Horsfield K, Woldenberg M J
Respir Physiol. 1986 Jan;63(1):97-107. doi: 10.1016/0034-5687(86)90033-2.
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 estimate 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.
通过计算机利用随机末梢和随机节段生长生成二叉分支树。在生长过程中，随着新分支的添加，这种树的分支比（Rb）会周期性振荡。随着树的增大，振荡幅度减小，并且Rb趋向于一个期望值。利用生长过程的逆过程对此现象进行了研究，即从现有树中通过末梢或节段去除分支。这些树要么是计算机生成的树，要么是哺乳动物支气管树的数据。由此获得的Rb振荡与生长过程中获得的振荡相似，并用于计算Rb的收敛值。此外，从减去最少分支数时首次出现的振荡的最大和最小Rb的平均值获得收敛Rb的估计值。将通过这些方法获得的Rb值与通过对分支数的对数相对于阶数的回归斜率取反对数获得的值进行比较。对于大树，结果相似，但对于小树，通过振荡平均值给出的Rb更可靠。我们发现支气管树的Rb值与随机节段生长生成的值不同，并且并不总是与随机末梢生长高度一致。因此，支气管树中必定存在其他一些生长过程。
