## 2 Materials and Methods  
### FE Model of the Intact Lumbar Spine  
An FE model of the lumbar spine has been created in previous studies by using FE software (ANSYS 14.0, ANSYS Inc., Canonsburg, PA, USA) [5; 11; 12; 16], as shown in Figure 1. Computer-assisted tomographic images of the normal ligamentous lumbar spine of a male subject were obtained using transverse slices at every 3 mm interval. Each CT slice was acquired from the coronal plane and enlarged in order to identify the different regions of the tissues. Furthermore, 43% of the cross-sectional area of the disc was defined as the nucleus, which is within the range of 30-50% reported in a previous study [16]. This FE model consists of L1-L5 vertebrae, intervertebral discs, posterior elements, and seven ligaments. The spinal disc consists of 12 double-cross-linked fiber layers embedded in the ground substance and incompressible nucleus pulposus. The disc ground substance was modeled using an incompressible, hyperelastic, two-parameter (C1 and C2) Mooney-Rivlin formulation. All seven ligaments were simulated using a two-node truss element (LINK 10) with uniaxial tension resistance-only behavior. The facet joint surfaces were treated as having sliding contact behavior by using an eight-node surface-to-surface contact element, and the coefficient of friction was set as 0.1. A more detailed description of the material properties of the spine FE model can be found in our previous studies, as listed in Table 1[5; 6; 11; 12].  
Figure 1: FE model of intact lumbar spine. Note: ALL = anterior longitudinal ligament; CL = capsular ligament; ISL = interspinous ligament; LF = ligamentum flavum; PLL = posterior longitudinal ligament; SSL = supraspinous ligament; TL = transverse ligament.  
\begin{table}
\begin{tabular}{l l c c c} \hline \hline \multicolumn{1}{c}{**Material**} & \multicolumn{1}{c}{**Element Type**} & \multicolumn{1}{c}{
\begin{tabular}{c} **Young’s Modulus** \\ **(MPa)** \\ \end{tabular} } & \multicolumn{1}{c}{**Poisson’s Ratio**} & \multicolumn{1}{c}{**Area (mm\({}^{2}\))**} \\ \hline \hline  
To verify the accuracy of the aforementioned FE model, a convergence test was conducted in a previous study [9]. Three mesh densities (coarse model: 4750 elements/4960 nodes; normal model: 27,244 elements/30,630 nodes; finest model: 112,174 elements/94,162 nodes) were selected to study the ROM in the intact lumbar spine (INT) model. The finest mesh density (FE model: 112,174 elements/94,162 nodes) was selected because the differences between the normal model and the finest model were within 1.03% in flexion (less than 0.2\({}^{\circ}\)), 4.39% in extension (less than 0.5\({}^{\circ}\)), 0.01% in torsion (less than 0.2\({}^{\circ}\)), and 0.001% in lateral bending (less than 0.1\({}^{\circ}\)) [10]. The element size was approximately 2.5 mm to confirm the accuracy of the FE analysis.  
To validate the FE model, the FE analysis results were compared with the results of the in vitro cadaveric tests [16] for the same loading conditions. For model validation [16; 17], the ROM in the five levels of the intact model was validated using previous cadaveric in vitro tests. The FE intact model displayed stiffer behavior in flexion, with a ROM value that was 4\({}^{\circ}\) less than that described in [PERSON]'s in vitro study. In addition, softer results were obtained in torsion compared with the in vitro test data; however, the differences were still within 2\({}^{\circ}\). Overall, the discrepancy between the in vitro tests and our FE simulation was within one standard deviation. The ROMs under four physiological motions fell within similar ranges, and the trends agreed well with the experimental results [17].