An artificial mandibular bone (P9-X.1135, Nissin Dental Products, Kyoto, Japan) with free-end edentulism of the left mandibular first premolar (no. 34), second premolar (no. 35), and first molar (no. 36) was used (Fig. 1). The model was composed of a two-layer structure of artificial cortical bone (urethane resin) and artificial cancellous bone (urethane resin foam).

Using the anatomical crown width diameter as a reference [20], we embedded three implants. The distance between the second premolar and mandibular first premolar implants was 8 mm. The distance between the first molar and second premolar implants was 10 mm.

An implant placement guide (Landmark Guide™, iCAT, Osaka, Japan) was fabricated to precisely embed the implants in the artificial mandible. A drilling machine (Enkoh’s, Enshu Industrial, Shizuoka, Japan) and implant placement guide were used to embed the implants perpendicular to the bottom surface of the artificial mandible. A drill used to form implant cavities (Brånemark System® Twist Drills, Nobel Biocare, Göteborg, Sweden) was mounted onto the drilling machine, and three implant cavities 3.0 mm in diameter and 10 mm in depth were formed. Then, in each of the implant cavities, an implant 3.75 mm in diameter and 10 mm in length (Brånemark System® Mk III, Nobel Biocare, Göteborg, Sweden) was embedded using 40 N cm of torque (Fig. 2).

Using models in which three implants were placed in a straight line (straight placement) as a reference, we also prepared two other types of models: (1) no. 35 was offset by 1.0 mm to the buccal side and no. 36 by 1.0 mm to the lingual side (buccal offset placement; B-offset), and (2) no. 35 was offset by 1.0 mm to the lingual side and no. 36 by 1.0 mm to the buccal side (lingual offset placement; L-offset) (Fig. 3). Three experimental models were prepared for each type of placement, i.e., a total of nine experimental models.

Using the anatomical crown width as a reference [20], it was determined that the occlusal surface view of the superstructure would be trapezoidal with a 7-mm buccolingual width in the mesial first premolar section, a 10-mm buccolingual width in the distal first molar section, and a 26-mm mesiodistal width (Fig. 4). The vertical dimension was 8 mm; the upper 4 mm was the thickness of the superstructure and the lower 4 mm was the abutment connection. Three loading points 2 mm in diameter and 0.2 mm in depth were applied to the occlusal surface of the first molar; these formed the buccal loading point (Fig. 4(a)), central loading point (Fig. 4(b)), and lingual loading point (Fig. 4(c)). The superstructure was made of titanium (ISUS, DENTSPLY Sankin, Tokyo, Japan) and fabricated using computer-aided design/computer-aided manufacturing (CAD/CAM). For each type of placement, we prepared three models by mounting the superstructure onto an artificial mandible model in which implants had been embedded; these served as the experimental models.