## 3 Results  
### Design  
Four different types of parametric models of bioimplants were built, using four different types of unit cells and filling. Implant models were built by replicating unit cells along three coordinate axes (X,Y,Z) to obtain a wire frame with the addition of a cylindrical base plate. The following unit cellswere constructed (see Figure 4): UC001--the cell built on the basis of tetrahedral diamond structure, with rib thickness of 0.4 mm, cell length (L) of 2.3 mm, cell width (W) of 2.3 mm, and cell height (H) of 1.7 mm; UC002--the cell built on the basis of the UC001 unit cell by removing dangling ribs, with rib thickness of 0.7 mm, L = 1.6 mm, W = 1.6 mm, H = 2.3 mm; UC003--the cell built by duplicating the UC002 unit cell along the X and Y axes, with the offset along the Z-axis by H/2, and along the X-axis by W/2, with rib thickness of 0.7 mm, L = 3.5 mm, W = 3.5 mm, H = 3.8 mm; UC004--the cell built by compressing the UC003 unit cell along X and Y axes by a factor of 2, with rib thickness of 0.3 mm, L = 2.0 mm, W = 2.0 mm, H = 4.1 mm. Based on the unit cells data, we modeled the bioimplants with the following wireframe (mesh) types: BI001--the wireframe built by replicating the UC001 unit cell along three coordinate axes--by a factor of 3 along X and Y axes, and by a factor of 5 along Z axis; BI002--the UC002 unit cell is replicated by a factor of 2 along X and Y axes, and by a factor of 4 along Z axis; BI003--the UC003 unit cell is replicated by a factor of 1 along X and Y axes, and by a factor of 3 along Z axis; BI004--the UC004 unit cell is replicated by a factor of 3 along X, Y, and Z axes. The above structures were limited by a 5 mm thick cylinder of 3.8 mm in diameter. These structures were then trimmed by using the SelBoundary operation. Dangling ribs in the structures were also deleted. A 2.5 mm thick cylinder of 4 mm in diameter was modeled as the implant base plate, allowing: (a) better adhesion of a part to a modeling base for 3D printing; (b) tight closure of the inlet hole of a bone defect; (c) machining of a part to the shape of the bone for better implantation into the defect. Modeling and unit cell replication parameters are given in Table 1. Implant models are shown in Figure 5.  
Figure 4: Unit cells used for implant modeling: (**a**) UC001—the unit cell built on the basis of tetrahedral diamond structure (rib thickness = 0.4 mm, cell length (L) = 2.3 mm, cell width (W) = 2.3 mm, cell height (H) = 1.7 mm); (**b**) UC002—the cell built on the basis of the UC001 unit cell by removing open ribs (rib thickness = 0.7 mm, L = 1.6 mm, W = 1.6 mm, H = 2.3 mm); (**c**) UC003—the cell built by replicating the UC002 unit cell along the X and Y axes by a factor of 2, with the offset along Z-axis by H/2, and along X-axis by W/2 (rib thickness of 0.7 mm, L = 3.5 mm, W = 3.5 mm, H = 3.8 mm); (**d**) UC004—the cell built by compressing the UC003 unit cell along X and Y axes by the factor of 2 (rib thickness =0.3 mm, L = 2.0 mm, W = 2.0 mm, H = 4.1 mm). To improve stiffness of the structure, we added an extra material between the cylindrical base plate and the wireframe, using the bounded blending operation. Figure 6 shows the result of the bounded blending operation applied to assign stiffness to the implant structure. In our case, the bounded blending operation includes the implicit functions of two geometric primitives: the cylindrical base plate and the wireframe; the R-function is union. The files of the BI001-BI004 models designed in Rhino software with the Symvol plugin can be found in the Supplementary Materials. The screenshots of the executed operations are also shown in the Supplementary Materials. File sizes of the models in various formats are given in Table 2.  
\begin{table}
\begin{tabular}{c c c c c c c} \hline \hline \multirow{2}{*}{**Model**} & \multirow{2}{*}{**Unit Cell**} & \multirow{2}{*}{\ \begin{tabular}{c} **Rib Thickness** \\ **T (mm)** \\ \end{tabular}  } & \multirow{2}{*}{ \begin{tabular}{c} **Cell Length L; Cell Width** \\ **W; Cell Height H (mm)** \\ \end{tabular}