Department of Physics, Ryerson University, Toronto, ON, Canada.
IEEE Trans Ultrason Ferroelectr Freq Control. 2011 Oct;58(10):2118-31. doi: 10.1109/TUFFC.2011.2061.
In ultrasound tissue characterization dealing with cellular aggregates (such as tumors), it can be hypothesized that cell microstructure and spatial distribution dominate the backscatter signal. Effects of spatial organization and size distribution of nuclei in cell aggregates on ultrasound backscatter are examined in this work using 2-D computer simulations. The nuclei embedded in cytoplasm were assumed to be weak scatterers of incident ultrasound waves, and therefore multiple scattering could be neglected. The fluid sphere model was employed to obtain the scattering amplitude for each nucleus and the backscatter echo was generated by summing scattered signals originating from many nuclei. A Monte Carlo algorithm was implemented to generate realizations of cell aggregates. It was found that the integrated backscattering coefficient (IBSC) computed between 10 and 30 MHz increased by about 27 dB for a spatially random distribution of mono-disperse nuclei (radius = 4.5 μm) compared with that of a sample of periodically positioned mono-disperse nuclei. The IBSC also increased by nearly 7 dB (between 10 and 30 MHz) for a spatially random distribution of poly-disperse nuclei (mean radius ± SD = 4.5 ± 1.54 μm) compared with that of a spatially random distribution of mono-disperse nuclei. Two different Gaussian pulses with center frequencies 5 and 25 MHz were employed to study the backscatter envelope statistics. An 80% bandwidth was chosen for each case with approximately 0.32 mm as the full-width at half-maximum (FWHM) for the first pulse and 0.06 mm for the second. The incident beam was approximated as a Gaussian beam (FWHM = 2.11 and 1.05 mm for those pulses, respectively). The backscatter signal envelope histograms generally followed the Rayleigh distribution for mono-disperse and poly-disperse samples. However, for samples with partially ordered nuclei, if the irradiating pulse contained a frequency for which ultrasound wavelength and scatter periodicity became comparable (d ~ λ/2), then the histograms were better fitted by the Nakagami distribution. This study suggests that the shape of an envelope histogram depends upon the periodicity in the spatial organization of scatterers and bandwidth of the ultrasound pulse.
在超声组织特征处理中涉及细胞聚集物（如肿瘤），可以假设细胞的微观结构和空间分布主导着背散射信号。本文采用二维计算机模拟研究了细胞聚集物中核的空间组织和大小分布对超声背散射的影响。假设嵌入细胞质中的核是入射超声波的弱散射体，因此可以忽略多次散射。采用流体球模型获得每个核的散射幅度，并通过对来自许多核的散射信号求和生成背散射回波。实现了蒙特卡罗算法来生成细胞聚集物的实现。结果发现，与周期性排列的单分散核（半径= 4.5μm）相比，对于单分散核的空间随机分布，在 10MHz 至 30MHz 之间计算的积分背散射系数（IBSC）增加了约 27dB。与空间随机分布的单分散核相比，对于空间随机分布的多分散核（平均半径±SD = 4.5±1.54μm），IBSC 也增加了近 7dB（在 10MHz 至 30MHz 之间）。使用中心频率为 5MHz 和 25MHz 的两个不同高斯脉冲来研究背散射包络统计。每种情况下选择 80%带宽，第一脉冲的半最大值全宽（FWHM）约为 0.32mm，第二脉冲为 0.06mm。入射束近似为高斯束（对于这些脉冲，FWHM 分别为 2.11mm 和 1.05mm）。对于单分散和多分散样本，背散射信号包络直方图通常遵循瑞利分布。然而，对于部分有序核的样本，如果辐照脉冲包含一个超声波长和散射周期变得可比的频率（d~λ/2），则直方图通过 Nakagami 分布更好地拟合。这项研究表明，包络直方图的形状取决于散射体空间组织的周期性和超声脉冲的带宽。
