On estimating the number density of random scatterers from backscattered acoustic signals

When an acoustic pulse interacts with an inhomogeneous, attenuating medium, the backscattered signals exhibit random fluctuations which are correlated with the physical properties of the medium. This paper proposes a robust model for characterizing the statistical nature of these backscattered signals. This model takes into account frequency-dependent attenuation, spatially varying media statistics, arbitrary beam geometries, and arbitrary pulse shapes. Based on this model, statistical estimation schemes are proposed for estimating both the attenuation coefficient and scatterer number density of the medium. Using appropriate simplifying assumptions, it is shown that this model is consistent with attenuation estimation algorithms currently used for ultrasonic tissue characterization. A statistical approach for estimating the number density of scatterers is described and its theoretical performance is evaluated. The algorithm for estimating the scatterer number density incorporates measurements of both the statistical moments of the backscattered signals and the point spread function of the acoustic system. The number density algorithm has been applied to simulated waveforms, waveforms obtained from ultrasonic phantoms with known number densities, and in vitro mammalian tissues. There is an excellent agreement between theoretical, simulation, and experimental results. The application of this technique to ultrasonic tissue characterization is also discussed.