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Morphometry of Airways

Keith Horsfield

10.1002/cphy.cp030307

Source: Supplement 12: Handbook of Physiology, The Respiratory System, Mechanics of Breathing

Originally published: 1986

Published online: January 2011

Full Article on Wiley Online Library



Abstract

The sections in this article are:

1 Definitions and Properties of Trees
2 Techniques of Airway Casting
2.1 Inflation
2.2 Fixation
2.3 Filling Pressure
2.4 Casting Material
3 Human Airway Morphometry
3.1 Definitions
3.2 Conducting Airways
3.3 Number of Conducting Airways
3.4 Variability of Airway Dimensions
3.5 Morphometric Parameters
3.6 Intra‐acinar Airways
3.7 Bifurcations
3.8 Branching Angle
3.9 Diameter Ratios
4 Determinants of Airway Size and Shape
4.1 Diameter Ratios, Length Ratios, and Branching Ratios
4.2 Branching Angles
5 Models of Airways
5.1 Symmetrical Model With Connectivity
5.2 Symmetrical Model Without Connectivity
5.3 Asymmetrical Models With Connectivity
5.4 Asymmetrical Models Without Connectivity
5.5 Merits and Demerits of the Models
6 Conclusion
Figure 1. Figure 1.

Terminology in branching trees. A, B, C: nodes and links in dichotomous branching. D: monopodial branching. E: generations in a symmetrical tree. F: generations in an asymmetrical tree. G: Horsfield orders in a symmetrical tree. H: Horsfield orders in an asymmetrical tree. I: Strahler orders, stage 1. J: Strahler orders, stage 2. K: symmetrical branching, delta = 0. L: asymmetrical branching, delta = 1. M: asymmetrical branching, delta = 4.
Figure 2. Figure 2.

Number, mean diameter, and mean length of branches in each Strahler order of a cast of the human bronchial tree. Straight lines represent the regression equations.
Figure 3. Figure 3.

Number, mean diameter, and mean length of branches in each Horsfield order of a cast of the human bronchial tree (same cast as in Fig. 2). Straight lines represent the regression equations.
Figure 4. Figure 4.

Branching patterns in human pulmonary acini. A: Weibel's 78 models. For simplicity only 1 alveolar duct system is shown. B: model from Ogawa 50. C: model from Parker, Horsfield, and Cumming 53. D: model from Hansen et al. 17. E: model from Pump 57. TB, terminal bronchiole; RBI, first‐generation respiratory bronchiole; AD1, first‐generation alveolar duct; ○, incomplete structure.


Figure 1.

Terminology in branching trees. A, B, C: nodes and links in dichotomous branching. D: monopodial branching. E: generations in a symmetrical tree. F: generations in an asymmetrical tree. G: Horsfield orders in a symmetrical tree. H: Horsfield orders in an asymmetrical tree. I: Strahler orders, stage 1. J: Strahler orders, stage 2. K: symmetrical branching, delta = 0. L: asymmetrical branching, delta = 1. M: asymmetrical branching, delta = 4.



Figure 2.

Number, mean diameter, and mean length of branches in each Strahler order of a cast of the human bronchial tree. Straight lines represent the regression equations.



Figure 3.

Number, mean diameter, and mean length of branches in each Horsfield order of a cast of the human bronchial tree (same cast as in Fig. 2). Straight lines represent the regression equations.



Figure 4.

Branching patterns in human pulmonary acini. A: Weibel's 78 models. For simplicity only 1 alveolar duct system is shown. B: model from Ogawa 50. C: model from Parker, Horsfield, and Cumming 53. D: model from Hansen et al. 17. E: model from Pump 57. TB, terminal bronchiole; RBI, first‐generation respiratory bronchiole; AD1, first‐generation alveolar duct; ○, incomplete structure.

