Allometric modeling and IH toxicology

The dependence of a biological variable X on body mass M is typically characterized by an allometric scaling law of the form  

In IH toxicology, the dose received by an animal is directly related to the amount of air inhaled. Minute volume (F ) is a commonly used respiratory measurement, and Bide et al. (2000) have reviewed the existing mammalian Fm data (as well as species body mass) for the purpose of supporting IH toxicology research. Table 9.1 provides F and M values from Bide et al for several mammalian species (non-anesthetized) that were used for allometric modelling in this chapter. An empirical relationship (for both anesthetized and nonanesthetized animals) of F, as a function of M has also been developed. Based on allometric scaling law, F should scale to the 0.75 power, but Bide et al found that F, scales to the 0.809 power [with standard error (SE) of 0.01 for this value] based on the available experimental data for nonanesthetized, adult mammals  

For typical whole body exposures, the exact inspired amount is usually not measured. In its place, a nominal dose (mg) can be calculated by multiplying the lethal IH dosage, LCtjo (mg min m ), by (m min )  

Toxicity is a function of many factors, and some of these i.e. metabolic, circulatory, etc.) may also scale allometrically in their effect. Allometric modeling can be used to empirically account for the cumulative effect of these factors and scale the nominal LD50 (mg) as a function of species body mass, as shown in eqn (9.4). A human estimate can be obtained from mammalian data by extrapolating to a 70 kg human.  

Instead of replacing the LD50 with the LCtjo, a better solution to the problem of non-independent parameters is to split the LD50 into two suitable components  

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