Complexity of spontaneous brain activity in mental disorders

Let's fail better: Using philosophical tools to improve neuroscientific research in psychiatry

Despite predictions that neuroscientific discoveries would revolutionize psychiatry, decades of research have not yet led to clinically significant advances in psychiatric care. For this reason, an increasing number of researchers are recognizing the limitations of a purely biomedical approach in psychiatric research. These researchers call for reevaluating the conceptualization of mental disorders and argue for a non-reductionist approach to mental health. The aim of this paper is to discuss philosophical assumptions that underly neuroscientific research in psychiatry and offer practical tools to researchers for overcoming potential conceptual problems that are derived from those assumptions. Specifically, we will discuss: the analogy problem, questioning whether mental health problems are equivalent to brain disorders, the normativity problem, addressing the value-laden nature of psychiatric categories and the priority problem, which describes the level of analysis (e.g., biological, psychological, social, etc.) that should be prioritized when studying psychiatric conditions. In addition, we will explore potential strategies to mitigate practical problems that might arise due to these implicit assumptions. Overall, the aim of this paper is to suggest philosophical tools of practical use for neuroscientists, demonstrating the benefits of a closer collaboration between neuroscience and philosophy.

Electrophysiological functional connectivity and complexity reflecting cognitive processing speed heterogeneity in young children with ADHD

Early intervention is imperative for young children with attention-deficit/hyperactivity disorder (ADHD) who manifest heterogeneous neurocognitive deficits. The study investigated the functional connectivity and complexity of brain activity among young children with ADHD exhibiting a fast cognitive processing speed (ADHD-F, n = 26), with ADHD exhibiting a slow cognitive processing speed (ADHD-S, n = 17), and typically developing children (n = 35) using wireless electroencephalography (EEG) during rest and task conditions. During rest, compared with the typically developing group, the ADHD-F group displayed lower long-range intra-hemispheric connectivity, while the ADHD-S group had lower frontal beta inter-hemispheric connectivity. During task performance, the ADHD-S group displayed lower frontal beta inter-hemispheric connectivity than the typically developing group. The ADHD-S group had lower frontal inter-hemispheric connectivity in broader frequency bands than the ADHD-F group, indicating ADHD heterogeneity in mental processing speed. Regarding complexity, the ADHD-S group tended to show lower frontal entropy estimators than the typically developing group during the task condition. These findings suggest that the EEG profile of brain connectivity and complexity can aid the early clinical diagnosis of ADHD, support subgrouping young children with ADHD based on cognitive processing speed heterogeneity, and may contain specific novel neural biomarkers for early intervention planning.

Dynamic brain entropy predicts risky decision-making across transdiagnostic dimensions of psychopathology

OBJECTIVES

Maladaptive risky decision-making is a common pathological behavior among patients with various psychiatric disorders. Brain entropy, which measures the complexity of brain time series signals, provides a novel approach to assessing brain health. Despite its potential, the dynamics of brain entropy have seldom been explored. This study aimed to construct a dynamic model of brain entropy and examine its predictive value for risky decision-making in patients with mental disorders, utilizing resting-state functional magnetic resonance imaging (rs-fMRI).

METHODS

This study analyzed the rs-fMRI data from a total of 198 subjects, including 48 patients with bipolar disorder (BD), 47 patients with schizophrenia (SZ), 40 patients with adult attention deficit hyperactivity disorder (ADHD), as well as 63 healthy controls (HC). Time series signals were extracted from 264 brain regions based on rs-fMRI. The traditional static entropy and dynamic entropy (coefficient of variation, CV; rate of change, Rate) were constructed, respectively. Support vector regression was employed to predict risky decision-making utilizing leave-one-out cross-validation within each group.

RESULTS

Our findings showed that CV achieved the best performances in HC and BD groups (r = -0.58, MAE = 6.43, R2 = 0.32; r = -0.78, MAE = 12.10, R2 = 0.61), while the Rate achieved the best in SZ and ADHD groups (r = -0.69, MAE = 10.20, R2 = 0.47; r = -0.78, MAE = 7.63, R2 = 0.60). For the dynamic entropy, the feature selection threshold rather than the time window length and overlapping ratio influenced predictive performance.

CONCLUSIONS

These results suggest that dynamic brain entropy could be a more effective predictor of risky decision-making than traditional static brain entropy. Our findings offer a novel perspective on exploring brain signal complexity and can serve as a reference for interventions targeting risky decision-making behaviors, particularly in individuals with psychiatric diagnoses.

EEG complexity in emotion conflict task in individuals with psychiatric disorders

Analyzing EEG complexity may help to elucidate complex brain dynamics in individuals with psychiatric disorders and provide insight into neural connectivity and its relationship with deficits such as emotion-related impulsivity. EEG complexity was calculated through multiscale entropy and compared between a heterogeneous psychiatric patient group and a healthy control group during the emotion conflict resolution task. Twenty-eight healthy adults and ten psychiatric patients were recruited and compared on the multiscale entropy of EEG acquired in the task. Our results revealed a lower multiscale entropy in the psychiatric patient group compared to the healthy group during the task. This decrease in multiscale entropy suggests reduced long-range interaction between the left frontal region and other brain regions during the emotion conflict resolution task among psychiatric patients. Notably, a positive correlation was observed between multiscale entropy and impulsivity measures in the psychiatric patient group, where the higher the EEG complexity during the emotion regulation task, the higher the level of self-reported impulsivity in the psychiatric patients. Such impulsivity was evident in both healthy individuals and psychiatric patients, with healthy individuals showing shorter reaction times on incongruent conditions compared to congruent conditions and psychiatric patients displaying similar reaction times in both conditions, This study highlights the significance of investigating EEG complexity and its potential applications in the transdiagnostic exploration of impulsivity in psychiatric disorders.

Exploring the disruptions of the neurophysiological organization in Alzheimer's disease: An integrative approach

BACKGROUND AND OBJECTIVE

Alzheimer's disease (AD) is a neurological disorder that impairs brain functions associated with cognition, memory, and behavior. Noninvasive neurophysiological techniques like magnetoencephalography (MEG) and electroencephalography (EEG) have shown promise in reflecting brain changes related to AD. These techniques are usually assessed at two levels: local activation (spectral, nonlinear, and dynamic properties) and global synchronization (functional connectivity, frequency-dependent network, and multiplex network organization characteristics). Nonetheless, the understanding of the organization formed by the existing relationships between these levels, henceforth named neurophysiological organization, remains unexplored. This work aims to assess the alterations AD causes in the resting-state neurophysiological organization.

METHODS

To that end, three datasets from healthy controls (HC) and patients with dementia due to AD were considered: MEG database (55 HC and 87 patients with AD), EEG1 database (51 HC and 100 patients with AD), and EEG2 database (45 HC and 82 patients with AD). To explore the alterations induced by AD in the relationships between several features extracted from M/EEG data, association networks (ANs) were computed. ANs are graphs, useful to quantify and visualize the intricate relationships between multiple features.

RESULTS

Our results suggested a disruption in the neurophysiological organization of patients with AD, exhibiting a greater inclination towards the local activation level; and a significant decrease in the complexity and diversity of the ANs (p-value ¡ 0.05, Mann-Whitney U-test, Bonferroni correction). This effect might be due to a shift of the neurophysiological organization towards more regular configurations, which may increase its vulnerability. Moreover, our findings support the crucial role played by the local activation level in maintaining the stability of the neurophysiological organization. Classification performance exhibited accuracy values of 83.91%, 73.68%, and 72.65% for MEG, EEG1, and EEG2 databases, respectively.

CONCLUSION

This study introduces a novel, valuable methodology able to integrate parameters characterize different properties of the brain activity and to explore the intricate organization of the neurophysiological organization at different levels. It was noted that AD increases susceptibility to changes in functional neural organization, suggesting a greater ease in the development of severe impairments. Therefore, ANs could facilitate a deeper comprehension of the complex interactions in brain function from a global standpoint.

