Xi rhythms: decoding neural oscillations to create full brain high resolution spectra parametric mapping

Neural oscillations excitability shape sensory, motor, and cognitive processes of the brain operation. To quantify the spectrum of brain magnetic and electrical recordings has become the main methodology to study neural oscillations. However, there is still lacking a valid approach, although the literatures on the spectrum decomposition is vast. In this work, we fit the neural spectrum by means of the Expectation Maximization algorithm, where the E step turns into a Winner filtering to separate multiple components and the M step is to fit each component by minimizing the smoothness penalized Whittle likelihood and shape-restricted regression, say, monotonicity, that is able to fit the diverse shape of each component. The decomposition allows characterizing the oscillation amplitude, resonance frequency, bandwidth, skewness, kurtosis, and slope of each component. This approach is termed as Xi rhythms, with Xi and rhythms standing for the background activity and multiple peaks. We apply it to: 1) multinational EEG database consisting of 535 subjects to create the quantitative spectrum norms (QSN); 2) large sample intracranial EEG (iEEG) dataset to infer the oscillations from recorded region to unrecorded areas within one subject and over inter-individuals and create the full brain high resolution statistical spectra parametric mapping. The statistical spectrum parameter mapping of iEEG promisingly provides an atlas and creates a norm for neural oscillations and quantitative electrophysiology study which can gain us more insightful understanding to brain dynamics, cognitive process and mental disorders.