## 2 Materials and Methods  
### Three-Dimensional Model Design  
This study was performed under approval of the Institutional Review Board of Korea University Medical Center (KUMC) (IRB no. MD13022). A randomly selected maxillary central incisor from the human tooth bank at the KUMC dental center was used to build the tooth model. The geometry of the tooth was obtained through optical scanning with an i500(r) intra-oral scanner (Medit Inc., Seongbuk-gu, Seoul, Korea) and 3D modelling with CAD software from Geomagic Wrap(r) (3D Systems Inc., Cary, NC, USA).  
Based on the obtained stereolithography model of the maxillary incisor, four different RAI FE models were constructed using 3D CAD software (Inventor, Autodesk GmbH, Munich, Germany). For the four RAI models, a standard identical abutment was created based on morphological expectation of the original tooth crown. Among the four RAI designs, the following three design modifications at the root surface were constructed to allow for no additional drilling: (1) Non-modified root surface (NM); (2) wedge shape added at mesial and distal root surface (WG); and (3) lattice shape added at root surface (LT). The fourth RAI design has anchorage in the root apex, implanted using the press-fit method after additional drilling in the root apex area: (4) apex-anchor added RAI (AA). Figure 1 shows the four RAI designs with descriptions of the different geometrical characteristics.  
The geometry of the tooth-supporting maxillary bone with 1.0 mm thick cortical bone was constructed in accordance with a previous study [23]. In the 3D geometry maxillary alveolar bone model, an empty socket after a tooth extraction was formed by subtracting with the root part of each RAI model made by modifying the original tooth shape for each experimental group. The outer geometry of the ceramic crown component is the same as that of the crown of scanned tooth. The inner socket of the ceramic crown was formed by subtracting the RAI abutment part with arbitrary designed but having the same shape in all experimental groups. The thickness of ceramic crown is 0.5 mm at the lingual side, 1.0 mm at the labial side, and 2.0 mm at the incisal side. Figure 2 shows a 2D sectional view of the experimental group NM to explain the mutual relationship with the components constituting one experimental group. Figure 3 is a 3D diagram depicting the components of each experimental group.  
Figure 1: Four modified root analogue implant (RAI) designs of each experimental group. Dimensions and notations of the geometric properties are as follows: H1: the height of implants without additional drilling protocol (=16.13 mm). H2: the height of implants with additional drilling protocol (=19.25 mm). NM-RAI: non-modified surface designed RAI; WG-RAI: wedge shape added at mesial and distal root surface of RAI. The height and width of the wedge are 0.6 mm and 1.0 mm, respectively; LT-RAI: lattice shape added at root surface RAI. The height of the protruding lattice and the width of the floor are equal to 0.3 mm; AA-RAI: apex-anchor added RAI. Thread protrusion is from 0.3 to 0.6 mm. Thread distance is 1.0 mm. H1 is the length value of the teeth scanned in this study. H2 is 3.12 mm added to the value of H1, which is the value that assumed the length of the implant drill apex tip to be 0.12 mm plus 3 mm, which is half of 6 mm, the shortest implant length of most commercial implants, in order to prevent too deep drilling.  
Figure 2: 2D sectional view of the non-modified root surface (MN) group to explain the mutual relationship with the components constituting one experimental group.