Effective scatterer diameter estimates for broad scatterer size distributions

Acoustic form factors have been used to model the frequency dependence of acoustic scattering in phantoms and tissues. This work demonstrates that a broad range of scatterer sizes, individually well represented by Faran theory or a Gaussian form factor, is not accurately described by a single effective scatterer from either of these models. Contributions from a distribution of discrete scatterer sizes for two different form factor functions (Gaussian form factors and scattering functions from Faran's theory) were calculated and linearly combined. Composite form factors created from Gaussian distributions of scatterer sizes centered at 50 µm with standard deviations of up to σ = 40 µm were fit to each scattering model between 2 and 12 MHz. Scatterer distributions were generated using one of two assumptions: the number density of the scatterer diameter distribution was Gaussian distributed, or the volume fraction of each scatterer diameter in the distribution was Gaussian distributed. Each simulated form factor was fit to a single-diameter form factor model for Gaussian and exponential form factors. The mean-squared error (MSE) between the composite simulated data and the best-fit single-diameter model was smaller with an exponential form factor model, compared with a Gaussian model, for distributions with standard deviations larger than 30% of the centroid value. In addition, exponential models were shown to have better ability to distinguish between Faran scattering model-based distributions with varying center diameters than the Gaussian form factor model. The evidence suggests that when little is known about the scattering medium, an exponential scattering model provides a better first approximation to the scattering correlation function for a broad distribution of spherically symmetric scatterers than when a Gaussian form factor model is assumed.