Boundary conditions of the model and simulation of occlusal adjustment

The boundary conditions used to verify the displaceability of teeth and analyze the distribution of occlusal forces are shown in Fig. 2a, b, respectively. In the former model, a vertical load was applied to the left canine with the restriction of nodes on the bottom of the mandible (Fig. 2a). FE analysis was performed under various loads following the construction of a load-displacement curve. In the FE models used to analyze the distribution of occlusal force, TMJs, maxillary teeth, and maxillary implants were replaced with appropriate springs to simplify the model (Fig. 2b).

The antagonists of the mandibular anterior teeth were assumed to be natural teeth, and those of mandibular implants were assumed to be either teeth or implants. According to the condition of the antagonists of the mandibular implants, the models with opposing natural teeth and implants were designated model-T and model-I, respectively.

The springs for the maxillary teeth or implants, except for the anterior teeth, were directed perpendicular to the occlusal plane. Each of those springs linked an external restricted node to the node corresponding to the occlusal central pit on a mandibular tooth, which allowed displacement perpendicular to the occlusal plane. The springs for temporomandibular joints linked an external restricted node to the top of the mandibular condyle. Nonlinear characteristics according to the load-displacement curves of the teeth and cartilage were given to the springs of the opposing teeth and TMJs, respectively. The springs for maxillary implants had linear compression characteristics. The springs for antagonists had little resistance under tension to simulate detachment. The properties of these springs were confirmed by load-displacement curves (Fig. 3) obtained using a simple FE model consisting of an element and a spring.

Occlusal adjustment was simulated by means of 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 that was assumed to be made by occlusal adjustment closed (Figs. 3, 4, and 5). The size of each gap was decided by trial and error (Table 2) so that the occlusal force, i.e., the reaction force of the springs on the occlusal surface, was similar to that calculated with the FE model with natural dentition (model-N, Fig. 6).