Knösche, T.

Laukner, M.

Lindner, D.

Petkovic, B.

Pliquett, U.

Poßner, L.

Seebeck, L.

Weise, K.

Wilhelmy, F.

Ziolkowski, M.

English

MPG.PuRe

   International Journal of Bioelectromagnetism Vol. 23, No. 1, pp. xx - xx, May 2021.  www.ijbem.org     A four-point measurement probe for brain tissue conductivity and permittivity characterization Lucas Poßnera, Lydia Seebeckb, Matthias Lauknerb, Florian Wilhelmyc, Dirk Lindnerc, Uwe Pliquettd, Bojana Petkovice, Marek Ziolkowskie, Thomas R. Knöschea and Konstantin Weisea,e   a Methods and Development Group Brain Networks, Max Planck Institute for Human Cognitive and Brain Sciences, Stephanstr. 1a, 04103 Leipzig, Germany b Institute for Electronics and Biomedical Information Technology, Leipzig University of Applied Sciences, Wächterstr. 13, 04107 Leipzig, Germany c Department of Neurosurgery, University Hospital Leipzig, Liebigstraße 20, 04103, Leipzig, Germany d Institute for Bioprocessing and Analytical Measurement Techniques, Rosenhof 1, 37308 Heilbad Heiligenstadt, Germany  e Advanced Electromagnetics Group, TU Ilmenau, Helmholtzplatz 2, 98693 Ilmenau, Germany Correspondence: Lucas Poßner, Methods and Development Group Brain Networks, Max Planck Institute for Human Cognitive and Brain Sciences,  Stephanstr. 1a, 04103 Leipzig, Germany Email: lpossner@cbs.mpg.de  Abstract. We present a measurement probe consisting of four platinum electrodes fused into soda-lime glass. The probe is based on a four-terminal sensing technique that uses separate pairs of current-carrying and voltage-sensing electrodes and performs more accurate measurements than the simpler and more usual two-terminal sensing technique. The electrodes are aranged within an area of 1 mm² allowing for local characterization of different brain tissues. The operation of the probe is demonstrated in situ on post mortem porcine brain tissue by measuring the impedance spectra of grey and white matter in a frequency range of 1 kHz < 𝑓 < 1 MHz. The conductivity and relative permittivity are derived from the impedance spectra using the geometry factor of the probe. The geometry factor is obtained experimentally by measuring the impedances of an electrolytical dilution series with known conductivities. The obtained conductivity of grey matter is in the order of 0.11 S/m and of white matter is in the order of 0.07 S/m over the acquired frequency range. Keywords: Bioimpedance, Bioimpedance spectroscopy, Electrodes, Brain tissue  1. Introduction The electric properties of in vivo human brain tissue are characterized by its electric conductivity and its relative permittivity. These properties are substantial for the modeling of invasive and non-invasive brain measurement and stimulation techniques, such as EEG, MEG, TMS, TES and DBS [Saturnino et al. 2019, Peterchev et al. 2012, Cho et al. 2015]. Further, these properties can be used for the classification of pathological tissue, such as glioma and other types of brain tumors [Jahnke et al. 2013]. These applications rely on the precise knowledge of the electric material parameters of brain tissue. Previous studies were conducted (i) taking a small number of subjects (≈10); (ii) using inappropriate measurement techniques such as monopolar measurements; (iii) measuring only at one frequency [Latikka et al. 2001, Koessler et al. 2017, Latikka and Eskola 2019]. In a previous study [Poßner et al. 2020] we used a commercial brain stimulation system and a two-point measurement probe to acquire the impedance of (which was not certified by peer review) is the author/funder. All rights reserved. No reuse allowed without permission. The copyright holder for this preprintthis version posted May 7, 2021. ; https://doi.org/10.1101/2021.04.29.441988doi: bioRxiv preprint  2 post mortem porcine brain tissue and showed that it is possible to distinguish grey and white matter tissue based on the measured impedances. Further investigations have shown that polarization effects at the electrodes of the two-point probe complicate the derivation of conductivity and permittivity values. In this work, we present a proof-of-principle study using a custom-made four-point measurement probe (Kurt-Schwabe-Institut für Meß- und Sensortechnik Meinsberg e.V., 04736 Waldheim, Germany) to obtain the conductivity and relative permittivity spectra of grey and white matter of post mortem porcine brain. 