Bulletin of Mathematical Biology

, Volume 38, Issue 3, pp 219–237 | Cite as

Distribution of end-points of a branching network with decaying branch length

  • William H. Warner
  • Theodore A. Wilson


The geometry of the human bronchial tree has been described as a network formed by successive dichotomous branching with constant branching angles and geometrically decaying branch lengths. Models having these properties and with randomly distributed branching planes are constructed. The distribution of the end points of the model networks are described by computing the variance of the distributions in the direction of the axis of the network and in the transverse directions. It is found that, for a given decay ratio, there is a branching angle for which the volume filled by the end points is a maximum. The advantages of the network with the decay ratio and branching angle of the human bronchial tree are discussed.


Dead Space Recursion Relation Bronchial Tree Daughter Branch Dimensionless Volume 
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Copyright information

© Society for Mathematical Biology 1976

Authors and Affiliations

  • William H. Warner
    • 1
  • Theodore A. Wilson
    • 1
  1. 1.Department of Aerospace Engineering and MechanicsUniversity of MinnesotaMinneapolisU.S.A.

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