EEG analysis with nonlinear excitable media

Journal of Clinical Neurophysiology

Volumn 22, Issue 5, 2005, Pages 314-329

  Chernihovskyi, Anton ^a   Mormann, Florian ^a   Müller, Markus ^b   Elger, Christian E ^a   Baier, Gerold ^b   Lehnertz, Klaus ^a  

^a UNIVERSITY OF BONN   (Germany)

^b UNIVERSIDAD AUTÓNOMA DEL ESTADO DE MORELOS   (Mexico)

Author keywords

Cellular neural networks; EEG; Epilepsy; Neuron models; Nonlinear dynamics; Nonlinear excitable media; Pattern recognition; Seizure detection; Seizure prediction; Synchronization; Time series analysis

Indexed keywords

ACTION POTENTIAL; ANALOG COMPUTER; ARTIFICIAL NEURAL NETWORK; BRAIN NERVE CELL; COMPUTER ANALYSIS; CORRELATION ANALYSIS; CORTICAL SYNCHRONIZATION; DYNAMICS; ELECTROENCEPHALOGRAPHY; HUMAN; MEDICAL INSTRUMENTATION; NERVE CELL EXCITABILITY; NEUROIMAGING; NEUROTRANSMISSION; NOISE; NONLINEAR SYSTEM; PREDICTION; REVIEW; SEIZURE; SIGNAL TRANSDUCTION; STATISTICAL ANALYSIS;

ANIMALS; ELECTROENCEPHALOGRAPHY; HUMANS; MODELS, THEORETICAL; NEURAL NETWORKS (COMPUTER); NEURONS; NONLINEAR DYNAMICS; PREDICTIVE VALUE OF TESTS; SEIZURES;

EID: 31944449492     PISSN: 07360258     EISSN: None     Source Type: Journal    
DOI: None     Document Type: Review

References (118)

