Similar trends were observed in the direction and magnitude of displacement between placements. Buccal loading exhibited considerable motion towards the buccal rotation/tilting of the implant bodies, and lingual loading exhibited little motion towards lingual displacement. This corresponds to the fact that there was more compressed displacement during buccal loading than during lingual loading.

In past reports where models were used, it was reported that compressive strain in the peri-implant bone occurs in sites close to the loading side and tensile strain occurs on the side opposite to the loading side [25, 28]. Concentration of stress leads to bone resorption [3–5]. In the experimental models in the present study as well, considerable compressive strain was observed in the loading-side peri-implant bone. Strain in the FEA models also exhibited considerable compressive strain on the loading side, similar to the experimental models. In terms of quantitative data for comparison with the experimental models, the length of the places where the strain gauges were applied was measured on the FEA models and the strain was calculated from the length before and after loading and compared with the experimental models. In previous verifications of offset placement with FEA models [15–18], the maximum stress that occurs in the peri-implant bone has been measured and compared with the observed stress distribution with straight placement. In the present study, we measured strain at the same sites in the experimental models and the FEA models, and therefore, we believe that it was possible to carry out a more multifaceted and objective assessment of the mechanical effects on the surrounding bone. The strain values for the experimental and FEA models showed similar trends with change in the loading site and placement of implants. However, the values of strain were different between the experimental and FEA models, the difference being greater than 10-fold at several sites. While comparing the experimental and FEA models, the difference in the accuracy of the cancellous bone and the difference in boundary conditions for the implant and the bone would affect the strain values. The cancellous bone in the experimental model was made of urethane resin foam that mimicked the trabecular structure. The cancellous bone of the FEA model, on the other hand, had a uniform structure, not a trabecular one. This seems to be the reason behind the difference in the strain values between the experimental and FEA models. While determining the boundary conditions between the implant and the artificial mandibular bone, immediate loading was assumed, but not osseointegration. The implant and artificial mandible in the FEA model were in complete contact. The coefficient of friction of the interface between the implants and artificial mandibular bones was set to zero. The boundary conditions of the experimental model were not bonded together, but they were completely fitted together mechanically. The difference in boundary conditions would affect the difference in strain values between the experimental and FEA models. Regarding how different placements affect strain, there was a trend for the strain to be greater when the loading site was at a greater distance from the load-supporting area (Fig. 15). In addition, there was not a significantly less strain site by offset placement. Anitua et al. [29] have reported that offset placement did not affect marginal bone loss around the implant in the oral cavity of the living body. Overloading of the peri-implant bone has been reported to result in bone resorption [3–5], and the concentration of considerable stress in the load-side peri-implant bone observed in our study confirms this. Hence, we conclude that our observation that offset placement did not reduce the stress around the peri-implant bone in both the experimental and FEA models is similar to that of the clinical report by Anitua et al. In addition, we also conclude that our results confirm the validity of both analyses. Thus, offset placement may not necessarily be more biomechanically effective than straight placement.