Impact of acoustic parameters on reflected signal from a hypothetical human cancellous bone - Biot’s theory application

Abstract

This work involves a numerical simulation study of the impact of physical and mechanical parameters describing hypothetical human cancellous bone on reflected ultrasound waves. 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 first 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; the Young’s modulus and the Poisson’s ratio. 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 each parameter on the reflected signal is studied and discussed.