DIAMETER-DEFINED STRAHLER SYSTEM AND CONNECTIVITY MATRIX OF THE PULMONARY ARTERIAL TREE

Diameter-defined Strahler system and connectivity matrix of the pulmon ary arterial tree. J. Appl. Physiol. 76(2): 882-892, 1994. - For model ing 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 s ome are connected in series; histograms of the diameters of vessels in the successive orders have wide overlaps; and the ''small-twigs-on-la rge-trunks'' phenomenon is not given a quantitative expression. To imp rove the accuracy of the hemodynamic circuit model, we made a distinct ion 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. I n an equivalent circuit, all elements of the same order are considered as arranged in parallel. Then, we follow the ordering method of Horsf ield and Strahler, with introduction of an additional rule for the ass ignment of order numbers. If D-n and SDn denote the mean and standard deviation of the diameters of vessels of order n, then our rule divide s the gap between D-n - SDn and D-n-1 + SDn-1 evenly between orders n and n - 1. Finally, we introduced a connectivity matrix with a compone nt in the mth row and the nth column that is the average number of ves sels of order m that grow out of the vessels of order n. This method w as applied to the rat. We found that the rat pulmonary arterial tree h as 11 orders of vessels and that the geometry is fractal within these orders. The ratios of diameters, lengths, and numbers of elements in s uccessive orders are 1.58, 1.60, and 2.76, respectively, The con necti vity matrix reveals interesting features beyond the fractal concept. N ew features are found in the variation of the total cross-sectional ar ea of elements with order numbers.