Large scale modeling of the piriform cortex for analyzing antiepileptic effects

The aim of this paper is to understand how we can model the brain as a so-called "large scale system" for analyzing epileptic behaviour. In particular, we explore a large scale network model suitable for the piriform cortex. Well known from clinical experiments for its chaotic behavior, the piriform cortex is easy to model because it appears to be almost independent of other portions of the brain. We describe its behavior by moving the analysis from the time space into the phase space of the EEG signals. Although the model of the piriform cortex contains hundreds of variables, useful information can be extracted from a single EEG signal which can be perceived as a time series computed from the artificial electrodes. This transformation, from the time space of a time series to the phase space, is considered mandatory to extract the nonlinear characteristics related with chaos. In the phase space, we analyze the attractor built from the EEG by computing the Largest Lyapunov Exponent(LLE), and the Kaplan-York dimension (D-KY). In addition, the analysis in the phase space opens the problem of measuring the synchronization between two coupled subsystems using the model of the piriform cortex. In particular, in this paper, we have opted to quantify this by means of the the nonlinear interdependence, i.e., the so-called S measure. This index is used to measure the synchronization between two systems in the phase space, and tends to better describe the interaction between the systems than the classical cross-correlation coefficient. The goal of studying the piriform cortex model is to see if we can generate certain desirable phenomena by modifying some of the underlying control parameters. We investigate, in this paper, the Problem of Stimulus Frequency, which is motivated by studies of the frequency of the olfactory stimuli as recognized by the piriform cortex via its bulb, which involves the dependence of the level of chaos as a function of the frequency of a stimulus that is globally applied in the network via the olfactory bulb.

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

[2]  P ? ? ? ? ? ? ? % ? ? ? ? , 1991 .

[3]  H. Abarbanel,et al.  Determining embedding dimension for phase-space reconstruction using a geometrical construction. , 1992, Physical review. A, Atomic, molecular, and optical physics.

[4]  James J. Wright,et al.  Dynamics of the brain at global and microscopic scales: Neural networks and the EEG , 1996, Behavioral and Brain Sciences.

[5]  R. Acharya U,et al.  Nonlinear analysis of EEG signals at different mental states , 2004, Biomedical engineering online.

[6]  C. Stam,et al.  Nonlinear dynamical analysis of EEG and MEG: Review of an emerging field , 2005, Clinical Neurophysiology.

[7]  James Theiler,et al.  Testing for nonlinearity in time series: the method of surrogate data , 1992 .

[8]  Walter J. Freeman,et al.  TUTORIAL ON NEUROBIOLOGY: FROM SINGLE NEURONS TO BRAIN CHAOS , 1992 .

[9]  Alistair I. Mees,et al.  Dynamics of brain electrical activity , 2005, Brain Topography.

[10]  R. Quiroga,et al.  Learning driver-response relationships from synchronization patterns. , 1999, Physical review. E, Statistical physics, plasmas, fluids, and related interdisciplinary topics.

[11]  J. Lamberts,et al.  Correlation Dimension of the Human Electroencephalogram Corresponds with Cognitive Load , 2000, Neuropsychobiology.

[12]  L. Pecora.  Synchronization conditions and desynchronizing patterns in coupled limit-cycle and chaotic systems , 1998 .

[13]  Joel L. Davis,et al.  An Introduction to Neural and Electronic Networks , 1995 .

[14]  J. Bower,et al.  Exploring parameter space in detailed single neuron models: simulations of the mitral and granule cells of the olfactory bulb. , 1993, Journal of neurophysiology.

[15]  John R. Terry,et al.  Topographic Organization of Nonlinear Interdependence in Multichannel Human EEG , 2002, NeuroImage.

[16]  W. Pritchard,et al.  Dimensional analysis of resting human EEG. II: Surrogate-data testing indicates nonlinearity but not low-dimensional chaos. , 1995, Psychophysiology.

[17]  L. Haberly.  Neuronal circuitry in olfactory cortex: anatomy and functional implications , 1985 .

[18]  J. Bower,et al.  The Book of GENESIS , 1998, Springer New York.

[19]  J. Hale.  Functional Differential Equations , 1971 .

[20]  Matthew A. Wilson,et al.  The simulation of large-scale neural networks , 1989 .

[21]  Jonathan D. Cryer,et al.  Time Series Analysis , 1986 .

[22]  R. Burke,et al.  Detecting dynamical interdependence and generalized synchrony through mutual prediction in a neural ensemble. , 1996, Physical review. E, Statistical physics, plasmas, fluids, and related interdisciplinary topics.

[23]  V. E. Bondarenko,et al.  Epilepsy-like phenomena in chaotic neural networks , 1996, Proceedings of International Conference on Neural Networks (ICNN'96).

[24]  P. Grassberger,et al.  A robust method for detecting interdependences: application to intracranially recorded EEG , 1999, chao-dyn/9907013.

[25]  J. Bower,et al.  Olfactory cortex: model circuit for study of associative memory? , 1989, Trends in Neurosciences.

[26]  Matthew A. Wilson,et al.  A Computer Simulation of Olfactory Cortex with Functional Implications for Storage and Retrieval of Olfactory Information , 1987, NIPS.

[27]  M. Hasselmo,et al.  Acetylcholine and memory , 1993, Trends in Neurosciences.

[28]  James M. Bower,et al.  Multiday Recordings from Olfactory Bulb Neurons in Awake Freely Moving Rats: Spatially and Temporally Organized Variability in Odorant Response Properties , 1997, Journal of Computational Neuroscience.

[29]  David J. Hand,et al.  Intelligent Data Analysis: An Introduction , 2005 .

[30]  Pierre Baldi,et al.  On the Use of Bayesian Methods for Evaluating Compartmental Neural Models , 1998, Journal of Computational Neuroscience.

[31]  Erol Başar,et al.  Biophysical and physiological systems analysis , 1976 .

[32]  Hans Lüders,et al.  Deep Brain Stimulation and Epilepsy , 2003 .