Correlations between ultrasonic guided wave velocities and bone properties in bovine tibia in vitro

Fatigue evaluation of long cortical bone using ultrasonic guided waves

Bone fatigue fracture is a progressive disease due to stress concentration. This study aims to evaluate the long bone fatigue damage using the ultrasonic guided waves. Two-dimensional finite-difference time-domain method was employed to simulate the ultrasonic guided wave propagation in the long bone under different elastic modulus. The experiment was conducted on a 3.8 mm-thick bovine bone plate. The phase velocities of two fundamental guided modes, A1 and S1, were measured by using the axial transmission technique. Simulation shows that the phase velocities of guided modes A1 and S1 decrease with the increasing of the fatigue damage. After 20,000 cycles of fatigue loading on the bone plate, the average phase velocities of A1 and S1 modes were 6.6% and 5.3% respectively, lower than those of the intact bone. The study suggests that ultrasonic guided waves can be potentially used to evaluate the fatigue damage in long bones.

Semi-analytical finite-element modeling approach for guided wave assessment of mechanical degradation in bones

Numerical models based on the Semi Analytical Finite-Element method are used to study the characteristics of guided wave modes supported by bone-like multi-layered tubular structures. The method is first validated using previous literature and experimental studies on phantoms mimicking healthy and osteoporotic conditions of cortical bone, and later used to study a trilayer marrow–bone–tissue system at varying mechanical degradation levels. The results show that bone condition strongly affects the modal properties of axially propagating guided waves and indicates that L(0,3) and F(1,6) are suitable modes for assessing the mechanical condition of the bone. The work here reports suitable modal selection and their dispersion properties which would the aid in development of a transduction mechanism for mechanical assessment of bones.

Relationships of the group velocity of the time-reversed Lamb wave with bone properties in cortical bone in vitro

The present study aims to investigate the feasibility of using the time-reversed Lamb wave as a new method for noninvasive characterization of long cortical bones. The group velocity of the time-reversed Lamb wave launched by using the modified time reversal method was measured in 15 bovine tibiae, and their correlations with the bone properties of the tibia were examined. The group velocity of the time-reversed Lamb wave showed significant positive correlations with the bone properties (r=0.55-0.81). The best univariate predictor of the group velocity of the time-reversed Lamb wave was the cortical thickness, yielding an adjusted squared correlation coefficient (r²) of 0.64. These results imply that the group velocity of the time-reversed Lamb wave, in addition to the velocities of the first arriving signal and the slow guided wave, could potentially be used as a discriminator for osteoporosis.

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

Long bones are good waveguides to support the propagation of ultrasonic guided waves. The low-order guided waves have been consistently observed in quantitative ultrasound bone studies. Selective excitation of these low-order guided modes requires oblique incidence of the ultrasound beam using a transducer-wedge system. It is generally assumed that an angle of incidence, θi, generates a specific phase velocity of interest, co, via Snell's law, θi=sin(-1)(vw/co) where vw is the velocity of the coupling medium. In this study, we investigated the excitation of guided waves within a 6.3-mm thick brass plate and a 6.5-mm thick bovine bone plate using an ultrasound phased array system with two 0.75-mm-pitch array probes. Arranging five elements as a group, the first group of a 16-element probe was used as a transmitter and a 64-element probe was a receiver array. The beam was steered for six angles (0°, 20°, 30°, 40°, 50°, and 60°) with a 1.6-MHz source signal. An adjoint Radon transform algorithm mapped the time-offset matrix into the frequency-phase velocity dispersion panels. The imaged Lamb plate modes were identified by the theoretical dispersion curves. The results show that the 0° excitation generated many modes with no modal discrimination and the oblique beam excited a spectrum of phase velocities spread asymmetrically about co. The width of the excitation region decreased as the steering angle increased, rendering modal selectivity at large angles. The phenomena were well predicted by the excitation function of the source influence theory. The low-order modes were better imaged at steering angle ⩾30° for both plates. The study has also demonstrated the feasibility of using the two-probe phased array system for future in vivo study.

Measuring the wavenumber of guided modes in waveguides with linearly varying thickness

Measuring guided waves in cortical bone arouses a growing interest to assess skeletal status. In most studies, a model of waveguide is proposed to assist in the interpretation of the dispersion curves. In all the reported investigations, the bone is mimicked as a waveguide with a constant thickness, which only approximates the irregular geometry of cortical bone. In this study, guided mode propagation in cortical bone-mimicking wedged plates is investigated with the aim to document the influence on measured dispersion curves of a waveguide of varying thickness and to propose a method to overcome the measurement limitations induced by such thickness variations. The singular value decomposition-based signal processing method, previously introduced for the detection of guided modes in plates of constant thickness, is adapted to the case of waveguides of slowly linearly variable thickness. The modification consists in the compensation at each frequency of the wavenumber variations induced by the local variation in thickness. The modified method, tested on bone-mimicking wedged plates, allows an enhanced and more accurate detection of the wavenumbers. Moreover, the propagation in the directions of increasing and decreasing thickness along the waveguide is investigated.