Modeling the electrical stimulation intensity dependence on stimulus frequency

The object of research is the process of electrical stimulation of human skeletal muscles during therapeutic therapy. The subject of study is a mathematical model of the electrostimulation characteristic, which relates the amplitude of muscle contraction and the frequency of the stimulating effect. The purpose of the work is to develop a mathematical model in the form of an analytical expression for describing the dependence of the amplitude of muscle contractions on the frequency of electrical stimuli. Methods used: methods of mathematical modeling, methods of structural and parametric identification of models, methods of approximation, methods of parametric optimization, methods of mathematical analysis. The results obtained: an analytical model in the form of a polynomial is proposed, which displays the dependence of the amplitude of muscle contraction on the frequency of stimuli; the degree of the polynomial is chosen and the coefficients of the model are obtained by parametric optimization; a model trajectory is built and the accuracy of modeling is estimated; an equation is obtained and its possible solutions are found to determine the optimal value of the stimulus frequency. The results can be used in the selection of individual effects of electrical stimulation during one session or with extrapolation over a number of sessions. Scientific novelty: an analytical description of the influence of the frequency of electrical stimuli on the mode of contraction of skeletal muscles has been obtained, which allows you to determine the individual optimal parameters of electromyostimulation.