If we ponder the difference between a human and a rat from the perspective of a pharmacologist, the first thing that generally strikes us is that a human is about 300 times larger (by body weight). However, it is not generally the case that a human dose of drug will be 300 times the rat dose. As a first approximation, observation suggests that drug doses tend to scale across species in proportion with body surface area, rather than body weight. A 70-kg human has a surface area of about 1.8 m2, and a 0.240-kg rat has a surface area of about 0.034 m2, so our second approximation suggests that the human dose should be about 50 times the rat dose. In other words,

D = a • W°67 (3.1)

where D is drug dose in a particular individual (of any species), a is a constant, and W is body weight. This is an example of an allometric equation, which asserts that many biological parameters (Y) relate across individuals or species by a power law:

Y a • Wb (3.2)

(Krishnan and Andersen, 1991; see also Dedrick, 1973; Boxenbaum, 1982; Mordenti, 1986; Yates and Kugler, 1986). Common sense tells us that a human and a rat differ in more than just size, that proportions of body parts also differ, in other words, the allometric constant b will not always equal 0.67. A number of literature values of a and b for various physiological parameters are summarized in Table 3.1. Krishnan and Andersen (1991) distinguish five general cases:

1. Parameters that decrease as body weight W increases; i.e., b < 0. An example is the number of heartbeats per unit time, for which b = —0.25.