Stress-Strain Response of the Human Spine Intervertebral Disc As an Anisotropic Body. Mathematical Modeling and Computation

Abstract

The paper deals with the biomechanical investigation on the human lumbar intervertebral disc under the static load. The disc is regarded as a two-phased ambient consisting of a fibrous outer part called annulus fibrosis and a liquid inner part nucleus pulposus. Due to the fibrous structure, the annulus fibrosis can be treated by using a special case of anisotropy-transversal isotropy. In the paper the corresponding tensor of material constants is derived. The tensor consequently incomes to the constitutive equations determining the stress-strain relation in the material. In order to study the mechanical behaviour the disc is observed within the motion segment, the basic unit for motion tracing. The motion segment involves two neighbouring vertebrae and the intervertebral disc between them that connect them both. When constitutive equations are accomplished, they can be incorporated in the finite element analysis. The illustrative example of the intervertebral disc L2/L3, the disc between the second and the third lumbar vertebrae the lumbar part of spine, with its computer implementation is performed. Finally the comparison of the results of using anisotropic and homogenized approach is provided. The comparison illustrates the eligibility of such a kind of approach.