Multiscale permutation entropy analysis of EEG recordings during sevoflurane anesthesia

Altered sleep onset transition in depression: Evidence from EEG activity and EEG functional connectivity analyses

OBJECTIVE

Sleep disorders constitute a principal diagnostic criterion for depression, potentially reflecting the abnormal persistence of brain activity during the sleep onset (SO) transition. Here, we sought to explore the differences in the dynamic changes in the EEG activity and the EEG functional connectivity (FC) during the SO transition in depressed patients.

METHODS

Overnight polysomnography recordings were obtained from thirty-two depressed patients and thirty-three healthy controls. The multiscale permutation entropy (MSPE) and EEG relative power were extracted to characterize EEG activity, and weighted phase lag index (WPLI) was calculated to characterize EEG FC.

RESULTS

The intergroup differences in EEG activity of relative power and MSPE were reversed near SO, which attributed to slower rates of change among depressed patients. Regarding the characteristics of the EEG FC network, depressed patients exhibited significantly higher inter-hemispheric and interregional WPLI values in both delta and alpha bands throughout the SO transition, concomitant with different dynamic properties in the delta band FC. During the process after SO, patients exhibited increased inter-hemispheric long-range links, whereas controls showed more intra-hemispheric ones. Finally, we found significant correlations in the dynamic changes between different EEG measures.

CONCLUSIONS

Our research revealed that the abnormal changes during the SO transition in depressed patients were manifested in both homeostatic and dynamic aspects, which were reflected in EEG FC and EEG activity, respectively.

SIGNIFICANCE

These findings may elucidate the mechanism underlying sleep disorders in depression from the perspective of neural activity.

Proposal of dental demineralization diagnosis with OCT echo based on multiscale entropy analysis

Optical coherence tomography (OCT) has been widely used for the diagnosis of dental demineralization. Most methods rely on extracting optical features from OCT echoes for evaluation or diagnosis. However, due to the diversity of biological samples and the complexity of tissues, the separability and robustness of extracted optical features are inadequate, resulting in a low diagnostic efficiency. Given the widespread utilization of entropy analysis in examining signals from biological tissues, we introduce a dental demineralization diagnosis method using OCT echoes, employing multiscale entropy analysis. Three multiscale entropy analysis methods were used to extract features from the OCT one-dimensional echo signal of normal and demineralized teeth, and a probabilistic neural network (PNN) was used for dental demineralization diagnosis. By comparing diagnostic efficiency, diagnostic speed, and parameter optimization dependency, the multiscale dispersion entropy-PNN (MDE-PNN) method was found to have comprehensive advantages in dental demineralization diagnosis with a diagnostic efficiency of 0.9397. Compared with optical feature-based dental demineralization diagnosis methods, the entropy features-based analysis had better feature separability and higher diagnostic efficiency, and showed its potential in dental demineralization diagnosis with OCT.

Multiscale information interaction at local frequency band in functional corticomuscular coupling

The multiscale information interaction between the cortex and the corresponding muscles is of great significance for understanding the functional corticomuscular coupling (FCMC) in the sensory-motor systems. Though the multiscale transfer entropy (MSTE) method can effectively detect the multiscale characteristics between two signals, it lacks in describing the local frequency-band characteristics. Therefore, to quantify the multiscale interaction at local-frequency bands between the cortex and the muscles, we proposed a novel method, named bivariate empirical mode decomposition-MSTE (BMSTE), by combining the bivariate empirical mode decomposition (BEMD) with MSTE. To verify this, we introduced two simulation models and then applied it to explore the FCMC by analyzing the EEG over brain scalp and surface EMG signals from the effector muscles during steady-state force output. The simulation results showed that the BMSTE method could describe the multiscale time-frequency characteristics compared with the MSTE method, and was sensitive to the coupling strength but not to the data length. The experiment results showed that the coupling at beta1 (15-25 Hz), beta2 (25-35 Hz) and gamma (35-60 Hz) bands in the descending direction was higher than that in the opposition, and at beta2 band was higher than that at beta1 band. Furthermore, there were significant differences at the low scales in beta1 band, almost all scales in beta2 band, and high scales in gamma band. These results suggest the effectiveness of the BMSTE method in describing the interaction between two signals at different time-frequency scales, and further provide a novel approach to understand the motor control.

Supplementary Information

The online version contains supplementary material available at 10.1007/s11571-022-09895-y.

High Variability Periods in the EEG Distinguish Cognitive Brain States

OBJECTIVE

To describe a novel measure of EEG signal variability that distinguishes cognitive brain states.

METHOD

We describe a novel characterization of amplitude variability in the EEG signal termed "High Variability Periods" or "HVPs", defined as segments when the standard deviation of a moving window is continuously higher than the quartile cutoff. We characterize the parameter space of the metric in terms of window size, overlap, and threshold to suggest ideal parameter choice and compare its performance as a discriminator of brain state to alternate single channel measures of variability such as entropy, complexity, harmonic regression fit, and spectral measures.

RESULTS

We show that the average HVP duration provides a substantially distinct view of the signal relative to alternate metrics of variability and, when used in combination with these metrics, significantly enhances the ability to predict whether an individual has their eyes open or closed and is performing a working memory and Raven's pattern completion task. In addition, HVPs disappear under anesthesia and do not reappear in early periods of recovery.

CONCLUSIONS

HVP metrics enhance the discrimination of various brain states and are fast to estimate.

SIGNIFICANCE

HVP metrics can provide an additional view of signal variability that has potential clinical application in the rapid discrimination of brain states.

An EEG-based attention recognition method: fusion of time domain, frequency domain, and non-linear dynamics features

Introduction

Attention is a complex cognitive function of human brain that plays a vital role in our daily lives. Electroencephalogram (EEG) is used to measure and analyze attention due to its high temporal resolution. Although several attention recognition brain-computer interfaces (BCIs) have been proposed, there is a scarcity of studies with a sufficient number of subjects, valid paradigms, and reliable recognition analysis across subjects.

Methods

In this study, we proposed a novel attention paradigm and feature fusion method to extract features, which fused time domain features, frequency domain features and nonlinear dynamics features. We then constructed an attention recognition framework for 85 subjects.

Results and discussion

We achieved an intra-subject average classification accuracy of 85.05% ± 6.87% and an inter-subject average classification accuracy of 81.60% ± 9.93%, respectively. We further explored the neural patterns in attention recognition, where attention states showed less activation than non-attention states in the prefrontal and occipital areas in α, β and θ bands. The research explores, for the first time, the fusion of time domain features, frequency domain features and nonlinear dynamics features for attention recognition, providing a new understanding of attention recognition.

