Functional Connectivity Analysis of Cerebellum Using Spatially Constrained Spectral Clustering.

The human cerebellum contains almost 50% of the neurons in the brain, although its volume does not exceed 10% of the total brain volume. The goal of this study is to derive the functional network of the cerebellum during the resting-state and then compare the ensuing group networks between males and females. Toward this direction, a spatially constrained version of the classic spectral clustering algorithm is proposed and then compared against conventional spectral graph theory approaches, such as spectral clustering, and N-cut, on synthetic data as well as on resting-state fMRI data obtained from the Human Connectome Project (HCP). The extracted atlas was combined with the anatomical atlas of the cerebellum resulting in a functional atlas with 46 regions of interest. As a final step, a gender-based network analysis of the cerebellum was performed using the data-driven atlas along with the concept of the minimum spanning trees. The simulation analysis results confirm the dominance of the spatially constrained spectral clustering approach in discriminating activation patterns under noisy conditions. The network analysis results reveal statistically significant differences in the optimal tree organization between males and females. In addition, the dominance of the left VI lobule in both genders supports the results reported in a previous study of ours. To our knowledge, the extracted atlas comprises the first resting-state atlas of the cerebellum based on HCP data.

Harnessing functional segregation across brain rhythms as a means to detect EEG oscillatory multiplexing during music listening.

OBJECTIVE: Music, being a multifaceted stimulus evolving at multiple timescales, modulates brain function in a manifold way that encompasses not only the distinct stages of auditory perception, but also higher cognitive processes like memory and appraisal. Network theory is apparently a promising approach to describe the functional reorganization of brain oscillatory dynamics during music listening. However, the music induced changes have so far been examined within the functional boundaries of isolated brain rhythms. APPROACH: Using naturalistic music, we detected the functional segregation patterns associated with different cortical rhythms, as these were reflected in the surface electroencephalography (EEG) measurements. The emerged structure was compared across frequency bands to quantify the interplay among rhythms. It was also contrasted against the structure from the rest and noise listening conditions to reveal the specific components stemming from music listening. Our methodology includes an efficient graph-partitioning algorithm, which is further utilized for mining prototypical modular patterns, and a novel algorithmic procedure for identifying 'switching nodes' (i.e. recording sites) that consistently change module during music listening. MAIN RESULTS: Our results suggest the multiplex character of the music-induced functional reorganization and particularly indicate the dependence between the networks reconstructed from the δ and ß H rhythms. This dependence is further justified within the framework of nested neural oscillations and fits perfectly within the context of recently introduced cortical entrainment to music. SIGNIFICANCE: Complying with the contemporary trends towards a multi-scale examination of the brain network organization, our approach specifies the form of neural coordination among rhythms during music listening. Considering its computational efficiency, and in conjunction with the flexibility of in situ electroencephalography, it may lead to novel assistive tools for real-life applications.

Assessment and conceptual remediation of basic calculation skills in elementary school students.

The specific domain model for math disabilities postulates a core number deficit which presents a prime target for remedial interventions. This longitudinal study identified two groups of Grade 3 students based on their basic calculation abilities: students with persistent difficulties through Grade 4 (PD group) and students whose performance improved into the average range (IP group). Baseline data revealed a distinct cognitive profile for students in the PD group featuring predominant deficits in symbolic number processing. A conceptual intervention based on explicit teaching of basic arithmetic procedures was implemented when students attended Grade 5 or 6. Students in the PD group benefited more from the programme, especially in performing written calculations and in multiplication speed. Statement of contribution What is already known on this subject? Most interventions focus on young students' basic arithmetical skills to prevent serious math problems in future. Few interventions target older students who often face persistent math difficulties. These interventions are usually procedural and focus on age-appropriate math skills. What does this study add? A conceptual intervention was implemented to remediate basic calculation deficits at the end of elementary school. The aim was to help students compensate for their gaps in knowledge and motivate them to engage in math activities. Neuropsychological testing of arithmetic abilities revealed difficulties in symbolic number processing.

Math anxiety: Brain cortical network changes in anticipation of doing mathematics.

