Journal of Computational Neuroscience

, Volume 19, Issue 2, pp 181–197 | Cite as

Oscillations in a Simple Neuromechanical System: Underlying Mechanisms

  • Murat SekerliEmail author
  • Robert J. Butera


A half-center neural oscillator was coupled to a simple mechanical system to study the closed-loop interactions between a central pattern generator and its effector muscles. After a review of the open-loop mechanisms that were previously introduced by Skinner et al. (1994), we extend their geometric approach and introduce four additional closed-loop mechanisms by the inclusion of an antagonistic muscle pair acting on a mass and connected to the half-center neural oscillator ipsilaterally. Two of the closed-loop mechanisms, mechanical release mechanisms, have close resemblance to open-loop release mechanisms whereas the latter two, afferent mechanisms, have a strong dependence on the mechanical properties of the system. The results also show that stable oscillations can emerge in the presence of sensory feedback even if the neural system is not oscillatory. Finally, the feasibility of the closed-loop mechanisms was shown by weakening the idealized assumptions of the synaptic and the feedback connections as well as the rapidity of the oscillations.


reciprocal inhibition afferent feedback oscillation mechanisms central pattern generator sensory feedback rhythmic movements simulation neuromechanical model neural oscillator escape and release mechanisms nullcline phase portrait 


