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Application of Nonlinear Dynamics in Medicine: Potential and Challenges

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

Deadline for manuscript submissions: closed (20 July 2022) | Viewed by 10568

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Dr. Peng Li

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Guest Editor

Department of Medicine, Brigham and Women's Hospital, Harvard Medical School, Boston, MA 02115, USA
Interests: Alzheimer's disease; biomedical signal processing; cardiovascular dynamics; fractal physiology; healthy aging; sleep
Special Issues, Collections and Topics in MDPI journals

Dr. Kun Hu

E-Mail Website
Guest Editor

Departments of Medicine and Neurology, Brigham and Women's Hospital, Harvard Medical School, Boston, MA 02115, USA
Interests: aging; cerebral autoregulation; cardiovascular control; circadian physiology; fractal physiology; motor function; nonlinear dynamics; sleep

Special Issue Information

Dear Colleagues,

Advances in wearable technology make it possible to monitor and record physiological signals such as motor activity, heart rate, and brain activity for longer periods, even when patients are ambulatory at home environments. How to extract health-related information reliably from these ambulatory recordings collected under non-control conditions is still a contemporary challenge in medicine, and addressing it will start a new era of remote medicine.

In the last two or three decades, many analytical tools based on the concepts of nonlinear dynamics, such as complexity, entropy, and fractal, have been proposed and approved to be able to better quantify complex signals with embedded nonlinear and nonstationary properties. However, the application of these tools in healthcare and clinics is still limited.

To collect ideas and evidence for the potential of applying nonlinear dynamic tools in medicine, as well as for the main barriers that hinder the application, this Special Issue will accept unpublished Original Research Articles, Reviews, Perspectives and Commentary Articles that are focused on or related to the following topics:

Development/improvement of nonlinear analytical tools for physiological data analysis;
Application of nonlinear analytical tools for diagnosis and prediction of diseases and health outcomes;
Opinions on the advantages and limitations of existing nonlinear analytical tools;
Insights into the applications and future directions of nonlinear dynamics in medicine.

Dr. Peng Li
Dr. Kun Hu
Guest Editors

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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

complexity
entropy
fractal
multiscale regulation
nonlinearity
nonstationarity
rhymicity

Published Papers (4 papers)

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Research

60 pages, 11229 KiB

Open AccessArticle

Complexity and Entropy in Physiological Signals (CEPS): Resonance Breathing Rate Assessed Using Measures of Fractal Dimension, Heart Rate Asymmetry and Permutation Entropy

by David Mayor, Tony Steffert, George Datseris, Andrea Firth, Deepak Panday, Harikala Kandel and Duncan Banks

Entropy 2023, 25(2), 301; https://doi.org/10.3390/e25020301 - 6 Feb 2023

Cited by 3 | Viewed by 2460

Abstract

Background: As technology becomes more sophisticated, more accessible methods of interpretating Big Data become essential. We have continued to develop Complexity and Entropy in Physiological Signals (CEPS) as an open access MATLAB^® GUI (graphical user interface) providing multiple methods for the modification and analysis of physiological data. Methods: To demonstrate the functionality of the software, data were collected from 44 healthy adults for a study investigating the effects on vagal tone of breathing paced at five different rates, as well as self-paced and un-paced. Five-minute 15-s recordings were used. Results were also compared with those from shorter segments of the data. Electrocardiogram (ECG), electrodermal activity (EDA) and Respiration (RSP) data were recorded. Particular attention was paid to COVID risk mitigation, and to parameter tuning for the CEPS measures. For comparison, data were processed using Kubios HRV, RR-APET and DynamicalSystems.jl software. We also compared findings for ECG RR interval (RRi) data resampled at 4 Hz (4R) or 10 Hz (10R), and non-resampled (noR). In total, we used around 190–220 measures from CEPS at various scales, depending on the analysis undertaken, with our investigation focused on three families of measures: 22 fractal dimension (FD) measures, 40 heart rate asymmetries or measures derived from Poincaré plots (HRA), and 8 measures based on permutation entropy (PE). Results: FDs for the RRi data differentiated strongly between breathing rates, whether data were resampled or not, increasing between 5 and 7 breaths per minute (BrPM). Largest effect sizes for RRi (4R and noR) differentiation between breathing rates were found for the PE-based measures. Measures that both differentiated well between breathing rates and were consistent across different RRi data lengths (1–5 min) included five PE-based (noR) and three FDs (4R). Of the top 12 measures with short-data values consistently within ± 5% of their values for the 5-min data, five were FDs, one was PE-based, and none were HRAs. Effect sizes were usually greater for CEPS measures than for those implemented in DynamicalSystems.jl. Conclusion: The updated CEPS software enables visualisation and analysis of multichannel physiological data using a variety of established and recently introduced complexity entropy measures. Although equal resampling is theoretically important for FD estimation, it appears that FD measures may also be usefully applied to non-resampled data. Full article

(This article belongs to the Special Issue Application of Nonlinear Dynamics in Medicine: Potential and Challenges)

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11 pages, 936 KiB

Open AccessArticle

Joint Angle Variability Is Altered in Patients with Peripheral Artery Disease after Six Months of Exercise Intervention

by Farahnaz Fallahtafti, Zahra Salamifar, Mahdi Hassan, Hafizur Rahman, Iraklis Pipinos and Sara A. Myers

