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Entropy
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Assessing Complexity in Physiological Systems through Biomedical Signals Analysis II
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Assessing Complexity in Physiological Systems through Biomedical Signals Analysis II

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

Deadline for manuscript submissions: 10 December 2024 | Viewed by 10804

Special Issue Editors

Prof. Dr. Paolo Castiglioni

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Guest Editor
IRCCS Fondazione Don Carlo Gnocchi, 20148 Milan, Italy
Interests: complexity in biosignals; physiological time series; fractals in medicine; cardiovascular modeling; physiology in extreme environments; rehabilitation medicine
Special Issues, Collections and Topics in MDPI journals
Prof. Dr. Luca Faes

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Guest Editor
Department of Energy, Information Engineering and Mathematical models (DEIM), University of Palermo, 90128 Palermo, Italy
Interests: time series analysis; information dynamics; network physiology; cardiovascular neuroscience; brain connectivity
Special Issues, Collections and Topics in MDPI journals
Dr. Gaetano Valenza

E-Mail Website
Guest Editor
Department of Information Engineering and Research Center“E. Piaggio”, University of Pisa, 56122 Pisa, Italy
Interests: biomedical signal and image processing; cardiovascular and neural modeling; wearable systems for physiological monitoring
Special Issues, Collections and Topics in MDPI journals
Dr. Andrea Faini

E-Mail Website
Guest Editor
Department of Cardiovascular, Neural and Metabolic Sciences, Istituto Auxologico Italiano, IRCCS, 20149 Milan, Italy
Interests: hypertension; echocardiography; signal analysis; cardiovascular medicine; biomedical signal processing; electrocardiography; advanced statistical analysis; heart rate variability

Special Issue Information

Dear Colleagues,

In the last few decades, the idea that most physiological systems are complex has become increasingly popular. Complexity is a ubiquitous phenomenon in physiology and medicine that allows living systems to adapt to external perturbations, preserving homeostasis, and originates from specific features of the system such as fractal structures, self-organization, nonlinearity, the presence of many interdependent components interacting at different hierarchical levels and time scales, and interconnections with other systems through physiological networks.

Biomedical signals generated by such systems may carry information on the system complexity, information that may help to detect physiological states, monitor health conditions over time, or predict pathological events. For this reason, the more recent trends in biomedical signals analysis are aimed at designing tools for extracting information on the system complexity from the derived time series, such as continuous electroencephalogram and electromyogram recordings, beat-by-beat values of cardiovascular variables, or breath-by-breath values of respiratory variables. Entropy has recently dedicated a Special Issue on these themes. Due to the interest it raised, the Special Issue was also published as a printed book in 2021.

However, important methodological issues on the complexity analysis of biomedical signals are still open. These include the development of methods that distinguish randomness from complexity; provide robust estimates on short series or from multivariate recordings; allow multivariate and/or multiscale estimates of predictability, entropy, and multifractality; parametrically represent the stochastic processes describing the data; or set the analysis parameters automatically.

Therefore, we are launching a second volume of the Special Issue aimed at collecting methodological contributions that may improve the use of complexity-based methods of signal analysis in physiological or clinical settings, as well as novel applications on biomedical signals illustrating the value of complexity analysis. Manuscripts reviewing the state-of-the-art of these topics are also welcome.

Dr. Paolo Castiglioni
Dr. Luca Faes
Dr. Gaetano Valenza
Dr. Andrea Faini
Guest Editors

Manuscript Submission Information

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. All submissions that pass pre-check are peer-reviewed. Accepted papers will be published continuously in the journal (as soon as accepted) and will be listed together on the special issue website. Research articles, review articles as well as short 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 thoroughly refereed through a single-blind 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 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
  • fractals
  • multiscale analysis
  • linear and nonlinear prediction
  • self-organization
  • chaos
  • information dynamics
  • symbolic dynamics
  • nonlinearity
  • heart rate variability
  • EEG

Related Special Issue

Published Papers (7 papers)

