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From a resin cast of a normal pulmonary arterial tree, the diameter, length, and number of branches in each order were determined for arteries from 25 to 300 micrometer in diameter. Histological sections 120-micrometer thick were cut from a normal human lung in which the pulmonary artery had been injected with a mixture of ink and gelatin. Similar measurements were made on arteries from 10 to 70 micrometer in diameter, and the mode of origin of the capillaries was studied. The data thus obtained were found to correspond reasonably well to values previously estimated by extrapolation from data for arteries of 100 micrometer or more in diameter. The branching rules apply down to arteries of about 10-15 micrometer in diameter, the estimated number of which is 73 million. Distal to these vessels, capillaries arise either directly from small arteries or indirectly via precapillaries which are given off in great numbers and diverse patterns from the small arteries

From a cast of a human pulmonary arterial tree, the diameter, length, order, and end branches of all intact branches down to those 0.8 mm in diameter were measured and corrections for broken branches were made. A sample of structures smaller than these (0.8-0.1 mm) was similarly measured. The values for branches less than 0.1 mm in diameter were found by extrapolation and comparison with known data for the precapillary vessels. Therefore, data or estimates for each order of branching in the pulmonary tree were obtained and calculations of cross-sectional area, volume, and flow were made.

A resin cast of the bronchial tree of a dog was studied down to branches of 0.5-mm diameter. The branches were ordered, and the number of branches, mean diameter, and mean length of branches in each order were determined. The model was developed from these data with the property that delta, the difference in order between the two daughter branches at a bifurcation, is identical for all parent branches of a given order. This property facilitates the use of the model for the calculation of physiological variables such as input impedance (Fredberg and Hoenig, ASME J. Biomech. Eng. 100: 57-66, 1978), and the comparison of such results with those obtained from symmetrical models (Sidell and Fredberg, ASME J. Biomech. Eng. 100: 131-138, 1978).

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Studies of bronchial tree data by West et al. (J. Appl. Physiol. 60: 1089-1097, 1986) have shown that plots of mean diameter against generation, using log-log scales, can be represented by a power function with harmonic modulations. Other studies have shown that the mean diameter of the airways is exponentially related to order of branching. This paper demonstrates that both observations are compatible with a fractal model of branching, and because airway branching is fractal, this may explain why both are also true of the bronchial tree. Furthermore, the exponential relationship of mean diameter with generation in the larger airways, demonstrated by Weibel, is shown to result from the exponential relation of diameter with order in the fractal model.

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