Abstract
What causes scattering of ultrasound from normal soft tissues such as the liver, thyroid, and prostate? Commonly, the answer is formulated around the properties of spherical scatterers, related to cellular shapes and sizes. However an alternative view is that the closely packed cells forming the tissue parenchyma create the reference media, and the long cylindrical-shaped fluid vessels serve as the scattering sites. Under a weak scattering or Born approximation for the extracellular fluid in the vessels, and assuming an isotropic distribution of cylindrical channels across a wide range of diameters, consistent with a fractal branching pattern, some theoretical predictions can be made. Our model predicts that backscatter increases as a power law of frequency, where the power law is determined by the fractal dimension. These results are consistent with the pioneering measurements of Campbell and Waag. Furthermore, the normalized histogram of echo amplitudes is found to be related to the classical Burr distribution, with the key power law parameter directly related to the fractal dimension, expected in the range of 2 to 3 for normal vasculature. Thus, the first and second order statistics of backscatter from soft vascularized tissues appear to be determined by fractal branching cylindrical vessels.
Published Version
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