Entropy 2022, 24(10), 1422; https://doi.org/10.3390/e24101422 - 6 Oct 2022

Viewed by 1494

Abstract

Supervised exercise therapy (SET) is a conservative non-operative treatment strategy for improving walking performance in patients with peripheral artery disease (PAD). Gait variability is altered in patients with PAD, but the effect of SET on gait variability is unknown. Forty-three claudicating patients with PAD underwent gait analysis before and immediately after a 6-month SET program. Nonlinear gait variability was assessed using sample entropy, and the largest Lyapunov exponent of the ankle, knee, and hip joint angle time series. Linear mean and variability of the range of motion time series for these three joint angles were also calculated. Two-factor repeated measure analysis of variance determined the effect of the intervention and joint location on linear and nonlinear dependent variables. After SET, walking regularity decreased, while the stability remained unaffected. Ankle nonlinear variability had increased values compared with the knee and hip joints. Linear measures did not change following SET, except for knee angle, in which the magnitude of variations increased after the intervention. A six-month SET program produced changes in gait variability toward the direction of healthy controls, which indicates that in general, SET improved walking performance in individuals with PAD. Full article

(This article belongs to the Special Issue Application of Nonlinear Dynamics in Medicine: Potential and Challenges)

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14 pages, 1026 KiB

Open AccessArticle

Entropy Analysis of Heart Rate Variability in Different Sleep Stages

by Chang Yan, Peng Li, Meicheng Yang, Yang Li, Jianqing Li, Hongxing Zhang and Chengyu Liu

Entropy 2022, 24(3), 379; https://doi.org/10.3390/e24030379 - 8 Mar 2022

Cited by 10 | Viewed by 3003

Abstract

How the complexity or irregularity of heart rate variability (HRV) changes across different sleep stages and the importance of these features in sleep staging are not fully understood. This study aimed to investigate the complexity or irregularity of the RR interval time series in different sleep stages and explore their values in sleep staging. We performed approximate entropy (ApEn), sample entropy (SampEn), fuzzy entropy (FuzzyEn), distribution entropy (DistEn), conditional entropy (CE), and permutation entropy (PermEn) analyses on RR interval time series extracted from epochs that were constructed based on two methods: (1) 270-s epoch length and (2) 300-s epoch length. To test whether adding the entropy measures can improve the accuracy of sleep staging using linear HRV indices, XGBoost was used to examine the abilities to differentiate among: (i) 5 classes [Wake (W), non-rapid-eye-movement (NREM), which can be divide into 3 sub-stages: stage N1, stage N2, and stage N3, and rapid-eye-movement (REM)]; (ii) 4 classes [W, light sleep (combined N1 and N2), deep sleep (N3), and REM]; and (iii) 3 classes: (W, NREM, and REM). SampEn, FuzzyEn, and CE significantly increased from W to N3 and decreased in REM. DistEn increased from W to N1, decreased in N2, and further decreased in N3; it increased in REM. The average accuracy of the three tasks using linear and entropy features were 42.1%, 59.1%, and 60.8%, respectively, based on 270-s epoch length; all were significantly lower than the performance based on 300-s epoch length (i.e., 54.3%, 63.1%, and 67.5%, respectively). Adding entropy measures to the XGBoost model of linear parameters did not significantly improve the classification performance. However, entropy measures, especially PermEn, DistEn, and FuzzyEn, demonstrated greater importance than most of the linear parameters in the XGBoost model.300-s270-s. Full article

(This article belongs to the Special Issue Application of Nonlinear Dynamics in Medicine: Potential and Challenges)

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15 pages, 2570 KiB

Open AccessArticle

Ischemic Stroke Risk Assessment by Multiscale Entropy Analysis of Heart Rate Variability in Patients with Persistent Atrial Fibrillation

by Ghina Chairina, Kohzoh Yoshino, Ken Kiyono and Eiichi Watanabe

Entropy 2021, 23(7), 918; https://doi.org/10.3390/e23070918 - 19 Jul 2021

Cited by 1 | Viewed by 2526

Abstract

It has been recognized that heart rate variability (HRV), defined as the fluctuation of ventricular response intervals in atrial fibrillation (AFib) patients, is not completely random, and its nonlinear characteristics, such as multiscale entropy (MSE), contain clinically significant information. We investigated the relationship between ischemic stroke risk and HRV with a large number of stroke-naïve AFib patients (628 patients), focusing on those who had never developed an ischemic/hemorrhagic stroke before the heart rate measurement. The

{CHA}_{2} {DS}_{2} - VASc

score was calculated from the baseline clinical characteristics, while the HRV analysis was made from the recording of morning, afternoon, and evening. Subsequently, we performed Kaplan–Meier method and cumulative incidence function with mortality as a competing risk to estimate the survival time function. We found that patients with sample entropy (

S_{E}^{(s)}

)

\geq

0.68 at 210 s had a significantly higher risk of an ischemic stroke occurrence in the morning recording. Meanwhile, the afternoon recording showed that those with

S_{E}^{(s)}

\geq

0.76 at 240 s and

S_{E}^{(s)}

\geq

0.78 at 270 s had a significantly lower risk of ischemic stroke occurrence. Therefore,

S_{E}^{(s)}

at 210 s (morning) and 240 s ≤ s ≤ 270 s (afternoon) demonstrated a statistically significant predictive value for ischemic stroke in stroke-naïve AFib patients. Full article

(This article belongs to the Special Issue Application of Nonlinear Dynamics in Medicine: Potential and Challenges)

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