Multiscale entropy analysis of biological signals: a fundamental bi-scaling law

Machine learning for hand pose classification from phasic and tonic EMG signals during bimanual activities in virtual reality

Myoelectric prostheses have recently shown significant promise for restoring hand function in individuals with upper limb loss or deficiencies, driven by advances in machine learning and increasingly accessible bioelectrical signal acquisition devices. Here, we first introduce and validate a novel experimental paradigm using a virtual reality headset equipped with hand-tracking capabilities to facilitate the recordings of synchronized EMG signals and hand pose estimation. Using both the phasic and tonic EMG components of data acquired through the proposed paradigm, we compare hand gesture classification pipelines based on standard signal processing features, convolutional neural networks, and covariance matrices with Riemannian geometry computed from raw or xDAWN-filtered EMG signals. We demonstrate the performance of the latter for gesture classification using EMG signals. We further hypothesize that introducing physiological knowledge in machine learning models will enhance their performances, leading to better myoelectric prosthesis control. We demonstrate the potential of this approach by using the neurophysiological integration of the "move command" to better separate the phasic and tonic components of the EMG signals, significantly improving the performance of sustained posture recognition. These results pave the way for the development of new cutting-edge machine learning techniques, likely refined by neurophysiology, that will further improve the decoding of real-time natural gestures and, ultimately, the control of myoelectric prostheses.

Benefits of Zero-Phase or Linear Phase Filters to Design Multiscale Entropy: Theory and Application

In various applications, multiscale entropy (MSE) is often used as a feature to characterize the complexity of the signals in order to classify them. It consists of estimating the sample entropies (SEs) of the signal under study and its coarse-grained (CG) versions, where the CG process amounts to (1) filtering the signal with an average filter whose order is the scale and (2) decimating the filter output by a factor equal to the scale. In this paper, we propose to derive a new variant of the MSE. Its novelty stands in the way to get the sequences at different scales by avoiding distortions during the decimation step. To this end, a linear-phase or null-phase low-pass filter whose cutoff frequency is well suited to the scale is used. Interpretations on how the MSE behaves and illustrations with a sum of sinusoids, as well as white and pink noises, are given. Then, an application to detect attentional tunneling is presented. It shows the benefit of the new approach in terms of p value when one aims at differentiating the set of MSEs obtained in the attentional tunneling state from the set of MSEs obtained in the nominal state. It should be noted that CG versions can be replaced not only for the MSE but also for other variants.

Inter-individual variability during neurodevelopment: an investigation of linear and nonlinear resting-state EEG features in an age-homogenous group of infants

Electroencephalography measures are of interest in developmental neuroscience as potentially reliable clinical markers of brain function. Features extracted from electroencephalography are most often averaged across individuals in a population with a particular condition and compared statistically to the mean of a typically developing group, or a group with a different condition, to define whether a feature is representative of the populations as a whole. However, there can be large variability within a population, and electroencephalography features often change dramatically with age, making comparisons difficult. Combined with often low numbers of trials and low signal-to-noise ratios in pediatric populations, establishing biomarkers can be difficult in practice. One approach is to identify electroencephalography features that are less variable between individuals and are relatively stable in a healthy population during development. To identify such features in resting-state electroencephalography, which can be readily measured in many populations, we introduce an innovative application of statistical measures of variance for the analysis of resting-state electroencephalography data. Using these statistical measures, we quantified electroencephalography features commonly used to measure brain development-including power, connectivity, phase-amplitude coupling, entropy, and fractal dimension-according to their intersubject variability. Results from 51 6-month-old infants revealed that the complexity measures, including fractal dimension and entropy, followed by connectivity were the least variable features across participants. This stability was found to be greatest in the right parietotemporal region for both complexity feature, but no significant region of interest was found for connectivity feature. This study deepens our understanding of physiological patterns of electroencephalography data in developing brains, provides an example of how statistical measures can be used to analyze variability in resting-state electroencephalography in a homogeneous group of healthy infants, contributes to the establishment of robust electroencephalography biomarkers of neurodevelopment through the application of variance analyses, and reveals that nonlinear measures may be most relevant biomarkers of neurodevelopment.

Advances in Multivariate and Multiscale Physiological Signal Analysis

Physiological systems are characterized by complex dynamics and nonlinear behaviors due to their intricate structural organization and regulatory mechanisms [...].

The Diagnosis of Congestive Heart Failure Based on Generalized Multiscale Entropy-Wavelet Leaders

Congestive heart failure (CHF) is a chronic heart condition associated with debilitating symptoms that can lead to mortality. The electrocardiogram (ECG) is a noninvasive and simple diagnostic method that can show detectable changes in CHF. However, manual diagnosis of ECG signals is often erroneous due to the small amplitude and duration of the ECG signals. This paper presents a CHF diagnosis method based on generalized multiscale entropy (MSE)-wavelet leaders (WL) and extreme learning machine (ELM). Firstly, ECG signals from normal sinus rhythm (NSR) and congestive heart failure (CHF) patients are pre-processed. Then, parameters such as segmentation time and scale factor are chosen, and the multifractal spectrum features and number of ELM hidden layer nodes are determined. Two different data sets (A, B) were used for training and testing. In both sets, the balanced data set (B) had the highest accuracy of 99.72%, precision, sensitivity, specificity, and F1 score of 99.46%, 100%, 99.44%, and 99.73%, respectively. The unbalanced data set (A) attained an accuracy of 99.56%, precision of 99.44%, sensitivity of 99.81%, specificity of 99.17%, and F1 score of 99.62%. Finally, increasing the number of ECG segments and different algorithms validated the probability of detection of the unbalanced data set. The results indicate that our proposed method requires a lower number of ECG segments and does not require the detection of R waves. Moreover, the method can improve the probability of detection of unbalanced data sets and provide diagnostic assistance to cardiologists by providing a more objective and faster interpretation of ECG signals.

