Synchronization Likelihood Research Articles

Graph Theoretical Analysis of Organization of Functional Brain Networks in ADHD

This article presents a new methodology for investigation of the organization of the overall and hemispheric brain network of patients with attention-deficit hyperactivity disorder (ADHD) using theoretical analysis of a weighted graph with the goal of discovering how the brain topology is affected in such patients. The synchronization measure used is the nonlinear fuzzy synchronization likelihood (FSL) developed by the authors recently. Recent evidence indicates a normal neocortex has a small-world (SW) network with a balance between local structure and global structure characteristics. Such a network results in optimal balance between segregation and integration which is essential for high synchronizabilty and fast information transmission in a complex network. The SW network is characterized by the coexistence of dense clustering of connections (C) and short path lengths (L) among the network units. The results of investigation of C show the local structure of functional left-hemisphere brain networks of ADHD diverges from that of non-ADHD which is recognizable in the delta electroencephalograph (EEG) sub-band. Also, the results of investigation for L show the global structure of functional left-hemisphere brain networks of ADHD diverges from that of non-ADHD which is observable in the delta EEG sub-band. It is concluded that the changes in left-hemisphere brain's structure of ADHD from that of the non-ADHD are so much that L and C can distinguish the ADHD brain from the non-ADHD brain in the delta EEG sub-band.

Does sleep restore the topology of functional brain networks?

Previous studies have shown that healthy anatomical as well as functional brain networks have small-world properties and become less optimal with brain disease. During sleep, the functional brain network becomes more small-world-like. Here we test the hypothesis that the functional brain network during wakefulness becomes less optimal after sleep deprivation (SD). Electroencephalography (EEG) was recorded five times a day after a night of SD and after a night of normal sleep in eight young healthy subjects, both during eyes-closed and eyes-open resting state. Overall synchronization was determined with the synchronization likelihood (SL) and the phase lag index (PLI). From these coupling strength matrices the normalized clustering coefficient C (a measurement of local clustering) and path length L (a measurement of global integration) were computed. Both measures were normalized by dividing them by their corresponding C-s and L-s values of random control networks. SD reduced alpha band C/C-s and L/L-s and theta band C/C-s during eyes-closed resting state. In contrast, SD increased gamma-band C/C-s and L/L-s during eyes-open resting state. Functional relevance of these changes in network properties was suggested by their association with sleep deprivation-induced performance deficits on a sustained attention simple reaction time task. The findings indicate that SD results in a more random network of alpha-coupling and a more ordered network of gamma-coupling. The present study shows that SD induces frequency-specific changes in the functional network topology of the brain, supporting the idea that sleep plays a role in the maintenance of an optimal functional network.

Functional connectivity changes in multiple sclerosis patients: A graph analytical study of MEG resting state data

Multiple sclerosis (MS) is characterized by extensive damage in the central nervous system. Within this field, there is a strong need for more advanced, functional imaging measures, as abnormalities measured with structural imaging insufficiently explain clinicocognitive decline in MS. In this study we investigated functional connectivity changes in MS using resting-state magnetoencephalography (MEG). Data from 34 MS patients and 28 age and gender-matched controls was assessed using synchronization likelihood (SL) as a measure of functional interaction strength between brain regions, and graph analysis to characterize topological patterns of connectivity changes. Cognition was assessed using extensive neuropsychological evaluation. Structural measures included brain and lesion volumes, using MRI. Results show SL increases in MS patients in theta, lower alpha and beta bands, with decreases in the upper alpha band. Graph analysis revealed a more regular topology in the lower alpha band in patients, indicated by an increased path length (λ) and clustering coefficient (γ). Attention and working memory domains were impaired, with decreased brain volumes. A stepwise linear regression model using clinical, MRI and MEG parameters as predictors revealed that only increases in lower alpha band γ predicted impaired cognition. Cognitive impairments and related altered connectivity patterns were found to be especially predominant in male patients. These results show specific functional changes in MS as measured with MEG. Only changes in network topology were related to poorer cognitive outcome. This indicates the value of graph analysis beyond traditional structural and functional measures, with possible implications for diagnostic and/or prognostic purposes in MS.