Evidence of Chaos in Electroencephalogram Signatures of Human Performance: A Systematic Review

(1) Background: Chaos, a feature of nonlinear dynamical systems, is well suited for exploring biological time series, such as heart rates, respiratory records, and particularly electroencephalograms. The primary purpose of this article is to review recent studies using chaos theory and nonlinear dynamical methods to analyze human performance in different brain processes. (2) Methods: Several studies have examined chaos theory and related analytical tools for describing brain dynamics. The present study provides an in-depth analysis of the computational methods that have been proposed to uncover brain dynamics. (3) Results: The evidence from 55 articles suggests that cognitive function is more frequently assessed than other brain functions in studies using chaos theory. The most frequently used techniques for analyzing chaos include the correlation dimension and fractal analysis. Approximate, Kolmogorov and sample entropy account for the largest proportion of entropy algorithms in the reviewed studies. (4) Conclusions: This review provides insights into the notion of the brain as a chaotic system and the successful use of nonlinear methods in neuroscience studies. Additional studies of brain dynamics would aid in improving our understanding of human cognitive performance.

Sulfobetaine-based ultrathin coatings as effective antifouling layers for implantable neuroprosthetic devices

Foreign body response (FBR), inflammation, and fibrotic encapsulation of neural implants remain major problems affecting the impedance of the electrode-tissue interface and altering the device performance. Adhesion of proteins and cells (e.g., pro-inflammatory macrophages, and fibroblasts) triggers the FBR cascade and can be diminished by applying antifouling coatings onto the implanted devices. In this paper, we report the deposition and characterization of a thin (±6 nm) sulfobetaine-based coating onto microfabricated platinum electrodes and cochlear implant (CI) electrode arrays. We found that this coating has stable cell and protein-repellent properties, for at least 31 days in vitro, not affected by electrical stimulation protocols. Additionally, its effect on the electrochemical properties relevant to stimulation (i.e., impedance, charge injection capacity) was negligible. When applied to clinical CI electrode arrays, the film was successful at inhibiting fibroblast adhesion on both the silicone packaging and the platinum/iridium electrodes. In vitro, in fibroblast cultures, coated CI electrode arrays maintained impedance values up to five times lower compared to non-coated devices. Our studies demonstrate that such thin sulfobetaine containing layers are stable and prevent protein and cell adhesion in vitro and are compatible for use on CI electrode arrays. Future in vivo studies should be conducted to investigate its ability to mitigate biofouling, fibrosis, and the resulting impedance changes upon long-term implantation in vivo.

Ordinal methods for a characterization of evolving functional brain networks

Ordinal time series analysis is based on the idea to map time series to ordinal patterns, i.e., order relations between the values of a time series and not the values themselves, as introduced in 2002 by C. Bandt and B. Pompe. Despite a resulting loss of information, this approach captures meaningful information about the temporal structure of the underlying system dynamics as well as about properties of interactions between coupled systems. This-together with its conceptual simplicity and robustness against measurement noise-makes ordinal time series analysis well suited to improve characterization of the still poorly understood spatiotemporal dynamics of the human brain. This minireview briefly summarizes the state-of-the-art of uni- and bivariate ordinal time-series-analysis techniques together with applications in the neurosciences. It will highlight current limitations to stimulate further developments, which would be necessary to advance characterization of evolving functional brain networks.

Permutation Entropy Analysis to Intracranial Hypertension from a Porcine Model

Intracranial pressure (ICP) monitoring is commonly used in the follow-up of patients in intensive care units, but only a small part of the information available in the ICP time series is exploited. One of the most important features to guide patient follow-up and treatment is intracranial compliance. We propose using permutation entropy (PE) as a method to extract non-obvious information from the ICP curve. We analyzed the results of a pig experiment with sliding windows of 3600 samples and 1000 displacement samples, and estimated their respective PEs, their associated probability distributions, and the number of missing patterns (NMP). We observed that the behavior of PE is inverse to that of ICP, in addition to the fact that NMP appears as a surrogate for intracranial compliance. In lesion-free periods, PE is usually greater than 0.3, and normalized NMP is less than 90% and p(s1)>p(s720). Any deviation from these values could be a possible warning of altered neurophysiology. In the terminal phases of the lesion, the normalized NMP is higher than 95%, and PE is not sensitive to changes in ICP and p(s720)>p(s1). The results show that it could be used for real-time patient monitoring or as input for a machine learning tool.

Neural complexity is a common denominator of human consciousness across diverse regimes of cortical dynamics

What is the common denominator of consciousness across divergent regimes of cortical dynamics? Does consciousness show itself in decibels or in bits? To address these questions, we introduce a testbed for evaluating electroencephalogram (EEG) biomarkers of consciousness using dissociations between neural oscillations and consciousness caused by rare genetic disorders. Children with Angelman syndrome (AS) exhibit sleep-like neural dynamics during wakefulness. Conversely, children with duplication 15q11.2-13.1 syndrome (Dup15q) exhibit wake-like neural dynamics during non-rapid eye movement (NREM) sleep. To identify highly generalizable biomarkers of consciousness, we trained regularized logistic regression classifiers on EEG data from wakefulness and NREM sleep in children with AS using both entropy measures of neural complexity and spectral (i.e., neural oscillatory) EEG features. For each set of features, we then validated these classifiers using EEG from neurotypical (NT) children and abnormal EEGs from children with Dup15q. Our results show that the classification performance of entropy-based EEG biomarkers of conscious state is not upper-bounded by that of spectral EEG features, which are outperformed by entropy features. Entropy-based biomarkers of consciousness may thus be highly adaptable and should be investigated further in situations where spectral EEG features have shown limited success, such as detecting covert consciousness or anesthesia awareness.

Complexity of Brain Dynamics as a Correlate of Consciousness in Anaesthetized Monkeys

The use of anaesthesia is a fundamental tool in the investigation of consciousness. Anesthesia procedures allow to investigate different states of consciousness from sedation to deep anesthesia within controlled scenarios. In this study we use information quantifiers to measure the complexity of electrocorticogram recordings in monkeys. We apply these metrics to compare different stages of general anesthesia for evaluating consciousness in several anesthesia protocols. We find that the complexity of brain activity can be used as a correlate of consciousness. For two of the anaesthetics used, propofol and medetomidine, we find that the anaesthetised state is accompanied by a reduction in the complexity of brain activity. On the other hand we observe that use of ketamine produces an increase in complexity measurements. We relate this observation with increase activity within certain brain regions associated with the ketamine used doses. Our measurements indicate that complexity of brain activity is a good indicator for a general evaluation of different levels of consciousness awareness, both in anesthetized and non anesthetizes states.

