Trabecular Structural Changes in a Vertebral Body with a Fixation Screw

Abstract

This chapter describes the effects of a spinal fixation screw on trabecular structural changes in a vertebral body, predicted by a three-dimensional simulation of trabecular remodeling. The entire vertebral body with a fixation screw and bone-screw interface were modeled using voxel finite elements. In the vertebral body, the implantation of the fixation screw caused a change in the mechanical environment of the cancellous bone, leading to trabecular structural changes at the cancellous bone level. The effects of the screw on the trabecular orientation were stronger in the regions above and below the screw compared to those in front of the screw. In the proximity of the bone-screw interface, the trabecular structural changes depended on the direction of the load applied to the screw. The bone resorption, predicted in the pull-out loading, is a candidate cause of screw loosening. The results indicate that the effects of implanted screws on trabecular structural changes are more important for long-term fixation.

This Chapter was adapted from Tsubota et al. (2003) with permission from Springer.

Appendix: Cancellous Bone Remodeling in a Normal Vertebral Body

In the case of a normal vertebral body, the trabecular surface remodeling simulation was conducted using a half-voxel model of a human L3 vertebral body (model N), as shown in Fig. 14.7a. The cortical shape of the model in the midsagittal plane was determined based on the photograph of the cross-section of the human vertebral body, available in the literature (Mosekilde 1990), as shown in Fig. 14.7b. Rotating the midsagittal section with regard to the central longitudinal axis, the three-dimensional shape of the cortical bone was constructed as an axisymmetric shell. The vertebral body diameter was 50  mm in the bilateral and anteroposterior directions, and its height was 25  mm in the axial direction.

Fig. 14.7

Voxel finite element model of half of a normal vertebral body (model N), assumed to be symmetric with respect to the central sagittal plane. (a) A three-dimensional image and compressive loading condition owing to the body weight (left), the fabric ellipsoid of the trabecular structure (top right), and the X ₂ − X ₃ cross-section (bottom right). (b) The shapes of the cortical and cancellous bones, constructed by rotating the midsagittal section (This figure was adapted from Tsubota et al. (2003) with permission from Springer)

The cancellous bone part was filled with toroidal trabeculae to a bone volume fraction of BVF = 0.46 and the degree of structural anisotropy of H ₁/H ₃ = 1.04, in which H ₁ and H ₃ were the maximum and minimum principal values of the fabric ellipsoid (Cowin 1985), respectively. As indicated by the fabric ellipsoid and by the image of the X ₂ − X ₃ cross-section in Fig. 14.7a, the trabecular structure was initially isotropic. The number of voxels for describing the bone was approximately 0.85 million, and the volume of each element was 250 μm × 250 μm × 250 μm. The bone part was assumed to be homogeneous and isotropic, and Young’s modulus E and Poisson’s ratio ν were set as E _b  = 20 GPa and ν _b  = 0.3 (An 1999; Zioupos et al. 1999). As a boundary condition , uniform compressive displacement U ₃ was applied to the upper plane at X ₃ = 25  mm to apply the total load F ₁ = 588 N as a body weight. The lower plane at X ₃ = 0  mm was fixed. The model parameters in the remodeling rate equation (Chap. 9) were set constant as threshold values Γ _u  = 1.0 and Γ _l  =  − 1.25, and the sensing distance was l _L  = 2.5 mm.

In remodeling simulation, an anisotropic trabecular structure was obtained owing to the trabecular formation and resorption for converging to a local state of uniform stress, as indicated by the image of the X ₂ − X ₃ cross-section and fabric ellipsoid of the trabecular structure in Fig. 14.8. The angle Θ ₃ between the maximum principal direction of the fabric ellipsoid and the X ₃ axis was 3^∘, consistent with the observation that the trabeculae in the vertebral body are oriented along the axial direction (Mosekilde 1990). The bone volume fraction BVF decreased to 0.37, and the degree of structural anisotropy H ₁/H ₃ increased to 1.47. The structural parameters BVF and H ₁/H ₃ obtained in the simulation better captured the experimental observation (Beuf et al. 2001) than the parameters of the initial isotropic structure.

Fig. 14.8

Trabecular structure in a normal vertebral body (model N) obtained from the remodeling simulation: the X ₂ − X ₃ cross-section (left) and the fabric ellipsoid (right) (This figure was adapted from Tsubota et al. (2003) with permission from Springer)