Neuronal avalanches and coherence potentials

Regular Article

Abstract

The mammalian cortex consists of a vast network of weakly interacting excitable cells called neurons. Neurons must synchronize their activities in order to trigger activity in neighboring neurons. Moreover, interactions must be carefully regulated to remain weak (but not too weak) such that cascades of active neuronal groups avoid explosive growth yet allow for activity propagation over long-distances. Such a balance is robustly realized for neuronal avalanches, which are defined as cortical activity cascades that follow precise power laws. In experiments, scale-invariant neuronal avalanche dynamics have been observed during spontaneous cortical activity in isolated preparations in vitro as well as in the ongoing cortical activity of awake animals and in humans. Theory, models, and experiments suggest that neuronal avalanches are the signature of brain function near criticality at which the cortex optimally responds to inputs and maximizes its information capacity. Importantly, avalanche dynamics allow for the emergence of a subset of avalanches, the coherence potentials. They emerge when the synchronization of a local neuronal group exceeds a local threshold, at which the system spawns replicas of the local group activity at distant network sites. The functional importance of coherence potentials will be discussed in the context of propagating structures, such as gliders in balanced cellular automata. Gliders constitute local population dynamics that replicate in space after a finite number of generations and are thought to provide cellular automata with universal computation. Avalanches and coherence potentials are proposed to constitute a modern framework of cortical synchronization dynamics that underlies brain function.

Keywords

European Physical Journal Special Topic Cellular Automaton Microelectrode Array Neuronal Group Avalanche Size 

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. 1.
    J.M. Beggs, D. Plenz, J. Neurosci. 23, 11167 (2003)Google Scholar
  2. 2.
    J.M. Beggs, D. Plenz, J. Neurosci. 24, 5216 (2004)CrossRefGoogle Scholar
  3. 3.
    C.V. Stewart, D. Plenz, J. Neurosci. 26, 8148 (2006)CrossRefGoogle Scholar
  4. 4.
    D. Plenz, T.C. Thiagarajan, Trends Neurosci. 30, 101 (2007)CrossRefGoogle Scholar
  5. 5.
    C.V. Stewart, D. Plenz, J. Neurosci. Meth. 169, 405 (2007)CrossRefGoogle Scholar
  6. 6.
    A. Mazzoni, F.D. Broccard, E. Garcia-Perez, P. Bonifazi, M.E. Ruaro, V. Torre, PLoS ONE 2, e439 (2007)ADSCrossRefGoogle Scholar
  7. 7.
    E.D. Gireesh, D. Plenz, Proc. Natl. Acad. Sci. USA 105, 7576 (2008)ADSCrossRefGoogle Scholar
  8. 8.
    S. Pajevic, D. Plenz, PLoS Comp. Biol. 5, e1000271 (2008)MathSciNetCrossRefGoogle Scholar
  9. 9.
    V. Pasquale, P. Massobrio, L.L. Bologna, M. Chiappalone, S. Martinoia, Neurosci. 153, 1354 (2008)CrossRefGoogle Scholar
  10. 10.
    T. Petermann, T. Thiagarajan, M.A. Lebedev, M.A. Nicolelis, D.R. Chialvo, D. Plenz, Proc. Natl. Acad. Sci. USA 106, 15921 (2009)ADSCrossRefGoogle Scholar
  11. 11.
    W.L. Shew, H. Yang, T. Petermann, R. Roy, D. Plenz, J. Neurosci. 9, 15595 (2009)CrossRefGoogle Scholar
  12. 12.
    G. Hahn, T. Petermann, S. Yu, W. Singer, D. Plenz, D. Nikolic, J. Neurophysiol. 104, 3312 (2010)CrossRefGoogle Scholar
  13. 13.
    T.L. Ribeiro, M. Copelli, F. Caixeta, H. Belchior, D.R. Chialvo, M.A. Nicolelis, et al., PLoS ONE 5, e14129 (2010)ADSCrossRefGoogle Scholar
  14. 14.
