is major organ of CL
`CLmetabolism ⬎⬎ CLrenal ⫹ CLbiliary
`Oxidative microsomal metabolism ⬎⬎ other metabolism
`fu(incubation matrix) ⫽ unity
`[S] ⬍ KM
`No inactivation of enzyme
`Equilibrium not approached
`
`In vitro rates and activities are representative of
`those that occur in vivo
`
`Liver is major organ of CL
`
`CLmetabolism ⬎⬎ CLrenal ⫹ CIbiliary
`Oxidative microsomal metabolism ⬎⬎ other metabo-
`lism
`
`fu(incubation matrix) ⫽ unity
`
`No inactivation of enzyme
`
`Mechanism of CL is similar across species
`Assumes no interspecies differences in intrinsic CL
`
`Turnover rate in human invitrosystem
`
`Plasma protein binding in human
`Turnover rate in human in vitro system
`
`Turnover rate in human in vitro system
`
`Plasma protein binding in human
`Turnover rate in human in vitro system
`
`Substrate saturation experiment in human in
`vitro system (Vmax/KM)
`Substrate saturation experiment in human in
`vitro system (Vmax/KM)
`Plasma protein binding in human
`
`Substrate saturation experiment in human in
`vitro system (Vmax/KM)
`Substrate saturation experiment in human in
`vitro system (Vmax/KM)
`Plasma protein binding in human
`
`Plasma protein binding in two or more species
`and human
`Intravenous pharmacokinetics in two or more
`species
`
`Intravenous pharmacokinetics in two or more
`species
`
`Plasma protein binding in two or more species
`and human
`Intravenous pharmacokinetics in two or more
`species
`
`Intravenous pharmacokinetics in two or more
`species
`
`Intravenous pharmacokinetics in monkey
`
`Intravenous pharmacokinetics in dog
`
`Intravenous pharmacokinetics in rat
`
`Empirical approach; assumes uniform intrinsic
`properties between preclinical species and
`humans
`
`A. Volume of distributions
`
`Average fraction unbound in tissues
`
`V1
`
`Dog-human proportionality
`
`Allometric scaling, excluding
`interspecies protein binding
`differences
`
`Allometric scaling, including interspecies
`protein binding differences
`
`B. Clearance
`Invitrot1/2, excluding protein binding,
`well-stirred model
`
`In vitro t1/2, including protein bind-
`ing, well-stirred model
`
`In vitro t1/2, excluding protein bind-
`ing, parallel tube model
`
`In vitro t1/2, including protein bind-
`ing, parallel tube model
`
`Enzyme kinetics, excluding fu, well-
`stirred model
`
`Enzyme kinetics, including fu, well-
`stirred model
`
`Enzyme kinetics, excluding fu, paral-
`lel tube model
`
`Enzyme kinetics, including fu, parallel
`tube model
`
`Allometric scaling, including inter-
`species fu and MLP differences
`
`Allometric scaling, excluding inter-
`species fu differences, including
`MLP differences
`
`Allometric scaling, including inter-
`species fu differences, excluding
`MLP differences
`
`Allometric scaling, excluding inter-
`species fu and MLP differences
`
`C. t1/2 and oral bioavailability
`Human vs. monkey
`
`Human vs. dog
`
`Human vs. rat
`
`V2
`
`V3a
`
`V3b
`
`C1a
`
`C1b
`
`C1c
`
`C1d
`
`C2a
`
`C2b
`
`C2c
`
`C2d
`
`C3a
`
`C3b
`
`C3c
`
`C3d
`
`T1
`
`T2
`
`T3
`
`Combinations of volume and CL
`predictions
`
`Tv(x)c(x)
`
`Data for particular CL and volume prediction
`methods
`
`Corresponding CL methods
`
`Fc(x)
`
`Data for particular CL methods
`
`Same assumptions for individual VD and CL
`prediction methods
`VDss prediction inappropriate for t1/2 prediction if
`multicompartmental pharmacokinetic behavior is
`anticipated
`
`Same assumptions for individual CL prediction
`methods
`Fraction absorbed is unity and no first-pass
`extraction by intestinal mucosa
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`50
`
`Obach et al.
`
`TABLE 3
`Values used for physiological constants in selected preclinical
`species and humans
`
`Species
`
`Vp
`
`Ve
`
`Vr
`
`Re/ia
`
`Body
`weight
`
`log10 body
`weight
`
`MLP
`
`liters/kg
`N.A. N.A.
`N.A.
`N.A.
