Euler stability of the human ligamentous lumbar spine. Part I: Theory

The human ligamentous lumbar spine was modelled in the frontal plane as an Euler column for the purpose of rigorously studying its mechanical stability. Using stiffness data obtained from testing cadaveric specimens, we simulated the vertebral bodies as rigid links and the intervertebral elastic behaviour as both linear (linear model) and exponential (exponential model). The linear model, with a higher initial stiffness, predicted a higher buckling load (67 N), and hence was more stable in upright posture than the exponential model (11 N). After buckling, the greatest lateral motion was predicted at L5-S1. The exponential model predicted postbuckling motion to be less than 5° at 100 N, while the linear model predicted an excessive 40° at L5-S1. In both models the injured spine, simulated with decreased intervertebral stiffness, was predicted to be more unstable by buckling at lesser loads and undergoing greater postbuckling lateral motion. Validation of this model was accomplished through experimentation described in Part II.