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

Abstract

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.

Method of diagnosing some diseases of the neuro-muscular system and features of data processing in software

“…The most ac curate quantitative characteristic of the neuromuscular ap paratus is obtained by evaluating the ability of the nerve and muscle to respond to pulses of a certain duration at certain current values by constructing a forceduration curve. The physiological basis of this method is that at constant amplitude of stimulation, the muscle is relatively insensitive to very short pulses, while the nerve is quite sensitive to them [4][5][6]. Since normally the nerve is gene rally more sensitive to current than the muscle, when stimulated with threshold and nearthreshold pulses in the motor point of the muscle, its contraction is a consequence of transsynaptic excitation coming from the nerve terminals irritated by the current [7,8].…”

“…In the practical determination of rheobase, a current pulse lasting 300 ms is used. Normally, rheobase is 4-8 mA [5,6]. The obtained rheobase value is plotted on the graph, where the values of the pulse durations in milliseconds are plotted along the abscissa axis, and the corresponding current values in milliamperes are plotted along the ordinate axis [6,10].…”

“…Studies of the influence of sinusoidal and rectangular signals for filling trapezoidal, bellshaped and sharpend pulses show that the optimal signals, at which the muscles contracted almost painlessly, were sharp pulses filled with a sinusoidal or rectangular signal [5][6][7].…”