ISSN 0869-6632 (Print)
ISSN 2542-1905 (Online)

For citation:

Molkov J. I., Sushik M. M., Kuznetsov A. S., Kozlov A. K., Zakharov D. G. The dynamical model of locomotor-like movements evoked by muscle vibration in humans. Izvestiya VUZ. Applied Nonlinear Dynamics, 1999, vol. 7, iss. 2, pp. 107-121. DOI: 10.18500/0869-6632-1999-7-2-107-121

This is an open access article distributed under the terms of Creative Commons Attribution 4.0 International License (CC-BY 4.0).
Full text PDF(Ru):
PDF icon 1999no2-3p107.pdf
(downloads: 0)
Language: 
Russian
Heading: 
Journal in the journal
Article type: 
Article
UDC: 
517.9
DOI: 
10.18500/0869-6632-1999-7-2-107-121

The dynamical model of locomotor-like movements evoked by muscle vibration in humans

Autors: 
Molkov Jaroslav Igorevich, Institute of Applied Physics of the Russian Academy of Sciences
Sushik Mihail Mihajlovich, Lobachevsky State University of Nizhny Novgorod
Kuznetsov Aleksej Sergeevich, Saratov State University
Kozlov Aleksandr Konstantinovich, Lobachevsky State University of Nizhny Novgorod
Zakharov Denis Gennadevich, National Research University "Higher School of Economics"
Abstract: 

A phenomenological model of central pattern generator is proposed for qualitative description, within the framework of ftraditional concepts of motoneural and skeleto—muscular sysiem of human leg, of dynamics of spontancous stepping movements evoked by muscle vibration. In particular, it describes bistability of «forward» and «backward» stepping and chaotic transitions between them. The model consists of two self-excited oscillators with nonlinear coupling, the action of which resembles qualitatively the action of a combination of excitatory and inhibitory chemical couplings typical for neural networks. The analysis is made on the example of the interaction of two identical Van der Pol - Duffing generators.

