A finite element model of the L5-S1 functional spinal unit: development and comparison with biomechanical tests in vitro

The main objective of this work is to develop a three-dimensional finite element model of the L5-S1 segment that is able to simulate its passive mobility measured in vitro. Due to their limited role in segment mobility, an isotropic linear elastic constitutive law was used for cartilage, cancellous and cortical bone. The intervertebral disk ground substance was modeled with a non-linear hyperelastic polynomial law. Fibers of the disk, as well as ligaments, were modeled with piecewise linear springs. Flexion-extension, axial rotation, and lateral bending torques were applied to the model. A comparison with the experimental results obtained on the same segment for these three major motions was conducted. The compliance of the segment subjected to pure torques was found to be similar between numerical and experimental results for all major motions. Coupled motions and translations were also similar, even in their amplitude. For lateral bending, the normal coupled motions originate from the geometry of the disk and not from the facet geometry.