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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