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

Poincaré plots are commonly used to visualize and quantify the most rapid component of heart rate variability (HRV), capturing the interdependence of successive beat-to-beat intervals. In this study, the analysis was enhanced by introducing the second-order Poincaré plot, where axes represented interval increments rather than consecutive intervals. Using data from healthy subjects at rest and during classical music listening, it was demonstrated that this method filtered out the elliptical shape observed in traditional Poincaré plots, which reflected slow HRV, thereby emphasizing faster variability. Ring-shaped patterns emerged in the plots for several participants, indicating heart rate correlation with respiratory cycles. For the other subjects, the plots displayed point clouds with positive, negative, or no serial correlation. Further analysis revealed that positive correlation arose during slow breathing, while negative correlation occurred with rapid breathing, corresponding to the ratio between respiratory frequency and heart rate. A simple oscillator model—consisting of a fast (cardiac) oscillator modulated by a slow (respiratory) oscillator—confirmed these findings. Although the study is primarily focused on HRV, the second-order Poincaré plot holds potential for broader applications in physiological and neurophysiological signal analysis.