The research protocol was reviewed and approved by the Research Ethics Committee at the School and Hospital of Stomatology, Fujian Medical University (No. 2017-CX-12).
Structures and geometric conditions of the computer aided design (CAD) model
A periapical film of the lower right first molar was taken by paralleling technique (Heliodent Plus, Sirona Dental Systems, Bernsheim, Germany) to generate a two dimensional (2D) image file (jpg). Microsoft Office PowerPoint 2007 (Microsoft, USA) was used to trace the points on the X-ray film (Fig. 1a), recorded the coordinate values of red points. The coordinate values of these points are imported into a FEA software (ANSYS v. 10; ANSYS Inc., Canonsburg, PA, USA) through ANSYS parametric design language (APDL) to create the 2D model.
There were three different model designs (Fig 1), viz., endocrown with 2 mm occlusal clearance, endocrown with 4 mm occlusal clearance and post-core crown. The restorations used two different crown materials, viz., zirconia (Zr) and lithia-disilicate reinforced glass ceramic (LDRGC), and three different post and core materials, viz., glass fiber (GF), stainless steel (SS) and metal cast (MC). There were ten kinds of combination in this study. Detailed flowchart showing the group distribution has been included in Fig 2. In the GF posts and SS posts, the cores were made of composite, while in the MC posts they were made of metal.
Endocrown and post-core crown designs
The Endocrown-2 mm designs were created with 2.0 occlusal clearance, 7.0 mm cavity depth, and 5.3 mm base width. The prepared cavity walls tapered with 6-8 degrees from the cavity base to the cavosurface (Fig. 1b). The Endocrown-4 mm designs were created with 4.0 occlusal clearance, 5.0 mm cavity depth, 5.3 mm base width and 6-8 degrees cavity walls taper (Fig. 1c). Jacket crown preparations were created with 2.0 mm occlusal clearance, 0.5-1.5 mm cervical clearance and shoulder margin, 6-8 degrees tapering angle for first molars, 14.0 mm post lengths. Rounded shoulder margins and anatomic occlusal reduction were incorporated in model (Fig. 1d).
The surrounding bone was modeled as cortical bone (1.5 mm thickness) and cancellous bone, which were assumed to be isotropic, homogeneous, and linearly elastic. A 0.2 mm periodontal ligament [17,18] was modeled around the roots. A 0.1 mm thick cement-imitating layer [17,18] was formed around the root part of the created post and under the crown. A small gap of cement was added to the bottom of the endocrown cavity, which was closer to the clinical situation. Perfect bonding was assumed at all the interfaces, including those between the teeth, the cores, the crowns, the posts and bones.
Material properties, mesh generation and boundary conditions
The Young’s modulus and Poisson’s ratios of the materials used are shown in Table 1 [18-26]. Material properties were assumed to be isotropic, homogenous, and linear-elastic, except the GF post. The material of GF post was anisotropic (Young’s modulus along its long axis was 38.5 GPa, and 12.0 GPa perpendicular to that axis).
For calculation purposes, each tooth model was divided into 2D 4-node structural solid elements (PLANE42). This element is defined by four nodes having two degrees of freedom at each node: translations in the nodal x and y directions. In model with endocrown-2 mm, 30,158 elements joined at 30,318 nodes were used. In model with endocrown-4 mm, 29,663 elements joined at 29,821 nodes were used. In model with post-core crown, 29,847 elements joined at 30,002 nodes were used. The aim of this preliminary FEA was to identify the regions with highest stress concentration within the restoration, especially those along the distal root inner and outer surface. These would be the regions to which shape optimization would be applied. Thus, the mesh around the distal root inner and outer surface was made much finer than those in the other areas, with an average element edge length of 0.05 mm.
Fixed zero-displacement in both the horizontal and vertical directions was defined at the horizontal and vertical cut-planes of the supporting bone. An axial load of 600 N [18,27] was applied to the central fossa of occlusal surface. MPS values were calculated by FEA along the distal root canal inner wall and the root outer surface (Fig 1b: 1→2→3→4). This FEA study focused on the distal root canal inner wall because the post was set in the distal root canal, from preliminary analysis the distal root canal inner wall was analyzed in greater detail. The stress distribution within the tooth/restoration cross-section was solved with the FEA software (ANSYS).