Detection of nonlinear interactions of EEG alpha waves in the brain by a new coherence measure and its application to epilepsy and anti-epileptic drug therapy

Rhythmic Network Modulation to Thalamocortical Couplings in Epilepsy

Thalamus interacts with cortical areas, generating oscillations characterized by their rhythm and levels of synchrony. However, little is known of what function the rhythmic dynamic may serve in thalamocortical couplings. This work introduced a general approach to investigate the modulatory contribution of rhythmic scalp network to the thalamo-frontal couplings in juvenile myoclonic epilepsy (JME) and frontal lobe epilepsy (FLE). Here, time-varying rhythmic network was constructed using the adapted directed transfer function between EEG electrodes, and then was applied as a modulator in fMRI-based thalamocortical functional couplings. Furthermore, the relationship between corticocortical connectivity and rhythm-dependent thalamocortical coupling was examined. The results revealed thalamocortical couplings modulated by EEG scalp network have frequency-dependent characteristics. Increased thalamus- sensorimotor network (SMN) and thalamus-default mode network (DMN) couplings in JME were strongly modulated by alpha band. These thalamus-SMN couplings demonstrated enhanced association with SMN-related corticocortical connectivity. In addition, altered theta-dependent and beta-dependent thalamus-frontoparietal network (FPN) couplings were found in FLE. The reduced theta-dependent thalamus-FPN couplings were associated with the decreased FPN-related corticocortical connectivity. This study proposed interactive links between the rhythmic modulation and thalamocortical coupling. The crucial role of SMN and FPN in subcortical-cortical circuit may have implications for intervention in generalized and focal epilepsy.

Complex network based models of ECoG signals for detection of induced epileptic seizures in rats

The automatic detection of seizures bears a considerable significance in epileptic diagnosis as it can efficiently lead to a considerable reduction of the workload of the medical staff. The present study aims at automatic detecting epileptic seizures in epileptic rats. To this end, seizures were induced in rats implementing the pentylenetetrazole model, with the electrocorticogram (ECoG) signals during, before and after the seizure periods being recorded. For this purpose, five algorithms for transforming time series into complex networks based on visibility graph (VG) algorithm were used. In this study, VG based methods were used for the first time to analyze ECoG signals in rats. Afterward, Standard measures in network science (graph properties) were made to examine the topological structure of these networks produced on the basis of ECoG signals. Then these measures were given to a classifier as input features so that the ECoG signals could be classified into seizure periods and seizure-free periods. Artificial Neural Network, considered a popular classifier, was used in this work. The experimental results showed that the method managed to detect epileptic seizure in rats with a high accuracy of 92.13%. Our proposed method was also applied to the recorded EEG signals from Bonn database to show the efficiency of the proposed method for human seizure detection.

Symbolic time series analysis of electroencephalographic (EEG) epileptic seizure and brain dynamics with eye-open and eye-closed subjects during resting states

Objective

Epilepsy is a neuronal disorder for which the electrical discharge in the brain is synchronized, abnormal and excessive. To detect the epileptic seizures and to analyse brain activities during different mental states, various methods in non-linear dynamics have been proposed. This study is an attempt to quantify the complexity of control and epileptic subject with and without seizure as well as to distinguish eye-open (EO) and eye-closed (EC) conditions using threshold-based symbolic entropy.

Methods

The threshold-dependent symbolic entropy was applied to distinguish the healthy and epileptic subjects with seizure and seizure-free intervals (i.e. interictal and ictal) as well as to distinguish EO and EC conditions. The original time series data was converted into symbol sequences using quantization level, and word series of symbol sequences was generated using a word length of three or more. Then, normalized corrected Shannon entropy (NCSE) was computed to quantify the complexity. The NCSE values were not following the normal distribution, and the non-parametric Mann–Whitney–Wilcoxon (MWW) test was used to find significant differences among various groups at 0.05 significance level. The values of NCSE were presented in a form of topographic maps to show significant brain regions during EC and EO conditions. The results of the study were compared to those of the multiscale entropy (MSE).

