We describe an analysis method that characterizes the correlation between coupled time-series functions by their frequencies and phases. It provides a unified framework for simultaneous assessment of frequency and latency of a coupled time-series. The analysis is demonstrated on resting-state functional MRI data of 34 healthy subjects. Interactions between fMRI time-series are represented by cross-correlation (with time-lag) functions. A general linear model is used on the cross-correlation functions to obtain the frequencies and phase-differences of the original time-series. We define symmetric, antisymmetric and asymmetric cross-correlation functions that correspond respectively to in-phase, 90° out-of-phase and any phase difference between a pair of time-series, where the last two were never introduced before. Seed maps of the motor system were calculated to demonstrate the strength and capabilities of the analysis. Unique types of functional connections, their dominant frequencies and phase-differences have been identified. The relation between phase-differences and time-delays is shown. The phase-differences are speculated to inform transfer-time and/or to reflect a difference in the hemodynamic response between regions that are modulated by neurotransmitters concentration. The analysis can be used with any coupled functions in many disciplines including electrophysiology, EEG or MEG in neuroscience.

Department of Neurology and Center of Clinical Neuroscience 1st Faculty of Medicine and General University Hospital Charles University Prague Prague Czech Republic

Department of Radiology Na Homolce Hospital Prague Czech Republic

Edmond and Lily Safra Center for Brain Sciences The Hebrew University of Jerusalem Jerusalem Israel

MRI Lab The Human Biology Research Center Department of Medical Biophysics Hadassah Hebrew University Medical Center Jerusalem Israel

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Sci Rep. 2017 Apr 10;7:45803. doi: 10.1038/srep45803. PubMed

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