Continuous Electrode Models and Application of Exact Schemes in Modeling of Electrical Impedance Measurements

The crucial issue in electrical impedance (EI) measurements lies in the galvanic interaction between the electrodes and the investigated material. This paper brings together the basic and applied research experience and combines their results with excellent properties. Consequently, innovative precise methodologies have emerged, enabling the direct modeling of EI measurements, free from the inaccuracies often associated with numerical approaches. As an outcome of the efficiency and robustness of the applied method, the conductivity of the material and the electrodes are represented by a common piecewise function, which is used to solve the differential equation modeling of the EI measurement. Moreover, this allows the possibility for modeling the conductivity of electrodes with continuous functions, providing an important generalization of the Complete Electrode Model (CEM), which has been widely used so far. The effectiveness of the novel approach was showcased through two distinct case studies. In the first case study, potential functions within both the material and the electrodes were computed using the CEM. In the second case study, calculations were performed utilizing the newly introduced continuous electrode model. The simulation results suggest that the new method is a powerful tool for biological research, from in vitro experiments to animal studies and human applications.