Three-dimensional finite element modeling of guided ultrasound wave propagation in intact and healing long bones

Abstract

The use of guided waves has recently drawn significant interest in the ultrasonic characterization of bone aiming at supplementing the information provided by traditional velocity measurements. This work presents a three-dimensional finite element study of guided wave propagation in intact and healing bones. A model of the fracture callus was constructed and the healing course was simulated as a three-stage process. The dispersion of guided modes generated by a broadband 1-MHz excitation was represented in the time-frequency domain. Wave propagation in the intact bone model was first investigated and comparisons were then made with a simplified geometry using analytical dispersion curves of the tube modes. Then, the effect of callus consolidation on the propagation characteristics was examined. It was shown that the dispersion of guided waves was significantly influenced by the irregularity and anisotropy of the bone. Also, guided waves were sensitive to material and geometrical changes that take place during healing. Conversely, when the first-arriving signal at the receiver corresponded to a nondispersive lateral wave, its propagation velocity was almost unaffected by the elastic symmetry and geometry of the bone and also could not characterize the callus tissue throughout its thickness. In conclusion, guided waves can enhance the capabilities of ultrasonic evaluation.

Ultrasonic evaluation of intact, healing and osteoporotic long bones

“…Finally, difficulties in obtaining bone specimens and the experimental artifacts associated with ultrasonic measurements can be avoided. Our research group has presented an extensive numerical research work to study the variation of the FAS velocity and the propagation of guided waves at different healing stages using the axial transmission method , Protopappas et al 2007, Vavva et al 2008a, Vavva et al 2008b). These studies revealed that the FAS velocity increases during the fracture healing process.…”

“…Concerning the FAS velocity, it was found to decrease in stage 1, remained the same up to stage 2, and then increased at stage 3. Nevertheless, when the FAS corresponded to a nondispersive lateral wave, its propagation velocity was almost unaffected by the elastic symmetry and geometry of the bone and could not characterize the callus tissue throughout its thickness (Protopappas et al 2007). …”

“…A 3D finite element study on guided wave propagation in intact and healing bones was also presented in (Protopappas et al 2007). The fracture healing process was simulated considering three successive stages.…”

“…More recently in (Potsika et al 2016b), we presented simulations of ultrasound propagation in healing long bones using the BEM to investigate the monitoring potential of backscattering parameters. The callus was modeled as a 2D, inhomogeneous medium consisting of the different ossification regions presented in (Protopappas et al 2007) with evolving material properties. The interaction of a plane wave at 100 kHz with healing long bones was investigated by calculating the acoustic pressure and scattering amplitude in the backward direction.…”

“…Emphasis is given on the experimental and numerical studies of our research group over the last decade which investigate bone healing and osteoporosis evolution using QUS , Protopappas et al 2007, Vavva et al 2008a, Potsika et al 2014, Vavva et al 2015, Potsika et al 2016a.…”