Blood Vessel Branching: Beyond the Standard Calculus Problem

  title={Blood Vessel Branching: Beyond the Standard Calculus Problem},
  author={J. Adam},
  journal={Mathematics Magazine},
  pages={196 - 207}
  • J. Adam
  • Published 2011
  • Mathematics
  • Mathematics Magazine
  • Summary Calculating the optimal angle for blood vessel branching is a standard calculus problem. However, optimality in that setting is judged by a cost functional that turns out not to give realistic results. We study a sequence of improvements to the cost functional, finally arriving at one that passes an important modeling test: From this last functional, we derive three empirical laws of blood vessel branching, originally proposed by German zoologist Wilhelm Roux. 
    19 Citations
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    • PDF
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    • 4
    Fluid Flow at Branching Junctions
    • 10
    • PDF
    Predicting bifurcation angle effect on blood flow in the microvasculature.
    • 12
    Solute dispersion in bifurcating networks
    • PDF
    A theoretical framework for determining cerebral vascular function and heterogeneity from dynamic susceptibility contrast MRI
    • 7


    Segment analysis of human coronary arteries.
    • 47
    Mathematics in Nature : Modeling Patterns in the Natural World
    • 23
    • PDF
    Introduction to the Calculus of Variations
    • 305
    Calculus, Early Transcendentals
    • 152
    • PDF
    On Growth and Form
    • 1,949
    Mathematical Biophysics, Vol
    • 2, Chapter XXVII, Dover, New York,
    • 1960
    The Branching Structure of Arterial Trees
    • Comments on Theoretical Biology
    • 1988
    Modern Fluid Dynamics, Vol
    • 1, Van Nostrand Reinhold, Wokingham, England,
    • 1968
    Modern fluid dynamics
    • 40