# Biomechanical Optimization of Lumbar Fusion Cages with a Porous Design: A Finite Element Analysis
## 3 Results
### Stability of Endplates  
The stability of the endplates following implantation of lumbar interbody fusion cages was evaluated through the range of motion (ROM) and displacement of the L3-L4 segment under motion conditions of axial compression (A-Compression), axial rotation (A-Rotation), flexion, extension, left bending (L-Bending), and right bending (R-Bending). These biomechanical parameters are essential for assessing the ability of fusion cages to maintain spinal stability and reduce the risk of subsidence. The results of displacement and ROM are detailed in Tables S1 and S2, respectively, and visually represented in Figures 4 and 5, comparing the performance of four cage designs: C-Cage, P-Cage, G-Cage, and V-Cage. Figure 3: The work flow diagram of the lumbar fusion cage with different structure designs implanted into the spine model. \begin{table}
\begin{tabular}{c c c c c c} \hline \hline
**Flexion** & **Extension** & **L-Bending** & **R-Bending** & **Rotation** & **Ref.** \\ \hline
9.4 & 4.3 & 5.5 & 5.3 & 2.2 & [PERSON] et al. [31] \\
8.7 & 4.1 & 5.2 & 5.3 & 2.0 & [PERSON] et al. [32] \\
7.8 & 3.8 & 5.5 & 5.5 & 2.0 & [PERSON] et al. [33] \\
9.2 & 4.1 & 5.3 & 5.2 & 2.1 & Present study \\ \hline \hline \end{tabular}
\end{table} 
Table 3: Comparison of the ROM of the complete finite element model in the present study (Deg). Figure 4: (**a**) Displacement and (**b**) range of motion (ROM) comparison for the L3–L4 segment implanted with different cage in the five common directions of motion. Figure 5: Simulation plots of displacement of the L3–L4 segment model implanted with the fusion cage under six different motion condition. The stability of the endplates was evaluated through the range of motion (ROM) based on simulated displacement of the L3-L4 segment. These displacement values, obtained from the finite element simulation output, serve as indicators to evaluate potential micromotion at the cage-endplate interface and subsequent subsidence risks. According to Figures 4a and 5, the C-Cage exhibited the largest displacements across all load conditions, suggesting heightened susceptibility to interfacial micromotion and subsidence. While a slight decrease in displacement was observed for P-Cage with a value of 0.026 mm, 0.251 mm, 0.251 mm, 0.364 mm, 0.163 mm, and 0.161 mm, for A-Compression, A-Rotation, flexion, extension, L-bending, and R-Bending, respectively. Remarkably, both G-Cage and V-Cage were found to demonstrate exceptional performance, a decline of 16% in extension displacement was reported for the V-Cage when compared to the C-Cage. The porous architectures facilitated uniform stress distribution across the endplate interface, effectively suppressing micromotion and lowering subsidence propensity. Range of motion (ROM) serves as a critical indicator for evaluating spinal kinematic stability, reflecting the ability of interbody fusion cages to constrain segmental motion and their impact on fusion efficacy and subsidence risks. In this study, ROM values were measured for the L3-L4 segment across five motion directions. According to Figure 4b and Table S2, the C-Cage exhibited the highest ROM values of 2.4\({}^{\circ}\), 10.5\({}^{\circ}\), 6.5\({}^{\circ}\), 6.6\({}^{\circ}\), and 6.8\({}^{\circ}\) for A-Rotation, flexion, extension, L-bending, and R-bending, respectively, indicating insufficient motion control and potential postoperative instability risks. The P-Cage with personalized morphology achieved marginal ROM reduction through optimized endplate congruency, though its efficacy remained limited. In contrast, both Gyroid-based porous cage (G-Cage) and Voronoi-inspired porous cage (V-Cage) significantly enhanced stabilization. Notably, V-Cage demonstrated superior performance, reducing ROM values to 1.7\({}^{\circ}\), 7.5\({}^{\circ}\), and 3.2\({}^{\circ}\) in a-rotation, flexion, and extension directions, respectively, representing reductions of approximately 29%, 29%, and 51% compared to C-Cage.