Abstract
In a previous study, nonlinear autoregressive (NLAR) models applied to ictal electroencephalogram (EEG) recordings in six patients revealed nonlinear signal interactions that correlated with seizure type and clinical diagnosis. Here we interpret these models from a theoretical viewpoint. Extended models with multiple nonlinear terms are employed to demonstrate the independence of nonlinear dynamical interactions identified in the ‘NLAR fingerprint’ of patients with 3/s seizure discharges. Analysis of the role of periodicity in the EEG signal reveals that the fingerprints reflect the dynamics not only of the periodic discharge itself, but also of the fluctuations of each cycle about an average waveform. A stability analysis is used to make qualitative inferences concerning the network properties of the ictal generators. Finally, the NLAR fingerprint is analyzed in the context of Volterra-Weiner theory.
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References
Akaike H (1974) A new look at statistical model identification. IEEE Trans Auto Control AC-19:716–723
Farmer JD, Ott E, Yorke JA (1983) The dimension of chaotic attractors. Physica 7D:153–180
Feigenbaum M (1983) Universal behavior in nonlinear systems. Physica 7D:16–39
Kawahara T (1980) Coupled Van der Pol oscillators — a model of excitatory and inhibitory neural interactions. Biol Cybern 39:37–43
Korenberg MJ (1973) Identifications of biological cascades of linear and static nonlinear systems. Proc 16th Midwest Symp Circuit Theory 18:1–9
Korenberg MJ (1987) Functional expansions, parallel cascades, and nonlinear difference equations. In: Marmarelis VZ (eds) Advanced methods of physiological system modelling. University of Southern California, Los Angeles
Marmarelis PZ, Marmarelis VZ (1978) Analysis of physiological systems: the white noise approach. Plenum, New York
Schiff ND, Victor JD, Canel A, Labar DR (1991) Nonlinear autoregressive analysis of ictal EEG records (Abstract P32. 40). Third IBRO World Congress of Neuroscience, Montreal, p 223
Schiff ND, Victor JD, Canel A, Labar DR (1995) Characteristic nonlinearities of 3/second ictal EEG identified by nonlinear autoregressive analysis. Biol Cybern 72:519–526
Victor JD, Canel A (1992) A relation between the Akaike criterion and reliability of parameter estimates, with application to noninear autoregressive modelling the ictal EEG. Ann Biomed Eng 20:167–180
Wilson HR, Cowan JD (1972) A mathematical theory of the functional dynamics of cortical and thalamic nervous tissue. Kybernetik 13:55–80
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Schiff, N.D., Victor, J.D. & Canel, A. Nonlinear autoregressive analysis of the 3/s ictal electroencephalogram: implications for underlying dynamics. Biol. Cybern. 72, 527–532 (1995). https://doi.org/10.1007/BF00199895
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DOI: https://doi.org/10.1007/BF00199895