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Year : 2021, Volume : 23, Issue : 2
First page : ( 188) Last page : ( 195)
Print ISSN : 0972-0979. Online ISSN : 0974-4517. Published online : 2021 May 1.
Article DOI : 10.5958/0974-4517.2021.00025.2

Mathematical modeling of mouse cell’s conductivity in pulsed electric field

Shigimaga V.A.11, Faizullin R.A.22, Osokina A.S.23

1department of Technical Systems and Technologies of Animal Husbandry, P. Vasilenko Kharkov National Technical University of Agriculture, Moscovsky Prospekt 45, Kharkov, 61000 (Ukraine)

2Federal State Budgetary Institution of Science, Udmurt Federal Research Center of the Ural Branch of the Russian Academy of Sciences, 34, T. Baramzina st., Izhevsk, 426 067 (Russia)

1e-mail: vash105@gmail.com;



Received:  10  October,  2020; Accepted:  3  March,  2021.


Based on the approximation by algebraic and transcendental functions, non-linear mathematical models were built for the experimentally obtained dependences of the conductivity of mouse’s reproductive and embryonic cells on the strength of pulsed electric field applied. The approximation of experimental data was performed by the use of least squares method. The finding of extrema, inflection, intersection and curvature of approximating functions were carried out. To find out these characteristic points, the classical mathematical analysis methods were used. For this, the well-known methods of analytical geometry and the algebraic methods for solving equations were used. In addition, to calculate the coordinates of intersection points and curvature, the 1st and 2nd derivatives of non-linear functions were determined. The relationship was established between the calculated coordinates of characteristic points and the modes of membrane electroporation during the linear growth of electric field strength applied to a cell. The constructed mathematical models of experimental conductometric curves made it possible to calculate the strength of pulsed electric field, which is necessary and sufficient for the implementation of any electro-manipulation technologies based on the phenomenon of electroporation.



Approximation, Cell conductivity, Electroporation, Mathematical analysis, Model.


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