EXPERIMENTAL MODELING AND MATHEMATICAL DESCRIPTION OF THE CHRONIC COMBINED TOXICITY AS A BASIS OF MULTI-FACTOR CHEMICAL HEALTH RISKS ANALYSIS

Some postulates of the theory and mathematical modeling of combined toxic effect are considered critically and their further development is suggested. To this end, results of experiments on rats exposed to repeated intraperitoneal injections of several binary and a three-factorial combination of chemicals, mostly toxic metals salts or metalcontaining nanoparticles were analyzed. Intoxications were quantitatively characterized with tens of functional, biochemical and morphometric indices. The mathematical description of combined effects was based both on common descriptive statistics and two mathematical models using analysis of variance ANOVA (a) and (b) mathematical theory of response surface construction which correlate with widely recognised paradigms of the combined toxicity theory- additivity of effects and doses additivity respectively. It was concluded that these paradigms are virtually interchangeable and should be considered as different methods of combined toxicity modelling rather than as representing fundamentally differing processes. Thus, the zero interactive response surface regression model seems preferable because it is invariant with respect to these paradigms. Within a mathematical model there exist not only three traditionally used types of combined toxicity (additivity, subadditivity and super additivity) but a lot of its variants depending on which effect is exactly considered and on its level, as well as on the dose levels and their ratio. A special attention is given to modeling opposing effects of toxics. The expedience of introducing a concept of a main (determinant) type of combined toxicity is emphasized, and criteria of its choice are proposed. For characterizing the three-factorial toxicity, a new health risk-oriented approach is suggested, the gist of which is a classification of effects depending on whether a binary combined toxicity type remains virtually the same or appears to be either more or less adverse when modeled against the background of the third toxic. The relevance of the above results to health risk analysis and management is briefly discussed.