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 . 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 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 Z k(ω)s are directly identified from noisy current and voltage myocardium measurements at the multisine measurement frequencies (i.e. nonparametric-in-frequency). © 2013 Institute of Physics and Engineering in Medicine.
- (periodically) time-varying electrical bioimpedance
- electrical impedance spectroscopy
- harmonic impedance spectra
- in vivo myocardial impedance
- multisine excitations
- parametric-in-time and nonparametric-in- frequency identification