### Issues

## Identification of general patterns and mathematical prediction of the synergistic interaction of hyperthermia with ionizing radiation or salts of heavy metals

«Radiation and Risk», 2020, vol. 29, No. 3, pp.106-117

*DOI: 10.21870/0131-3878-2020-29-3-106-117*

**Authors**

**Tolkaeva M.S.**– Environmental Engineer (Ecologist). Contacts: 4 Korolyov str., Obninsk, Kaluga region, Russia, 249035. Tel.: (484) 399-32-97; e-mail: This email address is being protected from spambots. You need JavaScript enabled to view it. .

**Belkina S.V.**– Head of Lab., C. Sc., Biol.

**Vorobey O.A.**– Junior Researcher

**Zhurakovskaya G.P.**– Lead. Researcher, D. Sc., Biol.

**Petin V.G.**– Chief Researcher, D. Sc., Biol., Prof. A. Tsyb MRRC.

A. Tsyb MRRC, Obninsk

**Abstract**

One of the directions in cancer treatment is the use of hyperthermia in combination with ionizing radiation or drugs. Some of the active drugs used include heavy metals. However, the study of their synergistic interaction with hyperthermia is fragmentary. The purpose of our study is to apply the mathematical model of synergism to identify common patterns of manifestation of synergistic effects at the simultaneous action of hyperthermia with ionizing radiation or salts of heavy metals on the survival of biological objects of various origins. In the experiments, biological objects of various origins were used - bacteriophages, bacterial spores, bacterial cells, diploid yeast cells and mammalian cells. To demonstrate the generality of the revealed patterns, we used the data on the survival rate of Chinese hamster cells published by other authors. To quantify the synergistic enhancement ratio, cell survival was determined after individual effects of hyperthermia, ionizing radiation, one of the heavy metals and their simultaneous action. The following salts of heavy metals were used – zinc sulfate, copper sulfate, cisplatin, lead iodide, and potassium dichromate. The results obtained are described and interpreted using the mathematical model of synergism, according to which the synergism is caused by the formation of additional effective damage due to the interaction of sublesions from each agent, which are not effective when they are used individually. For all analyzed cases of the hyperthermia interaction with ionizing radiation or heavy metals, the existence of an optimum temperature is demonstrated at which the greatest value of the synergistic enhancement ratio is recorded. The knowledge and consideration of the ideas described in this paper and the general patterns of synergistic effects will be useful for specialists using a combination of hyperthermia with physical or chemical agents, including heavy metals, in various practical areas of radiology, in particular for optimizing combined tumor treatment methods.

**Key words**

*combined action, hyperthermia, ionizing radiation, heavy metals, synergism, bacteriophage, bacteria, yeast cells, mammalian cells, mathematical model, sublesions, prediction.*

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