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Washout filter aided mean field feedback desynchronization in an ensemble of globally coupled neural oscillators

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Abstract

We propose an approach for desynchronization in an ensemble of globally coupled neural oscillators. The impact of washout filter aided mean field feedback on population synchronization process is investigated. By blocking the Hopf bifurcation of the mean field, the controller desynchronizes the ensemble. The technique is generally demand-controlled. It is robust and can be easily implemented practically. We suggest it for effective deep brain stimulation in neurological diseases characterized by pathological synchronization.

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References

  • Alberts WW, Wright EJ, Feinstein B (1969) Cortical potentials and parkinsonian tremor. Nature 221: 670–672

    Article  PubMed  CAS  Google Scholar 

  • Anderson PM, Fouad AA (1977) Power system control and stability. The Iowa State University Press, Ames

    Google Scholar 

  • Baltuch GH, Stern MB (2007) Deep brain stimulation for Parkinson’s disease. Informa Healthcare, New York

    Google Scholar 

  • Bazanella AS, Kokotovic PV, Silva ASE (2000) On the control of dynamic systems with unknown operating point. Int J Control 73(7): 600–605

    Article  Google Scholar 

  • Blakelock JH (1965) Automatic control of aircraft and missiles. Wiley, New York

    Google Scholar 

  • Crawford JD (1994) Amplitude expansions for instabilities in populations of globally-coupled oscillators. J Stat Phys 74: 1047–1084

    Article  Google Scholar 

  • Eckhorn R, Bauer R, Jordan W, Brosch M, Kruse W, Munk M, Reitboeck HJ (1988) Coherent oscillations: a mechanism of feature linking in the visual cortex? Multiple electrode and correlation analyses in the cat. Biol Cybern 60(2): 121–130

    Article  PubMed  CAS  Google Scholar 

  • Feng XJ, Shea-Brown E, Greenwald B, Kosut R, Rabitz H (2007) Optimal deep brain stimulation of the subthalamic nucleus—a computational study. J Comput Neurosci 23: 265–282

    Article  PubMed  Google Scholar 

  • Fisher RS, van Emde Boas W, Blume W, Elger C, Genton P, Lee P, Engel J Jr (2005) Epileptic seizures and epilepsy: definitions proposed by the International League Against Epilepsy (ILAE) and the International Bureau for Epilepsy (IBE). Epilepsia 46(4): 470–472

    Article  PubMed  Google Scholar 

  • Haken H (1993) Advanced synergetics: instability hierarchies of self-organizing systems. Springer, Berlin

    Google Scholar 

  • Hassouneh MA, Lee H-C, Abed EH (2004) Washout filters in feedback control: benefits, limitations and extensions. Proc 2004 American Control Conf, Boston, MA, pp 3950–3955

  • Hauptmann C, Popovych O, Tass PA (2005) Delayed feedback control of synchronization in locally coupled neuronal networks. Neurocomputing 65–66: 759–767

    Article  Google Scholar 

  • Hindmarsh JL, Rose RM (1984) A model of neuronal bursting using three coupled first order differential equations. Proc R Soc Lond, Ser B 221: 87–102

    Article  CAS  Google Scholar 

  • Kringelbach ML, Jenkinson N, Owen SLF, Aziz TZ (2007) Translational principles of deep brain stimulation. Nat Rev Neurosci 8: 623–635

    Article  PubMed  CAS  Google Scholar 

  • Kuramoto Y (1984) Chemical oscillations, waves and turbulence. Springer-Verlag, Berlin

    Google Scholar 

  • Lee HC (1991) Robust control of bifurcating nonlinear systems with applications. PhD thesis, University of Maryland

  • Lenz FA, Kwan HC, Martin RL, Tasker RR, Dostrovsky JO, Lenz YE (1994) Single unit analysis of the human ventral thalamic nuclear group. Tremor-related activity in functionally identified cells. Brain 117: 531–543

    Article  PubMed  Google Scholar 

  • McRuer D, Ashkenas I, Graham D (1973) Aircraft dynamics and automatic control. Princeton University Press, Princeton

    Google Scholar 

  • Milton J, Jung P (2003) Epilepsy as a dynamic disease. Springer, Berlin

    Google Scholar 

  • Nini A, Feingold A, Slovin H, Bergmann H (1995) Neurons in the globus pallidus do not show correlated activity in the normal monkey, but phase-locked oscillations appear in the MPTP model of parkinsonism. J Neurophysiol 74: 1800–1805

    PubMed  CAS  Google Scholar 

  • Pare D, Curro’Dossi R, Steriade M (1990) Neuronal basis of the parkinsonian resting tremor: a hypothesis and its implications for treatment. Neuroscience 35: 217–226

    Article  PubMed  CAS  Google Scholar 

  • Perlmutter JS, Mink JW (2006) Deep brain stimulation. Annu Rev Neurosci 29: 229–257

    Article  PubMed  CAS  Google Scholar 

  • Pikosky A, Rosenblum M, Kurths J (2001) Synchronization, a universal concept in nonlinear sciences. Cambridge University Press, Cambridge

    Google Scholar 

  • Popovych OV, Hauptmann C, Tass PA (2005) Effective desynchronization by nonlinear delayed feedback. Phys Rev Lett 94: 164102

