## 2 Methods and Materials
### Construction of 3D Model of Human Tibia
If the threshold segmentation range was set too small, it would result in missing tissue to be extracted, thereby causing the constructed model to lack some features. The target tissue of this study was the human tibia, and MIMICS recommended a threshold segmentation range of 226-3071. Based on this range, the selected tissues in the three views (sagittal, coronal, and horizontal) were observed layer by layer to ascertain whether any tissues were absent or superfluous. This was done to adjust the recommended threshold segmentation range. The final tibial threshold segmentation range selected in this article was 220-2474. After threshold segmentation, there were still many other bone tissues (femur, fibula, foot bones, etc.) connected to the tibia. To extract a complete and independent tibia model, it was necessary to separate the tibia from other bones. Firstly, the Multiple Slice Edit command was used to eliminate other bone pixels connected to the tibia. This operation required extra attention to detail by observing the images in the three views to determine which pixels needed to be eliminated, otherwise the generated 3D model would not conform to the anatomical structure of the tibia. Then, the Region Growing command was used to extract independent tibial masks. Due to interference factors such as noise and vibration during CT scanning, there were some abnormal cavities in the final mask obtained, so a cavity-filling operation was required. Manually filling the cavity layer by layer was tedious. The Calculate Polylines command was used to obtain the contour line of the tibial mask plate, whether the contour line was complete layer by layer was observed, and using the contour line to fill the cavity could greatly improve work efficiency [12]. However, CT scans were affected by factors such as noise, which resulted in the presence of abnormal cavities. Therefore, the generated contour lines were used to fill the cavities. The 3D model of the human tibia was constructed using the aforementioned method, which resulted in the formation of surface defects and an overall model that was relatively complex. Therefore, the model was first converted into a point cloud model. Then, the Geomagic Studio 2015 software was used for surface reconstruction, repairing surface defects, and streamlining the model. The first step in the surface reconstruction was point cloud simplification, which involved using a unified sampling method to reduce the number of point clouds in the model with an absolute sampling spacing of 0.48 mm. Second, the simplified point cloud model needed to be converted into a polygon model before being encapsulated with a maximum of 30 triangles during encapsulation. Mesh redrawing and noise reduction treatments were required because of the presence of surface imperfections, such as holes and nails, with the packaged model. This required setting target edge length to 0.8 mm, smoothness level to 3, smoothness to 70, and deviation limit to 1 mm. The models before and after polygon repair are shown in Figure 2.  
As shown in Figure 2, after polygon processing, the surface of the model was relatively smooth, without obvious defects such as holes or nails. This model was used as a basis to perform surface fitting on the tibial model. The selected surface was a NURBS surface, and the contour lines were manually drawn when performing surface fitting. Then, a surface patch (with 30 grids) was constructed based on the contour lines. Adaptive fitting considering the irregular shape of the surface patches was required to ensure the accuracy of the model. When fitting, the control point should not exceed 18 and the surface tension should be 0.3. Compared to models obtained through specialized software, the tibial 3D model obtained through the above method had good dimensional and structural universality. The axial functional gradient model could effectively avoid boundary abnormal stresses caused by discontinuous material properties, allowing the material properties of the model to continuously and smoothly change.