Optimal Experimental Design for Parametric Identification of the Electrical Behaviour of Bioelectrodes and Biological Tissues

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.