## 2 Numerical Modeling and Analysis
### Modeling Details  
The first step of the simulation process in the presented approach was to import into Abaqus finite element software the CAD file of a typical spinal brace obtained by laser scanning and subsequent conversion described in Section 2.2 for further processing. A numerical model of the spine with shell finite elements has been created, in which a cross-sectional thickness equal to 4 mm has been assigned (Figure 2a). Due to the complexity of the geometry of the brace, the abundance of curves, and general nonsymmetry, individual surfaces have been defined on the brace to achieve a better overview and higher accuracy for imposing loads and boundary conditions. For that purpose, the brace has been divided by planes parallel to the planes formed by the three main axes (Figure 2b). Material: Conventional spinal braces are commonly manufactured using materials such as polypropylene, polyethylene, and their variants. In a study by [PERSON] et al. [23], the elastic properties of polypropylene/ultra-high molecular weight polyethylene fiber were estimated, yielding a calculated value of approximately 1325 MPa. Additionally, the mechanical properties of materials used in traditional braces have been identified through experimental investigations in various studies [16; 17; 23; 24]. One of the key objectives of this study is to conduct a comparative analysis between traditional brace materials and those produced through additive manufacturing, particularly utilizing 3D-printed PLA. Consequently, polypropylene is initially chosen as the material for the spinal brace in the traditional context, featuring a modulus of elasticity (E) of 1000 MPa and a Poisson's ratio (v) of 0.2. Support and Load Conditions: This study builds upon the foundational work outlined in the work by [PERSON] et al. [18], aiming to simulate the structural behavior of a spinal brace in order to further refine and develop the scenario presented. The primary focus lies in optimizing the brace's topology, aligning with a key loading scenario akin to the Boston brace. In particular, the simulation in this study replicates the application of corrective forces generated by pulling the straps on the back of the brace. This action effectively tightens the brace around the human body, inducing corrective forces within the patient's body that serve to limit the progression of spinal inclination. The mechanism involves the transmission of these corrective forces through supporting pads situated on the inner part of the brace, facilitating a more even distribution of contact pressures. This approach is instrumental in achieving a smoother and more targeted application of corrective forces, contributing to the overall effectiveness of the spinal brace in managing spinal alignment. Figure 2: (**a**) CAD representation of spinal brace. (**b**) Division of the brace into individual surfaces to facilitate assignment of loads and boundary conditions. The developing tension of the tightening straps has been simulated in the model by imposing horizontal displacements in the tangential direction on the rear face of the brace, equal to 10 mm, as shown in Figures 3a and 4a. The clearance at the back of this specific brace is approximated to be in the range of 20-25 mm. The choice of imposed displacements of 10 mm on both sides of the rear face of the guardrail, as illustrated in Figure 3b, is based on the logical scenario of tensioning the straps until this clearance is filled. A key element of the numerical modeling of the brace is the simulation of its interaction with the human body. During the patient's movement, the brace-pad system (Figures 4b and 5) presses the human body to develop corrective forces. Pressures, normal to the contact surface, develop in part of the interaction surfaces, while the remaining part of the pad surfaces moves away and loses contact with the human skin, and zero pressure develops. At the same time, friction between the body and the brace develops in tangential directions over the contact surfaces.