Entropy and Complexity Analyses in Alzheimer's Disease: An MEG Study

Local signal variability and functional connectivity: Sensitive measures of the excitation-inhibition ratio?

A novel network version of permutation entropy, the inverted joint permutation entropy (JPEinv), holds potential as non-invasive biomarker of abnormal excitation-inhibition (E-I) ratio in Alzheimer's disease (AD). In this computational modelling study, we test the hypotheses that this metric, and related measures of signal variability and functional connectivity, are sensitive to altered E-I ratios. The E-I ratio in each neural mass of a whole-brain computational network model was systematically varied. We evaluated whether JPEinv, local signal variability (by permutation entropy) and functional connectivity (by weighted symbolic mutual information (wsMI)) were related to E-I ratio, on whole-brain and regional level. The hub disruption index can identify regions primarily affected in terms of functional connectivity strength (or: degree) by the altered E-I ratios. Analyses were performed for a range of coupling strengths, filter and time-delay settings. On whole-brain level, higher E-I ratios were associated with higher functional connectivity (by JPEinv and wsMI) and lower local signal variability. These relationships were nonlinear and depended on the coupling strength, filter and time-delay settings. On regional level, hub-like regions showed a selective decrease in functional degree (by JPEinv and wsMI) upon a lower E-I ratio, and non-hub-like regions showed a selective increase in degree upon a higher E-I ratio. These results suggest that abnormal functional connectivity and signal variability, as previously reported in patients across the AD continuum, can inform us about altered E-I ratios.

Supplementary Information

The online version contains supplementary material available at 10.1007/s11571-023-10003-x.

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

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

A primer on entropy in neuroscience

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

Applying machine learning techniques to detect the deployment of spatial working memory from the spiking activity of MT neurons

Neural signatures of working memory have been frequently identified in the spiking activity of different brain areas. However, some studies reported no memory-related change in the spiking activity of the middle temporal (MT) area in the visual cortex. However, recently it was shown that the content of working memory is reflected as an increase in the dimensionality of the average spiking activity of the MT neurons. This study aimed to find the features that can reveal memory-related changes with the help of machine-learning algorithms. In this regard, different linear and nonlinear features were obtained from the neuronal spiking activity during the presence and absence of working memory. To select the optimum features, the Genetic algorithm, Particle Swarm Optimization, and Ant Colony Optimization methods were employed. The classification was performed using the Support Vector Machine (SVM) and the K-Nearest Neighbor (KNN) classifiers. Our results suggest that the deployment of spatial working memory can be perfectly detected from spiking patterns of MT neurons with an accuracy of 99.65±0.12 using the KNN and 99.50±0.26 using the SVM classifiers.

Complexity analysis of heartbeat-related signals in brain MRI time series as a potential biomarker for ageing and cognitive performance

Getting older affects both the structure of the brain and some cognitive capabilities. Until now, magnetic resonance imaging (MRI) approaches have been unable to give a coherent reflection of the cognitive declines. It shows the limitation of the contrast mechanisms used in most MRI investigations, which are indirect measures of brain activities depending on multiple physiological and cognitive variables. However, MRI signals may contain information of brain activity beyond these commonly used signals caused by the neurovascular response. Here, we apply a zero-spin echo (ZSE) weighted MRI sequence, which can detect heartbeat-evoked signals (HES). Remarkably, these MRI signals have properties only known from electrophysiology. We investigated the complexity of the HES arising from this sequence in two age groups; young (18-29 years) and old (over 65 years). While comparing young and old participants, we show that the complexity of the HES decreases with age, where the stability and chaoticity of these HES are particularly sensitive to age. However, we also found individual differences which were independent of age. Complexity measures were related to scores from different cognitive batteries and showed that higher complexity may be related to better cognitive performance. These findings underpin the affinity of the HES to electrophysiological signals. The profound sensitivity of these changes in complexity shows the potential of HES for understanding brain dynamics that need to be tested in more extensive and diverse populations with clinical relevance for all neurovascular diseases.

SUPPLEMENTARY INFORMATION

The online version contains supplementary material available at 10.1140/epjs/s11734-022-00696-2.

Distinctive effects of executive dysfunction and loss of learning/memory abilities on resting-state brain activity

Dementia is a syndrome characterised by cognitive impairments, with a loss of learning/memory abilities at the earlier stages and executive dysfunction at the later stages. However, recent studies have suggested that impairments in both learning/memory abilities and executive functioning might co-exist. Cognitive impairments have been primarily evaluated using neuropsychological assessments, such as the Mini-Mental State Examination (MMSE). Recently, neuroimaging techniques such as magnetoencephalography (MEG), which assess changes in resting-state brain activity, have also been used as biomarkers for cognitive impairment. However, it is unclear whether these changes reflect dysfunction in executive function as well as learning and memory. In this study, parameters from the MEG for brain activity, MMSE for learning/memory, and Frontal Assessment Battery (FAB) for executive function were compared within 207 individuals. Three MEG parameters were used as representatives of resting-state brain activity: median frequency, individual alpha frequency, and Shannon’s spectral entropy. Regression analysis showed that median frequency was predicted by both the MMSE and FAB scores, while individual alpha frequency and Shannon’s spectral entropy were predicted by MMSE and FAB scores, respectively. Our results indicate that MEG spectral parameters reflect both learning/memory and executive functions, supporting the utility of MEG as a biomarker of cognitive impairment.

