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Allometric scaling to predict pharmacokinetic and pharmacodynamic parameters in man

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T O U L O U S E. Introduction to allometry ... Range of body size in mammals. Blue whale: 108 g. Shrew 2 g. Allometry is the study of size and its consequences ... – PowerPoint PPT presentation

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Title: Allometric scaling to predict pharmacokinetic and pharmacodynamic parameters in man


1
Allometric scaling to predict pharmacokinetic and
pharmacodynamic parameters in man
ECOLE NATIONALE VETERINAIRE T O U L O U S E
  • PL Toutain
  • UMR 181 Physiopathologie et Toxicologie
    Expérimentales
  • INRA, ENVT

2
Introduction to allometry
  • Allometry (a term coined by Huxley Tessier
    1936) is the study of size and its consequences

3
Range of body size in mammals
Blue whale gt108 g
Shrew 2 g
Allometry is the study of size and its
consequences
  • Interspecies allometric scaling is based on the
    assumption that there are anatomical,
    physiological and biochemical similarities among
    animals which can be described by simple
    mathematical models

4
Range of body size in mammalsextrapolation
within species
Young to adult
Adult to adult
5
Many allometric relationships have been
established between body size and organ weight as
well as body size and physiological process
6
Simple allometry
YaBWb
7
The power function
  • Y aBWb
  • Where Y is the parameter of interest, BW is the
    body weight, a b are the coefficient and
    exponent of the allometric equation respectively
  • The log transformation of this equation is
    represented as
  • log Y log a b x logBW
  • Linear plot slopeb and interceptlog A
  • the slope of the line (b) indicates the type of
    scaling relationship

8
Simple allometry the log-log transformation
logYlog a b log BW
bslope
YaBWb
log a is the Y-intercept
9
The scaling exponent (b) i.e. the slope defines
the type of scaling relationship
b1.25 Y increase faster than BW Positive
allometry
b1.0 Y increase proportionally with BW
(isometry)
b0.75 Y increase slower than BW Negative
allometry
10
The assumption behind the log-log transformation
  • It is assumed that there is a constant CV about
    the value of PK parameter associated with BW
    being considered

11
The log-log transformation
  • log-log transformation of the data will visually
    minimize the deviations from a regression line
  • A high R2 (e.g. 0.95) do not guarantee that all
    the data point will be close to the regression
    line
  • The extrapolation of this regression line to
    obtain a predicted human value may have a great
    uncertainty
  • The regression process does not treat the weight
    of each animal species comparably
  • Direct fitting of power function with
    incorporation of a weighting strategy has been
    shown not to improve the prediction performance

12
The log-log transformation
  • When there is a limited number of species
    associated with the regression analysis, each
    data point has the greatest impact on the
    prediction of Y for animals whose value of BW are
    closer to the deviant observation

13
  • How does a the distribution of body weight used
    in the regression analysis influence the
    prediction of Y
  • For any species included in the regression
    analysis, how does its location on the X-axis
    (i.e its value of BW relative to other observed
    data points) influence prediction of Y
  • Can we anticipate the impact on prediction error
    by the goodness of fit (R2) of the regression line

14
Number of species and the regression line
  • When there is a limited number of species
    associated with the regression analysis, each
    data point has the greatest impact on the
    prediction of Y for animals whose value of BW are
    closest to the deviant observation
  • When a midpoint species (dog in vet medecine) is
    the source of the error, the change is primarily
    in the intercept rather the slope consequently
    the resulting magnitude of prediction error is
    comparable throughout the range of BW values
    examined

