FEA is useful for mechanical simulations of a living body and has been used in implant dentistry research under careful consideration of the analysis conditions [32, 33]. Although some reports have demonstrated that bone density varies according to bone type and location, the material properties of the mandible were homogenous and isotropic in this study. However, the effect of this difference was considered to be negligible under the confirmation of the displacement of teeth and implants because of its far larger elastic modulus and far smaller strain than those of soft tissues, such as TMJs and PDL. Since the purpose of the present study was to examine the distribution of occlusal forces on the occlusal surface, occlusal forces should be mainly affected by the displaceability of TMJs and teeth, not by that of osseointegrated implants.

The FEMs in this study were based on those reported by Kasai et al. [14] and Kayumi et al. [15]. The displaceability of TMJs was regarded as that of the cartilage [30] because it has a far smaller elastic modulus than that of the TMJ disc [34, 35]. Therefore, the elastic modulus of the springs corresponding to TMJs was determined based on the thicknesses of the TMJ disc [36] and articular cartilage [35], the stress-strain curve of the intervertebral discs [30], and the displacement of the condyle [37, 38] in intercuspal clenching by indirect measurement. Although the material properties of the human body vary on an individual basis, the models used in this study were therefore considered to be appropriate to investigate the distribution of occlusal forces on the teeth, implants, and TMJs.

Based on previous literature [31, 39], occlusal loading of 200 N was considered to correspond with hard clenching. However, a previous study indicated that the maximum biting force (400 N) was better for occlusal adjustment with intercuspal clenching. Therefore, this study was performed with the assumption that the maximum functional force was 400 N. Occlusal loading of 100 N was considered to correspond with light clenching while loading of 200 N was considered to correspond with middle clenching. Calculations were also performed under a load of 800 N, which was assumed to be the maximum nonfunctional occlusal force, such as that exerted in nocturnal bruxism. Because of the difficulty of controlling nocturnal bruxism, this value was considered to be sufficient to include as the condition under maximum force [40]. However, Hattori et al. [41] described that neuromuscular regulatory systems control maximum clenching strength under various occlusal conditions. Therefore, the large force used in this study may not occur clinically in the SDA except in the case of nocturnal bruxism.