Frank A. Pintar

A non-linear finite element model of a spinal segment

Abstract Lumbar intervertebral joints play an important role in the etiology of low-back pain. An understanding of its mechanical response is essential both from the point of its normal function as well as injury prognosis. Since purely experimental investigations cannot provide complete information, mathematical models to supplement experimental records are necessary. In this study a finite element model of a lumbar intervertebral segment is developed to analyze the stress distributions and strain energy absorbing capacities. Experiments were conducted to obtain the geometry and load-deflection data. The nonlinear sigmoidal load-deflection behavior was divided into five distinct phases based on the variation of stiffness, defined by the instantaneous slope of the load-deflection diagram. The threshold of trauma was defined at the point at which the structure exhibited softening characteristics (this corresponds with the first drop of stiffness). Load at this level was termed as the micro failure of softening load. At the point of ultimate load, the specimen had zero stiffness. The non-linear axisymmetric (geometrical and material) model incorporated the cartilagenious and cortical bone, the endplates, and the disc. The nucleus pulposus was modeled using isoparametric quadrilateral fluid elements. The model was validated with experimental axial load-deflection data. To exercise the model, homogeneous, isotropic, and loading path independent material parameters were used for all the components of the spinal segment with the exception of the annulus. The Youngs modulus of annulus was estimated as a function of load level using the method of steepest descent. The disc absorbed about 84% of the total strain energy in the initial loading phase (ambient range), and at the threshold of failure, it gradually decreased to about 65%. The bony elements absorbed about 15% at the threshold. The nucleus pressure increased to about 11MPa at the threshold of trauma.