Structure and Topology Dynamics of Hyper-Frequency Networks during Rest and Auditory Oddball Performance

Hyper-brain hyper-frequency network topology dynamics when playing guitar in quartet

Ensemble music performance is a highly coordinated form of social behavior requiring not only precise motor actions but also synchronization of different neural processes both within and between the brains of ensemble players. In previous analyses, which were restricted to within-frequency coupling (WFC), we showed that different frequencies participate in intra- and inter-brain coordination, exhibiting distinct network topology dynamics that underlie coordinated actions and interactions. However, many of the couplings both within and between brains are likely to operate across frequencies. Hence, to obtain a more complete picture of hyper-brain interaction when musicians play the guitar in a quartet, cross-frequency coupling (CFC) has to be considered as well. Furthermore, WFC and CFC can be used to construct hyper-brain hyper-frequency networks (HB-HFNs) integrating all the information flows between different oscillation frequencies, providing important details about ensemble interaction in terms of network topology dynamics (NTD). Here, we reanalyzed EEG (electroencephalogram) data obtained from four guitarists playing together in quartet to explore changes in HB-HFN topology dynamics and their relation to acoustic signals of the music. Our findings demonstrate that low-frequency oscillations (e.g., delta, theta, and alpha) play an integrative or pacemaker role in such complex networks and that HFN topology dynamics are specifically related to the guitar quartet playing dynamics assessed by sound properties. Simulations by link removal showed that the HB-HFN is relatively robust against loss of connections, especially when the strongest connections are preserved and when the loss of connections only affects the brain of one guitarist. We conclude that HB-HFNs capture neural mechanisms that support interpersonally coordinated action and behavioral synchrony.

A phase-shifting anterior-posterior network organizes global phase relations

Prior research has identified a variety of task-dependent networks that form through inter-regional phase-locking of oscillatory activity that are neural correlates of specific behaviors. Despite ample knowledge of task-specific functional networks, general rules governing global phase relations have not been investigated. To discover such general rules, we focused on phase modularity, measured as the degree to which global phase relations in EEG comprised distinct synchronized clusters interacting with one another at large phase lags. Synchronized clusters were detected with a standard community-detection algorithm, and the degree of phase modularity was quantified by the index q. Notably, we found that the mechanism controlling phase modularity is remarkably simple. A network comprising anterior-posterior long-distance connectivity coherently shifted phase relations from low-angles (|Δθ| < π/4) in low-modularity states (bottom 5% in q) to high-angles (|Δθ| > 3π/4) in high-modularity states (top 5% in q), accounting for fluctuations in phase modularity. This anterior-posterior network may play a fundamental functional role as (1) it controls phase modularity across a broad range of frequencies (3-50 Hz examined) in different behavioral conditions (resting with the eyes closed or watching a silent nature video) and (2) neural interactions (measured as power correlations) in beta-to-gamma bands were consistently elevated in high-modularity states. These results may motivate future investigations into the functional roles of phase modularity as well as the anterior-posterior network that controls it.

Neural Synchrony and Network Dynamics in Social Interaction: A Hyper-Brain Cell Assembly Hypothesis

Mounting neurophysiological evidence suggests that interpersonal interaction relies on continual communication between cell assemblies within interacting brains and continual adjustments of these neuronal dynamic states between the brains. In this Hypothesis and Theory article, a Hyper-Brain Cell Assembly Hypothesis is suggested on the basis of a conceptual review of neural synchrony and network dynamics and their roles in emerging cell assemblies within the interacting brains. The proposed hypothesis states that such cell assemblies can emerge not only within, but also between the interacting brains. More precisely, the hyper-brain cell assembly encompasses and integrates oscillatory activity within and between brains, and represents a common hyper-brain unit, which has a certain relation to social behavior and interaction. Hyper-brain modules or communities, comprising nodes across two or several brains, are considered as one of the possible representations of the hypothesized hyper-brain cell assemblies, which can also have a multidimensional or multilayer structure. It is concluded that the neuronal dynamics during interpersonal interaction is brain-wide, i.e., it is based on common neuronal activity of several brains or, more generally, of the coupled physiological systems including brains.

