On fractal properties of arterial trees
On fractal properties of arterial trees
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DOI：
10.1006/jtbi.1998.0892
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发表时间：
1999-04-21
影响因子：
2
通讯作者：
Zamir, M
中科院分区：
文献类型：
--
作者：
Zamir, M
动脉树的分形特性的问题被认为是从广泛的树结构的人类心脏的右冠状动脉的数据。由于这棵树的高度不均匀的结构，研究的重点是纯粹的几何，而不是统计方面的分形特性。大量的动脉分叉组成的树被发现有一个混合程度的不对称在所有级别的树，包括深度的树，它已被普遍认为是对称的。还发现子血管与母血管的横截面积比在所有水平高度混合，具有高于和低于1.0的值，而不是像过去通常认为的那样始终高于1.0。幂律指数的计算值描述了动脉分叉处三个血管段的直径之间的理论关系，发现其范围远远超出了与立方和平方定律相关的两个值，并且没有明确支持其中一个或另一个。在整个树结构被发现有什么，我们称之为“伪分形”的属性，在这个意义上说，不同口径的血管显示相同的分支模式，但与一系列的值的分支参数。结果表明，更高程度的分形特征，其中的分支参数是恒定的整个树结构，是不太可能达到非均匀的血管结构。(C)北京：科学出版社.
The question of fractal properties of arterial trees is considered in light of data from the extensive tree structure of the right coronary artery of a human heart. Because of the highly non-uniform structure of this tree, the study focuses on the purely geometrical rather than statistical aspects of fractal properties. The large number of arterial bifurcations comprising the tree were found to have a mixed degree of asymmetry at all levels of the tree, including the depth of the tree where it has been generally supposed that they would be symmetrical. Cross-sectional area ratios of daughter to parent vessels were also found to be highly mixed at all levels, having values both above and below 1.0, rather than consistently above as has been generally supposed in the past. Calculated values of the power law index which describes the theoretical relation between the diameters of the three vessel segments at an arterial bifurcation were found to range far beyond the two values associated with the cube and square laws, and not clearly favoring one or the other. On the whole the tree structure was found to have what we have termed "pseudo-fractal" properties, in the sense that vessels of different calibers displayed the same branching pattern but with a range of values of the branching parameters. The results suggest that a higher degree of fractal character, one in which the branching parameters are constant throughout the tree structure, is unlikely to be attained in non-uniform vascular structures. (C) 1999 Academic Press.