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

Heart rate variability (HRV) is a non-invasive biomarker of autonomic nervous system activity, commonly analyzed using a Poincaré plot. This plot visualizes correlations between successive heartbeats (RR _i vs. RR _i+1 ) and quantifies autonomic regulation through SD1 and SD2 parameters. We introduce a second-order Poincaré plot, a natural extension that clarifies serial dependencies by plotting successive differences in RR intervals (ΔRR _i vs. ΔRR _i+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 ΔRR, while faster breathing induces negative ones. By visualizing serial dependencies that conventional HRV metrics miss, the second-order Poincaré 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.