# Allometric Scaling

 Weight 1 kg Weight 2 kg Dose 1 mg Exponent Dose 2 mg Ratio 1 mg/kg Ratio 2 mg/kg

This Javascript calculator estimates interspecies dosage scaling between animals of different weights via exponential allometry.

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 0.75-0.80.

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 half-life 0.25.

West & Brown (J Exp Bio 208, 1575-1592, 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:

 Species Weight, kg Human 65.00 Mouse 0.02 Hamster 0.03 Rat 0.15 Guinea Pig 1.00 Rabbit 2.00 Cat 2.50 Monkey 3.00 Dog 8.00

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.

 Property Allometric Exponent (a) Allometric Coefficient (b) Units Basal O2 consumption 0.734 3.8 ml/hr Endogenous N output 0.72 0.000042 g/hr O2 consumption by liver slices 0.77 3.3 ml/hr Clearance Creatine 0.69 8.72 ml/hr Inulin 0.77 5.36 ml/hr PAH 0.80 22.6 ml/hr Antipyrine 0.89 8.16 ml/hr Methotrexate 0.69 10.9 ml/hr Phenytoin 0.92 47.1 ml/hr Aztreonam 0.66 4.45 ml/hr Ara-C and Ara-U 0.79 3.93 ml/hr Volume of distribution (Vd) Methotrexate 0.918 0.859 l Cyclophosphamide 0.99 0.883 l Antipyrine 0.96 0.756 l Aztreonam 0.91 0.234 l Kidney weight 0.85 0.0212 g Liver weight 0.87 0.082 g Heart weight 0.98 0.0066 g Stomach and intestines weight 0.94 0.112 g Blood weight 0.99 0.055 g Tidal volume 1.01 0.0062 ml Elimination half-life Methotrexate 0.23 54.6 min Cyclophosphamide 0.24 36.6 min Digoxin 0.23 98.3 min Hexobarbital 0.35 80.0 min Antipyrine 0.07 74.5 min Turnover time Serum albumin 0.30 5.68 day-1 Total body water 0.16 6.01 day-1 RBC 0.10 68.4 day-1 Cardiac circulation 0.21 0.44 day-1