The Role of Fabric in the Large Strain Compressive Behavior of Human Trabecular Bone

Osteoporosis-related vertebral body fractures involve large compressive strains of trabecular bone. The small strain mechanical properties of the trabecular bone such as the elastic modulus or ultimate strength can be estimated using the volume fraction and a second order fabric tensor, but it remains unclear if similar estimations may be extended to large strain properties. Accordingly, the aim of this work is to identify the role of volume fraction and especially fabric in the large strain compressive behavior of human trabecular bone from various anatomical locations. Trabecular bone biopsies were extracted from human T12 vertebrae $(n=31)$⁠, distal radii $(n=43)$⁠, femoral head $(n=44)$⁠, and calcanei $(n=30)$⁠, scanned using microcomputed tomography to quantify bone volume fraction $(BV/TV)$ and the fabric tensor $(M)$⁠, and tested either in unconfined or confined compression up to very large strains $(∼70%)$⁠. The mechanical parameters of the resulting stress-strain curves were analyzed using regression models to examine the respective influence of $BV/TV$ and fabric eigenvalues. The compressive stress-strain curves demonstrated linear elasticity, yielding with hardening up to an ultimate stress, softening toward a minimum stress, and a steady rehardening followed by a rapid densification. For the pooled experiments, the average minimum stress was $1.89±1.77MPa$⁠, while the corresponding mean strain was $7.15±1.84%$⁠. The minimum stress showed a weaker dependence with fabric as the elastic modulus or ultimate strength. For the confined experiments, the stress at a logarithmic strain of 1.2 was $8.08±7.91MPa$⁠, and the dissipated energy density was $5.67±4.42MPa$⁠. The latter variable was strongly related to the volume fraction $(R2=0.83)$ but the correlation improved only marginally with the inclusion of fabric $(R2=0.84)$⁠. The influence of fabric on the mechanical properties of human trabecular bone decreases with increasing strain, while the role of volume fraction remains important. In particular, the ratio of the minimum versus the maximum stress, i.e., the relative amount of softening, decreases strongly with fabric, while the dissipated energy density is dominated by the volume fraction. The collected results will prove to be useful for modeling the softening and densification of the trabecular bone using the finite element method.