References
 1. Berend, N., C. Skoog, L. Waszkiewicz, and W. M. Thurlbeck. Maximum volumes in excised human lungs: effects of age, emphysema and formalin inflation. Thorax 35: 859–864, 1980.
 2. Bowes, C., G. Cumming, K. Horsfield, J. Loughhead, and S. Preston. Gas mixing in a model of the pulmonary acinus with asymmetrical alveolar ducts. J. Appl. Physiol.: Respirat. Environ. Exercise Physiol. 52t 624–633, 1982.
 3. Boyden, E. A. Segmental Anatomy of the Lungs. New York: McGraw‐Hill, 1955.
 4. Boyden, E. A. The structure of the pulmonary acinus in a child of six years and eight months. Am. J. Anat. 132: 275–300, 1971.
 5. Brock, R. C. The Anatomy of the Bronchial Tree With Special Reference to Lung Abscess. Oxford, UK: Oxford Univ. Press, 1946.
 6. Cohn, D. L. Optimal systems. II. The vascular system. Bull. Math. Biophys. 17: 219–227, 1955.
 7. Cumming, G., K. Horsfield, and S. B. Preston. Diffusion equilibrium in the lungs examined by nodal analysis. Respir. Physiol. 12: 329–345, 1971.
 8. Dawson, S. V., and K. E. Finucane. A prediction of the distribution of oscillatory flow in human airways. Bull. Physio‐Pathol. Respir. 8: 293–304, 1972.
 9. Eisman, M. M. Lung models: hollow, flexible reproductions. J. Appl. Physiol. 29: 531–533, 1970.
 10. Findeisen, V. Uber das Absetzen kleiner, in der Luft suspendierter Teilchen in der menschlichen Lunge bei der Atmung. Pfluegers Arch. Gesamte Physiol. Menschen Tiere 236: 367–379, 1935.
 11. Fowler, W. S. Lung function studies. III. Uneven pulmonary ventilation in normal subjects and in patients with pulmonary disease. J. Appl. Physiol. 2: 283–299, 1949.
 12. Fredberg, J. J., and A. Hoeing. Mechanical response of the lungs at high frequencies. J. Biomech. Eng. 100: 57–66, 1978.
 13. Haggett, P., and R. J. Chorley. Network Analysis in Geography. London: Arnold, 1969, p. 10–17.
 14. Haggett, P., and R. J. Chorley. Network Analysis in Geography. London: Arnold, 1969, p. 285–293.
 15. Hahn, H. L., P. D. Graf, and J. A. Nadel. Effect of vagal and tone on airway diameters and on lung volume in anesthetized dogs. J. Appl. Physiol. 41: 581–589, 1976.
 16. Hansen, J. E., and E. P. Ampaya. Lung morphometry: a fallacy in the use of the counting principle. J. Appl. Physiol. 37: 951–954, 1974.
 17. Hansen, J. E., and E. P. Ampaya. Human air space shapes, sizes, areas, and volumes., J. Appl. Physiol. 38: 990–995, 1975.
 18. Hansen, J. E., E. P. Ampaya, G. H. Bryant, and J. J. Navin. Branching pattern of airways and air spaces of a single human terminal bronchiole. J. Appl. Physiol. 38: 983–989, 1975.
 19. Heard, B. E. A pathological study of emphysema of the lungs with chronic bronchitis. Thorax 13: 136–149, 1958.
 20. Hess, W. R. Über die periphere Regulierung der Blutzirkulation. Pfluegers Arch. Gesamte Physiol. Menschen Tiere 168: 439–490, 1971.
 21. Hislop, A., D. C. F. Muir, M. Jacobsen, G. Simon, and L. Reid. Postnatal growth and function of the pre‐acinar airways. Thorax 27: 265–274, 1972.
 22. Hislop, A., and L. Reid. The similarity of the pulmonary artery branching system in siblings. Forensic Sci. 2: 37–52, 1973.
