Effect of physical and mechanical parameters on the reflected signal from the first interface of human cancellous bone—application of Biot's theory

Abstract

In this work, a simulated study on the effects of physical and mechanical parameters describing human cancellous bone on reflected ultrasound waves is proposed. The visco-inertial exchanges between the structure and the saturating fluid are described by the Biot theory modified by the Johnson model. A simplified expression of the reflection coefficient at the first interface is obtained in the frequency domain. This expression depends on three physical parameters which are porosity, tortuosity, and viscous characteristic length as well as the mechanical parameters; Young's modulus and Poisson's ratio. The reflected signal is calculated in the frequency domain by the product of the spectrum of the incident signal with 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. The results obtained are discussed and compared with those given in the literature.