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Mathematical Programming

, Volume 101, Issue 2, pp 365–385 | Cite as

Seizure warning algorithm based on optimization and nonlinear dynamics

  • Panos M. Pardalos
  • Wanpracha Chaovalitwongse
  • Leonidas D. Iasemidis
  • J. Chris Sackellares
  • Deng-Shan Shiau
  • Paul R. Carney
  • Oleg A. Prokopyev
  • Vitaliy A. Yatsenko
Article

Abstract.

There is growing evidence that temporal lobe seizures are preceded by a preictal transition, characterized by a gradual dynamical change from asymptomatic interictal state to seizure. We herein report the first prospective analysis of the online automated algorithm for detecting the preictal transition in ongoing EEG signals. Such, the algorithm constitutes a seizure warning system. The algorithm estimates STL max , a measure of the order or disorder of the signal, of EEG signals recorded from individual electrode sites. The optimization techniques were employed to select critical brain electrode sites that exhibit the preictal transition for the warning of epileptic seizures. Specifically, a quadratically constrained quadratic 0-1 programming problem is formulated to identify critical electrode sites. The automated seizure warning algorithm was tested in continuous, long-term EEG recordings obtained from 5 patients with temporal lobe epilepsy. For individual patient, we use the first half of seizures to train the parameter settings, which is evaluated by ROC (Receiver Operating Characteristic) curve analysis. With the best parameter setting, the algorithm applied to all cases predicted an average of 91.7% of seizures with an average false prediction rate of 0.196 per hour. These results indicate that it may be possible to develop automated seizure warning devices for diagnostic and therapeutic purposes.

Keywords

Temporal Lobe Epileptic Seizure Temporal Lobe Epilepsy Electrode Site False Prediction 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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References

