Skip to main content

Brain Dynamics and Modeling in Epilepsy: Prediction and Control Studies

  • Conference paper
Complex Dynamics in Physiological Systems: From Heart to Brain

Abstract

Epilepsy is a major neurological disorder characterized by intermittent paroxysmal neuronal electrical activity, that may remain localized or spread, and severely disrupt the brain’s normal operation. Epileptic seizures are typical manifestations of such pathology. It is in the last 20 years that prediction and control of epileptic seizures has been the subject of intensive interdisciplinary research. In this communication, we investigate epilepsy from the point of view of pathology of the dynamics of the electrical activity of the brain. In this framework, we revisit two critical aspects of the dynamics of epileptic seizures – the seizure predictability and seizure resetting – that may prove to be the keys for improved seizure prediction and seizure control schemes. We use human EEG data and the concepts of spatial synchronization of chaos, phase and energy to first show that seizures could be predictable in the order of tens of minutes prior to their onset. We then present additional statistical evidence that the pathology of the brain dynamics prior to seizures is reset mostly upon seizures’ occurrence, a phenomenon we have called seizure resetting. Finally, using a biologically-plausible neural population mathematical model that can exhibit seizure-like behavior, we provide evidence for the effectiveness of a recently devised seizure control scheme we have called “feedback decoupling”. This scheme also provides an interesting dynamical model for ictogenesis (generation of seizures).

This is a preview of subscription content, log in via an institution to check access.

Access this chapter

Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 169.00
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 219.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info
Hardcover Book
USD 219.99
Price excludes VAT (USA)
  • Durable hardcover edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. J. Engel Jr., P. C. Van Ness, T. B. Rasmussen and L. M. Ojemann, “Outcome with respect to epileptic seizures,” in Surgical Treatment of the Epilepsies, J. Engel Jr., Ed., New York: Raven Press, pp. 609–622, 1993.

    Google Scholar 

  2. J. Engel Jr., Seizures and Epilepsy. Philadelphia, PA: F. A. Davis Co., 1989.

    Google Scholar 

  3. J. Engel Jr. and T. A. Pedley, Epilepsy: a Comprehensive Textbook. Philadelphia, PA: Lippincott-Raven, 1997.

    Google Scholar 

  4. J. G. Milton, J. Gotman, G. M. Remillard and F. Andermann, “Timing of seizure recurrence in adult epileptic patients: a statistical analysis,” Epilepsia, vol. 28, pp. 471–478, 1987.

    Article  PubMed  CAS  Google Scholar 

  5. W. G. Lennox, Science and Seizures. New York: Harper, 1946.

    Google Scholar 

  6. W. Penfield, “The evidence for a cerebral vascular mechanism in epilepsy,” Ann. Int. Med., vol. 7, pp. 303–310, 1933.

    Google Scholar 

  7. F. M. Forster, Reflex Epilepsy, Behavioral Therapy and Conditioned Reflexes. Springfield: Thomas, 1977.

    Google Scholar 

  8. C. D. Binnie, A. J. Wilkins, F. C. Valdivia, F. J. J. Jimenez, J. Tejeiro, L. A. Peralta, A. Vaquero and E. G. Albea, “Ecstatic seizures by television,” J. Neurol. Neurosur. Psychiat., vol. 63, p. 273, 1997.

    CAS  Google Scholar 

  9. H. Degn, A. Holden and L. F. Olsen, Chaos in Biological Systems. New York: Plenum, 1987.

    Google Scholar 

  10. W. J. Freeman, “Simulation of chaotic EEG patterns with a dynamic model of the olfactory system,” Biol. Cybern., vol. 56, pp. 139–150, 1987.

    Article  PubMed  CAS  Google Scholar 

  11. A. Babloyantz and A. Destexhe, “Low dimensional chaos in an instance of epilepsy,” Proc. Natl. Acad. Sci. USA, vol. 83, pp. 3513–3517, 1986.

    Article  PubMed  CAS  Google Scholar 

  12. G. W. Frank, T. Lookman, M. A. H. Nerenberg, C. Essex et al., “Chaotic time series analysis of epileptic seizures,” Physica D, vol. 46, pp. 427–438, 1990.

