## Elementary Aspects

Allometric scaling is an empirical method for predicting physiological, anatomical, and pharmaco-kinetic measures across species in relation to time and size (Boxenbaum 1982; Boxenbaum and DiLea 1995; Ings, 1990). Allometric scaling is based on similarities among species in their physiology, anatomy, and biochemistry, coupled with the observation that smaller animals perform physiological functions that are similar to larger animals, but at a faster rate. The allometric equation is Y = aWb, and a log transformation of this formula yields the straight line:

Y = the pharmacokinetic or physiological variable of interest a = the allometric coefficient (and log a is the intercept of the line) W = body weight b = allometric exponent (slope of the line)

One of the first applications of allometric scaling was the use of the toxicity of anticancer agents in animals to predict toxicity in humans. It was observed that the toxic dose of a drug is similar among species when the dose is compared on the basis of body surface area (Freireich et al 1966). For most vertebrate species, the body weight/volume ratio varies very little, but the surface area/volume ratio increases as species become smaller. Allometric correction of dose multiples in toxicology (compared with proposed human doses) is thus important, especially when small rodents provide the principal toxicology coverage.

Body surface area (Y) is related to body weight (W, in kg) by the formula:

This allometric relationship between body surface area and species body weight then allows for a simple conversion of drug doses across species (Figure 10.3), and allometrically eqivalent doses of drugs (mg/kg) can be calculated for any species (Table 10.4). The conversion factor (km is simply the body weight divided by the body surface area. Thus, by using the km factors, the dose in Species 1 (in mg/kg) is equivalent to (kmspecies2/kmspecies1) times the dose in Species 2 (in mg/kg). For example, a 50 mg/kg dose of drug in mouse would be equivalent to a 4.1 mg/kg dose in human, i.e. approximately one-twelfth of the dose (Table 10.4). Likewise, the conversion factor can be used to calculate equivalent doses between any species. An equivalent dose in mg/kg in rat would be twice that for the mouse.

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