Dynamics of the brain at global and microscopic scales: Neural networks and the EEG

Abstract

There is some complementarity of models for the origin of the electroencephalogram (EEG) and neural network models for information storage in brainlike systems. From the EEG models of Freeman, of Nunez, and of the authors' group we argue that the wavelike processes revealed in the EEG exhibit linear and near-equilibrium dynamics at macroscopic scale, despite extremely nonlinear – probably chaotic – dynamics at microscopic scale. Simulations of cortical neuronal interactions at global and microscopic scales are then presented. The simulations depend on anatomical and physiological estimates of synaptic densities, coupling symmetries, synaptic gain, dendritic time constants, and axonal delays. It is shown that the frequency content, wave velocities, frequency/wavenumber spectra and response to cortical activation of the electrocorticogram (ECoG) can be reproduced by a “lumped” simulation treating small cortical areas as single-function units. The corresponding cellular neural network simulation has properties that include those of attractor neural networks proposed by Amit and by Parisi. Within the simulations at both scales, sharp transitions occur between low and high cell firing rates. These transitions may form a basis for neural interactions across scale. To maintain overall cortical dynamics in the normal low firing-rate range, interactions between the cortex and the subcortical systems are required to prevent runaway global excitation. Thus, the interaction of cortex and subcortex via corticostriatal and related pathways may partly regulate global dynamics by a principle analogous to adiabatic control of artificial neural networks.

Origin, structure, and role of background EEG activity. Part 2. Analytic phase

“…The sizes and durations of cones and avalanches give histograms that are fractal. The smallest and briefest are the most numerous, the distributions in time, space and frequency follow power laws, the patterns are self-similar across multiple scales (Ingber, 1995;Wright and Liley, 1996;Linkenkaer-Hansen, 2001;Hwa and Ferree, 2002), and estimates of the means and SD depend on the size of the measuring tool. These functional similarities indicate that neocortical dynamics is scale-free (Wang and Chen, 2003): the largest events are in the tail of a continuous distribution and share the same mechanism of onset with the smallest and the same brief time of onset despite their large size (Cover Illustration).…”

The Sleep Cycle Modelled as a Cortical Phase Transition

“…While our approach builds on, and freely borrows ideas from, earlier corticalcontinuum models developed by Freeman [4], Wright and Liley [23], Liley et al (7,8).…”

Simulated Electrocortical Activity at Microscopic, Mesoscopic, and Global Scales

“…Simple numerical simulations followed (Wright and Liley, 1996;Wright, 1997Wright, , 1999, leading to more advanced methods, including the development of wave equations (Robinson et al, 1997(Robinson et al, , 1998a(Robinson et al, , b, 2001. We have progressively introduced more refined physiological parameters, and descriptions of anatomical organization (Liley and Wright, 1994;Rennie et al, 1999Rennie et al, , 2000Rennie et al, , 2002, with the object of developing a single model to account for events in the brain at a number of different scales.…”