Reconsider phase reconstruction in chronobiological research from the modern signal processing perspective

Background: Phase is the most fundamental physical quantity when we study an oscillatory time series, and there are a lot of tools aiming to estimate phase. Most existing algorithms are developed based on the analytic function model. Unfortunately, this approach might not be suitable for several modern signals, particularly biomedical signals, due to the intrinsic complicated structure, including (possibly) multiple oscillatory components, each with time- varying frequency, amplitude, and non-sinusoidal oscillation. Due to the lack of consensus of model and algorithm, phases estimated from signals simultaneously recorded from different sensors for the same physiological system from the same subject might be different. All these might challenge reproducibility, communication, and scientific interpretation. Objectives: We need a standardized tool with theoretical supports over a unified model to extract phase. Methods: We systematically summarize existing models for phase and algorithms and discuss why we may face challenges with them. Then we introduce the adaptive non-harmonic model (ANHM) and how to define phase with this model and suggest applying algorithms that can separate oscillatory components and recover their fundamental components, e.g., the synchrosqueezing transformation (SST) or the continuous wavelet transform (CWT) with aproper time-varying bandpass filter, to extract the phase. Results: Two databases with different physiological signals, one for respiration and one for hemodynamic, with different clinical applications are explored. We report that the extracted phases following the definition, if properly extracted, are more uniform across different recording modalities and are immune to non-sinusoidal oscillation compared with traditional approaches. Conclusions: The proposed combination of ANHM and algorithms alleviates the above- mentioned challenges. We expect its scientific impact on a broad range of applications.