# Biomechanical Optimization of Lumbar Fusion Cages with a Porous Design: A Finite Element Analysis
## 2 Materials and Methods  
### Development of the Lumbar Spine FE Model  
The research object of this paper was a young and healthy male volunteer, aged 25 years old, 177 cm tall, 70 kg in weight, with no history of lumbar disease, and no deformity or degeneration of the lumbar spine was found in the X-ray examination. The study design based on volunteer was supported by Ethics Committee of First Affiliated Hospital of Ningbo University with informed consent obtained from the volunteer. The volunteer's spine was scanned using a dual-source CT scanner from Siemens CT (scanning conditions: 120 kV, 125 mA, layer thickness: 0.8 mm, top-down spiral axial scanning), and a total of 609 DICOM images of the lumbar spine were extracted. The L3-L4 lumbar segment was selected for this study due to its significant contribution to lumbar spine mobility and its frequent involvement in degenerative pathologies requiring fusion surgery, making it a clinically relevant and representative segment for comparing the biomechanical performance of different interbody cage designs. Focusing on a single segment allows for a clearer assessment of the cage design's direct impact while minimizing confounding factors from multi-segmental interactions in this initial comparative analysis. The CT data were processed in Mimics 21.0 (Materialise, Leuven, Belgium). Image denoising was performed, and optimal thresholds were established to distinguish bone from soft tissue boundaries. Soft tissue surrounding the vertebrae was removed based on the gray value in the range of 226-1672 Hu, followed by regional growth, smoothing, and gap-filling operations to produce a smooth, continuous vertebral outer contour. Cortical and cancellous bones were assigned using the gray value formula in Mimics, and intervertebral disks and cartilage were built in a preliminary three-dimensional model (Figure 1). Figure 1: A complete 3D model of the lumbar spine preparing process, from skeletal structure CT data of the lumbar spine to the final smoothed model with a repaired surface. The model was exported in STL format to Geomagic Studio 2016 (Geomagic Inc., Cary, NA, USA) for refinement. Protrusions and depressions were eliminated, surfaces were smoothed, and triangular meshes were fitted to create a continuous surface model. Solid models of cortical bone, cancellous bone, intervertebral disks, and endplates were then constructed using SolidWorks 2016 (Dassault Systemes, Paris, France), as shown in Figure 2.  
The assembled solid model was imported into Abaqus 2020 (Dassault Systemes, France) in IGES format for finite element analysis. In the L3-L4 segment, ligaments--including the anterior longitudinal, posterior longitudinal, supraspinous, interspinous, and intertransverse ligaments--were reconstructed. Material properties were assigned as follows: cortical bone, cancellous bone, and endplates were modeled as isotropic homogeneous elastic materials with thicknesses of 1.0 mm, 0.5 mm, and 0.5 mm (facet joint space), respectively. Facet joint cartilage was set to 0.25 mm thick with a surface-to-surface contact and friction coefficient of 0.1. The nucleus pulposus was modeled as an incompressible fluid using fluid elements to simulate its hydrostatic behavior, constituting 45% of the intervertebral disk volume, while the annulus fibrosus was modeled with 8 layers of fibers oriented at \(\pm\)30\({}^{\circ}\) to the transverse plane, comprising 55% of the intervertebral disk [21]. Ligaments, including the anterior longitudinal, posterior longitudinal, supraspinous, interspinous, and intertransverse ligaments, were modeled using nonlinear spring elements to simulate their physiological behavior (see Figure 2d) [22]. The finite element model of the L3-L4 single segment was generated using tetrahedral unit [23], convergence based on h-refinement with a 5% tolerance for stress and displacement, thus a total of 618,054 elements and 684,028 nodes, with an average mesh size of 0.1 mm.