Abstract
A method of calculating the volume of a tree distal to a cut at the origin of a branch, using branching, diameter and length ratios, has been developed. The method was applied to bronchial tree casts from human, dog, sheep, hamster, and rat lungs. It was found that the exponenta in the equation weight=k×diametera is approximately equal to 3.0 in sheep lung casts, as found by Hooper (1977), but it is greater than 3.0 in casts from the other four species.
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Hooper, G. 1977. “Diameters of Bronchi at Asymmetrical Divisions”.Resp. Physiol.,31, 291–294.
Horsfield, K. 1976. “Some Mathematical Properties of Branching Trees with Application to the Respiratory System.”Bull. Math. Biol.,38, 305–315.
— and G. Cumming. 1976. “Morphology of the Bronchial Tree in the Dog.”Resp. Physiol.,26, 173–182.
—, F. G. Relea and G. Cumming. 1976. “Diameter, Length and Branching Ratios in the Bronchial Tree”.Respir. Physiol.,26, 351–356.
Murray, C. D. 1927. “A Relationship Between Circumference and Weight in Trees and its Bearing on Branching Angles.”J. Gen. Physiol.,10, 725–729.
—. 1926. “The Physiological Principle of Minimal Work. 1. The Vascular System and the Cost of Blood Volume.”Proc. Natn. Acad. Sci., U.S.A.,12, 207–214.
Raabe, O. G., H. C. Yeh, G. M. Schum and R. F. Phalen. 1976.Tracheobronchial Geometry—Human, Dog, Rat, Hamster. Albuquerque: Lovelace Foundation for Medical Education and Research.
Uylings, H. B. M. 1977. “Optimization of Diameters and Bifurcation Angles in Lung and Vascular Tree Structures.”Bull. Math. Biol.,39, 509–519.
Weibel, E. R. 1963.Morphometry of the Human Lung, Berlin: Springer.
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Horsfield, K., Thurlbeck, A. Volume of the conducting airways calculated from morphometric parameters. Bltn Mathcal Biology 43, 101–109 (1981). https://doi.org/10.1007/BF02460943
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DOI: https://doi.org/10.1007/BF02460943