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  1. Bosco G, Poppele RE (2001) Proprioception from a spinocerebellar perspective. Physiological Reviews 81(2): 539–568.PubMedGoogle Scholar
  2. Brown TG (1914) On the nature of the fundamental activity of the nervous centres, together with an analysis of the conditioning of rhythmic activity in progression, and a theory of evolution of function in the nervous system. J. Physiol. (London) 48: 18–46.Google Scholar
  3. Dellow PG, Lund JP (1971) Evidence for central timing of rhythmical mastication. J. Physiol. 215: 1–13.PubMedGoogle Scholar
  4. DiPrisco GV, Wallen P, Grillner S (1990) Synaptic effects of intraspinal stretch receptor neurons mediating movement-related feedback during locomotion. Brain Research 530: 161–166.CrossRefPubMedGoogle Scholar
  5. Ekeberg O, Grillner S (1999) Simulations of neuromuscular control in lamprey swimming. Phil. Trans. R. Soc. Lond. B 354: 895– 902.CrossRefGoogle Scholar
  6. Ermentrout B (2002) Simulating, Analyzing, and Animating Dynamical Systems: A Guide to XPPAUT for Researchers and Students. Society for Industrial and Applied Mathematics, Philadelphia, PA.Google Scholar
  7. Feldman JL, Gautier H (1976) The interaction of pulmonary afferents and pneumotaxic center in control of respiratory pattern in cats. J. Neurophysiol. 39: 31–44.PubMedGoogle Scholar
  8. Graham BP, Redman SJ (1993) Dynamic behaviour of a model of the muscle stretch reflex. Neural Networks 6: 947–962.Google Scholar
  9. Grillner S (1981) Control of locomotion in bipeds, tetrapods, and fish. In: Papenheimer JR, Forster RE, Mammaerts W, Bullock TH, eds., Handbook of Physiology—The Nervous System II. American Physiological Society, Washington, D.C. pp. 1179– 1236.Google Scholar
  10. Grillner S, Perret C, Zangger P (1976) Central generation of locomotion in the spinal dogfish. Brain Res. 109: 255–269.CrossRefPubMedGoogle Scholar
  11. Grillner S, Wallen P, Brodin L, Lansner A (1991) Neuronal network generating locomotor behavior in lamprey: Circuitry, transmitters, membrane properties, and simulation. Annu. Rev. Neurosci. 14: 169–199.CrossRefPubMedGoogle Scholar
  12. Hatsopoulos NG (1996) Coupling the neural and physical dynamics in rhythmic movements. Neural Computation 8: 567–581.PubMedGoogle Scholar
  13. Henneman E, Olson CB (1965) Relations between structure and function in design of skeletal muscles J. Neurophysiol. 28(3): 581– 598.Google Scholar
  14. Hill AV (1953) The Mechanics of Active Muscle. Proceedings of the Royal Society of London. Series B: Biological Sciences (London) 141: 104–117.Google Scholar
  15. Hogan N (1990) Mechanical impedance of single- and multi-articular systems. In: Winters JM, Woo SLY, eds., Multiple Muscle Systems: Biomechanics and Movement Organization. Springer-Verlag, New York, pp. 149–164.Google Scholar
  16. Kopell N, Somers D (1995) Anti-phase solutions in relaxation oscillators coupled through excitatory interactions. J. Math. Biol. 33: 261–280.CrossRefPubMedGoogle Scholar
  17. Lin CC, Segel LA, Handelman GH (1974) Mathematics Applied to Deterministic Problems in the Natural Sciences. Macmillan, New York.Google Scholar
  18. Morris C, Lecar H (1981) Voltage oscillations in the barnacle giant muscle fiber. Biophys. J. 35: 193–213.PubMedGoogle Scholar
  19. Proske U, Wise AK, Gregory JE (1999) Movement detection thresholds at the human elbow joint. Progress in Brain Research 123: 143–147.PubMedGoogle Scholar
  20. Ramos CF, Stark LW (1990) Simulation experiments can shed light on the functional aspects of postural adjustments related to voluntary movements. In: Winters JM, Woo SLY, eds., Multiple Muscle Systems: Biomechanics and Movement Organization. Springer-Verlag, New York, pp. 507–517.Google Scholar
  21. Rinzel J, Ermentrout B (1989) Analysis of neural excitability and oscillations. In: Koch C, Segev I, eds., Methods in Neuronal Modeling: From Synapses to Networks. MIT Press, Cambridge, MA, pp. 135–171.Google Scholar
  22. Rossignol S, Lund JP, Drew T (1988) The role of sensory inputs in regulating patterns of rhythmical movements in higher vertebrates: A comparison between locomotion, respiration, and mastication. In: Cohen AH, Rossignol S, Grillner S, eds., Neural Control of Rhythmic Movements in Vertebrates. John Wiley & Sons, pp. 201–283.Google Scholar
  23. Rowat P, Selverston A (1997) Oscillatory mechanisms in pairs of neurons connected with fast inhibitory synapses. Journal of Computational Neuroscience 4: 103–127.CrossRefPubMedGoogle Scholar
  24. Simoni MF (2002) Synthesis and analysis of a physical model of biological rhythmic motor control with sensorimotor feedback. Ph.D. thesis, School of Electrical and Computer Engineering, Georgia Institute of Technology.Google Scholar
  25. Skinner FK, Kopell N, Marder E (1994) Mechanisms for oscillation and frequency control in reciprocally inhibitory model neural networks. Journal of Computational Neuroscience 1: 69– 87.CrossRefPubMedGoogle Scholar
  26. Taylor AL, Cottrell GW, Kristan WB (2002) Analysis of oscillations in a reciprocally inhibitory network with synaptic depression. Neural Computation 14(3): 561–581.CrossRefPubMedGoogle Scholar
  27. Terman D, Kopell N, Bose A (1998) Dynamics of two mutually coupled slow inhibitory neurons. Physica D 117: 241–275.Google Scholar
  28. VanVreeswijk C, Abbott LF, Ermentrout GB (1994) When inhibition not excitation synchronizes neural firing. Journal of Computational Neuroscience 1(4): 313–321.CrossRefPubMedGoogle Scholar
  29. Wadden T, Ekeberg O (1998) A neuro-mechanical model of legged locomotion: Single leg control. Biological Cybernetics 79: 161–173.CrossRefPubMedGoogle Scholar
  30. Wang XJ, Rinzel J (1992) Alternating and synchronous rhythms in reciprocally inhibitory model neurons. Neural Computation 4: 84–97.Google Scholar

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© Springer Science + Business Media, Inc. 2005

Authors and Affiliations

  1. 1.Laboratory for Neuroengineering and School of Electrical and Computer EngineeringGeorgia Institute of TechnologyAtlanta
  2. 2.Laboratory for Neuroengineering, School of Electrical and Computer Engineering and Wallace H. Coulter Dept. of Biomedical EngineeringGeorgia Tech/Emory UniversityAtlanta

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