Prediction of ultrasonic guided waves excitability to support the non-invasive assessment of human long bones

The characterization of bones via axial ultrasonic transmission techniques can be fully exploited only once the complexities of guided wave propagation are unveiled. Generally, plate/cylindrical waveguide models, where the soft tissues and their damping role are generally neglected, are used to identify the propagating waves in the bone. Here, a numerical strategy for a more rigorous simulation of guided wave propagation in elongated bones is proposed. First, from a computed tomography image of a human leg a three-dimensional finite element (FE) mesh of the problem is built by converting voxels into elements. At this level, the mechanical properties of bones and soft tissues can be obtained converting the Hounsfield units. If necessary, the FE mesh can be enhanced by smoothing the outer surfaces of the bone and/or skin. Next, time-transient three-dimensional explicit FE simulations are performed to simulate the propagation of stress waves along the bone with and without the soft tissues. The propagative energy is revealed by processing the bone time-responses with a 2D-FFT transform suitable for guided waves extraction. Finally, a representative bi-dimensional cross-section of the bone only is used to set the guided wave equation by means of a Semi-Analytical Finite Element (SAFE) formulation. Via SAFE, the dispersion curves are obtained and compared with the 2D-FFT energy map. The proposed strategy can support the research on non-invasive techniques based on stress waves for the assessment of long bones.