(250f) Computational Modeling of Ultrasound Wave Propagation in Healing Bones

The promising role of quantitative ultrasound in the monitoring of the fracture healing process has recently drawn the attention of many research groups worldwide. The recent use of computational methods for modeling wave propagation in bone has provided significant supplementary information about the underlying healing mechanisms and helped in interpreting experimental and clinical measurements. Computational studies have initially investigated whether the velocity of the First Arriving Signal (FAS) across fractured bones can be used as an indicator of healing. More recent research in the field has proposed the propagation of guided waves as an enhanced tool for the assessment of the fracture healing process due to their ability to reflect geometrical and material alteration in deeper cortical layers.  In our first 2D computational study, the bone was modeled as an isotropic plate and callus as a homogeneous and isotropic medium. The healing process was modeled as a 7-stage process and the callus material properties varied according to the examined healing stage. In a series of subsequent studies more realistic conditions were considered by assuming a) the presence of the overlying soft tissues b) the inhomogeneous nature of the callus material and c) the irregular 3D geometry and anisotropy of bone. The healing process was simulated as a 3-stage process.  In these studies, a decrease in the propagation velocity was observed at the first healing stages followed by a constant increase at later healing stages. Guided waves were found to be sensitive to geometrical and material changes in the callus tissue during the healing process.  The irregular geometry and anisotropy of the cortical bone and callus as well as the presence of the soft tissues were also found to significantly affect the propagating guided waves.

In our latest computational study we also accounted for the porous nature of the callus and we investigated the induced multiple scattering mechanisms. 2D models of healing bones were developed in which the callus material and geometrical properties were derived from scanning acoustic microscopy images of real bones. A negative dispersion was clearly observed, while the attenuation coefficient was found to increase exponentially with increasing frequency during the healing process.  The role of scattering phenomena was found to be more significant during the first healing stages. These studies should be regarded as a step towards the development of advanced quantitative tools for the evaluation of the healing course. However, safe conclusions can be drawn only when the results from computational studies are interpreted in combination with experimental and clinical research.