Key words: 
-
Acknowledgments: 
The authors are grateful to V.S. Gurfinkel, Y.S. Levik, O.B. Kazennikov, V.A. Selionov, and L.L. Rubchinsky for helpful discussions. This work was supported by the RFBR (grant RFBR-97-02-17526) and the Program for Support of Leading Scientific Schools of the Russian Federation (grant №. 96-15-96593).
Reference: 
  1. Delcomyn F. Neural basis оf rhythmic behavior in animals. Science. 1980;210(4469):492-498. DOI: 10.1126/science.7423199.
  2. Grillner S. Neurobiological bases оf rhythmic motor acts in vertebrates. Science. 1985;228:143-149. DOI: 10.1126/science.3975635.
  3. Collins JJ, Stewart IN. Coupled nonlinear oscillators and the symmetries оf animal gaits. J. Nonlinear Sci. 1993;3:349-392. DOI: 10.1007/BF02429870.
  4. Abarbanel HDI, Rabinovich MN, Selverston A, Bazhenov MV, Huerta R, Sushchik ММ, Rubchinskii LL. Synchronisation in neural networks. Phys. Usp. 1996;39(4):337-362. DOI: 10.1070/pu1996v039n04abeh000141.
  5. Shik ML, Severin FV, Orlovskii NG. Controlling walking and running through electrical stimulation of the middle brain. Biophysics. 1966;11:659-666. (in Russian).
  6. Mulloney B. Introduction: The neural basis of intersegmental coordination during locomotion. Seminars Neurosci. 1993;5(1):1-2. DOI: 10.1016/S1044-5765(05)80019-3.
  7. Gurfinkel VS, Levik YuS, Kazennikov OV, Selionov VA. Locomotor—like movements evoked by leg muscle vibration in humans. European J. Neurosci. 1998;10(5):1608-1612. DOI: 10.1046/j.1460-9568.1998.00179.x.
  8. Gurfinkel VS, Levik YuS, Kazennikov OV, Selionov VA. Is there a generator of human walking movements? Human Physiology. 1998;24(3):42. (in Russian).
  9. Kozlov AK, Sushchik MM, Molkov YaI. Phase bistability and chaos in the system of two identical Van der Pol-Duffing generators. Izvestiya VUZ. Applied Nonlinear Dynamics. 1999;7(1):68-80. (in Russian).
  10. Abarbanel HDI, Brown R, Sidorowich JJ, Tsimring LSh. The analysis оf observed chaotic data in physical systems. Rev. Моdern Phys. 1993;65(4):1331-1392. DOI: 10.1103/RevModPhys.65.1331.
  11. Abarbanel HDI. Tools for analyzing observed chaotic data. In: Guran A, editor. Smart Structures, Nonlinear Dynamics, and Control. N.Y.: Prentice Hall; 1995. P. 1-86.
  12. Badii R. Progress in analysis оf experimental chaos through periodic orbits. Rev. Modern Phys. 1994;66(4):1389-1415. DOI: 10.1103/RevModPhys.66.1389.
  13. Molkov YaI, Sushchik MM, Kuznetsov AS, Kozlov АК, Zakharov DG. Dynamic model of human locomotor movements caused by vibrational effects on muscles. Bulletin of the University of Nizhny Novgorod. Radiophysics. 1998;1:63-89. (in Russian).
  14. Frank Е. New life in аn old structure: Thе development of synaptic pathways in the spinal cord. Curr. Opin. Neurobiol. 1993;3(1):82-86. DOI: 10.1016/0959-4388(93)90039-2.
  15. Heagy JF, Carroll TL, Pecora LM. Synchronous chaos in coupled oscillator systems. Phys. Rev. E. 1994;50(3):1874-1885. DOI: 10.1103/PhysRevE.50.1874.
  16. Perez—Villar V, Munuzuri AP, Perez—Munuzuri V, Chua LО. Chaotic synchronization of a one—dimensional array of nonlinear active systems. Int. J. Bifurc. Chaos. 1993;3(4):1067-1074. DOI: 10.1142/S0218127493000891.
  17. Rubchinskii LL, Sushchik MM. Direct and inverse relationship between the disorder of spatial and temporal patterns in chains of chaotic autogenerators. Izvestiya VUZ. Applied Nonlinear Dynamics. 1999;7(1):81-87. (in Russian).
  18. Ermentrout B, Корell N. Learning of phase lags in coupled neural oscillators. Neural Computation. 1994;6(2):225-241. DOI: 10.1162/neco.1994.6.2.225.
  19. Collins JJ, Stewart IN. Coupled nonlinear oscillators and the symmetries оf animal gaits. J. Nonlinear Sci. 1993;3:349-392. DOI: 10.1007/BF02429870.
  20. Haken H, Kelso JAS, Bunz H. A theoretical model оf phase transitions in human hand movements. Biol. Cybern. 1985;51:347-356. DOI:  10.1007/Bf00336922
  21. Kelso JAS, Scholz JP, Schoner G. Nonequilibrium phase transitions in coordinated biological motion: critical fluctuations. Phys. Lett. A. 1986;118(6):279-284. DOI: 10.1016/0375-9601(86)90359-2.
  22. Buchanan JJ, Kelso JAS, Fuchs A. Coordination dynamics of trajectory formation. Biol. Cybern. 1996;74:41-54. DOI: 10.1007/BF00199136.
  23. Fuchs А, Jirsa VK, Haken H, Kelso JAS. Extending the HKB model of соordinated movement to oscillators with different eigen frequencies. Biol. Cybern. 1996;74(1):21-30. DOI: 10.1007/BF00199134.
  24. Sternad D, Turvey MT, Schmidt RC. Average phase difference theory аnd 1:1 phase entrainment in interlimb coordination. Biol. Cybern. 1992;67(3):223-231. DOI: 10.1007/BF00204395.
  25. Zakharov DG, Molkov YaI, Sushchik MM. Synchronized oscillations in a system of two coupled Van-der-Pol-Duffing oscillators. Radiophysics and Quantum Electronics. 1998;41(12):1037-1041. DOI 10.1007/BF02676498.
  26. Berge P, Pomeau Y, Vidal C. Order Within Chaos. Towards a Deterministic Approach to Turbulence. N.Y.: Wiley; 1987. 329 p.
  27. Schoner G, Kelso JAS. Dynamic pattern generation in behavioral and neural systems. Science. 1988;239(4847):1513–1520. DOI: 10.1126/science.3281253.
  28. Taga G, Yamaguchi Y, Shimizu H. Self—organized control of bipedal locomotion by neural oscillators in unpredictable environment. Biol. Cybern. 1991;65:147-159. DOI: 10.1007/BF00198086.
  29. Taga С. A model of the neuro—musculo—skeletal system for human locomotion. I. Emergence of basic gait. Biol. Cybern. 1995;73(2):97-111. DOI: 10.1007/BF00204048.
  30. Taga С. A model оf the neuro—musculo—skeletal system for human locomotion. II. Real-time adaptability under various constraints. Biol. Cybern. 1995;73(2):113-121. DOI: 10.1007/BF00204049.
Received: 
24.02.1999
Accepted: 
06.05.1999
Published: 
03.07.1999
  • 271 reads