Visibility graph similarity: A new measure of generalized synchronization in coupled dynamic systems

Synchronization is defined as interdependencies among coupled dynamic systems. In most coupled systems the intrinsic and internal variants, and the interdependencies among their subsystems are not accessible. Therefore, in order to quantify the interdependencies among the coupled systems, attempts have been made through measuring the synchronization between their outputs represented mostly as time series. In this paper a new method, called Visibility Graph Similarity (VGS), is presented as a method of measuring Generalized Synchronization. First, each time series is reconstructed as a trajectory in a state space. Next, a Distance Time Series (DTS) is created from a sequence of relative distances of the states to a reference state. Subsequently, a visibility graph (VG) is constructed using DTS. Then, a sequence of degrees of the VG, called Degree Sequence (DS), is obtained. Correlation of the DSs of two coupled systems is called VGS and is presented as a measurement of similarity of dynamics of the coupled systems. The synchronization measurement performance of the VGS is compared with synchronization likelihood (SL) and the classical cross correlation method using two identical and non-identical models of two coupled Henon map over the entire time domain. Also, it is compared with SL for tracing temporal synchronization using both models. It is shown that VGS provides a more accurate measure of the overall synchronization compared with SL. It is more reliable for measuring weak couplings compared with the cross correlation method. Moreover, VGS uses fewer parameters and detects the temporal synchronization sooner than the SL.

Modulating functional connectivity patterns and topological functional organization of the human brain with transcranial direct current stimulation

Transcranial direct current stimulation (tDCS) is a noninvasive brain stimulation technique that alters cortical excitability and activity in a polarity-dependent way. Stimulation for few minutes has been shown to induce plastic alterations of cortical excitability and to improve cognitive performance. These effects might be caused by stimulation-induced alterations of functional cortical network connectivity. We aimed to investigate the impact of tDCS on cortical network function through functional connectivity and graph theoretical analysis. Single recordings in healthy volunteers with 62 electroencephalography channels were acquired before and after 10 min of facilitatory anodal tDCS over the primary motor cortex (M1), combined with inhibitory cathodal tDCS of the contralateral frontopolar cortex, in resting state and during voluntary hand movements. Correlation matrices containing all 62 pairwise electrode combinations were calculated with the synchronization likelihood (SL) method and thresholded to construct undirected graphs for the θ, α, β, low-γ and high-γ frequency bands. SL matrices and undirected graphs were compared before and after tDCS. Functional connectivity patterns significantly increased within premotor, motor, and sensorimotor areas of the stimulated hemisphere during motor activity in the 60-90 Hz frequency range. Additionally, tDCS-induced significant intrahemispheric and interhemispheric connectivity changes in all the studied frequency bands. In summary, we show for the first time evidence for tDCS-induced changes in brain synchronization and topological functional organization.

Covariation of EEG Synchronization and Emotional State as Modified by Anxiolytics

The relationships between subjective estimation of emotional state and synchronization patterns in cortical emotional systems were investigated. The emotional state varied between groups using diazepam, buspirone, and placebo. The University of Wales Institute of Science and Technology Mood Adjective Checklist was used for the assessment of emotional state in the drug condition, yielding three estimates of emotional state: Energetic Arousal, Tension Arousal, and Hedonic Tone. These measures were correlated with the Synchronization Likelihood index of the resting EEG. Increased affective valence and arousal were related to an increased level of synchronization between frontal and right temporoparietal emotional areas. Two identified centers of synchronization, localized in the temporal and centroparietal regions, appeared to be functionally distinct. Stable relationships between subjective emotional state measures and cortical EEG synchronization patterns were confirmed, especially for the valence and energetic arousal estimation. A higher synchronization is associated with increased emotional valence and arousal, and this can thus be seen as a neural correlate of emotional experiences.

