Applying theoretical premises of binary toxicity mathematical modeling to combined impacts of chemical plus physical agents (A case study of moderate subchronic exposures to fluoride and static magnetic field)

Using Various Nonlinear Response Surfaces for Mathematical Description of the Type of Combined Toxicity

“…The results of this experiment were reported in the study by Katsnelson et al 28 Sodium fluoride solution was administered to rats by IP injection at a dose equivalent to 0.1 median lethal dose (LD 50 ) 3 times a week up to a total of 18 injections. Two-thirds of these rats and of the sham-injected ones were exposed to the whole body impact of a 25-mT static magnetic field (SMF) for 2 or 4 hours a day (note 1), 5 times a week.…”

“…54 However, in the experiments of our team, this type of combined toxicity occurred rather frequently. 8,9,22,24,28 Its distinctive feature is that for maintaining the level of effect while increasing the dose of one toxicant, it is necessary to increase the dose of the other as well. Consequently, for an action in opposite directions, the isobole-defining function Y ( x 1 , x 2 ) = Y 0 will be an increasing one.…”

“…In a series of publications, 22 -36 model (3) was used by us for analyzing the combined toxicities of various substances. It was shown that this model enables one to describe both the unidirectional action types (additivity, subadditivity, superadditivity) and oppositely directed actions of toxic agents in a certain region of experimental dose combinations.…”

Changes in the Dose–Response Relationship of One Toxicant Under Simultaneous Exposure to Another Toxicant

“…The dose–response lines having identical signs of their slopes: A, negative slope for the effect of the static magnetic field (acting alone or in the presence of fluoride) on the number of osteocytes in the compact bone tissue 20 ; B, positive slope for the effect of the nickel (acting alone or in the presence of chromium) on the of banded neutrophil percentage in blood smears. 19 …”

“…This issue takes us to the domain of a practically very important and theoretically complex problem of combined toxicity, to which our group has devoted a series of publications on the outcomes of its experimental and mathematical modeling. 14 -20 In these publications, based on our experiments involving a range of binary combinations, we gave primary consideration to the contradictory assessment of the so-called “type of combined action.” In particular, we postulated that (1) for this assessment, the widely recognized paradigms of effect additivity and dose additivity (Loewe additivity) are virtually interchangeable and might be regarded as different methods for modeling combined toxicity rather than as concepts reflecting fundamentally differing processes; (2) within both paradigms, there exist more than 3 traditionally recognized types of combined toxicity (additivity, subadditivity, and superadditivity), and we found at least 10 variants of it, depending on exactly which effect is considered and what its level is, as well as on dose levels and their ratio; (3) when dealing with multi-outcome chronic or subchronic combined intoxication, one may find some indices in respect to which 2 toxic agents act oppositely, and we proposed to discriminate between “hidden antagonism” (in the case of subadditivity of unidirectional effects) and “explicit antagonism” (in all cases of opposite effects).…”