## 2 Materials and Methods  
### Design of the Study  
The model design and overall experimental workflow of this study are illustrated in Figure 1. To design the model in each group, a maxillary tooth denitform model (D85 DP-500B.1, Nissin, Kyoto, Japan) was scanned using a laboratory scanner (Identica T500, Medit, Seoul, Korea), with the obtained data exported in the Standard Triangulated Language (STL) digital file format. The converted design file was then imported into modeling software (Meshmixer, Autodesk, San Rafael, CA, USA), the palate and other unnecessary structures were deleted, and a U-shaped model was designed. A cross-arch plate model was designed by attaching a 1.5-mm-thick cross-arch plate at the position of the palate (Figure 2). Figure 1: Workflow of the trueness and precision analysis for groups with healing abutment (HA). See the main text for the group definitions. R1 represents the most precise scan out of 28 scans after the precision analysis. One implant was placed at each position where a tooth was missing, with each implant designed to be placed in the same position in each model. Once the implant surgical guide was designed using Implant Studio software (3 Shape, Copenhagen, Denmark) and three-dimensionally printed using an SLA 3D printer (Form 3, Formlabs, Somerville, MA, USA), the implants were installed at the position of the missing teeth in each model by a single expert clinician. Since the implant positions were likely to affect the results, an implant surgical guide was used to ensure precise implant placement for each model. A hemisphere was fabricated on the labial/buocal side of the gingva corresponding to each tooth position on a curved line. The distance between the upper and lower hemispheres in each position was measured during the linear measurement process. The following six groups of experimental models were produced based on whether the HA was connected to the installed implant location and the location of missing teeth (Figure 2):  
1. HA-2: HA group with two missing teeth replaced with implants (first molar and second molar). 2. HA-3: HA group with three missing teeth replaced with implants (first premolar, second premolar, and first molar). 3. HA-4: HA group with four missing teeth replaced with implants (first premolar, second premolar, first molar, and second molar). 4. NHA-2: non-HA (NHA) group with two missing teeth replaced with implants (first molar and second molar). 5. NHA-3: NHA group with three missing teeth replaced with implants (first premolar, second premolar, and first molar). 6. NHA-4: NHA group with four missing teeth replaced with implants (first premolar, second premolar, first molar, and second molar). The maxilla and mandible were in a stable bite, with the area of missing teeth being on the right side of the model. This study compared three IOSs that are commonly used: CS3600(r) (version 3.1, Carestream, Dental, Atlanta, GA, USA), Trios 3(r) (3 Shape, Copenhagen, Denmark), and I500(r) (Medit, Seoul, Korea). The scanning performance is influenced by the scanning speed, and so each arch was scanned at the same speed by a single operator within about  
Figure 2: Images of the experimental models. HA groups and non-HA (NHA) groups are placed as follows: (**A**) HA-2, (**B**) HA-3, (**C**) HA-4, (**D**) NHA-2, (**E**) NHA-3, and (**F**) NHA-4. 90 s. In order to control the variance, this study kept the scanning process of all the IOSs at the same speed to compare the performance of IOSs during a certain limited period. All models with implants and HAs in position were scanned using a laboratory optical scanner (T500, Medit, Seoul, Korea), which can probe the surface of an object to obtain detailed 3D information. The acquired data included the maxillary and mandibular arches as well as information about bite registration. Each model was scanned eight times, and one of these scans was randomly selected as a reference scan for the trueness analysis of the IOSs.