Results

The results indicated that the dynamics of healthy subjects are more complex compared to epileptic subjects (during seizure and seizure-free intervals) in both EO and EC conditions. The comparison of the dynamics of epileptic subjects revealed that seizure-free intervals are more complex than seizure intervals. The dynamics of healthy subjects during EO conditions are more complex compared to those during EC conditions. Further, the results clearly demonstrated that threshold-dependent symbolic entropy outperform MSE in distinguishing different physiological and pathological conditions.

Conclusion

The threshold symbolic entropy has provided improved accuracy in quantifying the dynamics of healthy and epileptic subjects during EC an EO conditions for each electrode compared to the MSE.

Correlated EEG Signals Simulation Based on Artificial Neural Networks

In recent years, simulation of the human electroencephalogram (EEG) data found its important role in medical domain and neuropsychology. In this paper, a novel approach to simulation of two cross-correlated EEG signals is proposed. The proposed method is based on the principles of artificial neural networks (ANN). Contrary to the existing EEG data simulators, the ANN-based approach was leveraged solely on the experimentally acquired EEG data. More precisely, measured EEG data were utilized to optimize the simulator which consisted of two ANN models (each model responsible for generation of one EEG sequence). In order to acquire the EEG recordings, the measurement campaign was carried out on a healthy awake adult having no cognitive, physical or mental load. For the evaluation of the proposed approach, comprehensive quantitative and qualitative statistical analysis was performed considering probability distribution, correlation properties and spectral characteristics of generated EEG processes. The obtained results clearly indicated the satisfactory agreement with the measurement data.

A General Approach for Quantifying Nonlinear Connectivity in the Nervous System Based on Phase Coupling

Interaction between distant neuronal populations is essential for communication within the nervous system and can occur as a highly nonlinear process. To better understand the functional role of neural interactions, it is important to quantify the nonlinear connectivity in the nervous system. We introduce a general approach to measure nonlinear connectivity through phase coupling: the multi-spectral phase coherence (MSPC). Using simulated data, we compare MSPC with existing phase coupling measures, namely n : m synchronization index and bi-phase locking value. MSPC provides a system description, including (i) the order of the nonlinearity, (ii) the direction of interaction, (iii) the time delay in the system, and both (iv) harmonic and (v) intermodulation coupling beyond the second order; which are only partly revealed by other methods. We apply MSPC to analyze data from a motor control experiment, where subjects performed isotonic wrist flexions while receiving movement perturbations. MSPC between the perturbation, EEG and EMG was calculated. Our results reveal directional nonlinear connectivity in the afferent and efferent pathways, as well as the time delay (43 ± 8 ms) between the perturbation and the brain response. In conclusion, MSPC is a novel approach capable to assess high-order nonlinear interaction and timing in the nervous system.

Online Epileptic Seizure Prediction Using Wavelet-Based Bi-Phase Correlation of Electrical Signals Tomography

Considerable efforts have been made in order to predict seizures. Among these methods, the ones that quantify synchronization between brain areas, are the most important methods. However, to date, a practically acceptable result has not been reported. In this paper, we use a synchronization measurement method that is derived according to the ability of bi-spectrum in determining the nonlinear properties of a system. In this method, first, temporal variation of the bi-spectrum of different channels of electro cardiography (ECoG) signals are obtained via an extended wavelet-based time-frequency analysis method; then, to compare different channels, the bi-phase correlation measure is introduced. Since, in this way, the temporal variation of the amount of nonlinear coupling between brain regions, which have not been considered yet, are taken into account, results are more reliable than the conventional phase-synchronization measures. It is shown that, for 21 patients of FSPEEG database, bi-phase correlation can discriminate the pre-ictal and ictal states, with very low false positive rates (FPRs) (average: 0.078/h) and high sensitivity (100%). However, the proposed seizure predictor still cannot significantly overcome the random predictor for all patients.

