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Entropy
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Entropy-Based Biomechanical Research and Its Applications
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Entropy-Based Biomechanical Research and Its Applications

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

Deadline for manuscript submissions: closed (31 October 2022) | Viewed by 9277

Special Issue Editors

Dr. Li Li

E-Mail Website
Guest Editor
Department of Health Sciences and Kinesiology, Walter's College of Health Professions, Georgia Southern University, Statesboro, GA 30460, USA
Interests: biomechanics of human movement; aging; running injuries; gait analysis; the effects of specific pathologies on human movement (especially peripheral neuropathy, diabetes, and cerebral palsy)
Special Issues, Collections and Topics in MDPI journals
Dr. Brad Manor

E-Mail Website
Guest Editor
Hinda and Arthur Marcus Institute for Aging Research, Hebrew SeniorLife, Harvard Medical School, Boston, MA 02131, USA
Interests: balance; senescence; aging; mobility; fall; rehabilitative medicine; biomechanics; nonlinear signal processing
Special Issues, Collections and Topics in MDPI journals

Special Issue Information

Dear Colleagues,

Many sports, locomotion, ergonomic, pathological, and other observable phenomena exhibit time evolution and can be successfully modeled via suitable mathematical expression, usually in a set of differential equations. Because input-output relations between system quantities are generally non-proportional, associated dynamical behavior could be very complex or, under specific conditions, chaotic. Detection, description, analysis, quantification, and control of this random-like erratic motion associated with nonlinear dynamical systems is important due to universality (through dimensionless-less mathematical modeling) and several unique properties (sensitivity to initial conditions, mixing attractors, fractal dimension, long-term unpredictability, continuous frequency spectrum, etc.).

Besides application in information theory, entropy is a general measure commonly used to analyze complex systems. Like Lyapunov exponents or fractal dimensions, entropy describes the complexity of dynamics concerning system parameters, external forcing, initial conditions, or time instances.

Considering the recent advances in dynamic systems, this Special Issue will collect new ideas and describe promising methods arising from the field of analysis and modeling human behavior using complex nonlinear dynamical systems.

This Special Issue will accept original, unpublished papers and comprehensive reviews focused (but not restricted) on the following research areas:

  • Application of different entropy calculations in biomechanical analysis of human movements
  • Analysis of nonlinear dynamical systems with complex behavior
  • New chaotic systems with unique properties; both autonomous and driven
  • Experimental investigation of human movement with nonlinear dynamics
  • Advanced computational algorithms applied in human movements
  • Novel numerical methods dedicated to the quantitative analysis of dynamical human behaviors
  • Algorithms for analysis of time sequences and entropy calculation applied to human movements

Dr. Li Li
Prof. Dr. Brad Manor
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

  • approximate entropy
  • balance
  • biomechanics
  • complexity
  • correlation Entropy
  • electromyography
  • ergonomics
  • geometric entropy
  • Hilbert-Huang marginal spectrum entropy
  • injury risks
  • mobility (gait, walking, running)
  • movement control
  • multiscale entropy
  • muscle contraction
  • nonlinear analysis
  • permutation Entropy
  • postural control
  • sample entropy
  • Shannon - entropy
  • sports
  • stability
  • variability

Published Papers (5 papers)

