Estimation of Thickness and Speed of Sound for Transverse Cortical Bone Imaging Using Phase Aberration Correction Methods: An In Silico and Ex Vivo Validation Study

Abstract

Delay-and-sum (DAS) beamforming of backscattered echoes is used for conventional ultrasound imaging. Although DAS beamforming is well suited for imaging in soft tissues, refraction, scattering, and absorption, porous mineralized tissues cause phase aberrations of reflected echoes and subsequent image degradation. The recently developed refraction corrected multi-focus technique uses subsequent focusing of waves at variable depths, the tracking of travel times of waves reflected from outer and inner cortical bone interfaces, the estimation of the shift needed to focus from one interface to another to determine cortical thickness (Ct.Th), and the speed of sound propagating in a radial bone direction (Ct.ν11). The method was validated previously in silico and ex vivo on plate shaped samples. The aim of this study was to correct phase aberration caused by bone geometry (i.e., curvature and tilt with respect to the transducer array) and intracortical pores for the multi-focus approach. The phase aberration correction methods are based on time delay estimation via bone geometry differences to flat bone plates and via the autocorrelation and cross correlation of the reflected ultrasound waves from the endosteal bone interface. We evaluate the multi-focus approach by incorporating the phase aberration correction methods by numerical simulation and one experiment on a human tibia bone, and analyze the precision and accuracy of measuring Ct.Th and Ct.ν11. Site-matched reference values of the cortical thickness of the human tibia bone were obtained from high-resolution peripheral computed tomography. The phase aberration correction methods resulted in a more precise (coefficient of variation of 5.7%) and accurate (root mean square error of 6.3%) estimation of Ct.Th, and a more precise (9.8%) and accurate (3.4%) Ct.ν11 estimation, than without any phase aberration correction. The developed multi-focus method including phase aberration corrections provides local estimations of both cortical thickness and sound velocity and is proposed as a biomarker of cortical bone quality with high clinical potential for the prevention of osteoporotic fractures.