The bulletin of mathematical biophysics

, Volume 34, Issue 4, pp 431–438

Optimal branching structure of the vascular tree

  • Akira Kamiya
  • Tatsuo Togawa

DOI: 10.1007/BF02476705

Cite this article as:
Kamiya, A. & Togawa, T. Bulletin of Mathematical Biophysics (1972) 34: 431. doi:10.1007/BF02476705


Optimality in branching structure of the vascular tree was studied. Analysis on its physiological roles as the duct system for blood supply to the capillaries predicted that the vascular tree should be constructed with minimum volume under restriction of determinant pressure, flow and location at the origin and the terminals. Mathematical derivations of this conditional extremum problem yielded some equations expressing the relations between the radii of the branches and their branching angles, which provided numerical solutions for branching points of bi- and poli-terminal minimum volume trees. Comparison of the peritoneal vascular tree in a dog with the minimum volume one computed under the same restrictive conditions showed good agreement in their branching structure.

Copyright information

© N. Rashevsky 1968

Authors and Affiliations

  • Akira Kamiya
    • 1
  • Tatsuo Togawa
    • 1
  1. 1.Institute for Medical and Dental EngineeringTokyo Medical and Dental UniversityTokyoJapan

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