Simulation of acoustic guided wave propagation in cortical bone using a semi-analytical finite element method

Axial transmission techniques have been extensively studied for cortical bone quality assessment. However, the modeling of ultrasonic guided waves propagation in such a complex medium remains challenging. The aim of this paper is to develop a semi-analytical finite element method to simulate the propagation of guided waves in an irregular, multi-layer, and heterogeneous bone cross-section modeled with anisotropic and viscoelastic material properties. The accuracy of the simulations was verified against conventional time-domain three-dimensional finite element. The method was applied in the context of axial transmission in bone to investigate the feasibility of first arrival signal (FAS) to monitor degradation of intracortical properties at low frequency. Different physiopathological conditions for the intracortical region, varying from healthy to osteoporotic, were monitored through FAS velocity using a 10-cycle tone burst excitation centered at 32.5 kHz. The results show that the variation in FAS velocity is mainly associated with four of the eight modes supported by the waveguide, varying with velocity values between 550 and 700 m/s along the different scenarios. Furthermore, the FAS velocity is shown to be associated with the group velocity of the mode with the highest relative amplitude contribution at each studied scenario. However, because of the evolution of the mode with the highest contribution, the FAS velocity is shown to be limited to discriminate intracortical bone properties at low frequency.