Network-level permutation entropy of resting-state MEG recordings: a novel biomarker for early-stage Alzheimer’s disease?

Increasing evidence suggests that measures of signal variability and complexity could present promising biomarkers for Alzheimer’s disease (AD). Earlier studies have however been limited to the characterization of local activity. Here, we investigate whether a network version of permutation entropy could serve as a novel biomarker for early-stage AD. Resting-state source-space magnetoencephalography was recorded in 18 subjects with subjective cognitive decline (SCD) and 18 subjects with mild cognitive impairment (MCI). Local activity was characterized by permutation entropy (PE). Network-level interactions were studied using the inverted joint permutation entropy (JPE_inv), corrected for volume conduction. The JPE_inv showed a reduction of nonlinear connectivity in MCI subjects in the theta and alpha band. Local PE showed increased theta band entropy. Between-group differences were widespread across brain regions. Receiver operating characteristic (ROC) analysis of classification of MCI versus SCD subjects revealed that a logistic regression model trained on JPE_inv features (78.4% [62.5–93.3%]) slightly outperformed PE (76.9% [60.3–93.4%]) and relative theta power–based models (76.9% [60.4–93.3%]). Classification performance of theta JPE_inv was at least as good as the relative theta power benchmark. The JPE_inv is therefore a potential biomarker for early-stage AD that should be explored in larger studies.

Functional network disruption is a well-established finding in Alzheimer’s disease. Sensitive network-based biomarkers are however not available. We aimed to detect neuronal dysfunction at a predementia (mild cognitive impairment, MCI) stage of Alzheimer’s disease, by applying a network-level neural variability measure to magnetoencephalography data: the inverted joint permutation entropy (JPE_inv). This measure integrates information on local signal variability/complexity and nonlinear coupling. We found significant differences in JPE_inv between subjects with subjective cognitive decline and MCI, primarily in the theta band. The diagnostic ability of the JPE_inv was reported to be similar to that of relative theta power, the most potent neurophysiological biomarker of predementia Alzheimer’s disease to date.

Linear and Nonlinear Quantitative EEG Analysis during Neutral Hypnosis following an Opened/Closed Eye Paradigm

Hypnotic susceptibility is a major factor influencing the study of the neural correlates of hypnosis using EEG. In this context, while its effects on the response to hypnotic suggestions are undisputed, less attention has been paid to “neutral hypnosis” (i.e., the hypnotic condition in absence of suggestions). Furthermore, although an influence of opened and closed eye condition onto hypnotizability has been reported, a systematic investigation is still missing. Here, we analyzed EEG signals from 34 healthy subjects with low (LS), medium (MS), and (HS) hypnotic susceptibility using power spectral measures (i.e., TPSD, PSD) and Lempel-Ziv-Complexity (i.e., LZC, fLZC). Indeed, LZC was found to be more suitable than other complexity measures for EEG analysis, while it has been never used in the study of hypnosis. Accordingly, for each measure, we investigated within-group differences between rest and neutral hypnosis, and between opened-eye/closed-eye conditions under both rest and neutral hypnosis. Then, we evaluated between-group differences for each experimental condition. We observed that, while power estimates did not reveal notable differences between groups, LZC and fLZC were able to distinguish between HS, MS, and LS. In particular, we found a left frontal difference between HS and LS during closed-eye rest. Moreover, we observed a symmetric pattern distinguishing HS and LS during closed-eye hypnosis. Our results suggest that LZC is better capable of discriminating subjects with different hypnotic susceptibility, as compared to standard power analysis.

Exploring the Interactions Between Neurophysiology and Cognitive and Behavioral Changes Induced by a Non-pharmacological Treatment: A Network Approach

Dementia due to Alzheimer's disease (AD) is a neurological syndrome which has an increasing impact on society, provoking behavioral, cognitive, and functional impairments. AD lacks an effective pharmacological intervention; thereby, non-pharmacological treatments (NPTs) play an important role, as they have been proven to ameliorate AD symptoms. Nevertheless, results associated with NPTs are patient-dependent, and new tools are needed to predict their outcome and to improve their effectiveness. In the present study, 19 patients with AD underwent an NPT for 83.1 ± 38.9 days (mean ± standard deviation). The NPT was a personalized intervention with physical, cognitive, and memory stimulation. The magnetoencephalographic activity was recorded at the beginning and at the end of the NPT to evaluate the neurophysiological state of each patient. Additionally, the cognitive (assessed by means of the Mini-Mental State Examination, MMSE) and behavioral (assessed in terms of the Dementia Behavior Disturbance Scale, DBD-13) status were collected before and after the NPT. We analyzed the interactions between cognitive, behavioral, and neurophysiological data by generating diverse association networks, able to intuitively characterize the relationships between variables of a different nature. Our results suggest that the NPT remarkably changed the structure of the association network, reinforcing the interactions between the DBD-13 and the neurophysiological parameters. We also found that the changes in cognition and behavior are related to the changes in spectral-based neurophysiological parameters. Furthermore, our results support the idea that MEG-derived parameters can predict NPT outcome; specifically, a lesser degree of AD neurophysiological alterations (i.e., neural oscillatory slowing, decreased variety of spectral components, and increased neural signal regularity) predicts a better NPT prognosis. This study provides deeper insights into the relationships between neurophysiology and both, cognitive and behavioral status, proving the potential of network-based methodology as a tool to further understand the complex interactions elicited by NPTs.