Following our previous work regarding the involvement of math anxiety (MA) in math-oriented tasks, this study tries to explore the differences in the cerebral networks' topology between self-reported low math-anxious (LMA) and high math-anxious (HMA) individuals, during the anticipation phase prior to a mathematical related experiment. For this reason, multichannel EEG recordings were adopted, while the solution of the inverse problem was applied in a generic head model, in order to obtain the cortical signals. The cortical networks have been computed for each band separately, using the magnitude square coherence metric. The main graph theoretical parameters, showed differences in segregation and integration in almost all EEG bands of the HMAs in comparison to LMAs, indicative of a great influence of the anticipatory anxiety prior to mathematical performance.

Altered cross-frequency coupling in resting-state MEG after mild traumatic brain injury.

Cross-frequency coupling (CFC) is thought to represent a basic mechanism of functional integration of neural networks across distant brain regions. In this study, we analyzed CFC profiles from resting state Magnetoencephalographic (MEG) recordings obtained from 30 mild traumatic brain injury (mTBI) patients and 50 controls. We used mutual information (MI) to quantify the phase-to-amplitude coupling (PAC) of activity among the recording sensors in six nonoverlapping frequency bands. After forming the CFC-based functional connectivity graphs, we employed a tensor representation and tensor subspace analysis to identify the optimal set of features for subject classification as mTBI or control. Our results showed that controls formed a dense network of stronger local and global connections indicating higher functional integration compared to mTBI patients. Furthermore, mTBI patients could be separated from controls with more than 90% classification accuracy. These findings indicate that analysis of brain networks computed from resting-state MEG with PAC and tensorial representation of connectivity profiles may provide a valuable biomarker for the diagnosis of mTBI.

Genetic effects on source level evoked and induced oscillatory brain responses in a visual oddball task.

Stimuli in simple oddball target detection paradigms cause evoked responses in brain potential. These responses are heritable traits, and potential endophenotypes for clinical phenotypes. These stimuli also cause responses in oscillatory activity, both evoked responses phase-locked to stimulus presentation and phase-independent induced responses. Here, we investigate whether phase-locked and phase-independent oscillatory responses are heritable traits. Oscillatory responses were examined in EEG recordings from 213 twin pairs (91 monozygotic and 122 dizygotic twins) performing a visual oddball task. After group Independent Component Analysis (group-ICA) and time-frequency decomposition, individual differences in evoked and induced oscillatory responses were compared between MZ and DZ twin pairs. Induced (phase-independent) oscillatory responses consistently showed the highest heritability (24-55%) compared to evoked (phase-locked) oscillatory responses and spectral energy, which revealed lower heritability at 1-35.6% and 4.5-32.3%, respectively. Since the phase-independent induced response encodes functional aspects of the brain response to target stimuli different from evoked responses, we conclude that the modulation of ongoing oscillatory activity may serve as an additional endophenotype for behavioral phenotypes and psychiatric genetics.

ERP measures of math anxiety: how math anxiety affects working memory and mental calculation tasks?

There have been several attempts to account for the impact of Mathematical Anxiety (MA) on brain activity with variable results. The present study examines the effects of MA on ERP amplitude during performance of simple arithmetic calculations and working memory tasks. Data were obtained from 32 university students as they solved four types of arithmetic problems (one- and two-digit addition and multiplication) and a working memory task comprised of three levels of difficulty (1, 2, and 3-back task). Compared to the Low-MA group, High-MA individuals demonstrated reduced ERP amplitude at frontocentral (between 180-320 ms) and centroparietal locations (between 380-420 ms). These effects were independent of task difficulty/complexity, individual performance, and general state/trait anxiety levels. Results support the hypothesis that higher levels of self-reported MA are associated with lower cortical activation during the early stages of the processing of numeric stimuli in the context of cognitive tasks.

Comparison of brain network models using cross-frequency coupling and attack strategies.

Several neuroimaging studies have suggested that functional brain connectivity networks exhibit "small-world" characteristics, whereas recent studies based on structural data have proposed a "rich-club" organization of brain networks, whereby hubs of high connection density tend to connect among themselves compared to nodes of lower density. In this study, we adopted an "attack strategy" to compare the rich-club and small-world organizations and identify the model that describes best the topology of brain connectivity. We hypothesized that the highest reduction in global efficiency caused by a targeted attack on each model's hubs would reveal the organization that better describes the topology of the underlying brain networks. We applied this approach to magnetoencephalographic data obtained at rest from neurologically intact controls and mild traumatic brain injury patients. Functional connectivity networks were computed using phase-to-amplitude cross-frequency coupling between the δ and ß frequency bands. Our results suggest that resting state MEG connectivity networks follow a rich-club organization.

