Application of fractional calculus to ultrasonic wave propagation in human cancellous bone

Ultrasonic wave propagation in human cancellous bone is considered. Fractional calculus is used to describe the viscous interactions between fluid and solid structure. Reflection and transmission scattering operators are derived for a slab of cancellous bone in the elastic frame using Biot's theory. Experimental results are compared with theoretical predictions for slow and fast waves transmitted through human cancellous bone samples.