Assessment of the cortical bone thickness using ultrasonic guided waves: modelling and in vitro study

Determination of cortical bone thickness is warranted, e.g., for assessing the level of endosteal resorption in osteoporosis or other bone pathologies. We have shown previously that the velocity of the fundamental antisymmetric (or flexural) guided wave, measured for bone phantoms and bones in vitro, correlates with the cortical thickness significantly better than those by other axial ultrasound methods. In addition, we have introduced an inversion scheme based on guided wave theory, group velocity filtering and 2-D fast Fourier transform, for determination of cortical thickness from the measured velocity of guided waves. In this study, the method was validated for tubular structures by using numerical simulations and experimental measurements on tube samples. In addition, 40 fresh human radius specimens were measured. For tubes with a thin wall, plate theory could be used to determine the wall thickness with a precision of 4%. For tubes with a wall thicker than 1/5 of the outer radius, tube theory provided the wall thickness with similar accuracy. For the radius bone specimens, tube theory was used and the ultrasonically-determined cortical thickness was found to be U-Th = 2.47 mm +/- 0.66 mm. It correlated strongly (r(2) = 0.73, p < 0.001) with the average cortical thickness, C-Th = 2.68 +/- 0.53 mm, and the local cortical thickness (r(2) = 0.81, p < 0.001), measured using peripheral quantitative computed tomography. We can conclude that the guided-wave inversion scheme introduced here is a feasible method for assessing cortical bone thickness.