Experimental tests of planar strain theory for predicting bone cross-sectional longitudinal and shear strains.

Understanding of the diversity of skeletal loading regimes in vertebrate long bones during locomotion has been significantly enhanced by the application of planar strain theory (PST) to in vivo bone strain data. PST is used to model the distribution of longitudinal strains normal to the bone's transverse cross-section and the location of the neutral axis of bending. To our knowledge, the application of this theory to skeletal biomechanics has not been experimentally validated. We evaluated the accuracy of PST using strain measurements from emu tibiotarsi instrumented with four strain gauges and loaded in ex vivo four-point bending. Using measured strains from three-gauge combinations, PST was applied to predict strain values at a fourth gauge's location. Experimentally measured and predicted strain values correlated linearly with a slope near 1.0, suggesting that PST accurately predicts longitudinal strains. Additionally, we assessed the use of PST to extrapolate shear strains to locations on a bone not instrumented with rosette strain gauges. Guineafowl tibiotarsi were instrumented with rosette strain gauges and in vivo longitudinal and shear strains were measured during treadmill running. Individual-specific and sample-mean ratios between measured longitudinal strains from the medial and posterior bone surfaces were used to extrapolate posterior-site shear strain from shear strains measured on the medial surface. Measured and predicted shear strains at the posterior gauge site using either ratio showed trends for a positive correlation between measured and predicted strains, but the correlation did not equal 1.0 and had a non-zero intercept, suggesting that the use of PST should be carefully considered in the context of the goals of the study and the desired precision for the predicted shear strains.

Computationally derived endosteal strain and strain gradients correlate with increased bone formation in an axially loaded murine tibia model.

Osteoporosis is a common metabolic bone disorder characterized by low bone mass and microstructural degradation of bone tissue due to a derailed bone remodeling process. A deeper understanding of the mechanobiological phenomena that modulate the bone remodeling response to mechanical loading in a healthy bone is crucial to develop treatments. Rodent models have provided invaluable insight into the mechanobiological mechanisms regulating bone adaptation in response to dynamic mechanic stimuli. This study sheds light on these aspects by means of assessing the mechanical environment of the cortical and cancellous tissue to in vivo dynamic compressive loading within the mouse tibia using microCT-based finite element model in combination with diaphyseal strain gauge measures. Additionally, this work describes the relation between the mid-diaphyseal strains and strain gradients from the finite element analysis and bone formation measures from time-lapse in vivo tibial loading with a fluorochrome-derived histomorphometry analysis. The mouse tibial loading model demonstrated that cancellous strains were lower than those in the midshaft cortical bone. Sensitivity analyses demonstrated that the material property of cortical bone was the most significant model parameter. The computationally-modeled strains and strain gradients correlated significantly to the histologically-measured bone formation thickness at the mid-diaphyseal cross-section of the mouse tibia.