15
Influence on the predicted value in man of a 30
decrease of the clearance value for a given
species
16
ACCURACY OF ALLOMETRICALLY PREDICTED
PHARMACOKINETIC PARAMETERS IN HUMANS ROLE OF
SPECIES SELECTIONHuadong Tang and Michael
Mayersohn
Drug Metabolism Disposition, 2005, 33 (9)
1288-1293
17
ACCURACY OF ALLOMETRICALLY PREDICTED
PHARMACOKINETIC PARAMETERS IN HUMANS ROLE OF
SPECIES SELECTIONHuadong Tang and Michael
Mayersohn
Drug Metabolism Disposition, 2005, 33 (9)
1288-1293
As demonstrated by both theoretical and
literature experimentation, rats had no
significance in predicting human PK parameters as
long as the body weight of the rat is not the
smallest in the species used in the allometric
relationship.
18
Historical developmentsthe direct extrapolation
of doses from animals to man
19
The Use of Body Surface Area as a Criterion of
Drug Dosage in Cancer Chemotherapy Donald
Pinkel (Department of Pediatrics, Ronwell Park
Memorial Institute and University of Buffalo
School of Medicine, Buffalo, N.Y.) Cancer Res
1958 28 853-856
20
The use of body surface area as a criterion of
dosage regimen in cancer chemotherapy (From D
Pinkel Cancer Res 1958 28 853-856)
Mouse0.018
Body weight in Kg
Infant8
Child20
Rat0.25
Adult70
21
Body surface area in man
  • The DuBois and DuBois formula
  • BSA (m²) 0.20247 x Height(m)0.725 x
    Weight(kg)0.425
  • The Haycock formula
  • BSA (m²) 0.024265 x Height(cm)0.3964 x
    Weight(kg)0.5378
  • The Gehan and George formula
  • BSA (m²) 0.0235 x Height(cm)0.42246 x
    Weight(kg)0.51456
  • The Boyd formula
  • BSA (m2) 0.0003207 x Height(cm)0.3 x
    Weight(grams)(0.7285 - ( 0.0188 x LOG(grams) )

22
Comparison of toxicity data acquired during
clinical studies of 18 anticancer agents with
those obtained in mice, rats, dogs, and rhesus
monkeys uncovered close interspecies correlations
when doses were related to body surface, much
closer than when doses were related to mass. This
finding has guided numerous trials of anticancer
and other agents.
23
Comparison of toxicity data on anticancer agents
for the Swiss mouse and man (on a mg per m2
basis) From Freireich et al 1966
1000
100
Antimetabolites Alkylating agents Others
10
Maximum tolerated dose (mg per m2)
1.0
0.1
10
1000
Mouse LD10 mg per m2
24
Observed and predicted dosage (mg per m2) in man
using animal system (Freireich al 1966)
25
Interspecies scaling of maximum tolerated dose of
anticancer drugs
  • In general, small animal require larger dose than
    human to reach the MTD.
  • Wanatabe et al used the LD10 mice data from 25
    anticancer drugs and concluded that the MTD in
    human can be predicted from mice LD1 using a
    scaling power of 0.75
  • Actually the use of a fixed exponent cannot be
    justified

26
Slope actually from 0.60 to 0.84
Data from Freireich al 1966
27
Body weight or body surface area?
  • BSA is not directly measured but estimated with
    allometric equations
  • For a given species, it may exist several
    equations predicting BSA
  • There is no advantage using BSA over BW

28
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29
What is exactly a Dose?
30
The determination of an ED50 or any ED
Clearance x target EC50 Bioavailability
  • ED50
  • ED50 - is a hybrid parameter (PK and PD)
  • - is not a genuine PD drug parameter

31
What is a dose?
32
Cardiac output in mammals
In mL per minute
Body Weight in kg
33
Interpretation of body clearance
  • Interpretation of body clearance consists of
    calculating an extraction ratio

Body clearance (blood) Cardiac output
Ebody
34
What is a dose?
Cardiac output (L per day)
µg/L
µg per day
35
Dose (IV) for an hepatic cleared drug with a low
or a high hepatic extraction ratio (ER)
Low ER
The plasma protein binding and metabolism
activity are the major determinants for the
elimination of low hepatic clearance drugs
therefore it is not expected to have a good
allometric relationship with BW across species
for this kind of drug
High ER
Because hepatic blood flow is shown to have an
allometric relationship with BW, it is expected
that the elimination of high hepatic clearance
drug can show an allometric relationship with BW
36
Interspecies scaling of pharmacodynamic parameters
  • ED50

37
Interspecies scaling of pharmacodynamic parameters
  • Very little information is available for the
    prediction of pharmacodynamic (PD) parameters
    from animal to man
  • It is conceptually difficult to accept that the
    efficacy and potency of a drug will relate with
    body weight of the species

