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Journal of Computational Neuroscience

, Volume 19, Issue 1, pp 53–70 | Cite as

A Model of the Effects of Applied Electric Fields on Neuronal Synchronization

  • Eun-Hyoung Park
  • Ernest Barreto
  • Bruce J. Gluckman
  • Steven J. Schiff
  • Paul SoEmail author
Article

Abstract

We examine the effects of applied electric fields on neuronal synchronization. Two-compartment model neurons were synaptically coupled and embedded within a resistive array, thus allowing the neurons to interact both chemically and electrically. In addition, an external electric field was imposed on the array. The effects of this field were found to be nontrivial, giving rise to domains of synchrony and asynchrony as a function of the heterogeneity among the neurons. A simple phase oscillator reduction was successful in qualitatively reproducing these domains. The findings form several readily testable experimental predictions, and the model can be extended to a larger scale in which the effects of electric fields on seizure activity may be simulated.

Keywords

synchrony electric fields phase response seizure control 

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References

  1. Aksay E, Gamkrelidze G, Seung HS, Baker R, Tank DW (2001) In vivo intracellular recording and perturbation of persistent activity in a neural integrator. Nature Neuroscience 4: 184–193.CrossRefPubMedGoogle Scholar
  2. Bikson M, Lian J, Hahn PJ, Stacey WC, Sciortino C, Durand DM (2001) Suppression of epileptiform activity by high frequency sinusoidal fields in rat hippocampal slices. Journal of Physiology 531: 181–191.CrossRefPubMedGoogle Scholar
  3. Chan CY, Houndsgaard J, Nicholson C (1988) Effects of electric fields on transmembrane potential and excitability of turtle cerebellar Purkinje cells in vitro. Journal of Physiology (London) 402: 751–771.Google Scholar
  4. Chan CY, Nicholson C (1986) Modulation by applied electric fields of Purkinje and stellate cell activity in the isolated turtle cerebellum. Journal of Physiology (London) 371: 89–114.Google Scholar
  5. Cohen AH, Holmes PJ, Rand RH (1982) The nature of the coupling between segmental oscillators of the lamprey spinal generator for locomotion: A mathematical model. Journal of Mathematical Biology 13: 345–369.CrossRefPubMedGoogle Scholar
  6. Ermentrout GB (1981) n:m Phase-locking of weakly coupled oscillators. Journal of Mathematical Biology 12: 327–342.CrossRefGoogle Scholar
  7. Ermentrout GB and Kopell N (1984) Frequency plateaus in a chain of weakly coupled oscillators, I. SIAM Journal of Mathematical Analysis 15: 215–237.CrossRefGoogle Scholar
  8. Ermentrout GB (1996) Type I membranes, phase resetting curves, and synchrony. Neural Computation 8: 979–1001.PubMedGoogle Scholar
  9. Ermentrout GB, Kleinfeld D (2001) Traveling electrical waves in cortex: insights from phase dynamics and speculation on a computational role. Neuron 29(1): 33–44.CrossRefPubMedGoogle Scholar
  10. Ermentrout GB (2002) Simulating, Analyzing, and Animating Dynamical Systems: A Guide to XPPAUT for Researchers and Students, in Software, Environments, and Tools, SIAM, Philadelphia. (Free software downloading available at http://www.math.pitt.edu/~bard/xpp/xpp.html)
  11. Francis JT, Gluckman BJ, Schiff SJ, (2003) Sensitivity of Neurons to Weak Electric Fields, Journal of Neuroscience 23: 7255–7261.PubMedGoogle Scholar
  12. Gluckman BJ, Neel EJ, Netoff TI, Ditto WL, Spano ML, Schiff SJ (1996) Electric field suppression of epileptiform activity in hippocampal slices. Journal of Neurophysiology 76: 4202–4205.PubMedGoogle Scholar
  13. Gluckman BJ, Nguyen H, Weinstein SL, Schiff SJ (2001) Adaptive electric field suppression of epileptic seizures. Journal of Neuroscience 21: 590–600.PubMedGoogle Scholar
  14. Gluckman BJ, So P, Netoff TI, Spano ML, Schiff SJ (1998) Stochastic resonance in mammalian neuronal networks. Chaos 8: 588–598.CrossRefPubMedGoogle Scholar
  15. Golomb D, Hansel D (2000) The number of synaptic inputs and the synchrony of large, sparse neuronal networks. Neural Computation 12: 1095–1139.CrossRefPubMedGoogle Scholar
