Modelling of ECoG in temporal lobe epilepsy.

Subdural recordings of the e lectrical activity of the human brain g ive electrocorticograms (ECoG) almost free of artifacts and distortions by the skull and other intervening material. This paper discusses the modelling of the ECoG during the pre-ictal, ictal and post-ictal phases of an epileptic seizure. Optimum order linear autoregressive (AR) models are formed and the movement of the poles of the models are traced with time. Nonlinear extension to the AR models (NAR) is formulated based on the assumption of existence of nonlinear oscillations in the data. The optimum order of this model i s determined and its performance is compared with that of the linear AR models. The analysis of the data with NAR resulted in the satisfaction of sufficient conditions for limit cycles in the ictal phase.

[1]  S. H. Hsieh,et al.  THRESHOLD MODELS FOR NONLINEAR TIME SERIES ANALYSIS. , 1987 .

[2]  N. Andersen,et al.  ON POWER ESTIMATION IN MAXIMUM ENTROPY SPECTRAL ANALYSIS , 1978 .

[3]  J. Petruccelli,et al.  Detecting non-linearity in time series , 1986 .

[4]  T. Ozaki,et al.  Modelling nonlinear random vibrations using an amplitude-dependent autoregressive time series model , 1981 .

[5]  Åke Björck Iterative refinement of linear least squares solutions I , 1967 .

[6]  B. Van Der Pol,et al.  Forced Oscillations in a Circuit with Nonlinear Resistance , 1924 .

[7]  S. Haykin Nonlinear Methods of Spectral Analysis , 1980 .

[8]  J. Rissanen A UNIVERSAL PRIOR FOR INTEGERS AND ESTIMATION BY MINIMUM DESCRIPTION LENGTH , 1983 .

[9]  C. Granger,et al.  An introduction to bilinear time series models , 1979 .

[10]  Rangasami L. Kashyap,et al.  Optimal Choice of AR and MA Parts in Autoregressive Moving Average Models , 1982, IEEE Transactions on Pattern Analysis and Machine Intelligence.

[11]  J. Makhoul,et al.  Linear prediction: A tutorial review , 1975, Proceedings of the IEEE.

[12]  A. Babloyantz,et al.  Evidence of Chaotic Dynamics of Brain Activity During the Sleep Cycle , 1985 .

[13]  J. Makhoul Stable and efficient lattice methods for linear prediction , 1977 .

[14]  T.H. Crystal,et al.  Linear prediction of speech , 1977, Proceedings of the IEEE.

[15]  A. Babloyantz,et al.  Low-dimensional chaos in an instance of epilepsy. , 1986, Proceedings of the National Academy of Sciences of the United States of America.

[16]  H. Akaike A new look at the statistical model identification , 1974 .

[17]  M.G. Bellanger,et al.  Digital processing of speech signals , 1980, Proceedings of the IEEE.

[18]  Åke Björck,et al.  Iterative refinement of linear least squares solutions II , 1967 .

[19]  Hung Man Tong,et al.  Threshold models in non-linear time series analysis. Lecture notes in statistics, No.21 , 1983 .

[20]  S.M. Kay,et al.  Spectrum analysis—A modern perspective , 1981, Proceedings of the IEEE.