    C. Tetzlaff, S. Okujeni, U. Egert, F. Worgotter, M. Butz, PLoS Comput. Biol. 6, e1001013 (2010)MathSciNetCrossRefGoogle Scholar
  15. 15.
    P. Allegrini, P. Paradisi, D. Menicucci, A. Gemignani, Front Physiol. 1, 128 (2010)CrossRefGoogle Scholar
  16. 16.
    W.L. Shew, H. Yang, S. Yu, R. Roy, D. Plenz, J. Neurosci. 5, 55 (2011)CrossRefGoogle Scholar
  17. 17.
    A. Klaus, S. Yu, D. Plenz, PLoS One 6, e19779 (2011)ADSCrossRefGoogle Scholar
  18. 18.
    S. Yu, H. Yang, H. Nakahara, G. Santos, D. Nikolic, D. Plenz, J. Neurosci. 31, 17514 (2011)CrossRefGoogle Scholar
  19. 19.
    H. Yang, W. Shew, R. Rajarshi, D. Plenz, J. Neurosci. 32, 1061 (2012)CrossRefGoogle Scholar
  20. 20.
    T.C. Thiagarajan, M.A. Lebedev, M.A. Nicolelis, D. Plenz, PLoS Biology 8, e1000278 (2010)CrossRefGoogle Scholar
  21. 21.
    H.E. Stanley, Introduction to Phase Transitions and Critical Phenomena (Oxford University Press, New York, 1971)Google Scholar
  22. 22.
    P. Bak, How Nature Works: The Science of Self-Organized Criticality (Copernicus Books, New York, 1996)Google Scholar
  23. 23.
    H.J. Jensen, Self-Organized Criticality (Cambridge University Press, 1998)Google Scholar
  24. 24.
    D. Sornette, Critical Phenomena in Natural Sciences (Berlin, Springer Verlag, 2000)Google Scholar
  25. 25.
    S. Wolfram, Physica D 10, 1 (1984)MathSciNetADSCrossRefGoogle Scholar
  26. 26.
    W. Hordijk, C.R. Shalizi, J.P. Crutchfield, Physica D 154, 240 (2001)MathSciNetADSMATHCrossRefGoogle Scholar
  27. 27.
    J.K. Park, K. Steiglitz, W.P. Thurston, Physica D 19, 432 (2011)MathSciNetGoogle Scholar
  28. 28.
    D. Sornette, J. Terraspace Sci. Eng. 2, 1 (2009)Google Scholar
  29. 29.
    V. Braitenberg, A. Schüz, Anatomy of the cortex. Berlin Heidelberg (Springer-Verlag, New York, 1992)Google Scholar
  30. 30.
    M. Abeles, Corticonics: Neural Circuits of the Cerebral Cortex, 1st edn. (Cambridge University Press, New York Port Chester Melbourne Sydney, 1992)Google Scholar
  31. 31.
    M. Diesmann, M.O. Gewaltig, A. Aertsen, Nature 402, 529 (1999)ADSCrossRefGoogle Scholar
  32. 32.
    Y. Ikegaya, G. Aaron, R. Cossart, D. Aronov, I. Lampl, D. Ferster, et al., Science 304, 559 (2004)ADSCrossRefGoogle Scholar
  33. 33.
    C. Mehring, U. Hehl, M. Kubo, M. Diesmann, A. Aertsen, Biol. Cybern. 88, 395 (2003)MATHCrossRefGoogle Scholar
  34. 34.
    M.O. Gewaltig, M. Diesmann, A. Aertsen, Neural. Netw. 14, 657 (2001)CrossRefGoogle Scholar
  35. 35.
    A. Aertsen, M. Diesmann, M.O. Gewaltig, Propagation of Synchronous Spiking Activity in Feedforward Neural Networks, 90 edn. (1996), p. 243Google Scholar
  36. 36.