Spatiotemporal dynamics of maximal and minimal EEG spectral power

Oscillatory neural activities are prevalent in the brain with their phase realignment contributing to the coordination of neural communication. Phase realignments may have especially strong (or weak) impact when neural activities are strongly synchronized (or desynchronized) within the interacting populations. We report that the spatiotemporal dynamics of strong regional synchronization measured as maximal EEG spectral power-referred to as activation-and strong regional desynchronization measured as minimal EEG spectral power-referred to as suppression-are characterized by the spatial segregation of small-scale and large-scale networks. Specifically, small-scale spectral-power activations and suppressions involving only 2-7% (1-4 of 60) of EEG scalp sites were prolonged (relative to stochastic dynamics) and consistently co-localized in a frequency specific manner. For example, the small-scale networks for θ, α, β1, and β2 bands (4-30 Hz) consistently included frontal sites when the eyes were closed, whereas the small-scale network for γ band (31-55 Hz) consistently clustered in medial-central-posterior sites whether the eyes were open or closed. Large-scale activations and suppressions involving over 17-30% (10-18 of 60) of EEG sites were also prolonged and generally clustered in regions complementary to where small-scale activations and suppressions clustered. In contrast, intermediate-scale activations and suppressions (involving 7-17% of EEG sites) tended to follow stochastic dynamics and were less consistently localized. These results suggest that strong synchronizations and desynchronizations tend to occur in small-scale and large-scale networks that are spatially segregated and frequency specific. These synchronization networks may broadly segregate the relatively independent and highly cooperative oscillatory processes while phase realignments fine-tune the network configurations based on behavioral demands.

Probabilistic, entropy-maximizing control of large-scale neural synchronization

Oscillatory neural activity is dynamically controlled to coordinate perceptual, attentional and cognitive processes. On the macroscopic scale, this control is reflected in the U-shaped deviations of EEG spectral-power dynamics from stochastic dynamics, characterized by disproportionately elevated occurrences of the lowest and highest ranges of power. To understand the mechanisms that generate these low- and high-power states, we fit a simple mathematical model of synchronization of oscillatory activity to human EEG data. The results consistently indicated that the majority (~95%) of synchronization dynamics is controlled by slowly adjusting the probability of synchronization while maintaining maximum entropy within the timescale of a few seconds. This strategy appears to be universal as the results generalized across oscillation frequencies, EEG current sources, and participants (N = 52) whether they rested with their eyes closed, rested with their eyes open in a darkened room, or viewed a silent nature video. Given that precisely coordinated behavior requires tightly controlled oscillatory dynamics, the current results suggest that the large-scale spatial synchronization of oscillatory activity is controlled by the relatively slow, entropy-maximizing adjustments of synchronization probability (demonstrated here) in combination with temporally precise phase adjustments (e.g., phase resetting generated by sensorimotor interactions). Interestingly, we observed a modest but consistent spatial pattern of deviations from the maximum-entropy rule, potentially suggesting that the mid-central-posterior region serves as an "entropy dump" to facilitate the temporally precise control of spectral-power dynamics in the surrounding regions.

EEG state-trajectory instability and speed reveal global rules of intrinsic spatiotemporal neural dynamics

Spatiotemporal dynamics of EEG/MEG (electro-/magneto-encephalogram) have typically been investigated by applying time-frequency decomposition and examining amplitude-amplitude, phase-phase, or phase-amplitude associations between combinations of frequency bands and scalp sites, primarily to identify neural correlates of behaviors and traits. Instead, we directly extracted global EEG spatiotemporal dynamics as trajectories of k-dimensional state vectors (k = the number of estimated current sources) to investigate potential global rules governing neural dynamics. We chose timescale-dependent measures of trajectory instability (approximately the 2^nd temporal derivative) and speed (approximately the 1^st temporal derivative) as state variables, that succinctly characterized trajectory forms. We compared trajectories across posterior, central, anterior, and lateral scalp regions as the current sources under those regions may serve distinct functions. We recorded EEG while participants rested with their eyes closed (likely engaged in spontaneous thoughts) to investigate intrinsic neural dynamics. Some potential global rules emerged. Time-averaged trajectory instability from all five regions tightly converged (with their variability minimized) at the level of generating nearly unconstrained but slightly conservative turns (~100° on average) on the timescale of ~25 ms, suggesting that spectral-amplitude profiles are globally adjusted to maintain this convergence. Further, within-frequency and cross-frequency phase relations appear to be independently coordinated to reduce average trajectory speed and increase the variability in trajectory speed and instability in a relatively timescale-invariant manner, and to make trajectories less oscillatory. Future research may investigate the functional relevance of these intrinsic global-dynamics rules by examining how they adjust to various sensory environments and task demands or remain invariant. The current results also provide macroscopic constraints for quantitative modeling of neural dynamics as the timescale dependencies of trajectory instability and speed are relatable to oscillatory dynamics.

