RETRACTED: Experimental characterization of human cancellous bone via the first ultrasonic reflected wave – Application of Biot’s theory

Abstract

Abstract In this paper, enhanced characterization of human cancellous bone using reflected ultrasound waves is proposed using the Biot theory modified by the Johnson et al. model for viscous exchange between the structure and the saturating fluid. A simplified expression of the reflection coefficient at the first surface is obtained in the frequency domain. This expression is based on the three physical parameters which are porosity, tortuosity and viscous characteristic length, as well as on the mechanical parameters: Young modulus and poison ratio of the skeleton part. 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 inverse problem is solved numerically by minimizing between simulated and experimental reflected signals. Three physical parameters are inverted simultaneously: porosity, tortuosity and viscous characteristic length. Tests are performed using two samples of trabecular bone. Experimental results are compared with theoretical predictions, giving a good correlation.