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Entropy in Brain Networks

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A special issue of Entropy (ISSN 1099-4300). This special issue belongs to the section "Multidisciplinary Applications".

Deadline for manuscript submissions: closed (31 December 2020) | Viewed by 23863

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Prof. Dr. Jesús Poza

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Guest Editor

Biomedical Engineering Group, University of Valladolid, C/Plaza de Santa Cruz, 8, 47002 Valladolid, Spain
Interests: Alzheimer’s disease; electroencephalography (EEG); magnetoencephalography (MEG); biomedical engineering; signal processing
Special Issues, Collections and Topics in MDPI journals

Prof. Dr. María García

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Biomedical Engineering Group, Department of Theory of Signal and Communications and Telematic Engineering, University of Valladolid, 47011 Valladolid, Spain
Interests: nonlinear dynamics; brain dynamics; medical image analysis; artificial neural networks; pattern recognition

Dr. Javier Gomez-Pilar

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Guest Editor

1. Biomedical Engineering Group, E.T.S.I. de Telecomunicación, Universidad de Valladolid, Paseo Belén 15, 47011 Valladolid, Spain
2. Centro de Investigación Biomédica en Red en Bioingeniería, Biomateriales y Nanomedicina, (CIBER-BBN), 28029 Madrid, Spain
Interests: biomedical signal processing; computational neuroscience; network neuroscience; correlation networks; information theory; time-frequency analysis
Special Issues, Collections and Topics in MDPI journals

Special Issue Information

Dear Colleagues,

The human bain is the last biological frontier. Being a complex, hierarchical, and dynamical system governed by intricate nonlinear interactions at different levels, to disentangle the brain behavior and neural interactions has become a cutting-edge challenge. In order to obtain a comprehensive description of the structure and function of the brain, as well as how both interact with each other, modern neuroscience approaches rely on multilevel and multimodal analyses that frequently describe it as a complex network. Network neuroscience is hence becoming of paramount importance to provide further insight into brain functioning and structural organization. Notwithstanding, to unravel how the brain is organized and works, it is necessary to take a step forward and consider the nonlinear nature of such a system. Tools from information theory are well-suited for this task. In this regard, entropy is a powerful explanatory tool, which provides a theoretical and operational framework to obtain both quantitative and qualitative descriptions of the intrinsic properties of a system. Merging of network analysis with information theory methods can indeed help to provide novel descriptions of the fundamental basis of brain networks.

This Special Issue aims at exploring the role of entropy-based methodologies to further understand brain networks, encouraging novel studies focused on exploring the complex organization of structural networks and the mechanisms associated with the transmission and processing of brain information in functional networks. We welcome the submission of original research papers focused on basic research and applied methods that rely on entropy-based approaches to understand, characterize, and model structural and functional brain networks.

Prof. Dr. Jesús Poza
Prof. Dr. María García
Dr. Javier Gomez-Pilar
Guest Editors

Manuscript Submission Information

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Please visit the Instructions for Authors page before submitting a manuscript. The Article Processing Charge (APC) for publication in this open access journal is 2600 CHF (Swiss Francs). Submitted papers should be well formatted and use good English. Authors may use MDPI's English editing service prior to publication or during author revisions.

Keywords

entropy-based network analysis
nonlinear interactions
nonlinear dynamical systems
structural and functional brain networks
multimodal connectivity
spatiotemporal networks
metastability
microstates analysis
brain information flow
transmission and coding of neural information
fractal brain
multiscale networks
multilayer networks
hierarchical brain networks
neurodynamics
neurodegenerative diseases
cognitive neuroscience
computational neuroscience

Published Papers (10 papers)

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Editorial

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3 pages, 194 KiB

Open AccessEditorial

Entropy in Brain Networks

by Jesús Poza, María García and Javier Gomez-Pilar

Entropy 2021, 23(9), 1157; https://0-doi-org.brum.beds.ac.uk/10.3390/e23091157 - 02 Sep 2021

Viewed by 1498

Abstract

A thorough and comprehensive understanding of the human brain ultimately depends on knowledge of large-scale brain organization[...] Full article

(This article belongs to the Special Issue Entropy in Brain Networks)

Research

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16 pages, 907 KiB

Open AccessArticle

Exploring the Alterations in the Distribution of Neural Network Weights in Dementia Due to Alzheimer’s Disease

by Marcos Revilla-Vallejo, Jesús Poza, Javier Gomez-Pilar, Roberto Hornero, Miguel Ángel Tola-Arribas, Mónica Cano and Carlos Gómez

Entropy 2021, 23(5), 500; https://0-doi-org.brum.beds.ac.uk/10.3390/e23050500 - 22 Apr 2021

