A strain gauge (2630-100, Instron Japan, Kanagawa, Japan) was attached between the worktable and jig, and the change in the distance between the worktable and jig was measured under the assumption that it would be the same as the implant displacements under loading conditions (Fig. 6). Measurements were taken five times at each loading site, and the mean of the five measurements was considered the representative value of the loading site in that model.

Implant displacement measurements under loading conditions in the FEA models

All nodes at the bottom of the artificial mandible were completely restrained, 100 N of vertical load was applied to the three loading points, and an elastic analysis was performed. The vertical displacement of the loading points was assumed to be the displacement of the implants under loading conditions, and analyses were performed for the three loading sites (Fig. 7).

Measurements of the three-dimensional displacement in the FEA models

We analyzed the three-dimensional displacements of the three implants when 100 N of vertical load was applied. The assessment sites were the neck and tip of the implant, and the displacements of the implants under loading were analyzed with respect to the buccolingual direction (x-axis), the mesiodistal direction (y-axis), and the inferior-superior direction (z-axis).

Measurement of strain

Measurement of strain in the experimental models

An Instron-type universal testing machine was used to run a compression test during which strain was measured simultaneously. The strain gauges and a laptop computer (Latitude E5500, Dell, Texas, USA) were connected to a sensor interface (PCD-300B, Kyowa Electronic Instruments, Tokyo, Japan), and the strain in the peri-implant bone during the application of a 100-N load was measured.

Measurement of strain in the FEA models

The places on the experimental models where the strain gauges were applied were represented as coordinate points on the FEA models, and the strain in the FEA models was calculated by dividing the change in length between before and after loading by the length of the strain gauges.

Assessment of the stress distribution in the FEA models

An equivalent stress occurring in the peri-implant bone during loading was observed and assessed in a buccolingual cross-section of the no. 36 implant. The stress distributions were compared between placements.

Statistical analysis

Compressed displacement and strain values were examined by two-way analysis of variance using differences in load site and placement as factors. The level of significance was set to 5 %. Subsequently, Tukey’s method was used to perform a multiple comparison test, and for this also, the level of significance was set to 5 %.

PASW Statistics Ver18 (SPSS, Tokyo, Japan) was used for statistical processing.