Spectral-power associations reflect amplitude modulation and within-frequency interactions on the sub-second timescale and cross-frequency interactions on the seconds timescale

We investigated the global structure of intrinsic cross-frequency dynamics by systematically examining power-based temporal associations among a broad range of oscillation frequencies both within and across EEG-based current sources (sites). We focused on power-based associations that could reveal unique timescale dependence independently of interacting frequencies. Large spectral-power fluctuations across all sites occurred at two characteristic timescales, sub-second and seconds, yielding distinct patterns of cross-frequency associations. On the fast sub-second timescale, within-site (local) associations were consistently between pairs of β—γ frequencies differing by a constant Δf (particularly Δf ~ 10 Hz at posterior sites and Δf ~ 16 Hz at lateral sites) suggesting that higher-frequency oscillations are organized into Δf amplitude-modulated packets, whereas cross-site (long-distance) associations were all within-frequency (particularly in the >30 Hz and 6–12 Hz ranges, suggestive of feedforward and feedback interactions). On the slower seconds timescale, within-site (local) associations were characterized by a broad range of frequencies selectively associated with ~10 Hz at posterior sites and associations among higher (>20 Hz) frequencies at lateral sites, whereas cross-site (long-distance) associations were characterized by a broad range of frequencies at posterior sites selectively associated with ~10 Hz at other sites, associations among higher (>20 Hz) frequencies among lateral and anterior sites, and prevalent associations at ~10 Hz. Regardless of timescale, within-site (local) cross-frequency associations were weak at anterior sites indicative of frequency-specific operations. Overall, these results suggest that the fast sub-second-timescale coordination of spectral power is limited to local amplitude modulation and insulated within-frequency long-distance interactions (likely feedforward and feedback interactions), while characteristic patterns of cross-frequency interactions emerge on the slower seconds timescale. The results also suggest that the occipital α oscillations play a role in organizing higher-frequency oscillations into ~10 Hz amplitude-modulated packets to communicate with other regions. Functional implications of these timescale-dependent cross-frequency associations await future investigations.

Variation of functional brain connectivity in epileptic seizures: an EEG analysis with cross-frequency phase synchronization

Frequency coupling in nervous system is believed to be associated with normal and impaired brain functions. However, most of the existing experiments have been concentrated on the coupling strength within frequency bands, while the coupling strength between different bands is ignored. In this work, we apply phase synchronization index (PSI) to investigate the cross-frequency coupling (CFC) of Electroencephalogram (EEG) signals. The PSI matrixes for the multi-channel EEG signals are calculated from interictal to ictal period in each sliding time window. The results show that CFC changes obviously once seizure occurs between the different bands, and such alteration is earlier than the appearance of clinical symptoms in seizure. Considering the similar role of the within-frequency coupling (WFC), we further reconstruct multi-layered brain networks, including CFC networks and WFC networks. The graph metrics are applied to investigate the variation of network structure of the epileptic brain. Significant decreases/increases of the local/global efficiency are found in δ-β, δ-α, θ-α and δ-θ bands from the CFC network, while WFC network shows a significant decline in the local efficiency in θ and α bands. These findings suggest that CFC may provide a new perspective to observe the alteration of brain structure when seizure occurs, and the investigation of functional connectivity across the full frequency spectrum can give us a deeper understanding of epileptic brains.

Network topology dynamics of circulating biomarkers and cognitive performance in older Cytomegalovirus-seropositive or -seronegative men and women

Background

Cytokines are signaling molecules operating within complex cascade patterns and having exceptional modulatory functions. They impact various physiological processes such as neuroendocrine and metabolic interactions, neurotrophins’ metabolism, neuroplasticity, and may affect behavior and cognition. In our previous study, we found that sex and Cytomegalovirus (CMV)-serostatus may modulate levels of circulating pro- and anti-inflammatory cytokines, metabolic factors, immune cells, and cognitive performance, as well as associations between them.

