To prevent loosening or fracture of screws retaining the prosthesis to the implants in the posterior partially edentulous region, the use of staggered buccal and lingual offset placement or wide implants is suggested. However, it is not known how this usage compensates for the torque produced by lateral occlusal forces. This study evaluated the effectiveness of offset placement of three implants and a wide implant placement at the most posterior site. Three-dimensional geometric analysis was used to calculate the tensile force applied to gold screws in clinical situations with buccal or lingual loading perpendicular to cuspal inclination (10 or 20 degrees ). Four variations of the placement of three implants (3.75 mm) are: (1) straight; (2) buccal offset of the second implant; (3) lingual offset of the second implant; (4) a wide implant (5 mm) placement at most posterior site. The offset placement did not always decrease tensile force at the gold screw, but wide implant placement and decrease in cuspal inclination did.

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Further validity of finite element analysis (FEA) in implant biomechanics requires an increase of modelled range and mesh refinement, and a consequent increase in element number and calculation time. To develop a new method that allows a decrease of the modelled range and element number (along with less calculation time and less computer memory), 10 FEA models of the mandible with different mesio-distal lengths and elements were constructed based on three-dimensional graphic data of the bone structure around an osseointegrated implant. Analysis of stress distribution followed by 100 N loading with the fixation of the most external planes of the models indicated that a minimal bone length of 4.2 mm of the mesial and distal sides was acceptable for FEA representation. Moreover, unification of elements located far away from the implant surface did not affect stress distribution. These results suggest that it may be possible to develop a replica FEA implant model of the mandible with less range and fewer elements without altering stress distribution.

More validity of finite element analysis (FEA) in implant biomechanics requires element downsizing. However, excess downsizing needs computer memory and calculation time. To evaluate the effectiveness of a new algorithm established for more valid FEA model construction without downsizing, three-dimensional FEA bone trabeculae models with different element sizes (300, 150 and 75 micron) were constructed. Four algorithms of stepwise (1 to 4 ranks) assignment of Young's modulus accorded with bone volume in the individual cubic element was used and then stress distribution against vertical loading was analysed. The model with 300 micron element size, with 4 ranks of Young's moduli accorded with bone volume in each element presented similar stress distribution to the model with the 75 micron element size. These results show that the new algorithm was effective, and the use of the 300 micron element for bone trabeculae representation was proposed, without critical changes in stress values and for possible savings on computer memory and calculation time in the laboratory.

Double implants have been thought to have biomechanical advantages for single molar replacement. To evaluate the effectiveness of double implants versus a wide implant, the vertical forces and torque on each implant were calculated by three-dimensional geometric analysis. Buccal load (100N) perpendicular to cuspal inclination (20 degrees) was applied at the occlusal surface of the superstructure. The three kinds of load points (A, B, C) were 1.5, 3.5, and 5.5 mm from the mesial contact point, respectively. Three implants were compared: mesial and distal double implants (phi 3.3 mm), and a wide implant (phi 5 mm). The wide implant showed torque around the long axis (1.8-15.0 N x cm) whereas double implants had no torque. On the other hand, the vertical forces on the mesial double implant were both smaller (60%: loaded at point C) and larger (140%: loaded at point A) than the wide implant. Given the smaller surface area of the mesial double implant, this large force may generate much higher stress in the peri-implant bone. These results suggest that the biomechanical advantage of double implants for single molar replacement is questionable when the occlusal force is loaded at the occlusal surface near the contact point.