1. Allefeld C, Kurths J. (2004) An approach to multivariate phase synchronization analysis and its application to event-related potentials. Int J Bifurc Chaos 14:417-26.
2. Arena P, Fortuna L, Frasca M. (2002) Attitude control in walking hexapod robots: an analogic spatio-temporal approach. Int J Circ Theor Appl 30:349-62.
3. Babloyantz A, Destexhe A. (1986) Low-dimensional chaos in an instance of epilepsy. Proc Natl Acad Sci U S A 83:3513-7.
4. Baier G, Sahle S, Chen JP, Hoff AA. (1999) Local stimulation induces long-range order in spatial-temporal disorder. J Chem Phys 110:3251-5.
5. Baier G, Leder RS, Parmananda P. (2000) Human electroencephalogram induces transient coherence in excitable spatiotemporal chaos. Phys Rev Lett 84:4501-4.
6. Baier G, Müller M. (2004a) Nonlinear dynamic conversion of analog signals into excitation patterns. Phys Rev E 70:037201.
7. Baier G, Müller M. (2004b) Frequency-selective induction of excitation waves near sub- and supercritical Hopf bifurcation. Phys Lett A 330:350-7.
8. Barlow JS. (1985) Methods of analysis of nonstationary EEGs with emphasis on segmentation techniques: A comparative review. J Clin Neurophysiol 2:267-304.
9. Barth DS, MacDonald KD. (1996) Thalamic modulation of high-frequency oscillating potentials in auditory cortex. Nature 383:78-81.
10. Basar E. (1990) Chaos in brain function. Berlin: Springer.
11. Berger H. (1929) Über das Elektroenkephalogram des Menschen. Arch Psychiatr 87:35.
12. Blinowska KJ, Kus R, Kaminski M. (2004) Granger causality and information flow in multivariate processes. Phys Rev E 70:050902.
13. Chen YH, Rangarajan G, Feng JF, Ding MZ. (2004) Analyzing multiple onlinear time series with extended Granger causality. Phys Lett A 324:26-35.
14. Chernihovskyi A, Sowa R, Florin S, Elger CE, Lehnertz K. (2004) Pattern recognition in noisy and non-stationary time series with Cellular Neural Networks. In: Roska T, Gili M, Shi B, Zarandy A, eds. Proceedings of the 8th IEEE International Workshop on Cellular Neural Networks and Applications (CNNA2004). Budapest: Amulett'98 Kft.
15. Chua LO, Yang L. (1988a) Cellular neural networks: theory. IEEE Trans Circ Syst 35:1257-72.
16. Chua LO, Yang L. (1988b) Cellular neural networks: applications. IEEE Trans Circ Syst 35:1273-90.
17. Chua LO, Hasler M, Moschytz S, Neirynck J. (1995) Autonomous cellular neural networks: a unified paradigm for pattern formation and active wave propagation. IEEE Trans Circ Syst 42:559-77.
18. Chua LO. (1998) CNN: a paradigm for complexity. Singapore: World Scientific.
19. Chua LO, Roska, T. (2002) Cellular neural networks and visual computing. Cambridge UK: Cambridge University Press.
20. Cross MC, Hohenberg PC. (1993) Pattern formation outide from equilibrium. Rev Mod Phys 65:854-1112.
21. D'Alessandro M, Vachtsevanos G, Esteller R, Echauz J, Cranstoun S, Worrell G, Parish L, Litt B. (2005) A multi-feature and multi-channel univariate selection process for seizure prediction. Clin Neurophysiol 116:506-16.
22. Dayan P, Abbott LF. (2001) Theoretical neuroscience. Cambridge, Massachusetts, London, England: MIT Press.
23. Duke D, Pritchard W. (1991) Measuring chaos in the human brain. Singapore: World Scientific.
24. Elger CE. (2001) Future trends in epileptology. Curr Opin Neurol 14:185-6.
25. Elger CE, Lehnertz K. (1998) Prediction of epileptic seizures in humans from nonlinear dynamics analysis of brain electrical activity. Eur J Neurosci 10:786-9.
26. Elger CE, Mormann F, Kreuz T, Andrzejak RG, Rieke C, Sowa R, Florin S, David P, Lehnertz K. (2002) Characterizing the spatio-temporal dynamics of the epileptogenic process with nonlinear EEG analysis. In: Tetzlaff R, ed. Proceedings of the 7th IEEE International Workshop on Cellular Neural Networks and Their Applications. Singapore: World Scientific, pp 228-42.