Nonlinear Heart Rate Dynamics Before and After Paroxysmal Atrial Fibrillation Events

BACKGROUND

Heart rate complexity, derived from nonlinear heart rate variability (HRV), has been shown to help predict the outcomes of various diseases. Changes in heart rate complexity before and after paroxysmal atrial fibrillation (PAF) events are unclear.

OBJECTIVES

To evaluate changes in heart rate complexity through nonlinear HRV before and after PAF events.

METHODS

We enrolled 65 patients (72 ± 12.34 years old, 31 females) with 99 PAF events who received 24-hour Holter recording, and analyzed nonlinear HRV variables including Poincaré plot analysis, sample entropy (SampEn), and multiscale entropy (MSE). HRV analyses were applied to a 20-minute window before the onset and after the termination of PAF events. HRV parameters were evaluated and compared based on eight different 5-minute time segments, as we divided each 20-minute window into four segments of 5 minutes each.

RESULTS

SampEn and MSE_1~5 significantly decreased before the onset of PAF events, whereas SampEn, MSE_1~5 and MSE_6~20 significantly increased after the termination of PAF events. SD1 and SD2, which are nonlinear HRV parameters calculated via Poincaré plot analysis, did not significantly change before the PAF events, however they both decreased significantly after termination.

CONCLUSIONS

Heart rate complexity significantly decreased before the initiation and increased after the termination of PAF events, which indicates the crucial role of nonlinear heart rate dynamics in the initiation and termination of PAF.

Resting-state functional magnetic resonance imaging signal variations in aging: The role of neural activity

Resting‐state functional magnetic resonance imaging (rs‐fMRI) has been extensively used to study brain aging, but the age effect on the frequency content of the rs‐fMRI signal has scarcely been examined. Moreover, the neuronal implications of such age effects and age–sex interaction remain unclear. In this study, we examined the effects of age and sex on the rs‐fMRI signal frequency using the Leipzig mind–brain–body data set. Over a frequency band of up to 0.3 Hz, we found that the rs‐fMRI fluctuation frequency is higher in the older adults, although the fluctuation amplitude is lower. The rs‐fMRI signal frequency is also higher in men than in women. Both age and sex effects on fMRI frequency vary with the frequency band examined but are not found in the frequency of physiological‐noise components. This higher rs‐fMRI frequency in older adults is not mediated by the electroencephalograph (EEG)‐frequency increase but a likely link between fMRI signal frequency and EEG entropy, which vary with age and sex. Additionally, in different rs‐fMRI frequency bands, the fMRI‐EEG amplitude ratio is higher in young adults. This is the first study to investigate the neuronal contribution to age and sex effects in the frequency dimension of the rs‐fMRI signal and may lead to the development of new, frequency‐based rs‐fMRI metrics. Our study demonstrates that Fourier analysis of the fMRI signal can reveal novel information about aging. Furthermore, fMRI and EEG signals reflect different aspects of age‐ and sex‐related brain differences, but the signal frequency and complexity, instead of amplitude, may hold their link.

Brain variability in dynamic resting-state networks identified by fuzzy entropy: a scalp EEG study

Objective.Exploring the temporal variability in spatial topology during the resting state attracts growing interest and becomes increasingly useful to tackle the cognitive process of brain networks. In particular, the temporal brain dynamics during the resting state may be delineated and quantified aligning with cognitive performance, but few studies investigated the temporal variability in the electroencephalogram (EEG) network as well as its relationship with cognitive performance.Approach.In this study, we proposed an EEG-based protocol to measure the nonlinear complexity of the dynamic resting-state network by applying the fuzzy entropy. To further validate its applicability, the fuzzy entropy was applied into simulated and two independent datasets (i.e. decision-making and P300).Main results.The simulation study first proved that compared to the existing methods, this approach could not only exactly capture the pattern dynamics in time series but also overcame the magnitude effect of time series. Concerning the two EEG datasets, the flexible and robust network architectures of the brain cortex at rest were identified and distributed at the bilateral temporal lobe and frontal/occipital lobe, respectively, whose variability metrics were found to accurately classify different groups. Moreover, the temporal variability of resting-state network property was also either positively or negatively related to individual cognitive performance.Significance.This outcome suggested the potential of fuzzy entropy for evaluating the temporal variability of the dynamic resting-state brain networks, and the fuzzy entropy is also helpful for uncovering the fluctuating network variability that accounts for the individual decision differences.

Conditional Entropy: A Potential Digital Marker for Stress

Recent decades have witnessed a substantial progress in the utilization of brain activity for the identification of stress digital markers. In particular, the success of entropic measures for this purpose is very appealing, considering (1) their suitability for capturing both linear and non-linear characteristics of brain activity recordings and (2) their direct association with the brain signal variability. These findings rely on external stimuli to induce the brain stress response. On the other hand, research suggests that the use of different types of experimentally induced psychological and physical stressors could potentially yield differential impacts on the brain response to stress and therefore should be dissociated from more general patterns. The present study takes a step toward addressing this issue by introducing conditional entropy (CE) as a potential electroencephalography (EEG)-based resting-state digital marker of stress. For this purpose, we use the resting-state multi-channel EEG recordings of 20 individuals whose responses to stress-related questionnaires show significantly higher and lower level of stress. Through the application of representational similarity analysis (RSA) and K-nearest-neighbor (KNN) classification, we verify the potential that the use of CE can offer to the solution concept of finding an effective digital marker for stress.

