On the asymmetry of bifurcations in the bronchial tree.

The branching pattern of the conducting airways is significantly asymmetrical in the human, and even more so in other species. Although this asymmetry is believed to have an important effect on air flow and other transport processes in the bronchial tree, both experimental and theoretical studies have predominantly employed symmetrical model bifurcations. In this paper, published morphometric data for four species (human, dog, rat and hamster) is used to calculate the frequencies with which different degrees of asymmetry occur, and to examine the relationships between four of its manifestations, asymmetry of the cross-sectional areas, the lengths, the branching angles and the flow rates of the daughter branches. The observed characteristics are compared with some of the theoretical 'branching laws' which have been proposed. Quantification of the correlations between the different manifestations of asymmetry allows the geometrical characteristics to be specified for a range of realistic asymmetrical bifurcations, for use in either theoretical or experimental studies of transport in the bronchial tree.

[1]  A I Nikiforov,et al.  Morphometric variability of the human upper bronchial tree. , 1985, Respiration physiology.

[2]  O. Raabe,et al.  Factors influencing the deposition of inhaled particles. , 1976, Environmental health perspectives.

[3]  C. D. Murray.  THE PHYSIOLOGICAL PRINCIPLE OF MINIMUM WORK APPLIED TO THE ANGLE OF BRANCHING OF ARTERIES , 1926, The Journal of general physiology.

[4]  R. Schlesinger,et al.  Comparative morphometry of the upper bronchial tree in six mammalian species , 1981, The Anatomical record.

[5]  K. Horsfield,et al.  Morphology of the bronchial tree in man. , 1968, Journal of applied physiology.

[6]  C. G. Phillips,et al.  A diameter-based reconstruction of the branching pattern of the human bronchial tree. Part I. Description and application. , 1994, Respiration physiology.

[7]  C. G. Phillips,et al.  Diameter-based analysis of the branching geometry of four mammalian bronchial trees. , 1995, Respiration physiology.

[8]  B. B. Ross.  Influence of bronchial tree structure on ventilation in the dog's lung as inferred from measurements of a plastic cast. , 1957, Journal of applied physiology.

[9]  K. Horsfield,et al.  An asymmetrical model of the airways of the dog lung. , 1982, Journal of applied physiology: respiratory, environmental and exercise physiology.

[10]  C D Murray,et al.  The Physiological Principle of Minimum Work: I. The Vascular System and the Cost of Blood Volume. , 1926, Proceedings of the National Academy of Sciences of the United States of America.

[11]  Benoit B. Mandelbrot,et al.  Fractal Geometry of Nature , 1984 .

[12]  E. Weibel.  Morphometry of the Human Lung , 1965, Springer Berlin Heidelberg.

[13]  K. Horsfield,et al.  Computer simulation of the geometry of the human bronchial tree. , 1984, Bulletin of mathematical biology.

[14]  W. Hofmann,et al.  Analysis of human lung morphometric data for stochastic aerosol deposition calculations. , 1985, Physics in medicine and biology.

[15]  D E Olson,et al.  Models of the human bronchial tree. , 1971, Journal of applied physiology.

[16]  W. Hofmann,et al.  Monte Carlo Model for Aerosol Deposition in Human Lungs , 1988 .

[17]  C. G. Phillips,et al.  A diameter-based reconstruction of the branching pattern of the human bronchial tree. Part II. Mathematical formulation. , 1994, Respiration physiology.

[18]  K. Horsfield,et al.  Branching angles in the bronchial tree related to order of branching. , 1980, Respiration physiology.

[19]  O. Raabe,et al.  Application of an idealized model to morphometry of the mammalian tracheobronchial tree , 1978, The Anatomical record.

[20]  G Cumming,et al.  Angles of branching and diameters of branches in the human bronchial tree. , 1967, The Bulletin of mathematical biophysics.