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.
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.
The subject matter of the article is an electromyographic signal transducer, which are an integral part of devices for adaptive electrical stimulation of muscle structures based on reverse electromyographic communication. The goal of the work is to study the features, obtaining the corresponding theoretical relationships and computer modeling of a differential biopotential converter, providing amplification of the useful component and suppression of harmful interference, the spectra of which intersect. The following tasks were solved in the article: determining the effect of electrode width and electrode spacing on crosstalk; formation of the electrode-skin model and the input circuit of the transducer, obtaining theoretical relations for calculating the rejection coefficient, construction of the transducer circuit and its computer simulation. The following methods were used – methods of mathematical modeling of processes and technical devices; methods of analysis, structural and parametric synthesis of nonlinear electronic circuits; methods of machine design. The following results were obtained – a biopotential amplifier circuit with tracking feedback on power supply is proposed; modeling of dynamic processes by means of the Multisim program was carried out; on the basis of the constructed model of the electrode-skin input circuit and the obtained analytical relationships, the rejection coefficient of the input circuit of the equivalent circuit is calculated; the requirements for the signal registration module are formulated. Conclusions: The considered version of the electromyographic signal converter circuit based on tracking communication on power supply, effectively rejects 50 Hz common mode noise. On the basis of the constructed equivalent model of the input circuit of the amplifier, the theoretical relation for calculating the rejection coefficient of such amplifiers. The circuit is simulated in the Multisim program, the results confirmed the correctness of its functioning. The requirements for the interelectrode distance and the thickness of the electrodes themselves are also formulated. The results obtained can be used to design complexes for adaptive electrical stimulation.
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