Reorganization of Functional Networks in Mild Cognitive Impairment

Whether the balance between integration and segregation of information in the brain is damaged in Mild Cognitive Impairment (MCI) subjects is still a matter of debate. Here we characterize the functional network architecture of MCI subjects by means of complex networks analysis. Magnetoencephalograms (MEG) time series obtained during a memory task were evaluated by synchronization likelihood (SL), to quantify the statistical dependence between MEG signals and to obtain the functional networks. Graphs from MCI subjects show an enhancement of the strength of connections, together with an increase in the outreach parameter, suggesting that memory processing in MCI subjects is associated with higher energy expenditure and a tendency toward random structure, which breaks the balance between integration and segregation. All features are reproduced by an evolutionary network model that simulates the degenerative process of a healthy functional network to that associated with MCI. Due to the high rate of conversion from MCI to Alzheimer Disease (AD), these results show that the analysis of functional networks could be an appropriate tool for the early detection of both MCI and AD.

Functional community analysis of brain: A new approach for EEG-based investigation of the brain pathology

Analysis of structure of the brain functional connectivity (SBFC) is a fundamental issue for understanding of the brain cognition as well as the pathology of brain disorders. Analysis of communities among sub-parts of a system is increasingly used for social, ecological, and other networks. This paper presents a new methodology for investigation of the SBFC and understanding of the brain based on graph theory and community pattern analysis of functional connectivity graph of the brain obtained from encephalograms (EEGs). The methodology consists of three main parts: fuzzy synchronization likelihood (FSL), community partitioning, and decisions based on partitions. As an example application, the methodology is applied to analysis of brain of patients with attention deficit/hyperactivity disorder (ADHD) and the problem of discrimination of ADHD EEGs from healthy (non-ADHD) EEGs.

Decreased cortical connectivity and information flow in type 1 diabetes

Objective To investigate the effect of type 1 diabetes on EEG connectivity and information flow and study the relationship between these parameters and electrophysiological, neuropsychological and clinical variables. Methods Connectivity was assessed using several measures (phase coherence, phase lag index, synchronization likelihood and phase slope index) on 119 patients and 61 healthy controls over several frequency bands (between 0.5 and 45 Hz). Data was further correlated to EEG power, event related potentials, neuropsychological function and demographic variables. Results Multivariate test on the connectivity data showed a difference between patients and controls both with mastoid reference ( p < 0.01) and current source density estimates ( p < 0.04). Connectivity and information flow correlated with EEG power but not with event related potentials or neuropsychological function. Conclusions Connectivity and information flow are decreased in diabetes. These variables assess other functions of the brain than captured by the present cognitive tests. Several tests need to be performed in order to monitor the effect of diabetes on brain function. Significance The decrease in connectivity and cortical information flow are EEG abnormalities that add to the previously described EEG and ERP abnormalities described for type 1 diabetes.

Early dysfunction of functional connectivity in healthy elderly with subjective memory complaints

It is still an open question whether subjective memory complaints (SMC) can actually be considered to be clinically relevant predictors for the development of an objective memory impairment and even dementia. There is growing evidence that suggests that SMC are associated with an increased risk of dementia and with the presence of biological correlates of early Alzheimer's disease. In this paper, in order to shed some light on this issue, we try to discern whether subjects with SMC showed a different profile of functional connectivity compared with subjects with mild cognitive impairment (MCI) and healthy elderly subjects. In the present study, we compare the degree of synchronization of brain signals recorded with magnetoencephalography between three groups of subjects (56 in total): 19 with MCI, 12 with SMC and 25 healthy controls during a memory task. Synchronization likelihood, an index based on the theory of nonlinear dynamical systems, was used to measure functional connectivity. Briefly, results show that subjects with SMC have a very similar pattern of connectivity to control group, but on average, they present a lower synchronization value. These results could indicate that SMC are representing an initial stage with a hypo-synchronization (in comparison with the control group) where the brain system is still not compensating for the failing memory networks, but behaving as controls when compared with the MCI subjects.

Network analysis of resting state EEG in the developing young brain: structure comes with maturation.