  1. 1.
    Abarbanel, H.D.I.: Analysis of Observed Chaotic Data. Springer-Verlag, New York 1996Google Scholar
  2. 2.
    Athanasiou, G.G., Bachas, C.P., Wolf, W.F.: Invariant Geometry of Spin-glass States. Phy. Rev. B 35, 1965–1968 (1987)CrossRefGoogle Scholar
  3. 3.
    Babloyantz, A., Destexhe, A.: Low dimensional chaos in an instance of epilepsy. Proc. Natl. Acad. Sci. USA 83, 3513–3517 (1986)Google Scholar
  4. 4.
    Barahona, F.: On the computational complexity of spin glass models. J. Phys. A: Math. Gen. 15, 3241–3253 (1982)CrossRefMathSciNetGoogle Scholar
  5. 5.
    Barahona, F.: On the exact ground states of three-dimensional ising spin glasses. J. Phys. A: Math. Gen. 15, L611–L615 (1982)Google Scholar
  6. 6.
    Barahona, F., Grötschel, M., Jüger, M., Reinelt, G.: An application of combinatorial optimization to statistical physics and circuit layout design. Operations Research 36, 493–513 (1988)zbMATHGoogle Scholar
  7. 7.
    Barlow, J.S.: Methods of analysis of nonstationary EEGs with emphasis on segmentation techniques. J. Clin. Neutophysiol 2, 267–304 (1985)Google Scholar
  8. 8.
    Casdagli, M.C., Iasemidis, L.D., Sackellares, J.C., Roper, S.N., Gilmore, R.L., Savit, R.S.: Characterizing nonlinearity in invasive EEG recordings from temporal lobe epilepsy. Physica D 99, 381–399 (1996)CrossRefzbMATHGoogle Scholar
  9. 9.
    Casdagli, M.C., Iasemidis, L.D., Roper, S.N., Gilmore, R.L., Savit, R.S., Sackellares, J.C.: Nonlinearity in invasive EEG recordings from patients with temporal lobe epilepsy. Electroenceph. Clin. Neurophysiol. 102, 98–105 (1997)CrossRefGoogle Scholar
  10. 10.
    Shiau, D.S., Luo, Q., Gilmore, S.L., Roper, S.N., Pardalos, P.M., Sackellares, J.C., Iasemidis, L.D.: Epileptic seizures resetting revisited. Epilepsia. 41 (S7), 208–209 (2000)Google Scholar
  11. 11.
    Elger, C.E., Lehnertz, K.: Seizure prediction by non-linear time series analysis of brain electrical activity. Europ. J. Neurosci. 10, 786–789 (1998)CrossRefGoogle Scholar
  12. 12.
    Feber, F.: Treatment of some nonstationarities in the EEG. Neuropsychobiology 17, 100–104 (1987)Google Scholar
  13. 13.
    Frank, W.G., Lookman, T., Nerenberg, M.A., Essex, C., Lemieux, J., Blume, W.: Chaotic time series analyses of epileptic seizures. Physica D 46, 427–438 (1990)CrossRefzbMATHGoogle Scholar
  14. 14.
    Jansen, B.H., Cheng, W.K.: Structural EEG analysis. Int. J. Biomed. Comput. 23, 221-237 (1988)Google Scholar
  15. 15.
    Horst, H., Pardalos, P.M., Thoai, V.: Introduction to global optimization, Series on Nonconvex Optimization and its Applications. Kluwer Academic Publishers, Dordrecht, 1995Google Scholar
  16. 16.
    Iasemidis, L.D., Zaveri, H.P., Sackellares, J.C., Williams, W.J.: Phase space analysis of EEG in temporal lobe epilepsy. IEEE Eng. in Medicine and Biology Society, 10th Ann. Int. Conf., 1201–1203 (1988)Google Scholar
  17. 17.
    Iasemidis, L.D., Zaveri, H.P., Sackellares, J.C., Williams, W.J.: Linear and nonlinear modeling of ECoG in temporal lobe epilepsy. 25th Annual Rocky Mountain Bioengineering Symposium 24, 187–193 (1988)Google Scholar
  18. 18.
    Iasemidis, L.D., Zaveri, H.P., Sackellares, J.C., Williams, W.J., Hood, T.W.: Nonlinear dynamics of electrocorticographic data. J. of Clinical Neurophysiology 5, 339 (1988)Google Scholar
  19. 19.
    Iasemidis, L.D., Sackellares, J.C.: Long time scale spatio-temporal patterns of entrainment in preictal ECoG data in human temporal lobe epilepsy. Epilepsia 31, 621 (1990)Google Scholar
  20. 20.
    Iasemidis, L.D., Sackellares, J.C., Zaveri, H.P., Williams, W.J.: Phase space topography of the electrocorticogram and the Lyapunov exponent in partial seizures. Brain Topogr 2, 187–201 (1990)Google Scholar
  21. 21.
    Iasemidis, L.D.: On the dynamics of the human brain in temporal lobe epilepsy. Ph.D. dissertation, University of Michigan, Ann Arbor, (1991)Google Scholar
  22. 22.
    Iasemidis, L.D., Sackellares, J.C.: The evolution with time of the spatial distribution of the largest Lyapunov exponent on the human epileptic cortex. In: Measuring Chaos in the Human Brain, Duke, D.W., Pritchard, W.S. (eds.) World Scientific, Singapore, 1991, pp. 49–82Google Scholar
  23. 23.
    Iasemidis, L.D., Sackellares, J.C., Savit, R.S.: Quantification of hidden time dependencies in the EEG within the framework of nonlinear dynamics. In: Nonlinear dynamical analysis of the EEG, Jansen, B.H., Brandt, M.E. (eds.) World Scientific, Singapore, 1993, pp. 30–47Google Scholar
  24. 24.
    Iasemidis, L.D., Savit, R.S., Sackellares, J.C.: Time dependencies in partial epilepsy. Epilepsia 34S, 130–131 (1993)Google Scholar