Particle Swarm Optimization Fractional Slope Entropy: A New Time Series Complexity Indicator for Bearing Fault Diagnosis

Slope entropy (SlEn) is a time series complexity indicator proposed in recent years, which has shown excellent performance in the fields of medical and hydroacoustics. In order to improve the ability of SlEn to distinguish different types of signals and solve the problem of two threshold parameters selection, a new time series complexity indicator on the basis of SlEn is proposed by introducing fractional calculus and combining particle swarm optimization (PSO), named PSO fractional SlEn (PSO-FrSlEn). Then we apply PSO-FrSlEn to the field of fault diagnosis and propose a single feature extraction method and a double feature extraction method for rolling bearing fault based on PSO-FrSlEn. The experimental results illustrated that only PSO-FrSlEn can classify 10 kinds of bearing signals with 100% classification accuracy by using double features, which is at least 4% higher than the classification accuracies of the other four fractional entropies.

Consciousness as a multidimensional phenomenon: implications for the assessment of disorders of consciousness

Disorders of consciousness (DoCs) pose a significant clinical and ethical challenge because they allow for complex forms of conscious experience in patients where intentional behaviour and communication are highly limited or non-existent. There is a pressing need for brain-based assessments that can precisely and accurately characterize the conscious state of individual DoC patients. There has been an ongoing research effort to develop neural measures of consciousness. However, these measures are challenging to validate not only due to our lack of ground truth about consciousness in many DoC patients but also because there is an open ontological question about consciousness. There is a growing, well-supported view that consciousness is a multidimensional phenomenon that cannot be fully described in terms of the theoretical construct of hierarchical, easily ordered conscious levels. The multidimensional view of consciousness challenges the utility of levels-based neural measures in the context of DoC assessment. To examine how these measures may map onto consciousness as a multidimensional phenomenon, this article will investigate a range of studies where they have been applied in states other than DoC and where more is known about conscious experience. This comparative evidence suggests that measures of conscious level are more sensitive to some dimensions of consciousness than others and cannot be assumed to provide a straightforward hierarchical characterization of conscious states. Elevated levels of brain complexity, for example, are associated with conscious states characterized by a high degree of sensory richness and minimal attentional constraints, but are suboptimal for goal-directed behaviour and external responsiveness. Overall, this comparative analysis indicates that there are currently limitations to the use of these measures as tools to evaluate consciousness as a multidimensional phenomenon and that the relationship between these neural signatures and phenomenology requires closer scrutiny.

Double Feature Extraction Method of Ship-Radiated Noise Signal Based on Slope Entropy and Permutation Entropy

In order to accurately identify various types of ships and develop coastal defenses, a single feature extraction method based on slope entropy (SlEn) and a double feature extraction method based on SlEn combined with permutation entropy (SlEn&PE) are proposed. Firstly, SlEn is used for the feature extraction of ship-radiated noise signal (SNS) compared with permutation entropy (PE), dispersion entropy (DE), fluctuation dispersion entropy (FDE), and reverse dispersion entropy (RDE), so that the effectiveness of SlEn is verified, and SlEn has the highest recognition rate calculated by the k-Nearest Neighbor (KNN) algorithm. Secondly, SlEn is combined with PE, DE, FDE, and RDE, respectively, to extract the feature of SNS for a higher recognition rate, and SlEn&PE has the highest recognition rate after the calculation of the KNN algorithm. Lastly, the recognition rates of SlEn and SlEn&PE are compared, and the recognition rates of SlEn&PE are higher than SlEn by 4.22%. Therefore, the double feature extraction method proposed in this paper is more effective in the application of ship type recognition.

Electroencephalogram variability analysis for monitoring depth of anesthesia

Objective. In this paper, a new approach of extracting and measuring the variability in electroencephalogram (EEG) was proposed to assess the depth of anesthesia (DOA) under general anesthesia.Approach. The EEG variability (EEGV) was extracted as a fluctuation in time interval that occurs between two local maxima of EEG. Eight parameters related to EEGV were measured in time and frequency domains, and compared with state-of-the-art DOA estimation parameters, including sample entropy, permutation entropy, median frequency and spectral edge frequency of EEG. The area under the receiver-operator characteristics curve (AUC) and Pearson correlation coefficient were used to validate its performance on 56 patients.Main results. Our proposed EEGV-derived parameters yield significant difference for discriminating between awake and anesthesia stages at a significance level of 0.05, as well as improvement in AUC and correlation coefficient on average, which surpasses the conventional features of EEG in detection accuracy of unconscious state and tracking the level of consciousness.Significance. To sum up, EEGV analysis provides a new perspective in quantifying EEG and corresponding parameters are powerful and promising for monitoring DOA under clinical situations.

Consciousness and complexity: a consilience of evidence

Over the last years, a surge of empirical studies converged on complexity-related measures as reliable markers of consciousness across many different conditions, such as sleep, anesthesia, hallucinatory states, coma, and related disorders. Most of these measures were independently proposed by researchers endorsing disparate frameworks and employing different methods and techniques. Since this body of evidence has not been systematically reviewed and coherently organized so far, this positive trend has remained somewhat below the radar. The aim of this paper is to make this consilience of evidence in the science of consciousness explicit. We start with a systematic assessment of the growing literature on complexity-related measures and identify their common denominator, tracing it back to core theoretical principles and predictions put forward more than 20 years ago. In doing this, we highlight a consistent trajectory spanning two decades of consciousness research and provide a provisional taxonomy of the present literature. Finally, we consider all of the above as a positive ground to approach new questions and devise future experiments that may help consolidate and further develop a promising field where empirical research on consciousness appears to have, so far, naturally converged.

Exercise intervention protocol in children and young adults with cerebral palsy: the effects of strength, flexibility and gait training on physical performance, neuromuscular mechanisms and cardiometabolic risk factors (EXECP)

Background

Individuals with cerebral palsy (CP) have problems in everyday tasks such as walking and climbing stairs due to a combination of neuromuscular impairments such as spasticity, muscle weakness, reduced joint flexibility and poor coordination. Development of evidence-based interventions are in pivotal role in the development of better targeted rehabilitation of CP, and thus in maintaining their motor function and wellbeing. Our aim is to investigate the efficacy of an individually tailored, multifaceted exercise intervention (EXECP) in children and young adults with CP. EXECP is composed of strength, flexibility and gait training. Furthermore, this study aims to verify the short-term retention of the adaptations three months after the end of the EXECP intervention.