2. Methods 2.1 Measurement setup The probe consists of four platinum electrodes fused into soda-lime glass. The probe and an enlarged section of the tip are shown in Fig. 1. The electrodes are used in a four-point configuration with two current-carrying electrodes (E2, E3) and two voltage-sensing electrodes (E1, E4). This configuration minimizes the influence of the electrode polarization. The probe was connected to a commercial impedance analyzer (ISX-3 mini, Sciospec Scientific Instruments GmbH, 04828 Bennewitz, Germany). The impedances were measured within a frequency range of 1 kHz < 𝑓 < 1 MHz and with a current amplitude of 𝐼 = 100 μA.    Figure 1.  (a) Measurement probe consisting of four platinum electrodes (E1-E4) fused into soda-lime glass; (b) Magnification of the probe tip (frontal view); (c) Magnification of the probe tip (side view). (All measures in mm) 2.2 Measurement of post mortem porcine brain impedance The measurements were performed on post mortem porcine brain at its in situ position inside the head. The pig was regularly slaughtered in a slaughterhouse using electric stunning and the head was separated from the body. By the time of the measurement, it was dead for less than 2 hours. We performed a craniotomy on the porcine head, which left the brain undamaged. The cortex was cut with a scalpel and the impedances of grey and white matter were measured. 2.3 Derivation of the conductivity and relative permittivity The admittance 𝑌 = 1 𝑍⁄  of biological tissue is assumed to not have any inductive properties. Therefore, it can be written as 𝑌 = 𝐺 + 𝑗𝜔𝐶, where 𝐺 is the conductance and 𝐶 is the capacitance of the tissue. This can be written as the quotient of the complex conductivity 𝜎 and a geometry factor 𝑘: 𝑌 =(which was not certified by peer review) is the author/funder. All rights reserved. No reuse allowed without permission. The copyright holder for this preprintthis version posted May 7, 2021. ; https://doi.org/10.1101/2021.04.29.441988doi: bioRxiv preprint  3 𝜎 𝑘⁄ = (𝜎 + 𝑗𝜔𝜀0𝜀𝑟) 𝑘⁄ . The geometry factor 𝑘 depends on the geometry of the probe and the electric field distribution in the tissue. Using this relationship, the complex conductivity 𝜎 can be obtained from the measured admittance 𝑌 . This procedure was calibrated by obtaining the geometry factor experimentally. An electrolytical dilution series of saline was prepared with an initial concentration of 𝑐 = 194 m mol/l. The solution was diluted 5 times. After each step, the conductivity was measured using a conductivity meter (Cobra SMARTsense, PHYWE Systeme GmbH und Co. KG, 37079 Göttingen, Germany). The concentrations of the solutions and the corresponding conductivities are shown in Table 1.  Table 1. Concentration and conductivity of the prepared solutions Dilution Initial 1 2 3 4 5 Concentration/(m mol/l) 194 97 48.5 24.3 12.1 6.1 Conductivity/(S/m) 2.071 1.041 0.521 0.266 0.136 0.073  We used the probe to measure the admittance of the solutions within a frequency range of 100 Hz <𝑓 < 10 kHz. The absolute value of the admittance |𝑌| was constant and linear with respect to the conductivity 𝜎 and the phase angle 𝜑 was below 5°. Therefore, the susceptance of the admittance is neglected, and it can be set 𝑌 = 𝐺. The geometry factor 𝑘 is calculated by 𝑘 = 𝜎 𝐺⁄ . The obtained values are shown in Fig. 2. The geometry factor 𝑘 is calculated as 𝑘 = 219.78 1 m⁄ .    Figure 2. Relationship between the measured conductance and the conductivity of the solutions. 3. Results The impedances of grey and white matter were obtained in a measurement series with ten repetitions. This included the repeated application of the measurement probe on the respective tissues. The absolute values of the impedances and the corresponding phase angles are shown in Fig. 3(a) and (b), respectively, for both grey and white matter. The impedances differ significantly between the tissues (𝑝 ≪ 0.001, 𝑓 = 10 kHz). The electric conductivity and the relative permittivity of grey and white matter are calculated from the measured impedances by applying the previously obtained geometry factor 𝑘. The results are shown in Fig. 3(c) and (d), respectively.  