A three-dimensional model of the human airway tree.

A three-dimensional (3D) model of the human airway tree is proposed using a deterministic algorithm that can generate a branching duct system in an organ. The algorithm is based on two principles: 1) the amount of fluid delivery through a branch is proportional to the volume of the region it supplies; and 2) the terminal branches are arranged homogeneously within the organ. These principles define the basic process of branching: generation of the dimensions and directionality of two daughter branches is governed by the properties of the parent branch and the region the parent supplies. The algorithm is composed of nine basic rules and four complementary rules. When the contour of an organ and the position of the trunk are specified, branches are successively generated by the algorithm. Applied to the human lung, the algorithm generates an airway tree that consists of approximately 54,000 branches. Its morphometric characteristics are in good agreement with those reported in the literature. The algorithm and the 3D airway model are useful for studying the structure-function relationship in the lung.

[1]  C. D. Murray.  THE PHYSIOLOGICAL PRINCIPLE OF MINIMUM WORK , 1931, The Journal of general physiology.

[2]  C. Sparrow.  The Fractal Geometry of Nature , 1984 .

[3]  T B Martonen,et al.  Definition of Airway Composition Within Gamma Camera Images , 1994, Journal of thoracic imaging.

[4]  K. Horsfield,et al.  Relation between diameter and flow in branches of the bronchial tree. , 1981, Bulletin of mathematical biology.

[5]  T R Nelson,et al.  Modeling of lung morphogenesis using fractal geometries. , 1988, IEEE transactions on medical imaging.

[6]  Tatsuo Togawa,et al.  Theoretical relationship between the optimal models of the vascular tree , 1974 .

[7]  R. Crystal,et al.  The Lung: Scientific Foundations , 1991 .

[8]  R W Glenny,et al.  A computer simulation of pulmonary perfusion in three dimensions. , 1995, Journal of applied physiology.

[9]  B Suki,et al.  Branching design of the bronchial tree based on a diameter-flow relationship. , 1997, Journal of applied physiology.

[10]  T Togawa,et al.  Theoretical relationship between the optimal models of the vascular tree. , 1974, Bulletin of mathematical biology.

[11]  S. Werner,et al.  Targeted expression of a dominant negative FGF receptor blocks branching morphogenesis and epithelial differentiation of the mouse lung. , 1994, The EMBO journal.

[12]  H Kitaoka,et al.  Computer-assisted three-dimensional volumetry of the human pulmonary acini. , 1992, The Tohoku journal of experimental medicine.

[13]  J E Hansen,et al.  Human air space shapes, sizes, areas, and volumes. , 1975, Journal of applied physiology.

[14]  J. Ardell,et al.  Vascular tree structure affects lung blood flow heterogeneity simulated in three dimensions. , 1997, Journal of applied physiology.

[15]  H. Uylings.  Optimization of diameters and bifurcation angles in lung and vascular tree structures , 1977, Bulletin of mathematical biology.

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

[17]  Groat Ra.  Relationship of volumetric rate of blood flow to arterial diameter. , 1948 .

[18]  Groff Ae,et al.  Hepatic arterio-venous oxygen differences in patients with normal and diseased livers. , 1948 .

[19]  E A Zerhouni,et al.  Individual airway constrictor response heterogeneity to histamine assessed by high-resolution computed tomography. , 1993, Journal of applied physiology.

[20]  Sergey V. Buldyrev,et al.  Asymmetric Flow in Symmetric Branched Structures , 1998 .

[21]  Hideaki Yamashita,et al.  Roentgenologic anatomy of the lung , 1978 .

[22]  K K Pump,et al.  Morphology of the acinus of the human lung. , 1969, Diseases of the chest.

[23]  N. Suwa,et al.  Estimation of intravascular blood pressure gradient by mathematical analysis of arterial casts. , 1963, The Tohoku journal of experimental medicine.

[24]  E R Weibel,et al.  Morphometry of the human pulmonary acinus , 1988, The Anatomical record.

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

[26]  W M Thurlbeck,et al.  Roentgenographic appearance of the human pulmonary acinus. , 1971, Investigative radiology.

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

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

[29]  C A Dawson,et al.  A fractal continuum model of the pulmonary arterial tree. , 1992, Journal of applied physiology.

[30]  Keith Horsfield,et al.  Relation between diameter and flow in branches of the bronchial tree , 1981 .

[31]  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.