## 1 Introduction  
The dental implant has been a common treatment for missing teeth. The main material of a dental implant is titanium, which displays well-documented mechanical properties and biocompatibility [1] that allows the process of osseointegration between bone and dental implant and provides stability when biting forces are applied. Recent clinical studies have reported the success rate of dental implant to be upwards of 95% [2] and both the periodontal [3] and biomechanical causes [1] affect the peri-implant tissue.  
The esthetics of dental implants is affected by the peri-implant soft tissue and the underlying crestal bone [4; 5; 6]. Different implant characteristics such as its size, material (titanium vs. zirconia),roughness, surface modification (including grit-blasting, acid-etching, and anodization [7]), thread design, connection, and the prosthetic abutment design can influence the stress around immediately loaded implants [8; 9; 10; 11; 12; 13]. It has been found that immediate occlusal loading applies to the implant within two weeks of implant insertion before osseointegration [14]. For example, it was found that the strain was concentrated in the cortical bone around the implant neck and was influenced by the diameter of the implant [10; 15; 16].  
The design of platform switching [17] involves the implant-abutment interface being horizontally repositioned inwardly by using a prosthetic abutment with a smaller diameter, and this has been found to be beneficial by leaving less vertical distance necessary to establish the peri-implant biological width. The loss of crestal bone height is therefore inversely related to the discrepancy between the prosthetic abutment and the implant [18; 19] and it has been confirmed that the design of platform matching preserves peri-implant bone by a measurable degree [2; 20].  
In addition to this biological advantage, from the biomechanical point of view platform switching will decrease the stress in the bone surrounding an implant [21; 22]. The stress transmitted to the crestal bone was found to decrease when the prosthetic abutment diameter was reduced by 10% (to 4.5 mm) or 20% (to 4.0 mm) using 5 mm \(\times\) 13 mm implants, regardless of the presence of microthreads or a smooth surface or the direction of the applied force (90 or 15 degrees) [23]. However, only a few studies have investigated the biomechanics of the design concept of platform switching in immediately loaded implants [9; 13].  
This study used NobelActive (NA) implants (Nobel Biocare, Gothenburg, Sweden) to investigate the biomechanical effects of the design of platform switching as well as implant diameter in peri-implant bone. According to previous studies, the design of the NA implant--featuring self-tapping and bone-compressing properties--can increase its primary stability and potentially makes this kind of implant more suitable for immediate placement in fresh extraction sockets and where immediate loading is applied [24; 25; 26; 27]. The NA implant contains a built-in platform switching concept aimed at peri-implant bone maintenance; however, it is not yet well understood whether this implant affects the biomechanical environment of peri-implant bone.  
The purpose of this study was to elucidate the effects of loading types, diameter of platform, and implant diameter on peri-implant bone strain, especially for an immediately loaded implant with the design concept of platform switching.