Classification of cardiovascular time series based on different coupling structures using recurrence networks analysis

Ramírez-Ávila, Gonzalo Marcelo; Gapelyuk, Andrej; Marwan, Norbert; Walther, Thomas; Stepan, Holger; Kurths, Jüergen; Wessel, Niels

doi:10.1098/rsta.2011.0623

Cited by 25 publications

(7 citation statements)

References 66 publications

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“…These are complex networks constructed from the time series of chaotic dynamical systems, called recurrence networks (RNs) [ 20 ]. They have a wide range of practical applications [ 21 , 22 ] and the measures from these networks are used to characterize strange attractors in state space, typical of chaotic dynamical systems, as discussed in § 5 . The diversity of node degrees in the RNs was actually one of the motivations for us to search for a heterogeneity measure that could be used to compare the structural complexities of different chaotic attractors through the construction of RNs.…”

Section: Introductionmentioning

confidence: 99%

Measure for degree heterogeneity in complex networks and its application to recurrence network analysis

et al. 2017

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We propose a novel measure of degree heterogeneity, for unweighted and undirected complex networks, which requires only the degree distribution of the network for its computation. We show that the proposed measure can be applied to all types of network topology with ease and increases with the diversity of node degrees in the network. The measure is applied to compute the heterogeneity of synthetic (both random and scale free (SF)) and real-world networks with its value normalized in the interval false[0,1false]. To define the measure, we introduce a limiting network whose heterogeneity can be expressed analytically with the value tending to 1 as the size of the network N tends to infinity. We numerically study the variation of heterogeneity for random graphs (as a function of p and N) and for SF networks with γ and N as variables. Finally, as a specific application, we show that the proposed measure can be used to compare the heterogeneity of recurrence networks constructed from the time series of several low-dimensional chaotic attractors, thereby providing a single index to compare the structural complexity of chaotic attractors.

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Section: Introductionmentioning

confidence: 99%

Measure for degree heterogeneity in complex networks and its application to recurrence network analysis

et al. 2017

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“…The practical and powerful use of RP based methods has been demonstrated by their growing and interdisciplinary application, such as for cardiovascular health diagnosis, behavioral, cognitive and neurological studies, studying fluid dynamics and plasma, analysing optical effects, material health monitoring, palaeoclimate regime change detection, etc. [9][10][11][12][13][14][15][16]. In general, such studies have so far been restricted to rather low-dimensional systems.…”

Section: Introductionmentioning

confidence: 99%

Analysing spatially extended high-dimensional dynamics by recurrence plots

2015

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Recurrence plot based measures of complexity are capable tools for characterizing complex dynamics. In this letter we show the potential of selected recurrence plot measures for the investigation of even high-dimensional dynamics. We apply this method on spatially extended chaos, such as derived from the Lorenz96 model and show that the recurrence plot based measures can qualitatively characterize typical dynamical properties such as chaotic or periodic dynamics. Moreover, we demonstrate its power by analysing satellite image time series of vegetation cover with contrasting dynamics as a spatially extended and potentially high-dimensional example from the real world.

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“…Generally, coupling phenomena are very common in physiology [19][20][21][22][23][24][25][26][27]. Previous studies have developed a vast number of methods in order to measure coupling [22,28,29].…”

Section: Introductionmentioning

confidence: 99%

Measuring Electromechanical Coupling in Patients with Coronary Artery Disease and Healthy Subjects

Ji¹,

Liu

et al. 2016

Entropy

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Coronary artery disease (CAD) is the most common cause of death globally. To detect CAD noninvasively at an early stage before clinical symptoms occur is still nowadays challenging. Analysis of the variation of heartbeat interval (RRI) opens a new avenue for evaluating the functional change of cardiovascular system which is accepted to occur at the subclinical stage of CAD. In addition, systolic time interval (STI) and diastolic time interval (DTI) also show potential. There may be coupling in these electromechanical time series due to their physiological connection. However, to the best of our knowledge no publication has systematically investigated how can the coupling be measured and how it changes in CAD patients. In this study, we enrolled 39 CAD patients and 36 healthy subjects and for each subject the electrocardiogram (ECG) and photoplethysmography (PPG) signals were recorded simultaneously for 5 min. The RRI series, STI series, and DTI series were constructed, respectively. We used linear cross correlation (CC), coherence function (CF), as well as nonlinear mutual information (MI), cross conditional entropy (XCE), cross sample entropy (XSampEn), and cross fuzzy entropy (XFuzzyEn) to analyse the bivariate RRI-DTI coupling, RRI-STI coupling, and STI-DTI coupling, respectively. Our results suggest that the linear CC and CF generally have no significant difference between the two groups for all three types of bivariate coupling. The MI only shows weak change in RRI-DTI coupling. By comparison, the three entropy-based coupling measurements show significantly decreased coupling in CAD patients except XSampEn for RRI-DTI coupling (less significant) and XCE for STI-DTI and RRI-STI coupling (not significant). Additionally, the XFuzzyEn performs best as it was still significant if we further applied the Bonferroni correction in our statistical analysis. Our study indicates that the intrinsic electromechanical coupling is most probably nonlinear and can better be measured by nonlinear entropy-based measurements especially the XFuzzyEn. Besides, CAD patients are accompanied by a loss of electromechanical coupling. Our results suggest that cardiac electromechanical coupling may potentially serve as a noninvasive diagnostic tool for CAD.

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Classification of cardiovascular time series based on different coupling structures using recurrence networks analysis

Cited by 25 publications

References 66 publications

Measure for degree heterogeneity in complex networks and its application to recurrence network analysis

Measure for degree heterogeneity in complex networks and its application to recurrence network analysis

Analysing spatially extended high-dimensional dynamics by recurrence plots

Measuring Electromechanical Coupling in Patients with Coronary Artery Disease and Healthy Subjects

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