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Epilepsy: Extreme Events in the Human Brain

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Extreme Events in Nature and Society

Part of the book series: The Frontiers Collection ((FRONTCOLL))

Summary

The analysis of Xevents arising in dynamical systems with many degrees of freedom represents a challenge for many scientific fields. This is especially true for the open, dissipative, and adaptive system known as the human brain. Due to its complex structure, its immense functionality, and — as in the case of epilepsy — due to the coexistence of normal and abnormal functions, the brain can be regarded as one of the most complex and fascinating systems in nature. Data gathered so far show that the epileptic process exhibits a high spatial and temporal variability. Small, specific, regions of the brain are responsible for the generation of focal epileptic seizures, and the amount of time a patient spends actually having seizures is only a small fraction of his/her lifetime. In between these Xevents large parts of the brain exhibit normal functioning. Since the occurrence of seizures usually can not be explained by exogenous factors, and since the brain recovers its normal state after a seizure in the majority of cases, this might indicate that endogenous nonlinear (deterministic and/or stochastic) properties are involved in the control of these Xevents. In fact, converging evidence now indicates that (particularly) nonlinear approaches to the analysis of brain activity allow us to define precursors which, provided sufficient sensitivity and specificity can be obtained, might lead to the development of patient-specific seizure anticipation and seizure prevention strategies.

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References

  1. J. Engel Jr., T.A. Pedley: Epilepsy: a comprehensive text-book. (Lippincott-Raven, Philadelphia, PA 1997)

    Google Scholar 

  2. R.D. Traub, R.K. Wong: Science 216, 745 (1982)

    Article  ADS  Google Scholar 

  3. E.R.G. Sanabria, H. Su, Y. Yaari: J. Physiol. 532, 205 (2001)

    Article  Google Scholar 

  4. Y. Yaari, H. Beck: Brain Pathol. 12, 234 (2002)

    Article  Google Scholar 

  5. J. Engel Jr.: Seizures and epilepsy. (F.A. Davis Co., Philadelphia, PA 1989)

    Google Scholar 

  6. H. Berger: Archiv für Psychiatrie 87, 35 (1929)

    Google Scholar 

  7. E.J. Speckmann, C.E. Elger: In Electroencephalography, ed. E. Niedermeyer, F.H. Lopes da Silva (Williams and Wilkins, Baltimore, MD 1999), pp 15

    Google Scholar 

  8. E. Niedermeyer, F.H. Lopes da Silva: Electroencephalography. (Williams and Wilkins, Baltimore 1999)

    Google Scholar 

  9. E. Ott: Chaos in dynamical systems (Cambridge University Press, Cambridge, UK 1993)

    MATH  Google Scholar 

  10. H. Kantz, T. Schreiber: Nonlinear time series analysis (Cambridge University Press, Cambridge, UK 2003)

    Book  Google Scholar 

  11. T. Schreiber: Is nonlinearity evident in time series of brain electrical activity? In Chaos in Brain?, eds. au]K. Lehnertz, J. Arnhold, P. Grassberger, C.E. Elger (World Scientific, Singapore 2000) pp 13–22

    Chapter  Google Scholar 

  12. F.H. Lopes da Silva et al..: Rhythms of the brain: between randomness and determinism. In Chaos in Brain?, eds. K. Lehnertz, J. Arnhold, P. Grassberger, C.E. Elger (World Scientific, Singapore 2000) pp 63–76

    Chapter  Google Scholar 

  13. R.G. Andrzejak et al..: Phys. Rev. E 64, 061907 (2001)

    Article  ADS  Google Scholar 

  14. E. Başar: Chaos in Brain Function (Springer, Berlin Heidelberg New York 1990)

    Google Scholar 

  15. D. Duke, W. Pritchard: Measuring chaos in the human brain (World Scientific, Singapore 1991)

    Google Scholar 

  16. B.H. Jansen, M.E. Brandt: Nonlinear dynamical analysis of the EEG (World Scientific, Singapore 1993)

    Google Scholar 

  17. K. Lehnertz, J. Arnhold, P. Grassberger, C.E. Elger: Chaos in Brain? (World Scientific, Singapore 2000)

    Google Scholar 

  18. F. Takens: Detecting strange attractors in turbulence. In Lecture Notes in Mathematics 898, eds. D.A. Rand, L.S. Young (Springer, Berlin Heidelberg New York 1981) pp 366–381