`0.0313 0.265 0.364
`1.4
`0.0313 0.265 0.364
`1.4
`
`kg
`0.02
`0.25
`0.5
`
`⫺1.70
`⫺0.60
`⫺0.30
`
`years
`2.7
`4.7
`6.7
`
`Mouse
`Rat
`Guinea
`pig
`8.0
`0.48
`3.0
`1.4
`0.0314 0.179 0.322
`Rabbit
`20
`0.54
`3.5
`1.4
`0.0448 0.208 0.485
`Monkey
`20
`1.10
`12.5
`1.4
`0.0515 0.216 0.450
`Dog
`93
`1.84
`70
`1.4
`0.0436 0.151 0.380
`Human
`Some values were from Davies and Morris (1993) and Oie and Tozer (1979).
`NA, not available.
`a Re/i was assumed to be 1.4 for all species and all binding proteins.
`
`Allometry without protein binding (method V3a). In allo-
`metric scaling of volume of distribution, the physiological parameter
`used in the scaling was total body weight (Boxenbaum, 1982). In this
`method, plots were constructed of total volume of distribution in
`preclinical species (in units of liters per animal) vs. animal body
`weight (table 3) on a log-log scale for each compound in the analysis.
`Allometric equations in the form:
`
`log10VD ⫽ a 䡠 log10body weight(kg)
`
`⫹ b
`
`(4)
`
`were obtained by linear regression of the data points to determine
`the values a and b for each compound. These were then used, along
`with a standard value for human body weight (70 kg), to predict
`human volumes of distribution.
`Allometry corrected for protein binding (method V3b). An
`identical approach was taken as described above except that animal
`volume of distribution values were corrected for plasma protein
`binding using the following equation:
`
`VDfree
`
`⫽
`
`VDtotal
`fu
`
`(5)
`
`to yield free volumes of distribution. These values were then plotted
`as in method V3a to determine the allometric relationship for free
`volume of distribution vs. total body weight. The projected human
`free volume of distribution was then converted to total volume of
`distribution by VDfree(human) 䡠 fu(human).
`
`Methods for Predicting Human Clearance
`Three approaches were examined for their ability to accurately
`and successfully predict human CL, with each approach possessing
`important variations, leading to a total of 12 prediction methods
`(table 2): (1) methods in which first-order consumption of parent
`drug was monitored in liver microsomal incubations to yield in vitro
`t1/2 values (methods C1a–C1d), (2) methods in which Vmax and KMapp
`were determined and used in the calculation of CL⬘int (methods
`C2a–C2d) and (3) allometric scaling methods with and without con-
`siderations of interspecies differences in plasma protein binding
`and/or MLP (methods C3a–C3d).
`In vitro t1/2 methods. With methods C1a, C1b, C1c and C1d,
`values for intrinsic CL (CL⬘int) were calculated from in vitro t1/2 data
`obtained in an appropriate system (e.g., liver microsomes), which
`were then scaled up to represent the CL expected in an entire
`organism. The fundamental basis behind this simple approach lies in
`the derivation of the integrated Michaelis-Menten equation (Segel,
`1975):
`
`where Q is hepatic blood flow, and fu is the free fraction in blood.
`Values of 20 ml/min/kg for hepatic blood flow and 20 g of liver/kg of
`body weight were used in these calculations. Also, when the blood/
`plasma ratio was known to significantly differ from unity, plasma (or
`serum) CL values were converted to blood CL values by correcting
`with the blood/plasma ratio:
`
`Vm
`
`䡠 dt ⫽ ⫺
`
`⫹ 关S兴
`KMapp
`关S兴
`
`䡠 d关S兴
`
`(6)
`
`CLbl
`
`⫽
`
`CLp
`B/P
`
`(15)
`
`Downloaded from
`
`jpet.aspetjournals.org
`
` at ASPET Journals on March 6, 2016
`
`Vol. 283
`
`Over one t1/2 (i.e., when [S] ⫽ 0.5[S]t ⫽ 0, the following equation
`applies:
`
`Vm
`䡠 t1/2
`KMapp
`
`⫽ 0.693 ⫹
`
`0.5关S兴
`t⫽0
`KMapp
`
`(7)
`
`A necessary assumption in this approach, which is included in the
`experimental design, is that the substrate concentration used is well