Methods

Twenty-four children and young adults with spastic CP will be recruited to participate in a 9-month research project with a 3-month training intervention, consisting of two to three 90-min sessions per week. In each session, strength training for the lower limbs and trunk muscles, flexibility training for the lower limbs and inclined treadmill gait training will be performed. We will evaluate muscle strength, joint flexibility, neuromuscular and cardiometabolic parameters. A nonconcurrent multiple baseline design with two pre-tests and two post-tests all interspaced by three months is used. In addition to the CP participants, 24 typically developing age and sex-matched participants will perform the two pre-tests (i.e. no intervention) to provide normative data.

Discussion

This study has a comprehensive approach examining longitudinal effects of wide variety of variables ranging from physical activity and gross motor function to sensorimotor functions of the brain and neuromuscular and cardiometabolic parameters, providing novel information about the adaptation mechanisms in cerebral palsy. To the best of our knowledge, this is the first intervention study providing supervised combined strength, flexibility and gait training for young individuals with CP.

Trial registration number

ISRCTN69044459, prospectively registered (21/04/2017).

Altered EEG Signal Complexity Induced by Hand Proximity: A Multiscale Entropy Approach

Visual short-term memory (VSTM) is an important cognitive function that acts as a temporary storage for visual information. Previous studies have shown that VSTM capacity can be modulated by the location of one’s hands, where hand proximity enhances neural processing and memory of nearby visual stimuli. The present study used traditional event-related potentials (ERP) along with multiscale entropy (MSE) analysis to shed light on the neural mechanism(s) behind such near-hand effect. Participants’ electroencephalogram (EEG) data were recorded as they performed a VSTM task with their hands either proximal or distal to the display. ERP analysis showed altered memory processing in the 400–700 ms time window during memory retrieval period. Importantly, MSE analysis also showed significant EEG difference between hand proximal and distal conditions between scales 10 to 20, and such difference is clustered around the right parietal cortex – a region that is involved in VSTM processing and bimodal hand-eye integration. The implications of higher MSE time scale in the parietal cortex are discussed in the context of signal complexity and its possible relation to cognitive processing. To our knowledge, this study provides the first investigation using MSE to characterize the temporal characteristics and signal complexity behind the effect of hand proximity.

Multiscale Entropy Analysis: Application to Cardio-Respiratory Coupling

It is known that in pathological conditions, physiological systems develop changes in the multiscale properties of physiological signals. However, in real life, little is known about how changes in the function of one of the two coupled physiological systems induce changes in function of the other one, especially on their multiscale behavior. Hence, in this work we aimed to examine the complexity of cardio-respiratory coupled systems control using multiscale entropy (MSE) analysis of cardiac intervals MSE (RR), respiratory time series MSE (Resp), and synchrony of these rhythms by cross multiscale entropy (CMSE) analysis, in the heart failure (HF) patients and healthy subjects. We analyzed 20 min of synchronously recorded RR intervals and respiratory signal during relaxation in the supine position in 42 heart failure patients and 14 control healthy subjects. Heart failure group was divided into three subgroups, according to the RR interval time series characteristics (atrial fibrillation (HFAF), sinus rhythm (HFSin), and sinus rhythm with ventricular extrasystoles (HFVES)). Compared with healthy control subjects, alterations in respiratory signal properties were observed in patients from the HFSin and HFVES groups. Further, mean MSE curves of RR intervals and respiratory signal were not statistically different only in the HFSin group (p = 0.43). The level of synchrony between these time series was significantly higher in HFSin and HFVES patients than in control subjects and HFAF patients (p < 0.01). In conclusion, depending on the specific pathologies, primary alterations in the regularity of cardiac rhythm resulted in changes in the regularity of the respiratory rhythm, as well as in the level of their asynchrony.

Research on State Recognition and Failure Prediction of Axial Piston Pump Based on Performance Degradation Data

Degradation state recognition and failure prediction are the key steps of prognostic and health management (PHM), which directly affect the reliability of the equipment and the selection of preventive maintenance strategy. Given the problem that the distinction between feature vectors is not obvious and the accuracy of fault prediction is low, a method based on multi-class Gaussian process classification and Gaussian process regression (GPR) is studied by the vibration signal and flow signal in six degraded states of the axial piston pump. For degradation state recognition, the variational mode decomposition (VMD) was used to decompose the vibration signal, and obtaining intrinsic mode function (IMF) components with rich information. Subsequently, multi-scale permutation entropy (MPE) was employed to select feature vectors of IMF components in different states. In order to reduce feature dimensions and improve recognition performance, ReliefF was used to select feature vectors with high weight, then a method based on multi-class Gaussian process classification was established by using these feature vectors to realize the research on the degradation state recognition. The test results demonstrate that the method can effectively identify the degradation state. Its recognition rate reaches 98.9%. Besides, for failure prediction, through the analysis of the wear process and wear mechanism of the valve plate, the curve fitting between the flow and the wear amount was performed by GPR to realize the failure prediction of the axial piston pump. Depending on the evaluation index, the GPR obtained a better failure prediction effect. The results will assist in the realization of predictive maintenance, and which also has significant practical value in project items.

Information Integration and Mesoscopic Cortical Connectivity during Propofol Anesthesia

Background

The neurophysiologic mechanisms of propofol-induced loss of consciousness have been studied in detail at the macro (scalp electroencephalogram) and micro (spiking or local field potential) scales. However, the changes in information integration and cortical connectivity during propofol anesthesia at the mesoscopic level (the cortical scale) are less clear.

Methods

The authors analyzed electrocorticogram data recorded from surgical patients during propofol-induced unconsciousness (n = 9). A new information measure, genuine permutation cross mutual information, was used to analyze how electrocorticogram cross-electrode coupling changed with electrode-distances in different brain areas (within the frontal, parietal, and temporal regions, as well as between the temporal and parietal regions). The changes in cortical networks during anesthesia—at nodal and global levels—were investigated using clustering coefficient, path length, and nodal efficiency measures.

