## 2 Materials and Methods
### Rear-Impact Loading Conditions and Injury Measurement  
In this work, a computational biomechanics analysis was performed to simulate rear-end collisions with three impact speeds. A rear-end collision at 16 km/h was considered as a low-speed impact, which represents collision events under urban congested road conditions, such as collision events in parking lots or in front of traffic lights. This impact speed is currently included in Euro-NCAP whiplash testing [23]. A rear-end collision at 40 km/h is classified as a medium-speed collision, according to FMVSS 301 [24]. The vehicle speed is used to simulate a moderate rear-end collision when the vehicle drives on a city's main road. A speed of 56 km/h is specified in the frontal crash test during the UN R94 frontal-crash test [25], and it represents a high-speed rear-collision scenario in this study. Therefore, these three speeds cover a complete set of rear-end collision scenarios. The low-, medium-, and high-impact scenarios were modeled through three sled tests by applying corresponding acceleration pulses on the vehicle floor along the x-direction, as shown in Figure 6. The acceleration pulse of 16 km/h was derived from the Euro-NCAP low-speed whiplash test [23]. The pulse of 40 km/h was referenced from the car-crash test in a NHTSA report following FMVSS 301 [26]. [PERSON] et al. [27] reported an acceleration pulse for a 56 km/h collision speed, and this load represented an extreme rear-impact scenario. In this study, six simulation cases were performed with the combination of three different rear-impact speeds (16 km/h, 40 km/h, and 56 km/h) and two restraint systems (three point and four point). The responses of seatback rotation and head movements were recorded via the specification of nodal history curves for corresponding nodes in the finite element model assembly. Meanwhile, a cross-section was created between the first (C1) and second (C2) cervical vertebra to obtain the neck shear forces and moments of the THUMS, which were utilized to calculate the neck injury. Head and neck injuries are critical injury types in different collision scenarios, such as motorcyclist collisions with safety barriers and vehicle rear impacts. For instance, with respect to motorcyclist collisions with safety barriers, the head injury metric (HIC30) and neck injury metrics (F\({}_{\rm x}\), F\({}_{\rm y}\), F\({}_{\rm z}\), Mo\({}_{\rm x}\), Mo\({}_{\rm y}\), and M\({}_{\rm z}\)) were utilized to evaluate the protective effects of roadside safety equipment for motorcyclists [28]. Similarly, head and neck injuries of occupants are also the dominant injury types in vehicle rear impacts. The injury indices considered in this study include the Brain Injury Criteria (BrIC) [29], the Cumulative Strain Damage Measure (CSDM) [30], neck injury metrics (N\({}_{\rm ij}\) and N\({}_{\rm km}\)) [31; 32], and the Neck Injury Criterion (NIC) [33]. BrIC is calculated based on the angular velocity of the head's center of gravity. The CSDM is calculated based on strain distribution in brain tissue. For instance, the CSDM (0.25) has been widely utilized in the auto industry, and it reflects the  
Figure 5: Finite element model assembly of occupant restraint systems in zero-gravity seats with different seat belt systems: (**a**) three-point seat belt system. (**b**) four-point seat belt system. volume percentage of brain tissue, where the maximum principal strain is beyond 0.25. A higher value of the CSDM (0.25) reflects the higher possibility of experiencing diffuse axonal injury. The BrIC and CSDM (0.25) are not yet standardized and are only mentioned in regulations as potential assessment tools [34; 35]. In neck injury metric (N\({}_{\text{ij}}\)) is derived from the axial force and bending moment at the upper neck and is used to assess neck injuries in frontal impacts. In contrast, the neck injury metric (N\({}_{\text{km}}\)) is calculated based on the shear force and bending moment at the upper neck, and it better reflects whiplash injuries during rear-end collisions.