## 4 Discussion  
The goal of dental implant development is to find those conditions that have better optimal structure for favorable biomechanical transmission. The stress of each component within the implant system cannot come close to or be greater than the ultimate implant material strength. The stress transmitted from the implant to the bone must also be as favorable as possible because excess load may  
Figure 3: Stress patterns for implant stress (MPa) (**a**), abutment screw stress (MPa)(**b**), abutment stress (MPa) (**c**), and bone strain (micro strain) (**d**). Figure 2: Main effect plots of implant neck wall (**a**) and abutment screw size at each level for maximum implant, abutment, and abutment screw stresses and maximum bone strain (**b**). easily result in poor osseointegration, failing the major design criterion [2; 5; 6; 7; 8]. However, complicated biomechanical complications are often caused by multiple factors and their interactions, and it is difficult to evaluate and predict them solely by clinical study or experiments [9]. Experimental approaches or clinical observations cannot provide enough information to determine the detailed mechanical response and interactions relating to variations in the structure design parameters, such as the abutment screw size and implant neck thickness investigated in this study. Nonlinear FE analysis with reasonable interface conditions (contact) that could simulate the inherent flexibility within the implant system was employed to understand the biomechanical influence of abutment screw size with a hexagonal Morse taper three-piece internal connection implant and implant neck thickness on the surrounding bone. The finite element (FE) method can alter the parameters in a more controllable manner and has become a commonly used analytical tool in orthopedic/dental biomechanical studies [24; 25; 26]. Nevertheless, most related research focused only on different implant-abutment connections, i.e., internal friction and external hex connections, to influence the peri-implant crestal bone resorption [2; 5; 6; 7; 8]. However, many clinical trials have pointed out that abutment and abutment screw damage are the other two main reasons for implant failure [2; 5; 6; 7; 8]. The objective of this study was to evaluate and compare the mechanical effects of the implant neck wall thickness and abutment screw diameter on stability using 3D CAD technology and nonlinear FE analysis. We referred to the ISO14801 standard force application method and applied oblique force at a 30\({}^{\circ}\) angle to the implant axis to simulate the situation where a single tooth is severely oblique in a clinical situation. A load of 200 N is considered to be about two-thirds of the maximum occlusal force in the posterior teeth [23]. Our FE model also considered cortical and cancellous bones to mimic real anatomical status for elevating clinical responses. The unilateral implant neck wall thickness significantly influenced the mechanical response magnitude for the abutment (12%), abutment screw (22%), and implant (17%) stresses and bone strain (30%), which were observed to decrease by at least 12% when the wall thickness was increased from 0.45 mm to 0.5 mm (Figure 2a). This phenomenon was due to the increased structure stiffness at the implant neck, able to disperse the stress transmission from the abutment to the implant and from the abutment to the screw. The stress concentration was also reduced at the hexagon connection junction because a thickened implant neck wall can distribute more stress to the abutment Morse taper. The decrease in bone strain might also be due to a stronger implant neck wall causing difficulty in the force pushed and squeezed from implant to bone. ANOVA analysis showed that the abutment screw size influenced the structure stiffness, and the maximum stress decrease rates were 10% and 29% when the diameter increased from 1.4 mm to 1.6 mm and 1.8 mm, respectively.