Apparent- and Tissue-Level Yield Behaviors of L4 Vertebral Trabecular Bone and Their Associations with Microarchitectures

Abstract

The precise quantification of vertebral trabecular bone strength and the associations between the microarchitecture and nonlinear mechanics of trabecular bone under various loading conditions may provide insights into trabecular bone quality and trabecular strength prediction based on microarchitectures. In this research, 44 cubic L4 vertebral trabecular bone specimens (5 × 5 × 5 mm(3)) were selected from six male Chinese donors aged 62-70 years. For each vertebral trabecular cube, micro-computed tomography image-based nonlinear micro-finite element analyzes were conducted under compressive and tensile loadings along two orthogonal directions. A bilinear tissue constitutive model was used to describe the nonlinearity of bone tissue material. In each analysis, apparent Young's modulus and initial apparent yield point were determined; the average tissue von Mises stress at the apparent yield point was also calculated, and the amount of tissue elements yielded was obtained. Principal components (PCs) analysis revealed three independent components of the microarchitectural parameters of the vertebral trabecular bones; these three PCs can account for 80.744% of the total variability of trabecular microarchitectures; the first PC (PC1) included bone volume fraction, connectivity density and trabecular number; the second PC (PC2) comprised structure model index and degree of anisotropy; and the third PC (PC3) represented trabecular thickness and age. Multivariate linear regression analysis showed that the PCs were strongly predictive of the apparent- and tissue-level mechanical parameters of the vertebral trabecular bone. To gain further insights into the mechanical properties of trabecular bone, we divided the six vertebral bodies into two groups based on the microarchitectural parameters: high-quality group and low-quality group. We then compared the differences in the mechanical parameters between tension and compression, as well as along longitudinal and transverse loading directions. Results showed that the apparent Young's moduli of the high-quality group were significantly greater than those of the low-quality group in longitudinal and transverse directions. Only the apparent yield strains of the two groups under the longitudinal compressive loading condition were significantly different. The apparent yield stresses and the average tissue von Mises stresses of the trabeculae in the trabecular cubes of the high-quality group were significantly greater than those of the low-quality group under the four loading conditions. This study provided quantitative information regarding the nonlinear mechanical properties of vertebral trabecular bone. This study also described the associations of these mechanical properties with microarchitectures. Our findings may help estimate vertebral strength and the related fracture risk.

Keywords: Longitudinal direction; Nonlinear micro-finite element analysis; Trabecular bone; Transverse direction; Vertebral body; Yield behavior.