Results

In all cortical regions, and in both wakeful and unconscious states (early and late), the genuine permutation cross mutual information and the percentage of genuine connections decreased with increasing distance, especially up to about 3 cm. The nodal cortical network metrics (the nodal clustering coefficients and nodal efficiency) decreased from wakefulness to unconscious state in the cortical regions we analyzed. In contrast, the global cortical network metrics slightly increased in the early unconscious state (the time span from loss of consciousness to 200 s after loss of consciousness), as compared with wakefulness (normalized average clustering coefficient: 1.05 ± 0.01 vs. 1.06 ± 0.03, P = 0.037; normalized average path length: 1.02 ± 0.01 vs. 1.04 ± 0.01, P = 0.021).

Conclusions

The genuine permutation cross mutual information reflected propofol-induced coupling changes measured at a cortical scale. Loss of consciousness was associated with a redistribution of the pattern of information integration; losing efficient global information transmission capacity but increasing local functional segregation in the cortical network.

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Monitoring Depth of Anesthesia Based on Hybrid Features and Recurrent Neural Network

Electroencephalogram (EEG) signals contain valuable information about the different physiological states of the brain, with a variety of linear and nonlinear features that can be used to investigate brain activity. Monitoring the depth of anesthesia (DoA) with EEG is an ongoing challenge in anesthesia research. In this paper, we propose a novel method based on Long Short-Term Memory (LSTM) and a sparse denoising autoencoder (SDAE) to combine the hybrid features of EEG to monitor the DoA. The EEG signals were preprocessed using filtering, etc., and then more than ten features including sample entropy, permutation entropy, spectra, and alpha-ratio were extracted from the EEG signal. We then integrated the optional features such as permutation entropy and alpha-ratio to extract the essential structure and learn the most efficient temporal model for monitoring the DoA. Compared with using a single feature, the proposed model could accurately estimate the depth of anesthesia with higher prediction probability (P_k). Experimental results evaluated on the datasets demonstrated that our proposed method provided better performance than the methods using permutation entropy, alpha-ratio, LSTM, and other traditional indices.

Detection of Hypoglycemia Using Measures of EEG Complexity in Type 1 Diabetes Patients

Previous literature has demonstrated that hypoglycemic events in patients with type 1 diabetes (T1D) are associated with measurable scalp electroencephalography (EEG) changes in power spectral density. In the present study, we used a dataset of 19-channel scalp EEG recordings in 34 patients with T1D who underwent a hyperinsulinemic-hypoglycemic clamp study. We found that hypoglycemic events are also characterized by EEG complexity changes that are quantifiable at the single-channel level through empirical conditional and permutation entropy and fractal dimension indices, i.e., the Higuchi index, residuals, and tortuosity. Moreover, we demonstrated that the EEG complexity indices computed in parallel in more than one channel can be used as the input for a neural network aimed at identifying hypoglycemia and euglycemia. The accuracy was about 90%, suggesting that nonlinear indices applied to EEG signals might be useful in revealing hypoglycemic events from EEG recordings in patients with T1D.

Slope Entropy: A New Time Series Complexity Estimator Based on Both Symbolic Patterns and Amplitude Information

The development of new measures and algorithms to quantify the entropy or related concepts of a data series is a continuous effort that has brought many innovations in this regard in recent years. The ultimate goal is usually to find new methods with a higher discriminating power, more efficient, more robust to noise and artifacts, less dependent on parameters or configurations, or any other possibly desirable feature. Among all these methods, Permutation Entropy (PE) is a complexity estimator for a time series that stands out due to its many strengths, with very few weaknesses. One of these weaknesses is the PE’s disregarding of time series amplitude information. Some PE algorithm modifications have been proposed in order to introduce such information into the calculations. We propose in this paper a new method, Slope Entropy (SlopEn), that also addresses this flaw but in a different way, keeping the symbolic representation of subsequences using a novel encoding method based on the slope generated by two consecutive data samples. By means of a thorough and extensive set of comparative experiments with PE and Sample Entropy (SampEn), we demonstrate that SlopEn is a very promising method with clearly a better time series classification performance than those previous methods.

On the development of sleep states in the first weeks of life

Human newborns spend up to 18 hours sleeping. The organization of their sleep differs immensely from adult sleep, and its quick maturation and fundamental changes correspond to the rapid cortical development at this age. Manual sleep classification is specifically challenging in this population given major body movements and frequent shifts between vigilance states; in addition various staging criteria co-exist. In the present study we utilized a machine learning approach and investigated how EEG complexity and sleep stages evolve during the very first weeks of life. We analyzed 42 full-term infants which were recorded twice (at week two and five after birth) with full polysomnography. For sleep classification EEG signal complexity was estimated using multi-scale permutation entropy and fed into a machine learning classifier. Interestingly the baby’s brain signal complexity (and spectral power) revealed developmental changes in sleep in the first 5 weeks of life, and were restricted to NREM (“quiet”) and REM (“active sleep”) states with little to no changes in state wake. Data demonstrate that our classifier performs well over chance (i.e., >33% for 3-class classification) and reaches almost human scoring accuracy (60% at week-2, 73% at week-5). Altogether, these results demonstrate that characteristics of newborn sleep develop rapidly in the first weeks of life and can be efficiently identified by means of machine learning techniques.

Teaching Ordinal Patterns to a Computer: Efficient Encoding Algorithms Based on the Lehmer Code

Ordinal patterns are the common basis of various techniques used in the study of dynamical systems and nonlinear time series analysis. The present article focusses on the computational problem of turning time series into sequences of ordinal patterns. In a first step, a numerical encoding scheme for ordinal patterns is proposed. Utilising the classical Lehmer code, it enumerates ordinal patterns by consecutive non-negative integers, starting from zero. This compact representation considerably simplifies working with ordinal patterns in the digital domain. Subsequently, three algorithms for the efficient extraction of ordinal patterns from time series are discussed, including previously published approaches that can be adapted to the Lehmer code. The respective strengths and weaknesses of those algorithms are discussed, and further substantiated by benchmark results. One of the algorithms stands out in terms of scalability: its run-time increases linearly with both the pattern order and the sequence length, while its memory footprint is practically negligible. These properties enable the study of high-dimensional pattern spaces at low computational cost. In summary, the tools described herein may improve the efficiency of virtually any ordinal pattern-based analysis method, among them quantitative measures like permutation entropy and symbolic transfer entropy, but also techniques like forbidden pattern identification. Moreover, the concepts presented may allow for putting ideas into practice that up to now had been hindered by computational burden. To enable smooth evaluation, a function library written in the C programming language, as well as language bindings and native implementations for various numerical computation environments are provided in the supplements.

