Thoracic electrical bioimpedance in a Lissajous plane: Pre-post smoking changes and PCA of ellipse metrics

Thoracic electrical bioimpedance (TEB) provides non-invasive, radiation-free monitoring of breathing. The objective of this study was to evaluate a magnitude-phase representation of TEB as a geometric and descriptive framework for respiratory signals, using short-term smoking as a test perturbation rather than a primary physiological endpoint.

Twenty-eight adult smokers (17 women, 11 men) were measured immediately before and after smoking. TEB was acquired at 50 kHz using a four-electrode thoracic configuration, and tidal volume was recorded with a pneumotachometer. Changes in impedance magnitude (|ΔZ|) and phase (Δφ) were processed using mean-centering, Hanning windowing, Fourier transformation, Gaussian band filtering around the respiratory peak, and inverse reconstruction. Lissajous plots were constructed from Δ|Z|-Δφ signals, and geometric descriptors including semi-axes (δx, δy), inclination angle (θ), ellipse area (A), eccentricity (e), and baseline offsets were extracted. Paired statistical tests were applied according to data distribution, and principal component analysis (PCA) was used to organize multiple descriptors and reduce redundancy.

Univariate analyses showed no significant pre-post differences for most variables, except for a higher mean |ΔZ| amplitude in men. In PCA space, ellipse area (A) showed consistent differences between pre- and post-smoking distributions across sexes. These differences reflected changes in joint magnitude-phase dispersion rather than statistically significant physiological effects. Inclination, semi-axes, and eccentricity showed substantial overlap between conditions. PCA provided low-dimensional representations that facilitated visualization and comparison of magnitude-phase patterns. Significance. Representing TEB signals as magnitude-phase Lissajous ellipses provides an intuitive and reproducible geometric representation of breathing. Ellipse area is proposed as a composite geometric descriptor of joint magnitude-phase variability, intended for representation and comparison rather than direct physiological inference. This non-invasive and computationally simple framework uses standard hardware and may support future methodological developments in respiratory signal analysis. .