## 2 Materials and Methods  
### Geometrical Models  
Three-dimensional finite element models of IARPDs with two different implant locations and one conventional RPD, that is, a tooth assisted RPD, were constructed based on the reconstruction of the CBCT Kennedy Class I patient. The three finite element models were identified as: the conventional RPD; the IARPD PREMOLARS (IARPD PM), presenting the implants at the premolar regions; the IARPD MOLARS (IARPD MO), with the implants placed in the molar's region. The selected patient showed no signs of relevant systemic or oral diseases, including severe periodontal disease, and presented mandibular bilateral posterior edentulism missing three teeth per edentulous site and moderate resorption of the residual ridges.  
The geometries of the compact and trabecular bones of the mandible were created by the conversion of the CBCT scan raw medical data into 3D models and subsequent conversion to a CAD file by reverse engineering methods. Similarly, to the process of segmentation of the mandible bones, teeth segmentation allowed separating abutment teeth (34; 33; 43; 44) from the remaining teeth, while periodontal ligaments were modelled by offsetting the mesh of the root surface of each tooth (34; 33; 43; 44) by 0.25 to 0.3 mm. The 3D geometrical model of the acrylic portion of the RPD was obtained from the scanning of a conventional denture, which had been created over the plaster mode of the patient, using the inEOS(r) X5 laboratory scanner (Sirona Dental Systems Inc., Long Island City, NY, USA). The 3D model of the metal framework of the RPD was created over the scanned plaster model using the 3 Shape Dental System(tm) software and, posteriorly, assembled with the acrylics of the 3 rd and 4 th quadrants. Moreover, the external surface of the mandibular -plaster model of the patient was also scanned to create a 3D model of the coronal portion of the remaining teeth and soft tissue of the edentulous areas.  
The implants were created using s CAD tools (Solidworks(r) 2014, Dassault Systemes Pte. Ltd., Singapore) after feature extraction of the specific geometrical dimensions from official images of Straumann Standard Plus implants (O 4.1 mm) with regular platform and 10 mm long provided by the manufacturer (Institut Straumann AG, Basel, Switzerland). A ball attachment (patrix) and corresponding matrix were also created to establish the connection between prosthesis and the implant. In the assemblage of IARPD models the implants were placed as parallel as possible to the abutment teeth in the regions of the second premolar (Model IARPD PM) and of the extremity of metallic framework (Model IARPD MO), which corresponded to the virtual position of the first molar. To model the implant-bone contact, the implants were then trimmed from the cortical and cancellous bone bodies using Boolean operations. The same operation was performed on the soft tissue body to create the space required to the transmucosal portion of the implant. The matrices were aligned with the ball attachments of the implants and housed within the framework. The acrylic portions of the prostheses were also modified to accommodate the implants, ball attachments and matrices.  
A single plate was created to apply the prescribed load uniformly over the acrylic teeth of the removable partial denture. The plate was sketched in the horizontal plane of the mandible (parallel to the occlusal plane) and vertically extruded to obtain a final thickness of 10 mm. Additionally, a 10 mm diameter circle was included in the geometric centre of the sketch and extruded 25 mm for force application. After the assembly of all components of the models with implant-assisted removable partial dentures, the solid bodies were exported in the format of single Parasolid binary files.