title: Some considerations concerning the theory of combined toxicity: a case study of subchronic experimental intoxication with cadmium and lead.
abstract: Rats were exposed intraperitoneally (3 times a week up to 20 injections) to either Cadmium and Lead salts in doses equivalent to their 0.05 LD50 separately or combined in the same or halved doses. Toxic effects were assessed by more than 40 functional, biochemical and morphometric indices. We analysed the results obtained aiming at determination of the type of combined toxicity using either common sense considerations based on descriptive statistics or two mathematical models based (a) on ANOVA and (b) on Mathematical Theory of Experimental Design, which correspond, respectively, to the widely recognised paradigms of effect additivity and dose additivity. Nevertheless, these approaches have led us unanimously to the following conclusions: (1) The above paradigms are virtually interchangeable and should be regarded as different methods of modelling the combined toxicity rather than as reflecting fundamentally differing processes. (2) Within both models there exist not merely three traditionally used types of combined toxicity (additivity, subadditivity and superadditivity) but at least 10 variants of it depending on exactly which effect is considered and on its level, as well as on the dose levels and their ratio.
authors.affiliation: Institute of Industrial Ecology, the Urals Branch of the Russian Academy of Sciences, 20 Sofia Kovalevskaya Str., Ekaterinburg 620990, Russia. Electronic address: varaksin@ecko.uran.ru.
authors.forename: Anatoly N
authors.initials: AN
authors.lastname: Varaksin
authors.affiliation: Medical Research Center for Prophylaxis and Health Protection in Industrial Workers, 30 Popov Str., Ekaterinburg 620014, Russia. Electronic address: bkaznelson@etel.ru.
authors.forename: Boris A
authors.initials: BA
authors.lastname: Katsnelson
authors.affiliation: Institute of Industrial Ecology, the Urals Branch of the Russian Academy of Sciences, 20 Sofia Kovalevskaya Str., Ekaterinburg 620990, Russia. Electronic address: vpanov@ecko.uran.ru.
authors.forename: Vladimir G
authors.initials: VG
authors.lastname: Panov
authors.affiliation: Medical Research Center for Prophylaxis and Health Protection in Industrial Workers, 30 Popov Str., Ekaterinburg 620014, Russia. Electronic address: info@ymrc.ru.
authors.forename: Larisa I
authors.initials: LI
authors.lastname: Privalova
authors.affiliation: Medical Research Center for Prophylaxis and Health Protection in Industrial Workers, 30 Popov Str., Ekaterinburg 620014, Russia. Electronic address: info@ymrc.ru.
authors.forename: Ekaterina P
authors.initials: EP
authors.lastname: Kireyeva
authors.affiliation: Ural State Medical Academy, 3 Repin Str., Ekaterinburg 62028, Russia. Electronic address: usma@usma.ru.
authors.forename: Irene E
authors.initials: IE
authors.lastname: Valamina
authors.affiliation: Ural State Medical Academy, 3 Repin Str., Ekaterinburg 62028, Russia. Electronic address: usma@usma.ru.
authors.forename: Olga Yu
authors.initials: OY
authors.lastname: Beresneva
mesh_terms: D000818:Animals; D002104:Cadmium / Q000633:toxicity*; D005260:Female; D007854:Lead / Q000633:toxicity*; D007928:Lethal Dose 50; D051381:Rats; D059550:Toxicity Tests, Subchronic
chemical_list: D002104:Cadmium; D007854:Lead
keywords: Cadmium; Combined toxicity; Lead; Mathematical modelling