 23. Hogg, J. C., J. Williams, J. B. Richardson, P. T. Macklem, and W. M. Thurlbeck. Age as a factor in the distribution of lower‐airway conductance and in the pathologic anatomy of obstructive lung disease. N. Engl. J. Med. 282: 1283–1287, 1970.
 24. Honda, H. Description of the form of trees by the parameters of the tree‐like body: effect of branching angle and the branch length on the shape of the tree‐like body. J. Theor. Biol. 31: 331–338, 1971.
 25. Horsfield, K. Morphology of the Human Bronchial Tree. Birmingham, UK: Univ. of Birmingham, 1967. MD thesis.
 26. Horsfield, K. Analysis and Modelling of Branching Systems. Birmingham, UK: Univ. of Birmingham, 1972. PhD thesis.
 27. Horsfield, K. Some mathematical properties of branching trees with application to the respiratory system. Bull. Math. Biol. 38: 305–315, 1976.
 28. Horsfield, K. Morphology of branching trees related to entropy. Respir. Physiol. 29: 179–184, 1977.
 29. Horsfield, K. Postnatal growth of the dog's bronchial tree. Respir. Physiol. 29: 185–191, 1977.
 30. Horsfield, K. Are diameter, length and branching ratios meaningful in the lung? J. Theor. Biol. 87: 773–784, 1980.
 31. Horsfield, K. The science of branching systems. In: Scientific Foundations of Respiratory Medicine, edited by J. G. Scadding and G. Cumming. London: Heinemann, 1981, chapt. 5, p. 45–54.
 32. Horsfield, K. The structure of the tracheobronchial tree. In: Scientific Foundations of Respiratory Medicine, edited by J. G. Scadding and G. Cumming. London: Heinemann, 1981, chapt. 6, p. 54–70.
 33. Horsfield, K., and G. Cumming. Angles of branching and diameters of branches in the human bronchial tree. Bull. Math. Biophys. 29: 245–259, 1967.
 34. Horsfield, K., and G. Cumming. Morphology of the bronchial tree in man. J. Appl. Physiol. 24: 373–383, 1968.
 35. Horsfield, K., and G. Cumming. Morphology of the bronchial tree in the dog. Respir. Physiol. 26: 173–182, 1976.
 36. Horsfield, K., G. Dart, D. E. Olson, G. F. Filley, and G. Cumming. Models of the human bronchial tree. J. Appl. Physiol. 31: 207–217, 1971.
 37. Horsfield, K., W. Kemp, and S. Phillips. An asymmetrical model of the airways of the dog lung. J. Appl. Physiol.: Respirat. Environ. Exercise Physiol. 52: 21–26, 1982.
 38. Horsfield, K., and A. Thurlbeck. Volume of the conducting airways calculated from morphometric parameters. Bull. Math. Biol. 43: 101–109, 1981.
 39. Horsfield, K., and A. Thurlbeck. The relation between diameter and flow in branches of the bronchial tree. Bull. Math. Biol. 43: 681–691, 1981.
 40. Hughes, J. M. B., F. G. Hoppin, Jr., and J. Mead. Effect of lung inflation on bronchial length and diameter in excised lungs. J. Appl. Physiol. 32: 25–35, 1972.
 41. Hughes, J. M. B., H. A. Jones, A. G. Wilson, B. J. B. Grant, and N. B. Pride. Stability of intrapulmonary bronchial dimensions during expiratory flow in excised lungs. J. Appl. Physiol. 37: 684–694, 1974.
 42. Jackson, A. C., J. P. Butler, E. J. Millet, F. G. Hoppin, Jr., and S. V. Dawson. Airway geometry by analysis of acoustic pulse response measurements. J. Appl. Physiol.: Respirat. Environ. Exercise Physiol. 43: 523–536, 1977.
 43. Kamiya, A., and T. Togawa. Optimal branching structure of the vascular tree. Bull. Math. Biophys. 34: 431–438, 1972.
