Assessment of the effects of scatterer size distributions on effective scatterer diameter estimates

Scattering models used in most quantitative ultrasound studies assume distributions of identical scatterers. However, actual tissues may exhibit multiple levels of spatial scales. Therefore, the objective of the present study was to use both simulations and experiments to analyze the effects of scatterer size distributions when using a fluid-sphere model for estimating effective scatterer diameter (ESD). Simulations were conducted with populations of scatterers with uniformly distributed sizes within [25, 100], [25, 50], [50, 100], and [50, 75] m. Simulated backscatter coefficients (BSCs) used as inputs for the ESD estimator were obtained using two methods: (1) using portions of the theoretical BSC with different center frequencies between 1 and 40 MHz and 100% fractional bandwidth, and (2) processing simulated radiofrequency data from computer phantoms using f/4 transducers with center frequencies of 3, 6, 12, 24, and 36 MHz and 100% fractional bandwidth. Experiments were conducted using a gelatin phantom with Sephadex spheres ranging in diameter from 30 μm to 140 μm and 3.5, 7.5, 10, and 13 MHz focused transducers. ESD estimates obtained with both simulation methods were approximately inversely proportional to frequency and mostly independent of the underlying scatterer size distribution for sufficiently high analysis frequencies. For frequencies higher than 13 MHz the ESD estimates were below 50 μm for all considered size distributions even though two of them had no scatterers smaller than 50 μm. Further, the asymptotic behavior of ESD vs. frequency estimates was also observed experimentally. The results of this work highlight some of the effects of continuous scatterer size distributions when obtaining ESD estimates, and challenge the hypothesis that different frequency ranges are more sensitive to different spatial scales when using a single-size scattering model. Although the results presented here are not necessarily universal and most likely will be affected by the actual size distribution and frequency-dependent BSC of the individual scatterers, this work suggests that caution must be exerted when interpreting ESD estimates at different frequency ranges. This work was supported by a grant from the NIH R21CA139095.