Phase Synchrony (PS) and coherence analyses of stochastic time series - tools to discover brain tissue pathways traveled by electrical signals - are considered for the specific purpose of processing of the electroencephalogram (EEG).
We propose the Phase Synchrony Processor (PSP), as a tool for implementing phase synchrony analysis, and examine its properties on the basis of known signals. Long observation times and wide filter bandwidths can decrease bias in PS estimates. The value of PS is affected by the difference in frequency of the sequences being analyzed and can be related to that frequency difference by the periodic sinc function.
PS analysis of the EEG shows that the average PS is higher - for a number of electrode pairs - for non-ADHD than for ADHD participants. The difference is more pronounced in the \delta rhythm (0-3 Hz) and in the \gamma rhythm (30-50 Hz) PS. The Euclidean classifier with electrode masking yields 66 % correct classification on average for ADHD and non-ADHD subjects using the \delta and \gamma-1 rhythms.
We observed that the average \gamma-1 rhythm PS is higher for the eyes closed condition than for the eyes open condition. The latter may potentially be used for vigilance monitoring. The Euclidean discriminator with electrode masking shows an average percentage of correct classification of 78 % between the eyes open and eyes closed subject conditions.
We develop a model for a pair of EEG electrodes and a model-based MS coherence estimator aimed at processing short (i.e. 20 samples) EEG frames. We verify that EEG sequences can be modeled as AR(3) processes degraded by additive white noise with an average SNR of approximately 11-12 dB.
Application of the MS coherence estimator to the EEG suggests that MS coherence is generally higher for non-ADHD individuals than for ADHD participants when evaluated for the \theta rhythm of EEG. Also, MS coherence is consistently higher for ADHD subjects than for the majority of non-ADHD individuals when computed for the low end of the \delta rhythm (i.e. below 1 Hz).
ADHD produces more measurable effects in the frontal lobe EEG and for participants performing attention intensive tasks.