## 2 Materials and Methods
### LMS and PS Combination Model with Allograft Spacer  
The allograft spacer was constructed based on measuring the CornerstoneTM ASR (Medtronic Sofamor Danek, Memphis, TN, USA) using SolidWorks CAD drawings (Solidworks 2013, Dassault Systemes Solidworks Corporation, Waltham, MA, USA) and imported into ABAQUS to generate elements of 3D geometry. The mesh size of the allograft spacer was 0.5 mm. The boundary condition of the allograft spacer between the cortical bone and cancellous bone was accomplished through a \"tie\". Then, the meshed allograft spacer model was inserted into the C5-6 disc space of the previously constructed intact cervical FEM. The spacer had a length of 14 mm, a height of 7 mm, and a lordotic angle of 7\({}^{\circ}\), which were the best dimensions to fit the vertebral anatomy at the C5-6 level for the cervical model being used.  
The allograft spacers were inserted via an anterior surgical approach, which was previously described [22; 23; 24]. By simulating the surgical procedure, the anterior longitudinal ligament, the posterior longitudinal ligament, the superior and inferior endplates, and the anterior and posterior portions of the annulus fibrosus were excised. Then, the allograft spacer was positioned at the anterior margin of the vertebral body. Since our model was aimed at simulating the biomechanical behaviors after bony fusion, specific constraint conditions were imposed, especially at the bone-implant interface. In this study, the interface behavior was accomplished via a \"tie\" contact condition, which enabled the allograft spacer and vertebrae to be permanently bonded together and fully constrained.  
By incorporating the Poseidon cervical pedicle screw system (Medyssey, Jecheon, Korea) for posterior fixation, each lateral mass screw, pedicle screw, and their combination models were set. The PS was 28 mm in length and 3.5 mm in diameter, and the LMS was 14 mm in length and 3.5 mm in diameter. The rod had a thickness of 3.7 mm. Each screw was inserted as described below. The LMS position was defined as 1-mm medial and 1-mm cephalad in relation to the midpoint of the lateral mass. The insertion angle was set to 28\({}^{\circ}\) in the lateral direction and 15\({}^{\circ}\) in the superior direction. The PS position was set to 1-mm lateral to the center of the articular mass and near the end of the superior articular process. The C5-C6 segment was 40\({}^{\circ}\) medial and sagittally parallel to the inferior endplate [25; 26].  
\begin{table}
\begin{tabular}{c c c c} \hline \hline
**Component Name** & **Young’s Modulus (MPa)** & **Poisson’s Ratio (\(\
u\))** & **Ref.** \\ \hline Cortical bone & 12,000 & 0.3 & [16] \\ \hline Cancellous bone & 100 & 0.29 & [13] \\ \hline End plate & 500 & 0.4 & [17] \\ \hline Pedicle & 5000 & 0.3 & [19] \\ \hline Posterior element & 3500 & 0.29 & [11] \\ \hline Annulus matrix & 4.2 & 0.45 & [17] \\ \hline Annulus Fibers & 500 &
\begin{tabular}{c} Cross-sectional Area \\ 0.1(mm\({}^{2}\)) \\ \end{tabular} & [14] \\ \hline Nucleus pulposus & 1.0 & 0.499(Incompressible) & [17] \\ \hline Allospacer(Femoral cortical bone) & 18,200 & 0.38 & [20] \\ \hline Allospacer(Femoral cancellous bone) & 389 & 0.3 & [20] \\ \hline Posterior screw(Ti6 Al4V ELI) & 110,000 & 0.35 & [21] \\ \hline \hline \end{tabular}
\end{table}
Table 2: Material properties.  
Six types of postoperative posterior fixation models (Type 1: all LMS, Type 2: all pedicle screws (PS), Type 3: left (Lt) PS and right (Rt) LMS combination, Type 4: Lt LMS and Rt PS, Type 5: upper PS and lower LMS, and Type 6: upper LMS and lower PS) were constructed by modifying the intact model to simulate device implantation at C5-C6 (Figure 1).