# Finite Element Analysis (FEA) of Palatal Coverage on Implant Retained Maximly Overdentures
## 2 Materials and Methods  
Eight different three-dimensional finite element maxilla models were created and analyzed. The finite element models were designed as follows:  
1. Four-implant retained maxillary overdenture designed without and with full palatal coverage excluding a connecting bar. 2. Three-implant retained maxillary overdenture designed without and with full palatal coverage excluding a connecting bar. 3. Three-implant retained maxillary overdenture without and with full palatal coverage designed to connect the implant fixtures with a titanium bar. 4. Four-implant retained maxillary overdenture without and with full palatal coverage designed to connect the implant fixtures with a titanium bar. The abutment geometry and dimensions were made to replicate a two-millimeter (Zest Anchors) Locator(r) abutment for the three- and four-implant retained overdenture models excluding the connecting bar. The maxillary FEA prototype was created using computer-aided design (CAD) from a model supplied by Dentsply Sirona Inc. (Charlotte, North Carolina, United States). Due to the symmetrical nature of the maxilla, the finite element models were created using one half of the prototype to reduce computation time. The three-implant symmetric model contained one whole implant and another half implant (Figure 1). The symmetrical maxillary model with four-implants was fabricated using two implants as shown in Figure 2. The implant position and location are described in Figure 3. For both symmetrical models the implant diameter selected was 4 mm, and the implant length was 11 mm. The length of the implant above the surface of the cortical bone was 3.5 mm for all models. The thickness of the cortical bone was 2 mm in all cases. Figure 1: One half of the maxilla (three-implants model). Figure 2: One half of the maxilla (four-implants model). The jaw bone properties in the model were set with a Young's Modulus of 13.5 GPa for the cortical bone and 1.35 GPa for the cancellous bone. Poisson's ratio was set at 0.3 for both cortical and cancellous bones. The titanium bar connecting the implants had a Young's modulus of 107 GPa and a Poisson's ratio of 0.3. The polymethyl methacrylate (PMMA) was set with a Young's modulus of 3.4 GPa and a Poisson's ratio of 0.35. The interface between the cortical and cancellous bone layers and between the implant and each of the bone layers was assumed to be well bonded, which corresponds to good osseointegration. The implant-prosthesis interface was also well bonded. The lower surface of the model and the medial and distal planes of the bone were completely constrained. The boundary conditions were set with the bottom of the maxilla fixed. All the degrees of freedom (dof) were constrained on the bottom. The symmetrical boundary condition was imposed on the symmetry axis of the model. The interaction for the surfaces of the inner and outer bone were tied. The surfaces of the implants were also tied to the respective side and bottom surfaces of the inner and outer bone. Each model was composed of a mesh that had 41,000 elements and 60,000 nodes made of tetrahedron 3D quadratic solid elements, with an improved modified formulation (C3D10M) used to generate all the parts. A linearly varying load maximum at the position of the second implant (distal implant) and minimum at the model center (mesial implant) was applied on the denture such that the loads on the four-implants model were 187.5 N and 137.5 N respectively. For the three-implants model, the loads were also 187.5 N at the distal implant and 137.5 N at the center of the model. The connecting bar design loaded the bar directly, while the Locator(r) attachment design loaded the implant through the PMMA overdenture. The applied varying forces were simulated, with bucco-lingual loading angles ranging from 0 to 45 degrees. All computations were performed using ABAQUS(r)--the Finite Element software--for the analysis of finite element program. One-way analysis of variance (ANOVA) was performed to compare each model combination.