# Evaluating Commercial Electrical Neuromodulation Devices with Low-Cost Neural Phantoms
## 2 Materials and Methods
### Measurement Steps  
The substrate was prepared and left to acclimate to room temperature for 1 h. Stimulation electrodes were positioned in two separate configurations: parallel and perpendicular. Electrodes were 10 cm apart in each case. Before placement, measurement electrodes were calibrated with a common DC voltage source, a fresh AA battery at 1.5 V. The distance was factored into the electrode placement to calculate the voltage gradient [4; 22]. The absolute distance in the parallel case was higher, allowing more space for charge to dissipate into the material. The perpendicular case had a shorter distance between the stimulation electrodes. The measurement and stimulation devices were coated in conductive electrophysiological saline gel to reduce impedance. The voltage measured per distance was calculated for each and averaged. This measurement sequence was repeated twice per sample. If a material proved too pliable, the electrodes could shift during measurement.  
The stimulation electrodes were positioned on the surface for each device in both parallel and perpendicular configurations, as the electric field was perpendicular to the measurement [14; 30]. The deeper layers were farther from the stimulation, so the mea  
Figure 4: Schematic of stimulation and data acquisition system, including stimulation device, recording arrangement, and phantom.  
Figure 3: Measurement volumes in phantom container in Overhead View (**A**) and Lateral View (**B**).  
surements from each layer were averaged together to consolidate and filter readings, as in Equation (3).  
\[V_{avg}=\frac{1}{3}(V_{A2}+V_{B2}+V_{C2})+\frac{1}{3}(V_{A1}+V_{B1}+V_{C1})+\frac{ 1}{3}(V_{A0}+V_{B0}+V_{C0}) \tag{3}\]  
Averaging the voltage recordings from each cubic volume enabled robust, residual changes from electrical stimulation, as opposed to momentary shifts due to stimulation modality or noise [14; 30]. For both perpendicular and parallel electrode placements, the average electric field \(V_{avg}\) was calculated using Equation (3). Assuming both were the legs of a right-angled triangle, Pythagorean theorem was used to calculate the net average voltage \(V_{net,avg}\) in Equation (4) [14; 30]. The measured \(V_{net,avg}\) was then divided by the size of each cubic region to calculate the electric field.  
\[V_{net,avg}=\sqrt{\left(V_{net,parallel}\right)^{2}+\left(V_{net, perpendicular}\right)^{2}} \tag{4}\]  
The measured \(V_{net,avg}\) would reflect the measured efficiency. Reliable contact was key to low impedance, and thus high sensitivity, for the measurement electrodes. An efficiency factor \(EF\) was calculated for each device to measure potential power loss.  
\[EF\ (\%)=D_{obs}/D_{exp} \tag{5}\]  
As shown in Equation (5), the \(EF\) was the ratio of the observed dosage \(D_{obs}\) over the expected dosage \(D_{\text{exp}}\). The observed power was based on experimental measurements. The expected power was based on values from Equation (2). The combined percentage represented the fraction of power captured. If a material's efficiency factor was below 0.5%, it was excluded from future tests. Material cost and preparation time were also criteria for exclusion. The experiments were conducted at a lab maintained at 25 \({}^{\circ}\)C, at an indoor relative humidity of 50%. Each batch of materials was prepared in advance of the experiment. Hourly temperature and electrical measurements, without equipment, ensured that the samples were reliable at room temperature for at least 2 h. The \(EF\) depended on the reliability of the dosage measurement, including electrode geometry, electrode material, device configuration, and experimental design. As such, the \(EF\) could serve as a comparison method between phantom experiments for non-invasive neuromodulation devices.