Characterization of the Stages of Creative Writing With Mobile EEG Using Generalized Partial Directed Coherence

Two stages of the creative writing process were characterized through mobile scalp electroencephalography (EEG) in a 16-week creative writing workshop. Portable dry EEG systems (four channels: TP09, AF07, AF08, TP10) with synchronized head acceleration, video recordings, and journal entries, recorded mobile brain-body activity of Spanish heritage students. Each student's brain-body activity was recorded as they experienced spaces in Houston, Texas (“Preparation” stage), and while they worked on their creative texts (“Generation” stage). We used Generalized Partial Directed Coherence (gPDC) to compare the functional connectivity among both stages. There was a trend of higher gPDC in the Preparation stage from right temporo-parietal (TP10) to left anterior-frontal (AF07) brain scalp areas within 1–50 Hz, not reaching statistical significance. The opposite directionality was found for the Generation stage, with statistical significant differences (p < 0.05) restricted to the delta band (1–4 Hz). There was statistically higher gPDC observed for the inter-hemispheric connections AF07–AF08 in the delta and theta bands (1–8 Hz), and AF08 to TP09 in the alpha and beta (8–30 Hz) bands. The left anterior-frontal (AF07) recordings showed higher power localized to the gamma band (32–50 Hz) for the Generation stage. An ancillary analysis of Sample Entropy did not show significant difference. The information transfer from anterior-frontal to temporal-parietal areas of the scalp may reflect multisensory interpretation during the Preparation stage, while brain signals originating at temporal-parietal toward frontal locations during the Generation stage may reflect the final decision making process to translate the multisensory experience into a creative text.

Muscle Fatigue Analysis With Optimized Complementary Ensemble Empirical Mode Decomposition and Multi-Scale Envelope Spectral Entropy

The preprocessing of surface electromyography (sEMG) signals with complementary ensemble empirical mode decomposition (CEEMD) improves frequency identification precision and temporal resolution, and lays a good foundation for feature extraction. However, a mode-mixing problem often occurs when the CEEMD decomposes an sEMG signal that exhibits intermittency and contains components with a near-by spectrum into intrinsic mode functions (IMFs). This paper presents a method called optimized CEEMD (OCEEMD) to solve this problem. The method integrates the least-squares mutual information (LSMI) and the chaotic quantum particle swarm optimization (CQPSO) algorithm in signal decomposition. It uses the LSMI to calculate the correlation between IMFs so as to reduce mode mixing and uses the CQPSO to optimize the standard deviation of Gaussian white noise so as to improve iteration efficiency. Then, useful IMFs are selected and added to reconstruct a de-noised signal. Finally, considering that the IMFs contain abundant frequency and envelope information, this paper extracts the multi-scale envelope spectral entropy (MSESEn) from the reconstructed sEMG signal. Some original sEMG signals, which were collected from experiments, were used to validate the methods. Compared with the CEEMD and complete ensemble empirical mode decomposition with adaptive noise (CEEMDAN), the OCEEMD effectively suppresses mode mixing between IMFs with rapid iteration. Compared with approximate entropy (ApEn) and sample entropy (SampEn), the MSESEn clearly shows a declining tendency with time and is sensitive to muscle fatigue. This suggests a potential use of this approach for sEMG signal preprocessing and the analysis of muscle fatigue.

A Novel Detection Tool for Mild Cognitive Impairment Patients Based on Eye Movement and Electroencephalogram

BACKGROUND

Detecting subtle changes in visual attention from electroencephalography (EEG) and the perspective of eye movement in mild cognitive impairment (MCI) patients can be of great significance in screening early Alzheimer's disease (AD) in a large population at primary care.

OBJECTIVE

We proposed an automatic, non-invasive, and quick MCI detection approach based on multimodal physiological signals for clinical decision-marking.

METHODS

The proposed model recruited 152 patients with MCI and 184 healthy elderly controls (HC) who underwent EEG and eye movement signal recording under a visual stimuli task, as well as other neuropsychological assessments. Forty features were extracted from EEG and eye movement signals by linear and nonlinear analysis. The features related to MCI were selected by logistic regression analysis. To evaluate the efficacy of this MCI detection approach, we applied the same procedures to achieve the Clinical model, EEG model, Eye movement model, EEG+ Clinical model, Eye movement+ Clinical model, and Combined model, and compared the classification accuracy between the MCI and HC groups with the above six models.

RESULTS

After the penalization of logistic regression analysis, five features from EEG and eye movement features exhibited significant differences (p < 0.05). In the classification experiment, the combined model resulted in the best accuracy. The average accuracy for the Clinical/EEG/Eye movement/EEG+ Clinical/Eye movement+ Clinical/Combined model was 68.69%, 61.79%, 73.13%, 69.46%, 75.61%, and 81.51%, respectively.

CONCLUSION

These results suggest that the proposed MCI detection tool has the potential to screen MCI patients from HCs and may be a powerful tool for personalized precision MCI screening in the large-scale population under primary care condition.

