Bulletin of Mathematical Biology

, Volume 39, Issue 5, pp 509–520

Optimization of diameters and bifurcation angles in lung and vascular tree structures

  • H. B. M. Uylings

DOI: 10.1007/BF02461198

Cite this article as:
Uylings, H.B.M. Bltn Mathcal Biology (1977) 39: 509. doi:10.1007/BF02461198


An optimization model is described for lung and vascular tree structures. The model extends Murray's model, which is derived from minimal power dissipation due to the frictional resistance of laminar flow and the volume of the duct system. Instead of just laminar flow, it takes into account all types of steady flow, e.g. turbulent and laminar flow, and predicts which structural changes will occur among different parts of trees having different types of flow. The sensitivity of the optimal values is indicated and the model, predictions are compared with literature data.

Copyright information

© Society for Mathematical Biology 1997

Authors and Affiliations

  • H. B. M. Uylings
    • 1
  1. 1.Central Institute for Brain ResearchAmsterdamThe Netherlands

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