On the Relation of Bone Mineral Density and the Elastic Modulus in Healthy and Pathologic Bone

Osteoporosis could lead to the bone mechanical failure. To examine the bone health, mechanical properties are often estimated from the images of the bone density. Here, we review the relationships that have been experimentally determined between mineral density and the elastic modulus and factors that affect these relationships.

Studies, which have investigated the relation between the elastic modulus and bone mineral at the bulk scale, have shown that approximately 70% of variations in the elastic modulus can be explained based on the amount of mineral in bone. At the tissue level, however, higher resolution techniques are used to characterize the density and modulus more locally, and this leads to the correlation of mineral with modulus to be not as strong as that of the bulk level and often times, insignificant. This observation indicates the importance of structural hierarchy and mineral crystal organization in determining the local stiffness of the bone tissue. At the bulk level in bone (cm scale), modulus (E) is related to density (ρ) through a power law relationship (E ∝ ρ^α). At the tissue level (μm-mm scale), the relationship between the modulus and density is weak, likely due to the effect of microstructural features at small length scales.