Kernel Collaborative Representation-Based Automatic Seizure Detection in Intracranial EEG

Automatic seizure detection is of great significance in the monitoring and diagnosis of epilepsy. In this study, a novel method is proposed for automatic seizure detection in intracranial electroencephalogram (iEEG) recordings based on kernel collaborative representation (KCR). Firstly, the EEG recordings are divided into 4s epochs, and then wavelet decomposition with five scales is performed. After that, detail signals at scales 3, 4 and 5 are selected to be sparsely coded over the training sets using KCR. In KCR, l2-minimization replaces l1-minimization and the sparse coefficients are computed with regularized least square (RLS), and a kernel function is utilized to improve the separability between seizure and nonseizure signals. The reconstructed residuals of each EEG epoch associated with seizure and nonseizure training samples are compared and EEG epochs are categorized as the class that minimizes the reconstructed residual. At last, a multi-decision rule is applied to obtain the final detection decision. In total, 595 h of iEEG recordings from 21 patients with 87 seizures are employed to evaluate the system. The average sensitivity of 94.41%, specificity of 96.97%, and false detection rate of 0.26/h are achieved. The seizure detection system based on KCR yields both a high sensitivity and a low false detection rate for long-term EEG.

Early prediction of medication refractoriness in children with idiopathic epilepsy based on scalp EEG analysis

Refractory epilepsy often has deleterious effects on an individual's health and quality of life. Early identification of patients whose seizures are refractory to antiepileptic drugs is important in considering the use of alternative treatments. Although idiopathic epilepsy is regarded as having a significantly lower risk factor of developing refractory epilepsy, still a subset of patients with idiopathic epilepsy might be refractory to medical treatment. In this study, we developed an effective method to predict the refractoriness of idiopathic epilepsy. Sixteen EEG segments from 12 well-controlled patients and 14 EEG segments from 11 refractory patients were analyzed at the time of first EEG recordings before antiepileptic drug treatment. Ten crucial EEG feature descriptors were selected for classification. Three of 10 were related to decorrelation time, and four of 10 were related to relative power of delta/gamma. There were significantly higher values in these seven feature descriptors in the well-controlled group as compared to the refractory group. On the contrary, the remaining three feature descriptors related to spectral edge frequency, kurtosis, and energy of wavelet coefficients demonstrated significantly lower values in the well-controlled group as compared to the refractory group. The analyses yielded a weighted precision rate of 94.2%, and a 93.3% recall rate. Therefore, the developed method is a useful tool in identifying the possibility of developing refractory epilepsy in patients with idiopathic epilepsy.

Epileptic EEG classification based on kernel sparse representation

The automatic identification of epileptic EEG signals is significant in both relieving heavy workload of visual inspection of EEG recordings and treatment of epilepsy. This paper presents a novel method based on the theory of sparse representation to identify epileptic EEGs. At first, the raw EEG epochs are preprocessed via Gaussian low pass filtering and differential operation. Then, in the scheme of sparse representation based classification (SRC), a test EEG sample is sparsely represented on the training set by solving l1-minimization problem, and the represented residuals associated with ictal and interictal training samples are computed. The test EEG sample is categorized as the class that yields the minimum represented residual. So unlike the conventional EEG classification methods, the choice and calculation of EEG features are avoided in the proposed framework. Moreover, the kernel trick is employed to generate a kernel version of the SRC method for improving the separability between ictal and interictal classes. The satisfactory recognition accuracy of 98.63% for ictal and interictal EEG classification and for ictal and normal EEG classification has been achieved by the kernel SRC. In addition, the fast speed makes the kernel SRC suit for the real-time seizure monitoring application in the near future.

A new parametric feature descriptor for the classification of epileptic and control EEG records in pediatric population

This study evaluates the sensitivity, specificity and accuracy in associating scalp EEG to either control or epileptic patients by means of artificial neural networks (ANNs) and support vector machines (SVMs). A confluence of frequency and temporal parameters are extracted from the EEG to serve as input features to well-configured ANN and SVM networks. Through these classification results, we thus can infer the occurrence of high-risk (epileptic) as well as low risk (control) patients for potential follow up procedures.

Effect of oxcarbazepine on background EEG activity and cognition in epilepsy

BACKGROUND AND PURPOSE

Cognitive dysfunction related to antiepileptic drugs (AEDs) is an important issue in the management of patients with epilepsy. The aim of the present study was to evaluate relative long-term effects of oxcarbazepine (OXC) on cognition in drug-naive patients with epilepsy.

METHODS

Fifteen drug-naïve epilepsy patients were enrolled. Electroencephalogram (EEG) recordings and neuropsychological (NP) tests were performed before and after OXC monotherapy. The relative power of the discrete frequency bandwas obtained. In addition, interhemispheric and intrahemispheric spectral coherence was also calculated.