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Research

14 pages, 5658 KiB  
Article
Multifractal Multiscale Analysis of Human Movements during Cognitive Tasks
by Andrea Faini, Laurent M. Arsac, Veronique Deschodt-Arsac and Paolo Castiglioni
Entropy 2024, 26(2), 148; https://doi.org/10.3390/e26020148 - 08 Feb 2024
Viewed by 1063
Abstract
Continuous adaptations of the movement system to changing environments or task demands rely on superposed fractal processes exhibiting power laws, that is, multifractality. The estimators of the multifractal spectrum potentially reflect the adaptive use of perception, cognition, and action. To observe time-specific behavior [...] Read more.
Continuous adaptations of the movement system to changing environments or task demands rely on superposed fractal processes exhibiting power laws, that is, multifractality. The estimators of the multifractal spectrum potentially reflect the adaptive use of perception, cognition, and action. To observe time-specific behavior in multifractal dynamics, a multiscale multifractal analysis based on DFA (MFMS-DFA) has been recently proposed and applied to cardiovascular dynamics. Here we aimed at evaluating whether MFMS-DFA allows identifying multiscale structures in the dynamics of human movements. Thirty-six (12 females) participants pedaled freely, after a metronomic initiation of the cadence at 60 rpm, against a light workload for 10 min: in reference to cycling (C), cycling while playing “Tetris” on a computer, alone (CT) or collaboratively (CTC) with another pedaling participant. Pedal revolution periods (PRP) series were examined with MFMS-DFA and compared to linearized surrogates, which attested to a presence of multifractality at almost all scales. A marked alteration in multifractality when playing Tetris was evidenced at two scales, τ ≈ 16 and τ ≈ 64 s, yet less marked at τ ≈ 16 s when playing collaboratively. Playing Tetris in collaboration attenuated these alterations, especially in the best Tetris players. This observation suggests the high sensitivity to cognitive demand of MFMS-DFA estimators, extending to the assessment of skill/demand interplay from individual behavior. So, by identifying scale-dependent multifractal structures in movement dynamics, MFMS-DFA has obvious potential for examining brain-movement coordinative structures, likely with sufficient sensitivity to find echo in diagnosing disorders and monitoring the progress of diseases that affect cognition and movement control. Full article
(This article belongs to the Special Issue Assessing Complexity in Physiological Systems through Biomedical Signals Analysis II)
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11 pages, 990 KiB  
Article
Entropy-Based Multifractal Testing of Heart Rate Variability during Cognitive-Autonomic Interplay
by Laurent M. Arsac
Entropy 2023, 25(9), 1364; https://doi.org/10.3390/e25091364 - 21 Sep 2023
Viewed by 700
Abstract
Entropy-based and fractal-based metrics derived from heart rate variability (HRV) have enriched the way cardiovascular dynamics can be described in terms of complexity. The most commonly used multifractal testing, a method using q moments to explore a range of fractal scaling in small-sized [...] Read more.
Entropy-based and fractal-based metrics derived from heart rate variability (HRV) have enriched the way cardiovascular dynamics can be described in terms of complexity. The most commonly used multifractal testing, a method using q moments to explore a range of fractal scaling in small-sized and large-sized fluctuations, is based on detrended fluctuation analysis, which examines the power–law relationship of standard deviation with the timescale in the measured signal. A more direct testing of a multifractal structure exists based on the Shannon entropy of bin (signal subparts) proportion. This work aims to reanalyze HRV during cognitive tasks to obtain new markers of HRV complexity provided by entropy-based multifractal spectra using the method proposed by Chhabra and Jensen in 1989. Inter-beat interval durations (RR) time series were obtained in 28 students comparatively in baseline (viewing a video) and during three cognitive tasks: Stroop color and word task, stop-signal, and go/no-go. The new HRV estimators were extracted from the f/α singularity spectrum of the RR magnitude increment series, established from q-weighted stable (log–log linear) power laws, namely: (i) the whole spectrum width (MF) calculated as αmax − αmin; the specific width representing large-sized fluctuations (MFlarge) calculated as α0 − αq+; and small-sized fluctuations (MFsmall) calculated as αq− − α0. As the main results, cardiovascular dynamics during Stroop had a specific MF signature while MFlarge was rather specific to go/no-go. The way these new HRV markers could represent different aspects of a complete picture of the cognitive–autonomic interplay is discussed, based on previously used entropy- and fractal-based markers, and the introduction of distribution entropy (DistEn), as a marker recently associated specifically with complexity in the cardiovascular control. Full article
(This article belongs to the Special Issue Assessing Complexity in Physiological Systems through Biomedical Signals Analysis II)
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12 pages, 2651 KiB  
Article
Spatio-Temporal Fractal Dimension Analysis from Resting State EEG Signals in Parkinson’s Disease
by Juan Ruiz de Miras, Chiara-Camilla Derchi, Tiziana Atzori, Alice Mazza, Pietro Arcuri, Anna Salvatore, Jorge Navarro, Francesca Lea Saibene, Mario Meloni and Angela Comanducci
