, Volume 8, Issue 1, pp 288–295 | Cite as

Approximation of the Dependency of Trace Elements Concentrations in Internal Media upon their Contents in Environment Objects

  • Tunakova Yulia Alekseevna
  • Novikova Svetlana Vladimirovna
  • Faizullin Rashat Iskanderovich
  • Valiev Vsevolod Sergeevich


Models that demonstrate the dependency of a trace element content in the internal milieu of an organism upon that in external media objects of the environment were developed to identify dominant factors in ecology-mediated microelement imbalance in a human body. Based on the sets of experimental data obtained on trace element concentrations in the internal milieu (fluids) of a human body (blood) and accumulating media (hair), external fluids (drinking water), and deposit media (soil and snow cover), the degree of approximation of dependencies captured with different models was estimated, with the most adequate ones chosen. Linear, cubic, logistic, sigmoidal, parabolic functions, a polynomial of the fourth and fifth degrees, the Nelder–Mead optimization algorithm, and a Boltzmann function were applied to evaluate the approximation degree by different models. The selection of internal and external media demonstrating the best approximation results is justified.


Drinking water Trace element concentration Approximation model 



This study was supported by the Program of Competitive Growth of Kazan Federal University and subsidy allocated to Kazan Federal University for the state assignment in the sphere of scientific activities.

Compliance with Ethical Standards

Conflicts of Interest

The authors declare that they have no conflicts of interests.


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© Springer Science+Business Media, LLC, part of Springer Nature 2018

Authors and Affiliations

  1. 1.Kazan National Research Technical University named after A. N. Tupolev (KAI)KazanRussia
  2. 2.Institute of Fundamental Medicine and BiologyKazan Federal UniversityKazanRussia
  3. 3.Institute for Environmental Problems and Subsoil Use of the Academy of Sciences of TatarstanKazanRussia

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