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

A free plate model can predict guided modes propagating in tubular bone-mimicking phantoms

“…In previous investigations, more or less complex waveguide models, such as free plate 5 and tube models, 3,4,11 or bilayer models, [12][13][14] were applied and found to conform fairly well to experimental dispersion curves of guided modes in bone mimicking phantoms 3,5,12,14 and in ex vivo bone specimens. [3][4][5]13 On the other hand, more complex models involving more physical parameters would make the solution of the inverse problem more difficult to find. These considerations have implications regarding the choice of the model.…”

“…[3][4][5] Accuracy of estimates for bone characteristics depends on the chosen model for ultrasound propagation in the cortical bone (which represents the "forward problem") and on its ability to account for the complexity of the waveguide, including not only the elastic anisotropy, the tubular shape of bone and the presence of soft tissues, but also a variable thickness, irregular geometry, inhomogeneity, and absorption, for example. In previous investigations, more or less complex waveguide models, such as free plate 5 and tube models, 3,4,11 or bilayer models, [12][13][14] were applied and found to conform fairly well to experimental dispersion curves of guided modes in bone mimicking phantoms 3,5,12,14 and in ex vivo bone specimens. [3][4][5]13 On the other hand, more complex models involving more physical parameters would make the solution of the inverse problem more difficult to find.…”

“…Thus, applied to long bones such as the radius or tibia, guided waves based approaches would be expected to provide estimates of important bone quality factors like cortical thickness and stiffness which cannot easily be captured by X-ray densitometry techniques. [3][4][5] Measurements of guided waves in long bones have shown some diagnostic promises ex vivo 6,7 and in vivo.…”

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

“…3,10 Therefore, a suitable in vivo multi-layer model and a special signal processing technique must be implemented for consistency of mode identification and velocity estimation. [16][17][18] …”

Axial transmission assessment of trabecular bone at distal radius using guided waves

“…Each propagating mode interacts differently with the mechanical and geometrical aspects of the waveguide, and these multi-modal characteristics can be considered the main advantage of the method, once the sensitivity of the analysis can be improved through the selection of a desired group of modes in order to interrogate a specific region/parameter of the bone structure. Recent studies based on ultrasonic guided waves already showed considerable evidence that the multi-modal approach is more comprehensive and sensitive when compared to single velocity analysis [7,8].…”