MATHEMATICAL MODELING OF MOUSE CELL’S CONDUCTIVITY IN PULSED ELECTRIC FIELD (Applied Biological Research, 2023)
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.
Keywords: Approximation; cell conductivity; electroporation; mathematical analysis; model