# Numerical Analysis of EOD Helmet under Blast Load Events Using Human Head Model
## 3 Results and Discussion
### HIC and GSI Parameters  
The head injury criterion is used to calculate the probability of brain injury due to trauma and bases its calculations on the acceleration of the center of gravity and the time interval that it acts. The expression of HIC is as follow:  
\[HIC=\left\{\left[\frac{1}{t_{2}-t_{1}}\int_{t_{1}}^{t_{2}}a(t)dt\right]^{2.5}(t_{ 2}-t_{1})\right\}_{max} \tag{6}\]  
On the other side, the GSI criterion is based on the acceleration-time curve and was proposed by [PERSON] [51] through the following expression  
\[GSI=\int_{0}^{t}a(t)^{2.5}dt \tag{7}\]  
where \"\(a\)\" is the value of acceleration expressed in G's, and '\(t\)' is the time. According to this criterion, severe brain injuries occur (according to the AIS scale, presented later in Figure 10) if the GSI is greater than 1000. It is important to note that HIC and GSI, originally developed for blunt impact studies, are widely used in blast literature also, and have hence been used in this work. Table 6 shows the HIC values obtained, and the GSI values for all the cases studied. Figure 10: Probability of injury curves for different values of HIC parameter. \begin{table}
\begin{tabular}{c c c c} \hline \hline
**Case** & **TNT [kg]** & **Maximum Acceleration [m/s\({}^{2}\)–g]** & **Time a\({}_{\text{mix}}\) [ms]** \\ \hline \multirow{3}{*}{Without Helmet} & 0.050 & 3916.9–399.3 & 1.45 \\  & 0.075 & 5267–536.92 & 1.37 \\  & 0.100 & 6430.1–655.5 & 1.29 \\ \hline \multirow{3}{*}{With Helmet} & 0.050 & 771.6–78.7 & 3.92 \\  & 0.075 & 1109.3–113.1 & 3.68 \\ \cline{1-1}  & 0.100 & 1456.9–148.5 & 3.43 \\ \hline \hline \end{tabular}
\end{table} 
Table 5: Maximum acceleration and time for all cases studied. From the data presented in Table 6, it can be seen that the HIC value is reduced around 95% wearing helmet. In addition, GSI reduces by approximately 95% in all cases to values below the defined threshold value (1000). Therefore, in all the studied cases, according to the GSI criterion, there are no severe brain injuries when the protective helmet is used. The HIC value can be related to the probability of brain injury at each level of the AIS scale, according to the risk curves presented by [PERSON] et al. (2016) and shown in Figure 10.  
Each AIS level of injury carries a severity level associated with it, with AIS1 being the mildest and AIS6 being the highest severity ([PERSON] et al., 2016). For example, the AIS1 level involves a mild concussion without loss of consciousness, while the AIS6 would imply severe damage to the brain with fatal injuries. As presented in Table 7, on using the helmet, the probability of AIS \(\geq\) 1 brain injuries reduced 98%, 84%, and 46% for 0.050, 0.075, and 0.100 kg of TNT, respectively. For 0.05 kg explosive, the possibility of AIS level 3 and 4 injuries is completely eliminated by the use of the helmet, while AIS 1 and 2 injuries have only a small probability of occurrence on use of the helmet. On the other side, for intermediate cases (0.075 kg), the use of protective helmet plays an important role, as the probability of death (AIS 6 level injury), which is a near certainty without its use, gets eliminated with it. Helmet use also reduces that event to one with only a little probability of causing moderate injuries. Finally, in the case with 0.100 kg TNT studied, the use of helmet again eliminates chances of a fatal injury and sets to close zero the possibility of AIS 3 and AIS4 level injuries. However, the possibility of AIS1 and AIS2 level injuries are not negligible and have a probability of 54% and 20%, respectively. In addition, an analysis of the helmet applicability range was carried out. In order to determine the amount of TNT mass for which 3000 HIC value is reached (associated with a 100% probability of AIS 6 injury, implying severe brain damage leading to death), different explosive load states have been simulated. Figure 11 shows the curves obtained from this analysis.