A gompertz age-specitic mortality rate of aging, hormesis, and toxicity:dose response studies

Author(s): Boxenbaum, H., Ciraulo, D., Fournier, D.

Journal/Book: Drug Metbolism Review. 1989; 20, 1: 111-150.

Abstract: A Gompertz age-specific mortality rate model for aging, hormesis, and toxicity has been developed and tested. The basic underlying assumptions are: (1) the Napierian logarithm of age-specific mortality rate (Gompertzian) is a linear measure of the mean intensity of physiologic injury for a homogeneous mammalian population maintained in a uniform environment and kept free of preventable disease; (2) aging, hormesis, and toxicity superimpose their injury and age-specific mortality effects independent of one another; (3) with uniform toxicant exposure, nonrepairable increments of toxicity accumulate in an age independent fashion; (4) with uniform toxicant exposure, hormesis benefit accumulates at a constant age-independent rate but dissipates at a first-order rate; and (5) hormesis and toxicity dose-responses may be characterized by the logarithmic-logistic function. Six experimental data sets employing methylene chloride, gamma-radiation, hexachlorobenzene, and DDT administered to laboratory animals were shown to be consistent with the model. Although characterization of Gompertz functions was generally achievable, precision of logarithmiclogistic function parameter estimates was poor. Therefore, extrapolation of system behavior beyond the experimental dose region is precarious; nonetheless, some extrapolations were made in order to better visualize system properties.In general, hormetic effects do not approach toxic effects in magnitude of response. Coupled with their reversibility, hormetic benefit can nearly always be nullified by toxicity (e.g., see Fig. 17). Therein lies the danger of speculation about the human situation; although some evidence indicates that low exposures to toxic substances produces net beneficial effects in animals, unless we have extensive experimental data and are capable of extrapolating these data to man, we can never be quite sure how low we need go to get comparable results in man. In fact, the existence of longevity hormesis has not yet unequivocally been established to occur in man.

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