Modeling the Pressure-Flow Relation of Bifurcating Networks

  • David B. Reynolds


Despite a considerable number of measurements of the variation of pressure drop with flow rate through the bronchial tree (or physical models of it), reducing the data to a single relation is difficult. Much of the difficulty arises because of differences in geometry and experimental method. Integration of data obtained in vivo or in excised lungs depends strongly on controlling the experiment under isodimensional conditions. For example, during graded expirations the increasing pressure gradient with flow and the resulting decrease in bronchial caliber suggest that isovolume conditions may not be isodimensional. Consequently, experiments investigating pressure gradient in rigid models may be helpful in modeling the more complex situation in vivo.


Pressure Gradient Pressure Drop Inspiratory Flow Bronchial Tree Total Pressure Drop 
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  1. 1.
    Pedley, T.J., R.C. Schroter and M.F. Sudlow. Energy losses and pressure drop in models of human airways. Resp. Physiol. 9: 371–386, 1970.CrossRefGoogle Scholar
  2. 2.
    Schroter, R.C. and M.F. Sudlow. Flow patterns in models of the human bronchial airways. Resp. Physiol. 7: 341–355, 1969.CrossRefGoogle Scholar
  3. 3.
    Brech, R. and B.J. Bellhouse. Flow in branching vessels. Cardiovasc. Res. 7: 593–600, 1973.CrossRefGoogle Scholar
  4. 4.
    Douglass, R.W. and B.R. Munson. Viscous energy dissipation in a model of the human bronchial tree. J. Biomech. 7: 551–557, 1974.CrossRefGoogle Scholar
  5. 5.
    White, F.M. Viscous Fluid Flow. McGraw-Hill, New York, 1974, p. 123.Google Scholar
  6. 6.
    Reynolds, D.B. Modeling studies of the pressure-flow relationship of the central airways. Ph.D. Dissertation, Charlottesville, University of Virginia, 1978.Google Scholar
  7. 7.
    Pedley, T.J., R.C. Schroter and M.F. Sudlow. Gas flow and mixing in the airways. Bioengineering Aspects of the Lung. •J.B. West, ed. Marcel Dekker, Inc. New York, 1977.Google Scholar
  8. 8.
    Streeter, V.L. Fluid Mechanics. McGraw-Hill, New York, 1966, p. 266.Google Scholar
  9. 9.
    Jaeger, M.J. and H. Matthys. The pressure-flow characteristics of the human airways. Airway Dynamics. A Bouhuys, ed. Charles C. Thomas, Springfield, Ill. 1970, p. 21–32.Google Scholar
  10. 10.
    Round, G.F., T.G. Pal and I.A. Feuerstein. Viscous energy dissipation for steady flow in models of arterial bifurcations. J. Biomech. 10: 725–734, 1977.CrossRefGoogle Scholar
  11. 11.
    Wilson, T.A. Design of the bronchial tree. Nature 213: 668–669, 1967.CrossRefGoogle Scholar
  12. 12.
    Phalen, R.F., H.C. Yeh, G.M. Sebum, and O.G. Raabe. Application of an idealized model to morphometry of the mammalian tracheobronchial tree. Anat. Rec. 190: 167–176, 1970.CrossRefGoogle Scholar
  13. 13.
    Weibel, E.R. Morphology of the Human Lung.Academic Press, New York, 1963.Google Scholar
  14. 14.
    Jaffrin, M.Y. and P. Kesic. Airway resistance: a fluid mechanical approach. J. Appl. Physiol. 36: 354–361, 1974.Google Scholar
  15. 15.
    Dawson, S.V. and E.A. Elliott. Wave-speed limitation on expiratory flow–a unifying concept. J. Appl. Physiol.: Respirat. Environ. Exercise Physiol. 43: 498–515, 1977.Google Scholar

Copyright information

© Springer Science+Business Media New York 1980

Authors and Affiliations

  • David B. Reynolds
    • 1
  1. 1.Division of Biomedical EngineeringUniversity of VirginiaCharlottesvilleUSA

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