    Google Scholar 

  19. L. Glass: Nature 410, 277 (2001)

    Article  ADS  Google Scholar 

  20. T. Sauer, J. Yorke, M. Casdagli: J. Stat. Phys. 65, 579 (1991)

    Article  MathSciNet  MATH  ADS  Google Scholar 

  21. P. Grassberger, I. Procaccia: Phys. Rev. Lett. 50, 346 (1983)

    Article  ADS  MathSciNet  Google Scholar 

  22. J. Theiler: Phys. Rev. A 34, 2427 (1986)

    Article  ADS  Google Scholar 

  23. P. Grassberger, T. Schreiber, C. Schaffrath: Int. J. Bifurcation Chaos 1, 521 (1991)

    Article  MathSciNet  MATH  Google Scholar 

  24. K. Lehnertz, C.E. Elger: Phys. Rev. Lett. 80, 5019 (1998)

    Article  ADS  Google Scholar 

  25. F. Mormann et al..: Clin. Neurophysiol. (in press)

    Google Scholar 

  26. K. Lehnertz, C.E. Elger: Electroencephalogr. Clin. Neurophysiol. 95, 108 (1995)

    Article  Google Scholar 

  27. J. Martinerie et al.: Nature Med. 4, 1173 (1998)

    Article  Google Scholar 

  28. P.E. McSharry, L.E. Smith, L. Tarassenko: Nature Med. 9, 241 (2003)

    Article  Google Scholar 

  29. P. Grassberger, I. Procaccia: Phys. Rev. A 28, 2591 (1983)

    Article  ADS  Google Scholar 

  30. W. van Drongelen et al.: Pediatr. Neurol. 129, 207 (2003)

    Article  Google Scholar 

  31. H.R. Moser et al.: Pre-ictal changes and EEG analysis within the framework of Lyapunov theory

    Google Scholar 

  32. M. Le Van Quyen et al.: Neuroreport 10, 2149 (1999) In Chaos in Brain?, eds. K. Lehnertz, J. Arnhold, P. Grassberger, C.E. Elger (World Scientific, Singapore 2000) pp 96–111

    Article  Google Scholar 

  33. H. Kantz: Phys. Rev. E 49, 5091 (1994)

    Article  ADS  Google Scholar 

  34. L.D. Iasemidis et al.: Brain Topogr. 2, 187 (1990)

    Article  Google Scholar 

  35. L.D. Iasemidis et al.: J. Comb. Optimization 5, 9 (2001)

    Article  MathSciNet  MATH  Google Scholar 

  36. A. Wolf, J.B. Swift, L. Swinney, A. Vastano A: Physica D 16, 285 (1985)

    Article  ADS  MathSciNet  MATH  Google Scholar 

  37. M.T. Rosenstein, J.J. Collins, C.J. De Luca: Physica D 65, 117 (1993)

    Article  ADS  MathSciNet  MATH  Google Scholar 

  38. H. Kantz: Phys. Lett. A 185, 77 (1994)

    Article  ADS  Google Scholar 

  39. T. Schreiber: Int. J. Bifurc. Chaos 5, 349 (1995)

    Article  MATH  Google Scholar 

  40. A.S. Pikovsky, M.G. Rosenblum, J. Kurths: Synchronization — A universal concept in nonlinear sciences (Cambridge University Press, Cambridge, UK 2001)

