Advertisement

Journal of Combinatorial Optimization

, Volume 15, Issue 3, pp 276–286 | Cite as

Quantitative complexity analysis in multi-channel intracranial EEG recordings form epilepsy brains

  • Chang-Chia Liu
  • Panos M. Pardalos
  • W. Art Chaovalitwongse
  • Deng-Shan Shiau
  • Georges Ghacibeh
  • Wichai Suharitdamrong
  • J. Chris Sackellares
Original Paper

Abstract

Epilepsy is a brain disorder characterized clinically by temporary but recurrent disturbances of brain function that may or may not be associated with destruction or loss of consciousness and abnormal behavior. Human brain is composed of more than 10 to the power 10 neurons, each of which receives electrical impulses known as action potentials from others neurons via synapses and sends electrical impulses via a sing output line to a similar (the axon) number of neurons. When neuronal networks are active, they produced a change in voltage potential, which can be captured by an electroencephalogram (EEG). The EEG recordings represent the time series that match up to neurological activity as a function of time. By analyzing the EEG recordings, we sought to evaluate the degree of underlining dynamical complexity prior to progression of seizure onset. Through the utilization of the dynamical measurements, it is possible to classify the state of the brain according to the underlying dynamical properties of EEG recordings. The results from two patients with temporal lobe epilepsy (TLE), the degree of complexity start converging to lower value prior to the epileptic seizures was observed from epileptic regions as well as non-epileptic regions. The dynamical measurements appear to reflect the changes of EEG’s dynamical structure. We suggest that the nonlinear dynamical analysis can provide a useful information for detecting relative changes in brain dynamics, which cannot be detected by conventional linear analysis.

Keywords

Dynamical system Complexity analysis Electroencephalogram (EEG) Minimum embedding dimension 

