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Allometric scaling to predict pharmacokinetic and pharmacodynamic
parameters in man
PL ToutainUMR 181 Physiopathologie et Toxicologie Expérimentales
INRA, ENVT
ECOLENATIONALEVETERINAIRET O U L O U S E
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: >108 gShrew 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 mammals:extrapolation within species
Adult to adult Young to adult
5
Many allometric relationships have been established between body size and organ weight as well as body size and physiological process
6
y = 10x0.6
R2 = 1
0
20
40
60
80
100
120
140
160
180
0 20 40 60 80 100 120
Body weight
plas
ma
clea
ranc
e
Simple allometry
Y=aBWb
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: slope=b and intercept=log A
the slope of the line (b) indicates the type of scaling relationship
8
Simple allometry: the log-log transformation
y = 10x0.6
R2 = 1
1
10
100
1000
0.01 0.1 1 10 100
Body weight
pla
sma
clea
ran
ce
logY=log a +b log BW
b=slope
Y=aBWb
log a is the Y-intercept
9
0
2
4
6
8
10
12
0 2 4 6 8 10 12
Body weight
par
amet
er o
f in
tere
stThe scaling exponent (b) i.e. the slope defines the type of scaling relationship
b=1.25 Y increase faster than BW
Positive allometry
b=0.75Y increase slower than BW
Negative allometry
b=1.0 Y increase proportionally
with BW (isometry)
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
species BW (kg) CL CL CL CL
Mouse 0.03 0.72 8 0.72 8 0.72 8 0.5046
Rat 0.2 2.99 2.09 2.99 2.99
Rabbit 4 28.28 28.28 28.28 28.28
monkey 8 47.56 47.56 47.56 47.56
dog 15 76.21 76.21 54.25 76.21
Man 70 242 247 200 212
predicted bias 0% +2% +17% +12%
16
ACCURACY OF ALLOMETRICALLY PREDICTED PHARMACOKINETIC PARAMETERS IN HUMANS: ROLE OF SPECIES SELECTION
Huadong Tang and Michael Mayersohn
Drug Metabolism Disposition, 2005, 33 (9) 1288-1293
17
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.
ACCURACY OF ALLOMETRICALLY PREDICTED PHARMACOKINETIC PARAMETERS IN HUMANS: ROLE OF SPECIES SELECTION
Huadong Tang and Michael Mayersohn
Drug Metabolism Disposition, 2005, 33 (9) 1288-1293
18
Historical developments:the 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 Instituteand
University of Buffalo School of Medicine, Buffalo, N.Y.)
Cancer Res 1958 28 853-856
20
Methotrexatey = 0.3356x0.642
R2 = 0.9989
0
1
2
3
4
5
6
0 10 20 30 40 50 60 70 80
Body weight
do
se
pe
r d
ay
in m
g
Methotrexate y = 0.3356x0.642
R2 = 0.9989
0.01
0.1
1
10
0.01 0.1 1 10 100
Body weight
do
se p
er d
ay i
n m
g
Methotrexate y = 2.7102x + 0.0987
R2 = 0.9947
0
1
2
3
4
5
6
0 0.5 1 1.5 2
surface area
do
se
pe
r d
ay
in m
g
Mouse=0.018
Rat=0.25Infant=8
Adult=70
Child=20
Body weight in Kg
The use of body surface area as a criterion of dosage regimen in cancer chemotherapy
(From D Pinkel :Cancer Res 1958 28 853-856)
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
Mouse LD10 mg per m2
Max
imum
tol
erat
ed d
ose
(mg
per
m2 )
1000
100
10
1.0
0.110 1000
AntimetabolitesAlkylating agentsOthers
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
26Data from Freireich & al 1966
Slope actually from 0.60 to 0.84
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
29
What is exactly a Dose?
