# Biomechanical Optimization of Lumbar Fusion Cages with a Porous Design: A Finite Element Analysis
## 1 Introduction  
LUMbar interbody fusion (LIF) is a standard treatment for spinal instability due to degenerative disk disease and spinal deformities. The procedure involves a partial resection of vertebral elements and soft tissues, followed by the insertion of an interbody fusion cage to restore intervertebral spacing, spinal height, and natural curvature [1]. A variety of surgical techniques, implant designs, and grafting materials are utilized to promote biomechanically robust intervertebral fusion, stabilizing degenerated spinal segments, correcting alignment, and relieving pressure on the spinal canal [2]. Specifically, LIF accesses the L2-L5 intervertebral region via the anatomical corridor between the psoas major muscle and the aorta/inferior vena cava, preserving the structural integrity of the lamina and paraspinal musculature [3]. The deployment of an oversized fusion cage facilitates indirect decompression of neural elements by supporting the intervertebral disk while maintaining the posterior spinal architecture [4]. Despite its clinical success, LIF and the associated implantation of fusion cages can precipitate unintended biomechanical consequences, including adjacent segment degeneration (ASD) and cage subsidence [5]. Subsidence, characterized by the sinking of the cage into the vertebral endplate, is a prevalent complication that diminishes fusion segment height, disrupts spinal curvature, and risks nerve compression. These effects can compromise patient recovery, leading to persistent lower back pain and neurological deficits [6]. Emerging research attributes subsidence to factors such as an incompatible elastic modulus and suboptimal cage geometry, highlighting the need for innovative design solutions. Accordingly, refining fusion cage properties--through material modifications and the integration of microporous architectures--has become a focal point of investigation [7]. The morphological configuration of fusion cages plays a pivotal role in their optimization [8]. Conventional designs prioritize parameters such as contact surface area, intervertebral height restoration, and fixation stability. However, these standardized cages often fail to accommodate the anatomical variability among patients, resulting in suboptimal biomechanical outcomes [9]. Recent advancements in implant design have leveraged principles from bionics and biomechanics to introduce personalized approaches, which are gaining traction in the field. For example, [PERSON] et al. [10] engineered patient-specific multi-segment intervertebral implants tailored to individual spinal anatomies, achieving both safety and favorable clinical outcomes. Such customized designs enhance the conformity between the cage and vertebral endplates, optimize biomechanical performance, ensure even stress distribution across the vertebral interface, and improve load transmission underscoring the value of personalization in reducing postoperative complications. Beyond shape customization, the incorporation of porous architectures into fusion cage design offers additional advantages. By modulating the geometric properties of pore structures, cage stiffness can be precisely adjusted to prevent stress shielding while providing conduits for bone ingrowth, nutrient diffusion, and enhanced implant stability [11]. Porous configurations also lower the elastic modulus, mitigating stress shielding effects that can impede bone remodeling [12]. Among these structures, the Gyroid (G) scaffold stands out for its biomimetic resemblance to human bone, featuring high interconnectivity and tunable geometric parameters. Adjustments to its form can yield mechanical properties akin to cortical or cancellous bone, positioning it as a leading candidate for skeletal implants [13]. Studies indicate that Gyroid lattices outperform traditional scaffolds in elastic modulus and yield strength [14].