Models of Electrocortical Activity: Cerebral Rhythms, Synchronous Oscillation, and Relations to Cortical Stability

Agora 1999

A family of related models of electrocortical activity provide explanations of the origin of the cerebral rhythms, synchronous oscillation, and the emergence of spontaneous cortical activity. State-equations shown to reproduce generic properties of electrocortical activity are parametrised from physiological data, and modified to include realistic anatomical features. In these models, the occurrence of resonant phenomena in the delta, theta, alpha, beta, and gamma bands, depends upon strong and rapid negative feedback, particularly at inhibitory synapses. This feedback is only partially accounted for by membrane reversal potentials. Travelling wave activity is associated with highly damped solutions of the system's dispersion relations, and thus global resonant modes play little part. However, the formulation is compatible with an origin of alpha activity from thalamo-cortical resonance. With progressive increases in cortical activation, the power spectrum of electrocortical activity exhibits dominance of activity at progressively higher frequencies. At lower levels of cortical activation, associated with the theta, alpha, and beta bands, the simulated cortical system exhibits a single stable fixed point. Activity in the gamma band around 40 Hz, associated with large amplitude oscillations of pulse density, appears at higher levels of cortical activation, and is associated with an unstable fixed point. The transition between stable and unstable fixed points appears analogous to a thermodynamic phase transition, and features of fast and slow neurotransmission can be incorporated, to render the system stable in the large. Synchronous oscillation appears between co-active cortical sites, and does not depend upon non-linear phase locking, except at high degrees of cortical activation. Instead, synchrony is explained by analysis of the odd and even eigenfunctions of wave motion radiating from each of the co-active sites. The most complex application of this model attempts representation of electrocortical activity at the mini-columnar scale, by introducing a detailed specification of the inhibitory surrounds and patchy intrinsic connectivity of visual cortex. Quantitative specifications were obtained from a learning-rule model for visual cortical development. By this means, it is hoped to explore relations between rapid brain dynamics and synaptic plasticity of the Hebbian type. Testable predictions of this class of models included specific relations between 40 Hz and gamma band activity, and the slow electrocortical potentials.

Slide 1, Lecture Title and Authors

Slide 2, Aim/Principles

Slide 3, Mathematical Basis of Model

Slide 4, "Exploded" levels of brain modelling

Slide 5, List of parameter values and dimensions

Slide 6, Fixed points, linearisation, power spectrum and dispersion relation calculations

Slide 7, Fit to EEG

Slide 8, Cortico-thalamic model, fit to spectra and model root-locus diagram

Slide 9, Model with local feedback, dispersion relations

Slide 10, Table of real synaptic feedback mechanisms

Slide 11, Boiling porridge

Slide 12, Spectra from CCF

Slide 13, Two input ccf, cross-correlations and lag, first and second eigenfunctions, odd and even input diagrams

Slide 14, Moving bar simulations of spectra and cross-correlations

Slide 15, Zero-lag synchrony and spectra at increasing Q_ns

Slide 16, Patchy connectivity with orientation preference

Slide 17, Real orientation preference in shrew visual cortex with types of orientation preference junctional continuity

Slide 18, Simulation results of visual cortex orientation preference with types of junctional continuity

Slide 19, "Exploded" levels of brain modelling

Slide 20, Next Steps