4. Discussion The obtained conductivities of grey and white matter are in the order of 0.11 S/m and 0.07 S/m, respectively, over the acquired frequency range. These values are in the range of reported literature values obtained from human brain tissue (IT’IS database, 10 kHz: GM: 0.115 S/m; WM: 0.0695 S/m and Wagner et al. (2004), GM: 0.276 S/m; WM: 0.126 S/m). Differences can be explained by the different species and that our measurements were performed post mortem. The obtained relative permittivity values are lower than the reported literature values (IT’IS database, 10 kHz: GM: 22200; WM: 12500). Further, negative values were obtained at frequencies 10 kHz <  𝑓 < 50 kHz . This is due to the inductive behavior of the measured impedance in this frequency range which could arise from leakage currents through stray capacitances in the measurement chain. It can be observed that the variability between repeated applications of the measurement probe is higher for grey matter. The reason might be the inhomogeneity of this tissue originating from the layered structure of the cerebral cortex. (which was not certified by peer review) is the author/funder. All rights reserved. No reuse allowed without permission. The copyright holder for this preprintthis version posted May 7, 2021. ; https://doi.org/10.1101/2021.04.29.441988doi: bioRxiv preprint  4   Figure 3. (a) Absolute values of the obtained impedances; (b) Phase angles of the obtained impedances; (c) Calculated conductivities; (d) Calculated permittivities. 5. Conclusions With the presented four-point measurement probe it is possible to perform reliable impedance measurements. To obtain significant conductivity and permittivity values, the acquired impedances need to be compensated with respect to the electrical properties of the measurement chain (measurement fixtures, measurement probe) which is subject of future work. References Cho, J. H., Vorwerk, J., Wolters, C. H., & Knösche, T. R. (2015). Influence of the head model on EEG and MEG source connectivity analyses. Neuroimage, 110, 60-77. IT’IS database: https://itis.swiss/virtual-population/tissue-properties/database/dielectric-properties/ (accessed: 06.05.2021) Jahnke, H. G., Heimann, A., Azendorf, R., Mpoukouvalas, K., Kempski, O., Robitzki, A. A., & Charalampaki, P. (2013). Impedance spectroscopy—an outstanding method for label-free and real-time discrimination between brain and tumor tissue in vivo. Biosensors and Bioelectronics, 46, 8-14. Koessler, L., Colnat‐Coulbois, S., Cecchin, T., Hofmanis, J., Dmochowski, J. P., Norcia, A. M., & Maillard, L. G. (2017). In‐vivo measurements of human brain tissue conductivity using focal electrical current injection through intracerebral multicontact electrodes. Human brain mapping, 38(2), 974-986. Latikka, J., & Eskola, H. (2019). The resistivity of human brain tumours in vivo. Annals of biomedical engineering, 47(3), 706-713. Latikka, J., Kuurne, T., & Eskola, H. (2001). Conductivity of living intracranial tissues. Physics in Medicine & Biology, 46(6), 1611. Peterchev, A. V., Wagner, T. A., Miranda, P. C., Nitsche, M. A., Paulus, W., Lisanby, S. H., ... & Bikson, M. (2012). Fundamentals of transcranial electric and magnetic stimulation dose: definition, selection, and reporting practices.  Brain stimulation, 5(4), 435-453. Poßner, L., Laukner, M., Wilhelmy, F., Lindner, D., Pliquett, U., Petkovic, B., ... & Weise, K. (2020). In situ impedance measurements on postmortem porcine brain. Current Directions in Biomedical Engineering, 6(3), 143-146. Saturnino, G. B., Thielscher, A., Madsen, K. H., Knösche, T. R., & Weise, K. (2019). A principled approach to conductivity uncertainty analysis in electric field calculations. Neuroimage, 188, 821-834. Wagner, T. A., Zahn, M., Grodzinsky, A. J., & Pascual-Leone, A. (2004). Three-dimensional head model simulation of transcranial magnetic stimulation. IEEE Transactions on Biomedical Engineering, 51(9), 1586-1598.   (which was not certified by peer review) is the author/funder. All rights reserved. No reuse allowed without permission. The copyright holder for this preprintthis version posted May 7, 2021. ; https://doi.org/10.1101/2021.04.29.441988doi: bioRxiv preprint 

A four-point measurement probe for brain tissue conductivity and permittivity characterization

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A four-point measurement probe for brain tissue conductivity and permittivity characterization

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