The morphometric data on the branching pattern and vascular geometry of the human pulmonary arterial and venous trees are presented. Arterial and venous casts were prepared by the silicone elastomer casting method. Three recent innovations are used to describe the vascular geometry: the diameter-defined Strahler ordering model is used to assign branching orders, the connectivity matrix is used to describe the connection of blood vessels from one order to another, and a distinction between vessel segments and vessel elements is used to express the series-parallel feature of the pulmonary vessels. A total of 15 orders of arteries were found between the main pulmonary artery and the capillaries in the left lung and a total of 15 orders of veins between the capillaries and the left atrium in the right lung. The elemental and segmental data are presented. The morphometric data are then used to compute the total cross-sectional areas, blood volumes, and fractal dimensions in the pulmonary arterial and venous trees.

Through the use of simulated model experiments, data on blood cell distribution into a bifurcating capillary blood vessel are obtained. The results show that the movement of red blood cells at a bifurcation point is influenced by the difference in velocities of flow in the daughter branches. If the velocity of flow in one branch is slower than that in the other, the hematocrit decreases in the slower branch and increases in the faster branch. For velocity ratios sufficiently smaller than a certain critical value, the hematocrit ratio can be expressed by a linear relationship, (H1/H2) − 1 = a[(v1/v2) −1], in which v1, v2 and H1, H2 denote the particle velocities and tube hematocrits in the branches 1 and 2, respectively, and a is a dimensionless constant dependent upon a number of factors, the most important of which are the ratio of cell diameter to tube diameter, the shape and rigidity of the pellets, and the hematocrit in the feeding tube. For velocity ratios beyond a critical value, nearly all the cells flow into the faster branch. The smaller the feeding-tube hematocrit is, the smaller is the critical velocity ratio at which this phenomenon occurs. model experiment; critical velocity ratio; hematocrit: tube, feed-tube, discharge; velocity: particle, mean flow Submitted on August 15, 1977 Accepted on March 2, 1978

Recently, a complete set of data on the branching pattern of the cat's pulmonary arterial and venous trees and the elasticity of these blood vessels was obtained in our laboratory. Hence it becomes possible for the first time to perform a theoretical analysis of the blood flow in the lung of an animal based on a set of actual data on anatomy and elasticity. This paper presents an analysis of steady flow of blood in cat's lung. The effect of the vessel elasticity is embodied in the "fifth-power law" and the "sheet-flow" theory. The theory yields the pressure-flow relationship of the whole lung, the longitudinal pressure distribution, and the transit time of blood in the capillaries. These results are compared with available experimental data in the literature.

Morphometic data of the pulmonary artery in the cat's right lung are presented. Silicone elastomer casts of cat's right lung were made, and measured, counted and analyzed. The Strahler system is used to describe the branching pattern of the arterial vascular tree. These data are needed for any quantitative approach to the study of the pulmonary circulation. For all the pulmonary blood vessels of the cat lying between the main pulmonary artery and the capillary beds, there are a total of 10 orders of vessels in the right upper lobe, 9 orders of vessels in the right middle lobe and 11 orders of vessels in the right lower lobe. The ratio of the number of branches in successive orders of vessels or the branching ratio, is 3.58. The corresponding average diameter ratio is 1.72, whereas the average length ratio is 1.81.

The biophysical approach to the study of blood flow in the pulmonary vasculature requires a detailed description of vascular geometry and branching pattern. The description of the pulmonary venous morphometry in the dog is the focus of this paper. Silicone elastomer casts of a dog lung were made and were used to measure the diameters, lengths, and branching pattern of the pulmonary venous vasculature. The anatomic data are presented statistically with a diameter-defined Strahler ordering scheme, a rule for assigning the order numbers of the vessels on the basis of a diameter criterion. The asymmetric branching pattern of the pulmonary venous vasculature is described with a connectivity matrix. Results show that for the dog's right pulmonary venous tree 1) a total of 11 orders of vessels lay between the left atrium and the capillary bed; 2) the average ratios of the diameter, length, and number of branches of successive orders of veins were 1.701, 1.556, and 3.762, respectively; and 3) a fractal description of the tree geometry resulted in diameter and length fractal dimensions of 2.49 and 2.99, respectively. The morphometric data were used to compute the cross-sectional area, vascular volume, and Poiseuillean resistance in the venous vessels.