RESULTS

NP tests showed significant improvement in visuo-spatial, memory and executive function after OXC treatment. However, neither spectral power nor coherence changed significantly with OXC treatment.

CONCLUSIONS

Our study supports the notion that OXC has no significant cognitive side effect in patients with epilepsy.

EFFICIENT AUTOMATIC SELECTION AND COMBINATION OF EEG FEATURES IN LEAST SQUARES CLASSIFIERS FOR MOTOR IMAGERY BRAIN–COMPUTER INTERFACES

Discriminative features have to be properly extracted and selected from the electroencephalographic (EEG) signals of each specific subject in order to achieve an adaptive brain–computer interface (BCI) system. This work presents an efficient wrapper-based methodology for feature selection and least squares discrimination of high-dimensional EEG data with low computational complexity. Features are computed in different time segments using three widely used methods for motor imagery tasks and, then, they are concatenated or averaged in order to take into account the time course variability of the EEG signals. Once EEG features have been extracted, proposed framework comprises two stages. The first stage entails feature ranking and, in this work, two different procedures have been considered, the least angle regression (LARS) and the Wilcoxon rank sum test, to compare the performance of each one. The second stage selects the most relevant features using an efficient leave-one-out (LOO) estimation based on the Allen's PRESS statistic. Experimental comparisons with the state-of-the-art BCI methods shows that this approach gives better results than current state-of-the-art approaches in terms of recognition rates and computational requirements and, also with respect to the first ranking stage, it is confirmed that the LARS algorithm provides better results than the Wilcoxon rank sum test for these experiments.

A unified approach for detection of induced epileptic seizures in rats using ECoG signals

OBJECTIVE

Epileptic seizure detection is a key step for epilepsy assessment. In this work, using the pentylenetetrazole (PTZ) model, seizures were induced in rats, and ECoG signals in interictal, preictal, ictal, and postictal periods were recorded. The recorded ECoG signals were then analyzed to detect epileptic seizures in the epileptic rats.

METHODS

Two different approaches were considered in this work: thresholding and classification. In the thresholding approach, a feature is calculated in consecutive windows, and the resulted index is tracked over time and compared with a threshold. The moment the index crosses the threshold is considered as the moment of seizure onset. In the classification approach, features are extracted from before, during, and after ictal periods and statistically analyzed. Statistical characteristics of some features have a significant difference among these periods, thus resulting in epileptic seizure detection.

RESULTS

Several features were examined in the thresholding approach. Nonlinear energy and coastline features were successful in epileptic seizure detection. The best result was achieved by the coastline feature, which led to a mean of a 2-second delay in its correct detections. In the classification approach, the best result was achieved using the fuzzy similarity index that led to Pvalue<0.001.

CONCLUSION

This study showed that variance-based features were more appropriate for tracking abrupt changes in ECoG signals. Therefore, these features perform better in seizure onset estimation, whereas nonlinear features or indices, which are based on dynamical systems, can better track the transition of neural system to ictal period.

SIGNIFICANCE

This paper presents examination of different features and indices for detection of induced epileptic seizures from rat's ECoG signals.

DESIGN OF ASSISTIVE WHEELCHAIR SYSTEM DIRECTLY STEERED BY HUMAN THOUGHTS

Integration of brain–computer interface (BCI) technique and assistive device is one of chief and promising applications of BCI system. With BCI technique, people with disabilities do not have to communicate with external environment through traditional and natural pathways like peripheral nerves and muscles, and could achieve it only by their brain activities. In this paper, we designed an electroencephalogram (EEG)-based wheelchair which can be steered by users' own thoughts without any other involvements. We evaluated the feasibility of BCI-based wheelchair in terms of accuracies and real-world testing. The results demonstrate that our BCI wheelchair is of good performance not only in accuracy, but also in practical running testing in a real environment. This fact implies that people can steer wheelchair only by their thoughts, and may have a potential perspective in daily application for disabled people.

