Mathematical Phenomenology of Neural Stimulation by Periodic Fields

Abstract

Neuron synchronization has been hypothesized as the basic mechanism leading neurological phenomena like low electroencephalographic rhythm dimension or high coherence. Cognitive processes, such as associative memory, can also be explained in terms of neuron synchronization. Inspired by the analysis of an experiment on cortex periodic photostimulation, in resonance conditions, a simple network of integrate & fire (i & f) neurons, has been used to simulate cognitive perturbations by oscillatory and pulsate stimulation of the central nervous system (CNS). In view of realistic simulations of transcranial magnetic stimulation (TMS) phenomena, a discrete extension of the FitzHug–Nagumo nervous fiber model, endowed with regenerative nodes, has been developed too.

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References

  1. Abden, M.A. & Stuchly, M.A. (1994). Modeling of magnetic field stimulation of bent neurons. IEEE Transactions on biomedical Engineering, 41, 1092–1095.

    Google Scholar 

  2. Apollonio, F., D'Inzeo, G. & Tarricone, L. (1998). Modeling of neuronal cells exposed to RF fields from mobile telecommunication equipment. Bioelectrochemistry and Bioenergetics, 47, 199–205.

    Google Scholar 

  3. Balduzzo, M., Minelli, T.A. & Turicchia, L. (1999). Signal analysis and simulation of the EEG activity. Chaos Theory and Applications, 4, 7–14.

    Google Scholar 

  4. Barnes, F.S. (1992). Some engineering models for interactions of electric and magnetic fields with biological systems. Bioelectromagnetics Supplement, 1, 67–85.

    Google Scholar 

  5. Bendat, J.J. & Piersol, A.G. (1986). Random data. New York: Wiley.

    Google Scholar 

  6. Besthorn, C., Förstl, H., Geiger-Kabisch, C., Sattel, H., Gasser, T. & Schreiter-Grasser, U. (1994). EEG Coherence in Alzheimer disease. Electroencephalography and Clinical Neurophysiology, 90, 242–24

    Google Scholar 

  7. Boccaletti, S., Grebogi, C., Lai, Y.-C. Mancini, H. & Maza, D. (2000). The control of chaos. Physics Reports, 329, 103–197.

    Google Scholar 

  8. Burke, D., Kiernan, M.C. & Bostock, H. (2001). Excitability of human axons. Clinical Neurophysiology, 112, 1575–1585.

    Google Scholar 

  9. Clark, J.W. (1991). Neural network modeling. Physics in Medicine and Biology, 36, 1259–1317.

    Article  Google Scholar 

  10. Connors, B.W. & Amitai, Y. (1997). Making waves in the neocortex. Neuron, 18, 347–349.

    Article  PubMed  Google Scholar 

  11. Cook, M.R., Graham, C., Cohen, H.D. & Gerkovich, M.M. (1992). A replication study of human exposure to 60 Hz fields: Effects of neurobehavioral measures, Bioelectromagnetics, 13, 261–285.

    Google Scholar 

  12. Cracco, R.Q., Cracco, G.B., Maccabee, P.J., & Amassian, V.E. (1999). Cerebral function revealed by transcranial magnetic stimulation. Journal of Neuroscience Methods, 86, 209–219.

    Google Scholar 

  13. Deutsch, S. & Deutsch, A. (1993). Understanding the nervous system. New York: IEEE.

    Google Scholar 

  14. Draguhn, A., Traub, R.D., Schmitz, D. & Jefferys, J.G.R. (1998). Electrical coupling underlies high-frequency in the hippocampus in vitro. Nature, 394, 189–192.

    Google Scholar 

  15. Engelhardt, H., Gaub, H. & Sackman, E. (1984). Viscoelastic properties of erythrocyte membranes in hig-frequency electric field. Nature, 307, 378–380.

    Google Scholar 

  16. Ferro Milone, F., Minelli, T.A. & Turicchia, L. (1998). Neuron synchronization and human EEG phenomenology simulation. Nonlinear Dynamics, Psychology, and Life Sciences, 2, 21–33.

