Circular Phase-Space Indices: New Biomarkers for Heart Rate Modeling and Classification

Background/Introduction: In recent decades, nonlinear biomedical signal processing has captured the attention of many researchers. While existing methods (e.g. entropy, Lyapunov exponents) focus on abstract measures of signal irregularity, this study introduces a geometrically interpretable framework based on a novel circular phase-space reconstruction. This study intends to propose innovative biomarkers by analyzing the spatial density of the signal’s trajectory in this unique phase-space. Methods: Unlike traditional Poincaré plots, a circular phase-space is constructed by mapping the time series into (sin([Formula: see text], cos([Formula: see text], confining all points to a unit circle. To quantify the trajectory’s geometry, hypothetical circles (radii 0.1-1.0) are superimposed, and the normalized intersection counts between the trajectory and each circle are computed. These indices are extracted from the meditators’ and nonmeditators heart rate (HR) signals. The efficiency of the measures is assessed in both classification and modeling problems. For a typical classification problem, the performance of the [Formula: see text]-nearest neighbor ([Formula: see text]NN), support vector machine (SVM), and Naïve Bayes (NB) is appraised. For a modeling problem, a simple polynomial equation of degree two is proposed. Results: The results indicated that the proposed biomarkers, derived from the geometric structure of the circular phase-space, achieve 90% classification accuracy and enable dynamical modeling via a quadratic polynomial. Conclusions: In conclusion, this work pioneers the use of circular phase-space intersections to characterize HR dynamics, offering simplicity and interpretability over conventional nonlinear methods.