# On the Finite Element Modeling of the Lumbar Spine: A Schematic Review
## 1 Introduction  
The study of spine biomechanics has evolved over decades. Computational simulations provide a critical tool in light of the difficulty and complexity required to perform in vivo experiments on human spinal columns [1; 2; 3]. The biomechanics of the spine are extremely complex, and many different anatomical components are involved. In computational simulations, these components are modelled separately, each one being associated with specified modelling features according to their biomechanical response and constitutive model relationships [4; 5]. A complete finite element (FE) analysis of the spine requires the modelling of bone components, intervertebral discs, facet joints, and seven major spinal ligaments, as well as the cartilaginous endplates [5; 6; 7; 8]. The bone component consists of three parts: the cancellous bone (the innermost part), cortical bone (the outermost part), and posterior bony elements (which represent the vertebral arch where the bone marrow is inserted) [7]. The intervertebral disc is divided into the nucleus pulposus and the fibrous annulus, composed of the annular ground substance and reinforcing fibers. The three distinct parts of the disc should be modelled to simulate the correct biomechanics of the spinal column [7; 8]. Therefore, the facet joint needs to be represented in order to account for the relative movement between the spinal processes of the two vertebrae. The seven major ligaments represented in the FE model are the anterior longitudinal ligament (ALL), posterior longitudinal ligament (PLL), interspinous ligament (IL), intertransverse ligament (TL), flavian ligament (FL), supraspinous ligament (SL), and capsular ligament (CL) [5; 6]. Ligaments contribute to spinal stabilization byestablishing the follower force path-way, which passes through the rotation centers of the vertebrae [9; 10; 11; 12]. In an FE model of the lumbar spine, all these different components must be considered and modelled in order to ensure that the model is as reliable as possible. [PERSON] et al. [13] compared eight different finite element studies [14; 15; 16; 17; 18; 19; 20; 21] of the spine in a very comprehensive study. The eight element models were chosen according to the importance of the research carried out by the authors. The aim of the comparison was to observe whether it was possible to develop a prediction model of the lumbar spine's behaviour under certain loading conditions. From the different studies, a certain homogeneity and average of the results was observed. This homogeneity was achieved as a result of the correct and complex modelling of the different anatomical parts modelled by the authors in a comprehensive manner. The target of most biomechanical spine simulations is to evaluate the spinal loading conditions under physiological and pathological conditions [13; 22; 23]. Intradiscal pressure (IDP) and displacement measurements are the main parameters for analyzing the intervertebral disc mechanical response during the compression phase. Other analysis factors are the radial and circumferential internal stresses and the stretching in response to loading stresses. During flexion, extension, lateral bending, and rotation movements, the range of motion (ROM) is analyzed and examined [13; 22; 23; 24]. The final step of a computational simulation is to validate the so obtained finite element results using experimental testing. There are several types of in vivo experiments specific to the characterization and quantification of the mechanical response of the anatomical components [25; 26; 27; 28; 29; 30; 31; 32; 33; 34]. Several experiments involve simply testing the intervertebral disc among two pairs of vertebrae, then subjecting these to different stress states [25; 26; 29; 30; 33]. Other experiments concern the muscular trunk and the generation of follower forces. In such experiments, specimens are subjected to a simple compressive force and then a follower force, through which the obtained results can then be compared.