30
ED50 =
ED50 - is a hybrid parameter (PK and PD)
- is not a genuine PD drug parameter
Clearance x target EC50
Bioavailability
PD
PK
The determination of an ED50 or any ED%
31
What is a dose?
ilityBioavailab
ECclearanceDose caltherapeutiplasma
EROutputCardiacclearanceplasma _
750321 .)()/(_ kgBWdayLoutputCardiac
32
Cardiac output in mammals
750223 ._ BWoutputCardiac In mL per minute Body Weight in kg
33
Interpretation of body clearance
• Interpretation of body clearance consists of calculating an extraction ratio
Ebody = Body clearance (blood)
Cardiac output
34
What is a dose?
ilityBioavailab
ECERBWDose caltherapeuti
750321 .
µg/L
µg per day
Cardiac output (L per day)
35
Dose (IV) for an hepatic cleared drug with a low or a high hepatic extraction ratio (ER)
caltherapeutiECKm
VfuDose
max
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
caltherapeutiECBWDose 76068 .
Low ER
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
ED50 = Clearance x target EC50
Bioavailability
PD
Interspecies scaling of pharmacodynamic parameters
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 parameters:The 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 analysisE.-I. LEPIST & W.J. JUSKO, J. Vet. Pharmacol. Therap. 27, 211-218, 2004
ANTIINFLAMMATORY DRUG
41
42
Interspecies scaling of pharmacodynamic parameters:
the 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
ED50 = Clearance x target EC50
Bioavailability
Interspecies scaling of pharmacokinetic parameters
45
Half-life Systemic exposure
ClearanceVolume of distribution
bioavailability
Dosing regimenHow often?
Dosage regimen How much
Absorption
46
Acute toxicity of anticancer drugshuman versus mouse
0
2
4
6
8
10
12
14
0-1 0.4-0.6 0.6-1.2 2.0-3.0 >4 0
2
4
6
8
10
12
14
0-1 0.4-0.6 0.6-1.2 2.0-3.0 >4
Dose RatioExternal dose
AUC Ratio Internal dose
Fre
qu
ency
47
Interspecies scaling of clearance
48
Simple allometry: Diazepam
49
Scaling of antipyrine intrinsic clearance in 15 mammalian species
antipyrine in mammalsy = 8.2911x0.8922
R2 = 0.9713
0.1
1
10
100
1000
10000
0.01 0.1 1 10 100 1000
Body weight in kg
Intr
insi
c cl
eara
nce
in
mL
per
min
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
1. Simple allometry
2. Allometry with various biological correction factors
1. Product of maximum life-span (MLP) and clearance
2. Product of brain weight and clearance3. Ratio of clearance and GFR4. Two-term power equation5. Incorporation of molecular structure parameters6. incorporation of in-vitro data in in-vivo clearance7. 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
baBWClearance baBWMLPClearance baBWtBrainWeighClearance
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
510188
.
)( b
man
ClearanceMLPaClearance
225063604185 .. *_*.)( BWweightBrainyearsMLP
55
Prediction of Cefazolin Clearance in man: standard vs. corrected allometry (MLP)
Cefazolin y = 5.3801x0.7828
R2 = 0.9982
0.1
1
10
100
1000
0.01 0.1 1 10 100
Body weight
Cle
aran
ce
cefazolin MLP y = 3.7432x1.1068
R2 = 0.9906
0.01
0.1
1
10
100
1000
0.01 0.1 1 10 100
Body weight in kg
CL
X M
LP
Simple allometryPredicted: 141 mL/minActual: 61 mL/minError: 131%
Allometry with MLP as a correcting factorPredicted: 50.55mL/minActual: 61mL/minError:17.1%
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 man
Mahmood & Balian 1996
1. 0.55 ≤ b <0.71 : no correction factor is necessary
2. 0.71 ≤ b <1.00 MLP should be incorporated into scaling method
3. B>1.00 Brain weight should be incorporated into the scaling method
58
The « rule of exponents »to predict clearance in man for 50 drugs
Methods % Mean absolute error (MAE)
Simple allometry 106
CL x MLP 40
CL x brain Weight 49
Rule of exponents 25
Mahmood In interspecies pharmacokinetic scaling 2005 pp49
59
• 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
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
60Nagilla & 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
64Nagilla & Ward 2004
% o
utlie
rsInfluence of species, routes of elimination and correction factors
0.5-to twofold window
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
baBWGFRClearance /
BaBWflowBileCl _
baBWUDPGTCl UDPGT=UDP-glucuronyltransferase activity
69
Interspecies scaling of clearance
