Elsevier

Journal of Electrocardiology

Volume 43, Issue 6, November–December 2010, Pages 719-724
Journal of Electrocardiology

Analyzing temporal variability of standard descriptors of Poincaré plots

https://doi.org/10.1016/j.jelectrocard.2010.09.001Get rights and content

Abstract

The Poincaré map is a visual technique to recognize the hidden correlation patterns of a time series signal. The standard descriptors of the Poincaré map are used to quantify the plot that measures the gross variability of the time series data. However, the problem lies in capturing temporal information of the plot quantitatively. In this article, we propose a new formulation for calculating the standard descriptors SD1 and SD2 from localized measures SD1^w and SD2^w. To justify the importance of the temporal measure, SD1^w, SD2^w are calculated for the 2 case studies (normal sinus rhythm [NSR] vs congestive heart failure and NSR vs arrhythmia) and are compared with the performance using the overall measures (SD1, SD2). Using overall SD1, receiver operating characteristic areas of 0.72 and 0.86 were obtained for NSR vs congestive heart failure and NSR vs arrhythmia, and using the proposed method resulted in 0.82 and 0.89. Because we have shown that the overall SD1 and SD2 are functions of the respective localized measures SD1^w and SD2^w, we can conclude that use of localized measure provides equal or higher performance in pathology detection compared with the overall SD1 or SD2.

Introduction

The Poincaré plot, also named return map, is the simplest technique to describe the nonlinear dynamics of a phenomenon. This is a visual technique to recognize the hidden correlation patterns of a time series signal. The plot exploits the properties of the phase plane for 2-dimensional systems and provides a convenient method for discovering the existence of periodic or possibly more complex behavior such as quasi-periodic or chaotic motion.1 Researchers have put forward a number of techniques that attempt to quantitatively summarize the plot's geometric appearance.2, 3 The popular technique for measuring Poincaré plot, which was first proposed by Tulppo et al,2 is fitting an ellipse and measuring the dispersion of points along the minor axis (SD1) and the major axis (SD2). Kamen and Tonkin3 have extended the qualitative, visual classification system into a quantitative system by incorporating standard time-domain statistics. The definitions of the standard descriptors SD1 and SD2 in terms of linear statistics, given by Brennan et al,4 has shown that the standard descriptors guide the visual inspection of the distribution.

In general, Poincaré plot of a time series signal is constructed as a 2-dimensional plot by plotting consecutive points of the time series (ie, lag-1 plot). Use of Poincaré plots for characterizing abnormal cardiac function from heartbeat (RR) intervals has been found successful and proved integral to the heart rate variability (HRV) field.2, 4, 5, 6 The Poincaré plot is shown to provide prognostic information about mortality in post–myocardial infarction, chronic heart failure, and sudden infant death syndrome and about the risk of life-threatening ventricular arrhythmias in patients subjected to cardiac surgery.7, 8, 9, 10

The time-domain methods are ideal and better than frequency domain techniques for the analysis of long-term HRV signal.11 In HRV analysis, standard descriptor SD1 is considered to describe the short-term variability and SD2 the long-term variability as shown by Brennan et al.4 Although intuitive, the lack of temporal information is the primary limitation of the standard descriptors of the Poincaré plot. For analysis of long-term signal, inspection of temporal variation of any measure gives more insight than does the global measure. Hence, animating temporal progression of SD1 and SD2 for different physiologic condition can guide the interpretation of the quantitative methods and give insight into the degree of temporal dynamics. Temporal progression of SD1 and SD2 for normal sinus rhythm (NSR), congestive heart failure (CHF), and arrhythmia subjects is shown in Fig. 1. From the figures, it is apparent that overall SD1 and SD2 change tremendously with increasing number of RR intervals, especially in pathology (CHF and arrhythmia). Therefore, we hypothesize that the localized SD1 and SD2 may provide better insight to any specific pathology than the global measure.

In this study, we give a new formulation for calculating temporal SD1 and SD2 (localized measures) and compare it with existing standard descriptors, which are global in nature. We have used standard deviation (SD) as a metric to represent the temporal variability. Finally, the discriminating performance of the proposed metric is demonstrated using 2 case studies (NSR vs CHF and NSR vs arrhythmia) and compared with the existing standard descriptors.

Section snippets

Materials and method

In this section, the localized measurement of the standard descriptors (say, SD1^w, SD2^w) and the expression to connect these with the standard descriptors SD1 and SD2 of the plot are shown. This is followed by the presentation of the method to calculate SD1^w, SD2^w and of 355 subjects of 3 different groups, namely, NSR (54), CHF (29), and arrhythmia (272). A metric is defined for finding a global measure from temporal measures and compare the performance of SD1^w and SD2^w with overall SD1,

Results

Fig. 2 shows the localized values of SD1^w and SD2^w for NSR, CHF, and arrhythmia subjects, respectively. This provides more insight about the temporal variation of the signal or the change in temporal dynamics of the signal. We calculated 95% confidence intervals (CIs) of the mean variability of the standard descriptors for the 3 groups. For localized SD1, the CIs for NSR, CHF, and arrhythmia groups were found to be 0.0149-0.0210, 0.0245-0.0410, and 0.0441-0.0556 (all in seconds),

Discussion

A new formulation for calculating temporal SD1 and SD2 (localized measures) has been presented in this article. The proposed method is compared with existing standard descriptors, which are global in nature. Finally, the ability of the proposed method compared with the existing methods has been demonstrated using 2 case studies (discriminating NSR vs CHF and NSR vs Arrhythmia) as presented in the “Results” section.

The windowed calculation of time-domain features, SD1^w and SD2^w, provides more

Conclusion

In conclusion, this study provides a detailed visualization of temporal variation in HRV using temporal equivalent of the standard descriptors via SD1^w and SD2^w. It has revealed the possibility of using different metric on SD1^w and SD2^w rather than the commonly used overall SD1 or SD2. Use of simple metric such as SD has been shown to outperform than the existing standard descriptors in classifying pathology.

References (15)

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