An expression relating breaking stress and density of trabecular bone

Bone mineral density (BMD) is the principal diagnostic tool used in clinical settings to diagnose and monitor osteoporosis. Experimental studies on ex vivo bone samples from multiple skeletal locations have been used to propose that their breaking stress bears a power-law relationship to volumetric BMD, with a location-dependent index. We argue that a power-law cannot represent effects of trabecular removal, which is one of the leading causes of reduction in bone strength. A new expression, proposed on the basis of theoretical and numerical analysis of a mathematical model, is tested using previously published data on bone samples from iliac crest and vertebral body. It represents the experimental biomechanical data at least as well as the power-law, and provides means for extrapolating results from small biopsy samples to an entire bone. In addition, changes caused by trabecular thinning and anisotropy can be modeled by the expression