Characterization of volume scattering power spectra in isotropic media from power spectra of scattering by planes

Abstract

Relations between the power spectrum of scattering by a plane and by a volume of a statistically isotropic random medium are developed from two basic expressions. One gives the power spectrum of scattering by an n-dimensional isotropic medium as a one-dimensional transform of a rotationally symmetric correlation function of medium variations. The other describes the power spectrum of scattering by an (n-k)-dimensional cross section as a projection of the power spectrum in n-dimensional space. The results are used to determine the power spectrum of scattering by a volume from the power spectrum of scattering by a plane within the volume and also to relate the moments of power scattered in spaces of various dimensions. To illustrate the relations, calculations of power spectra and selected moments for volume scattering are made from power spectra having analytic forms as well as form power spectra computed in two dimensions from images of closely packed spheres and of pig liver sections. Numerical results obtained by processing power spectra having closed form expressions for volume scattering are in close agreement with theoretical values. Calculations for packed spheres show general concentrations of power explained by theory but required substantial smoothing of data in two dimensions to obtain consistent results because the images were not true cross sections. Results from sections of pig liver agree wth expected relationships. The theoretical expressions and numerical data indicate how quantitative information about the three-dimensional structure can be obtained from two-dimensional sections when the basic isotropy conditions are satisfied.

Experimental Application of Ultrafast Imaging to Spectral Tissue Characterization

“…Ultrasound tissue characterization using spectral methods has been extensively studied and validated, both theoretically and experimentally, over the last 30 y (Faran 1951;Insana and Brown 1993;Lizzi et al 1983Lizzi et al , 1988Waag et al 1983). Its clinical relevance was reported in studies on detection of inflammatory response (Tripette et al 2013), breast cancer treatment monitoring (Sadeghi-Naini et al 2013), detection of prothrombotic factors (Yu et al 2011) and prediction of coronary plaque composition (Nair et al 2002).…”

High-Frequency Quantitative Ultrasound Spectroscopy of Excised Canine Livers and Mouse Tumors Using the Structure Factor Model

“…In ocular malignant tumors, larger scatterer radii were estimated by ultrasound when compared to normal tissues and were related to clusters of melanin-laden histiocytes [5]. Waag et al related the ultrasound backscatter measurements to the lobule structures in the liver [7]. Oelze et al distinguished fibroadenomas (benign tumors) and carcinomas (malignant tumors) based on the QUS estimates [8].…”

Experimental validation of a convolution- based ultrasound image formation model using a planar arrangement of micrometer-scale scatterers

“…In the case of homogeneous scatterers placed in a homogeneous background, it is correct (up to a scaling factor) to set the estimated scattering function SF est to 1 where there is a scatterer, and set it to 0 where there is a background [17]. For a spherical scatterer in the plane of a linear array, SF est may be treated as a circular crosssection or as the projection of the sphere function onto the 2-D plane (similarly to [5], [17]). Alternatively, for acoustically compact spherical scatterers, SF est may be set to a collection of discrete points.…”

“…Waag et al [5] used images of pig liver lobules to investigate the relationship between backscattered spectra in 1-D, 2-D, and 3-D. Lizzi et al [6] used acoustic microscope data to estimate speed of sound maps of tissue, which were used to generate simulations of conventionalfrequency ultrasound images. The use of histology to estimate SF is also receiving increased attention: Mamou et al [7] generated 3-D acoustic impedance maps from 3-D volumes of H&E-stained histology, which was then used to estimate quantitative acoustic parameters [8]; Daoud and Lacefield [9] used histology images to derive spatial statistics of the SF.…”