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.

The dynamics of plant nutation

In this article we advance a cutting-edge methodology for the study of the dynamics of plant movements of nutation. Our approach, unlike customary kinematic analyses of shape, period, or amplitude, is based on three typical signatures of adaptively controlled processes and motions, as reported in the biological and behavioral dynamics literature: harmonicity, predictability, and complexity. We illustrate the application of a dynamical methodology to the bending movements of shoots of common beans (Phaseolus vulgaris L.) in two conditions: with and without a support to climb onto. The results herewith reported support the hypothesis that patterns of nutation are influenced by the presence of a support to climb in their vicinity. The methodology is in principle applicable to a whole range of plant movements.

Complexity of heart rate variability during moral judgement of actions and omissions

Recent research strongly supports the idea that cardiac activity is involved in the organisation of behaviour, including social behaviour and social cognition. The aim of this work was to explore the complexity of heart rate variability, as measured by permutation entropy, while individuals were making moral judgements about harmful actions and omissions. Participants (N = 58, 50% women, age 21-52 years old) were presented with a set of moral dilemmas describing situations when sacrificing one person resulted in saving five other people. In line with previous studies, our participants consistently judged harmful actions as less permissible than equivalently harmful omissions (phenomenon known as the "omission bias"). Importantly, the response times were significantly longer and permutation entropy of the heart rate was higher when participants were evaluating harmful omissions, as compared to harmful actions. These results may be viewed as a psychophysiological manifestation of differences in causal attribution between actions and omissions. We discuss the obtained results from the positions of the system-evolutionary theory and propose that heart rate variability reflects complexity of the dynamics of neurovisceral activity within the organism-environment interactions, including their social aspects. This complexity can be described in terms of entropy and our work demonstrates the potential of permutation entropy as a tool of analyzing heart rate variability in relation to current behaviour and observed cognitive processes.

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.

Circadian rhythm dynamics on multiscale entropy identifies autonomic dysfunction associated with risk of ventricular arrhythmias and near syncope in chronic kidney disease

BACKGROUND

A discordant biological clock could potentially induce sudden cardiac death (SCD). We aimed to evaluate the circadian change of heart rate variability (HRV) and its relationship to the risks of ventricular arrhythmia (VA) and near syncope in patients with chronic kidney disease (CKD).

METHODS

In this retrospective study, non-CKD and CKD patients were enrolled and underwent a 24-hour Holter examination for linear and nonlinear HRV analyses. The multiscale entropy (MSE) method was selected for nonlinear HRV analyses. The documented VAs or episodes of near syncope were classified as high-risk SCD group (n=8) and others as low-risk SCD group (n=21).

RESULTS

In linear analyses, time and frequency domains revealed no significant difference between groups. In nonlinear analyses with MSE, MSE₅, MSE_6-20, and MSE_{slope 5} were significantly lower (p=0.002, p<0.0001, and p=0.013) in the high-risk SCD group, compared to those in the low-risk SCD group, respectively. Comparing between daytime and nighttime within each group, the MSE₅ revealed no difference in the high-risk SCD group (p=0.128), whereas the daytime was significantly higher in the low-risk SCD group (p=0.048). The area under the curve (AUC) analysis revealed MSE_6-20 has the best predictive power associated with VAs and near syncope with a cut-off value of ≤24.64 (p<0.001).

CONCLUSIONS

Nonlinear analysis with MSE demonstrated the loss of circadian change in CKD patients and was associated with a higher risk for VAs and near syncope. The MSE method demonstrated the diurnal change of rhythm dynamics which identifies potential autonomic dysfunction leading to poor prognosis.

A perspective view on the nanomotion detection of living organisms and its features

The insurgence of newly arising, rapidly developing health threats, such as drug-resistant bacteria and cancers, is one of the most urgent public-health issues of modern times. This menace calls for the development of sensitive and reliable diagnostic tools to monitor the response of single cells to chemical or pharmaceutical stimuli. Recently, it has been demonstrated that all living organisms oscillate at a nanometric scale and that these oscillations stop as soon as the organisms die. These nanometric scale oscillations can be detected by depositing living cells onto a micro-fabricated cantilever and by monitoring its displacements with an atomic force microscope-based electronics. Such devices, named nanomotion sensors, have been employed to determine the resistance profiles of life-threatening bacteria within minutes, to evaluate, among others, the effect of chemicals on yeast, neurons, and cancer cells. The data obtained so far demonstrate the advantages of nanomotion sensing devices in rapidly characterizing microorganism susceptibility to pharmaceutical agents. Here, we review the key aspects of this technique, presenting its major applications. and detailing its working protocols.

Stress and Anxiety Measurement "In-the-Wild" Using Quality-aware Multi-scale HRV Features

Heart rate variability (HRV) has been studied in the context of human behavior analysis and many features have been extracted from the inter-beat interval (RR) time series and tested as correlates of constructs such as mental workload, stress and anxiety. Most studies, however, have been conducted in controlled laboratory environments with artificially-induced psychological responses. While this assures that high quality data are collected, the amount of data is limited and the transferability of the findings to more ecologically-appropriate settings (i.e., "in-the-wild") remains unknown. In this paper, we explore the use of motif-based multi-scale HRV features to predict anxiety and stress in-the-wild. To further improve their robustness to artifacts, we propose a quality-aware feature aggregation method. The new quality-aware features are tested on a dataset collected using a wearable biometric sensor from over 200 hospital workers (nurses and staff) during their work shifts. Results show improved stress/anxiety measurement over using conventional time- and frequency-domain HRV measures.