Functional connectivity and complexity analyses of resting-state fMRI in pre-adolescents demonstrating the behavioral symptoms of ADHD

Attention deficit hyperactivity disorder (ADHD) has been characterized by impairments among distributed functional brain networks, e.g., the frontoparietal network (FPN), default mode network (DMN), reward and motivation-related circuits (RMN), and salience network (SAL). In the current study, we evaluated the complexity and functional connectivity (FC) of resting state fMRI (rsfMRI) in pre-adolescents with the behavioral symptoms of ADHD, for pathology-relevant networks. We leveraged data from the Adolescent Brain and Cognitive Development (ABCD) Study. The final study sample included 63 children demonstrating the behavioral features of ADHD and 92 healthy control children matched on age, sex, and pubertal development status. For selected regions in the relevant networks, ANCOVA compared multiscale entropy (MSE) and FC between the groups. Finally, differences in the association between MSE and FC were evaluated. We found significantly reduced MSE along with increased FC within the FPN of pre-adolescents demonstrating the behavior symptoms of ADHD compared to matched healthy controls. Significant partial correlations between MSE and FC emerged in the FPN and RMN in the healthy controls however the association was absent in the participants demonstrating the behavior symptoms of ADHD. The current findings of complexity and FC in ADHD pathology support hypotheses of altered function of inhibitory control networks in ADHD.

The brain entropy dynamics in resting state

As a novel measure for irregularity and complexity of the spontaneous fluctuations of brain activities, brain entropy (BEN) has attracted much attention in resting-state functional magnetic resonance imaging (rs-fMRI) studies during the last decade. Previous studies have shown its associations with cognitive and mental functions. While most previous research assumes BEN is approximately stationary during scan sessions, the brain, even at its resting state, is a highly dynamic system. Such dynamics could be characterized by a series of reoccurring whole-brain patterns related to cognitive and mental processes. The present study aims to explore the time-varying feature of BEN and its potential links with general cognitive ability. We adopted a sliding window approach to derive the dynamical brain entropy (dBEN) of the whole-brain functional networks from the HCP (Human Connectome Project) rs-fMRI dataset that includes 812 young healthy adults. The dBEN was further clustered into 4 reoccurring BEN states by the k-means clustering method. The fraction window (FW) and mean dwell time (MDT) of one BEN state, characterized by the extremely low overall BEN, were found to be negatively correlated with general cognitive abilities (i.e., cognitive flexibility, inhibitory control, and processing speed). Another BEN state, characterized by intermediate overall BEN and low within-state BEN located in DMN, ECN, and part of SAN, its FW, and MDT were positively correlated with the above cognitive abilities. The results of our study advance our understanding of the underlying mechanism of BEN dynamics and provide a potential framework for future investigations in clinical populations.

Atypical instantaneous spatio-temporal patterns of neural dynamics in Alzheimer's disease

Cognitive functions produced by large-scale neural integrations are the most representative 'emergence phenomena' in complex systems. A novel approach focusing on the instantaneous phase difference of brain oscillations across brain regions has succeeded in detecting moment-to-moment dynamic functional connectivity. However, it is restricted to pairwise observations of two brain regions, contrary to large-scale spatial neural integration in the whole-brain. In this study, we introduce a microstate analysis to capture whole-brain instantaneous phase distributions instead of pairwise differences. Upon applying this method to electroencephalography signals of Alzheimer's disease (AD), which is characterised by progressive cognitive decline, the AD-specific state transition among the four states defined as the leading phase location due to the loss of brain regional interactions could be promptly characterised. In conclusion, our synthetic analysis approach, focusing on the microstate and instantaneous phase, enables the capture of the instantaneous spatiotemporal neural dynamics of brain activity and characterises its pathological conditions.

EEG Complexity Analysis of Brain States, Tasks and ASD Risk

Autism spectrum disorder is an increasingly prevalent and debilitating neurodevelopmental condition and an electroencephalogram (EEG) diagnostic challenge. Despite large amounts of electrophysiological research over many decades, an EEG biomarker for autism spectrum disorder (ASD) has not been found. We hypothesized that reductions in complex dynamical system behaviour in the human central nervous system as part of the macroscale neuronal function during cognitive processes might be detectable in whole EEG for higher-risk ASD adults. In three studies, we compared the medians of correlation dimension, largest Lyapunov exponent, Higuchi's fractal dimension, multiscale entropy, multifractal detrended fluctuation analysis and Kolmogorov complexity during resting, cognitive and social skill tasks in 20 EEG channels of 39 adults over a range of ASD risk. We found heterogeneous complexity distribution with clusters of hierarchical sequences pointing to potential cognitive processing differences, but no clear distinction based on ASD risk. We suggest that there is indication of statistically significant differences between complexity measures of brain states and tasks. Though replication of our studies is needed with a larger sample, we believe that our electrophysiological and analytic approach has potential as a biomarker for earlier ASD diagnosis.

Effect of Genetic Risk on the Relationship Between rs-fMRI Complexity and Tau and Amyloid PET in Alzheimer's Disease

Reduced functional magnetic resonance imaging (fMRI)-complexity in Alzheimer's disease (AD) progression has been demonstrated and found to be associated with tauopathy and cognition. However, association of fMRI-complexity with amyloid and influence of genetic risk (APOEɛ4) remain unknown. Here we investigate the association between fMRI-complexity, tau-PET, and amyloid-PET as well as influence of APOE genotype using multivariate generalized linear models. We show that fMRI-complexity has a strong association with tau but not amyloid deposition and that the presence of an APOEɛ4 allele enhances this effect. Thus fMRI-complexity provides a surrogate marker of impaired brain functionality in AD progression.

Modulation of Resting-State Brain Complexity After Bilateral Cerebellar Anodal Transcranial Direct Current Stimulation in Children with Autism Spectrum Disorders: a Randomized Controlled Trial Study

BACKGROUND

Autism spectrum disorders (ASD) are heterogeneous neurodevelopmental disorders characterized by aberrant neural networks. Cerebellum is best known for its role in controlling motor behaviors; however, recently, there have been significant reports showed that dysfunction in cerebellar-cerebral networks contributes significantly to many of the clinical features of ASD. Hereby, this is a randomized controlled trial (RCT) study examining the potential modulating effects of bilateral anodal tDCS stimulation over cerebellar hemispheres on the resting-state brain complexity in children with ASD.

METHODS

Thirty-six children with ASD (aged 4-14) years old were divided equally and randomly into a tDCS treatment group, which underwent 10 sessions (20-min duration, five sessions/per week) of bilateral anodal tDCS stimulation applied over left and right cerebellar hemispheres, and control group underwent the same procedures, but with sham tDCS stimulation. Resting-state brain complexity was evaluated through recording and calculating the approximate entropy (ApxEnt) values of the resting-state electroencephalograph (EEG) data obtained from a 64-channel EEG system before and after the interventions.

RESULTS

Repeated measures of ANOVA showed that tDCS had significant effects on the treatment group (Wilks' Lambda = 0.29, F (15, 16) = 2.67, p = 0.03) compared with the control group. Analyzed data showed a significant increase in the averaged ApxEnt values in the right frontal cortical region (F (1, 16) = 10.46, p = 0.005) after the bilateral cerebellar anodal tDCS stimulation. Besides, the Cohen's d effect size showed a large effect size (0.70-0.92) of bilateral cerebellar anodal tDCS on the ApxEnt values increases in the left and right frontal cortical regions, the right central cortical region, and left parietal cortical region. However, there were no any significant differences or increases in the brain complexity before and after the sham tDCS stimulation of the control group.

CONCLUSION

Bilateral cerebellar anodal tDCS modulated and increased the brain complexity in children with ASD with no any reported adverse effect. Hereby, cerebellum and cerebellar-cerebral circuitry would serve as a promising target for non-invasive brain stimulation and neuro-modulation as a therapeutic intervention.

Entropy and fractal analysis of brain-related neurophysiological signals in Alzheimer's and Parkinson's disease

Brain-related neuronal recordings, such as local field potential, electroencephalogram and magnetoencephalogram, offer the opportunity to study the complexity of the human brain at different spatial and temporal scales. The complex properties of neuronal signals are intrinsically related to the concept of 'scale-free' behavior and irregular dynamic, which cannot be fully described through standard linear methods, but can be measured by nonlinear indexes. A remarkable application of these analysis methods on electrophysiological recordings is the deep comprehension of the pathophysiology of neurodegenerative diseases, that has been shown to be associated to changes in brain activity complexity. In particular, a decrease of global complexity has been associated to Alzheimer's disease, while a local increase of brain signals complexity characterizes Parkinson's disease. Despite the recent proliferation of studies using fractal and entropy-based analysis, the application of these techniques is still far from clinical practice, due to the lack of an agreement about their correct estimation and a conclusive and shared interpretation. Along with the aim of helping towards the realization of a multidisciplinary audience to approach nonlinear methods based on the concepts of fractality and irregularity, this survey describes the implementation and proper employment of the mostly known and applied indexes in the context of Alzheimer's and Parkinson's diseases.