Permutation Entropy: Enhancing Discriminating Power by Using Relative Frequencies Vector of Ordinal Patterns Instead of Their Shannon Entropy

Many measures to quantify the nonlinear dynamics of a time series are based on estimating the probability of certain features from their relative frequencies. Once a normalised histogram of events is computed, a single result is usually derived. This process can be broadly viewed as a nonlinear IRn mapping into IR, where n is the number of bins in the histogram. However, this mapping might entail a loss of information that could be critical for time series classification purposes. In this respect, the present study assessed such impact using permutation entropy (PE) and a diverse set of time series. We first devised a method of generating synthetic sequences of ordinal patterns using hidden Markov models. This way, it was possible to control the histogram distribution and quantify its influence on classification results. Next, real body temperature records are also used to illustrate the same phenomenon. The experiments results confirmed the improved classification accuracy achieved using raw histogram data instead of the PE final values. Thus, this study can provide a very valuable guidance for the improvement of the discriminating capability not only of PE, but of many similar histogram-based measures.

Assessing spatiotemporal variability of brain spontaneous activity by multiscale entropy and functional connectivity

Brain signaling occurs across a wide range of spatial and temporal scales, and analysis of brain signal variability and synchrony has attracted recent attention as markers of intelligence, cognitive states, and brain disorders. However, current technologies to measure brain signals in humans have limited resolutions either in space or in time and cannot fully capture spatiotemporal variability, leaving it untested whether temporal variability and spatiotemporal synchrony are valid and reliable proxy of spatiotemporal variability in vivo. Here we used optical voltage imaging in mice under anesthesia and wakefulness to monitor cortical voltage activity at both high spatial and temporal resolutions to investigate functional connectivity (FC, a measure of spatiotemporal synchronization), Multi-Scale Entropy (MSE, a measure of temporal variability), and their relationships to Regional Entropy (RE, a measure of spatiotemporal variability). We observed that across cortical space, MSE pattern can largely explain RE pattern at small and large temporal scales with high positive and negative correlation respectively, while FC pattern strongly negatively associated with RE pattern. The time course of FC and small scale MSE tightly followed that of RE, while large scale MSE was more loosely coupled to RE. fMRI and EEG data simulated by reducing spatiotemporal resolution of the voltage imaging data or considering hemodynamics yielded MSE and FC measures that still contained information about RE based on the high resolution voltage imaging data. This suggested that MSE and FC could still be effective measures to capture spatiotemporal variability under limitation of imaging modalities applicable to human subjects. Our results support the notion that FC and MSE are effective biomarkers for brain states, and provide a promising viewpoint to unify these two principal domains in human brain data analysis.

Use of Multiple EEG Features and Artificial Neural Network to Monitor the Depth of Anesthesia

The electroencephalogram (EEG) can reflect brain activity and contains abundant information of different anesthetic states of the brain. It has been widely used for monitoring depth of anesthesia (DoA). In this study, we propose a method that combines multiple EEG-based features with artificial neural network (ANN) to assess the DoA. Multiple EEG-based features can express the states of the brain more comprehensively during anesthesia. First, four parameters including permutation entropy, 95% spectral edge frequency, BetaRatio and SynchFastSlow were extracted from the EEG signal. Then, the four parameters were set as the inputs to an ANN which used bispectral index (BIS) as the reference output. 16 patient datasets during propofol anesthesia were used to evaluate this method. The results indicated that the accuracies of detecting each state were 86.4% (awake), 73.6% (light anesthesia), 84.4% (general anesthesia), and 14% (deep anesthesia). The correlation coefficient between BIS and the index of this method was 0.892 (p<0.001). The results showed that the proposed method could well distinguish between awake and other anesthesia states. This method is promising and feasible for a monitoring system to assess the DoA.

Rolling Bearing Diagnosis Based on Composite Multiscale Weighted Permutation Entropy

In this paper, composite multiscale weighted permutation entropy (CMWPE) is proposed to evaluate the complexity of nonlinear time series, and the advantage of the CMWPE method is verified through analyzing the simulated signal. Meanwhile, considering the complex nonlinear dynamic characteristics of fault rolling bearing signal, a rolling bearing fault diagnosis approach based on CMWPE, joint mutual information (JMI) feature selection, and k-nearest-neighbor (KNN) classifier (CMWPE-JMI-KNN) is proposed. For CMWPE-JMI-KNN, CMWPE is utilized to extract the fault rolling bearing features, JMI is applied for sensitive features selection, and KNN classifier is employed for identifying different rolling bearing conditions. Finally, the proposed CMWPE-JMI-KNN approach is used to analyze the experimental dataset, the analysis results indicate the proposed approach could effectively identify different fault rolling bearing conditions.

Do Complexity Measures of Frontal EEG Distinguish Loss of Consciousness in Geriatric Patients Under Anesthesia?

While geriatric patients have a high likelihood of requiring anesthesia, they carry an increased risk for adverse cognitive outcomes from its use. Previous work suggests this could be mitigated by better intraoperative monitoring using indexes defined by several processed electroencephalogram (EEG) measures. Unfortunately, inconsistencies between patients and anesthetic agents in current analysis techniques have limited the adoption of EEG as standard of care. In attempts to identify new analyses that discriminate clinically-relevant anesthesia timepoints, we tested 1/f frequency scaling as well as measures of complexity from nonlinear dynamics. Specifically, we tested whether analyses that characterize time-delayed embeddings, correlation dimension (CD), phase-space geometric analysis, and multiscale entropy (MSE) capture loss-of-consciousness changes in EEG activity. We performed these analyses on EEG activity collected from a traditionally hard-to-monitor patient population: geriatric patients on beta-adrenergic blockade who were anesthetized using a combination of fentanyl and propofol. We compared these analyses to traditional frequency-derived measures to test how well they discriminated EEG states before and after loss of response to verbal stimuli. We found spectral changes similar to those reported previously during loss of response. We also found significant changes in 1/f frequency scaling. Additionally, we found that our phase-space geometric characterization of time-delayed embeddings showed significant differences before and after loss of response, as did measures of MSE. Our results suggest that our new spectral and complexity measures are capable of capturing subtle differences in EEG activity with anesthesia administration-differences which future work may reveal to improve geriatric patient monitoring.

