## 2 Materials and Methods  
### FEM of an Intact Cervical Spine  
A previously validated three-dimensional intact cervical spinal segment model of C3-6 in a 54-year-old male subject was used [9; 10]. The geometrical data of the multi-segmental cervical model were reconstructed from computed tomography (CT) images. The scanner operated at the following settings: ultra-high resolution with a transverse slice thickness of 0.5, and width of the pixel was 0.429 mm.  
The cervical Finite Element (FE) model included cortical bone, cancellous bone, posterior elements, annulus fibrosus, nucleus pulposus, and facet. In addition, anterior longitudinal ligaments, posterior longitudinal ligaments, intraspinous ligaments, ligament flava, and capsular ligaments were included. Ligament insertion points were matched from CT image. The spinal ligaments adopted the nonlinear load-displacement material property for the physiological nonlinear behavior of the ligaments (Table 1) [10; 11]. The cortical bone of the vertebrae was separately modeled from the inner cancellous bone because of its high stiffness. Although the thickness of the cortical bone varies depending on each vertebral body and on the location, an average value of 0.5 mm was used for the shell thickness in this study [12]. The vertebrae and discs were meshed using \"eight-node brick\" elements, and the posterior element was meshed using for-node brick elements. The material properties were assumed to be homogeneous and isotropic (Table 2) [13; 14; 15]. The mesh convergence was performed to confirm adequate mesh density among variable element sizes from 0.1 to 2.0 mm. Finally, a 0.5-mm element size was applied in our surgical model for the prediction of FE analysis results (implant and periphery, element size--0.5 mm; the others, 2 mm). No unusual stress patterns were presented in this study for this setting.  
The intervertebral disc was consisted of an annulus fibrosus and a nucleus pulposus bounded by the endplates. The fiber contents in the annulus fibrosus were modeled using tension-only truss elements, which carry only tensile forces. The annulus fiber was arranged in an alternating crisscross manner with an about 25\({}^{\circ}\) orientation [16; 17]. The facet cartilage joints were modeled 45\({}^{\circ}\) from the  
\begin{table}
\begin{tabular}{c c c c c c c c c c} \hline \hline \multicolumn{3}{c}{**ALL**} & \multicolumn{3}{c}{**PLL**} & \multicolumn{3}{c}{**LF**} & \multicolumn{3}{c}{**ISL**} & \multicolumn{3}{c}{**CL**} \\ \hline
**Load** & **Disp.** & **Load** & **Disp.** & **Load** & **Disp.** & **Load** & **Disp.** & **Load** & **Disp.** \\
**(N)** & **(mm)** & **(N)** & **(mm)** & **(N)** & **(mm)** & **(N)** & **(mm)** & **(N)** & **(mm)** \\ \hline
0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 \\ \hline
32 & 1.2 & 28 & 1.2 & 30 & 1.8 & 8.5 & 1.3 & 1.5 & 1.7 \\ \hline
60 & 2.5 & 50 & 2.2 & 55 & 3.5 & 10 & 2.8 & 29 & 3.6 \\ \hline
81 & 3.7 & 66 & 3.2 & 71 & 5.1 & 23 & 4.1 & 52 & 5 \\ \hline
100 & 4.8 & 79 & 3.4 & 95 & 6.9 & 28 & 5.5 & 86 & 7.5 \\ \hline
115 & 6 & 88 & 5 & 105 & 8 & 32 & 7 & 104 & 9.5 \\ \hline \hline \end{tabular}  
ALL = anterior longitudinal ligament, PLL = posterior longitudinal ligament, LF = ligament flavour, ISL = interspinous ligament, CL = capsule ligament, and Disp. = displacement.  
\end{table}
Table 1: The nonlinear material properties of the ligaments used in the Finite Element model [10].  
horizontal plane and soft frictionless, with an initial gap of 0.5 mm based upon CT imaging [16]. The segment angles used to create the cervical spine curvature for the model were as follows: C3-4: 4.5\({}^{\circ}\), C4-5: 1.87\({}^{\circ}\), and C5-6: 3.94\({}^{\circ}\)[18]. For this study, the general-purpose Finite element analysis (FEA) package ABAQUS (Abaqus 2017, Dassault Systemes Simulia Corp., Providence, RI, USA.) nonlinear geometry parameter (NLGEON = ON) in the ABAQUS step module was used.