Simulation of the electrical signal of the muscles to obtain the electromiosignal spectrum

The object of research is the process of skeletal muscle contraction under the influence of natural electrical impulses of the nervous system or under the conditions of external electrical stimulation. The subject of research is models that describe electrical processes in muscles during contraction. The work is aimed at building an analytical model of the skeletal muscle electrical signal, which makes it possible to calculate the spectral density of this signal for further analysis. Research methods are methods of mathematical modeling, theory of random processes and signals, methods of spectral analysis, methods of mathematical analysis. The model of the electrical signal of the muscle as the sum of random impulse signals corresponding to the signals of motor units is studied in the work. In this regard, a signal is analyzed, which, in contrast to the Gaussian process, is formed by summing a limited number of pulse signals. It is shown that the voltage distribution law of such a signal is expressed by the sum of Gaussian functions. In the course of the study, the structure of the electromyographic signal spectrum was obtained, presented as a sum of periodic pulses shifted in time relative to each other. The relationship between the statistical properties of a random phase difference and the type of signal power spectrum has been analytically established. The obtained theoretical relations make it possible to calculate the spectral density of the electromyographic signal depending on the number of motor units and various phase shifts between them, as well as depending on the chosen law of distribution of random variables. The results of a numerical experiment are presented for a different number of motor units and different ranges of time shifts in the case of a distribution of gauss of the probability density. The results obtained can be used in assessing the degree of dysfunction of skeletal muscles in various injuries (for example, in trauma, atrophy, etc.), as well as in choosing the optimal individual parameters of electrical stimulation during rehabilitation procedures or training processes for increasing muscle mass in athletes.