Heart rate variability (HRV) is concerned with the analysis of the intervals between heartbeats. An emerging analysis technique is the Poincaré plot, which takes a sequence of intervals and plots each interval against the following interval. The geometry of this plot has been shown to distinguish between healthy and unhealthy subjects in clinical settings. The Poincaré plot is a valuable HRV analysis technique due to its ability to display nonlinear aspects of the interval sequence. The problem is, how do we quantitatively characterize the plot to capture useful summary descriptors that are independent of existing HRV measures? Researchers have investigated a number of techniques: converting the two-dimensional plot into various one-dimensional views; the fitting of an ellipse to the plot shape; and measuring the correlation coefficient of the plot. We investigate each of these methods in detail and show that they are all measuring linear aspects of the intervals which existing HRV indexes already specify. The fact that these methods appear insensitive to the nonlinear characteristics of the intervals is an important finding because the Poincaré plot is primarily a nonlinear technique. Therefore, further work is needed to determine if better methods of characterizing Poincaré plot geometry can be found.

Brennan, Michael, Marimuthu Palaniswami, and Peter Kamen. Poincaré plot interpretation using a physiological model of HRV based on a network of oscillators. Am J Physiol Heart Circ Physiol 283: H1873-H1886, 2002; 10.1152/ajpheart.00405.2000.-In this paper, we develop a physiological oscillator model of which the output mimics the shape of the R-R interval Poincaré plot. To validate the model, simulations of various nervous conditions are compared with heart rate variability (HRV) data obtained from subjects under each prescribed condition. For a variety of sympathovagal balances, our model generates Poincaré plots that undergo alterations strongly resembling those of actual R-R intervals. By exploiting the oscillator basis of our model, we detail the way that low-and high-frequency modulation of the sinus node translates into R-R interval Poincaré plot shape by way of simulations and analytic results. With the use of our model, we establish that the length and width of a Poincaré plot are a weighted combination of low-and highfrequency power. This provides a theoretical link between frequency-domain spectral analysis techniques and time-domain Poincaré plot analysis. We ascertain the degree to which these principles apply to real R-R intervals by testing the mathematical relationships on a set of data and establish that the principles are clearly evident in actual HRV records.heart rate variability; quantitative beat-to-beat analysis THE STUDY OF HEART RATE variability (HRV) centers on the analysis of beat-to-beat fluctuations in heart rate. The series of time intervals between heartbeats, referred to as R-R intervals, are measured over a period of anywhere from 10 min to 24 h (15). Attention has focused on HRV as a method of quantifying cardiac autonomic function. In this study, we present new results in developing a novel mathematical model that describes the interactions between the sympathetic and the parasympathetic nervous systems and heart rate fluctuations over a short-term period of 5-10 min. Whereas our model is based on standard and already accepted physiological principles, the mathematical formulation permits in-depth numerical and analytic investigations yielding valuable insight into clinical R-R interval analysis techniques.Standard analysis techniques commonly estimate the levels of sympathetic and parasympathetic activity from the variability in the R-R intervals. Our attention has focused on two specific HRV analysis techniques. The first is the frequency domain spectral analysis of R-R intervals (2,4,6,14,20). R-R interval Poincaré plot analysis is the second technique, which is a newer nonlinear method (8-10, 21, 22). To date, R-R interval Poincaré plot analysis has not been clearly related to a physiological model of HRV. The main objective of our model is to provide insight into the significance of Poincaré plot morphology and not to accurately reproduce the complex autonomic activity of any particular individual.Our model emulates the differing varieties of Poincaré plot patterns seen in...

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