The 3D Spatial Autocorrelation of the Branching Fractal Vasculature
The 3D Spatial Autocorrelation of the Branching Fractal Vasculature
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DOI：
10.3390/acoustics1020020
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发表时间：
2019-06-01
期刊：
影响因子：
2.1
通讯作者：
Wood, Ronald W.
中科院分区：
文献类型：
--
作者：
Parker, Kevin J.;Carroll-Nellenback, Jonathan J.;Wood, Ronald W.
软组织内的分形分支脉管系统和分支系统的数学性质影响从血液速度到超声背向散射的广泛的重要现象。在分支网络的数学描述符中，空间自相关函数在组织和通过组织的波传播的统计测量中起着重要作用。然而，有开放的问题，分析模型的3D自相关函数的分支血管和软血管化组织的实验验证很少。为了解决这个问题，高分辨率计算机断层扫描的高度血管化胎盘灌注造影剂通过脐动脉进行了检查。发现空间自相关函数与幂律一致，然后在理论上预测其他相关函数的特定幂律行为，包括超声的反向散射。
The fractal branching vasculature within soft tissues and the mathematical properties of the branching system influence a wide range of important phenomena from blood velocity to ultrasound backscatter. Among the mathematical descriptors of branching networks, the spatial autocorrelation function plays an important role in statistical measures of the tissue and of wave propagation through the tissue. However, there are open questions about analytic models of the 3D autocorrelation function for the branching vasculature and few experimental validations for soft vascularized tissue. To address this, high resolution computed tomography scans of a highly vascularized placenta perfused with radiopaque contrast through the umbilical artery were examined. The spatial autocorrelation function was found to be consistent with a power law, which then, in theory, predicts the specific power law behavior of other related functions, including the backscatter of ultrasound.