Quantification of the roles of trabecular microarchitecture and trabecular type in determining the elastic modulus of human trabecular bone

Abstract

The roles of microarchitecture and types of trabeculae in determining elastic modulus of trabecular bone have been studied in microCT images of 29 trabecular bone samples by comparing their Young's moduli calculated by finite element analysis (FEA) with different trabecular type-specific reconstructions. The results suggest that trabecular plates play an essential role in determining elastic properties of trabecular bone.

Introduction: Osteoporosis is an age-related disease characterized by low bone mass and architectural deterioration. Other than bone volume fraction (BV/TV), microarchitecture of bone is also believed to be important in governing mechanical properties of trabecular bone. We quantitatively examined the role of microarchitecture and relative contribution of trabecular types of individual trabecula in determining the elastic property of trabecular bone.

Materials and methods: Twenty-nine human cadaveric trabecular bone samples were scanned at 21-mum resolution using a microCT system. Digital topological analysis (DTA) consisting of skeletonization and classification was combined with a trabecular type-specific reconstruction technique to extract the skeleton and identify topological type of trabeculae of the original trabecular bone image. Four different microCT-based finite element (FE) models were constructed for each specimen: (1) original full voxel; (2) skeletal voxel; (3) rod-reconstructed, preserving rod volume and plate skeleton; and (4) plate-reconstructed, preserving plate volume and rod skeleton. For each model, the elastic moduli were calculated under compression along each of three image-coordinate axis directions. Plate and rod tissue fractions directly measured from DTA-based topological classification were correlated with the elastic moduli computed from full voxel model.

Results: The elastic moduli of skeleton models were significantly correlated with those of full voxel models along all three coordinate axes (r(2) = 0.38 approximately 0.53). The rod-reconstructed model contained 21.3% of original bone mass and restored 1.5% of elastic moduli, whereas the plate-reconstructed model contained 90.3% of bone mass and restored 53.2% of elastic moduli. Plate tissue fraction showed a significantly positive correlation (r(2) = 0.49) with elastic modulus by a power law, whereas rod tissue fraction showed a significantly negative correlation (r(2) = 0.42).

Conclusions: These results quantitatively show that the microarchitecture alone affects elastic moduli of trabecular bone and trabecular plates make a far greater contribution than rods to the bone's elastic behavior.

FIG. 1

Results of DTA and reconstruction procedure on image of vertebral trabecular bone sample (3.2 × 3.2 × 2.1 mm³). (A) An original μCT image (full voxel model) of a trabecular bone sample. (B) Skeletonized image (skeleton model) of A. (C) Results of topological classification of B. Plate voxels are shown as dark gray, rod voxels in lighter shading. (D) Reconstructed structures with the trabecular type labeled for each voxel. (E) Rod-reconstructed model. (F) Plate-reconstructed model.

FIG. 2

Results of linear correlation analyses between the elastic modulus of the full voxel model and that of each of skeleton and plate- and rod-reconstructed models. The plots for the skeleton and rod-reconstructed models were almost superimposed on each other. For the results shown here, the elastic moduli were computed under compression along the z-axis of the image which was aligned with the principal orientation of trabeculae.

FIG. 3

Results of linear correlation analyses between the BV/TV of the full voxel models and that of each of skeleton and plate-and rod-reconstructed models.

FIG. 4

Illustrations of DTA on μCT images of three different trabecular bone samples (2.1 × 2.1 × 1.3 mm³). (Left) Original μCT image (full voxel model) of the trabecular bone sample. (Right) Skeletonized image (skeleton model). (A) Plate-to-rod ratio = 20.10, plate tissue fraction = 0.9526, Young’s modulus = 974.8 MPa. (B) Plate-to-rod ratio = 10.22, plate tissue fraction = 0.9109, Young’s modulus = 674.8 MPa. (C) Plate-to-rod ratio = 5.94, plate tissue fraction = 0.8559, Young’s modulus = 216.8 MPa.

FIG. 5

Results of correlation analyses between Young’s modulus ${\text{E}}_{\text{z}}^{\ast }$ of the full voxel model and that of (A) plate bone volume fraction (pBV/TV), (B) rod bone volume fraction (rBV/TV), (C) plate tissue fraction (pBV/BV), (D) rod tissue fraction (rBV/BV), (E) bone volume fraction (BV/TV), and (F) plate-to-rod ratio (pBV/rBV) by nonlinear regression of power laws.