# Electrically Equivalent Head Tissue Materials for Electroencephalogram Study on Head Surrogates
## 4 Results  
### Conductivity Test  
The carbon fiber (CF) of approximately 1000 \(\times\) 40 \(\upmu\)m was chosen to make multilayer head tissue material. The filler material was chosen depending on the processibility and targeted conductive properties. Figure 5a shows the conductivity of different CF and PDMS concentrations. The frequency range was considered from 0 to 1000 Hz. Note that the neural activities in a clinically significant and normal human brain occur between 0 and 200 Hz [44; 45]. We consider this as a low-frequency zone. High-frequency oscillation (HFO) can range up to 500 Hz in the epileptic region of a patient suffering from epilepsy [44; 46; 47]. In Figure 5a, we observe an increasing trend of conductivity with increasing CF concentrations. In addition, the conductivity of the composite within the targeted frequency zone is almost constant. From this study, we obtain a functional relation between CF concentration and the conductivity of the composites. Note that by varying the CF concentrations between 1% and 6%, the conductivities of the composite vary somewhere between 10\({}^{-5}\) (S/cm) to 10\({}^{-1}\) (S/cm). Table 2 shows the known electrical conductivities of different head tissue layers. It can be observed that the conductivities of head tissue layers vary between 10\({}^{-5}\) (S/cm) to 10\({}^{-2}\) (S/cm). As such, we can process different brain tissue layers with matching electrical conductivities by varying CF concentrations between 1% and 6%. Figure 5: (**a**) The effect of CF concentration on the conductivity of PDMS-CF composites. This study provides a functional relation between conductivity and CF concentration, which is then used to set the CF concentrations for different brain tissue layers based on their targeted conductivities. (**b**) Combined conductivity of 4-layer and 7-layer samples, which are nearly identical over the range of frequencies covered. Note that the 4-layered sample exhibits wider statistical variation than the 7-layered sample. (**c**) The conductivities of the whole skull and its sublayers (i.e., cortical and spongy layer) are shown. The inner and outer layer compact bones were made out of the same wt% composite. As the spongiform layer thickness is more than compact bones, the combined conductivity leans toward the spongiform bone’s conductivity. (**d**) The conductivities of brain tissue (combined white matter and grey matter), white matter, and grey matter are plotted. The required carbon fiber concentration for each layer of head tissue is shown in Table 3. The corresponding electrical conductivities of head tissue layers are shown in Figure 5b-d. Figure 5b shows the conductivity of 4-layer and 7-layer head tissue samples. Figure 5c,d highlight the conductivity values of the skull and brain tissue layers. Note the variation in properties between the combined layers and their sublayers. Collectively, the measured conductivities provide various combinations of Electrical conductivity values of different regions of brain tissue as well as the whole tissue. The targeted conductivity values were chosen from the statistical study of human head tissue [23] as shown in Figure 6. Note that the values and the statistics reported in Figure 6 include 56 previously conducted experimental data points on various head tissue layers. The comparison between the achieved value and recommended value is also shown in Figure 6. The recommended value came from paper [23], where the study performed a statistical procedure called'meta-analysis' for examining data from 56 independent studies and then determining average values. The median value has been taken from the boxplot diagram of the same study [23] which shows the variation in conductivity in different tissue layers. In Figure 6, the first and fourth solid line of each box is the first and third quartile accordingly. The third solid line of each box is the median of the study. Now, the recommended conductivity values [23] are available for a skull, its sublayers, CSF, brain