Euler Buckling as a Model for the Curvature and Flexion of the Human Lumbar Spine

The upright thoraco-lumbar spine resembles an Euler column buckled in the second mode (n = 2) when viewed in the sagittal plane. An advantage of n = 2 buckling is that further load can be carried without adopting a stooped posture. Flexion of the spine is considered as the first quarter cycle of an Euler pendulum. This is possible if the antagonistic muscles which control movement increase the bending stiffness, EI, to a value of about 15 N m². If the muscles are incapable of increasing EI sufficiently to support the weight of the body, or any excess load, the spine will be dynamically unstable. This conclusion is consistent with a static model which considers spinal instability as `loss of stiffness' and a dynamic model which suggests that it arises from ineffective adaptive control. The flexed spine resembles an n = 1 buckled column.