Network analysis is increasingly advancing the field of neuroimaging. Neural networks are generally constructed from pairwise interactions with an assumption of linear relations between them. Here, a high-order statistical framework to calculate directed functional connectivity among multiple regions, using wavelet analysis and spectral coherence has been presented. The mathematical expression for 4 regions was derived and used to characterize a quartet of regions as a linear, combined (nonlinear), or disconnected network. Phase delays between regions were used to obtain network's temporal hierarchy and directionality. The validity of the mathematical derivation along with the effects of coupling strength and noise on its outcomes were studied by computer simulations of the Kuramoto model. The simulations demonstrated correct directionality for a large range of coupling strength and low sensitivity to Gaussian noise compared with pairwise coherences. The analysis was applied to resting-state fMRI data of 40 healthy young subjects to characterize the ventral visual system, motor system and default mode network (DMN). It was shown that the ventral visual system was predominantly composed of linear networks while the motor system and the DMN were composed of combined (nonlinear) networks. The ventral visual system exhibits its known temporal hierarchy, the motor system exhibits center ↔ out hierarchy and the DMN has dorsal ↔ ventral and anterior ↔ posterior organizations. The analysis can be applied in different disciplines such as seismology, or economy and in a variety of brain data including stimulus-driven fMRI, electrophysiology, EEG, and MEG, thus open new horizons in brain research. Hum Brain Mapp 38:1374-1386, 2017. © 2016 Wiley Periodicals, Inc.

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Depression, anxiety and apathy are distinct neuropsychiatric symptoms that highly overlap in Parkinson’s disease (PD). It remains unknown whether each symptom is uniquely associated with a functional network dysfunction. Here, we examined whether individual differences in each neuropsychiatric symptom predict functional connectivity patterns in PD patients while controlling for all other symptoms and motor function. Resting-state functional connectivity MRI were acquired from 27 PD patients and 29 healthy controls. Widespread reduced functional connectivity was identified in PD patients and explained by either the neuropsychiatric or motor symptoms. Depression in PD predicted increased functional connectivity between the orbitofrontal, hippocampal complex, cingulate, caudate and thalamus. Apathy in PD predicted decreased caudate-thalamus and orbitofrontal-parahippocampal connectivity. Anxiety in PD predicted three distinct types of functional connectivity not described before: (i) increased limbic-orbitofrontal cortex; (ii) decreased limbic-dorsolateral prefrontal cortex and orbitofrontal-dorsolateral prefrontal cortices and (iii) decreased sensorimotor-orbitofrontal cortices. The first two types of functional connectivity suggest less voluntary and more automatic emotion regulation. The last type is argued to be specific to PD and reflect an impaired ability of the orbitofrontal cortex to guide goal-directed motor actions in anxious PD patients.