Ultrasound critical-angle reflectometry (UCR): a new modality for functional elastometric imaging

This paper discusses the measurement of velocity in a solid based on the analysis of the amplitude and phase of ultrasound waves reflected by a solid, a technique called ultrasound critical-angle reflectometry (UCR). To this end, the complete formulation of ultrasound wave reflection and refraction from a liquid-solid interface is described. Differences between this formulation and previously published ones are briefly discussed. Based on this analysis it is in particular possible to measure by this technique not only pressure but also, for the first time in such studies, shear wave velocities, an experimentally confirmed result. The measurement of the complete stiffness matrix of a transversely isotropic solid, specifically cortical bone, by applying UCR elastometry to any point on the solid's surface is demonstrated. Finally this method is extended to functional elastometric imaging. The techniques presented in this paper offer new opportunities for applications of UCR imaging to the assessment of bone metabolism, formation and disease and also to the analysis of composite materials in general.