Linear and Non-linear Analyses of EEG in a Group of ASD Children During Resting State Condition

This study analyses the spontaneous electroencephalogram (EEG) brain activity of 14 children diagnosed with Autism Spectrum Disorder (ASD) compared to 18 children with normal development, aged 5-11 years. (i) Power Spectral Density (PSD), (ii) variability across trials (coefficient of variation: CV), and (iii) complexity (multiscale entropy: MSE) of the brain signal analysis were computed on the resting state EEG. PSD (0.5-45 Hz) and CV were averaged over different frequency bands (low-delta, delta, theta, alpha, low-beta, high-beta and gamma). MSE were calculated with a coarse-grained procedure on 67 time scales and divided into fine, medium and coarse scales. In addition, significant neurophysiological variables were correlated with behavioral performance data (Kaufman Brief Intelligence Test (KBIT) and Autism Spectrum Quotient (AQ)). Results show increased PSD fast frequency bands (high-beta and gamma), higher variability (CV) and lower complexity (MSE) in children with ASD when compared to typically developed children. These results suggest a more variable, less complex and, probably, less adaptive neural networks with less capacity to generate optimal responses in ASD children.

Nonlinear features of gaze behavior during joint attention in children with autism spectrum disorder

Since children with autism spectrum disorder (ASD) might exhibit a variety of aberrant response to joint attention (RJA) behaviors, there is growing interest in identifying robust, reliable and valid eye-tracking metrics for determining differences in RJA behaviors between typically developing (TD) children and those with ASD. Previous eye-tracking studies have not been deeply investigated nonlinear features of gaze time-series during RJA. As a main motivation, this study aimed to extract three nonlinear features (i.e., complexity, long-range correlation, and local instability) of gaze time-series during RJA in children with ASD, which can be measured by fractal dimension (FD), Hurst exponent (H), and largest Lyapunov exponent (LLE), respectively. To illustrate our idea, this study adopted a publicly accessible database, including eye-tracking data collected during RJA from 19 children with ASD (7.74 ± 2.73) and 30 TD children (8.02 ± 2.89), and conducted a battery of nonparametric analysis of covariance (ANCOVA), where gender was used as covariable. Findings showed that gaze time-series during RJA in autistic children may generally have greater FD but lower H than that in TD controls. This implies that children with ASD possess more complex and unpredictable gaze behaviors during RJA than TD children. Furthermore, nonlinear metrics outperformed traditional eye-tracking metrics in obtaining higher identification performance with an accuracy of 82% and an AUC value of 0.81, distinguishing the differences between successful and failed RJA trails, and predicting the severity of ASD symptoms. Findings might bring some new insights into the understanding of the impairments in RJA behaviors for children with ASD.

Functional Connectivity and Complexity Analyses of Resting-State fMRI in Pre-Adolescents with ADHD

Attention deficit hyperactivity disorder (ADHD) has been characterized by impairments among distributed functional brain networks, e.g., the frontoparietal network (FPN), default mode network (DMN), and reward and motivation-related circuits (RMN). In the current study, we evaluated the complexity and functional connectivity (FC) of resting state fMRI (rsfMRI) in pre-adolescents with ADHD for pathology-relevant networks. We leveraged data from the Adolescent Brain and Cognitive Development (ABCD) Study. The final study sample included 63 children with ADHD and 92 healthy control children matched on age, sex, and pubertal development status. For selected regions in relevant networks, ANCOVA compared multiscale entropy (MSE) and FC between the groups. Finally, differences in the association between MSE and FC were evaluated. We found significantly reduced MSE along with increased FC within the FPN of pre-adolescents with ADHD compared to matched healthy controls. Significant partial correlations between MSE and FC emerged in fewer regions in the participants with ADHD than in the controls. The observation of reduced entropy is consistent with existing literature using rsfMRI and other neuroimaging modalities. The current findings of complexity and FC in ADHD support hypotheses of altered function of inhibitory control networks in ADHD.

A Bio-Inspired Chaos Sensor Model Based on the Perceptron Neural Network: Machine Learning Concept and Application for Computational Neuro-Science

The study presents a bio-inspired chaos sensor model based on the perceptron neural network for the estimation of entropy of spike train in neurodynamic systems. After training, the sensor on perceptron, having 50 neurons in the hidden layer and 1 neuron at the output, approximates the fuzzy entropy of a short time series with high accuracy, with a determination coefficient of R2~0.9. The Hindmarsh-Rose spike model was used to generate time series of spike intervals, and datasets for training and testing the perceptron. The selection of the hyperparameters of the perceptron model and the estimation of the sensor accuracy were performed using the K-block cross-validation method. Even for a hidden layer with one neuron, the model approximates the fuzzy entropy with good results and the metric R2~0.5 ÷ 0.8. In a simplified model with one neuron and equal weights in the first layer, the principle of approximation is based on the linear transformation of the average value of the time series into the entropy value. An example of using the chaos sensor on spike train of action potential recordings from the L5 dorsal rootlet of rat is provided. The bio-inspired chaos sensor model based on an ensemble of neurons is able to dynamically track the chaotic behavior of a spike signal and transmit this information to other parts of the neurodynamic model for further processing. The study will be useful for specialists in the field of computational neuroscience, and also to create humanoid and animal robots, and bio-robots with limited resources.

Multiscale entropy of ADHD children during resting state condition

This present study aims to investigate neural mechanisms underlying ADHD compared to healthy children through the analysis of the complexity and the variability of the EEG brain signal using multiscale entropy (MSE), EEG signal standard deviation (SDs), as well as the mean, standard deviation (SDp) and coefficient of variation (CV) of absolute spectral power (PSD). For this purpose, a sample of children diagnosed with attention-deficit/hyperactivity disorder (ADHD) between 6 and 17 years old were selected based on the number of trials and diagnostic agreement, 32 for the open-eyes (OE) experimental condition and 25 children for the close-eyes (CE) experimental condition. Healthy control subjects were age- and gender-matched with the ADHD group. The MSE and SDs of resting-state EEG activity were calculated on 34 time scales using a coarse-grained procedure. In addition, the PSD was averaged in delta, theta, alpha, and beta frequency bands, and its mean, SDp, and CV were calculated. The results show that the MSE changes with age during development, increases as the number of scales increases and has a higher amplitude in controls than in ADHD. The absolute PSD results show CV differences between subjects in low and beta frequency bands, with higher variability values in the ADHD group. All these results suggest an increased EEG variability and reduced complexity in ADHD compared to controls.

Supplementary Information

The online version contains supplementary material available at 10.1007/s11571-022-09869-0.

Cognitive Remediation and Schizophrenia: Effects on Brain Complexity

The objective of this study is to investigate nonlinear neural dynamics of chronic patients with schizophrenia following 3 months of cognitive remediation and to find correlations with neuropsychological measures of cognition. Twenty nine patients were randomized to Cognitive Training (CT) and Treatment as Usual (TAU) group. The system complexity is estimated by Correlation Dimension (D₂) and Largest Lyapunov Exponent (LLE) from the reconstructed attractor of the underlying system. Significant increase in dimensional complexity (D₂) over time is observed in prefrontal and medial frontal-central regions in eyes open and arithmetic condition; and posterior parietal-occipital region under eyes closed after 3 months. Dynamical complexity (LLE) significantly decreased over time in medial left central region under eyes closed and eyes open condition; prefrontal region in eyes open and lateral right temporal region in arithmetic condition. Interaction is significant for medial left central region with TAU group exhibiting greater decrease in LLE compared to CT group. The CT group showed significant correlation of increased D₂ with focused attention. In this study it is found that patients with schizophrenia exhibit higher dimensional and lower dynamical complexity over time indicating improvement in neurodynamics of underlying physiological system.

A primer on entropy in neuroscience

Entropy is not just a property of a system - it is a property of a system and an observer. Specifically, entropy is a measure of the amount of hidden information in a system that arises due to an observer's limitations. Here we provide an account of entropy from first principles in statistical mechanics with the aid of toy models of neural systems. Specifically, we describe the distinction between micro and macrostates in the context of simplified binary-state neurons and the characteristics of entropy required to capture an associated measure of hidden information. We discuss the origin of the mathematical form of entropy via the indistinguishable re-arrangements of discrete-state neurons and show the way in which the arguments are extended into a phase space description for continuous large-scale neural systems. Finally, we show the ways in which limitations in neuroimaging resolution, as represented by coarse graining operations in phase space, lead to an increase in entropy in time as per the second law of thermodynamics. It is our hope that this primer will support the increasing number of studies that use entropy as a way of characterising neuroimaging timeseries and of making inferences about brain states.

