Beyond Traditional Poincare Analysis: Second-Order Plots Reveal Respiratory Effects in Heart Rate Variability

Abstract

Heart rate variability (HRV) is a non-invasive biomarker of autonomic nervous system activity, commonly analyzed using a Poincare plot. This plot visualizes correlations between successive heartbeats (RRi vs. RRi+1) and quantifies autonomic regulation through SD1 and SD2 parameters. We introduce a second-order Poincare plot, a natural extension that clarifies serial dependencies by plotting successive differences in RR intervals ({Delta}RRi vs. {Delta}RRi+1). Applied to a PhysioNet dataset of 20 healthy individuals, this technique filtered out the slow HRV baseline of traditional elliptical plots to reveal distinct higher-order dynamics. These included ring-shaped structures indicating cardiorespiratory synchronization. A coupled-oscillator model, developed to simulate respiratory modulation, confirmed that these patterns are dictated by the respiratory frequency to heart rate ratio: slower breathing produces positive serial correlations in {Delta}RR, while faster breathing induces negative ones. By visualizing serial dependencies that conventional HRV metrics miss, the second-order Poincare plot extends the classical analysis framework. This tool provides a refined method for uncovering subtle dynamical features in HRV across diverse physiological and clinical states. HighlightsO_LISecond-order Poincare plots, plotting successive differences of RR intervals ({Delta}RRi vs. {Delta}RRi+1), extend traditional Poincare analysis to reveal rapid HRV dynamics. C_LIO_LIIn a dataset of 20 healthy individuals, second-order plots filtered out slow HRV components, highlighting respiratory modulation. C_LIO_LIRing-shaped patterns in some participants indicated strong cardiorespiratory coupling, while others showed positive or negative serial correlations linked to breathing rate. C_LIO_LIA coupled-oscillator model confirmed that the ratio of respiratory to heart rate frequency determines serial correlation patterns. C_LIO_LIThis method offers a novel tool for analyzing HRV dynamics, with potential applications in physiological and clinical research. C_LI