Periodic Distribution Entropy: Unveiling the complexity of physiological time series through multidimensional dynamics

Physiological signals, manifested as time series, reflect the internal transitions of physiological systems. Analyzing their complexity provides insights into the system's core characteristics. However, traditional techniques based on one-dimensional time series waveforms are limited, especially in the presence of noise. We introduce the Periodic Distribution Entropy (PDEn) as a solution. PDEn employs a high-dimensional strategy to model low-dimensional signals, aiming to measure complexity through the variability of attractor return map orbits. Our simulations indicate that PDEn is more resilient against different types and intensities of observational noise than other methods. In practical tests with real-world signal, where dynamical noise introduces more complexity, PDEn adeptly identifies atrial fibrillation from ECG data, exceeding other techniques in both effectiveness and consistency. Furthermore, PDEn efficiently distinguishes between healthy individuals and Parkinson's patients from the more intricate integrated multi-sensor gait signals. Following an analysis of physical mechanisms, we highlight PDEn's inherent advantage over alternative methods and, based on this, elucidate the connection between orbit heterogeneity and physiological pathological changes. Emphasizing its quantification strategy, PDEn stands out in precision and robustness, especially in detecting disease states from signals with noise, captured by medical devices in the real world.