Systematic Review on EEG Analysis to Diagnose and Treat Autism by Evaluating Functional Connectivity and Spectral Power

An abnormality in neural connectivity is linked to autism spectrum disorder (ASD). There is no way to test the concept of neural connectivity empirically. According to recent network theory and time series analysis findings, electroencephalography (EEG) can assess neural network architecture, a sign of activity in the brain. This systematic review aims to evaluate functional connectivity and spectral power using EEG signals. EEG records the brain activity of an individual by displaying wavy lines that depict brain cells' communication through electrical impulses. EEG can diagnose various brain disorders, including epilepsy and related seizure illness, brain dysfunction, tumors, and damage. We found 21 studies using two of the most common EEG analysis methods: functional connectivity and spectral power. ASD and non-ASD individuals were found to differ significantly in all selected papers. Due to high heterogeneity in the outcomes, generalizations cannot be drawn, and no single method is currently beneficial as a diagnostic tool. For ASD subtype delineation, the lack of research prevented the evaluation of these techniques as diagnostic tools. These findings confirm the presence of abnormalities in the EEG in ASD, but they are insufficient to diagnose. Our study suggests that EEG is useful in diagnosing ASD by evaluating entropy in the brain. Researchers may be able to develop new diagnostic methods for ASD which focuses on particular stimuli and brainwaves if they conduct more extensive studies with higher numbers and more rigorous study designs.

Automatic diagnosis of late-life depression by 3D convolutional neural networks and cross-sample Entropy analysis from resting-state fMRI

Resting-state fMRI has been widely used in investigating the pathophysiology of late-life depression (LLD). Unlike the conventional linear approach, cross-sample entropy (CSE) analysis shows the nonlinear property in fMRI signals between brain regions. Moreover, recent advances in deep learning, such as convolutional neural networks (CNNs), provide a timely application for understanding LLD. Accurate and prompt diagnosis is essential in LLD; hence, this study aimed to combine CNN and CSE analysis to discriminate LLD patients and non-depressed comparison older adults based on brain resting-state fMRI signals. Seventy-seven older adults, including 49 patients and 28 comparison older adults, were included for fMRI scans. Three-dimensional CSEs with volumes corresponding to 90 seed regions of interest of each participant were developed and fed into models for disease classification and depression severity prediction. We obtained a diagnostic accuracy > 85% in the superior frontal gyrus (left dorsolateral and right orbital parts), left insula, and right middle occipital gyrus. With a mean root-mean-square error (RMSE) of 2.41, three separate models were required to predict depressive symptoms in the severe, moderate, and mild depression groups. The CSE volumes in the left inferior parietal lobule, left parahippocampal gyrus, and left postcentral gyrus performed best in each respective model. Combined complexity analysis and deep learning algorithms can classify patients with LLD from comparison older adults and predict symptom severity based on fMRI data. Such application can be utilized in precision medicine for disease detection and symptom monitoring in LLD.

Enhanced temporal complexity of EEG signals in older individuals with high cognitive functions

Recent studies suggest that the maintenance of cognitive function in the later life of older people is an essential factor contributing to mental wellbeing and physical health. Particularly, the risk of depression, sleep disorders, and Alzheimer's disease significantly increases in patients with mild cognitive impairment. To develop early treatment and prevention strategies for cognitive decline, it is necessary to individually identify the current state of cognitive function since the progression of cognitive decline varies among individuals. Therefore, the development of biomarkers that allow easier measurement of cognitive function in older individuals is relevant for hyperaged societies. One of the methods used to estimate cognitive function focuses on the temporal complexity of electroencephalography (EEG) signals. The characteristics of temporal complexity depend on the time scale, which reflects the range of neuron functional interactions. To capture the dynamics, composed of multiple time scales, multiscale entropy (MSE) analysis is effective for comprehensively assessing the neural activity underlying cognitive function in the brain. Thus, we hypothesized that EEG complexity analysis could serve to assess a wide range of cognitive functions in older adults. To validate our hypothesis, we divided older participants into two groups based on their cognitive function test scores: a high cognitive function group and a low cognitive function group, and applied MSE analysis to the measured EEG data of all participants. The results of the repeated-measures analysis of covariance using age and sex as a covariate in the MSE profile showed a significant difference between the high and low cognitive function groups (F = 10.18, p = 0.003) and the interaction of the group × electrodes (F = 3.93, p = 0.002). Subsequently, the results of the post-hoct-test showed high complexity on a slower time scale in the frontal, parietal, and temporal lobes in the high cognitive function group. This high complexity on a slow time scale reflects the activation of long-distance neural interactions among various brain regions to achieve high cognitive functions. This finding could facilitate the development of a tool for diagnosis of cognitive decline in older individuals.

A Case Study on EEG Analysis: Embedding Entropy Estimations Indicate the Decreased Neuro-Cortical Complexity Levels Mediated by Methylphenidate Treatment in Children with ADHD

Objective: Complexity analysis is a method employed to understand the activity of the brain. The effect of methylphenidate (MPH) treatment on neuro-cortical complexity changes is still unknown. This study aimed to reveal how MPH treatment affects the brain complexity of children with attention deficit hyperactivity disorder (ADHD) using entropy-based quantitative EEG analysis. Three embedding entropy approaches were applied to short segments of both pre- and post- medication EEG series. EEG signals were recorded for 25 boys with combined type ADHD prior to the administration of MPH and at the end of the first month of the treatment. Results: In comparison to Approximate Entropy (ApEn) and Sample Entropy (SampEn), Permutation Entropy (PermEn) provided the most sensitive estimations in investigating the impact of MPH treatment. In detail, the considerable decrease in EEG complexity levels were observed at six cortical regions (F3, F4, P4, T3, T6, O2) with statistically significant level (p < .05). As well, PermEn provided the most meaningful associations at central lobes as follows: 1) The largeness of EEG complexity levels was moderately related to the severity of ADHD symptom detected at pre-treatment stage. 2) The percentage change in the severity of opposition as the symptom cluster was moderately reduced by the change in entropy. Conclusion: A significant decrease in entropy levels in the frontal region was detected in boys with combined type ADHD undergoing MPH treatment at resting-state mode. The changes in entropy correlated with pre-treatment general symptom severity of ADHD and conduct disorder symptom cluster severity.

EMD-based analysis of complexity with dissociated EEG amplitude and frequency information: a data-driven robust tool -for Autism diagnosis- compared to multi-scale entropy approach

OBJECTIVE

Autism spectrum disorder (ASD) is usually characterised by altered social skills, repetitive behaviours, and difficulties in verbal/nonverbal communication. It has been reported that electroencephalograms (EEGs) in ASD are characterised by atypical complexity. The most commonly applied method in studies of ASD EEG complexity is multiscale entropy (MSE), where the sample entropy is evaluated across several scales. However, the accuracy of MSE-based classifications between ASD and neurotypical EEG activities is poor owing to several shortcomings in scale extraction and length, the overlap between amplitude and frequency information, and sensitivity to frequency. The present study proposes a novel, nonlinear, non-stationary, adaptive, data-driven, and accurate method for the classification of ASD and neurotypical groups based on EEG complexity and entropy without the shortcomings of MSE.

APPROACH

The proposed method is as follows: (a) each ASD and neurotypical EEG (122 subjects × 64 channels) is decomposed using empirical mode decomposition (EMD) to obtain the intrinsic components (intrinsic mode functions). (b) The extracted components are normalised through the direct quadrature procedure. (c) The Hilbert transforms of the components are computed. (d) The analytic counterparts of components (and normalised components) are found. (e) The instantaneous frequency function of each analytic normalised component is calculated. (f) The instantaneous amplitude function of each analytic component is calculated. (g) The Shannon entropy values of the instantaneous frequency and amplitude vectors are computed. (h) The entropy values are classified using a neural network (NN). (i) The achieved accuracy is compared to that obtained with MSE-based classification. (j) The consistency of the results of entropy 3D mapping with clinical data is assessed.

MAIN RESULTS

The results demonstrate that the proposed method outperforms MSE (accuracy: 66.4%), with an accuracy of 93.5%. Moreover, the entropy 3D mapping results are more consistent with the available clinical data regarding brain topography in ASD.

SIGNIFICANCE

This study presents a more robust alternative to MSE, which can be used for accurate classification of ASD/neurotypical as well as for the examination of EEG entropy across brain zones in ASD.

