Enter weights for the two animals, the dose used for the first animal and an exponent for the allometric calculation. Generally, allometric scaling uses an exponent of 0.750.80. Click on Calculate! and the estimated dose for the second animal is provided, along with the ratio of dose to weight for both animals. As an example, if the dosage for a 0.25 kg rat is 0.1 mg, then using an exponent of 0.75, the estimated dosage for a 70 kg human would be 6.8 mg. While the dose to weight ratio for the rat is 0.4 mg/kg, the value for the human is only about 0.1 mg/kg. The calculator may also be used going from a large animal
to a small animal. For example, if the dosage for a 70 kg
human is 10 mg, then using an exponent of 0.80, the
estimated dosage for a 0.02 kg mouse would be 0.015 mg.
The dose to weight ratio would increase from 0.14 mg/kg
for the human to 0.73 mg/kg for the mouse. Other pharmacokinetics parameters often obey the
following exponentials: clearance 0.75, volume of
distribution 1.0, and elimination halflife 0.25. West & Brown (J
Exp Bio 208, 15751592, 2005) have explored the
reasons why metabolic rate scales as the ¾ power with body
weight, and derive a hydrodynamic theory to explain this
universal result. Besides explaining metabolic rates they
also show why lifespan goes like the +¼ power, heart rate
goes as the ¼ power, and hence all species have a similar
number of heartbeats during their lifetimes (about 1.5
billion). A similar consideration of scaling of blood flow
(+¾) and resistance (¾) explains why blood pressure
is constant across species. Hu and Hayton have discussed whether the basal metabolic
rate scale is a 2/3 or 3/4 power of body mass. The
exponent of 3/4 might be used for substances that are
eliminated mainly by metabolism or by metabolism and
excretion combined, whereas 2/3 might apply for drugs that
are eliminated mainly by renal excretion. Here's a list of typical animal weights:
Here is a list of other calculations that can be performed, taken from Ritschel and Banerjee (1986) without permission. To perform a calculation, stick 1.0 into Weight 1, the weight of the animal of interest into Weight 2, the allometric coefficient (b) into Dose 1, and the allometric exponent (a) into Exponent. The result will be provided in Dose 2, with the units as given in the table below.
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