On the calculation of theD-optimal multisine excitation power spectrum for broadband impedance spectroscopy measurements

Abstract

The successful application of impedance spectroscopy in daily practice requires accurate measurements for modeling complex physiological or electrochemical phenomena in a single frequency or several frequencies at different (or simultaneous) time instants. Nowadays, two approaches are possible for frequency domain impedance spectroscopy measurements: (1) using the classical technique of frequency sweep and (2) using (non-)periodic broadband signals, i.e. multisine excitations. Both techniques share the common problem of how to design the experimental conditions, e.g. the excitation power spectrum, in order to achieve accuracy of maximum impedance model parameters from the impedance data modeling process. The original contribution of this paper is the calculation and design of the D-optimal multisine excitation power spectrum for measuring impedance systems modeled as 2R-1C equivalent electrical circuits. The extension of the results presented for more complex impedance models is also discussed. The influence of the multisine power spectrum on the accuracy of the impedance model parameters is analyzed based on the Fisher information matrix. Furthermore, the optimal measuring frequency range is given based on the properties of the covariance matrix. Finally, simulations and experimental results are provided to validate the theoretical aspects presented.

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.…”

D-optimal input design for identification of a continuous system using sum of squares polynomial

“…Multisine input design has been considered in [14], [7], [8], [16]. This paper is inspired from [8].…”

“…A constrained optimization problem with a D-optimal cost function (8) and input-output power constraints were considered. In [8], the optimization variables were the moments, r 2k = ∞ 0 ω 2k φ u (ω)dω, k = 0, 1, · · ·2n. Once the optimal moments were determined, the input was parametrized as a multisine with…”

A pilot spectroscopy study on time-varying bioimpedance during electrically-induced muscle contraction

“…based on multisines signals [10], [11], [12]. Using the multifrequency approach, many frequencies are applied simultaneously (B) and the time to acquire a complete EIM spectrum is drastically reduced making it possible to measure the instantaneous impedance changes and temporal evolution of dynamic EIM, for example, during muscle contraction and relaxation and to collect both nonand fatigued muscle data.…”