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Special Issue "Entropy and Electroencephalography"

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A special issue of Entropy (ISSN 1099-4300).

Deadline for manuscript submissions: closed (31 July 2014)

Special Issue Editor

Guest Editor
Dr. Osvaldo Anibal Rosso

1. Departamento de Bioingeniería, Insitituto Tecnológico de Buenos Aires (ITBA), C1106ACD Av. Eduardo Madero 399, Ciudad Autónoma de Buenos Aires, Argentina
2. Instituto de Física, Universidade Federal de Alagoas (UFAL), BR 104 Norte km 97, 57072-970 Maceió, Alagoas, Brazil
3. Facultad de Ingeniería y Ciencias Aplicadas, Universidad de Los Andes, Santiago, Chile
Interests: time-series analysis; information theory; time-frequency transform; wavelet transform; entropy and complexity; non-linear dynamics and chaos; biological applications

Special Issue Information

Dear Colleagues,

Synchronous neuronal discharges create rhythmic potential fluctuations that can be recorded from the scalp through electroencephalography. The electroencephalogram (EEG) can be roughly defined as the mean brain electrical activity measured at different sites of the head. An EEG reflects characteristics of the brain activity itself and also yields clues concerning the underlying associated neural dynamics. The processing of information by the brain results in dynamical changes in its electrical activity; among the changing variables are time, frequency, and space. Therefore, concomitant studies require methods capable of describing the qualitative and quantitative signal variations in terms of time, frequency, and spatial localization.

The traditional way of analyzing brain electrical activity, on the basis of electroencephalography (EEG) records, relies mainly on visual inspection and years of training. Although such analysis is quite useful, its subjective nature precludes a systematic protocol.

Over the last few years, Information Theory-based quantifiers, such as entropy measures and related metrics, have emerged as particularly appropriate complexity measures in the study of time-series from biological systems (such as the brain). The reasons for this increasing success are manifold.

First, biological systems are typically characterized by complex dynamics. Even at rest, such systems’ dynamics have rich temporal structures. On the one hand, spontaneous brain activity encompasses a set of dynamically switching states, which are continuously re-edited across the cortex, in a non-random way. On the other hand, various pathologies are associated with the appearance of highly stereotyped patterns of activity. For instance, epileptic seizures are typically characterized by ordered sequences of symptoms. Entropy-based quantifiers seem particularly well-equipped to capture these structures (i.e., stereotyped patterns) in both healthy systems and in pathological states.

Second, while over the last few decades, a wealth of linear (and, more recently, nonlinear) methods for quantifying these structures from time-series have been devised, most of them, in addition to making restrictive hypotheses as to the type of underlying dynamics, are vulnerable to even low levels of noise. Even mostly deterministic biological time-series typically contain a certain degree of randomness (e.g., in the form of dynamical and observational noise). Therefore, analyzing signals from such systems necessitates methods that are model-free and robust. Contrary to most nonlinear measures, some entropy measures and derived metrics can be calculated for arbitrary real-world time-series and are rather robust with respect to noise sources and artifacts.

Finally, real-time applications for clinical purposes require computationally parsimonious algorithms that can provide reliable results for relatively short and noisy time-series. Most existing methods require long, stationary, and noiseless data. In contrast, methods utilizing quantifiers based upon entropy measure can be extremely fast and robust, and seem particularly advantageous when there are huge data sets and no time for preprocessing and fine-tuning parameters.

For this Special Issue, we welcome submissions related to time-series analysis using entropy quantifiers and related measures to study brain (electrical) activity that is recorded under normal and special conditions (e.g., conditions induced by anesthesia or  other drugs). We also welcome studies concerning pathological states (e.g., epilepsy, schizophrenia, etc.) and cognitive neuroscience. We envisage contributions that aim at clarifying brain dynamics characteristics using time-series recorded with electroencephalographic (EEG) techniques.  In addition, we hope to receive original papers illustrating entropic methods' wide variety of applications, which are relevant for studying EEG classification, determinism detection, detection of dynamical change prediction, and spatio-temporal dynamics.

