Modeling stress–strain state of screw transpedicular spine fixation system with variable structure of the vertebral body

Abstract

To ensure the stability of the spine in the postoperative period transpedicular fixation spine's elements is often used. Usually transpedicular system is formed from the rods that eventually form the frame structure type, attached with screws to the vertebrae. Such design must be rigid and take active part spine loads without significant deformation. Simple transpedicular system can be represented as: bone-1–transpedicular screw-1–Bar–transpedicular screw-2–bell-2–Cage–bell-1. This bar takes in about 20% and Cage takes in about 80% applied load. From the standpoint of improving the well-known structures interest should be given in their stress–strain state as a whole, and for each of the elements, in particular. This study was held in modeling of pedicle screw and the estimation of its deformation, taking into account the interaction with the body of vertebra, which has a variable structure. Vertebra has a complex structure provided with hard enough outer (cortical) layer and soft inner body. A simplified model can be considered with homogeneous materials characterized by different Young's modulus and Poisson's ratio. Transpedicular screw can be represented as a bar having a variable cross-section, located on an elastic base, characterized by different modulus of subgrade reaction. The modulus of subgrade reaction of the elastic foundation is changing stepwise at the transition from one layer of the vertebral body to another. In addition, it is assumed that the vertebra is rigidly clamped (conditionally stationary), and the load is transferred from the screw rod, being uniformly distributed along the length of the local section at the end of the screw. The numerical solution of this problem was obtained by using the generalized Heaviside function. Analysis of the solution indicates that the greatest strain occurs in the area of the screw located in the cortical layer of the vertebra, while the rest is practically not deformed. The same problem was solved by the finite element method in the medium CosmosDesignStar. At the same time 3D-models were used for the spinal segment, fixed transpedicular system. Results of solutions obtained by the two methods described above were sufficiently close, suggesting the adequacy of the proposed model with respect to the real conditions. Thus, the proposed technique can be used to analyze the stress–strain state of various screws, to assess the impact of new constructional elements of screws on the nature of their deformations, to develop improved designs of transpedicular systems, including their dynamics.