27. Esteller R, Echauz J, D'Alessandro M, Worrell G, Cranstoun S, Vachtsevanos G, Litt B. (2005) Continuous energy variation during the seizure cycle: towards an on-line accumulated energy. Clin Neurophysiol 116:517-26.
28. Faure P, Korn H. (2001) Is there chaos in the brain? I. Concepts of nonlinear dynamics and methods of investigation. Life Sci 324:773-93.
29. FitzHugh R. (1961) Impulses and physiological states in theoretical model of nerve membrane. Biophys J 1:445-66.
30. Franaszczuk PJ, Kudela P, Bergey GK. (2003) External excitatory stimuli can terminate bursting in neural network models. Epilepsy Res 53:65-80.
31. Friedrich R, Uhl C. (1996) Spatio-temporal analysis of human electroencephalograms: petit-mal epilepsy. Phys D 98:171-82.
32. Gabor AJ, Leach RR, Dowla FU. (1996) Automated seizure detection using a self-organizing neural network. Electroencephalogr Clin Neurophysiol 99:257-66.
33. Gotman J. (1982) Automatic recognition of epileptic seizures in the EEG. Electroencephalogr Clin Neurophysiol 54:530-40.
34. Gotman J. (1990) Automatic seizure detection: improvements and evaluation. Electroencephalogr Clin Neurophysiol 76:317-24.
35. Gotman J. (1999) Automatic detection of seizure and spikes. J Clin Neurophysiol 16:130-40.
36. Grey CM, Koenig P, Engel AK, Singer W. (1989) Oscillatory responses in cat visual cortex exhibit inter-columnar synchronization which reflects global stimulus properties. Nature 338:334-7.
37. Griffiths TD, Büchel C, Frackowiak R, Patterson RD. (1998) Analysis of temporal structure in sound by the human brain. Nat Neurosci 1:422-7.
38. Haken H. (1996) Principles of brain functioning: a synergetic approach to brain activity, behavior, and cognition. Berlin: Springer.
39. Harding GW. (1993) An automated seizure monitoring system for patients with indwelling recording electrodes. Electroencephalogr Clin Neurophysiol 86:428-37.
40. Hemmelmann C, Horn M, Reiterer S, Schack B, Susse T, Weiss S. (2004) Multivariate tests for the evaluation of high-dimensional EEG data. J Neurosci Meth 139:111-20.
41. Hilfiker P, Egli M. (1992) Detection and evolution of rhythmic components in ictal EEG using short segment spectra and discriminant analysis. Electroencephalogr Clin Neurophysiol 82:255-65.
42. Hodgkin AL, Huxley AF. (1952a) Currents carried by sodium and potassium ions through the membrane of the giant axon of Loligo. J Physiol 116:449-72.
43. Hodgkin AL, Huxley AF. (1952b) The components of membrane conductance in the giant axon of Loligo. J Physiol 116:473-96.
44. Hodgkin AL, Huxley AF. (1952c) The dual effect of membrane potential on sodium conductance in the giant axon of Loligo. J Physiol 116:497-506.
45. Hodgkin AL, Huxley AF. (1952d) A quantitative description of membrane current and its application to conduction and excitation in nerve. J Physiol 117:500-44.
46. Hopfield JJ. (1982) Neural networks and physical systems with emergent computational abilities. Proc Natl Acad Sci U S A 79:2554-8.
47. Hopfield JJ. (1984) (1984) Neurons with graded response have computational properties like those of two-state neurons. Proc Natl Acad Sci U S A 81:3088-92.
48. Iasemidis LD, Shiau DS, Pardalos PM, Chaovalitwongse W, Narayanan K, Prasad A, Tsakalis K, Carney PR, Sackellares JC.(2005) Long-term prospective on-line real-tune seizure prediction. Clin Neurophysiol 116:532-44.
49. Izhikevich EM. (2000) Neural excitability, spiking and bursting. Int J Bifurcat Chaos 10:1171-1266.
50. Izhikevich EM. (In press) Dynamical systems in neuroscience: The geometry of excitability and bursting. Cambridge, Massachusetts: MIT Press.