38
Allometry of pharmacokinetics and
pharmacodynamics of the muscle relaxant
metocurine in mammals
39
Interspecies scaling of pharmacodynamic
parametersThe case of Ketoprofen (sKTP)
  • Cat, goat, sheep, calf, horse
  • Endpoints inhibition of the synthesis of
    thromboxan (TXB2) and prostaglandinE2 (PGE2)
  • No relationship between IC50 (or other PD
    parameters) with BW

40
Modeling and allometric scaling of
s()-ketoprofen pharmacokinetics and
pharmacodynamics a retrospective analysis E.-I.
LEPIST W.J. JUSKO, J. Vet. Pharmacol. Therap.
27, 211-218, 2004 ANTIINFLAMMATORY DRUG
41
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42
Interspecies scaling of pharmacodynamic
parametersthe case of anaesthetic potency
minimum alveolar concentration (MAC)
  • Poor correlation between BW and MAC for several
    inhalation anesthetics
  • Travis Bowers 1991in Toxicol Ind Health 1991 7
    249-260

43
In vitro data Drug affinity drug potency
Drug potency from in vitro MIC for antibiotics
Benzodiazepine dose and benzodiazepine affinity
44
Interspecies scaling of pharmacokinetic parameters
Clearance x target EC50 Bioavailability
  • ED50

45
Absorption
Volume of distribution
Clearance
bioavailability
Half-life
Systemic exposure
Dosage regimen How much
Dosing regimen How often?
46
Acute toxicity of anticancer drugshuman versus
mouse
AUC Ratio Internal dose
Dose Ratio External dose
Frequency
47
Interspecies scaling of clearance
48
Simple allometry Diazepam
49
Scaling of antipyrine intrinsic clearance in 15
mammalian species
Boxenbaum Fertig Europ J Drug Metab
Pharmacokinet 1984 9 177-183
50
The concept of neoteny
  • Retention of juvenile characteristics in the
    adults of species
  • The modern man retained its juvenile
    characteristics of its ancestors (apes) through
    the retardation of somatic development for
    selected organs

51
Exemple of Neoteny
52
Interspecies scaling of clearance
  • Simple allometry
  • Allometry with various biological correction
    factors
  • Product of maximum life-span (MLP) and clearance
  • Product of brain weight and clearance
  • Ratio of clearance and GFR
  • Two-term power equation
  • Incorporation of molecular structure parameters
  • incorporation of in-vitro data in in-vivo
    clearance
  • Correction for protein binding

53
Simple allometry allometry with standard
correction factors (MLP and Brain weight)
  • Clearance or Clearance multiplied by MLP or
    Brain weight of several species are plotted
    against BW on a log-log plot

54
Product of maximum life-span (MLP) and clearance
  • The clearance of different species are multiplied
    by their respective MLP and are plotted against a
    function of BW on a log-log scale

55
Prediction of Cefazolin Clearance in man
standard vs. corrected allometry (MLP)
Simple allometry Predicted 141 mL/min Actual 61
mL/min Error 131
Allometry with MLP as a correcting
factor Predicted 50.55mL/min Actual
61mL/min Error17.1
56
Selection of a standard correction factor and the
so-called rule of the exponent
  • The random use of the different correction
    factors is of no practical value
  • Mahmood Balian 1996 investigated 40 drugs and
    found that the exponent of the simple allometry
    ranged from 0.35 to 1.39
  • Based on these exponents ,it was found that there
    are conditions under which only one of the three
    methods can be used preferentially for reasonably
    accurate prediction of clearance

Mahmood Balian 1996 xenobiotica 26 887-895
57
The  rule of exponents to predict clearance in
manMahmood Balian 1996
  • 0.55 b lt0.71 no correction factor is
    necessary
  • 0.71 b lt1.00 MLP should be incorporated into
    scaling method
  • Bgt1.00 Brain weight should be incorporated into
    the scaling method

58
The  rule of exponents to predict clearance in
man for 50 drugs
Mahmood In interspecies pharmacokinetic scaling
2005 pp49
59
A Comprehensive Analysis of the Role of
Correction Factors in the Allometric Predictivity
of Clearance from Rat, Dog, and Monkey to
Humans RAKESH NAGILLA, KEITH W. WARD
  • 103 compounds investigated
  • Standard allometry and allometry including
    various correction factor (MLP, brain weight,
    GFR) were performed
  • Scaling were performed on all compounds
    universally and on segregated subset based on
    allometric exponent, clearance, physicochemical
    properties etc
  • 776 allometric combinations with 27913 outcomes
    were preformed
  • A predicted-to-observed clearance ratio of 0.5 to
    twofold was preselected as the criterion for
    predictive success

