Quantitative Poincaré Plot

Abstract

Poincaré plot is a geometrical representation of a time series in a Cartesian plane. Points of the plot are duplets of the values of the time series and the distance (in number of values) between values of each duplet is the lag of the plot. Statistically, lag-1 Poincaré plot displays the correlation between consecutive samples in a graphical manner. It has been shown that Poincaré plot reveals patterns of heart rate dynamics resulting from nonlinear processes (Tulppo et al., Am. J. Physiol. 271:H244–H252, 1996; Brennan et al., IEEE Trans. Biomed. Eng. 48:1342–1347, 2001). The lag-1 RR interval Poincaré plot, a two-dimensional plot constructed by plotting consecutive RR intervals, is a representation of RR time series on phase space or Cartesian plane (Liebovitch and Scheurle, Complexity 5:34–43, 2000). It is extensively used for qualitative visualization of physiological signals. Poincaré plot is commonly applied to assess the dynamics of heart rate variability (Tulppo et al., Am. J. Physiol. 271:H244–H252, 1996; Acharya et al., Med. Biol. Eng. Comput. 44(12):1031–1051, 2006; Tulppo et al., Am. J. Physiol. 247:H810–H816, 1998; Toichi et al., J. Auton. Nerv. Syst. 62:79–84, 1997; Hayano et al., Nephrol. Dial. Transplant. 14:1480–1488, 1999). The quantitative analysis of Poincaré plot predominantly means the mathematical characterization of the shape of the plot. In the following sections we will discuss both the qualitative and quantitative techniques of Poincaré plot for analysing HRV signal.