Measuring the effects of sleep on epileptogenicity with multifrequency entropy

OBJECTIVE

We demonstrate that multifrequency entropy gives insight into the relationship between epileptogenicity and sleep, and forms the basis for an improved measure of medical assessment of sleep impairment in epilepsy patients.

METHODS

Multifrequency entropy was computed from electroencephalography measurements taken from 31 children with Benign Epilepsy with Centrotemporal Spikes and 31 non-epileptic controls while awake and during sleep. Values were compared in the epileptic zone and away from the epileptic zone in various sleep stages.

RESULTS

We find that (I) in lower frequencies, multifrequency entropy decreases during non-rapid eye movement sleep stages when compared with wakefulness in a general population of pediatric patients, (II) patients with Benign Epilepsy with Centrotemporal Spikes had lower multifrequency entropy across stages of sleep and wakefulness, and (III) the epileptic regions of the brain exhibit lower multifrequency entropy patterns than the rest of the brain in epilepsy patients.

CONCLUSIONS

Our results show that multifrequency entropy decreases during sleep, particularly sleep stage 2, confirming, in a pediatric population, an association between sleep, lower multifrequency entropy, and increased likelihood of seizure.

SIGNIFICANCE

We observed a correlation between lowered multifrequency entropy and increased epileptogenicity that lays preliminary groundwork for the detection of a digital biomarker for epileptogenicity.

An Overview of ICA/BSS-Based Application to Alzheimer's Brain Signal Processing

Alzheimer's disease (AD) is by far the most common cause of dementia associated with aging. Early and accurate diagnosis of AD and ability to track progression of the disease is increasingly important as potential disease-modifying therapies move through clinical trials. With the advent of biomedical techniques, such as computerized tomography (CT), electroencephalography (EEG), magnetoencephalography (MEG), positron emission tomography (PET), magnetic resonance imaging (MRI), and functional magnetic resonance imaging (fMRI), large amounts of data from Alzheimer's patients have been acquired and processed from which AD-related information or "signals" can be assessed for AD diagnosis. It remains unknown how best to mine complex information from these brain signals to aid in early diagnosis of AD. An increasingly popular technique for processing brain signals is independent component analysis or blind source separation (ICA/BSS) that separates blindly observed signals into original signals that are as independent as possible. This overview focuses on ICA/BSS-based applications to AD brain signal processing.

Magnetoencephalography: physics, techniques, and applications in the basic and clinical neurosciences

Magnetoencephalography (MEG) is a technique used to measure the magnetic fields generated from neuronal activity in the brain. MEG has a high temporal resolution on the order of milliseconds and provides a more direct measure of brain activity when compared with hemodynamic-based neuroimaging methods such as magnetic resonance imaging and positron emission tomography. The current review focuses on basic features of MEG such as the instrumentation and the physics that are integral to the signals that can be measured, and the principles of source localization techniques, particularly the physics of beamforming and the techniques that are used to localize the signal of interest. In addition, we review several metrics that can be used to assess functional coupling in MEG and describe the advantages and disadvantages of each approach. Lastly, we discuss the current and future applications of MEG.

Sleep/Wake Behavior and EEG Signatures of the TgF344-AD Rat Model at the Prodromal Stage

Transgenic modification of the two most common genes (APPsw, PS1ΔE9) related to familial Alzheimer's disease (AD) in rats has produced a rodent model that develops pathognomonic signs of AD without genetic tau-protein modification. We used 17-month-old AD rats (n = 8) and age-matched controls (AC, n = 7) to evaluate differences in sleep behavior and EEG features during wakefulness (WAKE), non-rapid eye movement sleep (NREM), and rapid eye movement sleep (REM) over 24-h EEG recording (12:12h dark-light cycle). We discovered that AD rats had more sleep-wake transitions and an increased probability of shorter REM and NREM bouts. AD rats also expressed a more uniform distribution of the relative spectral power. Through analysis of information content in the EEG using entropy of difference, AD animals demonstrated less EEG information during WAKE, but more information during NREM. This seems to indicate a limited range of changes in EEG activity that could be caused by an AD-induced change in inhibitory network function as reflected by increased GABAAR-β2 expression but no increase in GAD-67 in AD animals. In conclusion, this transgenic rat model of Alzheimer's disease demonstrates less obvious EEG features of WAKE during wakefulness and less canonical features of sleep during sleep.