Cited by 3 | Viewed by 2348

Abstract

Alzheimer’s disease (AD) is a neurodegenerative disorder which has become an outstanding social problem. The main objective of this study was to evaluate the alterations that dementia due to AD elicits in the distribution of functional network weights. Functional connectivity networks were obtained using the orthogonalized Amplitude Envelope Correlation (AEC), computed from source-reconstructed resting-state eletroencephalographic (EEG) data in a population formed by 45 cognitive healthy elderly controls, 69 mild cognitive impaired (MCI) patients and 81 AD patients. Our results indicated that AD induces a progressive alteration of network weights distribution; specifically, the Shannon entropy (SE) of the weights distribution showed statistically significant between-group differences (p < 0.05, Kruskal-Wallis test, False Discovery Rate corrected). Furthermore, an in-depth analysis of network weights distributions was performed in delta, alpha, and beta-1 frequency bands to discriminate the weight ranges showing statistical differences in SE. Our results showed that lower and higher weights were more affected by the disease, whereas mid-range connections remained unchanged. These findings support the importance of performing detailed analyses of the network weights distribution to further understand the impact of AD progression on functional brain activity. Full article

(This article belongs to the Special Issue Entropy in Brain Networks)

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43 pages, 2698 KiB

Open AccessArticle

The 2-D Cluster Variation Method: Topography Illustrations and Their Enthalpy Parameter Correlations

by Alianna J. Maren

Entropy 2021, 23(3), 319; https://0-doi-org.brum.beds.ac.uk/10.3390/e23030319 - 08 Mar 2021

Cited by 5 | Viewed by 2003

Abstract

One of the biggest challenges in characterizing 2-D image topographies is finding a low-dimensional parameter set that can succinctly describe, not so much image patterns themselves, but the nature of these patterns. The 2-D cluster variation method (CVM), introduced by Kikuchi in 1951, can characterize very local image pattern distributions using configuration variables, identifying nearest-neighbor, next-nearest-neighbor, and triplet configurations. Using the 2-D CVM, we can characterize 2-D topographies using just two parameters; the activation enthalpy (

ε_{0}

) and the interaction enthalpy (

ε_{1}

). Two different initial topographies (“scale-free-like” and “extreme rich club-like”) were each computationally brought to a CVM free energy minimum, for the case where the activation enthalpy was zero and different values were used for the interaction enthalpy. The results are: (1) the computational configuration variable results differ significantly from the analytically-predicted values well before

ε_{1}

approaches the known divergence as

ε_{1} \to 0.881

, (2) the range of potentially useful parameter values, favoring clustering of like-with-like units, is limited to the region where

ε_{0} < 3

and

ε_{1} < 0.25

, and (3) the topographies in the systems that are brought to a free energy minimum show interesting visual features, such as extended “spider legs” connecting previously unconnected “islands,” and as well as evolution of “peninsulas” in what were previously solid masses. Full article

(This article belongs to the Special Issue Entropy in Brain Networks)

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16 pages, 772 KiB

Open AccessArticle

Microcanonical and Canonical Ensembles for fMRI Brain Networks in Alzheimer’s Disease

by Jianjia Wang, Xichen Wu, Mingrui Li, Hui Wu and Edwin R. Hancock

Entropy 2021, 23(2), 216; https://0-doi-org.brum.beds.ac.uk/10.3390/e23020216 - 10 Feb 2021

Cited by 5 | Viewed by 2189

Abstract

This paper seeks to advance the state-of-the-art in analysing fMRI data to detect onset of Alzheimer’s disease and identify stages in the disease progression. We employ methods of network neuroscience to represent correlation across fMRI data arrays, and introduce novel techniques for network construction and analysis. In network construction, we vary thresholds in establishing BOLD time series correlation between nodes, yielding variations in topological and other network characteristics. For network analysis, we employ methods developed for modelling statistical ensembles of virtual particles in thermal systems. The microcanonical ensemble and the canonical ensemble are analogous to two different fMRI network representations. In the former case, there is zero variance in the number of edges in each network, while in the latter case the set of networks have a variance in the number of edges. Ensemble methods describe the macroscopic properties of a network by considering the underlying microscopic characterisations which are in turn closely related to the degree configuration and network entropy. When applied to fMRI data in populations of Alzheimer’s patients and controls, our methods demonstrated levels of sensitivity adequate for clinical purposes in both identifying brain regions undergoing pathological changes and in revealing the dynamics of such changes. Full article

(This article belongs to the Special Issue Entropy in Brain Networks)

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17 pages, 1594 KiB

Open AccessEditor’s ChoiceArticle

The Role of Entropy in Construct Specification Equations (CSE) to Improve the Validity of Memory Tests

by Jeanette Melin, Stefan Cano and Leslie Pendrill

Entropy 2021, 23(2), 212; https://0-doi-org.brum.beds.ac.uk/10.3390/e23020212 - 09 Feb 2021