Electroencephalography complexity in resting and task states in adults with attention-deficit/hyperactivity disorder

Analysing EEG complexity could provide insight into neural connectivity underlying attention-deficit/hyperactivity disorder symptoms. EEG complexity was calculated through multiscale entropy and compared between adults with attention-deficit/hyperactivity disorder and their peers during resting and go/nogo task states. Multiscale entropy change from the resting state to the task state was also examined as an index of the brain’s ability to change from a resting to an active state. Thirty unmedicated adults with attention-deficit/hyperactivity disorder were compared with 30 match-paired healthy peers on the multiscale entropy in the resting and task states as well as their multiscale entropy change. Results showed differences in multiscale entropy between individuals with attention-deficit/hyperactivity disorder and their peers during the resting state as well as the task state. The multiscale entropy measured from the comparison group was larger than that from the attention-deficit/hyperactivity disorder group in the resting state, whereas the reverse pattern was found during the task state. Our most robust finding showed that the multiscale entropy change from individuals with attention-deficit/hyperactivity disorder was smaller than that from their peers, specifically at frontal sites. Interestingly, individuals without attention-deficit/hyperactivity disorder performed better with decreasing multiscale entropy changes, demonstrating higher accuracy, faster reaction time and less variability in their reaction times. These data suggest that multiscale entropy could not only provide insight into neural connectivity differences between adults with attention-deficit/hyperactivity disorder and their peers but also into their behavioural performance.

Alteration of Neural Network Activity With Aging Focusing on Temporal Complexity and Functional Connectivity Within Electroencephalography

With the aging process, brain functions, such as attention, memory, and cognitive functions, degrade over time. In a super-aging society, the alteration of neural activity owing to aging is considered crucial for interventions for the prevention of brain dysfunction. The complexity of temporal neural fluctuations with temporal scale dependency plays an important role in optimal brain information processing, such as perception and thinking. Complexity analysis is a useful approach for detecting cortical alteration in healthy individuals, as well as in pathological conditions, such as senile psychiatric disorders, resulting in changes in neural activity interactions among a wide range of brain regions. Multi-fractal (MF) and multi-scale entropy (MSE) analyses are known methods for capturing the complexity of temporal scale dependency of neural activity in the brain. MF and MSE analyses exhibit high accuracy in detecting changes in neural activity and are superior with regard to complexity detection when compared with other methods. In addition to complex temporal fluctuations, functional connectivity reflects the integration of information of brain processes in each region, described as mutual interactions of neural activity among brain regions. Thus, we hypothesized that the complementary relationship between functional connectivity and complexity could improve the ability to detect the alteration of spatiotemporal patterns observed on electroencephalography (EEG) with respect to aging. To prove this hypothesis, this study investigated the relationship between the complexity of neural activity and functional connectivity in aging based on EEG findings. Concretely, MF and MSE analyses were performed to evaluate the temporal complexity profiles, and phase lag index analyses assessing the unique profile of functional connectivity were performed based on the EEGs conducted for young and older participants. Subsequently, these profiles were combined through machine learning. We found that the complementary relationship between complexity and functional connectivity improves the classification accuracy among aging participants. Thus, the outcome of this study could be beneficial in formulating interventions for the prevention of age-related brain dysfunction.

Shared increased entropy of brain signals across patients with different mental illnesses: A coordinate-based activation likelihood estimation meta-analysis

Entropy is a measurement of brain signal complexity. Studies have found increased/decreased entropy of brain signals in psychiatric patients. There is no consistent conclusion regarding the relationship between the entropy of brain signals and mental illness. Therefore, this meta-analysis aimed to identify consistent abnormalities in the brain signal entropy in patients with different mental illnesses. We conducted a systematic search to collect resting-state functional magnetic resonance imaging (rs-fMRI) studies in patients with psychiatric disorders. This work identified 9 eligible rs-fMRI studies, which included a total of 14 experiments, 67 activation foci, and 1383 subjects. We tested the convergence across their findings by using the activation likelihood estimation method. P-value maps were corrected by using cluster-level family-wise error p < 0.05 and permuting 2000 times. Results showed that patients with different psychiatric disorders shared commonly increased entropy of brain signals in the left inferior and middle frontal gyri, and the right fusiform gyrus, cuneus, precuneus. No shared alterations were found in the subcortical regions and cerebellum in the patient group. Our findings suggested that the increased entropy of brain signals in the cortex, not subcortical regions and cerebellum, might have associations with the pathophysiology across mental illnesses. This meta-analysis study provided the first comprehensive understanding of the abnormality in brain signal complexity across patients with different psychiatric disorders.

Multivariate Classification of Brain Blood-Oxygen Signal Complexity for the Diagnosis of Children with Tourette Syndrome

Tourette syndrome (TS) is a childhood-onset neuropsychiatric disorder characterized by the presence of multiple motor and vocal tics. Because of its varied clinical expressions and lack of reliable diagnostic biomarker, present TS diagnosis still depends on qualitative descriptions of symptoms. Our study aimed to investigate whether the complexity of resting state brain activity can serve as a potential biomarker for TS diagnosis, since it has been used successfully in various neuropsychiatric disorders, including two common TS comorbidities: attention-deficit hyperactivity disorder (ADHD) and obsessive-compulsive disorder (OCD). In the current study, we used both univariate analysis and multivariate searchlight analysis with both linear and non-linear classification methods to explore the group differences in the complexity of resting state brain blood oxygen level-dependent (BOLD) signals between 25 TS boys without comorbidity and 25 sex, age and educational years matched healthy controls (HCs). We also investigated the relation between symptom severity in TS patients (YGTSS scores) and complexity indices derived from different analysis methods. We found: i) univariate analysis revealed reduced complexity in TS patients in the left cerebellum, left superior frontal gyrus, and left medial frontal gyrus; ii) multivariate analysis with non-linear classification method achieved the highest performance (accuracy: 0.94, sensitivity: 0.96, specificity: 0.92, AUC: 0.95) in bilateral supplementary motor areas; iii) significant correlations were found between complexity index derived from multivariate analysis with non-linear classification method and Tic severity (YGTSS scores) in the left cerebellum (r = 0.523, with YGTSS phonic) and in the right supplementary motor area (r = 0.767, with YGTSS motor). Taken together, these results suggested that complexity of resting state BOLD activity is a highly effective index for differentiating TS patients from normal controls. It has a good potential to be a quantitative biomarker for TS diagnosis.

A Comparative Study of Functional Connectivity Measures for Brain Network Analysis in the Context of AD Detection with EEG

This work addresses brain network analysis considering different clinical severity stages of cognitive dysfunction, based on resting-state electroencephalography (EEG). We use a cohort acquired in real-life clinical conditions, which contains EEG data of subjective cognitive impairment (SCI) patients, mild cognitive impairment (MCI) patients, and Alzheimer’s disease (AD) patients. We propose to exploit an epoch-based entropy measure to quantify the connectivity links in the networks. This entropy measure relies on a refined statistical modeling of EEG signals with Hidden Markov Models, which allow a better estimation of the spatiotemporal characteristics of EEG signals. We also propose to conduct a comparative study by considering three other measures largely used in the literature: phase lag index, coherence, and mutual information. We calculated such measures at different frequency bands and computed different local graph parameters considering different proportional threshold values for a binary network analysis. After applying a feature selection procedure to determine the most relevant features for classification performance with a linear Support Vector Machine algorithm, our study demonstrates the effectiveness of the statistical entropy measure for analyzing the brain network in patients with different stages of cognitive dysfunction.

Signal complexity indicators of health status in clinical EEG

Brain signal variability changes across the lifespan in both health and disease, likely reflecting changes in information processing capacity related to development, aging and neurological disorders. While signal complexity, and multiscale entropy (MSE) in particular, has been proposed as a biomarker for neurological disorders, most observations of altered signal complexity have come from studies comparing patients with few to no comorbidities against healthy controls. In this study, we examined whether MSE of brain signals was distinguishable across patient groups in a large and heterogeneous set of clinical-EEG data. Using a multivariate analysis, we found unique timescale-dependent differences in MSE across various neurological disorders. We also found MSE to differentiate individuals with non-brain comorbidities, suggesting that MSE is sensitive to brain signal changes brought about by metabolic and other non-brain disorders. Such changes were not detectable in the spectral power density of brain signals. Our findings suggest that brain signal complexity may offer complementary information to spectral power about an individual's health status and is a promising avenue for clinical biomarker development.

