## 2 Materials and Methods  
A finite element model of 5-level intact lumbar spine was created using the software ANSYS 15.0 (ANSYS Inc., Canonsburg, PA, USA). The geometry of the intact vertebrae was obtained from the CT images of a healthy male. In order to simplify the model, a specialized command in ANSYS was used to rotate, translate and scale the L3 vertebral body to produce the L1, L2, L4 and L5 vertebral bodies. These bodies were then aligned as a lordotic intact lumbar spine (INT), as shown in Figure 1a. Details of model validation, material properties (Table 1) and convergency testing are included in previous studies [16; 17; 18; 19; 20]. Figure 1a illustrates the complete lumbar model including vertebrae (L1-L5), intervertebral discs (IVDs) and seven ligaments. The IVDs are composed of an annulus fibrosus and nucleus pulposus, with the ground substance embedded with 12 double-crosslinked fiber layers. The annulus fibrosus was considered as an incompressible and hyper-elastic material modeled using a 2-parameter (C1, C2) Mooney-Rivlin formulation [18], while the nucleus pulposus was considered as an incompressible fluid.  
Five finite element models were developed in this study: (a) intact lumbar spine (INT) without implants (Figure 1a); (b) INT model with augmentation with cement at L3 to simulate a burst fracture (30% cancellous bone were replaced by bone cement) with anatomical reduction (AwC); (c) AwC model with two-segment fixation at L2-L4 (AwC-TSF, Figure 1b); (d) AwC-TSF model with cement-augmented  
\begin{table}
\begin{tabular}{l l l} \hline \hline
**Material** & **Young’s Modulus (MPa)** & **Poisson’s Ratio** \\ \hline Cortical bone [18] & 12,000 & 0.2 \\ Cancellous bone [18] & 300/100 & 0.2 \\ Annulus fibrous [18] & Mononey-Rivlin & NA \\  & cl = 0.18, c2 = 0.045 & \\ Nucleus pulposus [18] & Mooney–Rivlin & NA \\  & cl = 0.12, c2 = 0.03 & \\ Ligaments [18] & Hyper-elastic & NA \\ Bone Cement [19] & 2300 & 0.33 \\ Pedicle screw (Titanium alloy) [20] & 113,000 & 0.3 \\ \hline \hline \end{tabular}
\end{table}
Table 1: The material properties of intact spine and instrumented models.  
Figure 1: Finite element model of the (**a**) intact (INT) lumbar spine implanted with (**b**) spinal posterior fixation system, cement augmentation at the L3 verteb and (**c**) the cement-augmented pedicle screws at L2 and L4 in AwC-TSF-S. ***The ligaments are: ALL, anterior longitudinal ligament; PLL, posterior longitudinal ligament; TL, transverse ligament; LF, ligamentum flavum; ISL, interspinous ligament; SSL, supraspinous ligament; CL, capsular ligament.  
(cylindrical cement volume 1.0 cm\({}^{3}\)) pedicle screws (AwC-TSF-S, Figure 1c); (e) INT model with an L3 burst fracture with anatomical reduction and two-segment fixation at L2/L4 only (TSF, Figure 1b). The implant used in this study was a CB PROT II Posterior Spinal System (Chin Bone Corp., Taiwan; US FDA 510(k): K142655), which is composed of titanium alloy screws of diameter 5.5 mm connected by titanium alloy rods (Figure 1b). All implants were modeled using 8-node solid elements.  
The interfaces between facet articular surfaces were treated as standard contact pairs at all levels. A hybrid multidirectional test method developed by [PERSON] [21] was used to assess the effect of implantation on the levels adjacent to the fusion segment. The upper surface of the first lumbar vertebra was first loaded with a 150 N axial load, and then subjected to a pure unconstrained moment. All degrees of freedom on the bottom nodes of the fifth vertebra of all models were constrained. The moment was increased in increments of 0.36 Nm until the ROM of the model (L1-L5) achieved 17\({}^{\circ}\) in flexion, 10\({}^{\circ}\) in extension, 12\({}^{\circ}\) in left lateral bending and 10\({}^{\circ}\) in left torsion.  
This study investigated lumbar motion and stress, including the ROM of each motion segment, the stiffness of fusion segments, stresses on endplates and pedicle screws, and peak disc stresses under flexion, extension, torsion and left lateral bending.