Structures and geometric conditions of the computer aided design (CAD) model
A mesio-distal cross-section of a lower right first molar was digitized and used to create 2-dimensional (2-D) models. 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.
Endocrown-2 mm-Zr: full zirconia endocrown with 2 mm occlusal clearance;
Endocrown-2 mm- LDRGC: full lithia-disilicate reinforced glass ceramic endocrown with 2 mm occlusal clearance;
Endocrown-4 mm-Zr: full zirconia endocrown with 4 mm occlusal clearance;
Endocrown-4 mm- LDRGC: full lithia-disilicate reinforced glass ceramic endocrown with 4 mm occlusal clearance;
GF post-Zr: glass fiber post + full zirconia crown;
GF post- LDRGC: glass fiber post + full lithia-disilicate reinforced glass ceramic crown;
SS post-Zr: stainless steel post + full zirconia crown;
SS post- LDRGC: stainless steel post + full lithia-disilicate reinforced glass ceramic crown;
MC post-Zr: metal cast post + full zirconia crown;
MC post- LDRGC: metal cast post + full lithia-disilicate reinforced glass ceramic crown.
In the GF posts and SS posts, the cores were made of composite, while in the MC posts they were made of metal. The model was created from radiographic image of a real tooth (Fig. 1a) using a FEA software (ANSYS v. 10; ANSYS Inc., Canonsburg, PA, USA) (17).
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 2-5 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 2-5 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, 2-5 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 ligamentwas modeled around the roots. A 0.1 mm thick cement-imitating layer was formed around the root part of the created post and under the crown. 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 elastic moduli and Poisson’s ratios of the materials used are shown in Table 1. 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 2-D 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, 4,596 elements joined at 4,701 nodes were used. In model with endocrown-4 mm, 4,582 elements joined at 4,693 nodes were used. In model with post-core crown, 4,657 elements joined at 4,759 nodes were used. The aim of this preliminary FEA was to identify the most highly stressed regions 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 0.2 mm.
Fixed zero-displacement in both the horizontal and vertical directions was defined at the horizontal and vertical cut-planes of the supporting bone. A load was applied that corresponded to static loading, assuming no vibrational or dynamic effects in the structure. To reflect the stress distribution at the moment of equilibrium, a simulated 100 N vertical occlusal load was applied to the distal marginal ridge. The von Mises stress values were calculated by FEA along the distal root canal inner wall and the root outer surface (Fig 1: A→B→C). We 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).