Nonlinear Response Analysis of the Human Ligamentous Lumbar Spine in Compression

Abstract

Basic questions regarding how extreme compressive loads can be tolerated by the spine without experiencing abnormal motions or instabilities remain unresolved. Two finite element models of the human lumbar spine were generated. The detailed model accounted for the three-dimensional irregular geometry, material and geometric nonlinearities, nonhomogeneous fiber-matrix nature of the discs, ligaments, and articulation at the facet joints. The nonlinear stability response of the model was predicted under an axial compression force (200 N to 700 N) applied at the L1 while the S1 was fixed. The effect of the presence of a combined flexion moment and a horizontal support on the response was investigated. Another nonlinear model using rigid bodies interconnected by deformable beam elements was also considered. The computed results under the axial compression loads indicated that the response is highly nonlinear with no bifurcation or limit point (critical load). The unconstrained lumbar spine is most flexible in the sagittal plane (least stiff plane). The existence of the horizontal support and the combined flexion moment significantly increased the load-bearing capacity of the lumbar spine; the lumbar spine resisted the axial compression force of 400 N with minimal displacements. Under axial compression force, the flexion moment tends to restrict the posterior translational movement of the lordotic lumbar spine, whereas the horizontal support constrains the coupled lateral motion. A slight decrease in the lordosis was predicted for the compression load of 400 N. It is postulated that the anterior location of the line of gravity of the upper-body weight is regulated to provide the required combined loads on the lumbar spine so higher compression can be tolerated by the spine at minimal energetic cost. In vivo experimental results support the validity of the model predictions.