scholarly journals A Review on the Nonlinear Dynamical System Analysis of Electrocardiogram Signal

2018 ◽  
Vol 2018 ◽  
pp. 1-19 ◽  
Author(s):  
Suraj K. Nayak ◽  
Arindam Bit ◽  
Anilesh Dey ◽  
Biswajit Mohapatra ◽  
Kunal Pal
Keyword(s):  
Signal Analysis ◽  
System Analysis ◽  
Nonlinear Dynamical System ◽  
Approximate Entropy ◽  
Recurrence Plot ◽  
Fluctuation Analysis ◽  
Ecg Signal ◽  
Poincaré Plot ◽  
Nonlinear Methods ◽  
Nonlinear Dynamical

Electrocardiogram (ECG) signal analysis has received special attention of the researchers in the recent past because of its ability to divulge crucial information about the electrophysiology of the heart and the autonomic nervous system activity in a noninvasive manner. Analysis of the ECG signals has been explored using both linear and nonlinear methods. However, the nonlinear methods of ECG signal analysis are gaining popularity because of their robustness in feature extraction and classification. The current study presents a review of the nonlinear signal analysis methods, namely, reconstructed phase space analysis, Lyapunov exponents, correlation dimension, detrended fluctuation analysis (DFA), recurrence plot, Poincaré plot, approximate entropy, and sample entropy along with their recent applications in the ECG signal analysis.

scholarly journals Nonlinear Methods Most Applied to Heart-Rate Time Series: A Review

Entropy ◽  
2020 ◽  
Vol 22 (3) ◽  
pp. 309 ◽  
Author(s):  
Teresa Henriques ◽  
Maria Ribeiro ◽  
Andreia Teixeira ◽  
Luísa Castro ◽  
Luís Antunes ◽  
...  
Keyword(s):  
Heart Rate ◽  
Recurrence Plot ◽  
Multiscale Entropy ◽  
Fluctuation Analysis ◽  
Mathematical Methods ◽  
Poincaré Plot ◽  
Nonlinear Methods ◽  
Plot Analysis ◽  
Heart Rate Dynamics ◽  
Recurrence Plot Analysis

The heart-rate dynamics are one of the most analyzed physiological interactions. Many mathematical methods were proposed to evaluate heart-rate variability. These methods have been successfully applied in research to expand knowledge concerning the cardiovascular dynamics in healthy as well as in pathological conditions. Notwithstanding, they are still far from clinical practice. In this paper, we aim to review the nonlinear methods most used to assess heart-rate dynamics. We focused on methods based on concepts of chaos, fractality, and complexity: Poincaré plot, recurrence plot analysis, fractal dimension (and the correlation dimension), detrended fluctuation analysis, Hurst exponent, Lyapunov exponent entropies (Shannon, conditional, approximate, sample entropy, and multiscale entropy), and symbolic dynamics. We present the description of the methods along with their most notable applications.

scholarly journals Cardio-Diagnostic Assisting Computer System

Diagnostics ◽  
2020 ◽  
Vol 10 (5) ◽  
pp. 322 ◽  
Author(s):  
Galya Georgieva-Tsaneva ◽  
Evgeniya Gospodinova ◽  
Mitko Gospodinov ◽  
Krasimir Cheshmedzhiev
Keyword(s):  
Frequency Domain ◽  
Computer System ◽  
Time Domain ◽  
Heart Rhythm ◽  
Recurrence Plot ◽  
Diagnostic Process ◽  
Control Group ◽  
Fluctuation Analysis ◽  
Poincaré Plot ◽  
Time Frequency