Simple and difficult mathematics in children: a minimum spanning tree EEG network analysis.

Sensor-level network characteristics associated with arithmetic tasks varying in complexity were estimated using tools from modern network theory. EEG signals from children with math difficulties (MD) and typically achieving controls (NI) were analyzed using minimum spanning tree (MST) indices derived from Phase Lag Index values - a graph method that corrects for comparison bias. Results demonstrated progressive modulation of certain MST parameters with increased task difficulty. These findings were consistent with more distributed network activation in the theta band, and greater network integration (i.e., tighter communication between involved regions) in the alpha band as task demands increased. There was also evidence of stronger intraregional signal inter-dependencies in the higher frequency bands during the complex math task. Although these findings did not differ between groups, several MST parameters were positively correlated with individual performance on psychometric math tasks involving similar operations, especially in the NI group. The findings support the potential utility of MST analyses to evaluate function-related electrocortical reactivity over a wide range of EEG frequencies in children.

A Graph theoretical approach to study the organization of the cortical networks during different mathematical tasks.

The two core systems of mathematical processing (subitizing and retrieval) as well as their functionality are already known and published. In this study we have used graph theory to compare the brain network organization of these two core systems in the cortical layer during difficult calculations. We have examined separately all the EEG frequency bands in healthy young individuals and we found that the network organization at rest, as well as during mathematical tasks has the characteristics of Small World Networks for all the bands, which is the optimum organization required for efficient information processing. The different mathematical stimuli provoked changes in the graph parameters of different frequency bands, especially the low frequency bands. More specific, in Delta band the induced network increases it's local and global efficiency during the transition from subitizing to retrieval system, while results suggest that difficult mathematics provoke networks with higher cliquish organization due to more specific demands. The network of the Theta band follows the same pattern as before, having high nodal and remote organization during difficult mathematics. Also the spatial distribution of the network's weights revealed more prominent connections in frontoparietal regions, revealing the working memory load due to the engagement of the retrieval system. The cortical networks of the alpha brainwaves were also more efficient, both locally and globally, during difficult mathematics, while the fact that alpha's network was more dense on the frontparietal regions as well, reveals the engagement of the retrieval system again. Concluding, this study gives more evidences regarding the interaction of the two core systems, exploiting the produced functional networks of the cerebral cortex, especially for the difficult mathematics.

The brain matures with stronger functional connectivity and decreased randomness of its network.

We investigated the development of the brain's functional connectivity throughout the life span (ages 5 through 71 years) by measuring EEG activity in a large population-based sample. Connectivity was established with Synchronization Likelihood. Relative randomness of the connectivity patterns was established with Watts and Strogatz' (1998) graph parameters C (local clustering) and L (global path length) for alpha (~10 Hz), beta (~20 Hz), and theta (~4 Hz) oscillation networks. From childhood to adolescence large increases in connectivity in alpha, theta and beta frequency bands were found that continued at a slower pace into adulthood (peaking at ~50 yrs). Connectivity changes were accompanied by increases in L and C reflecting decreases in network randomness or increased order (peak levels reached at ~18 yrs). Older age (55+) was associated with weakened connectivity. Semi-automatically segmented T1 weighted MRI images of 104 young adults revealed that connectivity was significantly correlated to cerebral white matter volume (alpha oscillations: r = 33, p<01; theta: r = 22, p<05), while path length was related to both white matter (alpha: max. r = 38, p<001) and gray matter (alpha: max. r = 36, p<001; theta: max. r = 36, p<001) volumes. In conclusion, EEG connectivity and graph theoretical network analysis may be used to trace structural and functional development of the brain.

Surface EEG shows that functional segregation via phase coupling contributes to the neural substrate of mental calculations.

