## 2 Materials and Methods
### Human Spine FE Model
#### 2.2.2 Spinal Fracture  
Four previous study models were referenced to generate the fractured spine model [32; 34; 35; 36]. Each study conducted a comparative analysis according to the screw type, fracture level, and CS screw insertion angle. Although the final goals were different, all the models used the same fixed segments and fracture implementation methods. The fixed site was T12-L2, and the fracture was implemented by removing part of the vertebral body of L1. However, in this study, a method of lowering the Young's modulus of the verteb was chosen to design the fractured spine model [37; 38]. The method of implementing a geometric fracture is the method used in [PERSON] et al. 's study [39]. This method calculated the defect volume inside the fractured spine and removed the defect site. Here, as for the bony defect area, the front side is the anterior margin of the vertebral body, the upper side is a transction paralleled to the upper endplate, and the lower side is an oblique section paralleled to the kyphotic correction angle. The main point here is that the size of the fracture site and the defect site is different for each patient according to the severity of the fracture. [PERSON] et al. 's study also selected fracture severity for a specific fracture patient as a representative model. Of course, as in [PERSON] et al. [14], fracture severity can be classified into moderate fractures and severe fractures. However, since this method requires direct modification of the geometry, this study adopted a method of implementing a fracture by adjusting the material properties so that the location and severity of the fracture can be adjusted without modifying the geometry. Figure 1: Composition of the human spine finite element (FE) model: (**a**) Overall shape of the intact FE model, (**b**) FE model of an intervertebral disc composed of nucleus pulposus and annulus fibrosus, and (**c**) six major ligaments of the spine; 2-node link element. We are only comparing the effects of different fixation segments and screw types on the stability of a fracture. The material properties of the rest of the vertebrae have a minor effect on such spine stability (the basic requirement to protect structures and prevent the early mechanical deterioration of spinal components [40]), so, we have maintained the properties of healthy bone in the rest of the vertebrae of the column. The method of fixation complements the upper and lower sections based on short-segmented fixation. As mentioned above, the screw type was either PS or CS, and the typical trajectory was selected based on the shape of the spine. Figure 2 shows the results of applying stress on the screw, obtained by constantly reducing the [PERSON]'s modulus of the verteba using FEA. In this Figure 2, \(Y_{1}\) denotes the [PERSON]'s modulus of the normal state (defined in a posterior fixed state without fracture), \(Y_{2}\) is half of \(Y_{1}\), \(Y_{3}\) is half of \(Y_{2}\), \(Y_{4}\) is 1/10 of \(Y_{1}\), \(Y_{5}\) is half of \(Y_{4}\), \(Y_{6}\) is 1/100 of \(Y_{1}\), and \(Y_{7}\) denotes the [PERSON]'s modulus of the FE model with the T12 segment completely removed. In this manner, the [PERSON]'s modulus of the verteba was reduced at a constant rate, and the stress on the screw due to the decrease in the stiffness of the verteba was calculated using FEA. A simulation was performed, wherein the stress on the spinal implant increased due to the fractured spine. The results of the simulation were compared with those in reference studies to determine the rate of reduction of [PERSON]'s modulus of the verteba that leads to a fracture [32]. To minimize the error of the results, a simulation was performed by implementing the fractured state of L1 in the T12-L2 fixation, as described in a comparative study. The equivalent stress of the screws obtained under similar conditions is summarized in Table 2. The fracture shape of the comparative paper [14; 32] is the same as that of [PERSON] et al.