## 4 Discussion  
In this study, the initial stability of a custom RAI design with drilling protocol was biomechanically evaluated by comparing it using a 3D FEA to other RAI designs without drilling protocols. Most previous research on the implantation of a patient-specific RAI after tooth extraction focuses mainly on achieving initial stability through modification of the root surface region, without considering additional drilling in the design of the RAI [19,20]. However, since the previous RAI implantation technique without additional drilling requires only a limited surface area (the tooth extraction socket), there is a limit to obtaining initial mechanical fixation immediately after implant placement. Therefore, we proposed a novel RAI design that requires additional drilling on surface area in addition to the surface of the tooth extraction socket. In addition, we performed experiments assuming the bone-to-implant interface is under a frictional contact condition. Most previous studies that performed biomechanical analysis of dental implants using the FE method set the contact condition between bones and dental implants as a bonded state [29, 30, 31]. This interface condition is only suitable for a fully osoe-integrated implant, which cannot be immediately applied in implantation stages. Therefore, in this study, frictional contact conditions were applied between the bones and dental implants, allowing the implant to slide on the bone. Assuming low COF values at the bone-to-implant interface can simulate the initial stability of immediate implantation conditions [32]. The initial stability of dental implants, in other words, the mechanical stability, can be achieved through mechanical interlocking between the implant-to-bone interface, irrespective of biological interaction; this is the most significant clinical issue with dental implantation [33]. According to the stress distribution results of this study, the modified-RAI-surface experimental groups (WD, LT, and AA), which added the penetration shape to the original tooth extraction socket surface, had a positive effect on the stress reduction of the cortical bone than the NM group without any surface modification. Similar to the findings of a previous study [19], this effect is expected to occur when the stress caused by an external load is more burdened on the cancellous bone region due to an increase in the mechanical fixation of that region (Figures 8 and 9). In addition, it should be considered that in the case of the LT group, the stress on the cancellous bone was significantly increased compared to the other groups, especially at a low COF, which may cause an overload on the cancellous bone. Therefore, the LT group results may be interpreted as follows: Over modification of the surface that induces excessive mechanical fixation may have a negative effect. However, in the AA group, which had a RAI that extended to the root apex rather than additional modification to the root surface, the stress concentration on the cortical bone was the lowest among all of the experimental groups and according to all COFs; the possibility of overload on the cancellous bone was also lower than in the LT group. Thus, it can be interpreted that the AA RAI design with additional drilling protocol can achieve favorable results in terms of stress distribution. In addition, Figure 8 showed that the region where the stress is very concentrated is closest to sharp margin of solid bodies of cortical bone. This region is the area around the dental implant neck, which coincides with the area where bone atrophy occurs due to overload in long-term clinical practice, which is similar to previous finite element analysis results and interpretations for dental implants [34].