Bones are known to contain spatial variations in mechanical properties. We refer to this variation as “mechanical heterogeneity”. Despite evidence that mechanical heterogeneity affects the mechanical behavior of bone and changes with age in ways that may increase risk of fracture, several knowledge gaps remain. For example, the macroscale mechanical consequences of aging-related changes in mechanical heterogeneity at the microscale are not well understood. In addition, methods to measure mechanical heterogeneity non-destructively are lacking. This dissertation presents a body of work that advances the study of mechanical heterogeneity in both types of bone tissue:​ cortical and trabecular.

A one-dimensional multiscale model was developed to investigate how agingrelated changes in the microconstituents of cortical bone drive mechanical consequences at the macroscale. Prior evidence indicates that these microconstituents, osteon and interstitial tissue, differ in their microstructural and mechanical properties;​ moreover, with aging, their respective volume fractions within cortical bone change, as do their mechanical properties. From the developed model, we found that aging-related changes in both the volume fractions and mechanical properties of the microconstituents, in addition to increased porosity, play important roles in aging-related decreases in the strength and toughness of cortical bone. For example, reduced ductility and increased strength of the interstitial tissue led to loss of toughness at the macroscale independently of the other aging-related changes. However, the model’s predictions were highly sensitive to post-yield parameters, due primarily to high uncertainty in the post-yield behaviors of both osteon and interstitial tissue. These results motivate further mechanical characterization of these microconstituents.

Elasticity imaging was explored as a method of measuring mechanical heterogeneity in trabecular bone. Simulated data were used to numerically verify the use of an elasticity imaging method to reconstruct the heterogeneous modulus of trabecular bone within a vertebra from a measurement of the displacement field and material anisotropy. Simulated data were also used to assess the impact of various factors on the sensitivity of modulus reconstructions to those inputs. We found the assumed form of the target modulus distribution had a substantial impact on the sensitivity of modulus reconstructions to error in the input displacement data. In contrast, the material anisotropy had minimal impact. Knowledge of modulus sensitivity to error in the inputs will allow investigators to estimate, for example, a minimum detectable change in modulus for a given amount of input error. Such knowledge indicates, for example, the requisite signal-to-noise ratio in the displacement data necessary to achieve the desired sensitivity in a given use case. Though developed in the context of reconstructing modulus in the vertebra, the analysis presented here may be applicable to a wide array of biological tissues.

With this analysis in hand, full-field displacement data obtained from prior experiments involving compression of cadaveric vertebrae were used to reconstruct the variation in modulus within the vertebral body. However, the signal-to-noise ratio in the data was insufficient. Given the relatively small yield strain of trabecular bone, methods that reduce displacement noise will be needed to enable elasticity imaging to infer a modulus distribution.

This dissertation employed multiple modeling techniques to investigate the role of mechanical heterogeneity in the mechanical behavior of bones. These techniques offer the tools necessary to, given the appropriate data, quantify and assess the mechanical heterogeneity in bone, which may be important for accurately assessing the risk of onset, and progression, of bone fractures.