A 4-pole Theory-Based Compensation Method using Multiple Loads for Impedance Spectroscopy of Porcine Brain Tissue

Abstract Accurate determination of the electrical properties of brain tissue—conductivity and relative permittivity—is essential for modeling and optimizing neurostimulation and neuroimaging and modulation techniques such as EEG, MEG, TMS, and TES. However, large discrepancies in reported conductivity values highlight the methodological challenges associated with impedance measurements. In this study, we present a systematic evaluation of compensation methods in impedance spectroscopy to improve measurement accuracy using a self-developed four-point platinum electrode designed for biological tissue applications. Three compensation algorithms—open-short, open-short-load, and multiple-load—were implemented and compared using an RC parallel test circuit that emulated typical measurement conditions, with load resistances ranging from 250 Ω to 5000 Ω. Quantitative error analysis demonstrated that the multiple-load method achieved the lowest normalized root mean square error (3.4%) and superior stability across frequencies from 100 Hz to 1 MHz. The calibrated probe was subsequently applied to post mortem porcine brain tissue, yielding conductivity values of grey matter of 0.109 S/m and white matter of 0.074 S/m. These results are significantly lower than standard simulation parameters of 0.275 S/m, and 0.126 S/m for grey and white matter, respectively. Finite-element simulations revealed that using the measured conductivities increased electric field predictions by 2.1% for TMS and 46% for TES in the maximum electric field magnitude, respectively. Our findings demonstrate that accurate impedance compensation is critical for reliable characterization of brain tissue and for enhancing the precision of neurostimulation modeling in the future.