    J.N. Teramae, T. Fukai, J. Comput. Neurosci. 22, 301 (2007)MathSciNetCrossRefGoogle Scholar
  37. 37.
    T.P. Vogels, L.F. Abbott, J. Neurosci. 25, 10786 (2005)CrossRefGoogle Scholar
  38. 38.
    A. Kumar, S. Rotter, A. Aertsen, J. Neurosci. 28, 5268 (2008)CrossRefGoogle Scholar
  39. 39.
    M. Abeles, G. Hayon, D. Lehmann, J. Comput. Neurosci. 17, 179 (2004)CrossRefGoogle Scholar
  40. 40.
    S. Kunkel, M. Diesmann, A. Morrison, Front Comput. Neurosci. 4, 160 (2011)Google Scholar
  41. 41.
    M. Abeles, H. Bergman, E. Margalit, E. Vaadia, J. Neurophysiol. 70, 1629 (1993)Google Scholar
  42. 42.
    A. Mokeichev, M. Okun, O. Barak, Y. Katz, O. Ben Shahar, I. Lampl, Neuron 53, 413 (2007)CrossRefGoogle Scholar
  43. 43.
    M.J. Rasch, A. Gretton, Y. Murayama, W. Maass, N.K. Logothetis, J. Neurophysiol. 99, 1461 (2008)CrossRefGoogle Scholar
  44. 44.
    E.A. Stern, M. Maravall, K. Svoboda, Neuron 31, 305 (2001)CrossRefGoogle Scholar
  45. 45.
    O. Shriki, J. Alstott, F.W. Carver, T. Holroyd, R. Henson, M.L. Smith, et al., Signatures of criticality in human brain dynamics. Soc. Neuroscience, Program No. 661.04 2011Google Scholar
  46. 46.
    K. Zhang, T.J. Sejnowski, Proc. Natl. Acad. Sci. USA 97, 5621 (2000)ADSCrossRefGoogle Scholar
  47. 47.
    W.L. Shew, T. Bellay, D. Plenz, J. Neurosci. Methods 192, 75 (2010)CrossRefGoogle Scholar
  48. 48.
    D. Plenz, D.R. Chialvo, Scaling properties of neuronal avalanches are consistent with critical dynamics [arXiv:0912 5369 2009]Google Scholar
  49. 49.
    A.K. Engel, P. Fries, W. Singer, Nat. Rev. Neurosci. 2, 704 (2001)CrossRefGoogle Scholar
  50. 50.
    W. Singer, Neuron 24, 49 (1999)CrossRefGoogle Scholar
  51. 51.
    C.M. Gray, P. Konig, A.K. Engel, W. Singer, Nature 338, 334 (1989)ADSCrossRefGoogle Scholar
  52. 52.
    M.N. Havenith, S.Yu, J. Biederlack, N.H. Chen, W. Singer, D. Nikolic, J. Neurosci. 31, 8570 (2011)CrossRefGoogle Scholar
  53. 53.
    G.G. Turrigiano, S.B. Nelson, Nat. Rev. Neurosci. 5, 97 (2004)CrossRefGoogle Scholar
  54. 54.
    I. Osorio, M.G. Frei, D. Sornette, J. Milton, Y-C. Lai, Phys. Rev. E 82, 021919 (2010)MathSciNetADSCrossRefGoogle Scholar
  55. 55.
    O. Kinouchi, M. Copelli, Nat. Phys. 2, 348 (2006)CrossRefGoogle Scholar
  56. 56.
    D. Millman, S. Mihalas, A. Kirkwood, E. Niebur, Nat. Phys. (2010) doi: 10.1038/nphys1757Google Scholar
  57. 57.
    J. Tabak, J. Rinzel, M.J. O’Donovan, J. Neurosci. 21, 8966 (2001)Google Scholar
  58. 58.
    W. Nisch, J. Bock, U. Egert, H. Hammerle, A. Mohr, Biosens. Bioelectron 9, 737 (1994)CrossRefGoogle Scholar
  59. 59.