Brain Entropy Mapping in Healthy Aging and Alzheimer's Disease

Alzheimer's disease (AD) is a progressive neurodegenerative disease, for which aging remains the major risk factor. Aging is under a consistent pressure of increasing brain entropy (BEN) due to the progressive brain deteriorations. Noticeably, the brain constantly consumes a large amount of energy to maintain its functional integrity, likely creating or maintaining a big "reserve" to counteract the high entropy. Malfunctions of this latent reserve may indicate a critical point of disease progression. The purpose of this study was to characterize BEN in aging and AD and to test an inverse-U-shape BEN model: BEN increases with age and AD pathology in normal aging but decreases in the AD continuum. BEN was measured with resting state fMRI and compared across aging and the AD continuum. Associations of BEN with age, education, clinical symptoms, and pathology were examined by multiple regression. The analysis results highlighted resting BEN in the default mode network, medial temporal lobe, and prefrontal cortex and showed that: (1) BEN increased with age and pathological deposition in normal aging but decreased with age and pathological deposition in the AD continuum; (2) AD showed catastrophic BEN reduction, which was related to more severe cognitive impairment and daily function disability; and (3) BEN decreased with education years in normal aging, but not in the AD continuum. BEN evolution follows an inverse-U trajectory when AD progresses from normal aging to AD dementia. Education is beneficial for suppressing the entropy increase potency in normal aging.

Serotonergic psychedelics LSD & psilocybin increase the fractal dimension of cortical brain activity in spatial and temporal domains

Psychedelic drugs, such as psilocybin and LSD, represent unique tools for researchers investigating the neural origins of consciousness. Currently, the most compelling theories of how psychedelics exert their effects is by increasing the complexity of brain activity and moving the system towards a critical point between order and disorder, creating more dynamic and complex patterns of neural activity. While the concept of criticality is of central importance to this theory, few of the published studies on psychedelics investigate it directly, testing instead related measures such as algorithmic complexity or Shannon entropy. We propose using the fractal dimension of functional activity in the brain as a measure of complexity since findings from physics suggest that as a system organizes towards criticality, it tends to take on a fractal structure. We tested two different measures of fractal dimension, one spatial and one temporal, using fMRI data from volunteers under the influence of both LSD and psilocybin. The first was the fractal dimension of cortical functional connectivity networks and the second was the fractal dimension of BOLD time-series. In addition to the fractal measures, we used a well-established, non-fractal measure of signal complexity and show that they behave similarly. We were able to show that both psychedelic drugs significantly increased the fractal dimension of functional connectivity networks, and that LSD significantly increased the fractal dimension of BOLD signals, with psilocybin showing a non-significant trend in the same direction. With both LSD and psilocybin, we were able to localize changes in the fractal dimension of BOLD signals to brain areas assigned to the dorsal-attenion network. These results show that psychedelic drugs increase the fractal dimension of activity in the brain and we see this as an indicator that the changes in consciousness triggered by psychedelics are associated with evolution towards a critical zone.

Complexity Analysis of EEG, MEG, and fMRI in Mild Cognitive Impairment and Alzheimer's Disease: A Review

Alzheimer's disease (AD) is a degenerative brain disease with a high and irreversible incidence. In recent years, because brain signals have complex nonlinear dynamics, there has been growing interest in studying complex changes in the time series of brain signals in patients with AD. We reviewed studies of complexity analyses of single-channel time series from electroencephalogram (EEG), magnetoencephalogram (MEG), and functional magnetic resonance imaging (fMRI) in AD and determined future research directions. A systematic literature search for 2000-2019 was performed in the Web of Science and PubMed databases, resulting in 126 identified studies. Compared to healthy individuals, the signals from AD patients have less complexity and more predictable oscillations, which are found mainly in the left parietal, occipital, right frontal, and temporal regions. This complexity is considered a potential biomarker for accurately responding to the functional lesion in AD. The current review helps to reveal the patterns of dysfunction in the brains of patients with AD and to investigate whether signal complexity can be used as a biomarker to accurately respond to the functional lesion in AD. We proposed further studies in the signal complexities of AD patients, including investigating the reliability of complexity algorithms and the spatial patterns of signal complexity. In conclusion, the current review helps to better understand the complexity of abnormalities in the AD brain and provide useful information for AD diagnosis.

Desynchronizing to be faster? Perceptual- and attentional-modulation of brain rhythms at the sub-millisecond scale

Neural oscillatory signals has been associated with many high-level functions (e.g. attention and working memory), because they reflect correlated behaviors of neural population that would facilitate the information transfer in the brain. On the other hand, a decreased power of oscillation (event-related desynchronization, ERD) has been associated with an irregular state in which many neurons behave in an uncorrelated manner. In contrast to this view, here we show that the human ERD is linked to the increased regularity of oscillatory signals. Using magnetoencephalography, we found that presenting a visual stimulus not only induced a decrease in power of alpha (8-12 Hz) to beta (13-30 Hz) rhythms in the contralateral visual cortex but also reduced the mean and variance of their inter-peak intervals (IPIs). This indicates that the suppressed alpha/beta rhythms became faster (reduced mean) and more regular (reduced variance) during visual stimulation. The same changes in IPIs, especially those of beta rhythm, were observed when subjects allocated their attention to a contralateral visual field. Those results revealed a new role of the event-related decrease in alpha/beta power and further suggested that our brain regulates and accelerates a clock for neural computations by actively suppressing the oscillation amplitude in task-relevant regions.