    Book  MATH  Google Scholar 

  41. F. Mormann et al.: Physica D 144, 358 (2000)

    Article  ADS  MATH  Google Scholar 

  42. K.V. Mardia: Probability and mathematical statistics: Statistics of directional data (Academy, London 1972)

    Google Scholar 

  43. P. Tass et al.: Phys. Rev. Lett. 81, 3291 (1998)

    Article  ADS  Google Scholar 

  44. J.P. Lachaux et al..: Hum. Brain Mapp. 8, 194 (1999)

    Article  Google Scholar 

  45. J. Arnhold et al.: Physica D 134, 419 (1999)

    Article  ADS  MATH  Google Scholar 

  46. T. Schreiber, A. Schmitz: Physica D 142, 346 (2000)

    Article  ADS  MathSciNet  MATH  Google Scholar 

  47. C.D. Binnie et al.: Electroencephalogr. Clin. Neurophysiol. 58, 498 (1984)

    Article  Google Scholar 

  48. J.G. Milton et al.: Epilepsia 28, 471 (1987)

    Article  Google Scholar 

  49. M. Balish, P.S. Albert, W.H. Theodore: Epilepsia 32, 642 (1991)

    Article  Google Scholar 

  50. E. Tauboll, A. Lundervold, L. Gjerstad: Epilepsy Res. 8, 153 (1991)

    Article  Google Scholar 

  51. L.D. Iasemidis et al.: Epilepsy Res. 17, 81 (1994)

    Article  Google Scholar 

  52. J. Bauer, W. Burr: Seizure 10, 239 (2001)

    Article  Google Scholar 

  53. W.G. Lennox: Science and seizures. (Harper, New York 1946)

    Google Scholar 

  54. R.B. Aird: Epilepsia 24, 567 (1983)

    Article  Google Scholar 

  55. P. Rajna et al.: Seizure 6, 361 (1997)

    Article  Google Scholar 

  56. P.B. Prichard, V.L. Holstrom, J. Giacinto: Ann. Neurol. 18, 265 (1985)

    Article  Google Scholar 

  57. S.S. Viglione, G.O. Walsh: Electroencephalogr. Clin. Neurophysiol. 39, 435 (1975)

    Google Scholar 

  58. Z. Rogowski, I. Gath, E. Bental: Biol. Cybern. 42, 9 (1981)

    Article  Google Scholar 

  59. R.B. Duckrow, S.S. Spencer: Electroencephalogr. Clin. Neurophysiol. 82, 415 (1992)

    Article  Google Scholar 

  60. H.H. Lange et al.: Electroencephalogr. Clin. Neurophysiol. 56, 543 (1983)

    Article  Google Scholar 

  61. J. Gotman, M.G. Marciani: Ann. Neurol 17, 597 (1985)

    Article  Google Scholar 

  62. J. Gotman, D.J. Koffler: Electroencephalogr. Clin. Neurophysiol. 72, 7 (1989)

    Article  Google Scholar 

  63. A. Katz et al.: Electroencephalogr. Clin. Neurophysiol. 79, 153 (1991)

    Article  Google Scholar 

  64. C.E. Elger, K. Lehnertz: Ictogenesis and chaos. In Epileptic seizures and syndromes, ed. P. Wolf (J. Libbey & Co, London 1994) pp 547–552

    Google Scholar 

  65. C.E. Elger, K. Lehnertz: Eur. J. Neurosci. 10, 786 (1998)

    Article  Google Scholar 

  66. M. Le Van Quyen et al.: Eur. J. Neurosci. 12, 2124 (2000)

    Article  Google Scholar 

  67. M. Le Van Quyen et al.: Lancet 357, 183 (2001)

    Article  Google Scholar 

  68. V. Navarro et al.: Brain 125, 640 (2002)

    Article  Google Scholar 

  69. I. Drury et al.: Exp. Neurol. 184, S9, (2003)

    Article  Google Scholar 

  70. B. Litt et al.: Neuron 30, 51 (2001)

    Article  Google Scholar 

  71. S. Gigola et al.: J. Neurosci. Meth. 138, 107 (2004)

    Article  Google Scholar 

  72. F. Mormann et al.: Epilepsy Res. 53, 173 (2003)

    Article  Google Scholar 

  73. F. Mormann et al.: Phys. Rev. E 67, 021912 (2003)

    Article  ADS  MathSciNet  Google Scholar 

  74. K. Schindler et al.: Clin. Neurophysiol 113, 604 (2002)

    Article  Google Scholar 

  75. J. Clin. Neurophysiol. (“Special Issue on Seizure Prediction”) 18, 191 (2001)

    Article  Google Scholar 

  76. B. Litt, K. Lehnertz: Curr. Opin. Neurol. 15, 173 (2002)

    Article  Google Scholar 

  77. H. Witte, L.D. Iasemidis, B. Litt. IEEE Trans. Biomed. Eng. (“Special Issue on Epileptic Seizure Prediction”) 50, 537 (2003)

    Article  Google Scholar 

  78. R.G. Andrzejak et al.: Phys. Rev. E 67, 010901 (2003)

    Article  ADS  MathSciNet  Google Scholar 

  79. R. Aschenbrenner-Scheibe et al.: Brain 126, 2616 (2003)

    Article  Google Scholar 

  80. M. Winterhalder et al.: Epilepsy Behav. 4, 318 (2003)

    Article  Google Scholar 

  81. T. Kreuz et al.: Phys. Rev. E 69, 061915 (2004)

    Article  ADS  Google Scholar 

  82. Y.C. Lai et al.: Phys. Rev. Lett. 91, 068102 (2003)

    Article  ADS  Google Scholar 

  83. W. de Clerq et al.: Lancet 361, 970 (2003)

    Google Scholar 

  84. B. Litt: Epilepsia 44(Suppl. 7), 30 (2003)

    Article  Google Scholar 

  85. W.H. Theodore, R.S. Fisher: Lancet Neurol. 3, 111 (2004)

    Article  Google Scholar 

  86. R.D. Traub, J.G.R. Jefferys, M.A. Whittington: J. Comput. Neurosci. 4, 141 (1997)

    Article  MATH  Google Scholar 

  87. F. Wendling et al.: Biol. Cybern. 83, 367 (2000)

    Article  Google Scholar 

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Authors and Affiliations

  1. Department of Epileptology, Universität Bonn, Bonn, Germany

    Klaus Lehnertz

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  1. Klaus Lehnertz
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Editors and Affiliations

  1. Interdisziplinäres Zentrum für Komplexe Systeme und Institut für Angewandte Mathematik, Universität Bonn, Wegelerstraße 6, 53115, Bonn, Germany

    Sergio Albeverio  & Volker Jentsch  & 

  2. Max-Planck-Institut für Physik komplexer Systeme, Nöthnitzer Straße 38, 01187, Dresden, Germany

    Holger Kantz

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© 2006 Center for Frontier Sciences

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Lehnertz, K. (2006). Epilepsy: Extreme Events in the Human Brain. In: Albeverio, S., Jentsch, V., Kantz, H. (eds) Extreme Events in Nature and Society. The Frontiers Collection. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-28611-X_6

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