    Article  Google Scholar 

  13. J. C. Principe, A. Rathie and J. M. Kuo, “Prediction of chaotic time series with neural networks and the issue of dynamical modeling,” Int. J. Bifurcat. Chaos, vol. 2, pp. 989–996, 1992.

    Article  Google Scholar 

  14. L. D. Iasemidis, H. P. Zaveri, J. C. Sackellares, W. J. Williams and T. W. Hood, “Nonlinear dynamics of electrocorticographic data,” J. Clin. Neurophysiol., vol. 5, p. 339, 1988.

    Article  Google Scholar 

  15. L. D. Iasemidis, H. P. Zaveri, J. C. Sackellares and W. J. Williams, “Linear and nonlinear modeling of ECoG in temporal lobe epilepsy”, in Proceedings of the 25th Annual Rocky Mountain Bioengineering Symposium, vol. 24, pp. 187–193, 1988.

    CAS  Google Scholar 

  16. L. D. Iasemidis, J. C. Sackellares, H. P. Zaveri and W. J. Williams, “Phase space topography of the electrocorticogram and the Lyapunov exponent in partial seizures,” Brain Topogr., vol. 2, pp. 187–201, 1990.

    Article  PubMed  CAS  Google Scholar 

  17. L. D. Olson, L. D. Iasemidis and J. C. Sackellares, “Evidence that interseizure intervals exhibit low dimensional dynamics,” Epilepsia, vol. 30, p. 644, 1989.

    Google Scholar 

  18. L. D. Iasemidis, J. C. Sackellares and W. J. Williams, “Localizing preictal temporal lobe spike foci using phase space analysis,” Electroencephalogr. Clin. Neurophysiol., vol. 75, pp. S63–S64, 1990.

    Google Scholar 

  19. L. D. Iasemidis, J. C. Sackellares and R. S. Savit, “Quantification of hidden time dependencies in the EEG within the framework of nonlinear dynamics”, in Nonlinear Dynamical Analysis of the EEG, B. H. Jansen and M. E. Brandt, Eds., Singapore: World Scientific, pp. 30–47, 1993.

    Google Scholar 

  20. L. D. Iasemidis, L. D. Olson, J. C. Sackellares and R. Savit, “Time dependencies in the occurrences of epileptic seizures: a nonlinear approach,” Epilepsy Res., vol. 17, pp. 81–94, 1994.

    Google Scholar 

  21. J. C. Sackellares, L. D. Iasemidis, A. Barreto, R. L. Gilmore, R. S. Savit, B. M. Uthman and S. N. Roper, “Computer-assisted seizure detection based on quantitative dynamical measures,” Electroenceph. Clin. Neurophysiol., vol. 95(2), p. 18P, 1995.

    Article  Google Scholar 

  22. L. D. Iasemidis and J. C. Sackellares, “The temporal evolution of the largest Lyapunov exponent on the human epileptic cortex,” in Measuring Chaos in the Human Brain, D. W. Duck and W. S. Pritchard, Eds., Singapore: World Scientific, pp. 49–82, 1996.

    Google Scholar 

  23. L. D. Iasemidis, J. C. Principe, J. M. Czaplewski, R. L. Gilman, S. N. Roper and J. C. Sackellares, “Spatiotemporal transition to epileptic seizures: A nonlinear dynamical analysis of scalp and intracranial EEG recordings,” in Spatiotemporal Models in Biological and Artificial Systems, F. L. Silva, J. C. Principe and L. B. Almeida, Eds., Amsterdam: IOS Press, pp. 81–88, 1997.

    Google Scholar 

  24. J. C. Sackellares, L. D. Iasemidis, R. L. Gilmore and S. N. Roper, “Epilepsy – when chaos fails,” in Chaos in the Brain? K. Lehnertz, J. Arnhold, P. Grassberger and C. E. Elger, Eds., Singapore: World Scientific, pp. 112–133, 2000.

    Google Scholar 

  25. L. D. Iasemidis, “Epileptic seizure prediction and control”, IEEE Transactions on Biomedical Engineering, vol. 50(5), pp. 549–558, 2003.