    Google Scholar 

  17. FitzHug, R. (1961). Impulses and physiological states in theoretical models of nerve membrane. Biophysics Journal, 1, 445–466.

    Google Scholar 

  18. Glass, A., Zappulla, R.A., Nieves, J. & Diamond, S.P. (1992). EEG Coherence as a predictor of spike propagation. Electroencephalography and Clinical Neurophysiology, 82, 10–16.

    Google Scholar 

  19. Goodman, R., Basset, C.A.L. & Henderson, A.S. (1983). Pulsing Electromagnetic Fields Induces Cellular Transcription. Science, 220, 1283–1285.

    Google Scholar 

  20. Graham, C., Cook, M.R., Cohen, H.D. & Gerkovich, M.M. (1994). Dose response study of human exposure to 60 Hz magnetic and electric fields, Bioelectromagnetics, 15, 447–463.

    Google Scholar 

  21. Grill, W.M. (1999). Modeling the effects of electric fields on nerve fibers. IEEE Transactions on biomedical Engineering, 46, 918–928.

    Google Scholar 

  22. Hodgkin, A. & Huxley, A. (1939). Action potentials recorded from inside a nerve fiber. Nature 144, 710–711.

    Google Scholar 

  23. Hodgkin, A. & Huxley, A. (1952). Currents carried by sodium and potassium ions through the membrane of the giant axon of Loligo. Journal of Physiology 116, 449–472.

    Google Scholar 

  24. Hopfield, J.J. (1994). Neurons, dynamics and computation. Physics Today, 47, 40–46.

    Google Scholar 

  25. Izhikevich, E.M. (1999). Weakly connected quasi-periodic oscillators, FM interactions, and multiplexing in the brain. SIAM Journal of Applied Mathematics, 59, 2193–2223.

    Google Scholar 

  26. Jing, H. & Takigawa, K. (2000). Observation of EEG coherence after repetitive transcranial magnetic stimulation. Clinical Neurophysiology, 111, 1620–1631.

    Google Scholar 

  27. Kantz, H., & Schreiber, T. (1995). Dimension estimates and physiological data. Chaos, 5, 143–154.

    Article  Google Scholar 

  28. Kantz, H. and Schreiber, T. Nonlinear time series analysis. (1997) Cambridge, MA: Cambridge University Press.

    Google Scholar 

  29. Kaplan, D. & Glass, L. (1995). Understanding the nonlinear dynamics. New York: Springer-Verlag.

    Google Scholar 

  30. King, R.W.P. (1999). Nerves in a human body exposed to low frequency electromagnetic field. IEEE Transactions on biomedical Engineering, 46, 1426–1431.

    Google Scholar 

  31. Kuramoto, Y., (1991). Collective Synchronization of Pulse Coupled Oscillators. Physica, D50, 15–30.

    Google Scholar 

  32. Lebedeva, N.N., Sulimov, A.V., Sulimova, O.P., Kotrovskaya, T.I. & Gailus, T. (2000). Cellular phone electromagnetic field effects on bio-electric activity of human brain. Critical Reviews in Biomedical Engineering, 28, 323–337.

    Google Scholar 

  33. Lopes da Silva, F.H. (1991). Neural mechanisms underlying brain waves: From neural membranes to networks. Electroencephalography and Clinical Neurophysiology 79, 81–93.

    Article  Google Scholar 

  34. Lopes da Silva, F.H. & Pfurtscheller, G. (1999). Basic concepts on EEG synchronization and desynchronozation. In G. Pfurtscheller & F.H. Lopes da Silva (Eds.), Handbook of elecroencephalography and clinical neurophysiology VI (pp. 3–11). Amsterdam: Elsevier.

    Google Scholar 

  35. Mann, K. and Roschke, J. (1996). Effects of pulsed High-frequency electromagnetic field on human sleep. Neuropsychobiology, 33, 41–47.

    Google Scholar 

  36. Miltner, W.H.R., Braun, C., Witte, H. & Taub, E. (1999). Coherence of the gamma band activity as a basis for associative learning. Nature, 397, 434–436.