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Research

21 pages, 2389 KiB  
Article
Considerations for Applying Entropy Methods to Temporally Correlated Stochastic Datasets
by Joshua Liddy and Michael Busa
Entropy 2023, 25(2), 306; https://doi.org/10.3390/e25020306 - 7 Feb 2023
Cited by 1 | Viewed by 1188
Abstract
The goal of this paper is to highlight considerations and provide recommendations for analytical issues that arise when applying entropy methods, specifically Sample Entropy (SampEn), to temporally correlated stochastic datasets, which are representative of a broad range of biomechanical and physiological variables. To [...] Read more.
The goal of this paper is to highlight considerations and provide recommendations for analytical issues that arise when applying entropy methods, specifically Sample Entropy (SampEn), to temporally correlated stochastic datasets, which are representative of a broad range of biomechanical and physiological variables. To simulate a variety of processes encountered in biomechanical applications, autoregressive fractionally integrated moving averaged (ARFIMA) models were used to produce temporally correlated data spanning the fractional Gaussian noise/fractional Brownian motion model. We then applied ARFIMA modeling and SampEn to the datasets to quantify the temporal correlations and regularity of the simulated datasets. We demonstrate the use of ARFIMA modeling for estimating temporal correlation properties and classifying stochastic datasets as stationary or nonstationary. We then leverage ARFIMA modeling to improve the effectiveness of data cleaning procedures and mitigate the influence of outliers on SampEn estimates. We also emphasize the limitations of SampEn to distinguish among stochastic datasets and suggest the use of complementary measures to better characterize the dynamics of biomechanical variables. Finally, we demonstrate that parameter normalization is not an effective procedure for increasing the interoperability of SampEn estimates, at least not for entirely stochastic datasets. Full article
(This article belongs to the Special Issue Entropy-Based Biomechanical Research and Its Applications)
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11 pages, 774 KiB  
Article
The Impact of Hoffmann Reflex on Standing Postural Control Complexity in the Elderly with Impaired Plantar Sensation
by Mengzi Sun, Fangtong Zhang, Kelsey Lewis, Qipeng Song and Li Li
Entropy 2023, 25(1), 64; https://doi.org/10.3390/e25010064 - 29 Dec 2022
Cited by 1 | Viewed by 1263
Abstract
In people with peripheral neuropathy (PN), impaired plantar sensation can cause adaptive changes in the central nervous system (CNS), resulting in changes in the standing postural control, which is reflected in the variability of standing output signals. Standard deviation (SD) and entropy are [...] Read more.
In people with peripheral neuropathy (PN), impaired plantar sensation can cause adaptive changes in the central nervous system (CNS), resulting in changes in the standing postural control, which is reflected in the variability of standing output signals. Standard deviation (SD) and entropy are reliable indicators of system variability, especially since entropy is highly sensitive to diseased populations. The relation between SD and entropy, CNS and center of pressure (COP) variability is unclear for people with severe PN. The purpose of this study was to explore the adaptability of the CNS to the severe of PN and its effect on the degree and complexity of COP variability. Here, people with PN were divided into less affected (LA) and more affected (MA) groups based on plantar pressure sensitivity. We studied Hoffmann reflex (H-reflex) and standing balance performance with the control group (n = 8), LA group (n = 10), and MA group (n = 9), recording a 30 s COP time series (30,000 samples) of double-leg standing with eyes open. We observed that the more affected group had less COP complexity than people without PN. There is a significant negative correlation between the SD and sample entropy in people without PN, less affected and more affected. The COP complexity in people without PN was inversely correlated with H-reflex. We concluded that: (1) The complexity of COP variability in patients with severe plantar sensory impairment is changed, which will not affect the degree of COP variability; (2) The independence of the COP entropy in the AP and ML directions decreased, and the interdependence increased in people with PN; (3) Although the CNS of people with PN has a greater contribution to standing balance, its modulation of standing postural control is decreased. Full article
(This article belongs to the Special Issue Entropy-Based Biomechanical Research and Its Applications)
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15 pages, 1806 KiB  
Article
Task Specific and General Patterns of Joint Motion Variability in Upright- and Hand-Standing Postures
by Moira Pryhoda, Karl M. Newell, Cassie Wilson and Gareth Irwin
Entropy 2022, 24(7), 909; https://doi.org/10.3390/e24070909 - 30 Jun 2022
Cited by 1 | Viewed by 1301
Abstract
The preservation of static balance in both upright- and hand-stance is maintained by the projection of center of mass (CM) motion within the region of stability at the respective base of support. This study investigated, from a degrees of freedom (DF) perspective, whether [...] Read more.
