Structure factor model-based approach for analyzing two-dimensional impedance map and studying scattering from polydisperse dense media

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A two-dimensional (2D) computational model of acoustic impedance constructed from histological tissue images, termed 2D impedance map (2DZM), was recently proposed to obtain quantitative information about tissue scattering (Luchies & Oelze 2016). However, this 2DZM approach was limited to isotropic and sparse media. The present study investigates the 2D structure factor model (SFM) in 2DZM approaches to take into account coherent scattering occurring in dense media. Studies of simulated 2DZMs were performed to evaluate the ability of 2D SFM-based approach to accurately quantify scattering. Polydisperse spheres with a gamma radius distribution were uniformly randomly distributed in a 3D volume to mimic a collection of whole cells. 2DZMs were obtained from simulated 3D media by performing perfect cross sections. The 2D backscatter coefficient (BSC) was computed by averaging the magnitude squared of the 2D Fourier transforms of 50 extracted 2D relative impedance contrast maps. The 2D BSC was fit to three theoretical models over the 1–100 MHz frequency range. A sparse fluid disc model (FDM) and a concentrated structure factor model (SFM) were compared to estimate the mean scatterer size and acoustic concentration for scatterer volume fractions ranging from 0.6% to 30%. In the case of the SFM, both monodisperse and polydisperse models were studied. Results demonstrated that the polydisperse SFM fitted satisfactorily the simulated BSCs of sparse and dense media. Scatterer radius and surface fraction estimates demonstrate the superiority of the 2D SFM-based approach over a wide range of studied volume fractions. Relative errors were less than 4% for the scatterer radius estimates and less than 10% for the surface fraction estimates when using the concentrated model (against 35% and 50%, respectively, when using the sparse model). The results establish the ability of the 2D SFM-based approach to accurately estimate scatterer properties from 2DZMs even in the challenging case of dense media.