Results

In the present study, we used a graph-theoretical approach to investigate the network topology dynamics of 22 circulating biomarkers and 11 measures of cognitive performance in 161 older participants recruited to undergo a six-months training intervention. For network construction, we applied coefficient of determination (R²) that was calculated for all possible pairs of variables (N = 33) in four groups (CMV⁻ men and women; CMV⁺ men and women). Network topology has been evaluated by clustering coefficient (CC) and characteristic path length (CPL) as well as local (E_local) and global (E_global) efficiency, showing the degree of network segregation (CC and E_local) and integration (CPL and E_global). We found that networks under consideration showed small-world networks properties with more random characteristics. Mean CC, as well as local and global efficiency were highest and CPL shortest in CMV⁻ males (having lowest inflammatory status and highest cognitive performance). CMV⁻ and CMV⁺ females did not show any significant differences. Modularity analyses showed that the networks exhibit in all cases highly differentiated modular organization (with Q-value ranged between 0.397 and 0.453).

Conclusions

In this work, we found that segregation and integration properties of the network were notably stronger in the group with balanced inflammatory status. We were also able to confirm our previous findings that CMV-infection and sex modulate multiple circulating biomarkers and cognitive performance and that balanced inflammatory and metabolic status in elderly contributes to better cognitive functioning. Thus, network analyses provide a useful strategy for visualization and quantitative description of multiple interactions between various circulating pro- and anti-inflammatory biomarkers, hormones, neurotrophic and metabolic factors, immune cells, and measures of cognitive performance and can be in general applied for analyzing interactions between different physiological systems.

Lifespan Changes in Network Structure and Network Topology Dynamics During Rest and Auditory Oddball Performance

Behavioral and physiological evidence suggests that developmental changes lead to enhanced cortical differentiation and integration through maturation and learning, and that senescent changes during aging result in dedifferentiation and reduced cortical specialization of neural cell assemblies. We used electroencephalographic (EEG) recordings to evaluate network structure and network topology dynamics during rest with eyes closed and open, and during auditory oddball task across the lifespan. For this evaluation, we constructed a hyper-frequency network (HFN) based on within- and cross-frequency coupling (WFC and CFC, respectively) at 10 oscillation frequencies ranging between 2 and 20 Hz. We found that WFC increased monotonously across the lifespan, whereas CFC showed a U-shaped relationship. These changes in WFC and CFC strengths coevolve with changes in network structure and network topology dynamics, namely the magnitude of graph-theoretical topology measures increased linearly with age (except for characteristic path length, which is going shorter), while their standard deviation showed an inverse U-shaped relationship with a peak in young adults. Temporal as well as structural or nodal similarity of network topology (with some exceptions) seems to coincide with variability changes, i.e., stronger variability is related to higher similarity between consecutive time windows or nodes. Furthermore, network complexity measures showed different lifespan-related patterns, which depended on the balance of WFC and CFC strengths. Both variability and complexity of HFNs were strongly related to the perceptual speed scores. Finally, investigation of the modular organization of the networks revealed higher number of modules and stronger similarity of community structures across time in young adults as compared with children and older adults. We conclude that network variability and complexity measures reflect temporal and structural topology changes in the functional organization and reorganization of neuronal cell assemblies across the lifespan.

Hyper-Frequency Network Topology Changes During Choral Singing

Choral singing requires the coordination of physiological subsystems within and across individuals. Previously, we suggested that the choir functions as a superordinate system that imposes boundary conditions on the dynamic features of the individual singers and found reliable differences in the network topography by analyzing within- and cross-frequency couplings (WFC and CFC, respectively). Here, we further refine our analyses to investigate hyper-frequency network (HFN) topology structures (i.e., the layout or arrangement of connections) using a graph-theoretical approach. In a sample of eleven singers and one conductor engaged in choral singing (aged between 23 and 56 years, and including five men and seven women), we calculated phase coupling (WFC and CFC) between respiratory, cardiac, and vocalizing subsystems across ten frequencies of interest. All these couplings were used for construction of HFN with nodes being a combination of frequency components and subsystems across choir participants. With regard to the network topology measures, we found that clustering coefficients (CCs) as well as local and global efficiency were highest and characteristic path lengths, correspondingly, were shortest when the choir sang a canon in parts as compared to singing it in unison. Furthermore, these metrics revealed a significant relationship to individual heart rate, as an indicator of arousal, and to an index of heart rate variability indicated by the LF/HF ratio (low and high frequency, respectively), and reflecting the balance between sympathetic and parasympathetic activity. In addition, we found that the CC and local efficiency for groups singing the same canon part were higher than for groups of singers constructed randomly post hoc, indicating stronger neighbor–neighbor connections in the former. We conclude that network topology dynamics are a crucial determinant of group behavior and may represent a potent biomarker for social interaction.