Problems of identifying periodontopathogenic bacterial flora and potential solutions to them by mathematical modeling of an effective dielectric response using the example of S. aureus (reference strain)
Authors:   Lashkarev Institute of Semiconductor Physics, National Academy of Sciences of Ukraine, Kyiv, Ukraine, Goncharenko A. , Burgonskyi V. ,   National Medical Academy of Postgraduate Education named after PL Shupyka, Kyiv, Ukraine, Mykolaichuk S. ,   National Medical Academy of Postgraduate Education named after PL Shupyka, Kyiv, Ukraine
Published: March 2021

The aim of the study was to create a multiparametric mathematical model describing the dielectric response of Staphylococcus aureus suspensions for its further use to interpret dielectric spectra and identify the parameters of periodontopathogenic bacterial flora, that would optimize diagnostic processes in periodontology. Materials and methods. The study was based on the use of the Bergman-Milton analytical spectral representation for the effective dielectric response, generalized to the case of inclusions (bacteria), which can be modeled as core-shell- spheroids. The developed software using the Matlab numerical computing environment allowed us to determine the effective dielectric conductivity and dielectric losses as a function of material and geometrical parameters of the bacterial suspension. The material parameters and the inclusion sizes (Staphylococcus aures – S. Aureus bacteria) were taken from literature sources; geometrical parameters characterizing the bacteria shape were considered as model variables. To illustrate the application of the method, the spectral density function of the simplest kind, sush as a homogeneous distribution of spheroidal shapes with a median corresponding to the spherical shape, was used. Results. The spectra of the real and imaginary part of the effective dielectric function εeff of S. Aureus aqueous suspensions in the frequency range of 1–104 KHz at different values of a nonsphericity parameter, characterizing the fluctuations of the bacterial shape around the spherical one, were calculated. It is shown that shape fluctuations can significantly affect Re εeff only at low frequencies, where they increase Re εeff. At high frequencies, the shape fluctuations only slightly reduce Re εeff. The imaginary part of the effective dielectric function (dielectric losses) shows a weak dependence on the nonsphericity parameter with in the entire frequency range. Other calculations indicate that the increase in the electrical conductivity of the plasma membrane, which characterizes S. Aureus dead bacteria, is accompanied by a marked decrease in Re εeff at frequencies below 1 MHz. Conclusion. By the example of S. Aureus, we demonstrated the use of a generalized spectral model of the effective dielectric response for the interpretation of the dielectric spectra of pathogenic microorganisms. The simplicity and analyticity of the model make it a convenient and promising tool for biophysical and medical studies. The generalized spectral model can be used to solve thel direct problem, namely to determine the influence of material and geometrical parameters of bacteria on their dielectric spectra, as well as to solve the inverse problem, which consists in finding the model parameters by processing the experimental dielectric spectra.