 44. Krahl, V. E. Anatomy of the mammalian lung. In: Handbook of Physiology. Respiration, edited by W. O. Fenn and H. Rahn. Washington, DC: Am. Physiol. Soc., 1964, sect. 3, vol. I, chapt. 6, p. 213–284.
 45. Leopold, L. B., and W. B. Langbein. The Concept of Entropy in Landscape Evolution. Washington, DC: US Dept. Interior, 1962, p. A1–A20. (Geological Survey Professional Paper 500‐A.).
 46. Miller, W. S. The Lung (2nd ed.). Springfield, IL: Thomas, 1947.
 47. Mon, E., and J. S. Ultman. Monte Carlo simulation of simultaneous gas flow and diffusion in an asymmetric distal pulmonary airway model. Bull. Math. Biol. 38: 161–192, 1976.
 48. Murray, C. D. The physiological principle of minimum work applied to the angle of branching of arteries. J. Gen. Physiol. 9: 835–841, 1926.
 49. Murray, C. D. The physiological principle of minimum work. I. The vascular system and the cost of blood volume. Proc. Natl. Acad. Sci. USA 12: 207–214, 1926.
 50. Nadel, J. A., W. G. Woolfe, and P. D. Graf. Powdered tantalum as a medium for bronchography in canine and human lungs. Invest. Radiol. 3: 229–238, 1968.
 51. Ogawa, C. The finer ramifications of the human lung. Am. J. Anat. 27: 315–332, 1920.
 52. Paiva, M. Gas transport in the human lung. J. Appl. Physiol. 35: 401–410, 1973.
 53. Palmes, E. D. Measurement of pulmonary air spaces using aerosols. Arch. Intern. Med. 131: 76–79, 1973.
 54. Parker, H., K. Horsfield, and G. Cumming. Morphology of distal airways in the human lung. J. Appl. Physiol. 31: 386–391, 1971.
 55. Pedley, T. J., R. C. Schroter, and M. F. Sudlow. Energy losses and pressure drop in models of the human airways. Respir. Physiol. 9: 371–386, 1970.
 56. Phalen, R. F., H. C. Yeh, O. G. Raabe, and D. J. Velasquez. Casting the lungs in‐situ. Anat. Rec. 177: 255–263, 1973.
 57. Phalen, R. F., H. C. Yeh, G. M. Schum, and O. G. Raabe. Application of an idealized model to morphometry of the mammalian tracheobronchial tree. Anat. Rec. 190: 167–176, 1978.
 58. Pump, K. K. The morphology of the finer branches of the bronchial tree of the human lung. Dis. Chest 46: 379–398, 1964.
 59. Pump, K. K. Morphology of the acinus of the human lung. Dis. Chest 56: 126–134, 1969.
 60. Raabe, O. G., H. C. Yeh, G. M. Schum, and R. F. Phalen. Tracheobronchial Geometry: Human, Dog, Rat, Hamster. Albuquerque, NM: Lovelace Found. Med. Educ. Res., 1976.
 61. Rahn, H., and B. B. Ross. Bronchial tree casts, lobe weights and anatomical dead space measurements in the dog's lung. J. Appl. Physiol. 10: 154–157, 1957.
 62. Rashevsky, N. The principle of adequate design. In: Foundations of Mathematical Biology, edited by R. Rosen. New York: Academic, 1973, vol. 3, p. 143–175.
 63. Rohrer, F. Der Strömungwiderstand in den menschlichen Atemwegen und der Einfluss der unregelmässigen Verzweigung des Bronchialsystems auf den Atmungsverlauf in verschiedenen Lungenbezirken. Pfluegers Arch. Gesamte Physiol. Menschen Tiere 162: 225–259, 1915.
 64. Ross, B. B. Influence of bronchial tree structure on ventilation of the dog's lung as inferred from measurements of a plastic cast. J. Appl. Physiol. 10: 1–14, 1957.
 65. Scherer, P. W., and A. I. Pack. Bronchial cross‐section from lung gas washout. J. Bioeng. 1: 347–356, 1977.
