Simulation study of the sensitivity of mechanical parameters on the reflected signal at the second interface of human cancellous bone—Application of Biot theory

Abstract

A simulation study of mechanical parameters sensitivity to reflected ultrasound waves at the second interface of a hypothetical human cancellous bone sample is proposed. The sample is considered as a biphasic porous medium saturated by a fluid. The visco-inertial exchanges between the structure and the saturating fluid are described by the Biot theory modified by the Johnson model. An analytical expression of the reflection coefficient at the second interface is obtained in the frequency domain. This expression depends on three physical parameters, which are the porosity, the tortuosity, and the viscous characteristic length, as well as on mechanical parameters, Young's modulus and Poisson's ratio of the solid and the skeletal frame of the medium. The reflected signal is calculated in the frequency domain by the product of the spectrum of the incident signal by the reflection coefficient. In the time domain, the reflected wave is obtained by taking the inverse Fourier transform of the reflected frequency signal. The effect of mechanical parameters on the reflected signal inside the medium is studied. The results obtained are discussed and compared to those given in the literature.