    Google Scholar 

  37. Minelli, T.A. & Turicchia, L. (1999). Progressive coherence patterns for EEG phenomenology, Nonlinear Dynamics, Psychology, and Life Sciences, 3, 129–142.

    Google Scholar 

  38. Mirollo, R.E., & S.H. Strogaz, S.H. (1990). Synchronization of pulse coupled oscillators, SIAM Journal of Applied Mathematics, 50, 1645–1662.

    Google Scholar 

  39. Munk, M.H.J., Roelfsema, P.R., Koenig, P., Engel, A.K. & Singer, W. (1996). Role of reticular activation in the modulation of intracortical synchronization. Science, 272, 271–274.

    Google Scholar 

  40. Murray, J.D. (1993). Mathematical biology. Berlin: Springer-Verlag.

    Google Scholar 

  41. Myers, J.M. (1999). Modelling the effect of an external electric field on the velocity of spike propagation in a nerve fiber. Physics Review E, 60, 5918–5925.

    Google Scholar 

  42. Nagarajan, S.S. (1996). A generalized cable equation for magnetic stimulation of axons. IEEE Transactions on Biomedical Engineering, 43, 304–312.

    Google Scholar 

  43. Nagumo, J. Aximoto, S. and Yoshizawa, S. (1962). An active pulse transmission simulating nerve axon. Proc. IRE 50, 2061–2071.

    Google Scholar 

  44. Nayfeh, A.H. & Balachandran, B. (1995). Applied nonlinear dynamics. NewYork: Wiley.

    Google Scholar 

  45. Nunez, P.L. (1995). Neocortical dynamics and human EEG rhythms. New York: Oxford University Press.

    Google Scholar 

  46. Oberfeld, G. (Ed.) (2000). Proceedings of the International Conference on Cell Tower Siting–Salzburg June 7–8 2000. Printing Office Federal State of Salzburg.

    Google Scholar 

  47. Pascual-Leone, A., Valls-Sole, J., Wassermann, E.M., Brasil Neto, J. P. & Hallett, M. (1994). Response to rapid rate transcranial magnetic stimulation of the human motor cortex. Brain, 117, 847–858.

    Google Scholar 

  48. Persinger, M.A., Richards, P.M., Koren, S.A. (1997). Differential entrainment of electroencephalographic activity by weak complex electromagnetic fields. Perception and Motor Skills 84, 527–536.

    Google Scholar 

  49. Preece, A.W., Wesnes, K.A. & Iwi, G.R. (1998). The effect of a 50 Hz magnetic field on cognitive functions in humans. International Journal of Radiation Biology, 74, 463–47.

    Google Scholar 

  50. Pyragas, K. (1998). Properties of generalized synchronization of chaos. Nonlinear Analysis: Modelling and Control, 3, 1–29.

    Google Scholar 

  51. Rattay, F. (1998). Analysis of the electrical excitation of CNS neurons. IEEE Transactions on Biomedical Engineering, 45, 766–772.

    Google Scholar 

  52. Rodriguez, E., George, N., Lachaux, J.P., Martinerie, J. Renault, B. & Varela, F.J. (1999). Perception shadow: long-distance synchronization of human brain activity. Nature, 397, 430–433.

    Article  PubMed  Google Scholar 

  53. Ruohonen, J., Ravazzani, P. & Grandori, F. (1998). Functional magnetic stimulation: theory and coil optimization. Bioelectrochemistry and Bioenergetics, 47, 213–219.

    Google Scholar 

  54. Sabah, N.H. (2000). Aspects of nerve conduction. IEEE Engineering in Medicine and Biology. November/December, 19(6), 111–118.

    Google Scholar 

  55. Sannita, W.G. (2000). Stimulus-specific oscillatory responses of the brain. Clinical Neurophysiology, 111, 565–583.

    Google Scholar 

  56. Scott, A. & Luzader, S.D. (1979). Coupled solitary waves in neurophysics. Physica Scripta, 20, 395–401.

    Google Scholar 

  57. Schnabel, V. & Struijk, J.J. (2001), Calculation of electric field in a multiple cylindrical volume conductor induced by magnetic coils. IEEE Transactions on Biomedical Engineering, 48, 78–86.

