Nonlinear EEG analysis based on a neural mass model

Abstract. The well-known neural mass model described by Lopes da Silva et al. (1976) and Zetterberg et al. (1978) is fitted to actual EEG data. This is achieved by reformulating the original set of integral equations as a continuous-discrete state space model. The local linearization approach is then used to discretize the state equation and to construct a nonlinear Kalman filter. On this basis, a maximum likelihood procedure is used for estimating the model parameters for several EEG recordings. The analysis of the noise-free differential equations of the estimated models suggests that there are two different types of alpha rhythms: those with a point attractor and others with a limit cycle attractor. These attractors are also found by means of a nonlinear time series analysis of the EEG recordings. We conclude that the Hopf bifurcation described by Zetterberg et al. (1978) is present in actual brain dynamics.

[1]  Tohru Ozaki.  The Local Linearization Filter with Application to Nonlinear System Identifications , 1994 .

[2]  A. J. Hermans,et al.  A model of the spatial-temporal characteristics of the alpha rhythm , 1982 .

[3]  F. H. Lopes da Silva,et al.  Models of neuronal populations: the basic mechanisms of rhythmicity. , 1976, Progress in brain research.

[4]  R Biscay,et al.  Measuring the dissimilarity between EEG recordings through a non-linear dynamical system approach. , 1995, International journal of bio-medical computing.

[5]  A A Borbély,et al.  All-night sleep EEG and artificial stochastic control signals have similar correlation dimensions. , 1994, Electroencephalography and clinical neurophysiology.

[6]  James J. Wright,et al.  Propagation and stability of waves of electrical activity in the cerebral cortex , 1997 .

[7]  Donald O. Walter,et al.  Mass action in the nervous system , 1975 .

[8]  H. Haken,et al.  Field Theory of Electromagnetic Brain Activity. , 1996, Physical review letters.

[9]  P. Valdés,et al.  A global scale factor in brain topography. , 1994, The International journal of neuroscience.

[10]  T. Ozaki.  A local linearization approach to nonlinear filtering , 1993 .

[11]  T. Ozaki.  2 Non-linear time series models and dynamical systems , 1985 .

[12]  P. Valdés,et al.  EEG spike and wave modelled by a stochastic limit cycle , 1996, Neuroreport.

[13]  J. Cowan,et al.  Excitatory and inhibitory interactions in localized populations of model neurons. , 1972, Biophysical journal.

[14]  J. C. Jimenez,et al.  Local Linearization method for the numerical solution of stochastic differential equations , 1996 .

[15]  Tohru Ozaki,et al.  The Role of the Likelihood Function in the Estimation of Chaos Models , 2000 .

[16]  D. Tjøstheim,et al.  Identification of nonlinear time series: First order characterization and order determination , 1990 .

[17]  X. Wang.  Multiple dynamical modes of thalamic relay neurons: Rhythmic bursting and intermittent phase-locking , 1994, Neuroscience.

[18]  N. Wiener,et al.  Nonlinear Problems in Random Theory , 1964 .

[19]  H. Tong.  Non-linear time series. A dynamical system approach , 1990 .

[20]  M. B. Priestley,et al.  Non-linear and non-stationary time series analysis , 1990 .

[21]  R. Jindra.  Mass action in the nervous system W. J. Freeman, Academic Press, New York (1975), 489 pp., (hard covers). $34.50 , 1976, Neuroscience.

[22]  F. L. D. Silva,et al.  Dynamics of EEGs as signals of neuronal populations: models and theoretical considerations , 1998 .

[23]  Nelson J. Trujillo-Barreto,et al.  The statistical identification of nonlinear brain dynamics: A progress report , 1999 .

[24]  Milan Palus,et al.  Nonlinearity in normal human EEG: cycles, temporal asymmetry, nonstationarity and randomness, not chaos , 1996, Biological Cybernetics.

[25]  J. E. Skinner,et al.  Chaos and physiology: deterministic chaos in excitable cell assemblies. , 1994, Physiological reviews.

[26]  D. Liley,et al.  Computer simulation of electrocortical activity at millimetric scale. , 1994, Electroencephalography and clinical neurophysiology.