Measuring synchronization in coupled simulation and coupled cardiovascular time series: A comparison of different cross entropy measures

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Percutaneous coronary intervention (PCI) is a common treatment method for patients with coronary artery disease (CAD), but its effect on synchronously measured heart rate variability (HRV) and pulse transit time variability (PTTV) have not been well established. This study aimed to verify whether PCI for CAD patients affects both HRV and PTTV parameters. Sixteen CAD patients were enrolled. Two five-minute ECG and finger photoplethysmography (PPG) signals were recorded, one within 24 h before PCI and another within 24 h after PCI. The changes of RR and pulse transit time (PTT) intervals due to the PCI procedure were first compared. Then, HRV and PTTV were evaluated by a standard short-term time-domain variability index of standard deviation of time series (SDTS) and our previously developed entropy-based index of fuzzy measure entropy (FuzzyMEn). To test the effect of different time series length on HRV and PTTV results, we segmented the RR and PTT time series using four time windows of 200, 100, 50 and 25 beats respectively. The PCI-induced changes in HRV and PTTV, as well as in RR and PTT intervals, are different. PCI procedure significantly decreased RR intervals (before PCI 973˘85 vs. after PCI 907˘100 ms, p < 0.05) while significantly increasing PTT intervals (207˘18 vs. 214˘19 ms, p < 0.01). For HRV, SDTS-only output significant lower values after PCI when time windows are 100 and 25 beats while presenting no significant decreases for other two time windows. By contrast, FuzzyMEn gave significant lower values after PCI for all four time windows (all p < 0.05). For PTTV, SDTS hardly changed after PCI at any time window (all p > 0.90) whereas FuzzyMEn still reported significant lower values (p < 0.05 for 25 beats time window and p < 0.01 for other three time windows). For both HRV and PTTV, with the increase of time window values, SDTS decreased while FuzzyMEn increased. This pilot study demonstrated that the RR interval decreased whereas the PTT interval increased after the PCI procedure and that there were significant reductions in both HRV and PTTV immediately after PCI using the FuzzyMEn method, indicating the changes in underlying mechanisms in cardiovascular system.

Section: Protocolmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Effect of a Percutaneous Coronary Intervention Procedure on Heart Rate Variability and Pulse Transit Time Variability: A Comparison Study Based on Fuzzy Measure Entropy

Zhang

Liu

et al. 2016

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“…On the other hand, whether ApEn or SampEn, the decision rule for vector similarity is based on the Heaviside function and it is very rigid because two vectors are considered as similar vectors only when they are within the tolerance threshold r, whereas the vectors just outside this tolerance are ignored [7,[19][20][21]. This rigid boundary may induce to the abrupt changes of entropy values when the tolerance threshold r changes slightly, and even failure to define the entropy if no vector-matching could be found for very small r [2,7,[19][20][21][22].…”

Section: Introductionmentioning

confidence: 99%

“…This rigid boundary may induce to the abrupt changes of entropy values when the tolerance threshold r changes slightly, and even failure to define the entropy if no vector-matching could be found for very small r [2,7,[19][20][21][22]. To enhance the statistical stability, we previously proposed a fuzzy measure entropy (FuzzyMEn) method, which used a fuzzy membership function to substitute the Heaviside function to make a gradually varied entropy value when r monotonously changes.…”

Section: Introductionmentioning

confidence: 99%

Determination of Sample Entropy and Fuzzy Measure Entropy Parameters for Distinguishing Congestive Heart Failure from Normal Sinus Rhythm Subjects

Zhao

Wei

Zhang

et al. 2015

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Entropy provides a valuable tool for quantifying the regularity of physiological time series and provides important insights for understanding the underlying mechanisms of the cardiovascular system. Before any entropy calculation, certain common parameters need to be initialized: embedding dimension m, tolerance threshold r and time series length N. However, no specific guideline exists on how to determine the appropriate parameter values for distinguishing congestive heart failure (CHF) from normal sinus rhythm (NSR) subjects in clinical application. In the present study, a thorough analysis on the selection of appropriate values of m, r and N for sample entropy (SampEn) and recently proposed fuzzy measure entropy (FuzzyMEn) is presented for distinguishing two group subjects. 44 long-term NRS and 29 long-term CHF RR interval recordings from http://www.physionet.org were used as the non-pathological and pathological data respectively. Extreme (>2 s) and abnormal heartbeat RR intervals were firstly removed from each RR recording and then the recording was segmented with a non-overlapping segment length N of 300 and 1000, respectively. SampEn and FuzzyMEn were performed Compared with SampEn, FuzzyMEn shows a better regularity when selecting the parameters m and r. In addition, FuzzyMEn shows a better relative consistency for distinguishing the two groups, that is, the results of FuzzyMEn in the NSR group were consistently lower than those in the CHF group while SampEn were not. The selections of m of 2 and 3 and r of 0.10 and 0.15 for SampEn and the selections of m of 1 and 2 whenever r (herein, rL = rG = r) are for FuzzyMEn (in addition to setting nL = 3 and nG = 2) were recommended to yield the fine classification results for the NSR and CHF groups.

“…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

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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.