# The Effectiveness of Dental Protection and the Material Arrangement in Custom-Made Mouthguards
## 2 Materials and Methods  
### Geometrical and Numerical Models  
Four 3D finite element models of a human maxilla were constructed based on the CBCT reconstruction of the patient. The selected patient showed no signs of relevant systemic or oral diseases, including severe periodontal disease, and presented normal dentition in the maxilla and mandible. The four finite element models are identified as: No Mouth Protection (NMP); Compact EVA Mouthguard (CMG); Foam EVA Mouthguard (FMG); Hollow EVA Mouthguard (HMG). Figure 1 shows two of the three mouthguard protections and Table 1 presents the main differences between them, namely the material used as well as the total thickness of each layer.  
\begin{table}
\begin{tabular}{l c c} \hline \hline
**Mouthguard Protection** & **Layer Thickness (mm)** & **Layer Material** \\ \hline Compact Eva (CMG) & 4 & EVA \\ Foam Eva (FMG) & \(1/2/1\) & EVA/EVA Foam/EVA \\ Hollow Eva (HMG) & \(1/2/1\) & EVA/hollow (space)/EVA \\ \hline \hline \end{tabular}
\end{table}
Table 1: Description of the three mouthguard protections, namely, thickness and material.  
The 3D geometries of the compact and trabecular bones of the maxilla were created by the conversion of the CBCT scan raw medical data into 3D models and, subsequently, were converted to a CAD file by reverse engineering methods [18]. Nevertheless, they were kept undistinguished. The selection of a different threshold for grey values allowed teeth segmentation to be separated from the maxillary bone, but periodontal ligaments were not modeled. The 3D geometrical model of the soft tissue was obtained from the scanning of the external surfaces of the patient maxilla, using an inEOS(r) X5 laboratory scanner (Sirona Dental Systems. Inc.: Erlangen, Germany). The 3D models of the mouthguard protections were created and processed using Geomagic Studio (Geomagic Studio 2013.0.1. Geomagic Inc.: Raleigh, NC, USA) and were posteriorly assembled with the maxillary bone and teeth. After the assembly of all components of the models, the solid bodies were exported in the format of single Parasolid binary files.  
All four models were imported into the ADINA system for linear and nonlinear finite element analysis (ADINA AUI version 9.3.1. ADINA R&D Inc.: Watertown, MA, USA). The numerical model of contacts among components was assured using two different contact modeling techniques: the glue mesh option, i.e., assuming that surfaces in contact are perfectly bonded together; the constraint function using Lagrange multipliers, assuring the possibility of relative motion between the contact surfaces. Glue contact was used to bond the outer surfaces of bone and the soft tissue inner surface as well as between maxilla bone and teeth. Relative motion was allowed between the three following contact pairs: soft-tissue/teeth, soft-tissue/mouthguard, and mouthguard/teeth.  
Assignment of the mesh density to the solid bodies of each component was made by promoting equally spaced subdivisions of the volume bodies using the desired element edge length [17]. In some cases, the subdivision of specific faces was recalculated with smaller sizes to promote a more refined mesh in areas requiring higher precision. Table 2 presents the mesh density attributed to each body and the refinement areas. The Delaunay free-form meshing algorithm assured the domains discretization, generating 8-node hexahedral elements. The 8-node elements included a mixed interpolation formulation (displacement and pressure-based) for the almost incompressible materials, i.e., displacements and pressure are interpolated. In addition, the 8-node elements included the incompatible modes features in the domains where the material was not incompressible; the addition of the incompatible modes increases the flexibility of the element, especially in bending solicitation.  
Figure 1: Geometrical model of two mouthguard protections: **(a)** Compact EVA Mouthguard (CMG); **(b)** Foam EVA Mouthguard (FMG).