Measuring anisotropy of elastic wave velocity with ultrasound imaging and an autofocus method: application to cortical bone

Abstract

This work investigates the feasibility of estimating the parameters of an exact transverse isotropy model in cortical bone. The model describes the anisotropy of the velocity of compressional and shear bulk elastic waves. We propose to achieve this with ultrasound imaging relying on the transmission of unfocused beams and with an autofocus method. The latter is based on the principle that the reconstructed ultrasound image shows optimal quality if the velocity model is correct. The autofocus approach is applied to a composite image of the interface between cortical bone and marrow. It is obtained by incoherent summation of four types of images exploiting four different ray paths in the cortical bone layer, three of them involving mode-converted shear waves. If the parameters of the model are correct, spatial co-localization of the interface appears in the four images. As a result, intensity and sharpness in the composite image are maximal.The five parameters of the model of transverse isotropy are successfully estimated in a tube made of a bone-mimicking material. The estimates are in good agreement with resonant ultrasound spectroscopy (RUS) measurements. The tube thickness is recovered with an error smaller than 0.3%. In vivo results at the forearm of a volunteer are promising, four parameters could be estimated and are in good agreement with ex vivo RUS measurements. Moreover x-ray peripheral computed tomography corroborates the thickness of the cortical bone layer in the ultrasound image. Weak-anisotropy and exact transverse isotropy models provide very close measurements of the thickness of the tube and the radius bone. Thus, we recommend using the model of weak transverse isotropy for real-time anatomical imaging because more computationally efficient. For material characterization however, the model of exact transverse isotropy is preferred because the elastic anisotropy of cortical bone is moderate, rather than weak.