Guided ultrasonic waves in long bones: modelling, experiment andin vivoapplication

Abstract

Existing ultrasound devices for assessing the human tibia are based on detecting the first arriving signal, corresponding to a wave propagating at, or close to, the bulk longitudinal velocity in bone. However, human long bones are effectively irregular hollow tubes and should theoretically support the propagation of more complex guided modes similar to Lamb waves in plates. Guided waves are attractive because they propagate throughout the bone thickness and can potentially yield more information on bone material properties and architecture. In this study, Lamb wave theory and numerical simulations of wave propagation were used to gain insights into the expected behaviour of guided waves in bone. Experimental measurements in acrylic plates, using a prototype low-frequency axial pulse transmission device, confirmed the presence of two distinct propagating waves: the first arriving wave propagating at, or close to, the longitudinal velocity, and a slower second wave whose behaviour was consistent with the lowest order Lamb antisymmetrical (A0) mode. In a pilot study of healthy and osteoporotic subjects, the velocity of the second wave differed significantly between the two groups, whereas the first arriving wave velocity did not, suggesting the former to be a more sensitive indicator of osteoporosis. We conclude that guided wave measurements may offer an enhanced approach to the ultrasonic characterization of long bones.

Use of multiple acoustic wave modes for assessment of long bones: Model study

“…Theoretical simulation studies on ultrasound axial propagation in model systems, confirmed by further experiments, demonstrated the possibility of ultrasonic assessment of CT by zero antisymmetric (A0) Lamb waves [15,16]. Propagation parameters of different acoustical wave modes were investigated in acrylic plates and tubes of varying wall thickness, where experimentally determined dispersion of the A0 Lamb wave velocity was in good correspondence with the theoretical predictions [17]. The velocities of longitudinal and guided waves in tibia were compared during studies in human subjects, in which different sensitivity of these types of waves to osteoporosis [17] and bone growth [18] was revealed.…”

“…Propagation parameters of different acoustical wave modes were investigated in acrylic plates and tubes of varying wall thickness, where experimentally determined dispersion of the A0 Lamb wave velocity was in good correspondence with the theoretical predictions [17]. The velocities of longitudinal and guided waves in tibia were compared during studies in human subjects, in which different sensitivity of these types of waves to osteoporosis [17] and bone growth [18] was revealed. Earlier, in the 1980-90s, a series of studies on bones was conducted by a Latvian group implementing "slow" type waves that they considered as an A0 Lamb or a flexural wave.…”

Ultrasonic evaluation of intact, healing and osteoporotic long bones

“…Specifically, in (Nicholson et al 2002, Bossy et al 2002) the cortical bone was modeled as a linear elastic homogeneous plate and the potential of ultrasound to reflect the thinning of the cortical cortex in osteoporotic bones was examined through FAS velocity and guided wave analysis. X-ray computed tomography was used in (Moilanen et al 2007) to establish more realistic 3D geometries of the human radius cortical bone and ultrasonically determine the thickness based on a guided wave analysis.…”

A numerical study of ultrasonic response of random cortical bone plates

“…This technique consists of use a set of ultrasonic transmitters and receivers placed on a line in contact with the skin along the bone axial axis. The analysis of the signals received can allow to estimate velocities of different kinds of wave propagating in the bone structure and thus to quantify some mechanical properties of bones (such as density, rigidity and thickness) [7][8][9][10][11]. The attenuation of cortical bone may also been evaluated by analyzing the reflected wave from bone surface [12].…”