Analysis of the Peak Resistance Frequency Method

Abstract

Objective: This study analyzes the peak resistance frequency (PRF) method described by Mercanzini et al., a method that can easily extract the tissue resistance from impedance spectroscopy for many neural engineering applications but has no analytical description thus far.

Methods: Mathematical analyses and computer simulations were used to explore underlying principles, accuracy, and limitations of the PRF method.

Results: The mathematical analyses demonstrated that the PRF method has an inherent but correctable deviation dependent on the idealness of the electrode-tissue interface, which is validated by simulations. Further simulations show that both frequency sampling and noise affect the accuracy of the PRF method, and in general, it performs less accurately than least squares methods. However, the PRF method achieves simplicity and reduced measurement and computation time at the expense of accuracy.

Conclusion: From the qualitative results, the PRF method can work with reasonable precision and simplicity, although its limitation and the idealness of the electrode-tissue interface involved should be taken into consideration.

Significance: This paper provides a mathematical foundation for the PRF method and its practical implementation.

Fig. 1

The electrode-tissue interface model with parasitic capacitance from the leads and other components in the system.

Fig. 2

The configuration of the microelectrodes. The inner pole consists of 80/20 Pt–Ir alloy, and the outer pole is stainless steel.

Fig. 3

Simulated impedance spectra for the double layer capacitance model with varying tissue resistivity (ρ = 0.5, 1, 2, 4, 8, 16, and 32 Ω·m; arrow indicates increasing resistivity). |Z_PRF| and φ_PRF are marked with asterisks.

Fig. 4

Simulated impedance spectra for the dependent double layer CPE model with varying tissue resistivity (same as Fig. 3). The PRF and |Z_PRF| are given for both simulation and calculation (upper panel, squares and circles with center dots, respectively), and only the simulated φ_PRF is shown (lower panel, asterisks). φ_PRF is independent of the tissue resistance; the impedance magnitude shows dispersion at low frequency.

Fig. 5

Simulated impedance spectra for the independent double layer CPE model with varying tissue resistivity (same as Fig. 3). Markers are the same as Fig. 4. φ_PRF increases with tissue resistance; impedance magnitude at low frequency is independent of tissue resistivity.

Fig. 6

Log–log plots of PRF versus resistivity for the CPE models. R² values for the log–log fitting are larger 0.99999.

Fig. 7

Relative errors (mean and standard deviation) of the resistivity extracted using the PRF method from 100 simulated impedance spectra with different frequency sampling density and noise levels. The curves where slightly shifted in the horizontal direction to avoid overlap of the error bars.

Fig. 8

Relative errors (mean and standard deviation) of the resistivity extracted using the least squares method from the same 100 simulated impedance spectra as in Fig. 7.