Handwriting movements for assessment of motor symptoms in schizophrenia spectrum disorders and bipolar disorder

The main aim of the present study was to explore the value of several measures of handwriting in the study of motor abnormalities in patients with bipolar or psychotic disorders. 54 adult participants with a schizophrenia spectrum disorder or bipolar disorder and 44 matched healthy controls, participated in the study. Participants were asked to copy a handwriting pattern consisting of four loops, with an inking pen on a digitizing tablet. We collected a number of classical, non-linear and geometrical measures of handwriting. The handwriting of patients was characterized by a significant decrease in velocity and acceleration and an increase in the length, disfluency and pressure with respect to controls. Concerning non-linear measures, we found significant differences between patients and controls in the Sample Entropy of velocity and pressure, Lempel-Ziv of velocity and pressure, and Higuchi Fractal Dimension of pressure. Finally, Lacunarity, a measure of geometrical heterogeneity, was significantly greater in handwriting patterns from patients than from controls. We did not find differences in any handwriting measure on function of the specific diagnosis or the antipsychotic dose. Results indicate that participants with a schizophrenia spectrum disorder or bipolar disorder exhibit significant motor impairments and that these impairments can be readily quantified using measures of handwriting movements. Besides, they suggest that motor abnormalities are a core feature of several mental disorders and they seem to be unrelated to the pharmacological treatment.

The distribution of information for sEMG signals in the rectal cancer treatment process

The electrical activity of external anal sphincter can be registered with surface electromyography. This signals are known to be highly complex and nonlinear. This work aims in characterisation of the information carried in the signals by harvesting the concept of information entropy. We will focus of two classical measures of the complexity. Firstly the Shannon entropy is addressed. It is related to the probability spectrum of the possible states. Secondly the Spectral entropy is described, as a simple frequency-domain analog of the time-domain Shannon characteristics. We discuss the power spectra for separate time scales and present the characteristics which can represent the dynamics of electrical activity of this specific muscle group. We find that the rest and maximum contraction states represent rather different spectral characteristic of entropy, with close-to-normal contraction and negatively skewed rest state.

EEG Analytics for Early Detection of Autism Spectrum Disorder: A data-driven approach

Autism spectrum disorder (ASD) is a complex and heterogeneous disorder, diagnosed on the basis of behavioral symptoms during the second year of life or later. Finding scalable biomarkers for early detection is challenging because of the variability in presentation of the disorder and the need for simple measurements that could be implemented routinely during well-baby checkups. EEG is a relatively easy-to-use, low cost brain measurement tool that is being increasingly explored as a potential clinical tool for monitoring atypical brain development. EEG measurements were collected from 99 infants with an older sibling diagnosed with ASD, and 89 low risk controls, beginning at 3 months of age and continuing until 36 months of age. Nonlinear features were computed from EEG signals and used as input to statistical learning methods. Prediction of the clinical diagnostic outcome of ASD or not ASD was highly accurate when using EEG measurements from as early as 3 months of age. Specificity, sensitivity and PPV were high, exceeding 95% at some ages. Prediction of ADOS calibrated severity scores for all infants in the study using only EEG data taken as early as 3 months of age was strongly correlated with the actual measured scores. This suggests that useful digital biomarkers might be extracted from EEG measurements.

Network Entropy for the Sequence Analysis of Functional Connectivity Graphs of the Brain

Dynamic representation of functional brain networks involved in the sequence analysis of functional connectivity graphs of the brain (FCGB) gains advances in uncovering evolved interaction mechanisms. However, most of the networks, even the event-related ones, are highly heterogeneous due to spurious interactions, which bring challenges to revealing the change patterns of interactive information in the complex dynamic process. In this paper, we propose a network entropy (NE) method to measure connectivity uncertainty of FCGB sequences to alleviate the spurious interaction problem in dynamic network analysis to realize associations with different events during a complex cognitive task. The proposed dynamic analysis approach calculated the adjacency matrices from ongoing electroencephalpgram (EEG) in a sliding time-window to form the FCGB sequences. The probability distribution of Shannon entropy was replaced by the connection sequence distribution to measure the uncertainty of FCGB constituting NE. Without averaging, we used time frequency transform of the NE of FCGB sequences to analyze the event-related changes in oscillatory activity in the single-trial traces during the complex cognitive process of driving. Finally, the results of a verification experiment showed that the NE of the FCGB sequences has a certain time-locked performance for different events related to driver fatigue in a prolonged driving task. The time errors between the extracted time of high-power NE and the recorded time of event occurrence were distributed within the range [−30 s, 30 s] and 90.1% of the time errors were distributed within the range [−10 s, 10 s]. The high correlation (r = 0.99997, p < 0.001) between the timing characteristics of the two types of signals indicates that the NE can reflect the actual dynamic interaction states of brain. Thus, the method may have potential implications for cognitive studies and for the detection of physiological states.

