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.

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.

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.

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.

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.

Material-specific difficulties in episodic memory tasks in mild traumatic brain injury.

The study examines acute, material-specific secondary memory performance in 26 patients with mild traumatic brain injury (MTBI) and 26 healthy controls, matched on demographic variables and indexes of crystallized intelligence. Neuropsychological tests were used to evaluate primary and secondary memory, executive functions, and verbal fluency. Participants were also tested on episodic memory tasks involving words, pseudowords, pictures of common objects, and abstract kaleidoscopic images. Patients showed reduced performance on episodic memory measures, and on tasks associated with visuospatial processing and executive function (Trail Making Test part B, semantic fluency). Significant differences between groups were also noted for correct rejections and response bias on the kaleidoscope task. MTBI patients' reduced performance on memory tasks for complex, abstract stimuli can be attributed to a dysfunction in the strategic component of memory process.

The influence of ageing on complex brain networks: a graph theoretical analysis.

OBJECTIVE: To determine the functional connectivity of different EEG bands at the "baseline" situation (rest) and during mathematical thinking in children and young adults to study the maturation effect on brain networks at rest and during a cognitive task. METHODS: Twenty children (8-12 years) and twenty students (21-26 years) were studied. The synchronization likelihood was used to evaluate the interregional synchronization of different EEG frequency bands in children and adults, at rest and during math. Then, graphs were constructed and characterized in terms of local structure (clustering coefficient) and overall integration (path length) and the "optimal" organization of the connectivity i.e., the small world network (SWN). RESULTS: The main findings were: (i) Enhanced synchronization for theta band during math more prominent in adults. (ii) Decrease of the optimal SWN organization of the alpha2 band during math. (iii) The beta and especially gamma bands showed lower synchronization and signs of lower SWN organization in both situations in adults. CONCLUSION: There are interesting findings related to the two age groups and the two situations. The theta band showed higher synchronization during math in adults as a result of higher capacity of the working memory in this age group. The alpha2 band showed some SWN disorganization during math, a process analog to the known desynchronization. In adults, a dramatic reduction of the connections in gray matter occurs. Although this maturation process is probably related to higher efficiency, reduced connectivity is expressed by lower synchronization and lower mean values of the graph parameters in adults.

Working memory in schizophrenia: an EEG study using power spectrum and coherence analysis to estimate cortical activation and network behavior.

This study examined regional cortical activations and cortico-cortical connectivity in a group of 20 high-functioning patients with schizophrenia and 20 healthy controls matched for age and sex during a 0- and a 2-back working memory (WM) task. An earlier study comparing schizophrenia patients with education level-matched healthy controls revealed less "optimally" organized network during the 2-back task, whereas a second study with healthy volunteers had suggested that the degree of cortical organization may be inversely proportional to educational level (less optimal functional connectivity in better educated individuals interpreted as the result of higher efficiency). In the present study, both groups succeeded in the 2-back WM task although healthy individuals had generally attained a higher level of education. First absolute power spectrum of the different frequency bands corresponding to the electrodes of each lobe was calculated. Then the mean values of coherence were calculated as an index of the average synchronization to construct graphs in order to characterize local and large scale topological patterns of cortico-cortical connectivity. The power spectra analyses showed signs of hypofrontality in schizophrenics with an asymmetry. Additionally, differences between the groups with greater changes during WM in healthy individuals were visible in all lobes more on the left side. The graph parameter results indicated decreased small-world architecture i.e. less optimal cortico-cortical functional organization in patients as compared to controls. These findings are consistent with the notion of aberrant neural organization in schizophrenics which is nevertheless sufficient in supporting adequate task performance.

Small-world networks and disturbed functional connectivity in schizophrenia.

Disturbances in "functional connectivity" have been proposed as a major pathophysiological mechanism for schizophrenia, and in particular, for cognitive disorganization. Detection and estimation of these disturbances would be of clinical interest. Here we characterize the spatial pattern of functional connectivity by computing the "synchronization likelihood" (SL) of EEG at rest and during performance of a 2Back working memory task using letters of the alphabet presented on a PC screen in subjects with schizophrenia and healthy controls. The spatial patterns of functional connectivity were then characterized with graph theoretical measures to test whether a disruption of an optimal spatial pattern ("small-world") of the functional connectivity network underlies schizophrenia. Twenty stabilized patients with schizophrenia, who were able to work, and 20 healthy controls participated in the study. During the working memory (WM) task healthy subjects exhibited small-world properties (a combination of local clustering and high overall integration of the functional networks) in the alpha, beta and gamma bands. These properties were not present in the schizophrenia group. These findings are in accordance with a partially inadequate organization of neuronal networks in subjects with schizophrenia. This method could be helpful for diagnosis and evaluation of the severity of the disease, as well as understanding the pathophysiologic mechanisms underlying cognitive dysfunction in schizophrenia.

Using graph theoretical analysis of multi channel EEG to evaluate the neural efficiency hypothesis.

Previous studies demonstrated that intelligence is significantly related to an impressive array of psychological, social, biological and genetic factors and that working memory (WM) can be considered as a general cognitive resource strongly related with a wide variety of higher order cognitive competencies and intelligence. Also, evaluating the WM of subjects might allow one to test the neural efficiency hypothesis (NEH). WM typically involves functional interactions between frontal and parietal cortices. We recorded EEG signals to study neuronal interactions during one WM test in individuals who had few years of formal education (LE) as compared to individuals with university degrees (UE). The two groups of individuals differed in the scores they obtained in psychological tests. To quantify the synchronization between EEG channels in several frequency bands, we evaluated the "synchronization likelihood" (SL), which takes into consideration nonlinear processes as well as linear ones. SL was then converted into graphs to estimate the distance from "small-world network" (SWN) organization, i.e., an optimally organized network that would give rise to the data. In comparison to LE subjects, those with university degrees exhibited less prominent SWN properties in most frequency bands during the WM task. This finding supports the NEH and suggests that the connections between brain areas of well-educated subjects engaged in WM tasks are not as well-organized in the sense of SWN.

Changes in linear and nonlinear EEG measures as a function of task complexity: evidence for local and distant signal synchronization.

The purpose of the present study was threefold: First, to replicate previous findings of changes in local gamma band power as a function of the complexity of a visuo-semantic processing task, second, to extend these findings in tasks delivered in the auditory modality, and third to explore the use of non-linear algorithms as indices of complexity and distant synchronization in the EEG signal. EEG was recorded from 28 scalp locations as participants performed three visual discrimination tasks designed to tap into increasingly more complex operations regularly involved in the recognition of living animate objects. Two auditory processing tasks involving the same stimuli, but requiring no semantic processing, served as controls. The degree of complexity of the semantic decision was associated with the predicted changes in local gamma power, as well as with broadband changes in the non-linear predictability of the signal (an index derived using an artificial neural network algorithm). These changes were observed at all scalp regions, a finding consistent with the wide cortical distribution of component processes involved in the tasks. In addition, the synchronization between temporal and parieto-occipital electrodes and the remaining recording sites was highest in the gamma bands and lowest in the alpha bands for the task that required the most complex visuo-semantic decision. This trend reversed with reduced task complexity, consistent with the view that multidimensional semantic decisions require the involvement of distributed cortical networks in auditory and visual association areas and in the frontal lobes.