Electrical bioimpedance spectroscopy in time-variant systems: Is undersampling always a problem?

During the last decades, Electrical Bioimpedance Spectroscopy (EBIS) has been applied mainly by using the frequency-sweep technique, across a range of many different applications. Traditionally, the tissue under study is considered to be time-invariant and dynamic changes of tissue activity are ignored by treating the changes as a noise source. A new trend in EBIS is simultaneous electrical stimulation with several frequencies, through the application of a multi-sine, rectangular or other waveform. This method can provide measurements fast enough to sample dynamic changes of different tissues, such as myocard. This high sampling rate comes at a price of reduction in SNR and the increase in complexity of devices. Although the frequency-sweep technique is often inadequate for monitoring the dynamic changes in a variant system, it can be used successfully in applications focused on the time-invariant or slowly-variant part of a system. However, in order to successfully use frequency-sweep EBIS for monitoring time-variant systems, it is paramount to consider the effects of aliasing and especially the folding of higher frequencies, on the desired frequency e.g. DC level. This paper discusses sub-Nyquist sampling of thoracic EBIS measurements and its application in the case of monitoring pulmonary oedema. It is concluded that by considering aliasing, and with proper implementation of smoothing filters, as well as by using random sampling, frequency-sweep EBIS can be used for assessing time-invariant or slowly-variant properties of time-variant biological systems, even in the presence of aliasing. In general, undersampling is not always a problem, but does always require proper consideration.