51. Jansen BH. (1991) Quantitative analysis of electroencephalograms: is there chaos in the future? Int J Biomed Comput 27:95-123.
52. Jansen BH, Brandt ME. (1993) Nonlinear dynamical analysis of the EEG. Singapore: World Scientific.
53. Kalitzin S, Velis D, Suffczynski P, Parra J, Lopes da Silva F. (2005) Electrical brain-stimulation paradigm for estimating the seizure onset site and the time to ictal transition in temporal lobe epilepsy. Clin Neurophysiol 116:718-28.
54. Kantz H, Schreiber T. (2003) Nonlinear time series analysis. Cambridge UK: Cambridge University Press.
55. Khan YU, Gotman J. (2003) Wavelet based automatic seizure detection in intracerebral electroencephalogram. Clin Neurophysiol 114:898-908.
56. Kiymik MK, Subasi A, Ozcalik HR. (2004) Neural networks with periodogram and autoregressive spectral analysis methods in detection of epileptic seizure. J Med Syst 28:511-22.
57. Klatchko A, Raviv G, Webber WR, Lesser RP. (1998) Enhancing the detection of seizures with a clustering algorithm. Electroencephalogr Clin Neurophysiol 106:52-63.
58. Koch C. (1999) Biophysics of computation. Oxford: Oxford University Press.
59. Korn H, Faure P. (2003) Is there chaos in the brain? II. Experimental evidence and related models. CR Biol 326:787-840.
60. Kudela P, Franaszczuk PJ, Bergey GK. (2003) Changing excitation and inhibition in simulated neural networks: effects on induced bursting behavior. Biol Cybern 88:276-85.
61. th Int. Workshop on CNNs and their Applications (CNNA'2000), Catania, pp 407-19.
62. Kunz R, Tetzlaff R. (2003) Spatio-temporal dynamics of brain electrical activity in epilepsy: analysis with Cellular Neural Networks (CNNs). J Circuit Syst Comp 12:825-44.
63. Laiho M, Paasio A, Kananen A, Halonen K. (2002) A mixed-mode polynomial-type CNN for analysing brain electrical activity in epilepsy. Int J Circ Theor Appl 30:165-80.
64. Laiho M, Paasio A, Kananen A, Halonen K. (2004) A mixed-mode polynomial cellular array processor hardware realization. IEEE T Circuits I 51:286-97.
65. Le Van Quyen M, Soss J, Navarro V, Robertson R, Chavez M, Baulac M, Martinerie J. (2005) Preictal state identification by synchronization changes in long-term intracranial EEG recordings. Clin Neurophysiol 116:559-68.
66. Lehnertz K, Elger CE. (1995) Spatio-temporal dynamics of the primary epileptogenic area in temporal lobe epilepsy characterized by neuronal complexity loss. Electroencephalogr Clin Neurophysiol 95:108-17.
67. Lehnertz K, Elger CE. (1998) Can epileptic seizures be predicted? Evidence from nonlinear time series analyses of brain electrical activity. Phys Rev Lett 80:5019-23.
68. Lehnertz K, Arnhold J, Grassberger P, Elger CE. (2000) Chaos in brain? Singapore: World Scientific.
69. Lehnertz K, Andrzejak RG, Arnhold J, Kreuz T, Mormann F, Rieke C, Widman G, Elger CE. (2001) Nonlinear EEG analysis in epilepsy: Its possible use for inter-ictal focus localization, seizure anticipation, and prevention. J Clin Neurophysiol 18:209-22.
70. Lehnertz K, Litt B. (2005) The First International Collaborative Workshop on Seizure Prediction: summary and data description. Clin Neurophysiol 116:493-505.
71. Litt B, Lehnertz K. (2002) Seizure prediction and the preseizure period. Curr Opin Neurol 15:173-7.
72. Lopes da Silva FH. (1993) EEG analysis: theory and practice. In: Niedermeyer E, Lopes da Silva FH, eds. Electroencephalography. Baltimore: Williams and Wilkins, pp 1097-123.
73. Lopes da Silva FH, Blanes W, Kalitzin SN, Parra J, Suffczynski P, Velis DN. (2003a) Epilepsies as dynamical diseases of brain systems: basic models of the transition between normal and epileptic activity. Epilepsia 44 Suppl 12:72-83.