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. Babloyantz A (1988) Chaotic dynamics in brain activity. In: Basar E (ed) Dynamics of sensory and cognitive processing by the brain. Springer, Berlin, pp 196–202 Google Scholar
  2. Babloyantz A, Destexhe A (1986) Low dimension chaos in an instance of epilepsy. Proc Natl Acad Sci USA 83:3513–3517 CrossRefGoogle Scholar
  3. Babloyantz A, Destexhe A (1987) The Creutizfeld–Jacob disease in the hierarchy of chaotic attractor. In: Markus M, Muller S (eds) From chemical to biological organization. Springer, Berlin, pp 307–316 Google Scholar
  4. Babloyantz A, Salazar JM, Nicolis C (1985) Evidence of chaotic dynamics of brain activity during the sleep cycle. Phys Lett A III:152–156 CrossRefGoogle Scholar
  5. Broomhead DS, King GP (1986) Physica D 20:217 zbMATHMathSciNetGoogle Scholar
  6. Cao L (1997) Practical method for determining the minimum embedding dimension of a scalar time series. Physica D 110:43–50 zbMATHCrossRefGoogle Scholar
  7. Casdagli MC, Iasemidis LD, Sackellares JC, Roper SN, Gilmore RL, Savit RS, (1996) Characterizing nonlinearity in invasive EEG recordings from temporal lobe epilepsy. Physica D 99(2–3):381–399. zbMATHGoogle Scholar
  8. Casdagli MC, Iasemidis LD, Savit RS, Gilmore RL, Roper SN, Sackellares JC (1997) Non-linearity in invasive EEG recordings from patients with temporal lobe epilepsy. Electroenceph Clin Neurophysiol 102:98–105 CrossRefGoogle Scholar
  9. Fell J, Roschke J, Beckmann P (1993) The calculation of the first positive Lyapunov exponent in sleep EEG data. Electroenceph Clin Neurophysiol 86:348–357 CrossRefGoogle Scholar
  10. Fraser AM, Swinney HL (1986) Independent coordinates for strange attractors from mutual information. Phys Rev A 33:1134–1140 CrossRefMathSciNetGoogle Scholar
  11. Grassberger P, Procaccia I (1983) Measuring the strangeness of strange attractors. Physica D 9:189–208 zbMATHCrossRefMathSciNetGoogle Scholar
  12. Iasemidis LD, Sackellares JC (1991) The evolution with time of the spatial distribution of largest Lyapunov exponent on the human epileptic cortex. In: Duke D, Pritchard W (eds) Measuring chaos in the human brain. World Scientific, Singapore, pp 49–82 Google Scholar
  13. Iasemidis LD, Sackellares JC (1996) Chaos theory and epilepsy. Neuroscientist 2:118–126 CrossRefGoogle Scholar
  14. Iasemidis LD, Sackellares JC, Zaveri H, Williams WJ (1990) Phase space topography and Lyapunov exponent of electrocardiograms in partial seizures. Brain Topogr 2:297–201 CrossRefGoogle Scholar
  15. Iasemidis LD, Sackellares JC, Savit RS (1993) Quantification of hidden time dependencies in the EEG within the framework of non-linear dynamics. In: Jansen BH, Brandt ME (eds) Nonlinear dynamical analysis of the EEG. 1990. World Scientific, Singapore, pp 30–47 Google Scholar
  16. Iasemidis LD, Principe JC, Czaolewski JM, Gilmore RL, Roper SN, Sackellares JC (1996) Spatiotemporal transition to epileptic seizures: a non-linear dynamical analysis of scalp and intracranial EEG recordings. In: Lopes da Silva F, Principe JC, Almeida LB (eds) Spatiotemporal models in biological and artificial systems. IOS, Amsterdam, pp 81–88 Google Scholar
  17. Kennel MB, Brown R, Abarbanel HDI (1992) Determining embedding dimension for phase-space reconstruction using a geometrical construction. Phys Rev A 45:3403–3411 CrossRefGoogle Scholar
  18. Martinerie JM, Albano AM, Mees AI, Rapp PE (1992) Phys Rev A 45:7058–7064 CrossRefGoogle Scholar
  19. Palus M (1996) Nonlinearity in normal human EEG: cycles, temporal asymmetry, nonstationarity and randomness, not chaos. Biol Cybern 75(5):389–396 zbMATHCrossRefMathSciNetGoogle Scholar
  20. Roschke J, Aldenhoff J (1991) The dimensionality of human’s electroencephalogram during sleep. Biol Cybern 64:307–313 CrossRefGoogle Scholar
  21. Sauer T, Yorke JA, Casdagli MC (1991) Embedology. J Stat Phys 65:579–616 zbMATHCrossRefMathSciNetGoogle Scholar
  22. Shatz CJ (1981) Brain Sci 214(4521):652–653 Google Scholar
  23. Takens F (1981) Detecting strange attractors in fluid turbulence. In: Rand D, Young L-S (eds) Dynamical systems and turbulence. Springer, Berlin, pp 366–381 CrossRefGoogle Scholar
  24. Thelier J, Rapp P (1996) Re-examination of the evidence for low-dimensional, non-linear structure in the human electroencephalogram. Electroenceph Clin Neurophysiol 98(3):213–22 CrossRefGoogle Scholar
  25. Whitney H (1936) Differentiable manifolds. Ann Math 37:645 CrossRefMathSciNetGoogle Scholar

Copyright information

© Springer Science+Business Media, LLC 2007

Authors and Affiliations

  • Chang-Chia Liu
    • 1
  • Panos M. Pardalos
    • 1
  • W. Art Chaovalitwongse
    • 2
  • Deng-Shan Shiau
    • 3
  • Georges Ghacibeh
    • 4
  • Wichai Suharitdamrong
    • 5
  • J. Chris Sackellares
    • 3
  1. 1.Department of Industrial and Systems Engineering, Biomedical EngineeringUniversity of FloridaGainesvilleUSA
  2. 2.Department of Industrial and Systems EngineeringRutgers UniversityPiscatawayUSA
  3. 3.Optima Neuroscience, Inc.Downtown Technology CenterGainesvilleUSA
  4. 4.Northeast Regional Epilepsy GroupHackensackUSA
  5. 5.Department of Industrial and Systems EngineeringUniversity of FloridaGainesvilleUSA

Personalised recommendations