Connectivity and the elastic properties of cancellous bone

Abstract

This study addresses the possible significance of trabecular connectivity for the mechanical quality of cancellous bone. A total of 141 cubic trabecular bone specimens collected from autopsy material from 56 individuals without any known bone or metastatic diseases were used. Age variation was in the range of 14 -91 years and a wide range of trabecular architecture was found. Each specimen was three-dimensionally reconstructed with a voxel size of either 20 or 25 m. Using the detailed three-dimensional reconstructions as input for microstructural finite-element models, the complete elastic properties of the trabecular architecture were obtained and maximum and mean stiffness could be calculated. Volume fraction and true three-dimensional architectural measurements of connectivity density and surface density were determined. Connectivity density was determined in an unbiased manner by the Euler number, which is a topological property. Using multiple regression analysis it was found that volume fraction explained by far the greatest part (84%-94%) of the variation in both mean and maximum stiffness. When connectivity density and surface density were included, the correlations increased marginally to 89%-95%. Noticeably negative regression coefficients were found for connectivity density. The results suggest that, in normal cancellous bone, the connectivity density has very limited value for assessment of elastic properties by morphological variables, but if a relation exists then stiffness decreases with increasing connectivity. (Bone 24:115-120; 1999) © 1999 by Elsevier Science Inc. All rights reserved.

Relationship between compressive properties of human os calcis cancellous bone and microarchitecture assessed from 2D and 3D synchrotron microtomography

“…The mechanical properties of the cancellous bone are significantly correlated with most of the morphological parameters. These results are akin to those in the literature for different human sites, using different architectural analyses and different mechanical characterization methods [5,18,20,31,60]. Yet, the Pearson coefficients obtained for the correlations between the mechanical properties and the 2D or 3D structural parameters are close.…”

“…It is interesting to note that the trabecular thickness (Tb.Th) appears underestimated in both studies when computed from the 3D MIL method (95 Am and 77 Am in our study), but that the mean direct trabecular thickness (Tb.Th*) and the mean value of the trabecular thickness evaluated these authors are very comparable (138 and 129 Am, respectively). Our values for 3D fractal dimensions (2.6 F 0.19) are higher than those Table 4 Pearson correlation coefficients (r) between the mechanical and architectural anisotropy parameters n = 16 SR ACT 3D analysis (10 Am) [59,60]. The mechanical properties of the cancellous bone are significantly correlated with most of the morphological parameters.…”

“…Even if significant correlations between architectural and mechanical properties are published in the literature, the fact that 3D standard parameters, 3D connectivity or 3D fractal dimension, can improve the assessment of the compressive strength by the bone volume fraction has not been well demonstrated. Kabel et al [60] concluded that the integration of the connectivity density in the multiple correlation, marginally improves the correlation between the mechanical stiffness and the bone volume fraction, whereas Ulrich et al [61] concluded there was a real improvement. In other respects, the fabric tensor built from MIL parameters has largely been used with the bone volume fraction to estimate the elastic properties of cancellous bone [34,62].…”

Increased femoral neck cancellous bone and connectivity in coxarthrosis (hip osteoarthritis)

“…Some studies have proposed that in normal cancellous bone, connectivity has limited value for assessment of elastic properties [23] and strength [25], although a relationship between loss of connectivity and loss of elastic modulus has been reported [25]. It has been suggested that skeletal fragility in vertebral osteoporosis is in part due to a loss of trabecular connectivity [39]; a loss of trabecular elements would increase loads and strain on the remaining trabeculae leading to a reduction in fatigue life.…”

Porous poly-ether ether ketone (PEEK) manufactured by a novel powder route using near-spherical salt bead porogens: Characterisation and mechanical properties

“…The connectivity density, which represents the ratio of the connecting holes, vertices (end points), and struts (bridges) in one unit volume, is also presented, which for dry and tapping processes are close to 9 and 6 per mm 3 , respectively. Thomsen et al [30] stated that human bone has a connectivity density less than 12 per mm 3 , and Kabel et al [31] found that in samples of humans between 14 and 91 years old, the connectivity density varied between 1 and 9 with a mean close to 3. The connectivity density measurements, in particular for the tapped structure, are in keeping with those expected for a material designed to resemble the structure of trabecular bone and suggested targets of 7 per mm 3 [1].…”