## 2 Materials and Methods
### Cervical Alignments  
Cobb Angles were used as cervical spine parameters and calculated per the 4-line method described by [PERSON] et al [15; 16]. This method involves drawing two parallel lines on the lateral radiograph. The first is a line from the inferior endplate of C2 to the posterior margin of the spinous process and the second parallel line is drawn from the inferior endplate of C7. Perpendicular lines are drawn from the two lines mentioned above and the angle subtended between the intersection of the perpendicular lines is defined as the cervical curvature angle. The angles created include the spino-cranial angle (SCA) which is defined as the angle between the C7 slope and the straight line joining the middle of the C7 end plate and the middle of the sella turcica. The cervical sagittal vertical axis (cSVA) is defined as the distance from a vertical plumb line dropped from the center of the C2 vertebral body to the posterior superior corner of the C7 vertebra. The FE model used for cervical validation had a C2-C7 Cobb angle of \(-\)5\({}^{\circ}\). This FE model was modified, and the three alignments were created by applying displacement/rotations to the cervical vertebrae until the appropriate alignment was obtained. For example, for creating a kyphotic model, the C7 vertebra was fixed and rotation at C2 was applied until C2-C7 = 10\({}^{\circ}\) (kyphosis)was obtained. From this method, the following alignments were created (a) intact-lordotic model (intact-L; C2-C7 angle: \(-10^{\circ}\), cSVA: 25 mm, the C7 slope: \(20^{\circ}\)), (b) intact-straight model (intact-S; C2-C7 angle: \(0^{\circ}\), cSVA: 31 mm, the C7 slope: \(22^{\circ}\)), and (c) intact-kyphotic model (intact-K; C2-C7 angle: \(10^{\circ}\), cSVA: 38 mm, the C7 slope: \(24^{\circ}\)) (Figure 1a-c).  
\begin{table}
\begin{tabular}{c c c c c} \hline
**Component** & **Material Properties** & **Constitute Relation** & **Element Type** & **Area (mm\({}^{2}\))** \\ \hline \hline
**Bone** & & & & \\ \hline \multirow{2}{*}{Vertebral cortical bone} & E = 10,000 Mpa & & & \\ \cline{2-5}  & v = 0.3 & & & \\ \hline \multirow{2}{*}{Vertebral cancellous bone} & E = 450 Mpa & & & \\ \cline{2-5}  & v = 0.25 & & & \\ \hline \multirow{2}{*}{Vertebrae-Posterior} & E = 3500 Mpa & & & \\ \cline{2-5}  & v = 0.25 & & & \\ \hline \multirow{2}{*}{Artificial bone} & E = 10,000 Mpa & & & \\ \cline{2-5}  & v = 0.3 & & & \\ \hline \multicolumn{5}{c}{**Intervertebral Disc**} & & & \\ \hline \multirow{2}{*}{Ground substance of annulus fibrosis} & C10 = 0.7 & & & \\ \cline{2-5}  & C01 = 0.2 & & & \\ \hline \multirow{2}{*}{Nucleus pulposus} & C10 = 0.12 & & & \\ \cline{2-5}  & C01 = 0.03 & & & \\ \cline{2-5}  & D1 = 0 & & & \\ \hline \multicolumn{5}{c}{**Ligaments**} & & & \\ \hline \multirow{2}{*}{Anterior Longitudinal Ligament} & 15.0 (\(<\)12\%), 30.0 (\(>\)12\%) & & & \\ \cline{2-5}  & v = 0.3 & & & \\ \hline \multirow{2}{*}{Posterior Longitudinal Ligament} & 10.0 (\(<\)12\%), 20.0 (\(>\)12\%) & & & \\ \cline{2-5}  & v = 0.3 & & & \\ \hline \multirow{2}{*}{Capsular Ligament} & 7.0 (\(<\)30\%), 30 (\(>\)12\%) & & & \\ \cline{2-5}  & v = 0.3 & & & \\ \hline \multirow{2}{*}{Ligamentum Flavum} & 5.0 (\(<\)25\%), 10.0 (\(>\)25\%) & & & \\ \cline{2-5}  & v = 0.3 & & & \\ \hline \multirow{2}{*}{Interspinous Ligament} & 4.0 (20–40\%), 8.0 (\(>\)40\%) & & & \\ \cline{2-5}  & v = 0.3 & & & \\ \hline \multicolumn{5}{c}{**Facet Joints**} & & & \\ \hline \multicolumn{5}{c}{Apophyseal Joints} & Non-linear Soft contact, GAPPUNI elements & - & - & - \\ \hline \end{tabular}
\end{table}
Table 1: Material properties assigned to the finite element model [12; 13; 14].