Determining the elastic modulus of mouse cortical bone using electronic speckle pattern interferometry (ESPI) and micro computed tomography: a new approach for characterizing small-bone material properties.

Mice phenotypes are invaluable for understanding bone formation and function, as well as bone disease. The elastic modulus is an important property of bones that can provide insights into bone quality. The determination of the elastic modulus of mouse cortical bone is complicated by the small dimensions of the bones. Whole bone bending tests are known to under estimate the elastic modulus compared to nanoindentation tests. The latter however provides information on extremely localized areas that do not necessarily correspond to the bulk elastic modulus under compression. This study presents a novel method for determining the bulk or effective elastic modulus of mouse cortical bone using the femur. We use Electronic Speckle Pattern Interferometry (ESPI), an optical method that enables the measurement of displacements on the bone surface, as it is compressed under water. This data is combined with geometric information obtained from micro-CT to calculate the elastic modulus. Roughly tubular cortical bone segments (2 mm) were cut from the diaphyses of femora of four week old C57BL/6 (B6) female mice and compressed axially using a mechanical tension-compression device. Displacements in the loading direction were mapped on the bone surface after loading the specimen. A linear regression of the displacement vs. axial-position enabled the calculation of the effective strain. Effective stress was calculated using force (N) data from the system's load cell and the mean cross-sectional area of the sample as determined by micro-CT. The effective elastic modulus (E) was calculated from the stress to strain ratio. The method was shown to be accurate and precise using a standard material machined to similar dimensions as those of the mouse femoral segments. Diaphyses of mouse femora were shown to have mean elastic moduli of 10.4+/-0.9 GPa for femora frozen for eight months, 8.6+/-1.4 GPa for femora frozen for two weeks and 8.9+/-1.1 GPa for the fresh femora. These values are much higher than those measured using three-point bending, and lower than values reported in the literature based on nanoindentation tests from mice bones of the same age. We show that this method can be used to accurately and precisely measure the effective elastic modulus of mouse cortical bone.