The mathematical analysis and the assessment of heart rate variability (HRV) based on computer systems can assist the diagnostic process with determining the cardiac status of patients. The new cardio-diagnostic assisting computer system created uses the classic Time-Domain, Frequency-Domain, and Time-Frequency analysis indices, as well as the nonlinear methods (Poincaré plot, Recurrence plot, Hurst R/S method, Detrended Fluctuation Analysis (DFA), Multi-Fractal DFA, Approximate Entropy and Sample Entropy). To test the feasibility of the software developed, 24-hour Holter recordings of four groups of people were analysed: healthy subjects and patients with arrhythmia, heart failure and syncope. Time-Domain (SDNN < 50 ms, SDANN < 100 ms, RMSSD < 17 ms) and Frequency-Domain (the spectrum of HRV in the LF < 550 ms2, and HF < 540 ms2) parameter values decreased in the cardiovascular disease groups compared to the control group as a result of lower HRV due to decreased parasympathetic and increased sympathetic activity. The results of the nonlinear analysis showed low values of (SD1 < 56 ms, SD2 < 110 ms) at Poincaré plot (Alpha < 90 ms) at DFA in patients with diseases. Significantly reducing these parameters are markers of cardiac dysfunction. The examined groups of patients showed an increase in the parameters (DET% > 95, REC% > 38, ENTR > 3.2) at the Recurrence plot. This is evidence of a pathological change in the regulation of heart rhythm. The system created can be useful in making the diagnosis by the cardiologist and in bringing greater accuracy and objectivity to the treatment.

NONLINEAR INDICES OF HEART RATE VARIABILITY FOR DIFFERENTIATING ARRHYTHMIAS

2013 ◽  
Vol 13 (04) ◽  
pp. 1350061 ◽  
Author(s):  
N. D. ASHA ◽  
K. PAUL JOSEPH
Keyword(s):  
Heart Rate ◽  
Heart Rate Variability ◽  
Normal Sinus Rhythm ◽  
Ventricular Tachyarrhythmia ◽  
Recurrence Plot ◽  
Largest Lyapunov Exponent ◽  
Fluctuation Analysis ◽  
Scaling Exponent ◽  
Poincaré Plot ◽  
Diagonal Length

Heart rate variability (HRV) is the temporal variation between sequences of consecutive heartbeats. Chaos and fractal-based measurements have been widely used for quantifying the HRV for cardiac risk stratification purposes. In this paper, five different sets of HRVs, viz., normal sinus rhythm (NSR), congestive heart failure (CHF), cardiac arrhythmia suppression trial (CAST), supra ventricular tachyarrhythmia (SVTA) and atrial fibrillation (AF), have been analysed using nonlinear parameters to fix the ranges of each parameter. Data were downloaded from the PhysioNet database with 15 sets in each case. The parameters used for analysis were Poincare plot measures: SD1, SD2 and SD12, largest Lyapunov exponent (LLE), correlation dimension (CD); recurrence plot measures: recurrence rate (REC), determinism (DET), mean diagonal length (L mean ), maximal diagonal length (L max ) and entropy (ENTR); detrended fluctuation analysis measures: scaling exponent (α) and fractal dimension (FD); sample entropy (SampEn); and approximate entropy (ApEn). Analysis of variance (ANOVA) was done for confirming the differences in parameter values between various cases. All parameters except LLE showed a significant statistical difference for different cases.

scholarly journals Dynamical System Analysis of Interacting Hessence Dark Energy inf(T)Gravity

2017 ◽  
Vol 2017 ◽  
pp. 1-14
Author(s):  
Jyotirmay Das Mandal ◽  
Ujjal Debnath
Keyword(s):  
Dynamical System ◽  
Autonomous System ◽  
System Analysis ◽  
Nonlinear Dynamical System ◽  
Computational Method ◽  
Dynamical Analysis ◽  
Dynamical System Theory ◽  
Nonlinear Dynamical ◽  
The Stability ◽  
The Universe

We have carried out dynamical system analysis of hessence field coupling with dark matter inf(T)gravity. We have analysed the critical points due to autonomous system. The resulting autonomous system is nonlinear. So, we have applied the theory of nonlinear dynamical system. We have noticed that very few papers are devoted to this kind of study. Maximum works in literature are done treating the dynamical system as done in linear dynamical analysis, which are unable to predict correct evolution. Our work is totally different from those kinds of works. We have used nonlinear dynamical system theory, developed till date, in our analysis. This approach gives totally different stable solutions, in contrast to what the linear analysis would have predicted. We have discussed the stability analysis in detail due to exponential potential through computational method in tabular form and analysed the evolution of the universe. Some plots are drawn to investigate the behaviour of the system(this plotting technique is different from usual phase plot and that devised by us). Interestingly, the analysis shows that the universe may resemble the “cosmological constant” like evolution (i.e.,ΛCDM model is a subset of the solution set). Also, all the fixed points of our model are able to avoid Big Rip singularity.

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