Optimal multisine excitation design for broadband electrical impedance spectroscopy

Abstract

Electrical impedance spectroscopy (EIS) can be used to characterize biological materials in applications ranging from cell culture to body composition, including tissue and organ state. The emergence of cell therapy and tissue engineering opens up a new and promising field of application. While in most cases classical measurement techniques based on a frequency sweep can be used, EIS based on broadband excitations enables dynamic biological systems to be characterized when the measuring time and injected energy are a constraint. Myocardial regeneration, cell characterization in micro-fluidic systems and dynamic electrical impedance tomography are all examples of such applications. The weakness of such types of fast EIS measuring techniques resides in their intrinsic loss of accuracy. However, since most of the practical applications have no restriction over the excitation used, the input power spectrum can be appropriately designed to maximize the accuracy obtained from the measurements. This paper deals with the problem of designing the optimal multisine excitation for electrical bioimpedance measurements. The optimal multisine is obtained by the minimization of the Cramer–Rao lower bound, or what is the same, by maximizing the accuracy obtained from the measurements. Furthermore, because no analytical solution exists for global optimization involving time and frequency domains jointly, this paper presents the multisine optimization approach partially in both domains and then combines the results. As regards the frequency domain approach, a novel contribution is made for the multisine amplitude power spectrum. In the time domain, multisine is optimized by reducing its crest factor. Moreover, the impact on the information and accuracy of the impedance spectrum obtained from using different multisine amplitude power spectra is discussed, as well as the number of frequencies and frequency distributions. The theory is supported by a set of validation measurements when exciting with the optimal and flat multisine signals and compared to a single frequency ac impedance analyzer when characterizing an RC circuit. In vivo healthy myocardium tissue electrical impedance measurements show that broadband EIS based on multisine excitations enable the characterization of dynamic biological systems.

The Theory and Fundamentals of Bioimpedance Analysis in Clinical Status Monitoring and Diagnosis of Diseases

“…Use of multi-sine excitation signals in bioimpedance measurements that is proposed in [78,79] helped increase the accuracy of the measured bioimpedance parameters. It has been validated using a set of optimal multi-sine measurements on 2R-1C equivalent electrical circuits, then applied on healthy myocardium tissue.…”

Interpulse multifrequency electrical impedance measurements during electroporation of adherent differentiated myotubes

“…Other attempts to study fast pore dynamics are based in time domain methods such as time-domain reflectometry [28] or time-domain dielectric spectroscopy [18]. In this work, a multisine-based approach [29] is used to perform for the first time fast EIS measurements (1 spectrum per millisecond) during the interpulse electroporation interval, with the aim of studying pore creation and resealing dynamics.…”

“…From all broadband excitation signals proposed in bioimpedance measurements, we used multisine excitation based on previous studies developed by our group (the reader is referred to the work by Sánchez et al for furher details [29]). Summarizing, the multisine burst consisted of 21 frequencies following a Bilateral Quasi-Logarithmic (BQL) distribution from 5 kHz to 1.313 MHz that was designed to concentrate a higher number of frequencies around the impedance relaxation central frequency and to minimize the intermodulation products at the selected frequencies, thereby increasing the Signal to Noise Ratio (SNR) and reducing the injected energy to the system [34].…”

Aspects of Using Chirp Excitation for Estimation of Bioimpedance Spectrum

“…For that reason, several types of broadband excitation signals (e.g., Maximal Length Sequence (Gawad et al, 2007), multisine (Sanchez et al 2011)) are preferable. However, in this chapter, we will focus on the use of chirp excitation due to several advantages of it: wide and flat amplitude spectrum (Nahvi & Hoyle, 2009) together with independent scalability in the time and frequency domain.…”