1. Simple allometry2. Allometry with various biological correction factors
1. Product of maximum life-span (MLP) and clearance2. Product of brain weight and clearance
3. Ratio of clearance and GFR4. Two-term power equation
5. Incorporation of molecular structure parameters
6. incorporation of in-vitro data in in-vivo clearance7. 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:
...._)()()( boundingHydrogenMWClLogCLLogCLLog dogratman
71
Interspecies scaling of clearance
1. Simple allometry2. Allometry with various biological correction
factors1. Product of maximum life-span (MLP) and clearance2. Product of brain weight and clearance
3. Ratio of clearance and GFR4. Two-term power equation5. Incorporation of molecular structure
parameters6. Correction for protein binding7. 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
1. Simple allometry2. Allometry with various biological correction factors
1. Product of maximum life-span (MLP) and clearance2. Product of brain weight and clearance
3. Ratio of clearance and GFR4. Two-term power equation5. Incorporation of molecular structure parameters6. Correction for protein binding
7. 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
caltherapeutiECKm
VfuDose
max
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
b
shepatocyteanimal
shepatocytehumananimal BWa
Cl
CLCl
)(
)(
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 BWLave et a., J Pham Sci., 1997, 86: 584-590
77
bBWaCl shepatocyteanimal
shepatocytehumanvivoinanimal Cl
ClCl
_
__
R2=0.525Predicted human clearance=196ml/min
R2=0.976Predicted human clearance=100mL/min
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
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
81
Incorporation of in-vitro data in in-vivo clearance
Methods %MAE
Simple allometry 164
CL x Brain Weight 61
In-vitro method 40
Rule of exponent 38
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
ED50 = Clearance x target EC50
Bioavailability
Bioavailability in man: prediction from rodents, primates & dogs ED%
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”
)()(% Hgabs ERffF 11
85
Bioavailability in man: prediction from rodents, primates & dogs
From Grass ADDR 2002 pp433
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
ut
uptp f
fVVVss
89
The minimal volume of distribution is 7.5 L (0.1 L/kg)
• VD = 7.5 + 7.5 x fu + 27L x fup
fuTVolume of distribution of albumin
Drug highly bound to plasma protein fu=very smal
No partitioningNo 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
Vfree (Unbound)Vtotal
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 Vβ
• 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
R2=0.14
R2=0.90
R2=0.94
HL
CL
VD
Allometric analysis of ciprofloxacin half-life, clearance and volume of distribution across
mammalsPoor correlation for HL
while correlation for CL and Vss are good
96
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
Morphine Fentanyl
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
01800750 .__.__.
_
oror
adult
childadultchildin BW
BWClCL
1. Classical allometric equation with different exponents
2. Correction of adult clearance by the estimated liver and kidney weight in children
3. The clearance were estimated using a specific method for a given age (decision tree)
• Child<1year: exponent=1• Child >1 years but <5 years: correction by liver and kidney weight• Child >5 years : allometric exponent of 0.75, 0.80 or 0.85
Mahmood BJCP 2006
101
Results
1. No single method was suitable for all drugs or for all age groups
2. 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
3. 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
Tested Exponents: 0.75, 0.89, 0.85 and 1.0L+K: liver and kidney weights correctionMixed : decision tree based upon age
Number of predictions in error (>100%) for 124 predictions
Mahmood BJCP 2006
103
Children <1 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 >5 years old
• One can use any exponent:(0.75, 0.80 or 0.85)
Mahmood BJCP 2006
106
Allometry in veterinary medicine
107
108
109
Conclusions:Advantages 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
112
Limits of allometric scaling
113
For more information, consult the Mahmood’ book