Cited by 16 | Viewed by 2485

Abstract

Commonly used rating scales and tests have been found lacking reliability and validity, for example in neurodegenerative diseases studies, owing to not making recourse to the inherent ordinality of human responses, nor acknowledging the separability of person ability and item difficulty parameters according to the well-known Rasch model. Here, we adopt an information theory approach, particularly extending deployment of the classic Brillouin entropy expression when explaining the difficulty of recalling non-verbal sequences in memory tests (i.e., Corsi Block Test and Digit Span Test): a more ordered task, of less entropy, will generally be easier to perform. Construct specification equations (CSEs) as a part of a methodological development, with entropy-based variables dominating, are found experimentally to explain (r

= \sqrt{R^{2}}

= 0.98) and predict the construct of task difficulty for short-term memory tests using data from the NeuroMET (n = 88) and Gothenburg MCI (n = 257) studies. We propose entropy-based equivalence criteria, whereby different tasks (in the form of items) from different tests can be combined, enabling new memory tests to be formed by choosing a bespoke selection of items, leading to more efficient testing, improved reliability (reduced uncertainties) and validity. This provides opportunities for more practical and accurate measurement in clinical practice, research and trials. Full article

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13 pages, 2104 KiB

Open AccessArticle

On the Variability of Functional Connectivity and Network Measures in Source-Reconstructed EEG Time-Series

by Matteo Fraschini, Simone Maurizio La Cava, Luca Didaci and Luigi Barberini

Entropy 2021, 23(1), 5; https://0-doi-org.brum.beds.ac.uk/10.3390/e23010005 - 22 Dec 2020

Cited by 5 | Viewed by 2720

Abstract

The idea of estimating the statistical interdependence among (interacting) brain regions has motivated numerous researchers to investigate how the resulting connectivity patterns and networks may organize themselves under any conceivable scenario. Even though this idea has developed beyond its initial stages, its practical application is still far away from being widespread. One concurrent cause may be related to the proliferation of different approaches that aim to catch the underlying statistical interdependence among the (interacting) units. This issue has probably contributed to hindering comparisons among different studies. Not only do all these approaches go under the same name (functional connectivity), but they have often been tested and validated using different methods, therefore, making it difficult to understand to what extent they are similar or not. In this study, we aim to compare a set of different approaches commonly used to estimate the functional connectivity on a public EEG dataset representing a possible realistic scenario. As expected, our results show that source-level EEG connectivity estimates and the derived network measures, even though pointing to the same direction, may display substantial dependency on the (often arbitrary) choice of the selected connectivity metric and thresholding approach. In our opinion, the observed variability reflects the ambiguity and concern that should always be discussed when reporting findings based on any connectivity metric. Full article

(This article belongs to the Special Issue Entropy in Brain Networks)

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12 pages, 1233 KiB

Open AccessArticle

Approximate Entropy of Brain Network in the Study of Hemispheric Differences

by Francesca Alù, Francesca Miraglia, Alessandro Orticoni, Elda Judica, Maria Cotelli, Paolo Maria Rossini and Fabrizio Vecchio

Entropy 2020, 22(11), 1220; https://0-doi-org.brum.beds.ac.uk/10.3390/e22111220 - 27 Oct 2020

Cited by 24 | Viewed by 2051

Abstract

Human brain, a dynamic complex system, can be studied with different approaches, including linear and nonlinear ones. One of the nonlinear approaches widely used in electroencephalographic (EEG) analyses is the entropy, the measurement of disorder in a system. The present study investigates brain networks applying approximate entropy (ApEn) measure for assessing the hemispheric EEG differences; reproducibility and stability of ApEn data across separate recording sessions were evaluated. Twenty healthy adult volunteers were submitted to eyes-closed resting EEG recordings, for 80 recordings. Significant differences in the occipital region, with higher values of entropy in the left hemisphere than in the right one, show that the hemispheres become active with different intensities according to the performed function. Besides, the present methodology proved to be reproducible and stable, when carried out on relatively brief EEG epochs but also at a 1-week distance in a group of 36 subjects. Nonlinear approaches represent an interesting probe to study the dynamics of brain networks. ApEn technique might provide more insight into the pathophysiological processes underlying age-related brain disconnection as well as for monitoring the impact of pharmacological and rehabilitation treatments. Full article

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20 pages, 3508 KiB

Open AccessArticle

A Novel Recognition Strategy for Epilepsy EEG Signals Based on Conditional Entropy of Ordinal Patterns

by Xian Liu and Zhuang Fu

Entropy 2020, 22(10), 1092; https://0-doi-org.brum.beds.ac.uk/10.3390/e22101092 - 29 Sep 2020

