## 2 Materials and Methods
### Data Analysis and Accident Reconstruction Case  
The validation of the material model for four types of EAs was assessed using CORA (CORrelation and Analysis) plus v 4.0.5 software from PDB--Partnership for Dummy Technology and Biomechanics. This rating represents an objective method to evaluate the overall time-history curves between simulation and experiment [39; 40; 41], using the phase shift, size, and shape ratings [42; 43; 44]. Detailed introduction and instructions can be found through its official website.  
In this study, both global and local head injury criteria were evaluated. The head kinematics, extracted from the accelerometer positioned at the head center of gravity (CG), were analyzed in terms of the resultant linear velocity/acceleration and the resultant angular velocity/acceleration. Following the recommendations in the ASTM standard [35], all the kinematics--time curves were filtered by a second-order Butterworth filter with a cutoff frequency of 300 Hz.  
Figure 4: (**a**) Setup of HIII drop test against different types of EAs, (**b**) corresponding HIII FE simulation model.  
In addition, the head injury criterion (HIC) was also derived. The HIC value was calculated [45] (see Equation (1)) based on the filtered resultant linear acceleration obtained from the simulated head impacts.  
\[\text{HIC}=\text{max}\Bigg{(}(t_{2}-t_{1})\bigg{[}\frac{1}{t_{2}-t_{1}}\int_{t_{ 1}}^{t_{2}}a(t)dt\bigg{]}^{2.5}\Bigg{)} \tag{1}\]  
where \(a\) is the resultant acceleration profile, \(t_{1}\) and \(t_{2}\) define the time interval that maximizes the HIC score; usually, \(t_{2}-t_{1}\) is considered as 15 ms. Angular kinematics has been proven to be highly related and associated with injuries such as concussions [34]. HIC does not take rotational motion or quantities into account; thus, angular kinematics and local tissue injury criteria such as stress and strain were also included in this study.  
The von Mises stress (VMS) of the skull bone and the 1 st principal Green-Lagrange strain (MPS) of the brain tissue were obtained using the LS-PrePost (version 4.7.23 64-bit, 29 September 2021). The MPS was defined as the 95 th percentile of the highest principal strain across all elements in the brain tissue to eliminate numerical instabilities for the entire brain from being disproportionately influenced by the response of a singular element [46; 47; 48]. The skull bone was originally modeled with an elastoplastic material model, where plasticity levels were set to 80 MPa for the cortical bone and 32.7 MPa for the trabecular bone [49]. The risk of skull fracture corresponding to linear acceleration and the risk of brain concussion related to the principal Green-Lagrange strain were evaluated using the risk functions presented by [PERSON] et al. [50] and [PERSON] et al. [51], respectively.  
A pedestrian fall accident scenario described in [52] was evaluated in this study (Case 3, front impact). In this case, an elderly man fell directly forward and hit the forehead off the ground without touching any other body part or having obstructions during the fall. The corresponding head injury record is \"Left sided chronic subdural hematoma. Right sided acute subdural hematoma. Midline shift to left\". During the accident reconstruction conducted using MADYMO, [PERSON] and [PERSON] [52] imposed an initial velocity and posture to a multi-body model representing a standing posture human, simulated the fall process, and thereby obtained the head kinematics just before the ground impact. The linear and angular velocities of the head before impact were then input into the head FE model in LS-DYNA as the initial conditions. The converted initial resultant linear velocity is 5.35 m/s (\(v_{xyz}=1.6,0,-5.1\)), and the rotational velocity is 1.36 rad/s, both applied to the center of gravity of the head in head-only simulations. All simulations were performed using an explicit dynamic solving method on a multi-core Linux cluster (8.1.1 Xeon 64, 4 CPUs, LS-Dyna revision 13.0.0, double precision).