Describing small-scale structure in random media using pulse-echo ultrasound

Abstract

A method for estimating structural properties of random media is described. The size, number density, and scattering strength of particles are estimated from an analysis of the radio frequency (rf) echo signal power spectrum. Simple correlation functions and the accurate scattering theory of Faran [J.J. Faran, J. Acoust. Soc. Am. 23, 405-418 (1951)], which includes the effects of shear waves, were used separately to model backscatter from spherical particles and thereby describe the structures of the medium. These methods were tested using both glass sphere-in-agar and polystyrene sphere-in-agar scattering media. With the appropriate correlation function, it was possible to measure glass sphere diameters with an accuracy of 20%. It was not possible to accurately estimate the size of polystyrene spheres with the simple spherical and Gaussian correlation models examined because of a significant shear wave contribution. Using the Faran scattering theory for spheres, however, the accuracy for estimating diameters was improved to 10% for both glass and polystyrene scattering media. It was possible to estimate the product of the average scattering particle number density and the average scattering strength per particle, but with lower accuracy than the size estimates. The dependence of the measurement accuracy on the inclusion of shear waves, the wavelength of sound, and medium attenuation are considered, and the implications for describing the structure of biological soft tissues are discussed.

Analysis of human fibroadenomas using three-dimensional impedance maps

“…The equation describing S(k) is (4) where z 0 is the acoustic impedance of the background material and z(r) is the spatially varying acoustic impedance at position r. The background impedance is defined as (5) where ρ 0 is the density and κ 0 is the compressibility of the background material. Likewise, the scatterer impedance is defined as (6) where ρ(r) is the spatially varying density and κ(r) is the spatially varying compressibility at position r. The connection between backscattered intensity and the acoustic impedance map of tissue is described by (4). This allows for the estimation of ultrasound parameters without necessitating the acoustic wave simulation that has been done in other impedance map work [9].…”

“…The acoustic intensity for the backscattered wave in (1) can be expressed by (2) where A is a proportionality constant [1]. Through methods described in [3], [5], and [6], the backscattered intensity can be computed as a function of frequency and related to the acoustic impedance of the underlying tissue. By making the assumption of weak scattering, which is appropriate in soft tissue, (2) can be rewritten as (3) where A′ is a new proportionality constant and S(k) is the squared magnitude of the Fourier transform of a relative impedance function [13].…”

“…For a plane wave of unit amplitude, the far field backscattered pressure from a scattering volume can be described by (1) where r is the distance to the scattering site, k is the spatial frequency or acoustic wave number (defined as the ratio of the angular frequency of the acoustic wave to the speed of sound in the medium), and Φ(k) is an angle distribution function [6], [8]. The acoustic intensity for the backscattered wave in (1) can be expressed by (2) where A is a proportionality constant [1].…”

Evaluation of in vivo Liver Tissue Characterization with Spectral RF Analysis versus Elasticity

“…The backscatterer coefficient was introduced in [6] and corresponds to the relative scattering cross-section per unit solid angle and volume. Indeed to compute the BSC, echoes from the media of interest are compared to specular echoes measured from a steel plate with a reflection coefficient of R=0.9 and placed at the focal length of the transducer.…”

High Frequency Quantitative Ultrasound Imaging of Solid Tumors in Mice

“…The Born approximation is valid when there is weak scattering and no multiple scattering. The first model was the spherical Gaussian model [5], the second model was derived from the Anderson model for fluid-filled sphere [6], and the third model was constructed by considering the cytoskeleton of cells. The spherical Gaussian model was used to describe the high frequency scattering initially because the spherical Gaussian model has been used previously to estimate scatterer properties in may tissues [3].…”