60
Nagilla Ward JPS 2004
61
No correction
MLP
Brain weight
Rule of the exponents
Nagilla Ward 2004
62
A Comprehensive Analysis of the Role of
Correction Factors in the Allometric Predictivity
of Clearance from Rat, Dog, and Monkey to Humans
  • When all three species were utilized in scaling
    using simple allometry, 48 of 103 compounds
    yielded a ratio (predicted/observed) that was not
    within twofold of the observed value
  • Incorporation of the empirical correction factor
    MLP or brain weight, either universally or
    judiciously according to the rule of exponents,
    failed to improve the predictive performance of
    the method.

63
A Comprehensive Analysis of the Role of
Correction Factors in the Allometric Predictivity
of Clearance from Rat, Dog, and Monkey to Humans
  • The success rate of allometric scaling ranged
    from 18 to 53
  • None of the correction factor resulted in
    substantially improved predictivity
  • None of the methods attempted in this study
    achieved a success rate greater than that
    observed by simply estimating human clearance
    based on monkey hepatic extraction

64
Influence of species, routes of elimination and
correction factors
outliers
Nagilla Ward 2004
0.5-to twofold window
65
Data set segregated based on physicochemical
properties
  • Within the classification of polar surface area
    (PSA), number of hydrogen bounds acceptors, cLogP
    and number of rotable bounds, the predictive
    success of the allometric scaling method remained
    similar with no improvement in prediction
    irrespective of the correction factor that was
    employed
  • Applying MLP, brain weight or the rule of
    exponents as correction factors resulted in no
    improvement in prediction

66
Value of the allometric approach
  • Conclusion the prospective allometric scaling ,
    with or without correction factors, represent a
    suboptimal technique for estimating human
    clearance based on in vivo preclinical data
  • Nagilla Ward J Pharmac Sci 2004 1à 2522-2534

67
See also Obach al for the value of allometry as
a predictive tool
68
Correction factors for renally and biliary
excreted drugs
  • Renally excreted drugs
  • Biliary excreted drugs

UDPGTUDP-glucuronyltransferase activity
69
Interspecies scaling of clearance
  • Simple allometry
  • Allometry with various biological correction
    factors
  • Product of maximum life-span (MLP) and clearance
  • Product of brain weight and clearance
  • Ratio of clearance and GFR
  • Two-term power equation
  • Incorporation of molecular structure parameters
  • incorporation of in-vitro data in in-vivo
    clearance
  • Correction for protein binding

70
Incorporation of molecular structure parameters
  • Wajima et al. 2002 suggested to use descriptors
    of drugs related to clearance to predict
    clearance in man e.g.
  • Molecular Weight ,Calculated partition
    coefficient (c log P Number of hydrogen bound
    acceptors (Ha)).
  • Then using some types of regression (multiple
    linear regression analysis, partial least square
    analysis or artificial neuronal network), a
    regression equation can be derived to predict
    clearance in man

71
Interspecies scaling of clearance
  • Simple allometry
  • Allometry with various biological correction
    factors
  • Product of maximum life-span (MLP) and clearance
  • Product of brain weight and clearance
  • Ratio of clearance and GFR
  • Two-term power equation
  • Incorporation of molecular structure parameters
  • Correction for protein binding
  • incorporation of in-vitro data in in-vivo
    clearance

72
Correction for protein binding
  • Protein binding varies considerably among animal
    species which in turn can influence the
    distribution and elimination of drugs
  • Theoretically unbound clearance should be
    predicted with more accuracy than the total
    clearance but in practical terms this is not the
    case (Mahmood, 2005)
  • Actually, the correction for binding simply adds
    more variability to the unbound clearance of the
    species

73
Interspecies scaling of clearance
  • Simple allometry
  • Allometry with various biological correction
    factors
  • Product of maximum life-span (MLP) and clearance
  • Product of brain weight and clearance
  • Ratio of clearance and GFR
  • Two-term power equation
  • Incorporation of molecular structure parameters
  • Correction for protein binding
  • incorporation of in-vitro data in in-vivo
    clearance

