## 2 Materials and Methods  
An in vitro experimental test including Periotest and strain gauge analyses was used to examine the influences of platform switching and implant diameter on the primary implant stability and the bone strain around immediately loaded implants. NA implants with a length of 11.5 mm and diameters of 3.5 mm, 4.3 mm, and 5.0 mm were employed (Figure 1), and designated as the NP3.5, RP4.3, and RP5.0 implants, respectively; the diameters of their corresponding abutments (Snappy(tm) abutment, Nobel Biocare, Goteborg, Sweden) are 3.0 mm, 3.4 mm, and 3.4 mm, respectively. Although the RP4.3 and RP5.0 implants had different diameters, their implant platforms were both 3.9 mm in diameter, which means that they possessed the same degree of platform switching in 0.5 mm after using a 3.4-mm-diameter abutment. The platform of NP3.5 implant was also 3.5 mm. Because the length of platform switching was obtained by subtracting diameter of abutment from diameter of implant platform, the NP3.5, RP4.3, and RP5.0 implants all had the same degree of platform switching (0.5 mm). Three specimens of rectangular synthetic trabecular bone (Sawbones model 1522-05, Pacific Research Laboratories, Vashon Island, WA, USA) were prepared for each implant group. The model of the trabecular bone with a density of 0.4 g/cm\({}^{3}\) and elastic modulus of 759 MPa was employed to simulate [PERSON]'s type 2 (D2) bone [28; 29]. A 2-mm-thick synthetic cortical layer (Sawbones model 3401-02, Pacific Research Laboratories, Vashon, WA, USA) with an elastic modulus of 16.7 GPa was then attached to the top of the trabecular bone to complete the preparation of the experimental bone model. The dimensions of each experimental bone model were around 45 mm \(\times\) 30 mm \(\times\) 43 mm (Figure 2). Figure 1: The RP5.0, RP4.3, and NP3.5 implants (from right to left). Figure 2: An experimental bone block with a 2-mm-thick synthetic cortical bone shell was prepared. After the implant was placed in the bone block, two rectangular rosette strain gauges were fixed onto the crest cortical region near the buccal (B) and lingual (L) sides of the implant. In order to simulate an immediately loaded implant, the interface between the implant and bone was prepared for contact only. After inserting the implants into the bone block and connecting titanium prosthetic abutments to the implants, the device of Periotest (Periotest Classic, Medizintechnik Gulden, Modautal, Germany) was used to measure the mobility of the implant. Periotest is one of the clinical noninvasive techniques and is easy to be used; therefore it is favorable for dentists to determine the initial implant stability after implantation. The process of the measurement was as follows: The tip of the device was perpendicularly positioned 2 mm from the prosthetic abutments and the instrument delivered calibrated impacts via a piston to the abutment four times per second for 4 s [30] as seen in Figure 3. Periotest values (PTVs) were obtained four times in each of four directions (buccal, lingual, mesial, and distal) for each model. Two kinds of occlusal loading--a vertical force and a 30 degree lateral force--were applied to the prosthetic abutments by a universal testing machine (JSV-H1000, Japan Instrumentation System, Nara, Japan) with a custom-made jig as seen in Figure 4. Both kinds of forces had a magnitude of 190 N [31], and the head speed when applying the loads was 1 mm/min.