Multi-Lag Analysis of Symbolic Entropies on EEG Recordings for Distress Recognition

Distress is a critical problem in developed societies given its long-term negative effects on physical and mental health. The interest in studying this emotion has notably increased during last years, being electroencephalography (EEG) signals preferred over other physiological variables in this research field. In addition, the non-stationary nature of brain dynamics has impulsed the use of non-linear metrics, such as symbolic entropies in brain signal analysis. Thus, the influence of time-lag on brain patterns assessment has not been tested. Hence, in the present study two permutation entropies denominated Delayed Permutation Entropy and Permutation Min-Entropy have been computed for the first time at different time-lags to discern between emotional states of calmness and distress from EEG signals. Moreover, a number of curve-related features were also calculated to assess brain dynamics across different temporal intervals. Complementary information among these variables was studied through sequential forward selection and 10-fold cross-validation approaches. According to the results obtained, the multi-lag entropy analysis has been able to reveal new significant insights so far undiscovered, thus notably improving the process of distress recognition from EEG recordings.

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.

Spatial complexity of brain signal is altered in patients with generalized anxiety disorder

BACKGROUND

Is it healthy to be chaotic? Recent studies have argued that mental disorders are associated with more orderly neural activities, corresponding to a less flexible functional system. These conclusions were derived from altered temporal complexity. However, the relationship between spatial complexity and health is unknown, although spatial configuration is of importance for normal brain function.

METHODS

Based on resting-state functional magnetic resonance imaging data, we used Sample entropy (SampEn) to evaluate the altered spatial complexity in patients with generalized anxiety disorder (GAD; n = 47) compared to healthy controls (HCs; n = 38) and the relationship between spatial complexity and anxiety level.

RESULTS

Converging results showed increased spatial complexity in patients with GAD, indicating more chaotic spatial configuration. Interestingly, inverted-U relationship was revealed between spatial complexity and anxiety level, suggesting complex relationship between health and the chaos of human brain.

LIMITATIONS

Anxiety-related alteration of spatial complexity should be verified at voxel level in a larger sample and compared with results of other indices to clarify the mechanism of spatial chaotic of anxiety.

CONCLUSIONS

Altered spatial complexity in the brain of GAD patients mirrors inverted-U relationship between anxiety and behavioral performance, which may reflect an important characteristic of anxiety. These results indicate that SampEn is a good reflection of human health or trait mental characteristic.

Mechanosensitivity of the BK Channels in Human Glioblastoma Cells: Kinetics and Dynamical Complexity

BK channels are potassium selective and exhibit large single-channel conductance. They play an important physiological role in glioma cells: they are involved in cell growth and extensive migrating behavior. Due to the fact that these processes are accompanied by changes in membrane stress, here, we examine mechanosensitive properties of BK channels from human glioblastoma cells (gBK channels). Experiments were performed by the use of patch-clamp method on excised patches under membrane suction (0-40 mmHg) at membrane hyper- and depolarization. We have also checked whether channel's activity is affected by possible changes of membrane morphology after a series of long impulses of suction. Unconventionally, we also analyzed internal structure of the experimental signal to make inferences about conformational dynamics of the channel in stressed membranes. We examined the fractal long-range memory effect (by R/S Hurst analysis), the rate of changes in information by sample entropy, or correlation dimension, and characterize its complexity over a range of scales by the use of Multiscale Entropy method. The obtained results indicate that gBK channels are mechanosensitive at membrane depolarization and hyperpolarization. Prolonged suction of membrane also influences open-closed fluctuations-it decreases channel's activity at membrane hyperpolarization and, in contrary, increases channel's activity at high voltages. Both membrane strain and its "fatigue" reduce dynamical complexity of channel gating, which suggest decrease in the number of available open conformations of channel protein in stressed membranes.

Sample Entropy of sEMG Signals at Different Stages of Rectal Cancer Treatment

Information theory provides a spectrum of nonlinear methods capable of grasping an internal structure of a signal together with an insight into its complex nature. In this work, we discuss the usefulness of the selected entropy techniques for a description of the information carried by the surface electromyography signals during colorectal cancer treatment. The electrical activity of the external anal sphincter can serve as a potential source of knowledge of the actual state of the patient who underwent a common surgery for rectal cancer in the form of anterior or lower anterior resection. The calculation of Sample entropy parameters has been extended to multiple time scales in terms of the Multiscale Sample Entropy. The specific values of the entropy measures and their dependence on the time scales were analyzed with regard to the time elapsed since the operation, the type of surgical treatment and also the different depths of the rectum canal. The Mann-Whitney U test and Anova Friedman statistics indicate the statistically significant differences among all of stages of treatment and for all consecutive depths of rectum area for the estimated Sample Entropy. The further analysis at the multiple time scales signify the substantial differences among compared stages of treatment in the group of patients who underwent the lower anterior resection.

