Adaptive Cardiorespiratory Separation With Harmonic Models and Filters: The Case of Electrical Impedance Tomography

Cardiorespiratory monitoring methods are vital in clinical and personal healthcare contexts, continuously delivering comprehensive insights into patient health. Among them, electrical impedance tomography, a non-invasive imaging modality, uniquely enables spatially resolved, real-time monitoring of both cardiac and respiratory functions. However, separating cardiac and respiratory signals remains a challenge due to spectral and spatial overlap, heart-lung interactions and nonstationarity. Existing signal processing techniques face limitations in adaptiveness, harmonic overlap handling, and real-time feasibility, restricting their clinical adoption. This work introduces two novel adaptive model-based approaches derived from a harmonic framework inspired by source-filter theory: harmonic least-squares, a deterministic estimator; and harmonically-constrained filtering, which employs harmonic priors and noise covariance approximations towards optimal separation. These algorithms were systematically validated using extensive synthetic and real-world datasets across diverse clinical scenarios. Monte Carlo simulations with a dynamic synthesizer and machine learning surrogate models provided robust performance evaluations, with insights into algorithm behavior through accumulated local effect plots. The proposed methods demonstrated superior performance compared to state-of-the-art approaches and achieved real-time processing capability, making them promising for integration into medical devices. Despite these advancements, further improvements in noise modelling, performance guarantees, and processing efficiency remain potential areas for future development.