Structure function: Theory, ultrasonic measurement, and histology

Ultrasonic scattering is determined by not only the properties of individual scatterers, but also the correlation among scatterer positions. The role of scatterer spatial correlation is significant for dense medium, but has not been fully understood. The effect of scatterer spatial correlation may be modeled by a structure function (three-dimensional Fourier transform of the scatterer positions) as a frequency-dependent factor in the backscatter coefficient (BSC) expression. To study the structure function, we have performed three steps: 1) we developed theoretical structure function models that take into account the polydispersity of spherical scatterers; 2) we developed the cell pellet biophantom technique to estimate the structure function from ultrasound backscattered data (11 - 105 MHz); 3) we developed algorithms for estimating the structure function from histology, independent of the acoustic measurements. The acoustically estimated and histologically estimated structure functions show consistent frequency dependency, which demonstrates the correlation between acoustically estimated structure function and scatterer position distribution observed in histology. Furthermore, fitting the theoretical polydisperse structure function model to the experimental structure functions yielded relatively accurate cell radius estimates (error < 16%). Our results suggest that the structure function is required for accurately modeling the acoustic scattering in dense medium.