Occupational functional plasticity revealed by brain entropy: A resting-state fMRI study of seafarers

Recently, functional magnetic resonance imaging (fMRI) has been increasingly used to assess brain function. Brain entropy is an effective model for evaluating the alteration of brain complexity. Specifically, the sample entropy (SampEn) provides a feasible solution for revealing the brain's complexity. Occupation is one key factor affecting the brain's activity, but the neuropsychological mechanisms are still unclear. Thus, in this article, based on fMRI and a brain entropy model, we explored the functional complexity changes engendered by occupation factors, taking the seafarer as an example. The whole-brain entropy values of two groups (i.e., the seafarers and the nonseafarers) were first calculated by SampEn and followed by a two-sample t test with AlphaSim correction (p < .05). We found that the entropy of the orbital-frontal gyrus (OFG) and superior temporal gyrus (STG) in the seafarers was significantly higher than that of the nonseafarers. In addition, the entropy of the cerebellum in the seafarers was lower than that of the nonseafarers. We conclude that (1) the lower entropy in the cerebellum implies that the seafarers' cerebellum activity had strong regularity and consistency, suggesting that the seafarer's cerebellum was possibly more specialized by the long-term career training; (2) the higher entropy in the OFG and STG possibly demonstrated that the seafarers had a relatively decreased capability for emotion control and auditory information processing. The above results imply that the seafarer occupation indeed impacted the brain's complexity, and also provided new neuropsychological evidence of functional plasticity related to one's career.

Decreased Complexity in Alzheimer's Disease: Resting-State fMRI Evidence of Brain Entropy Mapping

Alzheimer's disease (AD) is a frequently observed, irreversible brain function disorder among elderly individuals. Resting-state functional magnetic resonance imaging (rs-fMRI) has been introduced as an alternative approach to assessing brain functional abnormalities in AD patients. However, alterations in the brain rs-fMRI signal complexities in mild cognitive impairment (MCI) and AD patients remain unclear. Here, we described the novel application of permutation entropy (PE) to investigate the abnormal complexity of rs-fMRI signals in MCI and AD patients. The rs-fMRI signals of 30 normal controls (NCs), 33 early MCI (EMCI), 32 late MCI (LMCI), and 29 AD patients were obtained from the Alzheimer's disease Neuroimaging Initiative (ADNI) database. After preprocessing, whole-brain entropy maps of the four groups were extracted and subjected to Gaussian smoothing. We performed a one-way analysis of variance (ANOVA) on the brain entropy maps of the four groups. The results after adjusting for age and sex differences together revealed that the patients with AD exhibited lower complexity than did the MCI and NC controls. We found five clusters that exhibited significant differences and were distributed primarily in the occipital, frontal, and temporal lobes. The average PE of the five clusters exhibited a decreasing trend from MCI to AD. The AD group exhibited the least complexity. Additionally, the average PE of the five clusters was significantly positively correlated with the Mini-Mental State Examination (MMSE) scores and significantly negatively correlated with Functional Assessment Questionnaire (FAQ) scores and global Clinical Dementia Rating (CDR) scores in the patient groups. Significant correlations were also found between the PE and regional homogeneity (ReHo) in the patient groups. These results indicated that declines in PE might be related to changes in regional functional homogeneity in AD. These findings suggested that complexity analyses using PE in rs-fMRI signals can provide important information about the fMRI characteristics of cognitive impairments in MCI and AD.

Comparison of background EEG activity of different groups of patients with idiopathic epilepsy using Shannon spectral entropy and cluster-based permutation statistical testing

Idiopathic epilepsy is characterized by generalized seizures with no apparent cause. One of its main problems is the lack of biomarkers to monitor the evolution of patients. The only tools they can use are limited to inspecting the amount of seizures during previous periods of time and assessing the existence of interictal discharges. As a result, there is a need for improving the tools to assist the diagnosis and follow up of these patients. The goal of the present study is to compare and find a way to differentiate between two groups of patients suffering from idiopathic epilepsy, one group that could be followed-up by means of specific electroencephalographic (EEG) signatures (intercritical activity present), and another one that could not due to the absence of these markers. To do that, we analyzed the background EEG activity of each in the absence of seizures and epileptic intercritical activity. We used the Shannon spectral entropy (SSE) as a metric to discriminate between the two groups and performed permutation-based statistical tests to detect the set of frequencies that show significant differences. By constraining the spectral entropy estimation to the [6.25–12.89) Hz range, we detect statistical differences (at below 0.05 alpha-level) between both types of epileptic patients at all available recording channels. Interestingly, entropy values follow a trend that is inversely related to the elapsed time from the last seizure. Indeed, this trend shows asymptotical convergence to the SSE values measured in a group of healthy subjects, which present SSE values lower than any of the two groups of patients. All these results suggest that the SSE, measured in a specific range of frequencies, could serve to follow up the evolution of patients suffering from idiopathic epilepsy. Future studies remain to be conducted in order to assess the predictive value of this approach for the anticipation of seizures.

