The experimental models were fixed in a micro-CT scanner (inspeXio SMX-90CT, SHIMADZU, Kyoto, Japan) and scanned under the following imaging conditions: tube voltage, 90 kV; tube current, 109 nA; and slice thickness, 100 μm. FEA software (Mechanical Finder®, Research Center of Computational Mechanics, Tokyo, Japan) was used to construct three-dimensional FEA models from the resulting computed tomography (CT) data. The mesh was constructed of tetrahedral elements, and the total numbers of nodes and elements were approximately 270,000 and 1,500,000, respectively. For the Young’s modulus and Poisson ratio of each element, the artificial mandible manufacturer’s publicly disclosed values were used so that they would be similar to the physical properties of the experimental model. They were 628 MPa and 0.3 for artificial cancellous bone, 1,372 MPa and 0.3 for artificial cortical bone, and 100,800 MPa and 0.3 for the implant and superstructure (Table 1). 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.

To better understand how peri-implant bone is affected by differences in boundary conditions, two different kinds of models were fabricated by changing the boundary conditions between the implant and artificial mandibular bone. One was called a ‘contact model,’ in which the artificial mandible and implant 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 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 other was called a ‘fixation model,’ in which the artificial mandible and implant were completely bonded together. Delayed loading after the acquisition of osseointegration was assumed in this model. Fixation models were constructed by changing the boundary conditions of the contact model.