## 3 Results
In the CDI region, however, the damage area of the lower part appeared smaller when compared with the damage area in grade 10. Specifically, in the CDIII group, all the threaded parts in the upper and lower parts were almost eliminated. Specifically, CDIII-1 design was mostly damaged and destroyed in the upper part. The damage width in the vertical direction of the screw insertion direction was measured in the cross-sectional image (Figures 9 and 10) of the artificial bone that was finally removed from the screw. The results are shown in Figure 11a. The outer diameter was constant at 7.5\(\upmu\) although the damaged width increased sharply when the core diameter increased. Additionally, when the conical angle increased, the damaged width also showed a tendency to increase. Figure 2:0 (**a**) damaged width, (**b**) damaged thread height, and (**c**) increasing ratio of density of the artificial bone with the screw removed after the pullout test. Figure 2:1 Cross sectional images of the artificial bone (grade 20) with the screw removed after the pullout test. The height of the remained thread measured in the cross-sectional image (Figures 9 and 10) is shown in Figure 11b based on each density and screw design. When the core diameter and conical angle increased, the remained thread height tended to decrease irrespective of density, and the tendency was in agreement with the thread shape of the screw design. Though, when the core diameter increased, the damaged thread height decreased when compared with the actual thread height of the manufactured screw due to increases in the deformation and fracture. Specifically, when the core diameter increased, the thread height slightly decreased when the angle increased in the CDII and CDIII groups, with the exception of the CDI group with a high thread height. Conversely, the density of the damaged area was measured and compared with the density of the artificial bone prior to deformation and damage, and the values expressed as a percentage were termed as increasing ratio of density. The values were determined as the criterion of artificial bone damage and shown in the graph in Figure 11c. Irrespective of the density, the degree of damage of the artificial bone exhibited an increasing tendency with increases in the core diameter. In the CDI-CDII region, the degree of damage of grade 20 exceeded that for grade 10 although the degree of damage of grade 10 reversed and exceeded that of grade 20 in the CDIII group. When the distribution of the result values was linearized, the slope of grade 10 was steeper than that of grade 20. In order to more easily investigate the relationship between the core diameter and the conical angle through the 2D and 3D response surface analysis in Figures 12-14 are performed by ANSYS. So, the optimal screw design derived from the 2D and 3D response surface plots. In the 3D response surface plot, each x and y axes represent the conical angle and core diameter respectively, and the z axis denotes the pullout force. As shown in the image, the pullout force decreased when the core diameter and conical angle increased. Furthermore, in grade 10, the pullout force was high in the CDI group when the core diameter is 3.75o, and the pullout force increased when the conical angle was 8.58\({}^{\circ}\). At grade 10, the tendency of a gradual surface with each variable was manifested by proceeding at grade 20. The 3D response surface plot is shown in Figure 13 and indicates the effect of density, core diameter, and conical angle on the damage of the artificial bone. In grade 10, the damage showed an increasing tendency with increases in the conical angle although it exhibited a wide area and did not significantly affect the degree of damage. When the core diameter increased, the damage significantly  
Figure 2:2 3D and 2D response surface plot of the pullout force with variables of the pedicle screw and density: (**a**) and (**d**) grade 10 (**b**) and (**e**) medium density of grades 10 and 20, and (**e**) and (**f**) grade 20.  
increased.