RADIOELECTRONIC AND COMPUTER SYSTEMS

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.

skeletal muscles; electrical stimulation; stimulus amplitude; contraction amplitude; mathematical model; optimal parameters

Luca, De C. J. The use of surface electromyography in biomechanics. Journal of Applied Biomechanics, 1997, vol. 13, iss. 2, pp. 135-163.

Kim, J., Wichmann, T., Inan, O. T., DeWeerth, S. P. Analyzing the Effects of Parameters for Tremor Modulation via Phase-Locked Electrical Stimulation on a Peripheral Nerve. Journal of Personalized Medicine, 2022, vol. 12, iss. 1, pp. 76-91. DOI: 10.3390/jpm12010076.

Kosti´c, M., Koji´c, V., Iˇcagi´c, S., Andersson Ersman, P., Mulla, M. Y., Strandberg, J., Herlogsson, L., Keller, T., Štrbac, M. Design and Development of OECT Logic Circuits for Electrical Stimulation Applications. Applied Sciences, 2022, vol. 12, pp. 3985-4002. DOI: 10.3390/ app12083985.

Chuiko, G., Darnapuk, Y. Fractal nature of arterial blood oxygen saturation data. Radioelectronic and Computer Systems, 2022, no. 1(101), pp. 206-215. DOI: 10.32620/reks.2022.1.16.

Yeroshenko, O., Prasol, I., Datsok, O. Simulation of an electromyographic signal converter for adaptive electrical stimulation tasks. Innovative Technologies and Scientific Solutions for Industries, 2021, no. 1 (15), pp. 113-119. DOI: 10.30837/ITSSI.2021.15.113.

Datsok, O. M., Prasol, I. V., Yeroshenko, O. A. Construction of biotechnical system of muscular electrical stimulation [Pobudova biotekhnichnoyi systemy myazovoyi elektrostymulyatsiyi]. Bulletin of NTU "KhPI". Series: Informatics and modeling - isnyk NTU "KHPI". Seriya: Informatyka ta modelyuvannya, 2019, no. 13 (1338), pp. 165-175. DOI: 10.20998/2411-0558.2019.13.15. (In Ukrainian).

Carvalho, S., Correia, A., Figueiredo, J., Martins, J. M., Santos, C. P. Functional Electrical Stimulation System for Drop Foot Correction Using a Dynamic NARX Neural Network. Machines, 2021, vol. 9, pp. 253-271. DOI: 10.3390/ machines9110253.

Álvarez, D. M.-C., Serrano‐Muñoz, D., Fernández-Pérez, J. J., Gómez-Soriano, J., Avendaño-Coy, J. Effect of Percutaneous Electric Stimulation with High‐Frequency Alternating Currents on the Sensory‐Motor System of Healthy Volunteers: A Double‐Blind Randomized Controlled Study. Journal of Clinical Medicine, 2022, vol. 11, pp. 1832-1846. DOI: 10.3390/jcm11071832.

Pano-Rodriguez, A., Beltran-Garrido, J. V., Hernández-González, V. Effects of whole-body electromyostimulation on health and performance: a systematic review. BMC Complement Altern Med, 2019, vol. 87, pp. 1-14. DOI: 10.1186/s12906-019-2485-9.

Bersch, I., Friden, J. Electrical stimulation alters muscle morphological properties in denervated upper limb muscles. EBioMedicine, 2021, vol. 74, pp. 1397-1407. DOI: 10.1016/j.ebiom.2021.103737.

Gobbo, M., Maffiuletti, N. A., Orizio, C., Minetto, M. A. Muscle motor point identification is essential for optimizing neuromuscular electrical stimulation use. Journal of neuroengineering and rehabilitation, 2012, vol. 26, iss. 9, pp. 2600-2614. DOI: 10.1519/JSC.0b013e31823f2cd1.

Bekhet, A. H., Bochkezanian, V., Saab, I. M., Gorgey, A. S. The effects of electrical stimulation parameters in managing spasticity after spinal cord injury: a systematic review. American Journal of Physical Medicine and Rehabilitationthis link is disabled, 2019, vol. 98, iss. 6, pp. 484-499. DOI: 10.1097/phm.0000000000001064.

Bochkezanian, V., Newton, R. U., Trajano, G. S., Blazevich, A. J. Effects of Neuromuscular Electrical Stimulation in People with Spinal Cord Injury. Medicine and Science in Sports and Exercisethis link is disabled, 2018, vol. 50, iss. 9, pp. 1733-1739. DOI: 10.1249/MSS.0000000000001637.

