Quantitative ultrasound estimates from populations of scatterers with continuous size distributions

Although quantitative ultrasound imaging based on backscattering coefficients has proven potential for tissue characterization, the scattering models used in most studies assume distributions of identical scatterers. However, actual tissues may exhibit multiple levels of spatial scales. Therefore, the objective of the present study is to analyze the effects of scatterer size distributions when using a fluid-sphere model for estimating values of effective scatterer diameter (ESD) through both simulations and experiments. For simulations, ESD estimates were obtained at several analysis frequencies between 1 and 40 MHz from populations of scatterers with diameters ranging between 25 and 100 μm, 25 and 50 μm, 50 and 100 μm, and 50 and 75 μm. For sufficiently high analysis frequencies, the ESD estimates obtained through simulations were approximately inversely proportional to frequency and mostly independent of the underlying scatterer size distribution. Asymptotic expressions for the expected ESD estimates at low- and high-frequency limits were derived. Experiments were conducted using two gelatin phantoms with contrast agent spheres ranging in diameter from 30 to 140 μm and 70 to 140 μm, and 5-, 7.5-, 10-, and 13-MHz focused transducers. Not only was the asymptotic behavior of ESD versus frequency estimates observed experimentally, but also the experimental ESD estimates using the 10- and 13-MHz transducers were lower than the smallest scatterers present in the second phantom. These results may have a direct impact on how scatterer size estimates corresponding to specimens with different subresolution spatial scales should be interpreted.