Entropy 2023, 25(7), 1017; https://doi.org/10.3390/e25071017 - 02 Jul 2023
Viewed by 1209
Abstract
Complexity analysis of electroencephalogram (EEG) signals has emerged as a valuable tool for characterizing Parkinson’s disease (PD). Fractal dimension (FD) is a widely employed method for measuring the complexity of shapes with many applications in neurodegenerative disorders. Nevertheless, very little is known on [...] Read more.
Complexity analysis of electroencephalogram (EEG) signals has emerged as a valuable tool for characterizing Parkinson’s disease (PD). Fractal dimension (FD) is a widely employed method for measuring the complexity of shapes with many applications in neurodegenerative disorders. Nevertheless, very little is known on the fractal characteristics of EEG in PD measured by FD. In this study we performed a spatio-temporal analysis of EEG in PD using FD in four dimensions (4DFD). We analyzed 42 resting-state EEG recordings comprising two groups: 27 PD patients without dementia and 15 healthy control subjects (HC). From the original resting-state EEG we derived the cortical activations defined by a source reconstruction at each time sample, generating point clouds in three dimensions. Then, a sliding window of one second (the fourth dimension) was used to compute the value of 4DFD by means of the box-counting algorithm. Our results showed a significantly higher value of 4DFD in the PD group (p < 0.001). Moreover, as a diagnostic classifier of PD, 4DFD obtained an area under curve value of 0.97 for a receiver operating characteristic curve analysis. These results suggest that 4DFD could be a promising method for characterizing the specific changes in the brain dynamics associated with PD. Full article
(This article belongs to the Special Issue Assessing Complexity in Physiological Systems through Biomedical Signals Analysis II)
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8 pages, 2237 KiB  
Article
Autonomic Nervous System Influences on Cardiovascular Self-Organized Criticality
by Jacques-Olivier Fortrat and Guillaume Ravé
Entropy 2023, 25(6), 880; https://doi.org/10.3390/e25060880 - 30 May 2023
Viewed by 1152
Abstract
Cardiovascular self-organized criticality has recently been demonstrated. We studied a model of autonomic nervous system changes to better characterize heart rate variability self-organized criticality. The model included short and long-term autonomic changes associated with body position and physical training, respectively. Twelve professional soccer [...] Read more.
Cardiovascular self-organized criticality has recently been demonstrated. We studied a model of autonomic nervous system changes to better characterize heart rate variability self-organized criticality. The model included short and long-term autonomic changes associated with body position and physical training, respectively. Twelve professional soccer players took part in a 5-week training session divided into “Warm-up”, “Intensive”, and “Tapering” periods. A stand test was carried out at the beginning and end of each period. Heart rate variability was recorded beat by beat (Polar Team 2). Bradycardias, defined as successive heart rates with a decreasing value, were counted according to their length in number of heartbeat intervals. We checked whether bradycardias were distributed according to Zipf’s law, a feature of self-organized criticality. Zipf’s law draws a straight line when the rank of occurrence is plotted against the frequency of occurrence in a log–log graph. Bradycardias were distributed according to Zipf’s law, regardless of body position or training. Bradycardias were much longer in the standing position than the supine position and Zipf’s law was broken after a delay of four heartbeat intervals. Zipf’s law could also be broken in some subjects with curved long bradycardia distributions by training. Zipf’s law confirms the self-organized nature of heart rate variability and is strongly linked to autonomic standing adjustment. However, Zipf’s law could be broken, the significance of which remains unclear. Full article
(This article belongs to the Special Issue Assessing Complexity in Physiological Systems through Biomedical Signals Analysis II)
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22 pages, 3256 KiB  
Article
Visibility Graph Analysis of Heartbeat Time Series: Comparison of Young vs. Old, Healthy vs. Diseased, Rest vs. Exercise, and Sedentary vs. Active
by Alejandro Muñoz-Diosdado, Éric E. Solís-Montufar and José A. Zamora-Justo
Entropy 2023, 25(4), 677; https://doi.org/10.3390/e25040677 - 18 Apr 2023
Viewed by 1854
Abstract
Using the visibility graph algorithm (VGA), a complex network can be associated with a time series, such that the properties of the time series can be obtained by studying those of the network. Any value of the time series becomes a node of [...] Read more.
