The dependence of broadband ultrasound attenuation on phase interference in thin plates of variable thickness and curvature: a comparison of experimental measurement and computer simulation

Abstract

The measurement of broadband ultrasound attenuation describes the linear increase in ultrasound attenuation with frequency (dB/MHz); this is generally performed at the calcaneus, consisting of a high proportion of metabolically active cancellous bone. Although broadband ultrasound attenuation is not routinely implemented within clinical management since it cannot provide a reliable estimation of bone mineral density and hence clinical definition of osteopenia and osteoporosis, it offers a reliable means to predict osteoporotic fracture risk. One of the potential factors that can influence the accuracy of broadband ultrasound attenuation measurement is the effect of cortical end plates. This study aimed to explore this, performing a comparison of experimental study and computer simulation prediction. A total of three categories of thin discs were three-dimensional (3D) printed to replicate cortical shells of (1) variable constant thickness (planar), (2) variable constant thickness (curved), and (3) variable thickness. A through-transmission technique was used, where two single-element, unfocused, 1 MHz broadband transducers, as utilised clinically, were positioned coaxially in a cylindrical holder and immersed in water. Both quantitative and qualitative analyses demonstrated that broadband ultrasound attenuation measurements of the ‘planar’ and ‘curved’ discs were not statistically different (p-values > 0.01). A cyclic relationship between broadband ultrasound attenuation and disc thickness was observed; this was replicated within a computer simulation of phase interference created by a double-reflection echo within each disc (R² = 97.0%). Variable-thickness discs provided broadband ultrasound attenuation measurements ranging between 31.6 ± 0.1 and 40.60 ± 0.1 dB/MHz. Again applying the double-reflection echo simulation, a high level of agreement between experimental and simulation was recorded (R² = 93.4%). This study indicates that the cortical end plate can significantly affect the broadband ultrasound attenuation measurement of cancellous bone as a result of phase interference and, therefore, warrants further investigation to minimise its effect on clinical assessment.