    Google Scholar 

  58. Sebastian, J.L., Munoz, S., Rancho, M., & Miranda, J.M. (2001). Analysis of the influence of the cell geometry, orientation and cell proximity effects on the electric field distribution from direct RF exposure. Physics in Medicine and Biology, 46, 213–225.

    Google Scholar 

  59. Schurmann, K., Nikouline, V.V., Soljanlahti, S., Ollikainen, M., Basar, E., Ilmoniemi, R.J.(2001). EEG responses to combined somatosensory and transcranial magnetic stimulation. Clinical Neurophysiology, 112, 19–24.

    Google Scholar 

  60. Siebner, H.R., Willoch, F., Peller, M., Auer, C., Boecker, H., Conrad, B., and Bartenstein, P. (1998). Imaging brain activation induced by long trains of repetitive transcranial magnetic stimulation. NeuroReport, 9, 943–948.

    Google Scholar 

  61. Singer, W. (1994): The role of synchrony in neocortical networks, In E. Domany, J.L. van Hemmen and K. Shulten (Eds.). Models of neural networks II. (pp. 141–173). New York: Springer-Verlag.

    Google Scholar 

  62. Stuchly, M. & Dawson, T.W. (2000). Interaction of low-frequenchy electric and magnetic field with human body. IEEE Proceedings, 88, 643–664.

    Google Scholar 

  63. Suihko, V. (1998). Modeling direct activation of corticospinal axon using transcranial electrical stimulation. Electroencephalography and Clinical Neuriphysiology, 109, 238–244.

    Google Scholar 

  64. Thatcher, R.W., Krause, P.J. & Hrybyk, M. (1986). Cortico-cortical associations and EEG coherence: a two-compartimental model. Electroencephalography and Clinical Neurophysiology, 64, 123–143.

    Google Scholar 

  65. Traub, R.D., Jefferys, J.G.R. & Whittington, M.A. (1997). Simulation of gamma rhythms in networks of interneurons and pyramidal cells. Journal of Computational Neuroscience, 4, 141–150.

    Google Scholar 

  66. Trimmel, M., Schweiger, E. (1998). Effects of an ELF (50 Hz, 1 mT) electromagnetic field (EMF) on concentration in visual attention, perception and memory including effects on EMF sensitivity. Toxicology Letters, 96, 97, 377–382.

    Google Scholar 

  67. von Krosigk, M., Bald, T., & McCormick, D.A. (1993). Cellular mechanisms of synchronized oscillations in the thalamus. Science, 261, 361–364.

    PubMed  Google Scholar 

  68. Walsh, V. & Rushwort, M. (1999). A primer of magnetic stimulation as a tool for neurophysiology. Neuropsychologia, 37, 125–135.

    Google Scholar 

  69. Warman, E.N., Grill, W.M. & Durand, D.(1992). Modeling the effects of electric fields on nerve fibers: Determination of excitation thresholds. IEEE Transactions on Biomedical Engineering, 39, 1244–1254.

    Google Scholar 

  70. Whitle, P.(1998). Neural nets and chaotic carriers. New York: Wiley.

    Google Scholar 

  71. Zierhofer, C.M. (2001). Analysis of a linear model for electrical stimulation of axons. IEEE Transactions on Biomedical Engineering, 48, 173–184.

    Google Scholar 

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Correspondence to T. A. Minelli.

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Balduzzo, M., Milone, F.F., Minelli, T.A. et al. Mathematical Phenomenology of Neural Stimulation by Periodic Fields. Nonlinear Dynamics Psychol Life Sci 7, 115–137 (2003). https://doi.org/10.1023/A:1021460730922

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  • neuron synchronization
  • bioelectromagnetism
  • electromagnetic stimulation
  • binding
  • electrosmog
  • EEG
  • TMS