Quantitative simulation of wave propagation in a human leg to support the ultrasonic noninvasive assessment of human bones

This paper presents a dedicated Finite Element approach for quantitative time-transient simulations of stress and pressure waves propagation in biological structures as human bones. The tool, starting from a magnetic resonance image (MRI) as the one of a human leg, builds a three-dimensional finite element (FE) mesh by converting voxels into elements. This step does not require any segmentation or further geometric interpretation of the tissue structure, only the mechanical properties have to be provided via Hounsfield (HU) number density mapping. The proposed tool improves upon the usually adopted models taking into account the irregular geometry of the bone as well as the soft tissues and their damping role, typically neglected. The tool code can handle models of hundred millions of elements in a standard PC desktop, exceeding thus capabilities of commercially available FEM codes. Here, an application on a human leg is proposed to show the potential of the proposed tool. The results of the time-transient simulations are next exploited to validate the use of guided waves models for the non invasive ultrasonic diagnosis of elongated bones. In particular, the recorded time-waveforms are analyzed via the 2D Fast Fourier Transform and the frequency-wavenumber energy content of the propagating waves is extracted. Such information is compared with the guided waves dispersion curves predicted, considering a representative cross-section of the tibia, via a Semi Analytical Finite Element (SAFE) formulation. Some final considerations on the comparison of the extracted and predicted dispersion curves close the paper.