Dr. Osvaldo A. Rosso
Guest Editor

Submission

Manuscripts should be submitted online at www.mdpi.com by registering and logging in to this website. Once you are registered, click here to go to the submission form. Manuscripts can be submitted until the deadline. Papers will be published continuously (as soon as accepted) and will be listed together on the special issue website. Research articles, review articles as well as communications are invited. For planned papers, a title and short abstract (about 100 words) can be sent to the Editorial Office for announcement on this website.

Submitted manuscripts should not have been published previously, nor be under consideration for publication elsewhere (except conference proceedings papers). All manuscripts are refereed through a peer-review process. A guide for authors and other relevant information for submission of manuscripts is available on the Instructions for Authors page. Entropy is an international peer-reviewed Open Access monthly journal published by MDPI.

Please visit the Instructions for Authors page before submitting a manuscript. The Article Processing Charge (APC) for publication in this open access journal is 1400 CHF (Swiss Francs).


Published Papers (12 papers)

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Research

Open AccessArticle Instantaneous 3D EEG Signal Analysis Based on Empirical Mode Decomposition and the Hilbert–Huang Transform Applied to Depth of Anaesthesia
Entropy 2015, 17(3), 928-949; doi:10.3390/e17030928
Received: 9 December 2014 / Revised: 12 February 2015 / Accepted: 13 February 2015 / Published: 20 February 2015
PDF Full-text (1557 KB) | HTML Full-text | XML Full-text
Abstract
Depth of anaesthesia (DoA) is an important measure for assessing the degree to which the central nervous system of a patient is depressed by a general anaesthetic agent, depending on the potency and concentration with which anaesthesia is administered during surgery. We [...] Read more.
Depth of anaesthesia (DoA) is an important measure for assessing the degree to which the central nervous system of a patient is depressed by a general anaesthetic agent, depending on the potency and concentration with which anaesthesia is administered during surgery. We can monitor the DoA by observing the patient’s electroencephalography (EEG) signals during the surgical procedure. Typically high frequency EEG signals indicates the patient is conscious, while low frequency signals mean the patient is in a general anaesthetic state. If the anaesthetist is able to observe the instantaneous frequency changes of the patient’s EEG signals during surgery this can help to better regulate and monitor DoA, reducing surgical and post-operative risks. This paper describes an approach towards the development of a 3D real-time visualization application which can show the instantaneous frequency and instantaneous amplitude of EEG simultaneously by using empirical mode decomposition (EMD) and the Hilbert–Huang transform (HHT). HHT uses the EMD method to decompose a signal into so-called intrinsic mode functions (IMFs). The Hilbert spectral analysis method is then used to obtain instantaneous frequency data. The HHT provides a new method of analyzing non-stationary and nonlinear time series data. We investigate this approach by analyzing EEG data collected from patients undergoing surgical procedures. The results show that the EEG differences between three distinct surgical stages computed by using sample entropy (SampEn) are consistent with the expected differences between these stages based on the bispectral index (BIS), which has been shown to be quantifiable measure of the effect of anaesthetics on the central nervous system. Also, the proposed filtering approach is more effective compared to the standard filtering method in filtering out signal noise resulting in more consistent results than those provided by the BIS. The proposed approach is therefore able to distinguish between key operational stages related to DoA, which is consistent with the clinical observations. SampEn can also be viewed as a useful index for evaluating and monitoring the DoA of a patient when used in combination with this approach. Full article
(This article belongs to the Special Issue Entropy and Electroencephalography)
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Open AccessArticle Application of Entropy Measures on Intrinsic Mode Functions for the Automated Identification of Focal Electroencephalogram Signals
Entropy 2015, 17(2), 669-691; doi:10.3390/e17020669
