A new method to estimate time delays between EEG signals applied to beta activity of the olfactory cortical areas

A method based on coherence and phase spectra was developed to characterize the transmission of signals through neural networks that were assumed to have linear filter properties. The system is thought to consist of a frequency independent delay in series with a network that gives rise to a frequency dependent lag, the so-called minimum phase shift. The latter was estimated from the gain of the transfer function by means of Hilbert transform pairs. By subtracting the minimum phase shift from the phase differences between input and output, a corrected phase spectrum was obtained that represents the frequency independent delay. The slope of this spectrum was calculated and converted into the time delay. This method was applied to EEG signals recorded from different parts of the olfactory basal forebrain structures of the cat, in order to determine time delays for the beta activity. The results showed that the beta activity was propagated in a rostro-caudal direction. Along this rostro-caudal axis the conduction velocity slowed down from approximately 3 m/sec for the pathways between olfactory bulb and prepyriform cortex to 0.5 m/sec within the EC. These findings were compared to estimates of the conduction velocities in the lateral olfactory tract fibres and collaterals using transient responses. It is concluded that, to a first approximation, the linear approach gives physiologically meaningful results.