## 2 Materials and Methods  
### Modelling  
A cross-section of a bone block with a width of 10 mm and a vertical height of 17.5 mm was designed a with computer-aided design (CAD) software (Autodesk Inventor, San Francisco, CA, USA) based on a computed tomography (CT) scan of a patient, which modelled the correct geometries. The cortical area resulted to be 1.5 mm in thickness (Figure 1a). The implant model used had a diameter of 4 mm and a length of 9 mm, while the abutment had a length of 8.3 mm and the same diameter (Implacil De Bortoli, Sao Paulo, Brazil). The fillets depth was 0.4 mm. In Figure 1b, it is possible to observe both the drawing and dissected views, in which the Cone-Morse connection between implant and abutment is represented.  
The implant model has been equicrestally placed in the bone block so that the implant shoulder was at the same level of the crest. On the contrary, subcrestal patterns have been generated by the placement of the implant model at 1 mm and 2 mm below the crestal level, respectively (Figure 2). The software used to perform these placements was Ansys Workbench (Canonsburg, PA, USA).  
It is common practice to consider both cortical and trabecular bones as isotropic materials when utilizing a FEA study model to examine the behavior of bones in relation to dental implants. This would mean that the mechanical properties of the bone have been assumed to be uniform and not influenced by a specific direction [1]. The cortical bone is the outermost and most compact region of the bone, forming a protective layer around the inner trabecular bone. Instead, the trabecular bone, also known as spongy bone or cancellous bone, is a porous framework composed of bony trabeculae creating a three-dimensional network [2]. In the context of a FEA model, cortical bone is represented as a more rigid and stronger material, while trabecular bone is considered more flexible and less resistant. This difference in mechanical properties reflects the physical characteristicsof the bone itself. When developing an FEA model to simulate cortical and trabecular bone, specific values of [PERSON]'s modulus (stiffness measurement) and Poisson's modulus (deformability measurement) can be assigned to both bone types. However, it is important to note that parameter values can greatly vary depending on the anatomical location and individual variabilities. In addition, the mechanical characteristics are also dependent on density. Hence, chronic diseases or even aging can lead to a change in the density value that might compromise results. In this study, bone density belonging to category D3 according to the Misch classification was taken into account. It is possible to acquire the mechanical properties related to cortical and trabecular bones from biomechanical studies, experimental data, or scientific literature. Typical Young's modulus values for cortical bone can range from 13 to 20 GPa, while for trabecular bone the range is from 0.1 to 4 GPa. Conversely, Poisson's modulus for both types of bone can be considered around 0.3 [1; 2; 3]. Representing cortical and trabecular bone as isotropic materials could allow the simplification of modelling and analysis within FEA study; however, it is important to emphasize the complex biological nature of the bone and that its structure and mechanical properties could vary even within the same individual.  
The dimensions and properties assigned to the models related to the cortical bone, trabecular bone, and titanium implant used in this study are reported in Table 1.