Bochkezanian, V., Newton, R. U., Trajano, G. S., Vieira, A., Pulverenti, T. S., Blazevich, A. J. Effect of tendon vibration during wide-pulse neuromuscular electrical stimulation (NMES) on muscle force production in people with spinal cord injury (SCI). BMC Neurologythis link is disabled, 2018, vol. 18, iss. 1, pp. 1-10. DOI: 10.1186/s12883-017-0862-x.

Solberg, P. A., Kvamme, N. H., Raastad, T., Ommundsen, Y., Tomten, S. E., Halvari, H. Effects of different types of exercise on muscle mass, strength, function and well-being in elderly. Eur J Sport Sci, 2013, vol. 13, iss. 1, pp. 112-125.

Griffin, L., Decker, M. J., Hwang, J. Y., Wang, B., Kitchen, K., Ding, Z. Functional electrical stimulation cycling improves body composition, metabolic and neural factors in persons with spinal cord injury. Electromyogr Kinesiol, 2009, vol. 19, iss. 4, pp. 614-622.

Bersch, I., Tesini, S., Bersch, U., Frotzler, A. Functional electrical stimulation in spinal cord injury: clinical evidence versus daily practice. Artif Organs, 2015, vol. 39, iss. 10, pp. 849-54.

Allen, K., Goodman, C. Using electrical stimulation: A guideline for allied health professionals. Sydney, Sydney Local Health District and Royal Rehabilitation Center Publ., 2014. 11 p.

Dolbow, D. R., Gorgey, A. S., Sutor, T. W., Bochkezanian, V., Musselman, K. Invasive and non-invasive approaches of electrical stimulation to improve physical functioning after spinal cord injury. Journal of Clinical Medicinethis link is disabled, 2021, vol. 10, iss. 22, article no. 5356. DOI: 10.3390/jcm10225356.

Gorgey, A. S., Mahoney, E., Kendall, T., Dudley, G. A. Effects of neuromuscular electrical stimulation parameters on specific tension. Eur J Appl Physiol, 2006, vol. 97, iss. 6, pp. 737-744. DOI: 10.1007/s00421-006-0232-7.

Lopez-Rosado, R., Kimalat, A., Bednarczyk, M. Sullivan, J. E. Sensory Amplitude Electrical Stimulation via Sock Combined With Standing and Mobility Activities Improves Walking Speed in Individuals With Chronic Stroke: A Pilot Study. Front. Neurosci, 2019, vol. 13, article no. 337. DOI: 10.3389/fnins.2019.00337.

Bernstein, V. M., Farber, B. S. Involvement of Noise Immunity Systems of Myoelectric Control of Prostheses. Proceedings of Myo-Electrlc Control Symposium. Institute of Biomedical Engineering, UNB, Frederiction, New Brunswick, 1993, pp.42-43.

Bernstein, V. M., Slavutsky, J. L., Farber, B. S. Myoelectric Control of the Muscle Electrostimulation. Proceedings of Myo-Electric Control Symposium. Institute of Biomedical Engineering, UNB, Frederiction, New Brunswick, 1993, pp. 79-80.

Selivanova, K. G., Avrunin, O. G., Geletka, O. O. Mathematical modeling of electromyographic signal [Matematycheskoe modelyrovanye élektromyohrafycheskoho syhnala]. Bulletin of NTU "KhPI" Series "New solutions in modern technologies" - «Visnyk NTU «KHPI» Seriya «Novi rishennya v suchasnykh tekhnolohiyakh», 2014, no. 36 (1079), pp. 31-39. (In Russian).

Patrick Reilly, J. Survey of numerical electrostimulation models. Institute of Physics and Engineering in Medicine Physics in Medicine & Biology, 2016, vol. 61, iss. 12, pp. 4346–4363. DOI: 10.1088/0031-9155/61/12/4346.

Yeroshenko, O., Prasol, I. Simulation of the electrical signal of the muscles to obtain the electromiosignal spectrum. Technology Audit and Production Reserves, 2022, vol. 2, iss. 2(64), pp. 38–43. DOI: 10.15587/2706-5448.2022.254566.

Jung, J., Lee, D.-W., Son, Y. K., Kim, B. S., Shin, H. C. Volitional EMG Estimation Method during Functional Electrical Stimulation by Dual-Channel Surface EMGs. Sensors, 2021, vol. 21, pp. 8015-8032. DOI: 10.3390/s21238015.

Korn, G., Korn, T. Handbook of mathematics for scientists and engineers [Spravochnik po matematike dlya nauchnykh rabotnikov i inzhenerov]. Moscow, Nauka Publ., 2003. 832 p. (In Russian).