Department of Electrical and Computer Engineering, University of Rochester, Rochester, New York 14627, USA.
J Acoust Soc Am. 2019 Nov;146(5):3318. doi: 10.1121/1.5132934.
The issue of speckle statistics from ultrasound images of soft tissues such as the liver has a long and rich history. A number of theoretical distributions, some related to random scatterers or fades in optics and radar, have been formulated for pulse-echo interference patterns. This work proposes an alternative framework in which the dominant echoes are presumed to result from Born scattering from fluid-filled vessels that permeate the tissue parenchyma. These are modeled as a branching, fractal, self-similar, multiscale collection of cylindrical scatterers governed by a power law distribution relating to the number of branches at each radius. A deterministic accounting of the echo envelopes across the scales from small to large is undertaken, leading to a closed form theoretical formula for the histogram of the envelope of the echoes. The normalized histogram is found to be related to the classical Burr distribution, with the key power law parameter directly related to that of the number density of vessels vs diameter, frequently reported in the range of 2 to 4. Examples are given from liver scans to demonstrate the applicability of the theory.
软组织（如肝脏）超声图像的散斑统计问题有着悠久而丰富的历史。已经为脉冲回波干扰模式制定了一些理论分布，其中一些与光学和雷达中的随机散射体或衰落有关。这项工作提出了一种替代框架，其中假定主要回波是由充满充满组织实质的流体的血管的玻恩散射产生的。这些被建模为一个分支的、分形的、自相似的、多尺度的圆柱形散射体集合，由与每个半径处的分支数相关的幂律分布来控制。对从小尺度到大尺度的回波包络进行确定性的计算，从而得到回波包络的直方图的封闭形式理论公式。归一化的直方图被发现与经典的 Burr 分布有关，关键的幂律参数与血管的数量密度与直径的关系直接相关，通常报告的范围在 2 到 4 之间。从肝脏扫描中给出了一些示例，以证明该理论的适用性。
