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.

Cortical network analysis in patients affected by schizophrenia.

In the present study, we studied the structural changes of the brain functional network in a group of schizophrenic (SCHZ) patients during a 2-back working memory task. Cortical signals were obtained from scalp EEG signals through the high-resolution EEG technique, which relies on realistic head models and linear inverse solutions. Functional networks were estimated by computing the spectral coherence--i.e. a measure of synchronization in the frequency domain--between the time series of all the available cortical sources. To analyze those cortical networks we followed a theoretical graph approach by computing the network density as the total number of links and the node degree as the number of links of each cortical source. The major result suggest that in the Alpha2 frequency band (11-13 Hz) the cortical functional networks of the SCHZ patients present the largest differences when compared with those of a group of control (CTRL) subjects. In particular, the structure of the SCHZ network altered radically during the memory task, as the number of links that were different from the REST condition increased sensibly with respect to the CTRL network. In addition, a compensatory mechanism was found in the SCHZ patients during the correct performance of the memory task where the node degree showed a frontal asymmetry with higher activation of the left frontal lobe--i.e. higher number of connections--in the Alpha2 frequency band.

A decision support framework for the discrimination of children with controlled epilepsy based on EEG analysis.

BACKGROUND: In this work we consider hidden signs (biomarkers) in ongoing EEG activity expressing epileptic tendency, for otherwise normal brain operation. More specifically, this study considers children with controlled epilepsy where only a few seizures without complications were noted before starting medication and who showed no clinical or electrophysiological signs of brain dysfunction. We compare EEG recordings from controlled epileptic children with age-matched control children under two different operations, an eyes closed rest condition and a mathematical task. The aim of this study is to develop reliable techniques for the extraction of biomarkers from EEG that indicate the presence of minor neurophysiological signs in cases where no clinical or significant EEG abnormalities are observed. METHODS: We compare two different approaches for localizing activity differences and retrieving relevant information for classifying the two groups. The first approach focuses on power spectrum analysis whereas the second approach analyzes the functional coupling of cortical assemblies using linear synchronization techniques. RESULTS: Differences could be detected during the control (rest) task, but not on the more demanding mathematical task. The spectral markers provide better diagnostic ability than their synchronization counterparts, even though a combination (or fusion) of both is needed for efficient classification of subjects. CONCLUSIONS: Based on these differences, the study proposes concrete biomarkers that can be used in a decision support system for clinical validation. Fusion of selected biomarkers in the Theta and Alpha bands resulted in an increase of the classification score up to 80% during the rest condition. No significant discrimination was achieved during the performance of a mathematical subtraction task.

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.

Small-world properties of nonlinear brain activity in schizophrenia.

A disturbance in the interactions between distributed cortical regions may underlie the cognitive and perceptual dysfunction associated with schizophrenia. In this article, nonlinear measures of cortical interactions and graph-theoretical metrics of network topography are combined to investigate this schizophrenia "disconnection hypothesis." This is achieved by analyzing the spatiotemporal structure of resting state scalp EEG data previously acquired from 40 young subjects with a recent first episode of schizophrenia and 40 healthy matched controls. In each subject, a method of mapping the topography of nonlinear interactions between cortical regions was applied to a widely distributed array of these data. The resulting nonlinear correlation matrices were converted to weighted graphs. The path length (a measure of large-scale network integration), clustering coefficient (a measure of "cliquishness"), and hub structure of these graphs were used as metrics of the underlying brain network activity. The graphs of both groups exhibited high levels of local clustering combined with comparatively short path lengths--features consistent with a "small-world" topology--as well as the presence of strong, central hubs. The graphs in the schizophrenia group displayed lower clustering and shorter path lengths in comparison to the healthy group. Whilst still "small-world," these effects are consistent with a subtle randomization in the underlying network architecture--likely associated with a greater number of links connecting disparate clusters. This randomization may underlie the cognitive disturbances characteristic of schizophrenia.

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.

Detection of signs of brain dysfunction in epileptic children by recognition of transient changes in the correlation of seizure-free EEG.

Seizure-free EEG signals recorded from epileptic children were compared with EEG signals recorded from normal children. The comparison was based on the detection of transient events characterized by decrease in the correlation between different traces. For this purpose, a conceptually and mathematically simple method was applied. Two clear and remarkable phenomena, able to quantitatively discriminate between the two groups of subjects, were evidenced, with high statistical significance. In fact, it was observed that: (a) The number of events for the epileptic group was larger; (b) Applying restrictive criteria for event definition, the number of subjects in the epileptic group presenting events was larger. The results support the hypothesis of a decrease in brain correlation in children with epilepsy under treatment. This confirms the efficacy of the EEG signal in evaluating cortical functional differences not visible by visual inspection, independently of the cause (epilepsy or drugs), and demonstrate the specific effectiveness of the analysis method applied.

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.

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.

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.

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.

Neural networks involved in mathematical thinking: evidence from linear and non-linear analysis of electroencephalographic activity.

Using linear and non-linear methods, electroencephalographic (EEG) signals were measured at various brain regions to provide information regarding patterns of local and coordinated activity during performance of three arithmetic tasks (number comparison, single-digit multiplication, and two-digit multiplication) and two control tasks that did not require arithmetic operations. It was hypothesized that these measures would reveal the engagement of local and increasingly complex cortical networks as a function of task specificity and complexity. Results indicated regionally increased neuronal signalling as a function of task complexity at frontal, temporal and parietal brain regions, although more robust task-related changes in EEG-indices of activation were derived over the left hemisphere. Both linear and non-linear indices of synchronization among EEG signals recorded from over different brain regions were consistent with the notion of more "local" processing for the number comparison task. Conversely, multiplication tasks were associated with a widespread pattern of distant signal synchronizations, which could potentially indicate increased demands for neural networks cooperation during performance of tasks that involve a greater number of cognitive operations.

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.