NON-LINEAR DYNAMICS IN SPATIO-TEMPORAL PATTERNS OF ACTIVITY IN SIMULATED THALAMO-CORTICAL NEURAL NETWORKS AND SINGLE-UNIT RECORDINGS

Representation of information in the nervous system has often been considered to be contained in simultaneous discharge of a large set of neurons. Experimental evidence suggested that the sequence of spikes of a neuron is related to information processing in the network to which it belongs.

Most of the sensory information is centrally processed through the thalamo-cortical network, which can be represented to a certain extent by a range of parallel interconnected modules. The thalamus, far from being a mere relay station, participates in organizing a recurrent temporal pattern of activity.

The existence of so-called unspecific projections to both thalamus and cortex, such as forebrain cholinergic and dorsal raphe serotoninergic, suggests that global parameters may exert an important control over network activity.

The network activity is analyzed in the control-parameter plane defined by the kinetics of the post-synaptic potential and by the threshold potential. A 3D plot of this activity is done using a z-axis corresponding to the time needed to reach a stable mode of activity, either a recurrent spatiotemporal pattern mode as positive times or extinction mode as negative times.

For example,three different models of the thalamo-cortical (THACOR) circuit with 1, 2, and 4 modules, with the very same initial pattern of activation indicate that stable domains exist for all circuits, but sudden zones of transition, characterized by high "peaks" adjacent to deep "troughs", may be easily recognized.

Small changes of the control parameters induce the network to shift from stable time-locked mode to extinction mode and different initial patterns of activation may stabilize towards the same mode of activity, somewhat like attractors. Very sharp differences in activity may occur within a narrow range of the control parameters, whereas very large intervals may correspond to the same mode of activity. In the framework of the Theory of Catastrophes it is possible to represent such dynamic behavior by the Riemann-Hugoniot equation, given that the equilibrium surface represents the stable modes of activity with p.s.p. kinetics and the threshold potential as control parameters.

A complementary approach to the study the dynamical system is the analysis of single unit spike-trains. In order to investigate the existence of chaotic attractors, numerical methods from the standard theory of dynamical systems are used.

An embedding space was constructed using delay coordinates. The correlation integrals, which count the number of points falling in a hypersphere of preassigned radius, for any element of the time series, were computed. A deterministic structure is established when the slope of the correlation integral as a function of the radius is constant as the dimension of the embedding space is varied.

This slope provides an estimate of the so called "correlation dimension", which measures the size of the attractor. In a significant number of our samples, a deterministic structure with a low embedding dimension (between 2 and 6) could be determined.