74
Dose for an hepatic cleared drug with a low
hepatic ER and a total absorption
The plasma protein binding and metabolism
activity are the major determinants for the
elimination of low hepatic clearance drugs
therefore it is not expected to have a good
allometric relationship with BW across species
for this kind of drug as it is the case for
antipyrine ( the Clint of antipyrine in man is
only one-seventh of that which would be predicted
from other species)
75
Incorporation of in vitro data in in vivo
clearance (Lavé et al. 1997)
  • Clearances are normalized with in vitro data
    providing a more rational (mechanistic) approach
    for predicting metabolic clearance in man

For 10 extensively metabolized compounds,
adjusting the in vivo clearance in the different
animal species for the relative rates of
metabolism in vitro dramatically improved the
prediction of human clearance compared to the
approach in which clearance is directly
extrapolated using BW Lave et a., J Pham Sci.,
1997, 86 584-590
76
Interspecies Scaling of Bosentan, A New
Endothelin Receptor Antagonist and Integration of
in vitro Data into Allometric Scaling Thierry
Lave, Philippe Coassolo, Geneviève Ubeaud, Roger
Brandt, Christophe Schmitt, Sylvie Dupin, Daniel
Jaeck ane Ruby C. Chou Pharmaceutical Research,
13(1), 1996
Bosentan is an orally active, nonpeptide,
competitive antagonist of both ETA and ETB
(endothelin type A and B) receptors, mainly
eliminated by liver metabolism and characterized
by a very large interspecies variability
77
Interspecies Scaling of Bosentan, A New
Endothelin Receptor Antagonist and Integration of
in vitro Data into Allometric ScalingThierry
Lave, Philippe Coassolo, Geneviève Ubeaud, Roger
Brandt, Christophe Schmitt, Sylvie Dupin, Daniel
Jaeck ane Ruby C. Chou - Pharmaceutical Research,
13(1), 1996
R20.976 Predicted human clearance100mL/min
R20.525 Predicted human clearance196ml/min
78
Hepatocytes vs microsomes
  • Absence of phase II metabolism on liver
    microsomes, which could result in enzyme
    inhibition due to the accumulation of the
    oxidative metabolites

79
Incorporation of in vitro data in in vivo
clearance
Data of Lave al (J Pham Sci 1997 86 584-590) on
10 extensively metabolised drugs reanalysd by
Mahmood 2005
80
Lavé et al Pharmac Res 1996 13 pp97-101
81
Incorporation of in-vitro data in in-vivo
clearance
Data of Lave al (J Pham Sci 1997 86 584-590) on
10 extensively metabolised drugs reanalysd by
Mahmood 2005
82
Extrapolation of bioavailability
83
Bioavailability in man prediction from rodents,
primates dogs ED
Clearance x target EC50 Bioavailability
  • ED50

84
Absorption Bioavailability (F)
where fabs fraction absorbed from GI lumen fg
fraction metabolized by GI tissue ERH hepatic
extraction ratio, equivalent to hepatic first
pass effect 1 - F presystemic elimination
85
Bioavailability in man prediction from rodents,
primates dogs
From Grass ADDR 2002 pp433
86
In vivo prediction of absolute bioavailability
  • Correlation coefficient (R2)
  • Man vs rat 0.4
  • Man vs dog 0.3
  • Man vs primates 0.2
  • Caco-2 eversed sac

87
Extrapolation of Vss
88
Interspecies scaling of volumes of distribution
(Vd)
  • Where Vp, is the volume of plasma Vt is tissue
    volume and fup and fut are the fraction of
    unbound drug in plasma and tissues respectively
  • Usually a change in fut has a greater effect than
    fup on Vss

89
The minimal volume of distribution is 7.5 L (0.1
L/kg)
  • VD 7.5 7.5 x fu 27L x

fup fuT
Drug highly bound to plasma protein fuvery smal
Volume of distribution of albumin
No partitioning No tissue binding
V 7.5 L (not 3 L) which is the VD of
albumin Note plasma volume 3 L but plasma
protein (and drug) diffuse out of vascular space
and thus protein (and drug) will return through
the lymphatic system
90
Interspecies scaling of volumes of distribution
(Vd)
  • Because there is no allometric relationship
    between protein binding and BW, it will be
    difficult to project the Vd of drug in humans
    from data in animals
  • When a drug has a low binding to plasma and
    tissue proteins or when a drug only distribute
    extracellularly, the Vd of the drug reflect total
    body water or extracellular water
  • In these cases, the Vd in human can be predicted
    from data in animals because both the total body
    water and extracellular water decrease as animal
    size increases in an allometric manner.