    G.A. Worrell, S.D. Cranstoun, J. Echauz, B. Litt, NeuroReport 13, 2017 (2002)CrossRefGoogle Scholar
  60. 60.
    J.P. Hobbs, J.L. Smith, J.M. Beggs, J. Clin. Neurophysiol. 27, 380 (2010)CrossRefGoogle Scholar
  61. 61.
    A.F. Arnsten, J.X. Cai, B.L. Murphy, P.S. Goldman-Rakic, Psychopharmacology (Berl) 116, 143 (1994)CrossRefGoogle Scholar
  62. 62.
    V.S. Mattay, T.E. Goldberg, F. Fera, A.R. Hariri, A. Tessitore, M.F. Egan, et al., Proc. Natl. Acad. Sci. USA 100, 6186 (2003)ADSCrossRefGoogle Scholar
  63. 63.
    J.H. Krystal, D.C. D’Souza, D. Mathalon, E. Perry, A. Belger, R. Hoffman, Psychopharmacology (Berl) 169, 215 (2003)CrossRefGoogle Scholar
  64. 64.
    W.M. Abi-Saab, D.C. D’Souza, B. Moghaddam, J.H. Krystal, Pharmacopsychiatry 31, 104 (1998)CrossRefGoogle Scholar
  65. 65.
    M.P. Paulus, M.A. Geyer, L.H. Gold, A.J. Mandell, Proc. Natl. Acad. Sci. USA 87, 723 (1990)ADSCrossRefGoogle Scholar
  66. 66.
    E.V. Albano, Physica A 216, 213 (1995)ADSCrossRefGoogle Scholar
  67. 67.
    T.E. Harris, The Theory of Branching Processes (New York, Dover, 1989)Google Scholar
  68. 68.
    S. Zapperi, L.K. Baekgaard, H.E. Stanley, Phys. Rev. Lett. 75, 4071 (1995)ADSCrossRefGoogle Scholar
  69. 69.
    D. Eytan, S. Marom, J. Neurosci. 26, 8465 (2006)CrossRefGoogle Scholar
  70. 70.
    H.J. Luhmann, T. Mittmann, G. van Luijtelaar, U. Heinemann, Epilepsy Res. 22, 43 (1995)CrossRefGoogle Scholar
  71. 71.
    D.A. Prince, I. Parada, K. Scalise, K. Graber, X. Jin, F. Shen, Epilepsia 50, 30 (2009)CrossRefGoogle Scholar
  72. 72.
    M.J. Gutnick, B.W. Connors, D.A. Prince, J. Neurophysiol. 48, 1321 (1982)Google Scholar
  73. 73.
    B.W. Connors, Nature 310, 685 (1984)ADSCrossRefGoogle Scholar
  74. 74.
    D.J. Pinto, S.L. Patrick, W.C. Huang, B.W. Connors, J. Neurosci. 25, 8131 (2005)CrossRefGoogle Scholar
  75. 75.
    C.W. Eurich, J.M. Herrmann, U.A. Ernst, Phys. Rev. E Stat Nonlin. Soft. Matter Phys. 66, 066137 (2002)CrossRefGoogle Scholar
  76. 76.
    A. Levina, U. Ernst, J.M. Herrmann, Neurocomputing 70, 1877 (2008)CrossRefGoogle Scholar
  77. 77.
    A. Levina, J.M. Hermann, T. Geisel, Nat. Phys. 857, 2007 (Google Scholar
  78. 78.
    D. Plenz, Nature Physics (2010) doi: 10.1038/nphys1796Google Scholar
  79. 79.
    F. Omori, J. Coll, Sci. Imper. Univ. Tokyo. 7, 111 (1895)Google Scholar
  80. 80.
    T. Utsu, Y. Ogata, J. Phys. Earth. 43, 1 (1995)CrossRefGoogle Scholar
  81. 81.
    S. Marom, Prog. Neurobiol. 90, 16 (2010)CrossRefGoogle Scholar
  82. 82.
