BRANCHING RATIO AND GROWTH OF TREE-LIKE STRUCTURES
BRANCHING RATIO AND GROWTH OF TREE-LIKE STRUCTURES
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DOI：
10.1016/0034-5687(86)90033-2
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发表时间：
1986-01-01
期刊：
影响因子：
--
通讯作者：
WOLDENBERG, MJ
中科院分区：
文献类型：
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作者：
HORSFIELD, K;WOLDENBERG, MJ
利用随机末端和随机分段生长，由计算机生成二叉分枝树。这种树在生长期间的分枝率(Rb)随着新枝的增加而周期性地振荡。随着树的增大和RB向期望值收敛，振荡的幅度减小。这一现象是用生长过程的反转来研究的，即通过从现有树木上的枝条顶端或节段减去。这些要么是计算机生成的树，要么是哺乳动物的支气管树数据。由此得到的Rb的振荡与生长过程中得到的相似，并被用来计算Rb的收敛值。此外，从减去最少分支数后发生的第一次振荡的最大和最小Rb的平均值，得到收敛的Rb的估计式。将这些方法得到的Rb值与取对数对数法回归的斜率反对数得到的Rb值进行了比较。对于大树，结果是相似的，但对于较小的树，通过振荡的方法给出了更可靠的RB。我们发现，来自支气管树的Rb值不同于由随机节段生长产生的Rb值，并且与随机末端生长并不总是很好地一致。因此，一些其他的生长过程必须在支气管树中起作用。
Dichotomously branching trees were generated by computer using random terminal and random segmental growth. The branching ratio (Rb) of such a tree during growth oscillates periodically as new branches are added. The magnitude of the oscillations diminishes as the tree enlarges and Rb converges towards an expected value. This phenomenon was investigated using the reverse of the growth process, that is by terminal or segmental subtraction of branches from existing trees. These were either computer generated trees or mammalian bronchial tree data. The oscillations of Rb thus obtained were similar to those obtained during growth and were used to calculate convergent values of Rb. In addition, an esimate of convergent Rb was obtained from the mean of the maximum and minimum Rb of the first oscillation occurring when the least number of branches had been subtracted. Values of Rb obtained by these methods were compared with those obtained by taking the antilogarithm of the slope of the regression of log number of branches against order. With large trees the results are similar, but with smaller trees a more reliable Rb is given by the means of the oscillations. We find that Rb values from the bronchial trees are different from those generated by random segmental growth and are not always in good agreement with random terminal growth. Some other growth process must therefore be operative in the bronchial tree.