Validity of dimensional complexity measures of EEG signals

International Journal of Bifurcation and Chaos in Applied Sciences and Engineering

Volumn 7, Issue 1, 1997, Pages 173-186

  Pradhan, N ^a   Sadasivan, P K ^a  

^a NATIONAL INSTITUTE OF MENTAL HEALTH AND NEUROSCIENCES   (India)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 0030627320     PISSN: 02181274     EISSN: None     Source Type: Journal    
DOI: 10.1142/S021812749700011X     Document Type: Article

References (46)

1. Albano, A. M., Mees, A. I., deGuzman, G. C. & Rapp, P. E. [1987] " Data requirement for reliable estimation of correlation dimensions," in Chaos in Biological Systems eds. Degn, H., Holden, A. V. & Olsen, L. F. (Plenum, New York), pp. 207-220.
2. Albano, A. M. & Rapp, P. E. [1992] " On the reliability of dynamical measures of EEG signals," in Nonlinear Dynamical Analysis of the EEG, eds. Jansen, B. H. & Brandt, M. E. (World Scientific, Singapore), pp. 117-139.
3. Babloyantz, A., Salazar, J. M. & Nicolis, C. [1985] " Evidence of chaotic dynamics of brain activity during the sleep cycle," Phys. Lett. A111, 152-156.
4. Babloyantz, A. & Destexhe, A. [1986] " Low dimensional chaos in an instance of epilepsy," Proc. Natl. Acad. Sci. USA 83, 3513-3517.
5. Basar, E. [1990] Chaos in Brain Function (Springer Verlag, Berlin Heidelberg).
6. Birbaumer, N., Lutzenberger, W. & Flor, H. [1992] " Nonlinear EEG dynamics and mental imagery," Psychophysiol. 29, S19.
7. Dvorak, I., Siska, J., Wackermann, J., Hrudova, L. & Dostalek, C. [1986] " Evidence for interpretation of the EEG as a deterministic chaotic process with a low dimension," Activitas Nervosa Superior 28, 228-231.
8. Dvorak, I. & Holden, A. V. [1991] Mathematical Approaches to Brain Functioning Diagnostics (Manchester University Press).
9. Elbert, T., Ray, W. J., Kowalik, Z. J., Skinner, J. E., Graf, K. E. & Birbaumer, N. [1994] " Chaos and physiology, deterministic chaos in excitable cell assemblies," Physiol.Rev. 74, 1-47.
10. Ellner, S. [1988] " Estimating attractor dimensions from limited data: A new method, with error estimates," Phys. Lett. A133, 128-133.
11. Gallez, D. & Babloyantz, A. [1991] " Predictability of human EEG: A dynamical approach," Biol. Cybernetics 64, 381-391.
12. Glass, L., Kaplan, D. T. & Lewis, J. E. [1992] " Test for deterministic dynamics in real and model neural networks," in Nonlinear Dynamical Analysis of the EEG, eds. Jansen, B. H. & Brandt, M. E. (World Scientific, Singapore), pp. 233-249.
13. Gregson, R. A. M., Campbell, E. A. & Gates, G. R. [1992] " Cognitive load as a determinant of the dimensionality of the electroencephalogram: A replication study," Biol. Psych. 35, 165-178.
14. Hayashi, C. [1964] Nonlinear Oscillations in Physical Systems (McGraw Hill, New York).
15. Hayashi, N., Nakao, M. & Hirakawa, N. [1982] " Chaos in self sustained oscillation of an excitable biological membrane under sinusoidal simulation," Phys. Lett. A88, 265-266.
16. Huffman, R. E., Wei-Xing, S. & Bunney, B. S. [1995] " Nonlinear sequence dependent structure of nigral dopamine neuron interspike interval firing patterns," Biophys. J. 69, 128-137.
17. Jansen, B. H. [1991a] " Quantitative analysis of electroencephalograms: Is there chaos in the future?" Int. J. Biomed. Comput. 27, 95-123.
18. Jansen, B. H. [1991b] " Is it? and so what? - A critical review of EEG chaos," in Measuring Chaos in the Human Brain, eds. Duke, D. W. & Pritchard, W. S. (World Scientific, Singapore), pp. 83-96.
19. Jansen, B. H. & Brandt, M. E. eds. [1992] Nonlinear Dynamical Analysis of the EEC (World Scientific, Singapore).
20. Kowalik, Z. J. & Elbert, T. [1995] " A practical method for the measurements of the chaoticity of electric and magnetic brain activity," Int. J. Bifurcation and Chaos 5, 475-490.
21. Layne, S. P., Mayer-Kress, G. & Holzfuss, J. [1986] " Problems associated with dimensional analysis of electroencephalogram data," in Dimensions and Entropies in Chaotic Systems ed. Mayer-Kress, G. (Springer, New York), pp. 246-256.
22. Maritz, J. S. [1984] Distribution-Free Statistical Methods (Chapman and Hall, New York).
