Exploring and calibrating local curvature effect of cortical bone for quantitative ultrasound (QUS)

Apart from thinning of cortical layers, the local bone curvature, varying along bone periphery, modulates ultrasound waves as well, which is however often underestimated or overlooked in clinical quantitative ultrasound (QUS). A dedicated three-dimensional finite element modelling technique for cortical bones was established, for quantitatively exploring and calibrating the effect of local curvature of cortical bone on ultrasound. Using a correlation-based mode extraction technique, high-velocity group (HVG) and low-velocity group (LVG) wave modes in a human radius were examined. Experimental verification using acrylic cylinders and in vitro testing using a porcine femur were accomplished. Results coherently unravelled the cortical curvature exerts evident influence on bone-guided ultrasound when RoC/${\lambda}$ <1 for HVG mode and RoC/${\lambda}$ <2 for LVG mode (RoC/${\lambda}$: the ratio of local bone curvature radius to wavelength); the sensitivity of LVG mode to bone curvature is higher than HVG mode. It has also been demonstrated the local group velocity of an HVG or LVG mode at a particular skeletal site is equivalent to the velocity when propagating in a uniform cylinder having an outer radius identical to the radius of curvature at that site. This study provides a rule of thumb to compensate for the effect of bone curvature in QUS.