    K. Linkenkaer-Hansen, V.V. Nikouline, J.M. Palva, R.J. Ilmoniemi, J. Neurosci. 21, 1370 (2001)Google Scholar
  83. 83.
    A. Gal, D. Eytan, A. Wallach, M. Sandler, J. Schiller, S. Marom, J. Neurosci. 30, 16332 (2010)CrossRefGoogle Scholar
  84. 84.
    P. Shearer, E. Hauksson, G. Lin, Bull. Seismol. Soc. Amer. 95, 904 (2005)CrossRefGoogle Scholar
  85. 85.
    B. Enescu, Z. Struzik, K. Kiyono, Geophys. J. Int. 172, 395 (2008)ADSCrossRefGoogle Scholar
  86. 86.
    L. de Arcangelis, C. Godano, E. Lippiello, M. Nicodemi, Phys. Rev. Lett. 96, 051102 (2006)ADSCrossRefGoogle Scholar
  87. 87.
    N. Bertschinger, T. Natschlager, Neural Comput. 16, 1413 (2004)MATHCrossRefGoogle Scholar
  88. 88.
    R. Legenstein, W. Maass, Neural Netw. 20, 323 (2007)MATHCrossRefGoogle Scholar
  89. 89.
    D. Larremore, W. Shew, J. Restrepo, Phys. Rev. Lett. 106, 1 (2011)CrossRefGoogle Scholar
  90. 90.
    L. Pfeffer, ID, SCV, DP. IEEE Symposium on Computer-Based Medical Systems: CMBS (2004), p. 473, ISBN: 0-7695-2104-5Google Scholar
  91. 91.
    P. Ramo, S. Kauffman, J. Kesselia, O. Yli-Harja, Physica D 227, 100 (2007)MathSciNetADSCrossRefGoogle Scholar
  92. 92.
    C. Haldeman, J.M. Beggs, Phys. Rev. Lett. 94, 058101 (2005)ADSCrossRefGoogle Scholar
  93. 93.
    T.J. Gawne, B.J. Richmond, J. Neurosci. 13, 2758 (1993)Google Scholar
  94. 94.
    I.E. Ohiorhenuan, F. Mechler, K.P. Purpura, A.M. Schmid, Q. Hu, J.D. Victor, Nature 466, 617 (2010)ADSCrossRefGoogle Scholar
  95. 95.
    Y. Shu, A. Hasenstaub, D.A. McCormick, Nature 423, 288 (2003)ADSCrossRefGoogle Scholar
  96. 96.
    M. Okun, I. Lampl, Nat. Neurosci. 11, 535 (2008)CrossRefGoogle Scholar
  97. 97.
    L. de Arcangelis, H.J. Herrmann, Proc. Natl. Acad. Sci. USA 107, 3977 (2010)ADSCrossRefGoogle Scholar
  98. 98.
    L. de Arcangelis, C. Perrone-Capano, H.J. Herrmann, Phys. Rev. Lett. 96, 028107 (2006)ADSCrossRefGoogle Scholar
  99. 99.
    W. Rall, Biophys. J. 2, 145 (1962)ADSCrossRefGoogle Scholar
  100. 100.
    K.J. Friston, Neuroimage 5, 164 (1997)CrossRefGoogle Scholar
  101. 101.
    J.A.S. Kelso, Dynamic patterns: The Self-Organization of Brain and Behavior (MIT Press, Cambridge, MA, 1995)Google Scholar
  102. 102.
    M. Gardner, Sci. Am. 223, 120 (1970)CrossRefGoogle Scholar
  103. 103.
    E. Berlekamp, J.H. Conway, R. Guy, Winning Ways for Your Mathematical Plays (Academic Press, New York, 1982)Google Scholar
  104. 104.
    Cellular automata (MIT Press, Cambridge, 1990)Google Scholar
  105. 105.