Multichannel EEG traces from healthy subjects are used to investigate the brain's self-organisation tendencies during two different mental arithmetic tasks. By making a comparison with a control-state in the form of a classification problem, we can detect and quantify the changes in coordinated brain activity in terms of functional connectivity. The interactions are quantified at the level of EEG sensors through descriptors that differ over the nature of functional dependencies sought (linear vs. nonlinear) and over the specific form of the measures employed (amplitude/phase covariation). Functional connectivity graphs (FCGs) are analysed with a novel clustering algorithm, and the resulting segregations enter an appropriate discriminant function. The magnitude of the contrast function depends on the frequency-band (θ, α(1), α(2), ß and γ) and the neural synchrony descriptor. We first show that the maximal-contrast corresponds to a phase coupling descriptor and then identify the corresponding spatial patterns that represent best the task-induced changes for each frequency band. The principal finding of this study is that, during mental calculations, phase synchrony plays a crucial role in the segregation into distinct functional domains, and this segregation is the most prominent feature of the brain's self-organisation as this is reflected in sensor space.

An EEG study of brain connectivity dynamics at the resting state.

We investigated the dynamical behavior of resting state functional connectivity using EEG signals. Employing a recently introduced methodology that considers the time variations of phase coupling among signals from different channels, a sequence of functional connectivity graphs (FCGs) was constructed for different frequency bands and analyzed based on graph theoretic tools. In the first stage of analysis, hubs were detected in the FCGs based on local and global efficiency. The probability of each node to be identified as a hub was estimated. This defined a topographic function that showed widespread distribution with prominence over the frontal brain regions for both local and global efficiency. Hubs consistent across time were identified via a summarization technique and found to locate over forehead. In the second stage of analysis, the modular structure of each single FCG was delineated. The derived time-dependent signatures of functional structure were compared in a systematic way revealing fluctuations modulated by frequency. Interestingly, the evolution of functional connectivity can be described via abrupt transitions between states, best described as short-lasting bimodal functional segregations. Based on a distance function that compares clusterings, we discovered that these segregations are recurrent. Entropic measures further revealed that the apparent fluctuations are subject to intrinsic constraints and that order emerges from spatially extended interactions.

A novel symbolization scheme for multichannel recordings with emphasis on phase information and its application to differentiate EEG activity from different mental tasks.

UNLABELLED: Symbolic dynamics is a powerful tool for studying complex dynamical systems. So far many techniques of this kind have been proposed as a means to analyze brain dynamics, but most of them are restricted to single-sensor measurements. Analyzing the dynamics in a channel-wise fashion is an invalid approach for multisite encephalographic recordings, since it ignores any pattern of coordinated activity that might emerge from the coherent activation of distinct brain areas. We suggest, here, the use of neural-gas algorithm (Martinez et al. in IEEE Trans Neural Netw 4:558-569, 1993) for encoding brain activity spatiotemporal dynamics in the form of a symbolic timeseries. A codebook of k prototypes, best representing the instantaneous multichannel data, is first designed. Each pattern of activity is then assigned to the most similar code vector. The symbolic timeseries derived in this way is mapped to a network, the topology of which encapsulates the most important phase transitions of the underlying dynamical system. Finally, global efficiency is used to characterize the obtained topology. We demonstrate the approach by applying it to EEG-data recorded from subjects while performing mental calculations. By working in a contrastive-fashion, and focusing in the phase aspects of the signals, we show that the underlying dynamics differ significantly in their symbolic representations. ELECTRONIC SUPPLEMENTARY MATERIAL: The online version of this article (doi:10.1007/s11571-011-9186-5) contains supplementary material, which is available to authorized users.

Graph-based network analysis in schizophrenia.

Over the last few years, many studies have been published using modern network analysis of the brain. Researchers and practical doctors alike should understand this method and its results on the brain evaluation at rest, during activation and in brain disease. The studies are noninvasive and usually performed with elecroencephalographic, magnetoencephalographic, magnetic resonance imaging and diffusion tensor imaging brain recordings. Different tools for analysis have been developed, although the methods are in their early stages. The results of these analyses are of special value. Studies of these tools in schizophrenia are important because widespread and local network disturbances can be evaluated by assessing integration, segregation and several structural and functional properties. With the help of network analyses, the main findings in schizophrenia are lower optimum network organization, less efficiently wired networks, less local clustering, less hierarchical organization and signs of disconnection. There are only about twenty five relevant papers on the subject today. Only a few years of study of these methods have produced interesting results and it appears promising that the development of these methods will present important knowledge for both the preclinical signs of schizophrenia and the methods' therapeutic effects.

Mild traumatic brain injury: graph-model characterization of brain networks for episodic memory.

