## 2 Methods and Materials
### Construction of Finite Element Model of Human Tibia  
After constructing the 3D model of the human tibia using the above-described methods, an FEM of the tibia based on this 3D model was built. The Three-matic 8.0 software was used to locally refine and optimize the mesh of the model to ensure its accuracy and simulation effectiveness when constructing the FEM. Compared to other software, Three-matic has the ability to highly automate the design modification, FEA/CFD pre-processing, and mold design of STL files while also enabling design modifications for complex free-form surfaces. The mesh was homogenized to ensure the accuracy and reliability of the simulation. The number of triangular meshes on the surface of the model was minimized as much as possible while retaining accuracy to reduce the size of the model. Through the above operation, high-quality surface meshes were obtained with a mesh count of 66,780. For body meshes, traditional hexahedral elements could increase simulation accuracy, but generating hexahedral elements was prone to errors due to the irregular shape of the tibia. Using the appropriate tetrahedral elements could effectively ensure simulation accuracy during biomechanical analysis [13]. Therefore, let 10 elements were used as the body mesh of the model, with a maximum side length of 3 mm. The tet 10 elements had appropriate plasticity and creep as well as a large strain capacity. Each node had three degrees of freedom in the X, Y, and Z directions. The mesh quality distribution of the tibial model is shown in Figure 4.  
Figure 4: Body mesh of tibial model. Figure 3: Hand-drawn outline and the fitted tibia model. (**a**) Contour line. (**b**) Tibial model. In Figure 4, the quality of all grids is above the set maximum. The tibial material was assigned values after dividing the surface and body meshes of the tibial model. The common assignment methods included homogenization, binary assignment, and grayscale assignment. The homogeneous assignment method did not accurately capture the actual situation of the tibia. The binary assignment method was prone to abnormal stress mutations, and the grayscale assignment method was prone to producing non-bone materials in the model [14]. Therefore, a material assignment method based on the grayscale gradient was developed. This method divided the tibia into five regions for allocation. First, 10 layers of fault images were uniformly extracted from the small beam areas at both ends, and 20 layers of fault images were uniformly extracted in the backbone area. The MIMICS software was used to evenly set 10 detection lines on each layer of the fault image for CT value detection. Then, all data were extracted, data points within the medullary cavity were filtered and removed, and the mean method was used to obtain the average CT values of the two end-shaft and trabecular regions. Finally, the CT values were converted into material parameters and mapped to the model. This method could effectively prevent non-bone materials from appearing in the tibial model. Figure 5 shows the regional division of the tibial model. As shown in Figure 5, the tibial model includes five regions: the proximal trabecular (A1), distal trabecular (A2), and diaphyseal (A3) areas and a transition zone between the proximal trabecular and diaphyseal areas (A4 and A5, respectively). The boundaries of A1 and A2 are 68 mm and 282 mm, respectively. Furthermore, the distribution of CT values must be ascertained when assigning values to tibial materials. Based on the CT value detection results, data points in the medullary cavity can be proposed to obtain the average CT values of the trabecular and diaphyseal regions at both ends. This allows for the subsequent calculation of the apparent density and Young's modulus (YoM) of each region. This expression is shown in Equation (6). \[\left\{ \begin{array}{l}D=-13.4+1017*Gv\\ E=-388.8+5925*D\end{array} \right. \tag{6}\]  
\(D\) is the apparent density, \(Gv\) is the grayscale value, and \(E\) is the YoM.