Key result
The first order statistics of ultrasound speckle amplitude, intensity, and log amplitude from a fractal branching vasculature can be modeled by Burr, Lomax, and generalized logistic distributions.
Why the study?
Questions remain regarding the nature of ultrasound speckle from soft vascularized tissues, prompting analysis of cylindrical scattering structures arranged across a power law distribution of sizes.
Ultrasound speckle statistics from soft vascularized tissues can be modeled using Burr, Lomax, and logistic distributions, providing a theoretical framework that may help differentiate normal from pathological tissues such as fibrosis.
May support speckle-based tissue characterization; leaves open validation in human disease.
After 100 years of theoretical treatment of speckle patterns from coherent illumination, there remain some open questions about the nature of ultrasound speckle from soft vascularized tissues. A recent hypothesis is that the fractal branching vasculature is responsible for the dominant echo pattern from organs such as the liver. In that case, an analysis of cylindrical scattering structures arranged across a power law distribution of sizes is warranted. Using a simple model of echo strength and basic transformation rules from probability, we derive the first order statistics of speckle considering the amplitude, the intensity, and the natural log of amplitude. The results are given by long tailed distributions that have been studied in the statistics literature for other fields. Examples are given from simulations and animal studies, and the theoretical fit to these preliminary data support the overall framework as a plausible model for characterizing ultrasound speckle statistics.
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Parker et al. (2020) studied Ultrasound speckle modeling. Fractal branching vasculature model was evaluated on First order statistics of ultrasound speckle (amplitude, intensity, log amplitude). The first order statistics of ultrasound speckle amplitude, intensity, and log amplitude from a fractal branching vasculature can be modeled by Burr, Lomax, and generalized logistic distributions.
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