Ultrasonic propagation in cortical bone mimics

Abstract

Understanding the velocity and attenuation characteristics of ultrasonic waves in cortical bone and bone mimics is important for studies of osteoporosis and fractures. Three complementary approaches have been used to help understand the ultrasound propagation in cortical bone and bone mimics immersed in water, which is used to simulate the surrounding tissue in vivo. The approaches used were Lamb wave propagation analysis, experimental measurement and two-dimensional (2D) finite difference modelling. First, the water loading effects on the free plate Lamb modes in acrylic and human cortical bone plates were examined. This theoretical study revealed that both the S0 and S1 mode velocity curves are significantly changed in acrylic: mode jumping occurs between the S0 and S1 dispersion curves. However, in human cortical bone plates, only the S1 mode curve is significantly altered by water loading, with the S0 mode exhibiting a small deviation from the unloaded curve. The Lamb wave theory predictions for velocity and attenuation were then tested experimentally on acrylic plates using an axial transmission technique. Finally, 2D finite difference numerical simulations of the experimental measurements were performed. The predictions from Lamb wave theory do not correspond to the measured and simulated first arrival signal (FAS) velocity and attenuation results for acrylic and human cortical bone plates obtained using the axial transmission technique, except in very thin plates.

Propagation of time-reversed Lamb waves in bovine cortical bone in vitro

“…12 The longitudinal and the shear wave velocities assumed for cortical bone in calculating the group velocity were 4000 and 1800 m/s, respectively. 22 As found in Fig. 4, the experimental group velocities of the time-reversed Lamb waves showed a significant correlation with the cortical thickness (Pearson's correlation coefficient r ¼ 0.77) and tended to follow the theoretical group velocity of the A0 Lamb wave fairly well, consistent with the behavior of the SGW in long cortical bones.…”

The effect of boundary conditions on guided wave propagation in two-dimensional models of healing bone

“…First, for the simulation of the overlying soft tissues the bone was considered to be immersed in fluid (Model-1), as previously reported in [9,16,18]. More specifically, we used blood, which has properties close to those of the soft tissues.…”

“…Previous studies, such as [16,18] used boundary conditions (immersed plates) suitable in particular for studying the variation of the FAS velocity for various frequencies, plate-thicknesses or emitter-receiver distances. As we clearly demonstrated, such simplified boundary conditions are not suitable for guided waves in general.…”

“…Twodimensional (2D) computational simulations [14,[16][17][18] have used the Lamb wave theory to predict the expected properties and behavior of the modes propagating through intact bone-mimicking plates. Using low-frequency excitations (200 kHz), two waves could be detected in the waveform of the simulated signals; the fast wave which corresponds to the S0 Lamb mode, and a slower one which exhibits dispersion close to that of the A0 Lamb mode.…”

Excitation of ultrasonic Lamb waves using a phased array system with two array probes: Phantom and in vitro bone studies

“…The low-order 26 guided waves have been consistently observed in quantitative ultrasound bone studies. Selective excita- 27 tion of these low-order guided modes requires oblique incidence of the ultrasound beam using a trans- 28 ducer-wedge system. It is generally assumed that an angle of incidence, h i , generates a specific phase 29 velocity of interest, c o , via Snell's law, h i = sin À1 (v w /c o ) where v w is the velocity of the coupling medium.…”