Jiang Z L, Kassab G S, Fung Y C
Institute for Biomedical Engineering, University of California, San Diego, La Jolla 92093-0412.
J Appl Physiol (1985). 1994 Feb;76(2):882-92. doi: 10.1152/jappl.1994.76.2.882.
For modeling of a vascular tree for hemodynamic analysis, the well-known Weibel, Horsfield, and Strahler systems have three shortcomings: vessels of the same order are all treated as in parallel, despite the fact that some are connected in series; histograms of the diameters of vessels in the successive orders have wide overlaps; and the "small-twigs-on-large-trunks" phenomenon is not given a quantitative expression. To improve the accuracy of the hemodynamic circuit model, we made a distinction between vessel segments and vessel elements: a segment is a vessel between two successive nodes of bifurcation; an element is a union of a group of segments of the same order that are connected in series. In an equivalent circuit, all elements of the same order are considered as arranged in parallel. Then, we follow the ordering method of Horsfield and Strahler, with introduction of an additional rule for the assignment of order numbers. If Dn and SDn denote the mean and standard deviation of the diameters of vessels of order n, then our rule divides the gap between Dn--SDn and Dn--1 + SDn--1 evenly between orders n and n--1. Finally, we introduced a connectivity matrix with a component in the mth row and the nth column that is the average number of vessels of order m that grow out of the vessels of order n. This method was applied to the rat. We found that the rat pulmonary arterial tree has 11 orders of vessels and that the geometry is fractal within these orders. The ratios of diameters, lengths, and numbers of elements in successive orders are 1.58, 1.60, and 2.76, respectively. The connectivity matrix reveals interesting features beyond the fractal concept. New features are found in the variation of the total cross-sectional area of elements with order numbers.
为了构建用于血流动力学分析的血管树模型，著名的韦贝尔（Weibel）、霍斯菲尔德（Horsfield）和斯特拉勒（Strahler）系统存在三个缺点：尽管有些血管是串联连接的，但同一级别的血管都被视为并联；连续级别血管直径的直方图有很大重叠；“大树干上的小树枝”现象没有得到定量表达。为了提高血流动力学电路模型的准确性，我们对血管段和血管元件进行了区分：一个段是两个连续分叉节点之间的血管；一个元件是串联连接的同一级别的一组段的组合。在等效电路中，同一级别的所有元件都被视为并联排列。然后，我们遵循霍斯菲尔德和斯特拉勒的排序方法，并引入了一个额外的规则来分配序号。如果Dn和SDn分别表示第n级血管直径的平均值和标准差，那么我们的规则将Dn - SDn和Dn - 1 + SDn - 1之间的差距在第n级和第n - 1级之间平均分配。最后，我们引入了一个连通性矩阵，其第m行和第n列的元素是从第n级血管长出的第m级血管的平均数量。该方法应用于大鼠。我们发现大鼠肺动脉树有11级血管，并且在这些级别内几何形状是分形的。连续级别中元件的直径、长度和数量之比分别为1.58、1.60和2.76。连通性矩阵揭示了超越分形概念的有趣特征。在元件总横截面积随序号的变化中发现了新的特征。
