Implant displacement under loading conditions was measured using an Instron-type universal testing machine (Instron-5500R®, Instron Japan, Kanagawa, Japan) for the experimental model. The experimental models were placed on the worktable of an Instron-type universal testing machine, and compression tests were performed using a conical jig. A vertical load was applied at a rate of 0.5 mm/s on the three loading points. Using a report [23] stating that the maximum occlusal force applied to an implant superstructure in the molar region is 200 N as a reference, we selected 100 N for loading, to simulate the forces generated during mastication. 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.

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).

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).

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.