Harmonic impedance spectra identification from time-varying bioimpedance: theory and validation

The harmonic impedance spectra (HIS) of a time-varying bioimpedance Z(ω, t) is a new tool to better understand and describe complex time-varying biological systems with a distinctive periodic character as, for example, cardiovascular and respiratory systems. In this paper, the relationship between the experimental setup and the identification framework for estimating Z(ω, t) is set up. The theory developed applies to frequency response based impedance measurements from noisy current-voltage observations. We prove theoretically and experimentally that a voltage source (VS) and a current source (CS) analogue front end-based measurement lead, respectively, to a closed-loop and an open-loop HIS identification problem. Next, we delve into the estimation of the HIS by treating Z(ω, t), on the one hand, as a linear time-invariant (LTI) system within a short time window; and, on the other hand, as a linear periodically time-varying (PTV) system within the entire measurement interval. The LTI approach is based on the short-time Fourier transform (STFT), while the PTV approach relies on the information that is present in the skirts of the voltage and/or current spectra. In addition, direct and indirect methods are developed for estimating the HIS by using simple as well as more sophisticated techniques. Ultimately, the HIS and their uncertainty bounds are estimated from real measurements conducted on a periodically varying dummy impedance.