Gross electrocortical activity as a linear wave phenomenon with variable temporal damping, regulated by ascending catecholamine neurones.

We report critical tests for a theory of electrocortical wave processes, in which telencephalic dendritic potentials reflect the mass action of coupled oscillatory circuits exhibiting complicated and unspecified non-linearities, the whole system being driven by active cell firing. Specific assumptions were: stochastic independence for instantaneous coupling parameters in the system, an individual central tendency to the cycle time for each circuit, and the maintenance of steady state conditions. Application of the central limit theorem to the state transition matrix shows that the gross electrocortical waves should be linear waves, exhibiting a multitude of invariant resonant modes, with the natural frequencies of all the modes being clustered about a smaller number of center values. Ascending brain-stem neurones of at least the dopaminergic and noradrenergic classes should regulate both the power of noise-like signals driving the telencephalic resonant patterns, and the temporal damping of each resonance. We devised tests which involved between hemisphere comparisons of electrocortical spectra, before and after unilateral lesion of transhypothalamic ascending fibres, thus obtaining ratio power changes attributable to post lesion asymmetry of damping and driving, in modes of equivalent left-right center-frequencies. These ratio spectra were curve-fitted to an approximate theoretical expression, and the parameters obtained enabled tests of several specific predictions. Estimates of the center values for resonant mode frequencies, comparison of the relative changes in left/right phase with that expected from the ratio changes in power, and estimates of the surface-to-signal transformation of left and right signals made by a back-calculation, all conform to expectation from the theory, and are consistent across lesion of different types of ascending neurone.

State-changes in the brain viewed as linear steady-states and non-linear transitions between steady-states.

Preceding papers concern a linear theory of electrocortical waves and their regulation by brain-stem neurones, in conditions of steady-state. The present paper reconsiders the theory, and generalizes beyond the effects of the fibre systems so far studied. Relaxation and unification of the assumptions upon which the initial model was based is undertaken. It is shown that the generalised model may render state changes within the brain accessible to systematic description, using the EEG as dependent variable. It is proposed that a multitude of stable states are possible within the brain, each characterised by a set of damping parameters for separate linear resonant modes. Within each stable state, the set of sums of resonant modes characterises a sub-space of the total state-space. Transition between stable regions can occur with either perturbation by external signals, or by internal controls. Tentative consideration is given to the role of plastic changes leading to adaptive learning as an attribute of a system of this type.

Amplitude and phase relations of electrocortical waves regulated by transhypothalamic dopaminergic neurones: a test for a linear theory.

We have previously proposed that electrocortical activity (EEG) arises as a manifestation of linear waves generated by resonance among telencephalic neurones, and that this activity is controlled in part by ascending neurones from the brain-stem, which regulate the damping of each resonance. The present experiments focus on a specific class of ascending neurones, the mesotelencephalic dopaminergic cells, because these cells are thought to mediate important psychological effects, and are conveniently subject to selective lesion. A critical test of the theory is undertaken, by performing selective unilateral lesion, assessing the changes in the power spectrum of the EEG attributable to lesion, and determining whether the changes in phase of the EEG correspond to that predicted from the changes in power. Results support the theory, although the model order applicable in these experiments in inadequate. The consequences of these findings for automata theory, linear network theory and their application to mammalian brains are briefly discussed.