    Article  Google Scholar 

  26. K. Lehnertz and C. E. Elger, “Spatio-temporal dynamics of the primary epileptogenic area in temporal lobe epilepsy characterized by neuronal complexity loss,” Electroencephalogr. Clin. Neurophysiol., vol. 95, pp. 108–117, 1995.

    Article  PubMed  CAS  Google Scholar 

  27. K. Lehnertz and C. E. Elger, “Neuronal complexity loss of the contralateral hippocampus in temporal lobe epilepsy: a possible indicator of secondary epileptogenesis,” Epilepsia, vol. 36(S4), p. 21, 1995.

    Google Scholar 

  28. D. A. Scott and S. J. Schiff, “Predictability of EEG interictal spikes,” Biophys. J., vol. 69, pp. 1748–1757, 1995.

    Article  PubMed  CAS  Google Scholar 

  29. F. H. Lopes da Silva, J. P. Pijn and W. J. Wadman, “Dynamics of local neuronal networks: control parameters and state bifurcations in epileptogenesis,” Prog. Brain Res., vol. 102, pp. 359–370, 1994.

    Article  Google Scholar 

  30. L. D. Iasemidis, J. C. Sackellares, Q. Luo, S. N. Roper and R. L. Gilmore, “Directional information flow during the preictal transition,” Epilepsia, vol. 40(S7), pp. 165–166, 1999.

    Google Scholar 

  31. L. D. Iasemidis, J. C. Principe and J.C. Sackellares, “Measurement and quantification of spatiotemporal dynamics of human epileptic seizures,” in Nonlinear Biomedical Signal Processing, M. Akay, Ed., IEEE Press, vol. II, pp. 294–318, 2000.

    Google Scholar 

  32. J. C. Sackellares, L. D. Iasemidis, R. L. Gilmore and S. N. Roper, “Epilepsy – when chaos fails” in Chaos in the Brain?, K. Lehnertz, J. Arnhold, P. Grassberger and C. E. Elger, Eds., Singapore: World Scientific, pp. 112–133, 2000.

    Google Scholar 

  33. L. D. Iasemidis, D. S. Shiau, P. Pardalos and J. C. Sackellares, “Transition to epileptic seizures – an optimization approach into its dynamics”, in Discrete Problems with Medical Applications, D. Z. Du, P. M. Pardalos and J. Wang, Eds., DIMACS series, American Mathematical Society Publishing Co., vol. 55, pp. 55–74, 2000.

    Google Scholar 

  34. L. D. Iasemidis, P. Pardalos, J. C. Sackellares and D. S. Shiau, “Quadratic binary programming and dynamical system approach to determine the predictability of epileptic seizures,” J. Comb. Optim., vol. 5, pp. 9–26, 2001.

    Article  Google Scholar 

  35. L. D. Iasemidis, P. M. Pardalos, J. C. Sackellares and V. Yatsenko, “Global optimization approaches to reconstruction of dynamical systems related to epileptic seizures,” in Mathematical Methods in Scattering Theory and Biomedical Technology, C. V. Massalas et al., Eds., Singapore: World Scientific, pp. 308–318, 2002.

    Google Scholar 

  36. L. D. Iasemidis, D. S. Shiau, P. M. Pardalos and J. C. Sackellares, “Phase Entrainment and Predictability of Epileptic Seizures,” in Biocomputing, P. M. Pardalos and J. Principe, Eds., Kluwer Academic Publishers, pp. 59–84, 2002.

    Google Scholar 

  37. L. M. Hively, N. E. Clapp, C. S. Daw and W. F. Lawkins, “Nonlinear analysis of EEG for epileptic events,” ORNL/TM-12961, Oak Ridge National Laboratory, Oak Ridge, TN, 1995.

    Google Scholar 

  38. B. Litt, R. Esteller, J. Echauz, M. D. Alessandro, R. Shor, T. Henry, P. Pennell, C. Epstein, R. Bakay, M. Dichter and G. Vachtsevanos, “Epileptic seizures may begin hours in advance of clinical onset: A report of five patients,” Neuron, vol. 30, pp. 51–64, 2001.