74. Lopes da Silva FH, Blanes W, Kalitzin SN, Parra J, Suffczynski P, Velis DN. (2003b) Dynamical diseases of brain systems: different routes to epileptic seizures. IEEE Trans Biomed Eng 50:540-8.
75. McSharry PE, He T, Smith LA, Tarassenko L. (2002) Linear and non-linear methods for automatic seizure detection in scalp electro-encephalogram recordings. Med Biol Eng Comput 40:447-61.
76. Meron E. (1992) Pattern formation in excitable media. Phys Rep 218:1-66.
77. Mormann F, Lehnertz K, David P, Elger CE. (2000) Mean phase coherence as a measure for phase synchronization and its application to the EEG of epilepsy patients. Physica D 144:358-69.
78. Mormann F, Andrzejak RG, Kreuz T, Rieke C, David P, Elger CE, Lehnertz K. (2003a) Automated detection of a pre-seizure state based on a decrease in synchronization in intracranial EEG recordings from epilepsy patients. Phys Rev E 67:021912.
79. Mormann F, Kreuz T, Andrzejak RG, David P, Lehnertz K, Elger CE. (2003b) Epileptic seizures are preceded by a decrease in synchronization. Epilepsy Res 53:173-85.
80. Mormann F, Kreuz T, Rieke C, Andrzejak RG, Kraskov A, David P, Elger CE, Lehnertz K. (2005) On the predictability of epileptic seizures. Clin Neurophysiol 166:569-87.
81. Morris C, Lecar H. (1981) Voltage oscillations in the barnacle giant muscle fiber. Biophys J 193:193-213.
82. Müller M, Baier G, Galka A, Stephani U, Muhle H. (2005) Detection and characterization of changes of the correlation structure in multivariate time series. Phys Rev E 71:046116.
83. Murray JD. (1989) Mathematical biology. New York: Springer.
84. Murro AM, King DW, Smith JR, Gallagher BB, Flanigin HF, Meador K. (1991) Computerized seizure detection of complex partial seizures. Electroencephalogr Clin Neurophysiol 79:330-3.
85. Nagumo JS, Arimoto S, Yoshizawa S. (1962) An active pulse transmission line simulating nerve axon. Proc IRE 50:2061-70.
86. Osorio I, Frei MG, Wilkinson SB. (1998) Real-time automated detection and quantitative analysis of seizures and short-term prediction of clinical onset. Epilepsia 39:615-27.
87. Osorio I, Frei MG, Giftakis J, Peters T, Ingram J, Turnbull M, Herzog M, Rise MT, Schaffner S, Wennberg RA, Walczak TS, Risinger MW, Ajmone-Marsan C. (2002) Performance reassessment of a real-time seizure-detection algorithm on long ECoG series. Epilepsia 43:1522-35.
88. Parmananda P, Mahara H, Amemiya T, Yamaguchi T. (2001) Resonance induced pacemakers: A new class of organizing centers for wave propagation in excitable media. Phys Rev Lett 87:238302.
89. Parmananda P, Mena CH, Baier G. (2002) Resonant forcing of a silent Hodgkin-Huxley neuron. Phys Rev E 66:047202.
90. Pikovsky A, Rosenblum M, Kurths J. (2001) Synchronization: a universal concept in nonlinear sciences. Cambridge UK: Cambridge University Press.
91. Qu H, Gotman J. (1993) Improvement in seizure detection performance by automatic adaptation to the EEG of each patient. Electroencephalogr Clin Neurophysiol 86:79-87.
92. Rail W. (1969) Distribution of potential in cylindrical coordinates and time constants for a membrane cylinder. Biophys J 9:1509-41.
93. Rinzel J, Ermentrout BB. (1998) Analysis of neural excitability and oscillations. In: Koch C, Segev I, eds. Methods in neuronal modeling, 2nd ed. Cambridge, Massachusetts: MIT Press, pp. 251-92.
94. Roska T, Chua LO. (1993) The CNN universal machine: An analogic array computer. IEEE Trans Circ Syst II 40:163-73.
95. Roska T, Rodriguez-Vazquez A. (2000) Towards the visual microprocessor: VLSI Design and the use of Cellular Neural Network Universal Machines. Chichester: J. Wiley.
96. Saab ME, Gotman J. (2005) A system to detect the onset of epileptic seizures in scalp EEG. Clin Neurophysiol 116:427-42.
