2.2. Finite Element Modeling

A 3D model of the mandibular bone was extracted from CBCT images. The CT images consisted of 452 transversal sections with a slice thickness of 0.425 mm and a pixel width of 0.398 mm. The data were imported into Mimics (Materialise, Leuven, Belgium) and Geomagic (Geomagic Company, NC, USA) to generate the geometric model. Five different mandibular reconstruction surgical procedures were developed (Figure 1) [27, 28]. We printed 10 test models for each digital model and obtained 10 sets of measurements.

FE models and the number of nodes and elements of FE models.

Model A (single up, SU): two segments of the fibula replaced the mandibular body and the ramus, respectively. A single-layer fibula, lying in the direction of the alveolar ridge, was reconstructed for the mandibular body defect.

Model B (single down, SD): the ramus defect reconstructive design was the same as in Model A. A single-layer fibula, lying in the direction of the lower margin of the mandible, was reconstructed for the mandibular body defect.

Model C (double up, DU): the ramus defect reconstructive design was the same as in Model A. A double-barrel fibula was grafted to reconstruct the mandibular body defect, and the folded section was cut obliquely and fixed in the direction of the alveolar ridge.

Model D (double down, DD): the ramus defect reconstructive design was the same as in Model A. A double-barrel fibula was grafted to reconstruct the mandibular body defect, and the folded section was cut obliquely and fixed in the direction of the lower margin of the mandible.

Model E (distraction osteogenesis, DO): the ramus defect reconstructive design was the same as in Model A. A single-layer fibula was fixed to the lower margin of the mandible, and the height of the alveolar bone was distracted by oblique distraction osteogenesis to meet the requirement of a subsequent dental implant.

Implants were finally implanted into the grafted fibula and were modeled using SolidWorks (SolidWorks Corp., Dassault Systemes Concord, MA, USA). The finite element (FE) models were meshed using 10-node solid tetrahedral elements in ANSYS Workbench (Swanson Analysis Systems Co., Houston, TX, USA) [29]. The stress, strain, and displacement of each node of each connection section of each model were collected using ANSYS software. A global element edge length of 0.5 mm was implemented following a convergence test, which assessed the balance between modeling accuracy and cost. The detailed element assignment is listed in Table 1. The final model includes residual mandible, segmented fibula, 3 dental implants, TMJ discs, periodontal ligaments (PDL), and 9 teeth (32-47). The criteria used for the bone strain values for this FEA were according to a method described previously [30]. In brief, the genetically determined disuse-mode threshold strain range was classified as described elsewhere [30]. The various strain ranges are described below. The 50 microstrain is the strain where the maximal disuse-mode activity occurs and above which it begins to decline or turn off. 1000–1500 microstrain is the strain range whereby the mechanically controlled modeling function of increasing a bone's strength would usually turn on. 3000 microstrain is the bone's microdamage strain threshold range whereby irreversible microdamage can begin to accumulate. To promote bone remodeling, the strain associated with favorable models should be in the range of 50–3000 με under any conditions.

Material properties used in the FE models.

Two types of masticatory force (vertical 100 N and inclined 45°100 N) were modeled as a concentrated force and applied on the abutment to simulate physiological loading conditions (Figure 2). To simulate the boundary conditions, the top, medial, and distal borders of the condyle process were considered to be in contact with each other. The sliding contact was applied to define the interfaces between the condyle process and the disc in the ANSYS Workbench. Sliding between the interfaces was allowed during the simulation process. Other contact interfaces were bonded (Table 2).

Each model was applied with a vertical and inclined force of 100 N each. The three bone connective sections (S1, S2, and S3) were marked by the golden boxes and amplified.

Contact types set in FE models.