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OCR for page 175
APPENDIX B
A Model Illustrating Synergism
The practical significance of synergism might be considered in a simple
mathematical function based on exposure and magnitude of effect.
Nearly all the data available on interactions come from observations based
on high experimental or therapeutic doses. Drinking water standards are
predicated on low-dose exposures, conditions under which the synergism
data might not be duplicated. Although empirical data are lacking, some
formal statistical models of the impact of joint exposure suggest that, as the
dose (and the consequent effect) is reduced, the contribution of interaction
to total toxicity or action is disproportionately attenuated.
A simple mathematical model should help to make clear how this might
happen. This model is intended solely to be illustrative. The subcommittee
does not advocate the unquestioned use of this model, nor does it suggest
that it necessarily reflects the type of response to exposure to a mixture.
Suppose that the magnitudes of toxicity can be described by Equation
T= Bo + B1X! + B2x2 + BI2XLX2,
(1)
where T is average toxicity, Bo is background, BY is relative effect of agent
1, B2 is relative effect of agent 2, By is "interaction" effect, and x~ and x2
are concentrations of agents 1 and 2, respectively.
Consider the following two exposure patterns:
High: x~ = 5, x2 = 10
Low: x~ = 0.5, x2 = 1.0.
175
OCR for page 176
176 DRINKING WATER AND HEALTH
Assume that Be = 10, BY = 7, B2 = 5, and BE = 0.3. Then, the total
effect at a high dose with an interaction would be 110 and without an
interaction would be 95. At a lower dose, total toxicity with an interaction
would be 18.65 and without an interaction would be 18.5.
Thus, at high doses, the interaction makes an important contribution (about
15%) to the toxicity. At low doses, the interaction contribution is only 0.8%.
Representative terms from entire chapter:
total toxicity