Lempel-Ziv and multiscale Lempel-Ziv complexity in depression

There is a high demand for objective indicators in diagnosis of depression as diagnosis of depression is still based on psychiatrist's subjective judgment. A nonlinear method Lempel Ziv Complexity (LZC) has been previously successfully used for detection of neuronal or mental disorders based on electroencephalographic (EEG) signals. However, the method overlooks the high frequency content of EEG signals. Therefore, this study is aimed to find out whether the use of Multiscale Lempel Ziv Complexity (MLZC), considering also high frequencies, could overcome the limitations of LZC and better differentiate depression. In current study the EEG recordings were carried out on the groups of depressive and healthy subjects of 11 volunteers each. The LZC and MLZC were calculated on resting EEG signals in eyes open condition from 30 channels at a length of 2 minutes. The results revealed the incapability of traditional LZC to differentiate depressive subjects from healthy controls in eyes open condition, while MLZC differentiated two groups in numerous channels at different frequencies, giving the highest classification accuracy in channel F3 (86 %) at frequencies 9 and 15.5 Hz. The results indicate that the high frequency information, which is lost in calculation of traditional LZC, has a great value in differentiating between depressive and control groups.

Application of Higuchi's fractal dimension from basic to clinical neurophysiology: A review

BACKGROUND AND OBJECTIVE

For more than 20 years, Higuchi's fractal dimension (HFD), as a nonlinear method, has occupied an important place in the analysis of biological signals. The use of HFD has evolved from EEG and single neuron activity analysis to the most recent application in automated assessments of different clinical conditions. Our objective is to provide an updated review of the HFD method applied in basic and clinical neurophysiological research.

METHODS

This article summarizes and critically reviews a broad literature and major findings concerning the applications of HFD for measuring the complexity of neuronal activity during different neurophysiological conditions. The source of information used in this review comes from the PubMed, Scopus, Google Scholar and IEEE Xplore Digital Library databases.

RESULTS

The review process substantiated the significance, advantages and shortcomings of HFD application within all key areas of basic and clinical neurophysiology. Therefore, the paper discusses HFD application alone, combined with other linear or nonlinear measures, or as a part of automated methods for analyzing neurophysiological signals.

CONCLUSIONS

The speed, accuracy and cost of applying the HFD method for research and medical diagnosis make it stand out from the widely used linear methods. However, only a combination of HFD with other nonlinear methods ensures reliable and accurate analysis of a wide range of neurophysiological signals.

On the early diagnosis of Alzheimer's Disease from multimodal signals: A survey

INTRODUCTION

The number of Alzheimer's Disease (AD) patients is increasing with increased life expectancy and 115.4 million people are expected to be affected in 2050. Unfortunately, AD is commonly diagnosed too late, when irreversible damages have been caused in the patient.

OBJECTIVE

An automatic, continuous and unobtrusive early AD detection method would be required to improve patients' life quality and avoid big healthcare costs. Thus, the objective of this survey is to review the multimodal signals that could be used in the development of such a system, emphasizing on the accuracy that they have shown up to date for AD detection. Some useful tools and specific issues towards this goal will also have to be reviewed.

METHODS

An extensive literature review was performed following a specific search strategy, inclusion criteria, data extraction and quality assessment in the Inspec, Compendex and PubMed databases.

RESULTS

This work reviews the extensive list of psychological, physiological, behavioural and cognitive measurements that could be used for AD detection. The most promising measurements seem to be magnetic resonance imaging (MRI) for AD vs control (CTL) discrimination with an 98.95% accuracy, while electroencephalogram (EEG) shows the best results for mild cognitive impairment (MCI) vs CTL (97.88%) and MCI vs AD distinction (94.05%). Available physiological and behavioural AD datasets are listed, as well as medical imaging analysis steps and neuroimaging processing toolboxes. Some issues such as "label noise" and multi-site data are discussed.

CONCLUSIONS

The development of an unobtrusive and transparent AD detection system should be based on a multimodal system in order to take full advantage of all kinds of symptoms, detect even the smallest changes and combine them, so as to detect AD as early as possible. Such a multimodal system might probably be based on physiological monitoring of MRI or EEG, as well as behavioural measurements like the ones proposed along the article. The mentioned AD datasets and image processing toolboxes are available for their use towards this goal. Issues like "label noise" and multi-site neuroimaging incompatibilities may also have to be overcome, but methods for this purpose are already available.