97. Salinsky MC. (1997) A practical analysis of computer based seizure detection during continuous video-EEG monitoring. Electroencephalogr Clin Neurophysiol 103:445-9.
98. Schindler K, Wiest R, Kollar M, Donati F. (2001) Using simulated neuronal cell models for detection of epileptic seizures in foramen ovale and scalp EEG. Clin Neurophysiol 112:1006-17.
99. Schindler K, Wiest R, Kollar M, Donati F. (2002) EEG analysis with simulated neuronal cell models helps to detect pre-seizure changes. Clin Neurophysiol 113:604-14.
100. Schuster HG. (2001) Complex adaptive systems: an introduction. Saarbrücken, Germany: Scator Verlag.
101. Shoeb A, Edwards H, Connolly J, Bourgeois B, Treves ST, Guttag J. (2004) Patient-specific seizure onset detection. Epilepsy Behav 5:483-98.
102. Skarda CA, Freeman WJ. (1987) How brains make chaos in order to make sense of the world. Behav Brain Sci 10:161-95.
103. Sowa R, Chemihovsky A, Mormann F, Lehnertz K. (2005) Estimating phase synchronization in dynamical systems using Cellular Nonlinear Networks. Phys Rev E 71;061926.
104. Sowa R, Mormann F, Chernihovskyi A, Florin S, Elger CE, Lehnertz K. (2004) Estimating synchronization in brain electrical activity from epilepsy patients with Cellular Neuronal Networks. In: Roska T, Gili M, Shi B, Zarandy A, eds. Proceedings of the 8th IEEE International Workshop on Cellular Neural Nertrorks and Applications (CNNA2004). Budapest: Amulett'98 Kft.
105. Stam CJ. (2003) Chaos, continuous EEG, and cognitive mechanisms: a future for clinical neurophysiology. Am J End Technol 43:1-17.
106. Strasser P, Rössler OE, Baier G. (1996) Hyperchaos and chemical turbulence in enzymatic reaction-diffusion systems. J Chem Phys 104:9974-82.
107. Suffczynski P, Kalitzin S, Lopes Da Silva FH. (2004) Dynamics of non-convulsive epileptic phenomena modeled by a bistable neuronal network. Neuroscience 126:467-84.
108. Tetzlaff R, Kunz R, Ames C, Wolf D. (1999) Analysis of brain electrical activity in epilepsy with Cellular Neural Networks. In: IEEE Proceedings of the European Conference on Circuit Theory Design, pp 573-7.
109. Ulam S. (1952) Random processes and transformations. Proc Int Congress Math (Camb) 2:264-75.
110. van Putten MJ. (2003) Nearest neighbor phase synchronization as a measure to detect seizure activity from scalp EEG recordings. J Clin Neurophysiol 20:320-5.
111. Webber WR, Lesser RP, Richardson RT, Wilson K. (1996) An approach to seizure detection using artificial neural networks (ANN). Electroencephalogr Clin Neurophysiol 98:250-72.
112. Wendling F, Bellanger JJ, Bartolomei F, Chauvel P. (2000) Relevance of nonlinear lumped-parameter models in the analysis of depth-EEG epileptic signals. Biol Cybern 83:367-78.
113. Wendling F, Bartolomei F, Bellanger JJ, Chauvel P. (2002) Epileptic fast activity can be explained by a model of unpaired GABAergic dendritic inhibition. Eur J Neurosci 15:1499-508.
114. Wendling F, Bartolomei F, Bellanger JJ, Bourien J, Chauvel P. (2003) Epileptic fast intracerebral EEG activity: evidence for spatial decorrelation at seizure onset. Brain 126:1449-59.
115. Wilson SB, Scheuer ML, Plummer C, Young B, Pacia S. (2003) Seizure detection: correlation of human experts. Clin Neurophysiol 114:2156-64.
116. Wilson SB, Scheuer ML, Emerson RG, Gabor AJ. (2004) Seizure detection: evaluation of the Reveal algorithm. Clin Neurophysiol 115:2280-91.
117. Wolfram S. (1983) Statistical mechanics of cellular automata. Rev Mod Phys 55:601-44.
118. Yaylali I, Kocak H, Jayakar P. (1996) Detection of seizures from small samples using nonlinear dynamic system theory. IEEE Trans Biomed Eng 43:743-51.