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This paper considers the properties of parameters (natural frequencies and damping coefficients) obtained from segment-by-segment autoregression analysis of ECoG of rat. The use of a reference signal as control for parameter estimate errors, and multiple regression analyses indicate that the dependencies among parameters calculated from ECoG in the alert (desynchronised) state are of a form consistent with imposition of time-invariance assumptions (implicit in autoregression) on an inherently non-stationary, multimodal, linear and near-equilibrium "thermal" process.

A second test is undertaken for a theory of linear wave motion in electrocortical waves, under lateral hypothalamic control via regulation of damping. This test invokes a general property of linear systems, namely that wave motion with characteristic natural frequencies implies fixed phase velocities associated with each wavelength, independent of the changes in hypothalamic input. A means of testing the invariance of this dispersion relation at the point of recording is derived from a simplified biophysical model for waves in a dipole layer. The method avoids some problems implicit in direct spatio-temporal wave analysis. Results confirm that the model under test is internally consistent, and is also consistent with other findings concerning the origin and spatial nature of the EEG.

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.

An initial test for a theory of lateral hypothalamic regulation of electrocortical activity is undertaken. The theory supposes lateral hypothalamic input directly or indirectly damps telencephalic resonances involving linear wave phenomena, enabling this pathway to act as parametric control of information processing in cortical neural networks. Relative changes in left and right electrocortical power spectra are used to test for the presence of resonant modes with constant natural frequencies in conditions of asymmetrical damping, following unilateral lesion of the lateral hypothalamus. Natural frequency values for the modes clustered about center frequencies in the EEG band are obtained. This method has the advantage of minimising the effects of time-variation and the recorded signal's distortion from the electrocortical local spatial average, but limits consideration to five dominant modes of resonance. The uncertainty of true model order, and errors in curve-fitting impose limitations on the test.

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.

A linear model for electrocortical waves and their control by the lateral hypothalamus is proposed. It is argued that such a linear model is not in contradiction to non-linearity of neural elements on the microscopic scale. Telencephalic structures are treated as a mass of linked oscillators generating activity with a number of resonant modes. The lateral hypothalamus is regarded as controlling damping of activity in the telencephalic mass, and therefore exerting a specific parametric control over all signal processing in the cortical networks. An initial test is proposed to assess the constancy of telencephalic natural frequencies, with variation in lateral hypothalamic damping.