Modeling of electrostimulation characteristics to determine the optimal amplitude of current stimuli

The subject of research- the process of human skeletal muscles electrical stimulation during medical therapy. The subject of the study is a mathematical model of electrostimulation characteristics, which links the amplitude of muscle contraction and the stimulating effect amplitude. The current work develops a mathematical model in the form of an analytical expression to describe the muscle contraction amplitude dependence on electrical stimulus amplitude. Tasks to be solved: to analyze the dependence peculiarity of muscle contraction amplitude in stimulating impulse amplitude; conduct structural and parametric identification of the model; compare the results obtained using practical data, evaluate the model accuracy; use the obtained model for analytical description with the aim of a priori determination of the optimal stimulus amplitude. Methods used mathematical modeling method, methods of structural and parametric identification of models, approximation methods, parametric optimization methods, mathematical analysis methods. Results obtained an analytical model in the form of a 5th degree polynomial is proposed, which reflects the dependence of muscle contraction amplitude in the stimulus amplitude; the degree of the polynomial is selected and the coefficients of the model are obtained using parametric optimization; a model trajectory was built and the accuracy of modeling was estimated; an equation was obtained and its possible solutions were found to determine the optimal value of the stimulus amplitude; the practical application of the research results was substantiated. The results obtained can be used in the selection of individual effects of electrical stimulation during one session, as well as with extrapolation during the entire rehabilitation process. Scientific novelty: an analytical description showing the dependence of skeletal muscle contraction amplitude on the electrical stimulus amplitude was obtained, which allows determining individual optimal parameters of electromyostimulation.