91
Volume of distribution of propranolol
Vtotal
Vfree (Unbound)
For propranonol, Vf should be similar in humans
and other species However this is not a general
rule (e.g. large difference for Vf between
species for Beta-lactam antibiotics)
92
Interspecies scaling of volumes of distribution
(Vd)
  • Vc is the most important volume parameter which
    can be predicted with much more accuracy than Vss
    or Vß
  • The exponent of all three volume revolve around
    1.0 indicating that there exist a direct
    relationship between BW and volume
  • Correction for protein binding is not much help
    in improving the prediction of vomume in man

93
Extrapolation of half-life
94
Interspecies scaling of elimination half-life
  • Application of HL to the first time dosing to man
    is limited
  • HL is an hybrid parameter (clearance and Vd)
  • Conceptually, it is difficult to establish a
    relationship between HL and BW
  • Unlike clearance and Vd , the correlation of HL
    with BW has been found to be poor

95
Allometric analysis of ciprofloxacin half-life,
clearance and volume of distribution across
mammalsPoor correlation for HL while correlation
for CL and Vss are good
R20.14
HL
R20.90
CL
R20.94
VD
96
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97
Prediction of drug clearance in children from
adults
  • Origin of the difference between children and
    adults
  • Variation in body composition
  • Difference in liver and kidney function

98
Age-related changes clearance
Fentanyl
Morphine
99
Prediction of drug clearance in children from
adults
  • 41 drugs considered
  • 124 observations in children of different age
    groups
  • Infant, children, adolescent (from 1 day to 17
    years)

Mahmood BJCP 2006
100
Tested models
  • Classical allometric equation with different
    exponents
  • Correction of adult clearance by the estimated
    liver and kidney weight in children
  • The clearance were estimated using a specific
    method for a given age (decision tree)
  • Childlt1year exponent1
  • Child gt1 years but lt5 years correction by liver
    and kidney weight
  • Child gt5 years allometric exponent of 0.75,
    0.80 or 0.85

Mahmood BJCP 2006
101
Results
  • No single method was suitable for all drugs or
    for all age groups
  • The RMSE i.e. (MSE)0.5 was almost similar for
    exponent 0.75, 0.80 and 0.85 as well as the
    approach based on the liver and kidney weights
  • The lowest RMSE was seen with the mixed approach

Mahmood BJCP 2006
102
Percent root mean square (RMSE) and percent error
in the prediction of clearance in children by
several methods
Number of predictions in error (gt100) for 124
predictions
Tested Exponents 0.75, 0.89, 0.85 and 1.0 LK
liver and kidney weights correction Mixed
decision tree based upon age
Mahmood BJCP 2006
103
Children lt1 year old
  • The exponent 0.75 overpredicted the clearance by
    several folds
  • When exponent 1.0 (no exponent) was used on the
    BW the prediction of clearance was fairly
    reasonable and far less erratic than 0.75

Mahmood BJCP 2006
104
Children from 1 to 5 years old
  • The best approach appears to be the liver and
    kidney weights corrections

Mahmood BJCP 2006
105
Children gt5 years old
  • One can use any exponent
  • (0.75, 0.80 or 0.85)

Mahmood BJCP 2006
106
Allometry in veterinary medicine
107
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108
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109
ConclusionsAdvantages of interspecies PK scaling
  • Simple and easy to use
  • Require plasma concentration-time data from which
    PK parameters are calculated
  • Knowledge of elimination pathways, and plasma
    protein binding may be helpful but not necessary
  • Data analysis is short
  • 80 success rate if incorporation of hepatocytes
    information's

110
Limits of allometic scaling
111
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112
Limits of allometric scaling
113
For more information, consult the Mahmood book
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