*2.1. Generation of T10-L3 Finite Element Model*

A three-dimensional FE model of the T10-L3 thoracolumbar spine was created using 1 mm thin-cut axial computed tomography images obtained from a resin cast of an Asian male cadaver without spinal deformities or abnormalities (Figure 1). The images were imported into the software 3D-DOCTOR (Able Software Corp.) to reconstruct the geometric structure of the T10-L3 TL spine, and the corresponding mesh was prepared using the preprocessing software Patran (MSC Software). The mesh generation was performed with software Hypermesh (Altair Technologies Inc), and the FE models were imported into Abaqus 6.12 (Simulia Inc) to solve. In this study, we assumed linear and isotropic material properties for cancellous bone, cortical bone, posterior bony elements, endplate, and disc structures including annulus fiber layers, annulus ground substance, nucleus pulposus, and implant materials (Table 1). The material properties used in the present study were derived from the previous studies by Shin et al. and Wilcox et al. [16,17].

**Figure 1.** Finite element model of T10-L3 TL spine and simulation of L1 failure. The present finite element model of the intact spine (**left**) and simulated L1 failure (**right**). The weakened materials were indicated in blue.


**Table 1.** Material properties and mesh types of the FE model.

The model for a vertebra consisted of a vertebral body and a posterior element. For the vertebral body, a closed surface was first generated, consisting of cortical bones and endplates assigned to three-node shell elements (S3R). Considering the structures of the cortical bone and endplates of the vertebra, which cover the outer surface of the vertebral body and surround the cancellous bone, it is more reasonable to use shell elements than tetrahedral elements to represent the geometry of the cortex and endplates, and this modeling strategy was also reported in previous FE studies [18,19]. The thicknesses of the cortical bone and endplate were assigned as 0.35 mm and 0.5 mm, according to previous studies [20–22]

The interior of the cortical surface contained cancellous bone assigned to C3D4 continuum elements. The posterior element and the facet were modeled according to the original geometry using C3D4 tetrahedron elements as previously described [23,24]. A three-dimensional surface-to-surface contact with friction was assigned to simulate the facet contact behavior with a finite sliding interaction defined to allow random motions, including sliding, rotation, and separation. The friction characteristic was modeled with a classic isotropic Coulomb friction model with a friction coefficient of 0.1 [25].

The intervertebral discs (IVDs) were modeled with three different components: annulus fibers, annulus ground substance, and nucleus pulposus [25,26]. The IVDs were generated with the superior and inferior boundaries assigned to the endplates of the adjacent vertebra, and the outer boundaries of the IVDs were generated according to the scanned geometry. The annulus was constructed as a ring-shaped structure between the outer and inner annulus fibers. The annulus fibers were modeled with six layers of shell elements with a thickness of 1.5 mm. The annulus ground substance was defined between the two annulus fiber layers and was modeled by solid tetrahedral elements (C3D4). The nucleus pulposus was modeled by non-compressible solid tetrahedral linear elements (C3D4) inside the inner annulus fiber.

The ligamentous complex, including anterior longitudinal ligaments (ALL), posterior longitudinal ligaments (PLL), ligamentum flavum (LF), interspinous ligaments (ISL), and supraspinous ligaments (SSL), were modeled using hyperelastic, tension-only Truss elements (T3D2). The properties of the ligaments were adopted from Goel et al. [27]. The element types and number of elements used in the components of the spine are listed in Table 2.


**Table 2.** Element count and mesh type of the present intact model.
