Comparison of three methods of calculating strain in the mouse ulna in exogenous loading studies

Axial compression of mouse limbs is commonly used to induce bone formation in a controlled, non-invasive manner. Determination of peak strains caused by loading is central to interpreting results. Load-strain calibration is typically performed using uniaxial strain gauges attached to the diaphyseal, periosteal surface of a small number of sacrificed animals. Strain is measured as the limb is loaded to a range of physiological loads known to be anabolic to bone. The load-strain relationship determined by this subgroup is then extrapolated to a larger group of experimental mice. This method of strain calculation requires the challenging process of strain gauging very small bones which is subject to variability in placement of the strain gauge. We previously developed a method to estimate animal-specific periosteal strain during axial ulnar loading using an image-based computational approach that does not require strain gauges. The purpose of this study was to compare the relationship between load-induced bone formation rates and periosteal strain at ulnar midshaft using three different methods to estimate strain: (A) Nominal strain values based solely on load-strain calibration; (B) Strains calculated from load-strain calibration, but scaled for differences in mid-shaft cross-sectional geometry among animals; and (C) An alternative image-based computational method for calculating strains based on beam theory and animal-specific bone geometry. Our results show that the alternative method (C) provides comparable correlation between strain and bone formation rates in the mouse ulna relative to the strain gauge-dependent methods (A and B), while avoiding the need to use strain gauges.