COMBINATION OF HETEROGENEOUS EEG FEATURE EXTRACTION METHODS AND STACKED SEQUENTIAL LEARNING FOR SLEEP STAGE CLASSIFICATION

This work proposes a methodology for sleep stage classification based on two main approaches: the combination of features extracted from electroencephalogram (EEG) signal by different extraction methods, and the use of stacked sequential learning to incorporate predicted information from nearby sleep stages in the final classifier. The feature extraction methods used in this work include three representative ways of extracting information from EEG signals: Hjorth features, wavelet transformation and symbolic representation. Feature selection was then used to evaluate the relevance of individual features from this set of methods. Stacked sequential learning uses a second-layer classifier to improve the classification by using previous and posterior first-layer predicted stages as additional features providing information to the model. Results show that both approaches enhance the sleep stage classification accuracy rate, thus leading to a closer approximation to the experts' opinion.

Adaptive filtering and random variables coefficient for analyzing functional magnetic resonance imaging data

Functional magnetic resonance imaging (fMRI) is used to study brain functional connectivity (FC) after filtering the physiological noise (PN). Herein, we employ: adaptive filtering for removing nonstationary PN; random variables (RV) coefficient for FC analysis. Comparisons with standard techniques were performed by quantifying PN filtering and FC in neural vs. non-neural regions. As a result, adaptive filtering plus RV coefficient showed a greater suppression of PN and higher connectivity in neural regions, representing a novel effective approach to analyze fMRI data.

Phase synchronization in brain networks derived from correlation between probabilities of recurrences in functional MRI data

It is increasingly being recognized that resting state brain connectivity derived from functional magnetic resonance imaging (fMRI) data is an important marker of brain function both in healthy and clinical populations. Though linear correlation has been extensively used to characterize brain connectivity, it is limited to detecting first order dependencies. In this study, we propose a framework where in phase synchronization (PS) between brain regions is characterized using a new metric "correlation between probabilities of recurrence" (CPR) and subsequent graph-theoretic analysis of the ensuing networks. We applied this method to resting state fMRI data obtained from human subjects with and without administration of propofol anesthetic. Our results showed decreased PS during anesthesia and a biologically more plausible community structure using CPR rather than linear correlation. We conclude that CPR provides an attractive nonparametric method for modeling interactions in brain networks as compared to standard correlation for obtaining physiologically meaningful insights about brain function.

PHASE SYNCHRONIZATION OF NEURONAL NOISE IN MOUSE HIPPOCAMPAL EPILEPTIFORM DYNAMICS

Organized brain activity is the result of dynamical, segregated neuronal signals that may be used to investigate synchronization effects using sophisticated neuroengineering techniques. Phase synchrony analysis, in particular, has emerged as a promising methodology to study transient and frequency-specific coupling effects across multi-site signals. In this study, we investigated phase synchronization in intracellular recordings of interictal and ictal epileptiform events recorded from pairs of cells in the whole (intact) mouse hippocampus. In particular, we focused our analysis on the background noise-like activity (NLA), previously reported to exhibit complex neurodynamical properties. Our results show evidence for increased linear and nonlinear phase coupling in NLA across three frequency bands [theta (4–10 Hz), beta (12–30 Hz) and gamma (30–80 Hz)] in the ictal compared to interictal state dynamics. We also present qualitative and statistical evidence for increased phase synchronization in the theta, beta and gamma frequency bands from paired recordings of ictal NLA. Overall, our results validate the use of background NLA in the neurodynamical study of epileptiform transitions and suggest that what is considered "neuronal noise" is amenable to synchronization effects in the spatiotemporal domain.