23. Mayer-Kress, G. & Layne, S. P. [1987] " Dimensionality of the human electroencephalogram," in Perspectives in Biological Dynamics and Theoretical Medicine eds. Koslow, S. H., Madel, A. J. & Shlesinger, M. F. (The New York Academy of Sciences, New York), pp. 62-86.
24. McKenna, T. M., McMullen, T. A. & Shlesinger, M. F. [1994] " The brain as a dynamic physical system," Neurosci. 60, 587-605.
25. Nan, X. & Jinghua, X. [1988] " The fractal dimension of EEG as a physical measure of conscious human brain activities," Bull. of Math. Biol 50, 559-565.
26. Osborne, A. R. & Provenzale, A. [1989] " A finite correlation dimension for stochastic systems with power-law spectra," Physica D35, 357-381.
27. Palus, M. [1994] Nonlinearity in Normal Human EEG: Cycles and Randomness, Not Chaos Santa Fe Institute Publication Number 94-10-054. Santa Fe, NM: Santa Fe Institute.
28. Parikh, J. C. & Pratap, R. [1991] " A map describing EEG activity of human brain," Pramana J. Phys. 3, L347-L352.
29. Pijn, J. P., vanNeervan, J., Noest, A. & Lopes da Silva, F. H. [1991] " Chaos or noise in EEG signals: Dependence on state and brain site," Electroenceph. Clin. Neurophysiol. 79, 371-381.
30. Pradhan, N. & Narayana Dutt, D. [1993] " A nonlinear perspective in understanding the neurodynamics of EEG," Compt. Biol. Med. 23, 425-442.
31. Pradhan, N., Sadasivan, P. K., Chatterji, S. & Narayana Dutt, D. [1995] " Patterns of attractor dimensions of sleep EEG," Compt. in Biol. and Med. 25, 455-462.
32. Pradhan, N. & Sadasivan, P. K. [1996] " The nature of dominant Lyapunov exponent and attractor dimension curves of EEG in sleep," Compt. in Biol. Med. 26, 419-428.
33. Pritchard, W. S., Duke, D. W. & Krieble, K. K. [1995] " Dimensional analysis of resting human EEG II: Surrogate data testing indicate nonlinearity but not low dimensional chaos," Psychophysiol. 32, 486-491.
34. Rapp, P. E., Bashore, T. R., Martinerie, J. M., Albano, A. M., Zimmerman, I. D. & Mees, A. I. [1989] " Dynamics of brain electrical activity," Brain Topography 2, 99-118.
35. Rapp, P. E., Zimmerman, I. D., Albano, A. M., de Guzman, G. C., Greenbaum, N. N. & Bashore, T. R. [1986] " Experimental studies of chaotic neural behavior: Cellular activity and electroencephalographic signals," in Nonlinear Oscillations in Biology and Chemistry, Lecture Notes in Biomathematics 66, ed. Othmer, H. G. (Springer-Verlag, Berlin), p. 175-205.
36. Rapp, P. E. [1993] " Chaos in the neuroscience: Cautionary tales from the frontier," Biologist 40, 89-94.
37. Rapp, P. E., Albano, A. M., Schmah, T. I. & Farwell, L. A. [1993] " Filtered noise can mimic low dimensional chaotic attractors," Phys. Rev. E47, 2289-2297.
38. Rapp, P. E., Albano, A. M., Zimmerman, I. D. & Jimenez-Montano, M. A. [1994] " Phase-randomized surrogates can produce spurious identifications of non-random structure," Phys. Lett. A192, 27-33.
39. Rechtschaffen, A. & Kales, A. [1968] A Manual of Standardized Terminology, Technique and Scoring for Sleep Stages of Human Subjects Public Health Services, US Government Printing Office, Washington, DC.
40. Roschke, J., Mann, K. & Fell, J. [1994] " Nonlinear EEG dynamics during sleep in depression and schizophrenia," Int. J. Neurosci. 75, 271-284.
41. Schiff, S. J., Sauer, T. & Chang, T. [1994] " Discriminating deterministic versus stochastic dynamics in neuronal activity," Integ. Physiol. Behav. Sci. 29, 246-261.
42. Schuster, H. G. [1988] Deterministic Chaos. An Introduction Second Revised Edition (VCH Publishers, New York).
43. Snedecor, G. W. & Cochran, W. G. [1967] Statistical Methods Sixth Edition (Iowa State Univ. Press, Ames, Iowa).
44. Takens, F. [1985] " On the numerical determination of the dimension of an attractor," Lecture Notes in Mathematics 1125, 99-115.
45. Theiler, J., Eubank, S., Longtin, A., Galdrikian, B. & Farmer, J. D. [1992] " Testing for nonlinearity in time series: The method of surrogate data," Physica D58, 77-92.
46. Watt, R. C. & Hameroff, S. R. [1987] " Phase space analysis of human EEG during general anesthesia," in Perspectives in Biological Dynamics and Theoretical Medicine ed. Koslow, S. H., (New York Academy of Sciences, New York), pp. 286-288.