    Article  PubMed  CAS  Google Scholar 

  39. L. D. Iasemidis, D. S. Shiau, W. Chaovalitwongse, P. M. Pardalos, P. R. Carney and J. C. Sackellares “Adaptive seizure prediction system,” Epilepsia, vol. 43, pp. 264–265, 2002.

    Google Scholar 

  40. L. D. Iasemidis, D. S. Shiau, J. C. Sackellares, P. M. Pardalos and A. Prasad, “Dynamical resetting of the human brain at epileptic seizures: application of nonlinear dynamics and global optimization techniques,” IEEE Trans. Biomed. Eng., 51(3), pp. 493–506, 2004.

    Article  PubMed  Google Scholar 

  41. L. D. Iasemidis, A. Prasad, J. C. Sackellares, P. M. Pardalos and D.-S. Shiau, “On the prediction of seizures, hysteresis and resetting of the epileptic brain: insights from models of coupled chaotic oscillators,” in Order and Chaos, T. Bountis Ed. vol. 8, Publishing House of K. Sfakianakis, Thessaloniki: Greece, in press (Proceedings of the 14th Summer School on Nonlinear Dynamics: Chaos and Complexity, Patras, Greece, 2001).

    Google Scholar 

  42. K. Tsakalis, “Performance limitations of adaptive parameter estimation and system identification algorithms in the absence of excitation,” Automatica, vol. 32, pp. 549–560, 1996.

    Article  Google Scholar 

  43. K. S. Tsakalis, “Bursting scenaria in adaptive algorithms: Performance limitations and some remedies,” Kybernetika, vol. 33, pp. 17–40, 1997.

    Google Scholar 

  44. K. S. Tsakalis, L. D. Iasemidis, “Control aspects of a theoretical model for epileptic seizures,” Int. J. Bif. Chaos, vol. 16, pp. 2013–2027, 2006.

    Article  Google Scholar 

  45. K. Tsakalis, N. Chakravarthy, S. Sabesan, L. D. Iasemidis, and P. M. Pardalos, “A feedback control systems view of epileptic seizures,” Cybernetics Sys. Anal., vol. 42, pp. 483–495, 2006.

    Article  Google Scholar 

  46. N. Chakravarthy, S. Sabesan, L. D. Iasemidis, and K. Tsakalis, “Modeling and controlling synchronization in a neuron-level population model,” Int. J. Neural Sys., vol. 17(2), pp. 123–38, 2007.

    Article  Google Scholar 

  47. N. Chakravarthy, S. Sabesan, L. D. Iasemidis, and K. Tsakalis, “Controlling epileptic seizures in a neural mass model,” J. Comb. Optim., 2008 (in press).

    Google Scholar 

  48. M. Harrison et al., “Accumulated energy revisited” Clinical Neurophysiol., vol. 116, pp. 527–531, 2005.

    Article  Google Scholar 

  49. F. Mormann, T. Kreuz, R. G. Andrzejak, P. David, K. Lehnertz and C. E. Elger, “Epileptic seizures are preceded by a decrease in synchronization,” Epilepsy Res., vol. 53, pp. 173–185, 2003.

    Article  PubMed  Google Scholar 

  50. C. Hugenii, Horoloquium Oscilatorum, Paris, France, 1673.

    Google Scholar 

  51. M. G. Rosenblum, A. S. Pikovsky, J. Kurths, “Phase synchronization of chaotic oscillators,” Phys. Rev. Lett., vol. 76, pp. 1804–1807, 1996.

    Article  PubMed  CAS  Google Scholar 

  52. D. Gabor, Theory of communication, Proceedings of IEE London 93, pp. 429–457, 1946.

    Google Scholar 

  53. P. Panter, Modulation, Noise, and Spectral Analysis, McGraw-Hill, New York, 1965.

    Google Scholar 

  54. S. Sabesan, N. Chakravarthy, L. Good, K. Tsakalis, P. M. Pardalos and L. D. Iasemidis, “Global optimization and spatial synchronization changes prior to epileptic seizures”, University of Coimbra, Workshop on Optimization in Medicine, Coimbra, Portugal, July 20–22, 2005, Springer Verlag, pp. 103–125, 2007.

