Sinusoidal modeling of ictal activity along a thalamus-to-cortex seizure pathway I: new coherence approaches.

Understanding associations in neuronal circuitry is critical for tracing epilepsy pathways. Two new methods of measuring coherence between field potentials and EEG channels are proposed for modeling the level of linear association between channels during epileptic seizures. These methods rely upon modeling the repetitive clonic seizure activity as a sum of sinusoids with varying degrees of phase locking. Estimating the amplitude of sinusoids from correlation and cross-correlation time domain data, we can find the coherences from a ratio of these amplitudes. One method utilizes amplitude finding from the multiple signal classification (MUSIC) technique. The other method uses alterations in amplitude of individual sinusoids and their ratios in a matrix pencil equation formed from cross- and auto-correlation matrices. The corresponding generalized eigenvalues of these equations form the coherence ratios. This utilizes the estimation of signal parameters using rotational invariance techniques (ESPRIT) algorithm to arrive at coherence amplitude ratios. Simulations illustrate that the MUSIC method provides better noise immunity as it out-performs the conventional Fourier transform-based method for coherence estimation. Both coherence estimators reflect presence of sinusoidal components that are propagated or not propagated along a particular transmission pathway. We illustrate the value of both methods by examining the strength of correlation between seizure EEG from specific thalamic nuclei and cortex in a rodent model of generalized epilepsy. The pentylenetetrazol (PTZ) chemoconvulsant model in rats reflects selective activation of the anterior thalamic nucleus. Using both methods, this neuronal element has much larger coherence with cortex than another thalamic region, the posterior thalamus (p < 0.05). These methods isolate the unique contribution of anterior thalamus in the formation of an ictal network and corroborate earlier conventional or periodogram techniques.