Abstract

The electrical behaviour of a system, such as an electrode–tissue interface (ETI) or a biological tissue, can be used for its characterization. One way of accomplishing this goal consists of measuring the electrical impedance, that is, the opposition that a system exhibits to an alternating current flow as a function of frequency. Subsequently, experimental impedance data are fitted to an electrical equivalent circuit (EEC model) whose parameters can be correlated with the electrode processes occurring in the ETI or with the physiological state of a tissue. The EEC used in this paper is a reasonable approach for simple bio-electrodes or cell membranes, assuming ideal capacitances. We use the theory of optimal experimental design to identify the frequencies in which the impedance is measured, as well as the number of measurement repetitions, in such a way that the EEC parameters can be optimally estimated. Specifically, we calculate approximate and exact D-optimal designs by optimizing the determinant of the information matrix by adapting two of the most algorithms that are routinely used nowadays (REX random exchange algorithm and KL exchange algorithm). The D-efficiency of the optimal designs provided by the algorithms was compared with the design commonly used by experimenters and it is shown that the precision of the parameter estimates can be increased.

Highlights

  • The electrical behaviour of cells, biological tissues, or electrode-tissue interfaces can be used for their characterization [1–4]

  • Experimental impedance data are fitted to an electrical equivalent circuit (EEC), which is a mathematical model that approximates the electrical behaviour of the system under study

  • The EEC parameters give information about the physiological state of a tissue or about the electrode processes occurring in the electrode-tissue interface (ETI)

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Summary

Introduction

The electrical behaviour of cells, biological tissues, or electrode-tissue interfaces can be used for their characterization [1–4]. One way to do this is by measuring the electrical impedance, that is, the opposition that the system under study exhibits to an alternating current flow as a function of frequency. The EEC parameters give information about the physiological state of a tissue or about the electrode processes occurring in the electrode-tissue interface (ETI). It should be mentioned that the experimental impedance data are analysed by using an impedance function. This impedance function can be proposed from a plausible physical theory (that predicts the impedance) or from an EEC, that aids in the visualization of the physical processes occurring in the system under study [1]

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