    Article  PubMed  Google Scholar 

  • Popovych O, Hauptmann C, Tass PA (2006) Control of neuronal synchrony by nonlinear delayed feedback. Biol Cybern 95: 68–85

    Article  Google Scholar 

  • Popovych O, Hauptmann C, Tass PA (2008) Impact of nonlinear delayed feedback on synchornized oscillators. J Biol Phys 34: 367–379

    Article  Google Scholar 

  • Pyragas K, Payragas V, Kiss IZ, Hudson JL (2002) Stabilizing and tracking steady states of dynamical systems. Phys Rev Lett 89: 244103

    Article  PubMed  CAS  Google Scholar 

  • Pyragas K, Payragas V, Kiss IZ, Hudson JL (2004) Adaptive control of unknown unstable steady states of dynamical systems. Phys Rev E 70: 026215

    Article  CAS  Google Scholar 

  • Pyragas K, Popovych O, Tass PA (2007) Controlling synchrony in oscillatory networks with a separate stimulation-registration setup. Europhys Lett 80: 40002

    Article  Google Scholar 

  • Rodriguez-Oroz MC, Obeso JA, Lang AE, Houeto J-L, Pollak P, Rehncrona S, Kulisevsky J, Albanese A, Volkmann J, Hariz MI, Quinn NP, Speelman JD, Guridi J, Zamarbide I, Gironell A, Molet J, Pascual-Sedano B, Pidoux B, Bonnet AM, Agid Y, Xie J, Benabid AL, Lozano AM, Saint-Cyr J, Romito L, Contarino MF, Scerrati M, Fraix V, Van Blercom N (2005) Bilateral deep brain stimulation in Parkinson’s disease: a multicentre study with 4 years follow-up. Brain 128(10): 2240–2249

    Article  PubMed  CAS  Google Scholar 

  • Rosenblum M, Pikovsky A (2004a) Controlling synchronization in an ensemble of globally coupled oscillators. Phys Rev Lett 92: 114102

    Article  PubMed  Google Scholar 

  • Rosenblum M, Pikovsky A (2004b) Delayed feedback control of collective synchrony: an approach to suppression of pathological brain rhythms. Phys Rev E 70: 041904

    Article  Google Scholar 

  • Rosenblum M, Tukhlina N, Pikovsky A, Cimponeriu L (2006) Delayed feedback suppression of collective rhythmic activity in a neuronal ensemble. Int J Bifurc Chaos 16(7): 1989–1999

    Article  Google Scholar 

  • Rubin JE, Terman D (2004) High frequency stimulation of the subthalamic nucleus eliminates pathological thalamic rhythmicity in a computational model. J Comput Neurosci 16: 211–235

    Article  PubMed  Google Scholar 

  • Singer W, Gray CM (1995) Visual feature integration and the temporal correlation hypothesis. Annu Rev Neurosci 18: 555–586

    Article  PubMed  CAS  Google Scholar 

  • Steriade M, Jones EG, Llinas RR (1990) Thalamic oscillations and signaling. Wiley, New York

    Google Scholar 

  • Tass PA (1999) Phase resetting in medicine and biology: stochastic modeling and data analysis. Springer, Berlin

    Google Scholar 

  • Tass PA (2001a) Desynchronizing double-pulse phase resetting and application to deep brain stimulation. Biol Cybern 85: 343–354

    Article  PubMed  CAS  Google Scholar 

  • Tass PA (2001b) Effective desynchronization by means of double-pulse phase resetting. Europhys Lett 53: 15–21

    Article  CAS  Google Scholar 

  • Tass PA (2002) Desynchronization of brain rhythms with soft phaseresetting techniques. Biol Cybern 87: 102–115

    Article  PubMed  Google Scholar 

  • Tass PA (2003) A model of desynchronizing deep brain stimulation with a demand-controlled coordinated reset of neural subpopulations. Biol Cybern 89: 81–88

    Article  PubMed  Google Scholar 

  • The Deep-Brain Stimulation for Parkinson’s Disease Study Group (2001) Deep-brain stimulation of the subthalamic nucleus or the Pars Interna of the Globus Pallidus in Parkinson’s Disease. N Engl J Med 344:710–719

    Google Scholar 

  • Tukhlina N, Rosenblum M (2008) Feedback suppression of neural synchrony in two interacting populations by vanishing stimulation. J Biol Phys 34: 301–314

    Article  PubMed  Google Scholar 

  • Tukhlina N, Rosenblum M, Pikovsky A, Kurths J (2007) Feedback suppression of neuronal synchrony by vanishing stimulation. Phys Rev E 75(1): 011918

    Article  Google Scholar 

  • Wang HO, Abed EH (1995) Bifurcation control of a chaotic systems. Automatica 31: 1213–1226

    Article  Google Scholar 

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Correspondence to Ming Luo.

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Luo, M., Wu, Y. & Peng, J. Washout filter aided mean field feedback desynchronization in an ensemble of globally coupled neural oscillators. Biol Cybern 101, 241–246 (2009). https://doi.org/10.1007/s00422-009-0334-5

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  • DOI: https://doi.org/10.1007/s00422-009-0334-5

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