A general statistical model for ultrasonic backscattering from tissues

TLDR

Backscattered ultrasonic echoes from tissue are traditionally modeled by Rayleigh or K distributions, but these models are analytically complex. The study proposes a simpler generalized model using the Nakagami distribution. The model characterizes the envelope statistics of backscattered echoes from ensembles of scatterers with varying densities, cross sections, and regular spacing, and its validity was tested via computer simulations and phantom experiments. Results demonstrate the versatility of the Nakagami distribution and suggest it is a suitable, analytically simple model for tissue characterization across diverse scattering conditions.

Abstract

The backscattered ultrasonic echo from tissue can be described in terms of Rayleigh distribution or K distribution. Even though both generalized K distribution and homodyned K distribution can account for some of the scattering conditions that exist in tissues, the analytical complexity involved with these distributions is significant. A much simpler generalized model based on the Nakagami distribution is proposed here. This model can describe the statistics of the envelope of the backscattered echo from an ensemble of scatterers with varying number densities, varying cross sections, and the presence or absence of regularly spaced scatterers. Computer simulations and experiments on tissue-mimicking phantoms have been undertaken to test the validity of the model. Results clearly show the versatility of the Nakagami distribution and its parameter to model the backscattered envelope from tissues. It is suggested that Nakagami distribution may be a good model for use in tissue characterization because of its simple analytical nature and ability to encompass different scattering conditions.