## 2 Materials and Methods
### Numerical Simulation  
#### 2.3.1 Development of FE Models  
A three-dimensional (3D) geometric model of the thoracolumbar spine (Th7-L3) was built based on the spinal dimensions derived from the analysis of computed tomography (CT) images following the methodology presented in [PERSON] et al. [18] and [PERSON] et al. [19]. Based on the model obtained in the InVesalius 3.1.1 software, the geometric dimensions of nine vertebrae (Th7-L3) were obtained, which corresponded to the number of segments adopted in experimental tests. The values of each parametric dimension of the vertebrae included in the numerical model were confirmed against the vertebral dimensions reported in the literature [20; 21]. In addition, based on the model obtained from CT imaging, the position and inclination angle of individual vertebrae were measured in relation to the long axis of the spine in order to represent the geometry of the thoracolumbar spine.  
The geometric model of the thoracolumbar spine (Th7-L3) was created using the ANSYS Mechanical APDL 18.2 software. In addition to the vertebrae, the model also recreated the geometry of the IVDs, endplates, and ligament systems. In order to reduce excessive mobility of the thoracolumbar junction, a simplified muscular system was also recreated, which was modeled at the level of the Th8-Th9 and Th12-L1 motion segments(Figure 2A). The endplate thickness was modeled as 10% of the vertebral body height [22]. The model took into account the detailed structure of the IVD. Not only was differentiation assumed between the nucleus pulposus area and the annulus fibrosus, but also differences between the outer, medium, and inner layers of the annulus fibrosus itself (by differentiating their mechanical parameters). The geometry of the SOCORE transpedicular fixation system by NovaSpine was modeled to analyze the impact of using transverse connectors in PFS designs, and this system was also used during experimental tests. In order to optimize the running time of the numerical simulations, the screw geometry was simplified by omitting threads.  
Numerical simulations were carried out for four cases, similar to experimental tests (Figure 2). LSF4 TC1 was omitted as it was shown from experimental tests that the results did not have a significant impact compared to the other study groups.  
In the discrete model, the vertebrae and intervertebral discs were represented using SOLID187 10-node tetrahedral solid elements. Each vertebral body was characterized as cancellous bone encased in a layer of cortical bone with a thickness ranging from 0.5 to 1 mm [23]. Additionally, the presence of superior and inferior endplates was considered in all vertebrae. The elements used to describe the transpedicular fixation components, such as screws, rods, and transverse connectors, were also SOLID187 solid elements.  
Within the annulus fibrosus matrix of the IVD, three cylindrical layers of collagen fibers were modeled using SHELL181 four-node shell elements, each having six degrees of freedom at every node. These fibers within the individual layers of the IVD were inclined at a 30\({}^{\circ}\) angle and oriented alternately to the right and left [24].  
Furthermore, all four major types of ligaments typically found in the spine--namely, the anterior longitudinal ligament (ALL), posterior longitudinal ligament (PLL), inter  
Figure 2: Considered configurations of the numerical model: (**A**) physiological (P), (**B**) with compression fracture (F), (**C**) with LSF4, and (**D**) with LSF4 TC2.  
transverse ligament (ITL), and interspinous ligament (ISL)--were also represented using SHELL181 four-node shell elements in the model. As for the muscles, they were simulated using LINK180 two-node elements, with each node having three degrees of freedom.