`below the KMapp value, such that:
`
`0.5关S兴
`⬍⬍0.693
`KMapp
`
`Thus, the equation degenerates to:
`
`Vm
`䡠 t1/2
`KMapp
`
`⫽ 0.693
`
`Vm
`KMapp
`
`⫽
`
`0.693
`t1/2
`
`⫽ CL⬘
`int
`
`The in vitro t1/2 is incorporated into the following equation:
`
`CL⬘
`int
`
`⫽
`
`0.693 䡠 liver weight
`䡠 liver in incubation 䡠 fu共inc兲
`in vitro t1/2
`
`(8)
`
`(9)
`
`(10)
`
`(11)
`
`where in vitro t1/2 is in min, liver weight is in g/kg of body weight and
`liver in incubation refers to the g of liver/ml in the incubation,
`resulting in units of ml/min/kg for CL⬘int. The “liver in incubation”
`value was calculated from the amount of protein in the incubation
`and a scale-up factor from protein to g of liver. [For microsomes, this
`scale-up factor is 45 mg/g of liver (Houston, 1994).] This equation
`indicates that a value for binding to protein in the incubation be
`included, however, in this treatment, it was assumed to be zero (i.e.,
`fu(inc) ⫽ 1; see Discussion). Thus, the intrinsic CL values calculated
`were based on total concentrations, not free concentrations in the
`incubation. Full expansion of equation 11 yields the following:
`
`CL⬘
`int
`
`⫽ 0.693 䡠
`
`1
`t1/2(min)
`
`䡠
`
`g of liver weight
`kg of body weight
`
`䡠
`
`ml incubation
`mg of microsomal protein
`
`(12)
`
`䡠
`
`45mg of microsomal protein
`g of liver weight
`
`Conversion of intrinsic CL to CL involved the use of equations
`describing the well-stirred (equation 13) and parallel tube (equation
`14) models of hepatic CL (Pang and Rowland, 1977; Wilkinson and
`Shand, 1975):
`
`CLp
`
`⫽
`
`䡠 CL⬘
`Q 䡠 fu
`int
`䡠 CL⬘
`Q ⫹ fu
`int
`
`⫽ Q 䡠冉1 ⫺ e
`
`CLp
`
`冊
`
`(13)
`
`(14)
`
`⫺CLint 䡠 fu
`Q
`
`Apotex v. Cellgene - IPR2023-00512
`Petitioner Apotex Exhibit 1046-0005
`
`

`

`Downloaded from
`
`jpet.aspetjournals.org
`
` at ASPET Journals on March 6, 2016
`
`1997
`
`where CLbl represents CL in whole blood, and B/P is the blood to
`plasma concentration ratio.
`Methods C1b and C1d use equations 13 and 14, respectively, as
`written above. Methods C1a and C1c use equations 16 and 17, which
`represent variations on equations 13 and 14 in which fraction un-
`bound (fu) was removed:
`
`Q 䡠 CL⬘
`int
`Q ⫹ CL⬘
`int
`
`CLp
`
`⫽
`
`CLp
`
`⫽ Q 䡠冉1 ⫺ e
`
`Q 冊
`
`⫺CL⬘int
`
`(16)
`
`(17)
`
`Enzyme kinetic methods. With methods C2a, C2b, C2c and
`C2d, the enzyme kinetic parameters KMapp and Vmax measured in
`liver microsomal incubations were used to define intrinsic CL as:
`
`CL⬘
`int
`
`⫽
`
`Vmax
`KMapp
`
`(18)
`
`Intrinsic CL was scaled-up to predictions of CL as described above.
`Both the well-stirred and parallel tube models of hepatic CL (equa-
`tions 13, 14, 16 and 17) were applied. Methods C2a and C2c disre-
`garded the impact of protein binding (equations 16 and 17, respec-
`tively), whereas methods C2b and C2d included this parameter in
`the prediction (equations 13 and 14, respectively). As with the in
`vitro t1/2 methods, a standard value of 45 mg of microsomal protein/g
`of liver weight was used in the scale-up of in vitro intrinsic CL data,
`and values of 20 g of liver/kg of body weight and 20 ml/min/kg hepatic
`blood flow were also used.
`Allometric scaling with protein binding and MLP correc-
`tion factor (method C3a). In allometric scaling of CL, the physio-
`logical parameter used in the scaling was total body weight. In the
`case of this method, corrections for interspecies differences in both
`plasma protein binding and MLP (Boxenbaum, 1982) were applied.
`For plasma protein binding, free CL is defined as:
`
`CLp共free兲 ⫽
`
`CLp共total兲
`fu
`
`(19)
`
`F ⫽ Fa
`
`䡠 Fg
`
`Prediction of Human Pharmacokinetics
`
`51
`
`and CL predictions are combined to yield t1/2 predictions (methods
`TV1C1a, TV1C1b and so forth).