During childhood, brain structure and function changes substantially. Recently, graph theory has been introduced to model connectivity in the brain. Small-world networks, such as the brain, combine optimal properties of both ordered and random networks, i.e., high clustering and short path lengths. We used graph theoretical concepts to examine changes in functional brain networks during normal development in young children. Resting-state eyes-closed electroencephalography (EEG) was recorded (14 channels) from 227 children twice at 5 and 7 years of age. Synchronization likelihood (SL) was calculated in three different frequency bands and between each pair of electrodes to obtain SL-weighted graphs. Mean normalized clustering index, average path length and weight dispersion were calculated to characterize network organization. Repeated measures analysis of variance tested for time and gender effects. For all frequency bands mean SL decreased from 5 to 7 years. Clustering coefficient increased in the alpha band. Path length increased in all frequency bands. Mean normalized weight dispersion decreased in beta band. Girls showed higher synchronization for all frequency bands and a higher mean clustering in alpha and beta bands. The overall decrease in functional connectivity (SL) might reflect pruning of unused synapses and preservation of strong connections resulting in more cost-effective networks. Accordingly, we found increases in average clustering and path length and decreased weight dispersion indicating that normal brain maturation is characterized by a shift from random to more organized small-world functional networks. This developmental process is influenced by gender differences early in development.

Fuzzy Synchronization Likelihood with Application to Attention-Deficit/Hyperactivity Disorder

Synchronization as a measure of quantification of similarities in dynamic systems is an important concept in many scientific fields such as nonlinear science, neuroscience, cardiology, ecology, and economics. When interdependencies and connections of coupled dynamic systems are not directly accessible and measurable such as those of the neurons of the brain, quantification of similarities between their time series outputs is the best possible way to detect the existent interdependencies among them. In recent years, Synchronization Likelihood (SL) has been used as one of the most suitable algorithms in highly nonlinear and non-stationary systems. In this method, the likelihood of patterns is measured statistically, and then it is determined which patterns of the time series are similar to each other considering a threshold. But the degree of similarities is not considered in the decision. In this paper, a new measure of synchronization, fuzzy SL, is presented using the theory of fuzzy logic and Gaussian membership functions. The new fuzzy SL is compared with the conventional SL using both a standard problem from the chaos literature and a complicated real life neurological diagnostic problem, that is, the EEG-based diagnosis of Attention-Deficit/Hyperactivity Disorder (ADHD). The results of ANOVA analysis indicate the interdependencies measured by the fuzzy SL are more reliable than the conventional SL for discriminating ADHD patients from healthy individuals.

Feasibility of online seizure detection with continuous EEG monitoring in the intensive care unit

Continuous EEG (cEEG) is of great interest in view of the reported high prevalence of non-convulsive seizures on intensive care units (ICUs). Here, we describe our experiences applying a seizure warning system using cEEG monitoring. Fifty comatose ICU patients were included prospectively and monitored. Twenty-eight patients had post-anoxic encephalopathy (PAE) and 22 had focal brain lesions. A measure of neuronal interactions, synchronization likelihood, was calculated online over 10s EEG epochs and instances when the synchronization likelihood exceeded a threshold where marked as seizures. Five patients developed seizures. Our method detected seizures in three patients, in the other patients seizures were missed because of they were non-convulsive and had a focal character. The average false positive rate was 0.676/h. This is our first attempt to implement online seizure detection in the ICU. Despite problems with artifacts and that we missed focally oriented seizures, we succeeded in monitoring patients online. Given the relatively high occurrence of seizures, online seizure detection with cEEG merits further development for use in ICUs.

