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Advances in Gerontology

, Volume 9, Issue 3, pp 308–316 | Cite as

Kinetic Model of Aging Biological Species in Natural Habitat

  • A. A. ViktorovEmail author
  • V. A. KholodnovEmail author
  • A. V. Anofriev
Article
  • 2 Downloads

Abstract

It is found that the rate of change (kinetics) of the probability of death of representatives of living systems (LS) of different biological species—Drosophila, mice, rats, dogs, horses, and people in natural environments residing in different geographical areas—is described by a kinetic equation with similar values of the parameters. However, the kinetics of the probability of death of young people and rats, starting from birth, is more accurately described by a kinetic equation of a slightly different type, taking into account the prevailing process of development and adaptation of the organism to the environment. On the basis of a single kinetic approach to the description of the probability of death, an analytical model of the intensity of mortality in LS (approximation of the mortality rate—MR) is developed. It is shown that the approximation proposed by Gompertz to MR by an increasing exponent (law of Gompertz) is a special case of the unified mathematical model proposed in this paper.

Keywords:

aging uniform kinetics Drosofila mice rats dogs horses population of the Russian Federation mathematical model extrapolation 

Notes

ACKNOWLEDGMENTS

The authors express their sincere thanks to PhD V.Yu. Solov’ev for his constant interest in the work, valuable advice and discussion, to the graduate student E.E. Morozova and to the student of Moscow Engineering Physics Institute I.S. Zhuravlev for participating in the processing of experimental data, drawing pictures, and discussing the results.

COMPLIANCE WITH ETHICAL STANDARDS

The authors declare that they have no conflict of interest. This article does not contain any studies involving animals or human participants performed by any of the authors.

REFERENCES

  1. 1.
    Anisimov, V.N., Syndrome of accelerated aging under the influence of carcinogenic environmental factors, Ross. Fiziol. Zh. im. I.M. Sechenova, 2010, vol. 96, no. 8, pp. 817–833.Google Scholar
  2. 2.
    Waisman, N.Ya., Golubovsky, M.D., and Ilinskii, Yu.Yu., Differences in the parameters of longevity and its sexspecificity in human populations and modeling them in drosophila, Adv. Gerontol., 2013, vol. 3, no. 4, pp. 268–276.CrossRefGoogle Scholar
  3. 3.
    Viktorov, A.A. and Kholodnov, V.A., Kinetic theory for aging of living systems, Usp. Gerontol., 2013, vol. 26, no. 1, pp. 58–65.Google Scholar
  4. 4.
    Viktorov, A.A., Kholodnov, V.A., Gladkikh, V.D., and Alekhnovich, A.V., Influence of environment on aging of living systems: a mathematical model, Usp. Gerontol., 2013, vol. 26, no. 1, pp. 52–57.Google Scholar
  5. 5.
    Viktorov, A.A., Gladkikh, V.D., Ksenofontov, A.I., and Morozova, E.E., Forecasting environmental health risks based on the kinetic theory of aging of living systems, Adv. Gerontol., 2015, vol. 5, no. 3, pp. 141–146.CrossRefGoogle Scholar
  6. 6.
    Viktorov, A.A., Gladkikh, V.D., and Morozova, E.E., Aging of dogs and Drosophila as described based on the kinetic theory, Adv. Gerontol., 2017, vol. 7, no. 3, pp. 177–183.CrossRefGoogle Scholar
  7. 7.
    Gavrilov, L.A. and Gavrilova, N.S., Biologiya prodolzhitel’nosti zhizni (Biology of Life Expectancy), Moscow: Nauka, 1991.Google Scholar
  8. 8.
    Gerontologiya in silico. Stanovlenie novoi distsipliny. Matematicheskie modeli, ananliz dannykh i vychislitel’nye eksperimenty (Gerontology in silico. Development of New Science. Mathematical Modeling, Data Analysis, and Computational Experiments), Marchuk, G.I., Eds., Moscow: Binom. Laboratoriya Znanii, 2007.Google Scholar
  9. 9.
    Grigor’ev, Yu.G., Popov, V.I., Shafirkin, A.V., and Antipenko, Zh.B., Somaticheskie effekty khronicheskogo gamma-oblucheniya (Somatic Effects of Chronic Gamma-Radiation), Moscow: Energoatomizdat, 1986.Google Scholar
  10. 10.
    Darenskaya, N.G., Uchakov, I.B., Ivanov, I.V., et al., Ekstrapolyatsiya eksperimental’nykh dannykh na cheloveka: printsipy, podkhody, obosnovanie metodov i ikh uspol’zovaniya v fiziologii i radiobiologii (Extrapolation of Experimental Data to Humans: Principles, Approaches, the Substantiation of Methods and Their Use in Physiology and Radiobiology), Moscow: Istoki, 2004.Google Scholar
  11. 11.
    Urlanis, B.Ts., Evolyutsiya prodolzhitel’nosti zhizni (Evolution of Life Expectation), Moscow: Statistika, 1978.Google Scholar
  12. 12.
    Butov, A.A., Volkov, M.A., Anisimov, V.N., et al., A model of accelerated aging induced by 5-bromodeoxyuridine biogerontology, Biogerontology, 2002, vol. 3, pp. 175–182.CrossRefGoogle Scholar
  13. 13.
    David, J. and MacKay, C., Consistency of the Mortality of Chronically Irradiated Beagles with the Linear No-Threshold Model, Cambridge: Cavendish Laboratory, 2014.Google Scholar
  14. 14.
    Demin, V.F., Romanov, V.V., Soloviev, V.Y., and Zakharchenko, I.E., Harmonized approach to the health safety regulation in different areas of human activity, Med. Radiol. Radiat. Bezop., 2013, vol. 58, no. 5, pp. 26–34.Google Scholar
  15. 15.
    Sacher, G.A., Relation of lifespan to brain weight and body weight in mammals, in The Lifespan Animals, Wolstenholme, G.E.W. and O’Connor, M., Eds., Boston: Little and Brown, 1959, vol. 5, pp. 115–132.Google Scholar
  16. 16.
    Upton, A.C., Kimball, A.W., Furth, J., et al., Some delayed effects of atom-bomb radiations in mice, Cancer Res., 1960, vol. 20, pp. 1–60.Google Scholar
  17. 17.
    Viktorov, A.A. and Kholodnov, V.A., Kinetic theory for aging of living systems, Adv. Gerontol., 2013, vol. 3, no. 4, pp. 261–267.CrossRefGoogle Scholar
  18. 18.
    Viktorov, A.A., Kholodnov, V.A., Gladkikh, V.D., and Alekhnovich, A.V., Influence of environment on aging of living systems: a mathematical model, Adv. Gerontol., 2013, vol. 3, no. 4, pp. 255–260.CrossRefGoogle Scholar

Copyright information

© Pleiades Publishing, Ltd. 2019

Authors and Affiliations

  1. 1.Burnazyan Federal Medical Biophysical CenterMoscowRussia
  2. 2.Kotelnikov Institute of Radioengineering and ElectronicsMoscowRussia

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