Analysis of magnetoencephalography recordings from Alzheimer's disease patients using embedding entropies

The aim of this study was to examine the magnetoencephalography (MEG) background activity in Alzheimer's disease (AD) using three embedding entropies: approximate entropy (ApEn), sample entropy (SampEn), and fuzzy entropy (FuzzyEn). These three methods measure the time series regularity. Five minutes of recording were acquired with a 148-channel whole-head magnetometer from 36 AD patients and 24 elderly control subjects. Our results showed that MEG activity was more regular in AD patients than in controls. Additionally, FuzzyEn revealed statistically significant differences between the two groups (p <; 0.01, Bonferroni-corrected Mann-Whitney U-test), while ApEn and SampEn did not. The better discriminating results of FuzzyEn in comparison with the other entropy algorithms suggest that it is more efficient for the characterization of MEG activity in AD.

Incoordination between spikes and LFPs in Aβ1-42-mediated memory deficits in rats

Alzheimer's disease (AD) is a neurodegenerative disease that gradually induces cognitive deficits. Impairments of working memory have been typically observed in AD. It is well known that spikes and local field potentials (LFPs) as well as the coordination between them encode information in normal brain function. However, the abnormal coordination between spikes and LFPs in the cognitive deficits of AD has remained largely unexplored. As amyloid-β peptide (Aβ) is a causative factor for the cognitive impairments of AD, developing a mechanistic understanding of the contribution of Aβ to cognitive impairments may yield important insights into the pathophysiology of AD. In the present study, we simultaneously recorded spikes and LFPs from multiple electrodes implanted in the prefrontal cortex of rats (control and intra-hippocampal Aβ injection group) that performed a Y-maze working memory task. The information changes in spikes and LFPs during the task were assessed by calculation of entropy. Then the coordination between spikes and LFPs was estimated by the correlation of LFP entropy and spike entropy. Compared with the control group, the Aβ group showed significantly weaker coordination between spikes and LFPs. Our results indicate that the incoordination between spikes and LFPs may provide a potential mechanism for the cognitive deficits in working memory of AD.

Local active information storage as a tool to understand distributed neural information processing

Every act of information processing can in principle be decomposed into the component operations of information storage, transfer, and modification. Yet, while this is easily done for today's digital computers, the application of these concepts to neural information processing was hampered by the lack of proper mathematical definitions of these operations on information. Recently, definitions were given for the dynamics of these information processing operations on a local scale in space and time in a distributed system, and the specific concept of local active information storage was successfully applied to the analysis and optimization of artificial neural systems. However, no attempt to measure the space-time dynamics of local active information storage in neural data has been made to date. Here we measure local active information storage on a local scale in time and space in voltage sensitive dye imaging data from area 18 of the cat. We show that storage reflects neural properties such as stimulus preferences and surprise upon unexpected stimulus change, and in area 18 reflects the abstract concept of an ongoing stimulus despite the locally random nature of this stimulus. We suggest that LAIS will be a useful quantity to test theories of cortical function, such as predictive coding.

Influence of QRS complex detection errors on entropy algorithms. Application to heart rate variability discrimination

Signal entropy measures such as approximate entropy (ApEn) and sample entropy (SampEn) are widely used in heart rate variability (HRV) analysis and biomedical research. In this article, we analyze the influence of QRS detection errors on HRV results based on signal entropy measures. Specifically, we study the influence that QRS detection errors have on the discrimination power of ApEn and SampEn using the cardiac arrhythmia suppression trial (CAST) database. The experiments assessed the discrimination capability of ApEn and SampEn under different levels of QRS detection errors. The results demonstrate that these measures are sensitive to the presence of ectopic peaks: from a successful classification rate of 100%, down to a 75% when spikes are present. The discriminating capability of the metrics degraded as the number of misdetections increased. For an error rate of 2% the segmentation failed in a 12.5% of the experiments, whereas for a 5% rate, it failed in a 25%.

Analysis of complexity based EEG features for the diagnosis of Alzheimer's disease

As life expectancy increases, particularly in the developed world, so does the prevalence of Alzheimer's Disease (AD). AD is a neurodegenerative disorder characterized by neurofibrillary plaques and tangles in the brain that leads to neuronal death and dementia. Early diagnosis of AD is still a major unresolved health concern: several biomarkers are being investigated, among which the electroencephalogram (EEG) provides the only option for an electrophysiological information. In this study, EEG signals obtained from 161 subjects--79 with AD, and 82 age-matched controls (CN)--are analyzed using several nonlinear signal complexity measures. These measures include: Higuchi fractal dimension (HFD), spectral entropy (SE), spectral centroid (SC), spectral roll-off (SR), and zero-crossing rate (ZCR). HFD is a quantitative measure of time series complexity derived from fractal theory. Among spectral measures, SE measures the level of disorder in the spectrum, SC is a measure of spectral shape, and SR is frequency sample below which a specified percent of the spectral magnitude distribution is contained. Lastly, ZCR is simply the rate at which the signal changes signs. A t-test was first applied to determine those features that provide significant differences between the groups. Those features were then used to train a neural network. The classification accuracies ranged from 60-66%, suggesting they contain some discriminatory information; however, not enough to be clinically useful alone. Combining these features and training a support vector machine (SVM) resulted in a diagnostic accuracy of 78%, indicating that these feature carry complementary information.