P15-13 EEG synchronization likelihood co-varies with self-estimation of emotional valence modified by pharmaceuticals

P15-13 EEG synchronization likelihood co-varies with self-estimation of emotional valence modified by pharmaceuticals

Functional Connectivity in Mild Cognitive Impairment During a Memory Task: Implications for the Disconnection Hypothesis

Mild cognitive impairment (MCI) has been considered an intermediate state between healthy aging and dementia. The early damage in anatomical connectivity and progressive loss of synapses that characterize early Alzheimer's disease suggest that MCI could also be a disconnection syndrome. Here, we compare the degree of synchronization of brain signals recorded with magnetoencephalography from patients (22) with MCI with that of healthy controls (19) during a memory task. Synchronization Likelihood, an index based on the theory of nonlinear dynamical systems, was used to measure functional connectivity. During the memory task patients showed higher interhemispheric synchronization than healthy controls between left and right -anterior temporo-frontal regions (in all studied frequency bands) and in posterior regions in the γ band. On the other hand, the connectivity pattern from healthy controls indicated two clusters of higher synchronization, one among left temporal sensors and another one among central channels. Both of them were found in all frequency bands. In the γ band, controls showed higher Synchronization Likelihood values than MCI patients between central-posterior and frontal-posterior channels and a high synchronization in posterior regions. The inter-hemispheric increased synchronization values could reflect a compensatory mechanism for the lack of efficiency of the memory networks in MCI patients. Therefore, these connectivity profiles support only partially the idea of MCI as a disconnection syndrome, as patients showed increased long distance inter-hemispheric connections but a decrease in antero-posterior functional connectivity.

Functional network changes associated with sleep deprivation and fatigue during simulated driving: Validation using blood biomarkers

Objective Network analysis of electroencephalograph (EEG) signals to study the effect of fatigue and sleep deprivation in human drivers and its validation using blood biochemical parameters. Methods We present a new method of detection of human fatigue and sleepiness by studying the variation of functional interdependencies among EEG signals from various channels. An experiment has been designed to induce fatigue in 12 subjects through several stages over 36 h of sleep deprivation. The functional interdependency among the signals has been computed using synchronisation likelihood (SL), which measures the dynamical (both linear and non-linear) interdependency between two or more non-stationary time series. A network structure has been generated based on the likelihood values and is characterised by a number of standard network-characterising parameters at each stage. Finally, the trends in the network parameters have been validated using biochemical analysis of three blood parameters: glucose, blood urea and creatinine. Results An increasing trend in the degree of connectivity and clustering coefficient and a decreasing trend in the characteristic path length have been observed in some bands of signals at successive stages of the experiment. Conclusions Synchronisation of specific bands of the EEG signals from different cortical areas has been observed along with variation in network parameters at increased levels of fatigue and sleep deprivation. Significance The results indicate that the network parameters may be used to detect and quantify the level of fatigue and sleepiness.

‘Functional Connectivity’ Is a Sensitive Predictor of Epilepsy Diagnosis after the First Seizure

BackgroundAlthough epilepsy affects almost 1% of the world population, diagnosis of this debilitating disease is still difficult. The EEG is an important tool for epilepsy diagnosis and classification, but the sensitivity of interictal epileptiform discharges (IEDs) on the first EEG is only 30–50%. Here we investigate whether using ‘functional connectivity’ can improve the diagnostic sensitivity of the first interictal EEG in the diagnosis of epilepsy.Methodology/Principal FindingsPatients were selected from a database with 390 standard EEGs of patients after a first suspected seizure. Patients who were later diagnosed with epilepsy (i.e. ≥two seizures) were compared to matched non-epilepsy patients (with a minimum follow-up of one year). The synchronization likelihood (SL) was used as an index of functional connectivity of the EEG, and average SL per patient was calculated in seven frequency bands. In total, 114 patients were selected. Fifty-seven patients were diagnosed with epilepsy (20 had IEDs on their EEG) and 57 matched patients had other diagnoses. Epilepsy patients had significantly higher SL in the theta band than non-epilepsy patients. Furthermore, theta band SL proved to be a significant predictor of a diagnosis of epilepsy. When only those epilepsy patients without IEDs were considered (n = 74), theta band SL could predict diagnosis with specificity of 76% and sensitivity of 62%.Conclusion/SignificanceTheta band functional connectivity may be a useful diagnostic tool in diagnosing epilepsy, especially in those patients who do not show IEDs on their first EEG. Our results indicate that epilepsy diagnosis could be improved by using functional connectivity.

