Large scale modeling of the piriform cortex for analyzing antiepileptic effects

ABSTRACT

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.

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INDEX TERMS

Keywords:
Lyapunov exponents, chaos, nonlinear interdependence, piriform cortex