  16. Gutkin BS, Lang CR, Colby CL, Chow CC, Ermentrout GB (2001) Turning on and off with excitation: The role of spike-timing asynchrony and synchrony in sustained neural activity. Journal of Computational Neuroscience 11: 121–134.CrossRefPubMedGoogle Scholar
  17. Hansel D, Mato G, Meunier C (1995) Synchrony in excitatory neural networks. Neural Computation 7: 307–337.PubMedGoogle Scholar
  18. Hansel D, Sompolinsky H (1996) Chaos and synchrony in a model of a hypercolumn in visual cortex. Journal Computational Neuroscience 3: 7–34.CrossRefGoogle Scholar
  19. Kandel ER, Schwartz JH, Jessell TM (1991) Principles of Neural Science, 3rd ed. Appleton & Lange, Norwalk CT.Google Scholar
  20. Kuramoto Y (1984) Chemical Oscillations, Waves, and Turbulence. Springer, Berlin.Google Scholar
  21. McBain, CJ, Traynelis, SF, Dingledine, R (1990) Regional variation of extracellular space in the hippocampus. Science 249: 674–677.PubMedGoogle Scholar
  22. Munyan B, So P, Barreto E, Schiff SJ (2003), unpublished.Google Scholar
  23. Netoff TI, Schiff SJ (2002) Decreased neuronal synchronization during experimental seizures. Journal of Neuroscience 22: 7297–7307.PubMedGoogle Scholar
  24. Park EH, So P, Barreto E, Schiff SJ (2003) Electric field modulation of synchronization in neuronal networks. Neurocomputing 52–54: 169–175.Google Scholar
  25. Penfield W, Jasper H (1954) Epilepsy and the functional anatomy of the human brain. Little, Brown and Co., Boston MA, p. 896.Google Scholar
  26. Pikovsky AS, Rosenblum MG, Kurths J (2000) Phase synchronization in regular and chaotic systems. International Journal of Bifurcation and Chaos 10: 2291–2306.CrossRefGoogle Scholar
  27. Pikovsky AS, Rosenblum MG, Kurths J (2001) Synchronization a Universal Concept in Nonlinear Sciences. Cambridge University Press, Cambridge UK.Google Scholar
  28. Pinsky PF, Rinzel J (1994) Intrinsic and network rhythmogenesis in a reduced Traub model for CA3 neurons. Journal of Computational Neuroscience 1: 39–60. The erratum for this paper, published in volume 2, on page 275 (1995).CrossRefPubMedGoogle Scholar
  29. Rand RH, Holmes PJ (1980) Bifurcation of periodic motions in two weakly coupled van der Pol oscillators. International Journal of Nonlinear Mechanics 15: 387–399.CrossRefGoogle Scholar
  30. Rosenblum MG, Pikovsky AS, Kurths J (1996) Phase synchronization of chaotic oscillators. Physical Review Letters 76: 1804–1807.CrossRefPubMedGoogle Scholar
  31. Sharp PE, Blair HT, Cho J (2001) The anatomical and computational basis of the rat head-direction cell signal. Trends Neuroscience 24: 289–94.CrossRefGoogle Scholar
  32. Stein PSG (1976) Mechanisms of interlimb phase control. In: R Herman, S Grillner, P Stein, D Stuart, eds. Neural Control of Locomotion. Plenum Press, New York, NY, pp. 465–487.Google Scholar
  33. Tranchina D, Nicholson C (1986) A model for the polarization of neurons by extrinsically applied electric fields. Biophysical Journal 50: 1139–1159.PubMedGoogle Scholar
  34. Traub RD, Dudek FE, Taylor CP, Knowles WD (1985a) Simulation of hippocampal afterdischarges synchronized by electrical interactions. Neuroscience 14: 1033–1038.CrossRefGoogle Scholar
  35. Wang X-J (2001) Synaptic reverberation underlying mnemonic persistent activity. Trends Neurosci. 24: 455–63.CrossRefPubMedGoogle Scholar
  36. Winfree AT (1980) The geometry of biological time. Springer, New York, NY.Google Scholar

Copyright information

© Springer Science + Business Media, Inc. 2005

Authors and Affiliations

  • Eun-Hyoung Park
    • 1
    • 2
  • Ernest Barreto
    • 3
  • Bruce J. Gluckman
    • 3
  • Steven J. Schiff
    • 4
  • Paul So
    • 5
    Email author
  1. 1.The Krasnow Institute for Advanced StudyGeorge Mason UniversityFairfax
  2. 2.Department of Biomedical Engineering, Neural Engineering CenterCase Western Reserve UniversityCleveland
  3. 3.Department of Physics and Astronomy and The Krasnow Institute for Advanced StudyGeorge Mason UniversityFairfax
  4. 4.Department of Psychology and The Krasnow Institute for Advanced StudyGeorge Mason UniversityFairfax
  5. 5.Department of Physics and Astronomy and The Krasnow Institute for Advanced StudyGeorge Mason UniversityFairfax

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