Episodic memory is among the cognitive functions that can be affected in the acute phase following mild traumatic brain injury (MTBI). The present study used EEG recordings to evaluate global synchronization and network organization of rhythmic activity during the encoding and recognition phases of an episodic memory task varying in stimulus type (kaleidoscope images, pictures, words, and pseudowords). Synchronization of oscillatory activity was assessed using a linear and nonlinear connectivity estimator and network analyses were performed using algorithms derived from graph theory. Twenty five MTBI patients (tested within days post-injury) and healthy volunteers were closely matched on demographic variables, verbal ability, psychological status variables, as well as on overall task performance. Patients demonstrated sub-optimal network organization, as reflected by changes in graph parameters in the theta and alpha bands during both encoding and recognition. There were no group differences in spectral energy during task performance or on network parameters during a control condition (rest). Evidence of less optimally organized functional networks during memory tasks was more prominent for pictorial than for verbal stimuli.

Dynamic task-specific brain network connectivity in children with severe reading difficulties.

We investigated patterns of sensor-level functional connectivity derived from single-trial whole-head magnetoencephalography data during a pseudoword reading and a letter-sound naming task in children with reading difficulties (RD) and children with no reading impairments (NI). The Phase Lag Index (PLI), a linear and nonlinear estimator, computed for each pair of sensors, was used to construct graphs and obtain estimates of local and global network efficiency according to graph theory. In the 8-13 Hz (alpha band) and 20-30 Hz (gamma band) range, RD students showed significantly lower global efficiency than NI children, for the entire MEG recording epoch. RD students also displayed reduced local network efficiency in the alpha band. Correlations between phonological decoding ability and graph metrics were particularly evident during the task that posed significant demands for phonological decoding, and followed distinct time courses depending on signal frequency. Results are consistent with the notion of task-dependent, aberrant long- and short-range functional connectivity in RD children.

Tracking brain dynamics via time-dependent network analysis.

Complex network analysis is currently employed in neuroscience research to describe the neuron pathways in the brain with a small number of computable measures that have neurobiological meaning. Connections in biological neural networks might fluctuate over time; therefore, surveillance can provide a more useful picture of brain dynamics than the standard approach that relies on a static graph to represent functional connectivity. Using the application of well-known measures of neural synchrony over short segments of brain activity in a time series, we attempted a time-dependent characterization of brain connectivity by investigating functional segregation and integration. In our implementation, a frequency-dependent time window was employed and regularly spaced (defined as overlapping segments), and a novel, parameter-free method was introduced to derive the required adjacency matrices. The resulting characterization was compared against conventional approaches that rely on static and time-evolving graphs, which are constructed from non-overlapping segments of arbitrarily defined durations. Our approach is demonstrated using EEG recordings during mental calculations. The derived consecutive values of network metrics were then compared with values from randomized networks. The results revealed the dynamic small-world character of the brain's functional connectivity, which otherwise can be hidden from estimators that rely on either long or stringent time-windows. Moreover, by involving a network-metric time series (NMTS) in a summarizing procedure that was based on replicator dynamics, consistent hubs that facilitated communication in the underlying networks were identified. Finally, the scale-free character of brain networks was also demonstrated based on the significant edges selected with the introduced approach.

What does delta band tell us about cognitive processes: a mental calculation study.

Multichannel EEG recordings from 18 healthy subjects were used to investigate brain activity in four delta subbands during two mental arithmetic tasks (number comparison and two-digit multiplication) and a control condition. The spatial redistribution of signal-power (SP) was explored based on four consecutives subbands of the delta rhythm. Additionally, network analysis was performed, independently for each subband, and the related graphs reflecting functional connectivity were characterized in terms of local structure (i.e. the clustering coefficient), overall integration (i.e. the path length) and the optimality of network organization (i.e. the "small-worldness"). EEG delta activity showed a widespread increase in all subbands during the performance of both arithmetic tasks. The inter-task comparison of the two arithmetic tasks revealed significant differences, in terms of signal-power, for the two subbands of higher frequency over left hemisphere (frontal, temporal, parietal and occipital) regions. The estimated brain networks exhibited small-world characteristics in the case of all subbands. On the contrary, lower frequency subbands were found to operate differently than the higher frequency subbands, with the latter featuring nodal organization and poor remote interconnectivity. These findings possibly reflect the deactivation of default mode network and could be attributed to inhibitory mechanisms activated during mental tasks.