# A Female Multi-Body Head-and-Neck Model and Validation for Rear Impact Simulations
## 3 Model Details  
The stature and mass of the female model are selected as 160 cm and 50 kg, respectively, with a body mass index of 20 kg/m\({}^{2}\) to be in agreement with those of the volunteers in [PERSON] et al. [29] study. The inertial properties and geometrical features of the model are based on several studies from the literature, such as Chalmers University of Technology (ViVA project) and University of Michigan Transportation Research Institute, Ann Arbor, MI, USA (UMTRI) studies [22; 35; 36]. Figure 2: Average sled acceleration [29]. Based on [PERSON]'s study [37], the 35 th percentile female has a stature of 160.32 cm and a mass of 56 kg. Using this percentile, the head circumference, head breadth, head length, and neck circumference can be defined as 54.06 cm, 14.25 cm, 18.48 cm, and 30.91 cm, respectively [37]. The neck length is calculated as 10.25 cm. Also, in this study, constant density is assumed, and the density is selected as 0.91 g/cm\({}^{3}\) to be in agreement with the published data [22]. The head mass is defined as 3.47 kg, and its center of gravity is determined by applying uniform mass distribution [22]. The female model developed in this study has a head, a neck with seven cervical vertebrae (namely C1 to C7 from top to bottom) and T1, as represented in Figures 3 and 4. The configuration of the cervical vertebrae is derived from [PERSON]'s study [38], and an arc is created to define this configuration corresponding to the head-neck posture in a typical automotive seating position. The arc shown in Figure 3 with a radius of 228.75 mm and a sector angle of 25.96\({}^{\circ}\) was drawn in between O.C. (occipital condyles) and the lower end plate of C7, which approximates the curvature of the geometry of the cervical spine. The head and T1 anatomical coordinate systems used in the simulation model are shown in Figure 3. In the simulation model, the sled coordinate system, which is attached to the sled, has its \(x\) axis towards the left parallel to the ground, and its \(z\) axis is upward and vertical to the ground, which can be inferred from Figure 3; hence, the sled coordinate system is parallel to the head and T1 anatomical coordinate systems in the initial configuration as shown in Figure 3.  
With this arc, each vertebra and the surrounding soft tissues are modeled to have the geometry of a disc, and this arc divides these neck segments (i.e., discs) in half. The radius of  
Figure 4: The solid model of the cervical spine. Figure 3: The initial configuration of the head–neck model and the arc that approximates the initial configuration of the neck (adapted and modified from [16; 27]). the female neck disc is 4.92 cm, and the radius of the arc is 228.75 mm, as shown in Figure 4. The relative orientation between the discs was derived from the [PERSON] study [3]. Based on the neck geometry, the height of each vertebra was calculated; according to this, the first two vertebrae have a height of 14.5 mm, and the rest have a height of 14.4 mm. From the EvaRID data [22], the mass of the neck was found to be 0.663 kg, and the masses of the vertebrae are proportional to their heights. The inertial properties and relative orientations are shown in Table 1, where C0 represents the head. For the vertebrae from C1 to C6, the relative orientation corresponds to the angle of the corresponding vertebra relative to the vertebra below. The relative orientation of the head (C0) corresponds to the angle of the head anatomical coordinate system with respect to the C1 vertebra, as shown in Figure 3. The relative orientation of the vertebra C7 corresponds to the angle of C7 relative to the T1 anatomical coordinate system in Figure 3. In Table 1, the mass of the T1 vertebra is immaterial since, in the simulation, the T1 motion is specified as a function of time. The initial velocities of the head-neck system with respect to the sled coordinate system are given in Table 1, and it is considered that the whole head-neck system has the same velocity as the sled impact velocity before impact.