## 3 Results  
In order to effectively explain the deformation of the artificial bone at the contact area with the screw during the pullout behavior, the microstructure and compressive behavior of the artificial bone were observed first. Figure 1 shows the microstructure of an artificial bone with osteoporotic bone density (grade10 (0.16 g/cc)) and normal bone density (grade 20 (0.32 g/cc)). The cell size range of osteoporotic bone was 37-100 \(\upmu\)m, and normal bone exhibited a smaller cell size range than that of the osteoporotic bone as shown in the microstructures in Figure 1. The compressive behavior of the artificial bone that exhibit the aforementioned microstructure is shown in Figure 2. When the density of the artificial bone doubled, the yield compressive stress increased by approximately three to four times. Figure 1: Microstructure of artificial bone (**a**) grade 10 and (**b**) grade 20 via SEM. Table 1 shows the values of each experimental variable. Previous studies suggest that the insertion depth was fixed at 20 mm, and the pullout test was conducted by choosing screw sizes corresponding to 5.5, 6.5, and 7.5o, which are most commonly used for fracture treatment of vertebrae. The results indicate that the pullout force tended to increase with increases in repulsion force from compression due to screw volume and increases in contact area between the artificial bone and screw. Images of the pedicle screw designed and manufactured by considering the parameters which are the core diameter and conical angle are shown in the Figure 3. The Figure 3d shows the schematic diagram of pullout test. The core diameter and conical angle were determined as 3.75o, 4.1o, 5.5o, 5.72\({}^{\circ}\), 8.58\({}^{\circ}\), and 11.42\({}^{\circ}\), respectively, and the initial point at which the conical angle starts was fixed at 27.95 mm from the tip of the screw. When the core diameter increased and conical angle increased, the thread height at the top of the screw decreased. With respect to a pedicle screw used in patients, the purpose of the treatment and the patient's condition (i.e., bone thickness, density, and size) should be considered and applied to patients. Thus, the pedicle screw was completely inserted at 50 mm based on the length of the screw designed and manufactured in the study. Thus, the pullout force increased by approximately 4-5 times when compared with that in the previous study [12; 24]. The core diameter was determined as 3.75o, 4.1o, and 5.5o, and classified into CD I, II, and III groups, respectively. In addition, the pedicle screws with conical angles of 5.72\({}^{\circ}\), 8.58\({}^{\circ}\), and 11.42\({}^{\circ}\) are represented by CD(I/II/III)-1, CD(I/II/III)-2, and CD(I/II/III)-3, respectively. Figure 4 shows the pullout force-displacement curve of the pullout test based on each screw design and bone density. The initial linear region in the graph was termed as the elastic bond section, and its slope was different based on the design of the pedicle screw. In the pullout curve, the slope of the initial linear region of grade 10 that exhibits low density exceeded that of grade 20 on the whole. The schematic diagram of the pullout behavior of the screw is shown in Figure 5. \begin{table}
\begin{tabular}{c c c c c c c c c c} \hline
**Screw Design** & **CD** & **CD** & **CD** & **CD** & **CD** & **CD** & **CD** & **CD** & **CD** \\  & **I-1** & **I-2** & **I-3** & **II-1** & **II-2** & **II-3** & **III-1** & **III-2** & **III-3** \\ \hline Insertion depth (mm) & & & & & 50 & & & & \\ Outer diameter (\(\omega\)) & & & & & 7.5 & & & & \\ \hline Core diameter, CD (\(\omega\)) & 3.75 & 3.75 & 3.75 & 4.10 & 4.10 & 4.10 & 5.50 & 5.50 & 5.50 \\ Conical angle, CA (\({}^{\circ}\)) & 5.72 & 8.58 & 11.42 & 5.72 & 8.58 & 11.42 & 5.72 & 8.58 & 11.42 \\ \hline \end{tabular}
\end{table} 
Table 1: Screw design specifications. Figure 2: Compressive stress-strain curve of artificial bone. Figure 4: Pullout force–displacement curve of pedicle screws with (**a**) grade 10 and (**b**) grade 20.