Received: 8 December 2014 / Revised: 13 January 2015 / Accepted: 23 January 2015 / Published: 3 February 2015
Cited by 18 | PDF Full-text (1213 KB) | HTML Full-text | XML Full-text
Abstract
The brain is a complex structure made up of interconnected neurons, and its electrical activities can be evaluated using electroencephalogram (EEG) signals. The characteristics of the brain area affected by partial epilepsy can be studied using focal and non-focal EEG signals. In [...] Read more.
The brain is a complex structure made up of interconnected neurons, and its electrical activities can be evaluated using electroencephalogram (EEG) signals. The characteristics of the brain area affected by partial epilepsy can be studied using focal and non-focal EEG signals. In this work, a method for the classification of focal and non-focal EEG signals is presented using entropy measures. These entropy measures can be useful in assessing the nonlinear interrelation and complexity of focal and non-focal EEG signals. These EEG signals are first decomposed using the empirical mode decomposition (EMD) method to extract intrinsic mode functions (IMFs). The entropy features, namely, average Shannon entropy (ShEnAvg), average Renyi’s entropy (RenEnAvg ), average approximate entropy (ApEnAvg), average sample entropy (SpEnAvg) and average phase entropies (S1Avg and S2Avg), are computed from different IMFs of focal and non-focal EEG signals. These entropies are used as the input feature set for the least squares support vector machine (LS-SVM) classifier to classify into focal and non-focal EEG signals. Experimental results show that our proposed method is able to differentiate the focal and non-focal EEG signals with an average classification accuracy of 87% correct. Full article
(This article belongs to the Special Issue Entropy and Electroencephalography)
Open AccessArticle Enhanced Automatic Wavelet Independent Component Analysis for Electroencephalographic Artifact Removal
Entropy 2014, 16(12), 6553-6572; doi:10.3390/e16126553
Received: 31 July 2014 / Revised: 4 December 2014 / Accepted: 5 December 2014 / Published: 17 December 2014
Cited by 1 | PDF Full-text (18016 KB) | HTML Full-text | XML Full-text
Abstract
Electroencephalography (EEG) is a fundamental diagnostic instrument for many neurological disorders, and it is the main tool for the investigation of the cognitive or pathological activity of the brain through the bioelectromagnetic fields that it generates. The correct interpretation of the EEG [...] Read more.
Electroencephalography (EEG) is a fundamental diagnostic instrument for many neurological disorders, and it is the main tool for the investigation of the cognitive or pathological activity of the brain through the bioelectromagnetic fields that it generates. The correct interpretation of the EEG is misleading, both for clinicians’ visual evaluation and for automated procedures, because of artifacts. As a consequence, artifact rejection in EEG is a key preprocessing step, and the quest for reliable automatic processors has been quickly growing in the last few years. Recently, a promising automatic methodology, known as automatic wavelet-independent component analysis (AWICA), has been proposed. In this paper, a more efficient and sensitive version, called enhanced-AWICA (EAWICA), is proposed, and an extensive performance comparison is carried out by a step of tuning the different parameters that are involved in artifact detection. EAWICA is shown to minimize information loss and to outperform AWICA in artifact removal, both on simulated and real experimental EEG recordings. Full article
(This article belongs to the Special Issue Entropy and Electroencephalography)
Open AccessArticle Automatic Sleep Stages Classification Using EEG Entropy Features and Unsupervised Pattern Analysis Techniques
Entropy 2014, 16(12), 6573-6589; doi:10.3390/e16126573
Received: 18 July 2014 / Revised: 28 November 2014 / Accepted: 9 December 2014 / Published: 17 December 2014
Cited by 4 | PDF Full-text (1157 KB) | HTML Full-text | XML Full-text
Abstract
Sleep is a growing area of research interest in medicine and neuroscience. Actually, one major concern is to find a correlation between several physiologic variables and sleep stages. There is a scientific agreement on the characteristics of the five stages of human [...] Read more.