`Animal correlations (methods T1–T3). Assessment of animal/
`human t1/2 correlations were undertaken with a data set containing
`both data for in-house proprietary compounds and data from the
`scientific literature for which t1/2 data was available for rat, dog,
`monkey and human. Only compounds with t1/2 data for all four
`species were used in these analyses. To construct correlations, mea-
`sured t1/2 values in rat, dog or monkey were plotted vs. human t1/2
`values, and functions were derived from 1/x-weighted linear regres-
`sion. The predictions of human t1/2 were then obtained by inserting
`the animal t1/2 value into the regression equation.
`Combinations of human volume and clearance predictions
`[methods Tv(x)c(X)]. In this approach, each method for predicting
`the volume of distribution was combined with each method of pre-
`dicting CL to generate predictions of human t1/2 using the following
`formula:
`
`Predicted human t1/2
`
`⫽
`
`0.693 䡠 predicted human VD
`Predicted human CLp
`
`(20)
`
`All volume and CL combinations were tested, regardless of
`whether the individual volume and CL methods were originally from
`different types of approaches (e.g., volume predictions from allome-
`try were combined with CL predictions from in vitro data). This
`provided a total of 48 t1/2 prediction methods (four volume prediction
`methods ⫻ 12 CL prediction methods).
`
`Methods for Predicting Human Oral Bioavailability
`(Methods FC1a–FC3d)
`The methods for predicting human oral bioavailability used those
`described for CL (table 2), with a rearranged equation that accounted
`only for first-pass hepatic CL and accounted for neither the potential
`limitations on absorption from the GI tract (i.e., fraction absorbed,
`Fa, was assumed to be unity) nor potential first pass extraction by
`the gut wall tissue (Fg ⫽ 1):
`
`䡠冉1 ⫺
`
`冊 ⫽ 1 䡠 1 䡠冉1 ⫺
`
`CLp
`Q
`
`冊
`
`CLp
`Q
`
`(21)
`
`The values of CLp(free) were then corrected for interspecies differ-
`ences in MLP: [CLp(free)/MLP] for the various species. A list of MLP
`values used for the species are given in table 3. The log10[CLp(free)] (in
`units/MLP) was plotted vs. log10(body weight) for each individual
`compound. The functions obtained for each compound were subject to
`linear regression (to obtain the expression log10CLp ⫽ a 䡠 log10body
`weight ⫹ b), the values for CLp(free) for human, per MLP, were
`projected from the regression, and the total CL values were calcu-
`lated using the values for plasma protein binding in humans and
`human MLP.
`Allometric scaling without protein binding and without
`MLP correction factor (method C3b). This allometric method
`was carried out as described above using total CL and body weight,
`with no correction for interspecies differences in MLP.
`Allometric scaling with protein binding and without MLP
`correction factor (method C3c). This allometric method was car-
`ried out as described in C3b using free CL values and body weight,
`with no correction for interspecies differences in MLP.
`Allometric scaling without protein binding and with MLP
`correction factor (method C3d). This allometric method was car-
`ried out as described in C3a, except that CL values were not con-
`verted to free CL values before regression.
`
`Methods for Predicting Human t1/2
`Two approaches were examined for their ability to accurately and
`successfully predict human t1/2 (table 2): (1) methods that rely on
`direct correlations between animal and human t1/2 values (methods
`T1–T3) and (2) methods in which individual volume of distribution
`
`Thus, the number of oral bioavailability methods is equal to the
`number of CL methods (12).
`Success criteria. For volume of distribution and CL predictions,
`success was assessed by the geometric mean of the ratio of predicted
`and actual values. Thus:
`
`冏兺 log
`Average-fold error ⫽ 10
`
`冏
`
`Predicted
`Actual
`N
`
`(22)
`
`This approach prohibited poor overpredictions from being can-
`celed out by equally poor underpredictions; underpredictions were of
`equal value to overpredictions. It also did not allow any single outlier
`prediction from biasing conclusions concerning a particular predic-
`tion method. A method that predicted all actual values perfectly
`would have a value of 1; one that made predictions that were on
`average 2-fold off (100% above or 50% below) would have a value of
`2 and so forth. A prediction method with an average -fold error ⱕ2
`was considered successful.
`For t1/2, a similar calculation was made. In addition, a second
`success criterion was applied that was applicable to drug develop-
`ment and compound selection. In this criterion, the success rate of
`correctly placing compounds into an appropriate t1/2 zone was mea-
`sured. These predetermined zones were based on dosing regimens
`associated with half-lives (when considerations of disparate PK/PD
`relationships and wide therapeutic indices are ignored). The zones
`were 0 to 4 hr (three times daily), 4 to 12 hr (twice dail