Biomechanical Study of the Behavior of the Intervertebral Disc: Intact Lumbar Spine Versus Arthrodesis

Type of the study

This was a numerical study in silico. Von Mises stress distribution on IVD was analyzed from a validated FEM of lumbar spine (from L2 to L5), and compared to Von Mises stress distribution on IVD of the same subject, having an L3- L4 arthrodesis.

Geometrical model: Three-dimensional FEM is built up using scanner images (CT-scan Picker 5000) of a 40-year- old male. The geometrical model is generated from these files using SliceOmatic software. The finite element software Solidworks was used to conduct the numerical computing. Ligaments and muscles were not represented in the present model (Figure 1). Model with arthrodesis: We made modifications on the model to simulate an arthrodesis of L3-L4 stage: we replaced the L3-L4 disc with a bone graft, by changing the material properties of the disc to those of a vertebra, and fixed L3, L3- L4 space and L4 in one block by adding osteosynthesis with four pedicle screws and two rods (Figure 2). Material properties: The material properties of the model structures (Table 1) were taken from previous works [2]. Boundary conditions: Before proceeding to the application of loads and simulation, we defined boundary conditions which consisted in fixing all the elements of the lower base of the lumbar segment.

Loading

We applied loads on the upper surface of L2 (Figure 3) and observed Von Mises stress distribution on IVD for the two models. We studied the distribution of stress in axial compression after applying increasing loads of 400, 600, 800, 1000 and 1200 Newton (N). While knowing that the standing, relaxed position for a 70-kilogram man corresponds to a force of 400N, lifting an additional load of 20kg corresponds to a force of 600N and so on. We also studied the distribution of Von Mises stress in bending by using moments of force for the following values: 1.9 - 3.8 – 5.3 – 6.5 and 7.5 Newton- meter.

Validation of the Model

To validate our model, we compared the results with in vivo experimental data. We relied on the work of Wilke, et al. [3] who measured the pressure of the non-degenerated L4-L5 disc of a volunteer man, for several spatial positions and different load lifts. Von Mises stress on the healthy L4- L5 disc of our model were comparatively increased. This can be explained by the absence of ligaments and muscles, elements that allow movement and stabilize the spine, but are also essential for damping, transferring and distributing the loads. However, by comparing the evolution of stress as a function of loads between our model and experimental studies [4] or other FEM [2], we found that our model tends to follow the same linear behavior. We concluded that our model is reliable and valid for the study of IVD stress.

Von Mises Stress in Axial Compression

For the L2-L3 disc before and after arthrodesis, the stress increase linearly as the loads are increased for the two models. Stress increases significantly after arthrodesis (p=0.002). Likewise, for the L4-L5 disc stress increases linearly as the loads are increased for the two models. The difference was not significant between the models before and after arthrodesis (p=0.072). By comparing the sum of the stress undergone by the IVD on the healthy model, we find that the L4-L5 disc bears significantly more stress than the L2-L3 disc (p=0.008).

Von Mises Stress in Bending

The stress on L2-L3 and L4-L5 discs increase after arthrodesis, but the difference was not significant, with p equal to 0.151 and 0.44 respectively. However, the rate of stress increase at the L2-L3 disc was significantly higher compared to the rate of stress increase at the L4-L5 disc (p=0.032).