Sleep is a growing area of research interest in medicine and neuroscience. Actually, one major concern is to find a correlation between several physiologic variables and sleep stages. There is a scientific agreement on the characteristics of the five stages of human sleep, based on EEG analysis. Nevertheless, manual stage classification is still the most widely used approach. This work proposes a new automatic sleep classification method based on unsupervised feature classification algorithms recently developed, and on EEG entropy measures. This scheme extracts entropy metrics from EEG records to obtain a feature vector. Then, these features are optimized in terms of relevance using the Q-α algorithm. Finally, the resulting set of features is entered into a clustering procedure to obtain a final segmentation of the sleep stages. The proposed method reached up to an average of 80% correctly classified stages for each patient separately while keeping the computational cost low. Full article
(This article belongs to the Special Issue Entropy and Electroencephalography)
Open AccessArticle Ordinal Patterns, Entropy, and EEG
Entropy 2014, 16(12), 6212-6239; doi:10.3390/e16126212
Received: 9 October 2014 / Revised: 13 November 2014 / Accepted: 19 November 2014 / Published: 27 November 2014
Cited by 4 | PDF Full-text (882 KB) | HTML Full-text | XML Full-text
Abstract
In this paper we illustrate the potential of ordinal-patterns-based methods for analysis of real-world data and, especially, of electroencephalogram (EEG) data. We apply already known (empirical permutation entropy, ordinal pattern distributions) and new (empirical conditional entropy of ordinal patterns, robust to noise [...] Read more.
In this paper we illustrate the potential of ordinal-patterns-based methods for analysis of real-world data and, especially, of electroencephalogram (EEG) data. We apply already known (empirical permutation entropy, ordinal pattern distributions) and new (empirical conditional entropy of ordinal patterns, robust to noise empirical permutation entropy) methods for measuring complexity, segmentation and classification of time series. Full article
(This article belongs to the Special Issue Entropy and Electroencephalography)
Open AccessArticle A Quantitative Analysis of an EEG Epileptic Record Based on MultiresolutionWavelet Coefficients
Entropy 2014, 16(11), 5976-6005; doi:10.3390/e16115976
Received: 22 August 2014 / Revised: 7 November 2014 / Accepted: 11 November 2014 / Published: 17 November 2014
Cited by 1 | PDF Full-text (806 KB) | HTML Full-text | XML Full-text
Abstract
The characterization of the dynamics associated with electroencephalogram (EEG) signal combining an orthogonal discrete wavelet transform analysis with quantifiers originated from information theory is reviewed. In addition, an extension of this methodology based on multiresolution quantities, called wavelet leaders, is presented. In [...] Read more.
The characterization of the dynamics associated with electroencephalogram (EEG) signal combining an orthogonal discrete wavelet transform analysis with quantifiers originated from information theory is reviewed. In addition, an extension of this methodology based on multiresolution quantities, called wavelet leaders, is presented. In particular, the temporal evolution of Shannon entropy and the statistical complexity evaluated with different sets of multiresolution wavelet coefficients are considered. Both methodologies are applied to the quantitative EEG time series analysis of a tonic-clonic epileptic seizure, and comparative results are presented. In particular, even when both methods describe the dynamical changes of the EEG time series, the one based on wavelet leaders presents a better time resolution. Full article
(This article belongs to the Special Issue Entropy and Electroencephalography)
Open AccessArticle Comparative Study of Entropy Sensitivity to Missing Biosignal Data
Entropy 2014, 16(11), 5901-5918; doi:10.3390/e16115901
Received: 3 July 2014 / Revised: 5 August 2014 / Accepted: 3 November 2014 / Published: 10 November 2014
Cited by 3 | PDF Full-text (227 KB) | HTML Full-text | XML Full-text
Abstract
Entropy estimation metrics have become a widely used method to identify subtle changes or hidden features in biomedical records. These methods have been more effective than conventional linear techniques in a number of signal classification applications, specially the healthy–pathological segmentation dichotomy. Nevertheless, [...] Read more.
