Generalized Cross-Frequency Decomposition: A Method for the Extraction of Neuronal Components Coupled at Different Frequencies

Electroencephalography Alpha Traveling Waves as Early Predictors of Treatment Response in Major Depressive Episodes: Insights from Intermittent Photic Stimulation

Background: Early evaluation of treatment efficacy in adolescents and young adults with major depressive episodes (MDEs) remains a clinical challenge, often delaying timely therapeutic adjustments. Electroencephalography (EEG) alpha traveling waves, particularly those elicited by intermittent photic stimulation (IPS), may serve as biomarkers reflecting neural dynamics. This study aimed to investigate whether IPS-induced alpha traveling waves could predict early treatment outcomes in transitional-aged youth with MDEs. Methods: We recorded EEG signals from 119 patients aged 16-24 years at admission, prior to a standardized two-week treatment regimen. IPS was applied using multiple stimulus frequencies, and alpha traveling waves were analyzed in terms of directionality (forward vs. backward) and hemispheric lateralization. Results: Alpha traveling wave amplitudes varied across individuals, depending on stimulus frequency and hemisphere. Notably, a higher amplitude of backward alpha traveling waves at 10 Hz IPS in the left hemisphere significantly predicted positive early treatment response. In contrast, forward waves and right hemisphere responses did not show predictive value. Conclusions: IPS-induced backward alpha traveling waves in the left hemisphere may represent promising EEG biomarkers for early prediction of treatment efficacy in youth with MDEs. These findings offer a potential neurophysiological tool to support personalized treatment strategies and inform future clinical applications in adolescent and young adult depression.

Cross-frequency cortex-muscle interactions are abnormal in young people with dystonia

Sensory processing and sensorimotor integration are abnormal in dystonia, including impaired modulation of beta-corticomuscular coherence. However, cortex-muscle interactions in either direction are rarely described, with reports limited predominantly to investigation of linear coupling, using corticomuscular coherence or Granger causality. Information-theoretic tools such as transfer entropy detect both linear and non-linear interactions between processes. This observational case-control study applies transfer entropy to determine intra- and cross-frequency cortex-muscle coupling in young people with dystonia/dystonic cerebral palsy. Fifteen children with dystonia/dystonic cerebral palsy and 13 controls, aged 12-18 years, performed a grasp task with their dominant hand. Mechanical perturbations were provided by an electromechanical tapper. Bipolar scalp EEG over contralateral sensorimotor cortex and surface EMG over first dorsal interosseous were recorded. Multi-scale wavelet transfer entropy was applied to decompose signals into functional frequency bands of oscillatory activity and to quantify intra- and cross-frequency coupling between brain and muscle. Statistical significance against the null hypothesis of zero transfer entropy was established, setting individual 95% confidence thresholds. The proportion of individuals in each group showing significant transfer entropy for each frequency combination/direction was compared using Fisher's exact test, correcting for multiple comparisons. Intra-frequency transfer entropy was detected in all participants bidirectionally in the beta (16-32 Hz) range and in most participants from EEG to EMG in the alpha (8-16 Hz) range. Cross-frequency transfer entropy across multiple frequency bands was largely similar between groups, but a specific coupling from low-frequency EMG to beta EEG was significantly reduced in dystonia [P = 0.0061 (corrected)]. The demonstration of bidirectional cortex-muscle communication in dystonia emphasizes the value of transfer entropy for exploring neural communications in neurological disorders. The novel finding of diminished coupling from low-frequency EMG to beta EEG in dystonia suggests impaired cortical feedback of proprioceptive information with a specific frequency signature that could be relevant to the origin of the excessive low-frequency drive to muscle.

Detection of Cross-Frequency Coupling Between Brain Areas: An Extension of Phase Linearity Measurement

The current paper proposes a method to estimate phase to phase cross-frequency coupling between brain areas, applied to broadband signals, without any a priori hypothesis about the frequency of the synchronized components. N:m synchronization is the only form of cross-frequency synchronization that allows the exchange of information at the time resolution of the faster signal, hence likely to play a fundamental role in large-scale coordination of brain activity. The proposed method, named cross-frequency phase linearity measurement (CF-PLM), builds and expands upon the phase linearity measurement, an iso-frequency connectivity metrics previously published by our group. The main idea lies in using the shape of the interferometric spectrum of the two analyzed signals in order to estimate the strength of cross-frequency coupling. We first provide a theoretical explanation of the metrics. Then, we test the proposed metric on simulated data from coupled oscillators synchronized in iso- and cross-frequency (using both Rössler and Kuramoto oscillator models), and subsequently apply it on real data from brain activity. Results show that the method is useful to estimate n:m synchronization, based solely on the phase of the signals (independently of the amplitude), and no a-priori hypothesis is available about the expected frequencies.

