Four two-wire strain gauges (KFR-02N-120-C1-11, Kyowa Electronic Instruments, Tokyo, Japan) were applied to the no. 36 peri-implant bone surface [21]. The surface of the measurement site was polished with no. 320 sandpaper and then wiped clean with acetone, following which they were adhered with a special adhesive (CC-33A, Kyowa Electronic Instruments, Tokyo, Japan). The strain gauges were applied at four places—the mesial, distal, buccal, and lingual sides of the implant—and the strains they measured were designated as strain M, D, B, and L, respectively (Fig. 5).

The experimental models were fixed in a micro-CT scanner (ScanXmate-L090H, Comscantecno, Kanagawa, Japan) and scanned under the following imaging conditions: tube voltage, 90 kV; tube current, 10 μA; and slice thickness, 106 μm. FEA software (Mechanical Finder®, Research Center of Computational Mechanics, Tokyo, Japan) was used to construct three-dimensional FEA models from the resulting CT data. The mesh was constructed of tetrahedral elements, and the total numbers of nodes and elements were approximately 260,000 and 1,400,000, respectively. FEA models were prepared with appropriate physical properties (Table 1) determined by consulting the values published by the manufacturer of the artificial mandible models and Young’s modulus and Poisson’s ratio used in past research [22]. The implant, abutment, and superstructure were assumed to be a continuous structure made of titanium; no intervening conditions were set between the implant and abutment nor between the abutment and superstructure. The artificial cortical bone, artificial cancellous bone, implant, and superstructure were assumed to be homogeneous, isotropic, and linearly elastic. The boundary conditions for the implant and bone were a state of 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 reproduced by the contact model of FEA. Immediate loading was assumed in this model, because a state of contact was reproduced between the implant and artificial mandibular bone. The FEA models were made so as to correspond to each of the three experimental models with the respective placements, so nine FEA models were prepared similar to the experimental models.