## 2 Materials and Methods  
### Proximal Humerus Modeling  
Medical images of bone or biological tissue can be obtained by computed tomography (CT) or magnetic resonance imaging (MRI). These devices generate a set of images whose quantity and quality depend on the increments between each captured image and its resolution for each captured plane. The format used for this type of images is DICOM (digital imaging and communication in medicine), specially designed for the medical community because it contains captured patient images and both clinical and personal patient data. This avoids the incorrect assignment of images between different patients, and, in turn, standardizes the transmission of medical images.  
The DICOM images used for the present investigation were obtained from the website of the International Society for Biomechanics [19]. Images of the humerus were collected via CT at the Human Anatomy and Embryology Laboratory at the University of Brussels, Belgium. The humerus is considered a long bone, so the images were captured in three sections (distal, diaphysis and proximal); therefore, the reconstruction and union of the sections of interest was necessary. For the segmentation, the threshold of Hounsfield units (HU) was defined. That would allow identifying only the cortical bone tissue of the structure. The threshold defined for the present investigation was from \(-170\) to \(2380\) HU according to [PERSON] et al. [20] (Figure 1).  
3D Slicer v4.11 software [21] was selected to perform the segmentation of the images used in the present investigation since it is not only free to use but has also been used in biomechanical investigations such as that carried out by [PERSON] et al. [22].  
The integration, reduction and model simplification were carried out by Autodesk Meshmixer v3.5 software [23]. First, the models were imported in STL format to the software. After using the Boolean union tool, both structures were merged. Seeking to soften the union previously made between both structures, 3D sculpture tools were used within the same software. The whole process allowed the model to be reduced by 90% without losing its original shape, from 269,074 total triangles to 35,182. Model subtraction and conversion of the surfaces to solids was performed in ANSYS SpaceClaim(r) 2020.R2 software. After importing the models, the meshing of the surfaces was homogenized using the Regularize tool, for which a maximum element size of 1 mm and a 60\({}^{\circ}\) angle threshold were defined. Finally, the subtraction of the models was continued using the Substract tool, mesh homogenization and conversion of the models to solids (Figure 2).  
Figure 1: Preliminary 3D model of the structure of the humeral diaphysis. In the preliminary model, the remaining sections of the proximal and distal structures are observed (relative anterior (A), posterior (P) and lateral (L) position). In the boxes on the right side i.e., transverse (red box), coronal (green box) and sagittal (yellow box) planes, the segmentation imperfections can be observed according to the defined HU threshold.  
Figure 2: Model subtraction process to obtain a final model of the proximal humerus. The process begins (1) with the subtraction of the trabecular bone model (**B**) to the solid model of the proximal section (**A**), resulting in the empty structure of the proximal section of the humerus (**C**). Subsequently (2), the trabecular bone model (**B**) is added to the empty model (**C**), obtaining the final model composed of the cortical and trabecular structures (**D**).