Some comments on the absence of buckling of the ligamentous human spine in the sagittal plane

The human spine has an elaborate system of muscles and ligaments which serve to actuate this complex biomechanical system. In this paper, the buckling instabilities of the ligamentous spine are explored using a model based on Euler's elastica. The model features the intrinsic curvature and self-weight of the spine. With the help of nonlinear stability criteria, the stability of the spine and its buckled states are analyzed. Our main novel results demonstrate that the ligamentous spine in the sagittal plane remains stable under its self-weight and a terminal vertical load, and, following a pitchfork bifurcation, an unstable configuration of the spine is possible which is close to the unloaded spine.