Summary
To investigate the degree of interdependence of EEG signals, we have to use signal analysis methods. Three of these are described and their performance is compared: the cross-correlation (coherence and phase), the average amount of mutual information (AAMI) or the normalized AAMI, also called transmission coefficient T, and the correlation ratio h2 that is a general measure of nonlinear fit between any two signals. The three methods were applied to simulated and real signals in order to put in evidence how nonlinear relationships may affect differently these three measures of association. The nature of the interdependence between EEG signals is not characterized only by the degree of association, but also by the corresponding phase relationship. A basic question is whether such a phase shift can be interpreted as a transmission delay. However, a fundamental problem is that a phase shift may be difficult to interpret in terms of a biophysical model. A procedure is described in order to solve this problem. This involves computing the phase spectrum between the pair of signals, estimating the gain of the corresponding linear transfer function and the associated minimum phase. By subtracting the minimum phase from the phase spectrum, a corrected phase function can be obtained. From the slope of this phase function, a transmission delay can be estimated. This procedure is illustrated by applications to simulated and real EEG signals. It is demonstrated that from phase shifts we may estimate transmission delays between at least certain classes of EEG signals. In this way we can asses, unambiguously, how the transmission of information between different brain sites develops.
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References
Boeijinga, P.H. and Lopes da Silva, F.H. A new method to estimate time delays between EEG signals applied on beta activity of the olfactory cortical areas. Electroenceph. Clin. Neurophysiol., 1989, 73: 198–205.
Callaway, E. and Harris, P.R. Coupling between cortical potentials from different areas. Science, 1974, 183: 873–875.
Cohn, R. and Leader, H.S. Synchronization characteristics of paroxysmal EEG activity. Electroenceph. Clin. Neurophysiol., 1967, 22: 421–428.
De Lima, V.M.F., Pijn, J.P., Filipe, C.N., Lopes da Silva, F.H. The role of hippocampal commissures in the interhemispheric transfer of epileptiform afterdischarges in the rat: a study using linear and nonlinear regression analysis. Electroenceph. Clin. Neurophysiol., 1990 (In press).
Ende, H.W. van den. Beschrijvende statistiek voor gedragswetenschappen. Agon Elsevier, 1973.
Gel'fand, I.M. and Yaglom, A.M. Calculation of the amount of information about a random function contained in another such function. American Mathematical Society Translations, 1959, 12: 199–246.
Gevins, A.S. and Cutillo, B.A. Signals of cognition. In: F.H. Lopes da Silva, Storm van Leeuwen and A. Remond, (Eds.), Clinical Applications of Computer Analysis of EEG and other Neurophysiological Signals, Revised series, vol. 2, Handbook of Electroencephalography and Clinical Neurophysiology, 1986, 335–384. Elsevier, Amsterdam.
Gevins, A.S. and Remond, A. Methods of analysis of brain electrical and magnetic signals. In: Handbook of Electroencephalography and Clinical Neurophysiology, Revised series, vol. 1, 1987, 683, Elsevier, Amsterdam.
Gotman, J. Interhemispheric relations during bilateral spike and wave activity. Epilepsia, 1981, 22: 453–466.
Gotman, J. Measurement of small time differences between EEG channels: method and application to epileptic seizure propagation. Electroenceph. Clin. Neurophysiol., 1983, 56: 501–514.
Gotman, J. Interhemispheric interactions in seizures of focal onset: data from human intracranial recordings. Electroenceph. Clin. Neurophysiol., 1987, 67: 120–133.
Guilford, J.P. and Fruchter, B. Fundamental statistics in psychology and education. 6th ed. McGraw-Hill, 1985.
Lieb, J.P., Hoque, K., Skomer, C.E. and Song, X.W. Interhemispheric propagation of human mesial temporal lobe seizure: a coherence/phase analysis. Electroenceph. Clin. Neurophysiol., 1987, 67: 101–119.
Lopes da Silva, F.H. EEG analysis: theory and practice. In: E. Niedermeyer, and F. H. Lopes da Silva, (Eds.), Electroencephalography Basic Principles, Clinical Applications and Related Fields, 2nd edition, 1987, 871–899, Urban & Schwarzenberg, Baltimore-Munich.
Mars, N.J.I., Lopes da Silva, F.H., Van Hulten, K. and Lommen, J.G. Computer assisted analysis of EEGs during seizures; localization of an epileptogenic area. Electroenceph. Clin. Neurophysiol., 1977, 43: 575.
Mars, N.J.I. and Lopes da Silva, F.H. Propagation of seizure activity in kindled dogs. Electroenceph. Clin. Neurophysiol., 1983, 56: 194–209.
Mars, N.J.I., Thompson, P.M. and Wilkus, R.J. The spread of epileptic seizure activity in humans. Epilepsia, 1985, 26: 85–94.
Mars, N.J.I. and Lopes da Silva, F.H. EEG analysis methods based on information theory. In: A.S. Gevins and A. Remond, (Eds.), Handbook of Electroencephalography and Clinical Neurophysiology, Revised series, vol. 1. Elsevier, Amsterdam, 1987, 297–307.
Moddemeijer, R. Delay-estimation with application to electroencephalograms in epilepsy. Thesis, 1989. Repro University of Twente, Enschede.
Nunez, P.L. Methods to estimate spatial properties of dynamic cortical source activity. In: G. Pfurtscheller and F.H. Lopes da Silva, (Eds.), Functional Brain Mapping, 1988, 3–11, Huber Publ. Toronto.
Papoulis, A. The Fourier integral and its applications. McGraw-Hill, 1962.
Pfurtscheller, G. Some results of the analysis of epileptic seizure patterns by correlation-methods. In: Petsche and Brazier (Eds.), Synchronization of EEG Activity in Epilepsies, 1972. Springer-Verlag.
Pijn, J.P.M., Vijn, P.C.M., Lopes da Silva, F.H., Van Emde Boas, W. and Blanes, W. The use of signal-analysis for the localization of an epileptogenic focus: a new approach. Advances in Epileptology, 1989, 17: 272–276.
Rao, C.R. Linear statistical inference and its applications. 1961. John Wiley & Sons.
Shannon, C.E. and Weaver, W. The mathematical theory of communication. 1949, University of Illinois Press, Urbana, II.
Shaw, J.C. and Ongley, C. The measurement of synchronization. In: Petsche, and Brazier, (Eds.), Synchronization of EEG Activity in Epilepsies, 1972. Springer-Verlag.
Winer, B.J. Statistical principles in experimental design. Second edition, 1971. McGraw-Hill.
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Lopes da Silva, F., Pijn, J.P. & Boeijinga, P. Interdependence of EEG signals: Linear vs. nonlinear Associations and the significance of time delays and phase shifts. Brain Topogr 2, 9–18 (1989). https://doi.org/10.1007/BF01128839
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DOI: https://doi.org/10.1007/BF01128839