Neuron Synchronization and Human EEG Phenomenology Simulation

F. Ferro Milone1, T. A. Minelli2, L. Turicchia3
1Divisione Neurologica Ospedale di Vicenza, Università di Verona, Italy
2Dipartimento di Fisica dell'Università, Sez. INFN, Padova, Italy
3Padova, Italy

Tóm tắt

The observed low correlation dimension of the EEG—ascribed to the high synchronization degree of the brain activity—encourages the use of more or less realistic neural networks for the parametrization and classification of cerebral rhythms via simulation. We have therefore tried to explain the electrocortical activity in terms of synchronization using a map inspired to the integrate and fire neuron model. An extension apt to the heuristic simulation of the rhythm phenomenology is also presented and applied to the reproduction of chaos features in brain activity.

Tài liệu tham khảo

Ahiara, K., Takabe, T., & Toyoda, M. (1990). Chaotic neural networks. Physics Letters, A144, 333–340. Basar, E. (1990). Chaos in brain function. Berlin: Springer-Verlag. Battiston, L., Ferro Milone, F., Gabrieli, C., Minelli, T.A., Nofrate, V., & Pascolini, A. (1995). Non-linear analysis of EEG signals. In M. Costato, A. Degasperis, & M. Milani (Eds.), Nonlinear dynamics, SIF Conference Proceedings Vol. 48, (pp. 127–134). Bologna: SIF. Bauer, H.U., & Pawelzik, K. (1993). Alternating oscillatory and stochastic dynamics in a model for a neuronal assembly. Physica, D69, 380–393. Chen, C.-C. (1994). Threshold effects on synchronization of pulse coupled oscillators. Physical Review, E49, 2668–2672. Clark, J.W. (1991). Neural network modelling. Physics in Medicine and Biology, 36, 1259–1317. Cobb, S.R., Buhl, E.H., Halasy, K., Paulsen, O., & Somog yi, P. (1995). Synchronization of the neuronal activity in hippocampus by individual GABAergic interneurons. Nature, 378, 75–78. Freeman, W.J. (1979). Simulation of chaotic EEG patterns with a dynamic model. Biological Cybernetics, 56, 139–150. Gloor, P. (1975). Contribution of electroencephalography and electrocorticography to the surgical treatment of the epilepsies. In D.R. Purpura, J.K. Penry, and R.D. Walter (Eds.), Neurosurgical Treatment of the Epilepsies. Advances in Neurology (pp. 59–105). New York: Raven Press. Grassberger, P., & Procaccia, I. (1983). Measuring the strangeness of strange attractors. Physica, D9, 189–208. Guelfand, I.M., & Chilov, G.F. (1962). Les Distributions. Paris: Dunod. Hertz, J., Krogh, A., & Palmer, R.G. (1994). Introduction to the theory of neural computing. Reading: Addison-Wesley. Hopfield, J.J. (1994). Neurons, dynamics and computation. Physics Today, 47, 40–46. Kandel, E.R., Schwarz, J.H., & Jessel, T.M. (Eds.). (1994). Principles of neural science. Amsterdam: Elsevier. Kanou, M., Horio, Y., Aihara, K., & Nakamura, S. (1994). A current-mode implementation of a chaotic neuron model using a SI integrator. IEICE Transactions. Fundamentals, E77-A, 335–338. Kantz, H., & Schreiber, T. (1995). Dimension estimates and physiological data. Chaos, 5, 143–154. Krosigk von, M., Bald, T., & McCormick, D.A. (1993). Cellular mechanisms of synchronized oscillations in the thalamus. Science, 261, 361–364. Kuramoto, Y. (1991). Collective synchronization of pulse coupled oscillators. Physica, D50, 15–30. Liley, D.T.J., & Wright, J.J. (1994). A millimetric-scale simulation of electrocortical wave dynamics. Network, 5, 175 and 191–201. Liljenström, H. (1991). Modeling the dynamics of olfactory cortex. International Journal of Neural Systems, 2, 1–15. Lopes da Silva, F. (1991). Neural mechanisms underlying brain waves. Electroencephalography and Clinical Neurophysiology, 79, 81–93. Martin, J.H. (1994). The electrical activity in the cortical population of neurons: EEG and the pathogenetic mechanisms of the epilepsies. In E.R. Kandel et al. (Eds.). Mirollo, R.E., & Strogaz, S.H. (1990). Synchronization of pulse coupled oscillators, SIAM Journal of Applied Mathematics, 50, 1645–1662. Nunez, P.L., Silberstein, R.B., Cadusch, P.J., Wijesinghe, R.S., Westdorp, A.F., & Srinivasan, R. (1994). A theoretical and experimental study of high resolution EEG. Electroencephalography and Clinical Neurophysiology, 90, 40–57. Pedley, T.A., & Traub, R.D. (1990). Physiological basis of EEG. In D.D. Daly & T.A. Pedley (Eds.), Current Practice of Clinical Electroencephalography (pp. 107–137). New York: Raven Press. Saermark, K., Lebech, J. Bak, C.K., & Sabers, A. (1990). Magnetoencephalography and attractor dimension: Normal subjects and epileptic patients. In E. Basar (Ed.), Chaos in Brain Function (pp. 110–118). Berlin: Springer-Verlag. Singer, W. (1991). Response synchronization of cortical neurons. Ibro News, 19, 6–7. Steriade, M., Gloor, P., Llinas R.R., Lopes da Silva, F., & Mesulam, M.M. (1990). Basic mechanisms of cerebral rhythmic activities. Electroencephalography and Clinical Neurophysiology, 76, 481–508. Takens, F. (1981). Detecting strange attractors in turbulence. Lecture Notes in Mathematics, 898, 366–381. Tsodyks, M., Mikov, I., & Sompolinsky, H. (1993). Patterns of synchrony in inhomogeneous networks of oscillators with pulse interactions. Physical Review Letters, 71, 1280–1283. Turova, T.S., Mommaerts, W., & van der Meulen, E.C. (1994). Synchronization of firing times in a stochastic neural network model with excitatory connections. Stochastic Processes and Applications, 50, 173–186. West, B.J. (1990). Fractal Physiology and Chaos in Medicine. Singapore: World Scientific. Wright, J.J., Sergejev, A.A., & Liley, D.T.J. (1994). Computer simulation of the electrocortical activity at millimetric scale. Electroencephalography and Clinical Neurophysiology, 90, 365–375. Wright, J.J., & Liley, D.T.J. (1996). Dynamics of the brain at global and microscopic scales: Neural networks and the EEG. Behavioral and Brain Sciences, 19, 285–320. Wu, X., & Liljenström, H. (1994). Regulating the nonlinear dynamics of olfactory cortex. Network, 5, 47–60.