    Google Scholar 

  55. N. H. Packard, J. P. Crutchfield, J. D. Farmer and R. S. Shaw, “Geometry from time series,” Phys. Rev. Lett., vol. 45, pp. 712–716, 1980.

    Article  Google Scholar 

  56. F. Takens, “Detecting strange attractors in turbulence,” in Dynamical Systems and Turbulence, Lecture Notes in Mathematics, D. A. Rand and L. S. Young, Eds., Heidelberg: Springer-Verlag, 1981.

    Google Scholar 

  57. P. Grassberger and I. Procaccia, “Measuring the strangeness of strange attractors,” Physica D, vol. 9, pp. 189–208, 1983.

    Article  Google Scholar 

  58. P. Grassberger and I. Procaccia, “Characterization of strange attractors,” Phys. Rev. Lett., vol. 50, pp. 346–349, 1983.

    Article  Google Scholar 

  59. E. J. Kostelich, “Problems in estimating dynamics from data,” Physica D, vol. 58, pp. 138–152, 1992.

    Article  Google Scholar 

  60. H. D. I. Abarbanel, Analysis of Observed Chaotic Data, New York: Springer Verlag, 1996.

    Google Scholar 

  61. H. Haken, Principles of Brain Functioning: A Synergetic Approach to Brain Activity, Behavior and Cognition, Springer-Verlag, Berlin, 1996.

    Google Scholar 

  62. J. A. Vastano and E. J. Kostelich, “Comparison of algorithms for determining Lyapunov exponents from experimental data,” in Dimensions and Entropies in Chaotic Systems: Quantification of Complex Behavior, G. Mayer-Kress, Ed., Berlin: Springer-Verlag, 1986.

    Google Scholar 

  63. L. D. Iasemidis, D. S. Shiau, W. Chaovalitwongse, J. C. Sackellares, P. M. Pardalos, P. R. Carney, A. Prasad, B. Veeramani, and K. Tsakalis, “Adaptive epileptic seizure prediction system”, IEEE Trans. Biomed. Eng., vol. 50(5), pp. 616–627, 2003.

    Article  PubMed  Google Scholar 

  64. L. D. Iasemidis, D.-S. Shiau, P. M. Pardalos, W. Chaovalitwongse, K. Narayanan, A. Prasad, K. Tsakalis, P. Carney and J. C. Sackellares, “Long-term prospective on-line real-time seizure prediction”, J. Clin. Neurophysiol., vol. 116, pp. 532–544, 2005.

    Article  CAS  Google Scholar 

  65. W. Chaovalitwongse, L. D. Iasemidis, P. M. Pardalos, P. R. Carney, D.-S. Shiau and J. C. Sackellares, “Performance of a seizure warning algorithm based on nonlinear dynamics of the intracranial EEG”, Epilepsy Res., vol. 64, pp. 93–113, 2005.

    Article  PubMed  CAS  Google Scholar 

  66. C. Domb, in Phase Transitions and Critical Phenomena, C. Domb and M. S. Green, Eds., New York: Academic Press, 1974.

    Google Scholar 

  67. R. Esteller et al., “Continuous energy variation during the seizure cycle: Towards an on-line accumulated energy” Clinical Neurophysiology 116, pp. 517–526, 2005.

    Article  PubMed  Google Scholar 

  68. M. G. Rosenblum, A. S. Pikovsky, J. Kurths, “From phase to lag synchronization in coupled chaotic oscillators,” Phys. Rev. Lett., vol. 78, pp. 4193–4196, 1997

    Article  CAS  Google Scholar 

  69. V. S. Afraimovich, N. N. Verichev, M. I. Rabinovich, “General synchronization,” Izv VysshUch Zav Radiofizika, vol. 29, pp. 795–803, 1986.

    Google Scholar 

  70. N. F. Rulkov, M. M. Sushchik, L. S. Tsimring, H. D. I. Ababarnel, “Generalized synchronization of chaos in directionally coupled chaotic systems,” Phys. Rev. E, vol. 51, pp. 980–994, 1996.