Challenges and Future Perspectives on Electroencephalogram-Based Biometrics in Person Recognition

The emergence of the digital world has greatly increased the number of accounts and passwords that users must remember. It has also increased the need for secure access to personal information in the cloud. Biometrics is one approach to person recognition, which can be used in identification as well as authentication. Among the various modalities that have been developed, electroencephalography (EEG)-based biometrics features unparalleled universality, distinctiveness and collectability, while minimizing the risk of circumvention. However, commercializing EEG-based person recognition poses a number of challenges. This article reviews the various systems proposed over the past few years with a focus on the shortcomings that have prevented wide-scale implementation, including issues pertaining to temporal stability, psychological and physiological changes, protocol design, equipment and performance evaluation. We also examine several directions for the further development of usable EEG-based recognition systems as well as the niche markets to which they could be applied. It is expected that rapid advancements in EEG instrumentation, on-device processing and machine learning techniques will lead to the emergence of commercialized person recognition systems in the near future.

Bodily-Contact Communication Medium Induces Relaxed Mode of Brain Activity While Increasing Its Dynamical Complexity: A Pilot Study

We present the results of the analysis of the effect of a bodily-contact communication medium on the brain activity of the individuals during verbal communication. Our results suggest that the communicated content that is mediated through such a device induces a significant effect on electroencephalogram (EEG) time series of human subjects. Precisely, we find a significant reduction of overall power of the EEG signals of the individuals. This observation that is supported by the analysis of the permutation entropy (PE) of the EEG time series of brain activity of the participants suggests the positive effect of such a medium on the stress relief and the induced sense of relaxation. Additionally, multiscale entropy (MSE) analysis of our data implies that such a medium increases the level of complexity that is exhibited by EEG time series of our participants, thereby suggesting their sustained sense of involvement in their course of communication. These findings that are in accord with the results reported by cognitive neuroscience research suggests that the use of such a medium can be beneficial as a complementary step in treatment of developmental disorders, attentiveness of schoolchildren and early child development, as well as scenarios where intimate physical interaction over distance is desirable (e.g., distance-parenting).

Differential Entropy Preserves Variational Information of Near-Infrared Spectroscopy Time Series Associated With Working Memory

Neuroscience research shows a growing interest in the application of Near-Infrared Spectroscopy (NIRS) in analysis and decoding of the brain activity of human subjects. Given the correlation that is observed between the Blood Oxygen Dependent Level (BOLD) responses that are exhibited by the time series data of functional Magnetic Resonance Imaging (fMRI) and the hemoglobin oxy/deoxy-genation that is captured by NIRS, linear models play a central role in these applications. This, in turn, results in adaptation of the feature extraction strategies that are well-suited for discretization of data that exhibit a high degree of linearity, namely, slope and the mean as well as their combination, to summarize the informational contents of the NIRS time series. In this article, we demonstrate that these features are inefficient in capturing the variational information of NIRS data, limiting the reliability and the adequacy of the conclusion on their results. Alternatively, we propose the linear estimate of differential entropy of these time series as a natural representation of such information. We provide evidence for our claim through comparative analysis of the application of these features on NIRS data pertinent to several working memory tasks as well as naturalistic conversational stimuli.

Data Decomposition Techniques with Multi-Scale Permutation Entropy Calculations for Bearing Fault Diagnosis

This paper presents the local mean decomposition (LMD) integrated with multi-scale permutation entropy (MPE), also known as LMD-MPE, to investigate the rolling element bearing (REB) fault diagnosis from measured vibration signals. First, the LMD decomposed the vibration data or acceleration measurement into separate product functions that are composed of both amplitude and frequency modulation. MPE then calculated the statistical permutation entropy from the product functions to extract the nonlinear features to assess and classify the condition of the healthy and damaged REB system. The comparative experimental results of the conventional LMD-based multi-scale entropy and MPE were presented to verify the authenticity of the proposed technique. The study found that LMD-MPE’s integrated approach provides reliable, damage-sensitive features when analyzing the bearing condition. The results of REB experimental datasets show that the proposed approach yields more vigorous outcomes than existing methods.

Improved Multiscale Entropy Technique with Nearest-Neighbor Moving-Average Kernel for Nonlinear and Nonstationary Short-Time Biomedical Signal Analysis

Analysis of biomedical signals can yield invaluable information for prognosis, diagnosis, therapy evaluation, risk assessment, and disease prevention which is often recorded as short time series data that challenges existing complexity classification algorithms such as Shannon entropy (SE) and other techniques. The purpose of this study was to improve previously developed multiscale entropy (MSE) technique by incorporating nearest-neighbor moving-average kernel, which can be used for analysis of nonlinear and non-stationary short time series physiological data. The approach was tested for robustness with respect to noise analysis using simulated sinusoidal and ECG waveforms. Feasibility of MSE to discriminate between normal sinus rhythm (NSR) and atrial fibrillation (AF) was tested on a single-lead ECG. In addition, the MSE algorithm was applied to identify pivot points of rotors that were induced in ex vivo isolated rabbit hearts. The improved MSE technique robustly estimated the complexity of the signal compared to that of SE with various noises, discriminated NSR and AF on single-lead ECG, and precisely identified the pivot points of ex vivo rotors by providing better contrast between the rotor core and the peripheral region. The improved MSE technique can provide efficient complexity analysis of variety of nonlinear and nonstationary short-time biomedical signals.

