Article Summary

Title : Brain dynamics at multiple scales: can one reconcile the apparent low-dimensional chaos of macroscopic variables with the seemingly stochastic behavior of single neurons?
Authors : Sami El Boustani and Alain Destexhe
Year : 2009
Journal : International Journal of Bifurcation and Chaos
Volume : 20
Pages : 1687-1702

Abstract

Nonlinear time series analyses have suggested that the human electroencephalogram (EEG) may share statisti- cal and dynamical properties with chaotic systems. During slow-wave sleep or pathological states like epilepsy, corre- lation dimension measurements display low values, while in awake and attentive subjects, there is not such low dimen- sionality, and the EEG is more similar to a stochastic vari- able. We brie?y review these results and contrast them with recordings in cat cerebral cortex, as well as with theoreti- cal models. In awake or sleeping cats, recordings with mi- croelectrodes inserted in cortex show that global variables such as local ?eld potentials (local EEG) are similar to the human EEG. However, in both cases, neuronal discharges are highly irregular and exponentially distributed, similar to Poisson stochastic processes. To attempt reconcile these results, we investigate models of randomly-connected net- works of integrate-and-?re neurons, and also contrast global (averaged) variables, with neuronal activity. The network displays different states, such as “synchronous regular” (SR) or “asynchronous irregular” (AI) states. In SR states, the global variables display coherent behavior with low dimen- sionality, while in AI states, the global activity is high-dim- ensionally chaotic with exponentially distributed neuronal discharges, similar to awake cats. Scale-dependent Lyapunov exponents and ?-entropies show that the seemingly stochas- tic nature at small scales (neurons) can coexist with more coherent behavior at larger scales (averages). Thus, we sug- gest that brain activity obeys similar scheme, with seem- ingly stochastic dynamics at small scales (neurons), while large scales (EEG) display more coherent behavior or high- dimensional chaos.