Altered complexity in resting-state fNIRS signal in autism: a multiscale entropy approach

Objective.Feature extraction and recognition in brain signal processing is of great significance for understanding the neurological mechanism of autism spectrum disorder (ASD). Resting-state (RS) functional near-infrared spectroscopy measurement provides a way to investigate the possible alteration in ASD-related complexity of resting-state (RS) functional near-infrared spectroscopy (fNIRS) signals and to explore the relationship between brain functional connectivity and complexity.Approach.Using the multiscale entropy (MSE) of fNIRS signals recorded from the bilateral temporal lobes (TLs) on 25 children with ASD and 22 typical development (TD) children, the pattern of brain complexity was assessed for both the ASD and TD groups.Main results.The quantitative analysis of MSE revealed the increased complexity in RS-fNIRS in children with ASD, particularly in the left temporal lobe. The complexity in the RS signal and resting state functional connectivity (RSFC) were also observed to exhibit negative correlation in the medium magnitude.Significance.These results indicated that the MSE might serve as a novel measure for RS-fNIRS signals in characterizing and understanding ASD.

Interindividual Signatures of fMRI Temporal Fluctuations

The complexity and variability of human brain activity, such as quantified from Functional Magnetic Resonance Imaging (fMRI) time series, have been widely studied as potential markers of healthy and pathological states. However, the extent to which fMRI temporal features exhibit stable markers of inter-individual differences in brain function across healthy young adults is currently an open question. In this study, we draw upon two widely used time-series measures-a nonlinear complexity measure (sample entropy; SampEn) and a spectral measure of low-frequency content (fALFF)-to capture dynamic properties of resting-state fMRI in a large sample of young adults from the Human Connectome Project. We observe that these two measures are closely related, and that both generate reproducible patterns across brain regions over four different fMRI runs, with intra-class correlations of up to 0.8. Moreover, we find that both metrics can uniquely differentiate subjects with high identification rates (ca. 89%). Canonical correlation analysis revealed a significant relationship between multivariate brain temporal features and behavioral measures. Overall, these findings suggest that regional profiles of fMRI temporal characteristics may provide stable markers of individual differences, and motivate future studies to further probe relationships between fMRI time series metrics and behavior.

EEG microstate in obstructive sleep apnea patients

Obstructive sleep apnea (OSA) is a common sleep respiratory disease. Previous studies have found that the wakefulness electroencephalogram (EEG) of OSA patients has changed, such as increased EEG power. However, whether the microstates reflecting the transient state of the brain is abnormal is unclear during obstructive hypopnea (OH). We investigated the microstates of sleep EEG in 100 OSA patients. Then correlation analysis was carried out between microstate parameters and EEG markers of sleep disturbance, such as power spectrum, sample entropy and detrended fluctuation analysis (DFA). OSA_OH patients showed that the microstate C increased presence and the microstate D decreased presence compared to OSA_withoutOH patients and controls. The fifth microstate E appeared during N1-OH, but the probability of other microstates transferring to microstate E was small. According to the correlation analysis, OSA_OH patients in N1-OH showed that the microstate D was positively correlated with delta power, and negatively correlated with beta and alpha power; the transition probability of the microstate B → C and E → C was positively correlated with alpha power. In other sleep stages, the microstate parameters were not correlated with power, sample entropy and FDA. We might interpret that the abnormal transition of brain active areas of OSA patients in N1-OH stage leads to abnormal microstates, which might be related to the change of alpha activity in the cortex.

Long-Tailed Characteristic of Spiking Pattern Alternation Induced by Log-Normal Excitatory Synaptic Distribution

Studies of structural connectivity at the synaptic level show that in synaptic connections of the cerebral cortex, the excitatory postsynaptic potential (EPSP) in most synapses exhibits sub-mV values, while a small number of synapses exhibit large EPSPs ( >~1.0 [mV]). This means that the distribution of EPSP fits a log-normal distribution. While not restricting structural connectivity, skewed and long-tailed distributions have been widely observed in neural activities, such as the occurrences of spiking rates and the size of a synchronously spiking population. Many studies have been modeled this long-tailed EPSP neural activity distribution; however, its causal factors remain controversial. This study focused on the long-tailed EPSP distributions and interlateral synaptic connections primarily observed in the cortical network structures, thereby having constructed a spiking neural network consistent with these features. Especially, we constructed two coupled modules of spiking neural networks with excitatory and inhibitory neural populations with a log-normal EPSP distribution. We evaluated the spiking activities for different input frequencies and with/without strong synaptic connections. These coupled modules exhibited intermittent intermodule-alternative behavior, given moderate input frequency and the existence of strong synaptic and intermodule connections. Moreover, the power analysis, multiscale entropy analysis, and surrogate data analysis revealed that the long-tailed EPSP distribution and intermodule connections enhanced the complexity of spiking activity at large temporal scales and induced nonlinear dynamics and neural activity that followed the long-tailed distribution.

Identification of Electroencephalogram Signals in Alzheimer's Disease by Multifractal and Multiscale Entropy Analysis

Alzheimer's disease (AD) is the most common form of dementia and is a progressive neurodegenerative disease that primarily develops in old age. In recent years, it has been reported that early diagnosis of AD and early intervention significantly delays disease progression. Hence, early diagnosis and intervention are emphasized. As a diagnostic index for AD patients, evaluating the complexity of the dependence of the electroencephalography (EEG) signal on the temporal scale of Alzheimer's disease (AD) patients is effective. Multiscale entropy analysis and multifractal analysis have been performed individually, and their usefulness as diagnostic indicators has been confirmed, but the complemental relationship between these analyses, which may enhance diagnostic accuracy, has not been investigated. We hypothesize that combining multiscale entropy and fractal analyses may add another dimension to understanding the alteration of EEG dynamics in AD. In this study, we performed both multiscale entropy and multifractal analyses on EEGs from AD patients and healthy subjects. We found that the classification accuracy was improved using both techniques. These findings suggest that the use of multiscale entropy analysis and multifractal analysis may lead to the development of AD diagnostic tools.

Estimation of Granger causality through Artificial Neural Networks: applications to physiological systems and chaotic electronic oscillators

One of the most challenging problems in the study of complex dynamical systems is to find the statistical interdependencies among the system components. Granger causality (GC) represents one of the most employed approaches, based on modeling the system dynamics with a linear vector autoregressive (VAR) model and on evaluating the information flow between two processes in terms of prediction error variances. In its most advanced setting, GC analysis is performed through a state-space (SS) representation of the VAR model that allows to compute both conditional and unconditional forms of GC by solving only one regression problem. While this problem is typically solved through Ordinary Least Square (OLS) estimation, a viable alternative is to use Artificial Neural Networks (ANNs) implemented in a simple structure with one input and one output layer and trained in a way such that the weights matrix corresponds to the matrix of VAR parameters. In this work, we introduce an ANN combined with SS models for the computation of GC. The ANN is trained through the Stochastic Gradient Descent L1 (SGD-L1) algorithm, and a cumulative penalty inspired from penalized regression is applied to the network weights to encourage sparsity. Simulating networks of coupled Gaussian systems, we show how the combination of ANNs and SGD-L1 allows to mitigate the strong reduction in accuracy of OLS identification in settings of low ratio between number of time series points and of VAR parameters. We also report how the performances in GC estimation are influenced by the number of iterations of gradient descent and by the learning rate used for training the ANN. We recommend using some specific combinations for these parameters to optimize the performance of GC estimation. Then, the performances of ANN and OLS are compared in terms of GC magnitude and statistical significance to highlight the potential of the new approach to reconstruct causal coupling strength and network topology even in challenging conditions of data paucity. The results highlight the importance of of a proper selection of regularization parameter which determines the degree of sparsity in the estimated network. Furthermore, we apply the two approaches to real data scenarios, to study the physiological network of brain and peripheral interactions in humans under different conditions of rest and mental stress, and the effects of the newly emerged concept of remote synchronization on the information exchanged in a ring of electronic oscillators. The results highlight how ANNs provide a mesoscopic description of the information exchanged in networks of multiple interacting physiological systems, preserving the most active causal interactions between cardiovascular, respiratory and brain systems. Moreover, ANNs can reconstruct the flow of directed information in a ring of oscillators whose statistical properties can be related to those of physiological networks.

Diagnosis of Alzheimer's Disease by Time-Dependent Power Spectrum Descriptors and Convolutional Neural Network Using EEG Signal

Using strategies that obtain biomarkers where early symptoms coincide, the early detection of Alzheimer's disease and its complications is essential. Electroencephalogram is a technology that allows thousands of neurons with equal spatial orientation of the duration of cerebral cortex electrical activity to be registered by postsynaptic potential. Therefore, in this paper, the time-dependent power spectrum descriptors are used to diagnose the electroencephalogram signal function from three groups: mild cognitive impairment, Alzheimer's disease, and healthy control test samples. The final feature used in three modes of traditional classification methods is recorded: k-nearest neighbors, support vector machine, linear discriminant analysis approaches, and documented results. Finally, for Alzheimer's disease patient classification, the convolutional neural network architecture is presented. The results are indicated using output assessment. For the convolutional neural network approach, the accurate meaning of accuracy is 82.3%. 85% of mild cognitive impairment cases are accurately detected in-depth, but 89.1% of the Alzheimer's disease and 75% of the healthy population are correctly diagnosed. The presented convolutional neural network outperforms other approaches because performance and the k-nearest neighbors' approach is the next target. The linear discriminant analysis and support vector machine were at the low area under the curve values.

