Conformity to stochastic invariance of microstructure influences mechanical competence of trabecular bone

Bone fragility fractures are not solely determined by bone mineral density (BMD), as patients with similar BMD often exhibit markedly different fracture risks due to factors beyond bone mass. One such factor may be disruption of stochastic stability in trabecular bone microarchitecture, characterized by previously observed invariant probability distributions of trabecular size and spatial organization. This within-donor paired study tested the hypothesis that disruption of such stochastic stability (i.e., invariance) impairs mechanical competence, independent of bone volume fraction (BV/TV) and structural anisotropy. Trabecular bone cubes were digitally extracted from micro-CT models of human cadaveric proximal femurs. From the elderly donor group, thirteen BV/TV-matched cube pairs (N = 13 pairs) were identified from four donors, with each pair originating from the same anatomical location within the same femur. Within each pair, one cube exhibited invariant distributions, whereas the other showed significant deviations from at least one of these distributions. Micro-CT-based finite element simulations were performed to evaluate the elastic properties of the paired cubes. The results indicated that cubes not conforming to stochastic invariance exhibited consistent mechanical deficits, ranging from 6% to 35% across all stiffness tensor components relative to their paired counterparts. Analysis of covariance (ANCOVA) further confirmed that these mechanical deficits were independent of BV/TV and structural anisotropy within the current sample. Moreover, variances in the averaged measures of trabecular size and spatial arrangement were most likely associated with changes in stochastic stability status. These findings demonstrate that the stochastic organization of trabecular microstructure plays a distinct role in determining mechanical competence beyond conventional bone mass, morphometric, and fabric-based measures, providing mechanistic insight into bone fragility.