Ultrasonic propagation of reflected waves in cancellous bone: Application of Biot theory

An ultrasonic propagation in cancellous bone is considered using the Biot theory modified by the Johnson et al. Numerical simulations of reflected waves in the time domain are worked out by varying the modified Biot parameters. The sensitivity of different mechanical parameters: Young modulus and the Poisson ratio of the skeletal frame and physical parameters, porosity, tortuosity and viscous characteristic length are studied showing their effect on the reflected ultrasonic waves of the bone sample. The sensitivity of the modified Biot parameters with respect to the reflected wave depends strongly on the coupling between the solid and fluid phases of the cancellous bone. We show from these simulations that some parameters such as porosity and tortuosity play an important role on reflected wave, the remaining parameters have low sensitivity compared with the porosity and tortuosity. Experimental results for reflected waves by human cancellous bone samples are given and compared with theoretical predictions.