Identification of attention-deficit hyperactivity disorder based on the complexity and symmetricity of pupil diameter

Adult attention-deficit/hyperactivity disorder (ADHD) frequently leads to psychological/social dysfunction if unaddressed. Identifying a reliable biomarker would assist the diagnosis of adult ADHD and ensure that adults with ADHD receive treatment. Pupil diameter can reflect inherent neural activity and deficits of attention or arousal characteristic of ADHD. Furthermore, distinct profiles of the complexity and symmetricity of neural activity are associated with some psychiatric disorders. We hypothesized that analysing the relationship between the size, complexity of temporal patterns, and asymmetricity of pupil diameters will help characterize the nervous systems of adults with ADHD and that an identification method combining these features would ease the diagnosis of adult ADHD. To validate this hypothesis, we evaluated the resting state hippus in adult participants with or without ADHD by examining the pupil diameter and its temporal complexity using sample entropy and the asymmetricity of the left and right pupils using transfer entropy. We found that large pupil diameters and low temporal complexity and symmetry were associated with ADHD. Moreover, the combination of these factors by the classifier enhanced the accuracy of ADHD identification. These findings may contribute to the development of tools to diagnose adult ADHD.

Spontaneous neural activity relates to psychiatric traits in 16p11.2 CNV carriers: An analysis of EEG spectral power and multiscale entropy

Copy number variations (CNV) at the 16p11.2 chromosomal region are rare high-risk CNVs associated with various clinical features and psychiatric disorders including intellectual disability, developmental delays, and autism spectrum disorder. No study to date has investigated whether spontaneous neural activity is altered for 16p11.2 CNV carriers and whether this relates to psychiatric traits. The aim of this study is to examine the impact of 16p11.2 deletions (del) and duplications (dup) on spontaneous neural activity and its relationship to psychiatric problems. EEG was previously collected as part of the Simons Searchlight initiative. Using spectral power (delta, theta, alpha, and beta frequency bands), complexity index (CI), and multiscale entropy analysis techniques, we analyzed frontal resting-state EEG data collected from 22 16p11.2 del carriers, 14 dup carriers, and 13 controls. We then examined associations between neural activity and psychiatric traits, measured with the Child Behavior Checklist. Results indicated that EEG entropy was higher for del and dup compared to controls, respectively, at all timescales. CI was also higher for del and dup compared to controls. Theta power of 16p11.2 dup carriers was higher than controls. A strong association was found between entropy at higher timescales and anxiety problems. In addition, a strong correlation was found between theta power and pervasive developmental problems. Atypical spontaneous neural activity is implicated in 16p11.2 CNVs. With higher entropy or theta power, psychiatric traits increase in severity. Our findings provide evidence of the link between genotype, neural activity, and phenotypes in 16p11.2 CNVs.

Behavior needs neural variability

Human and non-human animal behavior is highly malleable and adapts successfully to internal and external demands. Such behavioral success stands in striking contrast to the apparent instability in neural activity (i.e., variability) from which it arises. Here, we summon the considerable evidence across scales, species, and imaging modalities that neural variability represents a key, undervalued dimension for understanding brain-behavior relationships at inter- and intra-individual levels. We believe that only by incorporating a specific focus on variability will the neural foundation of behavior be comprehensively understood.

A Study on Resting EEG Effective Connectivity Difference before and after Neurofeedback for Children with ADHD

Altered functional networks in attention deficit/hyperactivity disorder (ADHD) have been frequently reported, but effective connectivity has hardly been studied. Especially the differences of effective connectivity in children with ADHD after receiving neurofeedback (NF) training have been merely reported. Therefore, this study aimed to explore the effective networks of ADHD and the positive influence of NF on the effective networks. Electroencephalogram (EEG) data were recorded from 22 children with ADHD (including data from children pretraining and posttraining) and 15 age-matched healthy controls during an eyes-closed resting state. Phase transfer entropy (PTE) was used to construct the effective connectivity. The topological properties of networks and flow gain were measured separately in four bands (delta, theta, alpha, and beta). Results revealed the following: pretraining children with ADHD manifested a higher clustering coefficient and lower characteristic path length in the delta band than healthy controls; weakened anterior-to-posterior flow gain in the delta band, strengthened posterior-to-anterior flow gain in the alpha band and strengthened anterior-to-posterior flow gain in the beta band were observed in pretraining children with ADHD; The topological properties and flow gain in posttraining children with ADHD were close to those of healthy controls. Moreover, parent's SWAN presented significant improvements of ADHD symptoms after NF. Our findings revealed that the effective connectivity of ADHD was altered and that NF could improve the brain function of ADHD. The present study provided the first evidence that children with ADHD differed from healthy children in phase-based effective connectivity and that NF could reduce the differences.

Spatial variability of low frequency brain signal differentiates brain states

Temporal variability of the neural signal has been demonstrated to be closely related to healthy brain function. Meanwhile, the evolving brain functions are supported by dynamic relationships among brain regions. We hypothesized that the spatial variability of brain signal might provide important information about brain function. Here we used the spatial sample entropy (SSE) to investigate the spatial variability of neuroimaging signal during a steady-state presented face detection task. Lower SSE was found during task state than during resting state, associating with more repetitive functional interactions between brain regions. The standard deviation (SD) of SSE during the task was negatively related to the SD of reaction time, suggesting that the spatial pattern of neural activity is reorganized according to particular cognitive function and supporting the previous theory that greater variability is associated with better task performance. These results were replicated with reordered data, implying the reliability of SSE in measuring the spatial organization of neural activity. Overall, the present study extends the research scope of brain signal variability from the temporal dimension to the spatial dimension, improving our understanding of the spatiotemporal characteristics of brain activities and the theory of brain signal variability.

Measuring robust functional connectivity from resting-state MEG using amplitude and entropy correlation across frequency bands and temporal scales

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MRVE measures the dynamic variability of MEG signals at a range of temporal scales.

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MRVE correlation and AEC detected robust resting state functional connectivity.

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The most robust patterns were found for f_S=75Hz MRVE correlation and beta band AEC.

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Connectivity strength negatively correlates with local MRVE at fine time scales.

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Eye movement affects resting state connectivity measurements across frequencies.

Recent studies have shown how MEG can reveal spatial patterns of functional connectivity using frequency-specific oscillatory coupling measures and that these may be modified in disease. However, there is a need to understand both how repeatable these patterns are across participants and how these measures relate to the moment-to-moment variability (or ‘irregularity) of neural activity seen in healthy brain function. In this study, we used Multi-scale Rank-Vector Entropy (MRVE) to calculate the dynamic timecourses of signal variability over a range of temporal scales. The correlation of MRVE timecourses was then used to detect functional connections in resting state MEG recordings that were robust over 183 participants and varied with temporal scale. We compared these MRVE connectivity patterns to those derived using the more conventional method of oscillatory amplitude envelope correlation (AEC) using methods designed to quantify the consistency of these patterns across participants. Using AEC, the most consistent connectivity patterns, across the cohort, were seen in the alpha and beta frequency bands. At fine temporal scales (corresponding to ‘scale frequencies, fS = 30-150Hz), MRVE correlation detected mostly occipital and parietal connections. These showed high similarity with the networks identified by AEC in the alpha and beta frequency bands. The most consistent connectivity profiles between participants were given by MRVE correlation at fS = 75Hz and AEC in the beta band. The physiological relevance of MRVE was also investigated by examining the relationship between connectivity strength and local variability. It was found that local activity at frequencies fS≳ 10Hz becomes more regular when a region exhibits high levels of resting state connectivity, as measured by fine scale MRVE correlation (fS∼ 30-150Hz) and by alpha and beta band AEC. Analysis of the EOG recordings also revealed that eye movement affected both connectivity measures. Higher levels of eye movement were associated with stronger frontal connectivity, as measured by MRVE correlation. More eye movement was also associated with reduced occipital and parietal connectivity strength for both connectivity measures, although this was not significant after correction for multiple comparisons.