 66. Schroter, R. C., and M. F. Sudlow. Flow patterns in models of the human bronchial airways. Respir. Physiol. 7: 341–355, 1969.
 67. Sidell, R. S., and J. J. Fredberg. Non‐invasive inference of airway network geometry from broadband lung reflection data. J. Biomech. Eng. 100: 131–138, 1978.
 68. Slutsky, A. S., G. G. Berdine, and J. M. Drazen. Steady flow in a model of human central airways. J. Appl. Physiol.: Respirat. Environ. Exercise Physiol. 49: 417–423, 1980.
 69. Snyder, B., D. R. Dantzker, and M. J. Jaeger. Flow partitioning in symmetric cascades of branches. J. Appl. Physiol.: Respirat. Environ. Exercise Physiol. 51: 598–606, 1981.
 70. Strahler, A. N. Revision of Horton's quantitative factors in erosional terrain. Trans. Am. Geophys. Union 34: 345, 1953.
 71. Strahler, A. N. Quantitative analysis of watershed geomorphology. Trans. Am. Geophys. Union 38: 913–920, 1957.
 72. Thompson, D. On Growth and Form (2nd ed.). Cambridge, UK: Cambridge Univ. Press, 1952.
 73. Thurlbeck, A., and K. Horsfield. Branching angles in the bronchial tree related to order of branching. Respir. Physiol. 41: 173–181, 1980.
 74. Thurlbeck, W. M., and N.‐S. Wang. The structure of the lungs. In: Respiratory Physiology I, edited by J. G. Widdicombe. London: Butterworths, 1974, ser. 1, vol. 2, chapt. 1, p. 1–30. (Int. Rev. Physiol. Ser.).
 75. Timbrell, V., N. E. Bevan, A. S. Davies, and D. E. Munday. Hollow casts of lungs for experimental purposes. Nature London 255: 97–98, 1970.
 76. Tisi, G. M., V. D. Minh, and P. J. Friedman. In vivo dimensional response of airways of different size to transpulmonary pressure. J. Appl. Physiol. 39: 23–29, 1975.
 77. Tompsett, D. H. Anatomical Techniques. London: Livingstone, 1956.
 78. Uylings, H. B. M. Optimization of diameters and bifurcation angles in lung and vascular tree structures. Bull. Math. Biol. 39: 509–520, 1977.
 79. Weibel, E. R. Morphometry of the Human Lung. Berlin: Springer‐Verlag, 1963.
 80. Willson H. G. The terminals of the human bronchiole. Am. J. Anat. 30: 267–295, 1922.
 81. Wilson, T. A. Design of the bronchial tree. Nature London 213: 668–669, 1967.
 82. Woldehiwot, Z., and K. Horsfield. Diameter, length and branching angles of the upper airways in the dog lung. Respir. Physiol. 33: 213–218, 1978.
 83. Yeats, D. B., and N. Aspin. A mathematical description of the airways of the human lungs. Respir. Physiol. 32: 91–104, 1978.
 84. Yeh, H. C., and G. M. Schum. Models of human lung airways and their application to inhaled particle deposition. Bull. Math. Biol. 42: 461–480, 1980.
 85. Yeh, H. C., G. M. Schum, and M. J. Duggan. Anatomic models of the tracheobronchial and pulmonary regions of the rat. Anat. Rec. 195: 483–492, 1979.
 86. Young, T. On the functions of the heart and arteries. Philos. Trans. R. Soc. London 99: 1–31, 1808.
 87. Zamir, M. Optimality principles in arterial branching. J. Theor. Biol. 62: 227–251, 1976.

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Article Title: Morphometry of Airways
 

How to Cite

Keith Horsfield. Morphometry of Airways. Compr Physiol 2011, Supplement 12: Handbook of Physiology, The Respiratory System, Mechanics of Breathing: 75-88. First published in print 1986. doi: 10.1002/cphy.cp030307