Nonlinear Buckling Analysis for Etiological Study of Idiopathic Scoliosis

Abstract

This paper investigated buckling phenomena of the spine induced by the growth of vertebral bodies that have potential to cause idiopathic scoliosis. In the previous study, we presented a hypothesis that idiopathic scoliosis is a buckling phenomena induced by the growth of vertebral bodies based on the similarity of the clinical single and double-major curves with the results of the fourth and sixth buckling modes, respectively, as analyzed by the finite-elements method using linear buckling theory. However, this theory is valid for infinitesimal deformation and is not applicable to estimation of stability for post-buckling behavior. In this study, we developed a program to analyze deformation histories caused by the growth of vertebral bodies considering the geometrical nonlinearity and investigated buckling phenomena. We assumed that growth represents generation of non-elastic bulk strain. To exclude modes correctable by posture change, we considered constraints at the cervical spine. Using the developed program, we analyzed deformation histories induced by the growth of vertebral bodies and obtained deformation histories including buckling phenomena with side-bending modes similar to clinical curves. However, the magnitudes of deformations were in the sub-millimeter order that is too small for the etiology of idiopathic scoliosis by itself. Based on the results, we suggested that participation of other phenomena, such as bone remodeling caused by the stresses at the side-bending deformations, will be necessary.