Deterministic characteristics of spontaneous activity detected by multi-fractal analysis in a spiking neural network with long-tailed distributions of synaptic weights

Cortical neural networks maintain autonomous electrical activity called spontaneous activity that represents the brain's dynamic internal state even in the absence of sensory stimuli. The spatio-temporal complexity of spontaneous activity is strongly related to perceptual, learning, and cognitive brain functions; multi-fractal analysis can be utilized to evaluate the complexity of spontaneous activity. Recent studies have shown that the deterministic dynamic behavior of spontaneous activity especially reflects the topological neural network characteristics and changes of neural network structures. However, it remains unclear whether multi-fractal analysis, recently widely utilized for neural activity, is effective for detecting the complexity of the deterministic dynamic process. To verify this point, we focused on the log-normal distribution of excitatory postsynaptic potentials (EPSPs) to evaluate the multi-fractality of spontaneous activity in a spiking neural network with a log-normal distribution of EPSPs. We found that the spiking activities exhibited multi-fractal characteristics. Moreover, to investigate the presence of a deterministic process in the spiking activity, we conducted a surrogate data analysis against the time-series of spiking activity. The results showed that the spontaneous spiking activity included the deterministic dynamic behavior. Overall, the combination of multi-fractal analysis and surrogate data analysis can detect deterministic complex neural activity. The multi-fractal analysis of neural activity used in this study could be widely utilized for brain modeling and evaluation methods for signals obtained by neuroimaging modalities.

Entropy and the Brain: An Overview

Entropy is a powerful tool for quantification of the brain function and its information processing capacity. This is evident in its broad domain of applications that range from functional interactivity between the brain regions to quantification of the state of consciousness. A number of previous reviews summarized the use of entropic measures in neuroscience. However, these studies either focused on the overall use of nonlinear analytical methodologies for quantification of the brain activity or their contents pertained to a particular area of neuroscientific research. The present study aims at complementing these previous reviews in two ways. First, by covering the literature that specifically makes use of entropy for studying the brain function. Second, by highlighting the three fields of research in which the use of entropy has yielded highly promising results: the (altered) state of consciousness, the ageing brain, and the quantification of the brain networks' information processing. In so doing, the present overview identifies that the use of entropic measures for the study of consciousness and its (altered) states led the field to substantially advance the previous findings. Moreover, it realizes that the use of these measures for the study of the ageing brain resulted in significant insights on various ways that the process of ageing may affect the dynamics and information processing capacity of the brain. It further reveals that their utilization for analysis of the brain regional interactivity formed a bridge between the previous two research areas, thereby providing further evidence in support of their results. It concludes by highlighting some potential considerations that may help future research to refine the use of entropic measures for the study of brain complexity and its function. The present study helps realize that (despite their seemingly differing lines of inquiry) the study of consciousness, the ageing brain, and the brain networks' information processing are highly interrelated. Specifically, it identifies that the complexity, as quantified by entropy, is a fundamental property of conscious experience, which also plays a vital role in the brain's capacity for adaptation and therefore whose loss by ageing constitutes a basis for diseases and disorders. Interestingly, these two perspectives neatly come together through the association of entropy and the brain capacity for information processing.

Individual Cortical Entropy Profile: Test-Retest Reliability, Predictive Power for Cognitive Ability, and Neuroanatomical Foundation

The entropy profiles of cortical activity have become novel perspectives to investigate individual differences in behavior. However, previous studies have neglected foundational aspects of individual entropy profiles, that is, the test-retest reliability, the predictive power for cognitive ability in out-of-sample data, and the underlying neuroanatomical basis. We explored these issues in a large young healthy adult dataset (Human Connectome Project, N = 998). We showed the whole cortical entropy profile from resting-state functional magnetic resonance imaging is a robust personalized measure, while subsystem profiles exhibited heterogeneous reliabilities. The limbic network exhibited lowest reliability. We tested the out-of-sample predictive power for general and specific cognitive abilities based on reliable cortical entropy profiles. The default mode and visual networks are most crucial when predicting general cognitive ability. We investigated the anatomical features underlying cross-region and cross-individual variations in cortical entropy profiles. Cortical thickness and structural connectivity explained spatial variations in the group-averaged entropy profile. Cortical folding and myelination in the attention and frontoparietal networks determined predominantly individual cortical entropy profile. This study lays foundations for brain-entropy-based studies on individual differences to understand cognitive ability and related pathologies. These findings broaden our understanding of the associations between neural structures, functional dynamics, and cognitive ability.

Classification Methods Based on Complexity and Synchronization of Electroencephalography Signals in Alzheimer's Disease

Electroencephalography (EEG) has long been studied as a potential diagnostic method for Alzheimer's disease (AD). The pathological progression of AD leads to cortical disconnection. These disconnections may manifest as functional connectivity alterations, measured by the degree of synchronization between different brain regions, and alterations in complex behaviors produced by the interaction among wide-spread brain regions. Recently, machine learning methods, such as clustering algorithms and classification methods, have been adopted to detect disease-related changes in functional connectivity and classify the features of these changes. Although complexity of EEG signals can also reflect AD-related changes, few machine learning studies have focused on the changes in complexity. Therefore, in this study, we compared the ability of EEG signals to detect characteristics of AD using different machine learning approaches one focused on functional connectivity and the other focused on signal complexity. We examined functional connectivity, estimated by phase lag index (PLI) in EEG signals in healthy older participants [healthy control (HC)] and patients with AD. We estimated signal complexity using multi-scale entropy. Utilizing a support vector machine, we compared the identification accuracy of AD based on functional connectivity at each frequency band and complexity component. Additionally, we evaluated the relationship between synchronization and complexity. The identification accuracy of functional connectivity of the alpha, beta, and gamma bands was significantly high (AUC 1.0), and the identification accuracy of complexity was sufficiently high (AUC 0.81). Moreover, the relationship between functional connectivity and complexity exhibited various temporal-scale-and-regional-specific dependency in both HC participants and patients with AD. In conclusion, the combination of functional connectivity and complexity might reflect complex pathological process of AD. Applying a combination of both machine learning methods to neurophysiological data may provide a novel understanding of the neural network processes in both healthy brains and pathological conditions.

Lack of a Sense of Threat and Higher Emotional Lability in Patients With Chronic Microvascular Ischemia as Measured by Non-linear EEG Parameters

We aimed to investigate the non-linear features of the electroencephalogram (EEG) findings in patients with chronic microvascular ischemia (CMI) in order to determine the brain correlates of emotional impairment that could impact the risk of developing acute ischemia. We compared the EEG responses of patients with CMI and age-matched healthy volunteers to non-verbal emotionally charged sounds. We analyzed the EEG data, the psychological assessment of the stimuli, and the results of neuropsychological and behavioral testing. We assessed the (in)stability of the envelope's amplitude by calculating its average frequency and the ratio of its standard deviation to its mean. The non-linear features were lower in the patient group in the resting state. The emotional stimulation induced a decrease in the frequency of the envelope's amplitude in all subjects. Changes in the fractal dimension during stimulation were only seen in the patient group, and they correlated with symptoms of emotional lability. The lower ratio of the alpha-rhythm envelope's standard deviation to its mean in the right hemisphere correlated with a higher sense of threat. The EEG and behavioral correlates of emotional impairment in patients with CMI were found.

Prediction of treatment resistance in obsessive compulsive disorder patients based on EEG complexity as a biomarker

OBJECTIVE

This study aimed to identify an Electroencephalography (EEG) complexity biomarker that could predict treatment resistance in Obsessive compulsive disorder (OCD) patients. Additionally, the statistical differences between EEG complexity values in treatment-resistant and treatment-responsive patients were determined. Moreover, the existence of correlations between EEG complexity and Yale-Brown Obsessive Compulsive Scale (YBOCS) score were evaluated.

METHODS

EEG data for 29 treatment-resistant and 28 treatment-responsive OCD patients were retrospectively evaluated. Approximate entropy (ApEn) method was used to extract the EEG complexity from both whole EEG data and filtered EEG data, according to 4 common frequency bands, namely delta, theta, alpha, and beta. The random forests method was used to classify ApEn complexity.

RESULTS

ApEn complexity extracted from beta band EEG segments discriminated treatment-responsive and treatment-resistant OCD patients with an accuracy of 89.66% (sensitivity: 89.44%; specificity: 90.64%). Beta band EEG complexity was lower in the treatment-resistant patients and the severity of OCD, as measured by YBOCS score, was inversely correlated with complexity values.

CONCLUSIONS

The results indicate that, EEG complexity could be considered a biomarker for predicting treatment response in OCD patients.

SIGNIFICANCE

The prediction of treatment response in OCD patients might help clinicians devise and administer individualized treatment plans.