Correlation between longitudinal, circumferential, and radial moduli in cortical bone: Effect of mineral content

Previous studies indicate that changes in the longitudinal elastic properties of bone due to changes in mineral content are related to the longitudinal strength of bone tissue. Changes in mineral content are expected to affect bone tissue mechanical properties along all directions, albeit to different extents. However, changes in tissue mechanical properties along the different directions are expected to be correlated to one another. In this study, we investigate if radial, circumferential, and longitudinal moduli are related in bone tissue with varying mineral content. Plexiform bovine femoral bone samples were treated in fluoride ion solutions for a period of 3 and 12 days to obtain bones with 20% and 32% lower effective mineral contents. Transmission ultrasound velocities were obtained in the radial, circumferential, and longitudinal axes of bone and combined with measured densities to obtain corresponding tensorial moduli. Results indicate that moduli decreased with fluoride ion treatments and were significantly correlated to one another ( r 2 radial vs. longitudinal = 0.80, r 2 circumferential vs. longitudinal = 0.90, r 2 radial vs. circumferential = 0.85). Densities calculated from using ultrasound parameters, acoustic impedance and transmission velocities, were moderately correlated to those measured by the Archimedes principle ( r 2 = 0.54 , p < 0.01 ). These results suggest that radial and circumferential ultrasound measurements could be used to determine the longitudinal properties of bone and that ultrasound may not be able to predict in vitro densities of bones containing unbonded mineral.