Entropy estimation metrics have become a widely used method to identify subtle changes or hidden features in biomedical records. These methods have been more effective than conventional linear techniques in a number of signal classification applications, specially the healthy–pathological segmentation dichotomy. Nevertheless, a thorough characterization of these measures, namely, how to match metric and signal features, is still lacking. This paper studies a specific characterization problem: the influence of missing samples in biomedical records. The assessment is conducted using four of the most popular entropy metrics: Approximate Entropy, Sample Entropy, Fuzzy Entropy, and Detrended Fluctuation Analysis. The rationale of this study is that missing samples are a signal disturbance that can arise in many cases: signal compression, non-uniform sampling, or data transmission stages. It is of great interest to determine if these real situations can impair the capability of segmenting signal classes using such metrics. The experiments employed several biosignals: electroencephalograms, gait records, and RR time series. Samples of these signals were systematically removed, and the entropy computed for each case. The results showed that these metrics are robust against missing samples: With a data loss percentage of 50% or even higher, the methods were still able to distinguish among signal classes. Full article
(This article belongs to the Special Issue Entropy and Electroencephalography)
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Open AccessArticle Permutation Entropy Applied to the Characterization of the Clinical Evolution of Epileptic Patients under PharmacologicalTreatment
Entropy 2014, 16(11), 5668-5676; doi:10.3390/e16115668
Received: 12 August 2014 / Revised: 3 October 2014 / Accepted: 23 October 2014 / Published: 29 October 2014
Cited by 3 | PDF Full-text (691 KB) | HTML Full-text | XML Full-text
Abstract
Different techniques originated in information theory and tools from nonlinear systems theory have been applied to the analysis of electro-physiological time series. Several clinically relevant results have emerged from the use of concepts, such as entropy, chaos and complexity, in analyzing electrocardiograms [...] Read more.
Different techniques originated in information theory and tools from nonlinear systems theory have been applied to the analysis of electro-physiological time series. Several clinically relevant results have emerged from the use of concepts, such as entropy, chaos and complexity, in analyzing electrocardiograms and electroencephalographic (EEG) records. In this work, we develop a method based on permutation entropy (PE) to characterize EEG records from different stages in the treatment of a chronic epileptic patient. Our results show that the PE is useful for clearly quantifying the evolution of the patient along a certain lapse of time and allows visualizing in a very convenient way the effects of the pharmacotherapy. Full article
(This article belongs to the Special Issue Entropy and Electroencephalography)
Open AccessArticle Characterizing Motif Dynamics of Electric Brain Activity Using Symbolic Analysis
Entropy 2014, 16(11), 5654-5667; doi:10.3390/e16115654
Received: 9 September 2014 / Revised: 15 October 2014 / Accepted: 23 October 2014 / Published: 27 October 2014
PDF Full-text (21583 KB) | HTML Full-text | XML Full-text
Abstract
Motifs are small recurring circuits of interactions which constitute the backbone of networked systems. Characterizing motif dynamics is therefore key to understanding the functioning of such systems. Here we propose a method to define and quantify the temporal variability and time scales [...] Read more.
Motifs are small recurring circuits of interactions which constitute the backbone of networked systems. Characterizing motif dynamics is therefore key to understanding the functioning of such systems. Here we propose a method to define and quantify the temporal variability and time scales of electroencephalogram (EEG) motifs of resting brain activity. Given a triplet of EEG sensors, links between them are calculated by means of linear correlation; each pattern of links (i.e., each motif) is then associated to a symbol, and its appearance frequency is analyzed by means of Shannon entropy. Our results show that each motif becomes observable with different coupling thresholds and evolves at its own time scale, with fronto-temporal sensors emerging at high thresholds and changing at fast time scales, and parietal ones at low thresholds and changing at slower rates. Finally, while motif dynamics differed across individuals, for each subject, it showed robustness across experimental conditions, indicating that it could represent an individual dynamical signature. Full article