ANALYSIS OF ABSENCE SEIZURE GENERATION USING EEG SPATIAL-TEMPORAL REGULARITY MEASURES

Epileptic seizures are thought to be generated and to evolve through an underlying anomaly of synchronization in the activity of groups of neuronal populations. The related dynamic scenario of state transitions is revealed by detecting changes in the dynamical properties of Electroencephalography (EEG) signals. The recruitment procedure ending with the crisis can be explored through a spatial-temporal plot from which to extract suitable descriptors that are able to monitor and quantify the evolving synchronization level from the EEG tracings. In this paper, a spatial-temporal analysis of EEG recordings based on the concept of permutation entropy (PE) is proposed. The performance of PE are tested on a database of 24 patients affected by absence (generalized) seizures. The results achieved are compared to the dynamical behavior of the EEG of 40 healthy subjects. Being PE a feature which is dependent on two parameters, an extensive study of the sensitivity of the performance of PE with respect to the parameters' setting was carried out on scalp EEG. Once the optimal PE configuration was determined, its ability to detect the different brain states was evaluated. According to the results here presented, it seems that the widely accepted model of "jump" transition to absence seizure should be in some cases coupled (or substituted) by a gradual transition model characteristic of self-organizing networks. Indeed, it appears that the transition to the epileptic status is heralded before the preictal state, ever since the interictal stages. As a matter of fact, within the limits of the analyzed database, the frontal-temporal scalp areas appear constantly associated to PE levels higher compared to the remaining electrodes, whereas the parieto-occipital areas appear associated to lower PE values. The EEG of healthy subjects neither shows any similar dynamic behavior nor exhibits any recurrent portrait in PE topography.

APPLICATION OF EMPIRICAL MODE DECOMPOSITION (EMD) FOR AUTOMATED DETECTION OF EPILEPSY USING EEG SIGNALS

Epilepsy is a global disease with considerable incidence due to recurrent unprovoked seizures. These seizures can be noninvasively diagnosed using electroencephalogram (EEG), a measure of neuronal electrical activity in brain recorded along scalp. EEG is highly nonlinear, nonstationary and non-Gaussian in nature. Nonlinear adaptive models such as empirical mode decomposition (EMD) provide intuitive understanding of information present in these signals. In this study a novel methodology is proposed to automatically classify EEG of normal, inter-ictal and ictal subjects using EMD decomposition. EEG decomposition using EMD yields few intrinsic mode functions (IMF), which are amplitude and frequency modulated (AM and FM) waves. Hilbert transform of these IMF provides AM and FM frequencies. Features such as spectral peaks, spectral entropy and spectral energy in each IMF are extracted and fed to decision tree classifier for automated diagnosis. In this work, we have compared the performance of classification using two types of decision trees (i) classification and regression tree (CART) and (ii) C4.5. We have obtained the highest average accuracy of 95.33%, average sensitivity of 98%, and average specificity of 97% using C4.5 decision tree classifier. The developed methodology is ready for clinical validation on large databases and can be deployed for mass screening.

Wavelet coherence model for diagnosis of Alzheimer disease

This article presents a wavelet coherence investigation of electroencephalograph (EEG) readings acquired from patients with Alzheimer disease (AD)  and healthy controls. Pairwise electrode wavelet coherence is calculated over each frequency band (delta, theta, alpha, and beta). For comparing the synchronization fraction of 2 EEG signals, a wavelet coherence fraction is proposed which is defined as the fraction of the signal time during which the wavelet coherence value is above a certain threshold. A one-way analysis of variance test shows a set of statistically significant differences in wavelet coherence between AD and controls. The wavelet coherence method is effective for studying cortical connectivity at a high temporal resolution. Compared with other conventional AD coherence studies, this study takes into account the time-frequency changes in coherence of EEG signals and thus provides more correlational details. A set of statistically significant differences was found in the wavelet coherence among AD and controls. In particular, temporocentral regions show a significant decrease in wavelet coherence in AD in the delta band, and the parietal and central regions show significant declines in cortical connectivity with most of their neighbors in the theta and alpha bands. This research shows that wavelet coherence can be used as a powerful tool to differentiate between healthy elderly individuals and probable AD patients.

ARTIFICIAL NEURAL NETWORK BASED APPROACH TO EEG SIGNAL SIMULATION

In this paper a new approach to the electroencephalogram (EEG) signal simulation based on the artificial neural networks (ANN) is proposed. The aim was to simulate the spontaneous human EEG background activity based solely on the experimentally acquired EEG data. Therefore, an EEG measurement campaign was conducted on a healthy awake adult in order to obtain an adequate ANN training data set. As demonstration of the performance of the ANN based approach, comparisons were made against autoregressive moving average (ARMA) filtering based method. Comprehensive quantitative and qualitative statistical analysis showed clearly that the EEG process obtained by the proposed method was in satisfactory agreement with the one obtained by measurements.

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.