Analysis was performed according to the report by Kayumi et al. [15]. In linear finite element analysis (FEA), all teeth maintain perfect contact with antagonists with no stress on occlusal surfaces before loading. However, there must be some occlusal force on the occlusal surface when a mandible is in the intercuspal position. Since the displaceabilities of osseointegrated implants, natural teeth with PDLs, and TMJs are quite different from one another, the results of linear FEA under some occlusal loads should not correspond to real biomechanical conditions.

To verify the similarity of the FE models to the real stomatognathic system, “initializing” of models, i.e., modification of the condition of occlusal contact assuming the intercuspal position, was performed before analysis. This procedure was performed by modifying occlusal contacts on the implants so that the distribution of occlusal force was symmetrical under load 400 N [15]. The occlusal contacts were modified by altering the load displacement curves of the springs on the implants. The load displacement curve was shifted so that the spring provided little resistance to compressive forces until the gap closed, i.e., occlusal surface came in contact with antagonists (Fig. 7). The size of the gap was determined by trial and error, such that the occlusal force, namely, the reaction force of the springs on the occlusal surface, was distributed with approximate symmetry [14, 15] in models Im6, Im67, Im456, and Im4567. This size was determined so that the amount of reaction force on the most posterior teeth on both sides became as equal as possible. After initializing was completed, symmetric distribution of the reaction force on the teeth and the superstructures was confirmed in each model. Thereafter, the FEA was performed under the load conditions of loads 100, 200, and 800 N using the software package MSC.Marc2010 (MSC Software). The distribution of the reaction forces on the occlusal surface and the mandibular condyle, which were regarded as the occlusal force and the load on the TMJ, respectively, was investigated.