Contributions of trabecular rods of various orientations in determining the elastic properties of human vertebral trabecular bone

Abstract

Trabecular bone networks consist of two basic microstructural types: plates and rods. Although trabecular rods represent only a small fraction of total bone volume, their existence has important roles in failure initiation and progression. The goal of this study was to quantitatively examine the contributions of trabecular rods in various orientations to the anisotropic elastic moduli of human vertebral trabecular bone. Twenty-one human vertebral trabecular bone specimens were scanned by microcomputed tomography (microCT). A coordinate system of orthotropic axes representing the best elastic orthotropic symmetry was determined for each sample. Individual trabeculae segmentation (ITS), a 3D image analysis technique, was performed to identify each individual trabecular rod and determine its orientation in the orthotropic coordinate system. Next, three rod-removed images were created where longitudinal, oblique, or transverse trabecular rods were removed, respectively, from the original microCT images. The original and three categories of rod-removed images were then converted to finite element (FE) models for evaluation of their elastic moduli and anisotropy. Both the transverse and oblique rod-removal caused significant decreases in all six elastic moduli. However, the removal of longitudinal rods only caused significant changes in E(33), G(23), and G(31) but not in any transverse/in-plane elastic properties (E(11), E(22), and G(12)). The analysis of covariance (ANCOVA) with repeated measures was applied to detect the moduli change in the different models caused by the effects beyond just bone volume loss. The results suggested that the loss of transverse rods induced a significant decrease in in-plane mechanical competence, which was greater than what could be explained only by the associated bone volume loss. In contrast, the reduction in the axial Young's modulus caused by the loss of transverse rods was proportional to the bone volume decrease. Furthermore, the loss of longitudinal rods affected the axial Young's modulus through both bone volume loss and architectural change. With aging, the reduction in in-plane mechanical competence would be magnified by the preferential loss of transverse rods. The predictive ability of bone mineral density, a surrogate of BV/TV in clinical measurements, may reduce more quickly for transverse mechanical properties than for the axial mechanical properties.

Figure 1

Illustration of the ITS-based segmentation of trabecular rods on an image of a vertebral trabecular bone sample. According to the angle between the longitudinal axis and trabecular rod orientation, each individual rod was classified as transverse, oblique or longitudinal.

Figure 2

(A) Original, (B) longitudinal rod-removed model, (C) oblique rod-removed model, and (D) transverse rod-removed model of an image of a vertebral trabecular bone sample.

Figure 3

The normalized BV/TV and elastic moduli of longitudinal, oblique, and transverse rod-removed model. * indicates significant difference compared to the original model (repeated measures ANOVA tests, p<0.05).

Figure 4

Correlations between BV/TV and elastic moduli (A) E₁₁, (B) E₂₂, (C) E₃₃, (D) G₂₃, (E) G₃₁, and (F) G₁₂ of original, longitudinal rod-removed, oblique rod-removed and transverse rod-removed model. * Indicates significant difference of elastic moduli between rod-removed model and original model independent of bone volume fraction (repeated measures ANCOVA test with BV/TV as covariate, p<0.05).