Allometric scaling of pharmacokinetic parameters: A crucial step in discovery of New Chemical Entity

What is scaling in pharmacology?

Interpolation or extrapolation of drug dose or pharmacokinetic parameters to a species of interest.

Why Scaling of dose is required???

Mainly in three main situations:

1) To calculate FIH doses for clinical trials,

2) Dose extrapolation in veterinary practice and

3) Dose extrapolation for experimental purposes.

1. Linear extrapolation/simple scaling/isometric scaling method

2. Non linear extrapolation/allometric scaling method

Methods of scaling drugs

• mg/kg dose established for one species is applied across all species

• Advantage : simple• Problems arise when this method is applied to other

species

Linear extrapolation (method no.1)

This method assumes that -• any differences in species PK/PD are not clinically

relevant

• Dosage and weight are directly (linearly) proportional.

Linear extrapolation ( contd…)

Drawbacks of method no.1

• This method tends to overdose large animals and underdose small animals, which may be very clinically significant.

• Typically, this method is only effective with drugs that have large margins of safety and wide therapeutic ranges

Allometric scaling (method no.2)• Dedrick et al.

• drug pharmacokinetics has a nonlinear (allometric) relationship to weight.

• Allometric scaling has become the method of choice for interspecies extrapolation in drug discovery and development.

Allometric scaling (contd…)• It is the study of size and its consequences• Derieved from the Greek alloios meaning different

and is used to distinguish from isometric scaling • Based on the principle that major physiologic

processes are related to body weight raised to allometric exponent

• Figure changes as a function of size.

Rat Mice

Beagle dog Non human primates

Application requires gathering of species-specific PK data, such as half-life (t½), clearance (Cl), and volume of distribution (Vd), from multiple species.

The values of BW, CL, T1/2 and Vd are converted into logarithmic values and regression analysis for body weight and PK parameters is performed using SAS software Logarithmically transformed PK parameters (Y) and body weight (W) are fitted with the equation.

Log Y =b log W + c Where ‘Y’ is the parameter of interest, ‘W’ is the bodyweight and ‘b’ and ‘c’ are the intercept and slope respectively.

The following allometric equation is then applied.Y = aWb

Where ‘a’ is the anti-logarithm of ‘c’. Log-log plots of body weight Vs. Cl, T1/2and Vdss are made. Correlation coefficient (r2) is calculated of each correlation. The accuracy of extrapolated values was expressed as mean error (M.E %) using the equation -

M.E =

Where E is extrapolated value and O is observedvalue.

E-0 E X 100

BWCLT1/2Vd

Calculate r

Y=aWblogY=b log W+C

Allometric scaling of drug between Cl and BW

Allometric scaling of drug between Vd and BW

Allometric scaling of drug between T1/2 and BW

Interspecies difference between PK phase

Body metabolic rate

• As the size of the animal species gets larger the body surface area in relation to body weight decreses relatively

• Reason : transportation distance of nutrients…

• Absorption of lipophilic compounds is greater in dog

• Belladona is not toxic to rabbit

• Morphine produces CNS excitation in cats

• Absorption of orally administered drugs is faster in

monogastric animals

Species differences (size independent)

Rate of drug distribution

Determined by-

• Blood flow and rate of transport.

• Circulation time and blood flow can be scaled

allometrically

15 secs

60 secs

250 g

70 kg

Blood flow rate

Protein binding (Size independent)

• Drug affinity• No.of PBS• Efflux protein

Drug metabolism

• When a dose of aspirin was scaled for administration to cats, the cats experienced aspirin toxicity.

• Dogs lack acetylation.• Constitutive androstane receptor • Pregnane X receptor• Metabolites can also be biologically active

Drug elimination

• Compounds with molecular wt exceeding 350 with amphipathic structures or which undergo conjugation reaction are excreted in the bile.

Interspecies difference between PD phase

Dose response

Drug affinity (size independent) • Na/K ATPase transporter

• Dog,sheep and human are 1000 times more sensitive than rat and mice

• Gene regulation and expression

1. Drugs that are predominantly excreted renally.2. Drugs whose metabolism is primarily flow-limited.3. Drugs whose targets are not subject to large inter-species

differences in expression, affinity and distribution, or whose effects are not dependent on a receptor interaction .

4. Drugs that do not distribute extensively into tissues.

The following drugs follow simple allometric scaling

The following drugs are unlikely to follow simple allometric scaling-

1. Drugs that are highly protein-bound, but this can be corrected for by considering fu.

2. Drugs that undergo extensive metabolism(atropine). Important species differences in drug-metabolizing systems must be

considered.3. Drugs that undergo significant biliary excretion (MW > 350,

ampiphilic, conjugated)

The following drugs are unlikely to follow simple allometric scaling (contd…)

4. Drugs whose targets are subject to inter-species differences in expression, affinity and distribution.(morphine)

5. Drugs that undergo extensive renal secretion.

Conclusion • Interspecies allometric scaling has been widely used in the

prediction of pharmacokinetic parameters of a species of interest.

• Body weight, is the only required data.• Very important for dosing large (zoo) animals• Allometry is commonly used for determining the FIH dose

for Phase I human clinical drug trials.• Interspecies difference should be taken into consideration.• It is very simple and economic approach.

Thank you

• Tusko, who was an Asiatic elephant at the Lincoln Park Zoo in Oklahoma City.

• In 1962 ,Was given a dose of drug LSD, which had been estimated using a mg/kg method from cat

• Result …status epilepticus after 5 mins and finally died 1 hr and 35 mins later

• Dose administered : 297 mg• Corrected dose : 5.3 mg...

Correct translation of doses among and within species is of utmost importance…

Tragic example

Allometric scaling (contd…)

• Allometric scaling is a method of interspecies extrapolation that is commonly used to estimate human PK parameters from PK parameters measured in animals.