Using the visibility graph algorithm (VGA), a complex network can be associated with a time series, such that the properties of the time series can be obtained by studying those of the network. Any value of the time series becomes a node of the network, and the number of other nodes that it is connected to can be quantified. The degree of connectivity of a node is positively correlated with its magnitude. The slope of the regression line is denoted by k-M, and, in this work, this parameter was calculated for the cardiac interbeat time series of different contrasting groups, namely: young vs. elderly; healthy subjects vs. patients with congestive heart failure (CHF); young subjects and adults at rest vs. exercising young subjects and adults; and, finally, sedentary young subjects and adults vs. active young subjects and adults. In addition, other network parameters, including the average degree and the average path length, of these time series networks were also analyzed. Significant differences were observed in the k-M parameter, average degree, and average path length for all analyzed groups. This methodology based on the analysis of the three mentioned parameters of complex networks has the advantage that such parameters are very easy to calculate, and it is useful to classify heartbeat time series of subjects with CHF vs. healthy subjects, and also for young vs. elderly subjects and sedentary vs. active subjects. Full article
(This article belongs to the Special Issue Assessing Complexity in Physiological Systems through Biomedical Signals Analysis II)
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17 pages, 3668 KiB  
Article
Sample, Fuzzy and Distribution Entropies of Heart Rate Variability: What Do They Tell Us on Cardiovascular Complexity?
by Paolo Castiglioni, Giampiero Merati, Gianfranco Parati and Andrea Faini
Entropy 2023, 25(2), 281; https://doi.org/10.3390/e25020281 - 02 Feb 2023
Cited by 6 | Viewed by 2443
Abstract
Distribution Entropy (DistEn) has been introduced as an alternative to Sample Entropy (SampEn) to assess the heart rate variability (HRV) on much shorter series without the arbitrary definition of distance thresholds. However, DistEn, considered a measure of cardiovascular complexity, differs substantially from SampEn [...] Read more.
Distribution Entropy (DistEn) has been introduced as an alternative to Sample Entropy (SampEn) to assess the heart rate variability (HRV) on much shorter series without the arbitrary definition of distance thresholds. However, DistEn, considered a measure of cardiovascular complexity, differs substantially from SampEn or Fuzzy Entropy (FuzzyEn), both measures of HRV randomness. This work aims to compare DistEn, SampEn, and FuzzyEn analyzing postural changes (expected to modify the HRV randomness through a sympatho/vagal shift without affecting the cardiovascular complexity) and low-level spinal cord injuries (SCI, whose impaired integrative regulation may alter the system complexity without affecting the HRV spectrum). We recorded RR intervals in able-bodied (AB) and SCI participants in supine and sitting postures, evaluating DistEn, SampEn, and FuzzyEn over 512 beats. The significance of “case” (AB vs. SCI) and “posture” (supine vs. sitting) was assessed by longitudinal analysis. Multiscale DistEn (mDE), SampEn (mSE), and FuzzyEn (mFE) compared postures and cases at each scale between 2 and 20 beats. Unlike SampEn and FuzzyEn, DistEn is affected by the spinal lesion but not by the postural sympatho/vagal shift. The multiscale approach shows differences between AB and SCI sitting participants at the largest mFE scales and between postures in AB participants at the shortest mSE scales. Thus, our results support the hypothesis that DistEn measures cardiovascular complexity while SampEn/FuzzyEn measure HRV randomness, highlighting that together these methods integrate the information each of them provides. Full article
(This article belongs to the Special Issue Assessing Complexity in Physiological Systems through Biomedical Signals Analysis II)
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12 pages, 1398 KiB  
Article
Heart Rate Complexity and Autonomic Modulation Are Associated with Psychological Response Inhibition in Healthy Subjects
by Francesco Riganello, Martina Vatrano, Paolo Tonin, Antonio Cerasa and Maria Daniela Cortese
Entropy 2023, 25(1), 152; https://doi.org/10.3390/e25010152 - 12 Jan 2023
Viewed by 1478
Abstract
Background: the ability to suppress/regulate impulsive reactions has been identified as common factor underlying the performance in all executive function tasks. We analyzed the HRV signals (power of high (HF) and low (LF) frequency, Sample Entropy (SampEn), and Complexity Index (CI)) during the [...] Read more.
Background: the ability to suppress/regulate impulsive reactions has been identified as common factor underlying the performance in all executive function tasks. We analyzed the HRV signals (power of high (HF) and low (LF) frequency, Sample Entropy (SampEn), and Complexity Index (CI)) during the execution of cognitive tests to assess flexibility, inhibition abilities, and rule learning. Methods: we enrolled thirty-six healthy subjects, recording five minutes of resting state and two tasks of increasing complexity based on 220 visual stimuli with 12 × 12 cm red and white squares on a black background. Results: at baseline, CI was negatively correlated with age, and LF was negatively correlated with SampEn. In Task 1, the CI and LF/HF were negatively correlated with errors. In Task 2, the reaction time positively correlated with the CI and the LF/HF ratio errors. Using a binary logistic regression model, age, CI, and LF/HF ratio classified performance groups with a sensitivity and specificity of 73 and 71%, respectively. Conclusions: this study performed an important initial exploration in defining the complex relationship between CI, sympathovagal balance, and age in regulating impulsive reactions during cognitive tests. Our approach could be applied in assessing cognitive decline, providing additional information on the brain-heart interaction. Full article
(This article belongs to the Special Issue Assessing Complexity in Physiological Systems through Biomedical Signals Analysis II)
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