## 3 Results and Discussion
### Hyperextension Phase  
Once the kinetic energy is transferred to the head through the neck during the S-shape phase, it extends behind the torso. This extension moment results from the lever arm between the head's center of mass and the OC's pulling point. This, in turn, stretches the anterior ligaments and the annulus of the IVDs. Therefore, injuries are mostly limited to or originate from the spine's anterior column [8]. Patients that have experienced rear-end collision often sustain anterior ligament ruptures and disk separation, which lends weight to the hyperextension mechanism [12]. The degree of injury and symptom chronicity depends on the amount of extension that occurs. Figure 3b indicates that the neck experiences complex motion, in Arrangement C, comprised of hyperextension (>56\({}^{\circ}\)) combined with elevated compressive displacement (>120 mm). The extent of those relative motions is well beyond the neck's threshold tolerance levels [14]. Thus, the presence of head restraint in the vehicle is essential for the safety of the occupant. Although the head restraint in Arrangement B was misplaced, it had a significant impact in lowering the peak neck compression and extension by 72% and 91%, respectively (Figure 3b). On the other hand, Arrangement A has eliminated the relative kinematics since it supported the head in the former phase. Without head restraint support, the posterior and anterior spinal columns were subjected to sufficient compression and tension loads, respectively, to cause sprains and fractures in its osteoligamentous structure (Figure 4, C-iii). The former stresses were higher than 120 MPa owing to the interface between the C3-C6 spinous process (Figure 5c). Accordingly, microcracks initiation within their cancellous bones were likely to occur [24]. Besides, since the ISL, LF, and CL ligaments have failed in the cranivertebral region, the relative motions between the atlas and axis vertebas were no longer fully constrained. Hence, contact stresses between them were generated, as seen in Figure 4, C-iii. These stresses have up to a 20% probability of causing an unstable type II odontoid fracture in the C2 dens or initiating cancellous bone cracks in C1 and facet joints [25]. In this case, the immediate intervention of anterior screw fixation surgical treatment is required to provide rigid support for the fracture and unify with the preservation of altantoaxial rotation [25]. Disruption of the ALL ligament occurred at C3-C5 levels due to exposure to tensile stresses beyond 30 MPa, which exceeds its material capabilities (Figure 5a). Furthermore, stable avulsion fracture from the attachments to the inferior corner of the C4 vertebral body (Figure 4, C-iii). As stated by [PERSON] et al. [26], an added range of movement due to neck hyperextension can eventually cause long-term segmental spinal instability and spine degeneration. The PLL and CL ligaments did not endure harmful stresses since they are located on the middle neutral column, and thus their failure is not foreseen in this stage. Figure 5: Bar charts representing peak effective stress levels (MPa) recorded at (**a**) cervical ligaments, (**b**) intervertebral discs, and (**c**) cortical bony structure. Data bars labeled with (*) indicates failure occurred to the component. Regarding the IVDs, they undertook a complex combination of stresses beyond their physiological limit (greater than 3 MPa), especially at the C3-C4 interface (Figure 5b) [12]. Therefore, the probability of promoting radial fissures and disc prolapse (slipped disc) is very high [12]. It is worth mentioning that those injuries are hazardous and will require years to heal. All the previously mentioned neck injuries can be avoided by adjusting the head restraint properly, similar to Arrangement A. This allows the head restraint to absorb the head's kinetic energy and lower its relative rotational motion with the torso, which neglected neck extension.