Temporal Analysis of Cardiovascular and Respiratory Complexity by Multiscale Entropy Based on Symbolic Dynamics

The effect of an orthostatic stress on cardiovascular and respiratory complexity was investigated to detect impaired autonomic regulation in patients with vasovagal syncope (VVS). A total of 16 female patients and 12 age-matched healthy female subjects were enrolled in a passive 70° head-up tilt test. Also, 12 age-matched healthy male subjects were enrolled to study gender differences. Analysis was performed dynamically using various short-term (5 min) windows shifted by 1 min as well as by 20 min of orthostatic phase (OP) to evaluate local and global complexity. Complexity was determined over multiple time scales by the established method of refined composite multiscale entropy (RCMSE) and by a new proposed method of multiscale entropy based on symbolic dynamics (MSE-SD). Concerning heart rate variability (HRV) during OP, both methods revealed the highest complexity for female controls followed by lower complexity in male controls (p < 0.01) and by the lowest complexity in female patients (p < 0.01). For blood pressure variability (BPV), no gender differences in controls were shown by any method. However, MSE-SD demonstrated highly significantly increased BPV complexity in patients during OP (p < 0.01 on 4 time-scales after 7 min, p < 0.001 on 5 time-scales after 11 min) while RCMSE did not reveal considerable differences (p < 0.05 on 2 time scales after 7 min). Respiratory complexity was further increased in patients primary shown by MSE-SD. Findings indicated impaired autonomic regulation in VVS patients characterized by predominantly increased BPV complexity accompanied with decreased HRV complexity. In addition, results suggested extending the concept of complexity loss with disease.

Exploring resting-state EEG complexity before migraine attacks

Objective

Entropy-based approaches to understanding the temporal dynamics of complexity have revealed novel insights into various brain activities. Herein, electroencephalogram complexity before migraine attacks was examined using an inherent fuzzy entropy approach, allowing the development of an electroencephalogram-based classification model to recognize the difference between interictal and preictal phases.

Methods

Forty patients with migraine without aura and 40 age-matched normal control subjects were recruited, and the resting-state electroencephalogram signals of their prefrontal and occipital areas were prospectively collected. The migraine phases were defined based on the headache diary, and the preictal phase was defined as within 72 hours before a migraine attack.

Results

The electroencephalogram complexity of patients in the preictal phase, which resembled that of normal control subjects, was significantly higher than that of patients in the interictal phase in the prefrontal area (FDR-adjusted p < 0.05) but not in the occipital area. The measurement of test-retest reliability (n = 8) using the intra-class correlation coefficient was good with r1 = 0.73 ( p = 0.01). Furthermore, the classification model, support vector machine, showed the highest accuracy (76 ± 4%) for classifying interictal and preictal phases using the prefrontal electroencephalogram complexity.

Conclusion

Entropy-based analytical methods identified enhancement or “normalization” of frontal electroencephalogram complexity during the preictal phase compared with the interictal phase. This classification model, using this complexity feature, may have the potential to provide a preictal alert to migraine without aura patients.

Pattern Analysis of Oxygen Saturation Variability in Healthy Individuals: Entropy of Pulse Oximetry Signals Carries Information about Mean Oxygen Saturation

Pulse oximetry is routinely used for monitoring patients' oxygen saturation levels with little regard to the variability of this physiological variable. There are few published studies on oxygen saturation variability (OSV), with none describing the variability and its pattern in a healthy adult population. The aim of this study was to characterize the pattern of OSV using several parameters; the regularity (sample entropy analysis), the self-similarity [detrended fluctuation analysis (DFA)] and the complexity [multiscale entropy (MSE) analysis]. Secondly, to determine if there were any changes that occur with age. The study population consisted of 36 individuals. The “young” population consisted of 20 individuals [Mean (±1 SD) age = 21.0 (±1.36 years)] and the “old” population consisted of 16 individuals [Mean (±1 SD) age = 50.0 (±10.4 years)]. Through DFA analysis, OSV was shown to exhibit fractal-like patterns. The sample entropy revealed the variability to be more regular than heart rate variability and respiratory rate variability. There was also a significant inverse correlation between mean oxygen saturation and sample entropy in healthy individuals. Additionally, the MSE analysis described a complex fluctuation pattern, which was reduced with age (p < 0.05). These findings suggest partial “uncoupling” of the cardio-respiratory control system that occurs with aging. Overall, this study has characterized OSV using pre-existing tools. We have showed that entropy analysis of pulse oximetry signals carries information about body oxygenation. This may have the potential to be used in clinical practice to detect differences in diseased patient subsets.

Exploring the link between multiscale entropy and fractal scaling behavior in near-surface wind

The equivalency between the power law behavior of Multiscale Entropy (MSE) and of power spectra opens a promising path for interpretation of complex time-series, which is explored here for the first time for atmospheric fields. Additionally, the present manuscript represents a new independent empirical validation of such relationship, the first one for the atmosphere. The MSE-fractal relationship is verified for synthetic fractal time-series covering the full range of exponents typically observed in the atmosphere. It is also verified for near-surface wind observations from anemometers and CFSR re-analysis product. The results show a ubiquitous β ≈ 5/3 behavior inside the inertial range. A scaling break emerges at scales around a few seconds, with a tendency towards 1/f noise. The presence, extension and fractal exponent of this intermediate range are dependent on the particular surface forcing and atmospheric conditions. MSE shows an identical picture which is consistent with the turbulent energy cascade model: viscous dissipation at the small-scale end of the inertial range works as an information sink, while at the larger (energy-containing) scales the multiple forcings in the boundary layer act as widespread information sources. Another scaling transition occurs at scales around 1–10 days, with an abrupt flattening of the spectrum. MSE shows that this transition corresponds to a maximum of the new information introduced, occurring at the time-scales of the synoptic features that dominate weather patterns. At larger scales, a scaling regime with flatter slopes emerges extending to scales larger than 1 year. MSE analysis shows that the amount of new information created decreases with increasing scale in this low-frequency regime. Additionally, in this region the energy injection is concentrated in two large energy peaks: daily and yearly time-scales. The results demonstrate that the superposition of these periodic signals does not destroy the underlying scaling behavior, with both periodic and fractal terms playing an important role in the observed wind time-series.

