Interpretation of Impedance Spectra for Neural Stimulation Devices in Vitro
Authors: Eluagu Cynthia C. , Biney Bernard W. , Olivo Elizabeth , Dong QiWei , Wu Yupeng , Cogan Stuart , Otto Kevin John , Orazem Mark E. 
Published: December 2024

The interpretation of the physical properties of any given electrode device requires precise models for analyzing the impedance spectroscopy data and assessment of the data consistency with the Kramers-Kronig relations. In 1992, Shannon [1] studied the influence of charge reactions and charge density on macro electrodes and proposed safe levels of electrical stimulation for macro electrodes employed in brain stimulation. However, the current density performance of neural stimulation devices is dependent on the electrode size. By considering the contributions of both charging and faradaic current densities on the impedance spectroscopy data for microelectrode and ultra-microelectrode devices, we aim to develop accurate models and provide reliable data interpretation for the physical properties of neural stimulation devices.
We conducted electrochemical impedance spectroscopy (EIS) measurement for our 32-channel ultramicroelectrode device with site diameters ranging from 5 microns to 10 microns. The experiment was performed with the Gamry Reference 600+ Potentiostat, at open circuit conditions. The three-electrode-cell configuration consists of the working electrode, an Ag/AgCl reference, and a Platinum mesh counter electrode, immersed in phosphate-buffered saline. Impedance measurements were collected at an applied AC voltage of 25 mV rms with a frequency sweep from 10 kHz to 0.2 Hz at 10 points per decade.
The limits of the EIS measurements were assessed by plotting the accuracy contour plot for the Gamry Reference 600+ Potentiostat and the Reference 600+ Potentiostat connected to the 32-channel ultramicroelectrode device by a junction box. Methods for assessing potentiostat limits followed Gamry's recommendations, including open and shorted lead EIS measurements [2]. The accuracy of impedance measurement for the ultramicroelectrode device was evaluated using loops and terminal features on the device that enabled closed-circuit and open-circuit measurements, respectively.
The EIS data for the smaller electrodes (with diameters of 10 microns and 5 microns) were influenced by the capacitance of the cables; whereas, the larger/reference electrode (with an area of 4004 square microns) was unaffected by cable capacitance but was affected by ohmic impedance. The impedance spectra of the ultramicroelectrode device were regressed with a measurement model program [3] to compute the stochastic error structure and obtain parameters for accurate interpretation of the electrodes’ properties. Most of the data was consistent with the Kramers-Kronig relations.
The circuit element for the parasitic capacitance was added to the process model to fit the data points affected by the cable capacitance at high frequency. At open circuit, the model accounted for the constant element behavior of the electrode, and mass-transfer influenced by oxygen-reduction reactions. The capacitance of the electrodes was estimated by the application of Brug’s formula to the fitting parameters obtained from the process model analysis and the measurement model regression results. The capacitance calculated with the measurement model was consistent with the values of the parasitic capacitance obtained from the process model regression analysis.

References:

[1] R. V. Shannon, "A Model of Safe Levels for Electrical Stimulation,“ IEEE Transactions on Biomedical Engineering, 39, (1992), 424-426
[2]. Accuracy contour plots: Measurement and discussion, technical report, Gamry Instruments, Warminster, PA (2016).
[3]. W. Watson and M. E. Orazem, EIS: Measurement Model Program, Version 1.8, ECSArXiv, 2023, https://doi.org/10.1149/osf.io/g2fjm.