Ultrasound pulse propagation in dispersive media

Human tissues show dispersive ultrasound absorption, and it is important to understand how ultrasound pulses in the diagnostic frequency range, 1-10 MHz, propagate in such media. An uncomplicated wave-equation model for human soft tissues is postulated, and its dispersion law for absorption is demonstrated to be compatible with existing experimental findings. Propagative solutions for the simple one-dimensional, homogeneous case (no scattering) are derived. It is shown that the transmitted pulse consists of an undistorted, damped replica of the incident pulse, plus a depth-dependent, time-extended 'rumble', both of which travel at a fixed, finite velocity through the medium. The constancy of this (signal) velocity reconciles the predicted velocity dispersion with the observed weakness of such an effect in many tissues, and some consequences for the measurement of both velocity and absorption are indicated.