# Design and 3D Printing of Interbody Fusion Cage Based on TPMS Porous Structure
## 2 Materials and Methods
### Design and Performance Simulation Analysis of Porous Structure  
In the spinal bone, the pore sizes of different segments of the bone are different, and the distribution of the pore sizes are uneven. The optimal fusion cage bone implant should have similar mechanical and biological characteristics to the original spinal bone. It is of great significance to study how to optimize the spatial distribution of pore structure and pore structure in spinal implants. In this paper, through the construction method of TPMS, the implicit function equation model, the bionic porous structure model and the linear gradual porous structure model are constructed parametrically, and the pore shape, size, linear change rate, and other structural characteristics of the porous model are changed by adjusting the construction parameters of the model, to obtain the ideal porous structure implant parts [18; 19; 20; 21; 22]. The detailed design steps are shown in Figure 4.  
Step 1: pretreatment: construction of TPMS porous structural units. Taking the regular hexahedral mesh region as the design area, the porous material was designed by digging holes in each hexahedral mesh element; the corresponding relationship between the TPMS element parameters and density distribution was established.  
Step 2: homogenization process: we determined the equivalent tensor matrix of the microstructure unit. We extracted the hexahedral grid node information and element information, solved the overall stiffness matrix of the structure, constructed the correlation matrix, including grid node information and material properties. We used the proper orthogonal decomposition (POD) model reduction algorithm to model and map the finite element mesh, and calculate the equivalent elastic tensor matrix corresponding to each mesh sample.  
Step 3: structural optimization design: introducing the combinatorial approximation technique (combined approximation, CA), the equivalent tensor matrix of the grid structure was obtained from step (2) to assemble the elastic matrix. The approximate analytical expression of the displacement field was solved in the case of small disturbance of the stiffness matrix, and the optimization problem of the spatial distribution of porous structures was transformed into the standard geometric parameter optimization problem of the equivalent continuous solid model.  
Step 4: the method of moving asymptotes (MMA) was used to optimize the set region, and after, the pore shape parameters of each element were obtained, the corresponding  
Figure 4: TPMS pore structure parameters—performance mapping and pore structure spatial distribution optimization, comprehensive mechanical control process.  
porous structure was constructed. The approximate analytical relationship between the structural descriptor and the displacement field was established, which avoids multiple meshing and a finite element simulation, which will greatly accelerate the optimization design process. The core includes the correlation between porous structure parameters and properties and the correlation between properties and performance based on TPMS.  
To facilitate the application of pressure, considering the shape of the upper and lower end of the actual interbody fusion cage, a horizontal solid is added to the upper and lower surface of the best TPMS porous structure, as shown in Figure 5: