## 2 Materials and Methods  
A mandible 3D model was made using patient-derived cone-beam computed tomography (CBCT) images. The clinical model used presented a bilateral edentation of class I Kennedy. The mandible was also characterized by mandibular atrophy, bone field class II (bone height \(>\) 10 mm, bone crest width 2.5-5 mm), by the [PERSON] classification (1987) [13]. Ridge height in the third quadrant at implant sites was 2.4 mm higher than the alveolar ridge in the fourth quadrant. The 3D reconstruction of the mandible and the remaining teeth was performed using Slicer3D ([[http://www.slicer.org](http://www.slicer.org)]([http://www.slicer.org](http://www.slicer.org))) with further editing in Autodesk Fusion 360 (Autodesk, Inc., San Rafael, CA, USA) and Autodesk Inventor Professional version 2017 (Autodesk, Inc., San Rafael, CA, USA), as can be seen in Figure 1. The obtained model was then modified, simulating a bone augmentation in the posterior mandible. The height of the mandible ridge at the implant sites was increased by 3 mm, as shown in Figure 2. Both mandible models consisted of two macro-structures, a cortical bone layer with a 2 mm thickness, and an internal cancellous bone, as well as gingival tissue with a thickness of 2 mm and periodontal ligaments with a thickness of 0.2 mm (Figure 2). Implant-supported restorations were modeled for each defendulous area, consisting of implant, abutment, abutment screw, cement layer, and splinted ceramic crowns. In the atrophied mandible, implants measured 3.75 mm in diameter (D) and 8 mm in length (L) for implant sites 3.7, 4.5, 4.6, and 3.3 mm D with 10 mm L for implant site 3.6. These measurements were planned according to the available alveolar bone dimensions. In the virtually augmented mandible, all implants measured 4.2 mm D and 11.5 mm L.  
Simulations of physiological loading of the 3D models were performed using Simulation Mechanical version 2017 (Autodesk, Inc., San Rafael, CA, USA). For all simulation scenarios, a static model with linear and elastic material properties was selected. The mechanical properties of the assigned materials are presented for each element of the 3D analysis assembly in Table 1.  
The mandibular model was fixed in the simulation environment at the temporal-mandibular joint surfaces, with rotation restrictions around the Y and Z axes, to simulate the anatomical articulation of the structure and allow for physiological type rotation in the sagittal plane during mastication (Figure 3). Because the study model presented bilateral terminal edentation, restrictions were set on each one of the ceramic upper restorations at a time, simulating mastication conditions for each quadrant. Masticatory type forces corresponding to the pterygoid muscles (P) of 145 N and the masseter muscles (M) of 151 N were applied (Figure 3) [14]. Figure 1: Detailed views of the 3D model of the resorbed and the virtually augmented mandible with implants placed in sites 3.6, 3.7, 4.5, and 4.6, and remaining dentition. (**a**) Perspective view of modeled mandible with bone resorption and bilateral posterior edentation with implants placed. (**b**) Front view of modeled mandible with bone resorption and bilateral posterior edentation with implants placed. (**c**) Top view of modeled mandible with bone resorption and bilateral posterior edentation with implants placed. _Appl. Sci._**2020**, _10_, 401 \begin{table}
\begin{tabular}{c c c} \hline \hline
**Material** & **Young’s Modulus (MPa)** & **Poisson Coefficient** \\ \hline Cortical bone [15; 16; 17] & 13,700 & 0.3 \\ Cancellous bone [17; 18] & 1370 & 0.3 \\ Gingiva [19] & 19.6 & 0.3 \\ Dentina [20] & 18,600 & 0.31 \\ Periodantal ligament [21] & 69 & 0.45 \\ Ceramic [22] & 140,000 & 0.28 \\ Ti-6 Al-4V [23] & 110,000 & 0.35 \\ Cement [24] & 10,760 & 0.35 \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Material properties.