# A Female Multi-Body Head-and-Neck Model and Validation for Rear Impact Simulations
## 4 Validation of the Model  
The motion of T1, which is given as an input to the model, was used to validate the model against the volunteer data, as explained in Section 2. This T1 motion refers to the angular acceleration of T1 and the translational acceleration of the origin of the T1 accelerometer coordinate system. The T1 accelerometer coordinate system is shown in Figure 1. Figure 7 presents the average values of T1 accelerations recorded in the volunteer tests. The average angular displacement of T1, which is provided in the volunteer test results [29], was digitized to fit a not-a-knot cubic spline, which was differentiated twice and then filtered according to the SAEJ211 filter [41] together with the smoothing spline function of the Matlab R2014a software. The mean values of accelerations presented in Figure 7 were given as inputs for the T1 motion. Figure 7: T1 average accelerations as measured in the T1 accelerometer coordinate system. T1 acceleration in x-direction (**top left** figure). T1 acceleration in z-direction (**top right** figure). T1 angular acceleration (**bottom** figure). At the start of the impact, when time equals zero, the picture of one female volunteer [29] indicates that the head is flexed slightly with respect to T1, which is different from the initial configuration given in Figure 3. However, this initial flexion is not quantified in reference [29], from which the volunteer data is obtained. During the validations, it was observed that this initial flexion significantly affected the response of the model and provided better agreement with the volunteer motion. Therefore, during the validation and fine-tuning of the model, two different postures of the female head-neck system are considered, which are shown in Figure 8, where the head is flexed by 8 deg or 16 deg with respect to T1. In order to determine a natural and realistic posture of the cervical spine, a separate simulation was run in which T1 was fixed, and the head was allowed to fall under gravity without any reflex muscle activation. When the head flexion relative to T1 reached 8 deg or 16 deg, the posture of the cervical spine and the head were recorded to be used as the initial configuration in the subsequent impact simulation. The muscle activity of the volunteers is not reported in reference [29]. Therefore, at the start of the impact, it is not known how tense or how relaxed the volunteers were. Hence, during the validation of the head-neck model, the viscous damping function, which mimics the muscle activity pattern, is varied in accordance with the EMG signal shapes recorded from volunteer tests in the literature [42; 43; 44; 45; 46; 47; 48; 49]. Five cases are presented that produce similar biofidelic behavior regarding the motion of the 35 th percentile female model. These five cases are highlights from the validation and calibration of the model. The damping functions for cases 1 to 5 are displayed in Figure 9. In cases 1, 2, and 4, the initial head flexion prior to impact is 16 deg. In cases 3 and 5, the head is flexed by 8 deg before the impact. In cases 1, 2, 3, and 4, the scale factor for the stiffness function is 0.65, whereas for case 5, this scale factor is 0.40, as specified in Figure 5.  
Reference [29] provides the responses of the volunteers, which are displayed as top and bottom limits. Several responses of the volunteers and the female head-neck model have been examined to validate the model. In the plots showing the responses of the volunteers together with those of the female head-neck model, the displacements of the center of T1 are shown with respect to the sled expressed in the sled frame \(\mathcal{F}_{0}\) (see Figures 1 and 10). Similarly, the head C.G. displacements are shown with respect to the sled expressed in the sled frame \(\mathcal{F}_{0}\). The rotational displacements of the head and T1 are shown with respect to the sled around the \(y_{0}\) axis of the sled frame. The point at which the sled acceleration started to increase was designated as time zero.