  Recent theories examine the role of the fractal branching vasculature as a
primary site of Born scattering from soft normal tissues. These derivations
postulate that the first order statistics of speckle from tissue such as the
liver, thyroid, and prostate will follow a Burr distribution with a power law
parameter that can be related back to the underlying power law which governs
the branching network. However, the issue of scatterer spacing, or the number
of cylindrical vessels per sample volume of the interrogating pulse, has not
been directly addressed. This is now examined with a 3D simulation that varies
the number density and the governing power law parameter of an ensemble of
different sized cylinders. The Burr distribution is found to be an appropriate
model for the histogram of amplitudes from speckle regions, and the parameters
track the underlying conditions. These results are also tested in a more
general model of rat liver scans in normal vs. abnormal conditions, and the
resulting Burr distributions are also found to be appropriate and sensitive to
underlying scatterer distributions. These preliminary results suggest that the
classical Burr distribution may be useful in the quantification of scattering
of ultrasound from soft vascularized tissues.
