Time-invariant measurement of time-varying bioimpedance using vector impedance analysis

When stepped-sine impedance spectroscopy measurements are carried out on (periodically) time-varying bio-systems, the inherent time-variant (time-periodic) parts are traditionally ignored or mitigated by filtering. The latter, however, lacks theoretical foundation and, in this paper, it is shown that it only works under certain specific conditions. Besides, we propose an alternative method, based on multisine signals, that exploits the non-stationary nature in time-varying bio-systems with a dominant periodic character, such as cardiovascular and respiratory systems, or measurements interfered with by their physiological activities. The novel method extracts the best—in a mean square sense—linear time-invariant (BLTI) impedance approximation ZBLTI(jω) of a periodically time-varying (PTV) impedance ZPTV(jω, t) as well as its time-periodic part. Relying on the geometrical interpretation of the BLTI concept, a new impedance analysis tool, called vector impedance analysis (VIA), is also presented. The theoretical and practical aspects are validated through measurements performed on a PTV dummy circuit and on an in vivo myocardial tissue.