The preservation of static balance in both upright- and hand-stance is maintained by the projection of center of mass (CM) motion within the region of stability at the respective base of support. This study investigated, from a degrees of freedom (DF) perspective, whether the stability of the CM in both upright- and hand-stances was predicted by the respective dispersion and time-dependent regularity of joint (upright stance—ankle, knee, hip, shoulder, neck; hand stance—wrist, elbow, shoulder, neck) angle and position. Full body three-dimensional (3D) kinematic data were collected on 10 advanced level junior female gymnasts during 30 s floor upright- and hand-stands. For both stances the amount of the dispersion of joint angle and sway motion was higher than that of the CM and center of pressure (CP) with an inverse relation to time-dependent irregularity (SampEn). In upright-standing the variability of neck motion in the anterior–posterior direction was significantly greater than that of most joints consistent with the role of vision in the control of quiet upright posture. The findings support the proposition that there are both task specific and general properties to the global CM control strategy in the balance of upright- and hand-standing induced by the different active skeletal-muscular organization and the degeneracy revealed in the multiple distributional variability patterns of the joint angle and position in 3D. Full article
(This article belongs to the Special Issue Entropy-Based Biomechanical Research and Its Applications)
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14 pages, 3129 KiB  
Article
Estimating Information Processing of Human Fast Continuous Tapping from Trajectories
by Hiroki Murakami and Norimasa Yamada
Entropy 2022, 24(6), 788; https://doi.org/10.3390/e24060788 - 4 Jun 2022
Cited by 2 | Viewed by 2808
Abstract
Fitts studied the problem of information capacity and transfer in the speed–accuracy motor paradigm using a theoretical approach developed from Shannon and Weaver’s information theory. The information processing (bit/s) estimated in Fitts’ study is calculated from the movement time required to achieve the [...] Read more.
Fitts studied the problem of information capacity and transfer in the speed–accuracy motor paradigm using a theoretical approach developed from Shannon and Weaver’s information theory. The information processing (bit/s) estimated in Fitts’ study is calculated from the movement time required to achieve the required task index of difficulty but is essentially different from Shannon’s information entropy. Thus, we estimated the information entropy of multiple human movement trajectories and the mutual information among trajectories for the continuous aiming task in Fitts’ paradigm. Further, we estimated the information processing moment by moment. Two methods were considered: (1) encoded values encompassing the coordinates of the three dimensions and (2) coordinate values associated with each direction in the three dimensions. Information entropy indicates the magnitude of variation at each time point, and the structure of this variation varies with the index of difficulty. The ratio of entropy to mutual information was examined, and it was found that information was processed from the first half of the trajectory in difficult tasks. In addition, since these values calculated from the encoded method were higher than those from the conventional method, this method may be able to estimate these values successfully. Full article
(This article belongs to the Special Issue Entropy-Based Biomechanical Research and Its Applications)
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18 pages, 3304 KiB  
Article
Postural Complexity during Listening in Young and Middle-Aged Adults
by Charles Dane Napoli, Karen S. Helfer and Richard E. A. van Emmerik
Entropy 2022, 24(6), 762; https://doi.org/10.3390/e24060762 - 28 May 2022
Viewed by 1628
Abstract
Postural behavior has traditionally been studied using linear assessments of stability (e.g., center of pressure ellipse area). While these assessments may provide valuable information, they neglect the nonlinear nature of the postural system and often lead to the conflation of variability with pathology. [...] Read more.
Postural behavior has traditionally been studied using linear assessments of stability (e.g., center of pressure ellipse area). While these assessments may provide valuable information, they neglect the nonlinear nature of the postural system and often lead to the conflation of variability with pathology. Moreover, assessing postural behavior in isolation or under otherwise unrealistic conditions may obscure the natural dynamics of the postural system. Alternatively, assessing postural complexity during ecologically valid tasks (e.g., conversing with others) may provide unique insight into the natural dynamics of the postural system across a wide array of temporal scales. Here, we assess postural complexity using Multiscale Sample Entropy in young and middle-aged adults during a listening task of varying degrees of difficulty. It was found that middle-aged adults exhibited greater postural complexity than did young adults, and that this age-related difference in postural complexity increased as a function of task difficulty. These results are inconsistent with the notion that aging is universally associated with a loss of complexity, and instead support the notion that age-related differences in complexity are task dependent. Full article
(This article belongs to the Special Issue Entropy-Based Biomechanical Research and Its Applications)
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