  25. 25.
    Iasemidis, L.D., Olson, L.D., Sackellares, J.C., Savit, R. (1994): Time dependencies in the occurrences of epileptic seizures: a nonlinear approach. Epilepsy Research 17, 81–94 (1994)CrossRefGoogle Scholar
  26. 26.
    Iasemidis, L.D., Barreto, A., Gilmore, R.L., Uthman, B.M., Roper, S.N., Sackellares, J.C.: Spatio-temporal evolution of dynamical measures precedes onset of mesial temporal lobe seizures. Epilepsia 35S, 133 (1994)Google Scholar
  27. 27.
    Iasemidis, L.D., Sackellares, J.C.: Chaos theory and epilepsy. The Neuroscientist 2, 118–126 (1996)Google Scholar
  28. 28.
    Iasemidis, L.D., Principe, J.C., Sackellares, J.C.: Spatiotemporal dynamics of human epileptic seizures. In: 3rd Experimental Chaos Conference, Harrison, R.G., Weiping, L., Ditto, W., Pecora, L., Vohra, S. (eds.) World Scientific, Singapore, 1996, pp. 26–30Google Scholar
  29. 29.
    Iasemidis, L.D., Pappas, K.E., Gilmore, R.L., Roper, S.N., Sackellares, J.C.: Detection of the preictal transition state in scalp-sphenoidal recordings. Annual American Clinical Neurophysiology Society Meeting, Boston, 1996, pp. 5–10Google Scholar
  30. 30.
    Iasemidis, L.D., Pappas, K.E., Gilmore, R.L., Roper, S.N., Sackellares, J.C.: Preictal entrainment of a critical cortical mass is a necessary condition for seizure occurrence. Epilepsia 37S5, 90 (1996)Google Scholar
  31. 31.
    Iasemidis, L.D., Gilmore, R.L., Roper, S.N., Sackellares, J.C.: Dynamical interaction of the epileptogenic focus with extrafocal sites in temporal lobe epilepsy. Annals of Neurology 42, 429 (1997)Google Scholar
  32. 32.
    Iasemidis, L.D., Principe, J.C., Czaplewski, J.M., Gilmore, R.L., Roper, S.N., Sackellares, J.C.: Spatiotemporal transition to epileptic seizures: a nonlinear dynamical analysis of scalp and intracranial EEG recordings. In: Spatiotemporal Models in Biological and Artificial Systems, Silva, F.L., Principe, J.C., Almeida, L.B., (eds.) IOS Press, Amsterdam, 1997, pp. 81–88Google Scholar
  33. 33.
    Iasemidis, L.D., Sackellares, J.C., Gilmore, R.L., Roper, S.N.: Automated seizure prediction paradigm. Epilepsia 39S6, 207 (1998)Google Scholar
  34. 34.
    Iasemidis, L.D., Shiau, D.-S., Sackellares, J.C., Pardalos, P.M.: Transition to epileptic seizures: Optimization. In: DIMACS series in Discrete Mathematics and Theoretical Computer Science. Du, D.Z., Pardalos, P.M., Wang, J, (eds.) American Mathematical Society, Providence, 1999, pp. 55–74Google Scholar
  35. 35.
    Iasemidis, L.D., Principe, J.C., Sackellares, J.C.: Measurement and quantification of spatiotemporal dynamics of human epileptic seizures. In: Nonlinear biomedical signal processing. Akay, M. (ed.) IEEE Press, vol. II, 2000, pp. 294–318Google Scholar
  36. 36.
    Iasemidis, L.D., Pardalos, P.M., Sackellares, J.C., Shiau, D.-S.: Quadratic binary programming and dynamical system approach to determine the predictability of epileptic seizures. J. Combinatorial Optimization 5, 9–26 (2001)CrossRefzbMATHGoogle Scholar
  37. 37.
    Iasemidis, L. D., Shiau, D.-S., Pardalos, P.M., Sackellares, J.C.: Phase Entrainment and Predictability of Epileptic Seizures. In: Biocomputing. Pardalos, P.M., Principe, J.C., (eds.) Kluwer Academic Publishers, Dordrecht, 2001Google Scholar
  38. 38.
    Iasemidis, L.D., Shiau, D.S., Sackellares, J.C., Pardalos, P.M., Prasad, A.: Dynamical resetting of the human brain at epileptic seizures: application of nonlinear dynamics and global optimization techniques. IEEE Trans. Biomed Eng. (2002) submittedGoogle Scholar
  39. 39.
    Lehnertz, K., Elger, C.E.: Can epileptic seizures be predicted? Evidence from nonlinear time series analysis of brain electrical activity. Phys. Rev. Lett 80, 5019–5022 (1998)CrossRefGoogle Scholar
  40. 40.
    Le Van Quyen, M., Martinerie, J., Baulac, M., Varela, F.: Anticipating epileptic seizures in real time by non-linear analysis of similarity between EEG recordings. NeuroReport 10, 2149–2155 (1999)Google Scholar
  41. 41.
    Litt, B., Esteller, R., Echauz, J., Maryann, D.A., Shor, R., Henry, T., Pennell, P., Epstein, C., Bakay, R., Dichter, M., Vachtservanos, G.: Epileptic seizures may begin hours in advance of clinical onset: A report of five patients. Neuron 30, 51–64 (2001)CrossRefGoogle Scholar
  42. 42.
    Manuca, R., Savit, R.: Stationary and nonstationary in time series analysis. Physica D 99, 134–161 (1999)zbMATHGoogle Scholar
  43. 43.
    Martinerie, J., Van Adam, C., Le Van Quyen, M.: Epileptic seizures can be anticipated by non-linear analysis. Nature Medicine 4, 1173–1176 (1998)CrossRefGoogle Scholar