    N.H. Packard, Dynamics Patterns in Complex Systems, edited by J.A.S. Kelso, A.J. Mandell, M.F. Shlesinger (World Scientific, Singapore, 1988), p. 293Google Scholar
  106. 106.
    Cellular Automata: Proceedings of an Interdisciplinary Workshop (North Holland, Amsterdam, 1984)Google Scholar
  107. 107.
    P. Bak, K. Chen, M. Paczuski, Phys. Rev. Lett. 86, 2475 (2001)ADSCrossRefGoogle Scholar
  108. 108.
    N.M. Gotts, Int. J. Syst. Sci. 31, 873 (2000)MATHCrossRefGoogle Scholar
  109. 109.
    M. Mitchel, P. Hraber, J.P. Crutchfield, Complex Syst. 7, 89 (1993)Google Scholar
  110. 110.
    C.G. Langton, Physica D 42, 12 (1990)MathSciNetADSCrossRefGoogle Scholar
  111. 111.
    D. Hebb, The Organization of Behavior. A Neuropsychological Theory (Wiley, New York, 1949)Google Scholar
  112. 112.
    W.J. Freeman, Mass Action in the Nervous System (Academic Press, New York, 1975)Google Scholar
  113. 113.
    V. Braitenberg, J. Theor. Biol. 46, 421 (1974)CrossRefGoogle Scholar
  114. 114.
    V. Braitenberg, Lecture Notes in Biomathematics, Theoretical approches to complex systems Proceedings 1977, edited by R. Heim, G. Palm, vol. 21, 1st edn. (Springer Verlag, Berlin Heidelberg, New York, 1978), p. 171Google Scholar
  115. 115.
    V. Braitenberg, Architectonics of the Cerebral Cortex, edited by M.A.B. Brazier, H. Petsche (Raven Press, New York, 1978), p. 443Google Scholar
  116. 116.
    V. Braitenberg, A. Schüz, Spektrum Wiss 74 (1989)Google Scholar
  117. 117.
    M. Abeles, Local Cortical Circuits (Springer Verlag, Berlin, Heidelberg, New York, 1982), p. 1Google Scholar
  118. 118.
    M. Abeles Isr, J. Med. Sci. 18, 83 (1982)Google Scholar
  119. 119.
    H. Hammerle, U. Egert, A. Mohr, W. Nisch, Biosens. Bioelectron. 9, 691 (1994)CrossRefGoogle Scholar
  120. 120.
    U. Egert, D. Heck, A. Aertsen, Exp. Brain. Res. 142, 268 (2002)CrossRefGoogle Scholar
  121. 121.
    A. Toib, V. Lyakhov, S. Marom, J. Neurosci. 18, 1893 (1998)Google Scholar
  122. 122.
    C.M. Gray, P. Koenig, A.K. Engel, W. Singer, Nature 338, 334 (1989)ADSCrossRefGoogle Scholar
  123. 123.
    R. Eckhorn, R. Bauer, W. Jordan, M. Brosch, W. Kruse, M. Munk, et al., Biol. Cybern. 60, 121 (1988)CrossRefGoogle Scholar
  124. 124.
    W.J. Freeman, B.W. Van Dijk, Brain. Res. 422, 267 (1987)CrossRefGoogle Scholar
  125. 125.
    E. Rodriguez, N. George, J.P. Lachaux, J. Martinerie, B. Renault, F.J. Varela, Nature 397, 430 (1999)ADSCrossRefGoogle Scholar
  126. 126.
    F.J. Varela, J.P. Lachaux, E. Rodriguez, J. Martinerie, Nat. Rev. Neurosci. 2, 229 (2001)CrossRefGoogle Scholar
  127. 127.
    G.L. Gerstein, D.H. Perkel, Biophys. J. 453, 473 (1972)Google Scholar
  128. 128.
    A. Aertsen, G.L. Gerstein, Brain. Res. 340, 341 (1985)CrossRefGoogle Scholar
  129. 129.
