Spectral Synchronicity in Brain Signals

Brain activity following stimulus presentation and during resting state are often the result of highly coordinated responses of large numbers of neurons both locally (within each region) and globally (across different brain regions). Coordinated activity of neurons can give rise to oscillations which are captured by electroencephalograms (EEG). Most studies on resting state are based on functional magnetic resonance imaging data. In this paper, we examine EEGs as this is the primary data being used by our collaborators who are studying coordination of neuronal response during the execution of tasks such as learning, and memory formation, retention and retrieval. Developing new methods that address this research question is important because disruptions in coordination have been observed in a number of neurological and mental diseases such as schizophrenia, epilepsy and Alzheimer’s disease. In this paper, we develop the spectral merger clustering (SMC) method that identifies synchronized brain regions during resting state in a sense that these regions share similar oscillations or waveforms. The SMC method, produces clusters of EEGs which serve as a proxy for segmenting the brain cortical surface since the EEGs capture neuronal activity over a locally distributed region on the cortical surface. The extent of desynchronicity between a pair of EEGs is measured using the total variation distance (TVD) which gives the largest possible difference between the spectral densities of the pair of EEGs. We considered the spectral merger algorithm for clustering EEGs, which updates the spectral estimate of the cluster from a weighted average of the spectral estimate obtained from each EEG in the cluster. Numerical experiments suggest that the SMC method performs very well in producing the correct clusters. When applied to resting state EEG data, the SMC method gave results that partly confirms the segmentation based on the anatomy of ∗Centro de Investigación en Matemáticas, Guanajuato, Gto, México. ‡Department of Statistics, University of California, Irvine, USA. †UC Irvine Space-Time Modeling Group. 1 ar X iv :1 50 7. 05 01 8v 1 [ st at .A P] 1 7 Ju l 2 01 5 the cortical surface. In addition, the method showed how some regions, though not contiguously connected on the cortical surface, are spectrally synchronized during resting state. Moreover, the method demonstrates that brain organization, as expressed in cluster formation, evolves over resting state.