(This article belongs to the Special Issue Entropy and Electroencephalography)
Open AccessArticle Entropy-Complexity Characterization of Brain Development in Chickens
Entropy 2014, 16(8), 4677-4692; doi:10.3390/e16084677
Received: 21 July 2014 / Accepted: 20 August 2014 / Published: 21 August 2014
Cited by 3 | PDF Full-text (615 KB) | HTML Full-text | XML Full-text
Abstract
Electroencephalography (EEG) reflects the electrical activity of the brain, which can be considered chaotic and ruled by a nonlinear dynamics. Chickens exhibit a protracted period of maturation, and this temporal separation of the synapse formation and maturation phases is analogous to human [...] Read more.
Electroencephalography (EEG) reflects the electrical activity of the brain, which can be considered chaotic and ruled by a nonlinear dynamics. Chickens exhibit a protracted period of maturation, and this temporal separation of the synapse formation and maturation phases is analogous to human neural development, though the changes in chickens occur in weeks compared to years in humans. The development of synaptic networks in the chicken brain can be regarded as occurring in two broadly defined phases. We specifically describe the chicken brain development phases in the causality entropy-complexity plane H × C, showing that the complexity of the electrical activity can be characterized by estimating the intrinsic correlational structure of the EEG signal. This allows us to identify the dynamics of the developing chicken brain within the zone of a chaotic dissipative behavior in the plane H × C. Full article
(This article belongs to the Special Issue Entropy and Electroencephalography)
Open AccessArticle A Maximum Entropy Approach for Predicting Epileptic Tonic-Clonic Seizure
Entropy 2014, 16(8), 4603-4611; doi:10.3390/e16084603
Received: 24 June 2014 / Revised: 16 July 2014 / Accepted: 12 August 2014 / Published: 18 August 2014
Cited by 1 | PDF Full-text (695 KB) | HTML Full-text | XML Full-text
Abstract
The development of methods for time series analysis and prediction has always been and continues to be an active area of research. In this work, we develop a technique for modelling chaotic time series in parametric fashion. In the case of tonic-clonic [...] Read more.
The development of methods for time series analysis and prediction has always been and continues to be an active area of research. In this work, we develop a technique for modelling chaotic time series in parametric fashion. In the case of tonic-clonic epileptic electroencephalographic (EEG) analysis, we show that appropriate information theory tools provide valuable insights into the dynamics of neural activity. Our purpose is to demonstrate the feasibility of the maximum entropy principle to anticipate tonic-clonic seizure in patients with epilepsy. Full article
(This article belongs to the Special Issue Entropy and Electroencephalography)
Open AccessArticle Using Permutation Entropy to Measure the Changes in EEG Signals During Absence Seizures
Entropy 2014, 16(6), 3049-3061; doi:10.3390/e16063049
Received: 14 April 2014 / Revised: 26 May 2014 / Accepted: 27 May 2014 / Published: 30 May 2014
Cited by 13 | PDF Full-text (614 KB) | HTML Full-text | XML Full-text
Abstract
In this paper, we propose to use permutation entropy to explore whether the changes in electroencephalogram (EEG) data can effectively distinguish different phases in human absence epilepsy, i.e., the seizure-free, the pre-seizure and seizure phases. Permutation entropy is applied to analyze [...] Read more.
In this paper, we propose to use permutation entropy to explore whether the changes in electroencephalogram (EEG) data can effectively distinguish different phases in human absence epilepsy, i.e., the seizure-free, the pre-seizure and seizure phases. Permutation entropy is applied to analyze the EEG data from these three phases, each containing 100 19-channel EEG epochs of 2 s duration. The experimental results show the mean value of PE gradually decreases from the seizure-free to the seizure phase and provides evidence that these three different seizure phases in absence epilepsy can be effectively distinguished. Furthermore, our results strengthen the view that most frontal electrodes carry useful information and patterns that can help discriminate among different absence seizure phases. Full article
(This article belongs to the Special Issue Entropy and Electroencephalography)
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