Title: Allometric scaling to predict pharmacokinetic and pharmacodynamic parameters in man
1Allometric 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
2Introduction to allometry
- Allometry (a term coined by Huxley Tessier
1936) is the study of size and its consequences
3Range 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
4Range of body size in mammalsextrapolation
within species
Young to adult
Adult to adult
5Many allometric relationships have been
established between body size and organ weight as
well as body size and physiological process
6Simple allometry
YaBWb
7The 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
8Simple allometry the log-log transformation
logYlog a b log BW
bslope
YaBWb
log a is the Y-intercept
9The 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
10The 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
11The 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
12The 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
14Number 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
15Influence on the predicted value in man of a 30
decrease of the clearance value for a given
species
16ACCURACY OF ALLOMETRICALLY PREDICTED
PHARMACOKINETIC PARAMETERS IN HUMANS ROLE OF
SPECIES SELECTIONHuadong Tang and Michael
Mayersohn
Drug Metabolism Disposition, 2005, 33 (9)
1288-1293
17ACCURACY 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.
18Historical developmentsthe direct extrapolation
of doses from animals to man
19The 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
20The 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
21Body 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) )
22Comparison 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.
23Comparison 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
24Observed and predicted dosage (mg per m2) in man
using animal system (Freireich al 1966)
25Interspecies 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
26Slope actually from 0.60 to 0.84
Data from Freireich al 1966
27Body 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
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29What is exactly a Dose?
30The 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
31What is a dose?
32Cardiac output in mammals
In mL per minute
Body Weight in kg
33Interpretation of body clearance
- Interpretation of body clearance consists of
calculating an extraction ratio
Body clearance (blood) Cardiac output
Ebody
34What is a dose?
Cardiac output (L per day)
µg/L
µg per day
35Dose (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
36Interspecies scaling of pharmacodynamic parameters
37Interspecies 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
38Allometry of pharmacokinetics and
pharmacodynamics of the muscle relaxant
metocurine in mammals
39Interspecies 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
40Modeling 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
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42Interspecies 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
43In vitro data Drug affinity drug potency
Drug potency from in vitro MIC for antibiotics
Benzodiazepine dose and benzodiazepine affinity
44Interspecies scaling of pharmacokinetic parameters
Clearance x target EC50 Bioavailability
45Absorption
Volume of distribution
Clearance
bioavailability
Half-life
Systemic exposure
Dosage regimen How much
Dosing regimen How often?
46Acute toxicity of anticancer drugshuman versus
mouse
AUC Ratio Internal dose
Dose Ratio External dose
Frequency
47Interspecies scaling of clearance
48Simple allometry Diazepam
49Scaling of antipyrine intrinsic clearance in 15
mammalian species
Boxenbaum Fertig Europ J Drug Metab
Pharmacokinet 1984 9 177-183
50The 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
51Exemple of Neoteny
52Interspecies 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
53Simple 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
54Product 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
55Prediction 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
56Selection 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
57The 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
58The rule of exponents to predict clearance in
man for 50 drugs
Mahmood In interspecies pharmacokinetic scaling
2005 pp49
59A 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
60Nagilla Ward JPS 2004
61No correction
MLP
Brain weight
Rule of the exponents
Nagilla Ward 2004
62A 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.
63A 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
64Influence of species, routes of elimination and
correction factors
outliers
Nagilla Ward 2004
0.5-to twofold window
65Data 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
66Value 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
67See also Obach al for the value of allometry as
a predictive tool
68Correction factors for renally and biliary
excreted drugs
- Renally excreted drugs
- Biliary excreted drugs
UDPGTUDP-glucuronyltransferase activity
69Interspecies 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
70Incorporation 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
71Interspecies 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
72Correction 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
73Interspecies 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
74Dose 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)
75Incorporation 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
76Interspecies 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
77Interspecies 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
78Hepatocytes vs microsomes
- Absence of phase II metabolism on liver
microsomes, which could result in enzyme
inhibition due to the accumulation of the
oxidative metabolites
79Incorporation 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
80Lavé et al Pharmac Res 1996 13 pp97-101
81Incorporation 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
82Extrapolation of bioavailability
83Bioavailability in man prediction from rodents,
primates dogs ED
Clearance x target EC50 Bioavailability
84Absorption 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
85Bioavailability in man prediction from rodents,
primates dogs
From Grass ADDR 2002 pp433
86In 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
87Extrapolation of Vss
88Interspecies 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
89The minimal volume of distribution is 7.5 L (0.1
L/kg)
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
90Interspecies 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.
91Volume 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)
92Interspecies 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
93Extrapolation of half-life
94Interspecies 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
95Allometric 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
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97Prediction 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
98Age-related changes clearance
Fentanyl
Morphine
99Prediction 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
100Tested 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
101Results
- 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
102Percent 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
103Children 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
104Children from 1 to 5 years old
- The best approach appears to be the liver and
kidney weights corrections
Mahmood BJCP 2006
105Children gt5 years old
- One can use any exponent
- (0.75, 0.80 or 0.85)
Mahmood BJCP 2006
106Allometry in veterinary medicine
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109ConclusionsAdvantages 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
110Limits of allometic scaling
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112Limits of allometric scaling
113For more information, consult the Mahmood book