Sodium chloride solution
For reference purposes, we used NaCl (Sodium chloride ≥99 %, Carl Roth GmbH + Co. KG, Karlsruhe, Germany) to prepare the electrolyte solutions for providing the charge carrier in the physical head phantom. The conductivity of the sodium chloride solution was tested with a ProfiLine Cond 3310 (Xylem Analytics Germany Sales GmbH & Co. KG, Weilheim, Germany).
Agarose
We applied agarose (Agarose Broad Range, Carl Roth GmbH + Co. KG, Karlsruhe, Germany) as a solidifying agent in the NaCl solution with sufficient concentration to yield the mechanical strength of synthetic skins. We added 2 wt%, 3 wt%, and 4 wt% agarose to the heated electrolyte solution (approx. 65 °C) while stirring constantly. The milky dispersion was heated to approx. 80 °C until a clear solution emerged. The agarose electrolyte solution was kept in the liquid state, at around 65 °C, until poured into the casting mold. After cooling to room temperature, the agarose electrolyte solution formed a mechanically stable hydrogel.
Gypsum
In gypsum, the solid crystal embodies a structural conductivity barrier. We selected Stewaform (Glorex GmbH, Rheinfelden, Germany) as casting compound in order to allow the formation of a realistic skull-shaped compartment. The Stewaform powder was mixed with either deionized water or 0.17 % NaCl solution in the ratio of 2:1 to form a casting compound and poured in negative molds of the desired form and let dry at 40 °C for 2 hours. To protect the gypsum structures from dissolving when coming in contact with the NaCl solution, we infiltrated the gypsum for one minute in a two-component epoxy resin XTC-3d (Smooth-On Inc., Macungie, PA, USA) at a ratio of 2:1 (epoxy resin:hardener). The gypsum was then dried again at 40 °C for 10 min.
Reed sticks
We fit 80 reed sticks (diffusor sticks, Jörn Poppenhäger, Ottweiler, Germany) into a hollow plastic tube with an inner diameter of 29 mm and a length of 170 mm. In the middle, the tube incorporated two circular cut-outs with a diameter of 21 mm. Pellet and ring electrodes (MedCaT GmbH, Munich, Germany) were attached to the tube in 2.5 mm and 30 mm distance to the opening, respectively (cf. Figure 8 bottom). The tube including the electrode configurations was tightly sealed with silicone and the whole volume was filled with 0.17 % NaCl solution.
Impedance measurements
We tested the electrical properties of the material samples including agar hydrogel, gypsum, and reed sticks by means of four-electrode impedance measurements at room temperature. The temperature was monitored by a Traceable Excursion-Trac (VWR International bvba, Leuven, Belgium). The impedance of the measurement cell comprising of the material sample clamped between two NaCl solution compartments with a concentration of 0.17 % NaCl in deionized water was measured using a Gamry Reference 600 Plus (Gamry Instruments, Warminster, PA, USA) (Figure 8). The NaCl solution compartments held an outer pair of silver/silver-chloride ring electrodes with a distance of 160 mm to the sample for impressing an electric current, and an inner pair of silver/silver-chloride electrodes with 4 mm diameter for measuring the resulting potential difference. A more detailed description of the setup can be found in [31]. The reed sticks were tested in the above-mentioned double tube configuration.
We tested the impedance of 0.17 % NaCl solution (n=3), agarose hydrogels with 2 wt% (n=3), 3 wt% (n=3), and 4 wt% (n=3) agarose and each one gypsum sample with and without 0.17 % NaCl solution in the casting compound. The gypsum samples were also tested three times using this procedure after they have been dried at ambient air for at least 20 h. Each series of measurements were carried out over the frequencies of 0.1 Hz to 100 kHz and for 10 min at 1 Hz. There was a 30 min pause between each series of measurements.
Further, we tested three samples of agarose hydrogels with 2 wt% agarose and one gypsum sample with 0.17 % NaCl solution in the casting compound on an extended frequency range of 0.01 Hz to 100 kHz and for an extended duration of 60 min at 10 Hz. There was a 6 h pause between each series of measurements.
Simultaneous to measuring the impedances, we measured the temperature in the cell with an electrically insulated stainless steel probe connected to a Traceable® Excursion-Trac (VWR International bvba, Leuven, Belgium).
Conductivity calculation
The experimental measurements were carried out at ambient temperatures. To compare to existing literature values, the measure values were adjusted for the temperature difference. First, the impedance of the cell containing only NaCl solution, ZNaCl, was measured to use as the reference. The impedance can then be adjusted using
See formula 1 in the supplementary files.
where Z25 is the impedance adjusted to 25 °C, Zmeas is the measured impedance, ϑmeas in °C is the temperature at the time of measurement, and α is the linear factor (also called cell constant). The cell constant was determined through measurements of a cell containing 0.17 % NaCl solution only. The material conductivity is computed from the temperature-compensated net impedance Z25 using
See formula 2 in the supplementary files.
where d is the the material sample thickness/length and A is the surface area.
The tube configuration loaded with the reed sticks was measured in longitudinal and transverse direction. For both directions, we calculated the conductivity according to (2) with Z25 obtained from (1). The conductivity anisotropy was calculated as the ratio between longitudinal and transverse conductivity.