  44. 44.
    Mezard, M., Parisi, G., Virasoro, M.A.: Spin Glass Theory and Beyond. World Scientific, Singapore, (1987)Google Scholar
  45. 45.
    Olson, L.D., Iasemidis, L.D., Sackellares, J.C.: Evidence that interseizure intervals exhibit low dimensional dynamics. Epilepsia 30, 644 (1989)Google Scholar
  46. 46.
    Packard, N.H., Crutchfield, J.P., Farmer, J.D.: Geometry from time series. Phys. Rev. Lett. 45, 712–716 (1980)CrossRefGoogle Scholar
  47. 47.
    Palus, M., Albrecht, V., Dvorak, I.: Information theoretic test of nonlinearlity in time series. Phys. Rev. A 34, 4971–4972 (1993)Google Scholar
  48. 48.
    Pardalos, P.M., Rodgers, G.: Parallel branch and bound algorithms for unconstrained quadratic zero-one programming. In: Impact of recent computer advances on operations research. Sharda R, et al. (eds.) North-HollandGoogle Scholar
  49. 49.
    Pardalos, P.M., Rodgers, G.: Computational aspects of a branch and bound algorithm for quadratic zero-one programming. Computing 45, 131–144 (1990)MathSciNetzbMATHGoogle Scholar
  50. 50.
    Rapp, P.E., Zimmerman, I.D., Albano, A.M.: Experimental studies of chaotic neural behavior: cellular activity and electroencephalographic signals. In: Nonlinear Oscillations in Biology and Chemistry. Othmer HG, (ed.) Springer-Verlag, Berlin, 1986, pp. 175–805Google Scholar
  51. 51.
    Sackellares, J.C., Iasemidis, L.D., Pappas, K.E., Gilmore, R.L., Uthman, B.M., Roper, S.N.: Dynamical studies of human hippocampus in limbic epilepsy. Neurology 45S, 404 (1995)Google Scholar
  52. 52.
    Sackellares, J.C., Iasemidis, L.D., Gilmore, R.L., Roper, S.N.: Epileptic seizures as neural resetting mechanisms. Epilepsia 38 (S3), 189 (1997)Google Scholar
  53. 53.
    Sackellares, J.C., Iasemidis, L.D., Shiau, D.-S.: Detection of the preictal transition in scalp EEG. Epilepsia 40, 176 (1999)Google Scholar
  54. 54.
    Sackellares, J.C., Iasemidis, L.D., Gilmore, R.L., Roper, S,N.: Epilepsy - when chaos fails. In: Chaos in the brain? Lehnertz, K., Arnhold, J., Grassberger, P., Elger, C.E. (eds.) World Scientific, Singapore, 2002Google Scholar
  55. 55.
    Sackellares, J.C., Iasemidis, L.D., Pardalos, P.M., Shiau, D.-S.: Combined Application of Global Optimization and Nonlinear Dynamics to Detect State Resetting in Human Epilepsy. In: Biocomputing. Pardalos, P.M., Principe, J.C. (eds.) Kluwer Academic Publishers, Dordrecht, 2001Google Scholar
  56. 56.
    Takens, F.: Detecting strange attractors in turbulence. In: Dynamical systems and turbulence, Lecture notes in mathematics. Rand, D.A. and Young, L.S., (eds.) Springer-Verlag, Heidelburg, 1981Google Scholar
  57. 57.
    Theiler, J.: Spurious dimension from correlation algorithms applied to limited time-series data. Phys. Rev. A 34, 2427–2432 (1986)CrossRefGoogle Scholar
  58. 58.
    Theiler, J., Rapp, P.E.: Re-examination of the evidence for low-dimensional, nonlinear structure in the human electroencephalogram. Electroencephalogr. Clin. Neurophysiol. 98, 213–222 (1996)CrossRefGoogle Scholar
  59. 59.
    Wolf, A., Swift, J.B., Swinney, H.L., Vastano, J.A.: Determining Lyapunov exponents from a time series. Physica D 16, 285–317 (1985)CrossRefMathSciNetzbMATHGoogle Scholar
  60. 60.
    Wolf, A., Vastano, J.A.: Intermediate length scale effects in Lyapunov exponent estimation. In: Dimensions and Entropies in Chaotic Systems: Quantification of Complex Behavior. Mayer-Kress, G. (ed.) Springer-Verlag, Berlin, 1986 pp. 94–99Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2004

Authors and Affiliations

  • Panos M. Pardalos
    • 1
  • Wanpracha Chaovalitwongse
    • 2
  • Leonidas D. Iasemidis
    • 3
  • J. Chris Sackellares
    • 4
  • Deng-Shan Shiau
    • 5
  • Paul R. Carney
    • 6
  • Oleg A. Prokopyev
    • 7
  • Vitaliy A. Yatsenko
    • 8
  1. 1.Departments of Industrial and Systems Engineering and Biomedical EngineeringUniversity of FloridaUSA
  2. 2.Departments of Industrial and Systems Engineering and NeuroscienceUniversity of FloridaUSA
  3. 3.Departments of Biomedical Engineering and Electrical EngineeringArizona State UniversityUSA
  4. 4.Departments of Neuroscience, Neurology and Biomedical EngineeringUniversity of FloridaUSA
  5. 5.Department of NeuroscienceUniversity of FloridaUSA
  6. 6.Departments of Pediatrics, Neuroscience, and NeurologyUniversity of FloridaUSA
  7. 7.Department of Industrial and Systems EngineeringUniversity of FloridaUSA
  8. 8.Department of NeuroscienceUniversity of FloridaUSA

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