Using two-dimensional impedance maps to study weak scattering in sparse random media

Impedance maps (ZMs) have been proposed as a tool for modeling acoustic properties of tissue microstructure. Three-dimensional (3D) ZMs are constructed from a series of adjacent histological tissue slides that have been stained to emphasize acoustic impedance structures. The power spectrum of a 3DZM can be related to the ultrasound backscatter coefficient, which can be further reduced to a form factor. The goal of this study is to demonstrate the ability to estimate form factors using two-dimensional (2D) ZMs instead of 3DZMs, which have reduced computational and financial cost. The proposed method exploits the properties of isotropic media to estimate the correlation coefficient from slices before estimating the 3D volume power spectrum. Simulated sparse collections of objects were used to study the method by comparing the results obtained using 2DZMs to those predicted by theory. 2DZM analysis was conducted on normal rabbit liver histology and compared to 3DZM analysis of the same histology. The mean percent error between effective scatterer diameter estimates from 2DZMs and 3DZMs of rabbit liver histology was <10% when using three 2DZMs. The results suggest that 2DZMs are a feasible alternative to 3DZMs when estimating form factors for sparse collections of objects.