## 1 Introduction  
Ossoeintegrated dental implants have been accepted as one of the major treatment concepts for restoring completely and partially edentulous patients [1; 2; 3; 4; 5; 6]. The major factor that influences long-term implant use depends mainly on the biological stability provided by the osseointegration between the bone and implant interface (bone/implant interface) [2; 5; 6; 7; 8]. However, marginal bone remodeling around the implant is affected by implant mechanical behavior even after the bone/implant interface osseointegration is completed [2; 5; 6; 7; 8]. Overloading leads to marginal bone resorption, usually due to excess mechanical stress transferred from the bone/implant interface onto the supporting bone (crestal cortex) [2; 5; 6; 7; 8; 9]. Some studies have assessed the implant-abtument connection structure's effects on the marginal bone level change. High stress and marginal bone loss around the external hex connection structure were found [6; 10; 11; 12; 13; 14; 15; 16]. Besides resorption for the crestal cortex, internal components within the implant (abtument screw) may suffer failure or loosening when unfavorable stress is transferred from the abtument to the implant [2; 3; 4; 5; 9; 17].  
Implant-abutment connection design may be a primary factor influencing the force transmission mechanism at the implant-abutment and bone/implant interfaces [2; 5; 9; 17; 18]. Different implant-abutment connection designs, i.e., external hex and internal tri/hex connections are predicted to induce different micro motion and stress distribution patterns under occlusal loads [19]. Mechanical complications such as screw fracture or loosening may occur frequently when the occlusal load exceeds the preload applied when the implant-abutment was secured by the retaining screw (abutment screw) [2; 5; 9; 17; 18; 20; 21]. A retrospective study evaluated the implant component fracture type from 1289 implants to suggest directions for successful implant treatment. The study indicated that abutment screw fracture occurred most frequently in the maxillary anterior region [22].  
From the biomechanical perspective for internal implant-abutment connection, modifying the implant-abutment connection design, such as by increasing the abutment screw diameter or implant neck wall thickness, may enhance the strength of implant components to reduce the implant failure rate. However, the relationship between the unilateral wall thickness in the abutment, implant neck, and abutment screw diameter is mutually compensated, and few studies have addressed their interactions. The unilateral wall thickness in the abutment and implant neck are reduced when the corresponding hole diameter is increased to fit a larger-sized abutment screw. [PERSON] et al. indicated that the abutment screw diameter should preferably exceed \(\Phi\)1.4 mm and a unilateral wall thickness of \(>\)0.5 mm is an optimal selection for abutments [22]. However, this study only evaluated and compared the influence of abutment and fixation screw sizes for a 4.1 mm diameter implant in a mandibular model. Actually, different implant sizes for real clinical use with respect to different implant neck wall thickness are needed to understand their mechanical interactions.  
The aim of this study is to evaluate the mechanical interaction between the abutment screw size and unilateral neck wall thickness of the internal implant-abutment connection for three implant sizes using nonlinear finite element analysis. The main effect of abutment screw size and unilateral implant neck wall thickness on mechanical response (stress and strain) was also computed to identify the importance of each parameter.