The bioimpedance measurement/identification of time-varying biological systems Z(ω, t) by means of electrical impedance spectroscopy (EIS) is still a challenge today. This paper presents a novel measurement and identification approach, the so-called parametric-in-time approach, valid for time-varying (bio-)impedance systems with a (quasi) periodic character. The technique is based on multisine EIS. Contrary to the widely used nonparametric-in-time strategy, the (bio-)impedance Z(ω, t) is assumed to be time-variant during the measurement interval. Therefore, time-varying spectral analysis tools are required. This new parametric-in-time measuring/identification technique has experimentally been validated through three independent sets of in situ measurements of in vivo myocardial impedance. We show that the time-varying myocardial impedance Z(ω, t) is dominantly periodically time varying (PTV), denoted as ZPTV(ω, t). From the temporal analysis of ZPTV(ω, t), we demonstrate that it is possible to decompose ZPTV(ω, t) into a(n) (in)finite sum of fundamental (bio-)impedance spectra, the so-called harmonic impedance spectra (HIS) Zk(ω)s with [Formula: see text]. This is similar to the well-known Fourier series of a periodic signal, but now understood at the level of a periodic system's frequency response. The HIS Zk(ω)s for [Formula: see text] actually summarize in the bi-frequency (ω, k) domain all the temporal in-cycle information about the periodic changes of Z(ω, t). For the particular case k = 0 (i.e. on the ω-axis), Z0(ω) reflects the mean in-cycle behavior of the time-varying bioimpedance. Finally, the HIS Zk(ω)s are directly identified from noisy current and voltage myocardium measurements at the multisine measurement frequencies (i.e. nonparametric-in-frequency).

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The time-variant frequency response function (TV-FRF) uniquely characterizes the dynamic behaviour of a linear timevariant (LTV) system. This paper proposes a method for estimating nonparametrically the dynamic part of the TV-FRF from known input, noisy output observations. The arbitrary time-variation of the TV-FRF is modelled by Legendre polynomials. In opposition to existing solutions, the proposed method is applicable to arbitrary inputs.

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.

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