Age-dependent features of EEG-reactivity—Spectral, complexity, and network characteristics

Our goal was to measure indices characterizing EEG-reactivity in young and elderly subjects. It was hypothesized that EEG-reactivity as reflected by different measures would be lower in the elderly. In two age groups (young: N = 23, mean age = 21.5 ± 2.2 years; old: N = 25, mean age = 66.9 ± 3.6 years) absolute frequency spectra, Omega-complexity, synchronization likelihood and network properties (clustering coefficient and characteristic path length) of the EEG were analyzed in the delta, theta, alpha1, alpha2, beta1 and beta2 frequency bands occurring as a result of eyes opening. Absolute spectral power was higher in the young in the delta, alpha1 and alpha2 bands in the posterior area. The alpha1 peak frequency decreased following eyes opening in the young, while no change was observed in the elderly. Omega-complexity was higher in the elderly especially in the frontal area and increased following eyes opening. Values of the clustering coefficient, path length and that of the “small-world index” decreased as a result of eyes opening, the latter in the fast frequency range. The results suggest reduced reactivity in the elderly as shown by frequency spectra and decreased level of integrative activity particularly in the frontal area probably as a result of reduced interneuronal processing capacity. Indices of network characteristics reveal a shift towards more random topology especially in the beta frequencies caused by eyes opening.

Endophenotypes in a Dynamically Connected Brain

We examined the longitudinal genetic architecture of three parameters of functional brain connectivity. One parameter described overall connectivity (synchronization likelihood, SL). The two others were derived from graph theory and described local (clustering coefficient, CC) and global (average path length, L) aspects of connectivity. We measured resting state EEG in 1,438 subjects from four age groups of about 16, 18, 25 and 50 years. Developmental curves for SL and L indicate that connectivity is more random at adolescence and old age, and more structured in middle-aged adulthood. Individual variation in SL and L were moderately to highly heritable at each age (SL: 40–82%; L: 29–63%). Genetic factors underlying these phenotypes overlapped. CC was also heritable (25–49%) but showed no systematic overlap with SL and L. SL, CC, and L in the alpha band showed high phenotypic and genetic stability from 16 to 25 years. Heritability for parameters in the beta band was lower, and less stable across ages, but genetic stability was high. We conclude that the connectivity parameters SL, CC, and L in the alpha band show the hallmarks of a good endophenotype for behavior and developmental disorders.

The Lesioned Brain: Still a Small-World?

The intra-arterial amobarbital procedure (IAP or Wada test) is used to determine language lateralization and contralateral memory functioning in patients eligible for neurosurgery because of pharmaco-resistant epilepsy. During unilateral sedation, functioning of the contralateral hemisphere is assessed by means of neuropsychological tests. We use the IAP as a reversible model for the effect of lesions on brain network topology. Three artifact-free epochs (4096 samples) were selected from each electroencephalogram record before and after amobarbital injection. Functional connectivity was assessed by means of the synchronization likelihood. The resulting functional connectivity matrices were constructed for all six epochs per patient in four frequency bands, and weighted network analysis was performed. The clustering coefficient, average path length, small-world index, and edge weight correlation were calculated. Recordings of 33 patients were available. Network topology changed significantly after amobarbital injection: clustering decreased in all frequency bands, while path length decreased in the theta and lower alpha band, indicating a shift toward a more random network topology. Likewise, the edge weight correlation decreased after injection of amobarbital in the theta and beta bands. Network characteristics after injection of amobarbital were correlated with memory score: higher theta band small-world index and increased upper alpha path length were related to better memory score. The whole-brain network topology in patients eligible for epilepsy surgery becomes more random and less optimally organized after selective sedation of one hemisphere, as has been reported in studies with brain tumor patients. Furthermore, memory functioning after injection seems related to network topology, indicating that functional performance is related to topological network properties of the brain.