Cited by 11 | Viewed by 2272

Abstract

Epilepsy is one of the most ordinary neuropathic illnesses, and electroencephalogram (EEG) is the essential method for recording various brain rhythm activities due to its high temporal resolution. The conditional entropy of ordinal patterns (CEOP) is known to be fast and easy to implement, which can effectively measure the irregularity of the physiological signals. The present work aims to apply the CEOP to analyze the complexity characteristics of the EEG signals and recognize the epilepsy EEG signals. We discuss the parameter selection and the performance analysis of the CEOP based on the neural mass model. The CEOP is applied to the real EEG database of Bonn epilepsy for identification. The results show that the CEOP is an excellent metrics for the analysis and recognition of epileptic EEG signals. The differences of the CEOP in normal and epileptic brain states suggest that the CEOP could be a judgment tool for the diagnosis of the epileptic seizure. Full article

(This article belongs to the Special Issue Entropy in Brain Networks)

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20 pages, 4519 KiB

Open AccessArticle

Alteration of the Intra- and Inter-Lobe Connectivity of the Brain Structural Network in Normal Aging

by Chi-Wen Jao, Jiann-Horng Yeh, Yu-Te Wu, Li-Ming Lien, Yuh-Feng Tsai, Kuang-En Chu, Chen-Yu Hsiao, Po-Shan Wang and Chi Ieong Lau

Entropy 2020, 22(8), 826; https://0-doi-org.brum.beds.ac.uk/10.3390/e22080826 - 28 Jul 2020

Cited by 5 | Viewed by 2640

Abstract

The morphological changes in cortical parcellated regions during aging and whether these atrophies may cause brain structural network intra- and inter-lobe connectivity alterations are subjects that have been minimally explored. In this study, a novel fractal dimension-based structural network was proposed to measure atrophy of 68 parcellated cortical regions. Alterations of structural network parameters, including intra- and inter-lobe connectivity, were detected in a middle-aged group (30–45 years old) and an elderly group (50–65 years old). The elderly group exhibited significant lateralized atrophy in the left hemisphere, and most of these fractal dimension atrophied regions were included in the regions of the “last-in, first-out” model. Globally, the elderly group had lower modularity values, smaller component size modules, and fewer bilateral association fibers. They had lower intra-lobe connectivity in the frontal and parietal lobes, but higher intra-lobe connectivity in the temporal and occipital lobes. Both groups exhibited similar inter-lobe connecting pattern. The elderly group revealed separations, sparser long association fibers, commissural fibers, and lateral inter-lobe connectivity lost effect, mainly in the right hemisphere. New wiring and reconfiguring modules may have occurred within the brain structural network to compensate for connectivity, decreasing and preventing functional loss in cerebral intra- and inter-lobe connectivity. Full article

(This article belongs to the Special Issue Entropy in Brain Networks)

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18 pages, 6831 KiB

Open AccessArticle

Decoding Analysis of Alpha Oscillation Networks on Maintaining Driver Alertness

by Chi Zhang, Jinfei Ma, Jian Zhao, Pengbo Liu, Fengyu Cong, Tianjiao Liu, Ying Li, Lina Sun and Ruosong Chang

Entropy 2020, 22(7), 787; https://0-doi-org.brum.beds.ac.uk/10.3390/e22070787 - 18 Jul 2020

Cited by 7 | Viewed by 2820

Abstract

The countermeasure of driver fatigue is valuable for reducing the risk of accidents caused by vigilance failure during prolonged driving. Listening to the radio (RADIO) has been proven to be a relatively effective “in-car” countermeasure. However, the connectivity analysis, which can be used to investigate its alerting effect, is subject to the issue of signal mixing. In this study, we propose a novel framework based on clustering and entropy to improve the performance of the connectivity analysis to reveal the effect of RADIO to maintain driver alertness. Regardless of reducing signal mixing, we introduce clustering algorithm to classify the functional connections with their nodes into different categories to mine the effective information of the alerting effect. Differential entropy (DE) is employed to measure the information content in different brain regions after clustering. Compared with the Louvain-based community detection method, the proposed method shows more superior ability to present RADIO effectin confused functional connection matrices. Our experimental results reveal that the active connection clusters distinguished by the proposed method gradually move from frontal region to parieto-occipital regionwith the progress of fatigue, consistent with the alpha energy changes in these two brain areas. The active class of the clusters in parieto-occipital region significantly decreases and the most active clusters remain in the frontal region when RADIO is taken. The estimation results of DE confirm the significant change (p < 0.05) of information content due to the cluster movements. Hence, preventing the movement of the active clusters from frontal region to parieto-occipital region may correlate with maintaining driver alertness. The revelation of alerting effect is helpful for the targeted upgrade of fatigue countermeasures. Full article

(This article belongs to the Special Issue Entropy in Brain Networks)

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