Topographic Reconfiguration of Local and Shared Information in Anesthetic-Induced Unconsciousness

Theoretical consideration predicts that the alteration of local and shared information in the brain is a key element in the mechanism of anesthetic-induced unconsciousness. Ordinal pattern analysis, such as permutation entropy (PE) and symbolic mutual information (SMI), have been successful in quantifying local and shared information in neurophysiological data; however, they have been rarely applied to altered states of consciousness, especially to data obtained with functional magnetic resonance imaging (fMRI). PE and SMI analysis, together with the superb spatial resolution of fMRI recording, enables us to explore the local information of specific brain areas, the shared information between the areas, and the relationship between the two. Given the spatially divergent action of anesthetics on regional brain activity, we hypothesized that anesthesia would differentially influence entropy (PE) and shared information (SMI) across various brain areas, which may represent fundamental, mechanistic indicators of loss of consciousness. FMRI data were collected from 15 healthy participants during four states: wakefulness (W), light (conscious) sedation (L), deep (unconscious) sedation (D), and recovery (R). Sedation was produced by the common, clinically used anesthetic, propofol. Firstly, we found that that global PE decreased from W to D, and increased from D to R. The PE was differentially affected across the brain areas; specifically, the PE in the subcortical network was reduced more than in the cortical networks. Secondly, SMI was also differentially affected in different areas, as revealed by the reconfiguration of its spatial pattern (topographic structure). The topographic structures of SMI in the conscious states W, L, and R were distinctively different from that of the unconscious state D. Thirdly, PE and SMI were positively correlated in W, L, and R, whereas this correlation was disrupted in D. And lastly, PE changes occurred preferentially in highly connected hub regions. These findings advance our understanding of brain dynamics and information exchange, emphasizing the importance of topographic structure and the relationship of local and shared information in anesthetic-induced unconsciousness.

Multiscale Information Transfer in Functional Corticomuscular Coupling Estimation Following Stroke: A Pilot Study

Recently, functional corticomuscular coupling (FCMC) between the cortex and the contralateral muscle has been used to evaluate motor function after stroke. As we know, the motor-control system is a closed-loop system that is regulated by complex self-regulating and interactive mechanisms which operate in multiple spatial and temporal scales. Multiscale analysis can represent the inherent complexity. However, previous studies in FCMC for stroke patients mainly focused on the coupling strength in single-time scale, without considering the changes of the inherently directional and multiscale properties in sensorimotor systems. In this paper, a multiscale-causal model, named multiscale transfer entropy, was used to quantify the functional connection between electroencephalogram over the scalp and electromyogram from the flexor digitorum superficialis (FDS) recorded simultaneously during steady-state grip task in eight stroke patients and eight healthy controls. Our results showed that healthy controls exhibited higher coupling when the scale reached up to about 12, and the FCMC in descending direction was stronger at certain scales (1, 7, 12, and 14) than that in ascending direction. Further analysis showed these multi-time scale characteristics mainly focused on the beta1 band at scale 11 and beta2 band at scale 9, 11, 13, and 15. Compared to controls, the multiscale properties of the FCMC for stroke were changed, the strengths in both directions were reduced, and the gaps between the descending and ascending directions were disappeared over all scales. Further analysis in specific bands showed that the reduced FCMC mainly focused on the alpha2 at higher scale, beta1 and beta2 across almost the entire scales. This study about multi-scale confirms that the FCMC between the brain and muscles is capable of complex and directional characteristics, and these characteristics in functional connection for stroke are destroyed by the structural lesion in the brain that might disrupt coordination, feedback, and information transmission in efferent control and afferent feedback. The study demonstrates for the first time the multiscale and directional characteristics of the FCMC for stroke patients, and provides a preliminary observation for application in clinical assessment following stroke.

Improved Prediction of Falls in Community-Dwelling Older Adults Through Phase-Dependent Entropy of Daily-Life Walking

Age and age-related diseases have been suggested to decrease entropy of human gait kinematics, which is thought to make older adults more susceptible to falls. In this study we introduce a new entropy measure, called phase-dependent generalized multiscale entropy (PGME), and test whether this measure improves fall-risk prediction in community-dwelling older adults. PGME can assess phase-dependent changes in the stability of gait dynamics that result from kinematic changes in events such as heel strike and toe-off. PGME was assessed for trunk acceleration of 30 s walking epochs in a re-analysis of 1 week of daily-life activity data from the FARAO study, originally described by van Schooten et al. (2016). The re-analyzed data set contained inertial sensor data from 52 single- and 46 multiple-time prospective fallers in a 6 months follow-up period, and an equal number of non-falling controls matched by age, weight, height, gender, and the use of walking aids. The predictive ability of PGME for falls was assessed using a partial least squares regression. PGME had a superior predictive ability of falls among single-time prospective fallers when compared to the other gait features. The single-time fallers had a higher PGME (p < 0.0001) of their trunk acceleration at 60% of their step cycle when compared with non-fallers. No significant differences were found between PGME of multiple-time fallers and non-fallers, but PGME was found to improve the prediction model of multiple-time fallers when combined with other gait features. These findings suggest that taking into account phase-dependent changes in the stability of the gait dynamics has additional value for predicting falls in older people, especially for single-time prospective fallers.

Characterizing Normal and Pathological Gait through Permutation Entropy

Cerebral palsy is a physical impairment stemming from a brain lesion at perinatal time, most of the time resulting in gait abnormalities: the first cause of severe disability in childhood. Gait study, and instrumental gait analysis in particular, has been receiving increasing attention in the last few years, for being the complex result of the interactions between different brain motor areas and thus a proxy in the understanding of the underlying neural dynamics. Yet, and in spite of its importance, little is still known about how the brain adapts to cerebral palsy and to its impaired gait and, consequently, about the best strategies for mitigating the disability. In this contribution, we present the hitherto first analysis of joint kinematics data using permutation entropy, comparing cerebral palsy children with a set of matched control subjects. We find a significant increase in the permutation entropy for the former group, thus indicating a more complex and erratic neural control of joints and a non-trivial relationship between the permutation entropy and the gait speed. We further show how this information theory measure can be used to train a data mining model able to forecast the child’s condition. We finally discuss the relevance of these results in clinical applications and specifically in the design of personalized medicine interventions.