    G.L. Gerstein, A. Aertsen, J. Neurophysiol. 54, 1513 (1985)Google Scholar
  130. 130.
    A. Riehle, S. Grun, M. Diesmann, A. Aertsen, Science 278, 1950 (1997)ADSCrossRefGoogle Scholar
  131. 131.
    Gruen, M.Diesmann, F.Grammont, A.Riehle, A. Aertsen, J. Neurosci. Methods 94, 67 (1999)CrossRefGoogle Scholar
  132. 132.
    M. Abeles, Y. Prut, H. Bergman, E. Vaadia, A. Aertsen, Brain Theory: Spatio-Temporal Aspects of Brain Function, edited by A. Aertsen (Elsevier Science, Amsterdam, 1993)Google Scholar
  133. 133.
    G. Shahaf, D. Eytan, A. Gal, E. Kermany, V. Lyakhov, C. Zrenner, et al., PLoS Comput. Biol. 4, e1000228 (2008)MathSciNetCrossRefGoogle Scholar
  134. 134.
    V. Priesemann, M.H. Munk, M. Wibral, BMC Neurosci. 10, 40 (2009)CrossRefGoogle Scholar
  135. 135.
    S. Bornholdt, T. Rohl, Phys. Rev. E; Stat. Nonlin. Soft. Matter Phys. 67, 066118 (2003)CrossRefGoogle Scholar
  136. 136.
    M. Rubinov, O. Sporns, J.P. Thivierge, M. Breakspear, PLoS Comput. Biol. 7, e1002038 (2011)MathSciNetCrossRefGoogle Scholar
  137. 137.
    G.L. Pellegrini, L. de Arcangelis, H.J. Herrmann, C. Perrone-Capano, Phys. Rev. E Stat. Nonlin. Soft. Matter Phys. 76, 016107 (2007)ADSCrossRefGoogle Scholar
  138. 138.
    D. Lehmann, Int. J. Psychophysiol. 1, 267 (1984)MathSciNetCrossRefGoogle Scholar
  139. 139.
    D. Lehmann, H. Ozaki, I. Pal, Electroencephalogr Clin. Neurophysiol. 67, 271 (1987)CrossRefGoogle Scholar
  140. 140.
    D. Lehmann, P.L. Faber, S. Galderisi, W.M. Herrmann, T. Kinoshita, M. Koukkou, et al., Psychiatry Res. 138, 141 (2005)CrossRefGoogle Scholar
  141. 141.
    A.A. Fingelkurts, A.A. Fingelkurts, Int. J. Neurosci. 114, 843 (2004)CrossRefGoogle Scholar
  142. 142.
    A.A. Fingelkurts, A.A. Fingelkurts, Cogn. Process 7, 135 (2006)CrossRefGoogle Scholar
  143. 143.
    F.W. Ohl, H. Scheich, W.J. Freeman, Nature 412, 733 (2001)ADSCrossRefGoogle Scholar
  144. 144.
    F. Han, N. Caporale, Y. Dan, Neuron 60, 321 (2008)CrossRefGoogle Scholar
  145. 145.
    E.R. John, M. Shimokochi, F. Bartlett, Science 164, 1534 (1969)ADSCrossRefGoogle Scholar
  146. 146.
    W.J. Freeman, J. Integr. Neurosci. 2, 3 (2003)CrossRefGoogle Scholar
  147. 147.
    D. Lehmann, P.L. Faber, L.R. Gianotti, K. Kochi, R.D. Pascual-Marqui, J. Physiol. Paris 99, 29 (2006)CrossRefGoogle Scholar
  148. 148.
    J.J. McGuire, M.S. Boettcher, T.H. Jordan, Nature 434, 457 (2005)ADSCrossRefGoogle Scholar

Copyright information

© EDP Sciences and Springer 2012

Authors and Affiliations

  1. 1.Section on Critical Brain DynamicsNational Institute of Mental Health, NIHBethesdaUSA

Personalised recommendations