    Article  Google Scholar 

  71. H. Fujisaka and T. Yamada, “Stability theory of synchronized motion in coupled-oscillator systems,” Progr. Theor. Phys., vol. 69, pp. 32–37, 1983.

    Article  CAS  Google Scholar 

  72. L. D. Iasemidis and J. C. Sackellares, “Chaos theory in epilepsy,” The Neuroscientist, vol. 2, pp. 118–126, 1996.

    Article  Google Scholar 

  73. J. C. Sackellares, L. D. Iasemidis, R. L. Gilmore and S. N. Roper, “Epileptic seizures as neural resetting mechanisms”, Epilepsia, vol. 38(S3), p. 189, 1997.

    Google Scholar 

  74. D. S. Shiau, Q. Luo, R. L. Gilmore, S. N. Roper, P. Pardalos, J. C. Sackellares and L. D. Iasemidis, “Epileptic seizures resetting revisited”, Epilepsia, vol. 41(S7), p. 208, 2000.

    Google Scholar 

  75. W. A. Chaovalitwongse, L. D. Iasemidis, P. M. Pardalos, P. R. Carney, D.-S. Shiau and J. C. Sackellares, “Reply to comments by F. Morman, CE Elger, and K. Lehnertz on the performance of a seizure warning algorithm based on the dynamics of intracranial EEG”, Epilepsy Res., vol. 72, pp. 85–87, 2006.

    Article  PubMed  Google Scholar 

  76. W. A. Chaovalitwongse, L. D. Iasemidis, P. M. Pardalos, P. R. Carney, D.-S. Shiau and J. C. Sackellares, “Reply to comments by M. Winterhalder, B. Schelter, A. Achulze-Bonhage and J. Timmer on the performance of a seizure warning algorithm based on the dynamics of intracranial EEG”, Epilepsy Res., vol. 72, pp. 82–84, 2006.

    Article  Google Scholar 

  77. J. C. Sackellares, D.-S. Shiau, J. C. Principe, M. C. K. Young, L. K. Dance, W. Suharitdamrong, W. Chaovalitwongse, P. M. Pardalos and L. D. Iasemidis, “Predictability analysis for an automated seizure prediction algorithm”, J. Clinical Neurophysiol., vol. 23, pp. 509–520, 2006.

    Article  Google Scholar 

  78. P. Suffczynski, S. Kalitzin and F. H. L. Da Silva, “Dynamics of non-convulsive epileptic phenomena modeled by a bistable neuronal network”, Neuroscience, vol. 126, pp. 467–484, 2004

    Article  PubMed  CAS  Google Scholar 

  79. D. Liley, P. Cadusch and M. Dafilis, “A spatially continuous mean field theory of electrocortical activity”, Network: Comp. in Neural. Sys., vol. 13, pp. 67–113, 2002.

    Article  Google Scholar 

  80. E. Grassi, K. S. Tsakalis, S. Dash, S. V. Gaikwad, W. MacArthur and G. Stein, “Integrated system identification and PID controller tuning by frequency loop-shaping”, IEEE Trans. Control Sys. Tech., vol. 9, pp. 285–294, 2001.

    Article  Google Scholar 

  81. K. J. Astrom and L. Rundqwist, “Integrator windup and how to avoid it”, Proceedings of the 1989 American Control Conference, vol. 21–23, pp. 1693–1698, June 1989.

    Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Editor information

Editors and Affiliations

Rights and permissions

Reprints and permissions

Copyright information

© 2009 Springer Science+Business Media B.V.

About this paper

Cite this paper

Iasemidis, L., Sabesan, S., Chakravarthy, N., Prasad, A., Tsakalis, K. (2009). Brain Dynamics and Modeling in Epilepsy: Prediction and Control Studies. In: Dana, S.K., Roy, P.K., Kurths, J. (eds) Complex Dynamics in Physiological Systems: From Heart to Brain. Understanding Complex Systems. Springer, Dordrecht. https://doi.org/10.1007/978-1-4020-9143-8_12

Download citation

Publish with us

Policies and ethics