The structure function as new integral measure of spatial and temporal properties of multichannel EEG

The first-order temporal structure functions (SFs), i.e., the first-order statistical moment of absolute increments of scaled multichannel resting state EEG signals in healthy children and teenagers over a wide range of temporal separation (time lags) are computed. Our research shows that the sill level (asymptote) of the SF is mainly defined by a determinant of EEG correlation matrix reflecting the EEG spatial structure. The temporal structure of EEG is found to be characterized by power-law scaling or statistical-scale invariance over time scales less than 0.028 s and at least by two dominant frequencies differing by less than 0.3 Hz. These frequencies define the oscillation behavior of the SF and are mainly distributed within the range of 7.5-12.0 Hz. In this paper, we propose the combined Bessel and exponential model that fits well the empirical SF. It provides a good fit with the mean relative error fitting of 2.8 % over the time lag range of 1 s, using a sampling interval of 4 ms, for all cases under analysis. We also show that the hyper gamma distribution (HGD) fits to the empirical probability density functions (PDFs) of absolute increments of scaled multichannel resting state EEG signals at any given time lag. It means that only two parameters (sample mean of absolute increments and relevant coefficient of variation) may approximately define the empirical PDFs for a given number of channels. A three-dimensional feature vector constructed from the shape and scale parameters of the HGD and the sill level may be used to estimate the closeness of the real EEG to the "random" EEG characterized by the absence of temporal and spatial correlation.

A Comparison of Multiscale Permutation Entropy Measures in On-Line Depth of Anesthesia Monitoring

OBJECTIVE

Multiscale permutation entropy (MSPE) is becoming an interesting tool to explore neurophysiological mechanisms in recent years. In this study, six MSPE measures were proposed for on-line depth of anesthesia (DoA) monitoring to quantify the anesthetic effect on the real-time EEG recordings. The performance of these measures in describing the transient characters of simulated neural populations and clinical anesthesia EEG were evaluated and compared.

METHODS

Six MSPE algorithms-derived from Shannon permutation entropy (SPE), Renyi permutation entropy (RPE) and Tsallis permutation entropy (TPE) combined with the decomposition procedures of coarse-graining (CG) method and moving average (MA) analysis-were studied. A thalamo-cortical neural mass model (TCNMM) was used to generate noise-free EEG under anesthesia to quantitatively assess the robustness of each MSPE measure against noise. Then, the clinical anesthesia EEG recordings from 20 patients were analyzed with these measures. To validate their effectiveness, the ability of six measures were compared in terms of tracking the dynamical changes in EEG data and the performance in state discrimination. The Pearson correlation coefficient (R) was used to assess the relationship among MSPE measures.

RESULTS

CG-based MSPEs failed in on-line DoA monitoring at multiscale analysis. In on-line EEG analysis, the MA-based MSPE measures at 5 decomposed scales could track the transient changes of EEG recordings and statistically distinguish the awake state, unconsciousness and recovery of consciousness (RoC) state significantly. Compared to single-scale SPE and RPE, MSPEs had better anti-noise ability and MA-RPE at scale 5 performed best in this aspect. MA-TPE outperformed other measures with faster tracking speed of the loss of unconsciousness.

CONCLUSIONS

MA-based multiscale permutation entropies have the potential for on-line anesthesia EEG analysis with its simple computation and sensitivity to drug effect changes. CG-based multiscale permutation entropies may fail to describe the characteristics of EEG at high decomposition scales.

Using ordinal partition transition networks to analyze ECG data

Electrocardiogram (ECG) data from patients with a variety of heart conditions are studied using ordinal pattern partition networks. The ordinal pattern partition networks are formed from the ECG time series by symbolizing the data into ordinal patterns. The ordinal patterns form the nodes of the network and edges are defined through the time ordering of the ordinal patterns in the symbolized time series. A network measure, called the mean degree, is computed from each time series-generated network. In addition, the entropy and number of non-occurring ordinal patterns (NFP) is computed for each series. The distribution of mean degrees, entropies, and NFPs for each heart condition studied is compared. A statistically significant difference between healthy patients and several groups of unhealthy patients with varying heart conditions is found for the distributions of the mean degrees, unlike for any of the distributions of the entropies or NFPs.

Universal structures of normal and pathological heart rate variability

The circulatory system of living organisms is an autonomous mechanical system softly tuned with the respiratory system, and both developed by evolution as a response to the complex oxygen demand patterns associated with motion. Circulatory health is rooted in adaptability, which entails an inherent variability. Here, we show that a generalized N-dimensional normalized graph representing heart rate variability reveals two universal arrhythmic patterns as specific signatures of health one reflects cardiac adaptability, and the other the cardiac-respiratory rate tuning. In addition, we identify at least three universal arrhythmic profiles whose presences raise in proportional detriment of the two healthy ones in pathological conditions (myocardial infarction; heart failure; and recovery from sudden death). The presence of the identified universal arrhythmic structures together with the position of the centre of mass of the heart rate variability graph provide a unique quantitative assessment of the health-pathology gradient.