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Mathematical modeling of hands physiological tremor

DOI 10.18127/j15604136-201906-06


P.S. Tyugaeva – Student, Department “Medical and Technical Information Technology” (BMT-2), Bauman Moscow State Technical University
V.B. Akopyan – Dr. Sc. (Biol.), Professor, Department “Medical and Technical Information Technology” (BMT-2), Bauman Moscow State Technical University

Tremor is different frequencies and amplitudes involuntary rhythmic muscles contractions, aggravated by some pathologies of the nervous system for example by Parkinson’s disease, brain tumors or strokes, as well as at normal with fatigue and stress. The characteristic features of amplitude and frequency characteristics of pathological tremor carry valuable diagnostic information, are used phenomenologically in clinical practice to diagnose certain neurological diseases, and physiological tremor parameters are useful for assess the general condition of the body and, in particular, its physical and mental overwork. However, at present, the numerical characteristics of tremor are not established, standard methods for the study of tremor and requirements for technical characteristics of measuring instruments are not formulated. To improve the quality of diagnostics by using parameters of tremor, as an initial stage, a mathematical model of physiological hand tremor was developed. The input parameters of this model are the mass and length of the hand, and the output parameter is the function a(t), which describes the changes in time of the acceleration of the center of gravity of the hand. Analysis of the proposed model made it possible to formulate requirements for the technical characteristics of equipment for recording physiological hand tremor, to determine the sensitivity of accelerometers used to measure the acceleration amplitude, to determine the optimal frequency of discredit, and also to calculate the amplitude and frequency of physiological tremor at different input parameters. Presented model can be used in future as a basis for modeling and analysis of pathological types of tremor, because it relates such parameters of muscle contraction as the frequency of innervation of individual motor units and their number to the torque in the joint and, accordingly, to the acceleration and angle of rotation. Obtained results are compared with the data available in the literature. In some cases the experimentally obtained frequency characteristics may differ from those obtained as a result of modeling, since physiological tremor is caused by a number of factors, for example by mechanical fluctuations of a limb caused by breathing and a heartbeat, by physiological features of muscle contraction, etc.

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