An Empirical-Mathematical Approach for Calibration and Fitting Cell-Electrode Electrical Models in Bioimpedance Tests

Abstract

This paper proposes a new yet efficient method allowing a significant improvement in the on-line analysis of biological cell growing and evolution. The procedure is based on an empirical-mathematical approach for calibration and fitting of any cell-electrode electrical model. It is valid and can be extrapolated for any type of cellular line used in electrical cell-substrate impedance spectroscopy (ECIS) tests. Parameters of the bioimpedance model, acquired from ECIS experiments, vary for each cell line, which makes obtaining results difficult and—to some extent-renders them inaccurate. We propose a fitting method based on the cell line initial characterization, and carry out subsequent experiments with the same line to approach the percentage of well filling and the cell density (or cell number in the well). To perform our calibration technique, the so-called oscillation-based test (OBT) approach is employed for each cell density. Calibration results are validated by performing other experiments with different concentrations on the same cell line with the same measurement technique. Accordingly, a bioimpedance electrical model of each cell line is determined, which is valid for any further experiment and leading to a more precise electrical model of the electrode-cell system. Furthermore, the model parameters calculated can be also used by any other measurement techniques. Promising experimental outcomes for three different cell-lines have been achieved, supporting the usefulness of this technique.

Characterization and Monitoring of Titanium Bone Implants with Impedance Spectroscopy

“…The use of electrical impedance spectroscopy has been studied for cell culture monitoring in different works for a wide variety of applications, such as the study of cell proliferation [ 1 , 27 , 28 , 29 ], cell toxicity [ 30 ], or cellular differentiation [ 31 ]. In [ 28 ], an oscillation-based circuit was proposed for the measurement of electrical impedance in cell cultures. Figure 6 a shows the equivalent model proposed in [ 28 ] for modeling the electrical behavior of the cell culture and instrumentation system.…”

“…In [28], an oscillation-based circuit was proposed for the measurement of electrical impedance in cell cultures. Figure 6a shows the equivalent model proposed in [28] for modeling the electrical behavior of the cell culture and instrumentation system. toxicity [30], or cellular differentiation [31].…”

“… Electrical circuits used to model interfaces between impedance measurement electrodes and biological structures. ( a ) Electrical circuit used in [ 28 ], where Rgap models the resistance between the cell layer and the electrodes, Rs is the resistance between the cell layer and the reference electrode, R 1 and C 1 form the impedance of the area of the electrodes that is not covered by cells, and R 2 and C 2 model the impedance of the area of the electrodes covered by cells. ( b ) Electrical circuit used in [ 3 ], where R 0 models the overall electrolyte bulk behavior, R 1 and C 1 model the slower electrochemical phenomena (such as polarization due to mass diffusion), and R 2 and C 2 model the faster electrochemical phenomena (such as the polarization due to charge transfer).…”

Electrical Modeling of the Growth and Differentiation of Skeletal Myoblasts Cell Cultures for Tissue Engineering

“…An initial electrical model of the cell culture can be drafted based on some previous works [18,23] (see Figure 7a). R gap models the resistance between the cell layer and the electrodes; R s models the resistance between the cell layer and the reference electrode; R 1 and C 1 form the impedance of the area of the electrodes that are not covered by cells; and R 2 and C 2 model the impedance of the area of the electrodes that is covered by cells.…”

“…Equation 1is reproduced following the equations of the oscillation-based test model described in [18,23]:…”