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Sensory Feedback Mechanism Underlying Entrainment of Central Pattern Generator to Mechanical Resonance

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Abstract

Rhythmic body motions observed in animal locomotion are known to be controlled by neuronal circuits called central pattern generators (CPGs). It appears that CPGs are energy efficient controllers that cooperate with biomechanical and environmental constraints through sensory feedback. In particular, the CPGs tend to induce rhythmic motion of the body at a natural frequency, i.e., the CPGs are entrained to a mechanical resonance by sensory feedback. The objective of this paper is to uncover the mechanism of entrainment resulting from the dynamic interaction of the CPG and mechanical system. We first develop multiple CPG models for the reciprocal inhibition oscillator (RIO) and examine through numerical experiments whether they can be entrained to a simple pendulum. This comparative study identifies the neuronal properties essential for the entrainment. We then analyze the simplest model that captures the essential dynamics via the method of harmonic balance. It is shown that robust entrainment results from a strong, positive-feedback coupling of a lightly damped mechanical system and the RIO consisting of neurons with the complete adaptation property

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References

  • Av-Ron E, Parnas H, Segel L (1993) A basic biophysical model for bursting neurons. Biol Cybern 69(1):87–95

    Article  PubMed  CAS  Google Scholar 

  • Brown T (1911) The intrinsic factors in the act of progression in the mammal. Proc Roy Soc Lond B Biol Sci 84:308–319

    Article  Google Scholar 

  • Cohen A, Ermentrout G, Kiemel T, Kopell N, Sigvardt K, Williams T (1992) Modelling of intersegmental coordination in the lamprey central pattern generator for locomotion. Trends Neurosci 15(11):434–438

    Article  PubMed  CAS  Google Scholar 

  • Doyle J, Packard A, Zhou K (1991) Review of LFTs, LMIs, and μ. In: Proceedings of IEEE conference on decision and control pp 1227–1232

  • Efimov D, Fradkov A (2004) Excitation of oscillations in nonlinear systems under static feedback. In: Proceedings of IEEE conference on decision and control pp 2521–2526

  • Ekeberg O (1993) A combined neuronal and mechanical model of fish swimming. Biol Cybern 69(5/6):363–374

    Google Scholar 

  • Ermentrout G, Chow C (2002) Modeling neural oscillations. Physiol Behav 77:629–633

    Article  PubMed  CAS  Google Scholar 

  • Ermentrout G, Kopell N (1984) Frequency plateaus in a chain of weakly coupled oscillators. I SIAM J Math Anal 15(2):215–237

    Article  Google Scholar 

  • Fradkov A (1979) Speed-gradient scheme and its application in adaptive control problems. Autom Remote Contr 40(9):1333–1342 (Translated from Avtomatika i Telemekhanika 9:90–101, 1979.)

    Google Scholar 

  • Fradkov A (1999a) Exploiting nonlinearity by feedback. Physica D 128:159–168

    Article  Google Scholar 

  • Fradkov A (1999b) Feedback resonance in nonlinear oscillators. Proc Eur Contr Conf

  • Friesen W (1994) Reciprocal inhibition:A mechanism underlying oscillatory animal movements. Neurosci Biobehav Rev 18(4):547–553

    Article  PubMed  CAS  Google Scholar 

  • Friesen W, Stent G (1978) Neural circuits for generating rhythmic movements. Annu Rev Biophys Bioeng 7:37–61

    Article  PubMed  CAS  Google Scholar 

  • Fukuoka Y, Kimura H, Cohen A (2003) Adaptive dynamic walking of a quadruped robot on irregular terrain based on biological concepts. Int J Robot Res 22(3-4):187–202

    Article  Google Scholar 

  • Getting P (1989) Reconstruction of small neural networks. In: Koch C, Segev I (eds) Methods in Neuronal Modeling. MIT Press, Cambridge, pp 171–194

    Google Scholar 

  • Glad T and Ljung L (2000) Control theory – multivariable and nonlinear methods. Taylor & Francis, Boca Raton, London

    Google Scholar 

  • Hadeler K (1974) On the theory of lateral inhibition. Kybernetik 14:161–165

    Article  PubMed  CAS  Google Scholar 

  • Hindmarsh J, Rose R (1982) A model of the nerve impulse using two first-order differential equations. Nature 296(5853):162–164

    Article  PubMed  CAS  Google Scholar 

  • Hunt K, Sbarbaro D, Zbikowski R, Gawthrop P (1992) Neural networks for control systems – a survey. Automatica 28(6):1083–1112

    Article  Google Scholar 

  • Ijspeert A (2001) A connectionist central pattern generator for the aquatic and terrestrial gaits of a simulated salamander. Biol Cybern 84:331–348

    Article  PubMed  CAS  Google Scholar 

  • Iwasaki T, Zheng M (2002) The Lur’e model for neuronal dynamics. In: Proceedings of IFAC world congress July 21–26, 2002, Barcelona, Spain

  • Khalil H (1996) Nonlinear systems. Prentice Hall, Englewood Cliffs

    Google Scholar 

  • Lewis M, Etiennne-Cummings R, Hartmann M, Xu Z, Cohen A (2003) An in silico pattern generator:silicon oscillator, coupling, entrainment, and physical computation. Biol Cybern 88:137–151

    Article  PubMed  Google Scholar 

  • Matsuoka K (1985) Sustained oscillations generated by mutually inhibiting neurons with adaptation. Biol Cybern 52:367–376

    Article  PubMed  CAS  Google Scholar 

  • Matsuoka K (1987) Mechanisms of frequency and pattern control in the neural rhythm generators. Biol Cybern 56:345–353

    Article  PubMed  CAS  Google Scholar 

  • Ogata K (1996) Modern control engineering. Prentice Hall, Englewood Cliffs

    Google Scholar 

  • Ono K (1998) Self-excited natural periodical motion mechanism for efficient and robust locomotion. In: Proceedings of TITech COE/Super-Mechano Systems Workshop pp 32–43

  • Ono K, Takahashi R, Shimada T (2001) Self-excited walking of a biped mechanism. Int J Robot Res 20(12):953–966

    Article  Google Scholar 

  • Orlovsky G, Deliagina T, Grillner S (1999) Neuronal Control of Locomotion:From Mollusc to Man. Oxford University Press, Oxford

    Google Scholar 

  • Raney D, Slominski E (2004) Mechanization and control concepts for biologically inspired micro air vehicles. J Aircr 41(6):1257–1265

    Google Scholar 

  • Rinzel J (1985) Excitation dynamics:insights from simplified membrane models. Fed Proc 44(15):2944–2946

    PubMed  CAS  Google Scholar 

  • Taga G (1991) Self-organized control of bipedal locomotion by neural oscillators in unpredictable environment. Biol Cybern 65:147–159

    Article  PubMed  CAS  Google Scholar 

  • Wadden T, Ekeberg O (1998) A neuro-mechanical model of legged locomotion:single leg control. Biol Cybern 79:161–173

    Article  PubMed  CAS  Google Scholar 

  • Williamson M (1998) Neural control of rhythmic arm movements. Neural Netw 11:1379–1394

    Article  PubMed  Google Scholar 

Download references

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Iwasaki, T., Zheng, M. Sensory Feedback Mechanism Underlying Entrainment of Central Pattern Generator to Mechanical Resonance. Biol Cybern 94, 245–261 (2006). https://doi.org/10.1007/s00422-005-0047-3

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  • DOI: https://doi.org/10.1007/s00422-005-0047-3

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