Measures of entropy and complexity in altered states of consciousness

Quantification of complexity in neurophysiological signals has been studied using different methods, especially those from information or dynamical system theory. These studies have revealed a dependence on different states of consciousness, and in particular that wakefulness is characterized by a greater complexity of brain signals, perhaps due to the necessity for the brain to handle varied sensorimotor information. Thus, these frameworks are very useful in attempts to quantify cognitive states. We set out to analyze different types of signals obtained from scalp electroencephalography (EEG), intracranial EEG and magnetoencephalography recording in subjects during different states of consciousness: resting wakefulness, different sleep stages and epileptic seizures. The signals were analyzed using a statistical (permutation entropy) and a deterministic (permutation Lempel-Ziv complexity) analytical method. The results are presented in complexity versus entropy graphs, showing that the values of entropy and complexity of the signals tend to be greatest when the subjects are in fully alert states, falling in states with loss of awareness or consciousness. These findings were robust for all three types of recordings. We propose that the investigation of the structure of cognition using the frameworks of complexity will reveal mechanistic aspects of brain dynamics associated not only with altered states of consciousness but also with normal and pathological conditions.

A Review of Resting-State Electroencephalography Analysis in Disorders of Consciousness

Recently, neuroimaging technologies have been developed as important methods for assessing the brain condition of patients with disorders of consciousness (DOC). Among these technologies, resting-state electroencephalography (EEG) recording and analysis has been widely applied by clinicians due to its relatively low cost and convenience. EEG reflects the electrical activity of the underlying neurons, and it contains information regarding neuronal population oscillations, the information flow pathway, and neural activity networks. Some features derived from EEG signal processing methods have been proposed to describe the electrical features of the brain with DOC. The computation of these features is challenging for clinicians working to comprehend the corresponding physiological meanings and then to put them into clinical applications. This paper reviews studies that analyze spontaneous EEG of DOC, with the purpose of diagnosis, prognosis, and evaluation of brain interventions. It is expected that this review will promote our understanding of the EEG characteristics in DOC.

Feature ranking and rank aggregation for automatic sleep stage classification: a comparative study

BACKGROUND

Nowadays, sleep quality is one of the most important measures of healthy life, especially considering the huge number of sleep-related disorders. Identifying sleep stages using polysomnographic (PSG) signals is the traditional way of assessing sleep quality. However, the manual process of sleep stage classification is time-consuming, subjective and costly. Therefore, in order to improve the accuracy and efficiency of the sleep stage classification, researchers have been trying to develop automatic classification algorithms. Automatic sleep stage classification mainly consists of three steps: pre-processing, feature extraction and classification. Since classification accuracy is deeply affected by the extracted features, a poor feature vector will adversely affect the classifier and eventually lead to low classification accuracy. Therefore, special attention should be given to the feature extraction and selection process.

METHODS

In this paper the performance of seven feature selection methods, as well as two feature rank aggregation methods, were compared. Pz-Oz EEG, horizontal EOG and submental chin EMG recordings of 22 healthy males and females were used. A comprehensive feature set including 49 features was extracted from these recordings. The extracted features are among the most common and effective features used in sleep stage classification from temporal, spectral, entropy-based and nonlinear categories. The feature selection methods were evaluated and compared using three criteria: classification accuracy, stability, and similarity.

RESULTS

Simulation results show that MRMR-MID achieves the highest classification performance while Fisher method provides the most stable ranking. In our simulations, the performance of the aggregation methods was in the average level, although they are known to generate more stable results and better accuracy.

CONCLUSIONS

The Borda and RRA rank aggregation methods could not outperform significantly the conventional feature ranking methods. Among conventional methods, some of them slightly performed better than others, although the choice of a suitable technique is dependent on the computational complexity and accuracy requirements of the user.

Neural Correlates of Sevoflurane-induced Unconsciousness Identified by Simultaneous Functional Magnetic Resonance Imaging and Electroencephalography

BACKGROUND

The neural correlates of anesthetic-induced unconsciousness have yet to be fully elucidated. Sedative and anesthetic states induced by propofol have been studied extensively, consistently revealing a decrease of frontoparietal and thalamocortical connectivity. There is, however, less understanding of the effects of halogenated ethers on functional brain networks.

METHODS

The authors recorded simultaneous resting-state functional magnetic resonance imaging and electroencephalography in 16 artificially ventilated volunteers during sevoflurane anesthesia at burst suppression and 3 and 2 vol% steady-state concentrations for 700 s each to assess functional connectivity changes compared to wakefulness. Electroencephalographic data were analyzed using symbolic transfer entropy (surrogate of information transfer) and permutation entropy (surrogate of cortical information processing). Functional magnetic resonance imaging data were analyzed by an independent component analysis and a region-of-interest-based analysis.

RESULTS

Electroencephalographic analysis showed a significant reduction of anterior-to-posterior symbolic transfer entropy and global permutation entropy. At 2 vol% sevoflurane concentrations, frontal and thalamic networks identified by independent component analysis showed significantly reduced within-network connectivity. Primary sensory networks did not show a significant change. At burst suppression, all cortical networks showed significantly reduced functional connectivity. Region-of-interest-based thalamic connectivity at 2 vol% was significantly reduced to frontoparietal and posterior cingulate cortices but not to sensory areas.

CONCLUSIONS

Sevoflurane decreased frontal and thalamocortical connectivity. The changes in blood oxygenation level dependent connectivity were consistent with reduced anterior-to-posterior directed connectivity and reduced cortical information processing. These data advance the understanding of sevoflurane-induced unconsciousness and contribute to a neural basis of electroencephalographic measures that hold promise for intraoperative anesthesia monitoring.

Complexity analysis of fNIRS signals in ADHD children during working memory task

Attention-deficit/hyperactivity disorder (ADHD) is a prevalent neurodevelopmental disorder in children. Neuroimaging studies have revealed abnormalities of neural activities in some brain regions, including the frontal cortex, striatum, cerebellum, and occipital cortex. Recently, some investigators have demonstrated that nonlinear complexity analysis of neural activity may provide a new index to indicate ADHD. In the present study, we used the permutation entropy (PE) to measure the complexity of functional near-infrared spectroscopy (fNIRS) signals in children with and without ADHD during a working memory task, it was aimed to investigate the relationship between the PE values and the cortical activations, and the different PE values between the children with and without ADHD. We found that PE values exhibited significantly negative correlation with the cortical activations (r = -0.515, p = 0.003), and the PE values of right dorsolateral prefrontal cortex in ADHD children were significantly larger than those in normal controls (p = 0.027). In addition, the PE values of right dorsolateral prefrontal cortex were positively correlated to the ADHD index (r = 0.448, p = 0.012). These results suggest that complexity analysis of fNIRS signals could be a promising tool in diagnosing children with ADHD.