Harmoni: a Method for Eliminating Spurious Interactions due to the Harmonic Components in Neuronal Data

Cross-frequency synchronization (CFS) has been proposed as a mechanism for integrating spatially and spectrally distributed information in the brain. However, investigating CFS in Magneto- and Electroencephalography (MEG/EEG) is hampered by the presence of spurious neuronal interactions due to the non-sinusoidal waveshape of brain oscillations. Such waveshape gives rise to the presence of oscillatory harmonics mimicking genuine neuronal oscillations. Until recently, however, there has been no methodology for removing these harmonics from neuronal data. In order to address this long-standing challenge, we introduce a novel method (called HARMOnic miNImization - Harmoni) that removes the signal components which can be harmonics of a non-sinusoidal signal. Harmoni's working principle is based on the presence of CFS between harmonic components and the fundamental component of a non-sinusoidal signal. We extensively tested Harmoni in realistic EEG simulations. The simulated couplings between the source signals represented genuine and spurious CFS and within-frequency phase synchronization. Using diverse evaluation criteria, including ROC analyses, we showed that the within- and cross-frequency spurious interactions are suppressed significantly, while the genuine activities are not affected. Additionally, we applied Harmoni to real resting-state EEG data revealing intricate remote connectivity patterns which are usually masked by the spurious connections. Given the ubiquity of non-sinusoidal neuronal oscillations in electrophysiological recordings, Harmoni is expected to facilitate novel insights into genuine neuronal interactions in various research fields, and can also serve as a steppingstone towards the development of further signal processing methods aiming at refining within- and cross-frequency synchronization in electrophysiological recordings.

Cross-frequency phase coupling of brain oscillations and relevance attribution as saliency detection in abstract reasoning

reasoning is associated with the ability to detect relations among objects, ideas, events. It underlies the understanding of other individuals' thoughts and intentions. In natural settings, individuals have to infer relevant associations that have proven to be reliable or precise predictors. Salience theory suggests that the attribution of meaning to stimulus depends on their contingency, saliency, and relevance to adaptation. So far, subjective estimates of relevance have mostly been explored in motivation and implicit learning. Mechanisms underlying formation of associations in abstract thinking with regard to their subjective relevance, or salience, are not clear. Applying novel computational methods, we investigated relevance detection in categorization tasks in 17 healthy individuals. Two models of relevance detection were developed: a conventional one with nouns from the same semantic category, an aberrant one based on an insignificant common feature. Control condition introduced non-related words. The participants were to detect either a relevant principle or an insignificant feature to group presented words. In control condition they inferred that the stimuli were irrelevant to any grouping idea. Cross-frequency phase coupling analysis revealed statistically distinct patterns of synchronization representing search and decision in the models of normal and aberrant relevance detection. Significantly distinct frontotemporal functional networks with central and parietal components in the theta and alpha frequency bands may reflect differences in relevance detection.

Nonlinear interaction decomposition (NID): A method for separation of cross-frequency coupled sources in human brain

Cross-frequency coupling (CFC) between neuronal oscillations reflects an integration of spatially and spectrally distributed information in the brain. Here, we propose a novel framework for detecting such interactions in Magneto- and Electroencephalography (MEG/EEG), which we refer to as Nonlinear Interaction Decomposition (NID). In contrast to all previous methods for separation of cross-frequency (CF) sources in the brain, we propose that the extraction of nonlinearly interacting oscillations can be based on the statistical properties of their linear mixtures. The main idea of NID is that nonlinearly coupled brain oscillations can be mixed in such a way that the resulting linear mixture has a non-Gaussian distribution. We evaluate this argument analytically for amplitude-modulated narrow-band oscillations which are either phase-phase or amplitude-amplitude CF coupled. We validated NID extensively with simulated EEG obtained with realistic head modelling. The method extracted nonlinearly interacting components reliably even at SNRs as small as -15 dB. Additionally, we applied NID to the resting-state EEG of 81 subjects to characterize CF phase-phase coupling between alpha and beta oscillations. The extracted sources were located in temporal, parietal and frontal areas, demonstrating the existence of diverse local and distant nonlinear interactions in resting-state EEG data. All codes are available publicly via GitHub.

Predicting States of Abstract Reasoning Using EEG Functional Connectivity Markers

High order abstract reasoning is impaired in patients suffering from mental disorders especially from schizophrenia. Thought and language disorders typical of schizophrenia are presumably connected with the aberrant ability to filter out irrelevant associations. We hypothesized that EEG biomarkers in healthy population could be detected, extracted and validated with regard to the ability to abstract a general principle underlying presented words while ignoring irrelevant associations and retaining only relevant ones. We developed three models of abstract reasoning: a direct generalization presented by nouns from the same semantic category, a latent association based on a loose relation between the presented words, and no associations introduced by non-related words. In the present EEG study 17 healthy participants solved tasks trying to figure out a general principle in a group of words. Subsequently, we carried out a functional connectivity analysis in order to restore synchronous neuronal interactions in the theta-alpha frequency range. We used the obtained spatial patters restored individually and relevant phase locking values (PLVs) as features for the Support Vector Machine classifier with Gaussian kernel. The accuracy rating validated on an independent sample made up 62.5% which is a promising result if inter-subject variability in cognitive processing is taken into account. Being validated on the same sample, the accuracy reached 82%. The results indicate that spatial patterns of functional connectivity and PLVs can be used as predictors of types of abstract reasoning.