# Novel Design of Expandable Spinal Cage for Efficient Lumbar Spine Fusion Operation
## 3 FEA for Mechanical Performance Verification
### FEA Model and Results  
Finite element analysis was utilized for design verification of the expandable cage. Static structural analysis was performed using the Static Structural module of ANSYS 2021 R1, adhering to the ASTM F2077 standard. This process allowed us to evaluate the mechanical performance of the spinal cage.  
As shown in Figure 5, analysis was conducted based on a solid model. To simplify the analysis model as much as possible, it was composed of two main components: the fixture and two expandable cages. The fixture acts as a rigid body that does not deform, representing a metal block used to secure the cage in accordance with the ASTM F2077 standard. The mesh of this analysis model consisted of tetrahedral elements, with a total of 266,649 nodes and 146,169 elements. Since the prototype of the developed model is planned to be manufactured using Ti-6 Al-4V through additive manufacturing, the properties of these FEA models have been applied to all parts with tensile test results of Ti-6 Al-4V produced by additive manufacturing studied in the previous literature.  
The contact conditions and boundary conditions of the analysis model are defined as follows. First, for the contact conditions, the components constituting the expandable cage are defined to be in contact with each other with a friction coefficient of 0.38. Additionally, the metal block that comes into contact with spinal cage during actual experiments is treated to prevent sliding. Accordingly, a rough contact condition is applied between the fixture and the upper plate to prevent sliding.  
Second, for the boundary conditions of the analyzed model, a fixed condition is applied to the bottom of lower plate to prevent the cage from moving. A displacement condition is applied to the top of the fixture to perform compression tests and compression-shear tests. The displacement applied to the top of the fixture is a total of 1 mm, which is empirically determined to evaluate yield strength in accordance with the ASTM F2077 standard. In the  
\begin{table}
\begin{tabular}{c c c} \hline \hline
**Test** & **Parameter** & **Value** \\ \hline \multirow{3}{*}{Static axial compression} & Stiffness (N/mm) & 5914 \\ \cline{2-3}  & Yield load (N) & 6371 \\ \cline{2-3}  & Ultimate load (N) & 6989 \\ \hline \multirow{3}{*}{Static compression–shear} & Stiffness (N/mm) & 1435 \\ \cline{2-3}  & Yield load (N) & 1996 \\ \cline{1-1} \cline{2-3}  & Ultimate load (N) & 2147 \\ \hline \hline \end{tabular}
\end{table}
Table 1: The bottom 5% of mechanical performance of FDA-approved spinal cage.  
compression test, the cage is compressed vertically in the direction of arrow 1, as shown in Figure 5, while in the compression-shear test, the cage is compressed at a 45-degree angle in the direction of arrow 2. In this case, displacement in the direction perpendicular to the compression direction is not constrained to closely simulate the ASTM F2077 standard.  
As shown in Figures 6 and 7, compression analysis results are as follows: yield load is determined at the intersection of the blue line, offset by 2% from the initial slope, and for the load-displacement curve, the yield load is 11,463 N, exceeding the allowable criterion of 6371 N. Therefore, the designed expandable cage meets mechanical performance objectives under compression load. The initial yield occurs at a compression load of 1920 N on the axis of Sliding Block1.  
As shown in Figures 8 and 9, compression-shear analysis shows similar results. The yield load is 4360 N, surpassing the allowable criterion of 1996 N, confirming that the expandable cage also meets mechanical performance goals under compression-shear load. The initial yield under this condition occurs at a compression-shear load of 1128 N at the corner of the pillar where the lower plate axis is located.  
Figure 5: Boundary conditions for compressive analysis according to ASTM F2077 conditions.  
Figure 6: Load–displacement curve from compression analysis.